Let E and F be events with P(E) = 0.3, P(F) = 0.6 and P(EU F) = 0.7 a. P( EF) b. P(E|F) PECF) d. P( EF)

As per the concept of counting problem, the reason that the answers in part (a) and part (b) are not the same is because Q1 and Q2 are treated as two different coins in part (a) whereas they are effectively treated as the same coin in part (b). And the reason they are treated as one coin is because they both contribute the same amount to the sum of money.

Counting Problems

Basically, counting refers the process of finding the number of elements of a finite set of objects.

Given,

Suppose you have a nickel, two dimes, and a quarter. One of the dimes was minted in 1976, and the other one was minted in 1992.

While we looking into the given problem,

For A) states that,  If you choose at least one coin, this means you could choose 1, 2, 3 or 4 coins. Let us label the dime as D, the penny as P, the quarter minted in 1976 as Q1 and the quarter minted in 1992 as Q2.

Here in this process if you choose one coin, you could choose either D, P, Q1, or Q2. This gives us 4 possible sets.

And If you choose two coins, you choose the following sets of coins: DP, DQ1, DQ2, PQ1, PQ2, Q1Q2. This gives us 6 possible sets.

Then If you choose three coins, you could the following sets of coins: DPQ1, DPQ2, DQ1Q2, PQ1Q2. This gives us 4 possible sets.

So, If you choose four coins, you can only choose DPQ1Q2. This gives us 1 possible set.

So, the total number of different sets of coins you can form is 4 + 6 + 4 + 1 = 15 different sets of coins can be formed.

Similarly, for b) If you choose at least one coin, this means you could choose 1, 2, 3 or 4 coins.

Then If you choose one coin you could choose either D, P, Q1, or Q2. However, since Q1 and Q2 give us the same sum, they are effectively the same set. This gives us 3 possible sums.

So, If you choose two coins, you could choose the following sets of coins : DP, DQ, PQ, Q1Q2.And this gives us 4 possible sums

Then If you choose three coins, you could choose the following sets of coins: DPQ, DQ1Q2, PQ1Q2. And this gives us 3 possible sums

Then If you choose four coins, you can only choose DPQ1Q2. This gives us 1 possible sum.

So, the total number of different sums of coins you can form is 3 + 4 + 3 + 1 = 11 different sums of money can be produced.

Finally, c) The reason that the answers in part (a) and part (b) are not the same is because Q1 and Q2 are treated as two different coins in part (a) whereas they are effectively treated as the same coin in part (b). And the reason they are treated as one coin is because they both contribute the same amount to the sum of money.

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The direction of vector D is perpendicular to vector A, and it makes an angle of 90 degrees with vector A.

We are given that:

vector A + vector B = vector C

vector A - vector B = vector D

To find the direction of vector C,

we can use the fact that the tangent of the angle between vector A and vector C is equal to the ratio of their magnitudes.

That is:

tan(theta) = |vector C| / |vector A|

where theta is the angle between vector A and vector C.

Similarly, to find the direction of vector D,

we can use the fact that the tangent of the angle between vector A and vector D is equal to the ratio of their magnitudes.

That is:

tan(phi) = |vector D| / |vector A|

where phi is the angle between vector A and vector D.

We want to find the angle between vector A and vector D, which is equal to the supplement of the angle between vector A and vector C.

That is:

theta + phi = 180 degrees

Rearranging, we get:

phi = 180 degrees - theta

Substituting the equations for theta and phi, we get:

tan(180 degrees - phi) = |vector D| / |vector A| = tan(phi)

Simplifying, we get:

tan(180 degrees - phi) = tan(phi)

Using the identity tan(180 degrees - theta) = -tan(theta), we can rewrite this as:

-tan(phi) = tan(phi)

Solving for phi, we get:

2*phi = 180 degrees

phi = 90 degrees

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Complete question may be:

If, vector A + vector B = vector Cvector A - vector B = vector D, then find the direction of vector D is perpendicular to vector A?

Answer:

for

x= -4 and

x= 9

..............

Answer:

fourty-seven.......

Step-by-step explanation:

trust me

Answer:

The answer is graph C.

Step-by-step explanation:

Because both equations give the same line, it's infinitely solutions.

Since each serving contains 2/5 of a pound, then, the total weight of x servings would be:

If the total weight of x servings should be equal to the weight of the turkey, then:

Multiply both sides of the equation by 5/2:

Simplify the expressions on both sides of the equation:

Therefore, the number of adult servings from a 10 pound turkey, will be 25.

