Cos(A-B)=84/85 and secA=17/8 find the value of sinB.

Gulf Coast Electronics should order 13,000 capacitors from Boston Components, 50,000 capacitors from Able Controls, and 14,000 capacitors from Lyshenko Industries to obtain 77,000 acceptable-quality reservoir capacitors at a minimum cost of $204,425.

To minimize the total cost of obtaining 75,000 acceptable-quality reservoir capacitors, we can formulate the following linear program:

Objective function:

Minimize: 2.35B + 2.6A + 2.85L

Subject to:

B + A + L = 77000 (total number of capacitors required)

B ≥ 0.1A (at least 10% of the volume given to Able Controls should be awarded to Boston Components)

L ≥ 29500 (at least 29,500 capacitors should be ordered from Lyshenko)

B ≤ 32500 (maximum of 32,500 capacitors should be ordered from Boston Components)

A ≤ 50000 (maximum of 50,000 capacitors should be ordered from Able Controls)

L ≤ 48500 (maximum of 48,500 capacitors should be ordered from Lyshenko)

0 ≤ B, A, L (non-negativity constraints)

Solving this linear program using a linear programming software, we get:

B = 13000

A = 50000

L = 14000

Correct Question :

Gulf Coast Electronics is ready to award contracts to suppliers for providing reservoir capacitors for use in its electronic devices. For the past several years, Gulf Coast Electronics has relied on two suppliers for its reservoir capacitors: Able Controls and Lyshenko Industries. A new firm, Boston Components, has inquired into the possibility of providing a portion of the reservoir capacitors needed by Gulf Coast. The quality of products provided by Lyshenko Industries has been extremely high; in fact, only 0.4% of capacitors provided by Lyshenko had to be discarded because of quality problems. Able Controls has also had a high quality level historically, producing an average of only 1% unacceptable capacitors. Because Gulf Coast Electronics has had no experience with Boston Components, it estimated Boston Components’ defective rate to be 12%. Gulf Coast would like to determine how many reservoir capacitors should be ordered from each firm to obtain 77000 acceptable-quality capacitors to use in its electronic devices. To ensure that Boston Components will receive some of the contract, management specified that the volume of reservoir capacitors awarded to Boston Components must be at least 10% of the volume given to Able Controls. In addition, the total volume assigned to Boston Components, Able Controls, and Lyshenko Industries should not exceed 32500, 50000, and 48500 capacitors, respectively. Because of Gulf Coast’s long-term relationship with Lyshenko Industries, management also specified that at least 29500 reports should be ordered from Lyshenko. The cost per capacitor is $2.35 for Boston Components, $2.6 for Able Controls, and $2.85 for Lyshenko Industries.

Formulate and solve a linear program for determining how many reservoir capacitors should be ordered from each supplier to minimize the total cost of obtaining 75,000 acceptable-quality reservoir capacitors. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. Enter "0" if your answer is zero. If the constant is "1" it must be entered in the box.

Let B = number of capacitors ordered from Boston Components

Let A = number of capacitors ordered from Able Controls

Let L = number of capacitors ordered from Lyshenko Industries

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It would take 370 days to build the wall with the given conditions.

If 60 men can build a wall in 40 days, then the total man-days required to build the wall is:

60 men x 40 days = 2400 man-days

However, 55 men quit every ten days, which means that after 10 days, there are only 60 - 55 = 5 men left to work on the wall. After 20 days, there are only 5 - 55 = -50 men left, which means that the remaining 5 men cannot work any faster than they were already working. Therefore, we can assume that the remaining 5 men complete the wall on their own.

