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When rolling a pair of dice, there are 36 possible outcomes, each representing a unique combination of the numbers on the two dice.

Event A: "at least one die is a 3" is not mutually exclusive with Event B: "at least one die is a 6" or Event C: "the sum is 11"

Event A and Event B are mutually exclusive because when one of the die is a 6, the other die cannot be a 3 and vice versa.

Event A and Event C are not mutually exclusive because there are some outcomes where at least one die is a 3 and the sum is 11. For example (3,8), (4,7) and (6,5) are all outcomes where at least one die is 3 and the sum is 11.

Event B and Event C are not mutually exclusive because there are outcomes where at least one die is a 6 and the sum is 11. For example (5,6) and (6,5) are both outcomes where at least one die is a 6 and the sum is 11.

So, in conclusion, Event A and Event B are mutually exclusive, but Event A and Event C and Event B and Event C are not mutually exclusive.

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Answer:

The transaction amount for 3: -155.15

The transaction amount for 4: -223.75

Step-by-step explanation:

The decision between one sided and two sided alternative hypothesis is based on the statement of the null hypothesis and the alternative hypothesis appropriate for the context of the problem.

The hypothesis test is used to check if the observed data is consistent with the expected data or not. To do this, a null hypothesis and an alternative hypothesis are formulated. The decision between one sided and two sided alternative hypothesis is based on the statement of the null hypothesis and the alternative hypothesis appropriate for the context of the problem. The one-sided alternative hypothesis is used when the researcher is mainly interested in testing whether the population mean is either greater than or less than a given value. On the other hand, the two-sided alternative hypothesis is used when the researcher is mainly interested in testing whether the population mean is either different from or not different from a given value. The level of significance chosen for the test should be determined before the decision is made between one sided and two sided alternatives.

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Using the normal distribution and the central limit theorem, considering that this is a sample proportion, as we are dealing with percentages, it is found that there is a 0.1562 = 15.62% probability of getting less than 50% Democrats in a random sample of size 100.

Normal Probability Distribution

In a normal distribution with mean  and standard deviation , the z-score of a measure X

It measures how many standard deviations the measure is from the mean.  

After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample proportions of a proportion p in a sample of size n has mean  and standard deviation .

In this problem:

55% of the registered voters are Democrats, hence .

A sample of size 100 is taken, hence

The mean and the standard deviation of the sampling distribution of sample proportions

The probability of getting less than 50% Democrats in a random sample of size 100 is the p-value of Z when X = 0.5, hence:

By the Central Limit Theorem

has a p-value of 0.1562.

0.1562 = 15.62% probability of getting less than 50% Democrats in a random sample of size 100.

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If a machine closes 35 packages per minute. The number of packages the machine can close in 40 minutes is: 1400 packages.

Using this formula to  find the number of packages

Number of packages = Packages per minute machine closes ×   Number of minutes

Let plug in the formula

Number of packages =  35 packages per minute × 40 minutes

Number of packages =  1400 packages

Therefore we can conclude that the number of packages is 1400 packages.

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The complete question is:

A machine closes 35 packages per minute How many packages can the machine close in 40 minutes? Enter your answer in the box. packages?

The graph of "square root of 13" is 3.61 is seen below.

So, the graph of "square root of 13" = 3.61 is seen below.

As a result, the quotient obtained using the aforementioned division approach, or roughly 13 = 3.605, is the necessary square root of 13.

Plotting the number "square root of 13" on the number line is necessary.

since we are aware,

13 has a square root of 3.61.

In other words, we must write 3.61 on the number line.

Since 3.61 is between 3 and 4, it tends to lean more toward 4.

So, the graph of "square root of 13" = 3.61 is seen below.

The graph of "square root of 13" is 3.61 is seen below.

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A. The unit cost of the product follows a normal distribution with an expected value of ETB 305 and a standard deviation of ETB 5.

B. The expected value of the unit cost of the product is ETB 305 and the variance is ETB 25.

In order to calculate the standard deviation, follow the following steps:

1. Calculate the mean (average) of your data set.

2. For each data point, subtract the mean and square the result (the squared difference).

3. Sum all of the squared differences.

4. Divide the sum by the number of data points. This gives you the variance.

5. Take the square root of the variance to get the standard deviation.

Therefore, the correct answer is as given above

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The probability that the first item is not the first to be delivered is 0.6667

Let's call the events that the first, second, and third items arrive on the first day of February A, B, and C, respectively.

Therefore, the probability that one of the other two items arrives first is

1/3 + 1/3 = 2/3.

The probability that the first item is not the first to be delivered is

1 - 2/3 = 1/3

Evaluate

1 - 2/3 = 0.6667

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Using the ratio, if a certain piece of brass requires 10kg of zinc, the weight of the copper required for the same piece is 15 kg.

A ratio expresses the frequency with which one number contains another. If a fruit dish contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six. Similarly, the orange to lemon ratio is 6:8, while the orange to total fruit ratio is 8:14.

Here,

Given that a company uses copper and zinc in a weight-to-weight ratio of 3:2 to make bronze. As a result, the metal ratio can be written as,

3/2 = copper/zinc

Now, because the zinc weighs 10 kilograms.

As a result, the ratio can be depicted as,

3/2 = copper / zinc

3/2 = copper / 10kg

3 x 10 /2 =copper

30/2 = copper

15 = copper

As a result, if 10kg of zinc is required for a specific piece of bronze, the weight of copper required for the same piece is 15kilograms.

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Answer:

The cost of the wings per dollar is 18/15 = 1.2 wings per dollar.

Answer:

1.2

Step-by-step explanation:

Answer:

  A, B, C, D

Step-by-step explanation:

You want to know which of these equations have exactly one solution:

An equation in a single variable will have one solution if the variable terms on either side of the equal sign have different coefficients.

  A: coefficients are -13 and +13; one solution (x=25/26)

  B: coefficients are 12 and 13; one solution (x=0)

  C: coefficients are -13 and +13; one solution (x=-1/26)

  D: coefficients are 12 and 13; one solution (x=24)

All of the given equations have exactly one solution.

The parent function for f(x) = -1/2√x+4 can be transformed in a variety of ways to create new functions.

Shifting:

f(x) = -1/2√x+4 + c, where c is the amount of the shift on the y-axis

Reflecting:

f(x) = -1/2√-x+4, where the negative sign reflects the graph across the y-axis

Stretching:

f(x) = k(-1/2√x+4), where k is the amount of the stretch on the y-axis.

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Kris currently has $190 and wants to have at least $1,625 by the end of the summer. To find out how much money she needs to earn each weekend we need to subtract the money she already has from the money she wants to have and divide that by the number of weekends.

$1,625 - $190 = $1,435

$1,435 ÷ 8 = $179.38

So, Kris needs to earn at least $179.38 each weekend to reach her goal.

Answer choice C. Kris needs to earn at least $179.38 each weekend to meet her goal. is the best interpretation of the solution in the context of the problem.

The equations are 100x + 80y = 25600 and 50x + 160y = 18200.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Let x be the cost of a quail and y be the cost of a rabbit bought by the business lady.

Given that a business lady bought 100 quails and 80 rabbits for sh 25600.

100x + 80y = 25600

If she bought twice as many rabbits, number of rabbits = 80 × 2 = 160.

If she bought half as many quails, number of quails = 100/2 = 50

The equation is then,

50x + 160y = 25600 - 7400

50x + 160y = 18200

Hence the equations formed here at two situations are 100x + 80y = 25600 and 50x + 160y = 18200.

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if there are 5 people and 2 have to sit next to each other and 2 others cant sit next to each other, then 30 combinations possible

What are combinations?

A combination is a calculation that determines the number of possible arrangements in a collection of items in which the order of the selection does not matter. In combinations we can select the items in any order.

nn!/r!(n-r)!

Number of ways=5

=5!/2!2!

=5!/2*2

=5*4*3*2/2*2

=30

=30 ways

if there are 5 people and 2 have to sit next to each other and 2 others cant sit next to each other, then 30 combinations possible

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The 99% confidence interval for population proportion p is 0.117 < P < 0.243 for the true population proportion of people who received flu vaccinations this year when out of 200 people sampled, 36 received flu vaccinations this year.

Given that,

n = 200

x = 36

Point estimate = sample proportion

= x/n = 36/200 = 0.18

1 - p = 1 - 0.18 = 0.82

At a 99% level, the z is,

α = 1 - 0.99 = 0.01

α/2 = 0.005

Zα/2 = 0.005Z = 2.576

The margin of error = E = Zα/2 [tex]\sqrt{p(1-p)} /n[/tex]

= 2.576[tex]\sqrt{0.18*0.82} /200[/tex]

E = 0.063

A 99% confidence interval for population proportion p is,

p - E < P < p + E

0.18 - 0.063 < P < 0.18 + 0.063

0.117 < P < 0.243

Therefore, the 99% confidence interval for population proportion p is 0.117 < P < 0.243 for the true population proportion of people who received flu vaccinations this year when out of 200 people sampled, 36 received flu vaccinations this year.

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C) 1/2 is the value of P(A)

Independent events are events in probability and statistics that have no effect on each other and are not related to each other in any way, so the outcome of one event does not affect the outcome of the other event.

let the value of P(A) be x and the value of P(B) be y  given A and B are independent events

so P(A∩B) = P(A) * P(B)

=> x*y=1/6 ---(i)

now P(⁻A) = 1 - P(A) , P(B) = 1 - P(⁻B)

so P( ⁻A  ∩ ⁻B ) = (1-x)*(1-y)

=> 1 -x - y +xy = 1/3

=> x +y  =1+1/6-1/3

=> x + y = 5/6  ----(ii)

x - y = √(x+y)²-4xy

=> √(5/6)² - 4*1/6

=> √25/36 - 4/6

=> √(25-24)/36

=> √1/36

=> 1/6

so x-y = 1/6 ---(iii)

adding equation (ii) and (iii) we get

2x = 1

=> x = 1/2

so P(A)  = 1/2

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Complete question :

If A and B are independent events of random experiment such that P(A∩B)=1/6 and P( ⁻A  ∩ ⁻B )=1/3, then P(A)=?

a. 1/4b. 1/5c. 1/2s. 2/3

Step-by-step explanation:

To calculate how much should be placed in an account now to have $21,200 cash for a new car 7 years from now, we can use the formula for compound interest:

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

Where:

A = future value (amount of money after t years)

P = present value (amount of money now)

r = annual interest rate (as a decimal)

n = number of times the interest is compounded per year

t = number of years

In this case, we have:

A = $21,200

r = 0.064 (6.4% as a decimal)

t = 7

n = 1 (the interest is compounded annually)

So, we can solve for P:

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

P = $21,200 / (1 + 0.064)^(7)

P = $15,093.35

Therefore, the person should place $15,093.35 in an account now to have $21,200 cash for a new car 7 years from now, at an annual interest rate of 6.4%.

Answer:

2x, 2x + 2

Step-by-step explanation:

2x is even

2x + 2 = 2(x+1)

x and x+1 are consecutive integers

So multiplying both by 2 makes  them consecutive even integers

For example with x = 1

2x = 2, 2(x+1) = 2 . 2 = 4 which is next even consecutive integer

Answer:

2x, 2x + 2

Step-by-step explanation:

Each expression is divisible by 2, so it is even.

The probability of drawing the same color lollipop twice is 0.72.

According to the given question, 3 lollipops were picked up one by one, but after every draw, the lollipop is kept back in the jar. So it is a case of sampling with replacement.

Thereby, there will be 6 cases when the same color i.e red & yellow lollipops will be picked up 2 times i.e, rry, ryr, yrr, yry, yyr, ryy

(where r & y stand for red and yellow lollipops respectively)

And the corresponding probabilities for these six situations will be

(i) 3/5∗3/5∗2/5=18/125

(ii) 3/5∗2/5∗3/5=18/125

(iii)  2/5∗3/5∗3/5=18/125

(iv)  2/5∗3/5∗2/5=12/125

(v)  2/5∗2/5∗3/5=12/125

(vi)  3/5∗2/5∗2/5=12/125

Hence, the required probability will be the sum of all these probabilities i.e,

(i)+(ii)+(iii)+(iv)+(v)+(vi)

=3∗(18/125)+3∗(12/125)

=90/125

so, the probability that the same color Lollipop will be drawn two times is 90/125 or 0.72.

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The dealerships will each have sold 23 cars in 1 day.

The first step is to form a linear equation that represents the number of cars that are sold by the dealerships. A linear equation is an equation that has a single variable that is raised to the power of one.

The form of a linear equation that represents the total cars sold by the dealership is:

Total cars sold = cars already sold + (number of cars sold per day x number of days)

Total cars sold by Clarksville Cars= 15 + (8 x d)

= 15 + 8d

Total cars sold by Robinson's Autos = 13 + (10 x d)

= 13 + 10d

When the two dealerships are tied, the two above functions would be equal:

13 + 10d= 15 + 8d

In order to determine the value of d, take the following steps:

Combine and add similar terms:

10d - 8d = 15 - 13

2d = 2

Divide both sides of the equation by 2

d = 2 / 2

w = 1 week

Number of cars that would have been sold by each dealership =

13 + 10(1)

13 + 10 = 23 cars

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The center of the circle is (3 , -2) and the radius is 4 then the equation of circle is (x)² + (y)²-6x+4y = 3

What is a circle?

The circle is defined as the locus of the point traces around a fixed point called as the center and is equidistant from the outer trace.

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

The equation of the circle is,

( x - h )² + ( y - k )² = r²

(x-3)² + (y+2)² = 16

(x)² + (y)²-6x+9 +4y+4 = 16

(x)² + (y)²-6x+4y = 3

Compare the equations and find the center and radius,

Center = ( h,k) = ( 3, -2)

Radius = r = 4

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Answer: x= -1

Step-by-step explanation:

9x-3(x-5)=6x+3

9x-3x+15=6x+3

9x+6x-3x= 3-15

    15x-3x= -12

         12x= -12

            x= -1

a) The information not required in the tax computation is; the amount of the bill

b) The total bill is calculated as; $12.65

A percentage is defined as a number or ratio that is expressed as a fraction of 100.

The parameters are that a restaurant customer left ​$1.65 as a tip, the tax was 4 % and the tip was 15​% of the after tax cost. Thus;

Let the bill after the tax plus tip will be a and the bill after tax be b,

Therefore,

a = b + $1.65

Since $1.65 = 15% of b, then we have;

b = 1.65*100/15

b = 11

a = 11 + 1.65

a = 12.65

Hence, the total cost after the tip = $12.65

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The point (-5,3) is in the same quadrant as the fourth vertex of the square.

The given points are representing the points in the quadrant of the cartesian coordinate system. According to this any location on a 2-D plane is represented by 2 numbers, x and y, where x represents the horizontal displacement from the origin of the plane and y represents the vertical displacement from the origin.

Since the given points are the vertices of a square they must be in the form (c, d), (c, -d), (-c, -d), and (-c,d). So, from the given points only the B (-5,3) satisfies the given condition and forms the square.

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Sampling variation will have more impact on confidence interval but it is not accounted for by the margin of error.

What is Sampling variation?

The term "sampling variance" describes how much a sample estimate (a statistic) is likely to fluctuate from sample to sample due to the unique nature of each sample.

Sample Sizes and Variability are the factors which lead to sampling variation. As and when the sample size is changed i.e. either increased or decreased, the variability of samples fluctuates.

Since, Sam runs a large chain of car repair shops, this means he has large number of employees.

But his sample size is only of 10 employees whom he asks about their billable hours from which he constructs a 95% confidence interval for the true mean number of billable hours for all employees in the company.

Since, sampling variation is greatly affected by the sample size and variability, therefore it will have more impact on confidence interval.

Hence, sampling variation will have more impact on confidence interval but it is not accounted for by the margin of error.

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Since the options are missing in the question, here are the options from which answer is to be chosen

Answer:4x+3

Step-by-step explanation:

Given the following in the question if:

Volume of the box= 4x3+19x2+12z

Height of the box= x

width of the box =?

we have to find the width of the box, so as we know that

box is in the shape of cuboid, so

Volume of the cuboid = length * width * height

4x3+9x2+12x   =   x+4* width * x

width = 4x3+9x2+2x/x2+4x

we have to use long division method for this algebraic expression to divide and find width of the box.

we get width= 4x+3

Hence, the width of the box which in the shape of cuboid is 4x+3

Answer:

240

Step-by-step explanation:

C. 240

The expected value is calculated by taking the total sample size (300) and multiplying it by the hypothesized proportion of graduates who have full-time employment within 6 months of graduation (80%).

Expected value = 300 x (80/100) = 240

Answer:

[tex]y = \frac{1}{3} x - 4[/tex]

[tex]\it y=ax+b\\ \\ x=0 \Rightarrow y=-4 \Rightarrow b=-4 \Rightarrow y=ax-4\\ \\ x=3 \Rightarrow y=-3 \Rightarrow a\cdot3-4=-3\bigg|_{+4}\Rightarrow a\cdot3=1 \bigg|_{:3}\Rightarrow a=\dfrac{1}{3} \\ \\ Therefore, the\ equation\ of\ this \ line\ is: \ \ y=\dfrac{1}{3}x-4[/tex]