What is the price of a jacket that originally costs $125 but has a 25%
discount?

Answer:

D? I'm not sure tho so don't be mad if it's wrong

To maximize the $40,000 allocated to reach the most people, using linear programming, 10 TV ads and 175 radio ads should be used

The number of people reached is 595,000

Linear programming is a method of maximizing a straight-line or linear function that consists of two or more variables such as the cost and the number of people reached.

Let R represent the number of radio ads and let T represent the number of television ads.

The constraints are;

200·R + 500·T ≤ 40,000

R ≥ 10

T ≥ 10

The maximum value function is 7,000·T + 3,000·R

R ≥ T

R - T ≥ 0

R ≥ T

The equations are therefore;

200·R ≤ 40,000 - 500·T

R ≤ (40,000 - 500·T)/200 = 200 - 2.5·T

R ≤ 200 - 2.5·T

When R = T, we have;

T = 200 - 2.5·T

3.5·T = 200

T = 200 ÷ 3.5 ≈ 57.14

The value of the maximizing function, 7,000·T + 3,000·R, at the vertices of the feasible region are therefore;

(T, R)

At (10, 10); 7,000 × 10 + 3,000 × 10 = 100,000

At (10, 175); 7,000 × 10 + 3,000 × 175 = 595000

At (57.14, 57.14); 7,000 × 57.14 + 3,000 × 57.14 = 571400

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The ratio of F# to B to two decimal places is 1.50:1.

A ratio is simply used to compare two things or numbers.

In this case, the note F# has a frequency of 1,480 hertz and the note B has a frequency of 988 hertz.

The ratio of F to B will be:

= 1480 / 988

= 1.50

The ratio is 1.50:1.

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Answer:

3/2

Step-by-step explanation:

Answer:

Doesn't make a lot of sense. Can you be more specific.

Step-by-step explanation:

Weight of cat when 13 grams food is fed is 151.11 ounces.

Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign.  LHS = RHS (left hand side = right hand side) appears in all mathematical equations. You can solve equations to determine an unknown variable's value, which corresponds to an unknown quantity.

Given, the formula for weight,

W = 0.86[tex]g^{2}[/tex] - 0.01g + 5.9

    = 0.86[tex](13^{2} )[/tex] - 0.01*13 + 5.9

    = 0.86*169 - 0.13 + 5.9

    = 145.34 - 0.13 + 5.9

    = 151.11 ounces

Therefore, the weight of the cat will be 151.11 ounces.

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Cut off for the failing score is 60.

Percentage of the student failed is 12.5%.

What is standard deviation?

The term "standard deviation" (or "SD") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

What is normail distribution?

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

Given that,

mean = 72

standard deviation = 6

So,

(a) Cutoff score = mean-(2 x standard deviation)  [tex]=72-(2\times 6)[/tex][tex]= 72-12[/tex]  [tex]=60[/tex].

(b) In a normal distribution, 95% of students fall on both sides of mean in 2 standard deviations range. i.e., [tex]\frac{95}{2} = 47.5[/tex] of students between mean and (mean-2 x standard deviation). So, the percentage of students below 2 standard deviations from mean = 60-47.5 = 12.5%.

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Answer:

A denominator of 10: 5/10

A denominator of 100: 50/100

Answer:

a and c

Step-by-step explanation:

if you evaluate each one on either side of the equal sign you get the same number on both sides

[tex]7x^2+7y^2-28x+42y-35=0 \\ \\ x^2 +y^2-4x+6y-5=0 \\ \\ x^2+y^2-4x+6y=5 \\ \\ x^2-4x+4+y^2+6y+9=18 \\ \\ \boxed{(x-2)^2+(y+3)^2=18}[/tex]

So, the center is [tex](2,-3)[/tex] and the radius is [tex]3\sqrt{2}[/tex].

The value of the current assets is $44500.

Plants asset = $27000

Equity = $81000

The value of the current asset will be:

Cash $7,500

Prepaid Rent $12,000

Accounts Receivable $6,000

Merchandise Inventory $19,000,

Current asset = $44500

Plant assets will be:

Land $16,000

Building $11,000.