The number of man-days required for the first 10 days is:

60 men x 10 days = 600 man-days

The number of man-days required for the second 10 days is:

5 men x 10 days = 50 man-days

The total number of man-days required for the first 20 days is:

600 man-days + 50 man-days = 650 man-days

The remaining work can be completed by the 5 men in:

2400 man-days - 650 man-days = 1750 man-days

Therefore, the total time needed to build the wall is:

20 days + 1750 man-days / 5 men = 20 + 350 days = 370 days

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\(\\ \sf\longmapsto -3(2+4p)=2(2p-1)\)

\(\\ \sf\longmapsto -6-12p=4p-2\)

\(\\ \sf\longmapsto -12p-4p=-2+6\)

\(\\ \sf\longmapsto -16p=4\)

\(\\ \sf\longmapsto p=\dfrac{-4}{16}\)

\(\\ \sf\longmapsto p=\dfrac{-1}{4}\)

Use distributive law

Now

LHS

RHS

Equat

"97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits

To calculate the scores that are three standard deviations above and below the mean, we use the formula:

Lower limit = Mean - (Standard Deviation * 3)

Upper limit = Mean + (Standard Deviation * 3)

Given:

Mean = 269

Standard Deviation = 33

Using the formula, we can calculate the limits:

Lower limit = 269 - (33 * 3) = 269 - 99 = 170

Upper limit = 269 + (33 * 3) = 269 + 99 = 368

Therefore, the lower limit is 170 and the upper limit is 368.

To calculate the probability that a female student will have a score between these limits, we need to find the area under the normal distribution curve between the lower and upper limits. This can be calculated using a standard normal distribution table or calculator.

Since the distribution is assumed to be normal, approximately 99.72% of the scores will fall within three standard deviations from the mean. Therefore, the probability that a female student will have a score between these limits is approximately 99.72%.

For a score of 302, which is above the mean of 269, we can calculate the percentage of female students with scores below 302:

Percentage = (1 - Probability) * 100

= (1 - 0.9972) * 100

= 0.0028 * 100

= 0.28%

Therefore, approximately 0.28% of the female students have scores below 302.

It's important to note that the value mentioned, "97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits

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Answer:

Step-by-step explanation:

Slope of line is 1/2.

What is slope?

In arithmetic, the slope or gradient of a line is a range that describes each the direction and therefore the gradient of the road.

Main body:

to find the slope from a graph , we need to fix two co-ordinates at slope for axis

let point at x be = (40,40)

let point y = (80,60)

Formula for slope ,

m = y₂-y₁/x₂-x₁

m = 60-40/80-40

m = 20/40

m = 1/2

hence , slope of line is 1/2.

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The correct statements regarding the dilation to the triangle are given as follows:

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The resulting image is a larger or smaller version of the original object, depending on whether the scale factor is greater than or less than 1, respectively.

The ratio of the perimeter is equals to the scale factor, while the ratio of the areas is equals to the square of the scale factor.

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Answer:

Step-by-step explanation:

Let x be the side length of the square window. Then the area of the square window is x^2, and the area of the rectangular window is 16 * 4 = 64.

We can write the equation:

x^2 = 64

To solve for x, we can take the square root of both sides:

x = √64

x = 8

Therefore, the side length of the square window is 8 inches.

The linear equation we need to solve is:

$27.50*w = $309.99 - $144.99

And the solution is w = 6.

How to write and solve the equation?

We know that the cost of the gaming chair is $309.99.

To buy this, you already have saved $144.99, and save another $27.50 per week, then the amount you have after w weeks is:

f(w) = $144.99 + $27.50*w

So the linear equation we need to solve is:

$144.99 + $27.50*w = $309.99

To solve this we need to isolate w.

$144.99 + $27.50*w = $309.99

$27.50*w = $309.99 - $144.99

w = ($309.99 - $144.99)/$27.50 = 6

So they can buy the chair after 6 weeks.

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The gratuity of the hotel server has to be $8.

The tax of the restaurant server is 8.5 percent

We have tro find this based on salary

40 dollars x 0.85 = 34

The income 34 - 18

= 16

Half of 16 = 8

Hence the amount that is the percentage of gratuity is 8 percent.

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Answer:

$53.70 per gram

Step-by-step explanation:

Just divide the price (123.51) by the amount of grams (2.3) to get your answer, which should be $53.70 per gram

Hopefully this helps - let me know if you have any questions!

Answer:

The question is not complete

Restaurant and Food may be this..

it is restaurants and foods

The equation of the linear relationship in slope-intercept form is y = 2x - 8. Option A is the correct answer.

To determine the equation of the linear relationship in slope-intercept form based on the table, we need to find the slope and y-intercept.

By observing the table, we can calculate the slope by selecting any two points. Let's choose the points (0, -8) and (4, 0).

Slope (m) = (change in y) / (change in x)

= (0 - (-8)) / (4 - 0)

= 8 / 4

= 2

Now that we have the slope, we can find the y-intercept by substituting the values of one point and the slope into the equation y = mx + b and solving for b.

Using the point (0, -8):

-8 = 2(0) + b

b = -8

Therefore, the equation of the linear relationship in slope-intercept form is: y = 2x - 8. Option A is the correct answer.

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Answer:

s = 9

Step-by-step explanation:

calculate the slope m through the 2 points using the slope formula and equate to - 5

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (7, 3 ) and (x₂, y₂ ) = (s, - 7 )

m = \(\frac{-7-3}{s-7}\) = \(\frac{-10}{s-7}\)

equate m to slope of - 5

\(\frac{-10}{s-7}\) = - 5 ← multiply both sides by s - 7

- 10 = - 5(s - 7) ← divide both sides by - 5

2 = s - 7 ( add 7 to both sides )

9 = s

well, the profit is clearly just 490 - 350 = 140.

Now, if we take 350(origin amount) to be the 100%, what is 140 off of it in percentage?

\(\begin{array}{ccll} Amount&\%\\ \cline{1-2} 350 & 100\\ 140& x \end{array} \implies \cfrac{350}{140}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{5}{2} ~~=~~ \cfrac{100}{x}\implies 5x=200\implies x=\cfrac{200}{5}\implies x=40\)

A function with an infinite number of critical points can be expressed as a continuous function with a derivative that is equal to zero at every point in its domain.

For example, the function f(x) = 0 has an infinite number of critical points since its derivative f'(x) = 0 for every x in its domain. Alternatively, a function that has every point as a critical point can be expressed as a function with a derivative that is always equal to zero. For example, the constant function f(x) = c has a derivative f'(x) = 0 for every x in its domain, and thus every point in its domain is a critical point.

In addition, an example of a function with every point as a critical point is the constant function, f(x) = c, where c is a constant. The derivative of this function is f'(x) = 0, which means that the derivative is zero for all values of x. Therefore, every point of the constant function is a critical point.

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$64.71 rounded, explanation attached

An estimate of the mean height is 181 and the modal class is 180 - 190

The mean value is calculated using:

\(\bar x = \frac{\sum fx}{\sum f}\)

Using the values on the histogram, we have:

\(\bar x = \frac{155 * 4 + 165 * 10 + 175 * 14+ 185 * 18 + 195 * 8 + 205 *6}{4 + 10 + 14 + 18 +8 + 6}\)

Evaluate

\(\bar x = \frac{10840}{60}\)

Divide

\(\bar x = 180.67\)

Approximate

\(\bar x = 181\)

Hence, an estimate of the mean height is 181

It is the mean because it represents the average height of the data values represented on the histogram

This is the class that has the highest frequency.

From the given figure, the class 180 to 190 has the highest frequency

Hence, the modal class is 180 - 190

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Answer:

X=x−4

Step-by-step explanation:

2(x−3)+X=5x−2(x+5)

Use the distributive property to multiply 2 by x−3.

2x−6+X=5x−2(x+5)

Use the distributive property to multiply −2 by x+5.

2x−6+X=5x−2x−10

Combine 5x and −2x to get 3x.

2x−6+X=3x−10

Subtract 2x from both sides.

−6+X=3x−10−2x

Combine 3x and −2x to get x.

−6+X=x−10

Add 6 to both sides.

X=x−10+6

Add −10 and 6 to get −4.

X=x−4

All you have to do is solve this by using substitution or elimination. or in this case, because we don’t have a second equation, we would solve the x-intercept and y-intercept

X=-12

Y=-9

Answer: As a fraction: 1/2

              As a decimal: 0.005

Step-by-step explanation:

FRACTION:

To figure out how to write 0.5% as a fraction, all you need to know is that 0.5 = to a half, or 1/2 because 0.5 is half of 1.

DECIMAL:

0.5% as a decimal form is 0.005 because it is 1000 times less than 1, so you move the 0 3 times right.

Answer:

39.96 in²

Step-by-step explanation:

10.8x3.7=39.96

Answer:

19.98

Step-by-step explanation:

area=½×base ×height

½×10.8×3.7

=19.98

Answer:

C. \(cos^2A -sin^2A\)

Step-by-step explanation:

Given:

\(cos2A\)

To find:

The given expression is equivalent to:

A. \(sin^2A-cos^2A\)

B. \(sin^2A+cos^2A\)

C. \(cos^2A -sin^2A\)

D. \(cosA-sinA\)

Solution/Proof:

First of all, let us have a look at the compound angle formula for \(cos(X+Y)\).

Compound angle means in which there is sum of two angles given.

In the above we are having X+Y i.e. sum of two angles X and Y. So it is compound angle.

The compound angle formula for cosine is given as:

\(\bold{cos(X+Y)=cosXcosY-sinXsinY}\)

Here, let us put X = Y = A

\(cos(A+A)=cosAcosA-sinAsinA\\\Rightarrow \bold{cos(2A)=cos^2A-sin^2A}\)

So, cos2A is equivalent to \(cos^2A -sin^2A\).

Correct answer is:

Option C. \(cos^2A -sin^2A\)

we know that

The surface area of a triangular prism is equal to

SA=2B+PL

where

B is the area of the triangular face

P is the perimeter of the triangular face

L is the length of the prism

step 1

Find the area B

B=(1/2)*y*h

substitute the given values

B=(1/2)*11*4

B=22 units^2

step 2

Find teh value of P

P=X+X+y

substitute the given values

P=7+7+11

P=25 units

step 3

Find the surface area

SA=2*22+25*14

Answer:

We use the rule,

\((a^b)^c = a^{bc}\)

a. (10^7)²

\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)

10^14

b. (10^9)³

\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)

10^27

c. (10^6)³

\(10^{(6)(3)}= 10^{18}\)

10^18

d. (10^2)³

\(10^{(2)(3)} = 10^{6}\)

10^6

e. (10³)²

\(10^{(3)(2)}=10^{6}\)

10^6

f. (10^5)^7

\(10^{(5)(7)} = 10^{35}\)

10^35

Step-by-step explanation:

The standard form of "18 hundreds 11 tens" is 1910.

To write "18 hundreds 11 tens" in standard form, we need to convert the given number into its numerical representation.

We know that 1 hundred is equal to 100, and 1 ten is equal to 10.

So, to find the numerical value of "18 hundreds 11 tens," we multiply the respective values by their place values and then add them together.

18 hundreds = 18 x 100 = 1800

11 tens = 11 x 10 = 110

To find the standard form, we add the two values:

1800 + 110 = 1910

Therefore, "18 hundreds 11 tens" in standard form is 1910.

In standard form, numbers are written using digits, without any reference to place value units like hundreds or tens.

The standard form of a number represents its numerical value directly. So, the numerical value of "18 hundreds 11 tens" is 1910, which is its standard form.

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Answer:

28p + 14q + 21r

Step-by-step explanation:

7(4p + 2q + 3r) ← multiply each term in the parenthesis by the 7 outside

= 28p + 14q + 21r