What is the circumference and area of a circle with a radius of 4 meters? Round your answer to the nearest tenth. (Use 3.14 for Pi.)

In a statistical test, the null hypothesis to be made is that the sample proportions do not have any significant differences, which means an equal distribution. This is only rejected when the estimate is equal or less than 0.95. But since in this case it is >0.95, so therefore the null hypothesis is not rejected. Therefore:

False

Answer: All students passed except Gino

Step-by-step explanation:

divide 322 by 2 and then subtract the width

322 /2 = 161

161-72 = 89

 length is 89 feet

LaToya originally had 300 basketball cards. She gave away 3/4 of her collection, keeping 1/4 which is 75 cards. By solving the equation 1/4 x = 75, we find that x equals 300.

LaToya originally had a certain number of basketball cards. She gave half of them to Aaron and a fourth of them to her brother, leaving her with 75 cards. To find out how many cards she started with, let's define the total number of cards as x. Given that half and a fourth were given away, this means that 3/4 of x has been given to others, leaving her with 1/4 of her original number of cards.

Now, we can set up the equation: 1/4 x = 75. To solve for x, multiply both sides of the equation by 4, giving us x = 75 * 4, which equals 300. Therefore, LaToya originally had 300 basketball cards.

To find the number of cards LaToya started with, we can set up an equation based on the information given and solve for the unknown value.

To find the number of cards LaToya started with, we need to work backwards from the information given. We know that she has 75 cards left after giving half to her friends and a fourth to her brother. Let's assume that the number of cards she started with is 'x'.

If she gave half to her friends, that means she gave x/2 cards to her friends. Then, if she gave a fourth to her brother, she gave x/4 cards to her brother. So the total number of cards given away is x/2 + x/4 = 3x/4.

Since she has 75 cards left, we can set up the equation: x - 3x/4 = 75. Solving this equation will give us the value of x, which represents the number of cards LaToya started with.

Answer:

3

Step-by-step explanation:

The two numbers are 7 and 9, which are determined by setting up an algebraic equation based on the information that one number is 2 more than the other and the difference between their squares is 32.

The question involves finding two numbers where one number is 2 more than another and the difference between their squares is 32. To solve this problem, we denote the first number as ‘x’. Therefore, the second number will be '‘x+2’, as it is given to be 2 more than the first number. Next, we set up an equation based on the provided information that the difference between their squares is 32: ‘(x+2)² - x² = 32’.

Expanding the squared terms, we get ‘x² + 4x + 4 - x² = 32’. After simplifying the equation by canceling out ‘x²’ from both sides and subtracting 4 from both sides, we get ‘4x = 28’. Dividing both sides by 4 gives us ‘x = 7’. Thus, the first number is 7, and the second number is 7 + 2, which is 9.

The two numbers in question are 7 and 9, and they meet the criteria given in the problem statement.

The car speed in miles per minute is 0.8 miles per minute and the car will travel 1.6 miles in 2 minutes.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

The speed of the car = 48 miles per hour

Speed in miles per minute = 48/60 = 0.8 miles per minute

Time = 2 minutes

Speed = 0.8 miles per minute

Distance = 0.8×2 = 1.6 miles

Thus, the car speed in miles per minute is 0.8 miles per minute and the car will travel 1.6 miles in 2 minutes.

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If there are 2115 projects in total, then 665 projects will be covered by 133 science teachers. Therefore, an additional 290 volunteers are needed to judge the remaining projects, making the correct answer option A.

Step 1: Calculate projects judged by science teachers

The number of projects each teacher can judge is 5, so:

133 teachers * 5 projects per teacher = 665 projects

Step 2: Calculate additional projects

The total number of projects should be known to determine the additional requirement. Let's denote the total number of projects as P.

If P projects must be judged and 665 projects are already covered, then:

Remaining projects = P - 665

Each volunteer can also judge 5 projects. Let V be the number of volunteers needed:

Step 3: Solve for the fewest number of volunteers

We need enough volunteers to cover the remaining projects:

5 * V ≥ P - 665

To solve this, we need the total number of projects mentioned in options:

If P = 2115, then:

Remaining projects = 2115 - 665 = 1450

1450 / 5 = 290 volunteers

The correct answer is A (290).

The complete question is

The science fair judges will be science teachers and volunteers. Each judge will only have time to view 5 science fair projects. There are 133 science teachers. What is the fewest number of volunteers needed to have enough judges for all of the projects?

A 290

B 396

C 422

D 423

The interquartile range of the data set is 60

The interquartile range of the data set is the difference between the lower quartile (Q1) and the upper quartile (Q3)

From the given information:

We need to first identify the middle number(median) = 45

Thus:

IQR = 72.2 - 12.2

IQR = 60

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Reggie Jackson hit 5 home runs in 6 games sos he hit 5/6 = 0.833 home runs per game

lou gehrig hit 4 home runs in 4 games so he hit 4/4 = 1 home run per game

0.833 is less than 1 so Reggie Jackson hit fewer home runs per game

Using compound interest, the better investment is of 8.3% compounded annually.

The amount of money earned, in compound interest, after t years of the investment, is given by the following formula:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which the parameters are given as follows:

For the first option, of 8.3% compounded annually, the multiplier after each year is given as follows:

[tex](1 + \frac{0.083}{1}\right)^{1} = 1.083[/tex]

As the parameters are r = 0.083, n = 1.

For the second option, the parameters are given as follows:

r = 0.08, n = 4.

Hence the multiplier after each year of the investment is given by:

[tex](1 + \frac{0.08}{12}\right)^{12} = 1.0829[/tex]

Due to the higher multiplier, the first option is better, that is, 8.3% compounded annually.

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The 8% compounded quarterly has a higher effective annual rate than 8.3% compounded annually, thereby making it the better investment choice.

To determine which investment is better, we need to compare the effective annual rates (EAR) of the two options: 8.3% compounded annually vs. 8% compounded quarterly. The formula for EAR is (1 + i/n)n - 1, where i represents the interest rate and n is the number of compounding periods per year.

For the 8.3% compounded annually, the EAR is straightforward: (1 + 0.083/1)1 - 1 = 0.083 or 8.3%.

For the 8% compounded quarterly, we calculate the EAR as follows: (1 + 0.08/4)4 - 1 = (1 + 0.02)4 - 1 = (1.02)4 - 1 = 1.082432 - 1 = 0.082432 or 8.2432%.

Comparing the two EARs, the 8% compounded quarterly has a higher effective annual rate than the 8.3% compounded annually, making it the better investment.

Final answer:

To meet the client's investment goals with an investment return of $1,620 on a total of $26,000, the client should invest $8,000 in AAA bonds, $14,000 in A bonds, and $4,000 in B bonds. This is derived from setting up and solving a system of linear equations based on the conditions provided.

Explanation:

Part A: Investment Calculations

To solve for the amount to invest in each type of bond, we can set up a system of equations based on the given conditions. Let x be the amount invested in AAA bonds, y be the amount invested in A bonds, and z be the amount invested in B bonds. We are told that the client wants to invest twice as much in AAA bonds as in B bonds, which gives us the equation x = 2z. The total investment is $26,000, so we have x + y + z = $26,000. The desired annual return is $1,620, and this gives us another equation based on the yields: 0.04x + 0.06y + 0.11z = $1,620.

By solving this system of equations, we can find the amounts to invest in each bond.

From x = 2z, we can substitute for x in the other equations.

The total investment equation becomes 2z + y + z = $26,000, simplifying to 3z + y = $26,000.

The return equation becomes 0.08z + 0.06y + 0.11z = $1,620, simplifying to 0.19z + 0.06y = $1,620.

We can now solve these two new equations for y and z, and then find x using x = 2z.

After solving, we get:

z (B bonds) = $4,000

x (AAA bonds) = 2z = $8,000

y (A bonds) = $26,000 - x - z = $14,000

Part B: Investment Calculations with Updated Values

The process for part B is similar, but with the updated total investment of $38,000 and a desired return of $2,360. The equations are adjusted accordingly, and after solving, we would get the new investment amounts for AAA, A, and B bonds.

The client should invest $8,000 in AAA bonds, $14,000 in A bonds, and $4,000 in B bonds for the conditions in part A.

The limit of the given expression is undefined.

To find the limit of lim  θ→0  cos(4θ) - 1 / sin(7θ), we can simplify the expression first. Using the identity cos(2θ) = 2cos²θ - 1, we can rewrite the numerator as 2(cos²(2θ) - 1). The denominator, sin(7θ), can be rewritten as sin(2θ + 5θ). By applying the sum-to-product identities, we get sin(2θ)cos(5θ) + cos(2θ)sin(5θ), or cos(5θ)sin(2θ) + cos(2θ)sin(5θ).

Now, if we multiply both numerator and denominator by 1/sin(2θ)cos(5θ), we can simplify the expression further:

lim  θ→0 (2cos²(2θ) - 1) / (cos(5θ)sin(2θ) + cos(2θ)sin(5θ)) = lim  θ→0 (2cos(2θ) - 1/sin(2θ)) / (cos(5θ) + cos(2θ)tan(5θ)).

Now, we can substitute θ = 0 into the expression. Since cos(0) = 1 and sin(0) = 0, the denominator becomes cos(5(0)) + cos(2(0))tan(5(0)) = cos(0) + cos(0)tan(0) = 1 + 1(0) = 1. Thus, the limit is:

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{5x^3 + 2}\\\mathsf{= 5(-1)^3+2}\\\\\mathsf{(-1)^3}\\\mathsf{= -1\times-1\times-1}\\\mathsf{=1\times-1}\\\mathsf{= \bf -1}\\\\\mathsf{= 5(-1) + 2}\\\\\mathsf{5(-1)}\\\mathsf{= \bf -5}\\\\\mathsf{= -5 + 2}\\\mathsf{=\bf -3}\\\\\\\\\boxed{\boxed{\huge\text{Therefore, your answer is: \bf -3}}}\huge\checkmark\\\\\\\\\huge\text{Good luck on your assignment \& enjoy your day!}\\\\\\\frak{Amphitrite1040:)}[/tex]

54-36 =18

 they can make 18 bouquets

54/18 =3

36/18 =2

18 bouquets with 3 red and 2 white roses each

Answer:

3

GCF of 54 and 36 = 18

so, 18 bouquets

then,

54 red roses ÷ 18 = 3 red roses in each bouquet

divide total miles by time:

220 / 3.5 = 62.857

 rounded to nearest tenth = 62.9 miles per hour