The question is below.

The missing sides of the right triangle were obtained below.

Pythagoras' theorem 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 have that;

1) x = √26^2 - 10^2

x = 24

2) x = √20^2 + 14 ^2

x = 24.4

3) x = √50^2 - 30^2

x = 40

4) x = √15^2 + 5^2

x = 15.8

5) x = √12^2 + 20^2

x = 23.3

These are the sides that are missing.

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The surface area of the right square pyramid with the given base area and slant height would be = 221cm²

To calculate the surface area of the right square pyramid, the formula that should be used would be given below as follows. That is;

Surface area = a²+ 2al

where;

a² = area of base = 169cm²

a = side length of base = √169 = 13

l = slant height = 13 cm

S.A = 169+ 2(13×13)

= 169 + 52

= 221cm²

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7. Radius of circle P = 2       Radius of circle Q = 1

Coordinates of the point of tangency (4,2)

The equation of the tangency line is x = 4

8. AB is not a tangent. BC² ≠ AB² + AC²

9. The three radii of the circle are; CB, CF and CD

A diameter of the circle is BD

A tangent of the circle is GE

A chord of the circle is BD

A secant of the circle is AD

A point of tangency is F

7. To find the radius, identify the diameter of the circle. For the diagram, it can be said that the diameter of the circle P is 4.

The radius then is 4/2 = 2.

The radius of circle q is 2/2 = 1

You could also use the formula

Distance = sqrt((x2 - x1)² + (y2 - y1)²)

8. √4² + √12² = √160

√13 = 169

Therefore AB is not tangent. It is less than BC

9. The line that cuts the circle into two halves is the diameter. The lines than further cuts the diameter into equal parts are the radii's

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a) The total amount that the Scotts ended up paying for the townhome (including the down payment and the monthly payments) is $445,144.80.

b) The total interest paid on the mortgage is $213,144.80.

The down payment is the advance payment made on a mortgage or loan to satisfy the lending concerning the borrower's financial capacity.

The down payment reduces the mortgage liability, including interest.

The cost of the townhome = $232,000

The down payment for the town home made by the Scotts = $48,000

The mortgage = $184,000 ($232,000 - $48,000)

Monthly payment = $1,103.18

The mortgage period = 360 months (30 years x 12)

The total payment on the mortgage over the mortgage period = $397,144.80 (1,103.18 x 360)

The total payment, including the down payment = $445,144.80 ($397,144.80 + $48,000)

The total interest paid = $213,144.80 ($445,144.80 - $232,000)

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The Scotts bought a townhome for $232,000. They made a down payment of $48,000 and took out a mortgage for the rest. Over the course of 30 years they made monthly payments of $1,103.18 on their mortgage until it was paid off.

we can say that the pattern for how the numerator and denominator change in the fractions model is that they are multiplied or divided by the same non-zero integer.

Let's consider the fraction 2/ 3.

If we multiply both the numerator & the denominator by 2, we get 4 /6.

Also  multiplying both by 3, we will  get 6 /9

In general,  if we multiply the numerator and the denominator by the same non-zero integer, we get an equivalent fraction.

On the other hand, if we divide both the numerator and   the denominator by the same non-zero integer,

we also get an equivalent fraction. For example    if we divide 6/9 by 3, we get 2/3 again.

Hence , the above conclusion is correct.

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Full Question:

Fraction 2/ 3.

What pattern can you use to describe how the numerator and denominator change in the fraction models above?

It is very likely that a vacuum will last between 5.5 and 7.5 years.

This is because we can use the properties of the normal distribution to calculate that about 68% of the vacuum cleaners will fall within one standard deviation of the mean, which in this case is between 6.5 - 0.5 = 6 and

6.5 + 0.5 = 7

About 95% of the vacuum cleaners will fall within two standard deviations of the mean, which in this case is between 6 - 0.5 = 5.5 and 6.5 + 0.5 = 7

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Answer: The best estimate of the sum of the heights of the 5 mountains is between 130,000 and 135,000 ft. Therefore, option D is correct,

Step-by-step explanation: The best estimate of the sum of the heights of the five mountains listed is between 130,000 and 135,000 ft. These heights are already very high, so options A and B can be eliminated. Option C is too low, leaving option D as the best estimate.

Dhaulagiri: 26,810 ft

Nanga Parbat: 26,660 ft

Annapuma: 26,504 ft

Gasherbrum: 26,470 ft

Xixabangma: 26,286 ft

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Answer: (6,11π/6).

Step-by-step explanation:We need to find the radius r and the angle θ. Remember that r2=x2+y2, so

because of the signs of x and y, our angle is in quadrant IV. Therefore, we find that θ=11π/6.

So the final answer is (6,11π6).

If the helicopter flies 200 mph from the station nearest, the time it will it take to reach the ship is 0.52 hours

The numerical measurement between two entities or locations is defined as the distance, recorded in units such as kilometers, feet, meters, and miles. Determining the direct geometric line from point to point requires distinct models of calculation for both 2D and 3D geometry, most notably utilizing the Pythagorean theorem or the distance formula, respectively.

Physical sciences heavily rely on this notion, as it aids with computing rates that include: displacement, velocity, and acceleration. However, multiple factors - involving speed, direction, and time - can alter measured distances traveled by an object.

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The given Mayan number which is : :|| :|| in decimal (base 10) is 42.

The Mayan number system is a base-20 system that uses three symbols: a dot (.), a horizontal bar (|), and a shell-like symbol (:). The symbol for zero is a shell-like symbol (:).

To convert the given Mayan number to decimal (base 10), we need to understand the positional value of each symbol. Each position in the number represents a power of 20, with the rightmost position being 20⁰, the next position to the left being 20¹, and so on.

The Mayan number given, : :|| :||, can be broken down as follows:

The leftmost position has no symbol, which represents a value of 0.

The second position from the left has two shell-like symbols (:), which represents a value of 2x20¹ = 40.

The third position from the left has two horizontal bars (||), which represents a value of 2x20⁰ = 2.

The given Mayan number in decimal (base 10) is 40 + 2 = 42.

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Complete question is:

Convert the following Mayan number to decimal (base 10).

: :|| :||

When the number of milligrams reaches 11, the drug is to be injected again. We need approximately 6.7 hours between injections.

The given function is D(h)=30[tex]e^{-0.35h[/tex], which gives the number of milligrams D(h) of the drug in the patient's bloodstream h hours after it is injected.

When the drug is injected again, the number of milligrams in the bloodstream will be 11. Therefore, we need to find the value of h that satisfies the equation:

11 = 30[tex]e^{-0.35h[/tex]

To solve for h, we can first divide both sides by 30:

11/30 = [tex]e^{-0.35h[/tex]

Next, we take the natural logarithm of both sides:

ln(11/30) = ln([tex]e^{-0.35h[/tex])

Using the property of logarithms that ln(eˣ) = x, we can simplify the right side:

ln(11/30) = -0.35h

Finally, we can solve for h by dividing both sides by -0.35 and multiplying by -1:

h = (-1/0.35)ln(11/30)

Using a calculator, we get:

h ≈ 6.7

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Answer:

C

Step-by-step explanation:

given

cosΘ = [tex]\frac{9}{15}[/tex] = [tex]\frac{adjacent}{hypotenuse}[/tex]

then to find the third side (opposite) use Pythagoras' identity

opposite² + 9² = 15²

opposite² + 81 = 225 ( subtract 81 from both sides )

opposite² = 144 ( take square root of both sides )

opposite = [tex]\sqrt{144}[/tex] = 12

then

tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{12}{9}[/tex]

a) the   proportion of even numbers in the population is 2/3 or approximately 0.667.

b. Sample Proportions and Probability Distribution Table is attched.

c) c. The mean of the sampling distribution of the sample proportion of even numbers is approximately 0.3333.

d. The sample poportion is a biased estimator of the population proportion because   the  sample proportions do not target the proportion of even numbers in   the population.

a. The population consists of 2, 6, and 7. The proportion of even numbers in the population is 1/3 since only 6 is even.

b. We can find the proportion of even numbers in each sample as follows:

2,2:   2/2 = 1

2,6: 1/2 = 0.5

2,7: 1/2  = 0.5

6,2: 1/2 =   0.5

6,6:   2/2 = 1

6,7: 1/ 2 = 0.5

7, 2: 1/2 = 0.5

7,6: 1/2 = 0.5

 7,7: 0/2   =0

This means that

   0 ⇒     1/9

  0.5⇒    5/9

   1  ⇒    3/9 (or 1/3)

So the above is summarized onto the table attached.

C)  The mean of the sampling distribution    of the sample proportion of even numbers is the weighted average of the possible values of the sample proportion,

where the weights are the probabilities of each value. Hence,

(0 x 1/9) +   (0.5 x 6/9 ) + (1 x 2/  9)

= 1/3

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The pitch of the roof is equal to 1.14

Since pitch of the roof is the angle between the roof and the horizontal line.

Pitch (slope) = V/H

Where, V represents the rising vertical distance of an object.

H represents the horizontal distance an object runs through.

Substituting the selected points into the formula, we have;

Pitch (slope) = 32/28

Pitch (slope) = 1.14

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This is correct. If M is a subset of N and N is a subset of P, then, M is a subset of P.

This follows from the transitivity of the subset relation. In set theory, the transitive property states that if a relation applies between elements A and B, and between elements B and C, then it also applies between elements A and C.

For the subset relation, if M is a subset of N (M ⊆ N), this means that every element in M is also an element of N. Similarly, if N is a subset of P (N ⊆ P), every element in N is also an element of P.

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Answer:

BFD

Step-by-step explanation:

Supplementary angles add to 180, or will form a straight line.

< AFB and angle BFD will form a straight line so they are supplementary.

The stem and leaf plot that correctly represents the data sets is

Stem    Leaf

0      |  0, 3        

1       |  7, 7, 7, 1, 7,

2      |  8, 8, 2, 4, 0. 0

3      |   3, 1,

Option B is the correct answer.

We have,

The following data set shows the values collected by the manager.

{17, 0, 28, 17, 17, 20, 28, 11, 17, 22, 24, 33, 20, 31, 20, 3}

Now,

We make the stem and leaf plot as:

Stem    Leaf

0      |  0, 3        

1       |  7, 7, 7, 1, 7,

2      |  8, 8, 2, 4, 0. 0

3      |   3, 1,

Here,

3 can be written as 03 and 0 can be written as 00.

Thus,

The stem and leaf plot that correctly represents the data sets is

Stem    Leaf

0      |  0, 3        

1       |  7, 7, 7, 1, 7,

2      |  8, 8, 2, 4, 0. 0

3      |   3, 1,

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The coordinates of the vertices for the image of the triangle are A(−3, 6), B(0, 10), and C(−3, 3)

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

Triangle ABC has vertices at A(−3, 3), B(0, 7), and C(−3, 0)

If the preimage is translated 3 units up, then the transformation rule is

(x, y) = (x, y + 3)

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

A(−3, 3 + 3), B(0, 7 + 3), and C(−3, 0 + 3)

Evaluate

A(−3, 6), B(0, 10), and C(−3, 3)

Hence, the coordinates of the vertices for the image are A(−3, 6), B(0, 10), and C(−3, 3)

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A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.

The symbols W and L are variables.

The symbol P is a constant.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + W)

52 = 2(12 + 14)

52 = 2(26)

52 feet = 52 feet.

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The quadratic equation has only one solution if m = 14

For a quadratic equation:

ax² + bx + c = 0

The discriminant is:

D = b² - 4ac

If the discriminant is zero, then the quadratic has only one solution, here we have the equation:

2x² - 28x + 7m = 0

Then the discriminant is:

D = (-28)^2 - 4*2*7m

Now we need to solve:

(-28)^2 - 4*2*7m = 0

784 - 56m = 0

Solving that for m:

784/56 = m

14 = m

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When an object turns 90 degrees around in a circle, it turns 1/4 of the way around in a circle. Therefore, the correct statement is: "It turns 1/4 of the way around in a circle."

To understand why an object turning 90 degrees around in a circle turns 1/4 of the way around in a circle, it's helpful to consider the relationship between angles and circles.

A circle is a geometric shape that is defined by a set of points that are equidistant from a center point.

The distance from the center point to any point on the circle is called the radius of the circle. The circumference of a circle is the distance around the circle, and it is equal to 2π times the radius.

A circle has a total angle of 360 degrees. When an object turns 90 degrees around in a circle, it covers only a quarter of the total angle.

Therefore, it turns 1/4 of the way around in a circle.

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Your question seems incomplete, the probable complete question is:

Which statement about an object turning 90 degrees around in a circle is true?

It turns 1/4 of the way around in a circle

It turns 2/4 of the way around in a circle

It turns 3/4 of the way around in a circle

It turns 4/4 of the way around in a circle

The exponential function representing the lifting time on day n is given as follows:

a(n) = 2^(n - 1).

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

On the first day, the time is of one minute, while the amount doubles each day, hence the parameters a and b are given as follows:

a = 1, b = 2.

We take the day one at the reference day, not day zero, meaning that the function was shifted right one unit, hence the rule is given as follows:

a(n) = 2^(n - 1).

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Answer:

5 + 1/x = 11/5

Podemos simplificar esta ecuación multiplicando ambos lados por 5x, lo que da:

25x + 5 = 11x

Ahora, podemos resolver x aislando la variable en un lado de la ecuación:

25x - 11x = -5

14x = -5

x = -5/14

Por lo tanto, la solución a la ecuación es x = -5/14

The solution for integrals are -1/3 (2 + cos² (x))[tex]^\frac{3}{2}[/tex]  +C

If we are finding the following integral below

∫ (√2 + (cos x)² / secx × cscx) dx instead of ∫ (√(2 + cos²x)) / (secx × csc) dx

then

secx = 1/cosx and cscx = 1/sinx

∫ (√(2 + cos²x)) × sinx × cosx dx

givn that sin²x + cos²x = 1

sin²x = 1 - cos²x

u = cosx,

du = -sinx dx.

-∫ (√u) / (2sinxcosx) du.

-√u + C.

When you substitute the original equation into the result

1/3 (2 + cos²x)^(3/2) + C.

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The test statistic is z₀ = 2.65 and the P-value is 0.004. The null hypothesis is rejected at the 5% level of significance, and we conclude that there is sufficient evidence to suggest that the true proportion is greater than 0.8.

To test the hypothesis using the P-value approach, we can follow these steps:

Check whether the sample size is large enough for the normal approximation to the binomial distribution. The requirements are satisfied if np₀ >= 10 and n(1-p₀) >= 10,

where p₀ is the hypothesized proportion under the null hypothesis. In this case, p₀ = 0.8, n = 125, so np₀ = 100 and n(1-p₀) = 25, both of which are greater than 10.

Set up the null and alternative hypotheses.

The null hypothesis is H₀: p = 0.8 (the true proportion is 0.8).

The alternative hypothesis is H₁: p > 0.8 (the true proportion is greater than 0.8).

Calculate the test statistic.

Under the null hypothesis, the test statistic follows a standard normal distribution.

The test statistic is calculated as:

z₀ = (x - np₀) / sqrt(np₀(1-p₀))

where x is the number of successes in the sample.

Plugging in the values, we get:

z₀ = (105 - 1250.8) / √(1250.8 x 0.2)

z₀ = 2.65

Calculate the P-value.

The P-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample, assuming the null hypothesis is true.

Since this is a right-tailed test (H₁: p > 0.8), we calculate the area to the right of the test statistic.

Using a standard normal table or calculator, we find that the area to the right of z₀= 2.65 is 0.004.

Therefore, the P-value is 0.004.

Make a decision and interpret the results.

Using a significance level of α = 0.05, we compare the P-value to α.

Since the P-value (0.004) is less than α (0.05), we reject the null hypothesis.

We conclude that there is sufficient evidence to suggest that the true proportion is greater than 0.8 at a 5% level of significance.

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The mean of the data set is 3.33.

The variance of the data set is 0.47.

We have,

To find the mean of the data set,

We need to add up all the numbers and divide by the total number of values:

Mean = (2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 4) / 9

= 3.33 (rounded to two decimal places)

To find the variance,

We need to first find the squared difference between each value and the mean:

(2 - 3.33)^2 = 1.11

(2 - 3.33)^2 = 1.11

(3 - 3.33)^2 = 0.11

(3 - 3.33)^2 = 0.11

(3 - 3.33)^2 = 0.11

(4 - 3.33)^2 = 0.44

(4 - 3.33)^2 = 0.44

(4 - 3.33)^2 = 0.44

(4 - 3.33)^2 = 0.44

Next, we need to find the average of these squared differences:

Average of squared differences

= (1.11 + 1.11 + 0.11 + 0.11 + 0.11 + 0.44 + 0.44 + 0.44 + 0.44) / 9

= 0.47 (rounded to two decimal places)

Thus,

The mean of the data set is 3.33.

The variance of the data set is 0.47.

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Answer:

The amount of air needed to fill the basketball is approximately 533.16 cubic inches

Step-by-step explanation:

To find the amount of air needed to fill a basketball, we need to first calculate its volume. We can use the formula for the volume of a sphere, which is V = (4/3)πr^3, where π is approximately 3.14 and r is the radius of the sphere.

Since the diameter of the basketball is given, we need to first find the radius by dividing the diameter by 2:

r = 9.45 in / 2 = 4.725 in

Now we can plug in the value of r into the formula for the volume:

V = (4/3)πr^3 = (4/3)π(4.725 in)^3 = 533.16 in^3

Therefore, the amount of air needed to fill the basketball is approximately 533.16 approx cubic inches.

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The area of the rectangle is 81 square units. (option a)

To find the area of a rectangle, we need to know its length and width. We can determine these values by looking at the difference between the x-coordinates and the y-coordinates of the vertices.

In this case, we have the following coordinates: (-4,5), (5,5), (-4,-4), and (5,-4).

The length of the rectangle is the difference between the x-coordinates of the left and right vertices:

=> 5 - (-4) = 9.

The width is the difference between the y-coordinates of the top and bottom vertices:

=> 5 - (-4) = 9.

To find the area of the rectangle, we multiply its length by its width:

=> 9 x 9 = 81.

So, the correct answer is the (a), 81 square units.

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