5) Stacy ran 8 miles. She
recorded how long it took her to run each mile in minutes. How many times did Stacy run her fastest mile?

The height of the square pyramid is approximately 91.92 inches.

In a square pyramid, the slant height (s) is the hypotenuse of a right triangle formed by the height (h), half the length of the base (b/2), and the slant height (s). We can express this relationship as:

[tex]s^2 = (b/2)^2 + h^2[/tex]

Given that the length of one side of the base (b) is 25.2 in and the slant height (s) is 93.7 in, we can substitute these values into the equation:

[tex]93.7^2 = (25.2/2)^2 + h^2[/tex]

Simplifying:

[tex]8761.69 = 316.8 + h^2[/tex]

Subtracting 316.8 from both sides:

[tex]h^2 = 8444.89[/tex]

Taking the square root of both sides:

h ≈ 91.92 in

Therefore, the height of the square pyramid is approximately 91.92 inches.

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The unknown angle measure is 70 degrees.

We are given that;

The values 40° 70° 110° 180°

Now,

One possible equation to find the unknown angle measure is:

180 - 40 - 70 = ?

This equation is based on the fact that the sum of the angles in a triangle is 180 degrees. To solve for ?, we can subtract 40 and 70 from both sides of the equation:

180 - 40 - 70 = ? - 40 - 70 180 - 110 = ? 70 = ?

The solution is ? = 70 degrees.

Therefore, by equation the answer will be 70 degrees.

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The complete solution to the system is 25/17, 61/17, 2/17 respectively.

Using the Gauss-Jordan elimination method to find the solution of the system of linear equations represented by the given augmented matrix:

Starting matrix:

[1 -2/3 -1/3 | 1]

[1 -2 6 | -17]

[-3 -7 3 | -43]

Add Row 1 to Row 2 and Row 3:

[1 -2/3 -1/3 | 1]

[0 -4/3 17/3 | -18]

[0 -1 0 | -40]

Multiply Row 2 by -3/4:

[1 -2/3 -1/3 | 1]

[0 1 -17/4 | 27/2]

[0 -1 0 | -40]

Add Row 1 to Row 2 and Row 3:

[1 0 -7/4 | 19/2]

[0 1 -17/4 | 27/2]

[0 0 -17/4 | -13/2]

Multiply row 3 by -4/17:

[1 0 -7/4 | 19/2]

[0 1 -17/4 | 27/2]

[0 0 1 | 2/17]

Add Row 3 to Row 1 and Row 2:

[1 0 0 | 25/17]

[0 1 0 | 61/17]

[0 0 1 | 2/17]

Therefore, the solution of the system of linear equations is:

x = 25/17

y = 61/17

z = 2/17

So the solution is [25/17, 61/17, 2/17].

Thus the completed augmented matrix is:

[1 0 0 | 25/17]

[0 1 0 | 61/17]

[0 0 1 | 2/17]

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Answer:

Yes, (s + t)^2 is equivalent to s^2 + 2st + t^2. This can be shown through the process of expanding the expression (s + t)^2 using the FOIL method (multiplying first, outer, inner, and last terms).

First, we can rewrite (s + t)^2 as (s + t)(s + t).

Now, we do the multiplication and combine like terms:

s*s + s*t + t*s + t*t

s^2 + st + st + t^2

s^2 + 2st + t^2

The distance from the bottom of the building to the point where the ladder is touching the building for triangle 2, obtained using trigonometric ratio of tangent is 12 feet. The correct option is therefore;

12 feet

The trigonometric ratios are the value relationship between an interior angle of a right triangle and two of the sides of the triangle.

The right triangles are similar, therefore, the tangent of the angle the ladder makes with the ground are the same, which indicates;

tan(θ) = (Length of the side facing the angle θ) ÷ (Length of the side adjacent to the angle θ)

The side facing the angle is the distance from the bottom to the point where the ladder touches the building.

The adjacent to the angle is the horizontal distance from the bottom to the ladder to the building.

Therefore; tan(θ) = 18/12 = x/8

Where x = The distance from the bottom of the building to the point the ladder touches the building for triangle 2

18/12 = x/8

x = 18/12 × 8 = 12

The distance, x = 12 feet

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Answer:

12?

Step-by-step explanation:

I'm not too sure! I am in the middle of taking the test right now.

When t = 0, the value of n is approximately 3.93 million. The estimated number of people who moved to another state in 2005 is approximately 1.68 million. The predicted number of people who moved to another state in 2014 is approximately 6.81 million.

we need to substitute the given values of t (years since 1990) into the equation n = 0.03t² - 0.6t + 3.93. Let's calculate the values accordingly:

a. When t = 0 (which corresponds to the year 1990), we substitute this value into the equation:

n = 0.03(0)² - 0.6(0) + 3.93

n = 0 + 0 + 3.93

n ≈ 3.93

So, when t = 0, the value of n is approximately 3.93 million. In this context, it means that in the year 1990, around 3.93 million people moved to another state.

b. To estimate the number of people who moved to another state in 2005 (t = 2005 - 1990 = 15), we substitute this value into the equation:

n = 0.03(15)² - 0.6(15) + 3.93

n = 0.03(225) - 9 + 3.93

n = 6.75 - 9 + 3.93

n ≈ 1.68

Therefore, the estimated number of people who moved to another state in 2005 is approximately 1.68 million.

c. To predict the number of people who moved to another state in 2014 (t = 2014 - 1990 = 24), we substitute this value into the equation:

n = 0.03(24)² - 0.6(24) + 3.93

n = 0.03(576) - 14.4 + 3.93

n = 17.28 - 14.4 + 3.93

n ≈ 6.81

Hence, the predicted number of people who moved to another state in 2014 is approximately 6.81 million.

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The trend line that best fits the data in this problem is given by the following option:

Option D.

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

Hence the graph of the line of best fit should have the smallest possible residual values, meaning that the points on the scatter plot are the closest possible to the line.

As option D has the points the closest to the line, it is the correct option in the context of this problem.

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Answer:

90Y + 36

Step-by-step explanation:

just multiply the length by the width.

9 X (8y + 4 + 2y)

= 9 X (10y + 4)

= 90Y + 36

The correct probability from the two-way table is given as follows:

B. P(120 lb | 2,000 - 2,500 cal) is different of P(120 lb).

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Then the probabilities are given as follows:

Hence statement B is true.

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Factor of x ^2+7x−18 is (x−2)(x+9).

We have,

In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

We are given a polynomial expression in terms of variable x as:

x² - 7x + 18

so, we have,

x ^2+7x−18

=x ^2−2x+9x−18

=x(x−2)+9(x−2)

=(x−2)(x+9)

∴ x ^2+7x−18=(x−2)(x+9)

Hence, Factor of x ^2+7x−18 is (x−2)(x+9)

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complete question:

Factor completely x² - 7x + 18.

Prime

(x-9)(x-2)

(x-9)(x+2)

(x + 9)(x+2)

Answer:

Step-by-step explanation:

X is the horizontal line and Y is the vertical line. :)

The missing measurements on the triangle are given as follows:

m < H = 65º, y = 32.2, c = 35.5.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

The sum of the internal angle measures of a triangle is of 180º, hence the measure of angle H is given as follows:

m < H + 25 + 90 = 180

m < H = 65º.

Regarding the angle of 25º, we have that 15 is the opposite side, while y is the adjacent side, hence the measure of y is given as follows:

tan(25º) = 15/y

y = 15/tangent of 25 degrees

y = 32.2.

Applying the Pythagorean Theorem, the value of c is obtained as follows:

c² = 15² + (32.2)²

[tex]c = \sqrt{15^2 + 32.2^2}[/tex]

c = 35.5.

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The ratios associated to the line segment QR are QP : PR = 1 : 4 and QP : QR = 1 : 5.

In this problem we find a line segment defined by points Q(x, y) = (1, 7) and R(x, y) = (- 9, - 8) and whose partition point is P(x, y) = (- 1, 4), whose ratios must be found. First, find the lengths of line segments QP and PR by Pythagorean theorem:

QP = √[(- 1 - 1)² + (4 - 7)²]

QP = √[(- 2)² + (- 3)²]

QP = √13

PR = √[[- 9 - (- 1)]² + (- 8 - 4)²]

PR = √[(- 8)² + (- 12)²]

PR = 4√13

QR = 5√13

Second, determine the ratios:

QP : PR = √13 : 4√13

QP : PR = 1 : 4

QP : QR = √13 : 5√13

QP : QR = 1 : 5

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Answer:

1,000 - 50x > 600

-50x > -400

$0.00 < x < $8.00

1. In the short run, the firms in the competitive industry will earn positive profits because the market price is higher than the minimum of the average cost curve. The Option A.

2. If the market price is P4, the individual firm in a competitive industry will earn zero profit. The Option B

3. Firm would be encouraged to enter this market for all price that exceeds P4. The Option D,

When the market price is between P4 and P6, firms in a competitive industry are able to earn positive profits in the short run because the price is above their average variable cost (AVC) but below their average total cost (ATC).

This means that firms are covering their variable costs and also making a contribution towards their fixed costs. As a result, they are earning positive profits. But, in the long run the firms will enter the industry and increase supply causing market price to decrease towards P4 where firms earn zero economic profits in the long run.

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The measure of the angle BCA is 50 degrees.

The angles at the circumference subtended by the same arc are equal.

The angles at the circumference on the same segment theorem states that angles in the same segment of the circle are equal.

Therefore, let's use the theorem to find the angle ∠BCA in the circle.

Hence,

∠BCA = ∠BOA

Finally,

∠BCA =  50 degrees.

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The probability of just thunder is 0.196.

We have,

The probability of rain P(A) = 1/2

The probability of thunder and raining P(A ∩ B) = 1/3

The probability of rain and thunder P(A U B) = 11/30

Now,

Using the addition rule of probability.

P(A U B) = P(A) + P(B) - P(A∩B)

Substituting.

11/30 = 1/2 + P(B) - 1/3

11/30 - 1/2 + 1/3 = P(B)

P(B) = 0.196

The probability of just thunder is 0.196.

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The graph of its image after the composition is shown in graph.

We have to given that;

XY with endpoints are,

⇒ X (-3, 1) and Y (4,-5)

Now, After Translation (x, y)→(x, y + 2) we get;

X = (- 3, 1)

X' = (- 3, 1 + 2) = (- 3, 3)

Y = (4, - 5)

Y' = (4, - 3)

And, After Rotation: 90° about the origin.

That is, (x, y) = (y, - x)

The points of image are,

X'' = (3, 3)

Y'' = (- 3, - 4)

Thus, The graph of its image after the composition is shown in graph.

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The perimeter of the square that is given in the diagram above would be = 96cm

To calculate the perimeter of a square, the formula for the perimeter of a square should be used and this is given below.

That is ;

perimeter = 4a

where ;

a = side length = 24cm

Perimeter = 4× 24 = 96cm

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Given two points (7,-2) and (-3,-10), we can determine the slope of the line passing through them as follows:

slope = (y2 - y1) / (x2 - x1)

slope = (-10 - (-2)) / (-3 - 7)

slope = -8 / -10

slope = 4 / 5

Since we want a line perpendicular to this line, we need to find its negative reciprocal. The negative reciprocal of 4/5 is -5/4.

Now that we have the slope of the perpendicular line, we can use the point-slope form of a line to find its equation. The point-slope form is:

y - y1 = m(x - x1)

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

Using the point (-8,-12), we can substitute the values into the equation:

y - (-12) = -5/4(x - (-8))

y + 12 = -5/4(x + 8)

Simplifying, we get:

y + 12 = -5/4x - 10

y = -5/4x - 22

Therefore, the equation of the perpendicular line passing through the point (-8,-12) is y = -5/4x - 22 in point-slope form.

The dimensions of the rectangular horse pen are 40 feet (width) and 42 feet (length).

The area of a rectangle is expressed as:

Area = length × width

Given that,  the length of the pen will be 2 feet longer than the width, so the width is x feet and the length can be expressed as (x + 2) feet.

Using area of rectangle:

Area = length × width

1680 = (x + 2) × x

Simplify

1680 = x² + 2x

x² + 2x - 1680 = 0

Solve for x:

Using factoring

(x + 42)(x - 40) = 0

Hence:

x + 42 = 0 or x - 40 = 0

x = -42 or x = 40

Since we are dealing with dimensions, we use the positive value:

The valid solution is x = 40.

This represents the width of the horse pen.

The length can be found by adding 2 to the width:

Length = x + 2

Plug in x = 40

= 40 + 2

= 42

Therefore, the length is 42 feets.

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Answer:

The number of ways to construct a string of 4 digits without repetition can be found using the permutation formula.

The formula for finding the number of permutations of n objects taken r at a time without repetition is:

P(n, r) = n! / (n - r)!

Where n is the total number of objects and r is the number of objects being chosen.

In this case, we have 10 digits (0-9) to choose from, and we need to choose 4 digits without repetition. Therefore, the number of ways to construct a string of 4 digits without repetition is:

P(10, 4) = 10! / (10 - 4)!

P(10, 4) = 10! / 6!

P(10, 4) = (10 × 9 × 8 × 7) / (4 × 3 × 2 × 1)

P(10, 4) = 10,080

Therefore, there are 10,080 ways to construct a string of 4 digits without repetition using the digits 0-9.

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The earthquake registered 3.6 on the Richter scale.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function for this problem is given as follows:

R = log(A/0.0001)

The amplitude of the earthquake was of 0.3954, hence the magnitude of the earthquake is obtained as follows:

R = log(0.3954/0.0001)

R = 3.6.

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A) The total amount of the repair that is covered by the insurance is $2970.

B) He would need to pay $2000.

C) The insurance company will have to pay $2750.

A) To calculate the total amount of the repair that is covered, we need to consider the deductible and the 8% tax.

The repair cost before tax is $4750. Since the insurance adjuster approves any repairs, the deductible of $2000 needs to be subtracted from the repair cost.

Repair cost after deductible = $4750 - $2000 = $2750.

Now, we need to add the 8% tax to the repair cost after deductible.

Tax amount = 8% of $2750 = $2750 * 0.08 = $220.

Total amount of the repair that is covered = Repair cost after deductible + Tax amount

Total amount of the repair that is covered = $2750 + $220 = $2970.

Therefore, the total amount of the repair that is covered by the insurance is $2970.

B) If John has had no previous claims in the past year, he would be responsible for paying the deductible amount. In this case, John's deductible is $2000. So, he would need to pay $2000.

C) The insurance company will be responsible for paying the remaining amount after the deductible has been paid. In this case, the remaining amount is the total repair cost minus the deductible.

Amount insurance company has to pay = Total repair cost - Deductible

Amount insurance company has to pay = $4750 - $2000 = $2750.

Therefore, the insurance company will have to pay $2750.

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