A
Both data sets show additive relationships in data set I y is 5.5 more than X and in data set II y is five more than X

B Data set I shows a multiplicative relationship in which y is 5.5 more than x

C both data sets show multiplicative relationships In data set I y is 5.5 times x and in data set II y is 5 times x

D Data set I shows an additive relationship in which y is 4.5 more than x data set II shows a multiplicative relationship in which Y is five times X

Answer:

30

Step-by-step explanation:

1/3 of 60 is 20

40 would be left

1/4 of 40 is 10 so 30 would be left

The volume of the solid is a) 1/30 and b) 1/6.

When the solid’s base is located in the xy plane and the cross-section is taken perpendicular to the x-axis with known cross sectional area given by A(x) for all the x in the interval [a,b], then the volume of the solid is given as the definite integral of these cross-sectional areas.

V = ∫_a^b▒A(x)dx

By graphing the given equations, we see that the area is bounded by the line y= x+1 and parabola y=x^2+1 on the interval on x-axis as [0,1].

a) The base of each square has length

f(x) – g(x) = (x + 1) – (x^2 + 1) = x – x^2

and the solid is square.

The area of cross section is

A(x) = (x – x^2)^2 = x^2 – 2x^3 + x^4

Hence, the volume is

∫_0^1▒A(x)dx

∫_0^1▒〖(x^2-2x^3+x^4)dx〗

[1/3 x^3-1/2 x^4+1/5 x^5]1¦0

[1/3 -1/2  +1/5]

1/30

b) The base of each rectangle has length

f(x) – g(x) = x – x^2

and the height of each rectangle is 1.

The area of cross section is

A(x) = (x – x^2)(1) = x - x^2

Hence, the volume is

∫_0^1▒A(x)dx

∫_0^1▒〖(〖x-x〗^2)dx〗

[1/2 x-1/3 x^3]1¦0

[1/2 -1/3]

1/6

Learn more about Volume of the solid:

https://brainly.com/question/24259805

#SPJ4

Answer:

A

Step-by-step explanation:

Answer:

The width of the frame is 3 inches

Step-by-step explanation:

We are told that the inner rectangle is 10 inches by 16 inches.

It means the outer rectangle has to be (L = 10 + 2x) by (W = 16 + 2x),

Where x represents the width of the frame.

The perimeter of the frame is given by; p = 2L + 2W

p = 2(10+2x) + 2(16+2x)

We are given perimeter, P = 76

Thus;

2(10 + 2x) + 2(16 + 2x) = 76

Divide both sides by 2 to give;

(10+2x) + (16+2x) = 38

(10+16) + (2x+2x) = 38

4x = 38 - 26

4x = 12

x = 12/4 = 3

The width of the frame is x = 3 inches

After 10 years with a Compound interest rate of 1.9%, the amount in Carrie's account will be approximately $1777.87.

The amount that will be in Carrie's account after 10 years with compound interest, we can use the formula Pt = P0 ⋅ (1 + r)^t.

Given:

P0 = $1480 (initial deposit)

r = 1.9% = 0.019 (interest rate as a decimal)

t = 10 (number of years)

Substituting these values into the formula, we get:

Pt = $1480 ⋅ (1 + 0.019)^10

Using a calculator, we can evaluate the expression inside the parentheses:

(1 + 0.019)^10 ≈ 1.201223

Now we can calculate the final amount in Carrie's account:

Pt ≈ $1480 ⋅ 1.201223

Pt ≈ $1777.87

Therefore, after 10 years with a compound interest rate of 1.9%, the amount in Carrie's account will be approximately $1777.87.

To know more about Compound interest rate.

https://brainly.com/question/3989769

#SPJ11

Answer:

A. 1 + 3x = -89

B. x = -30

Step-by-step explanation:

Let the unknown variable be x.

A. Translating the word problem into an algebraic expression, we have;

1 + 3x = -89

B. To solve for the unknown variable;

1 + 3x = -89

3x = -89 -1

3x = -90

x = -90/3

x = -30

Check:

1 + 3x = -89

Substituting the value of x;

1 + 3(-30) = -89

1 + (-90) = -89

1 - 90 = -89

-89 = -89

The numeric value of the exponential expression in this problem is given by the following option:

A. 2^12.

The exponential expression for this problem is defined as follows:

8^x/2^y.

8 is the third power of 2, hence:

8 = 2^3.

When a term is elevated to two of it's powers, the powers are multiplied, hence:

(2^3)^x = 2^(3x).

Meaning that the exponential expression is then written as follows:

8^x/2^y = 2^(3x)/2^y.

When two terms of the same base and different exponents are divided, we keep the base and subtract the exponents, hence the expression is given as follows:

2^(3x)/2^y = 2^(3x - y).

As stated in the problem, the numeric value of the expression 3x - y is given as follows:

3x - y = 12.

Hence the entire expression is simplified as follows:

2^(3x - y) = 2^12.

Meaning that the correct option is given by option A.

More can be learned about exponential expressions at https://brainly.com/question/25537936

#SPJ1

Answer:A. 2^12.

Step-by-step explanation:i did it and got it right

Answer:

Step-by-step explanation:

why do you need help if you already did it?

Answer:

y = x + 6

using the equation:

y - y₁ = m(x - x₁)

y - 5 = 1(x - -1)

y - 5 = x + 1

y = x + 1 + 5

y = x + 6

note: "m" refers to slope and y₁ and x₁ the coordinates the line is passing through.

Answer:

x < -3

Step-by-step explanation:

4x + 1 > 9x + 16​

-15 > 5x

-3 > x

\(\implies {\blue {\boxed {\boxed {\purple {\sf { \: 8 \frac{1}{3}\:(or) \:8.333}}}}}}\)

\(\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}\)

\(3 \frac{3}{4} \times 2 \frac{2}{9} \)

➺\( \: \frac{15}{4} \times \frac{20}{9} \)

➺\( \: \frac{300}{36} \)

➺\( \: \frac{25}{3} \)

➺\( \: 8 \frac{1}{3} \)

➺\( \: 8.333\)

\(\large\mathfrak{{\pmb{\underline{\pink{Mystique35 }}{\orange{❦}}}}}\)

The rigid motion of the solid line figure is translated to the dotted line figure.

Translation describe a function that moves an object a certain distance.

In a translation, every point of the object must be moved in the same direction and for the same distance.

In translation, the object is not resized, rotated or reflected. The object usually remains the same but it moves a certain distance.

Therefore, the rigid motion maps the solid-line figure onto the dotted-line figure by translation

learn more on motion here:https://brainly.com/question/29166471

#SPJ1

Answer:

30

Step-by-step explanation:

150/5 = 30

Answer: 30

Step-by-step explanation:

Answer:

Step-by-step explanation:

Awnser=48

you

11.54 cm

Explanation

Step 1

draw and label

we have a right triangle, then

Step 2

Let

hence, we need a function that relates those values, it is sine function:

The sine function is a periodic function which is very important in trigonometry, it says for a rigth triangle, the sine of angle is the ratio of opposite side to hypotenuse: so

finally, replace and solve for h

therefore, the hypotenuse is

11.54 cm

I hope this helps you

Answer:

Initial value 4x and rate of change is 75

Step-by-step explanation:

Because the initial value is the value before something is taken or added to it. Rate of change is whats being taken from the initial value

Answer:

8, 6, 24 because 8+6+24=38

Answer:

24+12+2=38

Step-by-step explanation:

Answer:

Conditionally convergent

Step-by-step explanation:

Use alternating series test.

bₙ = n / √(n³ + 9)

lim(n→∞) bₙ

= lim(n→∞) [n / √(n³ + 9)]

= lim(n→∞) (n / √n³)

= lim(n→∞) (1 / √n)

= 0

The limit is 0, and bₙ is a decreasing series, so ∑aₙ converges.

Since bₙ > 1/n for n > 2, and 1/n diverges, ∑bₙ diverges.

(Alternatively, we could use limit comparison test to compare bₙ to n/√n³ and show that both diverge.)

Therefore, ∑aₙ is conditionally convergent.

Step-by-step explanation:

\( { \alpha }^{4} + { \beta }^{4} = ( {( { \alpha }^{2} })^{2} + {( { \beta }^{2} })^{2} \)

\( = {( { \alpha }^{2} + { \beta }^{2} })^{2} - 2( { \alpha }^{2} )( { \beta }^{2} )\)

\( {( {( \alpha + \beta )}^{2} - 2 \alpha \beta ) }^{2} - 2( { \alpha )}^{2} ( { \beta )}^{2} \)

I hope it helped you

Answer:

1. 766,536cm^3

2. 29,680,948cm^3

3. 41,620.8cm^3

Step-by-step explanation:

1. 123×82 = 10,086 10,086×76 = 766,536

2. 422×278 = 117,316 117,316×253 = 29,680,948

3. 87×2.3 = 200.1 200.1×208 = 41,620.8

Hope this helps! :)

In order to explain why -4 - 2 equals -8, let's start with the equation 0.2 = 0. By analyzing this equation, we can uncover the reason behind this seemingly counterintuitive result.

1. Begin with the equation 0.2 = 0.

2. Subtract 0.2 from both sides of the equation to isolate the variable: 0.2 - 0.2 = 0 - 0.2.

  This simplifies to 0 = -0.2.

3. Observe that the right side of the equation, -0.2, is a negative number.

4. Recall that subtracting a negative number is equivalent to adding its positive counterpart. Therefore, -0.2 is the same as +0.2.

5. Rewrite the equation as 0 = +0.2.

6. Notice that 0 on the left side of the equation is equal to 0 + 0, since any number added to zero remains unchanged.

7. Substitute 0 + 0 for 0 in the equation: 0 + 0 = +0.2.

8. Simplify the equation to 0 = +0.2.

9. Finally, recognize that a positive number cannot equal zero. Hence, the equation 0 = +0.2 is false.

10. As a result, the original equation 0.2 = 0 is invalid.

11. Therefore, the logical consequence is that any subsequent deductions based on this invalid equation would also be incorrect.

12. Consequently, -4 - 2 does not equal -8, as per the explanation derived from the flawed equation.

To summarize, by analyzing the equation 0.2 = 0, we can determine that subsequent deductions based on this equation are incorrect. Hence, -4 - 2 does not equal -8.

For more such questions on counterintuitive, click on:

https://brainly.com/question/17004386

#SPJ8

\(\\ \sf\longmapsto 2+y=-2x---(1)\)

\(\\ \sf\longmapsto -2x^2+8xy+42=y\dots(2)\)

From equation (1)

\(\\ \sf\longmapsto y=-2x-2\dots(3)\)

Put in eq(2)

\(\\ \sf\longmapsto -2x^2+8x(-2x-2)+42=-2x-2\)

\(\\ \sf\longmapsto -2x^2-16x^2-16x+42=-2x-2\)

\(\\ \sf\longmapsto -18x^2-16x+2x+42+2=0\)

\(\\ \sf\longmapsto -18x^2-14x+44=0\)

On solving

\(\\ \sf\longmapsto x=\dfrac{11}{9}\:or\;-2\)

Take it whole.

Put in eq(3)

\(\\ \sf\longmapsto y=-2(-2)-2=4-2=2\)

Hence

This means that for every 1 sheep on the farm, there are 0.25 horses. To find the total number of horses, we can multiply the number of sheep by 0.25:

\(12 * 0.25 = 3\)

Ratio refers to the quantitative relationship between two or more quantities, expressing the proportion of one quantity to the other(s). It is typically expressed as a fraction, where the numerator represents one quantity, and the denominator represents the other quantity.

For example, the ratio of the number of boys to the number of girls in a class of 30 students might be expressed as 2:3, which means there are 20 girls and 10 boys in the class. Similarly, the ratio of the length to the width of a rectangle might be expressed as 4:3, indicating that the length is four times greater than the width.

The ratio of sheep to horses is 4:1, which means that for every 4 sheep on the farm, there is 1 horse. We can also say that the total ratio of sheep and horses on the farm is 4+1=5.

To express the relationship between the chickens and the sheep, we need to use the fact that there are 32 chickens and 12 sheep on the farm. We can write this as a ratio:

\(chickens : sheep = 32 : 12\)

We can simplify this ratio by dividing both sides by 4:

\(chickens: sheep = 8: 3\)

This means that for every 8 chickens on the farm, there are 3 sheep.

To determine the number of horses on the farm, we can use the fact that the total ratio of sheep and horses is 5. We know that the ratio of sheep to horses is 4:1, so we can write:

\(sheep : horses = 4 : 1\)

We can simplify this ratio by dividing both sides by 4:

\(sheep : horses = 1 : 0.25\)

This means that for every 1 sheep on the farm, there are 0.25 horses. To find the total number of horses, we can multiply the number of sheep by 0.25:

\(12 * 0.25 = 3\)

To know more about denominator, visit:

https://brainly.com/question/17153086

#SPJ1

Answer:

no solution

y=x^3

y= 2-1 x 1

Step-by-step explanation:

Answer:

5x-3

Step-by-step explanation:

^^

Answer:

the answer is 5x-3,

because there is (5 times x) and (3 times -1), which equals

5x + (3 * -1), or 5x-3

using the sine ratio in trigonometry, the value of cos X in the triangle given in the image is: D. cos X = 5/13.

In trigonometry, the cosine ratio is a mathematical function that relates the angle of a right triangle to the ratio of the length of the adjacent side to the hypotenuse. The cosine ratio is defined as:

cos θ = adjacent side / hypotenuse

Where θ is the angle between the hypotenuse and the adjacent side.

Given the following:

θ = X

adjacent side = 5

hypotenuse = 13

Substitute:

cos X = 5/13

Learn more about trigonometry on:

https://brainly.com/question/12172664

#SPJ1

The slope of the line that passes through the points (-6,13) and (8,-29) is -3

Answer:

m= -3

-29-13= ‐42

8- (-6) = 14

Divide -42 and 14 which will equal -3

Answer:

C.

Step-by-step explanation:

Answer:

75%

Step-by-step explanation:

The fraction 3/4 is equivalent to 75%. Therefore, the percent Kevin will catch a fly ball is 75%.