Find the simplified form of the expression. Give your answer in scientific notation.

(9x10^5)(6x10^-7)
​

Answer:

MEAN = 14 (AS PER ESTIMATION)

MEDIAN = 17

Step-by-step explanation:

Mean=Sum of terms/No.of terms

Then,

→13+16+14+17+17+8+16/ = 101/7 = 14.428571....…

Median = The middle number

= 17

To find the area bounded by the curves y₁ = x³ and y₂ = 17x³ - 60x, we need to determine the points of intersection of the two curves.

Setting y₁ = y₂, we have:

x³ = 17x³ - 60x

Rearranging the equation:

16x³ - 60x = 0

Factoring out x:

x(16x² - 60) = 0

Setting each factor equal to zero:

x = 0

16x² - 60 = 0

Solving the quadratic equation:

16x² = 60

x² = 60/16

x² = 15/4

x = ±√(15/4)

x = ±(√15)/2

The points of intersection are x = - (√15)/2, 0, and (√15)/2.

To find the area bounded by the curves, we integrate the difference between the curves with respect to x over the interval [-(√15)/2, (√15)/2]:

Area = ∫[-(√15)/2, (√15)/2] (y₂ - y₁) dx

Area = ∫[-(√15)/2, (√15)/2] (17x³ - 60x - x³) dx

Area = ∫[-(√15)/2, (√15)/2] (16x³ - 60x) dx

Integrating term by term:

Area = [4x⁴ - 30x²] | [-(√15)/2, (√15)/2]

Evaluating the integral:

Area = [4((√15)/2)⁴ - 30((√15)/2)²] - [4((-(√15)/2)⁴ - 30((-(√15)/2)²)]

Area = [4(15/4) - 30(15/4)] - [4(15/4) - 30(15/4)]

Area = 15 - 15

Area = 0

Therefore, the area bounded by the curves y₁ = x³ and y₂ = 17x³ - 60x is 0.

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The standard form equation of the circle with the center (-1, 0) and circumference 8π is (x + 1)² + y² = 16.

To write the standard form equation of a circle, we use the formula:

(x - h)² + (y - k)² = r²

where (h, k) represents the center of the circle, and r represents the radius.

Given the center of the circle as (-1, 0) and the circumference of 8π, we can find the radius using the formula for circumference:

Circumference = 2πr

8π = 2πr

Dividing both sides by 2π:

4 = r

Now we have the center (-1, 0) and the radius r = 4. Plugging these values into the standard form equation, we get:

(x - (-1))² + (y - 0)² = 4²

Simplifying:

(x + 1)² + y² = 16

Therefore, the standard form equation of the circle with the center (-1, 0) and circumference 8π is (x + 1)² + y² = 16.

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Answer:

CE

Step-by-step explanation:

CE IS THE REQUIRED ANSWER FOR THE GIVEN QUESTION

There are 14,880 braids in total in the girls club.

To find the total number of hair braids in the girls club, you'll need to multiply the number of girls (372) by the number of braids per girl (40).

Your question: A girls club is trying to get into the record books for the most hair braids. There are 372 girls, and each girl braids her hair into 40 little braids. How many braids are there in total?

Step 1: Identify the number of girls, which is 372.

Step 2: Identify the number of braids per girl, which is 40.

Step 3: Multiply the number of girls (372) by the number of braids per girl (40) to get the total number of braids.

Total number of braids = 372 girls * 40 braids/girl = 14,880 braids

So, there are 14,880 braids in total in the girls club.

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Answer:

A. Zero

Step-by-step explanation:

12x+8=12x+8 - collecting like terms.

12x-12x=8-8

0=0

Hope it helps <3.

Answer:

8

Step-by-step explanation:

i hope this helps :)

Answer:

1:2

Step-by-step explanation:

By dividing both sides by 20 you will get 1:2 which is the same thing as 20:40 if you multiply 1:2 on both sides by 20

Answer:

1 : 2

Step-by-step explanation:

20 : 40

20/10 : 4/10

2 : 4

2/2 : 4/2

1 : 2

Answer:

113.1cm aka 113

Step-by-step explanation:

Answer:

12 pounds

Step-by-step explanation:

You have to divide the mass value by 16.

Percentage that like Mushroom and Pepperoni Pizza is: 30%

Bar charts are used to show statistical data from different observations. If this statistic is in percent format, the bar chart is called a percent bar chart. Percentage bar charts can be in both vertical and horizontal format.  

From the given bar chart, we see that:

Friends that like cheese = 4

Friends that like Mushroom = 2

Friends that like Pepperoni = 1

Friends that like Supreme = 3

Total number = 4 + 2 + 1 + 3 = 10

Percentage that like Mushroom and Pepperoni Pizza = (2 + 1)/10 * 100%

= (3/10) * 100%

= 30%

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Answer:

$7.68

Step-by-step explanation:

You must find the rate first, so in order to do that you divide the price by the quantity which is

3.20/5

which equals .64 and this number is the cost of potatoes per pound so to find 12 pounds you do

.64 * 12

which equals 7.68

Answer: 7.68

Step-by-step explanation:

First you find the rate where you do 3.20/5 which equals .64

Then you multiply the 12 and .64 and get 7.68

The coordiantes of M that divides AB in the ratio 1:2 are (2,1).

Coordinates are two numbers (Cartesian coordinates), or sometimes a letter and a number, that locate a specific point on a grid, known as a coordinate plane

To calculate the coordinate of M, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equatio 1 and 2 respectively

Hence, the coordinates of M are (2,1).

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We have calculated the steps for finding the tangent line at x = 1, the x-intercept of the tangent line, the tangent line at x1, and the x-intercept of the tangent line y2 for the function y = x^6 - 2.

A) (i) To divide (a^5 - b^5) by (a - b), we can use the factorization formula for the difference of fifth powers: a^5 - b^5 = (a - b)(a^4 + a^3b + a^2b^2 + ab^3 + b^4). Therefore, the division becomes:(a^5 - b^5)/(a - b) = (a - b)(a^4 + a^3b + a^2b^2 + ab^3 + b^4)/(a - b) = a^

4 + a^3b + a^2b^2 + ab^3 + b^4.

(ii) To divide (a^6 - b^6) by (a^3 - b^3), we can use the factorization formula for the difference of sixth powers: a^6 - b^6 = (a^3 - b^3)(a^3 + a^2b^3 + ab^3 + b^6). Therefore, the division becomes:

(a^6 - b^6)/(a^3 - b^3) = (a^3 - b^3)(a^3 + a^2b^3 + ab^3 + b^6)/(a^3 - b^3) = a^3 + a^2b^3 + ab^3 + b^6.

B) To find the derivative of f(t) = 6√t using the definition of the derivative, we can write:

f'(t) = lim(h->0) [(f(t+h) - f(t))/h].

Substituting f(t) = 6√t, we have:

f'(t) = lim(h->0) [(6√(t+h) - 6√t)/h].

To simplify this expression, we can use the difference of squares:

f'(t) = lim(h->0) [(6√(t+h) - 6√t)/h] * [(6√(t+h) + 6√t)/(6√(t+h) + 6√t)].

Simplifying further, we get:

f'(t) = lim(h->0) [(36(t+h) - 36t)/(h(6√(t+h) + 6√t))].

f'(t) = lim(h->0) [36/(6√(t+h) + 6√t)].

f'(t) = 6/(2√t) = 3/√t = 1/(3√t).

Therefore, d/dt [6√t] = 1/(3√t).

C) To find the derivative of f(t) = 5√t^2 using the definition of the derivative, we can write:

f'(t) = lim(h->0) [(f(t+h) - f(t))/h].

Substituting f(t) = 5√t^2, we have:

f'(t) = lim(h->0) [(5√(t+h)^2 - 5√t^2)/h].

Simplifying the expression, we get:

f'(t) = lim(h->0) [(5(t+h) - 5t)/(h(5√(t+h) + 5√t))].

f'(t) = lim(h->0) [5/(5√(t+h) + 5√t)].

f'(t) = 1/(√(t+h) + √t).

To simplify this further, we can multiply the numerator and denominator by (√(t+h) - √t):

f'(t) = [1/(√(t+h) + √t)] * [(√(t+h) - √t)/(√(t+h) - √t)].

f'(t) = (√(t+h) - √t)/(t+h - t) = (√(t+h) - √t)/h.

Taking the limit as h approaches 0, we have:

f'(t) = lim(h->0) [(√(t+h) - √t)/h] = 2/5√t.

Therefore, d/dt [5√t^2] = 2/5√t.

D) The function y = x^6 - 2.

The derivative of y with respect to x is y' = 6x^5.

To find the tangent line at x = 1, we substitute x = 1 into y' and evaluate:

y'(1) = 6(1)^5 = 6.

The slope of the tangent line at x = 1 is 6.

The point (1, f(1)) lies on the tangent line, so we need to find the value of f(1):

f(1) = (1)^6 - 2 = 1 - 2 = -1.

The tangent line at x = 1 passes through the point (1, -1) with a slope of 6. Using the point-slope form of a line, the equation of the tangent line is:

y + 1 = 6(x - 1).

To find the x-intercept of the tangent line in part (A), we set y = 0 and solve for x:

0 + 1 = 6(x - 1).

1 = 6x - 6.

6x = 7.

x = 7/6.

The x-intercept of the tangent line is x = 7/6.

To find the tangent line (#2) at x1, we substitute x = 7/6 into y' and evaluate:

y'(7/6) = 6(7/6)^5.

Simplifying the expression, we get:

y'(7/6) = 6(7^5)/(6^6).

To find the x-intercept of the tangent line y2, we set y = 0 and solve for x:

0 + f(7/6) = y'(7/6)(x - 7/6).

0 + (7/6)^6 - 2 = y'(7/6)(x - 7/6).

Solving for x, we have:

(7/6)^6 - 2 = y'(7/6)(x - 7/6).

x - 7/6 = ((7/6)^6 - 2)/y'(7/6).

x = ((7/6)^6 - 2)/y'(7/6) + 7/6.

The x-intercept of the tangent line y3 is x = ((7/6)^6 - 2)/y'(7/6) + 7/6.

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The system of equations is consistent and has a unique solution at (-4, 1).

To solve the system of equations by graphing, we can plot the lines represented by each equation on a coordinate plane and find their point of intersection.

The given system of equations is:

1) 3x + y = -3

2) 6x - 6y = -30

Let's graph these equations:

For equation 1, 3x + y = -3, we can rewrite it as y = -3x - 3.

For equation 2, 6x - 6y = -30, we can simplify it to x - y = -5, and then y = x + 5.

Now, let's plot these lines on a graph:

The line for equation 1, y = -3x - 3, has a slope of -3 and y-intercept of -3. It will have a negative slope, and we can plot two points on the line: (0, -3) and (-1, 0).

The line for equation 2, y = x + 5, has a slope of 1 and y-intercept of 5. We can plot two points on this line as well: (0, 5) and (-5, 0).

Plotting these lines on a graph, we can see that they intersect at the point (-4, 1).

Now, let's analyze the system:

Since the lines intersect at a single point, the system is consistent. The solution to the system is the coordinates of the point of intersection, which is (-4, 1).

In summary, the system of equations is consistent and has a unique solution of x = -4 and y = 1.

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Answer:

x= 5.5

Step-by-step explanation:

18=12x-48

-12x= -48-18

-12x= -66

x= -66/-12

x= 5.5

Answer:

Okay so first you distribute 6 into the parenthesis that gives you

18=12x-48

Then you add 48 on both sides

66=12x

then you divide

X=5.5

Step-by-step explanation:

The choice function c satisfies finite nonemptiness and choice coherence, but there does not exist a utility function U , which does not contradict the Fundamental Theorem of Mindless Economics.

A. To show that the choice function c satisfies finite nonemptiness, we need to demonstrate that for each choice set Bn, c(Bn) is non-empty.

To show that the choice function c satisfies choice coherence, we need to demonstrate that for any two choice sets Bn and Bm, if Bn ⊆ Bm, then c(Bn) ⊆ c(Bm).

From the given information, we have B1 = {x, y}, B2 = {y, z}, and B3 = {x, z}. Let's consider the possible pairs of choice sets:

B1 and B2: B1 ⊆ B2 since {x, y} is a subset of {y, z}. In this case, c(B1) = {x} and c(B2) = {y}. We can observe that {x} ⊆ {y}, which satisfies the condition of choice coherence.

B1 and B3: B1 ⊆ B3 since {x, y} is a subset of {x, z}. In this case, c(B1) = {x} and c(B3) = {z}. We can observe that {x} ⊆ {z}, which satisfies the condition of choice coherence.

B2 and B3: B2 ⊈ B3 since {y, z} is not a subset of {x, z}. Therefore, the condition of choice coherence does not apply in this case.

Overall, the choice function c satisfies finite nonemptiness and choice coherence, except for the pair of choice sets B2 and B3.

B. To show that there does not exist a utility function U: {x, y, z} → R that can produce these choices via the usual formula c(Bn) = {x ∈ Bn : U(x) ≥ U(y) for all y ∈ Bn}, we need to demonstrate that such a utility function does not exist.

Let's consider the pairs of choice sets B1 and B2:

For B1 = {x, y}, we have c(B1) = {x}. To satisfy the usual formula, we would need a utility function U(x) ≥ U(y). However, since there is no order or preference provided for x, y, and z, we cannot assign numerical values to them in a way that U(x) ≥ U(y) holds.

Similarly, for B2 = {y, z}, we have c(B2) = {y}. Again, we cannot assign numerical values to y and z that satisfy U(y) ≥ U(z) since there is no preference or order specified.

Therefore, there does not exist a utility function U: {x, y, z} → R that can produce these choices via the usual formula.

C. The answers to parts (a) and (b) do not contradict the Fundamental Theorem of Mindless Economics because the choices made by the individual in this scenario do not adhere to the assumptions of utility maximization based on preferences.

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The complete question is:

Suppose X = {X, Y, Z}, And B = {B1 , B2 , B3} Where B1 = {X, Y}, B2 = {Y, Z} And B3 = {X, Z}. We Have The Following Information About An Individual’s Choice Function: C (B1) = {X}, C (B2) = {Y}, And C (B3) = {Z}, A. Show That C Satisfies Finite Nonemptiness And Choice Coherence. B. Show That There Does Not Exist A Utility Function U : {X, Y, Z} → R, That Can.

Suppose X = {x, y, z}, and B = {B1 , B2 , B3} where B1 = {x, y}, B2 = {y, z} and B3 = {x, z}. We have the following information about an individual’s choice function:c (B1) = {x}, c (B2) = {y}, and c (B3) = {z},A. Show that c satisfies finite nonemptiness and choice coherence.

B. Show that there does not exist a utility function U : {x, y, z} → R, that can produce these choices via the usual formula (discussed in class): c (Bn) = {x ∈ Bn : U (x) ≥ U (y) for all y ∈ Bn} , for n = 1, 2, 3.

C.Explain why your answers to parts (a) and (b) do not contradict the Fundamental Theorem of Mindless Economics.

The quadrilateral is a parallelogram so it is Yes.

If a quadrilateral has a pair of parallel opposite sides, it’s a special polygon called parallelogram .The properties of a parallelogram are as follows:

The opposite sides are parallel and equal

The opposite angles are equal

The consecutive or adjacent angles are supplementary

If any one of the angles is a right angle, then all the other angles will be at right angle.

The quadrilateral is a parallelogram since the adjacent interior angles 75° and 105° are supplementary meaning they sum up to 180°

In conclusion, yes, the figure is a parallelogram.

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Answer:

D

Step-by-step explanation:

Boom

Answer:

$2.50

Step-by-step explanation:

6…=15

1…=15/6

2.50

Answer:

9 oatmeal cookies

Step-by-step explanation:

Answer:

150 children

Step-by-step explanation:

Ratio of adults to children= 8:5

Let the number of adults be 8 units and

the number of children be 5 units.

Total number of people

= 8 +5

= 13 units

Since there are 390 people,

13 units ----- 390 people

1 unit ----- 390 ÷13= 30 people

Number of children= 5 units

5 units ----- 30 ×5= 150 people

Thus, there are 150 children.

Answer:

C. 1,120 cubic inches

Explanation:

To find the total volume, we will divide the solid as follows:

The edge with a length equal to 10 in was calculated as:

18 in - 8 in = 10 in

Because 18 in is the length of the largest height of the figure and 8 in is the length of the smaller height.

Now, the volume of a rectangular prism can be calculated as:

Volume = Length x Width x Height

So, the volume of solid 1 is equal to:

V₁ = 12 in x 4 in x 10 in

V₁ = 480 in³

In the same way, the volume of solid 2 is equal to:

V₂ = 20 in x 4 in x 8 in

V₂ = 640 in³

Therefore, the total volume of the solid is the sum of both parts. Then:

V₁ + V₂ = 480 in³ + 640 in³

V₁ + V₂ = 1120 in³

So, the answer is C. 1,120 cubic inches

in this kind of exercises you need to work in 3 steps:

1. split your figure into shapes you know

2. calculate the area of those separate shapes

3. add the areas

1. (see picture)

2. shape 1 (triangle)

A= 8m×3m

A= 24m²

2. shape 2 (rectangle)

A= 8m×4m

A= 32m²

3.

total A= A1+ A2

A= 24m²+32m²

A= 56m²

Answer:

9 I believe

all i did was 45÷5 :/

Since there were three hours left to complete the distance of remaining 17.14 km from 120 km, there was plenty of time left to finish the race within the eight-hour time limit.

Distance is the length of the path traveled by an object from one point to another. For example, imagine walking from house to a nearby store. The distance between house and the store is the length of the path you took to get there. It is a scalar quantity, which means it has a magnitude (a numerical value) but no direction.

Distance is usually measured in units such as meters, kilometers, feet, or miles, depending on the context. For example, if you are measuring the distance between two cities, you might use kilometers or miles. If you are measuring the distance between two points in a laboratory, you might use meters or centimeters.

It's important to note that distance is a measure of the total length of the path traveled by an object, regardless of whether the path is straight or curved. For example, imagine driving from point A to point B, but path takes around a curved road. The distance traveled is the total length of the path taken, not just the straight-line distance between A and B.

Let d be the total distance of the race.

After 5 hours,still needed to travel 1/4 of the total distance, which means completed 3/4 of the total distance in 5 hours.

3/4 * d = 120 km - 1/4 * d (since the total distance is divided into 4 parts and you have completed 3 parts)

Multiplying both sides by 4 to eliminate the fraction,

3d = 480 - d

Adding d to both sides,

4d = 480

Dividing both sides by 4,

d = 120 km / 3 = 68.57 km (rounded to two decimal places)

So the total distance of the race is 68.57 km.

To find out how much distance still needed to cover, multiply the total distance by the fraction of the race that still had left to complete:

1/4 * 68.57 km = 17.14 km (rounded to two decimal places)

Therefore, still needed to cover 17.14 km to reach the finishing line.

Since there were three hours left to complete the remaining 17.14 km, there was plenty of time to finish the race within the eight-hour time limit.

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The function T((x, y)) = (x + y, x) is a linear transformation. Its matrix representation can be found by mapping the standard basis vectors and arranging the resulting vectors into a matrix.
The basic box representing the transformation can be drawn by considering the images of the standard unit vectors.

To show that T((x, y)) = (x + y, x) is a linear transformation, we need to demonstrate that it preserves vector addition and scalar multiplication.

Let's consider two vectors, u = (x₁, y₁) and v = (x₂, y₂), and a scalar c. The transformation of the sum of u and v is T(u + v), which is equal to (x₁ + y₁ + x₂ + y₂, x₁ + x₂). On the other hand, the sum of the individual transformations T(u) + T(v) is (x₁ + y₁, x₁) + (x₂ + y₂, x₂) = (x₁ + y₁ + x₂ + y₂, x₁ + x₂). Hence, T(u + v) = T(u) + T(v), satisfying the property of vector addition.

Similarly, the transformation of the scalar multiple of a vector c * u is T(cu), which is (cx + cy, cx). The scalar multiple of the transformation c * T(u) is c * (x + y, x) = (cx + cy, cx). Thus, T(cu) = c * T(u), demonstrating the property of scalar multiplication.

To find the matrix representation of the transformation T, we can map the standard basis vectors, i = (1, 0) and j = (0, 1), and arrange the resulting vectors into a matrix. Applying T to i and j, we have T(i) = (1, 1) and T(j) = (0, 0). Thus, the matrix representation of T is:

| 1 0 |

| 1 0 |

To draw the basic box representing the transformation, we consider the images of the standard unit vectors i and j. The image of i is (1, 1), and the image of j is (0, 0). Plotting these points on the coordinate plane, we can draw a box connecting them. This box represents the basic shape that gets transformed by the linear transformation T.

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Step-by-step explanation:

The given function is a quadratic function with a positive leading coefficient, therefore it opens upwards and has a minimum value. To find the minimum value of the function, we can use the formula:

x = -b/2a

where a = 1 and b = 6 are the coefficients of the quadratic function.

x = -6/2(1) = -3

Substitute x = -3 into the function to find the minimum value:

f(-3) = (-3)^2 + 6(-3) + 11 = 2

Therefore, the minimum value of the function is 2.