P(A)=0.60, p(b)=0..25 and p(A and B)=.15 what is p(A or B)?

Answer:

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(a) Sample space: 2^50 (1,024,000). Probability of exactly 20 heads: 0.000244140625.

(b) 6^2 (36). Probability of a sum of 4: 1/9.

(c) C(52,5) (2,598,960). Probability of a full house: 0.001441.

(d) 10^20 (10^19). Probability of bin 1 containing exactly 3 balls: 1/10^19.

(e) C(54,3) (19,323). Probability of at least one psychologist: C(24,1)/C(54,3) (0.841). Probability of exactly three psychologists: C(24,3)/C(54,3) (0.037).

(f) 3^10 (590,490). Probability of at least one of each type: 0.001690.

(a) The sample space consists of all the possible outcomes of flipping a fair coin 50 times, which is 2^50 (1,024,000). There are only two possible outcomes for each flip, heads or tails. The probability of getting exactly 20 heads is 0.000244140625.

(b) The sample space consists of all the possible outcomes of rolling a red and a blue 6-sided die, which is 6^2 (36). The probability of getting a sum of 4 is 1/9.

(c) The sample space consists of all the possible 5 card poker hands (selected from a single deck), which is C(52,5) (2,598,960). The probability of getting a full house (3 cards of one rank and 2 cards of another rank) is 0.001441.

(d) The sample space consists of all the possible ways of placing 20 labeled balls into 10 labeled bins, which is 10^20 (10^19). The probability of bin 1 containing exactly 3 balls is 1/10^19.

(e) The sample space consists of all the possible ways of selecting 3 of the 54 people attending the conference, which is C(54,3) (19,323). The probability of at least one psychologist being chosen is C(24,1)/C(54,3) (0.841). The probability of exactly three psychologists being chosen is C(24,3)/C(54,3) (0.037).

(f) The sample space consists of all the possible ways of buying ten cupcakes from the 3 different types, which is 3^10 (590,490). The probability that you have at least one of each type is 0.001690.

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At the significance level of a = 0.05, there is no strong statistical support for the manager's assertion.

Accepting it would be a type II error because the null hypothesis might not be true.

The 'null' and 'alternative' hypotheses should be

p 0.4 for H0 and p > 0.4 for Ha

q= 1-p= 1-0.4= 0.6

The alpha level for significance is 0.05.

For one-tailed tests, the crucial area is Z> ± 1.645

The sample proportion is p^= x/n= 38/90=0.42222

Using the z statistic

z= p^- p/ √pq

z= 0.422-0.4/ √0.4*0.6

z= 0.04536

We are unable to reject the null hypothesis since the calculated value of z=0.04536 does not fall within the crucial zone Z> 1.645.

The manager's assertion is not sufficiently supported by the available data.

When we reject the actual null hypothesis, we commit a type I mistake.

When we accept the incorrect null hypothesis, we make type II errors.

Accepting it would be a type II error because the null hypothesis might not be true.

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To much to right but have it in pic: \/ \/

Approximately 95% of housing prices are between a low price of $133,000 and a high price of $161,000.

These approximate percentages are defined by the Empirical Rule, for a normally distributed variable.

Hence the prices within two standard deviations of the mean are given as follows:

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1.  Every composite number can be expressed as a product of primes - True

2.  Some quadratic equation has infinite solution - True

3. False (ix-yl = |x-y|, which may not equal ly = |y|)

4. 2(3+√7)-2√7 = 6√7 - False

5. False (25,471,287 is divisible by 3)

6. √6 is not rational number - True

7. Between every two real numbers there is another real number -True

8. For any natural numbers a and b GCF (a, b) * LCM (a, b) = a*b. -True

9. Integer is not closed under division -True

10. False (The product of a non-zero rational number and an irrational number is not necessarily rational)

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Answer:

Step-by-step explanation:

Each bracelet need 7 inches of string. Jenna has a total of 16 feet of string.

Divide the total amount of string by the number of inches needed for each bracelet.

Step 1: Convert 16 feet into inches. 12 inches = 1 foot

16 feet x (12 inches/1 foot) = 192 inches

This is the total inches of string.

Note that feet and foot units cancel and you are left with inches.

Step 2: Find the number of bracelets that can be made. Use the answer from step 1. Each bracelet needs 7 inches of string.

Total inches of string / 7 inches of string for each bracelet

192 inches / 7 inches = 27.4

Round the answer to 27.

Same-sized rectangles are possible. However, because their sides might differ in length, they are not congruent.

Congruent refers to two rectangles having the same dimensions and shape. So, two rectangles are said to be congruent if their length and width are equivalent in size. The length and width of two rectangles must match for them to be congruent.

Also having the same area are congruent shapes, such as rectangles. However, congruent rectangles with the same area are not always the case. There are differences among rectangles. Figures that have the exact same shape but differ in size are referred to as similar figures.

These two polygons are incongruent because while their matching sides are equal, their corresponding angles are not. Despite the sides being the same size, they have different forms.

The complete question is:

Draw two rectangles that have the same area but are not congruent.

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The value of the equations are

n = 6

x = 20

b = -4

k = 176

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

-15 + n = -9   be equation (1)

On simplifying the equation , we get

Adding 15 on both sides of the equation , we get

n = -9 + 15

n = 6

Therefore , the value of n is 6

b)

x - 7 = 13   be equation (2)

On simplifying the equation , we get

Adding 7 on both sides of the equation , we get

x = 13 + 7

x = 20

Therefore , the value of x is 20

c)

14b = -56   be equation (3)

On simplifying the equation , we get

Dividing 14 on both sides of the equation , we get

b = - ( -56/14 )

b = -4

Therefore , the value of b is -4

d)

16 = k/11   be equation (4)

On simplifying the equation , we get

Multiply by 11 on both sides of the equation , we get

k = 16 x 11

k = 176

Therefore , the value of k is 176

Hence , the equations are solved

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Using the graph,  it's cheaper to use Company B instead of Company A; when the number of miles is less than 5 miles.

For us to solve this question, we need to first create an equation;

If A company initially supplies $30 and then $2 per mile, then the equation here is:

y = 2x + 30

If B company initially supplies $20 and then $4 per mile, then the equation is expressed as:

y = 4x + 20

Due to the fact that the two wages are asked to be equalized, we equate these two equations with each other and find the result.

2x + 30 = 4x + 20

2x = 10

x = 10/2

x = 5

This is the number of miles that both companies will charge a customer the same amount.

Then the time for which it is cheaper to use company B is when number of miles is less than 5.

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Step-by-step explanation:

based on you input, I would suggest you divide 70 by 4 to get 17.5.

that is the answer. trust.

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The actual speed of Mr Casey is 39.71 miles per hour and his estimation is greater than the actual speed at which he should travel.

Estimation is a roughly calculated answer of something for which we get an approximate result of it.

Given that, Mr. Casey needs to drive 278 miles in 7 hours. He estimates that he should drive at a speed of 50 miles per hour. We need to find whether his estimation correct or not,

We know that,

Speed = distance / time

Therefore, Mr. Casey's actual speed =

Speed = 278 / 7

= 39.71 miles per hour

As, he estimated his speed being 5o miles per hour, and actual speed is 39.71 miles per hour, therefore, his estimation is greater than the actual speed at which he should travel.

Hence, the actual speed of Mr Casey is 39.71 miles per hour and his estimation is greater than the actual speed at which he should travel.

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Answer:

seventy-five thousand two hundred thirty-two

Step-by-step explanation:

The activation energy for the given reaction is166 KJ/mol. (Option B)

Activation energy refers to the minimum amount of extra energy that is required by a reacting molecule to be converted into product. It is the minimum amount of energy required to energize or activate atoms or molecules so that they can undergo a chemical reaction or transformation. In order to calculate the activation energy (Ea), the Arrhenius equation is used which is given by:

k=Ae^((-E)/RT)

where k is the rate of chemical reaction, A is a constant depending on the chemicals involved, E is the activation energy, R is the universal gas constant, and T is the temperature.

The equation can be expressed as

ln⁡〖k=ln⁡〖A-(E/RT)lne〗  〗

2.303 log⁡〖k=2.303 log⁡〖A-E/RT〗 〗

log⁡〖k=log⁡〖A-E/2.303RT〗 〗

As there are two temperatures and two rate constants given, the Arrhenius equation is rearranged:

log⁡〖k2/k1=E/2.303(1/T1〗-1/T2)

According to the data,

k1 = 2.7 x 10^-4

T1 = 600 K

k2 = 3.5 x 10^-3

T2 = 650 K

R = 8.314

log⁡〖(3.5 x10^(-3))/(2.7 x 10^(-4) )=E/(2.303*8.314)(1/600〗-1/650)

E = 166208 J/mol or 166 KJ

Note: The question is incomplete. The complete question probably is: Calculate the activation energy (Ea) in kJ/mol for a reaction if the rate constant (k) is 2.7 × 10^-4 (M^−1sec^−1) at 600 K and 3.5 × 10^−3 (M−^1sec^−1) at 650 K. a. −166 kJ/mol b. 166 kJ/mol c. 1.64 kJ/mol d. 1.66 × 10^5 kJ/mol. (R

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Answer:

Exact Form:

21/10

Decimal Form:

2.1

Mixed Number Form:

2 1/10

Step-by-step explanation:

Answer:

5/4

Step-by-step explanation:

divide 20 and 16 by 4

20/4=5

16/4=4

Answer:

Car Value Depreciation Graph

The graph that represents the value of the car, y, in dollars, after x years is the graph that starts at $8,000 on the y-axis and decreases at a steady rate of 25% each year on the x-axis. It would be the graph V.

