What 5/8 divided by 1/2 ?

The opportunity cost of spending $90,000 on advertising but only producing 12,000 units can be calculated by comparing the benefits of the advertising investment to the potential alternative uses of that money.

First, let's calculate the total cost of producing 12,000 units. Fixed costs amount to $48,000, and variable costs are $8 per unit, resulting in a total cost of $48,000 + ($8 × 12,000) = $144,000.

Next, we need to calculate the potential sales revenue without advertising. With a price of $16 per unit, the potential sales revenue would be $16 × 12,000 = $192,000.

Now, let's calculate the potential sales revenue after advertising. The advertising multiplier is given as (30,000 + advertising) / 30,000. In this case, the multiplier would be (30,000 + 90,000) / 30,000 = 4.

Therefore, the potential sales revenue after advertising would be $192,000 × 4 = $768,000.

The opportunity cost is the difference between the potential sales revenue after advertising ($768,000) and the potential sales revenue without advertising ($192,000), which is $768,000 - $192,000 = $576,000.

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Step-by-step explanation:

9. 6x + 14

10. 5x + 12

11. 15x + 12y

12. -16f + 27

13. 39n + 24

Answer:

9.) 6x + 14

10.) 5x + 12

11.) 15x + 12y

12.) 27 - 16f

13.) 39n + 24

14.) 61m + 14

15.) 7x +6y

16.) 22n + 12

17.) 13x + 10y

18.) -6x + 15y +34

Step-by-step explanation:

2 times 3x, 2 times 4, plus 6

6x + 8 + 6

6x + 14

Answer:

25y+27x

Step-by-step explanation:

You cannot factor this any further

Answer:

C. -7/2

Step-by-step explanation:

7x + 2y = 5

2y= -7x + 5........ move x

y= -7/2 x + 5/2....divide by 2

Answer: S=19cm

Step-by-step explanation:

area = s^2

s(s-5)=266

s^2-5s=266

s^2-5s-266=0

(s-19)(s+14)=0

s=19cm

19 x 19 = 266

The original dimensions of the square cardboard sheet is 19 x 19.

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable, a≠0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given:

Let the length of each side of the original square cardboard be x cm.

After cutting off a strip of 3cm wide its dimension becomes

length = x cm and breadth= (x−5) cm

So, Area = x² - 5x

266 = x² - 5x

x² - 5x - 266= 0

x² - 19x + 14x - 266= 0

x(x - 19) + 14 (x - 19)= 0

(x- 19)( x + 14) = 0

x= 19, -14.

Hence, the original dimensions of the square cardboard sheet is 19 x 19.

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Answer:

corresponding angles, alternate exterior angles

Step-by-step explanation:

when you have to parallel lines cut be a transversal, you get different pairs of angles that are either equal or supplementary (add to 180).

For example, corresponding angles are congruent, and alternate exterior angles are congruent.

Answer: A) 1, 2, 4

Step-by-step explanation:

The range of a function is every y value.

Answer:

A. {1, 2, 4}

Step-by-step explanation:

Well let’s take a step back,

What is range?

Range is the amount of y-value son a graph or table.

So the range is (1, 4, 2)

The slope of the given lines are:

Graph 1 = 1/3

Graph 2 = -1/3

Graph 3 = 3

Graph 4 = -3

To find the slope (m) of a given line on a coordinate plane, choose any two points on the line, (x1, y1) and (x2, y2), then find the slope by plugging in the values of the coordinates into the formula below:

Slope of a line (m) = change in y / change in x = \(\frac{y_2 - y_1}{x_2 - x_1}\).

Find the slope of Graph 1:

Using two points on the line, (0, 0) and (3, 1):

Slope of graph 1 (m) = (1 - 0)/(3 - 0)

Slope of graph 1 (m) = 1/3

Find the slope of Graph 2:

Using two points on the line, (0, 0) and (-3, 1):

Slope of graph 2 (m) = (1 - 0)/(-3 - 0) = 1/-3

Slope of graph 2 (m) = -1/3

Find the slope of Graph 3:

Using two points on the line, (0, 0) and (1, 3):

Slope of graph 3 (m) = (3 - 0)/(1 - 0) = 3/1

Slope of graph 3 (m) = 3

Find the slope of Graph 4:

Using two points on the line, (0, 0) and (-1, 3):

Slope of graph 4 (m) = (3 - 0)/(-1 - 0) = 3/-1

Slope of graph 4 (m) = -3

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We get more money off when we follow order 1, that is, second deal follows first deal.

