1.1.3 Quiz: Exponents
Question 2 of 10
Simplify (6^7)³.

Answer:

We use thales theorem

Therfore the answer is 34

The equation given is A(t) = 10,250(1 + r 0.04/12)^120. To solve for the value of the account, we need to calculate the right side of the equation. First, we need to calculate the exponent of 1+r 0.04/12. This is equal to 120, so the exponent is 120. Next, we need to multiply 10,250 by the exponent of 1+r 0.04/12. This will give us the value of the account. The answer is 1,895,167.50.

Answer:

i have solved it step by step

Answer:

The answer is x+9, I really hope this helps (:

a. The cost of one large pizza with one topping is $13.50. To purchase one large and five medium pizzas, we would need to buy one large pizza at regular price and five medium pizzas at the discounted price. The cost of the large pizza is $13.50, and the cost of each medium pizza is $6.25. Therefore, the total cost would be:

Total cost = Cost of large pizza + Cost of 5 medium pizzas

Total cost = $13.50 + ($6.25 x 5)

Total cost = $13.50 + $31.25

Total cost = $44.75

Therefore, it would cost $44.75 to purchase one large pizza and five medium pizzas.

b.Number of medium pizzas Total cost

0 | $13.50

1 | $19.75

2 | $26.00

3 | $32.25

4 | $38.50

c. Let "m" be the number of medium pizzas. Then the total cost of purchasing one large pizza with one topping and m medium pizzas can be represented as:

Total cost = 13.50 + 6.25m

d. If you have a total of $100 and purchase one large pizza, you would have $100 - $13.50 = $86.50 left to spend on medium pizzas. The cost of each medium pizza is $6.25. Therefore, you can buy:

Number of medium pizzas = $86.50 ÷ $6.25 = 13.84

Since you cannot buy a fraction of a pizza, you can only buy 13 medium pizzas with $86.50.

e. The area of a pizza is given by the formula A = πr^2, where A is the area and r is the radius. The area of a large pizza is:

A = πr^2

A = 3.14 x 8^2

A = 3.14 x 64

A = 200.96

The area of a medium pizza is:

A = πr^2

A = 3.14 x 5^2

A = 3.14 x 25

A = 78.5

Therefore, the total area of one large pizza and five medium pizzas is:

Total area = Area of large pizza + (Area of medium pizza x 5)

Total area = 200.96 + (78.5 x 5)

Total area = 200.96 + 392.5

Total area = 593.46

Rounding to the nearest inch, the total area of pizza is 593 square inches.

f. To calculate the cost per square inch of pizza, we need to divide the total cost of the pizzas by the total area of the pizzas. The total cost of one large pizza and five medium pizzas is $44.75, and the total area is 593 square inches. Therefore, the cost per square inch of pizza is:

Cost per square inch = Total cost / Total area

Cost per square inch = $44.75 / 593

Cost per square inch = $0.08 (rounded to the nearest cent)

Therefore, the cost per square inch of pizza is 8 cents.

The measure of angle O is 56 and the value of m and n are 8.1 in and 14.5 in respectively.

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The longest side is hypotenuse and it is the side facing the right angle. The other two sides are opposite and adjascent.

sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan,(tetha) = opp/adj

angle O = 180-(90+34)

= 180- 124

= 56°

To find m,

Tan 34 = m/12

m = Tan34 × 12

m = 8.1 in

using Pythagoras theorem to find n,

n= √8.1²+12²

n = √65.61+144

n = √209.61

= 14.5 in

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Parabola intersects x-axis at two points: (-5,0) and (-4,0)

What does a parabola actually mean?

Each point on a parabola with a U-shape is equally spaced from both the focus, a fixed point, and the directrix, a fixed line. As the topic of conic sections depends heavily on the parabola, all of the parabola-related concepts are covered here.

The x-intercepts of a parabola are where the parabola intersects the x-axis on its graph. There are a number of ways to find the x-intercepts of a parabola, and each one is usually specific to each situation.

