rearrange the equation a = 1/2 b to make b the formula

The regression equation based on the information given about the sugar contents will be 0.18x - 20.84.

It should be noted that from the information, the accompanying data are the caloric contents and the sugar contents of 11 high-fiber breakfast cereals.

The sugar content will be:

a. 160 calories

= 0.18x - 20.84.

= 0.18(160) - 20.84

= 7.96

b. 90 calories

= 0.18x - 20.84.

= 0.18(90) - 20.84

= -4.64

c. 175 calories

= 0.18x - 20.84.

= 0.18(175) - 20.84

= 10.66

d. 208 calories

= 0.18x - 20.84.

= 0.18(208) - 20.84

= 16.6

Therefore, the sugar contents is illustrated above.

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Answer:

Step-by-step explanation:

9. D

10.D

11.E

12.D

Answer:

9.

[tex]x^2-4\\(x-2)(x+2)[/tex]

10.

[tex]x^2-25\\(x-5)(x+5)[/tex]

11.

[tex]36x^4-4x^2\\4x^2(9x^2-1)\\4x^2(3x+1)(3x-1)[/tex]

12.

[tex]x^2+100\\[/tex]

This polynomial cannot be factored by using the difference of squares method

Answer:

421/6 degrees

Step-by-step explanation:

The acute angles of a right triangle are complementary, so

[tex]10x+6+2x+7=90 \\ \\ 12x+13=90 \\ \\ 12x=77 \\ \\ x=\frac{77}{12}[/tex]

So, the acute angles measures 421/6 degrees and 119/6 degrees, and thus the larger angle is 421/6 degrees.

Answer:

  H

Step-by-step explanation:

Plane K is shown with two lines. Points on one of them are A, B, G. Points on the other one are G, M, N.

The point in plane K that is not shown on any line is point H.

Answer:

No.

Step-by-step explanation:

Negative decimal numbers are rational numbers since rational numbers include all the integers both positive and negative integers, decimal as well as a fraction because decimals can be written as fractions.

Answer:

60.

100 (total) - 40 (amount in the library Saturday morning) = 60.

Type: Percentages / Fractions

Answer:

See below

Step-by-step explanation:

[tex]A = \{2, 4, 6\}[/tex]

[tex]A^c =\{1, 3, 5\}\\B = \{4, 5, 6\}\\B^c = \{ 1,2, 3\}[/tex]

To prove 1 we have

[tex](A \bigcup B) = \{2, 4, 6\} \bigcup \{4, 5, 6\} = \{2, 4, 5, 6\}\\(A \bigcup B) ^c =\bold{\{1,3\}}\\A^c \bigcap B^c = {\{1, 3, 5\} \bigcap \{1, 2, 3\} =\bold{\{1,3\}}\\[/tex]

Hence proved

To prove 2

[tex](A \bigcap B) = \{2, 4, 6\} \bigcap \{4, 5, 6\} = \{4, 6\}\\\\(A \bigcap B)^c = \bold{\{1,2, 3, 5\}}\\A^c \bigcup B^c = \{1, 3, 5\} \bigcup \{1, 2, 3\} = \bold{\{1,2,3,5\}}\[/tex]

Hence proved

Notes

The complement of a set is the set of all elements not in the set

Here the set of all outcomes is {1, 2, 3,4,5, 6}

So if A = {2, 4, 6} then the complement of A s=is the set of outcomes not in A ie the set {1, 3, 5} which is the set of odd numbers on a die throw

The union of two sets is the set of all elements in both sets without duplication

The intersection of two sets is the set of all elements common to both sets

To estimate the amount of sales, x, will result in each of them earning the same amount for the week and we can set up the following equation:

T = R

825 + 0.06x = 1350 + 0.02x

Simplifying the equation, we get

x = 13125

We require a total of 13125 for the number of sales to maintain the same amount for Ramon and Teresa at the end of the week.

For this case, we can assume that the total salary for Teresa T is given by T = 825 + 0.06x

Where x represents the number of sales. And similarly the total salary of Ramon we have:

R = 1350 + 0.02x

We want to estimate the amount of sales, x, will result in each of them earning the same amount for the week and we can set up the following equation:

T= R

825 + 0.06x = 1350 + 0.02x

Multiply both sides by 100

[tex]$825 \cdot 100+0.06 x \cdot 100=1350 \cdot 100+0.02 x \cdot 100$[/tex]

82500 + 6x = 135000 + 2 x

Subtract 82500 from both sides

82500 + 6x - 82500 = 135000 + 2x - 82500

6x = 2x + 52500

Subtract 2x from both sides

6x - 2x = 2x + 52500 - 2x

4x = 52500

Divide both sides by 4

[tex]$\frac{4 x}{4}=\frac{52500}{4}$[/tex]

x = 13125

So then we require a total of 13125 for the number of sales to maintain the same amount for Ramon and Teresa at the end of the week.

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Using a linear function, it is found that it will take 13 hours for the candle to burn down to a height of .25 inches.

A linear function is modeled by:

y = mx + b

In which:

Considering the situation described, the y-intercept is of 10 while the slope is of -0.75, hence the height of the candle after t hours is given by:

h(t) = 10 - 0.75t

The height will be of 0.25 inches when h(t) = 0.25, hence:

0.25 = 10 - 0.75t

0.75t = 9.75

t = 9.75/0.75

t = 13 hours.

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Answer:

Step-by-step explanation:

Here's the solution

f^(-1)(x)=(\sqrt(5(x-10)))/(5), -(\sqrt(5(x-10)))/(5)

The value of the probability P(A and D) is 0.30

Using the probabilities on the tree diagram, we have the following parameters

P(A) = 0.5

P(D/A) = 0.6

The probability P(A and D) is then calculated using the following formula

P(A and D) = P(A) * P(D/A)

Substitute the known values in the above equation

P(A and D) = 0.5 * 0.6

Evaluate the product

P(A and D) = 0.30

Hence, the value of the probability P(A and D) is 0.30

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The missing length of the right triangle is 13.41 inches.

A right angle triangle has one of its angles as 90 degrees.

The side length of a right triangle can be found using Pythagoras theorem.

Therefore,

c² = a² + b²

where

Therefore,

x² = 18² - 12²

x² = 324 - 144

x² = 180

x = √180

x = 13.416407865

x = 13.41 inches

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If the Hansens want to reduce their expected estate tax liability prior to the death of either of the spouses, they could initiate a Marital Transfer.

A Marital transfer simply means that the Hansens should bequest their assets to each each other in case either of them die.

If this happens, the surviving spouse will not be charged any estate taxes because bequests to spouses are not subject to taxation.

To do this, the Hansens should put it into both of their wills that they plan to gift/ bequest their assets to their spouse if they die.

The big disadvantage of using a marital transfer however, is that the estate will still be subject to taxes when the surviving spouse dies. All the estate taxes that had been avoided would then be incurred by the estate but only after the death of both spouses.

In conclusion, they should use a marital transfer.

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The value of x in (1/6)/2 = x/3 is 1

The equation is given as

(1/6)/2 = x/3

Cross multiply in the above equation

x * 2 = (1/6) * 3

This gives

x * 2 = 1/2

Cross multiply

x = 2 * 1/2

This gives

x = 1

Hence, the value of x in (1/6)/2 = x/3 is 1

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Answer:

69500

Step-by-step explanation:

695 x 100 = 69500

to check answer divided 69500 by 100

which is equals to 695

695 is a hundred times smaller than 69500

multiplication is a method of finding the product of two or more numbers.

We need to find the number which 695 is a hundred times smaller than

Six hundred ninety five times smaller than

Let us consider the number to be x.

Let us multiply 695 with 100 to  get the value or answer of the above question.

Six hundred ninety five into hundred is sixty nine thousand five hundred

695 x 100 = 69500

To verify the answer is correct or not , divide 69500 by 100. if we get 695 out answer is correct

69500/100=695

Hence 695 is a hundred times smaller than 69500

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Answer + Step-by-step explanation:

the correct question:

For r ≠ 1 ,Prove using the mathematical induction method that :

[tex]1+\cdots+r^n =\frac{1-r^{n+1}}{1-r}[/tex]

………………………………………………………………………………………………………………

for n = 0 :

1⁰ = 1  and  (1 - r⁰⁺¹)/(1 - r) = (1 - r)/(1 - r) = 1

Then the property is true for n = 0.

For n ≥ 0 :

Suppose

[tex]1+\cdots+r^n =\frac{1-r^{n+1}}{1-r}[/tex]

And prove that

[tex]1+\cdots+r^{n+1} =\frac{1-r^{n+2}}{1-r}[/tex]

Since :

[tex]1+\cdots+r^{n+1} =(1+\cdots+r^n)+r^{n+1}[/tex]

Then

[tex]1+\cdots+r^n+r^{n+1} =\frac{1-r^{n+1}}{1-r}+r^{n+1}[/tex]

[tex]= \frac{1-r^{n+1}+r^{n+1}(1-r)}{1-r}[/tex]

[tex]= \frac{1-r^{n+2}}{1-r}[/tex]

Then according to the mathematical induction method

[tex]1+\cdots+r^n =\frac{1-r^{n+1}}{1-r}[/tex]

Where n is a natural number and r ≠ 1.

Answer:

Hola disculpa no me acuerdo

Step-by-step explanation:

De verdad que me encantaria ayudar pero no me acuerdo :(

Answer:

6

Step-by-step explanation:

Answer:

m = 3/2

Step-by-step explanation:

-7(m-1)= -(3m-1)

-7m + 7 = -3m + 1

-4m = -6

m = 3/2

Check.
-7(m-1)= -(3m-1)

-7(3/2 - 1) = -(3*3/2 - 1)

-7(1/2) = -(4.5 - 1)

-3.5 = -3.5

Use the distributive property to multiply −7 by m−1.

To find the opposite of 3m−1, find the opposite of each term.

The opposite of −1 is 1.

Add 3m to both sides.

Combine −7m and 3m to get −4m.

Subtract 7 from both sides.

Subtract 7 from 1 to get −6.

Divide both sides by −4.

Reduce the fraction -6/-4 to its lowest expression by extracting and canceling −2.

Answer: m=3/4 ✅

Answer:x>1

Step-by-step explanation:

Subract 11 from both sides

Answer:

(4,8)

Step-by-step explanation:

hihihihihihihihohihih

Answer:

2.8 metres each

Step-by-step explanation:

14/5

2.8

Answer: B: (1-5x²)³, all real numbers

Step-by-step explanation:

The notation [tex]f\circ g(x)[/tex] is called function composition, which is where you pass one function in as the value of another function. In other words, [tex]\( f\circ g(x)=f(g(x)) \)[/tex].

Since we have the values for f(x) and g(x), let's plug them in.

[tex]f(g(x))\\f(1-5x^2)\\(1-5x^2)^3[/tex]

Hence, the best answer choice is B, as all real numbers would work and it is the cube of 1 - 5x².

Using the probability concept, we have that:

A probability is given by the number of desired outcomes divided by the number of total outcomes.

The total number of students is given by:

26 + 3 + 9 + 10 + 6 + 5 + 7 = 66

Of those, 26 play only football, hence the probability is:

p = 26/66 = 13/33

Which means that option c is correct for question 19.

Of those same 66 students, 9 + 7 = 16 play baseball but not football, hence the probability is:

p = 16/66 = 8/33

Which means that option d is correct for question 20.

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Answer:

A

Step-by-step explanation:

If digits can be repeated, that means there are 10 options for each place in the pin code. 10*10*10*10 = 10,000

If digits can not be repeated, there are 10 options for the first digit, 9 options for the second digit, 8 options for the third digit, and 7 options for the fourth digit. 10*9*8*7 = 5040

Answer: 55

Step-by-step explanation: There is one simple theorem we need to know in order to solve for this.

Triangle Angle-Sum Property: All three angles interior angles of a triangle add up to 180°.

Thus, we could label the points A, B, and C, and set up an algebraic expression.

Let A = 27, B = 98, and C = x.

A + B + C = 180°.

Substituting A, B, and C we get:

27 + 98 + x = 180°.

Adding, we get:

125 + x = 180°

Subtracting 125 by 180, we get:

x = 55°

Thus, the angle X is 55°.

We could have simply solved this by just doing 180 - 98 - 27 = 55 in the first place, but I wanted to show you how I got such results.

Considering the definition of conditional probability, the probability that the team will win the second game given that they have already won the first game is 45.33%.

Probability is the greater or lesser chance that a given event will occur.

In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.

Conditional probability is the probability that a given event will occur given that another event occurs. The conditional probability operator is the │ sign.

In other words, the conditional probability is the probability of some event A , given the occurrence of some other event B and is denoted by P(A|B) and is read “the probability of A , given B ”.

Then, when an event influences the outcome of a second event, the probability of the second event is said to be a conditional probability and is calculated using the expression:

P(A|B)= P(A∩B) ÷ P(B)

where:

In this case, you know that:

Replacing in the definition of conditional probability:

P(A|B)= 0.34 ÷ 0.75

P(A|B)= 0.4533= 45.33%

Finally, the probability that the team will win the second game given that they have already won the first game is 45.33%.

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Hello and Good Morning/Afternoon!

Let's take this problem step by step:

Let's consider some facts:

 ⇒ angles are opposite each other

    ⇒ by the Vertical Angle Theorem

        ⇒ angles opposite each other are equal in measure

So:

 [tex]\hookrightarrow 4x + 12 = 64[/tex]

Let's solve

  [tex]4x + 12 = 64\\4x = 52\\x = 13[/tex]

x's value is 13

Answer: 13

Hope that helps!

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(a) The result of the long division is a - b + c.

(b) The result of the long division is 3 · m² + 2 · m + 1 + (12 · m³ - 16 · m + 6 · m²) / (m⁴ - 3 · m² + 4).

Long division is an algebraic procedure with which we can find the result of a division of two polynomials. Now we proceed to present the entire procedure explained:

(a) a² - b² + 2 · b · c - c² divided by a + b - c.

1) Multiply a + b - c by a and subtract it from a² - b² + 2 · b · c - c²: Result: a / Remainder: - b² - a · b + 2 · b · c + a · c - c²

2) Multiply a + b - c by - b and subtract it from the result of 1): Result: a - b / Remainder: b · c + a · c - c²

3) Multiply a + b - c by c and subtract it from the result of 2): Result: a - b + c / Remainder: 0

The result of the long division is a - b + c.

(b) 3 · m⁷ - 11 · m⁵ + m⁴ + 18 · m³ - 8 · m + 3 · m² + 4 divided by m⁴ - 3 · m² + 4.

1) Multiply m⁴ - 3 · m² + 4 by 3 · m³ and subtract it from 3 · m⁷ - 11 · m⁵ + m⁴ + 18 · m³ - 8 · m + 3 · m² + 4: Result: 3 · m³ / Remainder: 2 · m⁵ + m⁴ + 6 · m³ - 8 · m + 3 · m² + 4.

2) Multiply m⁴ - 3 · m² + 4 by 2 · m and subtract it from the result of 1): Result: 3 · m³ + 2 · m / Remainder: m⁴ + 12 · m³ - 16 · m + 3 · m² + 4.

3) Multiply m⁴ - 3 · m² + 4 by 2 · m and subtract it from the result of 2): Result: 3 · m² + 2 · m + 1 / Remainder: 12 · m³ - 16 · m + 6 · m².

The result of the long division is 3 · m² + 2 · m + 1 + (12 · m³ - 16 · m + 6 · m²) / (m⁴ - 3 · m² + 4).

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