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3 years ago

Which statements are true of all squares

Mathematics

1 answer:

mafiozo [28]3 years ago

8 0

Answer:

the diagonals of a square are congruent to each other - option 2 is true; the diagonals of a square are perpendicular and bisect each other - options 1 and 5 are true; a square is a rhombus, because all sides are congruent.

Step-by-step explanation:

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A telephone exchange operator assumes that 8% of the phone calls are wrong numbers. If the operator is right, what is the probab

Vera_Pavlovna [14]

Answer:

The probability that the sample proportion differ from the population proportion by greater than 3% is 0.0241.

Step-by-step explanation:

Let X = number of phone calls that are wrong numbers.

The proportion of phone calls that are wrong numbers is, p = 0.08.

A sample of n = 421 phone calls is selected to determine the proportion of wrong numbers in this sample.

The random variable X follows a Binomial distribution with parameters n and p.

The probability mass function of a Binomial distribution is:

$P(X=x)={421\choose x}0.08^{x}(1-0.08)^{421-x}$

Now, for the sample proportion to differ from the population proportion by 3% the value of the sample proportion should be:

$\hat p-p=0.03\\\hat p-0.08=0.03\\\hat p=0.11$ $\hat p-p=-0.03\\\hat p-0.08=-0.03\\\hat p=0.05$

So when the sample proportion is less than 5% or greater than 11% the difference between the sample proportion and population proportion will be greater than 3%.

If sample proportion is 5% then the value of X is,

$X=np=421\times 0.05=21.05\approx21$

Compute the value of P (X ≤ 21) as follows:

$P(X\leq 21)=\sum\limits^{21}_{x=0}{{421\choose x}0.08^{x}(1-0.08)^{421-x}}=0.0106$

If the sample proportion is 11% then the value of X is,

$X=np=421\times 0.11=46.31\approx47$

Compute the value of P (X ≥ 47) as follows:

$P(X\geq 47)=\sum\limits^{471}_{x=47}{{421\choose x}0.08^{x}(1-0.08)^{421-x}}=0.0135$

Then the probability that the sample proportion differ from the population proportion by greater than 3% is:

$P(\hat p-p>0.03)=P(X\leq 21)+P(X\geq 47)=0.0106+0.0135=0.0241$

Thus, the probability that the sample proportion differ from the population proportion by greater than 3% is 0.0241.

7 0

3 years ago

Select the correct answer.

m_a_m_a [10]

B).

hope this helps

5 0

4 years ago

Please help me... thank you

DanielleElmas [232]

Slope-intercept form:

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0) or (0,y)

For lines to be parallel, they have to have the SAME slope.

For lines to be perpendicular, their slopes have to be the opposite/negative reciprocals (flipped sign and number)

For example:

slope is 2

perpendicular line's slope is -1/2

slope is -2/3

perpendicular line's slope is 3/2

9.) First find the slope of line PQ. Use the slope formula and plug in the two points.

P = (4, 1) (x₁ , y₁)

Q = (8, 4) (x₂ , y₂)

$m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{4-1}{8-4}$

$m=\frac{3}{4}$

Line RS is parallel to line PQ, so they have the same slope of 3/4

$y=\frac{3}{4}x+b$

To find "b", plug in the point R = (3, -2) into the equation

$y=\frac{3}{4}x+b$

$-2=\frac{3}{4}(3)+b$

$-2=\frac{9}{4}+b$ Subtract 9/4 on both sides

$-2-\frac{9}{4}=b$ Make the denominators the same

$-\frac{8}{4} -\frac{9}{4}=b$

$-\frac{17}{4}=b$

$y = \frac{3}{4}x- \frac{17}{4}$

10.) Find the slope of line PQ

$m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{4-1}{8-4} =\frac{3}{4}$

Line RS is perpendicular to line PQ, so the slope of line RS is -4/3

y = -4/3x + b

Plug in the point R = (3, -2) into the equation to find "b"

y = -4/3x + b

-2 = -4/3(3) + b

-2 = -4 + b Add 4 on both sides

2 = b

$y = -\frac{4}{3}x+2$

8 0

3 years ago

What value for z makes this equation true?

Paladinen [302]

(10×10)+(10×5)=10z
100+50=10z
150=10z
z=15 which is C. Hope it help!

4 0

3 years ago

Read 2 more answers

PLEASE HELP FOR THIS QN

lilavasa [31]

Answer:

$5^8$

Step-by-step explanation:

$5^{2^{3}}$

$5^{2 \times 2 \times 2}$

$5^8$

$=390625$

8 0

4 years ago