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3 years ago

Is the dilation from A to B a reduction or enlargement?

Mathematics

2 answers:

WITCHER [35]3 years ago

8 0

Answer:

This is actually a reduction, and the scale factor of this dilation is 0.5.

Masteriza [31]3 years ago

4 0

It’s a because the factor reduce by itself

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A chemical company makes two brands of antifreeze. The first brand is 65% pure antifreeze, and the second brand is 90% pure anti

Murrr4er [49]

With amounts measured in gallons, let

x = amount of 65% antifreeze

y = amount of 90% antifreeze

1 gal of the 65% brand contains 0.65 gal of pure antifreeze; x gal would contain 0.65x gal. Similarly, y gal of the 90% brand contains 0.90y gal of pure antifreeze.

To obtain 120 gal of 80% antifreeze solution (which contains 0.80•120 = 96 gal of pure antifreeze), we must have

x + y = 120 … … … … … [total volume of antifreeze solution]

0.65x + 0.90y = 96 … [total volume of pure antifreeze]

Solve the first equation for y :

y = 120 - x

Substitute this into the second equation and solve for x :

0.65x + 0.90 (120 - x) = 96

0.65x + 108 - 0.90x = 96

0.25x = 12

x = 48

Solve for y :

y = 120 - 48

y = 72

6 0

2 years ago

A report indicated that 37% of adults had received a bogus email intended to steal personal information. Suppose a random sample

fiasKO [112]

Answer:

5.05% probability that no more than 34% had received such an email.

Step-by-step explanation:

We use the binomial approximation to the normal to solve this problem.

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:

$n = 700, p = 0.37$

$\mu = E(X) = np = 700*0.37 = 259$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{700*0.37*0.63} = 12.77$

In a random sample of 700 adults, what is the probability that no more than 34% had received such an email?

34% is 0.34*700 = 238

So this probability is the pvalue of Z when X = 238.

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

$Z = \frac{238 - 259}{12.77}$

$Z = -1.64$

$Z = -1.64$ has a pvalue of 0.0505

5.05% probability that no more than 34% had received such an email.

7 0

4 years ago

Give me a fraction that is greater than 1/3

Mumz [18]

1/2

...... should be correct

7 0

3 years ago

I do not understand this , please help!

puteri [66]

I don’t either djejsjnenekskekwnsjwjwjsnnensjskejsnnsnwjwjsnwnwnsbw

7 0

3 years ago

Solve the system by using a matrix equation <br><br>7x-4y=4 <br><br>10x-6y=2

Andrei [34K]

Answer:

<h2>The solution to the system of equation is x = 8, y = 13</h2>

Step-by-step explanation:

The system of equation using matrix equation can be solved using crammers rule. Given the equation;

7x-4y=4

10x-6y=2

The equation will be rewritten in the format AX = B

matrix A will be 2*2 matrix

X will be a column matrix containing the variables

B will be a column matrix

$\left[\begin{array}{cc}7&-4\\10&-6\\\end{array}\right] \left[\begin{array}{c}x&y\\\\\end{array}\right] = \right] \left[\begin{array}{c}4&2\\\\\end{array}\right]$

first we will find the determinant of the matrix A

$|A|=7(-6)-(10)(-4)\\|A|= -42+40\\|A|= -2$

To get the value of x, we will substitute the column matrix at the right hand side to replace the first column pf matrix A, then we look for the determinant and divide the determinant by the determinant of matrix A itself.

$|X|=\left[\begin{array}{cc}4&-4\\2&-6\\\end{array}\right]\\|X|= -24+8\\|X|=-16$

x = |X|/|A|

x = -16/-2

x = 8

Similarly for y, we will substitute the column matrix at the right hand side to replace the second column of matrix A, then we look for the determinant and divide the determinant by the determinant of matrix A itself.

$|Y|=\left[\begin{array}{cc}7&4\\10&2\\\end{array}\right]\\|Y|= 14-40\\|Y|=-26$

y = |Y|/|A|

y = -26/-2

y = 13

The solution to the system of equation is x = 8, y = 13

3 0

3 years ago