there is a 50% off sale at the video game store. during the sale sonia pays $30 for a new game. what was the orginal prce

The function f(x)=log[7]x is increasing. True or false

Ilia_Sergeevich [38]

I would say that the answer is true

7 0

3 years ago

Read 2 more answers

Can you answer at least one

Monica [59]

Answer:

15. 88%

Step-by-step explanation:

I did division

5 0

2 years ago

Read 2 more answers

adam prepares a meal of shrimp and brown rice. it must contain exactly 6 g of fat and 10 mg of iron. each 5oz serving of shrimp

jasenka [17]

Answer:

Adam needs 9/8 of a 5oz serving of shrimps (which equals to 5.625 oz) and 5/8 of a cup of brown rice (which is around 10 tablespoons).

Explanation:

You are given:

every serving of shrimp contains 2g of fat and 5mg of iron;

every serving of rice contains 6g of fat and 7mg of iron;

each meal should have 6g of total fat and 10mg of total iron.

You need to set a system of equation: let's call

s = quantity of shrimps

r = quantity of rice

The equation for the total fat will be: the quantity of fat in the serving of shrimps plus the quantity of fat in the serving of rice must be equal to 6g

2s + 6r = 6 (1)

Similarily:

the quantity of iron in the serving of shrimps plus the quantity of iron in the serving of rice must be equal to 10g

5s + 7r = 10 (2)

In order to solve the system, solve for s in equation (1):

s = (6-6r)/2 = 3 - 3r (3)

Substitute in equation (2):

5(3 - 3r) + 7r = 10

and solve for r:

15 - 15r + 7r = 10

8r = 5

r = 5/8

Substitute the value of r in equation (3):

s = 3 - 3×5/8 = 9/8

Therefore Adam would need 9/8 of a 5oz serving of shrimps and 5/8 of a 1 cup of brown rice for each meal.

6 0

3 years ago

A rack has a volume of 10 cm3 and a mass of 25g. What is the density?

valentinak56 [21]

Answer:

Step-by-step explanation:

density is mass divided by volume, so 25g divided by 10 cm = 2.5 g

4 0

3 years ago

A television station plans to ask a random sample of 400 city residents if they can name the news anchor on the evening news at

hodyreva [135]

Answer:

There is an 8.38% probability that the anchor will be fired.

Step-by-step explanation:

For each resident, there is only two possible outcomes. Either they can name the news anchor on the evening news at their station, or they cannot.

This means that the binomial probability distribution will be used in our solution.

However, we are working with samples that are considerably big. So i am going to aaproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X), \sigma = \sqrt{V(X)}$ .

In this problem, we have that:

400 city residents are going to be asked. So $n = 400$ .

Suppose that in fact 12% of city residents could name the anchor if asked. This means that $p = 0.12$ .

So,

$\mu = E(X) = 400*0.12 = 48$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{400*0.12*0.88} = 6.5$ .

They plan to fire the news anchor if fewer than 10% of the residents in the sample can do so.

What is the approximate probability that the anchor will be fired?

10% of the residents is 0.10*400 = 40 residents.

Fewer than 10% is 39 residents. So the probability that the anchor will be fired is the pvalue of Z when $X = 39$ .

So:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{39 - 48}{6.5}$

$Z = -1.38$

$Z = -1.38$ has a pvalue of 0.0838. This means that there is an 8.38% probability that the anchor will be fired.

5 0

3 years ago