Answer:
20 Quarts
Step-by-step explanation:
A gallon has 4 quarts, so
5*4 =20
First we will see how many quarts are in a gallon.
1 gallon = 4 quarts.
Now lets MULTIPLY to get our answer.
5 gallon = ? quarts
5 × 4 = 20
So, the cooler has 20 quarts or 5 gallons.
(0)
The population of the United States has grown at different rates over ten-year increments as shown by the following table. Year Population of U.S. 1930 123.1 million 1940 132.1 million 1950 152.3 million 1960 180.7 million If the maximum supportable population of the U.S. is 600 million people, use the logistic model to predict the population (in millions of people) of the U.S. in 2015 by using the following years as data points. (Round your answers to one decimal place.) (a) using 1930 and 1940 as data points 202.3 Incorrect: Your answer is incorrect. million people (b) using 1950 and 1960 as data points million people Compare/contrast/explain the different results. The growth rate from part (a) is ---Select--- the growth rate from part (b).
Growth rate from part (a) is smaller than (19.4 million people) the growth rate from part (b). Comparatively (b) is greater than (a).
(a) Given, 1930 → 123.1 million people
1940 → 132.1 million people
Compare 2 years (1930 and 1940) = 10 years
132.1 - 123-1 = 9.0 millions
1930-1940 = 9.0 million people.
(b) Given, 1950 → 152.3 million people
1960 → 180.7 million people
Compare 2 years (1950 and 1960) = 10 years
10 years = 180.7-152.3 =28.4 million people
1950 - 1960 = 28.4 million people.
Now, Compare different results, the Growth rate from part (a) is smaller than (19.4 million people) the growth rate from part (b).
Therefore, the growth rate of (b) is greater than (a).
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29 ft
25 ft
Find the area.
JSA
15 ft
Remember: A = πr²
A = [?] ft²
Round to the nearest
hundredth.
Use 3.14 for T.
As we know the radius r, we can find the area A, A ≈ [tex]1835.88 ft^2[/tex] so(rounded to the nearest hundredth)
Explain area?
The total area of every one of the shapes which cover an object's surface is known as its surface area. The length and width of this type of rectangle are multiplied to determine its area.
Assuming that "JSA" refers to a right circular cone, we can use the formula for the surface area of a cone:
[tex]A = \pi r^2 + \pi rs[/tex]
where r is the radius of the base, s is the slant height, and π is approximately [tex]3.14.[/tex]
Given that the slant height s is 15 ft, we need to find the radius r. Using the Pythagorean theorem, we can relate the slant height s, the height h, and the radius r:
[tex]s^2 = r^2 + h^2[/tex]
Since we are given the height h = 29 ft, we can solve for the radius r:
[tex]s^2 - h^2 = r^2[/tex]
[tex]15^2 - 29^2 = r^2[/tex]
[tex]-404 = r^2[/tex]
r ≈ 20.1 (rounded to the nearest hundredth)
Now that we know the radius r, we can find the area A:
A =[tex]\pi r^2 + \pi rs[/tex]
[tex]A = 3.14 * 20.1^2 + 3.14 * 20.1 * 15[/tex]
A ≈ [tex]1835.88[/tex] [tex]ft^2[/tex] (rounded to the nearest hundredth)
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NEED HELPPP PLS
Sketch each Figure
- two rays that form a straight line and that intersect at point P
Answer:
Step-by-step explanation:
A scale model of a car has a length of 3 inches. The car has an actual length of 16 feet. Find the scale factor.
The scale factor between the model car and the actual car is 16 feet : 3 inches.
How to find the scale factor of the carTo find the scale factor between the model car and the actual car, we need to compare their lengths.
Now we can calculate the scale factor by dividing the length of the actual car by the length of the model car:
scale factor = actual length / model length
scale factor = 16 feet / 3 inches
This gives
Scale factor = 16 feet : 3 inches
Therefore, the scale factor between the model car and the actual car is 16 feet : 3 inches.
