2. For two events A and B, if A and B are disjoint, and P(A)=0.1, P(B)-0.5, then P(AUB) = 3. X be a variable with the expected value E(X) = μ and he variance V(X) = 0², if Y = 5 x + 3, then E(Y) = E

Answer:

They biked for 1 hour and 38 minutes

Step-by-step explanation:

Here, we want to know the length of the biking time

Mathematically, from the time given;

if they had ended the biking by 2:47

They would have biked for 2 hours

But, as it can be seen, the biking stopped at 2:25 and that is (57-25 = 22 minutes earlier)

So, the length of their biking time would be;

1 hour and (60-22) minutes

and that is 1 hour 38 minutes

Solution:Given, the mean speed of the cars racing = 158.9 mph standard deviation = 6.7 mph

To find:What speed represents the 30th percentile for speeds of race cars at Talladega?

We need to find the z-score for the 30th percentile.From the standard normal distribution table, the z-score for the 30th percentile is -0.52.Using the formula for z-score we havez=(x-μ)/σwhere x is the speed of the carsμ is the mean speed = 158.9σ is the standard deviation = 6.7Substituting these values in the above equation we have-0.52=(x-158.9)/6.7Rearranging we get,x - 158.9 =\(-0.52 × 6.7x - 158.9 = -3.524x = 158.9 - 3.524x = 155.376\)The speed that represents the 30th percentile for speeds of race cars at Talladega is approximately 155.38 mph.

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x = 7

y = 8

All I did was assume x was 7 and y was 8. I added 4, 6, 7, 8, and 10 together. I got 35. Then, I divided by five (since that's how many numbers are shown) and I got 7 for the mean. 7 is the median, and the 7 is the mean gotten from 4, 6, 7, 8, and 10. Therefore, x must equal 7 and y must equal 8.

The probability that all four songs are liked will be 0.03418 and the probability of not liking the next four songs will be 0.99658.

The probability of an event occurring is defined by probability.

Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.

As per the given,

Total songs = 53

Like songs = 14

Probability of selecting and liking the first song = 14/53

Now since repetition is not allowed and one like the song has been chosen out of 14 thus, the remaining songs = 13, and total songs = 43 - 1 = 52

Probability of selecting liking the second song = 13/52

Probability of selecting liking the third song = 12/51

Probability of selecting liking the fourth song = 11/50

a)

The probability of liking all songs will be 14/53 x 13/52 x 12/51 x 11/50 = 0.03418.

b)

The probability of not liking the next four songs =1 - The probability of liking all songs

The probability of not liking the next four songs = 1 - 0.03418 = 0.96582.

Hence "The probability that all four songs are liked will be 0.03418 and the probability of not liking the next four songs will be 0.99658".

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The amount of tile needed to cover the pedestal will depend on the size and shape of the pedestal. In order to determine how much tile is needed, you will need to measure the surface area of the pedestal.

The pedestal's dimensions are height, breadth, and length.

Multiply the height, width, and length of the pedestal to calculate the surface area.

Multiply the surface area by the number of tiles needed to cover the pedestal. To determine the number of tiles needed, divide the surface area by the area of each tile.

For example, if the pedestal is 2 feet tall, 2 feet wide, and 4 feet long, the surface area is 16 square feet. If each tile has an area of 1 square foot, then it will take 16 tiles to cover the pedestal.

In conclusion, the amount of tile needed to cover the pedestal will depend on the size and shape of the pedestal and the size of the tiles. To determine the amount of tile needed, measure the surface area of the pedestal and then multiply it by the number of tiles needed to cover the pedestal.

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The pedestal's size and shape will determine how much tile is required to cover it. It will take 1176cm² of tiles to cover the pedestal.

You will need to measure the pedestal's surface area in order to figure out how many tiles you need. The height, width, and length of the pedestal are the same. To determine the surface area, multiply the pedestal's height, width, and length.

S = 2*s1 + s2 + 2*s3

= 96 + 480 + 600

= 1176

Divide the total number of tiles required to cover the pedestal by the surface area. Divide the surface area by the area of each tile to determine the required number of tiles.

The surface area, for instance, is 16 square feet if the pedestal is 2 feet tall, 2 feet wide, and 4 feet long. 16 tiles will be required to cover the pedestal if each tile has a surface area of one square foot.

In conclusion, the dimensions of the tiles and the pedestal's size will determine how much tile is required to cover the pedestal. Multiply the surface area of the pedestal by the number of tiles required to cover it to find the required quantity of tiles.

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Answer:

6x^3 - 16x^2 - 14x + 24

Step-by-step explanation:

Answer:

Step-by-step explanation:

(a) As the P-value is less than a = 0.10. So, we reject the null hypothesis.

(b) As the P-value is less than a = 0.01. So, we reject the null hypothesis.

(c) As the P-value is less than a = 0.01. So, we reject the null hypothesis.

(d) As the P-value is less than a = 0.02. So, we reject the null hypothesis.

What is the null hypothesis?

The null hypothesis asserts that no relationship exists between two sets of data or variables under consideration. The null hypothesis states that any empirically observed difference is due solely to chance and that no underlying causal relationship exists, hence the term "null."

Here, we have

(a) one-tail test, Zx= 1.46, and a = 0.10

We have to find the P-value for the following conditions and determine whether or not to reject the null hypothesis.

The P-value for the right-tailed test is defined as

P(Zx > 1.46) = 1 - P(Zx ≤ 1.46)

= 1 - 0.9276

= 0.0721

As the P-value is less than a = 0.10. So, we reject the null hypothesis.

(b) one-tail test, Zx = -2.48, and a = 0.01

We have to find the P-value for the following conditions and determine whether or not to reject the null hypothesis.

The P-value for the right-tailed test is defined as

P(Zx < -2.48) = 0.0066

As the P-value is less than a = 0.01. So, we reject the null hypothesis.

(c) two-tail test, Zx= -1.92, and a = 0.01

We have to find the P-value for the following conditions and determine whether or not to reject the null hypothesis.

The P-value for the right-tailed test is defined as

P(|Zx| > -1.92) = 2×P(Zx≤ -1.92)

= 2×0.0274

= 0.0549

As the P-value is greater than a = 0.01. So, we reject the null hypothesis.

(d) two-tail test, Zx = 2.76, and a = 0.02

We have to find the P-value for the following conditions and determine whether or not to reject the null hypothesis.

The P-value for the right-tailed test is defined as

P(|Zx| > 2.76) =2×P(Zx≤ -2.76)

= 2×0.0029

= 0.0058

As the P-value is less than a = 0.02. So, we reject the null hypothesis.

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You're correct answer would be $14.

\(35/20 = 1.75\)

\(8x1.75=14\)

Answer:

14

Given:

\(20 books= 35\)

Step-by-step explanation:

\(35/20=1.75\)

\(8*1.75= 14\)

The value of Nicholas' property in the market, considering a market capitalization rate of 5.75% compounded annually, is approximately $346,581.15 rounded to the nearest cent.

To calculate the value of Nicholas' property in the market, we need to determine the present value of the rental payments using the market capitalization rate of 5.75% compounded annually.

The value of Nicholas' property can be calculated using the formula for present value of an annuity:

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

where PV is the present value, P is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is $3,000 per month, the interest rate is 5.75% (or 0.0575) per year, and we need to calculate the present value over the entire holding period of the property.

To convert the interest rate to a monthly rate, we divide it by 12. So, the monthly interest rate is 0.0575 / 12 = 0.0047917.

Next, we need to determine the number of periods. Assuming Nicholas plans to hold the property for a certain number of years, we multiply the number of years by 12 to get the number of months.

Let's say Nicholas plans to hold the property for 10 years. The number of periods would be 10 * 12 = 120.

Plugging the values into the formula, we have:

PV = 3000 * (1 - (1 + 0.0047917)^(-120)) / 0.0047917.

Evaluating this expression, we find that the present value of the rental payments is approximately $346,581.15.

Therefore, the value of Nicholas' property in the market would be approximately $346,581.15 rounded to the nearest cent.

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Answer:

Y= (4, -5)

Step-by-step explanation:

________________

Z corresponds to D

W corresponds to A and

X correspondents to B

rotate it in your mind

from D to C gives you a good clue where to place Y.

4,-5 is correct

Answer:

y = 14x+8

Step-by-step explanation:

Since we are not told hat to find, we can fid the equation that represents the amount of money.

The general form of the equation in slope intercept form is expressed as

y = mx+c

m is the slope = 14

c is the y intercept = 8

Substitute

y = 14x + 8

Hence the required equation is y = 14x+8

Answer:

C

Step-by-step explanation:

Based on the given simple statements, "The scroll is open" and "The writings are visible," we can determine which compound statements would also be true.

The scroll is not open or the writings are visible.

This compound statement would be true. Since the first simple statement states that the scroll is open, the negation of this statement would be that the scroll is not open. The second simple statement states that the writings are visible, which aligns with this compound statement. Therefore, this compound statement is true.

