Luke is keeping track of the total number of hours he exercises. He started the summer having already put in 15 hours, and he then exercises 7 hours each week. The function to keep track of his exercise is f(x) = 7x + 15. What do the f(x) and x represent in Luke's situation? (2 points)

Group of answer choices

f(x) represents the total number of hours; x represents the number of weeks he exercises this summer

f(x) represents the total number of weeks that he has exercised; x represents the number of hours

f(x) represents the number of hours he exercises per day; x represents the number of weeks

f(x) represents the total number of hours that Luke has exercised; x represents the number of weeks he exercises per day

When a scalar quantities is multiplied by a matrix of size 9x10, the resulting matrix will also be of size 9x10.

If we perform the matrix computation cM, where c is a scalar and M is a matrix of size 9x10, the resulting matrix cM will also be of size 9x10.

This is because when we multiply a scalar by a matrix, each element in the matrix is multiplied by the scalar.

Therefore, the resulting matrix has the same dimensions as the original matrix.

To see why this is the case, consider a single element in the resulting matrix cM. Let's say the element is located at row i and column j.

Then, it is given by cM[i,j] = c*M[i,j]. Since M[i,j] is just a single element in the original matrix, multiplying it by the scalar c produces a new scalar.

Therefore, cM[i,j] is also a single element in the resulting matrix cM.

Since each element in the original matrix M is multiplied by the scalar c, the resulting matrix cM will have the same dimensions as the original matrix, i.e., 9x10.

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If Faith had met her goal, the mean would have increased from 60 to 100, the median would have remained the same at 60, and the mode would have changed from 60 to 100.

If Faith had met her goal, the mean, median, and mode would have changed. Let's assume her goal for the week was to read 100 pages.

Faith read only 60% of her goal, which is equivalent to 60 pages

(100 pages × 0.6).

If she had met her goal, she would have read 100 pages in total.

The mean would have changed from 60 pages to 100 pages.

Since we only have one data point (60), the median would have remained the same at 60.

The mode would be 60 since that is the only value we have.

If Faith had met her goal, the mode would have changed to 100, as 100 pages would appear most frequently.

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The value of x will be 18.67 for the given data of the triangle.

We have,

Thale's theorem:

When a line parallel to one side of a triangle intersects the other two sides in distinct points, the other two sides are divided in the same ratio.

Given that the sides of the triangle are divided into two parts,

For the left part the parts will be x and x + 7 for the right side the parts will be 16 and 22.

The ratio will be the same according to Thale's theorem. The value of x will be calculated as:-

x / ( x + 7 ) = 16 / 22

22x = 16x + 112

6x = 112

x = 112 / 6

x = 18.67

Therefore, the value of x will be 18.67.

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complete question;

Find the values of x and y. Find value of x.

Answer: 64 1/2

Step-by-step explanation:

Answer:

2³

Step-by-step explanation:

Square root of 64 = 8

exponential notation = 2×2×2 = 2³

Answer:

456

Step-by-step explanation:

Product means an answer derived from multiplication.  Therefore, if the product is 155952, and one value is 342, then the following equation is true:

342x = 155952, or 342 * x = 155952

Divide 155952 by 342 to get: 456.

Check the work in the equation:

342(456) = 155952

155952 = 155952, which is true, so the answer is 456.

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The required value of trigonometric ratios is,

sin 45° = 1/[tex]\sqrt{2}[/tex]

cos 30 = [tex]\sqrt{3}[/tex]/2

tan 60 = 1/  √3

We know that,

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Therefore,

sin 45° = 1/[tex]\sqrt{2}[/tex]

cos 30 = [tex]\sqrt{3}[/tex]/2

tan 60 = 1/  √3

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The true statement is that proves the congruence of both triangles is:

∠ABC ≅ ∠DCB;

alternate interior angles of parallel lines are congruent.

Here, we have

to prove that angles are congruent

From the complete question, we have the following highlights

Angles B and C are alternate interior angles

The triangles are bounded by parallel lines

The above highlights mean that:

Angles ABC and DCB are congruent, by the theorem of alternate interior angles of parallel lines

Hence, the true statement is (c)

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complete question:

Isabelle proves that the triangles are congruent by using the parallel lines to determine a second set of angles are congruent. What statement and reason could she have used? ∠ABC ≅ ∠BAC; corresponding angles of parallel lines are congruent. ∠CAB ≅ ∠DCB; alternate interior angles of parallel lines are congruent ∠ABC ≅ ∠DCB; alternate interior angles of parallel lines are congruent ∠ACD ≅ ∠ABD; corresponding angles of parallel lines are congruent.

Answer:

We can use the formula for compound interest to solve this problem. The formula is:

A = P * (1 + r/n)^(n*t)

where:

A = the amount of money after t years

P = the principal amount (the initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $5000, r = 0.03, n = 12 (since the interest is compounded monthly), and t = 10. Plugging these values into the formula, we get:

A = 5000 * (1 + 0.03/12)^(12*10)

A = 5000 * (1.0025)^120

A ≈ $6,621.36

So the investment will be worth approximately $6,621.36 after 10 years.

The side length of the square garden is 4 feet if the area of a square garden is the same as the area of a rectangular garden that is 8 ft long and 2 ft wide.

Length of the rectangular garden = 8 ft

Width of the rectangular garden = 2 ft

Area of rectangular garden =  length x width

Area of rectangle = 8 ft x 2 ft

Area of rectangular garden = 16 square feet

It is given that the area of the square garden is the same as the area of the rectangular garden. The area of the square garden is calculated as:

Area of square garden = side length x side length

Area of square garden = side length x side length = 16

To solve the equation, we need to make isolate it on one side of the equation.

Taking root on both sides:

[tex]\sqrt{(side length * side length)}[/tex] = [tex]\sqrt{16}[/tex]

side length = ± [tex]\sqrt{16}[/tex]

We need to take the positive root value:

side length =  [tex]\sqrt{16}[/tex]

side length = 4 ft

Therefore, we can conclude that the side length of the square garden is 4 feet.

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Answer:

Part A: 13440ft³

Part B: 2940ft³

Step-by-step explanation:

box volume:

20 x 28 = 560

560 x 24 = 13440ft³

Subtract gift volume:

13440 - 10500 = 2940ft³

Step-by-step explanation:

The total amount of money collected from the ticket sales is:

$5/ticket x 3000 tickets = $15,000

The expected value for a person that buys a ticket can be calculated by adding up the probabilities of winning each prize multiplied by the amount of money for each prize:

E(X) = (1/3000) x $500 + (1/3000) x $250 + (1/3000) x $125 + (1/3000) x $50 - (2996/3000) x $5

Simplifying this expression:

E(X) = $0.1666667 + $0.0833333 + $0.0416667 + $0.0166667 - $4.9833333

E(X) = -$4.65

Therefore, the expected value for a person that buys a ticket is -$4.65, which means that on average, a person can expect to lose $4.65 for every ticket they buy.

Answer: $0.31

Step-by-step explanation:

1/3000 tickets will be worth $500.

1/3000 tickets will be worth $250.

1/3000 tickets will be worth $125.

1/3000 tickets will be worth $50.

The remaining 2996/3000 tickets will be worth $0. (Nobody else wins.)

So (1/3000)x500 + (1/3000)x250 + (1/3000)x125 + (1/3000)x50 + (2996/3000)x0 = $0.31.

Please note: This question asks for expected value. Expected value is a measure of what you should expect to get per game. The payoff of a game is the expected value of the game minus the cost.

Answer:

[tex](- \infty, \infty)[/tex]

Third answer choice

Step-by-step explanation:

This is the graph of the function f(x) = tan(x)

We can see that the minimum value of f(x) tends to - ∞ and the maximum value tends to + ∞

So the range of f(x) is [tex](- \infty, \infty)[/tex]

This is the third answer choice (the one that is highlighted in orange)

This coal bag has a minimum weight of 2.925 kilograms.

We must determine the coal's minimum weight, which is 30 pieces.

One piece of coal weighs 100 g, accurate to the closest 5 g. As a result, the actual weight of a piece of coal may range between 97.5 g to 102.5 g.

We can multiply the minimum weight of one piece of coal (97.5 g) by 30 to determine the minimum weight of 30 pieces of coal:

Minimum weight of 30 pieces of coal = 97.5 g x 30 = 2925 g

Therefore, The sticker can be finished as follows:

This coal bag has a minimum weight of 2.925 kilograms.

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f(x) = x² and g(x) = 3(x + 1)² have the same minimum y-value and axis of symmetry, but they have different y-values at x = -2.

We have the function:

f(x) = x² and g(x) = 3(x + 1)² are both quadratic functions.

1. Minimum y-value:

For f(x) = x², the minimum y-value occurs at the vertex of the parabola, which is at (0, 0). The minimum y-value is 0.

For g(x) = 3(x + 1)², the minimum y-value occurs at the vertex of the parabola, which is at (-1, 0). The minimum y-value is also 0.

Therefore, both functions have the same minimum y-value.

2. Axis of symmetry:

For f(x) = x², the axis of symmetry is the vertical line that passes through the vertex of the parabola, which is x = 0.

For g(x) = 3(x + 1)², the axis of symmetry is also the vertical line that passes through the vertex of the parabola, which is x = -1.

Therefore, both functions have different equations but share the same axis of symmetry.

3. Y-value at x = -2:

For f(x) = x², the y-value at x = -2 is f(-2) = (-2)² = 4.

For g(x) = 3(x + 1)², the y-value at x = -2 is g(-2) = 3(-2 + 1)² = 3.

Therefore, the two functions have different y-values at x = -2.

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The mean of the data set is 16.7.

To find the mean of a data set, you add up all the values and divide by the number of values.

Adding up all the values, we get:

8 + 10 + 12 + 15 + 15 + 18 + 19 + 20 + 23 + 27 = 167

There are 10 values in the set, so we divide the sum by 10 to get the mean:

Mean = 167/10 = 16.7

Therefore, the mean of the data set is 16.7.

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The standard deviation of the sampling distribution of p is 0.028284

The mean of the sampling distribution of p can be found using the formula:

μp = p = 0.2

The standard deviation of the sampling distribution of p can be found using the formula.

Plugging in the given values, we get:

σp = ✓[(0.2*(1-0.2))/200 * (25000-200)/(25000-1)]

= ✓[(0.16/200) * (24800/24999)]

= ✓[0.0008 * 0.99204]

= ✓(0.0007936)

= 0.028284

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Answer:

[tex]\displaystyle{f(x)=(x-5)^2-24}[/tex]

Step-by-step explanation:

Given the function:

[tex]\displaystyle{f(x)=x^2-10x+1}[/tex]

Separate 1 out of the terms:

[tex]\displaystyle{f(x)=(x^2-10x)+1}[/tex]

Convert parentheses-terms to perfect square:

[tex]\displaystyle{f(x)=(x^2-10x+25)+1-25}[/tex]

Evaluate and/or simplify:

[tex]\displaystyle{f(x)=(x-5)^2-24}[/tex]

The correct expression that shows the slope of the line that passes through  (3, 6) and (-7, -4) is -4  - 6 / -7 - 3.

The slope of a line is the change in the dependent variable with respect to the change in the independent variable.

Therefore, the slope of a line is the change in y variable with respect to the change in x variable.

Hence,

m = slope = y₂ - y₁ / x₂ - x₁

Therefore, the line passes through (3, 6) and (-7, -4).

where

x₁ = 3

x₂ = -7

y₁ = 6

y₂ = -4

Therefore, the expression is -4  - 6 / -7 - 3.

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Answer:

answer A

Step-by-step explanation:

since 12/44 = 0.2727272727

i didnt get what you need but i assume you want the angle so it will be 360-130-80-70 = 80⁰

Answer:

500 times

Step-by-step explanation:

Divide the thickness of a cat hair by the thickness of a human hair.

4.0 × 10^-1 / 8.0 × 10^-4 =

= 0.5 × 10^3

= 500

500 times

Answer:

A. $4.90

Step-by-step explanation:

The requried function represents an absolute value parent function.

A graph is shown,

When we see at the points on the curve,
On x = -10 we have y = 10
simultaneously,
On x = 10 again we have y = 10

This implies that the function is an absolute value parent function.

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As per the combination method, there are 2,162,880 ways to choose 6 letters from 14 distinct letters, taking into account the order of the choices.

Since we are choosing 6 letters from 14 distinct letters, the number of ways to do this without taking into account the order is given by the combination formula:

C(14, 6) = 3003.

However, since we are also taking into account the order of the choices, we need to multiply the number of choices by the number of ways to arrange those choices.

The number of ways to arrange 6 letters is given by 6!, which represents the number of permutations of 6 objects.

Therefore, the total number of ways to choose 6 letters, with order taken into account, is given by the product of the number of combinations and the number of permutations:

C(14, 6) x 6! = 3003 x 720 = 2,162,880.

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Answer:

5.

Step-by-step explanation:

15.90 / 3.18 =

Answer:

4,875 gallons.

Step-by-step explanation:

1.5 gallons/hour

1.5 / 4 = 0.375 gallons/25mins

1.5 * 3 (hours) + 0.375 = 4.875 gallons

The length of the flat-screen television is approximately 40.01 inches.

Let's assume that the height of the flat-screen television is "h" inches.

From the problem statement, we know that the length of the screen is 175% of its height.

Mathematically, we can write:

Length = 1.75 x Height

We can substitute the value of "h" in this equation to find the length of the screen:

Length = 1.75 x h

Now, we also know that the diagonal length of the screen is 40 inches. Using the Pythagorean, we can write:

(Length)² + (Height)² = (Diagonal)²

Substituting the values we have, we get:

(1.75h)² + h² = (40)²

Expanding and simplifying:

3.0625h² = 1600

Dividing both sides by 3.0625:

h² = 522.24

Taking the square root of both sides (and ignoring the negative root since we're dealing with lengths):

h = 22.86 inches

Now we can use the equation we derived earlier to find the length:

Length = 1.75 x h

Length = 1.75 x 22.86

Length = 40.01 inches (rounded to two decimal places)

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Answer: A sales discount is a reduced price offered by a business on a product or service.

Step-by-step explanation:

Answer:

when the original selling price of a product does down. You'll be getting the same product at a lower price

Step-by-step explanation:

you can calculate the discount % by

NEW PRICE MULTIPLIED BY 100 DIVIDED BY OLD PRICE