19. You are laying on the ground looking up at a building. The distance between your head and the top of the
building is 60 feet. You need to look up at an angle of elevation of 55° to see the top of the building.
(Hint: draw a picture.)
a. How tall is the building?
b. How far is your head from
the base of the building?

Using simple interest his interest is $ 1165.50  

Simple interest is given by I = PRT/100 where

Given that Tucker deposits an amount of $7400 in an account that pays 3.15 % simple interest. Since he keep the amount in the account for 5 years without making any withdrawal or deposits, we need to find the amount of interest after 5 years.

Using the simple interest formula,

I = PRT/100

Given that

So, substituting the values of the variables into the equation, we have that

I = PRT/100

I = $ 7400 × 3.15 % × 5/100

= $ 74 × 315 × 5/100

= $ 116550/100

= $ 1165.50

So, his interest is $ 1165.50  

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The Inequality which ensure triangle exists is 22 > 4x > 7.

Inequality is defined as the relation between two quantities with the sign of inequality that is >, <, ≤ , ≥ ."

Theorem used In ΔABC,

AB + BC >AC

AC+ BC >AB

AC + AB > BC

According to the question,

In triangle ABC.

AC = 18units

BC = 6x units,

AB = 2x + 4 units

.

Substitute the value in the inequality to ensure triangle exists we get 4x > 7 and 22 > 4x.

From (1) and (2) inequality of triangle we get 22 > 4x > 7.

Hence, Inequality which ensure triangle exists is 22 > 4x > 7.

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Which inequality represents the values of that ensure triangle exists? a triangle with these side lengths: AC = 18 units, BC = 6x units, and AB = 2x + 4 units

Ben's house will be worth $490,523.96 in 9 years if the value continues to increase at a rate of 7% per year.

We can use the formula for compound interest, which is:

A = P × (1 + r)ⁿ

Where:

A = final amount

P = principal (starting value)

r = annual interest rate (expressed as a decimal)

n = number of compounding periods

In this case, the principal is $281,320, the annual interest rate is 7% (or 0.07 as a decimal), and the number of compounding periods is 9 years. Plugging in these values, we get:

A = $281,320 × (1 + 0.07)⁹

A = $281,320 × 1.743

A = $490,523.96

Therefore, Ben's house will be worth approximately $490,523.96 in 9 years if the value continues to increase at a rate of 7% per year.

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Answer:

[tex]15 + 45 = 3(5 + 15)[/tex]

The magnet's area is approximately 3.14 square inches.

What is circle?

Every point in a horizontal surface that is a certain distance above another point forms a circle (center).

The area of a circle is given by the formula:

[tex]A = \pi r^2[/tex]

where π is approximately equal to 3.14 and r is the radius of the circle. Since the diameter of the magnet is given as 2 inches, the radius is half of that, or 1 inch.

Plugging this value into the formula, we get:

[tex]A = 3.14 * 1^2[/tex]

A = 3.14 square inches

Therefore, the magnet's area is approximately 3.14 square inches.

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Answer:

In the explanation

Hope this helps!

Step-by-step explanation:

a.

1. LCM of 2 & 5 is 10

2. [tex]\frac{15x}{10} =\frac{12}{10}[/tex]  -> 15x = 12

3. x = [tex]\frac{12}{15}[/tex] or [tex]\frac{4}{5}[/tex]

b.

1. LCM of 3 & 9 is 9

2. 2x - [tex]\frac{6}{9}[/tex] = [tex]\frac{4}{9}[/tex]  ->  2x = [tex]\frac{10}{9}[/tex]  ->  [tex]\frac{18}{9} x[/tex] = [tex]\frac{10}{9}[/tex]  ->  x = [tex]\frac{10}{9}[/tex] × [tex]\frac{9}{18}[/tex]  ->  x = [tex]\frac{10}{18}[/tex]  ->  x = [tex]\frac{5}{9}[/tex]

3. x = [tex]\frac{5}{9}[/tex]

The measures of the other two angles in the parallelogram are both 143 degrees.

A parallelogram is a quadrilateral with two sides that are parallel to one another. A parallelogram has equal-length opposite sides and equal-length opposite angles. The internal angles that are extra to the transversal on the same side. A parallelogram's total interior angles add up to 360 degrees.

A parallelogram is formed by the junction of two parallel lines, and its opposite angles are equal.

Then, there are two 35 degree angles. Two further angles that are equivalent are noted: A parallelogram's angles add up to 360 degrees. Following that, x+x+37+37=360

2x=360-74

2x=286

x=143.

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The inverse of the graphs are added as an attachment

To plot the inverse of a graph, you can follow these steps:

See attachment for the graphs

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Answer:

31.97⁰ to the nearest hundredth.

Step-by-step explanation:

sin x = opposite side / hypotenuse

        = 9/17

x = 31.9657

Step-by-step explanation:

Welll.... there are EIGHT of them that total 1080

1080 / 8 = 135 degrees each

The correct options are:

C. It is a hyperbola.

D. It is in quadrants I and II.

The reciprocal parent function is given by:

f(x) = 1/x

The graph of this function is a hyperbola, which opens up and down, and has vertical asymptotes at x = 0 (the y-axis).

The graph is in quadrants I and II, since x > 0 for positive values of y, and x < 0 for negative values of y.

The graph does not go through the origin (0,0), since f(0) is undefined. It is not a parabola, since a parabola is a U-shaped curve, which is not the shape of the reciprocal parent function.

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Answer:

a = 2.1

Step-by-step explanation:

-3.7a + 1.7 = -6.07​

-3.7a = -7.77

a = 2.1

According to the given information, the perimeter of the given right-angle triangle is 30ft.

Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

We can use the Pythagorean theorem to find the length of the missing side of the right triangle, BC:

[tex]BC^2 = AB^2 - AC^2\\BC^2 = 13^2 - 12^2\\BC^2 = 169 - 144\\BC^2 = 25[/tex]

BC = 5

Now that we know all three sides of the triangle, we can find the perimeter by adding them together:

Perimeter = AB + AC + BC

Perimeter = 13 + 12 + 5

Perimeter = 30

Therefore, according to the given information, the perimeter of the given right-angle triangle is 30ft.

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Answer:

Step-by-step explan             456

The measure of the differences of all observations from the mean, expressed as a single number is called the "standard deviation". It is a commonly used measure of the amount of variability or dispersion within a set of data.

The standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences between each observation and the mean.

It is expressed in the same units as the data itself, and provides a way to understand how spread out the data is from the average or mean value.

A small standard deviation indicates that the data points tend to be close to the mean, while a large standard deviation indicates that the data points are more spread out.

The standard deviation can be used to compare the variability of different sets of data, and can also be used in statistical tests to determine if the difference between two sets of data is statistically significant.

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The correct statement is "The two triangles are the same shape but not the same size."

Both triangles will have three congruent sides and three congruent angles, which means they will be equilateral and equiangular. However, since the side lengths are different, the triangles will be different in size. In other words, one triangle will be larger than the other.

To see why they cannot be the same size, imagine drawing a line from one vertex of each triangle to the opposite side. Since both triangles are equilateral, these lines will bisect the opposite side and form two congruent right triangles. The hypotenuse of the larger triangle (with side length 5) will be longer than the hypotenuse of the smaller triangle (with side length 4), which means the two triangles are not the same size.

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The correct graph for the given data is given by option The bar graph x axis labeled sport and the y axis labeled number of students, with each having value as basketball -17, baseball-12, soccer - 27, and tennis - 44.

Because the data shows discrete categories (sports) and their related frequencies, the correct graph is a bar graph (number of students).

The x-axis is to be named "Sports" to represent the various sports (Basketball, Baseball, Soccer, and Tennis), and the y-axis has to be labelled "Number of Students" to reflect the frequency. The graph's bars will show the frequency of each sport, with the heights of the bars giving the number of students who identified each sport as their favourite. The right values for the bars should be based on the data provided:

[tex]Basketball: 17\\Baseball: 12\\Soccer: 27\\Tennis: 44[/tex]

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Answer:

To write a possible quadratic inequality, we first need to determine which quadratic function has roots at x = -0.5 and x = 1.5.

We know that the solution to the quadratic inequality is x < -0.5 or x > 1.5, which means that the parabola associated with our quadratic function should not intersect the x-axis between x = -0.5 and x = 1.5.

One quadratic function with roots at x = -0.5 and x = 1.5 is:

(x + 0.5)(x - 1.5) ≤ 0

To see why this is the case, we can use a graphing calculator to graph the quadratic function y = (x + 0.5)(x - 1.5) and observe that the function is negative (i.e., has a y-value less than zero) when x is less than -0.5 or greater than 1.5.

Alternatively, we can use the fact that the product of two factors is less than or equal to zero if and only if one factor is positive and the other is negative.

Since (x + 0.5) is positive for x > -0.5 and negative for x < -0.5, and (x - 1.5) is positive for x > 1.5 and negative for x < 1.5, the inequality (x + 0.5)(x - 1.5) ≤ 0 is true for x < -0.5 or x > 1.5, but false for -0.5 < x < 1.5.

Therefore, a possible quadratic inequality that satisfies the given set of values for x is:

(x + 0.5)(x - 1.5) ≤ 0

The difference in the two figure's areas is 96 square units.

The height of the horse trough is 4 feet.

No. 11

The area of Figure A is:

A = l * w = 12 * 8 = 96 square units

The area of Figure B is:

B = l * w = 16 * 12 = 192 square units

The difference in the two figure's areas is:

B - A = 192 - 96 = 96 square units

Therefore, the difference in the two figure's areas is 96 square units.

No. 12

We are given that the base area is 24 square feet, and the volume  is 96 cubic feet.

Volume = base area * height

96 = 24 * height

height = 96/24

height = 4 feet

Therefore, the height of the horse trough is 4 feet.

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Answer:...............

Step-by-step explanation:

...................

The true statements are:

A. Elena would be more likely to get an accurate estimate of the mean speed of the population by sampling 60 cars instead of sampling 30 cars.

C. Another random sample of 30 cars is likely to have a mean between 24 and 36 miles per hour.

Mean Absolute Deviation (MAD) is a measure of variability in a set of numerical data. It is calculated by finding the average absolute difference between each data point and the mean of the dataset.

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Step 1: The test statistic is 56.56.

Step 2: Using a chi-square distribution table with 30 degrees of freedom (n - 1), we find that the p-value is less than 0.0001.

Step 3: The rejection region for a left-tailed test with 30 degrees of freedom at the 10% level of significance is any test statistic less than 18.307.

Step 4: The test statistic of 56.56 is greater than the critical value of 18.307.

Step 5:  The 90% confidence interval for the variance of force on the helmets is [1615.46, 4123.82]

In statistics, variance is a measure of the spread or dispersion of a set of data points. It is calculated as the average of the squared differences from the mean.

Step 1: To test whether the standard deviation is significantly less than 40, we can use a chi-square test with the null hypothesis H0: [tex]σ^{2}[/tex] ≥ 1600 lbs² and the alternative hypothesis H1: σ² < 1600 lb[tex]s^{2}[/tex]. The test statistic is:

chi-square = (n - 1) *[tex]s^{2}[/tex] / [tex]σ^{2}[/tex]

where n is the sample size, [tex]s^{2}[/tex] is the sample variance, and [tex]σ^{2}[/tex] is the population variance under the null hypothesis.

Substituting the given values, we have:

chi-square = (31 - 1) * 2350 / 1600 = 56.56

Rounding to two decimal places, the test statistic is 56.56.

Step 2: To determine the p-value for a left-tailed test, we need to find the area under the chi-square distribution to the left of the test statistic. Using a chi-square distribution table with 30 degrees of freedom (n - 1), we find that the p-value is less than 0.0001.

Step 3: The rejection region for a left-tailed test with 30 degrees of freedom at the 10% level of significance is any test statistic less than 18.307.

Step 4: Since the test statistic of 56.56 is greater than the critical value of 18.307, we reject the null hypothesis and conclude that there is sufficient evidence to indicate that the standard deviation is significantly less than 40 at the 5% level of significance.

Step 5: To calculate a 90% confidence interval for the variance of force on the helmets, we can use the formula:

[(n - 1) * [tex]s^{2}[/tex]/ chi-square upper, (n - 1) * [tex]s^{2}[/tex] / chi-square lower]

where chi-square upper and chi-square lower are the upper and lower critical values, respectively, from the chi-square distribution table for 30 degrees of freedom at the 5% level of significance. Substituting the given values, we have:

chi-square upper = 45.722

chi-square lower = 18.307

[(31 - 1) * 2350 / 45.722, (31 - 1) * 2350 / 18.307] = [1615.46, 4123.82]

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However, each beaker would have the following if there were, say, five beakers: 2.5 units of water are equal to 8.5/5.

Typically, it is expressed in geometric units, which including cubic metres (m3), cubic centimetres (cm3), or cubic feet (ft3), depending on the length unit being used. A formula that is based on an object's shape can be used to determine its volume. The volume of such a rectangular prism, for instance, can be determined by utilizing the formula V = lwh, where l stands for length, w for width, and h for height. A cylinder's volume can be calculated using the formula V = r2h, where r denotes the circle of the base and h the height.

given

We can simply sum the numbers supplied to determine the total volume of water in all the beakers:

1/4 x 6 + 3/4 x 2 + 1/2 + 1 1/4 + 1 1/2 + 1 3/4

= 1.5 + 1.5 + 0.5 + 1.25 + 1.5 + 1.75 (converting mixed values to improper fractions)

= 8.5

8.5 units of water are therefore present in all of the beakers.

Each beaker will have 8.5 divided by the number of beakers if this water is distributed equally among them.

We are unable to provide a precise response since we are unsure of the number of beakers.

However, each beaker would have the following if there were, say, five beakers: 2.5 units of water are equal to 8.5/5.

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The two data sets that meet the given conditions for in centers, and variability is in the explanations.

Data Set 1 - Heights of Adults in a City:

Values in Data Set 1 (in inches): 64, 67, 65, 63, 66, 68, 62, 64, 67, 65, 63, 66, 68, 62

Story: The data set represents the heights of randomly sampled adults in a city. The city is known for having a relatively consistent height distribution, with the majority of adults falling within a similar height range. The heights in this data set range from 62 inches to 68 inches, with a center around 65 inches, which is the most common height among the sampled adults. The data set shows relatively low variability, with most heights clustering around the center, indicating that the population of adults in the city has a narrow height distribution.

Data Set 2 - Salaries of Employees in a Corporation:

Values in Data Set 2 (in thousands of dollars): 42, 45, 47, 48, 43, 50, 55, 44, 42, 45, 47, 48, 43, 50, 55

Story: The data set represents the salaries of randomly sampled employees in a large corporation. The corporation has a wide range of job positions, and as a result, the salaries of its employees show a higher variability compared to the heights of adults in the city. The salaries in this data set range from $42,000 to $55,000, with a center around $47,000, which is the most common salary among the sampled employees. The data set shows higher variability, with salaries spread out across a wider range, indicating that the population of employees in the corporation has a more diverse salary distribution. This could be due to differences in job roles, experience levels, and other factors that impact salaries within the corporation.

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The area under the X2 curve with 5 degrees of freedom to the right of 1.61, 9.24 and 15.09 is 0.078, 0.0001 and 0 respectively.

Area is a two-dimensional measure of a surface, such as a length multiplied by a width. It is used to measure the size of a space, such as a room, or a piece of land. Area can also be used to measure the size of a shape, such as a circle or a square. Area is usually measured in units such as square meters (m2) or square feet (ft2).

(a)1.61

The area under the X2 curve with 5 degrees of freedom to the right of 1.61 can be calculated using the following formula:

Area = 1 - Φ(x; df)

Where Φ(x; df) is the cumulative distribution function of the chi-square distribution, and df stands for the degrees of freedom.

For df = 5, Φ(1.61; 5) = 0.922.

Therefore, the area under the X2 curve with 5 degrees of freedom to the right of 1.61 is equal to 1 - 0.922 = 0.078.

(b) 9.24

For df = 5, Φ(9.24; 5) = 0.9999.

Therefore, the area under the X2 curve with 5 degrees of freedom to the right of 9.24 is equal to 1 - 0.9999 = 0.0001.

(c) 15.09

For df = 5, Φ(15.09; 5) = 1.

Therefore, the area under the X2 curve with 5 degrees of freedom to the right of 15.09 is equal to 1 - 1 = 0.

In conclusion, the area under the X2 curve with 5 degrees of freedom to the right of 1.61, 9.24 and 15.09 is 0.078, 0.0001 and 0 respectively.

Complete questions as follows-

find the area under the x2 -curve with 5 degrees of freedom to the right of (a) 1.61 (b) 9.24 (c) 15.09.

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The Monthly Budget for fast food is Option A. $136.

To determine how much money you should budget for fast food, we need to calculate the total amount of money you spend on fast food each week. To do this, we simply multiply the cost of one fast food meal by the number of meals you buy in a week, which is four in this case.

$850 x 4 = $3400 per week

Next, we need to figure out how much money you spend on fast food per month. To do this, we need to multiply the weekly amount by the number of weeks in a month. Most months have around four weeks, so we will use that as an estimate.

$3400 x 4 = $13600 per month

Therefore, the answer is Option A. $136. You should budget around $136 per month for fast food if you buy it four times a week and it costs you about $850 each time.

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The model predicts that the player should score around 17.47 points per game based on their 4.1 free throw attempts per game. However, the player's observed score of 13.7 points per game suggests that they may be underperforming compared to what would be expected based on this relationship.

Let us assume that the model predicts a linear relationship between points per game and free throw attempts per game, we can calculate the predicted value of points per game for this player using the regression equation

points per game = slope * free throw attempts per game + intercept

From the given data, we know that the slope of the regression line is 2.6 and the intercept is 7.1. Plugging in the values for this player, we get:

points per game = 2.6 * 4.1 + 7.1 = 17.47

So the model predicts that this player should score approximately 17.47 points per game, which is higher than the observed value of 13.7 points per game. This suggests that this player may be underperforming compared to what would be expected based on their free throw attempts per game.

However, just one player and there may be other factors that could affect their performance beyond just free throw attempts per game.

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after calculating both the expressions we can conclude that both expressions represent the same value of 12.

Mathematical operations including multiplication, division, addition, and subtraction are possible. The construction of an expression looks like this: Expression, number, and mathematical operator Numbers, variables, and functions are the elements of a mathematical expression (such as addition, subtraction, multiplication, and division, etc.). Expressions and phrases can be contrasted. Expressions are any equations that comprise numbers, variables, and an arithmetic operation. They are occasionally referred to as algebraic expressions. For instance, the value of m in the computation of 4m + 5 is the same as the word m in the provided equation, which has been separated from the figures 4m and 5 by the mathematical symbol +.

given,

Since subtracting a negative integer is equivalent to adding its positive counterpart, the expressions "10 - (-2)" as well as "-10 + 2" have the same meaning.

To be more precise, "10 - (-2)" denotes starting with a value of 10 and then deducting a negative value of -2. The positive value of an amount that is negative may be subtracted without affecting it, and vice versa. Therefore, "10 - (-2)" equals "10 + 2," making 12 the result.

The expression "-10 + 2" on the opposite hand suggests that we start with an amount of -10 and subsequently add a value of 2.

A positive number is equal to its negative counterpart when added to a negative number. Because of this, "-10 + 2" equals "-10 - (-2)", which also equals 12.

Therefore, both expressions represent the same value of 12.

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