7. These triangles are similar. Find the area of the smaller
triangle to the nearest whole number.
105 ft²
16 ft

12 ft

Answer
79 ft²
59 ft²
49 ft²
89 ft²

The area of the right triangle is 18.02 cm².

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The sum of angles in a triangle is 180 degrees.

Therefore, let's find the area of the right angle triangle as follows;

let's find the height and base of the triangle.

using trigonometric ratios,

cos 75 = adjacent / hypotenuse

cos 75 = base / 12

base = 3.10582854123

Therefore,

sin 75 = opposite / hypotenuse

sin 75 = h / 12

height = 11.5911099155

height = 11.59

Therefore,

area of the triangle = 1 / 2 × 3.11 × 11.59

area of the triangle = 36.0483518371 / 2

area of the triangle = 18.0241759186

area of the triangle = 18.02 cm²

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Answer: C-Cylinder

Step-by-step explanation:

In this problem, you are rotating the rectangle on the x axis. If you rotate it along this side, the rectangle makes it a cylinder.

Para aquellos que necesitas este respuesta en español: En este problema, estás girando el rectángulo sobre el eje x. Si lo giras a lo largo de este lado, el rectángulo lo convierte en un cilindro.

I hope this helps!

Answer:

The correct answer is (C), cylinder.

Explanation:

When the rectangle is rotated around the axis shown, it will create a three-dimensional shape with two parallel bases that are connected by a curved surface. This shape is called a cylinder.

The solution of  f(x)/g(x) is the function x ^5/2 + 6x^3/2 + 1

option C is correct.

Here, we have,

given that,

the functions are:

f(x) = x^3+6x^2+x^1/2

g(x) = x^1/2

so, we have,

f(x)/g(x)

= x^3+6x^2+x^1/2 / x^1/2

= x^3/ x^1/2  +6x^2/ x^1/2  +x^1/2/ x^1/2

=x ^5/2 + 6x^3/2 + 1

Hence, The solution of  f(x)/g(x) is the function x ^5/2 + 6x^3/2 + 1

option C is correct.

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The frequency distribution that matches the data {3,8,5,6,4,3,7,8,9,5,5,6,4,12,14,10,8} is C.

Number

of Shoes   Frequency

3-5                   7

6-8                  6

9-11                 2

12-14              2

A frequency distribution is a frequency table or chart that visually displays the actual number of observations in each range or class or the percentage of the observations.

In this frequency distribution, the group 3-5 has the highest frequency of 7 followed by 6-8 with 6 frequencies.

3,8,5,6,4,3,7,8,9,5,5,6,4,12,14,10,8

Number

of Shoes   Frequency

3-5              IIIIIII        7

6-8              IIIIII         6

9-11             II             2

12-14           II             2

Total                        17

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The graph of the solution of the inequality is attached

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

x - 4 < 5

Add 4 to both sides of the inequality

So, we have

x - 4 + 4 < 5 + 4

Evaluate the like terms

So, we have

x < 9

This means that the solution of the inequality is x < 9

See attachment for the graph

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Answer:

-----------------------

In the given right triangle we have an angle of 37° and adjacent leg of 11 units given.

Missing is the length of hypotenuse, x.

Use cosine function:

Plug in known values and solve for x:

To solve the compound inequality 2y + 3 ≥ -9 or -3y < -15, we'll solve each inequality separately and then combine the solutions.

First, let's solve the first inequality: 2y + 3 ≥ -9.

Subtract 3 from both sides:

2y ≥ -12

Divide both sides by 2 (note that dividing by a positive number does not change the inequality direction):

y ≥ -6

Next, let's solve the second inequality: -3y < -15.

Divide both sides by -3 (remember to reverse the inequality direction when dividing by a negative number):

y > 5

Now, let's combine the solutions. We have y ≥ -6 or y > 5.

In interval notation, we can express the solution as (-∞, -6] ∪ (5, ∞). This means that the solution includes all real numbers less than or equal to -6, as well as all real numbers greater than 5.

Answer: 1080

Step-by-step explanation:

12x10x9=1080

Hoped this helped?!

The total surface area of the square pyramid is 28 m²

An equation is an expression that is used to show how numbers and variables are related using mathematical operators

Given the square pyramid net:

Area of square base = 2 m * 2 m = 4 m²

Area of each triangle face = (1/2) * 2 m * 6 m = 6 m²

Area of the four triangle face = 4 * 6 m² = 24 m²

Total surface area = 24 m² + 4 m² = 28 m²

The total surface area is 28 m²

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An additional information that is needed to prove the triangles are congruent by the SAS Postulate is: D. ∠BAC ≅ ∠DAC.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.

Based on the side, angle, side (SAS) similarity theorem, we can logically deduce that ∆BAC is congruent to ∆DAC when the angles A (∠A) are congruent by the reflexive property.