The scroll is open or the writings are not visible.

This compound statement would not be true. Both simple statements state that the scroll is open and the writings are visible. So, the second part of this compound statement contradicts the given information.

The scroll is open or the writings are visible.

This compound statement would be true. It directly matches the given simple statements, where both the scroll being open and the writings being visible are mentioned. Therefore, this compound statement is true.

The scroll is not open or the writings are not visible.

This compound statement would not be true. Both simple statements state that the scroll is open and the writings are visible. So, neither part of this compound statement aligns with the given information.

The compound statements that would be true are:

The scroll is not open or the writings are visible.

The scroll is open or the writings are visible.

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Answer:

it is d, step 1: 14x - 21; step 2: 14x=22

Step-by-step explanation:

7(2x-3)=1   1. multiply 7 with (2x) and (-3)

14x-21=1    2. +21 on both sides

14x= 22      3. /14 on both sides

x=1.8

but I will say d is the correct answer

The dimensions of the largest field that can be enclosed with 136 ft of fencing are 72 ft by 64 ft. The area of the field is 4608 ft2.

The amount of fencing needed to enclose the field is equal to the sum of the lengths of all four sides. Since 136 ft of fencing is available, the sum of the lengths of all four sides must equal 136 ft.

Let x represent the length of one side and y represent the length of the other side. Then the equation for the amount of fencing needed can be written as follows:

x + x + y + y

= 136

Simplifying, we get:

2x + 2y = 136

To find the dimensions of the largest field that can be enclosed, we must maximize the area of the field. The area of the field is equal to the product of the lengths of the two sides:

A = xy

To maximize the area of the field, we must take the derivative of A with respect to x and set it equal to 0.

A' = y

Setting A' equal to 0, we get:

y = 0

Since y cannot be 0, this equation has no solution. To maximize the area of the field, we must instead take the derivative of A with respect to y and set it equal to 0.

A' = x

Setting A' equal to 0, we get:

x = 0

Since x cannot be 0, this equation has no solution. To maximize the area of the field, we must instead solve the equation 2x + 2y = 136 for x and y.

2x + 2y = 136

2x = 136 - 2y

x = 68 - y

Substituting x = 68 - y into A = xy, we get:

A = (68 - y)y

A = 68y - y2

Taking the derivative of A with respect to y and setting it equal to 0, we get:

A' = 68 - 2y

68 - 2y = 0

2y = 68

y = 34

Substituting y = 34 into x = 68 - y, we get:

x = 68 - 34

x = 34

Therefore, the dimensions of the largest field that can be enclosed with 136 ft of fencing are 34 ft by 34 ft. The area of the field is 4608 ft2.

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Answer:

x = 4

Step-by-step explanation:

2x+2=10

2x= 10-2

2x=8

x=8/2

x= 4

Answer:

X > 4

Step-by-step explanation:

2x + 2 > 10

subtract 2 from both sides

2x > 10 - 2

subtract 2 from 10 to get 8

2x > 8

divide both sides by 2

x > 8/2

divide 8 by 2 to get 4

x > 4

hope this helps!

Answer:2(3)+4(1)=10,

Step-by-step explanation:

To check if (3,1) is a solution to the system of equations 2x+y=7 and 2x+4y=10, we substitute x=3 and y=1 into the equations and check if the equations hold true.

6. Ashley

7. Points are represented by (x, y). Therefore, when proving that your answer is correct, you are to plug in the points into the corresponding values. With this problem, the original function was f(x) = -16x^2 + 96x

f(x) always means y, which means that whenever you plug in x into the other side of the function, you should get -112 because that is the y value in your given point. Ashley is correct because she plugged in -1 wherever x was in the function. In equations, solving the exponent comes before multiplying any numbers together, which is what she did: she squared the -1 and got 1. Now the equation reads to be -16(1)+96(-1)

-16 times 1 is just -16, and 96 times -1 is just -96, therefore when she added -16 and -96 together, she got -112, which is what she should’ve gotten since we were looking for the y value. That is why Ashley is correct.

Find the derivatives for the following functions

(a)  1(2) = sin(4x) (ar) (++)

(b) 17 marlos 96) +4 2

(a) Consider the given function f(x) = sin(4x) Differentiating both sides with respect to x,

we get df/dx = d/dx (sin 4x)df/dx = 4 cos(4x)

Therefore, the derivative of the given function f(x) = sin(4x) is df/dx = 4 cos(4x).

