6 x (2/3 divided by 2) + 0.5

The following relation are said to be the functions:

{(-5, 1), (-2, 0), (-1, 1), (2, 4), (6,3)}

Relation:

Relation in math is a set of ordered pairs defining the relation between two sets.

Given,

Here we have the following relation

{(-5, 1), (-5, 0), (-2, 1), (-1, 4), (6, 2)}

{(-5, 1), (-2, 0), (-2, 2), (3, 4), (6, 2)}

{(-5, 1), (-2, 0), (-1, 1), (2, 4), (6,3)}

{(-5, 3), (-2, 0), (-1, 2), (6, 4), (6,3)}

Now, we need to identify the which relations are the functions.

We know that the function means the relation in math such that each element of the domain is related to a single element in the codomain.

While we check this condition with each relation then we get,

{(-5, 1), (-5, 0), (-2, 1), (-1, 4), (6, 2)}

This one is not a relation because here -5 take two output values.

{(-5, 1), (-2, 0), (-2, 2), (3, 4), (6, 2)}

This one is not a relation because here -2 take two output values.

{(-5, 1), (-2, 0), (-1, 1), (2, 4), (6,3)}

This one is a function because each domain has exactly one co domain

{(-5, 3), (-2, 0), (-1, 2), (6, 4), (6,3)}

This one is not a relation because here -6 take two output values.

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₁₁C₈ * ₄C₃ as related to permutations is ₁₁P₈ / 8! * ₄P₃ / 3!

The term combination refers to a method of choosing where order does not matter. an instance forming 3 letter word from ABC. the combination is ₃C₃ = 1

In permutation, order matters hence in choosing or making selection specific order should be followed. an instance here is arranging the 3 letters word from ABC. ₃P₃ = 6

All the items above are different permutations however for combination they are same.

The difference mathematically is dividing by the number of arrangements

₃C₃ = 3! / (3!(3-3)!) = 3! / (3!* 0!) = 3! / 3! = 1

₃P₃ = 3! / (3-3)! = 3! / (0!) = 3! / 1 = 3! = 6

Therefore ₃C₃ = ₃P₃ / 3!

similarly

₁₁C₈ * ₄C₃ = ₁₁P₈ / 8! * ₄P₃ / 3!

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Considering the triangle given the variables are calculated to be

x = (5√6)/3

y = (10√6) / 3

Information given in the question

right angle triangle

The unknown variables is calculated using SOH CAH TOA

Definition of variables for the  right angle triangle

hypotenuse = y

opposite = 5√2

adjacent = x

The variable x is solved using tan, TOA, the angle is 60

tan 60 = Opposite / Adjacent

tan 60 = (5√2) / x

x = (5√2) / tan 60

x = (5√6)/3

The variable y is solved using sin, SOH, the angle is 60

sin 60 = Opposite / Hypotenuse

sin 60 = (5√2) / y

y = (5√2) / sin 60

y = (10√6) / 3

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The Original price of barbecue grill is 96.325.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

The final cost  barbecue grill is $79.95.

Discount = 25%

and Tax = 8%

let the original price be x

x- 0.25x + 0.08x = 79.95

0.83x = 79.95

x= 79.95/0.83

x = $96.325

Hence, the Original price of barbecue grill is 96.325.

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Answer:

P(les than/equal to 3): ½

Zach's investment is $100,000.

A ratio shows us the number of times a number contains another number.

Given that Zach, Kolby, and Peyton are investing a total of $350,000 to open a coffee shop. And their investments are in the ratio 1:2:0.5, respectively.
Therefore, Zach, Kolby, and Peyton's investment can be written as  1x, 2x, and 0.5x, respectively.

Now, the total sum of the investment of the three can be written as,

Zach's investment + Kolby's investment + Peyton's investment = $350,000

1x + 2x + 0.5x = $350,000

3.5x = $350,000

x = $350,000 / 3.5

x = 100,000

Further, Zach's investment can be written as,

Zach's investment = 1x = 1($100,000) = $100,000

Hence, Zach's investment is $100,000.

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If the temperatures on Earth continue to increase, the change in the pie graph would be C. Less than 2% of the Earth's water will be in polar ice caps.

The temperature of Earth has risen significantly in the last century as a result of human activity. This had led to the loss of polar ice caps due to them having melted into the oceans from the high temperatures.

This means that if the temperature of the planet should continue to increase, the polar ice caps we have will further be depleted. This would lead to less than 2% of the Earth comprising polar ice caps as is the case now.

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Answer: y+7=-4(x-2)

Answer: y+7=-4(x-2)

According to the following frequency table, the mean of the number points deducted from each student on an economics is 5.1

Frequency table:

Frequency table means the method of organizing raw data in a compact form by displaying a series of scores in ascending or descending order, together with their frequencies—the number of times each score occurs in the respective data set.

Given,

Here we need to determine the mean of the number of points deducted from each student on an economics test given in the follow grouped frequency table.

For the given table of data, the frequency table of the data is attached below.

In order to find the mean of the frequency table we have to use the following values,

The total frequency is 204

And the number of frequency is 40.

So, the mean is

=> 204/40

=> 5.1

Therefore, the mean of the data is 5.1

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Answer:

3.2 pages per minute

Step-by-step explanation:

Unit Rate: 64 / 20 = 3.2 pages per minute

A unit rate is just a measure of either how fast you can do one of something, or how fast you can do something in one unit of time :)

Answer:

Step-by-step explanation

64 pages ÷ 20 =

20 minutes ÷ 20 =

3.2 pages

1 minute

so she read 3.2 pages per minute

Answer:

$22,106.28

Step-by-step explanation:

[tex]CI=P(1+(\frac{r}{12}) )^{12t}[/tex], where [tex]P[/tex] is the principal, [tex]r[/tex] is the interest rate in decimal form, and [tex]t[/tex] is the time in years.

[tex]CI=\$11000.00(1+(\frac{0.07}{12}) )^{12(10)}[/tex]

[tex]CI=\$22106.28[/tex]

3-3(9x²+15x-15x+25)-4(6x²+9x-4x+6)

3-27x²-75-24x²-20-24

3-51x²-119

-116-51x²

An inequality that can be solved to show the number of chairs c Mrs. Smith can buy 8c ≤ 56

In this question we have been given Mrs. Boyer is buying folding chairs that are on sale for $8.

She has $56

We need to find an inequality that can be solved to show the number of chairs c Mrs. Smith can buy.

A price of one chair is $8

So, the price of 'c' number of chairs would be 8c

But she has $56

So, to find the number of chairs she can buy, we need to divide 56 by 8

We can write is as 8c = 56

⇒ c = 7

But she might buy less that 7 chairs.

So, we write above relation in inequality form as,

8c ≤ 56

Therefore, an inequality that can be solved to show the number of chairs c Mrs. Smith can buy 8c ≤ 56

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Answer:

27w+2=19w+6

27w+19w=6+2

w(27+19)=8

w(27+19)/27+19=8/27+19

w=8/(27+19)

The exponential function giving the concentration after t hours is given as follows:

[tex]C(t) = 0.00372(0.9359)^t[/tex]

The standard modelling of an exponential function is presented as follows:

[tex]y = a(b)^x[/tex]

The meaning of the variables of the equation are given as follows:

The initial value of the exponential function is given as follows:

a = 0.00372.

After eight hours, the concentration is given as follows:

C(8) = 0.00219.

Hence the rate of change is obtained as follows:

[tex]C(t) = 0.00372b^t[/tex]

[tex]0.00219 = 0.00372b^8[/tex]

[tex]b^8 = \frac{0.00219}{0.00372}[/tex]

[tex]b = \sqrt[8]{\frac{0.00219}{0.00372}}[/tex]

[tex]b = \left(\frac{0.00219}{0.00372}\right)^{\frac{1}{8}}[/tex]

b = 0.9359.

Hence the equation is:

[tex]C(t) = 0.00372(0.9359)^t[/tex]

The problem is given by the image at the end of the answer, and it asks for the exponential function modelling the situation.

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Using the t-distribution, it is found that:

a)

b)

The bounds of the confidence interval are given according to the rule presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are listed as follows:

The margin of error of the interval is:

[tex]M = t\frac{s}{\sqrt{n}}[/tex]

Then the interval can be interpreted as the sample mean plus/minus the margin of error.

For the confidence interval in this problem, using a calculator, the parameters are given as follows:

[tex]\mu = 1280.1111, s = 33.5799, n = 9[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 9 - 1 = 8 df, is t = 1.86.

Then the margin of error of the interval is:

M = 1.86 x 33.5799/sqrt(9) = 21.

Then the bounds of the interval are:

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Answer:

13

Step-by-step explanation:

56/7 = 8

13 - 5 = 8

15/7 = 13 - 5

The missing number in the expression is 13.

We have,

To find the missing number in the equation 56 / 7 =? - 5, solve for the unknown value.

