which rule explains why these triangles are congruent

True. In a continuous uniform distribution, all values within a specified interval are equally likely to occur. The mean or expected value of this distribution can be found by taking the average of the upper and lower limits of the interval.

This can be represented mathematically as (a+b)/2, where a and b are the lower and upper limits of the interval. For example, if we have a continuous uniform distribution on the interval [0,10], the mean value would be (0+10)/2 = 5.

This means that on average, we would expect a randomly selected value from this distribution to be around 5. It's important to note that the mean of a continuous uniform distribution is not affected by the shape or spread of the distribution, as all values have an equal chance of occurring.

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The answer is option C) 30,700

The problem involves using linear interpolation to estimate the population of Little Elm in 2020 based on the given data from 2010 and 2015.

To start, we need to calculate the annual growth rate of the population between 2010 and 2015. This can be done by taking the difference between the population in 2015 and the population in 2010, and then dividing that difference by the number of years in that time period:

Annual growth rate = (17,150 - 3,646) / 5 = 2,700

This means that, on average, the population of Little Elm grew by 2,700 people per year between 2010 and 2015.

Next, we can use this annual growth rate to estimate the population of Little Elm in 2020. To do this, we need to add 10 years of growth to the initial population of 3,646 (since we want to estimate the population in 2020, which is 10 years after 2010):

Estimated population in 2020 = 3,646 + (2,700 x 10) = 30,646

Therefore, the estimated population of Little Elm in 2020 is approximately 30,700, which corresponds to answer choice C.

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The area k of the triangle a = 3, c = 2, b = 135 degrees is approximately 1.06125 square units.

The area k of the triangle, we can use the formula:
k = (1/2) * b * c * sin(A)
where A is the angle opposite side a.
Find A, we can use the fact that the angles in a triangle add up to 180 degrees:
A + B + C = 180
Substituting in the given values, we get:
A + 135 + 180 = 360
A = 45 degrees
Now we can plug in all the values into the area formula:
k = (1/2) * 2 * 3 * sin(45)
k = 1.5 * 0.707
k = 1.06125
Therefore, the area k of the triangle is approximately 1.06125 square units.

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1. The statement "Each exterior angle of a regular hexagon is acute" is True.

2. The statement "The sum of the interior angles of a polygon is always a multiple of 180" is False.

3. The statement "In any polygon, the larger the number of vertices, the smaller the measure of an exterior angle" is True.

1. TRUE: Each exterior angle of a regular hexagon is acute.
A regular hexagon has six equal sides and six equal interior angles. The sum of the interior angles of a hexagon is (6-2) * 180 = 720 degrees. Since it's a regular hexagon, each interior angle is 720/6 = 120 degrees. The exterior angles are supplementary to the interior angles, so each exterior angle is 180 - 120 = 60 degrees. Since 60 degrees is less than 90 degrees, each exterior angle is acute.

2. FALSE: The sum of the interior angles of a polygon is always a multiple of 180.
The formula for the sum of the interior angles of a polygon is (n-2) * 180, where n is the number of vertices (or sides). As you can see, the result is always a multiple of 180.

3. TRUE: In any polygon, the larger the number of vertices, the smaller the measure of an exterior angle.
For a regular polygon, the measure of an exterior angle can be calculated as 360/n, where n is the number of vertices (or sides). As the number of vertices increases, the measure of an exterior angle decreases, since they are inversely proportional.

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The calculated two double inequalities that define shaded region are 1 ≤ y < 5 and -3 < x ≤ 2

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

The graph

On the graph, we have the following properties

Using the above as a guide, we have the following:

1 ≤ y < 5

-3 < x ≤ 2

Hence, the two double inequalities that define shaded region are 1 ≤ y < 5 and -3 < x ≤ 2

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The current scores of both Jenna and Kera in the game they were playing are

Jenny's current score is -15.

Kera's current score is 8.

In the given problem, we are given two players, Jenny and Kera, playing the game.

Jenny has -10 points, which means she already has negative points. He has since lost 5 more points. So his current score would be:

-10 - 5 = -15

So now Jenny has a score of -15.

Kera, meanwhile, has 22 points and 14 points to lose. So his current score would be:

22 - 14 = 8

So now Kera has 8 points.

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We get that the plane is about 2193.0 feet from the airport, Rounding to the nearest tenth

To solve the problem, we will use trigonometry and the tangent function, which relates the other facet of a right triangle to the adjoining aspect:

tan(theta) = opposite / adjacent

wherein theta is the angle of descent, opposite is the change in height, and adjacent is the space from the airplane to the airport.

