Anyone know this?? Thanks

Anyone Know This?? Thanks

Answers

Answer 1

9514 1404 393

Answer:

  x = 4

Step-by-step explanation:

The figure is a rhombus when the sides are the same length.

  21 -x = 2x +9

  12 = 3x . . . . . . . . add x-9 to both sides

  4 = x . . . . . . . . . . divide by 3


Related Questions

someone mind helping me in the question......thank you :) ....​

Answers

Answer:

NY: 4cm + 3cm = 7cm

XY: 8cm + 3cm = 11cm

   

Step-by-step explanation:

1. find the difference between XN and MN

2. use the difference to add to the value LN and LM

Alexandra and Maris are playing a game where they guess how many sides the regular polygon the other is holding has. Alexandra says her regular polygon has exactly 12 lines of symmetry. Maris says her regular polygon has an angle of rotational symmetry of 24°. How many sides does each regular polygon have?

Answers

The number of sides of Alexandra's regular polygon is 12.

The number of sides of Maris's regular polygon is 15.

What is a regulars polygon?

A regular polygon is denoted a area. The area bounded by equal length of arms. The angel between any two consecutive arms will same any other pair of consecutive arms.

The number of line of symmetry of a polygon is the same is the number of arm or sides of that polygon.

Thus the number of sides of a polygon that has 12 lines of symmetry is 12.

The angle of rotational symmetry of a polygon is 360°/n, where n is the number of arms.

Therefore,

Angle of rotational symmetry = 360°/n

Putting Angle of rotational symmetry = 24°:

24° = 360°/n

Multiply both sides by n

24n = 360

Divide both sides by 24:

n = 360/24

n = 15

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If no deposits or withdrawals
are made, money held in this
account may increase or
decrease.
This account may generate
income from a variety of
sources.
There is no risk of losing any
money put in this account.
Savings Account
Interest income is the only
way to earn money in this
type of account.
Investment Account

Answers

Answer:

Savings Account

There is no risk of losing any money put in this accountInterest income is the only way to earn money in this type of account

Investment Account

If no deposit or withdrawals are made, money held in this account may increase or decreaseThis account may generate income from a variety of sources

If 3(x+1)=4x-1, then x=

Answers

Answer:

X = 4

Step-by-step explanation:

To solve the equation 3(x+1) = 4x-1, we need to use the rules of algebra to isolate the variable "x" on one side of the equation and simplify the other side.

First, we can distribute the 3 on the left side of the equation to obtain 3x + 31 = 4x-1. This gives us 3x + 3 = 4x-1.

Next, we can subtract 3x from both sides of the equation to obtain 3 + 3 = 4x-1-3x. This simplifies to 3 = x-1.

Now we can add 1 to both sides of the equation to obtain 3+1 = x. This gives us the final solution x = 4.

Therefore, the solution to the equation 3(x+1) = 4x-1 is x = 4.

vi
18,500
-how did you divide this? 1,295 divided by 18,500

Answers

Answer:

0.07

Step-by-step explanation:

Question
There are two spinners. The first spinner has three equal sectors labeled 1, 2 and 3. The second spinner has four equal sectors labeled 3, 4, 5 and 6. The spinners are spun once.

What is the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner?

Answers

The number of possible outcomes that do not show 1 on the first spinner and 4 on the second spinner is 2.

What is sample space?

It is the total number of possible outcomes from a given set.

We have,

The sample space for when both the spinners are spun once.

S = {(1, 2, 3) x (3, 4, 5, 6)}

S = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 4), (3, 5), (3, 6)}

Now,

The number of total outcomes = 12

The number of outcomes that do not show 1 on the first spinner and 4 on the second spinner.

= {(2, 4), (3, 4)}

= 2

Thus,

The number of required possible outcomes is 2.

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a volunteer group decided to pick up trash along a stretch of road measuring five and one third miles. the group divided into five teams to cover an equal distance. What distance will each group have to cover?​

Answers

Answer: 1 [tex]\frac{1}{15}[/tex] miles

Step-by-step explanation:

     We will divide the length of the road, five and one-third miles by the number of groups, five teams, to find the answer to this question.

