To prove a polygon is a rectangle, which of the properties listed must be included in the proof?

Answer:

-3 + 8a

Step-by-step explanation:

multiply 3 by -1 as well as -8a by -1 and you'll get -3 + 8a

Answer:

He should have moved to the right.

Step-by-step explanation:

Ken moved 7 to the right which is correct because he needs to get 7º higher, but when he moved 2º to the left that would be a temperature decrease which is is incorrect.

Answer:

Sample Response: Ken’s error was showing a decrease in temperature by moving 2 units left on the number line. He should have moved 2 units right to represent an increase in temperature of 2°C.

Step-by-step explanation:

The arc length of the curve x =\(y^4/4 + 1/8y^2\), for 1 <= y <= 5, is approximately 33.93 units.

To find the arc length of the curve, we use the formula for arc length integration. Given the equation x = \(y^4/4 + 1/8y^2\) and the interval 1 <= y <= 5, we want to determine the length of the curve within this range.

First, we differentiate the equation with respect to y to obtain dx/dy. In this case, dx/dy = \(y^3 + 1/4y\). Then, we use the formula for arc length:

L = ∫[a,b] \(\sqrt{(1 + (dx/dy)^2)}\) dy

Plugging in the values from the given interval, a = 1 and b = 5, we integrate the expression \(\sqrt{(1 + (y^3 + 1/4y)^2)}\) with respect to y. Evaluating this integral gives us the arc length of the curve within the specified interval, which is approximately 33.93 units.

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Answer:

no

Step-by-step explanation:

8 is not grater than 9 so it would be 7 6 5 4 3 2 0r 1

Answer:

26 hours

Step-by-step explanation: divide 520 by 20 which gets you 26 .

to work 26 hours youll make exactly 520 dollars plus the for dollars is 560 which is more than 520

Answer:

6/15 divided by 6

Step-by-step explanation:

\(\frac{2}{5} / 6\\= \frac{6}{15} / 6\\\)

The line which contains the points (4,0) and (0,-2), value of y when x =3 is,  -1/2

The equation of a straight line is a relationship between x and y coordinates, The two point form of a straight line is y-y₁ =  y₂-y₁/x₂-x₁(x-x₁).

Given that,

The points, (4,0) and (0,-2)

Equation of line for given two points,

y-y₁ =  y₂-y₁/x₂-x₁(x-x₁)

y-0 =  -2 - 0/0-4(x-4)

y = 1/2(x - 4)

2y = x - 4

when x = 3,

y =  1/2(3 - 4)

y = - 1/2

Hence, the value of y is -1/2

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Answer:

each hot dog costs $2.85

Step-by-step explanation:

Answer:

2.85 dollars

Step-by-step explanation:

Answer: 9 per minute

Step-by-step explanation: 81 divided by 9 is 9 to double-check 9x9=81

a)The distribution of \(X_{1} +X_{2}+X_{3}\) is a normal distribution with mean μ = 180 and variance σ² = 36.(b)P( \(X_{1} +X_{2}+X_{3}\) > 185) ≈ P(Z > 5/6).(c) The distribution of Y - X is a normal distribution with mean μ = 5 and variance σ² = 27.(d)P(Y - X > 8) ≈ P(Z > 1.732)

(a) The sum of independent normal random variables follows a normal distribution. In this case, X1, X2, and X3 are independent normal random variables with a common mean μ1 = 60 and a common variance σ1² = 12. Therefore, the distribution of \(X_{1} +X_{2}+X_{3}\) is also a normal distribution with the following parameters:

Mean: μ = μ1 + μ1 + μ1 = 60 + 60 + 60 = 180

Variance: σ² = σ1² + σ1² + σ1² = 12 + 12 + 12 = 36

So, the distribution of \(X_{1} +X_{2}+X_{3}\) is a normal distribution with mean μ = 180 and variance σ² = 36.

(b) To find P(\(X_{1} +X_{2}+X_{3}\) > 185), we need to calculate the probability that the sum of X1, X2, and X3 exceeds 185. Since X1, X2, and X3 are normally distributed with a mean of 180 and a variance of 36, we can standardize the variable using the Z-score formula.

Z = (X - μ) / σ

Z = (185 - 180) / √36 = 5 / 6

Now, we need to find the probability that Z is greater than 5/6. We can look up this probability in the standard normal distribution table or use statistical software to find the corresponding value.

P(\(X_{1} +X_{2}+X_{3}\) > 185) ≈ P(Z > 5/6)

(c) The difference of independent normal random variables follows a normal distribution. In this case, Y - X is the difference between Y (with mean μ2 = 65 and variance σ2² = 15) and X (with mean μ1 = 60 and variance σ1² = 12).

The mean of Y - X is μ2 - μ1 = 65 - 60 = 5.

The variance of Y - X is σ2² + σ1² = 15 + 12 = 27.

Therefore, the distribution of Y - X is a normal distribution with mean μ = 5 and variance σ² = 27.

(d) To find P(Y - X > 8), we need to calculate the probability that the difference between Y and X exceeds 8. Since Y - X is normally distributed with a mean of 5 and a variance of 27, we can standardize the variable using the Z-score formula.

Z = (Y - X - μ) / σ

Z = (8 - 5) / √27 ≈ 1.732

Now, we need to find the probability that Z is greater than 1.732. We can look up this probability in the standard normal distribution table or use statistical software to find the corresponding value.

P(Y - X > 8) ≈ P(Z > 1.732)

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The expression given as (4-√5)(4+ √ 5) + 2√11 when rewritten is 11 + 2√11

Here, we have,

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

(4-√5)(4+ √ 5)

2√11

Rewrite the expression properly

So, we have the following representation

(4-√5)(4+ √ 5) + 2√11

Apply the difference of two squares to open the bracket

This gives

(4-√5)(4+ √ 5) + 2√11 = 16 - 5 + 2√11

Evaluate the like terms

So, we have the following representation

(4-√5)(4+ √ 5) + 2√11 = 11 + 2√11

Hence, the solution of the expression is 11 + 2√11

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Answer:

how many miles did they walk

Step-by-step explanation:

you didn't put the full question

Answer:

Step-by-step explanation:

2x4 = 8

2x3=6

Answer:26.5

Step-by-step explanation:

Remember that

An equilateral triangle has three equal sides and three equal interior angles

The measure of each interior angle is 60 degrees

so

In this problem

If the given angle (2x+4) is the measure of an interior angle

then

2x+4=60

2x=60-4

2x=56

If the given angle (2x+4) is the measure of an exterior angle

then

2x+4=120

2x=120-4

2x=116

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Area. of circle =πr²

Area. of circle =3×2×2

Area. of circle =12ft²

Answer:

Every hexagon tessellates.

Step-by-step explanation:

Hexagons always tessellates when perfectly combined and aligned especially when the x sides and the y sides are parallel to each other.

The statement "Box 1 is negatively skewed, and Box 2 is symmetric" is true.

Looking at shown the box-and-whisker plots, we can make the following observations:

Box 1 has a longer whisker on the left side than on the right side, which indicates that the data is skewed to the left.

Therefore, Box 1 is negatively skewed.

Box 2 has whiskers that are approximately the same length on both sides, which indicates that the data is symmetric.

Therefore, Box 2 is symmetric.

Based on these observations, we can conclude that:

A) Box 1 is negatively skewed, and Box 2 is symmetric.

Therefore, the correct answer is A.

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The missing figure is attached below.

The value of "x" is the unknown number that, when multiplied by 12, gives a result of 72. By solving the equation, we find that the unknown number is 6.

Let's call the unknown number "x". The statement "When 12 is multiplied by a number, the result is 72" can be represented mathematically as:

12 * x = 72

This equation states that when we multiply 12 by the unknown number "x", we obtain a product of 72. To find the value of "x", we need to solve this equation.

To solve for "x", we can divide both sides of the equation by 12:

(12 * x) / 12 = 72 / 12

Simplifying, we have:

x = 6

Therefore, the equation that fits the given statement is:

12 * x = 72

Where "x" is equal to 6.

