Find the Area Of each circle.

Mya would have both lessons on the same day again on the 12th day.

In order to determine when they would have the both lessons on the same day, the common multiple of 6 and 4 has to be determined. A multiple of a number is the product of an integer and that number. A common multiple is the multiple that is common to two or more numbers.

Multiple of 6 = 6, 12, 28, 24, 30, 36,

Multiple of 4 = 4, 8, 12, 16, 20, 24, 28

Common multiple = 12

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex] \qquad❖ \: \sf \: {b}^{2} - 9b + 14[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex] \qquad❖ \: \sf \:(b - 2) \sdot(b - 7)[/tex]

[tex] \qquad❖ \: \sf \:(b \sdot b) + (b \sdot - 7) - (2 \sdot b) - (2 \sdot - 7)[/tex]

[tex] \qquad❖ \: \sf \: {b}^{2} - 7b - 2b + 14[/tex]

[tex] \qquad❖ \: \sf \: {b}^{2} - 9b + 14[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex] \sf \:(b - 2) \sdot(b - 7) = {b}^{2} - 9b + 14[/tex]

Answer:

b² - 9b + 14

Step-by-step explanation:

(b - 2) × (b - 7)

= b×b - 7b - 2b + 2×7  (Expand)

= b² - (7b + 2b) + 14  (gather like terms)

= b² - 9b + 14

Using the normal distribution, the probability that x is less than 110 is:

A. 0.975.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given as follows:

[tex]\mu = 98, \sigma = 6[/tex]

The probability is the p-value of Z when X = 110, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{110 - 98}{6}[/tex]

Z = 2

Z = 2 has a p-value of 0.975.

Hence option A is correct.

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Answer:

Below in bold.

Step-by-step explanation:

Standard form is Ax + By = C

where A, B and C are integers  and A must be positive.

So the first 2 are already in standard form but the last 2 can be converted to standard form by multiplying each term by -1:

-12x+3y=27

= -1*-12x + -1*3y = -1*27

12x - 3y = -27   is the answer.

The last one is:

24x + 12y = -60.

Answer:

23 is the answer

If the p-value is smaller than the level of significance, then it indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null hypothesis is correct.

In this question,

A p-value is a probability, calculated after running a statistical test on data and it lies between 0 and 1. The p-value only tells you how likely the data you have observed is occurred under the null hypothesis.

One of the most commonly used p-value is 0.05. If the value is greater than 0.05, the null hypothesis is considered to be true. If the calculated p-value turns out to be less than 0.05, the null hypothesis is considered to be false, or nullified (hence the name null hypothesis).

A small p-value (< 0.05 in general) means that the observed results are unusual, assuming that they were due to chance only. Now, the smaller the p-value, the stronger the evidence that should reject the null hypothesis.

Hence we can conclude that if the p-value is smaller than the level of significance, then it indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null hypothesis is correct.

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Answer:

see explanation

Step-by-step explanation:

3- digit numbers starting with 5 are

528 and 582

3- digit numbers starting with 2 are

258 and 285

3- digit numbers starting with 8 are

825 and 852

there are 6 possible 3- digit numbers

258 , 285 , 528 , 582 , 825 , 852

68 is the wrong number in the sequence 808, 408, 208,108, 68

A number system is defined as a system of writing to express numbers.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The given sequence is 808, 408, 208,108, 68

Eight hundred eight, Four hundred and eight, two hundred and eight, one hundred eight and sixty eight.

808, 408, 208,108, 68

Let us find the difference between the consecutive numbers

400, 200, 100, 40

As we observe the first three terms having the common ratio where as 40 and 100 has different ratio.

Hence, 68 is the wrong number in the sequence 808, 408, 208,108, 68

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The function that represents the number of people at the fair after x hours is f(x) = 68 + 1.5x

What is the function that represent the number of people at the fair?

The function that represents the number of people at the fair is known as a linear function. A linear function is any function that graphs to a straight line. The dependent variable in the linear function increases by a constant number.

Linear functions can be represented by : y = mx + c

Where:

f(x) = 68 + (1.5x)

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[tex]f(1)[/tex] is [tex]81.[/tex]

To find  f(1):

f(n 1) = one-half(n).

f(3) = 9.

[tex]f(3) = 9If n = 1,f(2) = 9×3f(2) = 27If n = 0,f(1) = 27 ×3f(1) = 81[/tex]

A sequence is defined by the recursive function [tex]f(1)[/tex] is [tex]81.[/tex]

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Answer:

36

Step-by-step explanation:

Assuming I understand the question correctly

[tex]\text{one-halff(n)} = \frac{1}{2} f(n)[/tex]

We have the recursive relationship

[tex]f(n+1) = \frac{1}{2} f(n)[/tex]

[tex]f(3) = 9[/tex]

[tex]f(3) = \frac{1}{2} f(2)[/tex]

[tex]f(2) = \frac{1}{2} f(1)[/tex]

So

[tex]f(3) = \frac{1}{2} (\frac{1}{2} f(1) = \frac{1}{4} f(1) \\[/tex]

So [tex]f(1) = 4f(3) = 4(9) = 36[/tex]

Verifying

If f(1) = 36 then f(2) = (1/2)f(1) = (1/2)36 = 18

f(3) = (1/2) f(2) = (1/2)(18) = 9

When measuring variables, it is often preferable to use a small sample size because the smaller the sample the greater the chance of a spurious result.

Therefore, when measuring variables, it is often preferable to use a small sample size because the smaller the sample the greater the chance of a spurious result.

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The length of edge FC in the triangular prism is: 12 cm.

Volume of a right triangular prism = 1/2(Length of triangular base × height of triangular base × height of the prism).

Considering the image given showing a right triangular prism, we have the following:

Volume of triangular prism = 900 cubic centimeters

Length of triangular base = FC = ?

Height of triangular base = 10 centimeters

Height of the prism = 15 centimeters

Plugin the values

900 = 1/2(FC × 10 × 15)

900 = 1/2(FC × 150)

Multiply both sides by 2

2(900) = 2(1/2(FC × 150))

1,800 = FC × 150

Divide both sides by 150

1,800/150 = FC × 150/150

12 = FC

FC = 12 cm

The length of edge FC is: 12 cm.

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Answer: 12

Step-by-step explanation:

The value of x in the equation –x (–1) = 3x (–5) is x = 1

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the equation is given as

–x (–1) = 3x (–5)

Remove the bracket in the above equation

-x - 1 = 3x - 5

Collect the like terms in the above equation

3x + x = 5 - 1

Evaluate the like terms in the above equation

4x = 4

Divide both sides by 4 in the above equation

x = 1

Hence, the value of x in the equation –x (–1) = 3x (–5) is x = 1

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Answer:

-3, or D

Step-by-step explanation:

Based on the given perimeter of the polygon and the length of each side; the length of the longest side of the polygon is 29 cm

Perimeter of the polygon = x + (x + 6) + (x + 5) + (x + 1) + (x + 8) + (x + 4)

150 = x + x + 6 + x + 5 + x + 1 + x + 8 + x + 4

150 = 6x + 24

150 - 24 = 6x

126 = 6x

x = 126/6

x = 21

The longest side of the polygon is (x + 8)

= 21 + 8

= 29 cm

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Answer:

ph : perimeter = 4 sides of the base; p*h = the area of the sides of that prism

B : 2 areas of the base = top and bottom

A right prism consists of a rectangle and two undersides S night prism =

 S rectangle + 2S base

the length of the rectangle is the circumference of the base which is P  so A = ph + 2B

The expression x³+3x² is a cubic unit representation of the prism's volume.

Having 6 faces, 12 edges, and 8 vertices, a right rectangular prism is a three-dimensional object. Angles between the base and sides are right angles in a right rectangular prism. Rectangles make up each of the six faces.

We have provided that to:

In a right rectangular prism, the height is three units more than the base's length.

The square base has edges that are x units long.

How much volume does a rectangular prism have?

Volume of the rectangular prism = width × length × height

V =  W × L × H   ....................(1)

We've indicated that the

bigger by three than the base's length, h

and  the length of the base is x:

Hence,

               H = X +3

          Length of the base = X

           Width = X

Adding the values l h and w to the formula (1) yields,

V = W × L × H

= X × X × (X+3)

= (X²) × (X+3)

= X³ + 3X³

Consequently, the phrase

               X³ + 3X³

represents, in cubic units, the prism's volume.

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Algebraic expressions include both alphabet and number so that the value of the alphabet is to be determined. Thus the steps taken by Tyler are correct if x = 22.

ii. Tyler made no mistake.

Algebraic expressions include both alphabet and number so that the value of the alphabet is to be determined. The value of the alphabet in the expression would be determined by applying mathematical operations appropriately.

To solve the question given to Tyler, we have:

[tex]\sqrt{x + 3}[/tex] = -5

square both sides of the equation to have;

(x + 3) = [tex](-5)^{2}[/tex]

x + 3 = 25

collect like terms to get;

x = 25 - 3

  = 22

x = 22

1. Thus the equation is true if x = 22.

2. Tyler did not make any mistake in solving for x.

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Answer:

Below in bold,

Step-by-step explanation:

a. There's is only one card that fits this description so

Probability = 1/52.

b. There are 2 black Kings so

Probability = 2/52 = 1/26.

c. There are 2 of these - 7 of diamonds and 7 of hearts

so

Probability = 2/52 = 1/26.

d.  There 13 diamonds and 13 hearts so

Probability = 26/52 = 1/2.

e.  There  26 black cards

Probability = 26/52 = 1/2.

The correct powers of x are not displayed in several of the goods.

Algebra tiles are mathematical manipulatives that help pupils better comprehend algebraic thinking and its ideas. These tiles have shown to give beginning algebra pupils in elementary, middle, high, and college concrete models.

Blocks called algebra tiles can be used to symbolize constant, linear, and quadratic terms. Small yellow squares stand in for constant blocks, green rectangles for linear blocks, blue squares for quadratic blocks, and red squares for negative sides for all other types of blocks.

Future:

The image shows,

3x(2x - 1) = 6x² - 3x

This should be the appropriate representation on the tile:

_____+x _____ +x _____ +x

+x _ +x² ______+x² ______+x²

|

+x__ +x² _____ +x² ______+x²

|

- __ -x ______ -x _______-x

+6x² - 3x

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Horizontal asymptote y = 1.

Find the horizontal asymptote of the function:

Horizontal asymptotes are the lines perpendicular to the y-axis and meet the curve at infinity.

Horizontal asymptote y = 1.

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By the comparison test, the series converges.

We have

[tex]\dfrac1{k\sqrt{k+2}} \le \dfrac1{k \sqrt k} = \dfrac1{k^{3/2}}[/tex]

so we can compare to a convergent [tex]p[/tex]-series,

[tex]\displaystyle \sum_{k=1}^\infty \frac1{k\sqrt{k+2}} \le \sum_{k=1}^\infty \frac1{k^{3/2}} < \infty[/tex]

By the comparison test, the series converges.

What are convergence series and diverging series?

If the infinite series converges to a real number it is called converging if not then it is called diverging series.

If the larger series is convergent the smaller series must also be convergent. Likewise, if the smaller series is divergent then the larger series must also be divergent.

For this series to be converging it must follow the following :

⇒ [tex]| \frac{t_{n+1} }{t_{n} } | \leq 1[/tex]

⇒Putting n = 1

[tex]| \frac{t_{2} }{t_{1} } | \leq 1[/tex]

[tex]\t_{2} t_{1}[/tex] [tex]t_{2}[/tex]= 1/4

[tex]t_{1}[/tex]=1/[tex]\sqrt{2}[/tex]

[tex]\frac{t_{2} }{{t_{1} }}[/tex] = 1/2[tex]\sqrt{2[/tex]

⇒ t₂/t₁≤1

⇒ Hence it converges

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[tex]a = \frac{\pi.r {}^{2} }{4} = \frac{3.14 \times 10 {}^{2} }{4} = \frac{3.14 \times 100}{4} [/tex]

[tex]a = 78.5[/tex]

The conceptual and quantative relationship between  Alpha risk and Beta risk is related to the probability of accepting Null hypothesis. They are also known as Type 1 and type 2 error.

Alpha Risk:

Alpha risk is the risk that in statistical test a null hypothesis will be rejected when it is actually true. This is also known as a type I error, or a false positive. The term risk refers to chance or likelihood of making an incorrect decission.

Beta risk:

Beta risk represents the probability that a false hypothesis in a statistical test is accepted as true. Beta risk contrast with alpha risk, which measures the probability that a null hypothesis is rejected when it is actually true.

Determining the type of risk in a quantitative relationship is primarily based on sample size. The Sample Size directly affect the Alpha and Beta risk. If Sample size is larger, the Alpha and Beta risk will lower, and if the sample size is lower the risk of Beta and Alpha increases.

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Answer:

When x is -6, y will be 18

When x is -5 y will be 15

Step-by-step explanation:

Create a proportion

y/x

-9/3 = x/-6  What do we need to multiply 3 by to get 6?  -2, so we will multiply -9 by -2 to get 18

Some people like to solve by cross multiplying.

That would give us

(-9)(-6) = 3x  

54 = 3x  divide both sides by 3

18 = x

Set up the second problem as a proportion

-9/3 = x/-5  This is a little trickier.  I am trying to think what I have to multiply 3 by to get -5.  3(-5/3)  will give me -5, so I will multiply the top number that I know (-9) by (-5/3) to find my x.

(-9)(-5/3) = 45/3  or 15

Answer: 4.5

Step-by-step explanation:

2 + 0.5x

x = 5

2 + 0.5 ( 5 )

2 + 2.5

2 + 2.5 = 4.5

Hope this helps!

The line of best fit for the information in this graph is:

f(x) = 200x + 100.

To find the equation, we need to insert the points (x,y) in the calculator.

For this problem, the points (t,v) are given as follows:

(2, 500), (3, 700), (4, 900), (5, 110)

Hence, inserting these points into a calculator, the equation is given by:

f(x) = 200x + 100.

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Answer:

.....................................

The conjugate which is 3 - √7 is also a root of f(x).

The root of a polynomial function f(x) is the value of x for which f(x) = 0.

Now if a polynomial function has a root x = a + √b then the conjugate of x which is x' = a - √b is also a root of the function, f(x).

Given that the polynomial function, f(x), with rational coefficients has roots

3 + √7, then by the above, the conjugate which is 3 - √7 is also a root of f(x).

So, 3 - √7 is also a root of f(x).

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The equation that represents the  Myra's age given Talat age is as follows:

t = m + 5

Myra is 5 years younger than her sister Talat

Myra age is represented by m while Talat age is represented by t.

Hence,

m = age of Myra

t = age of Talat

Myra is 5 years younger than Talat. This means Talat is 5 years older than Myra.

Therefore, the equation that represents the  Myra's age given Talat age is as follows:

t = m + 5

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Answer:

Step-by-step explanation: