Two number cubes are rolled. What is the
probability that the sum of the numbers rolled is
either a 4 or a 10?
INI
1
2
3
First Number Cube
Second Number Cube
1 2 3 4 5 6
1.1 1.2 1.3 1.4 1.5 1.6
2,1 2,2 2,3 2,4 2,5 2,6
3,1 3,2 3,3 3,4 3,5 3,6
4,1 4,2 4,3 4,4 4,5 4,6
5,1 5,2 5,3 5,4 5,5 5,6
6,1 6,2 6,3 6,4 6,5 6,64
6,5 6,6
O 5/36
O 3/12
O 1/12
O 1/6

the expected return percentage is approximately 8.04%. , which is not among the provided answer options.

To calculate the expected return percentage, Expected return percentage = (Residual Income / Average Operating Assets) × 100

Plugging in the given values:

Expected return percentage = (58,250 / 5,675,000) × 100 ≈ 1.026% The expected return percentage is typically calculated by dividing the residual income by the average operating assets and expressing it as a percentage.

Now, to calculate the expected return percentage, we divide the required return by the average operating assets:

Expected Return Percentage = (Required Return on Average Operating Assets) / Average Operating Assets

Expected Return Percentage = $456,750 / $5,675,000

Calculating this division, we get:

Expected Return Percentage ≈ 0.0804

Converting this to a percentage, we find that the expected return percentage is approximately 8.04%.

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The rectangular travel board game will have a length of 16 inches.

To find the length of the board, we can set up an equation using the given information.

Let's assume the length of the board is L inches.
According to the problem, the width of the board is 9 inches shorter than the length.

So, the width would be (L - 9) inches.

The formula for the surface area of a rectangle is length multiplied by width.

Given that the surface area of the board is 112 square inches, we can set up the equation:

L * (L - 9) = 112

To solve this equation, we can distribute L to both terms inside the parentheses:

L² - 9L = 112

Next, we can move 112 to the left side of the equation by subtracting it from both sides:

L² - 9L - 112 = 0

Now, we have a quadratic equation. We can solve it by factoring or using the quadratic formula. Let's factor it:

(L - 16)(L + 7) = 0

Setting each factor equal to zero, we get two possible solutions:

L - 16 = 0 or L + 7 = 0

Solving for L, we find:

L = 16 or L = -7

Since length cannot be negative in this context, we can conclude that the length of the board is 16 inches.

The length of the board will be 16 inches.

We set up the equation L * (L - 9) = 112, where L represents the length of the board. Solving the equation, we find that the length of the board is 16 inches.

The rectangular travel board game will have a length of 16 inches.

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Answer: (x + 3)^2 + (y - 4)^2 = 49

Step-by-step explanation:

The equation of a circle given the center and radius: (x - h)^2 + (y - k)^2 = r^2

Given: center (-3,4) ; h = -3 and k = 4

diameter = 14

To find the radius: divide the diameter by 2 = 14/2 = 7 = r

Center: (-3,4) and radius: 7

Equation of a circle: (x - h)^2 + (y - k) ^2 = r^2

Substitute h = -3, k = 4, r = 7

(x - (-3))^2 + (y - 4)^2 = 7^2

Answer:

Equation of the circle: (x + 3)^2 + (y - 4)^2 = 49

Answer:

\(x=67, y=121, z=65\)

Step-by-step explanation:

One property of parallelogram is that opposite angles have the same measure, so we can write down:

\((y-9)=112\\y=121\)

Another property is that two adjacent angles are supplementary (meaning that they add up to 180 degrees). Thus, the following equations are true:

\((z+3)+112=180\\(x+1)+112=180\)

Solve the equations:

\((z+3)+112=180\\z+115=180\\z=65\\(x+1)+112=180\\x+113=180\\x=67\)

To check, add up all 4 angles and check if they sum up to 360 degrees:

\(x=67, y=121, z=65\\(y-9)+(x+1)+(z+3)+112=360\\(121-9)+(67+1)+(65+3)+112=360\\112+68+68+112=360\\360=360\)

And please ignore the fact that I cannot insert the degree sign :(

EXPLANATION

In order to order the real numbers from least to greatest we need to consider that we need to draw a number line.

The line scale marks are equally spaced and usually represent integers.

To plot a real number:

Draw and label a number line

Find where the number is on the number line and place a dot on the numbers.

Plotting Real numbers on the Number Line

Example: Graph the number 3/2 and -3.5 on a number line.

Comparing Real Numbers:

In order to compare the real numbers, we need to replace the blank with > , < or = to make a true sentence.

Example:

2/7 < 0.5

3/2 > 0.5

4/4 = 1

When we are asked to order numbers from least to greatest we can use the number line to help us to plotting the numbers and reordering them.

A strategy we can use here is to convert the numbers to decimals and then plot and/or order them as requested.

The c d f is (  1     : x≥4), b) mean is 2, c) the variance of x is 4/3 d) the value of f is 0.35 e) value of p is 0.375 and value of k is 1.4

a) F(x)=P(x ≤ x)=(  1     : x≥4

b) E(x)=∫^ (x)dx=2

c) ∫^4^0 x^ 2f(x)dx=4/3

d) f(x)=x/4,0<x<4)=0.35

e)P(1/2<X<2)=0.375

f)(p(x ≤ k)=F(K)=1.4

The pdf of x is
F(X)=1/4: 0<X<4
0 : otherwise


A) The c d f of x is
F(x)=P(x ≤ x)

=∫^ x f(t) αt
= ∫^ x1/4 αt
=1/4(t)^ x
=x/4,0<x<4
F(x)=(0: x≤0)        
      ( x/4:0<x<4)
     (  1     : x≥4)


B) We need, mean(x)
=E(x)=∫^ (x)dx

=1/4  ∫^4^ x dx
=1/4 (x^ 2/2)^ 4
=16/8
=2    

C) Here, E(X^2)          
=∫^4^0 x^ 2f(x)dx

=1/2∫^4^0 x^2 dx        
=1/4(x^ 3/3)^ 4^0
=16/3
Var(x)+E(X^2)-E^2(X)
=16/3-(2)^2
=4/3
       
d) F(1.4)=1.4/4   ∵   f(x)=(x/4,0<x<4)

=0.35


e)P(1/2<X<2)
=F(2)-F(1/2)

=2/4-1/2/4
=1/2-1/8=3/8              
=0.375

F) let R=35th percentile

so, we must have,
p(x ≤ K)=0.35           ∵  (p(x ≤ k)=F(K)
=K/4=0.35                    =k/4
k=1.4

Complete Question is given below

1. let x be a random variable with pdf . a) find the c d f f(x). b) find the mean of x. c) find the variance of x. d) find f (1.4). round to 3 decimal places. e) find P(1/2<X<2). f) find THE 35TH PERCENTILE.

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a. Salary is predicted to increase by approximately 0.012% if ros increases by 50 points.

The effect of ros on salary is not practically large.

b. The null hypothesis is that ros has no effect on CEO salary, and the alternative hypothesis is that ros has a positive effect.

The coefficient of ros is statistically insignificant at the 10% significance level, indicating that there is no evidence to support a positive effect of ros on salary.

c. Ros may not be included in the final model explaining CEO compensation in terms of firm performance since its coefficient is not statistically significant, suggesting that it has little impact on CEO salary after controlling for sales and role.

a. To calculate the percentage increase in salary if ros increases by 50 points, we can use the coefficient of ros from the regression equation. The coefficient of ros is 0.00024.

Percentage increase in salary = (Coefficient of ros) \(\times\) (Change in ros)

= 0.00024 \(\times\) 50 = 0.012

Therefore, the salary is predicted to increase by 0.012%, or 0.0012 in decimal form, if ros increases by 50 points.

To determine if ros has a practically large effect on salary, we need to consider the magnitude of the coefficient in relation to the overall scale of the data and other coefficients.

In this case, the coefficient of ros is relatively small (0.00024), suggesting that ros has a minor effect on CEO salary.

Therefore, ros does not have a practically large effect on salary.

b. To test the null hypothesis that ros has no effect on salary against the alternative that ros has a positive effect, we can perform a hypothesis test on the coefficient of ros.

The null hypothesis (H0) would be that the coefficient of ros is equal to zero (no effect), and the alternative hypothesis (Ha) would be that the coefficient is greater than zero (positive effect).

We can use the t-test statistic to test this hypothesis. With n = 209 and an alpha level of 0.10, we can compare the t-value for the coefficient of ros with the critical t-value from the t-distribution table.

If the t-value exceeds the critical t-value, we reject the null hypothesis in favor of the alternative.

c. Whether to include ros in a final model explaining CEO compensation in terms of firm performance depends on several factors.

Firstly, the coefficient of ros in the regression equation is relatively small (0.00024), indicating a minor effect on CEO salary.

Secondly, the p-value associated with the coefficient should be considered. If the p-value is less than the chosen significance level (e.g., 0.05), it suggests that the coefficient is statistically significant and not due to chance.

Additionally, other factors such as the theoretical significance of ros in relation to CEO compensation and the overall model fit (R2) should also be taken into account. If ros is theoretically meaningful and improves the overall model fit, it may be reasonable to include it in the final model. However, if ros is not theoretically relevant or does not contribute significantly to the model, it may be excluded.

Therefore, the decision to include ros in the final model should consider the statistical significance, theoretical relevance, and overall model fit, in addition to practical considerations and domain knowledge.  

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The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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(a) Example question: "How often do you look at social media while doing schoolwork?

(b) Sofie can select a simple random sample of students by using a random number generator to assign a unique identification number to each student in the online high school.

(c) The sample for Sofie's research is the 32 completed surveys she received. These surveys represent the responses of a subset of the population. The population, in this case, refers to all the students at the online high school.

(d) If Sofie uses only the completed surveys, she can conclude that approximately 50% (16 out of 32) of the students who completed the survey reported using social media while doing schoolwork.

(a) Please select one of the following options: never, rarely, occasionally, frequently, or always."

(b) She can then use the random number generator again to select a specific number of students from the entire population of students, ensuring that each student has an equal chance of being selected. For example, if there are 500 students in total and Sofie wants a sample size of 50, she can generate 50 random numbers and select the corresponding students based on their identification numbers.

(d) However, it is important to note that this conclusion is specific to the sample of completed surveys and cannot be generalized to the entire population of high school students.

To make an inference about the percent of all high school students who use social media while doing schoolwork, Sofie would need a larger and more representative sample that covers a wider range of students in the online high school.

Additionally, she should consider potential biases in the sample, such as non-response bias if the students who chose not to complete the survey have different social media usage patterns compared to those who did respond.

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The expected number of matchings goes to infinity as N › [infinity].

Matching in Graph Theory:A matching in Graph Theory is a set of edges of a graph where no two edges share a common vertex. In other words, a matching is a set of independent edges of a graph. A perfect matching in a Graph Theory is a matching of size equal to half the number of vertices in a graph.The expected number of matchings goes to 0 as N › [infinity]:The expected number of matchings goes to zero as N › [infinity] when |E| = 3/N. It is because 3/N is a relatively dense number of edges that are independent of the number of vertices that can exist between A and B. The expected number of matchings is thus very small in comparison to the total number of matchings possible as N › [infinity].The expected number of matchings goes to infinity as N › [infinity]:The expected number of matchings goes to infinity as N › [infinity] when |E| = 4.V. It is because 4.V is a relatively large number of edges that are independent of the number of vertices that can exist between A and B. The expected number of matchings is thus very large in comparison to the total number of matchings possible as N › [infinity]. Hence the expected number of matchings goes to infinity as N › [infinity].

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Answer:

Step-by-step explanation:

The implied utilization of the resources in the process can be calculated by dividing the demand rate by the total capacity of the resources. In this case, the total capacity is 1.1 + 0.93 = 2.03 clients per hour. Therefore, the implied utilization is 0.75 / 2.03 = 0.369 (or 36.9%).

The implied utilization represents the proportion of the available capacity that is being utilized to meet the demand. In this scenario, approximately 36.9% of the total capacity is being utilized to serve the clients. This indicates that there is still some unused capacity available in the process.

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Answer:

Reflexive Property of Congruence

Step-by-step explanation:

Reflexive Property of Congruence – "For any real number a, a ≅ a."

This means that line segment JP is congruent to line segment JP.

Comparing the estimated race time of approximately 73.152 seconds with the qualifying time of 90 seconds.

To create a model that estimates Tyler's race time based on the number of months in a 12-month period and his current race time, we can use the given information that his race time can be reduced by 1.5% per month.

Let's denote:

- N as the number of months Tyler has been practicing (with 0 ≤ N ≤ 12)

- T as Tyler's current race time in minutes and seconds (T ≥ 0)

- R as the qualifying time in minutes and seconds

To estimate Tyler's race time after N months of practice, we can use the formula:

Estimated race time = T * (1 - 0.015)^N

This formula accounts for the reduction of 1.5% per month. The expression (1 - 0.015)^N represents the cumulative reduction factor after N months.

The domain for this model is defined by the constraints mentioned earlier: 0 ≤ N ≤ 12 (months) and T ≥ 0 (current race time).

Now, let's use this model to estimate if Tyler will qualify for the state competition. Given that his current race time is 1 minute and 44 seconds (or 1 minute + 44 seconds = 104 seconds) and the qualifying time is 1 minute and 30 seconds (or 1 minute + 30 seconds = 90 seconds), we can substitute these values into the model.

Estimated race time = 104 * (1 - 0.015)^12

Estimated race time ≈ 104 * 0.708

Estimated race time ≈ 73.152 seconds

Comparing the estimated race time of approximately 73.152 seconds with the qualifying time of 90 seconds, we can conclude that Tyler's estimated race time is faster than the qualifying time. Therefore, based on the given conditions and the model, Tyler will likely qualify for the state swim competition.

Please note that this estimation assumes a constant reduction rate of 1.5% per month and does not account for other factors that may affect race times, such as physical fitness, training intensity, and individual performance improvements.

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Answer:

r=85

Step-by-step explanation:

r-76=9

add 76 to both sides

r=85

hope this is helpful

Answer: 85

Step-by-step explanation:

Since we're finding the placeholder of r and we're already subtracting, we need to add! What we need to do is add 76 + 9 which equals 85!

Hope this helps you! Good luck with your future work!

The maximum probability that a photon with the polarization state will be transmitted through the A filter is 1/2

To solve this problem, we need to use Malus' law, which states that the intensity of light transmitted through a polarizer is proportional to the square of the cosine of the angle between the polarization direction of the incoming light and the axis of the polarizer.

To find the overall probability that a photon will be transmitted through all three filters, we need to multiply the probabilities of each filter

P = 1/2 × cos²(θ) × 1

We are not given the angle θ, so we cannot calculate the exact value of P. However, we can calculate the maximum value of P, which occurs when the rotated filter is aligned with the A filter (i.e., θ = 0). In this case, P = 1/2.

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The given question is incomplete, the complete question is:

H filter Rotated filter Rotated filter followed by A filter An unpolarized photon beam is incident on a linear polarizing filter. The incoming photon flux is is 2.34 x 101 photons/m' /sec.  What is the probability that a photo with the polarization state be transmitted through a subsequent filter, that is aligned with the direction?

Answer:

Yes, it represents a function

Step-by-step explanation:

To check whether a graph is a function, we need to use the Line check. If an input has two outputs, then it is not a function. In this graph, we don't see one input has 2 outputs anywhere, so it is a function.

To prove ΔXWZ and ΔXYZ are congruent using sas congruence, ∠WXZ and ∠YXZ must be congruent.

In this question we have been given two triangles ΔXWZ and ΔXYZ.

We need to prove ΔXWZ and ΔXYZ are congruent using sas congruence.

To prove ΔXWZ and ΔXYZ are congruent using sas congruence we need

WX = XY                            ...........(given)      

∠W ≅ ∠Y                  

XZ  = XZ                            ..............(common side)

then ΔXWZ  ≅ ΔXYZ               ................(by SAS congruence rule)

By the SAS rule, the angle between the same side must be equal so ∠WXZ = ∠YXZ.

Therefore, it suffices to show that both triangles are congruent if ∠WXZ = ∠YXZ.

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Find a figure associated to given question below.

Answer:

infinitely many solutions

Step-by-step explanation:

Reduce the second equation by dividing all three terms by 3:  y + 1 = 2x.  Then compare this result to the first equation 2x - y = 1.  Noe that these two equations are identical.  Thus, the two lines coincide.  There are "infinitely many solutions."

To determine the constant amount that can be withdrawn each year for 20 years, we need to calculate the annuity payment using the present value of an annuity formula.

Inherited amount: RM300,000

Interest rate: 7% per year

Number of years: 20

Using the present value of an annuity formula:

PV = P * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present value (inherited amount)

P = Annuity payment (constant amount to be withdrawn each year)

r = Interest rate per period (7% or 0.07)

n = Number of periods (20 years)

Plugging in the values:

300,000 = P * [(1 - (1 + 0.07)^(-20)) / 0.07]

Solving this equation, we find that the constant amount that can be withdrawn each year is approximately RM15,000.

Therefore, the correct answer is A. RM15,000.

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Answer:

50%

Step-by-step explanation:

Let \(x\) be equal to the decimal when multiplied by 2 equals 1

\(2x=1\)

Divide both sides by 2

\(\frac{2x}{2} =\frac{1}{2} \\x=0.5\)

Multiply the decimal by 100 to get a percent

0.5×100=50%

I hope this helps!

-4x = y + 3

y = -4x - 3​ => 4x = -y - 3

-4x = y + 3

4x = -y - 3

----------------

0 = 0 (always true)

All Real Numbers

Answer:

x = x, y = -3 - 4x

Step-by-step explanation:

Subtract y from both sides of the equation.

-4x - y = 3

y = -4x - 3

Add 4x to both sides of the equation.

-4x - y = 3

y + 4x = -3

-4x - y = 3

Reorder the polynomial.

Add the two equations together to eliminate y from the system.

 -4x - y = 3

+ 4x + y = -3

          0 = 0

Since 0 = 0, the equations intersect at an infinite number of points.

Infinite number of solutions.

Solve one of the equations for y.

y = -3 - 4x

The solution is the set of ordered pairs that make y = -3 - 4x true.

Point form: (x, -3 -4x)

Equation Form: x = x, y = -3 - 4x

good luck, i hope this helps :)

Step-by-step explanation:

The perimeter of a parallelogram is twice the sum of the length of a longer and a shorter side.

The length can be evaluated by the distance formula between two points (x_1,y_1), (x_2, y_2)

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

For the longer side,

\(d=\sqrt{(7-(-4))^2+(3-2)^2}=\sqrt{122}\)

or the shorter side,

\(d=\sqrt{(7-6)^2+(3-(-2))^2}=\sqrt{26}\)

Therefore, the perimeter is given by,

\(2(\sqrt{122}+\sqrt{26})\approx254.2\)

mean =1.532

median = 6.98

standard deviation = 3.5

mean for heating degree days and broken down by season for the california

according to the given values we find the mean

mean =

-1.45+ -2.5+-4.5+1.056+3.67+6.98+3.78+2.67+4.87+3.45+2.97+-4.06/12

=1.532

median for heating degree days and broken down by season for the california  

according to the given values now we find the median

median = 6.98

standard deviation  for heating degree days and broken down by season for the california  

according to the given values now we find the standard deviation

standard deviation = square root of ∑(\(x_{i}\)- μ)^2/n

  = 3.5

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Answer:b would be 19 points

Step-by-step explanation:

Answer:

B)

Step-by-step explanation:

The answer is B) you have to devide the terms

Answer:

Step-by-step explanation:

This is a volume problem as indicated by the exponent on the unit feet. Cubed is a volume thing, whereas squared is an area thing, etc.

The volume for a box-shaped microwave is

V = l x w x h and we are given the length and the width, but those are in inches and they need to be in feet. That's the tricky part here...catching the inconsistency in the units!

18 inches = 1.5 ft and

14 inches = 7/6 feet

Filling in:

1.75 = 1.5 x 7/6 x h and

1.75 = 1.75h so

h = 1 foot

The size of the quarterly deposits in Shelby's RRSP account was approximately $147.40.

Let's denote the size of the quarterly deposits as \(D\). The total number of deposits made over 9 years is \(9 \times 4 = 36\) since there are 4 quarters in a year. The interest rate per period is \(r = \frac{3.50}{100 \times 12} = 0.0029167\) (3.50% annual rate compounded monthly).

Using the formula for the future value of an ordinary annuity, we can calculate the accumulated value of the RRSP fund:

\[55,000 = D \times \left(\frac{{(1 + r)^{36} - 1}}{r}\right)\]

Simplifying the equation and solving for \(D\), we find:

\[D = \frac{55,000 \times r}{(1 + r)^{36} - 1}\]

Substituting the values into the formula, we get:

\[D = \frac{55,000 \times 0.0029167}{(1 + 0.0029167)^{36} - 1} \approx 147.40\]

Therefore, the size of the quarterly deposits, rounded to the nearest cent, is approximately $147.40.

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Answer:

its 93 -_-

Step-by-step explanation:

If its wrong sorry

Answer: 8.6

same side s C and B

Answer: 7.2

Step-by-step explanation:

Since this is a right triangle we can use the Pythagorean theorem to solve for side b.

Pythagorean theorem: a²+b²=c²

Since the side length opposite the right angle is the hypotenuse we plug 11.2 in for C

(8.6)² + b²=(11.2)²

73.96 + b² = 125.44

b²=51.48

b = 7.17495644586

b=7.2