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]
An ice sculpture is melting from the heat. Assuming its height changes by negative 5 over 32 meters every hour, what will be the change in height after 4 hours?
Answer:
[tex]\frac{-5}{8} [/tex]
Step-by-step explanation:
Given : Height of an ice sculpture changes by negative 5 over 32 meters every hour.
To Find: what will be the change in height after 4 hours?
Solution:
Height changes in 1 hour by [tex]\frac{-5}{32}[/tex]
So, the change in height after 4 hours = [tex]\frac{-5}{32} \times 4[/tex]
= [tex]\frac{-5}{8} [/tex]
Hence,the change in height after 4 hours will be [tex]\frac{-5}{8} [/tex]
which has the greater capscity 7/8 of a cup. Or 2/8 of a gallon
A bank received an initial deposit of $15,000, kept a percentage of this money in reserve based on a reserve rate of 3%, and loaned out the rest. The amount it loaned out eventually was all deposited back into the bank. If this cycle continued indefinitely, how much money eventually resulted from the initial deposit?
A $50,000
B $45,000
C $500,000
D $19,500
Answer:
If this cycle continued indefinitely, how much money that eventually resulted from the initial deposit is
500,000 (C is the answer)
I need help deriving : (7x)/(3+x^2), I keep on deriving it wrong and I am not sure as to why
The derivative of [tex]\( f(x) = \frac{7x}{3 + x^2} \)[/tex] is [tex]\( f'(x) = \frac{-7x^2 + 21}{(3 + x^2)^2} \)[/tex].
To find the derivative of the function [tex]\( f(x) = \frac{7x}{3 + x^2} \)[/tex] , we can use the quotient rule. The quotient rule states that if you have a function [tex]\( g(x) = \frac{u(x)}{v(x)} \)[/tex] , then the derivative [tex]\( g'(x) \)[/tex] is given by:
[tex]\[ g'(x) = \frac{u'(x)v(x) - u(x)v'(x)}{[v(x)]^2} \][/tex]
In this case, let u(x) = 7x and v(x) = 3 +[tex]x^2[/tex] . Now, find the derivatives u'(x) and v'(x):
u'(x) = 7
v'(x) = 2x
Now, apply the quotient rule:
[tex]\[ f'(x) = \frac{(7)(3 + x^2) - (7x)(2x)}{(3 + x^2)^2} \][/tex]
Simplify the expression:
[tex]\[ f'(x) = \frac{21 + 7x^2 - 14x^2}{(3 + x^2)^2} \][/tex]
Combine like terms:
[tex]\[ f'(x) = \frac{-7x^2 + 21}{(3 + x^2)^2} \][/tex]
So, the derivative of [tex]\( f(x) = \frac{7x}{3 + x^2} \)[/tex] is [tex]\( f'(x) = \frac{-7x^2 + 21}{(3 + x^2)^2} \)[/tex].
Complete Question: What is the derivation of (7x)/(3+[tex]x^2[/tex]).
find 4 consecutive odd numbers such that the sum of the first and the forth is 27 less than three times the first
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?
Susan has 4 gallons of juice. How many cups of juice does she have?
A dolphin can swim at a speed of about 37 miles per hour. The fastest human swimmer can reach a speed of about 5.2 miles per hour. About how many times faster than humans are dolphins
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] .
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
Name the rule and find the next two numbers in the pattern 10,70,490
Answer:
Next numbers: 3430, 24010
Step-by-step explanation:
AS you can see you just need to discover the pattern by dividing the subsequent numbers by the direct number before that:
490/70=7
70/10=7
So both numbers indicate the patter on multiply by 7.
So to calculate the next number we first have to multiply 490*7= 3430
Now we just have to multiply the 3430 by 7 and that would be 24010.
So the next numbers would be 3430 and 24010,
Aaron finished his math assignment in 3/8 hours. then he completed his chemistry assignment in 1/4 hours. How much more time did Dan spend on his math assignment?
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
can someone help me please
the answer is A
see attached picture:
Lamar rented a movie. He started the movie at
11:39 PM and it ended at
1:13 AM. How long was the movie?
Which angle pairs are supplementary? Check all that apply
Answer:
b) ∠4 and ∠3
c) ∠4 and ∠5
e) ∠3 and ∠6
Step-by-step explanation:
Supplementary angles: If the two angles are supplementary, then the angles add upto 180 degrees.
We need to find which pairs add upto 180 degrees.
From the given figure, ∠4 + ∠3 = 180°
ii) ∠5 + ∠6 = 180°
iii) ∠4 + ∠5 = 180°
iv) ∠3 + ∠6 = 180°
v) ∠7 + ∠8 = 180°
So, the following pairs are supplementary.
b) ∠4 and ∠3
c) ∠4 and ∠5
e) ∠3 and ∠6
is 600 1/10th of 500-
Answer:
No
Step-by-step explanation:
600 is greater than 500 it would be 1.2 greater
Hope this helps!!
Stay Safe!!
slove for x=b - cb to get c by itsself
what is 12.1 rounded to the nearest whole number
The staff at Larry's Lawns spends their workday mowing lawns, raking, and bagging leaves. They work an average of twelve hours per day. The mowing and raking typically takes eight hours and an average of forty-eight bags of leaves are filled. Assuming the bags are filled at a constant rate, what is the average time it takes to fill one bag of leaves?
The average time it takes to fill one bag of leaves is 0.17 hours or 10 minutes.
Explanation:The average time it takes to fill one bag of leaves is 0.17 hours or 10 minutes.
To find the average time it takes to fill one bag of leaves, we need to divide the total time spent raking leaves by the number of bags filled. In this case, the total time spent raking leaves is 12 hours and the number of bags filled is 48.
Therefore, the average time it takes to fill one bag of leaves is:
Average time = Total time / Number of bags filled
Average time = 12 hours / 48 bags = 0.25 hours/bag = 15 minutes/bag.
Find the center of the circle that can be circumscribed about EFG with E(2,2),F(2,-2), and G(6,-2)
An athlete eats 0.35kg of protein per week while training. How much protein will she eat during 7 weeks of training?
The athlete will eat 2.45 kilograms of protein during 7 weeks of training.
To find out how much protein the athlete will eat during 7 weeks of training, we can simply multiply the amount of protein eaten per week by the number of weeks of training.
Given:
Protein eaten per week = 0.35 kg
Number of weeks of training = 7 weeks
Protein eaten during 7 weeks of training = 0.35 kg/week * 7 weeks
Now, calculate the result:
Protein eaten during 7 weeks of training = 2.45 kg
So, the athlete will eat 2.45 kilograms of protein during 7 weeks of training.
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write 6/7 in an equivalent form with the denominator of 35
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.
John is ordering 50 t-shirts. 30% of the shirts need to be small, how many shirts need to be small
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.
I start with 9-2x widgets. Each day, I produce 2x+1 widgets, and destroy 3-x widgets. After three days, how many widgets am I left with, in terms of x?
Final answer:
After three days, starting with 9-2x widgets, producing 2x+1 widgets daily, and destroying 3-x widgets daily, the student is left with 3 + 7x widgets, in terms of x.
Explanation:
Let's find out how many widgets are left after three days, starting with 9-2x widgets, producing 2x+1 widgets daily, and destroying 3-x widgets daily.
To calculate the total number of widgets after one day, we add the produced widgets (2x+1) and subtract the destroyed widgets (3-x) from the initial amount (9-2x):
At end of day 1: (9-2x) + (2x+1) - (3-x) = 9 - 2x + 2x + 1 - 3 + x = 7 + x
Repeat this process for two more days:
At end of day 2: (7+x) + (2x+1) - (3-x) = 7 + x + 2x + 1 - 3 + x = 5 + 4x
At end of day 3: (5+4x) + (2x+1) - (3-x) = 5 + 4x + 2x + 1 - 3 + x = 3 + 7x
Therefore, after three days, you are left with 3 + 7x widgets, in terms of x.
The student initially has 9-2x widgets, and each day there's a net change of 3x-2 widgets. After three days, the student is left with 7x+3 widgets.
Explanation:The student starts with 9-2x widgets. Each day, they produce 2x+1 widgets and destroy 3-x widgets. To find out how many widgets the student is left with after three days, we need to account for the daily production and the daily destruction of widgets and sum them up over the three days.
Let's calculate the daily net change in widgets. The number of widgets produced each day is 2x+1, and the number destroyed is 3-x, so the net change in widgets each day is:
(2x+1) - (3-x) = 2x + 1 - 3 + x = 3x - 2
Now, let's multiply this daily net change by three days:
3 days × (3x - 2) = 9x - 6
Finally, let's add this to the initial number of widgets to find the total:
(9-2x) + (9x - 6) = 9 - 2x + 9x - 6 = 7x + 3
Therefore, after three days, the student is left with 7x + 3 widgets in terms of x.
If someone helps me I will cash app you 1 dollar I need the steps not the answer how to solve it
*HELP* I've been stuck for mins. The graph shows the number of birdhouses Penn and his father can build if they have enough time to build no more than 10 birdhouses. What is the domain of this graph?
The answer to the question would be, All whole numbers from 0 to 10
If the graph shows the number of birdhouses Penn and his father can build if they have enough time to build no more than 10 birdhouses, the domain of the graph is given as [0, 10).
From the graph given, we are to find the domain of the graph. From the graph, we can see that;
The number of birdhouses is along the horizontal x-axisThe amount of time worked is along the vertical y-axisWe are to find the domain of the given graph. The domain of the graph is the input values for which the graph exists.
The domain of the graph is the values along the x-axis of the graph. Hence the domain of the graph is given as [0, 10).
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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.