When the polynomial P(x) = x3
+ 3x2
– 2Ax + 3,
where A is constant, is divided by x2
+ 1 and
remainder is –5x, then A is

After set s1.removeAll(s2), s1 is [1, 5].

After performing the operation s1.removeAll(s2) on sets s1 [1, 2, 5] and s2 [2, 3, 6], the set s1 would become [1, 5].

To determine the value of s1, the following steps has to be taken:

1. We have set s1 with elements [1, 2, 5] and set s2 with elements [2, 3, 6].
2. The removeAll() function is called on s1 with s2 as the argument: s1.removeAll(s2).
3. The removeAll() function will remove all elements from s1 that are also present in s2.
4. In our case, the number 2 is present in both sets, so it will be removed from s1.
5. After the operation, s1 will only contain the elements [1, 5].

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Step-by-step explanation:

[tex] \frac{r - p}{7} = s \\ cross \: multiply \\ 7s = r - p \\ \: \: move \: the \: variable \: to \: the \: \\ right \\ - p = 7s - r \\ change \: the \: signs \\ p = - 7s + r \\ p = r - 7s[/tex]

Answer:

p= -7S+r

Step-by-step explanation:

p=-7S+r ( gotta write at least 20 characters)

Step-by-step explanation:

The Key shows that 4 squares equals 8 games....so each single square is TWo games

tuesday = 22

wed = 10 games

Answer:

at all 32 or tue 22 and wed 10

Step-by-step explanation:

one equal 4 times separated square(quartered square) equals 8 video games then one part will be 2 because 8 divided by 4 is 2. back to the question,do it by your self

Answer:

First, we need to find the radius of the cylinder. We know that:

V = πr^2h

And we are given that V = 1,130.97 cubic inches. We also know that a cylinder is symmetrical, which means that the height of the cylinder is equal to the diameter of the circle. In other words, h = 2r.

Therefore, we can rewrite the formula as:

V = πr^2(2r)

1,130.97 = πr^3

r^3 = 359.82

r = 7.12 inches (rounded to two decimal places)

Now we need to find the amount of space on either side of the cylinder. We know that the pedestal is 18 inches across, so the total width is 18 inches. If we want an even amount of space on either side, we need to subtract the diameter of the cylinder from the width of the pedestal, and then divide the result by two.

Diameter = 2r = 2(7.12) = 14.24 inches

Space on either side = (18 - 14.24)/2 = 1.88 inches (rounded to two decimal places)

Therefore, if Consuela places the cylinder on a pedestal that is 18 inches across, there will be 1.88 inches of space on either side.

Answer:

y-intercept = (0,0)

x-intercepts (0,0), (-2, 0)

Step-by-step explanation:

For y-intercept

If you think about a graph, when does the graph intercept/hit y.   What is your value for x.   Your y-intercept is usually (0, y)   So in order to find the y-intercept you need to plug in x=0 to find y.

Equation:

y=16x²+32x       substitute x=0

y=16(0)²+32(0)

y=0

y-intercept = (0,0)

For x-intercept

When you have an x intercept it looks like (x, 0), so you must solve for x when y=0

Because this is a quadratic equation(parabola), you will get 2 x-intercepts.

y=16x²+32x

0=16x²+32x      > In order to solver for x, you must factor but in this case

                            you can take out the greatest common factor (GCF) =16x

0=16x(x +2)       >Typically when you factor you get 2 parentheses and set

                            each parenthesis equal to 0, but instead we've pulled

                            an x on the outside.  When there is an x outside you set

                            the outside equal to 0 as well as the parenthesis to

                            solve for x.

16x = 0                 (x+2)=0

x=0                           x= -2

x-intercepts (0,0), (-2, 0)

5.48% of the people in line waited for more than 28 minutes

Problems of normal distributions can be solved using the z-score formula.

In a set with mean  and standard deviation , the z-score of a measure X

Given Mean waiting time of 20 minutes with a standard deviation of 5 minutes.

This means that percentage of the people in line waited for more than 28 minutes.

The proportion is 1 subtracted by the p-value of Z when X = 28. So

Z = 1.6

This has a p-value of 0.9452.

1 - 0.9452 = 0.0548.

As a percentage,

0.0548*100% = 5.48%

Thus 5.48% of the people in line waited for more than 28 minutes

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The economic changes brought about by "rail-roads" are (a) Land prices rose and more land became available to settlers, (b) Copper mining developed as new technologies emerged, and (c) Transportation improved to bring the copper to market, So, correct option is (d).

The railroads brought about significant economic changes in several ways;

Option (a) : Land-prices rose and more land became available to settlers due to the expansion of railroads, making transportation faster, cheaper, and more reliable, thus leading to the settlement and development of previously unsettled or underdeveloped areas.

Option (b) : Copper mining developed as new technologies emerged, including steam-powered drills and machinery, which were made possible by the availability of rail transportation.

Option (c) : Transportation improved to bring the copper to market more quickly and efficiently than previously available methods, contributing to the growth of copper mining as a major industry.

Since, all are correct, the correct option is (d).

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The given question is incomplete, the complete question is

Select the economic changes brought about by the railroads.

(a) Land prices rose and more land became available to settlers.

(b) Copper mining developed as new technologies emerged

(c) Transportation improved to bring the copper to market

(d) All the options are correct.

Answer:

y = -8x

Step-by-step explanation:

-2-6 = -8

the slope was -2 that decreased by 6 would be -8.

Helping in the name of Jesus.

Answer:

2/3

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

A situation that could follow a binomial distribution is the number of heads that occur when flipping a "fair-coin" multiple times.

A "Binomial-Distribution" is defined as a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success.

In this case, flipping a "fair-coin" is an independent trial with two possible outcomes (heads or tails), and the probability of getting a heads on any given flip is 0.5.

Each "coin-flip" is independent of the others, and the probability of getting a heads on any given flip is always the same which is "0.5",

So, this situation fits the requirements for a binomial distribution.

The "binomial-distribution" can then be used to calculate the probability of getting a certain number of heads out of a fixed number of flips. For example, if we flip a coin 10 times, the probability of getting exactly-5 heads can be calculated using the binomial distribution formula.

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Answer:

0

Step-by-step explanation:

The limit of a sequence is the value that its terms approach.

We can present the limit of the terms in the sequence as:

[tex]\lim_{n \to \infty}\dfrac{1}{n^n}[/tex]

To evaluate this limit, we can plug infinity (the value that n is approaching) into the expression:

[tex]\lim_{n \to \infty}\dfrac{1}{n^n}[/tex]

[tex]= \dfrac{1}{\infty^\infty}[/tex]

We know that infinity to any positive power is still infinity. So, this expression simplifies to:

[tex]= \dfrac{1}{\infty}[/tex]

Any real number, no matter how large, is inconsequential (infinitely small) compared to infinity. Therefore, this expression evaluates to 0:

[tex]= 0[/tex]

So, the limit of the sequence [tex]\sum_{n=1}^{\infty} \dfrac{1}{n^n}[/tex] is 0.

__

Note: You could also deduce the limit of this sequence by plugging in larger and larger numbers:

[tex]\begin{array}{c | c | c}n & \text{seq. term} & \text{decimal} \\\cline{1-3} 2 & 1/4 & 0.25 \\3 & 1/81 & 0.012\\4 & 1/256 & 0.0039 \\5 & 1/3125 & 0.00032 \\... & ... & ... \\\infty & 1/\infty & 0\end{array}[/tex]

The probability that the Yankees will win when they score fewer than 5 runs is about 0.102.

Let A be the event that the Yankees win, and let B be the event that the Yankees score 5 or more runs. We know that;

P(A) = 0.53

P(B) = 0.51

P(A and B) = 0.43

We want to find the probability that the Yankees win when they score fewer than 5 runs. This can be expressed as;

P(A and not B)

We can use the formula;

P(A and B)=P(B | A) × P(A)

to find;

P(B | A) = P(A and B) / P(A)

= 0.43 / 0.53

≈ 0.811

This means that given the Yankees win a game, the probability that they score 5 or more runs is about 0.811. Therefore, the probability that they win when they score fewer than 5 runs is;

P(A and not B) = P(A) - P(A and B)

= 0.53 - (0.811 × 0.53)

≈ 0.102

Therefore, the probability that the Yankees will win is 0.102.

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The correct answer is A) 72÷14.

Divide the total number of cups of trail mix by the recommended serving size to determine how many servings are contained in the bag.

As a result, the expression that may be utilized is:

A) 72÷14

This expression represents dividing the total number of cups (312) by the suggested serving size (14):

312 ÷ 14 = 22.29

27 × 14

By multiplying the number of servings (27) by the recommended serving size (14), this expression shows the total number of cups. We are not informed of the bag's serving size.

72 × 14

By multiplying the number of servings (72) by the recommended serving size (14), this expression shows the total number of cups. We are not informed of the bag's serving size.

However, since we cannot have a fraction of a serving, the final result must be rounded to the nearest whole number:

22 portions

Therefore, the correct answer is A) 72÷14.

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Answer:

276

Step-by-step explanation:

let x = the number

(2/3)x - 70 = 45 + (1/4)x

2/3x - 1/4x = 45 + 70

8/12x - 3/12x = 115

5/12x = 115

x = 115(12/5) = 276

Double check the answer:

(2/3()276) - 70 = 45 + (1/4)(276)

114 = 114    answer is correct!

Answer:

Dear Kindergarten students,

Today, I am here to talk to you about place value and why it is important. Place value is the concept of understanding the value of a digit based on its position in a number. In other words, the position of a digit determines its value.

Let's take the number 123 for example. The digit 1 is in the hundreds place, the digit 2 is in the tens place, and the digit 3 is in the ones place. This means that 1 represents one hundred, 2 represents twenty, and 3 represents three. So when we put these digits together, we get the number 123.

Understanding place value is important because it helps us to read, write, and compare numbers. It also helps us to perform mathematical operations such as addition and subtraction more easily.

For instance, if we want to add two numbers such as 23 and 45, we need to line up the digits based on their place value. The ones place goes under the ones place, and the tens place goes under the tens place. Then we can add each column separately to get our answer of 68.

In summary, understanding place value is essential for working with numbers and performing mathematical operations accurately.

Thank you for listening!

Step-by-step explanation:

That what I would say

The five number summary used to construct the box plot are

The interquartile range is 25

Statistical data based on the minimum, first quartile, median, third quartile, and maximum are shown graphically in a box plot.

The numbers are defined as follows

The interquartile range is

= top quartile - bottom quartile

= 120 - 95

= 25

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Answer:

8

Step-by-step explanation:

8*10+142=222

22*8+46=222

The total value of the investment after 20 years with continuous compounding is $2,917.76.

Given information:

P = principal = $1000.

R = 5.5%

t = 20 years.

First, convert R as a percent to 'r' as a decimal

r = R/100

r = 5.5/100

r = 0.055 rates per year,

Then solve the equation for A:

The total value of the investment can be calculated using the formula:

A = P(1 + r/n[tex])^{nt}[/tex]

A = 1,000.00(1 + 0.055/1[tex])^{(1)(20)}[/tex]

A = 1,000.00(1 + 0.055[tex])^{(20)}[/tex]

A = $2,917.76

The total amount accrued, principal plus interest, with compound interest on a principal of $1,000.00 at a rate of 5.5% per year compounded 1 time per year over 20 years is $2,917.76.

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Based on the survey data, we can conclude that a higher proportion of teenagers own an iPod or MP3 player compared to young adults.

To determine if the difference is significant, we need to conduct a hypothesis test. We can begin by stating the null hypothesis as "there is no significant difference in the proportion of all teens and young adults who would say they own an iPod or MP3 player."

We can also state the alternative hypothesis as "there is a significant difference in the proportion of all teens and young adults who would say they own an iPod or MP3 player."

Next, we need to determine the test statistic and calculate the p-value to determine if the difference in the proportions is statistically significant. Assuming that the data follows a normal distribution, we can use a two-sample z-test to test our hypothesis.

Using a significance level of 0.05, we find that the test statistic is 3.07, and the p-value is 0.002. Since the p-value is less than the significance level, we can reject the null hypothesis and conclude that there is convincing evidence of a difference in the proportions of all teens and young adults who would say they own an iPod or MP3 player.

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First solve for the slope, m using the two points given. It doesn't matter which point you choose as point 1 or 2 as long as you're consistent.

m = (y2 - y1)/(x2 - x1)

point 1: (6.4, 2.6)

point 2:  (5.2, 9)

m = (9 + 2.6)/(5.2 + 6.4)

m = (9 + 2.6)/(5.2 + 6.4)

m = 11.6/11.6

m = 1

put the newly found slope into the linear equation for m

y = (1)x + b

y = x + b

Now solve for the y-intercept, b

by putting one of the given points

9 = 5.2 + b

b = 9 - 5.2

b = 3.8

final equation:

y = x + 3.8

To find the quotient of whole number divided by a unit fraction the steps are discussed below.

We have to divide a whole number by a unit fraction.

let the whole number be 10 and fraction is 1/2.

So, division is

= 10 / (1/2)

Now, Reciprocate the fraction in the denominator as

= 10 x 2/1

= 20

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In a series circuit, charges follow a single path, meaning that they flow through each component of the circuit one after another.

What is series circuit?

A series circuit is an electric circuit in which the components (such as resistors, capacitors, and inductors) are connected in a single path so that the current flows through each component in turn without branching off.

In a series circuit, charges follow a single path, meaning that they flow through each component of the circuit one after another. This means that the current passing through each component is the same, and the voltage is split between the components. If one component fails, the circuit is broken, and no current can flow.

In contrast, in a parallel circuit, charges have multiple paths to flow through. The current splits up and passes through each path independently, meaning that the current through each component is not necessarily the same.

The voltage across each component is the same, and the total current is the sum of the current through each path. If one component fails, the current can still flow through the other paths, and the circuit remains complete.

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Answer:

D. 15

Step-by-step explanation:

Use the Fundamental Theorem of Calculus to solve this problem. Since f(x) is the derivative of 1/3 x^3 - 2x^2 + 3x - 5, you have:

f(x) = d/dx (1/3 x^3 - 2x^2 + 3x - 5) = x^2 - 4x + 3

To find f(-2), you substitute x = -2 into the expression for f(x):

f(-2) = (-2)^2 - 4(-2) + 3 = 4 + 8 + 3 = 15

By Unitary method, 3 gallons = 12 quarts

We know that the  the unit conversion,

one liquid gallons is equals to the four liquid quarts

i.e., 1 gallon = 4 quarts

We need to find the 3 gallons to quarts.

Let us assume that x represents the required amount of liquid quarts.

By Unitary method,

⇒ x = 3 × 4

⇒ x = 12 quarts of liquid

Therefore, the unit conversion 3 gallons equals to 12 quarts.

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The simplification of the given expression is:

[tex]\sqrt[3]{\frac{6c}{-125} } = -\frac{\sqrt[3]{6c} }{5}[/tex]

Here we have an expression with a cube root:

[tex]\sqrt[3]{\frac{6c}{-125} }[/tex]

We can distribute the cube root over the fraction, then we will get:

[tex]\sqrt[3]{\frac{6c}{-125} } = \frac{\sqrt[3]{6c} }{\sqrt[3]{-125} } = \frac{\sqrt[3]{6c} }{-5}[/tex]

That is the expression simplified.

We can't keep simplifying this, because 6 is not a perfect cube and c is just a variable.

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Answer: The value of the expression 1/7 divided by 5 is,

⇒ 1 / 35

Step-by-step explanation:

What is the Division method?

The division method is used to distribute a group of things into equal parts. The division is just the opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

The expression is,

⇒ 1/7 divided by 5

Now, We can simplify as;

⇒ 1/7 divided by 5

⇒ 1 / 7 ÷ 5

⇒ 1 / 7×5

⇒ 1 / 35

Thus, The value of the expression 1/7 divided by 5 is,

⇒ 1 / 35

Answer:

The answer as follows

Step-by-step explanation:

Part I:

The graph of f(x) is a parabola with its vertex at the origin, opening upward.

To graph g(x), we can start by shifting f(x) 3 units to the right and 2 units up, according to the equation g(x) = (x - 3)² + 2. This means that the vertex of g(x) will be at the point (3, 2).

We can create a table of values for g(x) to plot some points and draw the graph:

| x  | g(x) |

|----|------|

| 0  | 11   |

| 1  | 8    |

| 2  | 5    |

| 3  | 2    |

| 4  | 5    |

| 5  | 8    |

| 6  | 11   |

Using these points, we can draw the graph of g(x) as a parabola that has the same shape as f(x), but is shifted to the right by 3 units and up by 2 units:

Part II:

The graph of g(x) is the graph of its parent function, f(x), shifted 3 units to the right and 2 units up. This means that every point on the graph of g(x) is 3 units to the right and 2 units up from the corresponding point on the graph of f(x).

In other words, the transformation that was applied to f(x) to get g(x) is a horizontal shift to the right by 3 units and a vertical shift up by 2 units. This is reflected in the equation g(x) = (x - 3)² + 2.

The area of the shaded segement is approximately 1.68 square inches.

The complete question is:

What is the area of the shaded segment shown in O below?

Hints:

Area of shaded segment = Area of sector - Area of triangle

Area of sector = (θ/360) × πr²

Area triangle = 1/2 × b × c × sin(A)

Given that;

Area of segment = Area of sector - Area of triangle.

Area of sector = (θ/360) × πr²

Area triangle = 1/2 × b × c × sin(A)

From the diagram:

Plug the values into the above formula and simplify.

Area of segment = Area of sector - Area of triangle.

Area of segment = ( (θ/360) × πr² ) - ( 1/2 × b × c × sin(A) )

Area of segment = ( (30/360) × 3.14 × 12² ) - ( 1/2 × 12 × 12 × sin(30) )

Simplify

Area of segment = 37.68 - 36

Area of segment = 1.68 in²

Therefore, the area of the segment is 1.68 in².

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