Unknown value = x

Starting with the equation 56 / 7 = x - 5, simplify the left side:

56 / 7 = x - 5

8 = x - 5

x = 8 + 5

x = 13

Thus,

The missing number in the expression is 13.

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The surface area of the cylinder in term of π is 6764πmm^2

A cylinder is a three-dimensional solid that contains two parallel bases connected by a curved surface. The bases are usually circular in shape. The perpendicular distance between the bases is denoted as the height “h” of the cylinder and “r” is the radius of the cylinder.

The total surface area of a cylinder is 2πr(r+h)

Where r is the radius and h is the height of the cylinder

therefore T.S.A= 2×38π(38+51)

T.S.A=76π×89

The total surface area(T.S.A) of the cylinder =6764πmm^2

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Answer: 7y = 38.11111111111   2y = 10.8888888889 the sum of these two equals to 49 so 11-49=-38 Hopefully you understood. But I didn't know what you wanted to know from this?

Step-by-step explanation: 11-(7y+2y)=-38

7y+2y=9y (basic math)

11-9y=-38  then you want to move -38 to the other side, and when you move it to the other side it changes its value then from -38 it becomes 38. Same for the -9y, we move it to the other side and it changes its value so now from -9y its 9y. So now are equation should look like this 11+38=9y.   11+38=49 => y=49÷9   y=5.44444444444   (49÷9) x 7 = 38.1111111111 and (49÷9) x 2 = 10.8888888889      

Answer:

y = 2(x - 1)^2 - 9

Step-by-step explanation:

The vertex form of a parabola is y = a(x - h)^2 + k

(h, k) is the vertex, aka (1, -9)

(x, y) is the point that is passed through aka (2, -7)

Using this, we can substitute these values into the equation.

First, let's work with the vertex

We know that h = 1 and k = -9:  y = a(x - 1)^2 - 9

Now, let's substitute in the point that was given: -7 = a(2 - 1)^2 - 9

Now, we can find the a-value by simplifying: -7 = a - 9   -->  a = 2

Finally, we can make the equation by taking our equation that we made with the vertex but just putting the a-value in since we know it.

y = 2(x - 1)^2 - 9 is the equation of the parabola in vertex form

I hope this helps! Let me know if it is wrong

Check the picture below.

[tex]~~~~~~\textit{initial velocity in meters} \\\\ S = -5t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&16\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&16\\ \qquad \textit{of the object}\\ h=\textit{object's height}&\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ 0=-5t^2+16t+16\implies 5t^2-16t-16=0 \\\\\\ (5t+4)(t-4)=0\implies t= \begin{cases} -\frac{4}{5}\\\\ 4 ~~ \textit{\LARGE \checkmark} \end{cases}[/tex]

the equation for meters is usually as you see in the picture but for this exercise it got rounded from -4.9 to -5, which is fine.

let's notice that "t"  has two values, however the seconds cannot be a negative value, so we dismiss that one.

The ball will strike the ground 4 seconds after it is thrown When an object is thrown upward, its height , in meters, is given by the quadratic equation S = -5t² + vt + h

To find the time at which the ball will hit the ground, we need to determine when the height (S) of the ball becomes zero. At that moment, the ball will be at ground level.

The height (S) of the ball is given by the quadratic equation:

S = -5t² + vt + h

where:

S = height of the ball in meters

t = time of flight in seconds

v = initial velocity in meters/second (upward velocity, so it's positive)

h = height above level ground from which the object is thrown

Given that the initial velocity (v) is 16 meters/second, and the height above the ground (h) is 16 meters, we can substitute these values into the equation:

S = -5t² + 16t + 16

Now, to find the time (t) at which the ball hits the ground, we need to solve for t when S = 0:

0 = -5t² + 16t + 16

This is a quadratic equation in standard form (ax² + bx + c = 0), and we can solve it by factoring or using the quadratic formula. In this case, let's use the quadratic formula:

The quadratic formula is given by:

t = (-b ± √(b² - 4ac)) / 2a

In our case, a = -5, b = 16, and c = 16. Plugging these values into the quadratic formula:

t = (-(16) ± √(16² - 4*(-5)16)) / 2(-5)

t = (-16 ± √(256 + 320)) / -10

t = (-16 ± √576) / -10

Now, find the two possible solutions for t:

t₁ = (-16 + √576) / -10

t₁ = (-16 + 24) / -10

t₁ = 8 / -10

t₁ = -0.8 seconds

t₂ = (-16 - √576) / -10

t₂ = (-16 - 24) / -10

t₂ = -40 / -10

t₂ = 4 seconds

We have two solutions for t: t = -0.8 seconds and t = 4 seconds. However, we can disregard the negative value for time, as time cannot be negative in this context.

