slove each problem include a diagram. a. A 6m long wheelchair ramp makes an angle of 15 with the ground. How high abouve the ground does the top end of the ramp reach. b.two treees are 120m apart. From the point halfway between them, then angle of the elevation to the top of the trees is 36 and 52. how much taller is one tree than the other.

The measure of the angle 4, m∠4, obtained from the measure formed by the diagonals of a rhombus is; m∠4 = 38°

The diagonals of a rhombus bisect the angles at the vertices of the rhombus

The diagonals of a rhombus are perpendicular bisectors of each other, therefore;

The measure of the angle m∠2 = 90°

Therefore; m∠1 = 90° - 52° = 38°

The triangle with base angles ∠1, and ∠4, is an isosceles triangle, with the base angles ∠1, and ∠4

The base angles of an isosceles triangle are congruent, therefore;

∠1 ≅ ∠4

m∠1 = m∠4

m∠4 = m∠1 = 38°

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Sue's total pay for the year based on the values will be £38110

Sue's total pay of year will have three parts

Fixed Salary for 12 months

 one month salary = £1410

 so 12 month salary = £1410 x 12 = £16920

26% of total profit

  Total cost to the company- £473,500

  Total income for the company - £549,000

  Profit =  Total income for the company - Total cost to the company

            =  £549,000 - £473,500 = £75500

   Sues income from profit = 26% of £75500 = (26 × 75500)/100 = £19630

Bonus if Sue sells at least 16 cars

  Given number of months when sue solds atleast 16 cars = 4

  So bonus income = 4 × 390 = £1560

Adding the three above parts

Sue's total pay for the year = £16920 + £19630 + £1560 = £38110

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Complete question

Ace autos sell cars and pay sue each month as follows

-salary of £1410

-26% of the total profit the company makes from her sales

- a £390 bonus if she sells at least 16 cars

The table shows information about the cars she sold last year

Total cost to the company- £473,500

Total income for the company - £549,000

Number of months when she sold at least 16 cars - 4

work out sues total pay for the year

1. All angles of a rectangle are right angles (90 degrees), while the angles of a parallelogram can be any angle other than 90 degrees.

2. The opposite sides of a rectangle are equal in length, whereas in a parallelogram, opposite sides are of equal length as well, but they may not be perpendicular to each other.

The questions are a bit unclear and have some spelling errors, but I will try my best to provide an answer:

- Mention the transformation of the brick when it is flipped or turned sideways:

If the brick is flipped over, the transformation it undergoes is called a reflection. This can also be thought of as a mirror image of the original brick. If the brick is turned sideways, the transformation it undergoes is called a rotation. In a rotation, the object is turned about a point, and the image of the object appears to have been rotated around that point.

- When the key is pushing the brick, without using or flipping the brick, what... (I'm not sure what the question is asking for, as it seems incomplete or there is some text missing.)

- What are the two differences between a rectangle and a parallelogram?

  In summary, the transformation of a flipped brick is a reflection, while a turned sideways brick undergoes a rotation. The differences between a rectangle and a parallelogram include the angles (all right angles for a rectangle and any angle other than 90 degrees for a parallelogram) and the opposite sides (equal length and perpendicular for a rectangle, equal length but not necessarily perpendicular for a parallelogram).

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The formula for the area Z (t) (in square meters) of the algae colony after t minutes: Z(t) = 13 * (1.02)² * t²

The area A(r) of a circular algae colony with radius r meters is given by

A(r) = pi * r²

The radius M(t) after t minutes is given by

M(t) = 1.02t

Substituting M(t) into the formula for A(r) gives

A(t) = pi * (1.02t)²

Simplifying gives

Z(t) = 13 * (1.02)² * t²

Therefore, the formula for the area Z (t) (in square meters) of the algae colony after t minutes: Z(t) = 13 * (1.02)² * t²

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Answer: 360 degrees.

Step-by-step explanation: The sum of the interior angles in a quadrilateral is always 360.

(you can check using the formula 180(n-2), where n is the number of sides.)

Answer:

x+3x-4=2x+x+5

Step-by-step explanation:

=4x-4= 3x+5

=4x-3x=5+4

= x=9. Done

The quadratic equation with the given roots is:

y = 0.5x² + 1.5x - 5

For a quadratic equation with a leading coefficient a, and roots:

x = h and x = k, we will get general formula:

y = a*(x - h)*(x - k)

Here we know that the roots are x = 2 and x = -5, replacing that we will get:

y = a*(x - 2)*(x + 5)

And we know that this quadratic passes through (1, -3), replacing these values:

-3 = a*(1 - 2)*(1 + 5)

-3 = a*(-1)*(6)

-3 = -6a

-3/-6 = a

0.5 = a

Replacing that:

y = 0.5*(x - 2)*(x + 5)

Expanding the quadratic we will get:

y = 0.5x² + 1.5x - 5

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Answer: 26.40

Step-by-step explanation:

The equation in slope-intercept form is,

y = - 2x + 2

We have to given that;

The point-slope equation is,

y - 6 = - 2 (x + 2)

Now, We can rewrite the equation in slope-intercept form as;

y - 6 = - 2 (x + 2)

y - 6 = - 2x - 4

y = - 2x - 4 + 6

y = - 2x + 2

Thus, the equation in slope-intercept form is,

y = - 2x + 2

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Answer:

Step-by-step explanation:

Make a plan:

Solve the problem:

Draw the conclusion:

Hope this helps!

Answer:

60 cm^3

Step-by-step explanation:

The formula for volume of a pyramid is

V = 1/3Bh, where B is the area of the base and h is the regular height (aka the altitude that connects the top of the pyramid and the base so we can simply ignore the slant height in the problem)

Step 1:  The base of a square pyramid is a square and the formula for area (A) of a square is A = s^2, where s is the side.

Since we're told that the length of the base side length is 6 cm, we can find the area of the base:

A = 6^2 = 36

Step 2:  Now, we can plug in 36 for B and 5 for h in the volume formula to find the volume:

V = 1/3(36)(5)

V = 12 * 5

V = 60 cm^3

Correct form of the area of compound shape is:

Given,

Compound shape including triangle and rectangle.

Firstly , calculate the area of rectangle:

Area of rectangle = l* b

l= length of rectangle

b =  breadth of rectangle

Thus,

Area of rectangle = 12*m

Secondly, area of triangle,

Area of triangle = 1/2 *b * h

b = base of triangle

h = height of triangle

Base of triangle = 12 - n

Then,

Area of triangle = 1/2* (12 - n) *m

Area of triangle = 6m - 0.5mn

Now to calculate the total area of the compound shape,

Total area = Area of rectangle  + Area of triangle

Total area = 12m + (6m - 0.5mn)

Total area = 18m - 0.5mn

Hence option 3 satisfies the area of the compound shape .

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The values of the angles x and y are ∠x = 110 and ∠y = 70

From the question, we have the following parameters that can be used in our computation:

The lines (parallel, transversal and others)

The measure of angle 1 is calculated as

∠1 = 180 - 140 -- angle on a straight line

So, we have

∠1 = 40

Next, we have

∠2 = 180 - 40 - 80 --- corresponding angles

So, we have

∠2 = 60

This means that

∠y = 180 - 60 - 50 -- angle on a straight line

So, we have

∠y = 70

This also means that

∠x = 180 - 60 - 10 -- angle in a triangle

So, we have

∠x = 110

Hence, the values of x and y are ∠x = 110 and ∠y = 70

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The probability that a randomly chosen person would score less than 86 is 0.8643, and the probability that a randomly chosen person would score more than 86 is 0.1357.

We consider X to be a random variable that represents the score of a person. So according to the question, X follows the given normal distribution and the given curve represents its distribution.

Now from the curve, we can see that the proportion of observation under the score 86 is 0.8643.

So we have,

P[X < 86] = 0.8643

A) We have to find the probability that a randomly chosen person would score less than 86. i.e, we have to find P[X < 86]

It is clearly given from the curve that, P[X < 86] = 0.8643

B) Now it is required to find the probability that a person chosen at random would score higher than 86 on this test. i.e P[X > 86]

P[X > 86] = 1 - P[X < 86]

= 0.1357

Therefore, the probability that a randomly chosen person would score less than 86 is 0.8643, and the probability that a randomly chosen person would score more than 86 is 0.1357.

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The height of the trapezoid is approximately 13.043 mm.

To find the height of a trapezoid, you can use the formula:

Area = 1/2 * (base1 + base2) * height

Given:

Area = 150 square millimeters

base1 = 7 mm , w

base2 = 16 mm

150 = 1/2 * (7 + 16) * height

150 =1/2 * 23 * height

Make height the subject of the formula

300 = 23 * height

height = 300 / 23

height = 13.043 mm (rounded to three decimal places)

Therefore, the height of the trapezoid is approximately 13.043 mm.

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The values of P and a such that [tex]f(x) = Pa^x[/tex] is an exponential growth function are given as follows:

C. P = 2; a = 3.

An exponential function has the definition presented according to the equation as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The conditions for an exponential growth function are given as follows:

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The equation of the graph in the required form is y = 5|x| - 5

From the question, we have the following parameters that can be used in our computation:

The graph (see attachment)

The graph is an absolute value graph

And it can be expressed in the form of y = a|x – h| + k

Where

Vertex = (h, k)

The vertex of the graph is (0, -5)

So, we have

y = a|x| - 5

Using the point on the graph, we have

a|1| - 5 = 0

So, we have

a = 5

This means that the equation of the graph is y = 5|x| - 5

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Without this information, it is not possible to determine if the sample accurately represents the overall distribution of eggs at the farmers' market.

It is impossible to say if the sample of eggs at the farmers' market is likely to be representative based on the information supplied. Jackson appears to have bought 17 eggs from each farmer, which suggests that he did so in an equal amount. It does not, however, provide data on the total number of farmers present at the market or their overall distribution of eggs.

Additional data, such as the total number of farmers present at the market, the average number of eggs each farmer generally has, and the variability in the number of eggs among the farmers, would be required to evaluate the sample's representativeness.

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Answer:

Step-by-step explanation:

To find the unit rate, we need to divide the distance traveled by the time taken.

In this case, the distance traveled is 9 miles, and the time taken is 36 minutes.

Unit rate = distance/time

Unit rate = 9 miles / 36 minutes

Simplifying the above expression by dividing both numerator and denominator by 9, we get:

Unit rate = 1 mile / 4 minutes

Therefore, the unit rate at which the go-kart is traveling is 1 mile per 4 minutes.

Answer:A

Step-by-step explanation:

Answer:

To calculate the future value (FV) of an investment with a given return on balance, monthly rate of return, monthly payment, and number of payments, you can use the future value of an ordinary annuity formula:

FV = P * ((1 + r)^n - 1) / r

Where:

FV = Future value

P = Monthly payment

r = Monthly rate of return (expressed as a decimal)

n = Number of payments

In this case, the return on balance and the monthly rate of return are provided separately. To incorporate the return on balance into the monthly rate of return, you can use the following formula:

Effective Monthly Rate of Return = (1 + Monthly Rate of Return) * (1 + Return on Balance) - 1

Let's calculate the effective monthly rate of return using the given values:

Return on Balance = 7.00% (expressed as a decimal) = 0.07

Monthly Rate of Return = 0.583% (expressed as a decimal) = 0.00583

Effective Monthly Rate of Return = (1 + 0.00583) * (1 + 0.07) - 1

= 1.00583 * 1.07 - 1

= 1.0761281 - 1

= 0.0761281

Now that we have the effective monthly rate of return, we can use the future value formula to calculate the future value:

FV = -$200 * ((1 + 0.0761281)^120 - 1) / 0.0761281

Please note that since the monthly payment is negative (-$200), it indicates that it is an outgoing payment or an investment with regular withdrawals.

Calculating the above formula will give you the future value of the investment.

I hope I was helpful

The expression that equals D + 3C in standard form is 2w² + 8w - 25.

To find an expression that equals D + 3C in standard form, we first need to simplify D and C.

Starting with D = 2w² - w - 7, we can rearrange the terms to put it in standard form:

D = 2w² - w - 7

D = 2w² - 2w + w - 7

D = 2w(w - 1) + (w - 7)

Next, simplifying C = 3w - 6:

C = 3w - 6

Now, we can substitute these expressions into D + 3C:

D + 3C = (2w² - w - 7) + 3(3w - 6)

Expanding and simplifying:

D + 3C = 2w² - w - 7 + 9w - 18

D + 3C = 2w² + 8w - 25

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The minimum grade needed to have overall grade of 85% in the class is 90%

A percentage is a number or ratio expressed as a fraction of 100. It is represented by by the symbol %.

Percentage can also be said as per 100

For example if there are total of 100 students in a class and their are 40 girls, the percentage of girls in the class is

40/100 × 100

= 40%

For the student to have a overall grade of 85%, the minimum grade in exam is calculated as

(100+70+80+x)/4 = 85

250+x = 340

x = 340 - 250

x = 90%

Therefore the minimum graded needed is 90%

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Answer:

  B, C, D

Step-by-step explanation:

You want to identify the shapes that are similar to polygon K.

Polygon K is a right triangle that has leg lengths in the ratio 4:2 = 2:1.

Polygons B, C, and D are right triangles similar to polygon K:

Polygons A and E are also right triangles, but have different ratios of leg lengths. In A they are 1/1, and in E they are 4/3. These triangles are not similar to triangle K.

__

Additional comment

Polygons similar to the same polygon are similar to each other. Rigid transformations such as reflection and rotation result in figures congruent to the original. Congruent figures are also similar.

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To find the measure of angle AB, we can use the fact that the sum of the angles in a triangle is 180 degrees.

Given:

Angle A = 65 degrees

Angle B = 91 degrees

We can subtract the sum of these two angles from 180 degrees to find angle AB:

Angle AB = 180 - (Angle A + Angle B)

Angle AB = 180 - (65 + 91)

Angle AB = 180 - 156

Angle AB = 24 degrees

Therefore, the measure of angle AB is 24 degrees.

The decimal value of point H is then approximately 0.033333.

How to solve:

We must translate the position of the third mark after 2 and 2 tenths into a decimal value in order to determine the decimal value of point H.

We can determine the distance between each tick mark by dividing the distance between the two end points (2.3 - 2.2 = 0.1) by the total number of tick marks (9) because there are nine tick marks between the end points.

To get to point H, we can multiply the distance between each tick mark by the number of ticks: 0.1 / 9 = 0.011111.

The decimal value of point H is then approximately 0.033333.

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Answer:

Step-by-step explanation:

The sum of 100,000 + 10,000,000,000,000 is 10,000,100,000,000.

The coffee club's assertion that the percentage of bags containing collectible cards is less than 0.2 is unsupported by sufficient data.

To test whether the coffee club's belief that the proportion of bags with collectable cards is less than 0.2 is supported by the sample, conduct a hypothesis test.

Null Hypothesis: The proportion of bags with collectable cards is equal to or greater than 0.2.

Alternative Hypothesis: The proportion of bags with collectable cards is less than 0.2.

Let p be the true proportion of bags with collectable cards in all Joe Coffee bags. Use a one-sample proportion test to test this hypothesis.

The test statistic is calculated as follows:

z = (p - p₀) / √(p₀(1-p₀)/n)

where p = sample proportion (11/65), p₀ = hypothesized proportion (0.2), and n = sample size (65).

Using a significance level of 0.05, the critical z-value for a one-tailed test is -1.645.

Calculating the test statistic:

z = ((11/65) - 0.2) / √(0.2(1-0.2)/65) = -1.469

Since -1.469 is not less than -1.645, we fail to reject the null hypothesis. There is not enough evidence to support the coffee club's belief that the proportion of bags with collectable cards is less than 0.2.

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