Event A has probability of 0.4 to occur and Event B has a probability of 0.5 to occur. Their union (A or B) has a probability of 0.7 to occur. Then:
(A) A and B are mutually exclusive.
(B) A and B are not mutually exclusive.
(C) A and B are independent.
(D) A and B are dependent.
(E) both (B) and (C).

A composite figure consists of two smaller figures - a rectangle and a Triangle. Therefore, the answer is 4 cm² (option a).

A composite figure that consists of two smaller figures - a rectangle and a triangle.

To find the area of the composite figure, we need to find the area of each smaller figure and add them up .Areaof rectangle to find the area of the rectangle, we need to multiply its length and width :Area of rectangle = 2 cm × 4 cm = 8 cm²Areaof triangle too find the area of the triangle, we need to use the formula :

Area of triangle = 1/2 × base ×heightT

he base of the triangle is 4 cm and the height is 2 cm, so:

Area of triangle = 1/2 × 4 cm × 2 cm = 4 cm²Area of composite figure To find the area of the composite figure, we need to add up the area of the rectangle and the area of the triangle: Area of composite figure = 8 cm² + 4 cm² = 12 cm². Therefore, the answer is 4 cm² (option a).

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In a group of 62 students, 27 are normal, 13 are abnormal, and 32 are normal-abnormal. We want to find the probability that a student picked at random is either normal or abnormal.

To calculate this probability, we need to consider the total number of students who are either normal or abnormal. This includes the students who are solely normal (27), solely abnormal (13), and those who are both normal and abnormal (32). We add these numbers together to get the total count of students who fall into either category, which is 27 + 13 + 32 = 72.

The probability of picking a student who is either normal or abnormal can be calculated by dividing the total count of students who are either normal or abnormal by the total number of students in the group. Therefore, the probability is 72/62 = 1.1613.

To find the probability of picking a student who is either normal or abnormal, we consider the total number of students falling into those categories. Since a student can only be classified as either normal, abnormal, or normal-abnormal, we need to count the students falling into each category and add them together. Dividing this sum by the total number of students gives us the probability. In this case, the probability is greater than 1 because there seems to be an error in the provided data, where the total count of students who are either normal or abnormal (72) exceeds the total number of students in the group (62).

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Answer:    F  2^4+2^3 .3^2

Step-by-step explanation:

16+2*36

2^4+72

2^4+2^3 .3^2

here 2^3=8

    and 3^2=9

so 8*9=72

Answer:

2 dollars donated.

Step-by-step explanation:

Answer:

18.18

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

just add them

them you get answer

Answer:

1.32

Step-by-step explanation:

total area = 33

33/5 1/2 = 6 .         X=6

5 1/2 x 1/2 = 2.75 .       6 x 1/2 = 3

2.75 x 3 = 8.25

new area = 8.25

8.25 x .13 = 1.32

Answer: 1. A 2. 1/5 3. 5/12 4. Not sure

Step-by-step explanation:

Answer:

x = 45

Step-by-step explanation:

[tex]\frac{x}{5} -7=2\\\\\frac{x}{5}=9\\\\x=45[/tex]

1)The average return for X is 14.9% and for Y is 21.84%.

2)The variance for X is 48.74 and for Y is 149.64.

3)The standard deviation for X is 6.98% and for Y is 12.23%.

What is Standard Deviation?

Standard deviation is a statistical measure that quantifies the amount of variability or dispersion in a dataset. It measures how spread out the values in a dataset are around the mean or average value. A low standard deviation indicates that the data points are close to the mean, while a high standard deviation indicates that the data points are spread out over a wider range.

[tex]\begin{document}\begin{tabular}{ccc}\topruleYear & X (\%) & Y (\%) \\\midrule1 & 22.1 & 27.3 \\2 & 17.1 & 4.1 \\3 & 10.1 & 29.3 \\4 & 20.2 & 15.2 \\5 & 5.1 & 33.3 \\\bottomrule\end{tabular}[/tex]

[tex]\textbf{1. Calculate the average returns for X and Y:}[/tex]

To calculate the average return for X, we sum up all the returns for X and divide by the number of observations:

[tex]\[\text{Average return for X} = \frac{{22.1 + 17.1 + 10.1 + 20.2 + 5.1}}{5} = 14.9\%\][/tex]

To calculate the average return for Y:

[tex]\[\text{Average return for Y} = \frac{{27.3 + 4.1 + 29.3 + 15.2 + 33.3}}{5} = 21.84\%\][/tex]

Therefore, the average return for X is 14.9% and for Y is 21.84%.

[tex]\textbf{2. Calculate the variances for X and Y:}[/tex]

To calculate the variance for X, we need to calculate the squared differences between each return and the average return for X, sum them up, and divide by the number of observations minus one:

[tex]\[\text{Variance for X} = \frac{{(22.1 - 14.9)^2 + (17.1 - 14.9)^2 + (10.1 - 14.9)^2 + (20.2 - 14.9)^2 + (5.1 - 14.9)^2}}{5-1} = 48.74\][/tex]

To calculate the variance for Y:

[tex]\[\text{Variance for Y} = \frac{{(27.3 - 21.84)^2 + (4.1 - 21.84)^2 + (29.3 - 21.84)^2 + (15.2 - 21.84)^2 + (33.3 - 21.84)^2}}{5-1} = 149.64\][/tex]

Therefore, the variance for X is 48.74 and for Y is 149.64.

[tex]\textbf{3. Calculate the standard deviations for X and Y:}[/tex]

To calculate the standard deviation for X, we take the square root of the variance for X:

[tex]\[\text{Standard deviation for X} = \sqrt{48.74} \approx 6.98\%\][/tex]

To calculate the standard deviation for Y:

[tex]\[\text{Standard deviation for Y} = \sqrt{149.64} \approx 12.23\%\][/tex]

Therefore, the standard deviation for X is 6.98% and for Y is 12.23%.

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Answer:

8851.86

Step-by-step explanation:

100-4.3= 95.7%

15000(.957)^12

Answer:

0.7

Step-by-step explanation:

Answer:

calm down rosie....  it's okay to not be too good at math... take Justin Timberlake.  in the show   "Friends with Benefits"  he's horrible at math but good at life.  so don't worry too much. You are still a good person.. even if you're bad at math :P

Step-by-step explanation:

now for the math part

as below

(A) The average cost per unit when 400 frames are produced is $525.

(B) The marginal average cost at a production level of 400 units is approximately $0.999 per frame. (C) The estimated average cost per frame if 401 frames are produced is approximately $524.19.

(A) Average cost per unit = Total cost / Number of frames

                    = C(x) / x

                    = (50,000 + 400x) / x

Substituting x = 400:

Average cost per unit = (50,000 + 400 * 400) / 400

                    = (50,000 + 160,000) / 400

                    = 210,000 / 400

                    = 525 dollars

So, the average cost per unit when 400 frames are produced is $525.

To find the marginal average cost at a production level of 400 units, we need to calculate the derivative of the average cost function:

(B) Marginal average cost = d/dx [(50,000 + 400x) / x]

                         = (400 - 50,000/x^2) / x

Substituting x = 400:

Marginal average cost = (400 - 50,000/400^2) / 400

                    = (400 - 50,000/160,000) / 400

                    = (400 - 0.3125) / 400

                    = 399.6875 / 400

                    = 0.999

The marginal average cost at a production level of 400 units is approximately 0.999 dollars per frame.

To estimate the average cost per frame if 401 frames are produced, we can use the average cost function:

(C) Average cost per unit = (50,000 + 400x) / x

Substituting x = 401:

Average cost per unit = (50,000 + 400 * 401) / 401

                    = (50,000 + 160,400) / 401

                    = 210,400 / 401

                    ≈ 524.19 dollars

Therefore, the estimated average cost per frame when 401 frames are produced is approximately $524.19.

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Answer:

the correct answer is d

hope it help

Answer:

Q:12) 9m-1.7m =7.3m

Q:13) 1.5m-0.8m=0.7

Q:14) 60cm-30cm= 30cm

Answer:

60 km

455 km

23 km

60 km

82.5 km

Step-by-step explanation:

Time = t

Speed = s

Distance is given by

[tex]d=s\times t[/tex]

t = 2 hours

s = 30 km/h

[tex]d=30\times 2=60\ \text{km}[/tex]

Distance driven is 60 km.

t = 7 hours

s = 65 km/h

[tex]d=65\times 7=455\ \text{km}[/tex]

Distance driven is 455 km

t = [tex]\dfrac{1}{2}\ \text{hours}=0.5\ \text{hours}[/tex]

s = 46 km/h

[tex]d=46\times 0.5=23\ \text{km}[/tex]

Distance driven is 23 km

t = 45 minutes = [tex]\dfrac{45}{60}=0.75\ \text{hours}[/tex]

s = 80 km/h

[tex]d=80\times 0.75=60\ \text{km}[/tex]

Distance driven is 60 km

t = [tex]1\dfrac{1}{2}\ \text{hours}=1.5\ \text{hours}[/tex]

s = 55 km/h

[tex]d=55\times 1.5=82.5\ \text{km}[/tex]

The distance driven is 82.5 km

The square root of 144 using the prime factorization method is 12.

When a number is multiplied by itself, the square of the number can be obtained.

The square root of 144 can be determined by the prime factorization method:

The prime factors of 144 are:

[tex]144 = 2 \times 2\times2 \times2 \times3 \times 3[/tex]

Since the square root can be obtained by forming the pair of the given number.

It can be written as:

144 = [tex]2^2 \times 3[/tex]

     =[tex]4 \times 3[/tex]

     = 12

Thus, the square root of 144 is 12.

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Answer:a

Step-by-step explanation:

Answer:

Approximately 19 bags of sand will be required.

Step-by-step explanation:

The statement misses the drawing of the sandbox which I have attached here. We can find the dimensions mentioned in the picture.

Length of box = 6.5 feet

Width of box = 5 ft

Height of box = 1.5 ft

Calculating the volume = V = length x width x height = 6.5 x 5 x 1.5 = 48.75 cubic ft

As given in the question, one sand bag has 2.6 cubic ft of sand

No of bags required = 48.75 / 2.6 = 18.75

The test statistic is approximately 0.45.

To calculate the test statistic for testing the null hypothesis H₀:p = 0.55 against the alternative hypothesis H₁:p ≠ 0.55, you can use the formula for the z-test statistic:

z = (p' - p) / √(p(1-p)/n)

where:

p' = sample proportion

p = hypothesized proportion under the null hypothesis

n = sample size

In this case, the sample proportion is p' = 55/96 = 0.5729 (rounded to 4 decimal places), p = 0.55, and n = 96.

Now let's calculate the test statistic:

z = (0.5729 - 0.55) / √(0.55 × (1-0.55) / 96)

z = (0.0229) / √(0.55 × 0.45 / 96)

z = (0.0229) / √(0.2475 / 96)

z = (0.0229) / √0.002578125

z = (0.0229) / 0.050773383

z ≈ 0.4502 (rounded to 4 decimal places)

Therefore, the test statistic is approximately 0.45.

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The volume of the solid S, where the base is a triangular region and cross-sections perpendicular to the y-axis are semicircles, can be found using calculus. The volume of S is (3π/8) cubic units.

In the first part, the volume of the solid S is (3π/8) cubic units.

In the second part, we can find the volume of S by integrating the areas of the cross-sections along the y-axis. Since the cross-sections are semicircles, we need to find the radius of each semicircle at a given y-value.

Let's consider a vertical strip at a distance y from the x-axis. The width of the strip is dy, and the height of the semicircle is the x-coordinate of the triangle at that y-value. From the equation of the line, we have x = (3/2)y.

The radius of the semicircle is half the width of the strip, so it is (1/2)dy. The area of the semicircle is then[tex](1/2)\pi ((1/2)dy)^2 = (\pi /8)dy^2.[/tex]

To find the limits of integration, we note that the base of the triangle extends from y = 0 to y = 2. Therefore, the limits of integration are 0 to 2.

Now, we integrate the area of the semicircles over the interval [0, 2]:

V = ∫[tex](0 to 2) (\pi /8)dy^2 = (\pi /8) [y^3/3][/tex] (evaluated from 0 to 2) = (3π/8).

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Answer:

-3/5 is the slope of the line.

Answer:

i) a) 4 lines

b) 1 line

c) 3 line

d) 2 line

ii) don't know

To determine the percentage of the segment that should participate in the baseball camp in order to make a $1500 profit, we need to calculate the breakeven point and then find the corresponding percentage.

The breakeven point is the point where the revenue equals the total cost, resulting in zero profit. In this case, the breakeven point can be calculated by adding the fixed cost (TFC) to the variable cost per person multiplied by the number of participants.

Given that the price per participant is $80 and the variable cost per person is $5, we can set up the equation:

80x - (5x + 9000) = 0

Simplifying the equation, we have:

75x - 9000 = 0

75x = 9000

x ≈ 120

So, the breakeven point is approximately 120 participants.

To calculate the percentage, we need to divide the breakeven point (120) by the segment size (10000) and multiply by 100:

(120/10000) * 100 ≈ 1.2%

Therefore, the percentage of the segment that should participate in the baseball camp to make a $1500 profit is not exactly 1.2%, but it is closest to option D) about 1.4%.

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Answer:

Cost of each cord = $7.5

Step-by-step explanation:

Given:

Discount rate = 30% = 0.30

Amount save by Lisa = $9

Number of charger = 4

Find:

Cost of each cord

Computation:

Total cost of 4 charger =  Amount save by Lisa[1/Discount rate]

Total cost of 4 charger =  9[1/0.30]

Total cost of 4 charger =  $30

Cost of each cord = Total cost of 4 charger / Number of charger

Cost of each cord = $30 / 4

Cost of each cord = $7.5

The NPV of the investment opportunity at a 6% interest rate is approximately $6,374. Taking into account the timing and value of the cash flows, it is advisable to take the opportunity.

The Net Present Value (NPV) of an investment opportunity calculates the present value of future cash flows discounted at a specific interest rate. Let's calculate the NPV at a 6% interest rate:

Year 1: Receive $500.

Year 2: Receive $1,500.

Year 10: Receive $10,000.

To find the NPV, we need to discount each cash flow back to its present value and sum them up:

NPV = (Cash flow at Year 1 / (1 + Interest rate)^1) + (Cash flow at Year 2 / (1 + Interest rate)^2) + (Cash flow at Year 10 / (1 + Interest rate)^10) - Initial investment

Plugging in the values, we get:

NPV = (500 / (1 + 0.06)^1) + (1500 / (1 + 0.06)^2) + (10000 / (1 + 0.06)^10) - 10000

≈ $6,374

Therefore, at a 6% interest rate, the NPV of the investment opportunity is approximately $6,374. Since the NPV is positive, it indicates that the investment is expected to generate a return greater than the cost of capital. Hence, it is advisable to take the opportunity.

(Note: The calculation for the NPV at 0% interest rate requires all future cash flows to be treated at their face value. Therefore, the NPV at a 0% interest rate would be equal to the sum of all future cash flows, which is $11,000 in this case.)

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