Gina sold 5/8 of a mushroom pizza and 3/4 of an onion pizza to the same family.How much pizza in all did the family buy?

A bullet is shot straight upward with an initial speed of 925 ft/s. The height of the bullet after t seconds is modeled by the f

never [62]

Answer:

462 ft/s

Step-by-step explanation:

The height of the bullet is modeled by:

h(t) = -16t² + 925t------------------------------------ (1)

The speed of the bullet is modeled by the first derivative of equation (1)

dh/dt= -32t + 925------------------------------------ (2)

At maximum height, dh/dt = 0

0 = -32t + 925

32t = 925

t = 925/32

= 28.91 seconds

This means that the total time to reach maximum height is 28.91 seconds

Substituting into equation (1) we can calculate the maximum height:

h = -16 (28.91)² +925 (28.91)

= -13,372.61 + 26,742.675

= 13,367.065 ‬ft

Average speed = Total distance/ Total time

= 13,367.065/28.91

= 462.368

≈ 462 ft/s

7 0

2 years ago

A helicopter flies 8 km due north from A to B. It then flies 5 km from B to C and returns to A as shown in the figure. Angle ABC

In-s [12.5K]

Please consider the attached graph.

We have been given that a helicopter flies 8 km due north from A to B. It then flies 5 km from B to C and returns to A as shown in the figure. The measure of angle ABC is 150°. We are asked to find the area of triangle ABC.

We will use trigonometric area formula to solve our given problem.

$A=\frac{1}{2}a\cdot c\cdot\text{sin}(b)$ , where angle b is angle between sides a and c.

For our given triangle $a=5,c=8$ and measure of angle b is 150 degrees.

$A=\frac{1}{2}(5)\cdot (8)\cdot\text{sin}(150^{\circ})$

$A=5\cdot 4\cdot(0.5)$

$A=10$

Therefore, the area of the triangle ABC is 10 square kilo-meters and option 'c' is the correct choice.

6 0

1 year ago

Ashley invests $9,720 in a one-month money market account paying 3.16% simple annual interest and $8,140 in a two-year CD yieldi

tester [92]

For the first investment. A = P(1 + rt); where p = 9,720, r = 0.0316 and t = 1/12
A = 9720(1 + 0.0316/12) = 9720(1.0026) = $9,746

For the second investment,
A = 8140(1 + 0.0323 x 2) = 8140(1.0646) = $8,666

Total amount she had = $9,746 + $8,666 = $18,412

5 0

2 years ago

Read 2 more answers

A sample of 1714 cultures from individuals in Florida diagnosed with a strep infection was tested for resistance to the antibiot

Damm [24]

Answer:

a) $p$ represent the real population proportion of people who showed partial or complete resistance to the antibiotic

b) $\hat p=\frac{973}{1714}=0.568$ represent the estimated proportion of people who showed partial or complete resistance to the antibiotic

c) We are confident (95%) that the true proportion of individuals in Florida diagnosed with a strep infection was tested for resistance to the antibiotic penicillin present partial or complete resistance to the antibiotic is between 54.5% to 59.1%.

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Part a

Description in words of the parameter p

$p$ represent the real population proportion of people who showed partial or complete resistance to the antibiotic

$\hat p$ represent the estimated proportion of people who showed partial or complete resistance to the antibiotic

n=1714 is the sample size required

$z_{\alpha/2}$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Part b

Numerical estimate for p

In order to estimate a proportion we use this formula:

$\hat p =\frac{X}{n}$ where X represent the number of people with a characteristic and n the total sample size selected.

$\hat p=\frac{973}{1714}=0.568$ represent the estimated proportion of people who showed partial or complete resistance to the antibiotic

Part c

The confidence interval for a proportion is given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.568 - 1.96 \sqrt{\frac{0.568(1-0.568)}{1714}}=0.545$

$0.568 + 1.96 \sqrt{\frac{0.56(1-0.56)}{1714}}=0.591$

And the 95% confidence interval would be given (0.545;0.591).

We are confident that about 54.5% to 59.1% of individuals in Florida diagnosed with a strep infection was tested for resistance to the antibiotic penicillin present partial or complete resistance to the antibiotic.

5 0

2 years ago

Grace read 9 books in 3 months what was her rate of reading Books per month

Lorico [155]

Answer:

3 books per month

Step-by-step explanation:

9 books ÷ 3 months = 3 books per month :)

7 0

2 years ago

Read 2 more answers