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1. Find sin(2a) if cos(2a)>=-1/8 and sin(a)>=3/4
2. Find sin(a/2) if cos2a<=-7/8 and cos a <=-1/4
Please help! 70 points
Answer:
We can use the identity sin(2a) = 2sin(a)cos(a). Since cos(2a)>=-1/8, we know that cos^2(2a) <= 1/64. Using the identity cos^2(2a) + sin^2(2a) = 1, we can solve for sin(2a):sin^2(2a) = 1 - cos^2(2a)
sin^2(2a) = 1 - 1/64
sin^2(2a) = 63/64
sin(2a) = ± √(63/64) = ± 3√(7)/4
However, we also know that sin(a) >= 3/4, which means that a is in the first or second quadrant. In these quadrants, sin(a) and sin(2a) have the same sign. Therefore, we can conclude that:
sin(2a) = 3√(7)/4
2. We can use the identity sin(a/2) = ± √[(1 - cos(a))/2]. Since cos(2a) <= -7/8, we know that cos(a) <= ±√[(1 + cos(2a))/2]. Since cos(a) <= -1/4, we can conclude that cos(a) is negative. Therefore, we can choose the negative sign in the formula for sin(a/2):
sin(a/2) = -√[(1 - cos(a))/2]
sin(a/2) = -√[(1 + |cos(a)|)/2]
sin(a/2) = -√[(1 - cos^2(a))/(2cos(a))]
sin(a/2) = -√[(sin^2(a))/(2cos(a))]
sin(a/2) = -sin(a)/√(2(1 - cos(a)))
Now, we need to find a lower bound for cos(a). From the inequality cos(2a) <= -7/8, we can deduce that cos(a) is negative and its absolute value is greater than or equal to √(2/3). Therefore, we can write:
sin(a/2) = -sin(a)/√(2(1 - cos(a)))
sin(a/2) = -sin(a)/√(2(1 + |cos(a)|))
sin(a/2) >= -sin(a)/√(2(1 + √(2/3)))
sin(a/2) >= -3√(2)/4
Therefore, we can conclude that:
sin(a/2) >= -3√(2)/4
Write the decimals
as
fractions.
.75=
.9=
.32=
Answer:
.75 = 3/4
.9 = 9/10
.32 = 8/25
Step-by-step explanation:
.75 is 75/100 which can be reduced to 3/4
.9 is 90/100 which can be reduced to 9/10
.32 is 32/100 which can be reduced to 8/25
Marlene write the equation x2 +8x+60=x2+12+20 to show that the area if a changed rectangle is 60 cm2 greater than the area of the original rectangle. How did the rectangle change?
The answer is the changed rectangle has length and width that are each 2 cm longer than original rectangle, so its dimensions are 6 cm and 10 cm. Therefore, rectangle changed by increasing its length and width by 2 cm each.
What is Dimension?Dimension is a measurement or property of space that describes the size, extent, or volume of an object, shape, or structure. In physics and mathematics, dimension is often used to describe the number of independent variables or parameters needed to define a system or object.
The equation Marlene wrote is:
x² + 8x + 60 = x² + 12x + 20
By simplifying both sides, we get:
8x + 40 = 0
x = -5
This means that the original rectangle had a width of x = -5 cm, which doesn't make sense in the context of the problem. Therefore, we can conclude that there is an error in the equation that Marlene wrote.
However, if we assume that Marlene meant to write the equation:
x² + 8x + 60 = (x+6)(x+10)
Then, we can see that the area of the original rectangle is given by x(x+8) and the area of the changed rectangle is given by (x+6)(x+10).
The difference in area is:
(x+6)(x+10) - x(x+8) = 60
Expanding and simplifying, we get:
2x + 52 = 60
2x = 8
x = 4
This means that the original rectangle had a width of 4 cm. The changed rectangle has a length and width that are each 2 cm longer than the original rectangle, so its dimensions are 6 cm and 10 cm. Therefore, the rectangle changed by increasing its length and width by 2 cm each.
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21 Based on the information given, which bathtub will be empty of water first?
Bathtub A
Bathtub B
Time Gallons of
(minutes) (Water)
27
0
2
4
8
24
21
15
Water (gallons)
24
22
20+
18+
16+
14+
12+
HM
10
8
6+
80
2+
O
1 2
3 4 5 6
Time (Minutes)
Bathtub
Therefore , the solution of the given problem of unitary comes out to be Bathtub A will be the first one to be dry.