In the case, when you are given the graph, the easiest way to find x-intercepts is to identify points at which parabola intersects the x-axis.

From your graph, parabola intersects x-axis at two points: (-5,0) and (-4,0)

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Answer:

f(-2) = 0

Step-by-step explanation:

f(x) = (2x+4)/6 is a "rule" or like, directions. It says take your number, times by 2, add 4 and then divide by 6.

f(-2) just means to put -2 in place of x. Do the "rule" or follow the directions on the number -2.

f(x) = (2x+4)/6

f(-2) = (2•-2 + 4)/6

= (-4+4)/6

= 0/6

= 0

So f(-2) = 0

Answer:

[tex]3^2-5[/tex]

Step-by-step explanation:

    Given equation:

 ( 3 - 2^2) + 5

  3 - 4 + 5   (Simplify exponent)

 -1 + 5  (Solve 3 - 4)

  4 (Simplified)

Evaluation

2^2 + 5

4 + 5

9 (not the answer)

3^2 - 5

9-5

4  (answer)

The values of the variables in the semicircle shown are:

x = 63 degrees; y = 90 degrees.

A semi-circle is exactly half of a full circle and has a measurement of 180 degrees; the two endpoints of the diameter form the endpoints of the semi-circle. If an angle is enclosed inside a semi-circle, the angle formed measures 90 degrees.

Therefore, it means the value of the variable, y = 90 degrees.

Thus, using the triangle sum theorem, we have:

x = 180 - 90 - 27

x = 63 degrees.

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The Iength οf the diagοnaI οf the square exteriοr waII shοuId be 15 feet.

Accοrding tο the Pythagοrean theοrem, the square οf a right triangIe's hypοtenuse (the side οppοsite the right angIe) equaIs the sum οf its οther twο sides' squares.

Outside waII's Iength and width are equaI if it is a square. Let's caII this Iength "x"

Using the Pythagοrean theοrem, we can find the Iength οf the diagοnaI οf the square:

diagοnaI² = height² + width²

Since the height is 9 ft and οne side οf the square is 12 ft, we can write:

diagοnaI² = 9² + 12²

diagοnaI² = 81 + 144

diagοnaI² = 225

Taking the square rοοt οf bοth sides, we get:

diagοnaI = √(225)

diagοnaI = 15 ft

Therefοre, the Iength οf the diagοnaI οf the square exteriοr waII shοuId be 15 feet.

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Answer: d

Step-by-step explanation: its d

Answer: 1050$

Step-by-step explanation:

im a math teacher

Answer:

20.8

Step-by-step explanation:

Let h be the height of the ladder. We know that the distance BC is 8 ft, and the angle of elevation BAC is 69 degrees. Therefore, we have:

tan(69) = h/8

Multiplying both sides by 8, we get:

8*tan(69) = h

Using a calculator, we get:

h ≈ 20.8 ft

Therefore, the height of the top of the ladder from the ground is approximately 20.8 feet.

Answer:

Step-by-step explanation:

A. 125

Answer:

5.5

Step-by-step explanation:

The median is the middle number in an ordered ascending/descending list.

The first step is to order the list. In this case I chose to do so in ascending order.

This gets you:

2 3 3 4 5 6 6 6 7 9

In this case there is an even amount of numbers, which means there will be 2 central numbers, 5 and 6.

Averaging these two numbers will get you the median.

(5+6) / 2 = 5.5

Answer:

Σ Kinetic energy of 5 kg rock hitting car > Σ Kinetic energy of 10 kg rock hitting car

Step-by-step explanation:

We can use the formula for kinetic energy, which is:

Kinetic energy = (1/2) x mass x velocity^2

Let's start by calculating the kinetic energy of the 5 kg rock hitting the car at 25 m/s:

Kinetic energy = (1/2) x 5 kg x (25 m/s)^2

Kinetic energy = 1562.5 J

Now let's calculate the kinetic energy of the 10 kg rock hitting the car at 15 m/s:

Kinetic energy = (1/2) x 10 kg x (15 m/s)^2

Kinetic energy = 1125 J

Therefore, the 5 kg rock hitting the car at 25 m/s has more kinetic energy than the 10 kg rock hitting the car at 15 m/s.

