12 A quality control inspector at a plant has found the probability of randomly selecting a defective
battery from a batch of batteries being produced is 0.02. The probability of rain that day has been
projected to be 0.75. If these two events are independent, what is the probability that on that particular
day, it rains, and the inspector chooses a defective battery from the batch being produced?
(1) 0.77
(3) 0.015
(2) 0.5
(4) 0.95

Answer:

Step-by-step explanation:

We are given a figure, consisting of a right triangle with a circle cut out of it.

To Calculate : area of the shaded region below,

First Let's find the Area of the right triangle:

Area(triangle) = 1/2 × Base × Height

= 1/2 × 56 × 56

= 1/2 × 3136

= 3136/2

= 1568 m².

Now, We are diameter of the circle = 20 m

Radius of the circle = 20/2 = 10 m

Acc. to question we have to use 3.14 as an

approximation for pi.

Area (circle) = 3.14 × 10 × 10

Area (circle) = 3.14 × 100

Area (circle) = 314 m²

Area of shaded region = Area of triangle - Area of circle =

= 1568 m² - 314 m²

= 1.254 square meters

Therefore, The approximate area of the shaded region is 1.254 square meters.

Option (a) is the required answer

The number of bacteria present at 5 hours is (b) 148.413

From the question, we were given,

f(t) = eᵗ

Then  f(t) = number of bacterials present at a particular time t.

f(5) = number of bacterial present at 5 hours

So, we have

f(5) = e⁵

f(5) = 148.413

Then this can be written in the whole number as 148  which implies that the second option is correct because using f(t) = eᵗ to describes the growth of a colony of bacteria will provide us with the answer

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If local supermarket offers a pack of 12 sodas for $3.48 on sale, and the local discount warehouse offers the soda in a 36-can case for $11.52, In terms of price per soda, the supermarket pack is the better value.

To determine which is the better value between the supermarket pack of 12 sodas for $3.48 and the discount warehouse 36-can case for $11.52, we need to calculate the price per soda for each option.

For the supermarket pack, the price per soda can be found by dividing the total cost by the number of sodas in the pack:

Price per soda = $3.48 / 12 = $0.29

For the discount warehouse case, the price per soda can be found by dividing the total cost by the number of sodas in the case:

Price per soda = $11.52 / 36 = $0.32

From these calculations, we can see that the price per soda is lower for the supermarket pack at $0.29 compared to $0.32 for the discount warehouse case. Therefore, in terms of price per soda, the supermarket pack is the better value.

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Answer:

x = 4√3

y = 8√3

Step-by-step explanation:

The interior angles of the given right triangle are 30°, 60° and 90°.

Therefore, the triangle is a special 30-60-90 triangle.

In a 30-60-90 triangle, the measures of its sides are in the ratio 1 : √3 : 2.  

Therefore, the formula for the ratio of the sides is b : b√3 : 2b where:

From inspection of the given triangle, the side opposite the 60° angle is 12 units in length. Therefore:

[tex]b\sqrt{3} = 12[/tex]

Solve the equation for b:

[tex]\begin{aligned}b&=\dfrac{12}{\sqrt{3}}\\\\b&=\dfrac{12 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}}\\\\b&=\dfrac{12\sqrt{3}}{3}\\\\b&=4\sqrt{3}\end{aligned}[/tex]

"x" is the side opposite the 30° angle. Therefore:

[tex]\begin{aligned}x& = b\\x& = 4\sqrt{3}\end{aligned}[/tex]

"y" is the side opposite the right angle. Therefore:

[tex]\begin{aligned}y&=2b\\y&=2 \cdot 4\sqrt{3}\\y&=8 \sqrt{3}\end{aligned}[/tex]

Therefore, the values of x and y are:

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The original price of this car is equal to $6,600.

In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

Assuming the original price is represented by the variable x, we have the following:

12.5/100 × x = x - 5,775

0.125x = x - 5,775

5,775 = (x - 0.125x)

5,775 = 0.875x

x = 5,775/0.875

x = $6,600.

In conclusion, we can logically deduce that the percentage Pat Bain paid is 87.5%.

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Company B needs approximately 55 applicants to apply in order to meet their hiring target of 30 new employees, taking into account the percentages of applicants who do not meet the requirements or pass the various stages of the hiring process.

Let's start with the total number of applicants needed to meet the hiring target of 30 new employees. We can call this number "x". We'll work backwards from there to find the number of applicants that need to apply in order to get 30 new employees.

We know that 5% of the remaining applicants fail the background investigation, which means that 95% pass. We also know that 23% of the remaining applicants do not show up for the interview, which means that 77% do show up.

