An analysis of the amount of fiber (in grams) and the potassium content(in milligrams) in servings of 77 breakfast cereals produced the regression model

answer:

£11.25

explanation:

2.75+1=3.75 this was one third so you have to multiply 3.75 by 3 so you get 11.25.

a. g(-2) = -4

g(-1) = 2

b. slope of g(x) on the interval = 2

Given,

a. g(x ) = f(2x)

g(-2) = 2(-2)

g(-2) = -4

g(1) = 2(1)

g(1) = 2

b. slope = g(b) -g(a)/b-a

g(0) = 2(0)

g(0)= 0

g(1) = 2(1)

g(1) = 2

therefore, g(1)-g(0)/1-0

slope = 2-0/1

slope = 2

hence we get the slope as 2.

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The compound interest is $2.5

What is Compound interest?

When you earn interest on both the money you've saved and the interest you earn, is called Compound interest.

Given that;

Principal amount = $1,000

Rate = .25%

Time = 1 year

Now,  Amount = P (1 + r)^t  

                      = 1,000 ( 1 + .25%)^1

                      = 1,002.5

And, Compound interest = P (1 + r)^t -  P

Now, Amount = 1,000 ( 1 + .25%)^1

                     = 1,002.5

Hence, Compound interest = 1,002.5 - 1,000

                                          = 2.5

So, The compound interest is $2.5.

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Answer:

A

Step-by-step explanation:

4360+(4360(0.511)) Equals 6590 when rounded up

The correct answer is Absolute change: 2230 and Percentage change: 51.1%. So, correct option is A.

To calculate the absolute change and percentage change, we need to subtract the initial measurement from the final measurement and then calculate the percentage change relative to the initial measurement.

Given that the population of Placerville grew from 4360 a decade ago to 6590 today, we can calculate the absolute change as follows:

Absolute change = Final measurement - Initial measurement

Absolute change = 6590 - 4360

Absolute change = 2230

Therefore, the absolute change in population is 2230.

To calculate the percentage change, we divide the absolute change by the initial measurement and multiply by 100:

Percentage change = (Absolute change / Initial measurement) * 100

Percentage change = (2230 / 4360) * 100

Percentage change ≈ 51.1%

Hence, the correct answer is:

a. Absolute change: 2230

Percentage change: 51.1%

Therefore, option a is the correct choice.

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You can use estimation to determine if your answer is reasonable by ensuring that the estimated answer does not have large outliers.

Estimation is a rough calculation or judgment using available information based on their face values without going into detail.

Estimation, which is based on approximation, helps to determine if a reasonable solution has been found before the events occur when the actual calculations are carried out.

Estimation ensures that the obtained data or results do not vary greatly from the central values. Estimation helps calculations without adequate data and when computations involve large numbers.

Thus, you can use estimation to determine if your answer is reasonable by ensuring that the estimated answer does not have large outliers.

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The letter at entry #123 will be S for the sequence C,S,S,S,S,S,C,S,S,S,S,S

The given sequence of letters is C,S,S,S,S,S,C,S,S,S,S,S

As per the given sequence, there are 12 letters in the sequence. To find the letter at #123 we continue the sequence till entry #120 or 10 iterations, the sequence will remain the same i.e C,S,S,S,S,S,C,S,S,S,S,S and then find the next 3 letters

So for entry #123, we will get the following value as per the sequence:

C,S,S

Hence, the letter at entry #123 will be S as per the given sequence of letters.

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Considering that they filed the taxes using the "married filing jointly" status, six exemptions can be claimed by the couple.

If a person and their spouse file taxes using the "married filing jointly" status, it means that two exemptions are claimed, one for the person and one for the spouse.

For this problem, the exemptions are given as follows:

2 + 4 = 6.

Hence:

Considering that they filed the taxes using the "married filing jointly" status, six exemptions can be claimed by the couple.

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Answer:

6

Step-by-step explanation:

simple 2+4=6

Answer: well i do not know

Step-by-step explanation: of well

Given that Bill saves 1/8 of his $92 income, the amount of money he saves is $11.5.

Given that;

Let the amount saved by be be represented by the variable x.