     (5 1/3) / 5 = (16/3) / 5 = (16/3) * (1/5) = 16/15 = 1 1/15 miles

* Note: We can use "keep change flip" when multiplying with fractions. Keep the first number, change to multiplication, flip to the reciprocal of the second number

Answer the following questions.
1) Choose the equation of a line parallel to the given equation and passing through a point P.
x+2 y=5 ; P=(2,-5)
y=-1/2 x-1
y=2 x-4
y=-2 x-1
y=-1/2 x-4

2) Choose the equation of a line parallel to the given equation and passing through a point P.
-3 x-y=-4 ; P=(1,4)
y=-3 x+5
y=-3 x+7
$y=1/3 x-3
$y=1/3x+7

Answers

The linear functions in this problem are given as follows:

1. y = -x/2 - 4.

2. y = -3x + 7.

How to define the linear functions?

Considering the options in these problems, the linear functions are defined in slope-intercept format, given as follows:

y = mx + b.

The coefficients of the function are given as follows:

m is the slope.b is the y-intercept.

The slope-intercept definition of the two equations presented in this problem are given as follows:

y = -0.5x - 5.y = -3x + 4.

When two linear functions are parallel, they have the same slope, hence the two functions will be given as follows:

y = -0.5x + b.y = -3x + b.

For item 1, when x = 2, y = -5, hence the intercept b is calculated as follows:

-5 = -0.5(2) + b

b = -5 + 1

b = -4.

For item 2, when x = 1, y = 4, hence the intercept b is calculated as follows:

4 = -3(1) + b

b = 7.

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Using the quadratic formula to solve 2x² = 4x-7, what are the values of x?
O2+√101

O 1± 101
2± √/10/
2
O 1± √√51

Answers

Answer:

x would be equal to 5 and the other one to your right would be 3 because O1t is aka known as a linear expression so you would have the multiply by 2 and use and exponent square

Name a pair of overlapping congruent triangles in the diagram. State whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL.
Given: LM≅LK; LN≅LJ

Answers

ΔLMJ and ΔLKN are congruent by SAS congruence postulate.

What is SAS and ASA congruence rule for triangles?

SAS : If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

ASA : If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

According to the given question:

The pair of overlapping congruent triangles in the diagram are:

ΔLMJ and ΔLKN

Now,

LM ≅ LK (Given)

LN ≅ LJ (Given)

∠LJM = ∠LNK (Angles opposite to equal sides are equal)

∴ ΔLMJ ≅ ΔLKN by SAS congruence of triangles

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A food company sells its corn flakes in boxes of two different sizes: the regular box and the family value box. For the family value box, the length, width, and height of the box have all been increased by 25%.

Answers

If the regular box has dimensions l, w, and h, then the dimensions of the family value box would be 1.25l, 1.25w, and 1.25h. This means that the volume of the family value box would be 1.25 * 1.25 * 1.25 = 1.953125 times the volume of the regular box. Since the family value box is 25% larger in each dimension, its volume is nearly double the volume of the regular box.

PLEASE HELP!!!!
Jamal works as a valet and a waiter at a restaurant. As a valet, Jon made $10.25 an hour and an additional $50.10 in tips, while at the restaurant he made $6.75 an hour and an additional $125 in tips. He made the same amount of money at both jobs last week.

Part A: Select the equation that can be used to determine the number of hours Jamal worked last week.

Part B: The total amount of money that Jamal made when both paychecks were the same is $

Answers

Since ,the amount is same in both jobs as valet and waiter thus the total amount of money he made is $538.9

What is equation?

Equation: a claim that two expressions with variable- and/or number-filled expressions are equivalent. Mathematical development has been sparked by the desire to find solutions to equations, which are really just questions.

Here,

Part A:

Jamal works as a valet made $10.25 an hour and an additional $50.10 in tips,

Thus number of hours be x

equation : 10.25x + 50.10 =0

or

Jamal works as a waiter made $6.75 an hour and an additional $125 in tips

equation : 6.75x + 125 = 0

Part B:

The total amount he made when both paychecks are same

=> 6.75x + 125 = 10.25x + 50.10

=> 10.25x-6.75x = 125-50.10

=>3.5x = 74.9

=>x=74.9/3.5 =21.4

Thus the total amount he made

10.25(21.4) + 50.1 = 269.45

and

Total amount = 2* 269.45=538.9

Since ,the amount is same in both jobs as valet and waiter thus the total amount of money he made is $538.9

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one and three fifths plus three and two thirds equals blank

Answers

Answer:  5 4/15

Step-by-step explanation:

1 3/5 + 3 2/3 = 8/5 + 11/3

Find the common denominator (5 and 3) = 15

So 8/5 equals to 24/15 because if 5 x 3 = 15 , 8 must also multiply by 3.

11/3 equals to 55/15 because if 3 x 5 = 15 , 11 must also multiply by 5.

Thus 24/15 + 55/15 = 79/15

This is an improper fraction, so converting to mixed number:

79/15 = 5 4/15 because 5 x 15 + 4 = 79

describe a procedure that you would use to localize the protein dynein in tissue sections of esophagus and trachea. indicate the results that you would expect from such an analysis.

Answers

Therefore, the five steps are taken to localize the protein dynein in tissue sections of the esophagus and trachea.

What is localization?

Any procedure that involves moving, attaching to, or otherwise maintaining a cell, substance, or cellular entity in one place, like an organelle or protein complex. Substance localisation can also be accomplished through selective degradation.

In this case,

the steps that are done in order to localize the protein dynein in tissue sections of the esophagus and trachea are as follows:

1. Histoclear removes the medium to enable the labeling of the antibodies

2. to rehydrate the sample, add water.

3. Using BSA blocking solution after Triton X- 100, which ruptures membranes and makes antigens more accessible to antibodies

(4) Add the dynein antibody.

5. include a secondary antibody that is likewise peroxidase-active (adds specificity)

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A librarian wants to check a sample of books from the library to get an idea of how many need replacing.
Why might simple random sampling be a good way to do this?
He will not need a list of all the books
He will take longer if he checks all the books instead of checking a few
He will have a more representative sample if he chooses randomly
He will be able to choose whichever books he likes because it is random

Answers

The reason why simple random sampling will be a good way to do the selection of bad books is; Option C: He will have a more representative sample if he chooses randomly

What is the importance of simple random sampling?

A simple random sample is defined as a randomly selected subset of a particular population. In this method of sampling, it will be noticed that each member of the population has an exactly equal chance of being selected.

The importance of simple random sampling is that it removes every form of bias as every member has an equal chance of being selected. Thus, it will give a good representation of what we want to research.

Now, in this case, since the librarian wants to check a sample of books from the library to get an idea of how many need replacing, it means that a random sampling method is good because;

He will have a more representative sample if he selects randomly as the definition earlier stated makes clear.

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what is the probability distribution that has a mean of 1 and a standard deviation of 0?

Answers

The required explanation of probability distribution that has a mean of 0 and a standard deviation of 1 is describe below.

What is probability distribution?

Probability distributions help to show our reality, empowering us to get evaluations of the likelihood that a specific occasion might happen, or gauge the inconstancy of event. They are a typical method for depicting, and potentially foresee, the likelihood of an occasion

According to question:

The mean of the z-scores is dependably 0. The standard deviation of the z-scores is dependably 1. The chart of the z-score dissemination generally has a similar shape as the first conveyance of test values. The amount of the squared z-scores is dependably equivalent to the quantity of z-score values.

Thus, it is dependable.

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Correct question:

A normal probability distribution can have any value of the mean or must have a standard deviation of 1 and a mean of 0?

What is the y-value of the solution for this system of equations:

4x - y = 10

x - 4 = y

Answers

The required value of y is obtained as -2.

What are the types of a system of equations?

The given system of equation can either have a unique solution, more than one solutions or no solution.

On this basis they are divided into two parts consistent and inconsistent.

A consistent system has one or more solutions while for an inconsistent system there are no solutions.

The given system of equations is as below,

4x - y = 10             (1)

x - 4 = y               (2)

Substitute the value of y from equation (2) into equation (1) to get,

4x - (x - 4) = 10

=> 3x + 4 = 10

=> 3x = 6

=> x = 2

Then, substitute x = 2 in  x - 4 = y  to get,

y = 2 - 4  = -2

Hence, the value of y for the given system of equations is -2.

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The answer to this question is -2

If the 8th term of a sequence is 256, and the 5th term of the sequence is 32, the common ratio is:

Answers

The geometric sequence have a common ratio of 2

Geometric Sequence

Geometric progression (GP) is a type of sequence where each next term is gotten by multiplying each previous term by a fixed number, which is called a common ratio.

In this problem, we must write out two equations to find the common ratio.

Let;

r = common ratioa = first term

The nth term of a GP is given as;

Tn = arⁿ⁻¹

T₈ = ar⁷

256 = ar⁷ ...eq(i)

T₅ = 32

32 = ar⁴ ...eq(ii)

Dividing equation (i) by equation (ii)

256 / 32 = ar⁷ / ar⁴

8 = r⁷⁻⁴

8 = r³

r = ∛8

r = 2

The common ratio of the geometric sequence is 2

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17. Which of the following statements about overhead expenses is true?
A. They contribute indirectly to the running of a business.
B. They contribute directly to the running of a business.
C. They're directly related to a specific department.
D. They're directly related to a specific product.

Answers

Thus ,the statement about overhead expenses which is true is option (B). .

What is overhead expenses?

In the business world, an ongoing expense of operating a business is known as overhead or an overhead charge .In contrast to operating costs like raw material and labor, overheads are expenses that cannot easily be connected to or associated with any one revenue unit.

Here,

the statement about overhead expenses  which is true is option (B).

Explanation :The costs of operating a firm that aren't directly connected to providing an item or service are referred to as overhead. These expenses might be either fixed, like rent, or variable, like transportation expenditures. Additionally, they may be semi-variable, like utilities. Thus contribute directly to the running of a business.

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f(x)=3x²+42-6
g(x)=62-5²-2
Find (f+g)(x).
O A. (f+g)(x) =-628+82 +42-4
O B. (f+g)(x) = 6r³-2r² +42-8
O c. (f+g)(x) = 9r³-2-8
OD. (f+g)(x) = 6x³+3x²-2-8

Answers

The composite function (f + g)(x) is (f + g)(x) = 9x² - x - 8

How to determine the composite function

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

f(x)=3x²+42-6

g(x)=62-5²-2

Express properly

So, we have the following representation

f(x) = 3x² + 4x -6

g(x) = 6x² - 5x - 2

The composite function is then calculated as

(f + g)(x) = f(x) + g(x)

So, we have

(f + g)(x) = 3x² + 4x -6 + 6x² - 5x - 2

Evaluate

(f + g)(x) = 9x² - x - 8

Hence, the function is (f + g)(x) = 9x² - x - 8

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Is (2, 10) a solution to this system of equations?
y = x + 8
y = 10x + 3
yes
Submit
no

Answers

Point (2,10) is not satisfying the linear function y = 10x + 3 thus it will be not the solution of the system of equations.

What is the equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

As per the given point (2,10)

Put it into y = x + 8

10 = 2 +  10 = 10 (satisfy)

Put it into y = 10x + 3

10 = 10 x 2 + 3 = 23 ≠ 10 (Not satisfy)

Hence "Point (2,10) will not be the system of equations' solution since it does not fulfill the linear function y = 10x + 3".

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Suppose there are two types of tickets to a show: advance and same-day. Advance tickets cost $25, and same-day tickets cost $20. For one performance, there were 65 tickets sold in all, and the total amount paid for them was $1450. How many tickets of each type were sold?
The number of Advance tickets sold:
The number of same-day tickets sold:

Answers

By solving a system of equations we will see that they sold 35 advanced tickets and 30 same-day ones.

How to find the number of each ticket sold?

Let's define the variables we will be using for this problem, these are:

x = number of same advance tickets.

y = number of same-day tickets.

With the given information we can write a system of equations:

x*$25 + y*$20 =  $1,450

x + y = 65

To solve the system we can isolate x on the second equation:

x = 65 - y

Now let's replace that in the other equation:

(65 - y)*$25 + y*$20 =  $1,450

$1,625 - y*$5 =  $1,450

$1,625 - $1,450 = $5*y

$175/$5 = y

35 = y

Then the value of x is:

x = 65 - 35 = 30

So they sold 35 advanced tickets and 30 same-day ones.

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For the given probability distribution, what is P(X<4) ?

Answers

Step-by-step explanation:

5. the most significant challenge that small businesses face is financial problems.

evaluate f(x)=-25x^4+3x^2+2

Answers

f(x)=-25x^4+3x^2+2 = f'(x)=-100x^3+6x

Take derivation

f'(x)=d/dx(-25x^4+3x^2+2)

Formula

d/dx(f+  g)=d/dx(f) + d/dx(g)

f'(x)=d/dx(-25x^4)+d/dx(3x^2)+d/dx(2)

Formula

d/dx(x^a)=ax^(a-1)

f'(x)=-25(4x^3)+3(2x)+0

f'(x)=-100x^3+6x

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Monica deposits ​$400 into a savings account that pays a simple interest rate of ​4.3% .Paul deposits ​$500 into a savings account that pays a simple interest rate of ​%4.2 Monica says that she will earn more interest in 1 year because her interest rate is higher. Is she​ correct? Justify your response.

Answers

Monica was wrong she will get less interest than Paul as Paul has invested a higher Principal amount than Monica.

What is simple interest?

Simple interest is based on the principal amount of a loan or the first deposit in a savings account.

                         [tex]A = P (1 + rt)\\\\A $ = final amount$\\P $ = initial principal balance$\\r $ = annual interest rate$\\t $ = time (in years)$[/tex]

Given that:

For Monica:

Principal (p) = $400

Rate (r) = 4.3% = 0.043

Year (t) = 1 year

Deposit Paul:

Principal = $500

Rate (r) = 4.2%  = 0.042

Year (t) = 1 year

Now calculate the interest amount for Monica and Paul, we get

For Monica:

             A = P(1 + rt)

             A = 400(1 + (0.043 × 1))

             A = 417.2

             A = $417.20

Now for Monica, Interest will be

           I = A - P

             = 417.20 - 400

           I = 17.20 dollars -----------(II)

For Paul:

             A = P(1 + rt)

             A = 500(1 + (0.042 × 1))

             A = 521

             A = $521 dollars

Now for Paul, Interest will be

           I = A - P

             = 521 - 500

           I = 21 dollars ---------------(II)

From (I) and (II), we can say that Paul will earn more interest than Monica.

Hence, Monica was wrong she will get less interest than Paul as Paul has invested a higher Principal amount than Monica.

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WHAT IS THE M(X) IN THE REGRETION EQUATION Y=20.23*X+516.1

Answers

The M(x) or the estimate slope is 20.23X

What is the regression equation?

A regression equation is used in stats to find out what relationship, if any, exists between sets of data. For example, if you measure a child’s height every year you might find that they grow about 3 inches a year. That trend (growing three inches a year) can be modeled with a regression equation.

[tex]Y_i=f(X_i, \beta)+e_i[/tex]        [tex]Y_i[/tex] = dependent variable

[tex]X_i[/tex] = independent variable

[tex]\beta[/tex] = unknown parameters

[tex]e_i[/tex] = error terms

Given here,  Y=20.23*X+516.1

Thus comparing it with the equation above we can deduce that

M(x) = 20.23x

Hence The M(x) or the estimate slope is 20.23X

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Calculate each sum or difference.
a) 43.78 +21.05 +52.29

Answers

Answer:

117.12

Step-by-step explanation:

43.78+21.05 = 64.83

64.83+52.29 = 117.12

The area of a rectangle is 9/10 square meter. The width is 2/5 meter. b. How many times greater is the length than the width? Write your answer in simplest form.

Answers

Answer:

Step-by-step explanation:

a = lw

l = a/w

l = (9/10)/(2/5) = (9/4)

l/w = (9/4)/(2/5) = 5 5/8 times greater

Answer:

4.5/2 = 2.25

Dif: 2.25/0.4 = 5.625 times greater

Hope this helps

may someone give me the answer

Answers

Answer:

x represents the number of hours.

(y) distance because the distance depends on the number of hours traveled.

