Seven times the sum of a number and 1

Use X as “Of a Number”

The surface area of a triangular prism is 288 square inches. If the triangle base is 8 inches, each rectangular face will be 8 inches broad and 10 inches long. The height of the triangular prism is 16 inches.

To find the height of the triangular prism, we need to use the formula for the surface area of a triangular prism:

Surface Area = 2(Area of the rectangular face) + (Perimeter of the base) x (Height)

We know that the rectangular face has a width of 8 inches and a length of 10 inches, so its area is:

Area of the rectangular face = 8 x 10 = 80 square inches

We also know that the surface area of the triangular prism is 288 square inches. Substituting these values into the formula, we get:

288 = 2(80) + (Perimeter of the base) x (Height)

Simplifying this equation, we get:

288 = 160 + 8(Height)

128 = 8(Height)

Height = 16 inches

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The correct system of equations which can be used to determine when the value of the cars, V , will be the same is,

⇒ 32,540 (1 - 0.35)ⁿ = 15,230 (1 - 0.15)ⁿ

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Car 1 purchased for $32,540 and decreases by 35% each month.

And,  Car 2 purchased for $15,230 and decreases by 15% each month.

Now, Let after n months the value of the cars, V , will be the same.

Hence, The value of car 1 after n months is,

⇒ 32,540 (1 - 0.35)ⁿ

And, The value of car 2 after n months is,

⇒ 15,230 (1 - 0.15)ⁿ

Thus, The correct system of equations which can be used to determine when the value of the cars, V , will be the same is,

⇒ 32,540 (1 - 0.35)ⁿ = 15,230 (1 - 0.15)ⁿ

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The production level that will maximize profit is approximately 122 units.  

How can we determine the production level that will maximize profit given the cost function and the demand function?

To find the production level that maximizes profit, we can calculate the profit function by subtracting the cost function from the revenue function. By determining the vertex of the resulting quadratic equation, we can identify the production level (x-coordinate of the vertex) at which profit is maximized.

To find the production level that will maximize profit, we need to determine the point where the cost function and the demand function intersect. The profit function can be calculated by subtracting the cost function from the revenue function (which is the product of the demand function and the production level).

Given:

Cost function: C(x) = 1700 - 7x (where x represents the production level) Demand function: p(x) = 1700 - 7x (where p(x) represents the price per unit)

To calculate the profit function, we subtract the cost function from the revenue function:

Profit function: P(x) = x * p(x) - C(x)

Now we substitute the given functions: P(x) = x * (1700 - 7x) - (1700 - 7x)

Simplifying further:

\(P(x) = 1700x - 7x^2 - 1700 + 7x\\ P(x) = -7x^2 + 1707x - 1700\)

To find the production level that maximizes profit, we need to determine the vertex of the quadratic equation P(x). The x-coordinate of the vertex represents the production level at which profit is maximized.

To find the x-coordinate of the vertex, we can use the formula  \(x =\frac{-b}{2a}\), where a, b, and c are the coefficients of the quadratic equation.

In this case, a = -7, b = 1707, and c = -1700. Substituting these values into the formula:

\(x=\frac{1707}{2*(-7)}\)

\(x=\frac{1707}{-14}\)

x ≈ 122.36

Rounding to the nearest whole number, the production level that will maximize profit is approximately 122 units.

Therefore, the production level that will maximize profit is approximately 122 units.

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The probability of selecting 2 men and 2 women from a group of 9 women and 7 men is 11%.

The probability of selecting 2 men and 2 women from a group of 9 women and 7 men is \($\frac{{7 \choose 2}{9 \choose 2}}{{16 \choose 4}}$\) which simplifies to\($\frac{63}{220}$\) or approximately 28.6%. The probability of selecting 2 men and 2 women from a group of 9 women and 7 men is 11%.

The probability of selecting 2 men and 2 women from a group of 9 women and 7 men can be calculated by using the formula for combination, nCr. In this case, we would be selecting 4 people from 16 individuals, so n = 16 and r = 4. The formula is nCr = n!/(r!(n-r)!). This can be simplified to 16C4 = 16!/ (4!(12!)). The answer is 1820/21168, which can be simplified to 86/792, or approximately 11%. Therefore, the probability of selecting 2 men and 2 women from a group of 9 women and 7 men is 11%.

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a. There are 10⁹ hertz in 1 giga hertz and 10^12 hertz in one terahertz

b. The channels frequency in hertz 6×10⁷hertz

c. The frequency of a microwave in hertz is 3× 10^10 hertz

d. The frequency of light is 10⁵ times greater than the frequency of the radio station

Frequency describes the number of waves that pass a fixed place in a given amount of time. So if the time it takes for a wave to pass is is 1/2 second, the frequency is 2 per second. If it takes 1/100 of an hour, the frequency is 100 per hour.

The S.I unit of frequency is hertz and it has other bigger unit stated as follows:

1 kilohertz = 10³hertz

1megahertz = 10⁶ hertz

1 gigahertz = 10⁹ hertz

1 tera hertz = 10^12 hertz

Therefore 60mega hertz = 60× 10⁶ = 6×10⁷

30 gigahertz = 30 × 10⁹ = 3 × 10^10

if the frequency of light is 1000 tera hertz and 100 mega hertz is the frequency of a radio station , then the frequency of light will be 1000×10^12 ÷ 100× 10⁶ = 10⁵ greater than the frequency of the radio station.

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Answer: Decrease it’s a negative

Step-by-step explanation:

Answer: 24 meters

Step-by-step explanation:

15/45 = 8/x

15x = 360

x = 24

The length of the bell tower's shadow is 24 meters. This can be answered by the concept of similar triangles.

To determine the length of the bell tower's shadow, we can use the concept of similar triangles. The height of the crane, the length of its shadow, and the height of the bell tower form one set of similar triangles. We can write the proportion:

height of crane / length of crane's shadow = height of bell tower / length of bell tower's shadow

Plugging in the given values, we get:

15 / 8 = 45 / x

Solving for x, we get x = 24.

Therefore, the length of the bell tower's shadow is 24 meters.

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Answer:

17 people surveyed own a cat.

Step-by-step explanation:

Let d stand for dog, c stand for cat, and b stand for both. In total, d + c + b = 100 people. The number of people who own a dog is four times the number of people who own a cat, so d = 4c. In the problem, it's given that 15 people own both a dog and a cat. So, b can be replaced with 15. Now, d + c + 15 = 100. This system of equations can be solved by substitution.

d = 4c

d + c + 15 = 100

4c + c + 15 = 100

5c + 15 = 100

5c = 85

c = 17

Check:

The number of dog owners is 4 * 17, or 68.

68 + 17 + 15 = 100

For a given input value mmm, the function ggg outputs a value nnn that satisfies the equation −2m−5n as n = -2mmm/5.

To find the value of nnn that satisfies the equation −2m−5n, you need to substitute the given input value mmm into the equation and solve for nnn.
1. Start with the equation −2m−5n.
2. Substitute the given input value mmm into the equation. So, the equation becomes −2mmm−5n.
3. Solve for nnn by isolating the variable n.
  - To do this, move the term with n to the other side of the equation. In this case, add 2mmm to both sides: −2mmm + 2mmm − 5n = 2mmm.
  - Simplify the equation: -5n = 2mmm.
  - To isolate n, divide both sides of the equation by -5: n = (2mmm)/(-5).
  - Simplify the expression: n = -2mmm/5.
Therefore, for a given input value mmm, the function ggg outputs a value nnn that satisfies the equation −2m−5n as n = -2mmm/5.

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Answer:

(0,0)

Step-by-step explanation:

Let's think about how the graph of this would look.

We know that y will be \(x^2\), meaning that if x was 0, y would be 0.

If x was 1, y would be 1

If x was 2, y would be 4.

Now let's think about negative numbers.

If x was -1, y would be 1 (since \(-1^2 = 1\)

If x was -2, y would be 4 (since \(-2^2 = 4\)).

This means that our graph would turn at the point where x and y are equal (excluding 1,1)

This is 0,0.

So 0,0 is the turning point of this graph.

Hope this helped!

Answer:

22,440

Step-by-step explanation:

204 = 2 * 2 * 3 * 17

1320 = 2 * 2 * 2 * 3 * 5 * 11

They both have 2 2's and a 3 in common, so use them once

2 * 2 * 3 * 17 * 2 * 5 * 11 = 22,440

Answer:

If you are factoring them out they both go into 12

Step-by-step explanation:

204: 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, and 204.

1320: 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 30, 33, 40, 44, 55, 60, 66, 88, 110, 120, 132, 165, 220, 264, 330, 440, 660, and 1320.

in both the of them the common factors are 1,2,3,4,6, and 12

Answer:

Both of them.

Step-by-step explanation:

Gina says the cost is 8t, which means you can easily find out the cost of each t-shirt if you know the the total cost too. Bindi says the total cost was 192, which is completely useless on its own, but paired with Gina's info, you can get the answer. Divide 192 by 8, and you get the cost of each t-shirt.

120 ways can the letters in the word spoon be arranged. So, The correct option is d) 120.

The word "spoon" has five letters, and we need to find the number of ways to arrange these letters. This can be done using the permutation formula, which is n!/(n-r)!, where n is the total number of items and r is the number of items being selected. In this case, we have five items and we need to arrange all of them, so r = 5. Therefore, the number of arrangements is 5!/(5-5)! = 5!/0! = 5x4x3x2x1 = 120.

To understand this concept better, consider that the first letter of "spoon" can be any of the five letters. Once we choose a letter for the first position, there are four letters left to choose from for the second position, three for the third position, two for the fourth position, and only one letter left for the fifth position. Multiplying these numbers gives us the total number of arrangements. Therefore, there are 120 ways to arrange the letters in the word "spoon". So the correct answer is d) 120.

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Answer: 9.97

Step-by-step explanation:

the answer to that is 9.97

Answer:

D.

Step-by-step explanation:

the composite function that can be used to determine the height, in meters, of the flare at any given time is:
h_meters(t) = 0.3048 * h(t)

To determine the height of the flare in meters at any given time, we can use the composite function. The composite function is obtained by converting the height in feet to meters.

The conversion factor to convert feet to meters is 0.3048. So, we can multiply the height in feet by 0.3048 to get the height in meters.

Therefore, the composite function that can be used to determine the height, in meters, of the flare at any given time is:

h_meters(t) = 0.3048 * h(t)  Where h(t) is the height of the flare in feet, and h_meters(t) is the height of the flare in meters.

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The degree, k, of each vertex in the graph g is 8.

Let's assume that every vertex in g has degree k. Since g is an undirected graph, each edge contributes to the degree of two vertices. Therefore, the sum of degrees of all vertices in g is equal to twice the number of edges in g.

Given that g has exactly 12 edges, the sum of degrees of all vertices is 2 * 12 = 24. Since g has only 3 vertices, the sum of their degrees must be 24.

If we assume that every vertex has degree k, then the sum of the degrees of the 3 vertices is 3k. Therefore, we can set up the equation 3k = 24.

Solving this equation, we find that k = 24 / 3 = 8. So, each vertex in g has a degree of 8.

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Katie is studying the polynomial f(x) =(2x-3) (x-4) (x^2-3) and determines the polynomial has three real roots.  you  disagree with Katies statement because the function has four real roots

Katie is studying the polynomial  and determines the polynomial has three real roots. Do you agree or disagree with Katie's statement? Explain your reasoning.

the complete question is

Katie is studying the polynomial f(x) =(2x-3) (x-4) (x^2-3) and determines the polynomial has three real roots. Do you agree or disagree with Katies statement? Explain your reasoning.

Write properties of function:

x intercept/zero: \(x_{1}\) = 3/2 ; \(x_{2}\) = 4 ; \(x_{3}\) = -\(\sqrt{3}\) ;  \(x_{4}\) = \(\sqrt{3}\)

Katie is studying the polynomial f(x) =(2x-3) (x-4) (x^2-3) and determines the polynomial has three real roots.  you  disagree with Katies statement because the function has four real roots

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Answer:

Jason runs faster then his friend.

Step-by-step explanation:

Jason's speed is represented by the equation y = 7x because he runs 7 miles in an hour. If his friend's speed is represented by y = 6x, then his friend runs a total of 6 miles in an hour.

Answer:

x=4 y=5

Step-by-step explanation:

The Excel function =40*RAND() generates random numbers between 0 and 40.

Since the RAND() function in Excel produces random numbers uniformly distributed between 0 and 1, multiplying it by 40 scales the range to 0 to 40.

The standard deviation of a uniform distribution with range a to b is given by (b - a) / sqrt(12). In this case, a = 0 and b = 40.which simplifies to approximately 11.55.

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Compare 1/7 to consecutive multiples of 1/9. This is easily done by converting the fractions to a common denominator of LCM(7, 9) = 63:

1/9 = 7/63

2/9 = 14/63

while

1/7 = 9/63

Then 1/7 falls between 1/9 and 2/9, so 1/7 = 1/9 plus some remainder. In particular,

1/7 = 1/9¹ + 2/63.

We do the same sort of comparison with the remainder 2/63 and multiples of 1/9² = 1/81. We have LCM(63, 9²) = 567, and

1/9² = 7/567

2/9² = 14/567

3/9² = 21/567

while

2/63 = 18/567

Then

2/63 = 2/9² + 4/567

so

1/7 = 1/9¹ + 2/9² + 4/567

Compare 4/567 with multiples of 1/9³ = 1/729. LCM(567, 9³) = 5103, and

1/9³ = 7/5103

2/9³ = 14/5103

3/9³ = 21/5103

4/9³ = 28/5103

5/9³ = 35/5103

6/9³ = 42/5103

while

4/567 = 36/5103

so that

4/567 = 5/9³ + 1/5103

and so

1/7 = 1/9¹ + 2/9² + 5/9³ + 1/5103

Next, LCM(5103, 9⁴) = 45927, and

1/9⁴ = 7/45927

2/9⁴ = 14/45927

while

1/5103 = 9/45927

Then

1/5103 = 1/9⁴ + 2/45927

so

1/7 = 1/9¹ + 2/9² + 5/9³ + 1/9⁴ + 2/45927

One last time: LCM(45927, 9⁵) = 413343, and

1/9⁵ = 7/413343

2/9⁵ = 14/413343

3/9⁵ = 21/413343

while

2/45927 = 18/413343

Then

2/45927 = 2/9⁵ + remainder

so

1/7 = 1/9¹ + 2/9² + 5/9³ + 1/9⁴ + 2/9⁵ + remainder

Then the base 9 expansion of 1/7 is

0.12512..._9

a. two critical points are (0,0) and (-2, -4). b. H has two positive eigenvalues, and (-2,-4) is a local minimum of f(x,y).

(a) To find the critical points of f(x,y), we need to find the partial derivatives of f(x,y) with respect to x and y, and then set them equal to zero.

∂f/∂x = 4x^3 - 8y

∂f/∂y = 4y - 8x

Setting these partial derivatives equal to zero and solving for x and y, we get:

4x^3 - 8y = 0 => y = x^3/2

4y - 8x = 0 => y = 2x

Substituting y = 2x into y = x^3/2, we get:

2x = x^3/2 => x(x^2 - 4) = 0

So we have two critical points: (0,0) and (-2, -4).

(b) To classify the critical points, we need to use the second partial derivative test. The Hessian matrix of f(x,y) is:

H = [12x^2 -8 -8-8 4 0-8 0 0]

At (0,0), we have H = [-8 -8; -8 4], which has determinant (-8)(4)-(-8)(-8) = 0 and trace -4. Since the determinant is zero, we cannot use the second partial derivative test at (0,0). Instead, we can observe that f(0,0) = 0, and f(x,y) is positive for all (x,y) not equal to (0,0). Therefore, (0,0) is a saddle point. At (-2,-4), we have H = [44 -8; -8 0], which has determinant (44)(0)-(-8)(-8) = 64 > 0 and trace 44 > 0. Therefore, H has two positive eigenvalues, and (-2,-4) is a local minimum of f(x,y).

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Answer:

40 students would choose rap. Hope this helps! BTW nice job scaring people off

It is 40 because the total in the graph is 50 so you have to multiply everything by 4

Answer:

i think it is 40 srry if i am wrong

Step-by-step explanation:

Answer:

ok hahahahahahahahahha

Answer:

laughs

Step-by-step explanation:

Answer:

Step-by-step explanation:

-1 3/4 = -1.75.

Answer:

20 inches

Step-by-step explanation:

Since there are 480 miles in total, we have to divide it by 12 so we can see how many half inches that would be.

480÷12 = 40

That would mean you can fit forty 12's in 480. Since 12 miles equals 1/2, you would multiply it by 40.

1/2 × 40 =20

This means that the distance between the cities on the map would be 20 inches.

Answer:

300 + 4x

Step-by-step explanation:

200 + 100 = 300

3x + x = 4x

(a plain variable like "x" always has an invisible one in front of it)

Answer:

Step-by-step explanation:

Stage 1

Stage 2

Stage 3

Equation for stage n: