mJWL=87 degrees. Find the value of x.

MJWL=87 Degrees. Find The Value Of X.

Answers

Answer 1

JWL = JWI + IWL

87 = (2x + 24) + (3x - 12)

87 = 5x + 12

5x = 75

x = 15

Hope this helps!

Answer 2

The value of the variable x will be 15. Then the correct option is A.

What is an angle?

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.

The measure of the angle ∠JWL will be 87°.

The angle ∠JWI and angle ∠IWL will be the linear angle.

Then the sum of the angle ∠JWI and angle ∠IWL is equal to the angle ∠JWI.

          ∠JWI + ∠IWL = 87°

(2x + 24) + (3x – 12) = 87

                    5x + 12 = 87

                           5x = 87 – 12

                           5x = 75

                             x = 75 / 5

                             x = 15

Thus, the value of the variable x will be 15.

Then the correct option is A.

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Related Questions

a site is 90m long and 45m wide what is the area of the site

Answers

Answer:4050m^2

Step-by-step explanation:

Assuming that the site is rectangular

Area= l x W

90 X 45

=4050

Answer:

1050m

How I got the answer: I assume the site is a rectangle so I'll use the formula for finding the area of a rectangle. Using the formula length times width I solved this problem. The length is 90m. The width is 45. When a question says x meters long it means the length is x meters. In other words long = length     wide = width in a math problem.  90 times 40 is 1050m

To make concrete, the ratio of cement to sand is 1 : 3. If cement and sand are sold in bags of equal mass, how many bags of cement are required to make concrete using 15 bags of sand?

Answers

Answer:

5 bags of cement are required.

Step-by-step explanation:

Since to make concrete, the ratio of cement to sand is 1: 3, if cement and sand are sold in bags of equal mass, to determine how many bags of cement are required to make concrete using 15 bags of sand the following calculation must be done:

Cement = 1

Sand = 3

3 = 15

1 = X

15/3 = X

5 = X

Therefore, 5 bags of cement are required.

Help Please ASAP!!! Not sure how to solve this problem. Can someone help me please? Thank you for your help!

Answers

Answer:

This question is formatted incorrectly

Step-by-step explanation:

uhhh I think something is wrong here

In each following find x. Leave answer in simplified radical form.

Answers

B because the number when u simply u get that

Determine whether the following problem involves a permutation or combination.​ (It is not necessary to solve the​ problem.)
How many different ​-letter passwords can be formed from the letters ​S, T​, U​, ​W, X​, Y​, and Z if no repetition of letters is​ allowed?

The problem involves (combination or permiation) because the (order or number) of letters selected (does or does not) matter.

Answers

Answer:

Step-by-step explanation:

The order matters

stuwxyz is different than zyxwuts

You have 7 letters

The number of permutations is 7! which is 7*6*5*4*3*2*1 = 5040

what is the quotient 3/8 ÷5/12

Answers

Answer:

9/10

Step-by-step explanation:

3/8 ÷5/12

Copy dot flip

3/8 * 12/5

Rewriting

3/5 * 12/8

3/5 * 3/2

9/10

find the total cost of 4 flats of plants at $12 each

Answers

Pretty sure it’s $48

WILL GIVE BRAINLIEST!!!

Find the number of all the 2-digit numbers satisfying the following congruences x ≡ 3(mod7), x ≡ 2(mod5).

Answers

Answer:

6 total

3 positive 2 digit numbers: 17, 52, 87

3 negative 2 digit numbers: -18, -53,-88

Step-by-step explanation:

We are given

x ≡ 3(mod7), x ≡ 2(mod5) and we want x to be two digits long.

x ≡ 3(mod7) means x-3=7k and

x ≡ 2(mod5) means x-2=5m where k and m are integers.

We need to find an x that satisfies both.

So some multiples of 7 are 7,14,21,28,35,42,49,56,63,70,77,84,91,98

Some multiples or 5 are

5,10 15,20,25,30 35,40,45,45,50,55,60,65,70

Now add 3 to first list for x=7k+3

10,17,24,31,38,45,52,59,66,73,80,87,94,101

Now add 2 to second list for x=5m+2

7,12 17,22,27,32 37,42,47,52,57,62,67,72

We only want to look at 2 digit numbers... just need to expand second list more:

Now add 2 to second list for x=5m+2

7,12,17,22,27,32,37,42,47,52,57,62,67,72,77,82,87,92,97,

That's all we need.

So let's write our lists and see the common numbers in them:

List 1: 10,17,24,31,38,45,52,59,66,73,80,87,94,101

List 2:

7,12,17,22,27,32,37,42,47,52,57,62,67,72,77,82,87,92,97

Common numbers: 17, 52, 87

Considering negative numbers as well:

x=7k+3:

3, -4, -11, -18, -25, -32,-39, -46, -53, -60, -67, -74, -81, -88, -95

x=5m+2:

2,-3,-8,-13,-18,-23,-28,-33,-38,-43,-48,-53,-58,-63,-68,-73,-78,-83,-88,-93,-98

Common 2digit numbers:

-18, -53,-88

-
An ice – cream cone is first filled to
rd of its capacity with strawberry and
3
then the remaining part of the cone
is equally filled with vanilla,
strawberry and chocolate. What
fraction of ice-cream filling is
strawberry?

Answers

Answer:

1/3

Step-by-step explanation:

1/3 is the correct answer as there are three flavours and are equally filled which will result to 1/3 of each flavour.

Hope it helps you. Have a good day

Which of the following pairs of functions are inverses of each other?
O A. f(x) = 8x? - 10 and g(x) = x +10
8
B. f(x) = {+8 and g(x) = 2x - 8
O C. f(x) = 18 - 9 and g(x) =
O D. f(x) = 3x2 +16 and g(x) = -
18
X+9
16

Answers

Answer:

A is the answer I guess so...

The functions f(x) = 18/x -9 and g(x) = 18/x+9 are inverse to each other.

What is a function?

A relation is a function if it has only One y-value for each x-value.

The  given function f(x)= 18/x - 9

Let us replace f(x) by y

y=18/x - 9

Now  x=18/y-9

Add 9 on both sides

x+9=18/y

Apply cross multiplication

y(x+9)=18

Divide both sides by x+9

y=18/(x+9)

f⁻¹(x)=18/(x+9)

Hence, the functions f(x) = 18/x -9 and g(x) = 18/x+9 are inverse to each other.

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For 0 less than or equal to theta less than 2(pi), what are thebsolutions to sin↑2(theta)=2(sin↑2)(theta/2)? ​

Answers

I assume the up arrows are supposed to indicate exponents, so that the equation is

sin²(θ) = 2 sin²(θ/2)

Recall the half-angle identity for sine,

sin²(θ/2) = (1 - cos(θ))/2,

as well as the Pythagorean identity,

sin²(θ) + cos²(θ) = 1

Rewrite the equation in terms of cosine and solve:

1 - cos²(θ) = 1 - cos(θ)

cos²(θ) - cos(θ) = 0

cos(θ) (cos(θ) - 1) = 0

cos(θ) = 0   or   cos(θ) - 1 = 0

cos(θ) = 0   or   cos(θ) = 1

[θ = arccos(0) + 2   or   θ = arccos(0) - π + 2]   or

… … … [θ = arccos(1) + 2]

(where n is any integer)

[θ = π/2 + 2   or   θ = -π/2 + 2]   or   [θ = 2]

In the interval 0 ≤ θ < 2π, we get the solutions θ = 0, π/2, and 3π/2.

(That is, for n = 0 in the first and third solution families, and n = 1 in the second family.)

Point P is plotted on the coordinate grid. If point S is 12 units to the left of point P, what are the coordinates of point S? On a coordinate grid from negative 12 to positive 12 in increments of 2, a point P is plotted at the ordered pair 6, negative 4. (6, −16) (−6, −16) (−6, −4) (6, 4)

Answers

9514 1404 393

Answer:

  (−6, −4)

Step-by-step explanation:

Translating a point 12 units left subtracts 12 from its x-coordinate.

  P(6, -4) +(-12, 0) = S(-6, -4)

A company manufactures televisions. The average weight of the televisions is 5 pounds with a standard deviation of 0.1 pound. Assuming that the weights are normally distributed, what is the weight that separates the bottom 10% of weights from the top 90%?​

Answers

Answer:

[tex]0.2564\text{ pounds}[/tex]

Step-by-step explanation:

The 90th percentile of a normally distributed curve occurs at 1.282 standard deviations. Similarly, the 10th percentile of a normally distributed curve occurs at -1.282 standard deviations.

To find the [tex]X[/tex] percentile for the television weights, use the formula:

[tex]X=\mu +k\sigma[/tex], where [tex]\mu[/tex] is the average of the set, [tex]k[/tex] is some constant relevant to the percentile you're finding, and [tex]\sigma[/tex] is one standard deviation.

As I mentioned previously, 90th percentile occurs at 1.282 standard deviations. The average of the set and one standard deviation is already given. Substitute [tex]\mu=5[/tex], [tex]k=1.282[/tex], and [tex]\sigma=0.1[/tex]:

[tex]X=5+(1.282)(0.1)=5.1282[/tex]

Therefore, the 90th percentile weight is 5.1282 pounds.

Repeat the process for calculating the 10th percentile weight:

[tex]X=5+(-1.282)(0.1)=4.8718[/tex]

The difference between these two weights is [tex]5.1282-4.8718=\boxed{0.2564\text{ pounds}}[/tex].

Answer:

0.2564

Step-by-step explanation:

90th percentile, we use the formula X=μ + Zσ,

Where u = mean and  sigma = standard deviation and Z = 1.282

The mean is 5 and sigma = .1

X = 5+1.282(.1)

X = 5.1282

10th percentile, we use the formula X=μ + Zσ,

Where u = mean and  sigma = standard deviation and Z = -1.282

The mean is 5 and sigma = .1

X = 5-1.282(.1)

X = 4.8718

The difference is

5.1282 - 4.8718

0.2564

{1,4,5,6,7,8} {7} find the intersection

Answers

9514 1404 393

Answer:

  {7}

Step-by-step explanation:

The only element common to both sets is 7. The intersection is {7}.

Use the figure to find x.

Answers

Answer:

[tex] x = 8.57[/tex]

Step-by-step explanation:

Here two triangles are given to us , which are attached to each other . Here we can use the concept of Trigonometry to find out the value of x. The angles of the triangle are 60° and 45° . Let the common side be p .

Step 1: Use the ratio of tan in upper triangle

[tex]\rm\implies tan60^o = \dfrac{perpendicular}{base} [/tex]

Substitute the respective values ,

[tex]\rm\implies \sqrt3=\dfrac{p}{7} [/tex]

Cross multiply ,

[tex]\rm\implies p = 7\sqrt3 [/tex]

Step 2: Use the ratio of cos in lower triangle

[tex]\rm\implies cos45^o = \dfrac{base}{hypontenuse} [/tex]

Substitute the respective values ,

[tex]\rm\implies \dfrac{1}{\sqrt2}=\dfrac{x}{7\sqrt3} [/tex]

Cross multiply ,

[tex]\rm\implies x= \dfrac{7\sqrt3}{\sqrt2} [/tex]

Put the approximate values of √2 and √3

[tex]\rm\implies x= \dfrac{7\times 1.732}{1.414} [/tex]

This equals to ,

[tex]\rm\implies \boxed{\blue{\rm \quad x = 8.57\quad}} [/tex]

Hence the value of x is 8.57 .

Answer:

The value of x is [tex]\frac{7\sqrt{6}}{2}[/tex]

Solution given:

AB=7

BD=x

<BAC=60°

<DBC=45°

In right angled triangle ABC

Tan 60°=opposite/adjacent

Tan 60°=BC/AB

Substitute value

[tex]\sqrt{3}[/tex]=[tex]\frac{BC}{7}[/tex]

BC=[tex]7\sqrt{3}[/tex]

again

againIn right angled triangle BCD

againIn right angled triangle BCDUsing Cos angle

Cos 45=adjacent/hypotenuse

Cos45°=BD/BC

Substituting value

[tex]\frac{\sqrt{2}}{2}=\frac{x}{7\sqrt{3}}[/tex]

Doing criss cross multiplication

[tex]\frac{\sqrt{2}}{2}*7\sqrt{3}=x[/tex]

x=[tex]\frac{7\sqrt{6}}{2}[/tex]

An online retailer processed 60 merchandise return requests from Wyoming and Montana in a day. Return requests from Montana were 5 times as many as those from Wyoming. How many return requests were from Wyoming?
A) 10
B) 25
C) 15
D) 20
E) 5

Answers

The answer is A.10 because five times 10 is equal to 50

The number of merchandise return requests for Wyoming is equal to 10.

Let merchandise return requests from Wyoming be W.

Let merchandise return requests from Montana be M.

Given the following data;

Total number of merchandise return requests for W and M = 60

Translating the word problem into an algebraic equation, we have;

[tex]W + M = 60[/tex]  .....equation 1

[tex]M = 5W[/tex]        ......equation 2

To find the value of W, we would solve the system of equations by using the substitution method;

Substituting eqn 2 into eqn 1, we have;

[tex]W + 5W = 60\\\\6W = 60\\\\W = \frac{60}{6}[/tex]

Wyoming, W = 10 merchandise return requests.

Therefore, the number of merchandise return requests for Wyoming is equal to 10.

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Is this true or false ??

Answers

Answer:  True

=============================================================

Explanation:

We'll use these two properties of integrals [tex]\displaystyle \text{If f(x) is an even function, then } \int_{-a}^{a}f(x)dx = 2\int_{0}^{a}f(x)dx[/tex]

[tex]\displaystyle \text{If f(x) is an odd function, then } \int_{-a}^{a}f(x)dx = 0[/tex]

These properties are valid simply because of the function's symmetry. For even functions, we have vertical axis symmetry about x = 0; while odd functions have symmetry about the origin.

------------------------

Here's how the steps could look

[tex]\displaystyle \int_{-7}^{7}(ax^8+bx+c)dx=\int_{-7}^{7}((ax^8+c)+bx)dx\\\\\\\displaystyle \int_{-7}^{7}(ax^8+bx+c)dx=\int_{-7}^{7}(ax^8+c)dx+\int_{-7}^{7}(bx)dx\\\\\\\displaystyle \int_{-7}^{7}(ax^8+bx+c)dx=\left(2\int_{0}^{7}(ax^8+c)dx\right)+(0)\\\\\\\displaystyle \int_{-7}^{7}(ax^8+bx+c)dx=2\int_{0}^{7}(ax^8+c)dx\\\\\\[/tex]

Therefore, the given statement is true. The values of a,b,c don't matter. You could replace those '7's with any real number you want and still end up with a true statement.

We can see that ax^8+c is always even, while bx is always odd.

------------------------

Side note:

For the second step, I used the idea that [tex]\int(f(x)+g(x))dx=\int f(x)dx+\int g(x)dx\\\\[/tex]

which allows us to break up a sum into smaller integrals.

True
Good job and hope you have a good day

How
many solutions are there to the equation below?
4(x - 5) = 3x + 7
A. One solution
B. No solution
O C. Infinitely many solutions
SUB

Answers

Answer:

A one solution

Step-by-step explanation:

4(x - 5) = 3x + 7

Distribute

4x - 20 = 3x+7

Subtract 3x from each side

4x-3x-20 = 3x+7-3x

x -20 = 7

Add 20 to each side

x -20+20 = 7+20

x = 27

There is one solution

Answer:

Step-by-step explanation:

Let's simplify that before we make the decision, shall we? We'll get rid of the parenthesis by distribution and then combine like terms.

4x - 20 = 3x + 7 and combining like terms and getting everything on one side of the equals sign:

1x - 27 = 0. Since that x has a power of 1 on it (linear), that means we have only 1 solution. If that was an x², we would have 2 solutions; if that was an x³, we would have 3 solutions, etc.

Samples of rejuvenated mitochondria are mutated (defective) in 3% of cases. Suppose 13 samples are studied, and they can be considered to be independent for mutation. Determine the following probabilities.
(a) No samples are mutated.
(b) At most one sample is mutated.
(c) More than half the samples are mutated.
Round your answers to two decimal places (e.g. 98.76).

Answers

Answer:

a) 0.6730 = 67.30% probability that no samples are mutated.

b) 0.9436 = 94.36% probability that at most one sample is mutated.

c) 0% probability that more than half the samples are mutated.

Step-by-step explanation:

For each sample, there are only two possible outcomes. Either it is mutated, or it is not. The probability of a sample being mutated is independent of any other sample, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Samples of rejuvenated mitochondria are mutated (defective) in 3% of cases.

This means that [tex]p = 0.03[/tex]

13 samples are studied

This means that [tex]n = 13[/tex]

(a) No samples are mutated.

This is P(X = 0). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{13,0}.(0.03)^{0}.(0.97)^{13} = 0.6730[/tex]

0.6730 = 67.30% probability that no samples are mutated.

(b) At most one sample is mutated.

