The population of city A is 23.5% of city B and the population of city B is 51% of city C. If city C has 9.89 million people, which of the following is the closest approximation of city A's population in millions?
0.95 million
1.2 million
1.25 million
1.3 million
1.42 million

f(x) = x + 1 is the monic quadratic polynomial used here

Given,

The monic quadratic polynomial f(x)

The remainder when f(x) divided by x - 1 is 2

The remainder when f(x) divided by  x - 3 is 4

We have to find f(x).

Monic Quadratic Polynomial;-

A monic polynomial in algebra is a univariate polynomial with a single variable and a leading coefficient of 1. Its leading coefficient is the highest degree nonzero coefficient.

Here,

The remainder when f(x) divided by x - 1 is 2

Assume f(x) / x - 1 = 1

Then,

f(x) = (x - 1) × 1 + 2

f(x) = x - 1 + 2

f(x) = x + 1

Next,

The remainder when f(x) divided by  x - 3 is 4

Assume f(x) / x - 3 = 1

Then,

f(x) = (x - 3) × 1 + 4

f(x) = x - 3 + 4

f(x) = x + 1

That is,

The monic quadratic polynomial used here is, f(x) = x + 1

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Answer:

5x^2-1x-3

Step-by-step explanation:

First bring the like terms together:

= 3x^2+2x^2+2x-3x-4+1

then solve it

Ans =5x^2-1x-3

I hope its useful

As we can see, the equality is equal for only one value of xx, which was the same as the one we found in part (a).
(a) [tex]x = \frac{L\pi }{4+\pi }[/tex]
(b) True
(c) Yes

What is maximum and minimum?

The smallest value in the data set is the minimum. The largest value in the data set is the maximum.

(a) The circumference of the circle is xx, which means that

[tex]P_ 1= 2\pi r\\x = 2\pi r\\r = \frac{x}{2\pi }[/tex]

The area of the circle is,

[tex]A_c = \pi r^2\\A_c = \frac{x^2}{4\pi }[/tex]

The circumference of the square is L - x, which means

[tex]P_2 = 4a \\L-x=4a\\a = \frac{L-x}{4}[/tex]

The area of the square is,

[tex]A_s = a^2\\A_s=\frac{(L-x)^2}{16}[/tex]

The sum of the areas of the circle and the square is

[tex]A = A_c + A_s\\A = \frac{x^2}{4\pi } +\frac{(L-x)^2}{16} \\A = \frac{4x^2+(L-x)^2\pi \pi }{16\pi } \\A = \frac{4x^2+(L^2 -2Lx+x^2)\pi }{16\pi } \\A = \frac{(4+\pi )x^2-2Lx\pi +L^2\pi }{16\pi }[/tex]

The derivative of the function of the total area is

[tex]A = \frac{4+\pi }{8\pi }x-\frac{L}{8}[/tex]

We solve the equation A'(x) = 0

[tex]\frac{4+\pi }{8\pi }x-\frac{L}{8}=0\\ \frac{4+\pi }{\pi }x=L\\ x = \frac{L\pi }{4+\pi }[/tex]

So, [tex]x = \frac{L\pi }{4+\pi }[/tex] is a critical point A, and it is a global minimum of A since

[tex]A"(x) = \frac{4+\pi }{8\pi } > 0[/tex] for all x.

(b) The area of the circle for [tex]x = \frac{L\pi }{4+\pi }[/tex] is

[tex]A_c = \frac{(\frac{L\pi }{4+\pi } )^2}{4\pi } \\A_c = \frac{(\frac{L^2\pi ^2}{(4+\pi )^2} )}{4\pi } \\A_c= \frac{L^2\pi }{4(4+\pi )^2}[/tex]

The area of the square for [tex]x = \frac{L\pi }{4+\pi }[/tex]  is

[tex]A_s = \frac{(L-\frac{L\pi }{4+\pi } )^2}{16}[/tex]

The ratio of the area is,

[tex]\frac{A_s}{A_c} = \frac{(\frac{(L-\frac{L\pi }{4+\pi })^2 }{16} )}{(\frac{L^2\pi }{4(4+\pi )^2} )}[/tex]

[tex]= \frac{(L - \frac{L\pi }{4+\pi })^2 }{16}*\frac{4(4+\pi )^2}{L^2\pi } \\ = \frac{L^2-\frac{2L^2\pi }{4+\pi }+(\frac{L\pi }{4+\pi } )^2 }{4} *\frac{(4+\pi )^2}{L^2\pi } \\= \frac{(4+\pi)^2 }{4\pi }-\frac{4+\pi }{2}+\frac{\pi }{4}\\ = \frac{4}{\pi }[/tex]

The ratio of the length of wire in the square to the length of wire in the circle for [tex]x = \frac{L\pi }{4+\pi }[/tex]  is

[tex]\frac{L-x}{x} =\frac{L-\frac{L\pi }{4+\pi } }{\frac{L\pi }{4+\pi } } \\= \frac{\frac{4L}{4+\pi } }{\frac{L\pi }{4+\pi } } \\= \frac{4}{\pi }[/tex]

As we can see (1) = (2)

(c) To prove this, we solve the equation

[tex]\frac{A_s}{A_c} = \frac{L-x}{x} \\ \frac{\frac{(L-x)^2}{16} }{\frac{x^2}{4\pi } } = \frac{L-x}{x}\\ \frac{(L-x)^2}{4}*\frac{\pi }{x^2} = \frac{L-x}{x} \\ \frac{L-x}{4} *\frac{\pi }{x} =1\\L\pi -\pi x=4x\\L\pi = (4 + \pi )x\\x = \frac{L\pi }{4+x}[/tex]

As we can see, the equality is equal for only one value of xx, which was the same as the one we found in part (a).

Hence,

(a) [tex]x = \frac{L\pi }{4+\pi }[/tex]

(b) True

(c) Yes

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Elastic demand for a good is defined as when the price of a good rises by 10% while the quantity required falls by 20%.

When a product's price changes, consumer demand is said to be elastic. Consumers will purchase significantly more if the price drops just a little. They won't buy as much if prices increase somewhat instead opting to wait for them to level out.

If all other variables remain constant, the ratio of a product's percent change in demand to its percent change in price determines whether a product's demand is elastic or inelastic.

It is neither elastic nor inelastic for an item's price to alter in proportion to its change in demand. In other words, a product has elastic demand if demand fluctuates more than price does.

Hence, Elastic demand for a good is defined as when the price of a good rises by 10% while the quantity required falls by 20%.

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The missing step was 2x-6+10x= 15+5x, the step where was applied the distributive property.

Applying the distributive property, the given radical expression can be represented by 15.

The properties of multiplication are:

For answering the question, you should solve the given expression step by step. After that, you should identify the missing step from the information given for the question.

The question gives:  2(x-3) + 10x = 5(3 + x), from the distributive property. you have

2x-6+10x= 15+5x     (step 1)

2x -5x +10x = 15+6  (step 2)

7x=21                       (step 3)

x=3                          (step 4)

See that step 1 (2x-6+10x= 15+5x ) is not shown in the question.

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Answer:

they could've walked 4 miles east to make the trip quicker. Would look alot nicer if i had grid paper

Step-by-step explanation:

_ _ _ _

| |

_ _ _ | |

Answer:

2x + 6

Step-by-step explanation:

If the number of months Hassan takes voice lessons is x, and he learns two pieces every month, you would multiply the number of months, x, together with the number of pieces he will learn each month, 2, making 2x.

Hassan already knows how to sing 6 vocal pieces, which you would add to 2x.

That makes 2x + 6.

It is true that in a one-way ANOVA situation, if the overall F value is statistically significant, then you know that all of the means are significantly different from one another.

ANOVA, which represents the analysis of variance, is a statistical test used to examine the distinction between the means of more than two groups.

One independent variable is used in a one-way ANOVA, while two independent variables are used in a two-way ANOVA.

In a one-way ANOVA scenario, the overall F value must be statistically significant for more than two of the means to be significantly different.

thus we can say that the given statement is true.

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Answer:

x = -7

Step-by-step explanation:

4x + 16 = -12   Subtract 16 from both sides

4x = -28  Divide both sides by 4

x = -7

Answer:

x = -7

Step-by-step explanation:

1. Subtract 16 from both sides

4x + 16 = -12

4x + 16 - 16 = -12 -16

2. Simplify

Subtract the numbers:

4x + 16 - 16 = -12 - 16

4x = -12 - 16

Subtract the numbers:

4x = -12 - 16

4x = -28

3. Divide both sides by the same factor

4x = -28

[tex]\frac{4x}{4}[/tex] = [tex]\frac{-28}{4}[/tex]

4. Simplify

Cancel terms that are in both the numerator and denominator:

[tex]\frac{4x}{4}[/tex] = [tex]\frac{-28}{4}[/tex]

x = [tex]\frac{-28}{4}[/tex]

Divide the numbers:

x = [tex]\frac{-28}{4}[/tex]

x = -7

Solution:

x = -7

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Answer:

Option 3 (Parentheses, division, multiplication, subtraction)

Step-by-step explanation:

Using PEMDAS, we can know that we need to solve the parentheses first. Next, we need to solve the multiplication and division, so we can eliminate the first option and last option. However, we need to solve the operations left to right, meaning we'd solve the division first. Therefore, the answer is option 3.

