Two numbers whose sum is 54 and whose difference is 4

P(A) = (4/36) * (3/6) = 1/18. Rounded to four decimal places, P(A) is 0.0556.  P(B) is 0.1111.  A and B are mutually exclusive because they cannot occur at the same time. If event A occurs (rolling a 4 or 5 first followed by an even number), then the sum of the two dice will be either 6 or 8. A and B are mutually exclusive because they cannot occur at the same time.  the lowest possible sum for event A is 6. Therefore, the two events are not independent.

a. To calculate P(A), we need to find the probability of rolling 4 or 5 first (which can occur in 4 out of 36 ways) and then rolling an even number (which can occur in 3 out of 6 ways). The probability of both events occurring is the product of their probabilities: P(A) = (4/36) * (3/6) = 1/18. Rounded to four decimal places, P(A) is 0.0556.

b. There are only 4 ways to get a sum of 5 or less: (1,1), (1,2), (2,1), and (1,3). There are a total of 36 possible outcomes when rolling two dice, so P(B) = 4/36 = 1/9. Rounded to four decimal places, P(B) is 0.1111.

c. A and B are mutually exclusive because they cannot occur at the same time. If event A occurs (rolling a 4 or 5 first followed by an even number), then the sum of the two dice will be either 6 or 8. But if event B occurs (the sum of the two dice is at most 5), then the sum of the two dice will be either 2, 3, 4, or 5. These two events cannot occur together because their outcomes are mutually exclusive.

d. A and B are not independent events. The occurrence of one event affects the probability of the other event. For example, if we know that event A has occurred (rolling a 4 or 5 first followed by an even number), then the probability of event B (the sum of the two dice is at most 5) is zero, since the sum of the two dice will be either 6 or 8. Similarly, if we know that event B has occurred (the sum of the two dice is at most 5), then the probability of event A (rolling a 4 or 5 first followed by an even number) is zero, since the lowest possible sum for event A is 6. Therefore, the two events are not independent.

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Answer:

t = 9 , u = 7

Step-by-step explanation:

for the 2 triangles to be congruent , then corresponding sides must be congruent, that is

QR = CD , so

5t = t + 36 ( subtract t from both sides )

4t = 36 ( divide both sides by 4 )

t = 9

and

DE = RS , so

6u = u + 35 ( subtract u from both sides )

5u = 35 ( divide both sides by 5 )

u = 7

Here, we are given the following values' = x4 + 6 x = −5 Δx = dx = 0.01To find: Δy and dy. In order to calculate Δy and dy, we will use the following formulas:Δy = f(x + Δx) − f(x)dy = f'(x) dx Where, f(x) = x4 + 6 x

We know that, Δx = dx = 0.01So, let's calculate the values of Δy and dy by putting the given values in the above formulas.Δy = f(x + Δx) − f(x)f(x + Δx) = (x + Δx)4 + 6 (x + Δx)Putting the given values in this formula we get, f(x + Δx) = (-5 + 0.01)4 + 6(-5 + 0.01) = 55.0184f(x) = x4 + 6 x Putting the given values in this formula we get, f(x) = (-5)4 + 6 (-5) = -605Δy = f(x + Δx) − f(x)= 55.0184 - (-605)= 660.0184 dy = f'(x) dx We will find f'(x) first.f(x) = x4 + 6 xf'(x) = 4x³ + 6Now, let's calculate the value of dy by putting the values of f'(x), dx and x in the given formula. dy = f'(x) dx= (4x³ + 6) dx= (4(-5)³ + 6) (0.01)= -499.4Now we can write the final  the given question as follows: Given values: y = x4 + 6 x = −5 Δx = dx = 0.01Formula used:Δy = f(x + Δx) − f(x)dy = f'(x) dx Where ,f(x) = x4 + 6 xf(x + Δx) = (x + Δx)4 + 6 (x + Δx)f(x) = x4 + 6 xf'(x) = 4x³ + 6Values of given variables:Δx = dx = 0.01x = -5Now, let's calculate the value of Δy by putting the given values in the formula.Δy = f(x + Δx) − f(x)f(x + Δx) = (x + Δx)4 + 6 (x + Δx)Putting the given values in this formula we get, f(x + Δx) = (-5 + 0.01)4 + 6(-5 + 0.01) = 55.0184f(x) = x4 + 6 x Putting the given values in this formula we get, f(x) = (-5)4 + 6 (-5) = -605Δy = f(x + Δx) − f(x)= 55.0184 - (-605)= 660.0184

Now, let's calculate the value of dy by putting the values of f'(x), dx and x in the given formula. dy = f'(x) dx= (4x³ + 6) dx= (4(-5)³ + 6) (0.01) = -499.4Therefore, Δy = 660.0184 and dy = -499.4.

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The expression which is equivalent to the expression given; -1/2 ( 1/4x - 3/8) according to the task content is; (-1/8)x + 3/16.

It follows from the task content that the expression which is equivalent to that given in the task content be determined.

On this note, by distributing the coefficient of.tne parents; we have;

-1/2 ( 1/4x - 3/8)

= {(-1/2) × (1/4)x} + {-1/2 × -3/8}

= (-1/8)x + 3/16

Ultimately, the expression which is equivalent to the expression given; -1/2 ( 1/4x - 3/8) according to the task content is; (-1/8)x + 3/16.

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The movie earned $1.21×10^7 in revenue per minute.

Revenue was earned per minute

we get,

we can divide the total revenue by the number of minutes.

When numbers are in scientific notation, we can divide in two separate steps.

First, let's divide the powers of ten, then we will divide the other numbers.

Because of the properties of exponents, we can subtract the exponent in the denominator from the exponent in the numerator to divide the powers of 10.

Now we can divide the numbers that are not powers of 10.

The problem asks us to round to two decimal places, so our final answer will have three digits including the ones place. Let's round

so the final answer will have three digits.

first number is 1.109 and

second number is .109

Now let's put the two results back together.

we get, $1.21

we get number after scientific notation

The movie earned $1.21×10^7 in revenue per minute.

Scientific Notation is the expression of a number n in the form

a∗10b

where a is an integer such that

1≤|a|<10

and b is an integer too.

Multiplication: To multiply numbers in scientific notation, multiply the decimal numbers. Then add the exponents of the powers of 10. Place the new power of 10 with the decimal in scientific notation form. If your decimal number is greater than 10, count the number of times the decimal moves to the left, and add this number to the exponent.

Division: To divide numbers in scientific notation, first divide the decimal numbers. Then subtract the exponents of your power of 10. Place the new power of 10 with the decimal in scientific notation form. If the resulting decimal number is less than 1, move the decimal point to the right and decrease the exponent by the number of places that the decimal point moved.

Large Numbers in Standard Form

n=101325=1.01325∗105

(Move the decimal point 5 places to the right)

Express Small Numbers in Standard Form

n=0.00092=9.2∗10−4

(Move the decimal point 4 places to the left.)

Multiplication:

(2.3∗104)∗(6.6∗107)

First Step -

2.3∗6.6=16.38

Second Step -

104∗107=1011

Because the new decimal number in step one is greater than 10, count the number of places the decimal moves to put the number between 1 and 10. Add this number to the exponent. In this case, the decimal point moves one place, so add 1 to the exponent.

1.638∗1012

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Answer:1.21*10^7

Step-by-step explanation:

i did kahn academy and this was the correct answer:)

Answer: R , y>6

Step-by-step explanation:

\(a^x\)  : domain is R

Range : y > 6

Answer:

tje answer is 4

Step-by-step explanation:

4x5=20

20-6=14

Answer:

f(x) = (x - 10) (x + 10)

Step-by-step explanation:

The equation looks like the difference of squares so 5 and 20 are out

-10 x -10 = 100

-10 x 10 = - 100

so (x - 10) (x + 10)

Answer:

r=21.424

Step-by-step explanation:

Volume = (1/3) . π . r² . h

3847 = (1/3) . π . r² . 8

3847 = (8/3)πr²

r²= 3847/(8/3)π

r² = 459

r= √459 = 21.424

As per the given information, we can conclude that the average distribution of colors in a bag of Skittles is:

- 20% of bags have an equal number of candies of each color. So, each color will have 100/6 = 16.67 (approx. 17) pieces of candy.

- 40% of bags have a 2-1-1-3-1-1 ratio of colors. Using this ratio, we can find out the number of pieces for each color:

- Red: 2/8 * 100 = 25

- Orange: 1/8 * 100 = 12.5 (approx. 13)

- Yellow: 1/8 * 100 = 12.5 (approx. 13)

- Green: 3/8 * 100 = 37.5 (approx. 38)

- Blue: 1/8 * 100 = 12.5 (approx. 13)

- Purple: 1/8 * 100 = 12.5 (approx. 13)

- 40% of bags have only red candies, which means the remaining colors have 0 pieces.

Therefore, the average distribution of colors in a bag of Skittles can be calculated as:

- Red: 40% * 100 = 40 pieces

- Orange: (20% * 17) + (40% * 13) = 4.4 + 5.2 = 9.6 (approx. 10)

- Yellow: (20% * 17) + (40% * 13) = 4.4 + 5.2 = 9.6 (approx. 10)

- Green: (20% * 17) + (40% * 38) = 4.4 + 15.2 = 19.6 (approx. 20)

- Blue: (20% * 17) + (40% * 13) = 4.4 + 5.2 = 9.6 (approx. 10)

- Purple: (20% * 17) + (40% * 13) = 4.4 + 5.2 = 9.6 (approx. 10)

Thus, the average distribution of colors in a bag of Skittles is 40 pieces of red, 10 pieces each of orange, yellow, blue, and purple, and 20 pieces of green.

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Answer:

79°c - (-3°c) = 82°c

Step-by-step explanation:

this is because we need to calculate the total gap between those numbers through number line. I have attached the photo, have a look over there.

Answer:

8 Boxes

Step-by-step explanation:

You need to take 338 and divide it by 48. The answer is 7.04. Since you can't just buy 0.04 of a box, you need to round up. Therefore the answer is 8.

The degree of freedom would be 36.

What is the degree of freedom in statistics?

It is a mathematical equation that tells how many values can vary and can aid in determining whether or not the results are statistically significant. In statistics, the most commonly encountered equation for determining degrees of freedom is df = N-1.

Que.16)

It is a statistic. Because it gives information about the sample.

Que.17)

Because 35 is close to 36.

Que.18)

degrees of freedom = n -1 = 37-1 = 36

Que .19)

\(C.I. = \bar{X} \ \pm \ t_{\alpha/2, n-1} \ \frac{s}{\sqrt{n}} \\ \\ \\ C.I. = 5.2 \pm 2.160 \ \frac{1.9}{\sqrt{14}} \\\\\\ C.I. = (4.1032, 6.2968)\)

\(t_{\alpha/2, n-1} = t_{0.05/2, 14-1} = 2.16\) it is obtained using t table.

Que. 20)

\(\\ C.I. = \bar{X} \pm z_{\alpha /2} \ \frac{\sigma }{\sqrt{n}} \\ \\ \\ C.I. = 93.2 \pm 2.58 \frac{16.9}{\sqrt{110}} \\\\\\ C.I. = (89.0427, 97.3573)\)

Hence, the degree of freedom would be 36.

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The equation that is equal to 72 is 8 x 9.

1. To find the equation that is equal to 72, we need to consider different mathematical operations and numbers that can be combined to yield the desired result.

2. One way to express 72 is through multiplication. Let's try different combinations of numbers to see if any multiplication equation equals 72.

3. We can start by examining factors of 72. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

4. By testing various combinations of these factors, we can determine which one equals 72.

5. After evaluating the different combinations, we find that the equation 8 x 9 equals 72.

6. Therefore, the equation 8 x 9 is the one that is equal to 72.

It's important to note that there might be other equations or operations that can also yield a result of 72, such as addition or subtraction, but based on the given information, multiplication is the operation used to obtain the desired outcome.

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The value of the angle \(y\) within the quadrilateral \(OABC\) inscribed the circle is 142°.

Let suppose that quadrilateral \(OABC\) is a parallelogram. Then, the following conditions must be fulfilled:

In addition, if we have a rhombus we have the additional condition as A, B and C lie on the circle:

\(\overline{OA} \cong \overline {AB} \cong \overline {BC} \cong \overline{OC}\) (4)

If we know that \(\angle AOC = 142^{\circ}\), then the value of \(\angle ABC = y = 142^{\circ}\).

Based on all these finding, we conclude that the value of the angle \(y\) within the quadrilateral \(OABC\) inscribed the circle is 142°.

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a) Corey's percentage increase in pay per hour is 14.2%.

b) When Dele invests $6,000 for 4 years at 3% per annum compound interest, the value of his investment (future value) at the end of 4 years is $15,757.12.

c) The worth of the car at the end of 2020 is $11,812.50, depreciating by 14% per annum.

a. Corey's original pay per hour = £12.36

Corey's new pay per hour = $14.11

Increase in pay = £1.75 (£14.11 - £12.36)

Percentage increase in pay = 14.2% (£1.75/£12.36 x 100)

b. Principal investment = $14,000

Investment period = 4 years

Compound interest rate = 3%

Compounding terms = Annually

The future value (FV) in 4 years:

N (# of periods) = 4 years

I/Y (Interest per year) = 3%

PV (Present Value) = $14,000

PMT (Periodic Payment) = $0

Results:

FV = $15,757.12

Total Interest = $1,757.12

c. Value of a car at the end of 2017 = $17,500

Depreciation rate per annum = 14%

Depreciation period = 3 years (Dec. 31, 2017 - Dece. 2020)

Value of the car at the end of 2020 = $11,812.50 ($17,500 x 1.14⁻³)

Thus, the car will reduce (depreciate) in value every year by 14%, making its value to be $11,812.50 at the end of 2020.

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Answer:

For X is (x=4y−4) and for Y is (y= 1 /4 x+1)

Step-by-step explanation:

Let's solve for x.

x−4y=−4

Step 1: Add 4y to both sides.

x−4y+4y=−4+4y

x=4y−4

Answer:

x=4y−4

Let's solve for y.

x−4y=−4

Step 1: Add -x to both sides.

x−4y+−x=−4+−x

−4y=−x−4

Step 2: Divide both sides by -4.

−4y /−4  =  −x−4 /−4

y= 1 /4 x+1

John initially had Php 132 and Mary initially had Php 252 (384 - 132).

Let's start by setting up the equations to solve for this problem.

Let x be the amount of money John had initially.

Then, Mary had (384 - x) initially.

After John gave Php 36 to Mary, John had (x - 36) left and Mary had (384 - x + 36) = (420 - x).

We are told that Mary had three times as much money as John after this transaction, so we can write:

3(x - 36) = 420 - x

Simplifying this equation gives:

3x - 108 = 420 - x

4x = 528

x = 132

Therefore, John initially had Php 132 and Mary initially had Php 252 (384 - 132).

Answer: Mary had Php 252 at first.

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Answer:

5 and 10

Step-by-step explanation:

The answer that refers to the total number of cases of a disease or a disorder in a specified population at a particular point in time is prevalence.

Prevalence is the total number of cases of a disease or disorder in a population at a given point in time, and does not include cases that have been resolved or previously diagnosed cases. It is an important measure of the health of a population, as it allows researchers to identify patterns in the distribution of a disease or disorder and helps inform public health strategies.

Prevalence is calculated by dividing the total number of cases of a disease or disorder in a population at a given point in time, by the size of the population. For example, if a population of 100,000 people has 500 cases of a particular disease, the prevalence would be 0.005 or 0.5%.

Prevalence is an important metric in epidemiology and public health, and is often used in combination with incidence rates to measure the health of a population. Incidence rates measure the number of new cases of a disease or disorder that occur in a population over a certain time period, whereas prevalence is a snapshot of the total number of cases of a disease or disorder in a population at a given point in time.

Knowing the prevalence of a disease or disorder in a population helps public health practitioners understand the magnitude of a health issue, inform public health strategies, and identify risk factors and trends in the distribution of a disease or disorder.

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Answer: y = -3x - 4

Step-by-step explanation:

Slope intercept form would be y = mx + b. To get your equation to this form you would need to isolate for y as shown:

3x + y = -4

y = -3x - 4 <-- Here I subtracted both sides by 3x

The probability of having one white ball is 1/20 or approximately 0.05.

To find the probability of selecting one white ball out of three balls, you need to know the number of white balls in the box and the total number of balls in the box. You also need to know whether the balls are being selected randomly or not.

Assuming that there is only one white ball in the box and the rest are some other color, and that the balls are being selected randomly.

The probability of selecting one white ball out of three would be:

Probability = (number of ways to select one white ball out of three) / (total number of ways to select three balls)

Since there is only one white ball, there is only one way to select one white ball out of three. The total number of ways to select three balls out of six is 6 choose 3, which is equal to 20.

Therefore, the probability of selecting one white ball out of three would be

Probability = (number of ways to select one white ball out of three) / (total number of ways to select three balls)

Probability = 1/20

Probability = approximately 0.05.

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The variable quantity "the number of heads in 50 tossed coins" is a discrete variable.

In statistics, a discrete variable is a variable that takes on a countable number of distinct values, while a continuous variable can take on an infinite number of values within a given range. In this case, the number of heads in 50 tossed coins can only take on a finite number of values (ranging from 0 to 50), and each value has a non-zero probability of occurring. Therefore, the variable is discrete. This is in contrast to a continuous variable, such as height or weight, which can take on any value within a certain range and is measured on a continuous scale.

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Answer:

600 calories

Step-by-step explanation:

120 (# of minutes in 2 hours) divided by 40 is 3, so multiply 200 by 3 and you get 600

Answer:

600 calories burnt

Step-by-step explanation:

What I started with is 200/40=5 calories burned per min

60 plus 60=120

5x120=600

Hope this helps

Answer:

Step-by-step explanation:

7. 2/5

8. 3/5

9. 2/5

10. 2/5

Answer:

Number 7: 2/5 chance or 40%

Number 8: 4/5 or 80% chance

Number 9: 2/5 chance

Number 10: 2/5 chance

Step-by-step explanation:

For each one, you put the total number of polygons at the bottom of the fraction or the denominator and the number of how many of them answer the question as the numerator.

Answer:

1.5 pounds

Step-by-step explanation:

The critical value zₐ/₂ that corresponds to an 83% level of confidence is approximately 1.381.

To find the critical value zₐ/₂, we need to determine the value that leaves an area of (1 - α)/2 in the tails of the standard normal distribution. In this case, α is the complement of the confidence level, which is 1 - 0.83 = 0.17. Dividing this value by 2 gives us 0.17/2 = 0.085.

To find the z-value that corresponds to an area of 0.085 in the tails of the standard normal distribution, we can use a standard normal distribution table or a statistical calculator. The corresponding z-value is approximately 1.381.

Therefore, the critical value zₐ/₂ that corresponds to an 83% level of confidence is approximately 1.381.

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a) The probability that in the next minute exactly 5 vehicles pass through the intersection is given as follows:

Formula used:

Poisson probability = (λ^k * e^-λ) / k! Where:λ = mean rate of vehicles through the intersection per minute k = the number of vehicles that pass through the intersection in the next minuteλ = 7k = 5

Therefore,Poisson probability =\(\frac{7^5 e^{-7}}{5!}\)

≈ 0.10464725

Rounded to 8 decimal places, the probability is ≈ 0.10464725.

b) The probability that in the next minute at most 2 vehicles pass through the intersection is given as follows:

Formula used:

Poisson probability = \(\frac{\lambda^k e^{-\lambda}}{k!}\) Where:λ = mean rate of vehicles through the intersection per minute k = the number of vehicles that pass through the intersection in the next minute Poisson probability for k = 0:λ = 7k = 0

Poisson probability for k = 1:

λ = 7k = 1Poisson probability for k = 2:

λ = 7k = 2

Therefore,Poisson probability for k ≤ 2 = P(k=0) + P(k=1) + P(k=2)

= \((7^0 e^{-7})/0! + (7^1 e^{-7})/1! + (7^2 e^{-7})/2!\)

≈ 0.09157819

Rounded to 8 decimal places, the probability is ≈ 0.09157819.

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The probability that the selected three digit number is an exact match with the winning three digit number = 1/1000

The 10 digits are 0, 1, 2, 3, 4, 5, 6,7, 8, 9. From these 10 digits 3 digits are selected.

Total number of ways of selecting a three-digit number = Number of ways of selecting a digit from 10 digits for each place(one's, ten's and hundred's place)

Thus a three-digit number can be selected in 10 x 10 x 10 = 1000 ways.

So there are 1000 possibilities for a three digit number.

From this only one choice matches exactly with the winning number.

So the number of favorable outcome = 1

Hence, The probability that the selected three digit number is an exact match with the winning three digit number = 1/1000

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