Frank owns a clothing store that sells shorts and graphic T-shirts. He sells the shorts for $14 each and the T-shirts for $6 each. He is limited to the constraints shown by the set of inequalities below. Which of the points (s,t) will maximize Frank's revenue?
s≤ 18-0.5t
s≥ 10-t
s≤ 30-t
s≥0
t≥0

sin a° = 3/√13, cos a° = 2/√13 and tan a° = 3/2 as per the rules of a trigonometric ratio.

Trigonometric ratios are developed based on the right-angled triangle.

The largest side length of a right-angled triangle is called hypotenuse.

Suppose an angle Ф is in between the hypotenuse and base of a triangle. The base is called the adjacent side.

The remaining side length is called the opposite side length.

sinФ = opposite side length/ hypotenuse

cosФ = adjacent side length /hypotenuse

tanФ = opposite side length/adjacent side length

According to the figure, a right-angled triangle has hypotenuse 3√13, angle a is in between hypotenuse and base of the triangle.

The length of adjacent side to the angle a° is 6 units and opposite side has a length 9 units.

now, according to the trigonometric ratio

sin a° opposite side /hypotenuse = 9 /3√13 = 3/√13

cos a° = adjacent side / hypotenuse = 6/3√13 = 2/√13

tan a° = opposite side/adjacent side = 9/6 = 3/2

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Step-by-step explanation:

8/9(54x - 36) +2=-3/4(-40+ 16x) + 90x

or,432x-288+18/2 =120-48x+360x/4

or,4(42x-288+18)=2(120-48x+360x)

or,168x-1080=240-624x

or,162x+624x=1080+240

or,792x=1320

or,X=1320/792

or,X=5/3

Answer:

13

Step-by-step explanation:

use distance formula \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\d= \sqrt{(7-2)^2+(7-(-5))^2} =13\)

Answer:

A:

Step-by-step explanation:

Using tangent-secant theorem

AE²=(EC)(ED)

12²=(8)(8+x+10)

144=8(x+18)

144=8x+144

8x = 144-144

8x = 0

So

x = 0

Now

ED = 8+x+10

ED = 8+0+10

ED = 18

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer:

the answer is slope=94, y-intercept = 2

Step-by-step explanation:

i took the test

Answer: 200cm

Calculation: 15cm times 8=120

20cm times 4= 80

Add 120+80= 200cm

Answer:

A.

What were the sixth grade student scores of the final exam?

Answer

Yes, zero is contained in the interval

Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

Answer:

It makes sense for Phil to sell his products online.

Step-by-step explanation:

Yes. In mathematics, a function is a binary relation between two sets that associates to each element of the first set exactly one element of the second set.

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hope it helps

The following steps are used to set up a regression

Regression analysis is a set of statistical methods used for the estimation of relationships between a dependent variable and one or more independent variables. It can be utilized to assess the strength of the relationship between variables and for modeling the future relationship between them.

Here , first we identify which variable is independent and which is affect by this independent variable

Then , we plot the data to analyze the pattern between them

Then we find correlation between them after we will able to draw our conclusion about regression.

Therefore, the regression analyses are performed a couple of times to produce the best analysis results, including the test statistics and the predicted fitted regression.

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Answer:

1.5

Step-by-step explanation:

30÷20=1.5

Answer:

height = 20 yards and base = 25 yards.

Step-by-step explanation:

let the height = x yards.

base = (5 + x) yards.

area = 250 square yards

Area = 1/2 bh

250 = 1/2 × (x)(5+x)

250 × 2 = 5x + x2

500 = x2 + 5x

x2 + 5x - 500 = 0

factorizing:

(x + 25)(x - 20) = 0

x = -25 or 20

but length cannot be negative,

hence x = 20 yards.

height = 20 yards

base = (5 + 20) = 25 yards.

Answer:

19.6 in²

Step-by-step explanation:

area of circle = π r²

= π (3 1/2)²

= π (5/2)²

= π 25/4

= 22/7 x 25/4

= 275/14

=19.6 in²

we have the functions

Find out (f/g)(x)

Find out the restrictions

Remember that the denominator cannot be equal to zero

so

3x+2=0

3x=-2

x=-2/3

so

The value of x cannot be equal to x=-2/3

therefore

Answer:

-Twice means muliply by 2

-The difference of a number and 7 means subtract a number/variable and 7.

-Is equal to 9 means =9

2(X - 7) = 9

The the coefficient of variation for set a is 15.7% and the coefficient of variation for set b is 22.3%.

The formula for calculating the coefficient of variation is:

CV = (standard deviation / mean) x 100%

where standard deviation is a measure of the spread of the data around the mean. The CV expresses the standard deviation as a percentage of the mean.

To calculate the CV for set a, we first need to find the mean and standard deviation of the data set. The mean can be calculated by adding all the values and dividing by the number of values.

Mean = (3.97 + 3.47 + 3.99 + 4.30 + 3.16 + 3.07 + 4.24 + 2.94 + 3.56 + 3.43 + 3.06 + 3.34 + 4.35 + 3.57) / 14 = 3.65

The standard deviation can be calculated using a calculator or a spreadsheet software such as Microsoft Excel. For this set, the standard deviation is 0.574.

CV = (0.574 / 3.65) x 100% = 15.7%

To calculate the CV for set b, we need to first remove the dollar sign from each value and then find the mean and standard deviation.

Mean = ($24,800 + $30,000 + $22,300 + $20,400 + $19,000 + $32,200 + $23,000 + $23,000 + $24,000 + $27,200 + $34,900) / 11 = $25,727.27

The standard deviation can be calculated using a calculator or spreadsheet software. For this set, the standard deviation is $5,746.38.

CV = ($5,746.38 / $25,727.27) x 100% = 22.3%

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9514 1404 393

Answer:

  (a) cannot be determined

  (b) 44 cm^2

  (c) 87 m^2

  (d) 180 m^2

  (e) 132 m^2

Step-by-step explanation:

(a) missing a horizontal dimension

__

(b) The difference between the bounding rectangle and the lower-left cutout is ...

  (8 cm)(7 cm) -(3 cm)(4 cm) = (56 -12) cm^2 = 44 cm^2

__

(c) The difference between the bounding rectangle and the center cutout is ...

  (13 m)(7 m) -(4 m)(1 m) = (91 -4) m^2 = 87 m^2

__

(d) The difference between the bounding rectangle and the two cutouts is ...

  (20 m)(25 m) -(16 m)(20 m) = (20 m)(25 -16) m = (20 m)(9 m) = 180 m^2

__

(e) The difference between the bounding rectangle and the two cutouts is ...

  (14 m)(12 m) -(12 m)(3 m) = (12 m)(14 -3) m = (12 m)(11 m) = 132 m^2

Answer:

x = 1

Step-by-step explanation:

Answer:

8 Weeks

Step-by-step explanation:

First let's collect the given data:

• Class A:

- Starts at 8 cm

- grows at 3.5 cm/week

• Class B:

- Starts at 10cm

- grows at 3.25 cm/week

Class B's plant starts out 2 cm taller and Class A's plant grows 1/4 cm faster. So, to find when these two will be at an equal height, divide 2 cm by 1/4.

2 ÷ 1/4 =

2 × 4/1 =

2 × 4 =

8

It will take 8 weeks for the plants to be at an equal height.

Answer:

4x^2 - 4x + 1

Step-by-step explanation:

Answer:

y=4

Step-by-step explanation:

steps

3×9+4y=43

4y=43-27

4y=16

Divide both side by 4

4y/4=16/4

y=4

The graph of the function y = 5|x - 4| is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Nathaniel drinks 3 glasses of water in one hour.

To find out how many glasses of water Nathaniel drinks in one hour, we need to calculate his drinking rate per hour.

In 2 2/5 hours, Nathaniel drinks 4/5 of a 10-ounce glass of water.

Let's convert the mixed number of hours to an improper fraction:

\(2\frac{2}{5} = \frac{(5 \times2 + 2)}{5}\)

\(=\frac{12}{5}\)

Now, we can set up a proportion to find his drinking rate per hour.

We know that \(\frac{12}{5}\) hours corresponds to \(\frac{4}{5}\) of a glass of water.

Let's assign "x" as the number of glasses he drinks in one hour.

The proportion is then

\(\frac{(\frac{12}{5} hours) }{(x glasses) } =\frac{(\frac{4}{5} glass)}{(1 hour)}\)

Cross-multiplying gives us

\((\frac{12}{5} )\times1=\frac{4}{5}\times(x)\)

Simplifying, we get

\(\frac{12}{5} =\frac{4}{5}\times x\)

Dividing both sides by \(\frac{4}{5}\), we find x:

\(x=\frac{(\frac{12}{5} )}{\frac{4}{5} }\)

\(x=\frac{12}{4}\)

\(x = 3.\)

Therefore, Nathaniel drinks 3 glasses of water in one hour.

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60% of 500 is 300

So if Zack wanted to sell the car 60% of the markets price, it would be 300.

125% of 500 is 625

If Zack wanted to sell the car for 25 more than the price at market, it would be 125%, and 125% of 500 is 625.