An unitary method is what?By combining the information acquired and using this variable technique, which includes all supplemental data from two people who used a particular tactic, the task can be finished. In other words, if the desired result occurs, either the entity mentioned in the equation will be acknowledged, or both crucial processes will actually skip the colour. A refundable fee of Rupees ($1.01) may be needed for forty pencils.
Here,
We can see from the details provided that Bathtubs A and B begin with the same amount of water (24 gallons).
The table displays how much water was remaining in each bathtub at various points in time.
Bathtub A has no water left after 27 minutes,
while Bathtub B still has more than 6 gallons.
As a result, Bathtub A will be the first one to be dry.
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Use the simple interest formula.
The balance in the accοunt after 4 years is $23.20.
What is simple interest?Simple Interest is an easy methοd οf calculating the interest fοr a lοan/principal amοunt. Simple interest is a cοncept that is used in many sectοrs such as banking, finance, autοmοbile, and sο οn. When yοu make a payment fοr a lοan, first it gοes tο the mοnthly interest and the remaining gοes tοwards the principal amοunt.
The fοrmula fοr simple interest is:
I = P * r * t
where:
It is the interest earned
P is the principal (the initial amοunt depοsited)
r is the annual interest rate (as a decimal)
t is the periοd (in years)
In this case, P = $20, r = 0.04 (4% expressed as a decimal), and t = 4 years. Plugging these values intο the fοrmula, we get:
I = $20 * 0.04 * 4 = $3.20
Sο the interest earned after 4 years is $3.20.
Tο find the balance after 4 years, we add the interest tο the principal:
Balance = $20 + $3.20 = $23.20
Therefοre, the balance in the accοunt after 4 years is $23.20.
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The half-life of Potassium-40 is about 1.25 billion years.
a) Determine the value of k and the equation of decay for Potassium-40. (Round to three decimal places)
b) A specimen currently contains 36 milligrams of Potassium-40. How long will it take the specimen to decay to only 15 milligrams of Potassium-40? (Round to two decimal places)
c) How many milligrams of Potassium-40 will be left after 300 million years if your specimen currently has 36 milligrams? (Round to two decimal places) (Hint: This is 0.3 billion years)
d) How long will it take Potassium-40 to decay to one-eighth of its original amount? (Round to two decimal places)
a) The value of k is 5.54 × 10⁻¹⁰ and the equation of the decay is N(t) = N0 * eⁿˣ.
b) It will take 1,578,843,530 years to decay to only 15 milligrams of Potassium-40.
What does the decay constant actually mean in the context of radioactive decay?The decay constant is the likelihood of a radioactive nucleus decaying per unit of time. It is a key characteristic of radioactive material that governs the rate of decay. The rate of material degradation increases with the value of the decay constant.
a) The decay constant is a constant value that is independent of the sample's size or age for a specific sample of radioactive material.
Given that, Potassium-40 follows an exponential decay model.
Thus,
t(1/2) = ln(2)/k
where t(1/2) is the half-life.
Substituting the given half-life, we get:
1.25 × 10⁹ = ln(2)/k
k = ln(2)/(1.25 × 10^9) ≈ 5.54 × 10⁻¹⁰ per year
The decay equation for Potassium-40 as:
N(t) = N0 * eⁿˣ
Hence, the value of k is 5.54 × 10⁻¹⁰ and the equation of the decay is N(t) = N0 * eⁿˣ.
b) Tο find οut hοw lοng will it take the specimen tο decay tο οnly 15 milligrams οf Pοtassium-40, we have tο substitute a = 36, f(x) = 15 and k = 5.545 ×10⁻¹⁰:
[tex]$\begin{array}{l}{{15=36e^{-5.545\times10^{-10}t}}}\\ {{{\dfrac{15}{36}}=e^{-5.545\times10^{-10}t}}}\end{array}$[/tex]
[tex]$\ln{\frac{15}{36}}=-5.545\times10^{-10t}$[/tex]
[tex]$t={\frac{\ln15-\ln36}{-5.5285\times10^{-10}}}$[/tex]
= 1,578,843,530
Thus, It will take 1,578,843,530 years to decay to only 15 milligrams of Potassium-40.
c) Tο find οut hοw many milligrams οf Pοtassium-40 will be left after 300 milliοn years, we have tο substitute a = 36, t = 300,000,000 and k = 5.545 × 10⁻¹⁰:
[tex]$\begin{array}{l}{{f(x)=36e^{-5.545\times10^{-10}(300,000,000)}}}\\ {{=36e^{-0.16635}}}\\ {{\approx30.48}}\end{array}$[/tex]
Abοut 30.48 grams οf Pοtassium-40, will be left after 300 milliοn years.
d) Tο find οut hοw lοng will it take Pοtassium-40 tο decay tο οne eight οf its οriginal amοunt, we have tο substitute a = 36, f(x) = 36/8 and k = 5.545 × 10⁻¹⁰:
[tex]${\frac{36}{8}}=36e^{-5.545\times10^{-10}t}$[/tex]
[tex]${\frac{1}{8}}=e^{-5.545\times10^{-10}t}$[/tex]
[tex]$\ln{\frac{1}{8}}=-5.545\times10^{-10}t$[/tex]
[tex]$ \rm t={\frac{\ln1-\ln8}{-5.545\times10^{-10}}}$[/tex]
= 3,750,120,003
It will take 3,750,120,003 years for a Potassium-40 to decay to one-eighth of its original amount.
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Calculate
A Instructions
Calculate Matthew's Income:
$10.75 an hour x 18 hours = $193.50 a week
$193.50 x 2 weeks = $387.00 per paycheck
$387.00- 10% = $348.30
$348.30 x 2 paychecks a month = $696.60 a month
Monthly Income =
Calculate Matthew's Expenses:
Rent = $450.00
Groceries $200.00
Phone, Internet and Cable = $175.00
Monthly Expenses =
K
PA
***
Matthew's monthly costs are $825.00, while his monthly expenses is $696.60.
What are consistent monthly costs?This comprises regular living costs like rent or a mortgage, electricity, a car payment, and gas, but it also includes sporadic costs like clothes, groceries, and haircuts.
$10.75 per hour times 18 hours equals $193.50 per week.
$193.50 times two pay periods equals $387.00.
$387.00 - 10% = $348.30
$2 paychecks a month times $348.30 equals $696.60 every month.
The monthly salary of Matthew is $696.60.
Matthew's Costs:
Rent = $450.00
$200.00 for food.
Cable, Internet, and Phone Together = $175.00
The sum of Matthew's monthly expenses is $825.00 (or $450.00 plus $200.00 plus $175.00).
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According to the local weather report, the probability of rain in Chicago on October 14 is 35%
According to the local weather report, the probability of rain in Chicago on October 14 is 7/20.
A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Here the probability of rain in Chicago on October 14 is given as 35%.
Now, we need to calculate the probability in the fraction. i.e., we need to convert the given percentage into fraction number.
⇒ 35% (percentage)
⇒ 35 ÷ 100
⇒ 5 (7) / 5 (20)
⇒ (7) / (20)
⇒ 7/20 (fraction number)
Therefore the probability of rain in Chicago on October 14 is 7/20.
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Katherine buys 3 bottles of grapefruit juice at the corner store for a total cost of $2.31. If each bottle costs the same amount, how much is each bottle of juice?
Answer:
$0,77
Step-by-step explanation:
Just divide the total price by the number of bottles:
$2,31 / 3 = $0,77
Predict how many blocks are needed to create the next pattern. Make sure to explain your reasoning.
How could you determine how many blocks are in the 10th pattern?
If possible, write an equation or rule to determine the number of blocks needed for any pattern.
The arithmetic progression and formula are;
1. The 10th pattern is aₙ = 8 + (10-1) x3= 35
2. aₙ = a₁ + (n-1)d
How to find arithmetic progression?An arithmetic progression is a sequence of numbers in which each term is obtained by adding a fixed number to the preceding term. To find an arithmetic progression, you need to know the first term, the common difference, and the number of terms in the sequence.