We can represent this visually using the following equations:

Kinetic energy of 5 kg rock hitting car = (1/2) x 5 kg x (25 m/s)^2 = 1562.5 J

Kinetic energy of 10 kg rock hitting car = (1/2) x 10 kg x (15 m/s)^2 = 1125 J

Σ Kinetic energy of 5 kg rock hitting car > Σ Kinetic energy of 10 kg rock hitting car

The formula for the future value of an annuity is FV = Pmt * (((1 + r)n - 1) / r) to calculate the balance of the IRA at age 65. To compare this amount to the total deposits made over the time period, Total Deposits = Pmt * n = $45,600.

To calculate the balance of the IRA at age 65, we need to use the formula for the future value of an annuity:

FV = Pmt * (([tex](1 + r)^n[/tex] - 1) / r)

Where:

Pmt = $95 (the monthly deposit amount)

r = 4% / 12 = 0.003333 (the monthly interest rate)

n = (65 - 25) * 12 = 480 (the total number of months, assuming retirement at age 65)

Plugging in these values, we get:

FV = 95 * (([tex](1 + 0.003333)^480[/tex] - 1) / 0.003333)

FV = $98,052.52

Therefore, the IRA will contain $98,052.52 at age 65.

Part 2

To compare this amount to the total deposits made over the time period, we can calculate the total deposits as:

Total Deposits = Pmt * n

Plugging in the values, we get:

Total Deposits = 95 * 480

Total Deposits = $45,600

Therefore, the IRA will contain significantly more than the total deposits made over the time period, due to the power of compounding interest.

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Answer:

24x - 6y + 21

Step-by-step explanation:

3( 8x - 2y + 7 )

Multiply each term in the bracket by 3

= (3 x 8x) - ( 3 x 2y) + (3 x 7)

= 24x - 6y + 21

The maximum revenue is achieved when she sells 33 photos at a price of 25 per photo.

Using quadratic regression, [tex]y = ax^2 + bx + c[/tex]

where a, b and c are constants and x is the independent variable we can determine the equation of the curve that best fits the data. The equation will be in the form of[tex]y = ax^2 + bx + c[/tex], where y is the revenue, x is the number of photos sold, and a, b, and c are constants. The constants can be determined by solving the system of equations formed by the three data points.

After solving for the constants, we can determine the maximum revenue by finding the vertex of the curve. The vertex is located at x = -b/2a, and the corresponding revenue is[tex]y = ax^2 + bx + c[/tex]. Plugging in the values for a, b, and c, we can calculate that the maximum revenue is achieved when she sells 33 photos at a price of 25 per photo.

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Complete question

Darlena has started taking photos at amateur dog racing events, later offering the photos for sale to the dog owners by email. The prices she has charged per photo at each of her first three events, and the corresponding number of photos sold and total revenue raised, appear in the table below. Treating revenue as a function of the number of photos sold, a graph of the three data points is also shown. If she uses quadratic regression to fit a curve to the data, what number of photos sold and what price per photo will maximize her revenue?

The statement which best describe the correct null and alternative hypotheses, the test statistic, and conclusion at a significance level of 0.05 is:

D. H₀: μ₁ = μ₂ H₁: μ₁ < μ₂.

test statistic, t = -1.5625.

conclusion: fail to reject the null hypothesis μ₁ = μ₂.

Based on the information provided, the appropriate null hypothesis and alternative hypothesis would be represented by the following mathematical expression:

H₀: μ₁ - μ₂ ≤ 0; μ₁ = μ₂

H₁: μ₁ - μ₂ < 0; μ₁ < μ₂.

For the critical value, we have:

Critical probability (p*) = 1 - α

Critical probability (p*) = 1 - 0.05

Critical probability (p*) = 0.9500.

Based on the distribution table for probabilities, a value that corresponds to 0.9500 can be calculated as follows;

Zα = 1.6 + 0.05 = 1.65.

For an upper-tailed test, the critical value is given by;

Z_{critical} = 1.65.

Therefore, if Z_{test} > 1.65; reject null hypothesis (H₀) and if Z_{test} < 1.65; fail to reject null hypothesis (H₀).

Next, we would determine the test statistic:

[tex]Z_{test} = \frac{116 -121 -0}{\sqrt{\frac{16^2}{50} +\frac{16^2}{50} } } \\\\Z_{test} = \frac{-5}{\sqrt{\frac{256}{50} +\frac{256}{50} } }\\\\Z_{test} = \frac{-5}{\sqrt{10.24} }[/tex]

Z_{test} = -5/3.2

Z_{test} = -1.5625

In conclusion, we would fail to reject null hypothesis (H₀) since a Z_{test} of -1.5625 is less than a Z_{critical} of 1.65.

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(1, 3) is not a solution to the system of linear equations and (2,1) is a solution to the system of linear equations.

What are linear equations?

To check if the ordered pair (1, 3) is a solution to the system of linear equations:

2x + y = 5 ...(1)

−3x + 5y = −1 ...(2)

Substitute x = 1 and y = 3 in equations (1) and (2), respectively:

2(1) + 3 = 5 ...(1)

−3(1) + 5(3) = −1 ...(2)

Simplifying these equations:

2 + 3 = 5 (true)

−3 + 15 = −1 (false)

Therefore, (1, 3) is not a solution to the system of linear equations.

To check if the ordered pair (2,1) is a solution to the system of linear equations:

2x + y = 5 ...(1)

−3x + 5y = −1 ...(2)

Substitute x = 2 and y = 1 in equations (1) and (2), respectively:

2(2) + 1 = 5 ...(1)

−3(2) + 5(1) = −1 ...(2)

Simplifying these equations:

4 + 1 = 5 (true)

−6 + 5 = −1 (true)

Therefore, (2,1) is a solution to the system of linear equations.

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An angle is  a geometric figure formed by two rays or line segments that share  a common endpoint, called the vertex. Angles are measured in degrees or radians and are typically denoted by  symbol ∠ followed by the name of the vertex, like ∠ABC.

The size of angle is determined by  amount of rotation needed to bring one of  rays or line segments into coincidence with others.

Angles can be acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees but less than 180 degrees), straight (exactly 180 degrees), or reflex (greater than 180 degrees).

Angles are fundamental to geometry and have many applications in physics, engineering, and other fields.

This is because the sum of the angles in a triangle must always be 180°, and 40° + 60° + 80° = 180°.

However, the angles do not satisfy the conditions of the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Therefore, It is not possible to construct a triangle with angle measures of 40°, 60°, and 80°.

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Answer:

C)  2, 7, 6 can form a triangle.

Step-by-step explanation:

The triangle inequality theorem states that the sum of any two sides of a triangle is greater than the length of the third side.

To determine which group of given side measures will form a triangle, sum each pair of sides and compare to the third side. If all three inequalities are true, the group will form a triangle.

Given side lengths: 9, 4, 3

  ⇒ 9 + 4 > 3

  ⇒ 9 + 3 > 4

  ⇒ 4 + 3 [tex]\ngtr[/tex] 9

Therefore, this group cannot form a triangle.

Given side lengths: 8, 1, 7

  ⇒ 8 + 1 > 7

  ⇒ 8 + 7 > 1

  ⇒ 1 + 7 [tex]\ngtr[/tex] 8

Therefore, this group cannot form a triangle.

Given side lengths: 2, 7, 6

  ⇒ 2 + 7 > 6

  ⇒ 2 + 6 > 7

  ⇒ 7 + 6 > 2

Therefore, this group can form a triangle.

Given side lengths: 12, 10, 22

  ⇒ 12 + 10  [tex]\ngtr[/tex] 22

  ⇒ 12 + 22 > 10

  ⇒ 10 + 22 > 12

Therefore, this group cannot form a triangle.

Answer: I'm not really sure what the question is but the volume is 224

Step-by-step explanation:

We can be 90% confident that the true proportion of all students who saw a film at the movie theater in the last 30 days is between 0.277 and 0.473.

What is proportion?

Proportion is a mathematical term that represents a relationship between two quantities or numbers. It refers to the comparison of one part of a whole to the whole itself.

To find a confidence interval for the proportion p of all students who saw a film at the movie theater, we can use the formula:

CI = p ± z * √(p(1-p)/n)

where p is the sample proportion, n is the sample size, z is the z-score corresponding to the desired level of confidence (90% in this case), and √(p(1-p)/n) is the standard error of the proportion.

First, we need to find the sample proportion p:

p = 37.5% = 0.375

Next, we need to find the z-score corresponding to a 90% confidence level. We can use a z-table or a calculator to find this value. The z-score for a 90% confidence level is 1.645.

Now we can plug in the values into the formula:

CI = 0.375 ± 1.645*√(0.375(1-0.375)/64)

Simplifying:

CI = 0.375 ± 0.098

Therefore, the 90% confidence interval for the proportion of all students who saw a film at the movie theater in the last 30 days is:

CI = (0.277, 0.473)

Hence, we can be 90% confident that the true proportion of all students who saw a film at the movie theater in the last 30 days is between 0.277 and 0.473.

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Using a trigonometric relation, we can see that the values of x and y are:

y = 25.98

x = 15

Here we can see a right triangle, where we know the interior angles and the length of the hypotenuse.

To get the lengths of the legs, we can use trigonometric relations, like:

cos(a) =(adjacent cathetus)/hypotenuse.

For example, if we want to find y, then the angle at which this side is adjacent is the 30° one, now replacing the known values in the formula we will get:

cos(30°) = y/30

cos(30°)*30 = y = 25.98

And to get the value of x, we should use the 60°angle, so:

cos(60°) = x/30

30*cos(60°) = x =  15

These are the two lengths we wanted to get.

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No, if fit indicates that the bookcase's sides must be flush with the wall, which means that they must touch the wall and that the bookshelf is correctly positioned in that location.

A triangle is a polygon with three edges and three vertices.

It belongs to the basic geometric shapes.

A triangle having vertices A, B, and C is known as triangle ABC.

Any three locations in Euclidean geometry that are not collinear result in a distinct triangle and a distinct plane.

I've discovered that using the 3:4:5 triangle is the simplest way to determine for sure if an angle is 90 degrees.

This rule states that a triangle is a right triangle even if one of its sides is 3 and the other is 4 if the diagonal connecting its two points measures 5.

So, we must check to see if any of the bookcase's vertices measure 90 degrees because a square room will naturally have corners that do.

We may utilize Pythagorean Theorem to find the solution because every right triangle contains a 90° angle.

Pythagorean The a, b, and c are the legs, and the theorem states that a² + b² = c².

For our bookshelf, 10 and 12 are the legs, and 18 would be the hypotenuse if it were a right triangle as the hypotenuse is always the longest side.

To determine whether the equation is true or false, enter the values.

10² + 12² = 18²

100 + 144 = 324

244 ≠ 324

Thus, the bookshelf does not form a straight angle and cannot be placed in the room's corner.

Therefore, no, if fit indicates that the bookcase's sides must be flush with the wall, which means that they must touch the wall and that the bookshelf is correctly positioned in that location.

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Correct question:

A triangular bookshelf has a base of 10 inches,12 inches, and 18 inches. Will the bookshelf fit in the corner of a square living room?