(b) Consider the given function f(x) = 17x6 + 4x2

Differentiating both sides with respect to x,

we getdf/dx = d/dx (17x6 + 4x2)df/dx = d/dx (17x6) + d/dx (4x2)df/dx = 102x5 + 8x

Therefore, the derivative of the given function f(x) = 17x6 + 4x2 is df/dx = 102x5 + 8x.

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Answer:

C. 2(4 × 5) = (2 × 4) × 5

Step-by-step explanation:

The associate property of multiplication is

a(bc) = (ab)c

You can change the grouping of a multiplication without changing the result.

Answer: C. 2(4 × 5) = (2 × 4) × 5

By answering the presented question, we may conclude that So Christian  equation spelled 16 words correctly, Sarah spelled 3x - 2 = 46 words correctly, and Leonard spelled 2x + 1 = 33 words correctly.

What is equation?

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilized in many different areas of mathematics, such as algebra, calculus, and geometry. Let's start by defining some variables to represent the number of words each student spelled correctly:

Let x be the number of words Christian spelled.

x + (3x - 2) + (2x + 1) = 95

6x - 1 = 95

6x = 96

x = 16

So Christian spelled 16 words correctly, Sarah spelled 3x - 2 = 46 words correctly, and Leonard spelled 2x + 1 = 33 words correctly.

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The volume of the right prism is 24,500 cubic inches.

To find the volume of a right prism, we multiply the area of the base by the height. In this case, since the base is a right triangle, we need to find the area of the triangle first.

Given:

Perpendicular height (height of the prism) = 35 inches

Base length (base of the right triangle) = 40 inches

Hypotenuse (the side opposite the right angle) = 37 inches

To find the area of the base, we can use the formula for the area of a right triangle:

Area = (1/2) * base * height

Plugging in the values, we have:

Area = (1/2) * 40 in * 35 in = 700 in²

Now that we have the area of the base, we can find the volume of the right prism:

Volume = Base area * Height

Volume = 700 in² * 35 in = 24,500 in³

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Answer:

2058

Step-by-step explanation:

every 5 years is 0.53 so you times that by 11 to get 7.61 and then half of .53 is .265 and round that up you get three more years so 2058 is the answer.

Answer:

y = 3x

Step-by-step explanation:

Given line slope = m = -1/3

   perpendicular line slope = - 1/m = 3

Point slope form through point 1, - 3

(y+3) = 3 ( x-1)       expand and rearrange

y -3 = 3x- 3

  y = 3x - 6  

Step-by-step explanation:

perp.: 3

y + 3 = 3(x - 1)

y + 3 = 3x - 3

y = 3x - 6

The option A is corret  quotient of X² + 3X + 2 divided by X + 1 is X + 2.

In HCF by long division method we first divide the greater number by the smallest number and then divide the smaller number by the remainder. We continue the process until we get 0 remainder. The divisor is the HCF of the given numbers.

To find the quotient of X² + 3X + 2 divided by X + 1 using the factorization method, we can first factor the dividend as follows:

X² + 3X + 2 = (X + 1)(X + 2)

Now we can rewrite the original expression as:

(X² + 3X + 2) / (X + 1) = (X + 1)(X + 2) / (X + 1)

Canceling out the common factor of (X + 1), we get:

(X² + 3X + 2) / (X + 1) = X + 2

Therefore, the quotient of X² + 3X + 2 divided by X + 1 is X + 2, which we have obtained using both polynomial long division and the factorization method.

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The length and width of a rectangle are 36cm and 4.5cm

Finding the Width:

The formula to find the perimeter of the rectangle is:

P=2(l+w),

where P is the perimeter, l be the length, and w be the width.

Now substitute the given values to solve for w, since we need to find the width.

The given information is:

the length of a rectangle is six inches more than eight times the width so the equation becomes:

L=8w+6

P=120

w=8w

now plug the values in the above formula:

P=2(l+w),

120=2(8w+6)+8w

120=16w+12+8w

120=24w+12

24w=108

w=4.5

To find the length just substitute in the L.

L=8(4.5)+6

L=30+6

L=36

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Answer:

y=3/4x-4

Step-by-step explanation:

The form is y=mx+b so isolate y

-4y=16-3x

y=-16/4-3x/-4

y=3/4x-4

Answer:

y = 3/4x - 4

Step-by-step explanation:

Slope intercept form: y = mx + b

3x - 4y= 16

-4y = 16 - 3x

4y = -16 + 3x

y = -4 + 3/4x

y = 3/4x - 4

Answer:

You could simply go to your course selection book (if there is one) and see if it's there. If not, then ask your guidance counselor for help or if you can automatically advance.

Step-by-step explanation: