20 points
Use Pythagoras' theorem to work out the
height of the equilateral triangle below.
Give your answer in centimetres
(cm)

Answer:

1.The  equation of best fit is ŷ = 2.69152X + 3.45818.

Step-by-step explanation:

By calculation, Irina should do 10 reps in each set

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

Sets = 8 reps

Increment = 25%

This means that

Reps = Sets * (1 + Increment)

substitute the known values in the above equation, so, we have the following representation

Reps = 8 * (1 + 25%)

Evaluate

Reps = 10

Hence, Irina should do 10 reps in each set

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1)

Given measure of angle 2 and angle 4:

∠2 = 5x + 24

∠4 = 6x - 9

Now the two lines are parallel to each other and have a transversal line.

Thus ∠2  and ∠4 form linear pair.

So,

∠2  + ∠4 = 180°
5x + 24 + 6x - 9 = 180°

x = 15.

Now,

∠2  = 5x + 24

∠2  = 5(15) + 24

∠2 = 99°

Hence the angle 2 is of 99° .

b)

Given,

Area of circle = 907.46 in²

Now,

Area of circle = πr²

Calculate r,

907.46 = πr²

r = 16.99 in

Now,

Diameter is double of radius.

d= 2r

d= 33.99 in

Thus diameter of the circle is 33.99 in.

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Check the picture below.

[tex]\cot(\theta )=\cfrac{\stackrel{adjacent}{4}}{\underset{opposite}{3}}\implies \cot^{-1}[\cot(\theta )]=\cot^{-1}\left( \cfrac{4}{3} \right) \\\\\\ \theta =\cot^{-1}\left( \cfrac{4}{3} \right)\implies \theta \approx 36.87^o ~~ \textit{\LARGE \checkmark}[/tex]

The first four terms of the geometric sequence with a first term of 3 and a common ratio of 2 are 3, 6, 12, and 24.

To find the first four terms of a geometric sequence with a first term (a1) of 3 and a common ratio (r) of 2, we can use the formula for the nth term of a geometric sequence:

[tex]an = a1 * r^(n-1)[/tex]

Substituting the given values, we have:

a1 = 3

r = 2

Let's calculate the first four terms (n = 1, 2, 3, 4) using the formula:

[tex]a1 = 3 * 2^(1-1) = 3 * 2^0 = 3 * 1 = 3\\a2 = 3 * 2^(2-1) = 3 * 2^1 = 3 * 2 = 6\\a3 = 3 * 2^(3-1) = 3 * 2^2 = 3 * 4 = 12\\a4 = 3 * 2^(4-1) = 3 * 2^3 = 3 * 8 = 24[/tex]

Therefore, the first four terms of the geometric sequence with a first term of 3 and a common ratio of 2 are 3, 6, 12, and 24.

In summary, the terms of the sequence are obtained by multiplying the first term (a1) by the common ratio (r) raised to the power of (n-1), where n represents the term number.

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Total volume of the figure is 9310.51 in³

Given,

Triangular prism and cuboid with dimensions.

Firstly calculate the volume of cuboid.

Volume of cuboid = l × b× h

l = length of cuboid = 23 in

b = width of cuboid = 16 in

h = height of cuboid = 18 in

Substitute in the formula,

Volume = 18 × 23×16

Volume = 6624 in³ .

Secondly calculate the volume of triangular prism,

Volume of triangular prism = [tex]\frac{1}{4} h\sqrt{-a^4 + 2(ab)^2 +2(ac)^2 - b^4 +2(bc)^2 - c^4}[/tex]

Substitute the values in the formula,

h= 21 in

a= 23 in

b = 16 in

c = 16 in

Volume = 2686.51 in³

Hence,

Total volume = (6624 + 2686.51) in³

Total volume = 9310.51 in³.

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Answer:

Step-by-step explanation:

You want to identify the x-intercepts on the graph.

An "x-intercept" is a point where the graph crosses or touches (intercepts) the x-axis. The y-value there is always 0.

The given graph crosses the x-axis where x = -2 and x = 3. This means the x-intercept points are ...

  (-2, 0) and (3, 0)

<95141404393>

Answer: B

Step-by-step explanation:

The length and width of this rectangle are 40 yards and 5 yards, respectively.

Let the width of the rectangle be represented by 'w'. Since the length of the rectangle is eight times the width, we can represent the length as '8w'.

The perimeter of a rectangle is found by adding all four sides. In this case, we know the perimeter is 90yd, so we can set up an equation as follows:

[tex]$$2w + 2(8w) = 90$$[/tex]

Simplifying the equation, we get:

[tex]$$2w + 16w = 90$$[/tex]

[tex]$$18w = 90$$$$w = 5$$[/tex]

So the width of the rectangle is 5 yards.

To find the length of the rectangle, we can substitute the value of the width (5) into the equation we used to represent the length.

[tex]$$8w = 8 \times 5 = 40$$[/tex]

So the length of the rectangle is 40 yards.

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The statement that Brock could use to qualify the distribution is that there is a peak at 22°C.

Brock can describe the distribution by stating that there is a peak of temperatures at 22°C. It is at this peak that the mean of the distributionc an be found.

A normal distribution such as the one shown in the diagram has a bell curve and the sample emans plotted can be used to indicate how close to the actual population the sample size is. So, option B is a way to describe the distribution.

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The mass of Box 1 is 450 grams, the mass of Box 2 is 300 grams, and the mass of Box 3 is 150 grams.

Given that,

The mass of Box 3 = 150 grams

Assume that,

Mass of Box 1 is "x"

And the mass of Box 2 "y".

We know that,

Box 1 has a mass that is three times more than Box 3,

Therefore,

⇒  3x150 = 450 grams

Then,

⇒ x = 450

Box 2 has a mass that is two-thirds the mass of Box 1,

so its mass is,

⇒ (2/3)x450 = 300 grams.

it  means, y = 300

Hence,

Masses are:

Box 1 is 450 grams

Box 2 is 300 grams

Box 3 is 150 grams

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Answer:

2.15E47

Step-by-step explanation:

First you want to simplify the simplified equation

4.3E23 x 5.0E23

Then you get your final answer:

2.15E47

The point on the number line represents the product is (a) point A

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

Product = (-4)(-2)(-1)

Express as products

So, we have

Product = (-4) * (-2) * (-1)

When the products are evaluated, we have

Product = -8

The point A is on -8

This means that the point on the number line represents the product is A

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The volume of the prism is 97.425 in³.

The volume of the prism is 5280 in³.

We have,

A.

The prism is an equilateral triangle prism.

So,

The area of an equilateral triangle can be calculated using the formula:

Area = (√(3) / 4) x side²

Substituting the given side length of 5 inches into the formula, we have:

Area = (√(3) / 4) x 5²

= (√(3) / 4) x 25

= 25  √(3) / 4

= 10.825 inches²

Now,

The volume of the prism.

= 10.825 x 9

= 97.425 in³

B.

The prism is a right triangular prism.

So,

base² + 16² = 34²

base² = 1156 - 256

base² = 900

base = 30

Now,

Area of the triangle.

= 1/2 x base x height

= 1/2 x 30 x 16

= 15 x 16

= 240 in²

The volume of the prism.

= 240 x 22

= 5280 in³

Thus,

The volume of the prism is 97.425 in³.

The volume of the prism is 5280 in³.

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Check the picture below.

[tex]\stackrel{ \textit{\LARGE Areas} }{\cfrac{1}{2}\cdot \pi (14)^2~~ + ~~\cfrac{1}{2}\cdot \pi (7)^2}\implies 98\pi ~~ + ~~24.5\pi\implies {\Large \begin{array}{llll} 122.5\pi \end{array}}[/tex]

a) The graph of the cost function for the Seattle factory starts with a flat line segment, then increases with a positive slope, and finally decreases with a negative slope.  b) The specific values for the slopes and endpoints depend on the exact calculations based on the given function, but this general description should provide an understanding of the cost structure over the specified domain.

a) To sketch a graph of the cost function for the Seattle factory, we'll use the given piecewise function and the specified domain [0, 42000].

First, we'll plot three points on the graph to represent the different parts of the function.

At 8000 units, the cost is 0.35.

At 20000 units, the cost is 0.75.

At 42000 units, the cost is 0.83 - (42000/200000).

Next, we'll connect the points with appropriate lines or curves based on the function's behavior over each part of the domain.

From 0 to 8000 units, the cost is constant at 0.35. This part of the graph will be a horizontal line segment at y = 0.35.

From 8000 to 20000 units, the cost increases. We'll draw an increasing line segment connecting the point (8000, 0.35) to the point (20000, 0.75). This represents a positive slope.

From 20000 to 42000 units, the cost decreases. We'll draw a decreasing line segment connecting the point (20000, 0.75) to the point (42000, 0.83 - (42000/200000)). This represents a negative slope.

b) Over each part of its domain, we can describe the function as follows:

From 0 to 8000 units, the cost is constant at 0.35. The function is constant with a slope of 0.

From 8000 to 20000 units, the cost increases. The function is increasing with a positive slope.

From 20000 to 42000 units, the cost decreases. The function is decreasing with a negative slope.

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A latent variable can assist in estimating a state's informal economy by accounting for unseen factors that impact the size and actions of the informal sector. MIMIC model estimates informal economy size and dynamics, identifies determinants, and explains its impact.

In the context of calculating the informal economy, a latent variable can represent the underlying construct of informal economic activity.

The MIMIC (Multiple Indicators Multiple Causes) model is a statistical technique commonly used to estimate latent variables. In the context of estimating the informal economy, the MIMIC model combines observed indicators (such as specific economic variables or survey data) with latent variables to estimate the size and characteristics of the informal sector.

The MIMIC model works by simultaneously estimating two components: the measurement model and the structural model. The measurement model links the observed indicators (such as employment in informal sectors, cash transactions, or informal business ownership) to the underlying latent variable (informal economy). The structural model then examines the relationship between the latent variable and its causes or determinants, which may include factors like regulatory environments, social norms, or economic conditions.

It provides a framework for quantifying and analyzing the informal sector, which is often challenging due to its unobservable nature and diverse activities.

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Answer:

3/10

Step-by-step explanation:

4+6+10

=20

6/20

=3/10

The hypotenuse of the smaller right triangle is calculated as approximately: C. 14 mm

If the ratio of the areas of two similar right triangles is 7:14, then the ratio of their corresponding sides will be equal to the ratio of their area s.

In this case, let x represent the hypotenuse of the smaller right triangle. Therefore, we have:

7/14 = x²/20²

Cross multiply:

14x² = 20² * 7

14x² = 2,800

x² = 2,800/14

x² = 200

x = √200

x ≈ 14 mm

The length of the hypotenuse of the smaller right triangle is calculated as 14 mm.

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12/8 = 3/2 (radians)

Changing the value of "a" in the equation r = ax alters the scale, proportionality, and direction of the relationship between the variables "r" and "x."

When you change the value of "a" in the equation r = ax, it affects the relationship between the variables "r" and "x" in the following ways:

Magnitude: The value of "a" determines the scale or magnitude of the relationship between "r" and "x." If "a" is a positive value, increasing its magnitude will cause the values of "r" and "x" to increase or decrease together.

If "a" is negative, increasing its magnitude will cause "r" and "x" to change in opposite directions.

Proportionality: The value of "a" determines the proportionality constant between "r" and "x." For example, if "a" is 2, it means that for every unit increase in "x," "r" will increase by 2 units.

Similarly, if "a" is 0.5, "r" will increase by 0.5 units for every unit increase in "x." The proportionality constant "a" determines the rate at which "r" changes relative to changes in "x."

Direction: The sign of "a" determines the direction of the relationship between "r" and "x." If "a" is positive, "r" and "x" will have the same direction of change.

For example, as "x" increases, "r" will also increase. Conversely, if "a" is negative, "r" and "x" will have opposite directions of change. As "x" increases, "r" will decrease, and vice versa.

Overall, changing the value of "a" in the equation r = ax alters the scale, proportionality, and direction of the relationship between the variables "r" and "x."

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Using the height and radius given, the surface area of the cylinder is 408.2m²

The surface area of a cylinder is the combined area of its curved surface (lateral surface) and its two circular bases. The formula for the surface area of a cylinder is:

A = 2πrh + 2πr²

where:

In the given question, the data are;

Substituting the value into the formula

A = 2π(5 * 8) + 2π(5)²

A = 408.2m²

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The Variance is approximately 422.12 and the standard deviation is approximately 20.54. These measures indicate that the data set has a relatively high dispersion or spread.

a) To find the mean, median, and mode of the given data set, we can perform the following calculations:

Mean: The mean is calculated by summing all the values and dividing by the total number of values.

Mean = (7 + 10 + 20 + 10 + 40 + 15 + 10 + 6 + 10 + 50 + 30 + 7 + 10 + 50 + 55 + 10 + 15 + 6 + 20 + 10 + 35 + 10 + 5 + 50 + 10) / 25

Mean = 357 / 25

Mean ≈ 14.28

Median: The median is the middle value of the data set when arranged in ascending order. If there is an even number of values, the median is the average of the two middle values.

Arranging the data set in ascending order: 5, 6, 6, 7, 7, 10, 10, 10, 10, 10, 10, 10, 10, 15, 15, 20, 30, 35, 40, 50, 50, 50, 55

Since there are 25 values, the median is the 13th value, which is 10.

Mode: The mode is the value(s) that appear most frequently in the data set.

In this case, the mode is 10, as it appears the most number of times (8 times)

Based on the mean, median, and mode, we can infer that the distribution of the data set is likely to be positively skewed, as there are some higher values that are pulling the mean towards the right.

b) To find the variance and standard deviation, we can use the following formulas:

Variance: The variance measures the spread of the data set.

Variance = Σ((xi - mean)^2) / n

where Σ represents the sum, xi represents each value, mean is the mean calculated earlier, and n is the total number of values.

Standard Deviation: The standard deviation is the square root of the variance and provides a measure of the dispersion of the data.

Standard Deviation = √Variance

Performing the calculations:

Variance = [(7 - 14.28)^2 + (10 - 14.28)^2 + ... + (10 - 14.28)^2] / 25

Variance ≈ 422.12

Standard Deviation = √Variance

Standard Deviation ≈ √422.12 ≈ 20.54

Therefore, the variance is approximately 422.12 and the standard deviation is approximately 20.54. These measures indicate that the data set has a relatively high dispersion or spread.

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The value of h is 24. 19

To determine the value, we need to know that the six different trigonometric identities.

These identities are listed as;

We also have that the ratios of these identities are;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the information given, we have that;

h sin 38 = 1.5

divide by the coefficient

h = 15/0. 62

Divide the values

h = 24. 19

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Since the independent variable x is not the base[tex], y=-10.2^x[/tex] does not represent an exponential function. Option A

To determine whether a function is exponential, we need to examine the form of the function and how the independent variable, in this case, x, is related to the dependent variable, y.

In an exponential function, the independent variable is typically the exponent, and the base is a constant. However, in the given function y = [tex]-10.2^x[/tex], the independent variable x is not the base of the exponent. The base is actually the constant -10.2.

In an exponential function, the variable x represents the exponent, and as x increases, the value of the function grows or decays at an exponential rate. However, in this case, the variable x is not in the exponent position. Instead, it is multiplied by -10.2.

Let's consider an example using different values of x:

For x = 1, y =[tex]-10.2^1[/tex]= -10.2

For x = 2, y =[tex]-10.2^2[/tex] = 104.04

For x = 3, y =[tex]-10.2^3[/tex] = -1061.208

As we can see, the values of y are not growing or decaying at an exponential rate as x increases. Therefore, the given function does not represent an exponential function.

It's important to note that the presence of an exponent alone does not make a function exponential. The relationship between the base, the exponent, and how the values change as the exponent varies determines whether a function is exponential or not.

In this case, since x is not the base and the values do not exhibit exponential growth or decay, the given function[tex]y = -10.2^x[/tex] does not represent an exponential function.

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ft cubed because they are three calculations we need to do but mainly 4 if you know wha tim saying :) Glad to help

Answer: The known solutions to f(x)=g(x) are x=1, x=7, and x=11. These are the values of x for which the values of f(x) and g(x) are equal according to the given table.

Answer:

the correct answers are:

1)1

2)3

3)7

4)9

Step-by-step explanation:

The known solutions to f(x) = g(x) can be determined by comparing the values of f(x) and g(x) in the given table. From the table, the matching values of f(x) and g(x) are:

1.x = 1: f(1) = 1, g(1) = 1

2.x = 3: f(3) = 3, g(3) = 3

3.x = 7: f(7) = 9, g(7) = 9

4.x = 9: f(9) = 11, g(9) = 11

Therefore, the correct answers are:

1)1

2)3

3)7

4)9

The grade for the missing test is 95.

To determine the grade for the missing test, we can use the information provided.

We know the average of all the tests, including the missing one, is 91.25.

Let's calculate the average using the given test grades: 90, 88, ?, 92.

The sum of the known test grades is: 90 + 88 + 92 = 270.

Since we have four tests in total, including the missing one, we can set up the equation:

(270 + ?) / 4 = 91.25

To find the missing grade, we can solve for the variable "?":

270 + ? = 91.25 x 4

270 + ? = 365

? = 365 - 270

? = 95

Therefore, the grade for the missing test is 95.

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