Hence,

1/8 of Bill's income = Amount saved

1/8 × $92 = x

Multiply the numerators

x = 1/8 × $92

x = $92/8

Divide 92 by 8

x = $11.5

Given that Bill saves 1/8 of his $92 income, the amount of money he saves is $11.5.

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Using the two column proof, it has been proved that m∠2 ≅ m∠3

From the given diagram, we can write the two column proof as follows;

Statement 1: m∠DHF = m∠EHG

Reason 1; Given

Statement 2; m∠2 + m∠1 = m∠DHF

Reason 2; Angle Addition Property

Statement 3; m∠1 + m∠3 = m∠GHE

Reason 3; Angle Addition Property

Statement 4; m∠2 ≅ m∠3

Reason 4; Definition of congruent angles

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Answer:

No solution for x

Step-by-step explanation:

Subtract 7 from both sides
==> [tex]5\left|x+1\right|+7-7=-38-7[/tex]

==> [tex]5\left|x+1\right|=-45[/tex]

Divide both sides by 5
==>   [tex]\frac{5\left|x+1\right|}{5}=\frac{-45}{5}[/tex]

==>  [tex]\left|x+1\right|=-9[/tex]

But this is not possible since absolute value cannot be negative

Hence the equation is inconsistent and therefore there are no solutions for x

Answer:

No solution

Step-by-step explanation:

5|x+1| + 7 = -38

5|x+1| = -38 - 7

5|x+1| = -45

Divide both sides by -5

|x + 1| = -9

Because of how the modulus works, whatever is inside it, whether positive or negative, will become positive.

And since the left side is always positive and the right side is always negative, there is no value of x that can satisfy the equation.

Therefore there is no solution to this equation

The input that makes the output of A to be three times the output of B is; x = 9

We are told that both Machines A and B have the same input. Thus;

Output of Machine A using Algebraic Properties is;

Output A = 5x - 4

Output of Machine B using Algebraic Properties is;

Output B = 3x + 8

We want to find the input that makes the output of A to be three times the output of B. Thus;

5x - 4 = 3(3x + 8)

5x - 4 = 9x + 24

9x - 5x = -4 - 24

4x = -28

x = -28/4

x = 9

Thus, we conclude that the input that makes the output of A to be three times the output of B is; x = 9

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Answer: 10

Step-by-step explanation:

There are 16th term in sequence.

Answer:

1 ÷ 64

Step-by-step explanation:

Answer:

Are of the parallelogram = 168 square feet

Step-by-step explanation:

I am not sure exactly what the question is asking for since the area of a parallelogram is simply the base x height and both are given

Are = 14 x 12 = 168 square feet

I have attached a picture with the decomposition of the parallelogram into a rectangle and two triangles.

ABCD is the parallelogram with base = 14 and height = 12

ABE and CDF are the two triangles each with base = 3 and height = 12

EBFD is a rectangle

All the dimensions are marked

I hope that helps and if you need any further clarification, please do ask

3x3=6

6-2=4.

Thats the answer!!! yayayayayayayayaya

Answer:

Step-by-step explanation:

Kate needs to read 2 books over summer vacation. She doesn't have the books yet so she's not sure how many pages are in each book. Kate doesn't want to wait until the last minute to read the books so she is planning to read the same number of pages each day of her summer vacation. If Kate's summer vacation is 72 days long, how can she write a variable expression to represent the number of pages she will need to read each day?

Answer: 1+9i

Step-by-step explanation:

(4+7i)-(3-2i)=

4+7i-3-(-2i)=

4+7i-3+2i=

4-3+7I+2I=1+9i

Answer:

Step-by-step explanation:

7 units long

Step-by-step explanation:

We are given a right triangle ABC

AB = 25 units

BC = 24 units

We are required to determine the length of AC

We are going to use the Pythagoras theorem;

According to the theorem, if a and b are the legs of a right triangle and c is the hypotenuse, then;

a² + b² = c²

In this case;

AB is the hypotenuse and BC is one of the legs of the triangle;

Therefore;

AB² = BC²+AC²

Rearranging the formula;

AC² = AB² - BC²

      = 25² - 24²

      = 625 - 576

      = 49

AC = √49

Thus, AC is 7 units long

HOPE THIS HELPS :)

Answer:

No

Step-by-step explanation:

A right triangle needs to have a right angle in this case this triangle does not. The next answer up is a triangle with 6,8, and 10 inches. This would give you a right triangle.

Also, To check if the sides are a right triangle, check if the sum of the squares of the two smaller sides equals the length of the square of the longest side.

I haven't used triangles in a long time..... so I kinda forget but the little I remember I used. Hope this helps!

Answer: No

Step-by-step explanation:  The given side lengths of the triangle are 4 inches, 6 inches, and 9 inches. To determine if the triangle is a right triangle, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's check if the given side lengths satisfy the Pythagorean theorem:

Using the Pythagorean theorem, we can calculate the squares of the side lengths:

4^2 = 16

6^2 = 36

9^2 = 81

Now, let's compare the sum of the squares of the two shorter sides to the square of the longest side:

16 + 36 = 52

81 = 81

Since 52 is not equal to 81, the given triangle is not a right triangle.

The function composite h(x) = f(x)g(x) is -10x² +  40x.

Option b)-10x² +  40x is the correct answer.

Given the functions in the question;

Since h(x) = f(x)g(x), replace the function designators in f(x)g(x) with the actual functions.

h(x) = f(x)g(x)

h(x) = ( 2x - 8 )( -5x )

Apply distributive property.

h(x) = ( 2x - 8 )( -5x )

h(x) = 2x(-5x) - 8(-5x)

Perform the operation to remove the parenthesis.

h(x) = -10x² +  40x

The function composite h(x) = f(x)g(x) is -10x² +  40x.

Option b)-10x² +  40x is the correct answer.

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Answer:

The answer is B

Step-by-step explanation:

<3

Answer:

CnA= {w, y}

Step-by-step explanation:

hope it helps

Answer:

Step-by-step explanation: it takes 60 peppers to make 3 pizzas we need 6 pizzas so we just take 60 x 2= 120. So we need 120 peppers to make 6 pizzas.

our number can be written as 44/2 = 22, the quotient between two integers, thus, our number is rational.

A number is rational if it can be written as the quotient between two integer numbers.

In this case, we want to prove that the number 22 is rational, so we just need to find two integers that, when we take the quotient between them, the outcome is 22.

This is kinda trivial, if we take for example the product between 22 and any integer, for example, 2, we get:

22*2 = 44

Solving for 22 we get:

22 = 44/2

There is our number written as the quotient between two integers, thus, our number is rational.

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Given the expression,

                         x+10=5

Rearrange variables to the left side of the equation,

                        x = 5 - 10

Calculate the sum or difference,

                        x = -5

Therefore,

The value of x is = -5

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The number line which represents the solution of the given absolute value inequality is |2x – 5| ≥ 3 is graph B : Points are at 1 and 4. Everything to the left of 1 and to the right of 4 is shaded.

An absolute value inequality is an equation of the form   |p| ≥ a or   |p| ≤ a

where p and are mathematical expressions.

Absolute rule for solving inequality: if |p| ≥ a then solution is  p ≤ (-a ) or

p ≥ a

Now for the given inequality  |2x – 5| ≥ 3 , applying above absolute rule we get :

(2x-5) ≤ -3   and (2x-5) ≥ 3

For 2x-5 ≤ -3

Adding 5 on sides we get:      2x-5+5 ≤-3+5

                                                         2x ≤ 2

On dividing both sides by 2:   (2x/2)   ≤ (2/2)

                                                       x    ≤ 1

which means that x are all number less than or equal to 1

On the number line, everything to left of 1 and point 1 on the number line

Now, For 2x-5 ≥ 3

Adding 5 on sides we get:      2x-5+5 ≥ 3+5

                                                         2x ≥ 8

On dividing both sides by 2:   (2x/2)   ≤ (8/2)

                                                      x    ≥ 4

which means that x are all numbers greater than or equal to 4

On the number line, everything to right of 4 and point 4 on the number line

Therefore, Graph B is the right answer which says that points are at 1 and 4 ,everything to the left of 1 and to the right of 4 is shaded.

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