pls help me ty very much​

The point where the line intersects the plane is (-1, 7, 13).

To find the point where the line intersects the plane, we need to substitute the equations of the line into the equation of the plane and solve for the parameter t.

Substituting x, y, and z from the equation of the line into the equation of the plane, we get:

x + y + z = 13

(-1) + (1 + t) + (1 + 2t) = 13

2t + 1 = 13

2t = 12

t = 6

Now we can substitute t = 6 back into the equations of the line to find the point of intersection:

x = -1

y = 1 + t = 1 + 6 = 7

z = 1 + 2t = 1 + 2(6) = 13.

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The largest area that can be enclosed with 6,500 meters of fencing without fencing the side along the river is approximately 1,083,333.33 square meters.

To find this answer, we can use the formula for the area of a rectangle, A = lw, where l is the length of the rectangle and w is the width of the rectangle.

Since we are not fencing the side along the river, the rectangle has three sides that are each of length x, and one side that is the length of the river, which we can call y. We know that the perimeter of the rectangle is 6,500 meters, so:

Solving for y, we get:

Now we can substitute y into the formula for the area of a rectangle:

Expanding this expression, we get:

A = 6,500x - 3x²

To find the maximum value of A, we can take the derivative of A with respect to x and set it equal to zero:

dA/dx = 6,500 - 6x = 0

Solving for x, we get:

x = 1,083.33

Substituting x back into the equation for y, we get:

Therefore, the largest area that can be enclosed is approximately:

A = 1,083.33(2,250.01) = 1,083,333.33 square meters.

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Complete Question:

Farmer Ed has 6,500 meters of​ fencing and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the​ river, what is the largest area that can be​ enclosed?

Answer:

9

Step-by-step explanation:

The probability that a randomly selected student has a typing speed of less than 38 words per minute is 15.87%.

What is normal distribution?

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

The formula for z-score is z = (x -μ)/σ

Where,

Z is standard score.

x is observed value.

μ is mean of the sample.

σ is standard deviation of the sample.

According to the given question.

The mean of the distribution is μ = 44

The standard deviation of the distribution is σ = 6

The observed value is x = 38

Therefore, z-score = (38 -44)/6 = -1

So, the are P(z > -1) = 15.87%

Hence, the probability that a randomly selected student has a typing speed of less than 38 words per minute is 15.87%.

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Answer:

43.3 m²

Explanation:

The surface area of the pyramid can be calculated as 4 times the area of one face.

So, the area of one face is equal to:

Where b is the base of the triangles and h is the height. So, replacing b by 5 m and h by 4.33 m, we get:

So, the surface area is equal to:

Therefore, the answer is 43.3 m²

Answer:

118

Step-by-step explanation:

you should have learned this in 1st grade

Answer: 14 boxes

Step-by-step explanation:

Divide 110 by 8 and you get 13.75. You will then round up to the nearest hole number to make sure that almost all the boxes have 8 muffins in each.

Answer

option C

Explanation:

Given the right angled triangle XYZ

The legs are Length YZ and Length ZX

Therefore, the legs are YZ AND ZX

When a crucial variable is excluded from a regression model, the results are referred to as omitted variable bias.

Regression analysis frequently encounters the issue of omitted variable bias, which occurs when an important independent variable is left out of the model and affects the estimates of the coefficients for the included variables.

This happens because one or more of the included independent variables as well as the dependent variable may be correlated with the variable that was left out. As a result, the intercept and coefficients of the included independent variables may be overestimated or underestimated.

Based on prior knowledge and theory, researchers should carefully consider which variables to include in the model to address this issue. They should then test for potential correlations between the included and

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Answer:

I think it's the 2nd one B but im not completely sure

Step-by-step explanation:

Answer: Inconsistent

Step-by-step explanation:

y = 3x + 4   → m = 3, b = 4

y = 3x + 3   → m = 3, b = 3

These equations have the same slope but different y-intercepts so they are parallel lines which means they will never intersect.

NOTES

one solution: consistent & independent        lines cross

infinite solutions: consistent & dependent     same line

no solution: inconsistent                                  parallel lines

The volume common to two spheres, each with radius r, if the distance between their centres is r/2 is V = (11/12)×π×r³.

The attached diagram shows 2 circumferences with radius r and separated centres by r/2.

Let´s call circumferences  1 and 2; by symmetry, rotating area A will produce a volume V₁ identical to a V₂, Obtained by rotating area B ( both around the x-axis), then the whole volume V will be:

V = 2× V₁

V₁ = ∫π×y²×dx         (1)

Now

( x - r/2)²  +  y² = r²       the equation of circumference 1

y² = r² - ( x - r/2)²

Plugging this value in equation (1)

V₁ = ∫π×[  r² - ( x - r/2)²]×dx        with integrations limits    0 ≤ x ≤ r/2

V₁ = π×∫ ( r² - x² + (r/2)² - r×x )×dx

V₁ = π× [  r²×x - x³/3 + (r/2)²×x - (1/2) × r × x²]    evaluate between 0 and r/2

V₁ = π× [(5/4)×r²×x - x³/3 - (1/2) × r × x²]

V₁ =  π× [(5/4)×r² × ( r/2 - 0 ) - (1/3)×(r/2)³ -  (1/2) × r × (r/2)²]

V₁ =  π× [ (5/8)×r³ - r³/24 - r³/8]

V₁ =  π× (11/24)×r³

Then

V = 2× V₁

V = 2×π×11/24)×r³

V = (11/12)×π×r³

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Answer:

=x^16y^26

Step-by-step explanation:

x^18y^24xy^2

x^16y^24xy^2

Answer:

D (x^16y^22)

Step-by-step explanation:

For edge

Each time the number of hours (on the x axis) goes up by 1, the cost (on the y axis) goes up by up by $2. So each hour costs $2.

You can pick two points on the graph, such as (1,2) and (2,4) to compute the slope using the slope formula below

m = (y2 - y1)/(x2 - x1)

m = (4-2)/(2-1)

m = 2/1

m = 2 we get a slope of 2

The slope is the rise/run

rise = change in cost = change in y

run = change in time = change in x

When the equation is solved for B, the equivalent equation is B = 8/A

The equation is given as:

BA = 8

To solve for the variable B, we simply divide both sides by A

So, we have:

BA/A = 8/A

Evaluate the expression on the right-hand side

BA/A = 8/A

Evaluate the expression on the left-hand side

B = 8/A

Hence, when the equation is solved for B, the equivalent equation is B = 8/A

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Answer:

\(\displaystyle \int_1^6\left|\frac{1}{x}-\frac{1}{x^2}\right|dx=\ln|6|-\frac{5}{6}\)

Step-by-step explanation:

We'll integrate with respect to x.

Recall that the area between some \(f(x)\) and some \(g(x)\) on the interval \([a, b]\) is given by:

\(\displaystyle \int_a^b|f(x)-g(x)|dx\)

The function \(x=6\) will be the upper bounds of our definite integral. The lower bounds will be the intersection of \(\displaystyle y=\frac{1}{x}\) and \(\displaystyle y=\frac{1}{x^2}\). Set the functions equal to each other and solve for x:

\(\displaystyle \frac{1}{x}=\frac{1}{x^2},\\\\x^2=x,\\x=1\)

Therefore, we'll be integrating the area between \(\displaystyle \frac{1}{x}\) and \(\displaystyle \frac{1}{x^2}\) on the interval \([1, 6]\). In integral notation, this is:

\(\displaystyle \int_1^6\left|\frac{1}{x}-\frac{1}{x^2}\right|dx\)

To evaluate this integral, recall that \(\displaystyle \int \frac{1}{x}dx=\ln|x|+C\) and \(\displaystyle \int \frac{1}{x^2}dx=\int x^{-2}dx=-x^{-1}+C=-\frac{1}{x}+C\).

Therefore,

\(\displaystyle \int_1^6\left|\frac{1}{x}-\frac{1}{x^2}\right|dx=\int_1^6\ln|x|-\left(-\frac{1}{x}\right)dx=\int_1^6\ln|x|+\frac{1}{x}dx\)

Solving yields:

\(\displaystyle\left \left(\ln|x|+\frac{1}{x}\right) \right \vert_1^6=\ln|6|+\frac{1}{6}-\left(\ln|1|+\frac{1}{1}\right)=\ln|6|+\frac{1}{6}-0-1=\boxed{\ln|6|-\frac{5}{6}}\)

Answer:

\(\ln 6 - \dfrac{5}{6}\)

Step-by-step explanation:

To find the area enclosed by curves and lines, use definite integration:

\(\displaystyle \int^b_a \text{f}(x)\:\:\text{d}x \quad \textsf{(where a is the lower limit and b is the upper limit)}\)

Definite integrals have limits.  The limits tell you the range of x-values to integrate the function between.

Given functions:

\(\begin{cases}y=\dfrac{1}{x}\\\\y=\dfrac{1}{x^2}\end{cases}\)

The upper limit has been given as x = 6.

The lower limit is the point of intersection of the two curves.

To find the lower limit, equate the functions and solve for x:

\(\implies \dfrac{1}{x}=\dfrac{1}{x^2}\)

\(\implies x=1\)

Therefore, the limits for this integration are x = 1 and x = 6.

To find the area enclosed by the two curves, the point of intersection and the line x=3, integrate the areas under both curves using definite integration and subtract the area under the lower curve from the area under the upper curve.

\(\begin{aligned}\displaystyle \int^6_1 \dfrac{1}{x}\:\:dx-\int^6_1 \dfrac{1}{x^2}\:\:dx & = \int^6_1\left(\dfrac{1}{x}-\dfrac{1}{x^2}\right)\:\:dx \\\\& = \int^6_1\left(\dfrac{1}{x}-x^{-2}\right)\:\:dx\\\\& = \left[\ln |x| + \dfrac{1}{x} \right]^6_1\\\\& = \left(\ln 6 + \dfrac{1}{6} \right) - \left(\ln 1 + \dfrac{1}{1} \right)\\\\& = \left(\ln 6 + \dfrac{1}{6} \right) - \left(0 +1\right)\\\\& = \ln 6 -\dfrac{5}{6}\end{aligned}\)

Integration Rules

\(\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}\)

Increase the power by 1, then divide by the new power.

\(\boxed{\begin{minipage}{3.5 cm}\underline{Integrating $\frac{1}{x}$}\\\\$\displaystyle \int \dfrac{1}{x}\:\text{d}x=\ln |x|+\text{C}$\end{minipage}}\)

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Answer:

Therefore, based on the given scatter plot, the set of numbers that matches the points is C. 8,9,8,10,8,11.

Step-by-step explanation:

The scatter plot shown represents a set of nine points on a coordinate plane. Each point consists of an x-coordinate and a y-coordinate. To determine which set of numbers corresponds to the scatter plot, we need to analyze the pattern in the given points.

Looking at the scatter plot, we observe that the x-coordinates range from 0 to 10 with an increment of 1, while the y-coordinates seem to vary.

Now let's examine the given answer choices:

A. .4,4,5,5,6,6

B. .4,10,4,11,4,12

C. 8,9,8,10,8,11

D. 10,10,10,11,10,12

Set C (8,9,8,10,8,11) among these answer choices matches the pattern observed in the scatter plot. The x-coordinates in the scatter plot range from 0 to 10, and the y-coordinates correspond to the numbers provided in set C.

Therefore, based on the given scatter plot, the set of numbers that matches the points is C.

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Answer:

A!!!!!!!!!!!!!!!!!!

Answer:

Step-by-step explanation:

Step one:

given data

Maya

P=$1650

r=5%= 0.05

t= 4 years

The simple interest expression is

A=P(1+rt)

A=1650(1+0.08*4)

A=1650(1+0.32)

A=1650(1.32)

A=1650*1.32

A=$2178

James

P=$1600

r=8%= 0.08

t=4years

The compound interest expression is

A=P(1+r)^t

A=1600(1+0.08)^4

A=1600(1.08)^4

A=1600*1.360

A=$2176

After 4 years Mayas' balance is $2178

After 4 years James' balance is $2176

the difference is =2178-2176=$2

The arithmetic sequence is:

3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43,....

