Let f = {(–2, 4), (–1, 2), (0, 0), (1, –2), (2, –5)}. Let g = {(–3, 3), (–1, 1), (0, –3), (1, –4), (3, –6)}. What is g(f(2))? -5 -1 2 The composition is undefined.
Jonathan can jog 3 2/5 miles in 7/8 hour.Find his average speed in miles per hour
The cost of a new house can be represented by the regression equation c = 120f + 90,000, where $120 is the cost per square foot and $90,000 is the cost of the lot. A new house on a lot costs $438,000. How many square feet does it have?
Answer: 2900 Square Feet
Step-by-step explanation: i took the test
a can of coffee weighs 13 ounces. what is the smallest number of cans that must be used to package 1,000 kilograms of coffee
A pair of jeans is on sale for 25% off the original price. Which expression represents the sale price? If the original price is $40, evaluate the expression to find the sale price. A: s=p-0.25p;$30 B: s=p-25;$15 C: s=p-0.25p;$10 D: s=p-0.25;$39.75
gerard is buying pencils in boxes of 10 he has 20 pencils but needs a total of 60 pencils
You need to fill a football with air to play with it. You know that your pump expels air at speed of 8.2 ft/s. The needle of your pump has a radius of 4.5 millimeters. What is the volume flow rate of the air being pumped into the football?
Answer:
The volume flow rate of the air being pumped into the football is approximately [tex]\( 5.261 \times 10^{-7} \)[/tex] cubic feet per second.
Explanation:
To find the volume flow rate of the air being pumped into the football, we first need to calculate the cross-sectional area of the needle of the pump.
Given:
- The radius of the needle, [tex]\( r = 4.5 \)[/tex] millimeters.
The cross-sectional area, [tex]\( A \)[/tex], of the needle can be calculated using the formula for the area of a circle:
[tex]\[ A = \pi r^2 \][/tex]
Converting the radius from millimeters to feet:
[tex]\[ r = \frac{4.5}{1000} \text{ feet} \][/tex]
Now, let's calculate the cross-sectional area:
[tex]\[ A = \pi \left( \frac{4.5}{1000} \right)^2 \][/tex]
[tex]\[ A \approx \pi \left( \frac{0.0045}{1000} \right)^2 \][/tex]
[tex]\[ A \approx \pi \times 2.025 \times 10^{-8} \text{ square feet} \][/tex]
Now, we can find the volume flow rate, [tex]\( Q \)[/tex], of the air being pumped into the football. The volume flow rate is the product of the cross-sectional area of the needle and the speed of the air:
[tex]\[ Q = A \times \text{Speed} \][/tex]
Given:
- Speed of the air, [tex]\( \text{Speed} = 8.2 \)[/tex] ft/s
Now, let's calculate the volume flow rate:
[tex]\[ Q = \pi \times 2.025 \times 10^{-8} \text{ square feet} \times 8.2 \text{ ft/s} \][/tex]
[tex]\[ Q \approx 5.261 \times 10^{-7} \text{ cubic feet/s} \][/tex]
Suppose you have a distribution, x, with mean = 13 and standard deviation = 3. define a new random variable y = 4x - 5. find the mean and standard deviation of y.
The mean and the standard deviation of y are given as follows:
Mean: 47.Standard deviation: 12.How does the subtraction and the multiplication affect the standard deviation?For the multiplication, we have that both the mean and the standard deviation are multiplied by the constant.
For the subtraction, we have that the mean is subtracted by the constant, while the standard deviation remains constant, since all observations are subtracted by the constant, the differences squared between each observation and the mean remain constant.
The original mean and standard deviation are given as follows:
Mean: 13.Standard deviation: 3.After the multiplication, they are given as follows:
Mean: 52.Standard deviation: 12.After the subtraction, they are given as follows:
Mean: 47.Standard deviation: 12.More can be learned about mean and standard deviation at https://brainly.com/question/14447368
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Final answer:
The mean and standard deviation of the new random variable y, derived from a distribution x with a given mean and standard deviation, are calculated by applying transformations, resulting in a mean of 47 and a standard deviation of 12.
