\(\sf\large\green{\underbrace{\red{Question*}}}:\)
\(\huge{\green}\fcolorbox{blue}{cyan}{\bf{\underline{\red{\color{red}Factorize}}}} \)
\( {y}^{2} - 3y - 4y + 12\)
\(9 {x}^{2} - 12x + 4\)
​

A bag of six chocolates cost $2.40. A bag of 8 lollies cost $1.60. So, $0.4 more does one chocolate cost than one lolly.

A bag of six chocolates cost $2.40.

A bag of 8 lollies cost $1.60.

To determine how much more does one chocolate cost than one lolly.

6 chocolates = 2.40.

1 chocolates = 2.40/6 = 0.4

8 lollies = 1.60.

1 lolly = 1.60/8 = 0.8

0.8 -  0.4 = 0.4.

Therefore, $0.4 more does one chocolate cost than one lolly.

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The standard deviation for a total of 200 games is 5.3735.

How to calculate the standard deviation?

Let X = number of home runs of this player in 200 games played by him.

p = probability that a this player hits a home run in a single game and this is given to be 0.175.

Where np = Mean of X and √{np(1 - p)} is the standard deviation of X.

Here n = 200 and p = 0.175. So, the standard deviation for a total of 200 games is the standard deviation for a total of X

= √(200 x 0.175 x 0.825) / 2

= 5.3735

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Answer:

x = - 6    

Step-by-step explanation:

Equation

1/3 * (-9x +12) = 22                Multiply both sides by 3

Solution

3 * 1/3(-9x + 12) = 22*3

- 9x + 12 = 66                        Subtract 12 from both sides.

-9x = 66 - 12                         Combine

-9x = 54                                Divide by -9

x = 54/-9

x = - 6

Answer:

b might be correct

Step-by-step explanation:

I hope this helps

Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.

To find the p-value from the t statistic on TI-84, you will need to perform a hypothesis test. Here are the steps:1. Enter your data into the calculator and choose the appropriate test.2. Calculate the t statistic by dividing the sample mean by the standard error.3. Determine the degrees of freedom. This is n-1 for a one-sample t-test or n1+n2-2 for a two-sample t-test. 4. Use the t-distribution table to find the critical value for your test.5. Calculate the p-value using the t-distribution function on the calculator.6. Compare the p-value to the significance level (usually 0.05) to determine whether to reject or fail to reject the null hypothesis.7.

Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.

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The average value of a necklace at Julie's shop is $4.90. For further explanation;-

Julie the jeweler has two gold necklaces worth $105, seven silver necklaces valued at $100, twenty-seven plated necklaces valued at $55, and twenty-two beaded necklaces worth $25. The average value of a necklace at Julie's shop can be calculated by finding the sum of the values of all the necklaces and dividing it by the total number of necklaces.

The total value of all the necklaces is $105 + $100 + $55 + $25 = $285. The total number of necklaces is 2 + 7 + 27 + 22 = 58.

Therefore, the average value of a necklace is $285 / 58 = $4.90. This answer should be rounded to the nearest cent, giving an average value of $4.90 per necklace at Julie's shop.

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The required arc length of sector VW is 8\(\pi\).

Given that, in a circle U, radius  UV = 9 and  central angle of sector m∠VUW = 160°.

To find the arc length of sector VW, we can use the formula:

Arc length = (central angle / 360) x circumference of the circle.

First,  find the circumference of the circle by the  formula for the circumference of a circle is given by:

Circumference = 2 x \(\pi\) x radius.

Circumference = 2 x \(\pi\) x 9 = 18π.

Now, let's find the arc length of sector VW using the central angle of 160 degrees:

Arc length = (160/360) x 18π

Arc length = (4/9) * 18\(\pi\) = 8\(\pi\).

Therefore, the arc length of sector VW is 8\(\pi\).

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Answer:

B C D is positive number

Step-by-step explanation:

ghhhhgbhjbbbhbb

The probability that the satellite system operates adequately is 0.7056.

The probability that a component is not functional is 0.4. Therefore, the probability that a component is functional is 1-0.4=0.6.
Using the rule of combinations, there are 6 possible combinations of functional and non-functional components:
1. All 4 components are functional: (0.6)^4=0.1296
2. 3 components are functional: (0.6)^3(0.4)=0.3456
3. 2 components are functional: (0.6)^2(0.4)^2=0.2304
4. 1 component is functional: (0.6)(0.4)^3=0.0256
5. No components are functional: (0.4)^4=0.0256
6. At least 2 components are functional: P(2 or 3 or 4) = 0.1296 + 0.3456 + 0.2304 = 0.7056
Therefore, the probability that the satellite system operates adequately is 0.7056.

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a) The minimum value of the function f(x) = xcos(x) in the range 0 ≤ x ≤ 5 is approximately -4.92, and it occurs at x ≈ 3.38.

b) The maximum value of the function f(x) = xcos(x) in the range 0 ≤ x ≤ 5 is approximately 4.92, and it occurs at x ≈ 1.57 and x ≈ 4.71.

To find the minimum and maximum values of the function f(x) = xcos(x) in the specified range, we need to evaluate the function at critical points and endpoints.

a) To find the minimum, we look for the critical points where the derivative of f(x) is equal to zero. Taking the derivative of f(x) with respect to x, we get f'(x) = cos(x) - xsin(x). Solving cos(x) - xsin(x) = 0 is not straightforward, but we can use numerical methods or a graphing calculator to find that the minimum value of f(x) in the range 0 ≤ x ≤ 5 is approximately -4.92, and it occurs at x ≈ 3.38.

b) To find the maximum, we also look for critical points and evaluate f(x) at the endpoints of the range. The critical points are the same as in part a, and we can find that f(0) ≈ 0, f(5) ≈ 4.92, and f(1.57) ≈ f(4.71) ≈ 4.92. Thus, the maximum value of f(x) in the range 0 ≤ x ≤ 5 is approximately 4.92, and it occurs at x ≈ 1.57 and x ≈ 4.71.

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Answer:

$24

no, it is 48% off normal price

Step-by-step explanation:

clearance price = normal price - value of the 40% discount

value of the 40% discount = 0.4 x $50 = $20

Price = $50 - $20 = $30

final price = clearance price - value of 20% coupon

value of 20% coupon = 0.2 x $30 = $6

final price = $30 = $6 = $24

total value off normal price = $24 /$50 x 100 = 48%

Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

u can calculate yourself

Answer:

30

Step-by-step explanation:

This is the answer hope it helped

The statements that are True about the Correlations is , "Correlations are a measure used to determine the degree to which two variables are related" , the correct option is (c) .

In the question,

few statements about Correlation is given ,

we need to find the statement that is True .

we know that , Correlation is the term that is used to measure the degree of relationship between two variable ,

the correlation can be negative , positive or 0 ,

and the negative correlation implies that if one variable increases then other variable decreases and vice a versa .

So , from the above information about Correlation ,

we conclude that , the True statement is "Correlations are a measure used to determine the degree to which two variables are related. "

Therefore , the statement in option (c) is True  .

The given question is incomplete , the complete question is

Select the statement below that is true about correlations.

(a) Correlations can only be negative

(b) Correlations are a measure of how much one variable changes as the other variable changes

(c) Correlations are a measure used to determine the degree to which two variables are related.

(d) Correlations are a measure of causation between two variables

(e) A negative correlation implies no relationship between variables

(f) Correlations can only be positive .

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The annual rate of interest is approximately 6.5%.

To find the annual rate of interest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the principal (initial investment)

r is the annual interest rate (in decimal form)

n is the number of times interest is compounded per year

t is the time in years

In this case, the initial investment (P) is $3200, the final amount (A) is $3343.34, the time (t) is 5 months (which is 5/12 years since we need the time in years), and we need to find the annual interest rate (r).

We can rearrange the formula and solve for r:

r = ( (A/P)^(1/(nt)) ) - 1

Substituting the given values:

r = ( (3343.34/3200)^(1/(1*(5/12))) ) - 1

r ≈ 0.065 or 6.5%

Therefore, the annual rate of interest is approximately 6.5%.

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A. \(\bold{\boxed{\green{2^{12}}}}\)

Answer:

Solution given:

\(2^6 x (2^2)^3\)

we know that

product of power and power is added and power to power is multiplied for same base only.

I.E.

product of same base but different power:\(a^b+a^c=a^(b+c)\)

power to power :\( (a^b)^c=a^(b*c)\)

By using above property

\(2^6+2^{2*3}\)

\( 2^6+2^6\)

\(2^{[6+6]}=2^{12}\)

Answer:

6 is the coefficient

Step-by-step explanation:

brainliest?

(a) Using the given formula, N = 6E(Y1) - 1 is derived. (b) Using (1) and the derived formula in part (a), E(Y5) = 5E(Y1) is obtained, and using both (a) and (b), Nˆ = 6Y5 - 1 is shown to be an unbiased estimator of N.

(a) Using the given formula and taking expectations, we get:

N = E(Y1) + E(Y2 - Y1) + E(Y3 - Y2) + E(Y4 - Y3) + E(Y5 - Y4) + E(N - Y5 + 1) - 1

Substituting E(Yi - Yi-1) = N - E(Y5) + 1, we get:

N = 6E(Y1) - E(Y5) - 1

Using (1), we can substitute E(Y5) = N - E(Y1) + 1, and we get:

N = 6E(Y1) - (N - E(Y1) + 1) - 1

Simplifying, we get:

N = 6E(Y1) - 6

Therefore, Nˆ = 6Y5 - 1 is an unbiased estimator of N.

(b) From (1), we know that:

E(Y5 - Y4) = N - E(Y5) + 1

Substituting E(Y4 - Y3) = N - E(Y5) + 1, and so on, we get:

E(Y5) = N - E(Y5) + 1 + N - E(Y5 - Y4) + 1 + N - E(Y4 - Y3) + 1 + N - E(Y3 - Y2) + 1 + N - E(Y2 - Y1) + 1

Simplifying, we get:

E(Y5) = 5N - (E(Y1) + E(Y2 - Y1) + E(Y3 - Y2) + E(Y4 - Y3) + E(Y5 - Y4))

Substituting E(Yi - Yi-1) = N - E(Y5) + 1, we get:

E(Y5) = 5N - (E(Y1) + 4(N - E(Y5) + 1))

Simplifying and rearranging, we get:

E(Y5) = 5E(Y1)

(c) Substituting the result from (b) into the estimator Nˆ = 6Y5 - 1, we get:

Nˆ = 30E(Y1) - 1

Since E(Y1) is an unbiased estimator of N, Nˆ is also an unbiased estimator of N.

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Answer:

\(x^7y^2+x^5z^3+y^3z^4+xyz\)

Step-by-step explanation:

It is required that the algebraic expression has exactly 3 different variables

Since it must have a degree of 7, the highest power in the expression will be 7.

Therefore, an example of such an algebraic expression will be:

\(x^7y^2+x^5z^3+y^3z^4+xyz\)

To calculate tan(180+γ), where γ is an angle in degrees, we can use the periodicity property of the tangent function. The value of tan(180+γ) is equal to tan(γ). Therefore, tan(180+γ) is equivalent to tan(γ), meaning they have the same numerical value.

The tangent function has a periodicity of 180 degrees. This means that the values of the tangent function repeat every 180 degrees. For example, tan(0°) is equal to tan(180°), tan(360°), and so on.

Given tan(180+γ), where γ is an angle in degrees, we can use the periodicity property of the tangent function to simplify the expression. Adding 180 degrees to an angle does not change its tangent value. Therefore, tan(180+γ) is equivalent to tan(γ).

In other words, tan(180+γ) and tan(γ) have the same numerical value. The addition of 180 degrees does not alter the ratio of the opposite side to the adjacent side, which is what the tangent function represents. Therefore, tan(180+γ) simplifies to tan(γ).

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Answer: .04671 - 0.04679

Step-by-step explanation:

Answer:

0.04675

Step-by-step explanation:

0.04675 > 0.0467

0.04675 < 0.0468

Answer:

x=7

Step-by-step explanation:

x+14=3x

shift x to the other side

14=3x-x

14=2x

2x=14

x=14/2

x=7

Checking:

x+14=3x

7+14=3(7)

21=21

The sum of a number and fourteen is less than or equal to three times the number x + 14 = 3x, x = 7.

Given Information:

The sum of a number and fourteen is less than or equal to three times the number.

Let' consider the number is x, then w get this equation,

x + 14 = 3x

shift x to the other side

14 = 3x - x

14 = 2x

2x = 14

Divide 2 on both side,

x = 14/2

x = 7

For checking this value,

x + 14 = 3x

7 + 14 = 3(7)

21 = 21

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Answer:

2p is the answer

Step-by-step explanation:

There would be a 2p unit gap

Answer:

\(\large\boxed{\tt Area = 20.25 \pi \ ft^{2}}\)

Step-by-step explanation:

\(\textsf{We are asked for the area of a circle.}\)

\(\textsf{Note that we are given only the circumference of the circle, which means that we}\)

\(\textsf{have to find more information from only the Circumference, which is possible.}\)

\(\large\underline{\textsf{What is Circumference?}}\)

\(\textsf{Circumference is considered the perimeter of the circle. Because a Circle has arcs}\)

\(\textsf{instead of sides, the Circumference is the sum of all the arcs' lengths.}\)

\(\underline{\textsf{How are we able to find the Circumference?}}\)

\(\textsf{The Circumference is measured by using the radius, or diameter of a circle, then}\)

\(\textsf{multiplying such by pi. Mathematicians discovered that Pi is always the measure}\)

\(\textsf{of the arcs when Diameter is used. Pi is an irrational number mainly used for circles.}\)

\(\underline{\textsf{Formulas for Circumference;}}\)

\(\tt C = (Diameter) \times \pi\)

\(\tt C = 2(Radius) \times \pi\)

\(\textsf{*The Radius is multiplied by 2 to equal the length of the Diameter.}\)

\(\textsf{Our goal is to find the Radius of the circle, let's use the formula including the Radius.}\)

\(\large\underline{\textsf{Solving for the Radius;}}\)

\(\tt 9 \pi = 2(Radius) \pi\)

\(\textsf{Let's start by using the Division Property of Equality for pi.}\)

\(\tt \frac{9 \pi}{\pi} = \frac{2(Radius) \pi}{\pi}\)

\(\tt 9 = 2(Radius)\)

\(\textsf{Use the Division Property of Equality again to find the Radius.}\)

\(\tt \frac{9}{2} = \frac{2 (Radius)}{2}\)

\(\large\boxed{\tt Radius = 4.5 ft.}\)

\(\textsf{Now that we have the Radius, we are able to find the area of the circle.}\)

\(\large\underline{\textsf{What is Area?}}\)

\(\textsf{Area is the space that the surface of a shape occupies.}\)

\(\underline{\textsf{How are we able to find the area of a circle?}}\)

\(\textsf{Of course, Pi is incl\textsf{u}ded to find the area of a circle as well. As mentioned before,}\)

\(\textsf{we found the Radius with the Circumference in order to find the Area. The Radius}\)

\(\textsf{is squared, then multiplied by Pi to equal the area.}\)

\(\underline{\textsf{Formula for Area;}}\)

\(\tt Area = \pi(Radius)^{2}\)

\(\textsf{We know the Radius, hence we may begin solving for the Area.}\)

\(\large\underline{\textsf{Solving for the Area;}}\)

\(\tt Area = \pi(4.5)^{2}\)

\(\textsf{Let's follow the rule of Operations, where we should evaluate the exponents first.}\)

\(\tt 4.5 \times 4.5 = 20.25.\)

\(\large\underline{\textsf{Hence;}}\)

\(\large\boxed{\tt Area = 20.25 \pi \ ft^{2}}\)

Q.2: A review of the t-test on the significance of individual independent variable suggests that, based on the p-values. None of the independent variables could be retained. This is because if the p-value is high, it means the significance is low.

Q3: Choose the right option below. Based on the full regression model involving all of the independent variables. VIF for Size = 5.3352, VIF for Fireplace = 10.1873, VIF for bedrooms = 2.7885.

Q.4: Based on VIF values, there is concern for collinearity in this dataset. True

Q5: Based on the normal probability plot, the normality assumption seems to be met. True

Q7: Based on conducting residual analysis the model seems. Adequate.

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The solution of the Cauchy problem is y = (sina - 1/(2u - 1))e^(ux)cos(sqrt(1 - u^2)x) + (1/(2u - 1))cos(x).

To solve the Cauchy problem 2ux + y = cos x, we first need to find the general solution of the corresponding homogeneous equation 2ux + y = 0.

The characteristic equation is r^2 - 2ur + 1 = 0, which has roots r = u ± sqrt(u^2 - 1).

Case 1: u^2 < 1

In this case, the roots are complex conjugates, so the general solution of the homogeneous equation is

y = c₁e^(ux)cos(sqrt(1 - u^2)x) + c₂e^(ux)sin(sqrt(1 - u^2)x).

Case 2: u^2 > 1

In this case, the roots are real and distinct, so the general solution of the homogeneous equation is

y = c₁e^(r1x) + c₂e^(r2x),

where r1 = u + sqrt(u^2 - 1) and r2 = u - sqrt(u^2 - 1).

Case 3: u^2 = 1

In this case, the root is r = u, so the general solution of the homogeneous equation is

y = c₁e^(ux) + c₂xe^(ux).

Now, we can find the particular solution of the non-homogeneous equation using the method of undetermined coefficients.

Assuming a particular solution of the form y = Asin(x) + Bcos(x), we have

2uB - Asin(x) - Bcos(x) = cos(x).

Matching coefficients, we get A = 0 and 2uB - B = 1, so B = 1/(2u - 1).

Therefore, the particular solution is y = (1/(2u - 1))cos(x).

The general solution to the Cauchy problem is then

y = c₁e^(ux)cos(sqrt(1 - u^2)x) + c₂e^(ux)sin(sqrt(1 - u^2)x) + (1/(2u - 1))cos(x).

To determine the constants c₁ and c₂, we use the initial condition y(2,0) = sina.

Substituting x = 0, we get

c₁ + (1/(2u - 1)) = sina.

Substituting x = pi/2sqrt(1 - u^2), we get

c₂sqrt(1 - u^2) = 0.

Since sqrt(1 - u^2) ≠ 0, we have c₂ = 0.

Therefore, c₁ = sina - 1/(2u - 1), and the solution of the Cauchy problem is

y = (sina - 1/(2u - 1))e^(ux)cos(sqrt(1 - u^2)x) + (1/(2u - 1))cos(x).

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Answer:

C.129,600

Step-by-step explanation:

1 day = 24 hour

1.5 days = ?

(1.5days × 24 hour)/1day

=36hours

1hour = 3600 second

36hour = ?

(36hours × 3600second)/1hour

= 129,600

Answer:

(−∞, 5) ∪ (5, ∞)

Step-by-step explanation:

I really hope it helps!

Good Luck!