Answer:

0.8 degrees per hour

Step-by-step explanation:

1 2/5 divided by 1 3/4

7/5 / 7/4

keep, change, flip the fraction

7/5 x 4/7

=4/5= 0.8

Answer:

-21

you "forget" the negative symbol and add like normal, then put the negative symbol in front of your answer

The volume available to carry instruments and cameras inside the cylindrical body of a TIROS weather satellite is approximately 26,336.5 cubic inches.

To find the volume of the cylindrical-shaped body of a TIROS weather satellite, we can use the formula for the volume of a cylinder: V = πr²h. In this case, the diameter is 42 inches, so the radius (r) is half of that, which is 21 inches. The height (h) is 19 inches.

Step 1: Calculate the radius (r) by dividing the diameter by 2.
r = 42 inches / 2 = 21 inches

Step 2: Calculate the square of the radius (r²).
r² = 21 inches × 21 inches = 441 square inches

Step 3: Multiply the square of the radius (r²) by the height (h).
Volume (V) = 441 square inches × 19 inches = 8379 cubic inches

Step 4: Multiply the result by π (approximately 3.1416).
V = 8379 cubic inches × 3.1416 ≈ 26,336.5 cubic inches

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If you only have $10 and the book costs $20, No, you cannot buy the book. However, if you have $25, Yes, you can afford the book and still have $5 left after the purchase.

In scenario A, where you have $10 and the book costs $20, you cannot buy the book. The cost of the book exceeds the amount of money you have, leaving you $10 short. In this case, you would need to find an additional $10 in order to afford the book.

In scenario B, where you have $25 and the book costs $20, you can buy the book. With $25, you have enough funds to cover the full price of the book. After purchasing the book, the remaining amount found by subtraction of the cost of the book from the amount you have (ie) the remaining amount = the amount you have - the cost of the book = $25 - $20 = $5

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The given question is

You want to read a certain book.

A. This book costs $ 20. If you only have$ 10, can you buy the book?

B. If you have $ 25, can you buy the book?

Thee factory is able to provide 94.38 boxes per hour to the warehouse.

Rate = (2000 - 1245) / 8 = 94.38 boxes per hour

Therefore, the factory is able to provide 94.38 boxes per hour to the warehouse.

Boxes added in 40 hours = rate * time = 94.38 * 40 = 3,775.2

Therefore, the inventory at the end of a 40-hour work week would be:

1245 + 3775.2 = 5020.2 boxes

rate = (50000 - 1245) / time

Simplifying this equation, we get:

time = (50000 - 1245) / rate = 511.64 hours (rounded to two decimal places).

Therefore, it will take approximately 511.64 hours to fill the warehouse to its 50,000 box capacity,

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Answer:

A) 24

Step-by-step explanation:

Answer:

m = 24

Step-by-step explanation:

The value of y when x = 0 is 10

The equation is given as

y = x² - 7x + 10

So, we have

y = (0)² - 7(0) + 10

Evaluate

y = 10

In (a), we have

x = 0 and y = 10

This means that the graph crosses the y-axis at y = 10

See attachment for graph

We have

x² - 7x + 10 = 0

Expand

x² - 2x - 5x + 10 = 0

Factorize

(x  - 2)(x - 5) = 0

So, we have

x = 2 and x = 5

In (c), we have

x = 2 and x = 5 and y = 0

This means that the graph crosses the x-axis at x = 2 and x = 5

See attachment for graph

See attachment for graph

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Answer:

Consider the quadratic equation

x

2

+

4

x

+

4

=

0

, which, on the left side, is also a perfect square trinomial. Factoring to solve:

⇒

(

x

+

2

)

(

x

+

2

)

=

0

⇒

x

=

−

2

and

−

2

Two identical solutions! Recall that the solutions of a quadratic equation are the x intercepts on the corresponding quadratic function.

So, the solutions to the equation

x

2

+

5

x

+

6

=

0

, for example, will be the x intercepts on the graph of

y

=

x

2

+

5

x

+

6

.

Similarly, the solutions to the equation

x

2

+

4

x

+

4

=

0

will be the x intercepts on the graph of

y

=

x

2

+

4

x

+

4

.

Since there is really only one solution to

x

2

+

4

x

+

4

=

0

, the vertex of the function

y

=

x

2

+

4

x

+

4

lies on the x axis.

Now, think of the discriminant of a quadratic equation. If you don't have previous experience with it, don't fret.

We use the discriminant,

b

2

−

4

a

c

, to verify how many solutions, and the solution type, a quadratic equation of the form

a

x

2

+

b

x

+

c

=

0

may have without solving the equation.

When the discriminant equals less than

0

, the equation will have no solution. When the discriminant equals exactly zero, the equation will have exactly one solution. When the discriminant equals any number more than zero, there will be exactly two solutions. If the number in question that you get as a result is a perfect square in the latter case, the equation will have two rational solutions. If not, it will have two irrational solutions.

I've already shown that when you have a perfect square trinomial, you will have two identical solutions, which is equal to one solution. Hence, we can set the discriminant to

0

and solve for

c

.

Where

a

=

1

,

b

=

14

and

c

=

?

:

b

2

−

4

a

c

=

0

14

2

−

4

×

1

×

c

=

0

196

−

4

c

=

0

4

c

=

196

c

=

49

Thus, the perfect square trinomial with

a

=

1

and

b

=

14

is

x

2

+

14

x

+

49

. We can verify this by factoring.

x

2

+

14

x

+

49

=

(

x

+

7

)

(

x

+

7

)

=

(

x

+

7

)

2

Practice exercises:

Using the discriminant, determine the values of

a

,

b

,

or

c

that render the trinomials perfect squares.

a)

a

x

2

−

12

x

+

4

b)

25

x

2

+

b

x

+

64

c)

49

x

2

+

14

x

+

c

Step-by-step explanation:

The inequality that describes this scenario is 75 + 11.50S ≥ 55. This inequality represents a situation where someone has an initial balance of 75 dollars and is earning 11.50 dollars per hour of work.

The inequality states that the total earnings must be greater than or equal to 55 dollars. In other words, the person needs to work a certain number of hours to earn enough money to meet the 55-dollar requirement. This inequality can be solved for S (the number of hours worked) by subtracting 75 from both sides and dividing by 11.50. This would give the minimum number of hours required to meet the 55-dollar requirement. Overall, this inequality provides a clear guideline for the minimum amount of work needed to meet a specific financial goal.

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A function which models P(t), the number of pollen grains per square centimeter t years after the first year the grains were deposited is: D) P(t) = 310(1.01)^t.

An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function is represented by this formula:

f(x) = eˣ

Generally speaking, a mathematical model for any quantity (pollen grains) that increases by r percent per unit of time is an exponential function of this form:

P(t) = I(1 + 0.01r)^t

Where:

Substituting the given parameters into the formula, we have;

P(t) = 300(1 + 0.01r)^t

P(t) = 310(1.01)^t

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Complete Question:

Keith modeled the growth over several hundred years of a tree population by estimating the number of the trees’ pollen grains per square centimeter that were deposited each year within layers of a lake’s sediment. He estimated there were 310 pollen grains per square centimeter the first year the grains were deposited, with a 1% annual increase in the number of grains per square centimeter thereafter. Which of the following functions models P(t), the number of pollen grains per square centimeter t years after the first year the grains were deposited?

A) P(t) = 310^t

B) p(t) = 310^{1.01t}

C) P(t) = 310(0.99)^t

D) P(t) = 310(1.01)^t

Answer:

x = 30

Step-by-step explanation:

The perpendicular bisector is cutting a line at a right angle, two sides of the line will be equal to each other which allows us to write the following equation:

2x - 20 = 70 - x transfer like terms to the same side of the equation:

2x + x = 70 + 20 notice how the signs of the expressions changed from "-" to "+" when transferred

3x = 90 divide both sides by 3

x = 30

Bob's distance from his home is equal to 4 miles.

In order to calculate Bob's distance from his home, we would have to apply Pythagorean's theorem.

Mathematically, Pythagorean's theorem is given by this mathematical expression:

a² + b² = c²

Where:

a, b, and c represents the side lengths of a right-angled triangle.

Substituting the parameters, we have:

c² = a² + b²

5² = 3² + b²

25 = 9 + b²

b² = 25 - 9

b²  = 16

b = √16

b = 4 miles.

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a ball of radius 13 has a round hole of radius 3 drilled through its center. then the volume of the resulting solid is 8.5528 x 10³  units³

The radius of the ball is 13 units.

Its volume is

V₁ = (4π*13³)/3

    = 9.2028 x 10³ units³

The drilled hole has the approximate shape of a solid cylinder with radius = 3 and length = 26. Its volume is

V₂ = π*(3²)*26

    = 0.650 x 10³ units³

The volume of the resulting solid is

V₁ - V₂ = 8.5528 x 10³

Answer: 8.5528 x 10³  units³

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Answer:

Step-by-step explanation:

How to Use the Equivalent Expression Calculator?

The procedure to use the equivalent expression calculator is as follows:

Step 1: Enter an algebraic expression in the input field

Step 2: Now click the button “Submit” to get the equivalent expression

Step 3: Finally, the equivalent expression for the given algebraic expression will be displayed in a new window.

What is an Algebraic Expression?

An algebraic expression is an expression that consists of variables, coefficients, constants, and mathematical operators such as addition, subtraction, multiplication, and division. Generally, if two things are the same, then it is called equivalent. Similarly, in mathematics, the equivalent expressions are the expressions that are the same, even though the expression looks different. But if the values are plugged into the expression, both expressions give the same result.

Example

Question:

Write the equivalent expression for the given expression: 3x+9

Solution:

Given expression: 3x+9

Take 3 outside from the expression, and we get,

= 3(x+3), which is called the equivalent expression

Answer:

Hello!

Number 2 and 4 is wrong, other than that everything else is all good.

\(2)\)  \(6x^4 - 12x^5 + 90x^1^{3}\)

The Greatest common factor is 6x^4.

The GCF needs to have the smallest exponent from the variables.

The correct answer should be 6x^4 ( 1 - 2x + 15x^9)

\(4)\)  \(x^2 - 36\)

x (x - 36) is wrong because if we use the distributive property, the answer would be x^2 - 36x. Notice that there shouldn't be a variable multiplying 36.

The correct answer would be (x - 6)(x + 6)

x^2 + 6x - 6x - 36

x^2 - 36.

Hope this helps!

The correct answer is option b. 15.77%. The annual discount rate, also known as the discount rate or the rate of return, can be calculated using the present value formula.

Given that a cash flow of £52 million in 5 years' time is currently valued at £25 million, we can use this information to solve for the discount rate.

The present value formula is given by PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of years.

In this case, we have PV = £25 million, CF = £52 million, and n = 5. Substituting these values into the formula, we can solve for r:

£25 million = £52 million / (1 + r)^5.

Dividing both sides by £52 million and taking the fifth root, we have:

(1 + r)^5 = 25/52.

Taking the fifth root of both sides, we get:

1 + r = (25/52)^(1/5).

Subtracting 1 from both sides, we obtain:

r = (25/52)^(1/5) - 1.

Calculating this value, we find that r is approximately 0.1577, or 15.77%. Therefore, the annual discount rate is approximately 15.77%, corresponding to option b.

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The sample mean of data is 24.19 and median is 3.54. The sign test and hypothesis testing. The boxplot for observation is present above figure. Yes, it support assumption that we are sampling from a normal distribution.

We have a sample data with values 1.48, 4.10, 2.02, 56.59, 2.98, 1.51, 76.49, 50.25, 43.52, 2.96. Also, here consider a sample from a normal distribution with unknown mean and variance, and the hypothesis that the population median (which is the same as the mean in this case) is 3.

Hypothesis testing parameters are

\(Н_0 : \mu = 3 \)

\(H_a : \mu ≠ 3 \)

The sample mean is called the average and it is defined as the ratio sum of data values divided by number of data values.

Median is a statistical measure. It is equals to the middle data value obtained by ordering the data values in ascending order. In case of odd number of data values it is middle value and in case of even number of data values it become mean of two middle values. Here we use Excel function to determine the mean and median values. So, see the above figure, excel command for mean is

'= mean (column contain data values)' and for median '= median ( same column)'. So, mean = 24. 19 and median

= 3.54 . The sign test for hypothesis testing of observations also present in above figure. P-value of test = 0.623 > 0.05 , That is no evidence to reject the null hypothesis. So, population mean = 3. The boxplot of observations also present in above figure.

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Answer:

11) D. 144 b/m

12) B. As exercise levels increase, heart rate increases

13) D. Transporting wastes away from cells

14) B. Capillaries

15) This is because during excercise you increase the skin blood flow in order to enable ¨heat dissipation¨. Then after the increase in blood flow to the muscles decides to have an increase which causes it to have a cardiac output which is in direct proportion to the increase in oxygen consumption.

Step-by-step explanation:

A because 2 is half of 4 and 18 is half of 36.

Step-by-step explanation: because 2 is half of 4 and 18 is half of 36.

Answer:

Step-Opens up with a vertex at (4,-1)by-step explanation:

The use of color-coded file labels will save you approximately 6.67 hours each month (4 weeks) in completing your filing tasks. To calculate the time saved each month using color-coded file labels, we need to consider the time saved per day and multiply it by the number of workdays in a month.

Given that it takes 20 minutes less each day to complete filing tasks with color-coded file labels, this translates to a time savings of 1/3 hour per day (20 minutes = 1/3 hour).

Now, let's calculate the total time saved in a month:

Time saved per day = 1/3 hour

Number of workdays in a month = 4 weeks * 5 days/week = 20 days

Total time saved in a month = Time saved per day * Number of workdays in a month

                            = (1/3 hour) * 20 days

                            = 20/3 hours

                            ≈ 6.67 hours

Therefore, the use of color-coded file labels will save you approximately 6.67 hours each month (4 weeks) in completing your filing tasks.

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