5
Which expressions are equivalent? Select all that apply.
A 3(x + 2) + 4x and 7x + 6
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B 2(x + 3) + 2x and 4x + 3
C -2 + 4(x + 3) and 4x + 10
D 3x + 5(x-1) and 8x-5
E
5x - 2(x + 4) and 3x + 8
F
4 - 5(x + 2) and 5x-6

Answer:

y x y x y is simplified as y³

Step-by-step explanation:

Hoped this helped.

We will see that the total number of ways in which we can distribute 20 different prizes among 180 people is:

C =  6.818e46

Here we need to count how many selections do we have. Each prize will be a selection, so we have 20 selections.

Now we need to count the numbers of 6for each selection.

For the first prize, there are 180 options.

For the second prize, there are 179 options (because one person already got a prize).

For the third prize, there are 178 options.

And so on.

The total number of combinations is given by the product between the numbers of options:

C = 180*179*178*...*161*160 = 6.818e46

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Answer:

Perimeter of ΔLMN = 80 units

Step-by-step explanation:

From the figure attached,

m∠K = m∠N = 58°

m∠J = m∠M = 76°

m∠I = m∠L = 46°

Therefore, ΔKJI and ΔNML are the similar triangles.

By the property of similar triangles,

"Corresponding sides of two similar triangles are proportional"

\(\frac{JK}{NM}= \frac{JI}{ML}= \frac{KI}{NL}\)

\(\frac{9}{NM}= \frac{11}{27.5}= \frac{12}{30}\)

\(\frac{9}{NM}= \frac{12}{30}\)

NM = \(\frac{9\times 30}{12}\)

NM = 22.5

Perimeter of the triangle LMN = ML + NM + NL

                                                  =  27.5 + 22.5 + 30

                                                  = 80 units

Answer:

0.25

Step-by-step explanation:

Answer:

25% as a decimal is 0.25 I think

Step-by-step explanation:

From the probability distribution for the number of defective items in a random sample, the expected value of X is 2.82.

To calculate the expected value of X, we need to multiply each possible value of X by its corresponding probability and sum them up.

The expected value of X, denoted as E(X) or μ, is calculated using the formula:

E(X) = ∑ (x * p(x))

where x represents each possible value of X and p(x) represents the corresponding probability.

In this case, the probability distribution for X is given as follows:

x: 0 1 2 3 4

p(x): 0.1 0.15 0.13 0.07 0.55

To calculate the expected value, we perform the following calculations:

E(X) = (0 * 0.1) + (1 * 0.15) + (2 * 0.13) + (3 * 0.07) + (4 * 0.55)

E(X) = 0 + 0.15 + 0.26 + 0.21 + 2.2

E(X) = 2.82

The expected value represents the average value or mean of the probability distribution. In this case, it represents the average number of defective items we expect to find in a random sample based on the given probabilities.

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X-6y<-12 in slope intercept form is y > 1/6X + 2

The total cost for operating both game booths at the County Fair is $1068.

To determine the total labor cost for Neill's two game booths, we need to calculate the number of hours worked by each employee during the three-day County Fair.

Let's assume that Neill and his employees work 8 hours per day for three days, which is a total of 24 hours per employee. Then we can calculate the labor costs as follows:

For the Guess Your Age booth:

Neill pays his Guesser $13.50 per hour, so the total labor cost for 1 employee is $13.50 x 24 = $324.

For the Tell Your Fortune booth:

Neill pays the fortune teller $17.25 per hour, so the total labor cost for 1 employee is $17.25 x 24 = $414.

Therefore, the total labor cost for both booths is $324 + $414 = $738.

In addition to the labor costs, Neill also incurs permit fees for each booth. The permit fee for the Guess Your Age booth is $145, and the permit fee for the Tell Your Fortune booth is $185. Therefore, the total permit fee is $145 + $185 = $330.

Adding the labor costs and permit fees together, the total cost for operating both game booths at the County Fair is:

$738 (labor) + $330 (permits) = $1068

Therefore, the total cost for operating both game booths at the County Fair is $1068.

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The statement is true.

When the block is in equilibrium, each spring is stretched an additional ∆x. This implies that the forces from the two springs are balanced, and the block is not experiencing any net force in the equilibrium position.

When the block is set into oscillation with amplitude a, it will pass through its equilibrium point during the oscillation. At the equilibrium point, the displacement of the block is zero, and it changes direction. At this point, the block has its maximum speed v, as it is accelerating towards the equilibrium position.

The speed of the block decreases as it moves away from the equilibrium position, reaches zero at the maximum displacement (amplitude), and then starts accelerating towards the equilibrium point again. Therefore, when the block passes through its equilibrium point, it has its maximum speed v.

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The 18th term of the arithmetic sequence -13, -9, -5, -1, 3,... is 55. Thus, the right answer is option A. which is A(18) = 55

Arithmetic Progression is a sequence of numbers in which the difference between two numbers in the series is a fixed definite value.

The specific number in the arithmetic progression is calculated by

\(a_n=a_1+(n-1)d\)

where \(a_n\) is the term in arithmetic progression at the nth term

\(a_1\) is the initial term in the arithmetic progression

d is the difference between two consecutive terms

In the given question, \(a_1\) = -13

d = -9 - (-13) = 4

Therefore, to calculate the 18th term,

\(a_{13}=a_1+(18-1)d\)

= -13 + (17) 4

= -13 + 68

= 55

Hence, the 18th term of the above AP is 55

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After considering the given data and given set of options we conclude that sequence projects a divergence therefore the correct option is diverges.  

To estimate and find whether the sequence \(an = 3 + 5n^2 / 1+n\) converges or diverges, we can apply the following steps:
We can apply divison of both the numerator and denominator of the sequence by \(n^2\) to get an equivalent expression: \(an = (5/n) + 3n / (1/n + 1).\)
As n comes towards infinity, the term 5/n approaches zero and the term 3n approaches infinity.
Hence, the sequence diverges to infinity.
Finally, the sequence \(an = 3 + 5n^2 / 1+n\)diverges.
Then after carefully evaluating we can projects that,l the sequence diverges which can be seen in the given figure.
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Answer:

Only 1 flavour ??

Only 1 flavour ??anyway ....

Only 1 flavour ??anyway ....number of different ice cream desserts

desserts= 3 x 1 x 4

= 12

Answer:

x       y

0     -2

1       -1

2       -0.56

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Because it looks rigid

Answer:

3966

Step-by-step explanation:

Use order of operations to solve this problem:

In your case, there are no parentheses or exponents, so we can skip right the the multiply and divide step. The first multiplication is 98*63=6174. The next step is to do 32*69=2208. Then you minus 6174-2208=3966.

Hope this helps!

Answer:

65%

Step-by-step explanation:

Knowing that 52/80 are red.

To find the percent of marbles are red you do

52/80 * 100 = 65

Hence, 65% of the marbles are red.

[RevyBreeze]

At any given time (10 minutes) a total of 300 skiers are riding the chairlift. Below, you will learn how to solve the problem.

We are told that a single chairlift at Seven Springs Resort discharges 1800 skiers/hour, if we want to know how many skiers are riding in 10 minutes we will use a rule of three.

1800 skiers → 60 minutes

       X         ← 10 minutes

X = 10*1800/60

X = 300 skiers

We conclude that at any given time (10 minutes) a total of 300 skiers are riding the chairlift.

A rule of three is used when we have three known values and only one unknown.

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If the yearly cost for the dental claims are normally distributed , then the yearly cost at which 35% of the employee fall at or below is $91.35  .

In the question ,

it is given that ,

the yearly cost for the dental claims are normally distributed ;

and the mean (μ) is 105 , standard deviation(σ) is 35 .

we know that the z value that corresponds to 35th percentile from standard normal table is : z = -0.385  ;

let the yearly cost be "x" ;

the yearly cost can be calculated using the formula ;

x = z×(σ) + μ

x = (-0.385)×35 + 105

Simplifying further ,

we get ;

x = 91.525

x ≈ 91.53

Therefore , the correct option is (d) 91.53  .

The given question is incomplete , the complete question is

The yearly cost of dental claims for the employees of the local shoe manufacturing company is normally distributed with a mean of $105 and a standard deviation of $35. what is the yearly cost at which 35% of the employees fall at or below is ?

(a) $118.48

(b) $127.29

(c) $82.71

(d) $91.53

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There is no 7th period, so no you aren't in 7th period.

Answer:

C. the same

Step-by-step explanation:

4.80 divided by 12 equals .40

6.40 divided by 16 equals .40

The range of the function g(x) is given as follows:

[0, ∞).

From the graph of the function given in this problem, y assumes all real non-negative values, hence the interval notation representing the range of the function is given as follows:

[0, ∞).

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Answer:

liner Y=9(2x)  Y=5x-3

Step-by-step explanation:

The equations which are linear are

a) y = 9( 2x )

b) y = ( 5x + 3 )2

d) y = 5x - 3

The equations which are non linear are

c) y = 8x²

e) y = 3x² + 2x - 1

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

a)

Let the equation be y = 9( 2x )

Now , on simplifying the equation , we get

y = 18x

Now , this is a linear equation in 2 variables of the from y = mx + c

So , the equation is linear

b)

Let the equation be y = ( 5x + 3 )2

Now , on simplifying the equation , we get

y = 10x + 6

Now , this is a linear equation in 2 variables of the from y = mx + c

So , the equation is linear

c)

Let the equation be y = 8x²

Now , on simplifying the equation , we get

y = 8x²

This is a quadratic equation , and is not linear

So , the equation is non linear

d)

Let the equation be y = 5x - 3

Now , on simplifying the equation , we get

y = 5x - 3

Now , this is a linear equation in 2 variables of the from y = mx + c

So , the equation is linear

e)

Let the equation be y = 3x² + 2x - 1

Now , on simplifying the equation , we get

y = 3x² + 2x - 1

This is a quadratic equation , and is not linear

So , the equation is non linear

Hence ,

The equations which are linear are y = 9( 2x ) , y = ( 5x + 3 )2 and y = 5x - 3

The equations which are non linear are y = 8x² and y = 3x² + 2x - 1

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To find y, we need to substitute ug(x) for u in yf(u). So, y = f(ug(x)).

We are given yf(u) and ug(x). Here, u is the argument of the function yf and x is the argument of the function ug. To find y, we need to first substitute ug(x) for u in yf(u). This gives us yf(ug(x)). However, we want to find y, not yf(ug(x)). To do this, we can note that yf(ug(x)) is just a function of x, since ug(x) is a function of x. So, we can write y as y = f(ug(x)), where f is the function defined by yf.

To find y, we need to substitute ug(x) for u in yf(u) and then write the result as y = f(ug(x)). This allows us to express y as a function of x, which is what we were asked to do.

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The firm's cash coverage ratio can be calculated using the formula:

Cash Coverage Ratio = (Operating Income + Depreciation) / Interest Expense.  Therefore, the firm's cash coverage ratio is approximately 6.93.

The cash coverage ratio is a financial metric used to assess a company's ability to cover its interest expenses with its operating income. It provides insight into the company's ability to generate enough cash flow to meet its interest obligations.

In this case, we first calculated the operating income by subtracting the cost of goods sold (COGS) and selling, general, and administrative expenses (SG&A) from the sales revenue. The resulting operating income was $143,106.

Since the question didn't provide information about the depreciation expenses, we assumed it to be zero. If depreciation expenses were given, we would have added them to the operating income.

The interest expense was given as $20,650, which we used to calculate the cash coverage ratio.

By dividing the operating income by the interest expense, we found the cash coverage ratio to be approximately 6.93. This means that the company's operating income is about 6.93 times higher than its interest expenses, indicating a favorable position in terms of covering its interest obligations.

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Answer:

\( \frac{2}{4} , \frac{3}{4} \\ 1 \frac{2}{4} \\ 2 \frac{1}{4} \)

The area of triangle is 47.906 square unit.

Having three sides, three angles, and three vertices, a triangle is a closed, two-dimensional object. A polygon also includes a triangle.

Triangle's characteristics

s = (AB+BC+CA)/2

s = (14+12+8)/2

s = 17

Area of triangle using Heron's formula is:

A = √{s(s-a)(s-b)(s-c)}

A =  √{17(17-14)(17-12)(17-8)}

A = 47.906 square unit

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Answer:

x = (14/3,6)

Step-by-step explanation:

-3(x-2) < 8

taking negative sign to opposite side relational operator changes.

3(x-2) >8

Similarly

3(x-2)<12

Now

8< 3(x-2) < 12

dividing by 3

8/3 < x-2 < 4

adding 2

8/3 +2 < x < 6

Therefore x = (14/3, 6)

Hope it helps ...

Answer:

14

Step-by-step explanation:

Replace each instance of x with 0 to find f(0):

f(0) = (3/2)(0) + 14 = 14

\(\huge{\mathbb{\tt {PROBLEM:}}}\)

\({\boxed{\boxed{\tt {If f(x) =3/2x +14 \: then \: find \: the \: value \: of \: f(0)}}}}\)

\(\huge{\mathbb{\tt {ANSWER:}}}\)

\({\mathbb{14}}\)

\(\huge{\mathbb{\tt {EXPLANATION:}}}\)

\({\boxed{\boxed{\tt {You \: must \: be \: replaced \: each \: instance \: of \: x \: with \: 0 \: to \: find \: f(0)}}}}\)

\({\boxed{\boxed{\tt { f(0)=(3/2)(0)+14=14}}}}\)

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The first model of inequality satisfy the problem i.e 2w + 2* 4w ≤ 106

A rectangle is a four-sided, two-dimensional flat shape. The opposite sides of a rectangle's four sides are parallel and equal to one another. It belongs to a category of quadrilaterals where each of the four angles is a straight angle or measures 90 degrees. A particular kind of parallelogram that has all of its angles equal is the rectangle. A square is a rectangle with four equally sized sides. Let's now explore the characteristics of the rectangle in this essay.

Rectangles' essential characteristics are as follows:

A rectangle is a parallelogram.

The Perimeter of the rectangle is 2a + 2b where a and b are the two sides

Now , if w is the width of the rectangle then, the length is 4w given in problem.

Perimeter,

2w + 2* 4w

As it is given in the problem

2w + 2* 4w ≤ 106

The first model of inequality satisfy the problem.

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Answer:

The answer is X equals 12

Step-by-step explanation:

I hope you get it right!