Explanation:
The question asks us to find the mean and standard deviation of a new random variable y = 4x - 5, given a distribution, x, with a mean of 13 and a standard deviation of 3. To calculate the mean of y, we use the transformation y = 4x - 5. The mean of y can be found by substituting the mean of x into this equation, giving us 4(13) - 5 = 52 - 5 = 47. To find the standard deviation of y, we multiply the standard deviation of x by the coefficient of x in the equation, resulting in 3 * 4 = 12. Therefore, the mean of y is 47, and the standard deviation is 12.
misty is building a triangular plainting bed. two of the sides have lengths of eight feet and five feet. what are the possible lengths for the third side?
The length of the third side of the triangle Misty is building should be more than 3 feet and less than 13 feet, according to the Triangle Inequality Theorem.
Explanation:This question pertains to the numerical properties of a triangle, in which two side lengths of the triangle are provided, specifically eight feet and five feet. The length of the third side of the triangle is not set, but it has certain parameters due to the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the possible lengths of the third side would be greater than the absolute difference of the two given sides (eight feet and five feet), and less than the sum of the lengths of the two given sides. Thus, the third side's length should be more than 3 feet (8 - 5) and less than 13 feet (8 + 5).
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Find the exact circumference of a circle with the given radius. 36 inches C = 72 in. 36 in. 18 in. IN PIE TERMS PLEASE!!!!!:)
Answer:
The circumference of a circle is [tex]72\pi [/tex] .
Step-by-step explanation:
Forrmula
[tex]Circumference\ of\ a\ circle = 2\pi r[/tex]
Where r is the radius of the circle .
As given in the question
The radius of the circle is 36 inches .
Put all the values in the formula
[tex]Circumference\ of\ a\ circle = 2\times 36\pi [/tex]
[tex]Circumference\ of\ a\ circle = 72\pi [/tex]
Therefore the circumference of a circle is [tex]72\pi [/tex] .
While free diving in the ocean Samantha once set a record by diving 525 feet in 3 1/2 minutes how many feet per minute did she dive?
If sinθ =4/5 , then cosθ = _____.
Answer:
cosθ = [tex]\frac{3}{5}[/tex] .
Step-by-step explanation:
Given : If sinθ =4/5 .
To find : cosθ = _____.
Solution : We have given that sinθ =4/5 .
By the trigonometric identity
cos²θ + sin²θ = 1.
Plugging the value of sinθ =4/5 .
cos²θ + [tex](\frac{4}{5}) ^{2}[/tex] = 1.
cos²θ + [tex]\frac{16}{25}[/tex] = 1.
On subtracting [tex]\frac{16}{25}[/tex] from both sides
cos²θ = 1 - [tex]\frac{16}{25}[/tex] .
cos²θ = [tex]\frac{25 -16}{25}[/tex] .
Taking square root both sides.
[tex]\sqrt{cos^{2}theta} = \sqrt{\frac{9}{25}}[/tex] .
cosθ = [tex]\frac{3}{5}[/tex] .
Therefore, cosθ = [tex]\frac{3}{5}[/tex] .
a 26 inch piece of Steel is cut into three pieces so that the second piece is twice as long as the first piece and the third piece is 2 in more than three times the length of the first piece find the links of the pieces
Explain why you add to find the sum of two integers, but subtract to find the sum of a positive and negative integer
Write the quadratic equation whose roots are -2 and 3, and whose leading coefficient is 3
The Florida Everglades welcomes about 2x10 to the third power visitors per day. Based on this, about how many visitors come to the Everglades per week?
if f(x)=4-x^2 and g(x)=6x, which expression is equivalent to (g-f)(3)?
Three consecutive integers whose sum is 36
The Sears tower in Chicago is 1,454 feet tall. Write the height as an integer
Each U.S. penny weighs 2.5 grams. How many pennies,x is how many pennies it an equation, are on scale if their total weight is 37.5 grams:A. 2.5+x=37.5 x=12,B. 2.5x=37.5 x=15, C. x-2.5=37.5 x=40,D. 2.5x=37.5 x=18???? please answer quick.
find 4 consecutive odd numbers such that the sum of the first and the forth is 27 less than three times the first
Express the side length of a square as a function of the length d of the square’s diagonal. then express the area as a function of the diagonal length.
The population of a town grew from 20,000 to 28,000. The continuous growth rate is 15%. The equation 20,000e^0.15t=28,000 represents the situation, where t is the number of years the population has been growing. About how many years has the population of the town been growing? Use a calculator and round your answer to the nearest whole number.
A. 2 years
B.9 years
C. 17 years
D. 22 years
The correct option is: A. 2 years
Explanation
The given growth equation is: [tex]20000e^0^.^1^5^t = 28000[/tex], where [tex]t[/tex] is the number of years the population has been growing.
For finding the number of years, we will solve the above equation for [tex]t[/tex].
First, dividing both sides by 20000, we will get........
[tex]\frac{20000e^0^.^1^5^t}{20000}=\frac{28000}{20000}\\ \\ e^0^.^1^5^t = 1.4[/tex]
Now taking 'natural log' on both sides, we will get........
[tex]ln(e^0^.^1^5^t)=ln(1.4)\\ \\ 0.15t*ln(e)= ln(1.4)\\ \\ 0.15t*1=ln(1.4)\\ \\ t=\frac{ln(1.4)}{0.15}=2.243..... \approx 2[/tex]
So, the population of the town has been growing about 2 years.
The town has been growing for 17 years
Exponential functionsGiven the exponential function
Given the expressions 20,000e^0.15t=28,000
We are to find the value of "t" which is the time.
e^0.15t = 28000/20000
e^0.15t = 7/5
e^0.15t = 1.4
Take the ln of both sides
lne^0.15t = ln 1.4
0.15t = 2.639
t = 2.639/0.15
t = 17years
Hence the town has been growing for 17 years
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The heights of women aged 20 to 29 are approximately normal with mean 64 inches and standard deviation 2.7 inches. men the same age have mean height 69.3 inches with standard deviation 2.8 inches. what are the z-scores for a woman 6 feet tall and a man 6 feet tall? what information do the z-scores give that the actual heights do not?
The mean amount spent by a family of four on food per month is $500 with a standard deviation of $75. assuming that the food costs are normally distributed, what is the probability that a family spends less than $410 per month? 0.2158 0.8750 0.0362 0.1151
Answer:
0.1151
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 500, \sigma = 75[/tex].
What is the probability that a family spends less than $410 per month?
This probability is the pvalue of Z when X = 410. So:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{410 - 500}{75}[/tex]
[tex]Z = -1.2[/tex]
[tex]Z = -1.2[/tex] has a pvalue of 0.1151. This is the answer.
Armand ran the 100-yard dash in 17.18 seconds. Arturo's time has an 8 with a vaule 10 times the value of 8 in armand's time. What could be arturo's tome on the 100-yard dash?
Answer:
26.89 seconds
Step-by-step explanation:
Any number with an 8 in the tenths place will have an 8 with 10 times the value of the 8 in the hundredths place in Armand's time.
If someone helps me I will cash app you 1 dollar I need the steps not the answer how to solve it
Write 24.652 as a mixed number.
For the given conditional statement, determine which of the following option(s) has a truth value of true. Select all that apply.
If a polygon is regular, then it has congruent angles and congruent sides.
conditional
converse
inverse
contrapositive
Answer:
Conditional and Converse.
Step-by-step explanation:
If a polygon is regular, then it has congruent angles and congruent sides.
We can say that;
Hypothesis is : If a polygon is regular
Conclusion is : then it has congruent angles and congruent sides.
A conditional statement will not be true when the hypothesis is true but the conclusion is false. In the given statement, the above conditional statement has a truth value of true.
We can write the converse statement as : If it has congruent angles and congruent sides, then the polygon is regular.
This also has a truth value of true.
So, correct options are :
Conditional and converse
When ordering a certain type of computer, there are 3 choices of hard drive, 4 choices for the amount of memory, 2 choices of video card, and 3 choices of monitor. in how many ways can a computer be ordered?
Answer:
72 possible combinations
Step-by-step explanation:
The features in a computer (C) are:
Hard drive (h): 3 choicesAmount of memory (a): 4 choicesVideo card (v): 2 choicesMonitor (m): 3 choicesAll the possible combinations can be found using the following expression.
C = h × a × v × m = 3 × 4 × 2 × 3 = 72
There are 72 possible combinations to set up a computer.