The conjugate of the expression √x - 5 - 2 when x > 5 is -(√x - 3) / (√x + 2).
The conjugate of an expression is obtained by multiplying both the numerator and denominator of the expression by the conjugate of the denominator.
We have the following expression below:
√x - 5 - 2
To determine the conjugate of the expression above, we first consider the denominator:
√x - 5
The conjugate of this expression is:
√x + 5
Therefore, to obtain the conjugate of the expression given above, we multiply the numerator and denominator by √x + 5.√x - 5 - 2 * √x + 5 / √x - 5 - 2 * √x + 5
This expression simplifies to:
-(√x - 3) / (√x - 5 + 2 * √x + 5)= -(√x - 3) / (√x + 2)
Therefore, the conjugate of the expression √x - 5 - 2 when x > 5 is -(√x - 3) / (√x + 2).
Learn more about conjugate from the given link
https://brainly.in/question/17696198
#SPJ11
Virinia is baking loaves of bread. For each loaf of bread, she uses 16 of a teaspoon of baking powder and 4 cups of flour. Virinia has a total of 47 of a teaspoon of baking powder and 15 cups of flour. She bakes as many whole loaves of bread as she can with the baking powder she has. What fraction of the flour did Virnia use?
Virinia used 11.75 cups of flour, which is equivalent to 47/4 cups of flour. This represents a fraction of 47/60 of the total flour she had.
Virinia uses 16/1 (or 16) teaspoons of baking powder per loaf of bread. Since she has a total of 47 teaspoons of baking powder, she can bake 47/16 (or 2.9375) loaves of bread. However, since she can only bake whole loaves, she can make 2 loaves of bread using the available baking powder.
For each loaf of bread, Virinia uses 4 cups of flour. Since she has 15 cups of flour in total, she can bake 15/4 (or 3.75) loaves of bread. However, she can only bake 2 whole loaves, as mentioned earlier.
Therefore, the number of loaves Virinia can bake is limited by the baking powder, resulting in 2 loaves. For these 2 loaves, she uses a total of 2 * 4 = 8 cups of flour.
To find the fraction of flour she used, we divide the amount of flour used (8 cups) by the total amount of flour she had (15 cups), giving us 8/15. This fraction can be simplified to 47/60, which represents the proportion of flour Virinia used.
To learn more about proportion click here, brainly.com/question/31548894
#SPJ11
If the triangle fgh is similar to the triangle rst, which side is proportional to side fh?
If the triangle fgh is similar to the triangle rst, the side proportional to side FH is RS.
When two triangles are similar, their corresponding sides are proportional in length.
This means that if one side of a triangle is in proportion to another, then the two triangles are similar triangles.
Two triangles are similar if they have the same shape but not necessarily the same size.
Let's say that ABC is a triangle and DEF is another triangle, and if the ratio of the corresponding sides of ABC and DEF is constant, then the two triangles are similar. Therefore, FH side of triangle FGH is proportional to the RS side of triangle RST when the two triangles are similar.
Hence, we can write the proportion as below:
FH/FM=HG/TS=GF/SR;
in the above proportion, FM=TS and GF=HG.
Therefore if the triangle fgh is similar to the triangle rst, the side proportional to side FH is RS.
learn more about similar triangles here:
https://brainly.com/question/29191745
#SPJ11
West junior High needs to fill its swimming pool with water. Determine the amount of water it needs by finding the volume of the pool. Use the drop-down menus to complete the statements. First, write the. Next, use parentheses when you substitute
for l,w, and h. Now, simplify by
50, 25, and 3. The volume of the pool is
m3
To determine the amount of water needed to fill the swimming pool at West Junior High, we need to find the volume of the pool.
To determine the amount of water needed to fill the swimming pool at West Junior High, we need to find the volume of the pool. The volume of a rectangular prism (such as a swimming pool) is calculated by multiplying its length, width, and height.
Given that the length (l) is 50 meters, the width (w) is 25 meters, and the height (h) is 3 meters, we can substitute these values into the volume formula.
The volume of the pool can be calculated as follows:
V = l * w * h
Substituting the given values:
V = 50 * 25 * 3
Now, let's simplify this expression:
Multiplying 50 by 25 gives us 1250:
V = 1250 * 3
Multiplying 1250 by 3 gives us 3750:
V = 3750
Therefore, the volume of the pool is 3750 cubic meters. This means that West Junior High needs 3750 cubic meters of water to fill its swimming pool.
To learn more about volume - brainly.com/question/28058531
#SPJ11
Paul and Krystal spent 1 1/2 hours at the pool. For half of that time, they swam laps. What equation can be used to find the amount of time they spent swimming laps?
The equation to find the amount of time Paul and Krystal spent swimming laps is: Time spent swimming laps = (1/2) × Total time spent at the pool
To calculate the time Paul and Krystal spent swimming laps, we need to find half of the total time they spent at the pool, which is 1 1/2 hours.
Step 1: Convert 1 1/2 hours to an improper fraction.
1 1/2 = (2/2 + 1/2) = 3/2
Step 2: Multiply the total time by half.
Time spent swimming laps = (1/2) × (3/2) = 3/4 hours
Paul and Krystal spent 3/4 hours swimming laps. To convert this fraction to a mixed number, we divide the numerator (3) by the denominator (4):
3 ÷ 4 = 0 remainder 3
The result is 0 hours and 3/4 hours, which is equivalent to 45 minutes. Therefore, Paul and Krystal spent 45 minutes swimming laps during their 1 1/2-hour pool session.
To know more about Amount, visit
https://brainly.com/question/25720319
#SPJ11
Thirty-six of the staff of 80 teachers at a local intermediate school are certified in Cardio-Pulmonary Resuscitation (CPR). In 180 days of school, what is the mean, variance, and standard deviation of the number of days can we expect that the teacher on bus duty will likely be certified in CPR?
The mean number of days that we can expect the teacher on bus duty to be certified in CPR is 81. The variance is 36, and the standard deviation is 6
The mean, or expected value, is given by the product of the probability and the number of trials. In this case, the probability of a teacher being certified in CPR is 36/80, and the number of trials is 180. So the mean is (36/80) * 180 = 81.
To calculate the variance, we need to multiply the probability of success (36/80) by the probability of failure (1 - 36/80) and then multiply by the number of trials (180). The variance is (36/80) * (1 - 36/80) * 180 = 36.
The standard deviation is the square root of the variance. So the standard deviation is √36 = 6.
In summary, the mean number of days that we can expect the teacher on bus duty to be certified in CPR is 81. The variance is 36, and the standard deviation is 6. These values indicate the average, spread, and variation in the number of days a certified CPR teacher would be on bus duty during 180 school days.
Learn more about standard deviation here:
https://brainly.com/question/29758680
#SPJ11
Make a number line and mark all the points that represent the following values of x.
-2.5
The point that represents the value of x = -2.5 on the number line is -2.5.
To make a number line and mark all the points that represent the value of x = -2.5,
Draw a straight line and place a point on it to represent zero. This will be the starting point for the number line.Mark the positive values to the right of zero. These values will increase as you move to the right.Mark the negative values to the left of zero. These values will decrease as you move to the left.Identify the point -2.5 on the number line by marking a point exactly in between -2 and -3.The number line will look like this:In this case, x is a constant value equal to -2.5.
Therefore, only one point needs to be marked on the number line representing the value of x = -2.5. This point will be exactly in between -2 and -3, as shown above.
Therefore, the point that represents the value of x = -2.5 on the number line is -2.5.
The number line has to be labeled to indicate which values are positive and which are negative.
The scale can be arbitrary, but it should be consistent throughout the number line.
Learn more about number line from the given link;
https://brainly.com/question/24644930
#SPJ11
Two similar hexagons have a scale factor of 5:2. If the perimeter of the larger hexagon is 45cm, what is the perimeter of the smaller hexagon?
The perimeter of the smaller hexagon is 18 cm.
Given that two similar hexagons have a scale factor of 5:2. If the perimeter of the larger hexagon is 45cm.
What is the perimeter of the smaller hexagon?
We know that the ratio of the perimeters of two similar polygons is equal to the ratio of their corresponding sides. Therefore, if the larger hexagon has a perimeter of 45 cm, the perimeter of the smaller hexagon can be found by multiplying the perimeter of the larger hexagon by the reciprocal of the scale factor.The ratio of the perimeters of two similar polygons is equal to the ratio of their corresponding sides.
Therefore, if the larger hexagon has a perimeter of 45 cm, the perimeter of the smaller hexagon can be found by multiplying the perimeter of the larger hexagon by the reciprocal of the scale factor.Similarly, if the scale factor is 5:2, the reciprocal of the scale factor is 2:5.
Hence the perimeter of the smaller hexagon can be calculated as follows:Perimeter of the smaller hexagon = (2 / 5) × 45= 18 cm
Thus, the perimeter of the smaller hexagon is 18 cm.
Learn more about hexagon here,
https://brainly.com/question/30384520
#SPJ11
A local movie theater is trying to find the best price at which to sell popcorn. To reach its goal of making at least $50,000 from popcorn sales this year, the theater decided to hire a consulting firm to analyze its business. The firm determined that the best-case scenario for the theater’s revenue generated from popcorn sales, while meeting its revenue goals, is given by this system of inequalities, where r represents the revenue in tens of thousands of dollars and p represents the sale price of popcorn in dollars
The point of (4, 6) is not a solution of this system.
The point of (6, 5) is a viable solution of this system.
How to determine the true statement about the system's possible solution?Based on the information provided above, we can logically deduce that the best-case scenario for the revenue generated from popcorn sales by the theater, while meeting its revenue goals, is represented by the following system of inequalities:
r ≤ -0.23p² + 2.25p
r ≥ 5
For the ordered pair (4, 6), we would evaluate the system of inequalities as follows;
r ≤ -0.23p² + 2.25p
6 ≤ -0.23(4)² + 2.25(4)
6 ≤ -3.68 + 36
6 ≤ 32.32
r ≥ 5
6 ≥ 5.
For the ordered pair (6, 5), we would evaluate the system of inequalities as follows;
r ≤ -0.23p² + 2.25p
5 ≤ -0.23(6)² + 2.25(6)
5 ≤ -5.22
5 ≤ 32.32
r ≥ 5
5 ≥ 6
In conclusion, a viable solution (p, r) is (6, 5).
Read more on linear equation here: brainly.com/question/25858757
#SPJ4
Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Suppose for the purposes of this question that historically the population mean time spent in Heavenly Chocolate's retail stores has been 26 minutes. Use the appropriate hypothesis test to determine if there is evidence in the data to conclude that the mean value on the website is greater than the mean at the retail store at the 0.05 level of significance.
In which case p-value < 0.05 we can reject H₀ and we can conclude there is evidence in the data to conclude that the mean value on the website is greater than 26 minutes.
Given:
Mean time spent in Heavenly Chocolate's retail stores has been 26 minutes. and if there is evidence in the data to conclude that the mean value on the website is greater than the mean at the retail store at the 0.05 level of significance.
H₀ : μ = 26
H₁ : μ = 26
Here, mentioned that there is evidence to support the claim μ = 26
Therefore, in which case p-value < 0.05 we can reject H₀ and we can conclude μ > 26.
Learn more about null hypothesis here:
https://brainly.com/question/30821298
#SPJ4
Incomplete Question:
This Question is about the variable 'Time' which is the number of minutes a customer who ultimately made a purchase spent on the website Suppose for the purposes of this question that historically the population mean time spent in Heavenly Chocolate's retail stores has been 26 minutes. Use the appropriate hypothesis test to determine if there is evidence in the data to conclude that the mean value on the website is greater than the mean at the retail store at the 0.05 level of significance.
Moving to another question will save this response. Question 6 Find the Sample standard Deviation to 2 dp for the following set of data 25-20-18-15-22 O a. 3.80 O b.381 O c. 14.51 O d. 14.50 Moving to another question will save this respons
The sample standard deviation to 2 decimal places for the given set of data is 5.39 (option E).
To find the sample standard deviation(SD) for the given set of data {25, 20, 18, 15, 22}, we can use the following formula:
$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n}(x_i-\overline{x})^2}$
Where $s$ is the Sample SD ,$n$ is the number of observations,$x_i$ is the $i^{th}$ observation, and$\overline{x}$ is the mean of the observations.
Using the above formula, we can find the sample standard deviation as follows:
First, we need to find the mean of the observations:
$\overline{x} = \frac{1}{n}\sum_{i=1}^{n}x_i = \frac{25+20+18+15+22}{5} = 20$
Substituting the values in the formula:
$s = \sqrt{\frac{1}{5-1} [(25-20)^2 + (20-20)^2 + (18-20)^2 + (15-20)^2 + (22-20)^2]}$$s = \sqrt{\frac{1}{4} [25 + 0 + 4 + 25 + 4]} = \sqrt{\frac{58}{2}} = \sqrt{29} \approx 5.3852$
Therefore, the Sample SD to 2 decimal places for the given set of data is 5.39 (option E).
Option E is the correct answer.
To learn more about standard deviation refer to:
https://brainly.com/question/13336998
#SPJ11
In an acute-angled triangled PQR, with PQ=10m, PR=15m, PRQ=40°. Evaluate PPQR.
Answer: PPQR is 58.982°.
The given problem can be easily solved using trigonometry.
Let's solve the problem step by step
:Given, PQ = 10mPR = 15m Angle PRQ = 40°
We need to find PPQR We can solve this by using the sine rule.
As per the sine rule: sin(PQR) / QR
= sin(RPQ) / RP.... (1)
We can use cosine rule for QR. As per the cosine rule: QR² = RP² + RQ² - 2RP * RQ * cos(PQR).... (2)
We know the value of PQ and PR, we can easily find the value of RP.
Using Pythagoras theorem, PR² = PQ² + QR²QR²
= PR² - PQ²QR = √(PR² - PQ²)QR
= √(15² - 10²) = √(225 - 100) = √125
We can use equation (1) to find sin(PQR)sin(PQR) / √125
= sin(40) / 15sin(PQR)
= (√125 * sin(40)) / 15
We can use equation (2) to find cos(PQR)QR² = RP² + RQ² - 2RP * RQ * cos(PQR)√125²
= RP² + 10² - 2RP * 10 * cos(PQR)125
= RP² + 100 - 20RP * cos(PQR)20RP * cos(PQR)
= RP² - 25RP * cos(PQR) = (RP - 125/20)cos(PQR)
= (RP - 25/4) / RQ sin(PQR) / √125
= sin(40) / 15sin(PQR) = (√125 * sin(40)) / 15
Using equation (1): sin(PQR) / √125 = sin(40) / 15sin(PQR)
= (√125 * sin(40)) / 15sin(PQR) = 0.4501PPQR
= 180 - PRQ - PQR = 180 - 40 - (180 * 0.4501)
= 180 - 40 - 81.018 = 58.982°
To know more about trigonometry visit:
https://brainly.com/question/11016599
#SPJ11
Y=3x-7 Missing value
The complete table for the function are
x -2 -1 1 3
y -13 -10 -4 2
How to complete the missing parts of the table for the function.From the question, we have the following parameters that can be used in our computation:
The function equation and the incomplete table of values
This is given as
y = 3x - 7
From the table, the missing values are at
x = -2, x = -1, 1 and x = 3
So, we have
y = 3(-2) - 7 = -13
y = 3(-1) - 7 = -10
y = 3(1) - 7 = -4
y = 3(3) - 7 = 2
Read more about functions at
brainly.com/question/27915724
#SPJ1
Question
y = 3x - 7
Missing value for
x -2 -1 1 3
y
The i intensity l of light varies inversely as the square of the distance d from the light source. If the intensity of light 4 feet from a source is 40 foot candles, wrote the complete variation equation
l = 640/d2. The complete variation equation for the intensity of light, l, varies inversely as the square of the distance, d, from the light source can be written as:
l = k/d2
In this equation, k represents the constant of variation. To find the specific equation, we need to use the given information. According to the problem, when the distance is 4 feet (d = 4), the intensity of light is 40 foot candles (l = 40).
Plugging these values into the equation, we have:
40 = k/42
40 = k/16
To solve for k, we multiply both sides of the equation by 16
640 = k
Therefore, the complete variation equation for the intensity of light is:
l = 640/d2
Learn more about intensity here: brainly.com/question/17583145
#SPJ11
There are three numbers: 4, 26 and 18. A fourth number creates a group average of 12. What is this fourth number
The fourth number that will create a group average of 12 for the numbers 4, 26 and 18 is 0.
To solve this problem, you will need to use the formula for calculating the average or arithmetic mean. You can calculate the average of a group of numbers by adding them together and then dividing the sum by the number of numbers in the group.
There are three numbers: 4, 26 and 18. To find the fourth number that will create an average of 12 for the four numbers, we can use the formula for calculating the average. We can write this formula as:
(4 + 26 + 18 + x) / 4 = 12
where x is the fourth number we need to find.
To solve for x, we can multiply both sides of the equation by 4 to eliminate the fraction:
4 + 26 + 18 + x = 48
Then, we can simplify the left side by combining like terms:
48 + x = 48
Finally, we can solve for x by subtracting 48 from both sides of the equation:
x = 0
Therefore, the fourth number is 0.
Learn more about Arithmetic mean:
https://brainly.com/question/28268656
#SPJ11
A traffic engineer states that the mean improvement is between 582.5 and 727.5 vehicles per hour. With what level of confidence can this statement be made
The confidence level with which this statement can be made is this: 90%
How to determine the confidence levelTo determine the confidence level for the given measurements, we will first determine the z-score with the formula: z = (x − μ)/ σ
First;
z * 311./√50
= 727.5 - 582.5 /2
= 72.5
z score = 72.5 *√50/ 311.7
= 1.6447
But, Z ≤ 1.6447 = 0.95, and,
Z > 1.6447 = 0.05
α/2 = 0.05
So, 1 - α = 0.09 or 90%.
Learn more about confidence intervals here:
https://brainly.com/question/15712887
#SPJ4
What is the volume of a sphere with a radius of 30. 5 cm, rounded to the nearest tenth of a cubic centimeter?
The volume of a sphere with a radius of 30.5 cm is approximately 46619.5 cm³ when rounded to the nearest tenth of a cubic centimeter.
The volume of a sphere can be calculated using the formula:
V = (4/3) * π * r^3
Where V is the volume, π is a constant approximately equal to 3.14, and r is the radius of the sphere.
Substituting the given radius value into the formula:
V = (4/3) * 3.14 * (30.5 cm)^3
Calculating the volume:
V ≈ (4/3) * 3.14 * (30.5 cm)^3 ≈ 46619.53 cm^3
Rounding to the nearest tenth of a cubic centimeter, the volume of the sphere is approximately 46619.5 cm^3.
To learn more about sphere click here : brainly.com/question/15044609
#SPJ11
a binomial distribution with an n of 15 and a probability of success of 20 percent, what is theprobability of 10
The probability of getting exactly 10 successes in a binomial distribution with n = 15 and a probability of success of 20% is approximately 0.0264, or 2.64%.
To calculate the probability of getting exactly 10 successes in a binomial distribution with n = 15 and a probability of success of 20%, we can use the binomial probability formula:
P(X = k) = (n choose k) * (p^k) * ((1-p)^(n-k))
Where:
P(X = k) is the probability of getting exactly k successes
n is the number of trials
p is the probability of success
k is the number of successes
Substituting the given values into the formula:
P(X = 10) = (15 choose 10) * (0.2^10) * ((1-0.2)^(15-10))
Calculating this:
P(X = 10) = (3003) * (0.2^10) * (0.8^5)
P(X = 10) ≈ 0.0264
To know more about binomial distribution refer here:
https://brainly.com/question/29137961#
#SPJ11
2100 in the ratio of 3:5:7 , how much will the three boys get each
In a ratio of 3:5:7, if a total amount of 2100 is to be divided among three boys, the first boy will receive 3 parts, the second boy will receive 5 parts, and the third boy will receive 7 parts of the total amount.
To find out how much each boy will receive, we need to determine the value of one part of the ratio. The total number of parts in the ratio is 3 + 5 + 7 = 15.
To calculate the value of one part, we divide the total amount (2100) by the total number of parts (15):
Value of one part = 2100 / 15 = 140.
Now we can determine the amount each boy will receive by multiplying the value of one part by their respective ratios.
The first boy will receive 3 parts, so his share will be 3 * 140 = 420.
The second boy will receive 5 parts, so his share will be 5 * 140 = 700.
The third boy will receive 7 parts, so his share will be 7 * 140 = 980.
Therefore, in the ratio of 3:5:7, the first boy will receive 420, the second boy will receive 700, and the third boy will receive 980.
To learn more about ratio here brainly.com/question/13419413
#SPJ11
the weights of 6-week-old poults are normally distributed with a mean 9.0 pounds and standard deviation of 2.8 pounds. A turkey farmer wants to provide a money-back gaurantee that her 6-week poults will weiht at least a certain amount. What weight should she guarantee so that she will have to give her customer's money back only 1% of the time
The turkey farmer should guarantee a weight of 13.45 pounds to have to give her customers' money back only 1% of the time.
To determine the weight the turkey farmer should guarantee, we need to find the value that corresponds to the 99th percentile of the normal distribution. Using the mean (9.0 pounds) and standard deviation (2.8 pounds) provided, we can calculate this value.
To find the 99th percentile, we can use the Z-score formula: Z = (X - μ) / σ, where Z is the standard score, X is the value we're looking for, μ is the mean, and σ is the standard deviation. Rearranging the formula to solve for X, we have X = Z * σ + μ.
Since we want the 99th percentile, we need to find the Z-score that corresponds to that percentile. Using a standard normal distribution table or calculator, we find that the Z-score for the 99th percentile is approximately 2.33.
Plugging the values into the formula, we have X = 2.33 * 2.8 + 9.0 = 13.45 pounds. Therefore, the turkey farmer should guarantee a weight of at least 13.45 pounds to have to give her customers' money back only 1% of the time.
Learn more about Guarantee
brainly.com/question/32193758
#SPJ11
Suppose that past history shows that 5% of college students are sports fans. A sample of 10 students is to be selected. Find the probability that at most 1 student is a sports fan.
The probability that at most 1 student is a sports fan is 0.9143.
Let us consider a binomial distribution,
where p = 5/100 = 0.05, q = 1 - 0.05 = 0.95, n = 10
We are required to find the probability of at most 1 student being a sports fan
P (x ≤ 1) = P (x = 0) + P (x = 1)P (x = 0)
= [tex]nCx * p^x * q^(n-x)P (x = 0) = 10C0 * 0.05^0 * 0.95^10P (x = 0) = 0.5987369392P (x = 1) = nCx * p^x * q^(n-x)P (x = 1) = 10C1 * 0.05^1 * 0.95^9P (x = 1)[/tex]
= 0.3155915129P (x ≤ 1) = P (x = 0) + P (x = 1)P (x ≤ 1)
= 0.5987369392 + 0.3155915129P (x ≤ 1)
= 0.9143284521
Therefore, the probability that at most 1 student is a sports fan is 0.9143.
To know more about probability visit:-
https://brainly.com/question/31828911
#SPJ11
About 80 percent of the elderly in the United States are comprised of which of the following groups? non-Hispanic Whites African Americans Asian Americans Latinos
According to data from the U.S. Census Bureau, as of 2020, approximately 80 percent of the elderly population (age 65 and older) in the United States is comprised of non-Hispanic Whites. This group represents the majority of the elderly population in the country.
However, it is important to note that the composition of the elderly population can vary across different regions and states within the U.S.
Non-Hispanic Whites: As mentioned earlier, non-Hispanic Whites make up the largest proportion of the elderly population in the United States. This is due to factors such as historical demographics and immigration patterns.
African Americans: African Americans constitute a significant portion of the elderly population in the United States. According to the U.S. Census Bureau's 2020 data, African Americans represent around 9% of the elderly population.
Asian Americans: Asian Americans make up a smaller percentage of the elderly population compared to non-Hispanic Whites and African Americans. The exact proportion can vary depending on the specific Asian ethnic groups, as the Asian American population is diverse, including individuals with origins from various countries such as China, India, the Philippines, and more.
Latinos: The Latino population, which includes individuals of Hispanic or Latino origin, represents a growing segment of the U.S. population. However, the percentage of Latinos among the elderly population is relatively smaller compared to non-Hispanic Whites and African Americans.
The specific proportion varies depending on factors such as immigration patterns and birth rates.
It's important to note that these percentages may change over time due to demographic shifts, immigration trends, and other factors that influence the U.S. population composition.
Additionally, the distribution of the elderly population across racial and ethnic groups can vary across different regions and states within the United States.
Learn more about non-Hispanic Whites at https://brainly.com/question/15142742
#SPJ11
How do I solve this question?
Answer:
x = 7
Step-by-step explanation:
We can identify the figure formed by 2 radii, (6x - 3), and (3x + 18) as a kite because it is a quadrilateral symmetric around a center line.
The radii sides are congruent, and therefore, the other two sides must be congruent as well. So, we can solve for x by equation (6x - 3) and (3x + 18).
[tex]6x - 3= 3x + 18[/tex]
↓ subtracting 3x from both sides
[tex]3x - 3= 18[/tex]
↓ adding 3 to both sides
[tex]3x = 18 + 3[/tex]
[tex]3x = 21[/tex]
↓ dividing both sides by 3
[tex]\boxed{x = 7}[/tex]
A worker on scaffolding 60 ft above the ground needs to lift a 400 lb bucket of cement from the ground to a point 40 feet above the ground by pulling on a rope weighing 5 lb/ft. How much work is required
The worker needs to do 8150 ft-lb of work to lift the bucket.
The bucket has to be lifted 60-40=20 feet. As the worker pulls the bucket, the weight of the rope has to be overcome. Therefore, the work done in lifting the bucket through a distance of 20 ft is given by;
Work done = (work done in lifting the bucket + work done in lifting the rope)
Work done in lifting the bucket= Force × distance= 400 lbs × 20 ft= 8000 ft-lb
As the weight of the rope varies, an average weight can be considered for convenience.
Therefore, the weight of the rope is taken as the average weight over the distance it is lifted, which is 30 feet.
So, work done in lifting the rope= force × distance= 5 lbs/ft × 30 ft= 150 ft-lb
Therefore, the total work done by the worker= 8000 + 150= 8150 ft-lb
Thus, the worker needs to do 8150 ft-lb of work to lift the bucket.
learn more about Work done here:
https://brainly.com/question/13662169
#SPJ11
Suppose that a company owns 400 computers. Each computer has an 11% probability of not working. Suppose we randomly select 25 computers. What is the probability that at least 22 will work in good condition
The probability that at least 22 out of 25 computers will work in good condition is approximately 0.0250, or 2.5%.
To calculate the probability that at least 22 out of 25 computers will work in good condition, we can use the binomial distribution formula.
The binomial distribution formula is given by:
[tex]P(X = k) = C(n, k) \times p^k \times (1 - p)^{(n - k)[/tex]
Where:
P(X = k) is the probability of getting exactly k successes,
C(n, k) is the number of ways to choose k items from a set of n items (also known as the binomial coefficient),
p is the probability of success on a single trial, and
n is the total number of trials.
In this case, n = 25 (the total number of computers selected), k ranges from 22 to 25 (at least 22 working computers), and p = 0.89 (probability of a computer working, which is 1 - 0.11).
Let's calculate the probability using these values:
P(X ≥ 22) = P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25)
[tex]P(X = k) = C(25, k) \times 0.89^k \times 0.11^{(25 - k)[/tex]
[tex]P(X = 22) = C(25, 22) \times 0.89^{22} \times 0.11^3[/tex]
[tex]P(X = 23) = C(25, 23) \times 0.89^{23} \times 0.11^2[/tex]
[tex]P(X = 24) = C(25, 24) \times 0.89^{24} \times 0.11^1[/tex]
[tex]P(X = 25) = C(25, 25) \times 0.89^{25} \times 0.11^0[/tex]
Calculate the binomial coefficients, we can find:
P(X = 22) ≈ 0.0210
P(X = 23) ≈ 0.0038
P(X = 24) ≈ 0.0002
P(X = 25) ≈ 0.0000
Finally, summing up these probabilities:
P(X ≥ 22) ≈ 0.0210 + 0.0038 + 0.0002 + 0.0000
≈ 0.0250
Therefore, the probability that at least 22 out of 25 computers will work in good condition is approximately 0.0250, or 2.5%.
Learn more about binomial distribution click;
https://brainly.com/question/29163389
#SPJ4
A game at an arcade is in the form of a large wheel that a player spins. The wheel is programmed to give 2 tickets 50% of the time, 5 tickets 25% of the time, 10 tickets 23% of the time, and 100 tickets 2% of the time. If a player spins the wheel once, what is the expected number of tickets the player will win
The expected number of tickets the player will win when the wheel is spun once is 6.55.
To find out the expected number of tickets a player will win by spinning the wheel once, we need to multiply the probability of each outcome by the number of tickets that correspond to that outcome, and then add up these products.
This is because the expected value is the sum of each outcome multiplied by its probability.
Let's denote the number of tickets that the player wins by X.
Then, X = 2 with probability 0.5
X = 5 with probability 0.25
X = 10 with probability 0.23
X = 100 with probability 0.02
Therefore, the expected value of X is given by:
E(X) = 2(0.5) + 5(0.25) + 10(0.23) + 100(0.02)
E(X) = 1 + 1.25 + 2.3 + 2
E(X) = 6.55
Therefore, the expected number of tickets the player will win is 6.55.
Learn more about probability here:
https://brainly.com/question/32117953
#SPJ11
Marty's Barber Shop has one barber. Customers have an arrival rate of 2.1 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that no units are in the system
The probability that no units are in the system is 0.467 or 46.7%.
The probability that no units are in the system of Marty's Barber Shop can be calculated as follows:
To find out the probability that no units are in the system, the number of arrivals (λ) and the service rate (μ) are needed. It is given that the arrival rate is 2.1 customers per hour and the service rate is 4 per hour.
From the given data, the formula to calculate the probability of no units in the system is:
P0=1−λμ
P0 = 1 - λ/μ
Now, putting the values, we get : P0=1−2.14=0.4670.467 = 46.7%
The probability that no units are in the system is 0.467 or 46.7%.
Hence, the answer is 46.7%.
Learn more about probability here https://brainly.com/question/14210034
#SPJ11
a. The process standard deviation is 15 , and the process control is set at plus or minus 1 standard deviation. Units with weights less than 8.85 or greater than 9.15 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)
The probability of a defect is 0.0013.
Given that the process standard deviation is 15, we can assume the process average is 9 (which is the mean of the given defect range).
Therefore, the defect range can be written as:
P(weight < 8.85) = P(X < 8.85 - 9) = P(X < -0.15)
and
P(weight > 9.15) = P(X > 9.15 - 9) = P(X > 0.15)
Since the standard deviation is 15, and the process control is at plus or minus 1 standard deviation, the range of values for defects can be written as:
P(-1×15 < X < 1×15) = P(-15 < X < 15)
Now, using the Normal distribution, we can calculate the probability of defects by finding the area under the distribution curve, outside of the process control. This is certainly outside the scope of this question, but the answer (to 4 decimals) is 0.0013.
Therefore, the probability of a defect is 0.0013.
Learn more about the standard deviation visit:
brainly.com/question/13905583.
#SPJ4
If one U.S. dollar was worth Canadian dollars when Sal went to a debate tournament in Toronto, and he had in U.S. currency as spending money, how much was his money worth in Canadian dollars
Sal's $100 in U.S. currency would be worth 131 Canadian dollars if he exchanged it at the prevailing exchange rate.
If one U.S. dollar was worth 1.31 Canadian dollars when Sal went to a debate tournament in Toronto, and he had $100 in U.S. currency as spending money, his money would be worth 131 Canadian dollars. This is because you can convert U.S. dollars to Canadian dollars by multiplying the amount in U.S. currency by the exchange rate.
Exchange rate is the value of one currency in relation to another. The exchange rate between the U.S. dollar and the Canadian dollar varies depending on market conditions, but as of August 2021, the exchange rate is approximately 1 U.S. dollar to 1.31 Canadian dollars.
Therefore, Sal's $100 in U.S. currency would be worth 131 Canadian dollars if he exchanged it at the prevailing exchange rate.
To learn more about exchange rate here:
brainly.com/question/13717814#
#SPJ11
you have four pieces of a chain necklace, which you wish to join into a single circle of 12 links. it costs $2 to open a link, and 3$ to close a link you have 15 dollars how can you do this
The four pieces of chain necklaces into a single circle of 12 links, you need to open six links (1.5 links for each necklace) and then close two links, which will cost $18.
To join four pieces of chain necklaces into a single circle of 12 links, you need to open eight links (two links for each necklace), and then close three links. Since it costs $2 to open a link, opening eight links will cost $16 (8 × $2), and it costs $3 to close a link, so closing three links will cost $9 (3 × $3). Therefore, the total cost will be $16 + $9 = $25.
However, you only have $15, which is less than the total cost of joining the necklaces. Therefore, you need to find another solution to join the necklaces. You can open six links (1.5 links for each necklace) and then close two links. Opening six links will cost $12 (6 × $2), and closing two links will cost $6 (2 × $3).
To know more about cost visit:-
https://brainly.com/question/14566816
#SPJ11
While in Los Angeles, you meet a vendor selling smoothies. He said he made $1065 yesterday and sold 250 smoothies. If a green smoothie costs $4 and a strawberry-banana smoothie costs $4. 50, how many of each type did he sell? You must use matrices and show your work!
The vendor sold 120 green smoothies and 130 strawberry-banana smoothies.
To solve this problem using matrices, we can set up a system of equations based on the given information.
Let's define:
x = the number of green smoothies sold
y = the number of strawberry-banana smoothies sold
Based on the information provided, we can form two equations:
Equation 1: The total revenue from green smoothies and strawberry-banana smoothies should be equal to $1065.
4x + 4.50y = 1065
Equation 2: The total number of smoothies sold should be equal to 250.
x + y = 250
Now, we can represent this system of equations using matrices.
Let's define the matrices:
A = [[4, 4.50], [1, 1]]
X = [[x], [y]]
B = [[1065], [250]]
Now, the matrix equation is given by AX = B.
Multiplying both sides by the inverse of matrix A, we can solve for X:
A^(-1)AX = A^(-1)B
IX = A^(-1)B
X = A^(-1)B
To find the inverse of matrix A, we can use matrix algebra or any suitable method (e.g., row reduction). However, in this case, since matrix A is a 2x2 matrix, we can easily find its inverse:
A^(-1) = 1/(4 * 1 - 4.50 * 1) * [[1, -4.50], [-1, 4]]
Evaluating the inverse of matrix A, we have:
A^(-1) = [[1/(-0.5), -4.50/(-0.5)], [-1/(-0.5), 4/(-0.5)]]
= [[-2, 9], [2, -8]]
Now, we can find the solution for X:
X = [[-2, 9], [2, -8]] * [[1065], [250]]
= [[-2 * 1065 + 9 * 250], [2 * 1065 - 8 * 250]]
= [[-2130 + 2250], [2130 - 2000]]
= [[120], [130]]
The solution to the system of equations is x = 120 and y = 130.
Learn more about inverse of matrix from :
https://brainly.com/question/27924478
#SPJ11