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As the degrees of freedom increase, the Chi-square distribution becomes less skewed.

Option C is the correct answer.

We have,

The Chi-square distribution is a probability distribution that is commonly used in statistics.

It is often used in hypothesis testing and in constructing confidence intervals for population variances.

The shape of the Chi-square distribution depends on the degrees of freedom (df). The degrees of freedom represent the number of independent pieces of information used to estimate a parameter or make an inference.

When the degrees of freedom are small, such as 1 or 2, the Chi-square distribution is highly skewed to the right.

This means that the distribution has a long tail on the right side and is concentrated toward the lower values.

However, as the degrees of freedom increase, the Chi-square distribution becomes less skewed.

The distribution becomes more symmetrical and approaches a bell shape, similar to the shape of a normal distribution. This means that the values are more evenly spread out and there is less concentration towards the lower values.

Therefore,

As the degrees of freedom increase, the Chi-square distribution becomes less skewed.

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Answer:

When an exponent of the power is an even number and the base is a negative number, the value is always positive.

Answer:

domain= [-5,5]

range= [-3,3]

Step-by-step explanation:

the domain is with the x axis you have to look for the farthest x axis which would be - 5 in this case and the closest axis which is 5 so the x can be anywhere between - 5 and 5

then for the range is with the y axis you would look for the farthest y axis which is - 3 and the closes which is 3 so the y can be anywhere in between - 3 and 3

The expression which is equivalent to -32^3/5 is  -32768 / 125.

We are given that;

Expression=-32^3/5

Now,

To find an equivalent expression for -32^3/5 is to use the property of exponents that says [tex](a/b)^n = a^n / b^n.[/tex] Applying this property, we get:

-32^3/5 = (-32)^3 / 5^3

Now we can simplify the numerator and denominator by cubing them:

-32^3/5 = -32768 / 125

This is an equivalent expression for -32^3/5. There may be other ways to find equivalent expressions, such as factoring or using common denominators.

Therefore, by the expression the answer will be -32768 / 125.

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Answer:

-8 and 4

Step-by-step explanation:

P= -2

-2+6 = 4

-2-8= -8

The expression -2(5 + 7x) + 5(x + 5) is equivalent to the expression -9x + 15. So, the answer is option B: 15 - 9x.

To simplify the expression -2(5 + 7x) + 5(x + 5), we can distribute the coefficients and simplify further.

Starting with the expression -2(5 + 7x):

-2(5 + 7x) = -2 × 5 - 2 × 7x

= -10 - 14x

= -14x - 10

Now let's simplify the expression 5(x + 5):

5(x + 5) = 5 × x + 5× 5

= 5x + 25

Finally, combining the two simplified expressions:

-14x - 10 + 5x + 25

Combining like terms:

(-14x + 5x) + (-10 + 25)

-9x + 15

Therefore, the expression -2(5 + 7x) + 5(x + 5) is equivalent to the expression -9x + 15.

So, the answer is option B: 15 - 9x.

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Based on the information, A. There is a 99% chance that the proportion of students who eat cauliflower on Jane's campus is between 5.03% and 17.83%.

Calculate the sample proportion:

= x / n = 4 / 35

= 0.1143

Calculate the Agresti and Coull's adjustment factor:

zα/2 = z(1 - α/2) = z(1 - 0.99/2)

= 2.576

Calculate the margin of error:

= 2.576 √(0.1143(1 - 0.1143) / 35)

= 0.064

Calculate the confidence interval:

= 0.1143 ± 0.064

= (0.0503, 0.1783)

We are 99% confident that the true proportion of students who eat cauliflower on Jane's campus is between 5.03% and 17.83%.

In other words, if we were to repeat this study many times, we would expect to obtain a confidence interval that includes the true proportion of students who eat cauliflower on Jane's campus 99% of the time.

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Answer:

-4

Step-by-step explanation:

i jus did this question

Two reports that could be used to verify the accuracy of retirement contributions for the most recent payroll period are the Payroll Summary Report and the Retirement Contribution Report.

Two reports that could be used to verify the accuracy of retirement contributions for the most recent payroll period are:

Payroll Summary Report: This report provides a summary of the payroll transactions for the period, including details of employee wages, deductions, and employer contributions.

It should include a specific section or breakdown for retirement contributions, showing the individual employee contributions and the corresponding employer contributions.

By reviewing this report, one can ensure that the retirement contributions have been accurately calculated and remitted.

Retirement Contribution Report: This report specifically focuses on the retirement contributions made by both employees and the employer.

It should provide a detailed breakdown of the contributions for each employee, including the employee's contribution amount, the employer's matching or non-elective contribution amount, and any additional details related to the retirement plan.

This report allows for a comprehensive review of the retirement contributions to verify if they match the expected amounts based on employee records and plan guidelines.

By comparing the information in these reports with the employees' individual contribution records and the retirement plan requirements, it is possible to verify that the retirement contributions were accurately remitted for the most recent payroll period.

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Step-by-step explanation:

To multiply the polynomials (8v - 5)(v + 7), we can use the distributive property:

(8v - 5)(v + 7) = 8v(v + 7) - 5(v + 7)

Now we can simplify by multiplying each term:

8v(v + 7) - 5(v + 7) = 8v^2 + 56v - 5v - 35

Finally, we can combine like terms to get the simplified expression:

8v^2 + 51v - 35

Therefore, (8v - 5)(v + 7) = 8v^2 + 51v - 35.

The additional information is needed to prove the triangles are congruent by the SAS Postulate is <ACB = <ACD.

We have, CB = CD

As, The SAS Congruence Theorem states that if two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of another triangle, then the two triangles are congruent.

In triangle ACB and ACD

AC = AC (common)

CB=  CD (given)

Now, to prove using SAS rule we need only one angle which is in between the two congruent sides then

<ACB = <ACD

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The values are x = 2 and NS = 3.5.

Given is a circle with center S, we need to find the missing measure,

K = 16, MP = 8, LP = 2x+4, and PS = 3.5, we need to find the measures of x and NS.

We know that the perpendicular drawn from the center of a circle bisect the chords into two halves,

And the perpendiculars are congruent.

Therefore,

MP = PL

2x+4 = 8

x+2 = 4

x = 2

Also,

NS = PS

So, NS = 3.5

Hence the values are x = 2 and NS = 3.5.

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Answer:

65/100 that is the answer to this question

Rounded to the nearest hundredth, the value of y at [tex]x = 7[/tex] is approximately [tex]12.78[/tex], according to the concept of linear regression line.

To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form [tex]y = mx + b[/tex], where m represents the slope and b represents the y-intercept.

Using the provided data, the linear regression line equation is:

[tex]\[ y = 1.3642x + 3.2324 \][/tex]

To find the value of [tex]y[/tex] at [tex]x = 7[/tex], we substitute [tex]x = 7[/tex] into the equation:

[tex]\[ y = 1.3642(7) + 3.2324 \][/tex]

Simplifying the equation, we get:

[tex]\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \][/tex]

In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is [tex]y = 1.3642x + 3.2324[/tex]. By substituting [tex]x = 7[/tex] into the equation, we find that the estimated value of y is approximately [tex]12.78[/tex]. This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.

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Applying the angle of intersecting secants theorem, the measure of arc LN in the circle is: 56°.

Given the circle in the image above where the two secants intersect outside the circle, the angle of intersecting secants theorem states that:

external angle formed = 1/2 * (the measure of arc KP - the measure of arc LN)

Plug in the values:

20 = 1/2 * (96 - m(LN))

2 * 20 = 96 - m(LN)

40 = 96 - m(LN)

m(LN) = 96 - 40

m(LN) = 56°

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Answer:

A. mBC = 71

B. mAB = 142

C. AD = 30

D. BD = 30

E. YD = 16

F. DC = 18

Step-by-step explanation:

A. mBC = mAC = 71

B. mAB = mBC + mAC = 71 + 71 = 142

C. AD = AB/2 = 60/2 = 30

D. BD = AD = 30

E. YA^2 = YD^2 + AD^2

YD^2 = YA^2 - AD^2 = 34^2 - 30^2 = 1156 - 900 = 256

YD = √256 = 16

F. DC + YD = YC

DC = YC - YD = 34 - 16 = 18

The equation of the circle is (x - 2)² + (y - 3)² = 36

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

The circle

Where, we have

Center = (a, b) = (2, 3)

Radius, r = 6 units

The equation of the circle is represented as

(x - a)² + (y - b)² = r²

So, we have

(x - 2)² + (y - 3)² = 6²

Evaluate

(x - 2)² + (y - 3)² = 36

Hence, the equation is (x - 2)² + (y - 3)² = 36

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Answer:
147 floors

Explanation:

To determine the number of floors in the Burj Khalifa, we can use the information provided. We know that Andre stood 1000 meters away from the building and looked up at a 39.62-degree angle using a laser rangefinder. Let's calculate the height of the Burj Khalifa using basic trigonometry.

First, we can find the height of the building using the tangent function:

tan(angle) = height / distance

tan(39.62 degrees) = height / 1000 meters

height = tan(39.62 degrees) * 1000 meters

height ≈ 747.97 meters

Now, let's calculate the number of floors in the Burj Khalifa. We are given that each floor is 5.079 meters tall.

Number of floors = height / height of each floor

Number of floors = 747.97 meters / 5.079 meters

Number of floors ≈ 147.23 floors

Since we cannot have fractional floors, we can round the number down to the nearest whole number.

Therefore, there are approximately 147 floors in the Burj Khalifa.