If C(x) = 4x2 - 3, find the following. (a) C(0) (b) c(-1) (c) C(-4) (d) o (-3) Let f(x) = 3 + x + x2 and h = 0. (a) Does f(8 + 1) = f(8) + f(1)? O Yes No (b) Find f(x + n). (c) Does f(x + n) = f(x) + f(h)? Yes No (d) Does f(x + n) = f(x) + h? O Yes No (e) Find f(x + h) - f(x) and simplify.

The coordinates of the point P on directed line segment that partitions AB in the ratio 1:2 is (4, 0)

Given the point A (-2, 4) and B(7, -2). The coordinate of the point P on the line segment that partitions AB in the ratio 1:2, is expressed as:

\(P(X, Y) = (\frac{ax_1+bx_2}{a+b}, \frac{ay_1+by_2}{a+b})\)

Substitute the given coordinates where a = 1 and b = 2

\(P(X, Y) = (\frac{1(-2)+2(7)}{1+3}, \frac{1(4)+2(-2)}{1+2})\\P(X, Y) = (\frac{-2+14}{3}, \frac{4-4}{1+2})\\P(X, Y) = (\frac{12}{3},\frac{0}{3})\\P(X, Y) = (4, 0)\\\)

Hence the coordinate of point P is (4, 0)

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Answer:

Step-by-step explanation:

A. 4^5*4^5 = 4^(5+5) = 4^10 ≠ 4^15

B.  (5^4)^5 = 5^(4*5) = 5^20

C. 3^1*3^0 = 3^(1+0) = 3^1 ≠ 3^0

D. 6^20/6^10 = 6^(20 - 10) = 6^10 ≠ 6^2

7x5 -7 x 2 =21

5x-2x =21

Combine like terms

3x=21

Divide both sides by 3

x=21/3

x=7

The amount of water that will serve the entire container exists 3/10 gallons.

An expression exists a sentence with a minimum of two numbers or

variables and at least one math function.

Given: 1 over 5 gallons of water serve 2 over 3 of the container.

(1/5) gallon / (2/3) container = x gallons / 1 container

cross-multiplying the above equation, we get

1/5 = (2/3)x

multiply both sides by the reciprocal of 2/3 = 3/2

(3/2) (1/5) = x = 3/10 gallons serve the total container

Each 1/10 of a gallon serve 1/3 of the container

So 3(1/10) gallons serve 3(1/3)bins

3/10 gallons serve a whole container.

The amount of water that will serve the entire bin container exists 3/10 gallons.

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The probability of choosing a defective product from a factory with a 30% defect rate is equal to 0.3 or 30%.

Determining the percentage of defective goods among all the things produced is necessary to assess the likelihood that a randomly chosen item from a factory with a 30% defective rate will be defective.

We can utilize the idea of probability to calculate the percentage of defective goods if we suppose that the factory produces a huge number of items. In this instance, the ratio of the number of defective products to the total number of produced items determines the likelihood of choosing a defective item.

Therefore, We can anticipate 30 faulty items out of 100 produced by the factory. As a result, the chance of choosing a flawed item is 30/100, which can be expressed as 0.3 or 30%.

In general, The probability of choosing a defective product from a factory with a 30% defect rate is equal to 0.3 or 30%.

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The number of seats in each row of the hall is 40

Given that there are 3200 seats overall and that there are twice as many rows as there are seats in each row.

The total capacity of the hall=3200

Number of rows= 2 ( number of seats in each row)

Let's assume the number of seats in each row=x

⇒Number of rows=2x

The total capacity of the hall = (number of rows)( number of seats in each row)

The total capacity of the hall=3200

3200 = (2x) × (x)

[number of rows=2x, number of seats in each row=x]

3200 = 2\(x^{2}\)

1600=\(x^{2}\)

x=40

There are 80 rows with 40 seats in each row.

Hence, the Number of seats in each row=40 and the Number of rows=80

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Answer:

C)

Step-by-step explanation:

Answer:

0.017741

Step-by-step explanation:

Answer:

A =d

B=e

C=f.

.

. Hbivubhxhkivyvu

As per the details given, there are 37 dots in the 5th step.

To locate the pattern and decide the range of dots in the 5th step, allow's examine the given records:

Step 1: 6 dots

Step 2: 14 dots

Step 3: 21 dots

Looking on the variations between consecutive steps, we will see that the quantity of additional dots in each step is growing via eight.

In other phrases, the distinction among Step 1 and Step 2 is eight, and the difference between Step 2 and Step 3 is likewise eight.

Thus, we can preserve this sample to decide the quantity of dots within the 4th and 5th steps:

Step 4: 21 + 8 = 29 dots

Step 5: 29 + 8 = 37 dots

Therefore, there are 37 dots in the 5th step.

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Answer:

Step-by-step explanation:

The easiest way is to use the distributive rule. 15¾ = 15+ ¾

15¾*8 = (15+¾)8 = 15*8 + ¾*8 = 120+6 = 126

The algebraic expression that represents the phrase "fourteen increased by a number" is 14 + y. which is the correct answer that would be an option (A).

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The given statement is "fourteen increased by a number"

According to the given question, translate the phrase into an algebraic expression:

⇒ 14 + y

This is because the phrase "increased by" means to add a certain number to 14.

The variable y represents the number that is being added to 14.

Thus, the algebraic expression that represents the phrase "fourteen increased by a number" is 14 + y.

Hence, the correct answer would be option (A).

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An algebraic expression which models the given context would be written as s + 0.02s = 1.05s.

Price can be define as an amount of money which is primarily set by the seller of a good (product), and it must be paid by a buyer to the seller, so as to enable the acquisition of this good (product).

An algebraic expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

Let s represent the price of a pair of shoes.

Therefore, an algebraic expression which models the given context would be written as follows:

s + 0.02s = 1.05s.

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Answer:

one proportion is 15 miles over 2.5 hours -  yesterday is M miles over 4 hours (?)

Step-by-step explanation:

Answer:

1. 1/2 or 18/36

2. 14/19

3. 3/1

4. 5/23

5. 14/52 or 7/26

Step-by-step explanation:

i think i did these right

Answer:

Step-by-step explanation:

Just divide them, put em over each other to make fractions lel

18/36

14/19

3/5

5/23

May I please have a Brainliest? I put a lot of thought and effort into my answers, so I would really appreciate it!

A rectangle with area of 12 square units would have sides of length 4 units and 3 units. Area would therefore be 4 x 5.

A rectangle must be such that one side is longer than the other side.

The area of a rectangle is found as:

= Length x Width

As the area is 12, the length and width have to be numbers that when multiplied, will give you 12.

The factors of 12 which allow this to happen are:

= 1, 2, 3, 4, 6, 12

From here you can use 3 and 4.

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Answer:

Step-by-step explanation:

Area of a circle = πr²

where

r is the radius

From the question

r = 14 m

π = 3.14

The area of the circle is

A = 3.14 × ( 14 ) ²

= 3.14 × 196

= 615.44

We have the final answer as

Hope this helps you

Answer:

forty four thousand thirty eight

Step-by-step explanation:

Answer:

forty four thousand thirty eight

Step-by-step explanation:

combine the words for the number place + digits.

hope this helps!

Answer:

\(y=\displaystyle\frac{1}{2} x-3\)

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: \(y=mx+b\) where m is the slope and b is the y-intercept (the value of y when x=0)

1) Determine the slope (m)

\(m=\displaystyle\frac{y_2-y_1}{x_2-x_1}\) where two points on the line are \((x_1,y_1)\) and \((x_2,y_2)\)

Plug in the given points (4,-1) and (0,3)

\(m=\displaystyle\frac{-1-(-3)}{4-0}\\\\m=\displaystyle\frac{2}{4}\\\\m=\displaystyle\frac{1}{2}\)

Therefore, the slope of the line is \(\displaystyle\frac{1}{2}\). Plug this into  \(y=mx+b\) :

\(y=\displaystyle\frac{1}{2} x+b\)

2) Determine the y-intercept (b)

\(y=\displaystyle\frac{1}{2} x+b\)

The y-intercept occurs when x=0. Because we're given that (0,-3), the y-intercept is therefore -3.

\(y=\displaystyle\frac{1}{2} x-3\)

I hope this helps!

Answer:

A. f(-3) = 2 is true, based on the table.

B. f(0) = 10 is false, since f(0) = 3 based on the table.

C. The domain for f(x) is the set (-5, -3, 0, 2, 6, 7, 9, 10, 13) is true, since these are all the values of x for which f(x) is defined.

D. The range for f(x) is all real numbers is false, since the values of f(x) are only 0, 1, 2, and 3.

Step-by-step explanation:

The injury probability p that makes the decision maker indifferent between entering now and waiting until next year is approximately 0.26.

To calculate this probability, we need to set the expected values of entering now and waiting until next year equal to each other and solve for p. Let EMV₁ be the expected value of entering now and EMV₂ be the expected value of waiting until next year. Then we have:

EMV₁ = -1000p + 5000(1-p)

EMV₂ = 0.9(-1000p) + 0.1(5000)

Setting EMV₁ equal to EMV₂, we get:

-1000p + 5000(1-p) = 0.9(-1000p) + 0.1(5000)

Solving for p, we get:

p ≈ 0.26

Therefore, if the probability of injury is greater than 0.26, the decision maker should wait until next year to enter the market, and if the probability of injury is less than 0.26, the decision maker should enter the market now.

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The given vectors are:
Vector A = (-11, b, 2)
Vector B = (b, b^2, b)

The values of b for which the given vectors are orthogonal are 0, -3, and 3.

To find the values of b for which the given vectors are orthogonal, we need to use the dot product of the vectors.

To determine if two vectors are orthogonal, their dot product should be equal to zero.

The dot product is calculated as follows:

Dot Product (A, B) = A1 * B1 + A2 * B2 + A3 * B3

Substituting the components of Vector A and Vector B:

(-11 * b) + (b * b^2) + (2 * b) = 0

Now, simplify the equation:

-11b + b^3 + 2b = 0
b^3 - 9b = 0

Factor the equation:

b(b^2 - 9) = 0

Now, we can find the values of b:

b = 0
b^2 - 9 = 0
b^2 = 9
b = ±3

So, the values of b for which the given vectors are orthogonal are 0, -3, and 3.

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The UCL (Upper Control Limit) using sigma = 3 for this process would be 30. The UCL utilizing sigma=3 for this process would be 28.036.

In statistical process control, the upper control limit (UCL) is utilized as a device to identify when to stop a process due to a high variation.

A process that exceeds its UCL will result in defective or inconsistent items, which should be avoided.

Marble Inc. produces high-end countertops from a variety of materials. The company employs the process of randomly selecting one countertop to count the number of blemishes as a means of monitoring the quality of its production processes.

The formula for calculating UCL is as follows: UCL = average of blemishes + 3 × standard deviation For ten samples with a different number of blemishes in each sample, the UCL is determined.

Using the given formula for UCL using sigma= 3: UCL = (2+3+4+5+6+7+8+9+10+17)/10 + 3 × √[(2-9.1)² + (3-9.1)² + (4-9.1)² + (5-9.1)² + (6-9.1)² + (7-9.1)² + (8-9.1)² + (9-9.1)² + (10-9.1)² + (17-9.1)²]/10UCL = 28.036

From the above calculations, the UCL utilizing sigma=3 for this process would be 28.036.

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(1) Recall the angle sum identity for cosine:

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

So

cos(π/3) cos(5π/6) - sin(π/3) sin(5π/6) = cos(π/3 + 5π/6)

= cos(7π/6)

= -√(3)/2

(2) Recall the half-angle identity:

cos²(x) = (1 + cos(2x))/2

Since π/2 < 7π/12 < π, you should expect cos(7π/12) < 0. So solving for cos(x) above, we have

cos(x) = -√[(1 + cos(2x))/2]

Then

cos(7π/12) = -√[(1 + cos(7π/6))/2]

= -√[(1 - √(3)/2)/2]

= -√[1/2 - √(3)/4]

You could stop there, or continue and try to de-nest the radicals to end up with

= (√(2) - √(6))/4

(3) Recall the angle sum formula for tangent:

tan(x - y) = (tan(x) - tan(y))/(1 + tan(x) tan(y))

Then

(tan(122°) - tan(32°))/(1 + tan(122°) tan(32°)) = tan(122° - 32°)

= tan(90°)

which is undefined, since tan(x) = sin(x)/cos(x), and cos(90°) = 0.

(4) Recall the double angle identity for sine:

sin(2x) = 2 sin(x) cos(x)

Then

2 sin(15°) cos(15°) = sin(30°)

= 1/2

(5) Use the double angle identity for cosine:

cos(2x) = 2 cos²(x) - 1

Then

12 cos²(θ) - 6 = 6 (2 cos²(θ) - 1)

= 6 cos(2θ)

(6) Use the sine double angle identity mentioned in (4):

7 cos(4x) sin(4x) = 7/2 (2 cos(4x) sin(4x))

= 7/2 sin(8x)

Consult the other question you commented on [19739123 in the URL] for details on (7) and (8).

The following are the answer to each statement;

1. The book is $18

2. Giselle can earn up to $18 pulling weeds for her grandma.

3. Giselle's grandma pays her $1 for every 5 weeds she pulls

4. Giselle does not have to use any of her own money towards the purchase of the book when she pulls 90 weeds.

5. Giselle only needs to pull 18 weeds to not use any of her own money

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The inequality that describes the problem is x < 180 × 4, which means that the total amount of money Mr. Dawson wants to spend on groceries in April should be less than $180 multiplied by 4, or $720.

Mr. Dawson is making a grocery budget for the month of April. He plans to split the budget equally among 4 shopping trips and wants to stay under budget. To figure out the maximum amount of money he should spend on groceries in April, he needs to calculate the total amount of money he should spend for all 4 shopping trips. To do this, he multiplies the maximum amount of money he should spend per trip, $180, by the number of trips, 4. This gives us $180 × 4 = $720. Therefore, Mr. Dawson should spend less than $720 on groceries in April. The inequality that describes the problem is x < 180 × 4, which means that the total amount of money Mr. Dawson wants to spend on groceries in April should be less than $720. This inequality ensures that Mr. Dawson will stay under budget and be able to complete his 4 shopping trips for the month of April.

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=====================================================

Explanation:

Problem 1

Add up the given probabilities in the bottom row:

0.12+0.32+0.25+0.13 = 0.82

For any probability distribution, all of the probabilities must add to 1. This represents 100%. If x is the probability of getting 0 accidents, then x+0.82 = 1 solves to x = 0.18

Having 0.18 in that blank spot will add to the other probabilities to get a total sum of 1.

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

Problem 2

Add up every probability that corresponds to "2 accidents" or more.

0.32+0.25+0.13 = 0.70

There's a 70% chance of having 2 or more accidents.

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

Problem 3

Add in a third row that multiplies the first two rows. If x = number of accidents, and P(x) = probability, then we'll have an x*P(x) row. Check out the table in the attached image.

After determining that third row, add up those products.

0 + 0.12 + 0.64 + 0.75 + 0.52  = 2.03

For any given day, we expect there should about 2.03 accidents on average.

This lines up with the table showing that P(x) is largest when x = 2; ie 0.32 is the largest probability in the table corresponding to having 2 accidents.

For more information, check out "expected value".