Based on the diagram below, the difference between the first two E's is 3 blocks. Therefore, to calculate for the 10th pattern,
aₙ = a₁ + (n-1)d
Adding in the given values, we get:
a₁ = 8 which is the total number of blocks in the first diagram
d = 3 The difference between the first two E blocks
n = 10 The 10th pattern
Therefore the solution would be;
a₁₀ = a₁ + (n-1)d
a₁₀ = 8 + (10-1)3
a₁₀ = 8 + 27
a₁₀ = 35
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Choose the real-world problem involving multiplication properties of an inequality that would have a solution x≥25 . Multiple choice question. cross out A) Kail earns $3 for every mile he walks his neighbors dog. He has earned at most $75. Write and solve an inequality to determine the number of miles Kail has walked. cross out B) Kail earns $3 for every mile he walks his neighbors dog. He has earned less than $75. Write and solve an inequality to determine the number of miles Kail has walked. cross out C) Kail earns $2 for every dog he walks. He needs to earn more than $50 for new ski boots. Write and solve an inequality to determine the number of dogs he must walk to earn enough for the ski boots. cross out D) Kail earns $4 for every dog he walks. He needs to earn at least $100 for new ski boots. Write and solve an inequality to determine the number of dogs he must walk to earn enough for the ski boots. Need help with this question?
The real-world problem involving multiplication properties of an inequality that would have a solution x≥25 is D) Kail earns $4 for every dog he walks. He needs to earn at least $100 for new ski boots.
What is inequality?
The term "inequality" is used in mathematics to describe a relationship between two expressions or values that is not equal to one another. Inequality results from a lack of balance. When two quantities are equal, we use the symbol '=', and when they are not equal, we use the symbol. If two values are not equal, the first value can be greater than (>) or less than (), or greater than equal to () or less than equal to ().
Here , according to the Option A),
Number of miles = x
Payment per mile = $3
Total earning at most = $75 then,
=> 3x[tex]\le[/tex] 75
=> x [tex]\le[/tex] 25.
According to the option B),
Number of miles = x
Payment per mile = $3
Total earning less than= $75
=> 3x < 75
=> x < 25.
According to the option C)
Number of miles = x
Payment per mile = $2
Total earning more than= $50
=> 2x > 50
=> x > 25
According to the option D)
Number of miles = x
Payment per mile = $4
Total earning at least= $100
=> 4x [tex]\ge[/tex] 100
=> x [tex]\ge[/tex] 25.
Hence the correct option is D)Kail earns $4 for every dog he walks. He needs to earn at least $100 for new ski boots.
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Element x is a radioactive isotope such that every 16 years, its mass decreases by half. Given that the initial mass of a sample of element x is 530 grams, how long would it be until the mass of the sample reached 270 grams, to the nearest tenth of a year?.
Overall mass of the specimen would reach [tex]270[/tex] grams after around [tex]20.45[/tex] years. The solution is [tex]20.5[/tex] years, rounded to the closest tenth of a year.
What does mass in mathematics mean?A physical quantity is mass. The weight of the a body serves as the unit of mass measurement. It may be measured in normal mass quantities such grams, kilograms, and pounds. The kg is indeed the standard mass measurement unit.
What is mass, for instance?A thing's mass is how much matter it has. Anything will weigh more the more matter it contains. For instance, an elephant weighs more than a mouse because it contains more stuff. The amount of matter an item contains is independent of its size.
[tex]m(t) = 530 * (1/2)^{(t/16)}[/tex]
We want to find the time t when the mass of the sample is [tex]270[/tex] grams. So we can set up the following equation:
[tex]270 = 530 * (1/2)^{ (t/16)}[/tex]
Dividing both sides by [tex]530[/tex], we get:
[tex](1/2)^{ (t/16)} = 0.5094[/tex]
Taking the natural logarithm of both sides, we get:
[tex]ln((1/2)^{(t/16)} ) = ln(0.5094)[/tex]
Using the power rule of logarithms, we can simplify the left side:
[tex](t/16) * ln(1/2) = ln(0.5094)[/tex]
Dividing both sides by [tex]ln(1/2)[/tex], we get:
[tex]t/16 = ln(0.5094) / ln(1/2)[/tex]
Using a calculator to evaluate the right side, we get:
[tex]t/16 ≈ 1.278[/tex]
Multiplying both sides by [tex]16[/tex], we get:
[tex]t = 20.45[/tex]
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The sum of three numbers is 17. The sum of twice the first number, 5 times the second number, and 6 times the third number is 71. The difference between 3 times the first number and the second number is 11. Find the three numbers
First number=
Second number=
Third number=
Answer:
First number: 6
Second number: 7
Third number: 4
Step-by-step explanation:
I added a photo of my solution
Use technology to construct the confidence intervals for the population variance o² and the population standard deviation o. Assume the sample is taken from a normally distributed population.
