Change y = – 2/3 x + 7 into standard form

Answer:

a) From A ∩ A' = ∅, we have;

A ∩ (A' ∪ B) = A ∩ B

b) From A ∩ (A' ∩ B') = (A ∩ A') ∩ B' and A ∩ A' = ∅, we have;

A ∩ (A ∪ B)' = ∅

Step-by-step explanation:

a) By distributive law of sets, we have;

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

From the complementary law of sets, we have;

A ∩ A' = ∅

Therefore, for A ∩ (A' ∪ B) = A ∩ B, we have

A ∩ (A' ∪ B) = (A ∩ A') ∪ (A ∩ B) (distributive law of sets)

A ∩ A' = ∅ (complementary law of sets)

Therefore;

(A ∩ A') ∪ (A ∩ B) = ∅ ∪ (A ∩ B)  = (A ∩ B) (Addition to zero identity property)

∴  A ∩ (A' ∪ B) = A ∩ B

b) By De Morgan's law

(A ∪ B)' = A' ∩ B'

Therefore, A ∩ (A ∪ B)' = A ∩ (A' ∩ B')

By associative law of sets, we have;

A ∩ (A' ∩ B') = (A ∩ A') ∩ B'

A ∩ A' = ∅ (complementary law of sets)

Therefore, (A ∩ A') ∩ B' = ∅  ∩ B' = ∅

Which gives;

A ∩ (A ∪ B)' = ∅.

Answer:

about 72 dollars

Step-by-step explanation

"about" tells us to round our numbers. Therefore, 7.8 becomes 8. As each pound is $8.99, we multiply the two and get 71.92, which is "about" 72.

Answer:

$72

Step-by-step explanation:

To find the cost, multiply the price per pound by the number of pounds.

8.99(7.8)

= 70.12

This is closest to $72

Answer:

7450

Step-by-step explanation:        

Move the decimal to the right 3 times.

The standard notation is 7450

Standard and scientific notation are the ways to represent numbers mathematically. We write numbers in standard and scientific notations using the rules for respective mathematical concepts. Here, 7.56×1011 7.56 × 10 11 is a scientific notation. 756,000,000,000 756 , 000 , 000 , 000 is standard notation.

Given:

7.45 x 10^3

So, when there is multiplication in decimals then the decimal point would shift to the right side.

Then,

7.45* 1000

=7450

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Answer:

10

Step-by-step explanation

50 divided by 10 is 5 so

50 times 2 which is 100 divided by 10 is 10

Answer:

a) Suzette ran for 4 hours

b) Suzette biked for 5 hours

Step-by-step explanation:

Speed is rate of distance traveled, it is the ratio of distance traveled to time taken. It is given by:

Speed = distance / time

The total distance ran and biked by Suzette (d) = 80 miles, while the total time ran and biked by Suzette (t) = 9 hours.

For running:

Her speed was 5 miles per hour, let the total hours Suzette ran be x and the total distance she ran be p, hence since Speed = distance / time, therefore:

5 = p / x

p = 5x

For biking:

Her speed was 12 miles per hour, let the total hours Suzette ran be y and the total distance she ran be q, hence since Speed = distance / time, therefore:

12 = q / y

q = 12y

The total distance ran and biked by Suzette (d) = Distance biked + distance ran

d = p + q

80 = p + q

80 = 5x + 12y                 (1)

The total time taken to run and bike by Suzette (t) = time spent to bike + time spent to run

t = x + y

9 = x + y                         (2)

Solving equation 1 and equation 2, multiply equation 2 by 5 and subtract from equation 1:

7y = 35

y = 35/7

y = 5 hours

Put y = 5 in equation 2:

9 = x + 5

x = 9 -5

x = 4 hours

a) Suzette ran for 4 hours

b) Suzette biked for 5 hours

Answer:

B

Step-by-step explanation:

it is defined for all values so D=R

also we can get any value

so Range =R

Answer:

B

Step-by-step explanation:

because that's odd power function it can take both, negative and positive values

Answer:

25 + 10h = 50+5h

Step-by-step explanation:

Black Diamond Ski Resort

25 + 10h

Bunny Hill Ski Resort

50+5h

We want when they are equal

25 + 10h = 50+5h

Answer:

10x + 25 = 5x + 50

Step-by-step explanation:

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      Hi my lil bunny!

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Let's solve your inequality step-by-step.

[tex]x(x+2)<x[/tex]

[tex]x^2 + 2x < x[/tex]

Let's find the critical points of the inequality.

[tex]x^2 + 2x = x[/tex]

[tex]x^2 + 2x - x - x[/tex]  (Subtract x from both sides)

[tex]x^2 + x = 0[/tex]

[tex]x ( x + 1 ) = 0[/tex] (Factor left side of equation)

[tex]x = 0 |OR| x + 1 = 0[/tex] (Set factors equal to 0)

[tex]x = 0 |OR| x = -1[/tex]

Check intervals in between critical points. (Test values in the intervals to see if they work.)

[tex]x < - 1[/tex] (Doesn't work in original inequality)

[tex]-1 < x < 0[/tex] (Works in original inequality)

[tex]x > 0[/tex]  (Doesn't work in original inequality)

So the answer is : [tex]-1 < x < 0[/tex]

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If this helped you, could you maybe give brainliest..?

❀*May*❀

Answer:

  Bobby has $300 in the yearbook fund and earns $13.50 for each yearbook sold.

Step-by-step explanation:

The value of the expression when x is zero is 300. For each increment of 1 in x, the value of the expression increases by 13.50. This best matches the scenario ...

  Bobby has $300 in the yearbook fund and earns $13.50 for each yearbook sold.

Answer:

(B) -266

Step-by-step explanation:

The formula to find the nth term in a sequence is:

[tex]x_{n} = a + d(n-1)[/tex], where a is the first term and n is the "difference."

Looking at this equation, we can see that the number decreases by 7 each time and the first term is 70.

So:

[tex]x_n = 70 + -7(n-1)[/tex]

Solve for the equation:

[tex]x_n = 70 + -7n+7\\x_n = -7n+77[/tex]

Since we want to find the 49th term:

[tex]x_9 = -7(49) + 77\\x_9 = -343+77\\x_9 = -266[/tex]

Hope this helped!

Answer:

A. unbiased estimator.

Step-by-step explanation:

In Statistics, an estimator is a statistical value which is used to estimate a parameter. Parameters are the determinants of the probability distribution. Therefore, to determine a normal distribution we would use the parameters, mean and variance of the population.

A function of random variables used to estimate a parameter of a distribution is an unbiased estimator.

An unbiased estimator is one in which the difference between the estimator and the population parameter grows smaller as the sample size grows larger. This simply means that, an unbiased estimator captures the true population value of the parameter on average, this is because the mean of its sampling distribution is the truth.

Also, we know that the bias of an estimator (b) that estimates a parameter (p) is given by; [tex]E(b) - p[/tex]

Hence, an unbiased estimator is an estimator that has an expected value that is equal to the parameter i.e the value of its bias is equal to zero (0).

Generally, in statistical analysis, sample mean is an unbiased estimator of the population mean while the sample variance is an unbiased estimator of the population variance.

Answer: B statistic

Step-by-step explanation:

it just is trust me

Answer:

Step-by-step explanation:

It is convenient to let a graphing calculator draw the graph for you. It can also display the solution: (x, y) = (6, 18).

__

The equations of interest are ...

  x + 2y = 42 . . . . . . revenue from sale of x cookies and y chips

  y = 3x . . . . . . . . . . 3 times as many chips as cookies

Answer:

\underline{\text{Variable Definitions:}}

Variable Definitions:

​

x=

x=

\,\,\text{the number of packs of cookies sold}

the number of packs of cookies sold

y=

y=

\,\,\text{the number of bags of chips sold}

the number of bags of chips sold

Each pack of cookies sells for $1, so xx packs of cookies will bring in 1x1x dollars. Each bag of chips sells for $2, so yy bags of chips will bring in 2y2y dollars. Therefore, the total amount 1x+2y1x+2y equals \$42:$42:

1x+2y=42

1x+2y=42

Since Kylie sold 3 times as many bags of chips as packs of cookies, she sold more bags of chips, so if we multiply 3 by the number of packs of cookies sold, we will get the number of bags of chips sold, meaning yy equals 3x.3x.

y=3x

y=3x

\underline{\text{Write System of Equations:}}

Write System of Equations:

​

1x+2y=

1x+2y=

\,\,42

42

y=

y=

\,\,3x

3x

\underline{\text{Solve for }y\text{ in each equation:}}

Solve for y in each equation:

​

\begin{aligned}\color{indianred}{1x}+2y = 42\hspace{10px} & \hspace{10px}\color{green}{y}\color{green}{=}\color{green}{3x} \\[10px] 2y = \color{indianred}{-1x}+42\hspace{10px} & \hspace{10px} & \\[10px] \frac{2y}{2} = \frac{-1x+42}{2}\hspace{10px} & \hspace{10px} & \\[10px] \color{blue}{y} \color{blue}{= -\frac{1}{2}x+21}\hspace{10px}\hspace{10px} & \hspace{10px} & \end{aligned}

1x+2y=42

2y=−1x+42

2

2y

​

=

2

−1x+42

​

y=−

2

1

​

x+21

​

y=3x

​

​

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Compare the coordinates of corresponding vertices.

C(7, - 2 ) → C'(- 3, 7 )

x- direction 7 → - 3 , that is - 10 of a shift

y- direction - 2 → 7, that is + 9 of a shift

Thus the translation rule is

(x, y ) → (x - 10, y + 9 )

Answer and Step-by-step explanation: The described right triangle is in the attachment.

As it is shown, AC is the hypotenuse and BC and AB are the sides, so use Pytagorean Theorem to find the unknown measure:

AC² = AB² + BC²

[tex]AB^{2} = AC^{2}-BC^{2}[/tex]

[tex]AB =\sqrt{AC^{2}-BC^{2}}[/tex]

[tex]AB =\sqrt{7^{2}-4.5^{2}}[/tex]

[tex]AB =\sqrt{28.75}[/tex]

AB = 5.4

Then, right triangle ABC measures:

AB = 5.4cm

BC = 4.5cm

AC = 7cm

variable is in power so it exponential.

the constant and coefficient both are positive so it is exponential Growth.

Answer:

Below

Step-by-step explanation:

6)

The sum that we have is 85 +99

We want to express it as the product of a whole number thar is greater than 1 and a sum of two whole numbers.

Notice that: 85 = 84+1

● 85 + 99 = 84 + 1 + 99 = 84 + 100

84 and 100 are even numbers so we can factor using 2.

● 84 + 100 = 2(42 +50)

2 is greater than one and 42+50 is the sum of two whole numbers so all the conditions are satisfied.

■■■■■■■■■■■■■■■■■■■■■■■■■■

7)

Dasha go on business trips every 9 months while Charlie go every 6 months.

They came back at the same time.

So Charlie has to wait 6 months before going and Dasha nine months.

Dasha will be alone home for 3 months so she doesn't need to hire someone.

Here is what happens:

● Both Dasha and Charlie are home.

● After 6 months Charlie go and Dasha is at home

● after 3 months Dasha goes also and Charlie is home

● after 3 months charlie go and Dasha is home

● after 3 months both are home.

● aftet 3 months they both go

So the period is:

● 6+3+3+3+3 = 18

So after 18 months they should hire someone.

The picture below makes the understanding easier. ( x is Charlie and y is Dasha)

■■■■■■■■■■■■■■■■■■■■■■■■■■

8)

Pime factorisation

● 96÷2= 48

● 48÷2= 24

● 24 ÷ 2 = 12

● 12 ÷ 2 = 6

● 6÷2 = 3

● 3÷3 = 1

=> 96 = 2 × 2 ×2×2×2 ×3 =2^5 ×3

● 80÷ 2 = 40

● 40 ÷ 2 = 20

● 20÷2 = 10

● 10÷2 = 5

● 5÷5 = 1

=> 80 = 2×2×2×2×5 = 2^4 × 5

So the GCF is 2^4 wich is 16

He can make 16 party

● 80÷16 = 5

There will be 5 boxes of raisin in each one

● 96÷16 = 6

There will be 6 pencils in each party

Answer:

[tex]\Large \boxed{p^2 +3p-18}[/tex]

Step-by-step explanation:

[tex]( p + 6 )( p - 3 )[/tex]

Expand brackets.

[tex]p(p-3)+6(p-3)[/tex]

[tex]p^2 -3p+6p-18[/tex]

Combine like terms.

[tex]p^2 +3p-18[/tex]

Answer:

p² + 3p - 18

Step-by-step explanation:

(p + 6) (p-3)

Break it apart to make it easier to see:

p(p-3) = p² - 3p

6(p-3) = 6p - 18

Add both parts together(Combine Like terms):

p² - 3p + 6p - 18 = p² + 3p - 18

Answer:

[tex]\Large \boxed{\mathrm{A) \ 0 }}[/tex]

Step-by-step explanation:

3x + 4y = 7

-3x - 4y = 7

Add both equations.

0x + 0y = 14

0 = 14

There are no solutions.

Answer:

A) 0

Step-by-step explanation:

Adding both equations.

0 + 0 = 14

0 = 14 (no solutions)

Answer:

#3 would be the first one and #4 would be the third answer.

Step-by-step explanation:

i'm so sorry for the wait

There is no one set answer because there are many ways to estimate here.

35 rounds to 40

9 rounds to 10

She got rid of 10 shirts out of 40, so 10/40 = 1/4 = 0.25 = 25% is the estimated percentage of shirts she got rid of. This is one possible estimate.

Using a calculator, the actual percentage is 9/35 = 0.2571 = 25.71% approximately. So our estimate isn't too bad. Our estimate is an underestimate.

Answer:

18 : 30

Step-by-step explanation:

Our ratio could look like this:

Number of games won : Number of games played

6 : 10

=> .6 : 1

Let's check whether the 1st option is correct.

=>  18 : 20

=> 1 x 20 = 20

=> .6 x 20 = 12

=> 12 : 20 is not equal to 18 : 20

The second option is 100% incorrect because the number of games won is greater than the number of games played.

let's check whether the 3rd option is correct.

=> 18 : 30

=> 1 x 30 = 30

=> .6 x 30 = 18

18 : 30 = 18: 30

So, the 3rd option is correct.

Answer:

18:30

Step-by-step explanation:

The ratio of games is 6 won out of 10 games

The ratio at the bottom that is 6:10 is

18:30

Divide each side by 3

18/3 : 30/3

6:10

Answer:

2.64 km

Step-by-step explanation:

24*110=2640 meters

2640/1000=2.64 km

Answer:

D. 860 square inches

Answer:

D: 860 square inches

Step 1.

Remember:

w = 8

x = 5

y = 20

z = 11.3

Let's start with the bottom rectangular prism. The front and back of it is x * x

(5 * 5), so the from and back is 25 + 25 = 50.

The three long sides are x * y (5*20), so the three long rectangles are 100 * 3 = 300. The bottom shape is 350 in total.

Step 2.

The top two rectangles are w * y, (8 * 20) so the two top rectangles are 160 * 2 = 320.

The triangles are w * w / 2 (8 * 8/2) (64 / 2) (32), so the two triangles are 64.

We subtract x from z to get 6.3.

Then, we multiply 6.3 by 20. We get 126. Finally, we add all the values together to get our final answer.

350 + 384+126 = 860

Our answer is D: 860.

Answer:

$240

Step-by-step explanation:

The amount they spend on a monthly basis for transportation = percentage represented on the circle covered by transportation ÷ 100% × the total monthly income.

= [tex] \frac{5}{100} * 4800 [/tex]

[tex] = 0.05 * 4800 = 240 [/tex]

Money spent on transportation = $240

Answer: the cash that is Paid each is 240$

Answer:

70.83 ft³

Step-by-step explanation:

The volume of a pyramid is:

[tex]\frac{bh}{3}[/tex], where b is the base area and h is the height.

Let's first find the area of the base.

[tex]17\cdot5=85\\85\div2=42.5[/tex]

Multiplying this by 5:

[tex]42.5\cdot5=212.5[/tex]

Dividing by 3:

[tex]212.5\div3=70.83[/tex].

Hope this helped!

Answer: |p-72% |≤ 4%

Step-by-step explanation:

Let p be the population proportion.

The absolute inequality about p using an absolute value inequality.:

[tex]|p-\hat{p}| \leq E[/tex] , where E = margin of error, [tex]\hat{p}[/tex] = sample proportion

Given:  A poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% .

|p-72% |≤ 4%

⇒    72% - 4% ≤ p ≤ 72% +4%

⇒  68%  ≤ p ≤  76%.

i.e. p is most likely to be between 68% and 76% (.

The conclusion about p using an absolute value inequality is in the range of 29.8% to 34.2%.

An expression using absolute functions and inequality signs is known as an absolute value inequality.

We know that the absolute value inequality about p using an absolute value inequality is written as,

[tex]|p-\hat p| \leq E[/tex]

where E is the margin of error and [tex]\hat p[/tex] is the sample proportion.

Now, it is given that the poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76%. Therefore, p can be written as,

[tex]|p-0.72|\leq 0.04\\\\(0.72-0.04)\leq p \leq (0.72+0.04)\\\\0.68 \leq p\leq 0.76[/tex]

Thus, the p is most likely to be between the range of 68% to 76%.

Similarly, the proportion of people who like dark chocolate more than milk chocolate was 32% with a margin of error of 2.2%. Therefore, p can be written as,

[tex]|p-\hat p|\leq E\\\\|p-0.32|\leq 0.022\\\\(0.32-0.022)\leq p \leq (0.32+0.022)\\\\0.298\leq p\leq 0.342[/tex]

Thus, the p is most likely to be between the range of 29.8% to 34.2%.

Hence, the conclusion about p using an absolute value inequality is in the range of 29.8% to 34.2%.

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Answer:

To find the perimeter of a rectangle or square you have to add the lengths of all the four sides

The area is measurement of the surface of a shape.

Hope this helps! （づ￣3￣）づ╭❤～

Answer:

-5r + 8r +5

= (-5+8)r+5 (we can calculate number in same variabe)

= 3r +5

hope it helps ^°^

Answer:

3r + 5.

Step-by-step explanation:

-5r + 8r + 5

= 8r - 5r + 5

= 3r + 5.

Hope this helps!

Answer:

Therefore, perimeter of the given triangle is 18.300 cm.

Step-by-step explanation:

Area of the triangle ABC = [tex]\frac{1}{2}(\text{AB})(\text{BC})(\text{SinB})[/tex]

10 = [tex]\frac{1}{2}(3.2)(8.4)(\text{SinB})[/tex]

Sin(B) = [tex]\frac{10}{3.2\times 4.2}[/tex]

B = [tex]\text{Sin}^{-1}(0.74405)[/tex]

B = 48.08°

By applying Cosine rule in the given triangle,

(AC)² = (AB)² + (BC)²-2(AB)(BC)CosB

(AC)² = (3.2)² + (8.4)² - 2(3.2)(8.4)Cos(48.08)°

(AC)² = 10.24 + 70.56 - 35.9166

(AC)² = 44.88

AC = [tex]\sqrt{44.8833}[/tex]

AC = 6.6995 cm

Perimeter of the ΔABC = m(AB) + m(BC) + m(AC)

                                      = 3.200 + 8.400 + 6.6995

                                      = 18.2995

                                      ≈ 18.300 cm

Therefore, perimeter of the given triangle is 18.300 cm

The product of (4z² + 7z – 8) and (–z + 3) is -4z³ + 5z² + 29z - 24

(4z² + 7z – 8) and (–z + 3)

= -4z³+ 12z² - 7z² + 21z + 8z - 24

= -4z³ + 5z² + 29z - 24

Therefore, the product of (4z² + 7z – 8) and (–z + 3) is -4z³ + 5z² + 29z - 24

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