Megan paid $2.52 in sales tax on an item that cost $36.00 before tax. At that rate, how much would she pay in sales tax for an item that costs $40.00 before tax? ​

No, the trapezoids are not similar because their corresponding angles do not have the same measures.

The given trapezoids ABCD and EFGH can be analyzed to determine if they are similar. Similarity in geometric figures implies that their corresponding angles are congruent, and their corresponding sides are proportional.

Let's examine the angles of the trapezoids:

In trapezoid ABCD:

Angle A = 137 degrees

Angle B = 90 degrees

Angle C = 90 degrees

Angle D = 43 degrees

In trapezoid EFGH:

Angle E = 136 degrees

Angle F = 90 degrees

Angle G = 90 degrees

Angle H = 44 degrees

By comparing the angles, we can observe that angles B and F are both right angles (90 degrees) in both trapezoids. Additionally, angles C and G are also right angles (90 degrees) in both trapezoids.

However, angles A and E, as well as angles D and H, do not have the same measures. Angle A measures 137 degrees in trapezoid ABCD, while angle E measures 136 degrees in trapezoid EFGH. Similarly, angle D measures 43 degrees in trapezoid ABCD, while angle H measures 44 degrees in trapezoid EFGH.

Since the corresponding angles in the two trapezoids do not have the same measures, we can conclude that trapezoids ABCD and EFGH are not similar.

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Hence, there is a 0.68 percent probability that the fifth driver will be the one that police officer summons over while wearing a safety belt.

The word "probability" derives from the Latin word "propitiate," which means "credibility, probability," from the noun probabilism in the 14th century (see probable). The phrase was first used in a mathematical meaning in 1718.

Part A:

The likelihood that precisely 3 drivers are buckled up can be determined using the binomial probability formula:

P(X = 3) = (5 choose 3) × (0.68)³ × (0.32)²

Where (5 choose 3) = 10 is the number of ways to choose 3 drivers out of 5.

P(X = 3) = 10 × 0.68³ × 0.32²

P(X = 3) = 0.267

Consequently, there is a 0.267 percent chance that all 3 drivers are buckled up.

Part B:

The fifth driver will be pulled by by the police officer since 4 other drivers have already been stopped. We are looking for the likelihood that the motorist is wearing a safety belt.

Since 68% of drivers are safety belt wearers, there is a 0.68 percent chance that the following motorist will be as well.

Thus, there is a 0.68 percent chance that the next vehicle the police officer pulls over is driven by a person wearing a safety belt.

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The statement that the one with a higher coefficient of variation exhibits higher variability is true.

The coefficient of variation expresses the proportionate level of variability present in a random variable and can be determined by dividing the mean by the standard deviation.

If the coefficient of variation is higher, it means that the random variable shows more variation in relation to its mean.

To illustrate, suppose that the average height of a set of males is 6 feet with a standard deviation of 2 inches.

The variance ratio would result in a coefficient of variation of 0. 033 Suppose that a group of females has an average height of 5 feet with a standard deviation of 1 inch.

The women's coefficient of variation is calculated to be 0. 02 The variance of men's height in relation to their average height is indicated by their higher coefficient of variation.

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Answer:

1,800 lbs of sand

900 lbs of gravel

600 lbs of cement

Step-by-step explanation: 11*300=3,300. 300*6=1,800, 300*3=900, and 300*2=600. This is correct because if you add 1,800+900+600 you get 3,300.

Without additional information about the model house, it is impossible to accurately describe the surface that Molly does not need to paint. It could be any surface that will not be visible when the model house is displayed, such as the underside of a roof, the back of a wall, or the bottom of a floor.

By the SSS Congruence Theorem, △ABC ≅ △DEF.

What does a math congruent mean?

Congruent refers to having precisely the same form and size. Even after the forms have been flipped, turned, or rotated, the shape and size ought to remain constant.

What is the SSS rule?

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle.

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Answer:

Find the exact value using trigonometric identities.

100

Step-by-step explanation:

The exact value of 2 divided by (0.01) 2 is 20000.

We are given that;

2 divided (0.01)2

Now,

To find the exact value of 2 divided by (0.01) 2, we can use the following steps:

Rewrite 0.01 as a fraction: 0.01 = 1/100

Square both the numerator and the denominator: (0.01) 2 = (1/100) 2 = 1/10000

Flip the fraction and multiply by 2: 2 / (0.01) 2 = 2 x 10000/1 = 20000

Therefore, by algebra the answer will be 20000.

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Answer: The first one is nonlinear, the second is nonlinear, and the third is linear.

Step-by-step explanation: The first one is nonlinear because when you calculate slope you get different numbers.

7-4/2-1 = 3/1= 3

4-3/1-0= 1/1= 1

Also when you graph it, it does not become a line. I can attach an image for evidence (Credits to other person who answered and commented on my answer thanks for finding my mistake.)

The second one has an exponent on the x, so it is not linear.

The third is a line so it is linear.

Answer:

Nonlinear, Nonlinear, Linear

Step-by-step explanation:

For if you graph 1 and 2 you will see both are not increasing evenly like a straight line, only the graph 3 shows a linear line.

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

Answer:

B and D

Step-by-step explanation:

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

\(3x+y=5\implies y=\stackrel{\stackrel{m}{\downarrow }}{-3}x+5\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so we're really looking for the equation of a line that has a slope oif -3 and it passes through (2 , -4)

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- 3}(x-\stackrel{x_1}{2}) \implies y +4 = - 3 ( x -2) \\\\\\ y+4=-3x+6\implies {\Large \begin{array}{llll} y=-3x+2 \end{array}}\)

now, keeping in mind that perpendicular lines have negative reciprocal slopes

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ -3 \implies \cfrac{-3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-3} \implies \cfrac{1}{ 3 }}}\)

so for this one, we're looking for the equation of a line whose slope is 1/3 and it passes through (2 , -4)

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{2}) \implies y +4 = \cfrac{1}{3} ( x -2) \\\\\\ y+4=\cfrac{1}{3}x-\cfrac{2}{3}\implies y=\cfrac{1}{3}x-\cfrac{2}{3}-4\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x-\cfrac{14}{3} \end{array}}\)

a) Composite function fog(x) = 3/(x+3)

b) Domain of fog(x) in interval notation = (-∞,-3)∪(-3,∞)

A function is a process or a relation that associates each element 'a' of a set A , to a single element 'b' of another set B.

Given functions,

f(x) = x/(x+2)

g(x) = 6/x

a) (fog)(x) = f(g(x))

= f(6/x)

= (6/x)/((6/x) + 2)

= 6/x((6/x) + 2)

= 6/(6 + 2x)

= 3/(x+3)

fog(x) = 3/(x+3)

b) Domain of (fog)(x)

y = 3/(x+3)

For domain y = 0

⇒ x+3  = 0

⇒ x  = -3

But the function gets undefined for x = -3

So, Domain x ≠ -3

⇒ x > -3 or x < -3

Domain set Interval Notation : (-∞,-3)∪(-3,∞)

Hence, value of composite function

fog(x) = 3/(x + 3)

Domain of fog(x) : (-∞,-3)∪(-3,∞)

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Answer:

\(f^{-1}(x) = \sqrt[3]{\frac{x -4}{5}} +2\)

Step-by-step explanation:

Given

\(f(x) = 5(x - 2)^3 + 4\)

Required

Determine the inverse

\(f(x) = 5(x - 2)^3 + 4\)

Replace f(x) with y

\(y = 5(x - 2)^3 + 4\)

Swap the positions of x and y

\(x = 5(y - 2)^3 + 4\)

Make y the subject

\(x -4= 5(y - 2)^3\)

Divide by 5

\(\frac{x -4}{5}= (y - 2)^3\)

Take cube roots of both sides

\(\sqrt[3]{\frac{x -4}{5}}= y - 2\)

Add 2 to both sides

\(\sqrt[3]{\frac{x -4}{5}} +2 = y\)

\(y = \sqrt[3]{\frac{x -4}{5}} +2\)

Replace y with \(f^{-1}(x)\)

\(f^{-1}(x) = \sqrt[3]{\frac{x -4}{5}} +2\)

The sine of 585 degrees is approximately -0.707.

To find the sine of 585 degrees, we need to understand the periodic nature of the sine function. The sine function has a period of 360 degrees or 2π radians, which means it repeats its values after every full revolution.

To evaluate the sine of 585 degrees, we can subtract 360 degrees repeatedly until we obtain an angle within the first revolution.

585 degrees - 360 degrees = 225 degrees

Now we have an angle of 225 degrees, which is within the first revolution. The sine function can be evaluated for this angle.

The sine of 225 degrees can be calculated using various methods, such as using a calculator or referring to a trigonometric table. The approximate value of the sine of 225 degrees is -0.707.

Therefore, sin(585 degrees) ≈ sin(225 degrees) ≈ -0.707.

The negative sign indicates that the angle lies in the third quadrant of the unit circle, where the sine function is negative.

It's important to note that when working with angles beyond the first revolution, it's common to reduce them to an equivalent angle within the first revolution to simplify calculations and make use of known trigonometric values.

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We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

The given system of equations are 2x-1/3y = -2...(1)

3x+y=1...(2)

We solve this system of equations by using substitution method.

Let us solve for x in equation to substitute it in equation (2).

2x=-2+1/3y

Divide both sides of equation by 2.

x=-1+1/6y

Now plug in the value of x in equation 2.

Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

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The Area of that shape is 8 2 times 4 is 8

Step-by-step explanation:

10 × n = 360

n = 360 ÷ 10

n = 36

So, n = 36

(3 × 4) × 5 = k × (5 × 4)

12 × 5 = k × 20

60 = k × 20

k = 60 ÷ 20

k = 3

So, k = 3

Answer:

\(n = 36 \\ k = 3\)

Step-by-step explanation:

#1

\(10 \times n = 360 \\ 10n = 360 \\ \frac{10n}{10} = \frac{360}{10} \\ n = 36\)

#2

\((3 \times 4) \times 5 = k \times (5 \times 4) \\ 12 \times 5 = k \times 20 \\ 60 = 20k \\ \frac{60}{20} = \frac{20k}{20} \\ 3 = k\)

Hope this helps you.

Let me know if you have any other questions:-)

Step-by-step explanation:

\(3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{15}{9} \\ \)

Given the number 96.08, we look at the digits after the decimal point:

therefore, the digit in the tenth place is 0 and the digit in the hudnredths place is 8

The probability of the sample mean being less than 25.3 is given as follows:

0.9713 = 97.13%.

The sample mean would not be considered unusual, as it has a probability that is greater than 5%.

The z-score of a measure X of a normally distributed variable that has mean represented by \(\mu\) and standard deviation represented by \(\sigma\) is obtained by the equation presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The parameters for this problem are given as follows:

\(\mu = 25, \sigma = 1.3, n = 68, s = \frac{1.3}{\sqrt{68}} = 0.1576\)

The probability of a score less than 25.3 is the p-value of Z when X = 25.3, hence:

Z = (25.3 - 25)/0.1576

Z = 1.9

Z = 1.9 has a p-value of 0.9713.

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Step-by-step explanation: you forgot to put the graph

Answer:

The larger number is 51.3. (to 3 s.f.)

Step-by-step explanation:

Let the smaller number be x and the larger number be y.

Given that the sum of the 2 numbers is 52,

x +y= 52 -----(1)

One number is 76 times the second number. Since we have made y to be the larger number,

y= 76x -----(2)

Substitute equation (2) into (1):

x +76x= 52

Simplify:

77x= 52

Divide both sides by 77:

x= 52 ÷77

\(x = \frac{52}{77} \)

x= 0.675 (3 s.f.)

Substitute the value of x into (2):

\(y = 76( \frac{52}{77} )\)

\(y = 51 \frac{25}{77} \)

y= 51.3 (3 s.f.)

We can write the quadratic in standard form as:

y = x² -18x - 1053

For a quadratic equation whose solutions are:

x = x₁

x = x₂

We can write it as:

y = (x - x₁)*(x - x₂)

Here the solutions are:

x = 9 + 9√13

x = 9 - 9√13

Then we can write the quadratic as:

y = (x - 9 - 9√13)*(x - 9 + 9√13)

Expanding that:

y = x² -18x - 81*13

y = x² -18x - 1053

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Answer:

1) 5m

2) 0.25tan

Step-by-step explanation:

Differentiate the function/equation with respect to x and solve for the derivative, dy/dx. The value of dy/dx at the given point is the slope of the tangent line to the curve at that point. Then use the point-slope formula to get the equation of the tangent.

1.

\(y = \dfrac{x^2}{x+2} \implies \dfrac{dy}{dx} = \dfrac{2x\times(x+2) - x\times1}{(x+2)^2} = \dfrac{x(x+4)}{(x+2)^2}\)

When x = 2, the derivative is

\(\dfrac{dy}{dx}\bigg|_{x=2} = \dfrac{2(2+4)}{(2+2)^2} = \dfrac34\)

Then the equation of the tangent line at (2, 1) is

\(y - 1 = \dfrac34 (x - 2) \implies \boxed{y = \dfrac{3x}4 - \dfrac12}\)

2.

\(x^3 + 2y^2 = 10y \implies 3x^2 + 4y \dfrac{dy}{dx} = 10 \dfrac{dy}{dx} \implies \dfrac{dy}{dx} = \dfrac{3x^2}{10-4y}\)

When x = 2 and y = 1, the derivative is

\(\dfrac{dy}{dx}\bigg|_{(x,y)=(2,1)} = \dfrac{3\times2^2}{10-4\times1} = 2\)

Then the tangent at (2, 1) has equation

\(y - 1 = 2 (x - 2) \implies \boxed{y = 2x - 3}\)

Answer:

Step-by-step explanation:

Answer:

It is not true. 19 - 10 = 9.

:) Hope this helps