a) The null hypothesis is that there is no difference in the proportion of homeowners using water filters among the three communities. The alternative hypothesis is that at least one community has a different proportion of homeowners using water filters than the other communities.
b) To calculate the expected count for the bottom right cell, we can use the formula:
Expected count = (row total x column total) / grand total
The row total for Community C and the column total for No are both 100, and the grand total is 300. Therefore:
Expected count = (100 x 100) / 300 = 33.33
The expected count of 33.33 for the bottom right cell means that if there were no difference in the proportions of homeowners using water filters among the three communities, we would expect 33.33 of the 100 homeowners in Community C to answer 'No' to the question about water filters.
c) To determine what we can conclude from the Chi-square statistic of 13.22, we need to compare it to the critical value for a Chi-square distribution with (3-1) x (2-1) = 2 degrees of freedom at the desired level of significance. Let's assume a level of significance of 0.05. From a Chi-square distribution table, the critical value with 2 degrees of freedom at 0.05 level of significance is 5.99.
Since 13.22 is greater than 5.99, we can reject the null hypothesis and conclude that there is a significant difference in the proportion of homeowners using water filters among the three communities. However, we cannot determine from this test alone which communities have different proportions of homeowners using water filters. We would need to conduct further tests, such as post-hoc tests, to investigate the specific differences among the communities.
A bicyclist travelled for T = 1.6 hours at a constant speed of R = 20 kilometers (km) per hour. Use the formula
D = R · T
to find the total distance traveled in kilometers.
Answer: The formula D = R * T relates the distance traveled (D) to the rate of speed (R) and the time elapsed (T). Using the given values, we can substitute R = 20 km/h and T = 1.6 h to find:
D = R * T = 20 km/h * 1.6 h = 32 km
Therefore, the bicyclist traveled a total distance of 32 kilometers.
Step-by-step explanation:
Find the measure of angle 1 state, the value only do not use units did not right angle one equals
Find the measurement of angle to state the value only do not use units do not right angle two equals in your response
The required angle 1 between the side and diagonal of a square is approximately 45 degrees.
What is the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
Let's assume that the length of one side of the square is 'a'.
Then the length of the diagonal of the square is given by the Pythagorean theorem:
d² = a² + a² = 2a²
d = a * √(2)
To find the angle between the side and the diagonal, we can use the cosine function:
cos(Ф) = adjacent/hypotenuse = a / (a * √(2))
cos(Ф) = 1 / √(2)
Ф= cos⁻¹(1/√(2))
Ф≈ 45°
Therefore, the angle between the side and diagonal of a square is approximately 45 degrees.
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If Michael earns $150 a week from his part-time job, and 20% of his paycheck is
deducted for taxes, his estimated monthly income should be
His estimated monthly income should be $480.
Find the general solution of the differential equation.
6y (4) +83y" +100y = 0
y(x) =
Refer to the attached image.
A triangle has two sides of length 7 and 10. What is the largest possible whole-number length for the third side?
Answer:
The largest possible whole-number length for the third side of a triangle with two sides of length 7 and 10 is 13. This is due to the fact that the two given lengths must be added together, and then subtracted from the third side in order to create a valid triangle. Therefore, the third side must be at least 13 in order to create a triangle.
Expand the logarithm fully using the properties of logs. Express the final answer in terms of \log x log x. log7x2
Therefore, the expansion of log(7x²) using the properties of logarithm is
log 7 + 2log x, expressed in terms of log x.
What exactly is a logarithm?The mathematical idea of a logarithm illustrates the opposite of a power. It follows that the exponential that must be multiplied by bc to get the value of a number, x, is equal to its ground logarithm. As an illustration, 1000 = 103, so log10 = 3 is 1000's base-10 logarithm, which is 3. As an example, the square of ten is now only one twentieth of the base-10 exponential of ten, which is two. Log 100 = 2. Mathematicians use the logistic (or log) notion to respond to problems like these.
Here,
Using the product rule of logarithms, we can write:
log(7x²) = log 7 + log(x²)
Using the power rule of logarithms, we can write:
log(7x²) = log 7 + log(x²) = log 7 + 2log x
Therefore, the expansion of log(7x²) using the properties of logs is:
log 7 + 2log x, expressed in terms of log x.
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Can someone please answer these questions for me i cant figure them out!! (brainliest promised)
What is the fractional equivalent of the repeating decimal n = 0.1515... ?
Answer the questions to find out.
1. How many repeating digits does the number represented by n have? (2 points)
2. You need to multiply n by a power of 10 to help you find the fraction. Decide on the power of 10 to multiply by, and tell how you identified that number. (2 points)
3. Write an equation where the left side is your power of 10 times n and the right side is the result of multiplying 0.1515... by that power. (2 points)
4. Write the original equation, n = 0.1515... underneath your equation from question 3. Then subtract the equations. Show your work. (2 points)
5. Write n as a fraction in simplest form. Show your work. (2 points)
The fractional equivalent of the repeating decimal is 15/99
What does division of fractions mean?
A fraction is divided into additional equal pieces when it is divided into fractions. For instance, if you had three-fourths of a pizza remaining and divided each slice into two pieces, you would have received six slices, which would be equivalent to six-eighths of the entire pizza.
n = 0.1515...-------(1)
multiply n by 100 =10²
The reason we multiply x by 100 is because 0.1515... has 2 repeating digits and 100 has two zeros.
100n=15.15......--------(2)
Subtract (1) from (2)
100n=15.15...
n = 0.1515....
___________
99n=15
=> n=15/99
The fractional equivalent of the repeating decimal is 15/99
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Solve for x: 48:36::4:x
Answer:
x=3
Step-by-step explanation:
the answer is 3 because 3*12=36 and 4*12=48
What is the answer to this problem?
3x+6+x-2+8(x-3)+-4-4+x+1+-2(x+2)+6+7x+-8x=?
Answer:
Step-by-step explanation:
Let's simplify the given expression by combining like terms:
3x + 6 + x - 2 + 8(x - 3) - 4 - 4 + x + 1 - 2(x + 2) + 6 + 7x - 8x
First, let's simplify the expression inside the parentheses:
8(x - 3) = 8x - 24
Now we can combine like terms:
3x + x + x + 7x - 8x + 6 - 2 - 4 - 4 + 1 + 6 - 2( x + 2) + 8x - 24
Simplifying further:
6x - 2 - 4 - 4 + 8x - 2(x + 2) - 17
6x + 8x - 2x - 2(2) - 25
12x - 4 - 25
12x - 29
Therefore, the answer to the given expression is 12x - 29.
Answer:
hope this helps!!
Step-by-step explanation:
Exercice 1:
Sur 100 étudiants, on considère les ensembles M de ceux qui étudient les mathématiques, E de ceux qui étudient
l'économie et G de ceux qui étudient la gestion. Sur ces 100 étudiants, 55 étudient les mathématiques, 9 les mathéma-
tiques et la gestion, 7 les mathématiques et l'économie, 8 l'économie et la gestion, 6 les mathématiques et la gestion
mais pas l'économie, 80 les mathématiques ou la gestion et 12 l'économie seulement.
(a) Combien d'étudiants suivent les trois matières ?
(b) Combien sont-ils a étudier les mathématiques ?
(c) Combien sont-ils a étudier la gestion?
(d) Combien sont-ils a étudier l'économie?
(e) Combien n'étudient aucune de ces trois matières ?
Answer:
(a) Pour trouver le nombre d'étudiants qui suivent les trois matières, on peut utiliser la formule suivante:
A music industry researcher wants to estimate, with a 95% confidence level, the proportion of young urban people (ages 21 to 35 years) who go to at least 3 concerts a year. Previous studies show that 42% of those people (21 to 35 year olds) interviewed go to at least 3 concerts a year. The researcher wants to be accurate within 1% of the true proportion. Find the minimum sample size necessary.
For many years the only way to test if a person had tuberculosis (TB) required a laboratory procedure that could take up to several weeks to produce a definite result. There are now DNA-based tests to detect TB that can be done in a couple of hours.
We have the following data on a DNA test for TB
· If a person does not have TB then the DNA test always is negative.
· If a person does have TB, then the DNA test will be positive 94% of the time.
Assume that we will use the test in Africa where the rate of incidence of TB is 450 per 100,000.
Has TB
Does not have TB
Row Totals
Test result: negative
Test result: positive
P
Column Totals
Q
100,000
What is the value of P?
· 100,000
· 99,550
· 450
· 423
For many years the only way to test if a person had tuberculosis (TB) required a laboratory procedure that could take up to several weeks to produce a definite result. There are now DNA-based tests to detect TB that can be done in a couple of hours. We have the following data on a DNA test for TB • If a person does not have TB then the DNA test always is negative. • If a person does have TB, then the DNA test will be positive 94% of the time. Assume that we will use the test in Africa where the rate of incidence of TB is 450 per 100,000. Has TB Does not have TB Row Totals Test result: negative Test result: positive P Column Totals Q 100,000 What is the value of P? • 100,000 • 99,550 • 450 • 423
The number of positive results for all persons with TB will be D. 423
How to calculate the value of PProbability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true
Rate of incidence of TB is 450 per 100,000
Column Totals of "Has TB" = (450 / 100,000) * Grand Total = (450 / 100,000) * 100,000 = 450
If a person does have TB, then the DNA test will be positive 94% of the time.
Therefore, P = Number of positive results for all persons with TB:
= 0.94 * 450
= 423
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A basketball player makes 40% of his shots from the free throw line. Suppose that each of his shots can be considered independent and that he throws 3 shots. Let x = the number of shots that he makes. What is the sample space for x?.
The probability of throwing 3 shots is 100% and the sample space is set of all possible real number.
Probability is the measure of the likelihood that a given event will occur. In this case, the event is a basketball player making a shot from the free throw line.
Since the player has a 40% success rate, we can calculate the probability of him making x number of shots, where x is the number of shots that he throws.
Since the shots are independent of each other, the sample space for x is the set of all possible numbers of shots that he can make, from 0 to the total number of shots (3 in this case).
Therefore, the sample space for x is {0, 1, 2, 3}, which means that the player has a 0% probability of making 0 shots, a 40% probability of making 1 shot, an 80% probability of making 2 shots, and a 100% probability of making all 3 shots
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Financial institutions often offer lower auto loan rates for new cars than used ones. A local credit union advertises new car loans at 2.79% APR and used car loans at 3.29% both for up to 72 months.
Tyresa wants to buy a car but doesn’t want to spend more than $350 a month for a maximum of four years. What is the maximum loan amount she can take out for a new car and a used car using the advertised rates?
Use the formula, A = P[(1 + r/n)^nt - 1] / r/n(1 + r/n)^nt , where P is the monthly payment, r is the annual interest rate, n is the number times interest is compounded in one year, and t is the number of years. Show all of your steps.
Using the loan rates we know that the maximum loan amount Tyresa needs to pay for 4 years which is 48 months is $330.81 for the new car.
What are loan rates?The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal or the loaned amount.
Typically, a loan's interest rate is expressed as an annual percentage rate, or APR (APR).
The annual cost of a loan to a borrower is referred to as the interest rate and is indicated as a percentage.
APR represents the total yearly cost of a loan to the borrower, including all fees.
The APR is stated as a percentage, just like an interest rate.
Thus, we discover that using the present value formula:
Pv = C[(1-(1+i)n/i)]
Now, calculate for the new car as follows:
Pv = 350[(1-(1+2.79%/12)2.79%/12)]
Pv = $15879.04
Loan amount each month: 15879.04/48 months = $330.81
Similarly, calculate for the old car as follows:
Pv = 350[(1-(1+3.29%/12)3.29%/12)]
Pv = $15721.34
Loan amount each month: 15721.34/48 months = $327.52
Therefore, using the loan rates we know that the maximum loan amount Tyresa needs to pay for 4 years which is 48 months is $330.81 for the new car.
