Guys, can you please help me find the 2 values of k so that an each trinomial can be factored over the integers for me, please? :)

a). 2x²–7x+k
b). kx²–5x+3

To find σg(X)^2, we need to calculate the variance of the function g(X) = 4X^2 + 2, where X is a random variable with a given density function. The density function is defined as f(x) = (3/2)(x + 1) for 0 ≤ x and 0 elsewhere. By calculating the variance of g(X), we can determine the value of σg(X)^2.

To calculate the variance of g(X), we first need to find the mean of g(X), denoted as E[g(X)]. For a continuous random variable, the mean is calculated as the integral of the function multiplied by the density function. In this case, we have:

E[g(X)] = ∫(4X^2 + 2) * f(x) dx

Substituting the given density function, we have:

E[g(X)] = ∫(4X^2 + 2) * (3/2)(X + 1) dx

After simplifying and evaluating the integral, we can find the value of E[g(X)].

Next, we calculate the variance of g(X), denoted as Var[g(X)]. The variance is calculated as the expectation of the squared difference between g(X) and its mean, E[g(X)]^2. In mathematical terms:

Var[g(X)] = E[(g(X) - E[g(X)])^2]

By substituting the values of g(X) and E[g(X)], we can evaluate this expression and find the value of Var[g(X)].

Finally, to find σg(X)^2, we take the square root of Var[g(X)], i.e., σg(X) = √Var[g(X)]. After calculating Var[g(X)], we can determine the value of σg(X) to three decimal places as needed.

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2.5(cos 5π/6  + i sin 5π/6) is the polar form  of the complex number

Complex numbers are numbers that are expressed in the form of a+ib, where a and b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1)

Given: the complex number (5√3)/4 - 5/4 i

In polar form:

(5√3)/4 - 5/4 i = r(cosθ + isinθ)

θ  = tan⁻¹( (-5/4) / (5√3 /4) )

θ = -30°

θ = -30+180 = 150°

θ = 5π/6

r = √( (5√3)/4)² +(- 5/4)²) = 2.5

Thus,

(5√3)/4 - 5/4 i = r(cosθ + isinθ)

r(cosθ + isinθ) = 2.5(cos 5π/6  + i sin 5π/6 )

Therefore, the polar form  of the complex number is 2.5(cos 5π/6  + i sin 5π/6)

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Answer:

For example

Here Domain and range both are set of all real numbers

The solution to the given problem is [ln|a+8| - 2/3 (a+8)^(3/2)] - [ln|8| - 2/3 (8)^(3/2)].

Given functions are f(x)=√x+8, g(x) = 1/(x+8).Now let's find the x-intercept of the two functions:f(x)=√x+8

To find the x-intercept, we need to put f(x) = 0 and solve for x.√x + 8 = 0√x = -8

The square root of a number cannot be negative, so there are no x-intercepts.

Now let's find the y-intercept of the two functions:f(x)=√x+8

When we substitute x = 0 in the function, we get:f(0) = √0+8 = √8g(x) = 1/(x+8)

When we substitute x = 0 in the function, we get:g(0) = 1/(0+8) = 1/8

Therefore, the y-intercepts are: (0, √8) and (0, 1/8).

Now let's sketch the two functions to determine the range of integration.

It can be observed that the two functions intersect at x = 0. Therefore, the limits of integration are 0 and a.

The area between the two functions is given byA = ∫[g(x) - f(x)] dx from 0 to aA = ∫[1/(x+8) - √x+8] dx from 0 to a

Now let's integrate the function with respect to x.A = [ln|x+8| - 2/3 (x+8)^(3/2)] from 0 to aA = [ln|a+8| - 2/3 (a+8)^(3/2)] - [ln|8| - 2/3 (8)^(3/2)]

The area between the two curves is [ln|a+8| - 2/3 (a+8)^(3/2)] - [ln|8| - 2/3 (8)^(3/2)].

Hence, the solution to the given problem is [ln|a+8| - 2/3 (a+8)^(3/2)] - [ln|8| - 2/3 (8)^(3/2)].

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Answer:

B. 12.5%

Step-by-step explanation:

Find how much was unused:

120 - 105

= 15

To find what percent this is, divide it by 120:

15/120

= 0.125

Multiply this by 100:

0.125(100)

= 12.5

So, 12.5% of the wire went unused

The correct answer is B. 12.5%

The sign of the discriminant \(b^{2}-4ac\) of a quadratic equation determines how many real solutions there are to that quadratic equation.

The value of the expression is the discriminant of a quadratic equation in standard form : This quantity specifies how many different ways a quadratic problem can be solved.

Solutions to quadratic equations can be 0, 1, or 2. If the discriminant has a positive value, then there are two genuine solutions for x, and the graph of the solution has two different x-intercepts. There is only one actual solution for x if the discriminant's value is zero, which means that the solution's graph only has one x-intercept.

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Answer:

4ft

Step-by-step explanation:

A percentage is a way to describe a part of a whole.  The most improbable simulation for this coin is heads are 9.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

The most improbable simulation for this coin for heads is the frequency of heads coming up out of 20 which is far from the estimated frequency. Since out of these 20 times 75% of the times the head will come up. Therefore, the number of times the head will come up can be written as,

\(75\%\ of\ 20\\\\= \dfrac{75}{100} \times 20\\\\= 15\)

Now it is estimated that at least 15 times out of 20, the head will come up. Thus, the most improbable simulation for this coin is heads are 9.

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Answer:

A coin is biased to display heads 75% of the time. It is tossed 20 times, and the outcomes are recorded. The most improbable simulation for this coin is

9 heads.

Step-by-step explanation:

Given the following question:

Point A = (7, 4) = (x1, y1)

Point B = (3, 6) = (x2, y2)

To find the slope use rise over run:

m = -0.5

Hello!

If y varies jointly with x and z, it'll mean that x and z are being multiplied by a factor "k", to equal y.

To give you a visual, this is what I mean.

\(y=kxz\)

That means we'll want to find \(k\) with the first point we're given: \((2,20,5)\)

\(20=k(2)(5)\)

\(20=10k\)

\(k=2\)

Which means our equation is:

\(y=2xz\)

Now, let's plug in the \(x\) and \(z\) from the other point to find \(y\).

\(y=2(3)(6)\)

\(y=36\)

Hope this helps!

Answer:

Hello!

If y varies jointly with x and z, it'll mean that x and z are being multiplied by a factor "k", to equal y.

To give you a visual, this is what I mean.

That means we'll want to find  with the first point we're given:

Which means our equation is:

Now, let's plug in the  and  from the other point to find .

Step-by-step explanation:

Answer:

The triangle is not equilateral.

Step-by-step explanation:

Distance formula:

\( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Distance from (a, a) to (-a, -a):

\( d_1 = \sqrt{(-a - a)^2 + (-a - a)^2} \)

\( d_1 = \sqrt{(-2a)^2 + (-2a)^2} \)

\( d_1 = \sqrt{8a^2} \)

Distance from (-a, -a) to (-3a, 3a):

\( d_2 = \sqrt{(-3a - (-a))^2 + (3a - (-a))^2} \)

\( d_2 = \sqrt{(-2a)^2 + (4a)^2} \)

\( d_2 = \sqrt{20a^2} \)

Distance from (-3a, 3a) to (a, a):

\(d_3 = \sqrt{(-3a - a)^2 + (3a - a)^2}\)

\(d_3 = \sqrt{(-4a)^2 + (2a)^2}\)

\(d_3 = \sqrt{20a^2}\)

The three sides do not have the same length, so the triangle is not equilateral.

If the gross income per month is $4000 , then the monthly disposable income will be $2920   .

To find the monthly disposable income, we subtract the various taxes from the gross income.

The Federal tax is = 10% of $4000 = $400  ;

The State tax is = 7% of $4000 = $280  ;

The City tax is = 3% of $4000 = $120  ;

and the Social security tax is = 7% of $4000 = $280  ;

So , the Total monthly tax is = $400 + $280 + $120 + $280 = $1080  ;

We know that the Monthly disposable income = Gross income - Total tax ;

⇒ Monthly disposable income = $4000 - $1080  ;

⇒ Monthly disposable income = $2920  .

Therefore, the monthly disposable income after taxes is $2920.

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A substitute is a good or service that buyers can quickly swap out for another. For instance, a one-dollar bill can be used in place of another dollar bill.

In business and economics, a replacement, or substitutable good, is a good or service that consumers perceive as just being substantially the same as or reasonably similar to some other good. Consumers are given options and alternatives through substitutes, which also spur competition and lower prices in the market.

Here are a few examples of replacement goods:

1. A $1 bill can be exchanged for four quarters.

2. Coke against Pepsi

3. Regular vs. premium gas

4. Butter and lard

5. Tea and coffee

6. Apples and oranges

7. Comparing driving a car to riding a bike

8. Books in general and e-books

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Answer:

same

Step-by-step explanation:

they are both the same triangles stuck together they both have angles of 35 degrees

The linear speed of the tip of the minute hand is \( \frac{{4 \pi \, \text{cm}}}{{15 \, \text{min}}} \).

To find the linear speed \( v \) of the tip of the minute hand of a clock, we need to consider the distance traveled by the tip in a given time.

The minute hand completes one full revolution in 60 minutes, which corresponds to a distance equal to the circumference of a circle with a radius of 8 cm.

The circumference of a circle is given by the formula \( C = 2 \pi r \), where \( r \) is the radius.

In this case, the radius \( r \) is 8 cm, so the circumference is \( C = 2 \pi (8) = 16 \pi \) cm.

Since the minute hand covers the circumference of the circle in 60 minutes, we can calculate the linear speed by dividing the distance traveled (circumference) by the time taken.

Therefore, \( v = \frac{{16 \pi \, \text{cm}}}{{60 \, \text{min}}} \).

To simplify the answer, we can divide both the numerator and denominator by 4:

\( v = \frac{{4 \pi \, \text{cm}}}{{15 \, \text{min}}} \).

So, the linear speed of the tip of the minute hand is \( \frac{{4 \pi \, \text{cm}}}{{15 \, \text{min}}} \).

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Based on the variable declarations and initializations you provided:
int a = 2; int b = 6; int c = 3;
An expression that evaluates to false would be one where the conditions are not met. For example:
(a + b == c)
This expression checks if the sum of a and b is equal to c. In this case, (2 + 6) is not equal to 3, so the expression evaluates to false.

One possible solution is:
The given variable declarations and initializations are:
int a = 2;
int b = 6;
int c = 3;

To evaluate which of the following expressions is false, we need to look at each expression and see if it produces a Boolean value of false.
a < b || c > b

This expression is true because 2 is less than 6 and 3 is greater than 6. Therefore, the OR operator (||) returns true because at least one of the operands is true.
a + b > c && c - a < b

This expression is true because 2 + 6 is greater than 3 and 3 - 2 is less than 6. Therefore, the AND operator (&&) returns true because both operands are true.
b % c == a || c * b < a

This expression is false because 6 % 3 is equal to 0, which is not equal to 2. Therefore, the equality operator (==) returns false. Moreover, 3 times 6 is 18, which is not less than 2. Therefore, the second operand is also false. Therefore, the OR operator (||) returns false because both operands are false.

Therefore, the expression "b % c == a || c * b < a" evaluates to false.

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Answer:

c

Step-by-step explanation:

gm=cm+rg

gm-cm=rg

m(g-c)/g-c = rg/g-c

m=r g/g-c

     -3m=4m-15

-3m-4m=-15

-7m=-15

-15/-7m

= -2.14

-15/-3-4= 2.14

Answer:

The answer is C. I just got it right

Step-by-step explanation:

The expected operational time of the machine is 6.75

For given x , y > 0 , the lifetime of the machine is max{x , y} because it stops when the two component will fail.

The life expectancy if therefore the expectancy of max{x, y}

t = E [ max{x,y} ]

So, the max{x , y} can be x or y

We have three integral

I₁ = \(\frac{1}{162}\int\limits^9_0 \, dx \int\limits^{18-x}_{x} y \. dy\)

Solving the integration

=> I₁ =  729 / 162

=> 4.5

I₂ = \(\frac{1}{162}\int\limits^9_0 \, dx \int\limits^{x}_{0} y \. dy\)

=> I₂ = 121.5/162

=> 0.75

=> I₃ = \(\frac{1}{162}\int\limits^9_0 \, dx \int\limits^{18-x}_{x} x \. dy\)

=> I₃ = 243 / 162

=>  1.5

So . the total is 4.5 + 0.75 + 1.5

=>  6.75 is expected operational time

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Answer:

Independent then dependent

Step-by-step explanation:

Yes. YES!

Answer:

Give me some hint please

Answer:

2. d) L = 10, W = 20

3. c) P = 100

Step-by-step explanation:

2. 2L + W = 40

W = 40 - 2L

A = L x W

= L (40 - 2L)

= 2L^2 + 40L

=-2 (L^2 - 20L)

= -2 (L^2 - 20^2 + 100 - 100)

= -2 (L^2 - 20L + 100) +200

= -2 (L - 10)^2 +200

L = 10

W = 40 - 2(10

=20

3. c. P = 2(L + W)

= 2(49 + 1)

= 100

a. P = 53

b. P = 32.5

d. P = 28

An infinite geometric series is one in which each term is equal to the preceding term multiplied by a fixed non-zero number, known as the common ratio.

The first term is called a1, and the common ratio is represented by r.In this particular question, we are required to find the value of a1 and r for an infinite geometric series. The partial sum S2 will also need to be found.For a geometric sequence that is infinite, the formula for the partial sum, Sn, is:Sn = a1 / (1-r), where a1 is the first term and r is the common ratio.To solve for a1, it is necessary to know two other variables: the common ratio r and the value of the first term a1. S2 is the sum of the first two terms, so: S2 = a1 + arTo find S2, we must first determine a1 and r. a1 is the first term in the sequence, and r is the common ratio. We can obtain both a1 and r by dividing the second term by the first term.The formula is:r = (ar/a1) = a2/a1 Substitute the value of r and a1 into the formula for S2 to obtain the result: S2 = a1 + ar = a1 + a1r = a1(1+r) Therefore, the value of a1 is a constant number that will appear in the series, and the common ratio, r, will be multiplied by this number to obtain the next value in the series.

So, a1 is the first term, and r is the common ratio of the infinite geometric series. S2, the sum of the first two terms, is found by using the formula S2 = a1 + ar where a1 is the first term and r is the common ratio.

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The value of the sample statistic is used to estimate the value of the population parameter.

The sample statistic is the value that is calculated from the sample data, which is used to make inferences about the population parameter. Sample statistics are used to estimate population parameters. A sample statistic is an estimate of a population parameter that is obtained from a sample, whereas a population statistic is a value that is computed from a population.

Therefore, the correct answer is a. sample statistic.

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Answer:

116 cm squared

Step-by-step explanation:

The area of the triangle is 28 cm squared.

The area of the parallelogram is 88 cm squared.

The total area of the composite figure would be 116 cm squared.

Answer:

triangle:28

parallelogram:88

total area:116

Step-by-step explanation:

8×7=56

triangle->56÷2

=

\( {28}^{2} \)

parallelogram->11cm×8cm

=

\( {88}^{2} \)

total area->28cm²+88cm²=116cm²

We can use the stars and bars method to fix this issue. This provides us a total of 191 allocations from which to choose: 191 choose 11 is equal to frac(191!11!180!) = 6,176,424,853,430.

ii. There are two options available for each of the 10 journeys since each one can be either express or local. Therefore, there are a total of $210 = 1024 potential sequences.

iii. Three scenarios should be taken into account: when there are three, four, or five vehicles in the train.

If there are 3 cars in the train, there are $7 choose 3 = 35 options to select them.

If there are 4 cars in the train, there are $7 * 4 * 35 options to select the cars.

If there are 5 cars in the train, there are 7 * 5 * 21 options to select the cars.

$35+35+21=91 is the total amount of trains that could run.

iv. This issue can be resolved by combining permutation and combination. Selecting the first two or three intermediate stations for the express train is necessary. There are $8choose 2+$8choose 3=28+56=84$ different methods we can allocations this.

Therefore, (84 times 1) + (84 times 2) = 252 is the total number of possible express train trips.

v. We need $20ngeq $20 to ensure that we have opened each of the three doors in every conceivable combination. Using the n-solve, we obtain: n = log 20(20) / 2 = 1.

To ensure that the same three doors have been opened six times, we must make at least one halt.

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Graph  has been transformed from the graph of y = x³ by a horizontal shift of 4 units to the right then by a reflection over the x-axis, and 5 units upward of vertical shift.

A function from a set X to a set Y assigns to each element of X exactly one element of Y.

The given function is y = -(x-4)³ + 5.

Let us use algebraic methods to understand the transformation of the graph of this function.

First, we can observe that the parent function is y = x³ has been transformed to y = -(x-4)³ by replacing x with (x-4).

This transformation gives  a horizontal shift of the graph of 4 units to the right.

then negative sign in front of the function reflects the graph over the x-axis, resulting in an upside-down graph.

Finally, the entire graph is shifted vertically upward by 5 units, as observed  by the constant term +5 in the equation.

Hence,  the graph  has been transformed from the graph of y = x³ by a horizontal shift of 4 units to the right then by a reflection over the x-axis, and 5 units upward of vertical shift.

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To find the exact value of the expression

tan⁡15∘−sin⁡15∘cos⁡15∘tan15∘−cos15∘sin15∘

​, we can use the fundamental trigonometric identities and the complementary angle theorem.

First, let's rewrite

tan⁡15∘tan15∘

in terms of sine and cosine. We know that

tan⁡�=sin⁡�cos⁡�

tanθ=cosθ/sinθ

​, so we have:

tan⁡15∘=sin⁡15∘cos⁡15∘

tan15∘=cos15∘sin15∘

​

Now, let's substitute this expression back into the original expression:

tan⁡15∘−sin⁡15∘cos⁡15∘=sin⁡15∘cos⁡15∘−sin⁡15∘cos⁡15∘

tan15∘−cos15∘sin15∘​=cos15∘sin15∘​−cos15∘sin15∘

​

Using a common denominator, we can combine the terms:

sin⁡15∘−sin⁡15∘cos⁡15∘=0

cos15∘sin15∘−sin15∘​=0

Therefore, the exact value of the expression

tan⁡15∘−sin⁡15∘cos⁡15∘tan15∘−cos15∘sin15∘​

is 0.

The exact value of the expression using trigonometric identities: tan⁡15∘−sin⁡15∘cos⁡15∘tan15∘−cos15∘sin15∘​is 0.

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The future value of the $10,000 investment after 7 years, at an interest rate of 6% per year, compounded annually, is approximately $14,185.10.

To calculate the future value (FV) of an investment of $10,000 at an interest rate of 6% per year, compounded annually, after 7 years, we can use the formula:

FV = P(1 + r)^n

Where:

P is the principal amount (initial investment) = $10,000

r is the interest rate per period = 6% = 0.06

n is the number of periods = 7

Plugging in the values, we have:

FV = $10,000(1 + 0.06)^7

Calculating the expression inside the parentheses first:

(1 + 0.06)^7 ≈ 1.41851

Now, multiply the principal amount by the calculated expression:

FV ≈ $10,000 * 1.41851 ≈ $14,185.10

Therefore, the future value of the $10,000 investment after 7 years, at an interest rate of 6% per year, compounded annually, is approximately $14,185.10.

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Answer:

D

Step-by-step explanation:

one way to write a quadratic equation is using the y = (x-s) (x-r) where r and s are positive zeros. another way to solve this and think about it would be to plug in your points and equate both sides. 

example:(3,0) (8,0)0 = (3-8) (3-3)0 = 00 = (8-8) (8-3)0=0

To yield a linear graph, the variables that should be plotted on the horizontal and vertical axes depend on the nature of the process being repeated by the student. If the process involves measuring the dependent variable y for different values of an independent variable x, then x should be plotted on the horizontal (x-axis) and y on the vertical (y-axis). This is because the independent variable is usually plotted on the x-axis, while the dependent variable is plotted on the y-axis. The resulting graph will show how y varies with respect to x, and if the relationship between x and y is linear, the graph will be a straight line.

On the other hand, if the process involves measuring the dependent variable y for different values of another independent variable z, then z should be plotted on the horizontal (x-axis) and y on the vertical (y-axis). This is because in this case, the variable being plotted on the x-axis is still the independent variable, while the dependent variable is still plotted on the y-axis.

In summary, the choice of variables to plot on the horizontal and vertical axes to yield a linear graph depends on the nature of the process being repeated by the student, and whether the process involves measuring the dependent variable y for different values of an independent variable x or another independent variable z.

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