At a local bodega, the cost of a banana at the corner store is $1.50, and the cost of a

How many liters of a 10% antifreeze solution and a 40% antifreeze solution must be mixed to make 15 liters of a 25% solution? Ro

butalik [34]

Answer:

7.5 liters of a 10% antifreeze solution AND

7.5 liters of a 40% antifreeze solution

Step-by-step explanation:

According to the question,we were asked to find out how many liters of 10% anti freeze solution and 40% anti freeze each to make a 15 liters 25% mixture

Let’s call

the amount of liters needed of our 10% solution “x”. So, how

many liters do we need of the 40% solution? Well, there are 15

liters in total, x liters have been spoken for, so what remains

of our allotted 10 liters then, is 15-x.

Now let's solve for "x"

10% of x + 40% of (15 - x) = 25% of 15 liters

0.1x + 0.4(15 - x) = 0.25(15)

0.1x + 6 - 0.4x = 3.75

Collect the like terms and we have

0.3x = 2.25

x = 2.25 × 3

X = 7.5(Liters for the 10% anti freeze solution)

The 40% solution= 15 - 7.5 = 7.5 liters

Since "X" was used to fill for the unknown amount of 10% anti freeze solution,we have 7.5 liters of the 10% solution and another 7.5 liters for the 40% solution to end up with 15 liters of the desired 25% solution.

8 0

3 years ago

The function f(x) is graphed on the coordinate plane. What is f(−4) ?

Dmitry_Shevchenko [17]

If you are trying to find the degree of f(-4) the answer is 1.

4 0

3 years ago

How can Doug use place value pattern to check his answer?

MAVERICK [17]

He can use it to make sure he lined his place values up properly

3 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 $\mu = E(X), \sigma = \sqrt{V(X)}$ .