5% of all widgets are defective. there is a 30% chance that a widget was produced at the foo factory. if a widget was produced at the foo factory, then there is a 4% chance that the widget is defective.

a.) what is the probability that a widget was produced at the foo factory AND is defective?

b.) are "produced at the foo factory" and "defective" independent events? justify.

Answer:

the area is 816

Step-by-step explanation:

Step-by-step

12 + 5 = 17

17 / 2 = 8.5

8.5 * 96 = 816

the area is 816

Work done by a force field in moving an object from a to b is calculated using the line integral of the vector field. For the force field F(x, y) = 2y3/2i + 3xyj and the points a(1, 1) and b(3, 9), we consider a path from a to b, compute the line integral separately for each segment, and sum the results.

In physics and vector calculus, the work done by a force field (like the one in your question) in moving an object from a to b is calculated using the line integral of the vector field along the path taken. For your specific question where the force field is given by F(x, y) = 2y3/2i + 3xyj with the object moving from a(1, 1) to b(3, 9), the work done is computed as follows:

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we know that

the volume of a solid oblique pyramid is equal to

[tex]V=\frac{1}{3}*B*h[/tex]

where

B is the area of the base

h is the height of the pyramid

in this problem we have that

B is a square

[tex]B=b^{2}[/tex]

where

[tex]b=x\ cm[/tex]

so

[tex]B=x^{2}\ cm^{2}[/tex]

[tex]h=(x+2)\ cm[/tex]

substitute in the formula of volume

[tex]V=\frac{1}{3}*x^{2}*(x+2)\\ \\V=\frac{1}{3}*[x^{3} +2x^{2}]\ cm^{3}[/tex]

therefore

the answer is

[tex]V=\frac{1}{3}*[x^{3} +2x^{2}]\ cm^{3}[/tex]

We have been given that an apartment complex offers apartments with four different​ options, designated by a through  d.

From the given directions we have

Therefore, from the fundamental theorem of counting principle number of available apartments are

[tex]4\times 3\times 5\times 2 =120[/tex]

Hence, 120 apartments options are available.

Answer:

its B i think

Step-by-step explanation:

yall needa just say the answer not explain like.smh

Keiko has 1.43 meters of rope left after cutting away 2.57 meters from her 4-meter rope. This is found by subtracting the length of rope she cut away from the initial length of the rope.

The question asks how much rope Keiko has left after cutting away 2.57 meters from a 4 meter rope. To find the answer, we can perform a simple subtraction operation: 4 meters (initial length of rope) - 2.57 meters (length of rope cut away). The result of this calculation should give us the length of rope that Keiko has left.

So, let's perform the calculation:

4 meters - 2.57 meters = 1.43 meters

Therefore, Keiko has 1.43 meters of rope left after cutting away 2.57 meters from her 4 meter rope.

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Final answer:

To find the area of a cake given its circumference, calculate the radius and plug it into the area formula A = πr². Finally, round to the nearest hundredth to get the area value.

Explanation:

To find the area of a circle, you use the formula A = πr², where r is the radius of the circle. Given the circumference of the cake is 25 1/7 inches, we can calculate the radius as r = Circumference / (2π) = 25 1/7 / (2 x 22/7) = 25 1/7 / (44/7) = 25 1/7 / 6.2857 ≈ 3.99 inches.

Now, substitute the radius into the area formula: A = 3.14 x (3.99)² ≈ 50.03 square inches. Therefore, the area of the cake is approximately 50.03 square inches.

Answer:

See attached diagram

Step-by-step explanation:

Let x be the number of times the app is opened and y be your monthly income (in dollars).

If an advertiser pays you  $0.005 each time the app is opened, then he pays you $0.005x for all times the app is opened. Since an advertiser pays you $20 per month, then the total income is

y=20+0.005x.

Plot this line on the coordinate plane (see attached diagram).

Answer:

C

Step-by-step explanation:

Gross income(81,031) - adjustments(9,678) - exemptions(3,650•4 = 14,600) - STANDARD deduction(8,350)

$81,031 - $2,914 - $1,939 - $4,825 - $14,600 - $8350 = $48,403

itemized deductions = $6,560 which is less than the Standard deduction of $8,350, so you would use the Standard deduction

The total taxable income is b. $41,843..

To find Bianca and Dave's taxable income, we'll follow these steps:

Calculate the Total Exemptions:
They have 4 exemptions worth $3,650 each.
Total exemptions = 4 × $3,650 = $14,600.

Calculate Adjustments and Deductions:  

Total adjustments and deductions = $2,914 + $1,939 + $4,140 + $4,825 + $2,420 = $16,228.

Determine the Standard Deduction:
For married filing jointly, the standard deduction is $8,350.

Calculate Adjusted Gross Income (AGI):
AGI = Combined Gross Income - Adjustments
AGI = $81,031 - (Business Expenses + Business Losses + Retirement Contributions)
AGI = $81,031 - ($2,914 + $1,939 + $4,825) = $81,031 - $9,678 = $71,353.

Calculate Total Deductions:
In this case, we will take the higher of the total adjustments/deductions calculated or the standard deduction.
Total official deductions = max(Total adjustments and deductions, Standard Deduction)
Total deductions = max($16,228, $8,350) = $16,228.

Calculate Taxable Income:
Taxable Income = AGI - Total Deductions - Total Exemptions
Taxable Income = $71,353 - $16,228 - $14,600
Taxable Income = $71,353 - $30,828 = $40,525.

Where the above pictogram is given, note that the number of children who read fewer books than Carlos are two in number. Namely:

To derive the number of children who read fewer books than Carlos, we only need to count the number of people whose books are less than four.

Using the picture graph key, we know that:

Ryan read 4 books

Gwen = 2

Anna = 6

Henry = 3

Since 2 and 3 are less than 4 which was read by Carlos, then the number of children who read fewer books than Carlos are two in number.

Full Question:

Although part of your question is missing, you might be referring to this full question:

Read Picture Graphs

Use the picture graph above. Write or draw to explain.

4. Carlos read 4 books. How many children read fewer books than Carlos?

_  children ?

The solutions for the triangle are:   ∠A = 51.833...° , ∠B = 70.880...° and ∠C = 57.286...°

Explanation

For finding the unknown angles, we need to use Cosine rule. The formulas are...

[tex]cos A = \frac{b^2+c^2-a^2}{2bc} \\ \\ cos B= \frac{a^2+c^2-b^2}{2ac}\\ \\ cos C= \frac{a^2+b^2-c^2}{2ab}[/tex]

Given that the length of three sides of the triangle as : [tex]a= 11.4, b= 13.7[/tex] and [tex]c=12.2[/tex]

Thus,

[tex]cosA= \frac{(13.7)^2+(12.2)^2 -(11.4)^2}{2(13.7)(12.2)} \\ \\ cosA= \frac{206.57}{334.28} \\ \\ cosA= 0.61795... \\ \\ A= cos^-^1 (0.61795...)= 51.833... degree\\ \\ \\ \\  cos B= \frac{(11.4)^2+(12.2)^2 -(13.7)^2}{2(11.4)(12.2)}\\ \\ cos B= \frac{91.11}{278.16} \\ \\ cos B= 0.3275...\\ \\ B= cos^-^1 (0.3275...)= 70.880... degree \\ \\ \\ \\ cos C= \frac{(11.4)^2+(13.7)^2 -(12.2)^2}{2(11.4)(13.7)}\\ \\ cos C= \frac{168.81}{312.36} \\ \\ cos C= 0.54043...\\ \\ C= cos^-^1 (0.54043...)= 57.286... degree[/tex]

Answer

To simplify the answer above this one, it is

C) A=51.8 B=70.9 C=57.3

Step-by-step explanation:

I got it right on edge

Osman can calculate the cost to replace the unusually shaped picture window by determining its area and then using the formula C = (Area of the window × $8) + $35 to find the total cost. The final total should be rounded to the nearest cent. However, without the window's dimensions, an exact cost cannot be calculated.

To calculate the cost to replace the unusually shaped picture window in Osman's parents' living room, we must first determine the area of the window to find out how many square feet of glass are needed. Once we have the area, we can multiply by the cost per square foot and add the installation fee. Unfortunately, the question does not provide the necessary dimensions of the window, so we cannot proceed with the exact calculations. However, I will provide a general formula that Osman could use to calculate the replacement cost.

Let's assume that the dimensions of the window are provided and that we have managed to calculate the area, A, in square feet. The cost of the replacement glass will then be A × $8. After calculating this, Osman would need to add the installation fee, which is $35. So the total cost to replace the window, C, would be calculated using the formula:

C = (A × $8) + $35

Once Osman replaces the window, if the total calculated cost is not a whole number, he should round it to the nearest cent.

An axiom in Euclidean geometry states that in space, there are 2 points that lie on the same line.

This is called the two-point postulate. According to Euclidean geometry, in space, there are at least two points, and through these points, there exists exactly one line. This means that there is only one single line that could pass between any two points. This is a mathematical truth. It is known as an axiom because an axiom refers to a principle that is accepted as a truth without the need for proof.