Find the area of the following
trapezoid:
8 cm
5 cm
4 cm
16 cm
A = [?] cm2

Answer:

4

Step-by-step explanation:

Answer:

B; There is only one (x,y) solution and y is negative

Step-by-step explanation:

First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.

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Step-by-step explanation:

π ∫₀¹ x² dx

This integral is obtained using disk method.  Each disk has a volume of V = πr²t, so the radius is r = x.

The region is 0 ≤ y ≤ x, 0 ≤ x ≤ 1.

Revolved around the x-axis, the resulting shape is a cone.

If the shape were a paraboloid, the integral would have been:

π ∫₀¹ (x²)² dx

π ∫₀¹ x⁴ dx

No, this shape does not belong in a group of shapes that have more than one pair of perpendicular sides.

In order to determine if the shape belongs to a group of shapes with more than one pair of perpendicular sides, we need to examine the number of right angles in the shape.

A right angle is a 90-degree angle, and shapes with perpendicular sides have right angles at their intersections. By counting the number of right angles in the shape, we can determine if it has more than one pair of perpendicular sides.

If the shape has only one right angle, then it does not have more than one pair of perpendicular sides. But if it has two or more right angles, then it would belong to the group of shapes that have more than one pair of perpendicular sides.

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Answer:

Subtraction property of equality

Step-by-step explanation:

5(-4x^2 +4)+ 1 = -x^2 +6 Given

                     -1             -1

= 5(-4x^2 +4) = -x^2 +5 Subtraction property of equality

Emily uses subtraction on both sides the equation to even the equation and getting rid of a like term.

Hope this helps :)

2p= 32"

1) The perimeter (2p) is the sum of the sides.

2) Since a square has four congruent sides, and each one, in this case, measures 8 "

Then we can write:

2p = 8 +8 + 8+8

2p = 32 inches

3) So the Perimeter is 32"

(a) The region Y₁ < 1/2 and Y₂ > 1/4 corresponds to the rectangle,

{(y₁, y₂) : 0 ≤ y₁ < 1/2 and 1/4 < y₂ ≤ 1}

Integrate the joint density over this region:

\(P\left(Y_1<\dfrac12,Y_2>\dfrac14\right) = \displaystyle\int_0^{\frac12}\int_{\frac14}^1 (y_1+y_2)\,\mathrm dy_2\,\mathrm dy_1 = \boxed{\dfrac{21}{64}}\)

(b) The line Y₁ + Y₂ = 1 cuts the support in half into a triangular region,

{(y₁, y₂) : 0 ≤ y₁ < 1 and 0 < y₂ ≤ 1 - y₁}

Integrate to get the probability:

\(P(Y_1+Y_2\le1) = \displaystyle\int_0^1\int_0^{1-y_1}(y_1+y_2)\,\mathrm dy_2\,\mathrm dy_1 = \boxed{\dfrac13}\)

Y₁ and Y₂ are not independent because

P(Y₁ = y₁, Y₂ = y₂) ≠ P(Y₁ = y₁) P(Y₂ = y₂)

To see this, compute the marginal densities of Y₁ and Y₂.

\(P(Y_1=y_1) = \displaystyle\int_0^1 f(y_1,y_2)\,\mathrm dy_2 = \begin{cases}\frac{2y_1+1}2&\text{if }0\le y_1\le1\\0&\text{otherwise}\end{cases}\)

\(P(Y_2=y_2) = \displaystyle\int_0^1 f(y_1,y_2)\,\mathrm dy_1 = \begin{cases}\frac{2y_2+1}2&\text{if }0\le y_2\le1\\0&\text{otherwise}\end{cases}\)

\(\implies P(Y_1=y_1)P(Y_2=y_2) = \begin{cases}\frac{(2y_1+1)(2y_2_1)}4&\text{if }0\le y_1\le1,0\ley_2\le1\\0&\text{otherwise}\end{cases}\)

but this clearly does not match the joint density.

The y-coordinate of -3f(x-1) when x = 0 is -63

From the question, we have the following parameters that can be used in our computation:

The table of values

So, we have

-3f(x - 1)

When x = 0, we have

y = -3f(0 - 1)

This gives

y = -3f(-1)

From the table, we have

y = -3 * 21

Evaluate

y = -63

Hence, the y-coordinate is -63

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Answer:

19

Step-by-step explanation:

-9b -5 -7b = -309

-16b - 5 = -309

16b = 309 - 5

16b = 304

b = 304 ÷ 16

b = 19

Answer:

x = 20

Step-by-step explanation:

Sum of 12, 8, 6, 4 and x is:

S = 12 + 8 + 6 + 4 + x = 30 + x

\(\dfrac{2}{5}S = \dfrac{2}{5}\cdot 30 + \dfrac{2}{5}x\\\\=12 + \dfrac{2}{5}x\\\\\\\textrm{But left side is nothing but x}\\\\\textrm{So we get }x = 12 + \dfrac{2}{5}x\\\\\rm{Subtract $\dfrac{2}{5}x$ from both sides}\\\\x - \dfrac{2}{5}x = 12\\\\\dfrac{3}{5}x = 12\\\\x = \dfrac{12 \cdot 5}{3} \\\\x = 20\\\\\)

Verify

12 + 8 + 6 + 4 + 20 = 50

(2/5) x 50 = 20

The correct statement:

The slope is positive because as the age increases, the value increases.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

The table:

x → y

5 →  0.75

10 → 5.75

15 →  10.75

20 → 15.75

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

m = 15.75 - 10.75 / 20 - 15

m = 1

Therefore, the slope is positive because as the age increases, the value increases.

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The value of the square root of 7 is,

⇒ √7 = 2.645

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

WE have to given that;

To find the value of the square root of 7 .

Since, the square root of 7 is,

⇒ √ 7

⇒ 2.645

Thus, The value of the square root of 7 is,

⇒ √7 = 2.645

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9: What is the probability of beef tips being the preferred new menu item?

To find the probability of a customer preferring beef tips over the other menu items, divide the quantity of customers that preferred beef tips over the total number of customers that participated in the survey:

28 / (42 + 28 + 30) = 28/100 = 28%

There is a 28% chance that beef tips is the new preferred menu item.

11: Out of a similar group of 375 customers, predict how many more customers will prefer chicken carbonara to shrimp scampi.

There are 100 customers that participated in the pre-existing survey. A grand total of 375 participants in a similar survey would mean that each food's preference would grow in a similar fashion.

100 * 3.75 = 375

You can then multiply each response group by 3.75 to find how many people prefer chicken carbonara and shrimp scampi.

42 * 3.75 = 157.5

30 * 3.75 = 112.5

Then, subtract the quantities to find out how many more people prefer chicken to shrimp.

157.5 - 112.5 = 45 people.

13: Predict the number of times that Giorgianna's name will be drawn in 32 weeks. Round to the nearest whole number.

There are five people in the group, and one is chosen as the team leader every week. 1 divided by 5 is .2, so the probability of being chosen as team leader is 20%.

You can multiply 0.2 by 32 to represent how many times the experiment will be run. The product is 6.4 times, so Giorgianna's name will likely be drawn 6 times within 32 weeks.

Answer:

9.) 7/ 25. 11). 45. 13) 6

Step-by-step explanation:

Explanation shown below;

For 13;

The probability of chosen Georgianna is 1/5

The number of times the draw would be conducted would be 32

Hence Georgianna would be chosen [ 1/5. * 32 = 6. 4 = 6[to the nearest whole]

Answer: A.

Step-by-step explanation: we just need to distribute and see that the only plausible answer is a because when distributed it equals 3x=6

Step-by-step explanation:

51 and 51

maybe

Answer:

4

Step-by-step explanation:

The required reverse Euclidean algorithm is the solution to the modular equation (5x) mod 91 is

x = 6(mod 91).

Given that (5*x) mod 91 =32.

To solve the modular equation (5*x) mod 91 =32 using reverse Euclidean algorithm is to find the modular inverse of 5 modulo 91.

Consider  (5*x) mod 91 =32.

5x = 32(mod 91)

Apply the Euclidean algorithm to find GCD of 5 and 91 is

91 = 18 * 5 + 1.

Rewrite it in congruence form,

1 = 91 - 18 *5

On simplifying the equation,

1 = 91 (mod 5)

The modular inverse of 5 modulo 91 is 18.

Multiply equation by 18 on both sides,

90x = 576 (mod91)

To obtain the smallest positive  solution,

91:576 = 6 (mod 91)

Divide both sides by the coefficient of x:

x = 6 * 90^(-1).

Apply the Euclidean algorithm,

91 = 1*90 + 1.

Simplify the equation,

1 + 1 mod (90)

The modular inverse of 90 modulo 91 is 1.

Substitute the modular inverse in the given question gives,

x = 6*1(mod 91)

x= 6 (mod91)

Therefore, the solution to the modular equation (5x) mod 91 is

x = 6(mod 91).

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Answer:

C. The shaded area represents both 2/3 and 6/9 of the whole shape.

Answer:

y - 2 / 4 is equivalent to 1/4y - 1/2

\(\displaystyle\\\frac{1}{4} y-\frac{1}{2} =\frac{1}{4} y-\frac{1}{4}\times2=\frac{1}{4} (y-2)\)

Answer:The square root of 16 is rational.

Step-by-step explanation:

The required linear functions are H = 30 + 10t and S = 45 + 7t and the number of weeks at which the saving would get the same is 5 weeks.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
H = 30 + 10t - - - - - (1)
S = 45 + 7t  - - - - - -(2)
According to the conditions,
30 + 10t = 45 + 7t
-3t = -15
t = 5 weeks

Thus, the required linear functions are H = 30 + 10t and S = 45 + 7t, and the number of weeks at which the saving would get the same is 5 weeks.

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Answer:

(y+2) / y

Step-by-step explanation:

Just do what is says     f(x ) = (y+2) / y

Answer:

35 x 2.51 = 87.85

36 x 2.51 = 90.36

If he cannot spend more than 90 than the maximum amount he can afford is 35.

Step-by-step explanation:

Answer: 35.8565737052

Answer:

sorry i cant help thanks

Step-by-step explanation:

Answer:

$258.10

Step-by-step explanation:

The simplified expression of x(3x + 5)-5(2x - 1) is 3x² - 5x + 5

From the question, we have the following parameters that can be used in our computation:

x(3x + 5)-5(2x - 1)

Open the brackets

So, we have

3x² + 5x - 10x + 5

Evaluate the like terms

So, we have

3x² - 5x + 5

Hence, the simplified expression is 3x² - 5x + 5

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Answer:  -2

Step-by-step explanation:

4y/4 = -8/4

     y = -2

Answer:

Step-by-step explanation:

Answer is -2