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A 7 in. medium-angle grinder is on sale for $117.60 and is marked as being 20% off. What was the original list price?
(Type a whole number or an exact decimal. If the decimal does not terminate round two decimal places)
Answer:
the original list price of the grinder was $147
Step-by-step explanation:
If the sale price is 20% off the original price, then the sale price is 100% - 20% = 80% of the original price. We can set up the equation:
Sale price = 0.8 * original price
We know the sale price is $117.60, so we can substitute and solve for the original price:
117.60 = 0.8 * original price
original price = 117.60 / 0.8
original price = 147
Therefore, the original list price of the grinder was $147.
5 Use three of the terms below to fill in the two
expressions. Each term may be used only once. Both
of your expressions must be equivalent to 0.5x + 1.5.
0.5
2
X
+
+
0.25x
3
0.75
Both expressions 0.5 + 2(0.25x) + 0.75(3-x) and 2 - 2(0.75x) - 3(0.25x) are equivalent to 0.5x + 1.5, and they satisfy the condition that each term is used only once.
How did we arrive at this assertion?One possible solution is:
0.5 + 2(0.25x) + 0.75(3-x) = 0.5x + 1.5
Simplifying this expression:
0.5 + 0.5x + 0.5x + 2(0.25x) + 2.25 - 0.75x = 0.5x + 1.5
0.5x + 0.5x - 0.75x = 1.5 - 0.5 - 2.25
0.25x = -0.25
x = -1
Substituting x = -1 into 0.5x + 1.5:
0.5(-1) + 1.5 = 0.5 + 1.5 = 2
Therefore, another equivalent expression is:
2 - 2(0.75x) - 3(0.25x) = 0.5x + 1.5
Simplifying this expression:
2 - 1.5x = 0.5x + 1.5
2 - 1.5x - 0.5x = 1.5
-2x = -0.5
x = 0.25
Substituting x = 0.25 into 0.5x + 1.5:
0.5(0.25) + 1.5 = 0.125 + 1.5 = 1.625
Therefore, both expressions 0.5 + 2(0.25x) + 0.75(3-x) and 2 - 2(0.75x) - 3(0.25x) are equivalent to 0.5x + 1.5, and they satisfy the condition that each term is used only once.
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given pseudo code, write the method in JAVA, pseudocode had different parameters PLEASE WRITE WITH ONLY INT[] ARR AS PARAMETER
public static Triple getMaxSubArray(int[] arr) This method returns a triple that represents the maximum subarray. The first element of the triple is the index in arr where the maximum subarray starts, the middle element of the triple is where the index in the arr where maximum subarray ends, and the last element of the triple is the maximum subarray sum
findMaxSubarry(arr,low,high)
if high==low return (low,high,arr[low])
else
mid = mid point of arr
(l-low,l-high,l-sum) = findMaxSubarray(arr,low,mid)
(r-low,r-high,r-sum) = findMaxSubarray(arr,mid+1,high)
c-low,c-high,c-sum) = findMaxCrossing(arr,low,mid,high)
if l-sum ≥ r-sum and l-sum ≥ c-sum
return (l-low,l-high,l-sum)
else if r-sum ≥l-sum and r-sum ≥ c-sum
return (r-low,r-high,r-sum)
else
return (c-low,c-high,c-sum)
findMaxCrossing(arr,low,mid,high)
l-sum = MIN
sum = 0
for i=mid downto low
sum = sum arr[i]
if sum > l-sum
l-sum = sum
max-left = i
r-sum = MIN
sum = 0
for j=mid+1 to high
sum = sum + arr[j]
if sum > r-sum
r-sum = sum
max-right = j
return (max-left,max-right,l-sum+r-sum);
The Pseudocode is discussed below.
What is JAVA?Java is a high-level, class-based, object-oriented programming language that is designed to have as few implementation dependencies as possible.
Given is to write a Pseudo code.
In computer science, pseudo - code is a plain language description of the steps in an algorithm or another system.Pseudo - code often uses structural conventions of a normal programming language, but is intended for human reading rather than machine reading.Pseudocode is an artificial and informal language that helps programmers develop algorithms. Pseudocode is a "text-based" detail (algorithmic) design tool is an artificial and informal language that helps programmers develop algorithms. Pseudocode is a "text-based" detail (algorithmic) design toolTherefore, the Pseudocode is discussed above.
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5x2 + 2x − 3) − (2x2 − 3x + 7) expressed as a trinomial
Answer:
13x-16
Step-by-step explanation:
I am assuming that you mean 5*(2 + 2x − 3) − (2*2 − 3x + 7).
That equals 10x-5+3x-11=13x-16
Which exponential function is represented by the graph? O f(x) = 213x) O f(x) = 3(3x) O f(x) = 3(2x) O F(x) = 2(2x)
The exponential function that is represented by the graph is f(x) = 2(2x).
This is because the graph shows a function with a base of 2 and an exponent of x. The function f(x) = 2(2x) has a base of 2 and an exponent of x, so it matches the graph.
To verify this, we can plug in some values of x into the function and see if they match the points on the graph. For example, when x = 0, the function gives us f(0) = 2(2^0) = 2(1) = 2, which matches the point (0, 2) on the graph. Similarly, when x = 1, the function gives us f(1) = 2(2^1) = 2(2) = 4, which matches the point (1, 4) on the graph.
Therefore, the correct answer is f(x) = 2(2x).
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Suppose ABC is a right triangle with sides a, b, and c and right angle at C. Use the Pythagorean theorem to find the unknown side length. Then find the values of the six trigonometric functions for angle B. Rationalize the denominators when applicable.
a=8, b=15
The six trigonometric functions' values for angle B in this right triangle are as follows: Tan(B) = 8/15 CSC(B) = 17/8 Sin(B) = 8/17 Cos(B) = 15/17 Tan(B) = 8/15 (rationalized denominator)
cot(B) = 15/8 sec(B) = 17/15.
The length of the unknown side, which in this case is the hypotenuse c, can be determined using the Pythagorean theorem:[tex]c2 equals a2 + b2; c2 equals 82 + 152; c2 equals 64 + 225^2 = 289 \sc = √289 \sc = 17[/tex]
Thus, the hypotenuse's length is 17.
We must first get the measure of angle B before we can determine the values of the six trigonometric functions for that angle. Since angle C is a right angle and the total of the angles in a triangle is 180 degrees, we can calculate angle B's measure as follows:
angle B is equal to 90 times angle A, or 90 times angle B.
For now, since we lack sufficient data to estimate the size of angle A, angle B will be specified in terms of an unknowable angle. We are still able to calculate the six trigonometric functions for angle B using the ratios of the triangle's side lengths.
B = opposite/hypotenuse = a/c = 8/17;
B = adjacent/hypotenuse = b/c = 15/17;
B = opposite/adjacent = a/b = 8/15;
B = hypotenuse/opposite = c/a = 17/8;
B = cos(B) = (rationalized denominator)
Hypotenuse/nearby = c/b = 17/15; adjacent/opposite = b/a = 15/8; sec(B) = c/b = 17/15; cot(B) = b/a = 15/8.
For angle B in this right triangle, the values of the six trigonometric functions are as follows:
sin(B) = 8/17
cos(B) = 15/17
tan(B) = 8/15
csc(B) = 17/8 (rationalized denominator)
sec(B) = 17/15
cot(B) = 15/8
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In one season, a basketball player missed 50% of her free throws. How many free throws did she attempt if she made 183 free throws?
Answer:
Step-by-step explanation:
50% of 366 is 183, therefore your answer is 366.
If a customer uses a discount code that offers a 25% discount and free shipping, the hammer will cost $17.25. There is no sales tax if the customer buys the hammer online.
What is the original price of the hammer from the online retailer?
Answer:
the answer is 21.56
Step-by-step explanation:
have a nice day.
