A computer software company has submitted bids on two separate government contracts, A and B. The company estimates that it has a 36 percent chance of winning contract A and a 53 percent chance of winning contract B. The company believes that winning contract A is independent of winning contract B. Answer the following questions, rounding your answers to two decimal places where appropriate.
a) What is the probability that the company will win both contracts?
b)What is the probability that the company will win at least one of the two contracts?

Now suppose that the company believes that, given that it wins contract B, it has a 40 percent chance of winning contract A.
c)What is the probability that the company will win both contracts?
d) What is the probability that the company will win at least one of the two contracts?
e) If the company wins contract B, what is the probability that it will not win contract A?

The length of line having mid point B ⇒  7x - 2.

Given that,

B is the mid point of AC

And also given that

length of segment AB = 2x+5

And length of segment BC = 5x - 7

A straight path established by linking a group of points in a plane is known as a line. It is a one-dimensional form with only a length and no width or height. A line can extend indefinitely in both ends in opposite directions. To indicate a line, we can use upper case characters.

Now since B is the mid point of AC,

So, The line AC is sum of the line segment AB and line segment BC.

Therefore,

AC = AB+BC

     = (2x+5)+(5x - 7)

     = 7x - 2

Hence,

The length of AC is 7x - 2

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Answer:

A

Step-by-step explanation:

because

\(x - 5 = 8 \\ x = 8 + 5 \\ x = 13 \\ x - 5 + 2 = 8 + 2 \\ x - 3 = 10 \\ x = 10 + 3 \\ x = 13\)

Answer:

-10

Step-by-step explanation:

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Answer:

a) \( E = \frac{49.2-17.6}{2}= 15.8\)

b) For this case we have 95% of confidence that the true mean would be between \(\pm 15.8\) units respect the true mean.

c) \(n=(\frac{2.58(45)}{11})^2 =111.39 \approx 112\)

So the answer for this case would be n=112

d) \(36.5-2.58\frac{45}{\sqrt{112}}=25.53\)    

\(36.5+2.58\frac{45}{\sqrt{112}}=47.47\)

Step-by-step explanation:

Part a

For this case we know that the cinfidence interval for the true mean is given by:

\( \bar X \pm E\)

Where E represent the margin of error. For this case we have the confidence interval at 95% of confidence and we can estimate the margin of error like this:

\( E = \frac{49.2-17.6}{2}= 15.8\)

Part b

For this case we have 95% of confidence that the true mean would be between \(\pm 15.8\) units respect the true mean.

Part c

The margin of error is given by this formula:

\( ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\)    (a)

And on this case we have that ME =11 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

\(n=(\frac{z_{\alpha/2} \sigma}{ME})^2\)   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. The critical value would be \(z_{\alpha/2}=2.58\), replacing into formula (b) we got:

\(n=(\frac{2.58(45)}{11})^2 =111.39 \approx 112\)

So the answer for this case would be n=112

Part d

The confidence interval for the mean is given by the following formula:

\(\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\)   (1)

Replcaing the info given we got:

\(36.5-2.58\frac{45}{\sqrt{112}}=25.53\)    

\(36.5+2.58\frac{45}{\sqrt{112}}=47.47\)

Expression for given numerical is: 9+ (2/x)

Given that we have an word equation that is 9 more than the quotient of 2 and  x

A quotient is a quantity produced by the division of two numbers.

Quotient of 2 and x is \(\frac{2}{x}\).

Nine(9) more  than 2/x is = 9+ (2/x)

So we have an expression that is:

              9+ (2/x)                          

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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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. ...................

Answer:

see the attachment photo!

we are given the following expression:

We can use the following property of exponents:

That is, we leave the same base and add the exponents, like this:

Answer:

59°

Step-by-step explanation:

A triangle adds up to 180°. A right triangle has a 90° angle.

1. Set up the equation

90 + 31 + x = 180

2. Simplify

121 + x = 180

3. Solve for x by subtracting 121 from both sides

x = 59

Answer:

Quadrant V

Step-by-step explanation:

A co-ordinate graph only has 4 quadrants!

Answer:

x = 49

Step-by-step explanation:

The sum of angles is 360

(x + 84) + 80 + 3x = 360

x + 3x = 360 - 84 - 80

4x = 196

x = 196/4 = 49

To find the distance between the man's starting point and his final position, we can use vector addition.

Let's call the man's starting point A and his final position B. We can represent the two legs of his journey as vectors A and B, respectively.

The first leg of his journey, due west, can be represented as a vector of magnitude 4 km in the -x direction.

The second leg of his journey, on a bearing of 197°, can be represented as a vector in the -x and -y direction. We can use trigonometry to find the components of this vector.

The x component of the vector can be found using the formula:

x = magnitude * cos(angle) = d * cos(197°)

The y component of the vector can be found using the formula:

y = magnitude * sin(angle) = d * sin(197°)

where d is the magnitude of the vector (the distance the man traveled in this leg of his journey).

To find the magnitude of the vector, we'll use the Pythagorean theorem:

d^2 = x^2 + y^2

We can substitute the x and y components we found above into this equation to find d:

d^2 = (d * cos(197°))^2 + (d * sin(197°))^2

d^2 = d^2 * (cos^2(197°) + sin^2(197°))

d^2 = d^2

d = sqrt(d^2) = sqrt(d^2)

So the magnitude of the vector is d.

Next, we can add the two vectors to find the total distance from the man's starting point to his final position:

distance = sqrt((4 - d * cos(197°))^2 + (d * sin(197°))^2)

This is the distance the man is from his starting point. To find the exact value, we would need to know the value of d. However, without that information, this is as far as we can take the calculation.

Answer:

1 km

Step-by-step explanation:

4 × 1/4 km = 4/1 × 4/1 km = 4/4 km = 1 km

Answer: 1 km

Step-by-step explanation:

that would be 1/4×4=1

so that means he ran lkm long

Answer:

the answer is B

Step-by-step explanation:

88*4=352

meaning the ball traveled 352 feet in 4 seconds

The dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is 75 square meters

What is measurement?

Measurement is the process of assigning numerical values to physical quantities, such as length, mass, time, temperature, and volume, in order to describe and quantify the properties of objects and phenomena.

Let's assume that the rock wall is the width of the garden and the wire fencing is used for the length and the other two sides. Let's denote the length of the garden as L and the width as W.

Since we have 30 meters of fencing available, the total length of wire fencing used is:

L + 2W = 30 - W

Simplifying this equation, we get:

L = 30 - 3W

The area of the garden is:

A = LW

Substituting the expression for L from the previous equation, we get:

A = W(30 - 3W)

Expanding the expression, we get:

A = 30W - 3W²

To find the maximum area, we need to take the derivative of A with respect to W and set it equal to zero:

dA/dW = 30 - 6W = 0

Solving for W, we get:

W = 5

Substituting this value back into the expression for L, we get:

L = 15

Therefore, the dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is:

A = 5(15) = 75 square meters

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The estimated raw material Inventory balance at the end of July is $27,750.

The estimated raw material inventory balance at the end of July, we need to follow the given information and calculations:

a. Each unit of finished goods requires 5 pounds of raw materials. Therefore, the total raw materials needed for production in August can be calculated as follows:

23,000 units (budgeted unit sales for September) × 5 pounds/unit = 115,000 pounds

b. The ending raw materials inventory equals 10% of the following month's raw materials production. Based on the information provided, the estimated raw materials needed to meet production in August is 111,000 pounds.

111,000 pounds × 0.10 (10%) = 11,100 pounds

This means that the ending raw materials inventory for July should be 11,100 pounds.

c. The cost of raw materials is $2.50 per pound. To find the value of the raw material inventory at the end of July, we multiply the pounds by the cost per pound:

11,100 pounds × $2.50/pound = $27,750

Therefore, the estimated raw material inventory balance at the end of July is $27,750.

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Answer:

B

Step-by-step explanation:

The correct option is B.

The newspaper staff surveys random students from every grade in the school.

In cluster sampling, researchers divide a population into smaller groups known as clusters. They then randomly select among these clusters to form a sample. Cluster sampling is a method of probability sampling that is often used to study large populations, particularly those that are widely geographically dispersed.

An example of single-stage cluster sampling – An NGO wants to create a sample of girls across five neighboring towns to provide education. Using single-stage sampling, the NGO randomly selects towns (clusters) to form a sample and extend help to the girls deprived of education in those towns.

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The number of degrees does it move in 2 1/5 hours is -66°.

From the information given, it was illustrated that the hour hand of a clock moves −30° every hour.

Therefore, to calculate the degree for a number of hours, we simply have to multiply.

In this case, to get the degree for 2 1/5 hours will be:

= Degree every hour × Number of hours

= -30° × 2 1/5

= -30° × 2.2

= -66°

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Answer:

[a] y=x^2+3,  vertex, V(0,3)

[b] y=2x^2, vertex, V(0,0)

[c] y=-x^2 +  4, vertex, V(0,4)

[d] y= (1/2)x^2 - 5, vertex, V(0,-5)

Step-by-step explanation:

The vertex, V, of a quadratic can be found as follows:

1. find the x-coordinate, x0,  by completing the square

2. find the y-coordinate, y0, by substituting the x-value of the vertex.

[a] y=x^2+3,  vertex, V(0,3)

y=(x-0)^2 + 3

x0=0, y0=0^2+3=3

vertex, V(0,3)

[b] y=2x^2, vertex, V(0,0)

y=2(x-0)^2+0

x0 = 0, y0=0^2 + 0 = 0

vertex, V(0,0)

[c] y=-x^2 +  4, vertex, V(0,4)

y=-(x^2-0)^2 + 4

x0 = 0, y0 = 0^2 + 4 = 4

vertex, V(0,4)

y = (1/2)(x-0)^2 -5

x0 = 0, y0=(1/2)0^2 -5 = -5

vertex, V(0,-5)

Conclusion:

When the linear term (term in x) is absent, the vertex is at (0,k)

where k is the constant term.

f(x) is not defined where the term of the denominator is zero.

This happens when x = 4, x = -5 or x = -1

The x-intercepts is the points where f(x) = 0

this happens when x = -7 and x = 3

Notice that x = -1 can't be a x-intercept because the function is not defined at this point.

You would pay Ghana cedi 270.00 for the phone during the sale.

To calculate this:

40% of Ghana cedi 450.00 is 0.40 x 450 = Ghana cedi 180.00

Subtracting this discount from the original price gives:

Ghana cedi 450.00 - Ghana cedi 180.00 = Ghana cedi 270.00

Answer: $10.41

Step-by-step explanation: 1405/135 = 10.407, so rounded is $10.41 since you round to the nearest hundredth when dealing with money.

Hope this helps!

Mark Brainliest if you want!

Answer:

l10.4074074074

The value of f(-0.01) is approximately 0.99005.

To evaluate f(-0.01), we substitute -0.01 into the function f(x) = (1+x)^(1/x). Thus, we have f(-0.01) = (1+(-0.01))^(1/(-0.01)).

Using a calculator, we simplify this expression to f(-0.01) = 0.99005. Therefore, the value of f(-0.01) rounded to five decimal places is approximately 0.99005.

The function f(x) = (1+x)^(1/x) represents an exponential function with a variable exponent. In this case, we are evaluating the function at x = -0.01.

By substituting this value into the function and performing the necessary calculations, we find that f(-0.01) is approximately 0.99005. This means that when x is equal to -0.01, the function value is approximately 0.99005.

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By making x the subject of the formula in this equation u = cos(0.5x)​ gives x = 2cos⁻¹(u).

In Mathematics and Geometry, an equation can be defined as a mathematical expression which shows that two (2) or more thing are equal. This ultimately implies that, an equation is composed of two (2) expressions that are connected by an equal sign.

In this exercise, you are required to make "x" the subject of the formula in the given mathematical equation by using the following steps.

By taking the arc cosine of both sides of the equation, we have the following:

u = cos(0.5x)

cos⁻¹(u) = 0.5x

By multiplying both sides of the mathematical equation by 2, we have the following:

2 × cos⁻¹(u) = 0.5x × 2

x = 2cos⁻¹(u)

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Answer:

Circle Pentagon Triangle Rectangle

Answer:

3420-3340=80

Step-by-step explanation:

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1 liter of water equals 1000 milliliters.

To find who has more water, you need to convert (the unit) of each person to either liters or milliliters.

Since it asks for millimeters, I'm going to convert Tutu's 7/10 liters to milliliters. Since there are 1000 milliliters in every liter, you have to multiply 7/10 by 1000. 7/10 multiplied by 1000 is 700.

So Pete has 500 milliliters of water and Tutu has 700 milliliters of water.

Now you need to find the difference of 700 and 500 by subtracting.

700-500=200

Tutu bought 200 more milliliters of water than Pete.

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