Answer:

The answer is Parentheses multiplication division subtraction

Step-by-step explanation:

Always remember

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Answer:

1st blank = 6x

2nd blank = 12

3rd blank = 2

4th blank = 2

5th blank = 8

6th blank = 5

Answer:

17

Step-by-step explanation:

I hope this helps!!!

3/4 3/4 3/4 3/4= 3 hours

3 hours equals 4 shifts

you do this 4 times and it equals 12 hours, and 16 . Then you have 3/4 left which equals a shift. So 16+1=17

A. There is enough data to conclude that the average one-time gift giving exceeds $75. with a 5% loss

B. The probability of receiving a sample mean one-time gift donation of $80 or more is the p-value.

What is a p-value?

The p-value, under the assumption that the null hypothesis is true, is the likelihood of receiving findings from a statistical hypothesis test that are at least as severe as the observed results. The p-value provides the minimal level of significance at which the null hypothesis would be rejected as an alternative to rejection points. The alternative hypothesis is more likely to be supported by greater evidence when the p-value is lower.

P-value is frequently utilized by government organizations to increase the credibility of their research or reports. The United States Census Bureau, for instance, mandates that any analysis with a p-value higher than 0.10 be accompanied by a statement stating that the difference is not statistically significant from zero.

A)

One wants to determine whether there is any proof that the average one-time gift giving exceeds $75.

The right response is thus E, i.e. E. H0:75 Vs H1:>75

Track down the test statistic.

n=54(sample size) (sample size)

Observed mean: 80

Observed standard deviation: 12

valid value=75

test statistic = (12[tex]\sqrt54[/tex])/(80-75)=3.06

Get the p-value by using the R-command shown below:

Lower. Tail=FALSE, p norm (3.06, 0, 1)

There is a 0.001 p-value.

What is the result of this experiment?

At a 5% threshold of significance, we reject H0 since the p-value is less than 0.05. (Los).

A. Dismiss the null theory. There is enough data to conclude that the average one-time gift giving exceeds $75. with a 5% loss

B)

In this situation, explain what the p-value means.

Take into account that the sample mean (Xbar) has a mean of 75 and a standard deviation of 12[tex]\sqrt54[/tex].

The chance that (Xbar) is larger than 80 is then equal to the p-value that was determined before.

The probability of receiving a sample mean one-time gift donation of $80 or more, given that the population mean one-time gift donation is $75, is represented by the p-value, which is B.

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The second number used by Ameekah to represent the consecutive integers is (x + 1).

Let 'x' be the first number written by Ameekah.

Then, the second number will be obtained by adding one to first number.

= x + 1

Thus, the second number used by Ameekah to represent the consecutive integers is (x + 1).

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Answer:

"B" is correct, "x + 1"

Step-by-step explanation:

Have a Jocular Day

the probability that a randomly selected set of 2 will include 1 a and 1 b is 35/66

The probability is equal to the variety of possible outcomes. the total number of outcomes that could occur. For instance, there is only one way to get a head and there are a total of two possible outcomes, so the probability of flipping a coin and getting heads is 1 in 2. Writing P(heads) = 12

Classical

Empirical

Subjective.

Axiomatic

There are 66 equally likely outcomes, or C(5+7,2) =C(12,2)=66 possible outcomes. Only C(5,1)*C(7,1)=35 of these contain 1A and 1B. thus, the likelihood is 35/66.

The value of the solution is 35/66

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Answer: 8

Step-by-step explanation: 16/2 is simply 16 ÷ 2 in fraction form,

16 ÷ 2 = 8

The maximum area to enclose a rectangular pasture with one side of the pasture up against a river is equal to 500,000 square feet.

As given in the question,

Let 'x' represents the length of the rectangular pasture

And 'y' represents the width of the rectangular pasture

Condition:

One side of the pasture is up against a river

Perimeter of the rectangular pasture with one side up against river

= x + 2y

⇒ 2000 = x + 2y

⇒x= 2000 - 2y

Area of the rectangular pasture

=( 2000 - 2y )( y )

= - 2 ( y² - 1000y)

= -2( y² - 1000y + 250000 - 250000 )

= -2 (y - 500 )² + 500, 000

Maximum area is at y = 500

Maximum area is 500,000

Therefore, the maximum area of the given rectangular pasture is 500,000 square pasture.

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Yes, if Trapezoid abcd has vertices a(2, 4), b(5, 4), c(7, 1), and d(0, 1) , ABCD is an isosceles trapezoid.

Since, If in a trapezoid two opposite nonparallel sides are equal then it is called isosceles trapezoid.

In trapezoid ABCD sides are AB, BC, CD and DA.

According to the question,  A≡(2,4) B≡(5,4) C≡(7,1) and D≡(0,1)

After making the diagram of ABCD, we found that DA and BC are nonparallel sides.

And, by the distance formula BC = √((7 - 5)² + (1 - 4)²) =

⇒ BC =√(4 + 9)

⇒BC = √13 unit.

Similarly, DA = √((0 - 2)² + (1 - 4)²)

DA  = √(4 + 9)

⇒ DA  = √13 unit.

Thus, In trapezoid ABCD, two non parallel sides BC and DA are equal.

Therefore, trapezoid ABCD is a isosceles trapezoid.

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The amount of ham Ms.D  has left is [tex]6\frac{3}{4}[/tex] pounds.

Ms.D bought [tex]8\frac{1}{2}[/tex] pounds of ham from Excellente Hambaked Shop.  She gave [tex]1\frac{3}{4}[/tex] pounds of ham to Mr.Chavir. The number of pounds of ham she has left can be calculated as follows:

Hence, the amount of hams in pounds she has left is the difference between what she had and the amount of pounds of hams she gave to Mr Chavir.

Therefore,

Amount bought by Ms.D  = [tex]8\frac{1}{2}[/tex] pounds

Amount given to Mr.Chavir.  = [tex]1\frac{3}{4}[/tex] pounds

Therefore,

Amount of she has left = [tex]8\frac{1}{2}[/tex] - [tex]1\frac{3}{4}[/tex]

Amount of she has left = [tex]\frac{17}{2} - \frac{7}{4}[/tex]

Amount of she has left = [tex]\frac{34-7}{4}[/tex]

Amount of she has left = [tex]\frac{27}{4}[/tex]

Amount of she has left = [tex]6\frac{3}{4}[/tex] pounds

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When a linear transformation is done to a nonzero vector in linear algebra, the vector is said to have an eigenvector, or characteristic vector, which only changes by a scalar amount. The scaling factor for the eigenvector is the appropriate eigenvalue, frequently represented as lambda.

When a linear transformation is done to a nonzero vector in linear algebra, the vector is said to have an eigenvector, or characteristic vector, which only changes by a scalar amount. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by.

Hence, characteristic polynomial of A and A^T are the same, therefore their eigenvalues are also same.

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The measure of an angle ∠TQU is 26.6° if  PQ=3 and QR=4

In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. These are referred to as dihedral angles. An angle can also be defined by two intersecting curves, which is the angle of the rays lying tangent to the respective curves at their point of intersection.

Angle can also refer to a rotation or the measurement of an angle. This measurement is the ratio of the length of a circular arc to its radius.

Given,

Rectangle PQRS has PQ=3 and QR=4

The points T and U are on side PS such that PT=US=1

As PQRS is rectangle so opposite sides of rectangle should be equal.

PS=QR and PQ=RS

QR=4, PS=4

But, PS=PT+TU+US

4=1+TU+1

TU=4-2

TU=2

And PU=PT+TU

1+2=3

PU=3

Consider, ΔQPU, Right angled at P.

We know that,

tan Q=PU/PQ

tan Q=3/3

tan Q=1

Q=tan⁻¹

Q=45°

∠PQU=45°

Now, let us consider ΔQPT is right angled at P

tan Q=PT/PQ

tan Q=1/3

Q= tan⁻¹(1/3)

Q=18.43°

∠PQT=18.43°

∠PQU=∠PQT+∠TQU

45°=18.43°+∠TQU

∠TQU=45°-18.43°

∠TQU=26.57°

∠TQU≈26.6°

Therefore, the measure of ∠TQU is 26.6°.

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Answer: -2

Step-by-step explanation:

(x - 5) (x + 2) = 0

(x - 5) = 0

(x - 2) = 0

Add 5 to both sides, then simplify. After that, you will subtract 2 from both sides. Simplify again, and the solution is -2.