H(x) = 50x

H(5) = 50(5)

H(5) - 250 miles

After 5 hours of driving at 50 miles per hour, the car has traveled 250 miles.

Step-by-step explanation:

A manufacturer puts tires on two cars (four tires each). Each tire has a 10% probability of being flat. Assume the manufacturer puts four tires on one car first and then another four on the next car second. What's the probability that there is at least one car that has no working tires?

Answers

The probability that there is at least one car that has no working tires is given as follows:

0.0002 = 0.02%.

What is the binomial distribution formula?

The mass probability formula, giving the probability of x successes, is of:

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

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

The parameters are given by:

n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.

For each car, the parameters are given as follows:

p = 0.9, n = 4.

Hence the probability that a car has no working tires is given as follows:

P(X = 0) = (1 - 0.9)^4 = 0.0001.

Hence the probability that two cars have working tires is given as follows:

P(X = 2) = (1 - 0.0001)² = 0.9998.

The probability that at least one has no working tires is given as follows:

P(X < 2) = 1 - 0.9998 = 0.0002 = 0.02%.

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simplify:3x + 42 - 34 1. Order from smallest to largest:Number of pennies in a stack that is 1 ft highNumber of books in a stack that is 1 ft highNumber of dollar bills in a stack that is 1 ft highNumber of slices of bread in a stack that is 1 ft high What is the volume of a cylinder, in cubic centimeters, with a height of 8 centimetersand a base diameter of 16 centimeters? Round to the nearest tenths place Axton Betz-Hamilton describes her childhood as typical for a rural kid. Her father worked as a department manager for a regional grocery store chain. What did her mother do for a living? * please help will mark brainlyist HELP HELP ASAP ASAP WILL MARK BRAINLIEST PLEASE EASY POINTS A gas goes from 1L at 273 K to 2 L when heated. What is the new temp? For some metal alloy, a true stress of 345 MPa (50040 psi) produces a plastic true strain of 0.02. How much will a specimen of this material elongate when a true stress of 412 MPa (59760 psi) is applied if the original length is 480 mm (18.90 in.)? Assume a value of 0.22 for the strain-hardening exponent, n. Line B in the given graph represents the reaction with an enzyme added to substrates. How did the enzyme affect the reaction? John is a 37 year old married business owner. He runs a dry cleaning service with 3 locations in Toledo, Ohio. His personal obligations are the home he owns with his wife, who works for a large consulting firm, the healthcare of his family and his commitment toward saving for his three childrens college educations. John knows that two of his locations require a large cash infusion to pay for new equipment. Although his wifes job provides the family health insurance, it also places the family in a higher income tax bracket. John would like to minimize his taxes and protect his family. What form of ownership would you suggest for him? Why? If a gray fly is crossed with a heterozygous black fly, which combination below represents the parental cross? Please help! What is -(1/2) to the fourth power? A boy who is riding his bicycle, moves with an initial velocity of 5 m/s. ten second later, he is moving at 15 m/s. what is his acceleration Throughout the movie, Wendell Smith (the African American reporter) chronicles Jackie Robinsons first season in Major League Baseball. Why does he have such a personal stake in the success of Jackie Robinson? (Think about how he is treated as a reporter.) I just need the inequality/equation please! Stephanie is saving money to buy a computer next year. So far she has saved $200. Write an inequality to show how much she needs to save each month for the next year so she has at least $1200 to spend on the computer, then solve the inequality. complete the table below to show the differences bettween algebraic expression and equation helpp ill give brainlist 2. Would you put on heavily colored or dark color clothes during cool weather? whyor why not? Which statement best describes the difference between weather and climate? a. Weather is studied by earth scientists, while climate is studied by life scientists b. Weather describes rainfall, while climate describes temperature. c. Weather describes current conditions, while climate describes conditions over long periods. d. Weather describes the condition of the atmosphere, while climate describes the condition of the land. A researcher assesses self-esteem among college students at the beginning of the semester using a self-report questionnaire, as well as three months later at the end of the semester among the same sample of college students using the exact same self-report measure of self-esteem. The researcher determines that there is a significant positive relationship between self-esteem measured at the beginning and end of the college semester for the students sampled. This demonstrates how correlations can be used to demonstrate _____.