Plant asset = $16000 + $11000 = $27000

Stockholders equity will be:

Common stock = $30000

Retained earnings = $51000

Equity = $81000

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Answer: (7/x) + 10

A quotient is a result you get after dividing two numbers, for example, 10 divided by 2 is 5. 5 is the quotient because it's the result of 10/2. Hence, the quotient of seven and a number is simply (7/x), x being any number. And that value is added to 10, leaving us with the expression (7/x) + 10.

Answer:

I think B. 3.85 units

Step-by-step explanation:

The number of boys were playing tag are 5.

What is equation?

Two expressions joined by an equal sign form a mathematical statement known as an equation. An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.

Given: Some students were playing tag on a playground. The number of girls was three less than twice the number of boys. If there were 7 girls.

Suppose the number of boys are x,

So, the number of girls are, 2x - 3.

There are 7 girls.

So, 2x - 3 = 7

2x = 10

x = 10/2

x = 5

Therefore, the number of boys were playing tag are 5.

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Juan must add a volume of 7 cubic feet for the enlarged sandbox.

The volume occupied by the sandbox (V), in cubic feet, is represented by the volume formula for a parallelpiped:

V = w · l · h

Where:

Juan wants to know the additional amount of sand required for the enlarged sandbox. If we know that the initial volume is equal to a cubic foot and each length is double, then we find that the resulting volume for sandbox is:

V' = (2 · w) · (2 · l) · (2 · h)

V' = 8 · (w · l · h)

V' = 8 · V

V = 8 ft³

The addition of sand is found by the following subtraction:

ΔV = V' - V

ΔV = 8 ft³ - 1 ft³

ΔV = 7 ft³

An additional volume of 7 cubic feet is needed for the sandbox.

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With the help of unitary method it can be found out that Tomás has to buy more 3650 grams of oranges if he wants to reach 5 kg.

It is given to us that -

Tomás first chose a tray with oranges whose label says 1,350 gram

We have to find out more grams of oranges that he should buy if he wants to reach 5 kilogram.

We know that

1 kilogram = 1000 grams

=> 1000 grams = 1 kilogram ----- (1)

By unitary method, we can find out the number of kilograms equivalent to 1350 grams of oranges.

From equation (1), we have

1000 grams = 1 kilogram

=> 1350 grams = (1/1000) * 1350

=> 1350 grams = 1.35 kilograms ----- (2)

Now, from equation (2), we can see that Tomás first chose 1,350 grams of oranges which is equal to 1.35 kilograms of oranges.

This implies that the more kilograms of oranges that Tomás has to buy to reach 5 kilograms is given by -

(5 - 1.35) kilograms

= 3.65 kilograms

From equation (1), we have

1 kilogram = 1000 grams

=> 3.65 kilograms = 3.65 * 1000 grams

=> 3.65 kilograms = 3650 grams.

Thus, by solving through unitary method we find out that Tomás has to buy more 3650 grams of oranges if he wants to reach 5 kg.

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The reminder of the equation using the long division method is 70X - 12.

long division method :

Four main steps to solving this problem:

[tex]x^2 - 3$\overline{)x^5 + 24x^3- 5x - 12}$( x^3 + 25x\\\\[/tex]

           x₅ + 3 x³

          (-)    (-)                              

                 25x³ - 5x   -   12

                 25x³ - 75x

                 (-)      (+)                          

                            70x  - 12              

here

divisor - (x² - 3)

dividend - (x⁵ + 2x12x² - 5x - 12)

quotient - (x³ +25x)

the given question is incomplete the correct question is

Use long division to divide.

(x⁵ + 2x12x² - 5x - 12) / (x² - 3)

The reminder of the equation using the long division method is 70X - 12.

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Using the double-declining-balance method of depreciation, the completion of the table as shown is as follows:

Year Cost   Accumulated   Book Value  Depreciation Accumulated  Book

                   Depreciation        B.O.Y         Expense      Depreciation   Value

                        B.O.Y                                                               E.O.Y       E.O.Y

1    $29,000          $0           $29,000         $11,600            $11,600   $17,400

2   $29,000    $11,600          $17,400          $6,960           $18,560  $10,440

3   $29,000   $18,560          $10,440           $4,176           $22,736   $6,264

The double-declining-balance method is one of the depreciation methods in use, but it allocates more cost to the earlier years of the asset's life.

This depreciation method uses twice the straight-line rate, which is computed as the product of 100/estimated useful life multiplied by 2.

For each year's depreciation expense, the double rate is applied at the end of the year's balance.

For the last year, the difference between the previous year's ending balance and the residual value is taken as the depreciation expense.

Auto  = $29,000

Estimated useful life = 5 years

Residual = $2,000

Depreciable amount = $27,000 ($29,000 - $2,000)

Straight-line depreciation rate = 20% (100/5)

Double-declining depreciation rate = 40% (20% x 2)

1st year = $11,600 ($29,000 x 40%)

2nd year = $6,960 ($17,400 x 40%)

3rd year =  $4,176 ($10,440 x 40%)

4th year = $2,506 ($6,264  x 40%)

5th year = $1,758 ($3,758 - $2,000)

Year Cost   Accumulated   Book Value  Depreciation Accumulated  Book

                   Depreciation        B.O.Y         Expense      Depreciation   Value

                        B.O.Y                                                               E.O.Y       E.O.Y

1    $29,000          $0           $29,000         $11,600            $11,600   $17,400

2   $29,000    $11,600          $17,400          $6,960           $18,560  $10,440

3   $29,000   $18,560          $10,440           $4,176           $22,736   $6,264

4   $29,000  $22,736           $6,264          $2,506           $25,242   $3,758

5  $29,000  $25,242            $3,758           $1,758           $27,000  $2,000

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Answer: hours

Step-by-step explanation:

minutes would be way too many

seconds - just self explanatory

days- would be less than one

hours is the only possible solution

Upon graphing of the function rule h = 8 - 0.4j, we see that the graph is continuous.

We are given the function as; h = 8 - 0.4j

Let h represent the height in inches on the y-axis and let j represent the amount of juice in ounces on the x-axis.

We are told that the height of the juice in a 20-oz bottle depends on the amount of juice. This means that j is an independent variable and h is dependent variable.

The function  represents the height of juice after drinking j ounces of juice. Therefore as the juice is being drank, the height of the juice in bottle will change continuously. Therefore, the graph of our given function will be continuous because we can drink fractions of an ounce juice.

The equation of a line in slope-intercept form is given as;

y = mx + b

where;

m is Slope of line

b is y-intercept

If we rewrite our function slope-intercept form of equation, we will get;

h = -0.4j + 8

Thus;

Slope = -0.3

y-intercept = 8.

The graph is as plotted in the attached file

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The acceleration when the car comes to a full stop is 20.76 meters per square second.

Here we have the velocity function:

v(t) = -3t^2 + 18t + 9

To find the acceleration we need to differentiate with respect to the variable t, so we will get the acceleration:

a(t) = 2*(-3)*t + 1*18

a(t) = - 6*t + 18

Now, the car will come to a stop when the velocity is equal to zero, so we need to solve:

-3t^2 + 18t + 9 = 0

Dividing all by -3 we get:

(-3t^2 + 18t + 9)/-3 = 0

t^2 - 6t - 3 = 0

The solutions are:

[tex]t = \frac{6 \pm \sqrt{(-6)^2 - 4*1*-3} }{2*1} \\\\t = \frac{6 \pm 6.92}{2}[/tex]

We only care for the positive solution:

t = (6 + 6.92)/2 = 6.46

The acceleration at that time is:

a(6.46) =  - 6*6.46 + 18 = -20.76

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=====================================================

Explanation:

Unfortunately the U from "universal set" and the union symbol look almost identical.

What I'll do to avoid confusion is to let E represent the set of everything we care about, aka universal set.

E = {f, g, h, p, q, r, x, y, z}

Feel free to use other notation if it makes better sense to you.

From this set, we'll erase items that are found inside set A = {f, g, p, q}

So we go from this

E = {f, g, h, p, q, r, x, y, z}

to this

A' = {h, r, x, y, z}

Everything found in here is guaranteed to not be inside set A.

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

The next step is to union set A' with set B. This is where we combine those two sets into a larger set of items. Toss out any duplicates. Each unique letter is to be listed once.

A' u B = {h, r, x, y, z}  U  {g, h, q, x, y}

A' u B = {h, r, x, y, z,        g, h, q, x, y}

A' u B = {g, h, q, r, x, y, z}

It's recommended you sort the items in a consistent fashion.

Set this result aside for now, and come back to it later.

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

Go back to the set of everything, aka universal set.

E = {f, g, h, p, q, r, x, y, z}

Cross off stuff found in set C, so we guarantee to form the opposite or complement set C'

C' = set of everything NOT found in C

C' = erase "p,q,x,y,z" from set E

C' = {f, g, h, r}

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

To recap we found

Intersect those sets by looking at what they have in common. This is the overlapped region between the sets.

The three items in common are: {g, h, r}  which forms the final answer.

Answer:

the lamp of post is 24 of the same

Answer:

9.8 * 100 = 980

0.040 * 1000 = 40

61 / 10 = 6.1

8.909 * 100 = 890.9

Step-by-step explanation:

The farmer should use 1200 pounds of type 1 mixture and 800 pounds of type 2 mixture to satisfy the given conditions

From given information,

Type 1: 45 percent of protein in the supplement is x pounds

Type 2: 20 percent of the protein in the supplement is (2000 - x) pounds

Also Mixture A 35% of the protein in the supplement is 2000 pounds

According to the equation after removing the percentage sign we have

45x + 20(2000-x)= 35*2000

45x + 40000 - 20x = 70000

25x = 30000

x = 1200

Now for type 2 mixture we have

2000 - 1200 = 800 pounds

Therefore, the farmer should use 1200 pounds of type 1 mixture and 800 pounds of type 2 mixture to satisfy the given conditions

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The average rate of change of the resistance of the thermistor for each degree change in the temperature, when the temperatures changes from 0 °C and 2 °C is A. 4 ohms/°C

The average is calculated by adding the values in the dataset then dividing the result by the count of the numbers or values in the set. The average is also known as the arithmetic mean.

The function for finding the resistance of the thermistor is; R(t) = t³ + 5

The unit of the R = Ohms

The unit of t = Degrees Celsius, °C

The resistance of the thermistor when the temperature is t = 0 °C is found as follows;

R(0) = 0³ + 5 = 5

Therefore;

When the temperature is 0 °C the resistance of the thermistor is 5 Ohms

When the temperature is t = 2 °C, we have;

R(2) = 2³ + 5 = 13

The resistance of the thermistor at t = 2 °C is 13 Ohms

The average rate of change of a function, f(x), is found using the formula;

[tex]A(x) = \dfrac{f(x_2) - f(x_1) }{x_2-x_1}[/tex]

The average rate of change of the resistance per degree change in the temperature, between the temperature interval of 0 °C and 2 °C is therefore;

[tex]A(x) = \dfrac{R(2) - R(0)}{2 - 0}[/tex]

Which gives;

[tex]A(t) = \dfrac{13 -5}{2 - 0}= 4[/tex]

The average rate of change of the resistance of the thermistor between the temperatures of t = 0 °C and t = 2 °C is 4 Ohms/°C

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From the equation E(d) = 38d + 500, The initial electricity is 500W and the build up is 38W per day

An equation is an expression showing the relationship between two or more numbers and variables.

The standard equation of a straight line is:

y = mx + b

Where m is the rate of change and b is the y intercept

Let E represent the electricity from the solar panels after d days.

Since:

E(d) = 38d + 500

The y intercept is 500 and the slope is 38

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The mean age is equal to: 44.09.

The standard deviation is equal to: 10.07.

First of all, we would determine the median of each class interval as follows:

Median 1 = (25 + 34)/2 = 29.5

Median 2 = (35 + 44)/2 = 39.5

Median 1 = (45 + 54)/2 = 49.5

Median 1 = (55 + 64)/2 = 59.5

Next, we would calculate the mean age by using this mathematical expression:

Mean age = ∑fx/∑f

Substituting the given parameters into the formula, we have;

Mean age = [(24.3 × 29.5) + (36.1 × 39.5) + (36.7 × 49.5) + (20.9 × 59.5)]/(24.3 + 36.1 + 36.7 + 20.9)

Mean age = [716.85 + 1,425.95 + 1,816.65 + 1,243.55]/118

Mean age = [5,203]/118

Mean age = 44.09.

Now, we can calculate the standard deviation as follows:

Standard deviation, S = √((∑f(xi - μ)²/∑f)

Standard deviation, S = √((24.3 × (29.5 - 44.09)² + (36.1 × (39.5 - 44.09)² + (36.7 × (49.5 - 44.09)² + (20.9 × (59.5 - 44.09)²)/(24.3 + 36.1 + 36.7 + 20.9))

Standard deviation, S = √((5172.70 + 760.56 + 1,074.14 + 4,963.08)/118)

Standard deviation, S = √(11,970.48/118)

Standard deviation, S = √101.5

Standard deviation, S = 10.07.

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The present value of $2525 per year, at a discount rate of 10 percent, if the first payment is received 9 years from now and the last payment is received 24 years from now is; $9215.77

An annuity is defined as a fixed amount of cash that is received or paid periodically over a certain period of time. This would mean that the amount in each cash flow of the annuity would be equal and occur for a specific period of time.

The formula for present value is;

PV = P[1 - (1 + r)⁻ⁿ)/r]

where;

PV is present value

P is periodic cash flow

r is interest rate

n is time

We are given the following;

Periodic cash flow (P) = $2525 /Year

Interest rate (r) = 10% /Year = 0.1

Time (n) = 16 Year (from 9 years to 24 years)

Thus;

PV = 2525[1 - (1 + 0.1)⁻¹⁶)/0.1]

PV = $19754.86

This is the present value in 9 years

Thus, the present value in 24 years which is now will be expressed by the formula;

PV = FV/(1 + i)^(t)

where;

PV is present value

FV is future value

i is interest rate

t is time

Thus;

PV = 19754.86/(1 + 0.1)^(8)

PV = $9215.77

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Answer:

It's option B, (f • g)(x) = 3x^3 + 6x^2 - 5x - 10

Step-by-step explanation:

In this problem, we are dealing with a branch of functions called composite functions. What the difference is between normal and composite functions is that we instead of defining a value for f(x), take two functions, f(x) and g(x), in the form of f and g. For instance, h(x) = g.

• Take the products of both functions.

f(x)g(x) = 3x²+5 • x-2

• Next, expand the functions. We expand by combining like terms.

= 3x^3 - 6x^2 + 5x - 10

Since the function cannot be simplified further, this leads to option B being our answer.

Hope this helps!

Answer: Let us assume speed of jet in still air =x

speed of wind =y

Jet flying against the wind

Relative speed of the jet = speed of jet in still air -speed of the wind=x-y

distance covered =3426

time =6 hours

distance = speed * time

3426=(x-y)*6

x-y =3426/6

x-y=571——(1)

Jet flying with the wind

Relative speed of the jet = speed of jet in still air +speed of the wind=x+y

distance covered =4026

time =6 hours

distance = speed * time

4026=(x+y)*6

x+y =4026/6

x+y=671———-(2)

solving 1 and 2 we get

x+y=671

x-y=571

x=621

y=50

speed of jet in the still air =x= 621 miles per hour

Step-by-step explanation: