Tyler poured a total of 15 cups of water into 2 equal-sized bottles and filled each bottle. How much water was in each bottle?

△RST is dilated with the rule DT,1/3 (x, y), where the center of dilation is T(3, –2).

dmitriy555 [2]

△RST is dilated with the rule DT,1/3 (x, y), where the center of dilation is T(3, –2).

The distance between the x-coordinates of R and T is 3 .

The distance between the y-coordinates of R and T is 6.

R' is 1 unit left,2 units up from T, so the coordinates of R' are (2,0)

6 0

2 years ago

Read 2 more answers

A bank account earned 3.5% continuously compounded annual interest. After the initial deposit, no deposits or withdrawals were m

aalyn [17]

This question is incomplete. Below is the complete question:

A bank account earned 3.5% continuously compounded annual interest. After the initial deposit, no deposits or withdrawals were made. At the end of an 8 year period, the balance in the account was $13231.30. what is the amount of the initial deposit?

Answer: The initial deposit is $10,001

Step-by-step explanation:

To solve this we need to utilize the continuous compounding interest formula:-

Fv = Pv × e^(i × t)

Where, Fv = the future value

Pv = present value

i = the interest rate

t = the time in years

e = a mathematical constant that is usually approximated by 2.7183

In this case, the Fv = 13,231.30

i = 3.5% or 0.035

t = 8 years

e = 2.7183

Pv = ? (The unknown variable).

13,231.30 = Pv × [2.7183^(0.035 × 8)]

13,231.30 = Pv × [2.7183^(0.28)]

13,231.30 = Pv × 1.323

Pv = 13,231.30/1.323

Pv = $10000.98

= $10,001

Therefore the initial deposit is $10,001

8 0

2 years ago

Suppose that 20% of the adult women in the United States dye or highlight their hair. We would like to know the probability that

Rasek [7]

Answer:

71.08% probability that pˆ takes a value between 0.17 and 0.23.

Step-by-step explanation:

We use the binomial approxiation to the normal to solve this question.

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:

$p = 0.2, n = 200$ . So

$\mu = E(X) = np = 200*0.2 = 40$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.2*0.8} = 5.66$

In other words, find probability that pˆ takes a value between 0.17 and 0.23.

This probability is the pvalue of Z when X = 200*0.23 = 46 subtracted by the pvalue of Z when X = 200*0.17 = 34. So

X = 46

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

$Z = \frac{46 - 40}{5.66}$

$Z = 1.06$

$Z = 1.06$ has a pvalue of 0.8554

X = 34

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

$Z = \frac{34 - 40}{5.66}$

$Z = -1.06$

$Z = -1.06$ has a pvalue of 0.1446

0.8554 - 0.1446 = 0.7108

71.08% probability that pˆ takes a value between 0.17 and 0.23.

6 0

2 years ago

Given directed line segment QS , find the coordinates of R

Degger [83]

Answer:

The answer is below

Step-by-step explanation:

The question is not complete, what are the coordinates of point Q and R. But I would show how to solve this.

The location of a point O(x, y) which divides line segment AB in the ratio a:b with point A at ( $x_1,y_1$ ) and B( $x_2,y_2$ ) is given by the formula: