Let a,b,c and d be distinct real numbers. Showthat the equation(x − b)(x − c)(x −d) + (x − a)(x −c)(x − d) + (x −a)(x − b)(x − d) +(x − a)(x − b)(x −

Answer:

$600

Step-by-step explanation:

90/0.15

Answer:

g(f(x)) = 6x - 14

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

g(x) = 3x + 1

f(x) = 2x - 5

Step 2: Find

Answer:

A, they are skew

Step-by-step explanation:

Skew means that they are not perpendicular and they are not parallel.

Sorry if it turns out wrong.

Answer: 10

Step-by-step explanation: I got this correct on Edmentum.

The probability that an endure all battery selected at random will last more than 610 hours is 0.3%

What is the Z score?

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. If a Z-score is 0, it indicates that the data point's score is identical to the mean score.

Z score is used to determine by how many standard deviations the raw score is above or below the mean, The z score is given by:

\(z = \frac{x - \mu}{\sigma}\)

where,

x = raw score

μ = mean

σ = standard deviation

Given that μ = 500, σ = 40, for x > 610:

z = (610 - 500) / 40

= 2.75

From the normal distribution table, P(z > 2.75) = 1 - P(z < 2.75) = 1 - 0.9970 = 0.0030 = 0.3%

Hence, the probability that an endure all battery selected at random will last more than 610 hours is 0.3%

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Answer:

C

Step-by-step explanation:

Answer:

C) There are infinitely many solutions since -5=-5 is a true statement.

Step-by-step explanation:

In a Quadratic equation 4x² - 13x + k = 0 , one root of this equation is 12 times more than the another root. Find the value of k.

One root of quadratic equation is 12 times more than the another root.

Let , the one root of the quadratic equation is m and the another is n then according to the Question ,

Given quadratic equation is 4x² - 13x + k = 0

\(\begin{gathered} \star \sf \: a = 4 \\ \\ \star \sf \: b = - 13 \\ \\ \star \sf \: c = k\end{gathered}\)

\(\sf \: sum \: of \: roots = - \dfrac{b}{a}\)

So,

\(\begin{gathered} \star \sf \: m + n = - \frac{( - 13)}{4} \\ \\ \sf \: substituting \: the \: value \: of \: n \: from \: equation \: (i) \\ \\ \mapsto \sf \: m + 12m = \frac{13}{4} \\ \\ \mapsto \sf \: 13m = \frac{13}{4} \\ \\ \mapsto \sf m = \frac{13}{4 \times 13} \\ \\ \mapsto \boxed{ \sf m = \frac{1}{4} }\end{gathered}\)

\(\begin{gathered} \sf \star \: n = 12m \\ \\ \mapsto \sf \: n = 12 \times \frac{1}{4} \\ \\ \mapsto \boxed{\sf n = 3}\end{gathered}\)

Now, we know that :-

\(\sf \: product \: of \: roots = \dfrac{c}{a}\)

So,

\(\begin{gathered} \star \sf \: m \times n = \frac{k}{4} \\ \\ \mapsto \sf \frac{1}{4} \times 3 = \frac{k}{4} \\ \\ \mapsto \sf k = \frac{1}{4} \times 4 \times 3 \\ \\ \mapsto \boxed{\sf k = 3 }\end{gathered}\)

Answer:

A one tailed test

Step-by-step explanation:

Chi-Square Distributions That Are Positively Skewed Have A Research Hypothesis That Is A One-Tailed Test.

Chi-Square distributions are positively skewed, with the degree of skew decreasing with increasing degrees of freedom.

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One-Tailed Test

Chi-Square distributions that are positively skewed have a research hypothesis that is a One-Tailed Test.

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The only value of c that satisfies the initial condition g(2) = 5 is c = -3.

The graph of a function f consists of three line segments, with points (1,2), (2,3), and (3,4).

An antiderivative of f is a function g such that g'(x) = f(x). That is, g is the "opposite" of the derivative of f. The values of c in an antiderivative g(x) = f(x) + c are determined by the initial condition g(2) = 5, since g'(2) = f(2) = 3.

So, in order to determine the value of c, we need to integrate f(x) and find the value of g(2). The integral of f(x) is

g(x) = x² + 2x + c

Substituting x = 2 into this equation, we get

g(2) = 4 + 4 + c = 8 + c

Now, since g(2) = 5, we can solve for c:

5 = 8 + c

c = -3

Therefore, the only value of c that satisfies the initial condition g(2) = 5 is c = -3.

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The insurance company expects the interest rate to be around 4.16%.

To find the expected interest rate, we can use the formula for present value of an annuity:

PV = PMT x (1 - (1 + r)^(-n)) / r

Where:

PV = present value of the annuity, which is the amount the insurance company needs to deposit

PMT = payment per period, which is $45,000

r = interest rate per period, which is what we need to find

n = total number of periods, which is unknown

We know that the insurance company needs to deposit $2,500,000 to make the payments, so we can set:

PV = $2,500,000:

$2,500,000 = $45,000 x (1 - (1 + r)^(-n)) / r

To solve for r, we can use trial and error or an iterative method. Here, we'll use trial and error.

Let's assume n = 20, which is a reasonable number of years for an insurance policy. Then we can solve for r:

$2,500,000 = $45,000 x (1 - (1 + r)^(-20)) / r

$2,500,000r = $45,000 x (1 - (1 + r)^(-20))

(1 + r)^(-20) = 1 - ($45,000 / $2,500,000) x r

1 + r = (1 - ($45,000 / $2,500,000) x r)^(-1/20)

r ≈ 0.0416 or 4.16%

Therefore, the insurance company expects the interest rate to be around 4.16%.

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Answer:

Step-by-step explanation:

Volume of the box  =  x³ +11x² + 20x – 32        I think the ' is a typo for ³

      the width is x-1    and the height is x+8      

Find an expression for the length

       Vol = LWH    solve L

        Vol / (WH)   =  L     so

L  =  (x³ +11x² + 20x – 32) / (x-1) (x+8)      

                    so it would help to factor the numerator

       (x³ +11x² + 20x – 32)       I'm willing to bet (x-1) and  (x+8) are factors

                                               but I will plot the equation to find the three roots

        (x³ +11x² + 20x – 32)  = (x-1) (x+8) (x+4)

L  =  (x³ +11x² + 20x – 32) / (x-1) (x+8)

   =  (x-1) (x+8) (x+4) / (x-1) (x+8)           the (x-1) and (x+8) cancel out leaving

L =   (x + 4)

Answer:

its the second one because i think it is im not sure if u get it wrong dont blame me i said i think it is

Step-by-step explanation:

because i think it is

The solution to the proportion 2.14 = X/12, rounded to the nearest tenth, is X = 25.7.

To solve the proportion 2.14 = X/12, we can cross-multiply and solve for X.

Cross-multiplying means multiplying the numerator of the first fraction (2.14) by the denominator of the second fraction (12), and vice versa.

So, 2.14 * 12 = X * 1.

The result of multiplying 2.14 and 12 is 25.68. Therefore, X * 1 can be simplified to just X.

Thus, X = 25.68.

Rounding to the nearest tenth, X is approximately 25.7.

So, the solution to the proportion is X = 25.7.

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Answer:

Area = 77.1

Step-by-step explanation:

The are of a right triangle is

\( \frac{1}{2} \times base \times height\)

our base and height are 6 for both triangles, so we shall find the area of one of the triangles...

\( \frac{1}{2} \times 6 \times 6 = 18\)

multiply this by 2

\(2 \times 18 = 36\)

Now find the area of the whole circle

\(area = \pi {r}^{2} \)

our radius is 6, therefore:

\(area = \pi {6}^{2} = 113.1\)

Finally, subtract the area of the two triangles from the total are of the circle. The difference left over is our answer

\(113.1 - 36 = 77.1\)

Answer:

Exact Area = 36pi - 36  square meters

Approximate Area = 77.04 square meters (when using pi = 3.14)

================================================

Explanation:

The circle has radius r = 6 meters. The area of the circle is...

A = pi*r^2

A = pi*6^2

A = 36pi

This is the exact area in terms of pi.

Because we have two right triangles, and each right triangle has the same leg length, we can effectively use the SAS theorem to prove the triangles are congruent. Therefore, both of the triangles shown have the same area. One triangle is a rotated copy of the other.

The area of one of the triangles is base*height/2 = 6*6/2 = 18 square meters. That means two of them combine to an area of 18*2 = 36 square meters.

Subtract this from the area of the circle to get the green shaded area

green area = (circle area) - (triangle areas)

green area = (36pi) - (36)

green area = 36pi - 36

This is the exact area in terms of pi. If you want the approximate area, then replace pi with its approximate value. Let's say we go for pi = 3.14

That means,

green area = 36pi - 36

green area = 36*3.14 - 36

green area = 77.04 square meters approximately

Use more decimal digits in pi to get a more accurate area value.

Plotting the data on a graph can help you identify the outliers or points that don't fit the pattern.

The dataset, you can use it to identify the points that don't fit the pattern.

The points that don't fit the pattern in a dataset.

The points that don't fit the pattern in a dataset, you can use several methods such as:

Visualization:

Plotting the data on a graph can help you identify the outliers or points that don't fit the pattern.

You can use various graph types such as scatter plots, line graphs, box plots, etc., to visualize the data.

Statistical methods:

You can use statistical methods such as standard deviation, z-score, or regression analysis to identify the outliers or points that don't fit the pattern.

Domain knowledge:

If you have domain knowledge about the dataset, you can use it to identify the points that don't fit the pattern.

If you know that a particular event occurred during a specific period, you can use it to explain the anomaly in the data.

The points that don't fit the pattern, you can investigate why they don't fit the pattern.

It could be due to measurement errors, data entry errors, or a genuine anomaly in the data.

Understanding why certain data points don't fit the pattern can provide insights into the data and improve the accuracy of the analysis.

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Answer:

there arent

Step-by-step explanation:

Δ is negative

Answer:

2300000

Step-by-step explanation:

Answer:

1.3d-2d =-17-8

1d=25

d=25/1

d=25

2.2n-5n=-10+7

-3n=-3

N= -3/-3

N=1

3.p+6p=13+15

7p=28

p=28/7

p=4

4. 3(y+7)

3y+21

2y+3=3y+21

2y-3y=21-3

-1y=18

y=18/-1

y=-18

Given the value of (cot(theta) = frac{6}{5}) and (tan(theta)), we can determine the value of (theta) by using the relationship between tangent and cotangent.

By taking the reciprocal of (cot(theta)), we find (tan(theta) = frac{5}{6}). Therefore, (theta) is an angle such that (tan(theta) = frac{5}{6}).

The tangent and cotangent functions are reciprocal to each other. If (cot(theta) = frac{6}{5}), then we can find the value of (tan(theta)) by taking the reciprocal:

[tan(theta) = frac{1}{cot(theta)} = frac{1}{frac{6}{5}} = frac{5}{6}]

Hence, the angle (theta) that satisfies both (cot(theta) = frac{6}{5}) and (tan(theta) = frac{5}{6}) is the same angle.

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If m is a nonzero integer, then m^(1/m) is not always greater than 1.

The statement is false.

To determine if m^(1/m) is greater than 1, we can consider different values of m. For positive values of m, such as m = 2, m^(1/m) = 2^(1/2) = √2, which is approximately 1.414 and greater than 1.

However, if we consider negative values of m, such as m = -2, m^(1/m) = (-2)^(1/(-2)) = (-2)^(-1/2), which is equal to 1/√(-2). Since the square root of a negative number is not defined in the real number system, the value of m^(1/m) is not defined for negative values of m.

Therefore, the statement that m^(1/m) is always greater than 1 for nonzero integers m is false.

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Answer:

Shirt = $7

Sweatshirt = $12

Step-by-step explanation:

Let T represent shirts and S to represent sweatshirts

you bought 3T + 4S = 69

your friend bought 6T + 2S = 66 multiply second equation by -2

-2 x 6T + 2S = 66

-12T - 4S = -132 now find the sum of this and first equation

3T + 4S -12T - 4S = 69 - 132 add like terms

-9T = -63 divide both sides by -9

T = 7 this is the cost of one shirt to find the cost of a sweatshirt we replace the T in any equation with 7

3T + 4S = 69

3*7 + 4S = 69

21 + 4S = 69 subtract 21 from both sides

4S = 48 divide both sides by 4

S = 12

we simplify it to \(F = \bar{x} \cdot z \cdot \bar{y} \cdot w\). This involves breaking down the negations and using the rules of De Morgan's theorems to express the original expression in a simpler form.

By applying De Morgan's theorems to the expression \(F=\overline{(x+\bar{z}) \bar{y} w}\), we can simplify it using the following rules:

1. De Morgan's First Theorem: \(\overline{A+B} = \bar{A} \cdot \bar{B}\)

2. De Morgan's Second Theorem: \(\overline{A \cdot B} = \bar{A} + \bar{B}\)

Let's apply these theorems to simplify the expression step by step:

1. Applying De Morgan's First Theorem: \(\overline{x+\bar{z}} = \bar{x} \cdot z\)

2. Simplifying \(\bar{y} w\) as it does not involve any negations.

After applying these simplifications, we get the simplified expression:

\[F = \bar{x} \cdot z \cdot \bar{y} \cdot w\]

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Answer:

The equation that models the population growth is y = 90,000(1.02)^x

Step-by-step explanation:

The formula of the exponential growth is y = a \((b)^{x}\), where

Let us solve the question

∵ At x = 0, the population y = 90,000

→ That means the initial value is 90,000

∴ a = 90,000

→ Substitute it in the form of the equation above

∴ y = 90,000 \((b)^{x}\)

→ To find b use any values from the table to substitute x and y

∵ At x = 1, y = 91,800

∵ 91,800 = 90,000 \((b)^{1}\)

∴ 91,800 = 90,000 b

→ Divide both sides by 90,000

∵ \(\frac{91,800}{90,000}\) = \(\frac{90,000b}{90,000}\)

∴ 1.02 = b

→ Substitute it in the equation above

∵ y = 90,000 \((1.02)^{x}\)

∴ The equation that models the population growth is y = 90,000(1.02)^x

Answer: g(-3) is 9 .

Step-by-step explanation:

So there are two functions  and  the first function says that to get the solution x has to be greater than 4   and -3 which is the input is not greater than 4  so you can't use that function to solve for g(-3).

using the second function , it says that  x has to be less or equal to 4. And -3 is indeed less than 4 so you have to use the second function to solve for g(-3)  

g(x) = -2x + 3     Input -3  and solve

g(-3) = -2(-3) + 3

g(-3) = 6 + 3

g(-3) = 9  

If there are n men and n women in the group, we can first arrange the men and women separately in alternate positions. We can treat the men as a single group and arrange them in n! ways, and similarly, we can treat the women as a single group and arrange them in n! ways.

Next, we need to arrange the two groups (men and women) in alternate positions to satisfy the given condition. Since we need to place the youngest person (who could be a man or a woman) at the beginning of the row, we have two cases:

Case 1: The youngest person is a man

In this case, the men must start the arrangement, followed by the women. Since there are n men and n women, there are n! ways to arrange the men and n! ways to arrange the women. We can fix the youngest man at the beginning of the row, so there are (n-1)! ways to arrange the remaining n-1 men. Similarly, there are (n-1)! ways to arrange the n-1 women. Therefore, the total number of arrangements in this case is:

n! * n! * (n-1)! * (n-1)!

Case 2: The youngest person is a woman

In this case, the women must start the arrangement, followed by the men. Since there are n women and n men, there are n! ways to arrange the women and n! ways to arrange the men. We can fix the youngest woman at the beginning of the row, so there are (n-1)! ways to arrange the remaining n-1 women. Similarly, there are (n-1)! ways to arrange the n-1 men. Therefore, the total number of arrangements in this case is:

n! * n! * (n-1)! * (n-1)!

To get the total number of arrangements that satisfy the given condition, we need to add the number of arrangements in Case 1 and Case 2:

n! * n! * (n-1)! * (n-1)! + n! * n! * (n-1)! * (n-1)!

= 2 * n! * n! * (n-1)! * (n-1)!

= 2 * (n!)^2 * (n-1)!

Therefore, the total number of ways to arrange the people in a row with alternating men and women, starting with the youngest person, is 2 * (n!)^2 * (n-1)!.

Each class is approximately 58 minutes long.

To find the length of each class, we need to subtract the time spent on lunch and switching rooms from Jayla's total time in school.

Given information:

Total time in school: 7 hours = 7 * 60 minutes = 420 minutes

Lunch period: 30 minutes

Time spent switching rooms: 42 minutes

To find the total time spent in classes, we subtract the time for lunch and switching rooms from the total time in school:

Total time in classes = Total time in school - Lunch period - Time spent switching rooms

Total time in classes = 420 minutes - 30 minutes - 42 minutes

Total time in classes = 348 minutes

Since Jayla has 6 classes that are all the same length, we can divide the total time in classes by the number of classes to find the length of each class:

Length of each class = Total time in classes / Number of classes

Length of each class = 348 minutes / 6 classes

Length of each class ≈ 58 minutes

Consequently, each class lasts about 58 minutes.

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A real-world problem that involves equal shares could be splitting a pizza equally among a group of friends. In this example, the equal share is approximately 1.5 slices per person.

Let's say there are 8 friends and they want to share a pizza.

Each friend wants an equal share of the pizza.

To find the equal share, we need to divide the total number of slices by the number of friends. If the pizza has 12 slices, each friend would get 12 divided by 8, which is 1.5 slices.

However, since we can't have half a slice, each friend would get either 1 or 2 slices, depending on how they decide to split it.

This ensures that everyone gets an equal share, although the number of slices may differ slightly.

In this example, the equal share is approximately 1.5 slices per person.

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Step-by-step explanation:

Pathagory and Theorem

a^2+b^2=c^2

(x-3)^2+(x-4)^2=6^2

expand:

2x^2-14x+25=36

2x^2-14x-11=0

x=(\sqrt{71}+7)/2

perimeter=(x-3)+(x-4)+6=2x-1

insert the value for x into 2x-1

\(\sqrt{71}\)+6=perimeter

Hope that helps :)

9514 1404 393

Answer:

  2x -1

Step-by-step explanation:

The perimeter is the sum of the side lengths.

  P = 6 + (x -4) + (x -3)

  P = 2x -1 . . . . . . collect terms

The perimeter is 2x -1.

_____

Additional comment

There is nothing in the problem statement that suggests this is a right triangle. Without knowing at least one angle, we cannot solve for a numerical value for the perimeter. The problem title suggests we're to leave the result in polynomial form.

Answer:

x≤ 1

Step-by-step explanation:

3x-6≤ -3

+6

3x≤ 3/3