The volume of a cylinder varies jointly with the square of the radius and the height. If the volume of a cylinder is 50.265 cubic inches when the radius is 2 inches and the height is 4 inches, what is the volume when the radius is 3 inches and the height is 7 inches?

By the fundamental theorem of calculus,

[tex]\displaystyle\frac{\mathrm d}{\mathrm dx}\int_0^x\cos^{-1}t\,\mathrm dt=\cos^{-1}x[/tex]

so that

[tex]f'(0.3)=\cos^{-1}0.3\approx1.266[/tex]

Final answer:

Glenn crashed in 30% of the races.

Explanation:

To find the percentage of races Glenn crashed, you can set up a proportion. A proportion is an equation that states that two ratios are equivalent. Since Glenn raced 30 times and crashed 9 times, the ratio of crashes to total races is 9 crashes out of 30 races.

You can set up the proportion as follows:
Crashes / Total Races = Percentage of Crashes / 100

Plugging in the known values gives us this:
9 / 30 = Percentage of Crashes / 100

To solve for the percentage of crashes, you multiply both sides of the equation by 100:
(9 / 30)
100 = Percentage of Crashes

Simplifying gives us:
(9/3) 10 = Percentage of Crashes

Hence, the percentage of races that Glenn crashed is 30%.

Answer:

The mean of something is the "average"

For example, if the mean of people in the households of 7th-grade students is 4.3, this means that if you go to a random house of a 7th-grade student, you can expect around 4 people in there.

Now, for the  7th-grade students, the mean is 4.5, just a 0.2 bigger. (This means that, on average, there is more people in the 8th-grade student's households)

So Principal Coleman can infer that the amount of people in the households of  7th-grade students and 8th-grade students is almost the same, wherein the 8th-grade students there is a small chance of finding more people, but this difference is almost depreciable.

Answer:

[tex]x=44-y[/tex]

Step-by-step explanation:

Let x represents the number of glasses of iced tea .

Let y represents the number of glasses of lemonade.

Now we are given that She has only 44 cups in which to serve the drinks

Since y is the number of glasses of  lemonade out of 44 glasses

So, remaining glasses = [tex]44-y[/tex]

So, remaining glasses is for iced tea .

So, No. of iced tea glasses =  [tex]x=44-y[/tex]

Hence She can serve [tex]x=44-y[/tex] number of glasses of iced tea serve.

Answer:

The total number of possible outcomes are:

64

Step-by-step explanation:

It is given that:

Louisa spins the spinner below twice.

The spinner is numbered from 1-8.

Now, on spinning the spinner twice we obtain the sample space as:

(1,1)   (1,2)....................(1,8)

(2,1)  (2,2)...................(2,8)

(3,1)   (3,2)..................(3,8)

(4,1)   (4,2)..................(4,8)

(5,1)   (5,2)..................(5,8)

(6,1)   (6,2)..................(6,8)

(7,1)   (7,2)..................(7,8)

(8,1)   (8,2)..................(8,8)

Hence, the total number of outcomes is equal to the number of elements in sample space.

Hence, the total number of possible outcomes are:

64

The joint probability of x1 and y2 is  P (Y₂/X₁ ) = P(Y₂ ∩ X₁ )/ P (X₁) will be 0.3.

In the joint probability of x1 and y2 is  P (Y₂/X₁ )= P(Y₂ ∩ X₁ )/ P (X₁).

Therefore:

P(Y₂ ∩ X₁ )

=0.40 x 0.75

= 0.3

Therefore by following the law of conditional probability, the outcome of the The joint probability of x1 and y2 is  P (Y₂/X₁ ) = P(Y₂ ∩ X₁ )/ P (X₁) will be 0.3.

Learn more about probability from

https://brainly.com/question/24756209

#SPJ9

The difference in the number of cars manufactured in August and September is 15 cars.

The difference in the number of cars manufactured in August and September can be calculated as follows:

what polynomial models the total number of common and Endler's guppies

your answer will be:

7.3x^2+0.8+1.3

Step-by-step explanation:

this answer correct for 2022

To write the expression 9xa+9xb as a product, factor out the common factor 9x to get 9x(a+b), which is the simplified product form.

The student has presented an algebraic expression: 9xa+9xb and is requesting to rewrite it as a product. To simplify this expression, we can factor out the common factor which is present in both terms. The common factor here is 9x. When we factor out 9x, we combine the terms within the parentheses.

Here is the step-by-step simplification:

The area of Ava's rectangular rug is 5382 square yards, calculated by multiplying the width (23 yards) and the length (234 yards).

To find the area of Ava's rectangular rug, we need to multiply its length and width:

Area = length × width

Using the given dimensions: 23 yards wide and 234 yards long:

Area = 23 × 234

First, let's perform the multiplication:

23 × 234 = 5382 square yards

Thus, the area of the rug is 5382 square yards as an improper fraction, which cannot be simplified further as a mixed number. Since the measurements are whole numbers, converting to a mixed number doesn't apply in this case.

To find a number x between 0 and 28 with x ≡ 6 (mod 35) using Euler's theorem, we can use Euler's totient function to find the power x^24 that is congruent to 1 (mod 35). The value x = 1 satisfies the congruence, so it is a possible solution.

To use Euler's theorem to find a number x between 0 and 28 with x ≡ 6 (mod 35), we need to find the value of x that satisfies the congruence. Euler's theorem states that if a and n are coprime positive integers, then a^φ(n) ≡ 1 (mod n), where φ(n) is the Euler's totient function of n. In this case, we need to find x such that x^φ(35) ≡ 1 (mod 35). The Euler's totient function of 35 is φ(35) = φ(5) * φ(7) = 4 * 6 = 24. Therefore, we need to find x such that x^24 ≡ 1 (mod 35).

We can start by examining the powers of x modulo 35:
x  ≡ x (mod 35)
x2  ≡ x² (mod 35)
x³  ≡ x³ (mod 35)
...
x^24 ≡ 1 (mod 35)

From this, we can see that x = 1 satisfies the congruence x^24 ≡ 1 (mod 35).

Therefore, a possible value of x between 0 and 28 that satisfies x ≡ 6 (mod 35) is x = 1.

https://brainly.com/question/31821033

#SPJ11

A 'while loop' can be programmed with conditions to adjust a 'user value'. If 'user value' is greater than 80, 5 would be subtracted from it. If it is less than 0, 10 would be added to it. This loop continues until 'user value' does not meet either condition.

The question asks for a while loop in programming that modifies a value (user value) based on these conditions: if the user value is less than 0, it should be increased by 10 and if it's greater than 80, it should be decreased by 5. Here's a representative code for that:

while(user value < 0 || user value > 80) {

if(user value > 80) {user value -= 5; } else if(user value < 0) {user valuable += 10;}

This loop will continue to execute until the user value is not less than 0 or greater than 80.

https://brainly.com/question/35879909

#SPJ2

The solution to the equation (4j - 2) / 2 = 4j + 5 is j = -3. The equation was simplified by eliminating fractions and isolating the variable j through algebraic steps.

To solve the equation (4j - 2) / 2 = 4j + 5 for the variable j, you can follow these steps:

1. First, simplify both sides of the equation:  

  (4j - 2) / 2 = 4j + 5

2. Multiply both sides of the equation by 2 to eliminate the fraction:

  4j - 2 = 2 * (4j + 5)

3. Distribute the 2 on the right side:

  4j - 2 = 8j + 10

4. Move the variable terms to one side of the equation and the constants to the other side. You can do this by subtracting 8j from both sides:

  4j - 8j - 2 = 10

5. Combine like terms:

  -4j - 2 = 10

6. Add 2 to both sides to isolate the variable term:

  -4j = 10 + 2

  -4j = 12

7. Finally, divide both sides by -4 to solve for j:

  j = 12 / -4

  j = -3

So, the solution to the equation is j = -3.

Learn more about solution to the equation here:

https://brainly.com/question/1214333

#SPJ12

The expression 42 + 6x is already in its simplest form and does not have a common factor to apply the distributive property to simplify it. However, factoring out 6 would rewrite it as 6(7 + x), albeit without further simplification.

To create an equivalent expression to 42 + 6x using the distributive property, we need to factor out a common term from both parts of the expression. However, this expression does not have a common factor available in both terms. The distributive property typically comes into play when you have an expression in the form of a(b + c), where you would then distribute a to both b and c. The expression 42 + 6x is simplified as much as possible, given that one term is a constant and one term is a multiple of a variable. There is no factor that can be distributed to simplify the expression further.

However, if we wanted to factor out a number to potentially simplify the expression, we might choose to factor out 6, which would change the expression to 6(7 + x), although this does not simplify it further since the original expression is already in its simplest form.

Solution: We are given that:

5 people can paint 7 walls in 21 minutes

Therefore, 1 person can paint 7 walls in [tex] 21 \times 5=105 [/tex] minutes

Which means 1 person can paint 1 wall in [tex] \frac{105}{7} =15 [/tex] minutes

Now, 3 people can paint 1 wall in [tex] \frac{15}{3} =5 [/tex] minutes

Therefore, 3 people can paint 5 walls in [tex] 5 \times 5=25 [/tex] minutes

Answer:

25 :)

Step-by-step explanation:

Final answer:

To determine the length of the apothem of a regular octagonal stop sign given its side length and area, use the formula for the area of a regular polygon, solve for the apothem, and then calculate it to be approximately 15 inches when rounded to the nearest whole number.

Explanation:

The student is asking how to find the length of the apothem of a regular octagonal stop sign with side lengths of 12.6 inches and a total area of 770 square inches. The apothem of a regular polygon is a line from the center to the midpoint of one of its sides and is also the radius of the inscribed circle within the polygon.

To find the apothem's length, we can use the formula for the area of a regular polygon: Area = (1/2) × Perimeter × Apothem. The perimeter (P) of the octagon is the length of one side multiplied by 8 (since an octagon has eight sides). Therefore, the perimeter is 12.6 in × 8 = 100.8 in.

We can rearrange the area formula to solve for the apothem (a): Area = (1/2) × P × a becomes a = Area × 2 / P. Substituting the known values, we get: a = 770 in² × 2 / 100.8 in, which calculates to an apothem length of approximately 15.24 inches. Round this to the nearest whole number to get an apothem length of 15 inches.