Given,

There are two deals in an online electronics retailer.

First deal: 10% off on your total purchase = x × (90/100)

Second deal: $20 off on a purchase of minimum $100 = x - 20

x be the money we spend.

We have to spend a minimum of $100.

They allowed us to use both deals.

We have to find the order of deals.

Lets check:

Order 1:

First deal, then Second deal.

First deal, x = 100

ie, x × (90/100) = 100 × (90/100) = 90

Second deal, x = 90

ie, x - 20 = 90 - 20 = 70

100 - 70 = 30

ie, $30 will get off when we apply this order.

Order 2:

Second deal, then first deal.

Second deal, x = 100

x - 20 = 100 - 20 = 80

First deal, x = 80

ie, x × (90/100) = 80 × (90/100) = 72

100 -72 = 28

ie, $28 will get off when we apply this order.

So, we can go for order 1.

Now lets check the same with x = 150 and x = 500

x = 150

Order 1:

First deal, then Second deal.

First deal: x = 150

ie, x × (90/100) = 150 × (90/100) = 135

Second deal, x = 135

ie, x - 20 = 135 - 20 = 115

150 - 115 = 35

ie, $35 will get off when we apply this order.

Order 2:

Second deal, then first deal.

Second deal, x = 150

x - 20 = 150 - 20 = 130

First deal, x = 130

ie, x × (90/100) = 130 × (90/100) = 117

150 - 117 = 33

ie, $33 will get off when we apply this order.

So, we can go for order 1.

x = 500

Order 1:

First deal, then Second deal.

First deal: x = 500

ie, x × (90/100) = 500 × (90/100) = 450

Second deal, x = 450

ie, x - 20 = 450 - 20 = 430

500 - 430 = 70

ie, $70 will get off when we apply this order.

Order 2:

Second deal, then first deal.

Second deal, x = 500

x - 20 = 500 - 20 = 480

First deal, x = 480

ie, x × (90/100) = 480 × (90/100) = 432

500 - 432 = 68

ie, $68 will get off when we apply this order.

So, we can go for order 1.

Lets  conclude that,

We get more money off when we follow order 1, that is, second deal follows first deal.

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Answer:

A. The rate of change of the cost of the taxi ride is $3.00 per minute.

Step-by-step explanation:

The DEXA is the most accurate form of body composition measurement.

What is an x-ray?

An X-ray is a rapid and painless technique which is commonly used to generate images of the internal parts of a human body. It is a very effective and convenient way of looking for bone damages and other problems.

Explanation

The statement 'the dual-energy x-ray absorptiometry (DEXA) is the gold standard measurement for body composition is true. Here, the gold standard means the most accurate form of measurement.

Hence, the given statement is true.

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Answer:

the product of 3, and a number increased by 2

A. The function G(x) = -9x + 2 is a solution of the one-dimensional Laplace's Equation.

B. The function G(x) = 4x² + 3x - 1 is not a solution to the one-dimensional Laplace's Equation.

A. The one-dimensional Laplace's Equation is given by ∂²G/∂x² = 0. To demonstrate that G(x) = -9x + 2 satisfies this equation, we need to show that its second derivative with respect to x is zero. Taking the derivative of G(x) with respect to x, we have dG/dx = -9. Taking the second derivative, we have d²G/dx² = 0. Since the second derivative of G(x) is zero, it satisfies the one-dimensional Laplace's Equation, ∂²G/∂x² = 0.

B. To determine if G(x) = 4x² + 3x - 1 satisfies the one-dimensional Laplace's Equation (∂²G/∂x² = 0), we need to compute its second derivative with respect to x. Taking the derivative of G(x) = 4x² + 3x - 1 with respect to x, we have dG/dx = 8x + 3. Taking the second derivative, we have d²G/dx² = 8. Since the second derivative of G(x) is not zero, G(x) = 4x² + 3x - 1 does not satisfy the one-dimensional Laplace's Equation, ∂²G/∂x² = 0.

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The exact value  of \(sin 2x\) is \(4√5/9.\)

Given that \(sec x = 3/2 and csc y = 3\)where x and y are in the 2x = 2 sin x quadrant, we need to find the exact value of sin 2x.

In the first quadrant, we have the following values of the trigonometric ratios:\(cos x = 2/3 and sin y = 3/5\)

Also, we know that sin \(2x = 2 sin x cos x.\)

Now, we need to find sin x.

Having sec x = 3/2, we can use the Pythagorean identity

\(^2x + 1 = sec^2xtan^2x + 1 = (3/2)^2tan^2x + 1 = 9/4tan^2x = 9/4 - 1 = 5/4tan x = ± √(5/4) = ± √5/2\)

As x is in the first quadrant, it lies between 0° and 90°.

Therefore, x cannot be negative.

Hence ,\(tan x = √5/2sin x = tan x cos x = √5/2 * 2/3 = √5/3\)

Now, we can find sin 2x by using the value of sin x and cos x derived above sin \(2x = 2 sin x cos xsin 2x = 2 (√5/3) (2/3)sin 2x = 4√5/9\)

Therefore, the exact value  of sin 2x is 4√5/9.

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Answer:

2 and 5

Step-by-step explanation:

five plus two equals 7

Answer:

5 & 2

Step-by-step explanation:

X + y = 7

X × y = 10

Solve with the help of trial & error method.

Factors of 10 - 1, 5, 2, 10

Let's take 5 as X & 2 as y.

X + y = 7 --- 5 + 2 = 7

X × y = 10 --- 5 × 2 = 10

Hence, the two numbers that multiply to 10 and add to 7 are 5 & 2

Integrate the density over the disk \(D\) given by

\(D = \{(x,y) ~:~ x^2 + y^2 \le 2^2\}\)

or more conveniently, in polar coordinates by

\(D' = \left\{(r,\theta) ~:~ 0 \le r \le 2 \text{ and } 0\le \theta\le2\pi\right\}\)

Since the density depends on the distance from the origin, we have

\(\rho(r) = \left(1\dfrac{\rm lb}{\mathrm{in}^6}\right)r^3 - \left(2\dfrac{\rm lb}{\mathrm{in}^4}\right)r + 5\dfrac{\rm lb}{\mathrm{in}^3}\)

(Note the units in each coefficient ensure that \(\rho\) is measured in lb/in³.)

Then the mass (in lb) of the puck is

\(\displaystyle \iint_{D'} r\,\rho(r)\,dr\,d\theta = \int_0^{2\pi} \int_0^2 r (r^3 - 2r + 5) \, dr \, d\theta \\\\ ~~~~~~~~ = 2\pi \int_0^2 (r^4 - 2r^2 + 5r) \, dr \\\\ ~~~~~~~~ = 2\pi \left(\frac{2^5}5 - \frac{2\cdot2^3}3 + \frac{5\cdot2^2}2\right) = \boxed{\frac{332\pi}{15}}\)

The best approximation for the area of this circle is approximately 50.2 m².Option (c) is the correct answer.

To determine the best approximation for the area of this circle, we need to use the formula for the area of a circle, which is given by A = πr².

Here, we are given the value of π to be approximately equal to 3.14.

Now, we need to determine the radius of the circle.

From the diagram, we can see that the diameter of the circle is 8 meters.

Therefore, the radius is half of this, which is 4 meters.

Substituting the values of π and r into the formula, we get: A = πr²= 3.14 × 4²= 3.14 × 16= 50.24 (to two decimal places)

Therefore, the best approximation for the area of this circle is approximately 50.2 m².Option (c) is the correct answer.

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Answer:

B. 16

Step-by-step explanation:

A. 4

B. 16

C. 36

D.64

Answer:

$20.96

Step-by-step explanation:

He has $638.54 in his account and writes a check for $159.50. The amount of money he needs to stay at or above $500 is denoted by x.

638.54 - 159.50 + x >= 500

After writing a check, Malcom has $479.04 left in his account, which is below his cutoff.

479.04 + x >= 500

He must add at least x amount of dollars to his account to avoid a fee.

x >= 20.96

In order to avoid a fee, Malcom must add a minimum of $20.96 to his account.