So, the ball will strike the ground 4 seconds after it is thrown.

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Solving for X the value is = 45, 6

acc to our question-

90/x=90/x+15+1/2

(15-x)90 - 90x/15x-x^2 = 5

x= 45 or 6

hence, for X the value is = 45, 6

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The equation that shows the relationship between the number of hours Jack's crew works, x, and the total number of yards of pavement laid, y will be;

⇒ y = 40 + 15x

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Sanjay and his paving crew laid 40 yards of new pavement.

And, They can lay 15 yards of new pavement per hour.

Now,

Let the number of hours Jack's crew works = x

And, The total number of yards of pavement laid = y

Hence, We can formulate;

An equation that shows the relationship between x and y will be;

y = 15x + 40

Thus, The equation that shows the relationship between the number of hours Jack's crew works, x, and the total number of yards of pavement laid, y will be;

⇒ y = 40 + 15x

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The corresponding angles form the given figure are ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8 and ∠3 and ∠7. Therefore, option D is the correct answer.

From the given figure, we need to identify the corresponding angles.

The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.

From the figure, ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8 and ∠3 and ∠7 are the corresponding angles.

The corresponding angles form the given figure are ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8 and ∠3 and ∠7. Therefore, option D is the correct answer.

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If  the total amount of period costs incurred to sell 9,000 units is closest to: D) $49,500.

First step is to find the variable selling and administrative expense per unit

Sales commissions $ 0.50

Add variable administrative expense 0.50

Variable selling and administrative expense per unit $ 1.00

Now let find the total amount of period costs

Total variable selling and administrative expense $9,000

($1.00 per unit × 9,000 unit)

Add total fixed selling and administrative expense 40,500

Total period cost $ 49,500

Therefore the correct option is D.

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The complete question is:

Shelp Corporation has provided the following information:

Cost per Unit Cost per Period

Direct materials $ 7.15

Direct labor $ 3.35

Variable manufacturing overhead $ 1.40

Fixed manufacturing overhead $ 81,000

Sales commissions $ 0.50

Variable administrative expense $ 0.50

Fixed selling and administrative expense $ 40,500

For financial reporting purposes, the total amount of period costs incurred to sell 9,000 units is closest to:

A) $33,000

B) $9,000

C) $40,500

D) $49,500

Using the z-score tables, the number of babies that weighed more than 10 pounds is; 43

A probability distribution that can be considered to be symmetric about the mean is the normal distribution, which can often be referred to as the Gaussian distribution. This depicts to us the concept of data being close to the mean occurring more often than data that are considered far from the mean. The normal distribution usually has a bell curve graph.

We are given that;

The total number of babies is 908.

Mean of the normal distribution is 7.2 pounds.

Standard deviation of the normal distribution is 1.5 pounds.

The formula of z score is given by;

z = (x - μ)/σ

where;

x is sample mean

μ is population mean

σ is standard deviation

We are given that;

x = 10

μ = 1.5

σ = 7.2

Thus;

z = (10 - 7.2)/1.5

z = 1.86667

The P-value from Z-Table gives us:

P(x > 10) = 1 - P(x < 10) = 0.030974

The number of babies that weighed more than 10 pounds is;

(0.030974 × 908) ≈ 43

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The area of the city block is 13.23 kilometers².

The city block is 3 times as long as it is wide. In this case, the width can be represented by w. The length will be 3w.

Therefore, perimeter will be:

= 2(length + width)

= 2(3w + w) = 16.8

8w = 16.8

Divide

w = 16.8 / 8

w = 2.1

Length = 3w = 3 × 2.1 = 6.3km

The area will be:

= Length × Width

= 6.3 × 2.1

= 13.23km²

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Answer:

The area of the city block is 13.23 kilometers².

Step-by-step explanation:

Answer:

Step-by-step explanation:

x²-4x+2=0

x²-4x=-2

x²-4x+4=-2+4

(x-2)²=2

x-2=±√2

x=2±√2

x=2+√2≈2+1.41≈3.41

x=2-√2≈2-1.41≈0.59

so roots lie between 0 and 4.

Answer: im pretty sure the answer is c

Step-by-step explanation:

if the answer is  not c im sorry but i hope this helps! Have a good day!