1.What is a number that is a multiple of two or more numbers​

The average rate of change for the function f(x) = −3x4 + 2x3 − 5x2 + x + 5, from x = −1 to x = 1 is 3.

Option A is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = −3\(x^4\) + 2x³ - 5x² + x + 5, from x = −1 to x = 1.

f(-1) = 3 x 1 + 2 x -1 - 5 x 1  - 1 + 5

f(-1) = 3 - 2 - 5 - 1 + 5

f(-1) = 3 - 3

f(-1) = 0

f(1) = 3 x 1 + 2 x 1 - 5 x 1 + 1 + 5

f(1) = 3 + 2 - 5 + 1 + 5

f(1) = 6

Now,

The average rate of change.

= ( f(1) - f(-1) ) / (1 - (-1) )

= (6 - 0) / (1 + 1)

= 6 / 2

= 3

Thus,

The average rate of change for the function is 3.

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Step-by-step explanation:

x is 10

FO is x+10

OG is 10+10

FG is x+3x

Answer:

67 ÷ 9 = 7.444

Step-by-step explanation:

its too blurry I can't see the numbers

The degrees of freedom in the denominator of the f-statistic calculation is 2.

The number of distinct bits of information required to construct a statistic is called the degrees of freedom, which is frequently denoted by the letters v or df.

For the stated question-

degrees of freedom df = n - 1

n = 3 groups

df = 3 - 1

df = 2

Thus, the degrees of freedom in the denominator of the f-statistic calculation is 2.

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Answer:

13 dollars.

Step-by-step explanation:

Before selling, the store bought the sweaters for 9$ each.

117 divided by 13 = 9

After selling, the store sold the sweaters for 22$ each.

286 divided by 13 = 22

22 - 9= 13

Answer:

9 : 2 : 4

Step-by-step explanation:

Given

72 : 16 : 32 ( divide each part of the ratio by 8, the LCM of 72, 16, 32 )

= 9 : 2 : 4

Answer:

Given - Radius of ring is 9 millimeters

To find - Circumference

Solution -

9 millimeters = 0.9 centimeters

Circumference of circle = 2 × pie × r

= 2 × 3.14 × 0.9

= 6.28 × 0.9

= 5.652

Answer:y =-3x/4+2

Step-by-step explanation:

Slope= -3/4

The line is passing through (0,2).

y-2=(x-0)*-3/4

or

y =-3x/4+2

The value of x in the remote angles of the triangle  is 22.

The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.  

In other words the sum of the remote interior angle is equals to the external angle.

Therefore,

110 = 3x + 2x

110 = 5x

divide both sides by 5

110 / 5 = 5x / 5

x = 22

Therefore, using exterior angle theorem, the value of x is 22.

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The actual solution must be approximated to the tenth place.

How do you solve an equation to the nearest tenth?

To round the decimal number to its nearest tenth, look at the hundredth number. If that number is greater than 5, add 1 to the tenth value. If it is less than 5, leave the tenth place value as it is, and remove all the numbers present after the tenth place.

To estimate the tenth place, you have to determine the actual solution and the approximate.

Assume the solution to the system of equations is:

(x, y), (1.25, 1)

1.25 is to the hundredth place.

So, the next thing is to approximate 1.25 to 1.3 (the tenth place).

So, we have:

(x, y), (1.3, 1)

Hence, the actual solution must be approximated to the tenth place.

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Answer: x + 1/4 = 1

Step-by-step explanation: the sum of something is to add and if you are adding 1/4 to x they need to be on the same side and “is” is a good indicator of where or when the equal sign needs to go.

Answer:

x + 1/4 = 1

x = 3/4

Step-by-step explanation:

If the directions are to write an equation, then you get:

x + 1/4 = 1

"Sum" means adding.

If you are also asked to solve, then subtract 1/4 from both sides of the equation.

x + 1/4 = 1

x = 1 - 1/4

x = 3/4

It takes 210 minutes at the end of Sunday to achieve the goal.

Given that you want an average of at least 30 active minutes each day during the week, to determine how many active minutes do you need on a Sunday to achieve your goal, the following calculation must be performed:

Therefore, it takes 210 minutes at the end of Sunday to achieve the goal.

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Answer:

there is no slope. y = 4, the line is horizontal

Answer:

615,000

Step-by-step explanation:

Given that:

Whole number rounded to the nearest ten thousand is 620,000

Let x = the whole number

HTh__ TTh ____ Th ____ H ____ T ____ U

6_____ 2 ______ 0 ____ 0 ____ 0 ____ 0

The ten thousand digit is 0 ;

To round to the nearest 10 thousand, the thousand digit is rounded up to 1 and added to the ten thousand digit if it up to 5 or above and rounded down to 0 if below 5 with all subsequent digits(hundred, tens and unit) rounded to Zero..

Hence,

The whole number will could be range between :

615,000 - 619,999

Hence, the least possible value for the number is 615,000.

Answer:

$127.75

Step-by-step explanation:

Multiply the cost by the area to find the total cost

Answer:

18.75%

Step-by-step explanation:

720 - (209+376) =

720 - 585 = 135

135/720 = 0.1875 --> 18.75%

Answer:

it transformed each point 2 units to the left and 10 units down.

function notation; f(x)= (2+x) -10

Step-by-step explanation:

The probability that a person does not have the disease given a positive test result is approximately 0.4754, rounded to four decimal places.

The probability of getting a negative result when a randomly selected person undergoes the test can be calculated by considering the complementary probability of getting a positive result.

Since 5% of the population suffers from the disease, the probability of an individual having the disease is 0.05. The probability of a positive test result given that the person has the disease is 0.99. Thus, the probability of a negative result given that the person has the disease is 1 - 0.99 = 0.01.

Similarly, the probability of a negative result given that the person does not have the disease can be calculated. Since 95% of the population does not have the disease, the probability of an individual not having the disease is 0.95. The probability of a positive test result given that the person does not have the disease is 0.05. Thus, the probability of a negative result given that the person does not have the disease is 1 - 0.05 = 0.95.

Therefore, the probability of getting a negative result when a randomly selected person undergoes the test is 0.01 (or 1%) rounded to three decimal places.

Now, let's calculate the probability that a person does not have the disease given that the test result is positive. This can be found using Bayes' theorem.

Let A represent the event that a person has the disease, and B represent the event that the test result is positive. We want to calculate P(A' | B), which is the probability of not having the disease given a positive test result.

According to Bayes' theorem:

P(A' | B) = (P(B | A') * P(A')) / P(B)

P(B | A') is the probability of a positive test result given that the person does not have the disease, which is 0.05.

P(A') is the probability of not having the disease, which is 0.95.

P(B) is the probability of a positive test result, which can be calculated by considering the two scenarios:

P(B | A) * P(A) is the probability of a positive test result given that the person has the disease, which is 0.99, multiplied by the probability of having the disease, which is 0.05.

P(B | A') * P(A') is the probability of a positive test result given that the person does not have the disease, which is 0.05, multiplied by the probability of not having the disease, which is 0.95.

So, P(B) = (P(B | A) * P(A)) + (P(B | A') * P(A')) = (0.99 * 0.05) + (0.05 * 0.95) = 0.0995.

Substituting these values into the formula, we get:

P(A' | B) = (0.05 * 0.95) / 0.0995 ≈ 0.4754

Therefore, the probability that a person does not have the disease given a positive test result is approximately 0.4754, rounded to four decimal places.

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The formula for calculating the effective annual rate of interest with quarterly compounding is:

(1 + r/4)^4 - 1 = A/P

where r is the quarterly interest rate, A is the final amount, and P is the principal.

In this case, P = $2,000, A = $3,000, and the time period is 7 years or 28 quarters.

So we have:

(1 + r/4)^4 - 1 = 3000/2000

(1 + r/4)^4 = 1.5

1 + r/4 = (1.5)^(1/4)

r/4 = (1.5)^(1/4) - 1

r = 4[(1.5)^(1/4) - 1]

To get the effective annual rate, we need to convert the quarterly rate to an annual rate by multiplying by 4:

effective annual rate = 4[(1.5)^(1/4) - 1] ≈ 8.84%

Therefore, the effective annual rate of interest at which $2,000 will grow to $3,000 in seven years if compounded quarterly is approximately 8.84%, rounded to 2 decimal places.

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Answer:

50

Step-by-step explanation:

Answer:

Cos(15) = Cos(45-30)

Sin(15) = Sin(45-30)

Cos(45-30) - Sin(45-30)

Simplifying both brackets

Recall

Cos(A+B) = CosACosB - SinASinB (For cosine... The sign is always the opposite during expansion. If you look... Cos(A+B) became negative during its expansion;So if It was Cos(A–B)... Its expansion is CosACosB + SinASinB)]

Sin(A+B) = SinACosB + CosASinB

Now let's go!

Cos(45-30) = Cos45Cos30 + Sin45Sin30

From Trig

Cos45 = 1/√2

Cos30 = √3/2

Sin45 = 1/√2

Sin30 = 1/2

Substituting

Cos(45-30) = (1/√2).(√3/2) + (1/√2).(1/2)

= √3/(2√2) + 1/(2√2)

= 1 + √3/(2√2).

For

Sin(45 - 30)

= Sin45cos30 – Cos45Sin30

= (1/√2).(√3/2) – (1/√2).(1/2)

= √3/(2√2) – 1/2√2

= √3 – 1/(2√2)

So the question was

Cos15 - Sin15

Substituting...

1 + √3 / 2√2 – (√3 - 1)/ 2√2

When the Minus interacts with the parenthesis

We have

1 + √3 - √3 + 1 / (2√2)

= 2/2√2

= 1/√2.

THE ANSWER IS 1/√2 AND NOT 1/2.

YOU CAN VERIFY THIS WITH YOUR CALCULATOR ALSO.

YOU'LL HAVE 0.7071 WHICH IS SAME AS 1/√2.

HAVE A GREAT DAY!

Answer:

x= 4/5

y= 2/5

Step-by-step explanation:

3x-y=2

2x+y=5

solve them so that they are in y=mx+b form

3x-y-3x=2-3x

-y= -3x+2

y= 3x -2

2x+y -2x= 2-2x

y= -2x+2

now use the substitution method to get your points

3x -2= -2x+2

3x -2+2= -2x+2+2

3x= -2x+4

3x+2x= -2x+4+2x

5x=4

x= 4/5

now substitute x into any of the 2 equations

y= 3x -2

y= 3(4/5) -2

y= 2 2/5 -2

y= 2/5

Hope this helped!

Answer:

5.3

Step-by-step explanation:

We know that the bottom of the ladder is 15 feet from the wall, and it touches the wall 80 feet above the ground.  Imagine it like two points on a graph.  One is at the origin (0,0).  That represents the bottom of the ladder.  The next one is at (80,15), which represents where the top is.  To find slope, we divide rise (y-values) over the run (x-values).  The y value increases by 80, while the x increases by 15.  80 divided by 15 equals about 5.3

The solutions of the equation are x = 15 and x = -20

The equation is given as:

the absolute value quantity two fifths times x plus 1 end quantity minus 7 equals 0

Rewrite the equation properly as:

|2/5x + 1| - 7 = 0

Add 7 to both sides

|2/5x + 1| = 7

Remove the absolute bracket

2/5x + 1 = 7 and 2/5x + 1 = -7

Subtract 1 from both sides

2/5x = 6  and 2/5x = -8

Solve for x

x = 15 and x = -20

Hence, the solutions of the equation are x = 15 and x = -20

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Answer:

B. x = -20 and x = 15

Step-by-step explanation:

Good luck! Hope this helped :)

The selling price that gives the maximum profit is $32.

So, the correct answer is B) $32.

Given that the profit of a company is given by the function, P = -25x² + 1600x - 3600.

We need to find the selling price to gives the maximum profit.

To find the selling price that gives the maximum profit, we need to determine the value of x that corresponds to the vertex of the quadratic function.

The vertex of a quadratic function in the form of P(x) = ax² + bx + c is given by the formula x = -b / (2a).

In this case, the profit function is P(x) = -25x² + 1600x - 3600, where a = -25, b = 1600, and c = -3600.

Using the formula for the x-coordinate of the vertex, we have:

x = -b / (2a)

= -1600 / (2×(-25))

= -1600 / (-50)

= 32

Therefore, the selling price that gives the maximum profit is $32.

So, the correct answer is B) $32.

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it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

What is Integers?

A whole number is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+, and √2 are not. The set of integers consists of zero, positive natural numbers, also called integers or counting numbers, and their additive inverses.

To prove that there are no integers x, y, z such that x² + y² = 8z + 3, we can use the concept of modulo arithmetic.

First, let's consider the possible values of x² and y² modulo 8:

For any integer n, n² modulo 8 can only be 0, 1, or 4.

Now, let's examine the possible values of 8z + 3 modulo 8:

8z modulo 8 is always 0.

3 modulo 8 is equal to 3.

Therefore, the possible values of x² + y² modulo 8 can only be 0, 1, or 4, while 8z + 3 modulo 8 is equal to 3. Since 0, 1, and 4 are not equal to 3 modulo 8, there are no integers x, y, z that satisfy the equation x² + y² = 8z + 3.

Hence, it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

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Answer:

\(\huge\boxed{y=\dfrac{4}{3}x-1}\)

Step-by-step explanation:

Let

\(k:y=m_1x+b_1\\l:y=m_2x+b_2\)

then

\(k\perp l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\k\ ||\ l\iff m_1=m_2\)

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

We have:

\(y=-\dfrac{3}{4}x-3\to m_1=-\dfrac{3}{4}\)

Let

\(y=m_2x+b_2\)

Therefore

\(m_2=-\dfrac{1}{-\frac{3}{4}}=\dfrac{4}{3}\Rightarrow y=\dfrac{4}{3}x+b_2\)

Substitute

\((0,\ -1)\to x=0;\ y=-1\)

\(-1=\dfrac{4}{3}\cdot0+b_2\\\\b_2=-1\)