Find the area of square ABCD shown below. Round to the nearest tenth if necessary.
O
D
y
O
A
B
square units

The correct solution of the triangle is seen in option D

In this case, we would need to use the sine rule so as to solve the triangle as we have in the problem that is before us here. The sine rule states that;

a/Sin A = b/SinB = c/SinC

We know that we can be able to obtain the angle C using the sine rule;

29/Sin 42 = 33/SinC

SinC = 33Sin42/29

C = Sin-1(33Sin42/29)

C = 49.6 degrees

The angle B is now;

180 - (42 + 50)

B = 88.4 degrees

Then;

b/Sin 88 = 29/Sin42

b = 29 Sin 88/Sin42

b = 28.98/0.669

b = 43.3

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The 58th percentile of the lengths is 489.4 mm.

The 58th percentile of the lengths is calculated from normal distribution curve as shown below.

The mean of the distribution is at the 50th percentile.

The 58th percentile is between the mean and 1 standard deviation above the mean.

Mean (50%) = 480 mm

58% = ?

1 standard deviation above the mean (84%)= M + S.D = 480 mm + 40 mm = 520 mm

We are going to interpolate, to find the approximate value of the length.

50 ----- 480 mm

58 ----- ?

84 ------- 520 mm

(58 - 50)/(84 - 50) = (x - 480)/(520 - 480)

0.235(40) = x - 480

9.4 = x - 480

x = 489.4 mm

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Answer:

The answer and step by step explanation is above

The expressions that are equivalent to 3^8 are:

We have to solve these out

3^8. = 6561

From the options

A. 3^2x3^4

= 9 x 81

= 729

B  3²x3^6

= 9 x 729

= 6561

C.  3^16/3^2

= 43046721/9

= 4782969

d. 3^12/3^4

= 531441 / 81

= 6561

E.  (3^4)²

= 3⁴ x 3⁴

= 3⁴⁺⁴

= 3⁸

= 6561

F. (3¹)^7

= 3⁷

= 2187

The expressions that are equivalent to 3^8 are:

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The measure of angle in degrees is 63 degree

We are given that;

The triangle ABC inscribed in the circle.

Now,

m<BAC-63

From isosceles triangle CBD,

m/CBD=m/BCD = 32

This implies that,

m/BDC+32+32=180

m/BDC+64 = 180

m/BDC=180-64

m/BDC = 126

m/BAC =1/2(m/BDC)

= 1/2(126)

= 63

Therefore, by the triangles the answer will be 63 degrees.

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The phrase, raise to the power of is used when referring to exponents because the power or strength increases with the addition of more numbers. For instance, 2 raised to the power of 1 is not as strong as 2 raised to the power of 100.

The usage of this phrase stems from the fact that numbers tend to increase in strength as they are raised to an increasing number of figures.  

The strength that numbers carry differs as they increase or decrease. Just as 10 is greater than 1 or 2, so will different powers of exponents differ in strengths.

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The question's single element is divided into

A composite shape is a geometrical figure formed from two or multiple elementary shapes layered and intermixed.

These simpler elements may comprise of

As the base forms are overlapped or mixed to create an entirely new shape, they form a composite figure with a combined outline more intricate than any single component.

The single element in the question is separated to form

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If we use the variable n to represent the unknown number, then "15 more than twice a number" can be written as:

2n + 15

Answer:

The answer is 15+2n

Step-by-step explanation:

15 more than twice a number =15+2n

The volume of the pyramid is determined as 433.33 mm³.

The volume of the right square pyramid is calculated by applying the following formula.

V = ¹/₃a²h

where;

The volume of the pyramid is calculated as follows;

V = ¹/₃ (10 mm)² x ( 13 mm )

V = 433.33 mm³

Thus, the volume of the pyramid is calculated from the formula stated.

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If in the set A ⊂ B then the statement A U B = B

A set is a collection of well defined items.

Since we have A ⊂ B, we want to determine which statement of the set is true. To determine that, we proceed as follows.

So, if A ⊂ B then the statement A U B = B

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Answer: Translation

Step-by-step explanation:

      To get from the pre-transformation shape (red) to the transformed image (blue), a translation takes place. This is where the shape is not rotated, reflected, or stretched, but simplify "slided" or "shifted" somewhere else.

Answer:

C = 117.92° or 118°

Step-by-step explanation:

Law of Cosine: [tex]c^2=a^2+b^2-2ab*cos(C)[/tex]

Plug in your values to solve for C°

A = 50 , B = 55 , C = 90

[tex]90^2=50^2+55^2-(2*50*55)*cos(C)[/tex]

[tex]8100=2500+3025-5500*cos(C)[/tex]

Subtract 2500 and 3025 to move to other side.

[tex]8100-2500-3025=-5500*cos(C)[/tex]

[tex]2575=-5500*cos(C)[/tex]

Divide -5500 to leave cos(C) byitself

[tex]-\frac{2575}{5500} =cos(C)[/tex]

Inverse Cos(C) to get C byitself solving it in degree.

[tex]C=cos^{-1}(-\frac{2575}{5500} )[/tex]

C = 117.916339°

Round to Hundredths place or Whole Degree.

C = 117.92° or 118°

240° is the coterminal angle of 23×π÷3.

First, we can simplify 23 times π over 3 by noticing that 2π is equivalent to 6 pi over 3, so we can add 2π to 23 times pi over 3 until we get an angle between 0 and 2π (or 0 and 360 degrees).

23 times π over 3 is equivalent to an angle of 360 degrees times (23 times π over 3)/(2π), which simplifies to 360 degrees times 23/2, or 4140 degrees.

To find a coterminal angle between 0 and 360 degrees, we can subtract 360 degrees until we get an angle in that range.

4140 - 360(11) = 240

Therefore, a coterminal angle of 23 times pi over 3 between 0 and 360 degrees is 240 degrees.

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Answer:

100 + 5f = 40

5f = -60

f = -12 feet per minute (decrease of 12 feet per minute)

Answer: 20


Realistically : In this hypothetical scenario, if 5 + 5 equals 9, then the basic principles of mathematics are no longer applicable, and any further calculations cannot be accurately determined. However, in the real world, 5 + 5 equals 10, and therefore 10 + 10 would equal 20.

Answer:

20

Step-by-step explanation:

The account will be worth approximately $13,268.58 in 20 years if it is opened with an initial deposit of $6,500 and earns 3.6% interest compounded semi-annually.

The formula accrued amount in a compounded interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Principal P = $6,500

Compounded semi-annually n = 2

Time t = 20 years

Interest rate r = 3.6%

Accrued amount A = ?

First, convert R as a percent to r as a decimal

r = R/100

r = 3.6/100

r = 0.036

Plug in the given values into the above formula.

A = P( 1 + r/n )^( n × t )

A = $6,500( 1 + 0.036/2 )^( 2 × 20 )

A = $6,500( 1 + 0.036/2 )^( 40 )

A = $6,500( 1 + 0.018 )^( 40 )

A = $13,268.58

Therefore, the accrued amount in 20 years is $13,268.58.

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The solutions to the inequality word problem are:

2) a + $68.50 ≥ $175

3) A He needs to save at least $106.50 more.

2) We are told that  Marshall wants to save at least $175 for a new video game system and some games.

So far, he has saved $68.50.

If the amount of money he needs to save extra is a, then the inequality we have:

a + $68.50 ≥ $175

3) a + $68.50 ≥ $175

subtracting $68.50 from both sides gives:

a ≥ 175 - 68.5

a ≥ $106.5

He needs to save at least $106.50 more.

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The quadratic function x² - 10x + 20 in vertex form is f(x) = (x - 5)² -5. The vertex of this parabola is (5, 15).

To convert the quadratic function in standard form, f(x) = ax² + bx + c, to vertex form, f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola, follow these steps:

Complete the square by adding and subtracting (b/2a)²inside the parentheses:

f(x) = x² - 10x + 20

f(x) = (x²- 10x + 25) - 5

Factor the expression inside the parentheses as a perfect square:

f(x) = (x - 5)² -5

Write the function in vertex form by pulling out the value of a from the perfect square:

f(x) = 1(x - 5)² -5

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Answer:

Median: 31

Mode: 31

Range: 67

Step-by-step explanation:

Median: To find the median, we first need to arrange the numbers in order from smallest to largest:

25, 29, 31, 31, 69, 80, 92

The middle number is 31, so the median is 31.

Mode: The mode is the number that appears most frequently in the set. In this case, the number 31 appears twice, which is more than any other number. So, the mode is 31.

Range: The range is the difference between the largest and smallest numbers in the set. The smallest number is 25 and the largest number is 92, so the range is:

92 - 25 = 67.

Therefore, the median is 31, the mode is 31, and the range is 67.

Answer:

The median of the given set of numbers is 31, the mode is 31, and the range is 67.

Step-by-step explanation:

To find the median, we need to first arrange the numbers in order from smallest to largest:

25, 29, 31, 31, 69, 80, 92

There are seven numbers in the list, which means the middle number will be the fourth number: 31.
Therefore, the median is 31.

To find the mode, we need to determine which number appears most frequently in the list.
In this case, the number 31 appears twice, which is more than any other number in the list.

Therefore, the mode is 31.

To find the range, we need to subtract the smallest number from the largest number. The smallest number is 25 and the largest number is 92, so the range is:

92 - 25 = 67

Therefore, the range is 67.

The length of the segment in circle (9) is the radius x = 6. And the length of the segment in (10) is x = 8.9

A circle is a two-dimensional shape that is defined as a set of points that are equidistant from a single fixed point, called the center. The radius of a circle is the distance from the center to any point on the circumference. All radii of a circle are equal in length. While the diameter of a circle is a straight line passing through the center of the circle and touching two points on the circumference. The diameter is always twice the length of the radius.

For question (9):

the segments indicated as x and 6 are radii of the circle so;

x = 6

For question (10):

the radius = 31.6/2 = 15.8

also;

the radius = 6.9 + x

so;

x = 15.8 - 6.9

x = 8.9.

Therefore, the The length of the segment in circle (9) is the radius x = 6. And the length of the segment in (10) is x = 8.9

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Answer:

F1 8,-2 F2 -5,-3

Step-by-step explanation:

An inequality to represent the domain of the situation: 0 ≤ x ≤ 6

An inequality to represent the range of the situation: 4 ≤ y ≤ 24

If the equation of the function is [tex]c(x) = n(1.35)^x[/tex], the value of n is: 4.

In Mathematics and Geometry, a domain refers to the set of all real numbers for which a particular function is defined.

Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph of this logarithmic function shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [0, 6] or 0 ≤ x ≤ 6.

Range = [4, 24] or 4 ≤ y ≤ 24.

Next, we would determine the value of n by using the y-intercept (0, 4);

[tex]c(x) = n(1.35)^x\\\\4=n(1.35)^0[/tex]

n = 4.

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The given data results in the following Frequency Distribution

Class Frequency

21-27 3

28-34 8

35-41 7

42-48 8

49-55 4

In statistics, frequency distribution is a way of organizing data into categories, or intervals, and counting how many observations fall into each category. It helps us understand the distribution of data and identify patterns within it.

To construct a frequency distribution using 5 classes, we need to first determine the range of the data:

Range = Maximum value - Minimum value

= 52 - 21

= 31

We can then calculate the width of each class:

Width = Range / Number of classes

= 31 / 5

= 6.2

Since we cannot have a fractional width, we round up to the nearest whole number. The class width is therefore 7.

Next, we need to determine the class intervals, or boundaries, which are the values that define each class. We start with the minimum value and add the class width successively:

Class 1: 21-27

Class 2: 28-34

Class 3: 35-41

Class 4: 42-48

Class 5: 49-55

We can now count how many observations fall into each class. The resulting frequency distribution is shown below:

Class Frequency

21-27 3

28-34 8

35-41 7

42-48 8

49-55 4

In this frequency distribution, we can see that the majority of the observations fall into the middle three classes, with fewer observations in the first and last classes. This suggests that the data is roughly symmetric and evenly distributed around the center.

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Answer:

1. s < 40

2. w ≤ 12

3. D ≥ 110

4. D ≤ 3 1/2

5. w ≥ 30

6. m ≥ 45

7. t ≠ 21

8. c < 45

9. D > 1/5

10. s ≠ 45 5/6

11. h ≥ 48

12. P ≠ 5

The linear equation for the scenario is y = x - 12

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

Represent the original amount with x

and the amount left with y

So, we have

Amout left = x - 12

Using the variable representtaion, we have

y = x - 12

Hence. the scenario is y = x - 12

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The surface area of the given composite figure is: 484.38 cm²

The formula for the area of a rectangle is:

Area = Length * Width

The formula for the area of a square is:

Area = side * side

The surface area is simply the area of each of the surfaces of the figure.

Thus, surface area of the given composite figure is:

4(13 * 10) + (10 * 10) + (10 * 10) - 3π(5²))

= 484.38 cm²

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a) The point estimate of the population proportion of adults who lack confidence they will be able to afford health insurance in the future is 0.57

b) At 90% confidence, the margin of error is 0.0324.

c) The 90% confidence interval is (0.5376, 0.6024).

d) The 95% confidence interval is (0.5314, 0.6086).

(a) The point estimate of the population proportion of adults who lack confidence they will be able to afford health insurance in the future can be found by dividing the number of respondents who lack confidence (575) by the total number of respondents (1,007):

Point estimate = 575/1007 = 0.57 (rounded to two decimal places)

(b) The margin of error can be calculated using the formula:

Margin of error = z√(p'(1-p')/n)

where z is the z-score associated with the desired level of confidence, p' is the point estimate, and n is the sample size. For a 90% confidence level, the z-score is 1.645.

Margin of error = 1.645√(0.57*(1-0.57)/1007) ≈ 0.0324 (rounded to four decimal places)

(c) The 90% confidence interval can be calculated using the formula:

Point estimate ± Margin of error

Substituting the values:

0.57 ± 0.0324

The 90% confidence interval is (0.5376, 0.6024) (rounded to four decimal places).

(d) The 95% confidence interval can be calculated in the same way, but with a different z-score. For a 95% confidence level, the z-score is 1.96.

Margin of error = 1.96√(0.57(1-0.57)/1007) ≈ 0.0386 (rounded to four decimal places)

0.57 ± 0.0386

The 95% confidence interval is (0.5314, 0.6086) (rounded to four decimal places).

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