A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t² + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s.

the solution to be eliminated is -0.2s this is because time do not have negative values

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a.

It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be real or complex.

Considering the given function, the answer is both real one is negative the other is positive.

The solution in this case represents time, and time of negative value do not apply in real life

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Answer:

Solve what's in the parentheses

Step-by-step explanation:

You always solve what's in the parentheses first.

The portion of the variance in y that is not explained by the regression model is measured by the variance option known as SSE.

The statistical term variance is defined as the dispersion or spread of a set of data points around the mean.

Variance is the difference between each number in the set and the mean, then squared and summed up. The results of this calculation are divided by the number of data points minus one. The formula for variance can be represented as:

\($\sigma^2 =\frac{\sum (x - \bar{x})^2}{N-1}$$\)

Where\($$\sigma^2= Variance$$\)

\($x = Each\ individual\ data\ point$$$  \bar{x} = The\ mean \value \ of \ the \ set \ of \ data \  points$$\\$N = The \ number \ of  \ data \  points$$\)

There are three types of variance:

Population variance is a statistical term used to describe the average spread of values in an entire population of data points. It is typically denoted by the Greek letter sigma (σ) squared. Since it is almost impossible to gather all the data points in the population, population variance is usually estimated from a random sample of data.

Sample variance, on the other hand, is used to estimate population variance based on a random sample of data points. It is the average of the squared differences from the mean. This type of variance is denoted by the letter s squared, and it is a close estimate of the population variance.

Hence, option 3 is the correct answer.

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The probabilities are given as follows:

The Poisson distribution was used, as we have only the mean of the distribution, and the Poisson distribution was then approximated to the normal.

The z-score of a measure X of a normally distributed variable that has mean represented by \(\mu\) and standard deviation represented by \(\sigma\) is obtained by the equation presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

For the Poisson distribution, the standard deviation is the square root of the mean, hence the mean and the standard deviation for the normal distribution are given as follows:

\(\mu = 150, \sigma = \sqrt{150} = 12.15\)

The probability of less than 100 customers per day, using continuity correction, is one subtracted by the p-value of Z when X = 99.5, hence:

Z = (99.5 - 150)/12.15

Z = -4.16

Z = -4.16 has a p-value of 0.

The probability of more than 185 customers is one subtracted by the p-value of Z when X = 184.5, hence:

Z = (184.5 - 150)/12.15

Z = 2.84

Z = 2.84 has a p-value of 0.9977.

Hence:

1 - 0.9977 = 0.0023 = 0.23%.

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Answer:

No; equation

Step-by-step explanation:

2x+5 = 10 is not an expression rather it's an equation because it has an equal sign. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign.

Step-by-step explanation:

mnnchddhxgijzdzjdzfjdzurizfzifzirzzfizdi

The total number of people's who attended the fair, in terms of c and a is

c + a = 2200

where, c = children and a = adults

Total number of adults who attended the fair are 700 and total number of children who attended the fair are 1500.

We have given that ,

Admission fee for children= $1.50

Admission fee for adults = $4.00

total people enter into fair = 2200

total collection from 2200 people's = $5,050

let consider ,

c --> the number of children that attended the fair

a --> the number of adults that attended the fair,

First, write the two equations letting c = children and a = adults :

c + a = 2200 ---(1)

1.50 (c) + 4.00(a) =5050 ---(2)

Now, we use substitution, c = 2200 − a

plug this value in equation ( 2)

1.50 (2200 - a) + 4.00(a) = 5050

Simplify it

=> 3300 - 1.5a + 4a = 5050

=> 2.5 a = 1750

=> a = 700

Using the first equation ...

c = 2200 - a

=> c = 2200 - 700

=> c = 1500

therefore, there were 700 adults and 1500 children .

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Answer: ΔDEB ≅ ΔCEA; SAS

Step-by-step explanation:

          Using the diagram below, we can see that these two triangles share an angle, meaning that angle in both triangles is congruent. Next, we see dashed lines representing congruence for two of the other sides. This means these two triangles are proved congruent by SAS;

    S = Side

    A = Angle

    S = Side

          See attached for a visual.