Rearranging the formula, we get:

adjacent = contrary / tan(theta)

because the angle of descent is 13 ranges and the alternate in height is from 500 ft, we've got:

contrary = 500 ft

theta = 13 stages

Substituting these values into the formula, we get:

adjacent = 500 ft / tan(13 ranges)

using a calculator, we find that tan(13 stages) is about 0.228, so:

adjacent = 500 feet / 0.228 = 2192.98 feet

Therefore, we get that the plane is about 2193.0 feet from the airport.

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The standard form of the quadratic relation y=2(x-2)^2-18 is y=2x^2-8x-14.

The standard form of a quadratic relation is y=ax^2+bx+c, where a, b, and c are constants. To convert y=2(x-2)^2-18 to standard form, we need to expand the squared term and simplify the expression.

First, we expand the squared term to get y=2(x^2-4x+4)-18. Then, we distribute the 2 to get y=2x^2-8x+8-18. Finally, we simplify by combining like terms to get the standard form y=2x^2-8x-14.

This quadratic relation is a parabola with a vertex at (2,-18) and it opens upwards since the coefficient of x^2 is positive. The axis of symmetry is a vertical line passing through the vertex, and the y-intercept is -14.

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The volume of the material used to make the insulated collar is 1060.56 cubic inches.

The volume of the material used to make the insulated collar can be determined as follows.

1. Identify the given dimensions:

inner radius (r) = 3 inches,

outer radius (R) = 5 inches, and

height (h) = 21 inches.

2. Use the formula for the volume of a cylinder:

V = πr^2h.

3. Calculate the volume of the outer cylinder with radius R:

V_outer = πR^2h = 3.14 * (5^2) * 21 ≈ 1653.3 cubic inches.

4. Calculate the volume of the inner cylinder with radius r:

V_inner = πr^2h = 3.14 * (3^2) * 21 ≈ 592.74 cubic inches.

5. Subtract the volume of the inner cylinder from the volume of the outer cylinder to find the volume of the material used:

V_material = V_outer - V_inner ≈ 1653.3 - 592.74 ≈ 1060.56 cubic inches.

The volume of the material is approximately 1060.56 cubic inches, rounded to the nearest hundredth.

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Based on the inscribed angle theorem, the measure of angle JKL in the circle is: m<JKL = 121°.

Where an inscribed angle is subtended by an arc it intercepts, the measure of the inscribed angle is equal to half of the the measure of the intercepted arc in the circle, based on the inscribed angle theorem.

Angle JKL is the inscribed angle that is subtended by arc JML. Find the measure of arc JML.

Measure of arc JML = 360 - 53 - 65

Measure of arc JML = 242°

m<JKL = 1/2(measure of arc JML) [inscribed angle theorem]

Substitute:

m<JKL = 1/2(242)

m<JKL = 121°

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The ladder must be situated at an angle of approximately 63.43° to reach the top of the 9 ft wall.

How to find the angle of elevation at which the ladder must be situated?

Certainly, here's an illustration of the problem:

           |\

           | \

           |   \  9 ft

           |     \

ladder |       \

  (10 ft)|_____\

      wall

To find the angle of elevation at which the ladder must be situated, we can use the trigonometric function of sine. Let θ be the angle of elevation. Then:

sin θ = opposite / hypotenuse

In this case, the opposite side is the height of the wall (9 ft), and the hypotenuse is the length of the ladder (10 ft). So:

sin θ = 9/10

Using a calculator or a trigonometric table, we can find the angle whose sine is 9/10:

θ ≈ 63.43°

Therefore, the ladder must be situated at an angle of approximately 63.43° to reach the top of the 9 ft wall.

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The p-value for the hypothesis test is 0.04. This means that if the null hypothesis is true

To find the p-value, we need to conduct a hypothesis test.

The null hypothesis is that there is no difference in blood pressure before and after taking the medication:

H0: μd = 0

The alternative hypothesis is that there is a difference in blood pressure before and after taking the medication:

Ha: μd ≠ 0

where μd is the population mean difference in blood pressure before and after taking the medication.

We are given that the sample size is n = 36, the sample mean difference is ¯d = 2.4, and the sample standard deviation is s = 4.5.

We can calculate the t-statistic as:

t = (¯d - 0) / (s / sqrt(n)) = (2.4 - 0) / (4.5 / sqrt(36)) = 2.13

Using a t-distribution table with 35 degrees of freedom (df = n - 1), we find that the two-tailed p-value for t = 2.13 is approximately 0.04.

Therefore, the p-value for the hypothesis test is 0.04. This means that if the null hypothesis is true (i.e., if there is really no difference in blood pressure before and after taking the medication), there is a 4% chance of observing a sample mean difference as extreme or more extreme than 2.4. Since this p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is evidence that the drug affects blood pressure.

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Answer:

Here is the complete magic square:

-3 4 -1

2 0 -2

1 -4 3

Every row, column, and long diagonal adds to 0.

The estimate from direct proportionality is higher than the prediction from KLEIBER's law.

a. For a 180 kilogram lion, we can use KLEIBER's law: R = 73.3*(180^0.75) = 6136.5 Calories per day. For an 80 kilogram human, we can use the same formula: R = 73.3*(80^0.75) = 1537.6 Calories per day.

b. If metabolic rate and mass were directly proportional, we could use the ratio of the masses to find the basal metabolic rate for an 80 kilogram human.

The ratio of the masses is 80/180 = 0.44. We can multiply this by the basal metabolic rate for the lion to get an estimate for the human: 0.44*6136.5 = 2701.26 Calories per day.

This estimate is higher than the prediction from Kleiber's law for an 80 kilogram human (1537.6 Calories per day). KLEIBER's law indicates that smaller organisms have a higher metabolic rate per kilogram of mass than do larger organisms.

Therefore, the estimate from direct proportionality is higher than the prediction from KLEIBER's law.

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If Holly cuts 6 ribbons into fifths for her craft project, after cutting, she has a total of 30 one-fifth-size ribbons (6 ribbons x 5 cuts each).

Holly has cut 6 ribbons into fifths for her craft project. This means that she has a total of 30 ribbons, each with a size of one-fifth. To understand this better, we can break it down into fractions. Each ribbon is one-fifth of a whole ribbon, and since Holly has cut 6 ribbons, she has 6 times one-fifth, which equals 30. So, to answer the question, Holly has 30 ribbons, each with a size of one-fifth. These ribbons can be used for various crafts, such as creating bows, wrapping presents, or decorating cards. The possibilities are endless, and with 30 ribbons, Holly can get creative and make a lot of beautiful crafts.

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The situation provided is exponential growth and the equation is

p = 225 * 1.133ˣ

This scenario represents a significant improvement as the number of students increases each year.

The basic approach to incremental growth is:

[tex]P = P_{0} * (1 + r)^t[/tex]

where:

P. = initial population

r = increase in decimal form

t = time in years

Here

P₀ = 225 (initial population in 2021).

r = 13.3% = 0.133 (growth rate as decimal) .

t = x (time in years from the opening of the school in 2021)

Substituting these values ​​in the formula we get:

[tex]p = 225 * (1 + 0.133)^x[/tex]

Simplifying further, we get:

p = 225 * 1.133ˣ

This is the equation that predicts school population x years after the school opens in 2021

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The variance of the data set is 0.318652.

To find the variance of this data set, we need to use the formula:
variance = Σ(x - μ)² / n
Where Σ represents the sum, x is the value of each data point, μ is the mean value, and n is the number of data points.

Using this formula, we can calculate the variance as follows:

Variance = [(5.07 - 4.312)² + (3.57 - 4.312)² + (5.32 - 4.312)² + (3.19 - 4.312)² + (3.49 - 4.312)² + (4.25 - 4.312)² + (4.76 - 4.312)² + (5.19 - 4.312)² + (3.94 - 4.312)² + (4.34 - 4.312)²] / 10

Variance = [0.225769 + 0.449769 + 0.370656 + 1.323856 + 0.716164 + 0.006544 + 0.175684 + 0.382884 + 0.135556 + 0.000484] / 10

Variance = 3.18652 / 10

Variance = 0.318652

Therefore, the variance of the data set is 0.318652.

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The volume of the prism is 78 cubic feet.The volume of a prism is given by the formula V = Bh, where B is the area of the base and h is the height of the prism.

In this case, the base of the prism is a right triangle with legs measuring 3 feet and 4 feet, so its area is (1/2)(3)(4) = 6 square feet. The height of the prism is 13 feet. Therefore, the volume of the prism is V = Bh = (6)(13) = 78 cubic feet.To understand this calculation, think of the prism as a stack of identical, parallel cross sections. Each cross section is a copy of the base, with an area of 6 square feet.

The height of each cross section is the same, and equal to the height of the prism, which is 13 feet. To find the total volume of the prism, we add up the volumes of all these cross sections, which is equal to the area of the base times the height of the prism.

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The answer is 2143.6.

The Equation of the line which is parallel to the line "y = 3x + 6", and also passes through (4,7) is "y = 3x - 5".

In order to find an equation of a line which passes through point (4,7) and is parallel to line "y = 3x + 6", we use the fact that parallel lines have the same slope.

The given line ""y = 3x + 6" has a slope of 3,

So, the "parallel-line" we want to find must also have a slope of 3.

Now, by using the "point-slope" form of the equation of a line, which is : y - y₁ = m(x - x₁),

where m is slope and (x₁, y₁) is a point on the line,

So, we substitute "m = 3" and (x₁, y₁) = (4,7) to get:

⇒ y - 7 = 3(x - 4),

⇒ y - 7 = 3x - 12,

⇒ y = 3x - 5

Therefore, the equation of the required line is y = 3x - 5.

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The Colorado hikers are at an altitude of 8753.1694 feet.

Here we have been given the equation T = -1. 83a + 212.

Here, T is the boiling point in Fahrenheit of water, while a is the altitude of the place.

We know that the campers in hiing in Colorado boil water for ea. The water boils at a temperature of 196°F, we need to find the altitude.

Here we are going to clearly take T = 196°F

Substituting the value in the above equation will give us

196 = - 1.83a + 212

Taking the variable to the Right Hand Side will give us

196 + 1.83a = 212

Taking 196 to LHS to separate the constant and variable will give us

1.83a = 212 - 196

Solving LHS gives us

1.83a = 16

Taking 1.83 to the other side will give us

a = 16/1.83

or, a = 8.7431694 thousands feet

= 8753.1694 feet

Hence, the Colorado hikers are at an altitude of 8753.1694 feet.

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The required inequalities are h + l ≤ 20, 10h + 15l ≥ 240 and 20h + 25l ≥ 440

Given, for tutoring elementary students in math Susan earns $10 per hour. She earns $15 per hour for cleaning in the library.

Let h be the number of hours Susan works in one week tutoring elementary students.

Let l be the number of hours Susan works in one week cleaning the library.

Given that each week Susan cannot work more than 20 hours.

So, h + l ≤ 20 ....(1)

Susan's total earnings must be at least $240 per week.

10h + 15l ≥ 240    ...(2)

Multiplying equation (1) by 10

10h + 10l ≤ 200    ...(3)

Adding equations (2) and (3)

20h + 25l ≥ 440

Thus, the three required inequalities are h + l ≤ 20, 10h + 15l ≥ 240 and 20h + 25l ≥ 440

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Mato will pay about $700 more in interest than Kika ($625 - $1,300 = $675, which rounds to $700). The answer is C: Mato; $700

Mato will pay more in interest because he has a higher interest rate and a shorter repayment period. To calculate the amount of interest each will pay, we can use the formula:

Interest = (Loan amount) x (Interest rate) x (Time in years)

For Kika:
Interest = $5,000 x 0.052 x 5
Interest = $1,300

For Mato:
Interest = $5,000 x 0.075 x (2/12)
Interest = $625

Therefore, Mato will pay about $700 more in interest than Kika ($625 - $1,300 = $675, which rounds to $700). The answer is C: Mato; $700.

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The payback period for the auto is approximately 8 years.

Buy-Rite Pharmacy has purchased an auto for delivering prescriptions. The auto was purchased for $26,000, and it has a useful life of 6 years with a $5,500 salvage value. By delivering prescriptions, the pharmacy aims to increase gross revenues by at least $33,500 per year. The pharmacy will incur a cost of $28,000 per year for these prescriptions.

Using the straight-line method, the annual depreciation of the auto is ($26,000 - $5,500) / 6 = $3,917. This means that the total cost of the auto over 6 years will be $26,000 - $5,500 + ($3,917 x 6) = $43,502.

To calculate the payback period, we need to determine how long it will take for the increased gross revenues to cover the cost of the auto.

The net increase in revenues will be $33,500 - $28,000 = $5,500 per year. Therefore, the payback period is $43,502 / $5,500 = 7.9 years, which is rounded to 8 years.

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The constant of proportionality between y and x in the graph is 3

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

The graph

On the graph, we have the following readings

(x, y) = (1, 3)

Using the above as a guide, we have the following:

The constant of proportionality between y and x in the graph is

k = y/x

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

k = 3/1

Evaluate

k = 3

Hence, the constant of proportionality between y and x in the graph is 3

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Answer:

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

Let the original number be n.

We are given that 30% of n is 14.99.

Set up an equation to reflect this relation:

Solve it for n:

The area of the whole figure is 31.5 sq. units.

The area of a given figure connotes its expanse in a 2 dimensional plane. The shape and size of a given figure determines how to calculate its area.

From the given question, the figure given can be likened to a rhombus. So that;

area of a rhombus = (diagonal 1 * diagonal 2)/ 2

Then,

area of the figure = (diagonal 1 * diagonal 2)/ 2

where: diagonal 1 = 7.5, and diagonal 2 = 8.4

So that;

area of the figure = (7.5*8.4)/ 2

                             = 63/ 2

                             = 31.5

The area of the whole figure is 31.5 sq. units.

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Answer:

x=2

Step-by-step explanation:

2x+y=10

3x=y

2x+3x=10

5x=10

x=2