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3 years ago

5

on their first three plays, the number of yards gained by a football team was -4, -7, and 2. find the total change in yards on t

hese tree plays.

1 answer:

maria [59]3 years ago

7 0

Answer:

-9

Step-by-step explanation:

The answer is -9 because,

-4 + -7 = -11

Same sign, so you add the numbers and keep the sign.

-11 + 2 = -9

Different signs, subtract the problem. Keep the sign of the BIGGER number.

I hope this helps!

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Tom and Jerry both invested the same amount for 8 years. If Tom’s rate of return is 9% and Jerry’s rate is 10% compounded annual

Margarita [4]

Answer:

The correct option is;

(f) 7.6%

Step-by-step explanation:

The given parameters are;

The number of years Tom and Jerry are investing their money, t = 8 years

The rate of return for Tom's investment, r₁ = 9%

The rate of return for Jerry's investment, r₂ = 10%

The rate at which the interest is compounded, n = Annually = 1

Let P represent the equal amount of money each of Tom and Jerry invested separately

The amount, A, of the investment is given by the following formula;

$A = P \times \left (1 + \dfrac{r}{n} \right ) ^{n \times t}$

Substituting the known values for Tom, gives;

$A = P \times \left (1 + \dfrac{0.09}{1} \right ) ^{1 \times 8} = P \times 1.09^8 \approx 1.993\cdot P$

The amount Tom has after 8 years ≈ 1.993·P

Substituting the known values for Jerry, gives;

$A = P \times \left (1 + \dfrac{0.1}{1} \right ) ^{1 \times 8} = P \times 1.1^8 \approx 2.144\cdot P$

The amount Jerry has after 8 years ≈ 2.144·P

The percentage amount Jerry has more than Tom after 8 years, PA is given as follows;

$PA = \dfrac{2.144 \cdot P - 1.993 \cdot P}{1.993 \cdot P} \times 100 = 7.57651781234\% \approx 7.6 \%$

The amount Jerry will have after 8 years than Tom = PA ≈ 7.6%.

5 0

3 years ago

I'm having trouble with the second to last step in the fifth question.

inysia [295]

Answer:

Step-by-step explanation:

let me asnswer it on paper hold on

4 0

3 years ago

i don't understand how to make it into a graphing form? how do you find the center and radius? (I'm confused because it has a 4x

Vilka [71]

Answer: $\bold{(x-2)^2+(y-3)^2=\dfrac{1}{4}}$

Center = (2, 3) radius = $\bold{\dfrac{1}{2}}$

<u>Step-by-step explanation:</u>

When both the x² and y² values are equal and positive, the shape is a circle. Complete the square to put the equation in format:

(x-h)² + (y-k)² = r² where

(h, k) is the vertex
r is the radius

1) Group the x's and y's together and move the number to the right side

4x² - 16x + 4y² - 24y = -51

2) Factor out the 4 from the x² and y²

4(x² - 4x ) + 4(y² - 6y ) = -51

3) Complete the square (divide the x and y value by 2 and square it)

$4[x^2-4x+\bigg(\dfrac{-4}{2}\bigg)^2]+4[y^2-6y+\bigg(\dfrac{-6}{2}\bigg)^2]=-51+4\bigg(\dfrac{-4}{2}\bigg)^2+4\bigg(\dfrac{-6}{2}\bigg)^2$

= 4(x - 2)² + 4(y - 3)² = -51 + 4(-2)² + 4(-3)²

= 4(x - 2)² + 4(y - 3)² = -51 + 4(4) + 4(9)

= 4(x - 2)² + 4(y - 3)² = -51 + 16 + 36

= 4(x - 2)² + 4(y - 3)² = 1

4) Divide both sides by 4

$(x-2)^2+(y-3)^2=\dfrac{1}{4}$

(h, k) = (2, 3)
$r=\dfrac{1}{2}$

6 0

3 years ago

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the e

Korolek [52]

Answer:

A sample of 499 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is given by:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

In this question, we have that:

$\pi = 0.21$

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a pvalue of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 90% confidence level with an error of at most 0.03

We need a sample of n, which is found when $M = 0.03$ . So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.03 = 1.645\sqrt{\frac{0.21*0.79}{n}}$

$0.03\sqrt{n} = 1.645\sqrt{0.21*0.79}$

$\sqrt{n} = \frac{1.645\sqrt{0.21*0.79}}{0.03}$

$(\sqrt{n})^2 = (\frac{1.645\sqrt{0.21*0.79}}{0.03})^2$

$n = 498.81$

Rounding up

A sample of 499 is needed.

8 0

3 years ago

Ronald brought a jacket on Friday that had original price if $45. It was on sale at 10% off its original price. Which formula sh

trapecia [35]

The answer is D 1.1(45-45(.7))

3 0

2 years ago