Common difference = 4

First term = 3

The formula for the sum of the first n terms of an arithmetic sequence is:

Sₙ = ⁿ/₂[2a + (n − 1)d]

where:

n = the number of terms to be added.

a = the first term in the sequence.

d = common difference

We are told that sum of the first 9 term is 171. Thus:

(9/2) [2a + (9 − 1)d]  = 171

(2a + 8d) = 38   ----(1)

Sum of the next 5 term is 235.

Thus, sum of the first 14 terms = 235 + 171 = 406

(14/2) [2a + (14 − 1)d]  = 406

7(2a + 13d) = 406

2a + 13d = 58    -----(2)

Subtract eq 1 from eq 2 to get:

5d = 20

d = 4

2a + 13(4) = 58

2a = 58 - 52

a = 3

Sequence is:

3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43,....

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Answer:

Step-by-step explanation:From the issue, we may deduce that:

x + y = 50 She desires to produce 50 ounces of the combination (because to this).

(0.35x) + (0.60y) = 0.55(x+y) (because we're calculating the amount of salt in each solution and the combination contains 55% salt)

We may take the first equation and replace it in the second equation:

(0.35x) + (0.60y) = 0.55(50) (50)

0.35x + 0.60y = 27.5 when x is substituted.

A system of two equations with two variables is now available:

x + y = 50\s0.35x + 0.60y = 27.5

To determine one of the variables in terms of the other, we may utilize the first equation. Let's figure out y:

y = 50 - x

We now change y in the second equation to the following expression:

0.35x + 0.60(50-x) = 27.5

Finding the value of x:

0.35x + 30 - 0.6x = 27.5

0.25x= -2.5

x= -10

Since the number of ounces cannot be negative, the answer is illogical. As a result, you should double-check your calculations or determine if the issue statement contains a mistake.

To get the answer, you can also try an alternative approach like substitution or elimination. Then, double-check your calculations.

Given information:h(t) = -5t² + 12t + 14 where t is measured in seconds.a) How high is the rock off the ground when it is thrown?For h(0), the initial height of the rock is required.h(0) = -5(0)² + 12(0) + 14 = 14 meters.

For h(t), the rock's maximum height needs to be found to determine the time when the rock hits the ground. In order to determine the maximum height, first, we need to find the time of maximum height using the formula:

tmax = -b/2a = -12/2(-5) = 1.2s

Now, h(1.2) can be found to determine the maximum height:

h(1.2) = -5(1.2)² + 12(1.2) + 14 = 20.8 meters

Therefore, the rock is in the air for (1.2*2) 2.4 seconds.c) For what times is the height of the rock greater than 17 metres?This means h(t) > 17. Solving this inequality gives:-

5t² + 12t + 14 > 17

=> -5t² + 12t - 3 > 0

=> (-5t + 3)(t - 1) > 0

From part c, we know that the rock's height is greater than 17 metres between 0 and 0.6 seconds and after 1 second. Therefore, the time the rock is above 17 metres is the sum of these two time periods:0.6 seconds + (2 - 1) seconds = 1.6 seconds.

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The equation of the surface of revolution generated by revolving x = (1/z)^z about the z-axis is x = e^(-y).

To find the equation of the surface of revolution, we start with the parametric equation x = (1/z)^z, y = t, z = t. We eliminate the parameter t by substituting z for t in the equation x = (1/z)^z. Simplifying further, we obtain x = e^(-y).

This equation represents the surface of revolution generated by revolving the curve x = (1/z)^z about the z-axis. The exponentiation by e^(-y) signifies that the x-coordinate changes exponentially as the y-coordinate varies.

Therefore, as we revolve the curve around the z-axis, it forms a surface with an exponential decay in the x-direction. Hence, the equation x = e^(-y) describes the surface of revolution.

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Answer:

9:thirty one

Step-by-step explanation:

Add 46 twenty and 5three then add the answer in 7:thirty

(a) Ω = {1, 2, 3, 4} × {1, 2, 3, 4}, F = power set of Ω, P assigns equal probability (1/16) to each outcome.

(b) X1 and X2 represent the values of the first and second rolls, respectively.

(c) X is the random variable defined as the maximum value from the two rolls, with state space Sx = {1, 2, 3, 4}.

(d) pX(1) = 1/16, pX(2) = 3/16, pX(3) = 5/16, pX(4) = 7/16.

(e) The cumulative distribution function Fx of X:

Fx(1) = 1/16, Fx(2) = 1/4, Fx(3) = 9/16, Fx(4) = 1.

(a) The underlying probability space (Ω, F, P) for the random experiment can be specified as follows:

- Sample space Ω: {1, 2, 3, 4} × {1, 2, 3, 4} (all possible outcomes of the two rolls)

- Event space F: The set of all possible subsets of Ω (power set of Ω), representing all possible events

- Probability measure P: Assumes each outcome in Ω is equally likely, so P assigns equal probability to each outcome.

Since the two rolls are assumed to be independent, the joint probability of any two outcomes is the product of their individual probabilities. Therefore, P({i} × {j}) = P({i}) × P({j}) = 1/16 for all i, j ∈ {1, 2, 3, 4}.

(b) Two independent random variables X1 and X2 can be defined as follows:

- X1: The value of the first roll

- X2: The value of the second roll

These random variables are independent because the outcome of the first roll does not affect the outcome of the second roll.

(c) The random variable X can be defined as follows:

- X: The maximum value from the two rolls, i.e., X = max(X1, X2)

The state space Sx for X can be determined as Sx = {1, 2, 3, 4} (the maximum value can range from 1 to 4).

(d) The probability mass function px of X can be computed as follows:

- pX(1) = P(X = 1) = P(X1 = 1 and X2 = 1) = 1/16

- pX(2) = P(X = 2) = P(X1 = 2 and X2 = 2) + P(X1 = 2 and X2 = 1) + P(X1 = 1 and X2 = 2) = 1/16 + 1/16 + 1/16 = 3/16

- pX(3) = P(X = 3) = P(X1 = 3 and X2 = 3) + P(X1 = 3 and X2 = 1) + P(X1 = 1 and X2 = 3) + P(X1 = 3 and X2 = 2) + P(X1 = 2 and X2 = 3) = 1/16 + 1/16 + 1/16 + 1/16 + 1/16 = 5/16

- pX(4) = P(X = 4) = P(X1 = 4 and X2 = 4) + P(X1 = 4 and X2 = 1) + P(X1 = 1 and X2 = 4) + P(X1 = 4 and X2 = 2) + P(X1 = 2 and X2 = 4) + P(X1 = 3 and X2 = 4) + P(X1 = 4 and X2 = 3) = 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 = 7/16

(e) The cumulative distribution function Fx of X can be computed as follows:

- Fx(1) = P(X ≤ 1) = pX(1) = 1/16

- Fx(2) = P(X ≤ 2) = pX(1) + pX(2) = 1/16 + 3/16 = 4/16 = 1/4

- Fx(3) = P(X ≤ 3) = pX(1) + pX(2) + pX(3) = 1/16 + 3/16 + 5/16 = 9/16

- Fx(4) = P(X ≤ 4) = pX(1) + pX(2) + pX(3) + pX(4) = 1/16 + 3/16 + 5/16 + 7/16 = 16/16 = 1

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Answer:

-0.25n + 1

Step-by-step explanation:

Difference between all numbers: -0.25

Hence,

\(t_n = -0.25n + 1\)

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The probability that micah is included in the group of students chosen is ²⁸²⁸²⁸C₃₃₂ / ²⁸²⁸²⁸C₃₃₃

According to the question,

Total number of students in class = 282828

Micha's roll number = 111

Micha's teacher is randomly selecting students

Number of students to be selected = 333

So , Total number of ways to select 333 students from 282828 is

=> ²⁸²⁸²⁸C₃₃₃

Now , We have to find the probability that micah is included in this sample.

So, Lets fixed the place of micah

Number of students left after fixing micah place = 333 - 1

=> 332

Number of ways to select these 332 = ²⁸²⁸²⁸C₃₃₂

Therefore , Probability = ²⁸²⁸²⁸C₃₃₂ / ²⁸²⁸²⁸C₃₃₃

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In a case whereby sheri’s cab fare was $32, with a 20% gratuity and no taxes. sheri's write a check to the cab driver for $40, this can be considered as being reasonable amount because it is  $1.60 more to the cab driver.

A gratuity is a sum of money that customers typically give to specific service sector employees, including those in the hotel industry, in addition to the service's base charge for the work they have completed.

Given ; Sheri’s cab fare was $32 and the percentage of gratuity is 20%

amount of gratuity = 20% 0f 32 = 6.40

The fare of the cab  + gratuity = 32 + 6.40 = 38.40

Check to the cab driver for $40 ,  implies ($40 - $38.40)= $1.60 more to the cab driver.

Hence, it is reasonable.

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Answer:

34°

Step-by-step explanation:

A triangle measures 180°

An isosceles triangle has two angles and sides with equal measurements.

We know that one angle is 112°. Thus, we can use that to form an equation to solve for the unknown values:

112° + x + x = 180°

112° + 2x = 180°

2x = 68

x = 34°

The other two angles each measure 34°.

Check:

112 + 34 + 34 = 180

hope this helps and is right!! p.s. i really need brainliest :)

Answer:

34°

Step-by-step explanation:

Sum of interior angles of a triangle is 180°

Two of the interior angles of an Isosceles triangle are equal

Given one of the interior angles is 112° then the remaining two angle must be equal:

⇒ 112 + 2x = 180

⇒ 2x = 68

⇒ x = 34°

1. To have 50, 4-ounce portions of green beans, we need to find how many pounds of fresh green beans should be bought.

Firstly, we'll need to find out how many ounces are needed to have a total of 50 portions of 4-ounces each.

50 portions of 4 ounces each = 50 × 4 = 200 ounces.

To find the total weight in ounces of the green beans that need to be purchased, we divide 200 by 0.85 (as 85% of fresh green beans are edible) as follows:

Total weight in ounces = 200/0.85 = 235.29 ounces.

1 pound is equal to 16 ounces, so to find the total weight in pounds of fresh green beans, we divide 235.29 by 16 as follows:

Total weight in pounds = 235.29/16 = 14.7 pounds.

Therefore, approximately 15 pounds of fresh green beans should be purchased.

2. We need to find out how much whole fish we need to buy to obtain 10 pounds of fish after it has been cleaned (with 40% yield).

We can solve for this using the formula: Yield% = (edible portion ÷ raw portion) × 100.

We can rearrange the formula as: Edible portion = (yield% ÷ 100) × raw portion

We need a 40% yield, so substituting the given values in the formula above, we get:

Edible portion = (40 ÷ 100) × Raw portion

Let's say Raw portion is R. We need 10 pounds of edible portion, so:

10 pounds = (40 ÷ 100) × R10 ÷ (40 ÷ 100) = R25 = R

Therefore, 25 pounds of whole fish should be purchased.

3. We are serving 60 people with half-pound strip sirloin, so we need to find how many pounds of sirloin should be brought in, assuming that 20% of it will be wasted after trimming.

Each serving requires a half-pound, so 60 people need a total of 60 × 0.5 = 30 pounds of sirloin.

To find out the total weight of sirloin that should be brought in, we can use the formula:

Total weight of sirloin = Required weight of sirloin ÷ (1 - Waste%)

Required weight of sirloin = 30 pounds

Waste% = 20% = 0.2

Substituting these values into the formula, we get:

Total weight of sirloin = 30 ÷ (1 - 0.2)= 30 ÷ 0.8= 37.5 pounds.

So, approximately 38 pounds of sirloin should be brought in.

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Answer:

50 km

Step-by-step explanation:

So the map has a scale of 1 cm: 20 km. Next, you look at how far they are apart and see if the scale and the distance on the map are the same measurement. In this case, they are both centimeters so they stay the same. Then, all you do is multiple the real size, 20 km, by

2.5

1

. Then, 20 x 2.5=50. So the answer is 50 km

Answer:

$3.36 per pound

Step-by-step explanation:

The information gives us that 1/4 a pound of salad costs $0.84, to get to one pound all we have to do is multiply $0.84 by 4 to get our pound price.

0.84*4= $3.36

Brainliest would be appreciated! :-)