This is:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{13,0}.(0.03)^{0}.(0.97)^{13} = 0.6730[/tex]

[tex]P(X = 1) = C_{13,1}.(0.03)^{1}.(0.97)^{12} = 0.2706[/tex]

Then

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.6730 + 0.2706 = 0.9436[/tex]

0.9436 = 94.36% probability that at most one sample is mutated.

(c) More than half the samples are mutated.

This is:

[tex]P(X > 6.5) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13)[/tex]

Then

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 7) = C_{13,7}.(0.03)^{7}.(0.97)^{6} \approx 0[/tex]

Using two decimal digits precision, all will be 0. So

0% probability that more than half the samples are mutated.

1/4 + 4/10 what is the answer plz give correct

Answers

Answer:

0.65 is the correct answer

Step-by-step explanation:

hopes it helps

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

[tex]\boxed{\frac{13}{20}}[/tex]

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the answer...}}\\\\\frac{1}{4} +\frac{4}{10}\\------------\\LCM(4,10) = 20\\\\\rightarrow \frac{1}{4}=\frac{1*5}{4*5} = \frac{5}{20}\\\\\rightarrow \frac{4}{10}=\frac{4*2}{10*2}=\frac{8}{20}\\\\\\\rightarrow\frac{5}{20}+ \frac{8}{20} = \boxed{\frac{13}{20}}\\\\\\\text{The answer is in it's simplest form.}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.    

Brendan has $65 worth of balloons and flowers delivered to his mother. He pays the bill plus an 8.5% sales tax and an 18% tip on the total cost including tax. He also pays a $10 delivery fee that is charged after the tax and tip. How much change does he receive if he pays with two $50 bills? Round to the nearest cent.

Answers

Answer:

its 6.78 i believe

Step-by-step explanation:

Which explains whether or not the graph represents a direct variation?

Answers

Answer:

The slope is 3 and equation of the line is y=3x. I think the answer is the 1st option

Step-by-step explanation:

Given:

y=3x

Direct variation equations have the form:

y=kx,

where

k is the constant of proportionality

so k=3

If a 5 meter long metal bar has 40 kg mass then what is the mass of a metal bar 3 meters long

Answers

24 kg

Step-by-step explanation:

You start by calculating the linear mass density of the rod:

d = m/L = (40 kg)/(5 m) = 8 kg/m

So for a 3-m long bar, the mass can be calculated as follows:

m = d×L = (8 kg/m)(3 m) = 24 kg

A​ half-century ago, the mean height of women in a particular country in their 20s was inches. Assume that the heights of​ today's women in their 20s are approximately normally distributed with a standard deviation of inches. If the mean height today is the same as that of a​ half-century ago, what percentage of all samples of of​ today's women in their 20s have mean heights of at least ​inches?

Answers

Answer:

0.26684

Step-by-step explanation:

Given that :

Mean, μ = 62.5

Standard deviation, σ = 1.96

P(Z ≥ 63.72)

The Zscore = (x - μ) / σ

P(Z ≥ (x - μ) / σ)

P(Z ≥ (63.72 - 62.5) / 1. 96) = P(Z ≥ 0.6224)

P(Z ≥ 0.6224) = 1 - P(Z < 0.6224)

1 - P(Z < 0.6224) = 1 - 0.73316 = 0.26684

What type of object is pictured below?
O A. Point
O B. Ray
C. Segment
D. Line

Answers

Answer:

It is a ray because there are two points with a line passing through them which is extenging on one side but not on the other.

It would be b, a ray

See above. okokokoookkokokokokkkkokokkokokkok

Answers

Answer:

B

Step-by-step explanation:

B is the correct answer

Work out the area of a rectangle with base, b = 36mm and perimeter, P = 94mm.​

Answers

Answer:

396

Step-by-step explanation:

A = bw

A = 36w

P = 2w + 2b

94 = 2w + 2(36)

94 = 2w + 72

-72           -72

--------------------

22 = 2w

----    ----

2       2

11 = w

A = 36(11)

A = 396

The area of the rectangle will be 396.

A random sample of 10 sales receipts for internet sales results in a mean sale amount of $66.30 with a standard deviation of $15.75. Using this data, find the 98% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases. Assume that the population variances are not equal and that the two populations are normally distributed. Step 1 of 3 : Find the point estimate that should be used in constructing the confidence interval.

Answers

Answer:

ur mum s house

Step-by-step explanation:

myueudifigkgkgogkvkcv

1289 +(-1236) + (2434) =
0 -1431
O 2345
O 2487
0 -1956

Answers

Answer:

This answer is 2487

which will be the third one

Hope this help

plzz help with this question

Answers

Answer: 51 liters of fuel are required

Step by step: start by seeing how many times 476 can go into 1428

(1428/476=3)

Then take your sum of that and multiply it by 17 since that’s the number that correlates with 476

(17x3=51) therefore your answer is 51 liters

Other Questions
Colin was so ................. because of his exam that he could not sit still for five minutes.A. on the verge B. on edge C. on border D. on rim At the end of the day, Isaac hears a car pull in the driveway. A few minutes later, his father walks through the side door to the house. Isaac smiles, then runs to the door to greet his father. This scene is repeated for several days. Then, one evening, Isaac runs to the side door as soon as he hears a car pull into the driveway. Isaac's behavior of running to the door when he hears the car can best be described as which of the following?A. Conditioned stimulusB. Conditioned responseC. Unconditioned stimulusD. Unconditioned response Generally, local governments get the least amount of funding from:A. property taxB. income tax C. sales taxD. state government Simplify:64(3x2)+4x16x28x+148x2 180 X 26 X = ? What are some ways to increase the likelihood that children and adolescents participate in regular physical activity? Also i need help to give someone a Brainliest. 2- Completar las siguientes palabras que tienen relacin con la AMISTAD :CON_ _ AN_ _ _ EAL _ A _ EMP _ _ T _ A_ ARI _ O A _ REC _ _ CO _ _ REN _ _ __ OL _ _ AR _ _ AD A _ U _ _ _ F _ _ TO The area of a rectangle is 44 m^2, and the length of the rectangle is 3 m less than twice the width. Find the dimensions of the rectangle.length : width : Phosphates have been banned in most dishwashing detergents in order toprotect the environment. Why were phosphates removed from dishwasherdetergents?A. Because they buffer cells from extremes in pHB. Because they increase the acidity of water and cause acid rainC. Because they increase the salinity of water and pollute drinkingwaterD. Because they cause algal blooms that starve fish of oxygen A security guard, dressed in plain clothes, was working for a discount store when a customer got into a heated argument with a cashier over the store's refund policy. Without identifying himself as a security guard, the security guard suddenly grabbed the customer's arm. The customer attempted to push the security guard away, and the security guard knocked the customer to the floor, causing injuries. The customer sued the discount store for battery on a theory of vicarious liability for the injuries caused by the security guard. The store filed an answer to the customer's complaint, asserting the affirmative defense of contributory negligence. The customer has moved to strike the affirmative defense. Traditional rules of contributory negligence apply. Should the trial court grant the customer's motion The Northern Division of Southwest Clothing Inc. forecasts (has budgeted) the following income statement for the upcoming year: Sales $850,000 Variable Costs (520,000) Contribution Margin 330,000 Fixed Costs (480,000) Operating loss ($150,000) Unfortunately, every other division in the company is also expecting an operating loss for the coming year. The company's management is considering shutting down the Northern Division and has determined that $350,000 of the $480,000 Fixed Costs shown would be eliminated if that happens. If the Northern Division is shutdown, what is the change (impact) in Southwest's forecast operating results The most prominent of the nineteenth-century socialists were the German theorists Karl Marx and Friedrich Engels. They argued that human history has been a struggle between social classes, and that the future lay with the working class because capitalism would grind to a halt. True False is -66 rational or irrational ? A chemist determines by measurements that 0.0550 moles of nitrogen gas participate in a chemical reaction. Calculate the mass of nitrogen gas that participates.Be sure your answer has the correct number of significant digits. A group of high school students were surveyed about their handedness and their favorite sport. The results are displayed below.Which of the following statements is not true, according to the graph?The left-handed group has a higher percentage of people who prefer baseball.The right-handed group has a lower percentage of people who prefer basketball.The percentage of people who prefer soccer has a lower percentage in the left-handed group.The percentage of people who prefer football is approximately the same for the right- and left-handed groups. What is the value of 3x^2 + 4y^2 if x = 2 y = 1 Plz help me out with this please solve thanks! A car travels 12 km in 15 minutes.Work out the average speed of the car in km/h.