Answer:

8

Step-by-step explanation:

Josh is 6 years older than 5 times Kim's age. The sum of their ages is less than 54. What is the oldest Kim could be?

J + k < 54 when  J = 5k + 6 so:

5k + 6  + k < 54

6k + 6 < 54

subtract 6 from both sides:

6k + 6 - 6 < 54 - 6

6k < 48

divide both sides by 6:

6k/6 < 48/6

k < 8

Kim could be 8 at maximum.

The required confidence interval for the difference of means is (-18.52, -13.48).

Statisticians use  confidence intervals to gauge vulnerability in an example variable. For instance, a scientist chooses various examples haphazardly from a similar populace and registers a certainty span so that each example might be able to perceive how it might address the genuine worth of the populace variable. The subsequent datasets are different where a few stretches incorporate the genuine populace boundary and others don't.

[tex]n_{a}[/tex] = 18 represent the sample of A

[tex]n_{b}[/tex] = 18 represent the sample of B

μₐ = 39 represent the mean sample  for A

μᵇ =  represent the mean sample for B  

σ = 9 represent the sample deviation for A

σ = 6 represent the sample deviation for B

α = 0.01 represent the significance level

Confidence =99% or 0.99

confidence interval for the difference of means is given by the following formula,

μₐ - μᵇ± [tex]t_{\frac{α}{2}}[/tex][tex]\sqrt{\frac{S_{a}}{n_{a}} +\frac{S_{b}}{n_{b}} }[/tex]

39 - 55 ± 2.756[tex]\sqrt{\frac{9}{18} +\frac{6}{18} }[/tex]

-16 - 2.756(0.912) =  -18.52

-16 + 2.756(0.912) = -13.48

Thus, required confidence interval is (-18.52, -13.48).

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The rule with describes the expression 8,4,10,6,12,8,14 is the alternating numbers gets increased by 2

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the expression be represented as A

Now , the expression A is

A = 8,4,10,6,12,8,14

Taking out the alternate numbers from the expression A , we get

A₁ = 8 , 10 , 12 , 14

So ,the values of A₁ increases by 2

And ,Taking out the alternate numbers from the expression A , we get

A₂ = 4 , 6 , 8 , 10

So , the values of A₂ also increases by 2

Hence , the alternating numbers in the expression increases by 2

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Answer:

B. Falls

Step-by-step explanation:

The likelihood that a player will score more than 24 points in a randomly chosen game is 0.0013 or 0.13%.

To compute the probability for the a data point, we must first get the value's z-score.

Mean = μ = 15 points

SD = σ = 3 points

When calculating the likelihood that a score will be higher than 24, the z-score for 24 is:

z-score = (x-μ)/σ

z = (24-15)/3

z = 9/3

z = 3

The chance of z3 must now be determined using the z-score table, and it will be deducted from 1 to determine the likelihood of z>3.

P(z < 3) = 0.9987

P(z > 3) = 1 - P(z < 3)

P(z > 3) = 1 - 0.9987

P(z > 3) = 0.0013 = 13%

Thus, the probability that a player will score more than 24 points in a randomly chosen game is 0.0013 or 0.13%.

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Answer:

11. (-4, 5)

12. (0, 2)

Step-by-step explanation:

The solution from the graph is to determine the point of intersection of the two rays. And find the x and y values corresponding to that point.

In 11, the point of intersection is at x = -4, y =5

In 12, the point of intersection is at x = 0, y = 2

I am not clear on what they want you to do for checking the solution. You could mathematically solve for the set of equations.

I think what they mean is to check if your reading of the point coordinates from the graph is correct.
In which case just plug in the values of x and y into both equations in each problem and find if they are consistent

Let's take Problem 12 which has a solution of x = 0, y = 2

Plug in these values into each of the equations:

For 2x - y = -2, with x = 0, y = 2
2(0) - 2 = 0 - 2 = -2 so consistent

For 2x + 4y = 8
2(0) + 4(2) = 0 + 8 = 8

So both equations are consistent with the values read off the graph.

Use the same technique for the others

Hope that helps

The number of gallons that can be filled is 18 gallons.

Rate demonstrates how many times one number can fit into another number. It contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

In this case, the number of hours in 3 days will be:

= 24 × 3

= 72 hours.

Since the leaky faucet is losing water and is filling a 5-gallon bucket every 20 hours. The gallon filled in 72 hours will be represented by x.

5/20 = x/72

Cross multiply

20x = 72 × 5

20x = 360

x = 360/20

x = 18

There'll be 18 gallons

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