In this equation, the value of "x" is the unknown number that, when multiplied by 12, gives a result of 72. By solving the equation, we find that the unknown number is 6.

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a) To graph the marginal utility of x, we need to find the derivative of the utility function with respect to x. Given that y=1, the utility function becomes U=x^(1/5). Taking the derivative of U with respect to x, we get dU/dx = (1/5)x^(-4/5). This represents the marginal utility of x.

When we graph the marginal utility of x, we put the marginal utility on the vertical axis and x on the horizontal axis. Since x^(-4/5) is positive for all positive values of x, the graph of the marginal utility of x will have a positive slope that decreases as x increases. The shape of the graph will resemble a downward-sloping curve that approaches zero as x approaches infinity.

b) The MRS (Marginal Rate of Substitution) for this consumer is the rate at which the consumer is willing to trade one good for another while keeping the total utility constant. In this case, the MRS is the negative ratio of the marginal utility of x to the marginal utility of y. Mathematically, MRS = -(dU/dx)/(dU/dy).

Since y is a constant and dU/dy = 0, the MRS simplifies to MRS = -(dU/dx)/0 = undefined. This means that the consumer is not willing to trade any amount of y for x, as the marginal utility of y is zero. The consumer only derives utility from x and does not value y in terms of marginal utility.

The graph of the marginal utility of x will have a positive slope that decreases as x increases. The MRS for this consumer is undefined, indicating that the consumer does not value y in terms of marginal utility.

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Answer:

64x

Step-by-step explanation:

Hello!

Using the exponent rule \(\frac{a^b}{a^c} = a^{b - c}\), we can simplify the fraction.

The simplified expression is 64x.

Answer:

Drawing the first marble would be 4/17 then putting that one aside and picking another green marble would be 3/17

Step-by-step explanation:

The predicted selling price for an observed selling price of 233.1 and square footage of 1385 is $235.96 (thousands of dollars). The error is 1.24 and the squared error is 1.5376.

Selling price is the amount of money that a seller charges for a product or service. It is usually determined by factors such as the cost of materials, labor costs, overhead, and the desired profit margin. In some cases, the selling price may also be affected by factors such as the product's demand, competitive pricing, and market conditions.

The equation used to predict the selling price is Predicted Selling Price (Thousands of Dollars)=23.11 +0.15 Square Footage.
For the given data, we have
Observed Selling Price = 233.1
Square Footage = 1385

Therefore,
Predicted Selling Price (Thousands of Dollars) = 23.11 + 0.15*1385
= 23.11 + 207.75
= 230.86.

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Answer:

read the answers below.

Step-by-step explanation:

d = dog

d = c + 8

ch = chickens

ch = d -2

gp = guinia pigs

gp = c - 3

d + c + ch + gp = 59

gp = c- 3

gp = d -8 - 3

gp = d - 11

d + d-8 + d - 2 + d-11 = 59

4d -8 - 2 - 11 = 59

4d - 21 = 59

4d - 21 + 21 = 59 + 21

4d = 80

4d/4 = 80/4

d = 20

========

c = d - 8

c = 20 - 8

c = 12

========

ch = d - 2

ch = 20 - 2

ch = 18

=========

gp = d - 11

gp = 20 - 11

gp = 9

Answer:

a. 7m+19

b. You caught more fireflies, your friend caught less

Step-by-step explanation:

Answer:

Expression: 7m +19

Who has More? Me/You

The expression which is equivalent to (14x)⁰y-⁷z as required in the task content is; z / y⁷.

It follows from the task content that the expression which is equivalent to the given expression (14x)⁰y-⁷z is to be determined.

Recall from the laws of indices that a⁰ = 1 where a represents any mathematical entity.

Therefore, the resulting expression is;

1 • y -⁷ • z

= z • 1 / y⁷

= z / y⁷.

Ultimately, the resulting expression which is equivalent is; z / y⁷.

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Answer:

G(6)=13

Step-by-step explanation:

G(6)=2(6)+1 or G(6)=12+1 which is 13 hope this helps ur welcome

Answer:

12

Step-by-step explanation:

g(6)=2(6)+1

=12+1

=13

Answer:

55 games

Step-by-step explanation:

What we have to figure out is the total amount of games they played the whole year. We know they won 20% of their games, which equates to 11 games won in total. In order to find the total amount of games we will need to set up the equation \(g = 11/20\)%. We solve this accordingly: \(g = (11/20) *100\); \(g = (.55)*100\); \(g = 55\).

The area under the curve over [2,5] is 24.

Given function is f(x) = 2xIntervals [2, 5] is given and it is to be divided into subintervals.

Let us consider n subintervals. Therefore, width of each subinterval would be:

$$
\Delta x=\frac{b-a}{n}=\frac{5-2}{n}=\frac{3}{n}
$$Here, we are using right-hand end point. Therefore, the right-hand end points would be:$${ c }_{ k }=a+k\Delta x=2+k\cdot\frac{3}{n}=2+\frac{3k}{n}$$$$
\begin{aligned}
\therefore R &= \sum _{ k=1 }^{ n }{ f\left( { c }_{ k } \right) \Delta x } \\&=\sum _{ k=1 }^{ n }{ f\left( 2+\frac{3k}{n} \right) \cdot \frac{3}{n} }\\&=\sum _{ k=1 }^{ n }{ 2\cdot\left( 2+\frac{3k}{n} \right) \cdot \frac{3}{n} }\\&=\sum _{ k=1 }^{ n }{ \frac{12}{n}\cdot\left( 2+\frac{3k}{n} \right) }\\&=\sum _{ k=1 }^{ n }{ \frac{24}{n}+\frac{36k}{n^{ 2 }} }\\&=\frac{24}{n}\sum _{ k=1 }^{ n }{ 1 } +\frac{36}{n^{ 2 }}\sum _{ k=1 }^{ n }{ k } \\&= \frac{24n}{n}+\frac{36}{n^{ 2 }}\cdot\frac{n\left( n+1 \right)}{2}\\&= 24 + \frac{18\left( n+1 \right)}{n}
\end{aligned}
$$Take limit as n → ∞, so that $$
\begin{aligned}
A&=\lim _{ n\rightarrow \infty  }{ R } \\&= \lim _{ n\rightarrow \infty  }{ 24 + \frac{18\left( n+1 \right)}{n} } \\&= \boxed{24}
\end{aligned}
$$

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Given function f(x) = 2x. The interval is [2,5]. The number of subintervals, n is 3.

Therefore, the area under the curve over [2,5] is 21.

From the given data, we can see that the width of the interval is:

Δx = (5 - 2) / n

= 3/n

The endpoints of the subintervals are:

[2, 2 + Δx], [2 + Δx, 2 + 2Δx], [2 + 2Δx, 5]

Thus, the right endpoints of the subintervals are: 2 + Δx, 2 + 2Δx, 5

The formula for the Riemann sum is:

S = f(c1)Δx + f(c2)Δx + ... + f(cn)Δx

Here, we have to find a formula for the Riemann sum obtained by dividing the interval [2.5] subintervals and using the right hand endpoint for each ck. The width of each subinterval is:

Δx = (5 - 2) / n

= 3/n

Therefore,

Δx = 3/3

= 1

So, the subintervals are: [2, 3], [3, 4], [4, 5]

The right endpoints are:3, 4, 5. The formula for the Riemann sum is:

S = f(c1)Δx + f(c2)Δx + ... + f(cn)Δx

Here, Δx is 1, f(x) is 2x

∴ f(c1) = 2(3)

= 6,

f(c2) = 2(4)

= 8, and

f(c3) = 2(5)

= 10

∴ S = f(c1)Δx + f(c2)Δx + f(c3)Δx

= 6(1) + 8(1) + 10(1)

= 6 + 8 + 10

= 24

Therefore, the Riemann sum is 24.

To calculate the area under the curve over [2, 5], we take the limit of the Riemann sum as n → ∞.

∴ Area = ∫2^5f(x)dx

= ∫2^52xdx

= [x^2]2^5

= 25 - 4

= 21

Therefore, the area under the curve over [2,5] is 21.

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