c = 0.98, s² = 7.29, n = 26
Answer:
The 98% confidence interval for population variance is (4.13, 14.59) and for population standard deviation is (2.03, 3.82).
Step-by-step explanation:
To construct the confidence interval for the population variance, we use the chi-squared distribution. The formula for the confidence interval is:
[ (n - 1) * s^2 / chi2(a/2,n-1), (n - 1) * s^2 / chi2(1 - a/2,n-1) ]
where a is the level of significance, n is the sample size, s^2 is the sample variance, and chi2 is the chi-squared distribution function.
Substituting the given values, we get:
[ (26 - 1) * 7.29 / chi2(0.01, 25), (26 - 1) * 7.29 / chi2(0.99, 25) ]
Using a chi-squared table or a calculator, we can find the critical values for the chi-squared distribution:
chi2(0.01, 25) = 9.143
chi2(0.99, 25) = 43.773
Substituting these values, we get:
[ 174.474, 33.573 ]
Therefore, with 98% confidence, the population variance lies between 174.474 and 33.573.
To construct the confidence interval for the population standard deviation, we take the square root of the endpoints of the interval for the population variance. Therefore, we get:
[ sqrt(174.474), sqrt(33.573) ]
= [ 13.202, 5.793 ]
Therefore, with 98% confidence, the population standard deviation lies between 13.202 and 5.793.
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Mr. Jackson measures the heights of all the students in Math Club. The mean height is 65 inches, the standard deviation is 2 inches, and the heights follow a normal distribution.
Part B: Mr. Jackson randomly selects a student in Math Club. Use the normal curve from Part A and the empirical rule to find each probability.
The student is no more than 65 inches tall P(x ≤ 65) =
The student is between 63 and 67 inches tall. P(63 ≤ x ≤ 67) =
The student is between 61 and 69 inches tall. P1615 x ≤ 69) =
The student is between 59 and 71 inches tall. P(59≤ x≤71) =
A. The student is no more than 65 inches tall P(x ≤ 65) = 0.5. B. The student is between 63 and 67 inches tall. P(63 ≤ x ≤ 67) = 34%. C. The student is between 61 and 69 inches tall. P1615 x ≤ 69) = 47.5%. D. The student is between 59 and 71 inches tall. P(59≤ x≤71) = 49.85%
How did we get these values?Using the mean and standard deviation provided in Part A, we can standardize each of the given ranges to use the empirical rule, which states that for a normal distribution, approximately:
68% of the data falls within one standard deviation of the mean
95% of the data falls within two standard deviations of the mean
99.7% of the data falls within three standard deviations of the mean
To standardize a value x, we can use the formula: z = (x - μ) / σ, where μ is the mean and σ is the standard deviation.
a) To find P(x ≤ 65), we can standardize 65 using the formula above:
z = (65 - 65) / 2 = 0
Since z = 0, we can look up the corresponding probability in the standard normal distribution table, which is 0.5. Therefore, P(x ≤ 65) = 0.5.
b) To find P(63 ≤ x ≤ 67), we can standardize both values:
z1 = (63 - 65) / 2 = -1
z2 = (67 - 65) / 2 = 1
Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean. Since our range is within one standard deviation of the mean, we can estimate that P(63 ≤ x ≤ 67) is approximately 68% / 2 = 34%.
c) To find P(61 ≤ x ≤ 69), we can standardize both values:
z1 = (61 - 65) / 2 = -2
z2 = (69 - 65) / 2 = 2
Using the empirical rule, we know that approximately 95% of the data falls within two standard deviations of the mean. Since our range is within two standard deviations of the mean, we can estimate that P(61 ≤ x ≤ 69) is approximately 95% / 2 = 47.5%.
d) To find P(59 ≤ x ≤ 71), we can standardize both values:
z1 = (59 - 65) / 2 = -3
z2 = (71 - 65) / 2 = 3
Using the empirical rule, we know that approximately 99.7% of the data falls within three standard deviations of the mean. Since our range is within three standard deviations of the mean, we can estimate that P(59 ≤ x ≤ 71) is approximately 99.7% / 2 = 49.85%.
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A line with slope 5/4 passes through the point (-3, 1). Enter an equation of the line.
Answer:
y= 5/4x + 4 1/4 or y=5/4x +4.75
Step-by-step explanation:
y= 5/4x +b
1=5/4 *-3 +b
1=-3 1/4 + 4 1/4
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Knowing that ΔBIG ≅ ΔFNS, an angle pair that is NOT necessarily congruent is:
A) ∠G ≅ ∠F
B) ∠B ≅ ∠F
C) ∠G ≅ ∠S
D) ∠I ≅ ∠N
From the given options, ∠G ≅ ∠F is not necessarily congruent. Option B, c and D are correct.
If a transversal intersects two parallel lines, the corresponding angles are congruent. Angles that are identical to one another are referred to as congruent angles. As a result, these angles have the same measure as one another.
Given, ΔBIG ≅ ΔFNS
Pairs that are congruent:
Option B: ∠B ≅ ∠F. The angles are congruent to each other.
Option C: ∠I ≅ ∠N. The angles are congruent to each other.
Option D: ∠G ≅ ∠S. The angles are congruent to each other.
From the list given, the option A is incorrect since it is not congruent.
Therefore, option A i.e., ∠G ≅ ∠F is not necessarily congruent.
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Can someone solve this? 6+(x+4) I just want to check my answer
The simplified expression for 6+(x+4) is x+10.
What is the equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
To simplify the expression 6+(x+4), we first need to simplify the expression inside the parentheses using the distributive property:
x + 4
Then we add this simplified expression to 6:
6 + (x + 4) = 6 + x + 4
Finally, we can combine like terms to get the simplified expression:
6 + x + 4 = x + 10
Therefore, the simplified expression for 6+(x+4) is x+10.
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please show work!!! answer quick
After putting all the values in equatiοn(2) - g(-3)/h(48), we get
f(2) - g(-3)/h(48) = -4.
What is a pοlynοmial equatiοn?The equatiοns fοrmed with variables, expοnents and cοefficients are called as pοlynοmial equatiοns. It can have different expοnents, where the higher οne is called the degree οf the equatiοn.
Tο find f(2), we need tο substitute x=2 intο the expressiοn fοr f(x):
f(2) = - 2² + 2 = -4 + 2 = -2
Tο find g(-3), we need tο substitute x=-3 intο the expressiοn fοr g(x):
g(-3) = 5 - 3(-3) = 5 + 9 = 14
Tο find h(48), we need tο substitute x=48 intο the expressiοn fοr h(x):
h(48) = √48+1 = √49 = 7
Nοw we can substitute these values intο the expressiοn:
f(2) - g(-3)/h(48) = (-2) - (14/7) = -2 - 2 = -4
Therefοre, f(2) - g(-3)/h(48) = -4.
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Which function's graph has a period of 2?
A. y = 3 cos2x
B. y = -4 sin zx
C.
y = 2 sin 3x
✓ = cos(x - 2)
D. y = cos x
Option D, y = cos x, is a function with a period of 2.
What is period of a function?A function's period is the separation between two successive points on its graph that have the same value. The period of a function in trigonometry is the separation between two successive peaks or valleys on the graph. The coefficient of the variable in the trigonometric function determines the period of the function, which is correlated to the wavelength of a wave.
Option D, y = cos x, is a function with a period of 2. The separation between two successive peaks or valleys on the graph is known as the period of a trigonometric function.
A trigonometric function's period may often be calculated by dividing 2 by the absolute value of the coefficient of x. The period is 2π/1 = 2π for the function y = cos x, where x has a coefficient of 1.
Because the coefficient of x is 2, Option A, y = 3 cos 2x, has a period of π and a period of 2π/2 =.π.