Similarly, 12% of the remaining applicants do not pass the pre-screening assessment, which means that 88% do pass. Finally, 10% of all applicants do not meet the basic business requirements for the job, which means that 90% do meet the requirements.

Putting all of this information into the following equation;

0.9x × 0.88 × 0.77 × 0.95 = 30

Simplifying and solving for x, we get;

x = 30 / (0.9 × 0.88 × 0.77 × 0.95)

x ≈ 55.24

Therefore, Company B needs approximately 55 applicants.

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Answer:

35 pages per minute

Step-by-step explanation:

175/5= 35

Check

35 x 5 = 175

175/35= 5

Answer:

C

Step-by-step explanation:

if the mean and median are the same, the graph will be symmetrical

The formula of the nth term of the sequence is f(n) = 8 *0.7r^(n - 1)

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

a=_1=8, r=0.7

Express properly

So, we have

First term, a = 8

Common ratio, r = 0.7

The above definition is of a geometric sequence that has a first term of 8 and a common ratio of 0.7

Using the above as a guide, we have the following:

f(n) = a * r^(n - 1)

substitute the known values in the above equation, so, we have the following representation

f(n) = 8 *0.7r^(n - 1)

Hence, the nth term of the sequence is f(n) = 8 *0.7r^(n - 1)

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The equation that represents the circle is (x + 1)² + (y - 1)² = 16

The equation of a circle with center (h,k) and radius r is:

(x - h)² + (y - k)² = r²

To find the equation of the circle with center (-1,1) and radius 4, we need to shift the center of the circle to (-1,1).

We can do this by replacing x with (x - (-1)) = (x + 1) and y with (y - 1) in the equation of the original circle. This gives:

(x + 1)² + (y - 1)² = 16

This equation represents a circle with center (-1,1) and radius 4.

Therefore, the correct option is (O) (x + 1)² + (y - 1)² = 16.

The other options do not have the correct center or radius to describe the circle.

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As indicated by the question, the company's prices have been declining. As a result, a sharp increase is not anticipated, nor is a significant change in the following 30 days.

a public market where business stock and its derivatives can be traded at a set price on a regulated exchange. This means that there is little chance of a big shift in the stock price during the next 30 days.

Look at the query to comprehend the printing company's pricing pattern. The price of this printing company's shares has decreased, according tothe inquiry. It has fallen steadily over time.

Investors shouldn't anticipate a sudden increase in the price of this company's shares because the question doesn't indicate one. However, 30 days is a relatively small period of time to indicate any movement in the stock's price.

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If she can give out 12 to each of her friends and have 3 left over. or she can give 9 out to each of her friends and have 12 left over, Malaika has 3 friends who can receive candies.

Let's suppose Malaika has "c" candies, and "f" is the number of friends she has.

According to the problem statement, we have two equations:

c = 12f + 3

c = 9f + 12

To solve for "f", we can set the two equations equal to each other:

12f + 3 = 9f + 12

Simplifying the equation, we get:

3f = 9

Dividing both sides by 3, we get:

f = 3

We can verify our solution by plugging "f=3" back into one of the original equations:

c = 12f + 3

c = 12(3) + 3

c = 39

So, Malaika has 39 candies in total. We can also check the other equation to make sure it is true:

c = 9f + 12

c = 9(3) + 12

c = 39

Both equations are true, so our solution of "f=3" is correct.

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Answer:

Step-by-step explanation:

You are looking for the tangent ratio, which is opposite side over adjacent side.  Using the tangent ratio of an angle of 37°.

tan37° = x/89

.75355405 = x/89

.75355405 · 89 = x/89 · 89/1

67.06 = x

rounded to 67.1

Answer:

67.1? that's what I got lol

The area of the triangle that has height of √6 and a base of √24 is calculated as: 6 square units.

The area of a triangle = 1/2 * b * h, where:

h is the height of the triangle, and

b is the base length of the triangle.

Given the following:

Height of triangle = √6

Base length of the triangle = √24

Plug in the values:

Area of triangle = 1/2 * √24 * √6

= (√24 * √6) / 2

= √144 / 2

= 12/2

Area of triangle = 6 square units.

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Answer:

Beth has $752

Step-by-step explanation:

First we lay out what we know:

Beth: 3x+20

Will: x

Dennis: x+20

Next we write the equation:

3x+20+20+x+x=1260

Then we add any numbers that can be added to each other:

5x+40=1260

Then we solve,

We first minus 40 from both sides of the equation,

5x+40=1260

-40 -40

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

5x=. 1220

Last we divide 1220 by 5,

5x=1220

÷5. ÷ 5

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

x=244

Now that we know that x is 244 we fill in the blanks,

Beth: 732+20

Will: 244

Dennis: 244+20

Then we just solve the equations,

Beth: 732+20=752

Will: 244

Dennis: 244+20=264

That's it,

if you want to check your work you can add them all up and if they equal 1260 it's correct.

752+244+264=1260

Your welcome, have a good day/night.

The finance charge for Sandra Lazzaro, using the average daily balance method, is $13.63.

The average daily balance is one of the methods for computing the finance charges (interest and other fees).

The average daily balance method uses the balance owed at the end of each day of the billing period, and not the balance owed at the end of the week, month, or year.

Billing period for the credit card = 31 days

Unpaid credit card balance = $750

Payment made three days before month-end = $600

Finance charge rate per month = 2.2%

Method = Average daily balance

Day        Description    Amount    Average Balance

1 - 28     Balance           $750       $21,000 ($750 x 28 days)

29 - 31   Payment        -$600       $-1,800 ($600 x 3 days)

31           Total                              $19,200

Average daily balance = $619.35 ($19,200 ÷ 31)

Finance charge = $13.63 ($619.35 x 2.2%)

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Answer:

h=5

Step-by-step explanation:

Substituting in 92 for s,
92=4lw+2wh
Substituting in 9 for l,
92=4(9)(w)+2wh

Substituting 2 for w,

92=4(9)(2)+2(2)(h)

Simplifying by multiplying terms

92=72+4h

Subtract 72 on both sides

20=4h

Divide by 4 on both sides

5=h

1. The standard quantity of plastic allowed to make 3,500 helmets is 2,310 kilograms.

2. The standard materials cost allowed to make 3,500 helmets is $16,170.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

1. The standard quantity of kilograms of plastic (SQ) allowed to make 3,500 helmets can be calculated as:

SQ = Standard quantity per unit × Actual output

= 0.66 kg/helmet × 3,500 helmets

= 2,310 kg

Therefore, the standard quantity of plastic allowed to make 3,500 helmets is 2,310 kilograms.

2. The standard materials cost allowed (SQ × SP) to make 3,500 helmets can be calculated as:

Standard materials cost allowed = Standard price × Standard quantity allowed

= $7.00/kg × 2,310 kg

= $16,170

Therefore, the standard materials cost allowed to make 3,500 helmets is $16,170.

3. The materials spending variance can be calculated as the difference between the actual cost incurred and the standard cost allowed:

Materials spending variance = Actual materials cost - Standard materials cost allowed

= $16,401 - $16,170

= $231 (Favorable)

Therefore, the materials spending variance is $231 (Favorable).

4. The materials price variance and the materials quantity variance can be calculated as follows:

Materials price variance = (Actual price - Standard price) × Actual quantity

= ($16,401/2,485 kg - $7.00/kg) × 2,485 kg

= $9,141.77 (Unfavorable)

Materials quantity variance = (Actual quantity - Standard quantity allowed) × Standard price

= (2,485 kg - 2,310 kg) × $7.00/kg

= $1,225 (Unfavorable)

Therefore, the materials price variance is $9,141.77 (Unfavorable) and the materials quantity variance is $1,225 (Unfavorable).

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The margin of error is E = 0.67.

We can use the formula:

E = z* (σ / sqrt(n))

Where

In this case, we are given that C = 0.95, σ = 3.4, and n = 100. We can use a standard normal distribution table to find the z-score that corresponds to a 95% confidence level, which is approximately 1.96.

Substituting the values:

E = 1.96 * (3.4 / sqrt(100))

E = 1.96 * 0.34

E = 0.6664

Rounding to two decimal places, the margin of error is approximately 0.67.

Therefore, the margin of error is E = 0.67.

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1) The amount is php 340,060

2) The rate is 13%

3) The amount is  php 137,622

Compound interest is commonly used in many types of financial products, such as savings accounts, CDs, and loans.

1)

[tex]A = P(1 + r/n)^nt\\A = 80000( 1 + 0.16)^9.75\\A = php 340,060[/tex]

2)

[tex]12300 = 9750(1 + r)^2\\12300/9750 = (1 + r)^21.26 = (1 + r)^2\\ln 1.26 = 2 ln1 + r\\ln 1.26/2 = ln1 + r\\0.12 = ln1 + r\\e^{0.12} = 1 + r\\r = e^{0.12} - 1\\r = 0.13\\r = 13%[/tex]

3)

[tex]A = 50000(1 + 0.15/2)^2 * 7\\A = php 137,622[/tex]

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Using multiplication operation, the amount of pension that Edith will receive after 4 years of service and using the vesting percentage and the pension multiplier is $49,725.

The pension amount is the product of the multiplication of the average salary, the vesting percentage and the pension multiplier factor.

Multiplication operation is one of the four basic mathematical operations, including addition, subtraction, and division.

Edith's average salary = $65,000

The number of years of service = 4 years

Pension Multiplier = 2%

Pension multiplier factor = 1.02 (100% + 2%)

Vesting percentage = 75%

Pension to be received = $49,725 ($65,000 x 75% x 1.02)

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Answer:

4x - 1 > 15

4x > 16

x > 4

The solution set is all numbers greater than 4.

Answer:

x^3-18x^2+108x-216

There is a formula for this simplification, and you can write the answer directly if you remember the formula.

The probability of hitting the shaded region is 0.755 or 75.5%.

To find the probability of hitting the shaded region, we need to find the area of the shaded region and divide it by the area of the entire square.

Let's label the side length of the small square as x.

Then, we know that the diagonal of the small square is 7, so we can use the Pythagorean theorem to solve for x:

x^2 + x^2 = 7^2

2x^2 = 49

x^2 = 24.5

So the area of each white square is x^2 = 24.5 square units.

Let's label the side length of the large square as y.

Then, we know that the diagonal of the large square is 20, so we can use the Pythagorean theorem to solve for y:

y^2 + y^2 = 20^2

2y^2 = 400

y^2 = 200

So the area of the large square is y^2 = 200 square units.

Now, we can find the area of the shaded region by subtracting the area of the two white squares from the area of the large square:

Area of shaded region = Area of large square - 2 * Area of white square

= 200 - 2(24.5)

= 151

Therefore, the probability of hitting the shaded region is:

Probability = Area of shaded region / Area of entire square

Probability = 151 / 200

Probability = 0.755 or 75.5% (rounded to one decimal place)

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Answer: x<4/3

Step-by-step explanation: 17-5=12/9

Answer:

B

Step-by-step explanation:

This is a linear function.

:D

Once again, we get the same answer: Kristin had $32 before receiving the $18 for cleaning the attic. we solve this by forming equation and solving it

what is equation ?

An equation is a mathematical statement that shows that two expressions are equal. It usually consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems in various fields, including mathematics, physics, engineering

In the given question,

Let's use "x" to represent the amount of money Kristin had before receiving the $18 for cleaning the attic. We can set up the following equation:

x + 18 = 50

This equation represents the total amount of money Kristin has now, which is $50, after receiving the $18 for cleaning the attic. To solve for "x", we can subtract 18 from both sides of the equation:

x + 18 - 18 = 50 - 18

x = 32

Therefore, Kristin had $32 before receiving the $18 for cleaning the attic.

Alternatively, we can also use a diagram to represent the situation. We can draw a rectangle to represent the total amount of money Kristin has now, which is $50. We can then divide the rectangle into two parts: one part representing the $18 she received for cleaning the attic, and the other part representing the amount of money she had before. We can label this unknown amount as "x", and set up the following equation:

x + 18 = 50

This equation is the same as the one we set up earlier. To solve for "x", we can again subtract 18 from both sides of the equation:

x + 18 - 18 = 50 - 18

x = 32

Once again, we get the same answer: Kristin had $32 before receiving the $18 for cleaning the attic.

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Answer: 5 and 2

Step-by-step explanation:

In an arithmetic sequence, the difference between consecutive terms is constant. Since the third and fourth terms are -1 and -4, the common difference is -4 - (-1) = -3. Therefore, the second term is -1 - (-3) = 2 and the first term is 2 - (-3) = 5. So the first and second terms of the sequence are 5 and 2 respectively.

Using the properties of a parallelogram, the values of x and y are:

x = 9; y = 22.

Since the opposite sides are parallel and equal to each other in the parallelogram above, therefore, Opposite angles are equal (or congruent) while the consecutive angles are supplementary to each other.

Therefore, we have:

6y = 180 - 48

6y = 132

Divide both sides by 6:

6y/6 = 132/6

y = 22

(5x + 3) + 6y = 180

5x + 3 + 6(22) = 180

5x + 135 = 180

5x = 180 - 135

5x = 45

x = 9

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The probability that ten hats given to ten people will consist of more blue caps than red caps is given as follows:

a. 0.2.

Here, we have to calculate a probability:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The outcomes in which there are more blue than red caps are those in which the number of zeros is greater than the number of ones, hence the number of desired outcomes is of:

2. (simulation number 7 and simulation number 10).

Hence the probability is of:

p = 2/10

p = 0.2.

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