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Part A: What is the area of the parallelogram? Show your work. (5 points) Part B: How can you decompose this parallelogram into two triangles? If this parallelogram what decomposed into two triangles, what would be the area of each triangle? ​

Step-by-step explanation:

[tex]\frac{( \csc x+1)( \csc x-1)}{ \csc ^2x} = \frac{ { \csc }^{2} x - 1}{ \csc^{2} x} \\ = 1 - \sin^{2} x = \cos^{2} x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

b. Since csc theta = 1/sin theta, we can multiply both sides by sin theta and you will end up with

[tex] \cos^{2} \theta + \sin^{2} \theta = 1[/tex]

which is an identity.

Complete question is;

Assume the random variable X is normally distributed with mean μ = 50 and standard deviation σ = 7. What is the probability P (X > 42)?

Answer:

P(X > 42) = 0.1271

Step-by-step explanation:

We are given;

mean; μ = 50

Standard deviation; σ = 7

Formula for the z-score is;

z = (x - μ)/σ

Thus;

z = (42 - 50)/7

z = -1.14

Since we are looking for P (X > 42), then let's look up this z-value from the z-distribution table attached.

We have;

P(X > 42) = 0.1271

Answer:

$66.3

Step-by-step explanation:

price of a ticket without discount = $78

discount  % = 15%

discount amount = ?

price of a discounted ticket = ?

discount amount = discount% of price of a original ticket

=15/100 * $78

=$1170/100

=$ 11.7

price of the discounted ticket = $78 - $11.7

=$66.3

The discounted price of the stadium's normal ticket is  $66.3

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A stadium's normal ticket price is $78 and As a special promotion they offer 15% off.

Therefore, The discounted price of the ticket should be (100 - 15)% = 85% of the original price which is,

= (85/100)×78.

= $66.3 is the discounted price.

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Answer:

no solution

Step-by-step explanation:

[tex]\dfrac{2x - 6}{4} > \dfrac{x - 3}{2}[/tex]

The LCD is 4, so multiply both sides of the inequality by 4.

[tex]4 \times \dfrac{2x - 6}{4} > 4 \times \dfrac{x - 3}{2}[/tex]

[tex]2x - 6 > 2 \times (x - 3)[/tex]

[tex]2x - 6 > 2x - 6[/tex]

Subtract 2x from both sides.

[tex]-6 > -6[/tex]

Since -6 = -6, the above statement is false, so there are no solutions.

Answer: no solution

Answer:

35°

Step-by-step explanation:

From the sketch made, to obtain B we use the cosine angle formula :

We have 2 so des and an included angle

Cos B = (a² + c² - b²) / 2ac

First we obtain the side c

c² = a² + b² - 2ab CosC

c² = 11.2² + 6.7² - 2(11.7 * 6.7) * cos 72

c = 11.13

Using the value of c

Cos B = (a² + c² - b²) / 2ac

CosB = (11.2² + 11.13² - 6.7²) / (2*11.2*11.13)

Cos B = 204.4269 / 249.312

B = Cos^-1(204.4269 / 249.312)

B = 34.9°

Answer:

umm not sure on this one either 9328.71

Step-by-step explanation:

9514 1404 393

Answer:

  C

Step-by-step explanation:

The step shown indicates that y was eliminated from the equations. For choices A, B, D, this is done by adding the equations together (the y-coefficients are opposites). The result of doing that gives x-terms of 4x, 0x, and 0x, respectively. These x-terms do not match the one given: 2x.

For choice C, the y-term is eliminated by subtracting twice the second equation from the first. Doing that gives ...

  (4x +2y) -2(x +y) = (14) -2(3)

  4x +2y -2x -2y = 14 -6 . . . . eliminate parentheses

  2x = 8 . . . . . . . . . . . . . . collect terms

Answer:

x=7

Step-by-step explanation:

take 30 degree as reference angle

using sin tan rule

tan 30=opposite/adjacent

[tex]\frac{1}{\sqrt{3} }[/tex]=x/[tex]7\sqrt{3}[/tex]

[tex]\frac{1}{\sqrt{3} }[/tex] *[tex]7\sqrt{3}[/tex]

[tex]7\sqrt{3} /\sqrt{3}[/tex]

7=x

Answer:

-2.41: -2.14: -2.1: -11/8: 7/50

Answer:

c

Step-by-step explanation:

Answer:

I think there is no solution.

Step-by-step explanation:

Substitute:

Z = -3y-5x+25

X = 3y-2z-13

Put into the last formula:

14(3y-2z-13)-2y+3(-3y-5x+25) = 48

Then:

14(3y-2(-3y-5x+25)-13)-2y+3(-3y-5(3y-2z-13)) = 48

So:

14(3y-2(-3y-5(3y-2z-13)+25)-13)-2y+3(-3y-5(3y-2(-3y-5x+25)-13)) = 48

And so on.

Answer:

The total mass of Earth's hydrosphere is about 1.4 × 1018 tonnes, which is about 0.023% of Earth's total mass. At any given time, about 20 × 1012 tonnes of this is in the form of water vapor in the Earth's atmosphere (for practical purposes, 1 cubic meter of water weighs one tonne).

Step-by-step explanation:

Answer:

4+(3 times x)= height of balloon.   x = seconds

Step-by-step explanation:

I hope this helps you! :D

Answer:

1/2 or 0.5

Step-by-step explanation:

All possible odd values on a 6-sided die include 1, 3, and 5; that is 3 values out of 6 total values. 3/6 or 1/2 is a 0.5 probability.

Answer:

The p-value of the test is 0.1611>0.01, which means that there is not significant evidence at the 1% significance level that less than 34% of fathers take no responsibility for child care

Step-by-step explanation:

A journal article reports that 34% of fathers take no responsibility for child care. A group of fathers believes that this estimate is too high.

At the null hypothesis, we test if the proportion is of at least 34%, that is:

[tex]H_0: p \geq 0.34[/tex]

At the alternative hypothesis, we test if the proportion is less than that, that is:

[tex]H_1: p < 0.34[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.34 is tested at the null hypothesis:

This means that [tex]\mu = 0.34, \sigma = \sqrt{0.34*0.66}[/tex]

In a random sample of 80 fathers, it was found that 23 of those fathers take no responsibility for child care.

This means that [tex]n = 80, X = \frac{23}{80} = 0.2875[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.2875 - 0.34}{\frac{\sqrt{0.34*0.66}}{\sqrt{80}}}[/tex]

[tex]Z = -0.99[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion below 0.2875, which is the p-value of Z = -0.99.

Looking at the Z-table, Z = -0.99 has a p-value of 0.1611.

The p-value of the test is 0.1611>0.01, which means that there is not significant evidence at the 1% significance level that less than 34% of fathers take no responsibility for child care

Answer:

iv. q/6E0

Step-by-step explanation:

Electric flux formula:

The electic flux formula, of a charge q is given by, through an entire cube, is given by:

[tex]E = \frac{q}{E_o}[/tex]

In which [tex]E_o[/tex] is a constant related to the material.

The electric flux through any one face of the cube is:

Key-word is face, and a cube has 6 faces, with the force distributed evenly throughout it. Thus

[tex]E_f = \frac{1}{6} \times \frac{q}{E_o} = \frac{q}{6E_o}[/tex]

And the correct answer is given by option iv.

Answer:

14

Step-by-step explanation:

So let's think smart.  If you look at the image I made a diagram.  The 3 squares I colored in represent 3/4.  It takes 14 3/4 strips to cover 10 1/2 inches.

The Number of 3/4 inch strips required to cover 10 1/2 inches of caulk will be 14

The total inches of caulk to be covered = 10 1/2 inches

The fraction of inch strip to be used = 3/4 inches

To obtain the number of 3/4 inch strop required ;

We divide the total inches of caulk by 3/4

Hence,

10 1/2 ÷ 3/4

21/2 ÷ 3/4

Change the sign to × and take the reciprocal of 3/4 ;

21/2 × 4/3

(21 × 4) / (2 × 3) = 84 / 6

84 / 6 = 14

Hence, the number of 3/4 inch strip required is 14

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Answer:

[tex]P(6am-12\ noon) = 0.305[/tex]

[tex]P(12\ noon - 6pm) = 0.143[/tex]

[tex]P(6pm-12\ midnight) = 0.322[/tex]

[tex]P(12\ midnight - 6am) =0.230[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{cc}{Time} & {Inventors} & {6am - 12\ noon} & {295} & {12\ noon -6pm} & {138} & {6pm - 12\ midnight} & {311} & {12\ midnight - 6am} & {222} & {Total} & {966} \ \end{array}[/tex]

Required

The probability of each time interval

To do this, we simply divide the number of inventors in the interval by the total inventors (966)

So, we have:

[tex]P(6am-12\ noon) = \frac{6am-12\ noon}{Total}[/tex]

[tex]P(6am-12\ noon) = \frac{295}{966}[/tex]

[tex]P(6am-12\ noon) = 0.305[/tex]

[tex]P(12\ noon - 6pm) = \frac{12\ noon - 6pm}{Total}[/tex]

[tex]P(12\ noon - 6pm) = \frac{138}{966}[/tex]

[tex]P(12\ noon - 6pm) = 0.143[/tex]

[tex]P(6pm-12\ midnight) = \frac{6pm-12\ midnight}{Total}[/tex]

[tex]P(6pm-12\ midnight) = \frac{311}{966}[/tex]

[tex]P(6pm-12\ midnight) = 0.322[/tex]

[tex]P(12\ midnight - 6am) =\frac{12\ midnight - 6am}{Total}[/tex]

[tex]P(12\ midnight - 6am) =\frac{222}{966}[/tex]

[tex]P(12\ midnight - 6am) =0.230[/tex]

Answer:

hi, yes the option B is the correct answer

Answer:

B

Step-by-step explanation:

Answer:

B EDGE

Step-by-step explanation:

Perpendicular Definition:

[tex] \large \boxed{m_1m_2 = - 1}[/tex]

Slopes of two different equations multiply each others and must equal to -1. We can also say that the perpendicular occurs only if both equations are negative reciprocal to each others. For example, we are given the equation of y = 2x. The perpendicular to y = 2x would be y = (-1/2)x. See how both are reciprocal to each others.

From the equation below:

[tex] \large{x + 5y = - 2}[/tex]

Since the equation is in the form of Ax+By = C. It is better to use the another slope formula which is:

[tex] \large \boxed{m = - \frac{A}{B} }[/tex]

From the equation above, use the slope formula to find the slope.

[tex] \large{m = - \frac{1}{5} }[/tex]

Therefore the equation has a slope of -1/5. Next to find the perpendicular equation to the original equation. Since our slope is -1/5 - that means the negative reciprocal of -1/5 is 5. Therefore the slope of perpendicular line is 5.

Next we will be using the point-slope form below:

[tex] \large \boxed{y - y_1 = m(x - x_1)}[/tex]

Given the y1 and x1 or (x1,y1) are the points. Our perpendicular slope is 5 which passes through the point (3,0). Substitute both slope and the point in.

[tex] \large{y - 0 = 5(x - 3)}[/tex]

Simplify in the slope-intercept form as we get:

[tex] \large{y = 5x - 15}[/tex]

Answer

Hope this helps and let me know if you have any doubts!

Given:

The equation of a line is:

[tex]2y+3x=10[/tex]

The line is dilated by factor 3.

To find:

The result of dilation.

Solution:

The equation of a line is:

[tex]2y+3x=10[/tex]

For [tex]x=0[/tex],

[tex]2y+3(0)=10[/tex]

[tex]2y+0=10[/tex]

[tex]y=\dfrac{10}{2}[/tex]

[tex]y=5[/tex]

For [tex]x=2[/tex],

[tex]2y+3(2)=10[/tex]

[tex]2y+6=10[/tex]

[tex]2y=10-6[/tex]

[tex]2y=4[/tex]

Divide both sides by 2.

[tex]y=\dfrac{4}{2}[/tex]

[tex]y=2[/tex]

The given line passes through the two points A(0,5) and B(2,2).

If the line dilated by factor 3 with origin as center of dilation, then

[tex](x,y)\to (3x,3y)[/tex]

Using this rule, we get

[tex]A(0,5)\to A'(3(0),3(5))[/tex]

[tex]A(0,5)\to A'(0,15)[/tex]

Similarly,

[tex]B(2,2)\to B'(3(2),3(2))[/tex]

[tex]B(2,2)\to B'(6,6)[/tex]

The dilated line passes through the points A'(0,15) and B'(6,6). So, the equation of dilated line is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-15=\dfrac{6-15}{6-0}(x-0)[/tex]

[tex]y-15=\dfrac{-9}{6}(x)[/tex]

[tex]y-15=\dfrac{-3}{2}x[/tex]

Multiply both sides by 2.

[tex]2(y-15)=-3x[/tex]

[tex]2y-30=-3x[/tex]

[tex]2y+3x=30[/tex]

Therefore, the equation of the line after the dilation is [tex]2y+3x=30[/tex].

Answer:

390 yds

Step-by-step explanation:

Take the amount of wood per birdhouse and multiply by the number of birdhouses being made

78 * 5 =390 yds

Answer:

390 yds

Step-by-step explanation:

Take the amount of wood per birdhouse and multiply by the number of birdhouses being made

78 * 5 =390 yds

Hope this helps!!!

Answer:

The opposite of a number is the number on the other side of 0 number line, and the same distance from 0.

9514 1404 393

Answer:

  4

Step-by-step explanation:

2/3 = 4/6

There are four 1/6-cup servings of rice in 4/6 cups of rice.

Answer:

Option 4) -$45 per month; the amount of money withdrawn per month.

Step-by-step explanation:

The rate of change is 45. Before he began taking money out to pay for his classes[month 0], he had $190. Since then, every month, $45 have been withdrawn.