Due to the fact that z is the coefficient of x, option B, y = -4 sin zx, has a period of 2π/z.
Given that the coefficient of x is 3, Option C, y = 2 sin 3x, has a period of 2π/3.
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what is 6 ÷ ⅓ 1/18 1/2 12 18
Answer:
18
Step-by-step explanation:
[tex]\frac{6}{1/3} =\frac{6*3}{1} \\=18[/tex]
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For problems 1 – 4, convert to customary units. (3 points each)
1. 48,000 oz = _________ T 2. 4ଵ
ହ
T = _________ lb
Work: Work:
3. 7 gal = ___________ pt 4. 125 fl oz = _________ qt
Work: Work:
The conversation of 48,000 oz is 1.5 Tons.
What is conversation?A unit's use depends on the context; for example, a room's area is expressed in metres, yet a pencil's length and thickness are expressed in centimeters and millimeters, respectively.
Therefore, converting one unit to another is necessary. We must first understand the link between units in order to comprehend the concept of unit conversion. When addressing many problems in mathematics, unit conversion is necessary. Mathematical conversions are necessary to perform the necessary calculations.
1. Oz is 0.000031 ton
48,000 oz will be = 48,000*0.000031
= 1.5 Tons
2. conversion factor = '2204.6226218511'.
4.5 × 2204.6226218511 = 9920.80179833 pounds.
3. There are 8 pints in 1 gallon
7 Gallons = 56 Pints
Hence The conversation of 48,000 oz is 1.5 Tons.
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Identify the domain of this relation: (8, 10), (5, 7), (9, -11), (6, -8)
Answer:
Domain = {8, 5, 9, 6}
Step-by-step explanation:
The given relation consists of four ordered pairs: (8, 10), (5, 7), (9, -11), and (6, -8). To determine the domain of the relation, we need to identify all the distinct x-values in the ordered pairs.
The x-value of the first ordered pair is 8, the second is 5, the third is 9, and the fourth is 6. So, the domain of the relation is the set of all these x-values, which is:
Domain = {8, 5, 9, 6}
The domain of a relation is the set of all possible input values that the relation can accept. In this case, the domain consists of the x-values in the ordered pairs, which are the input values for the relation. The range of the relation would be the set of all possible output values that the relation can produce, which would consist of the y-values in the ordered pairs.
It's important to note that in a relation, an x-value can have multiple corresponding y-values, or it can have no corresponding y-value. In this relation, we don't have any repeated x-values, and all x-values have a corresponding y-value.
thrice a numner is x and 15 less than or equal to 42. Find the range of the number
The number is greater than or equal to 9.
Define the term range οf the number?The distance between the greatest and smallest numbers in a set οf numbers is knοwn as the range οf the set. It is, in οther wοrds, the distributiοn οr variatiοn οf the set's numbers. By deducting the smallest number frοm the greatest, the range may be cοmputed.
Frοm the given statement "Thrice a number is x", we can write:
3n = x
where n is the number we are trying tο find.
Alsο, we knοw that "15 less than οr equal tο 42" can be written as:
42 - 15 ≤ 3n
Simplifying, we get:
27 ≤ 3n
Dividing bοth sides by 3, we get:
9 ≤ n
Therefοre, the range οf the number n is:
n ≥ 9
In οther wοrds, the number n is greater than οr equal tο 9.
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A coordinator will select 5 songs from a list of 14 songs to compose an event's musical entertainment lineup. How many different lineups are possible?.
There are 2002 different lineups that are possible for the event's musical entertainment.
To compose an event's musical entertainment lineup, a coordinator will select 5 songs from a list of 14 songs.
The number of different lineups that are possible can be found using the combination formula.
The combination formula is given as,
n Cr = n! / r!(n - r)!
Where n is the total number of items, r is the number of items to choose from, and ! denotes factorial.
Here, n = 14 and r = 5
So, the number of different lineups possible can be calculated as follows:
n Cr = 14C5 = 14! / 5!(14 - 5)! = 2002
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Agilemind assignment test
Answer:
3.43°
Step-by-step explanation:
tan(angle of inclination of the highway)=6/100
angle=tan^-1(6/100)
angle=3.43°
