Consider the following figure:
The value of a is

Essentially just count the tick marks between the two letters.

JL= 5

JK= 3

KP= 9

NP= 2

JP= 12

LN= 5

The asked lengths are from the number line:

JK = 3, JL = 5, KP = 9, NP = 2, JP = 12 and LN = 5.

Given that is a number line we need to find the asked values,

1. JK =

K = -4 and J = -7

So, JK = -4-(-7)

JK = -4+7

JK = 3

2. JL =

J = -7 and L = -2

So, JL = -2-(-7)

JL = -2+7

JL = 5

3. KP =

K = -4 and P = 5
So, KP = 5-(-4)

KP = 9

4. NP =

N = 3 and P = 5

So, NP = 5-3

NP = 2

5. JP =

J = -7 and P = 5

So, JP = 5-(-7)

JP = 12

6. LN =

L = -2 and N = 3

So, LN = 3-(-2)

LN = 5

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The factor of given expression is 6(5-v-3w) and 2(15-3v-9w). correct option is c and d.

Given that factor 30-6v-18w.

Equivalent expressions are expressions that work the same way, even if they look different. If two algebraic expressions are equivalent, the two expressions have the same value if we enter the same values ​​for the variables.

For option A

Factor the expression:

2(15-2v)≠6(5-v-3w)

get the result: False

Answer: False

For option B

Factor the expression:

3(10-3v+6w)≠6(5-v-3w)

get the result: False

For option C

Factor the expression:

6(5-v-3w)=6(5-v-3w)

get the result: True

For option D

Factor the expression:

6(5-v-3w)=2(15-3v-9w)

get the result: True

Hence, the equivalent expression of the factor 30-6v-18w is 6(5-v-3w) and 2(15-3v-9w).

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The number of solutions to the system is 1

A linear equation is a equation that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

y = 4x + 8

4y = 4x - 8

Substitute y = 4x + 8 in 4y = 4x - 8

4(4x + 8) = 4x - 8

Expand the equation

16x + 32 = 4x - 8

Evaluate the like terms

12x = - 40

Divide by 12

x = -10/3

The above means that the number of solutions to the system is 1

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Answer:

21

Step-by-step explanation:

(-4)(-2)+2(6+5)

(8)+2(11)

10+11

21

Hope this helps! :)

Answer:32

Step-by-step explanation: First, we do parentheses. 6+5 = 11. Next, we have to do multiplication (-4)(-2) is positive 8 because there are two negatives. 8+2 is 10 + 2(11) is 10+22 which is 32

Answer:

Step-by-step explanation:

The sum of interior angles of a quadrilateral is 360°.

If we consider the measure of one of the unknown angles to be [tex]x[/tex]°, we can set up the following equation:

[tex]x + x + 75^\circ + 117^\circ = 360^\circ[/tex]

Now we can solve for [tex]x[/tex]:

⇒ [tex]2x + 192^\circ = 360^\circ[/tex]

⇒ [tex]2x = 360^\circ - 192^\circ[/tex]        [subtracting 192° from both sides]

⇒ [tex]2x = 168^\circ[/tex]

⇒ [tex]x = \frac{168^\circ}{2}[/tex]                      [dividing both sides by 2]

⇒ [tex]x = \bf84^\circ[/tex]

Therefore, the other two angles each have a measure of 84°.

The critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881

The scatter plot of the election is added as an attachment

From the scatter plot, we have the following highlights

Start by calculating the degrees of freedom (df) using

df =n - 2

Substitute the known values in the above equation

df = 8 - 2

Evaluate the difference

df = 6

Using the critical value table;

At a degree of freedom of 6 and significance level of 0.01, the critical value is

z = 0.834

From the list of given options, 0.834 is between  -0.881 and 0.881

Hence, the critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881

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Answer:

36

Step-by-step explanation:

[tex]\sqrt{24a}=12\sqrt{6} \\ \\ 24a=864 \\ \\ a=36[/tex]

The cost of goods sold using LIFO is $99.

Using this formula

Cost of goods sold=(March 3 Purchased units × March 3 Purchase price)+ [(March 3 Purchased units -March 9 sold units)×March 1 Beginning inventory cost]

Let plug in the formula

Cost of goods sold=(15 units×$3.90)+[(22 units-15 units)×$5.80]

Cost of goods sold=$58.5+(7 units×$5.80)

Cost of goods sold=$58.5+$40.6

Cost of goods sold=$99.1

Cost of goods sold=$99 (Approximately)

Therefore the cost of goods sold using LIFO is $99.

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The relationship of the graph g(x) = (x − 2)^3 + 6 compare to the parent function of f(x) = x^3 is that g(x) is shifted 2 units to the right and 6 units up.

Translations is a transformation technique that changes the position of an object from one point on the plane to another.

Given the function below

g(x) = (x − 2)^3 + 6

The function compared to f(x) = x^3, shows a translation of f(x) by 2 unit to the right along the horizontal and vertical translation of the function 6 units up

Hence the relationship of the graph g(x) = (x − 2)^3 + 6 compare to the parent function of f(x) = x^3 is that g(x) is shifted 2 units to the right and 6 units up.

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Answer:

g(x) is shifted 6 units to the left and 2 units down.

Step-by-step explanation:

took the test

Answer 1:

1.23456789 × (10-6) = 4.93827156

Answer 2:

(1.23456789 × 10) - 6 = 6.3456789

Answer 3:

1.23456789 × [tex]10^{-6}[/tex] = 0.000000123456789

Hope this helped! :)

Answer:

  x = 3

Step-by-step explanation:

Maybe you want the value of x such that ...

  4(6^x) = 864

Dividing by 4 gives ...

  6^x = 216

You may know that 216 = 6^3. Using that, we can equate exponents:

  6^x = 6^3

  x = 3

Alternatively, we can use logarithms to find x. Taking logs gives ...

  x·log(6) = log(216)

  x = log(216)/log(6) = 3

Answer:

x=3/2 y=1/2

Step-by-step explanation:

Check the picture below.

The factor of such equation described as having the number 3 as a root can be determined as; (x-3).

It follows from the task content that; we are required to determine a possible factor of a polynomial in the event that such polynomial has a root of 3.

The implication of a polynomial having a root of 3 is that; such a polynomial has 3 to be one of it's zeros.

Hence, a linear equation which holds for such polynomial is that; x = 3 and when expressed as a linear factor, the linear factor is; (x-3).

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Step-by-step explanation:

x = number of heavy equipment operators

y = number of general laborers

x + y = 37 (37 people were hired)

out if this we get e.g.

x = 37 - y

124x + 82y = 3916 (daily rate for each role, in total 3916)

now we use the first equation in the second :

124(37 - y) + 82y = 3916

4588 - 124y + 82y = 3916

672 - 42y = 0

672 = 42y

y = 16

x = 37 - y = 37 - 16 = 21

21 heavy equipment operators were hired.

16 general laborers were hired.

The detail  Description on how to create a number line with the above  points is given below:

Note that we were given the following: points 4, 1, 25, and opposite of 2. The step to take  to First draw on Number Line.

Since Numbers with a negative sign are known to be less than zero ( Right of zero is shown by ‘+’ sign and to the left of zero is shown by ‘–’ sign while the + sign numbers can be depicted as simply numbers)

Then:

Therefore, The detail  Description on how to create a number line with the above points given above is correct:

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The probability of obtaining a success is 0.010935.

Given that the probability of obtaining success is P(X>=5),n=6,p=0.3.

We are required to find the probability of obtaining a success if the probability is P(X>=5).

Probability is basically likeliness of happening an event among all the events possible.

Binomial distribution is basically the discrete probability distribution of the number of successes in a sequence of n independent experiments.

[tex](a+b)^{n} =nC_{0}p^{0} (1-p)^{n-0}+-----------nC_{n} p^{n} (1-p)^{0}[/tex]

We have to just put n=6 anr r=6 and 5 one by one to get the probability.

P(X>=5)=[tex]6C_{5}(0.3)^{5} (0.7)^{1} +6C_{6}(0.3)^{6} (0.7)^{0}[/tex]

=6!/5!1!8*0.00243*0.7+0.000729

=6*0.00243*0.7+0.000729

=0.010206+0.000729

=0.010935

Hence the probability of obtaining a success if the probability is P(X>=5) is 0.010935.

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The total product cost per unit.

TPC= $33

This is further explained below.

Generally, The direct materials cost per unit, the direct labor cost per unit, the variable overhead cost per unit, and the fixed overhead cost per unit make up the total product cost per unit.

The total costs of the product may be calculated by adding up the costs of all of the direct materials, all of the direct labor and all of the overhead expenses of the production process. 1 Information such as the cost of manufacturing on a per-unit basis may assist a company in determining an acceptable selling price for the final product.

Generally, the equation for total product cost per unit. is  mathematically given as

TPC= 20 + 10 + 2 + 1

TPC= $33

In conclusion, the total product cost per unit.

TPC= $33

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Answer:

$33

Step-by-step explanation:

Answer:

600

Step-by-step explanation:

250/1 times 6/ 100 times 40/1

The probability is p = 2/5, the correct option is the third one.

There is a total of 6 socks, such that 4 are black and 2 are blue.

Then the probability of first getting a black sock is the quotient between the number of black socks and the number of blue socks, which gives:

P = 4/6

Now there are 5 socks in total, such that 3 are black and 2 blue.

Then the probability of getting another black one is:

Q = 3/5

The joint probability (getting the two black socks) is given by the product of the individual probabilities:

p = (4/6)*(3/5) = 2/5

The correct option is the third one.

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there are two expressions that can represent the length of the rectangle, these two expressions are:

L = x

or

L = (4x + 12)

Remember that for a rectangle of length L and width W, the area is given by:

A = L*W

In this case, we know that the area is:

[tex]A = 4x^2 + 12x[/tex]

We can factorize that expression into:

[tex]A = x*(4x + 12)[/tex]

So there are two expressions that can represent the length of the rectangle, these two expressions are:

L = x

or

L = (4x + 12)

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The value of the function g(x) = x -3/2x + 1 for x = -1 is g(-1) = 4

The function is given as:

g(x) = x -3/2x + 1

The value is given as:

x = -1

Substitute the known values in the above equation

i.e. we substitute the -1 for x in the above equation

So, we have:

g(-1) = -1 -3/2(-1) + 1

Expand the bracket

g(-1) = -1 -3/-2 + 1

Evaluate the sum and the difference

g(-1) = -4/-1

Evaluate the quotient

g(-1) = 4

Hence, the value of the function g(x) = x -3/2x + 1 for x = -1 is g(-1) = 4

So, the complete parameters are:

g(x) = x -3/2x + 1

x = -1

g(-1) = 4

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Hello,

The triangle be right only if : 18² = 8² + 12²

We have : 18² = 18 × 18 = 324

and 8² + 12² = 8 × 8 + 12 × 12 = 208

324 ≠ 208 → the triangle can not be a right triangle

Step-by-step explanation:

First thing first, let find the x value of where P and Q both meet y=5, we know that y=5, and y=2x^2+7x-4, so using transitive law,

[tex]5 = 2 {x}^{2} + 7x - 4[/tex]

[tex]2 {x}^{2} + 7x - 9[/tex]

[tex]2 {x}^{2} - 2x + 9x - 9[/tex]

[tex]2x(x - 1) + 9(x - 1)[/tex]

[tex](2x + 9)(x - 1) = 0[/tex]

[tex]x = 1[/tex]

[tex]2x + 9 = 0[/tex]

[tex]x = - \frac{9}{2} [/tex]

Now, to find the gradient of the curve let take the derivative of both sides

[tex]5 = 2 {x}^{2} + 7x - 4[/tex]

[tex]0 = 4x + 7[/tex]

[tex]4x + 7[/tex]

Plug in -9/2, let call that point P

[tex]4( \frac{ - 9}{2} ) + 7 = - 11[/tex]

Plug in 1, let call that point Q

[tex]4(1) + 7 = 11[/tex]

So the gradient of the curve at point P (-9/2,5) is -11

The gradient of the curve at point Q (1,5) is 11.

Answer:

[tex]s=\frac{u}{r} -\frac{t}{r}[/tex]

Step-by-step explanation:

You have to move the variables (r and t) with u to isolate s.

[tex]rs+t=u[/tex]

   [tex]-t[/tex]       [tex]-t[/tex]

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

[tex]rs=u-t[/tex]

÷ [tex]r[/tex]       ÷ [tex]r[/tex]

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

[tex]s=\frac{u}{r} -\frac{t}{r}[/tex]

Answer:

7

Step-by-step explanation:

→ Find the scale factor

30 ÷ 25 = 1.2

→ Multiply answer by 20

20 × 1.2 = 24

→ Equate equation to 24

4x - 4 = 24

→ Add 4 to both sides

4x = 28

→ Divide both sides by 4

x = 7