Which of the following tables shows a valid probability density function? Select all correct answers. Select all that apply: O x P(X = x) 0 0.37 1 0.06 2 0.01 3 0.56 O x P(X = x) 0 3/8 1 3/8 2 1/4O x P(X = x) 0 1/8 1 1/8 2 1/8 3 3/8 4 1/4O x PX =x) 0 0.03 1 0.01. 2 0,61 3 0.31 4 0.21 O x P(X = x) 0 1/10 1 3/10 2 4/5 3 -1/5
The tables that show a valid probability density function, are tables 1 to 3
How to determine the tablesFrom the question, we have the following parameters that can be used in our computation:
Table of values
For a table to show a valid probability density function, the following must be true
Sum of P(X = x) = 1
Using the above as a guide, we have the following:
Table 1: Sum = 0.37 + 0.06 + 0.01 + 0.56 = 1
Table 2: Sum = 3/8 + 3/8 + 1/4 = 1
Table 3: Sum = 1/8 + 1/8 + 1/8 + 3/8 + 1/4 = 1
Table 4: Sum = 0.03 + 0.01 + 0.61 + 0.31 + 0.21 = 1.17
Table 5: Sum = 1/10 + 3/10 + 4/5 + 1/5 = 1.4
Hence, the tables are tables 1 to 3
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The time to complete a construction project is normally distributed with a mean of 60 weeks and a standard deviation of 4 weeks. Solve all following questions both manually (by looking up the Z table) and using Excel.
(1) (2 pts for manual calculation; 2 pts for using Excel) What is the probability the project will be finished in 62 weeks or less?
(2) (2 pts for manual calculation; 2 pts for using Excel) What is the probability the project will take longer than 65 weeks?
(3) (2 pts for manual calculation; 2 pts for using Excel) What is the probability the project will be finished between 62 and 66 weeks?
1. The probability the project will be finished in 62 weeks or less is 0.6915. 2.The probability the project will be finished in longer than 65 days is 0.8944.
What is standard score?The standard score in statistics is the amount of standard deviations that a raw score (i.e., an observed value or data point) deviates from or exceeds the mean of the thing being observed or measured. Standard scores are positive for raw scores above the mean and negative for raw scores below the mean.
It is determined by deducting the population mean from a given raw score, then dividing the result by the population standard deviation. Standardizing or normalising is the process of transforming a raw score into a standard score.
Given that,
mean = 60 weeks
SD = 4 weeks
1. P (p ≤ 62) = P(z ≤ 62)
The z-score is given by:
z-score = x - mean / SD
Substituting the values we have:
z-score = 62 - 60/4 = 2/4 = 0.5
P(z ≤ 0.5) = 0.6915 (Using the z -table)
Hence, the probability the project will be finished in 62 weeks or less is 0.6915.
Similarly,
2. P(z > 65) = P(z > 1.25) = 0.8944
Hence, the probability the project will be finished in longer than 65 days is 0.8944.
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what is 5 - 1/4 as a simplest form?
5 - 1/4 in simplest form is 19/4.
Define the simplest form.The phrase "expressing a number, fraction, or statement in its simplest form" has a mathematical meaning. This signifies that further simplification or reduction of the result would cause a change in the result's value.
By dividing the numerator and denominator by their 4 greatest common factors, for instance, the fraction 4/8 can be made simpler. In its simplest form, this gives us 1/2. A different number, such as 0.5, which is not in its simplest form, results from additional simplification.
To simplify 5 - 1/4, we need to find a common denominator and combine the terms. The common denominator is 4, so we can write:
5 - 1/4 = 20/4 - 1/4
= (20 - 1)/4
= 19/4
Therefore, 5 - 1/4 in simplest form is 19/4.
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Adam is planning
a rectangular patio that will have an area of
16x2 1 20x square feet. The length of the patio
will be x 1 5 feet. Write an expression to
represent the width of the patio.
Answer:
The width of the patio is 15 feet
Step-by-step explanation:
We can start by using the formula for the area of a rectangle:
Area = length x width
In this case, we know that the area of the patio is given by:
16x^2 + 20x square feet
And we also know that the length of the patio is x + 5 feet. So we can substitute these values into the formula to get:
16x^2 + 20x = (x + 5) x width
Simplifying the right-hand side by multiplying x + 5 by width, we get:
16x^2 + 20x = width x^2 + 5x
To solve for the width, we can move all the terms with width to the left-hand side and all the other terms to the right-hand side:
width x^2 - 16x^2 + 20x - 5x = 0
Simplifying the left-hand side by combining like terms, we get:
width x^2 - 16x^2 + 15x = 0
Factoring out x, we get:
x (width x - 16x + 15) = 0
Now we can solve for the width by setting each factor equal to zero and solving for x:
x = 0 or width x - 16x + 15 = 0
Since the length and width of the patio must be positive values, we can disregard the solution x = 0. So we are left with:
width x - 16x + 15 = 0
We can factor this quadratic equation by finding two numbers whose product is 15 and whose sum is -16. These numbers are -1 and -15, so we can write:
(width x - 1)(x - 15) = 0
Setting each factor equal to zero and solving for x, we get:
width x - 1 = 0 or x - 15 = 0
width x = 1 or x = 15
Since the length of the patio is x + 5, which is 20 feet, we know that x = 15 is the correct solution. So we can substitute x = 15 into the expression for the width:
width x = 1, x = 15, so we choose x = 15
width x - 16x + 15 = (15) x - (16)(15) + 15 = 15 feet
Therefore, the width of the patio is 15 feet.
If f(x)=3x^2+1 and g(x)=1-x, what is the value of (f-g)(2)?
Answer:
14
Step-by-step explanation:
To find the value of (f-g)(2), we first need to compute the function (f-g), which is defined as the difference between f(x) and g(x), and then evaluate it at x=2.
So, (f-g)(x) = f(x) - g(x)
Substituting the given functions, we get:
(f-g)(x) = (3x^2 + 1) - (1-x)
(f-g)(x) = 3x^2 + x
Now, to find (f-g)(2), we substitute x=2 into the expression we just obtained:
(f-g)(2) = 3(2)^2 + 2
(f-g)(2) = 3(4) + 2
(f-g)(2) = 12 + 2
(f-g)(2) = 14
Therefore, the value of (f-g)(2) is [14.]
What is the length of CG??
The length of CG is approximately 5.4 units.
Describe Triangles?A triangle is a closed geometric figure that is formed by connecting three straight line segments called sides. These sides meet at three points called vertices. Triangles are one of the simplest and most fundamental shapes in geometry and can be found in many natural and man-made objects.
Triangles can be classified into different types based on their sides and angles.
By sides:
Equilateral triangle: all three sides are equal in length.
Isosceles triangle: two sides are equal in length.
Scalene triangle: all three sides are different in length.
By angles:
Acute triangle: all three angles are acute (less than 90 degrees).
Right triangle: one angle is a right angle (exactly 90 degrees).
Obtuse triangle: one angle is an obtuse angle (greater than 90 degrees).
Triangles have many properties and are used in various fields such as architecture, engineering, physics, and mathematics. They are also commonly used in trigonometry to solve problems involving angles and distances.
We can use the property of similar triangles to solve this problem.
First, let's label the intersection point of FG and BC as point H. Also, let's label the length of CG as x.
Since FG is parallel to AC, we can use the property of similar triangles to find that triangles ABF and HBG are similar.
Therefore, we can set up the proportion:
AB/FB = HG/GB
Plugging in the given values, we get:
10/63 = (x + 57)/57
Solving for x, we get:
x = 5.4
Therefore, the length of CG is approximately 5.4 units.
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Using the arithmetic operation the value for x in the equation (x – 7)2 = 36 is obtained as 25.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The given equation is (x – 7)2 = 36.
Use the arithmetic operation of multiplication -
2x - 14 = 36
Collect all the like terms -
2x = 36 + 14
Use the arithmetic operation of addition -
2x = 50
Use the arithmetic operation of division -
x = 50/2
x = 25
Therefore, the value is 25.
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PLS ANSWER MY QUESTION QUICKLY
Answer:
B
Step-by-step explanation:
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