The total price is obtained following these two steps:

The first step is obtain the price without taxes, which is done adding the price of all the items in the data-set.

Then the proportion is applied, relative to the sales tax of 7%.

The percentage of a sales tax of 7% is given as follows:

107%.

Hence the multiplier relative to this sales tax is given as follows:

1.07.

The problem is incomplete, hence the answer was given in general terms.

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The ΔABC reflects across x-axis with point a=2 and scale factor of x+2 to form the ΔA'B'C'.

What is reflection?

A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.

The vertices of ΔABC is given as -

A(–4, –2), B(–2, 6), and C(4, 4)

The vertices of ΔA'B'C' is given as -

A′(–2, –2), B′(0, –10), and C′(6, –8)

To find the scale factor of the reflection use the formula -

x + a = x' and y + b = y'

Substitute the values in the equation.

For vertex A and A' -

x1 + a = x1'

-4 + a = -2

a = -2 + 4

a = 2

y1 + b = y1'

-2 + b = -2

b = -2 + 2

b = 0

For vertex B and B' -

x2 + a = x2'

-2 + a = 0

a = 0 + 2

a = 2

y2 + b = y2'

6 + b = -10

b = -10 - 6

b = -16

For vertex C and C' -

x3 + a = x3'

4 + a = 6

a = 6 - 4

a = 2

y3 + b = y3'

4 + b = -8

b = -8 - 4

b = -12

It can be seen that the values of a is constant whereas the values of y varies. This happens due to reflection of coordinates across the x-axis.

Therefore, the reflection happens across the x axis.

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The likelihood of randomly selecting a chocolate chip cookie from the batch is unlikely. Therefore, option C is the correct answer.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

Given that, the baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies.

P(chocolate chip) = 0.25

In probability, larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 0.5 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Here, 0.25<0.5

Therefore, option C is the correct answer.

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Answer:unlikely

Step-by-step explanation:

Equation for the cost of company A: f(x) = 15 + x

Equation for the cost of company B: g(x) = 45 + x/2

For 80 miles, company B is cheaper than company A.

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.

Given,

Company A charges an initial fee of $15 for the rental plus $1 per mile driven

f(x) = 15 + x

Company B charges an initial fee of $45 for the rental plus $0.50 per mile driven

g(x) = 45 + 0.5x

g(x) = 45 + x/2

x is number of miles

For 80 miles company A charges

f(80) = 15 + 80

        = 95

For 80 miles company B charges

g(80) = 45 + 80/2

         = 85

By the above calculation, Company B is cheaper than Company A for 80 miles drive.

Hence,

f(x) = 15 + x is Equation for the cost of company A

g(x) = 45 + x/2 is Equation for the cost of company B

Company B is cheaper than company A for drive of 80 miles.

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Here is the attached image for the answer. If you write it in in slope-intercept form, y=mx+b. You will get the answer below in the attached image.

The value of given expression 12*9  is 108

What is Algebraic expression ?

Algebraic expressions are the concept of expressing numbers the usage of letters or alphabets without specifying their real values. The basics of algebra taught us how to express an unknown fee using letters which includes x, y, z, and so forth. these letters are known as here as variables. An algebraic expression can be a aggregate of both variables and constants. Any price that is placed before and accelerated through a variable is a coefficient.

Given expression ,

12*9 = (3*4) * (3*3)

= 9*(3*4)

= 9* 12

= 108

Hence, The value of given expression 12*9 is 108

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The mistake of Derek is that 72 divided by 8 is 9, not 8.

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

Given is an equation that Derek is trying to solve.

The equation is 8d = 72.

8d = 72

In the first step, Derek divided both sides of the equation by 8, which is a correct way to solve the problem.

We have to divide both sides of the equation by 8.

8d / 8 = 72 / 8

This step is correct.

After dividing, in the left hand side, there will be only 'd' remaining and in the right hand side, 27/8 = 9.

d = 9

But Derek got 8 instead of 9 in the right hand side.

Hence the value of d is 9 and not 8, which is the mistake of Derek.

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Answer:

x = 58.67

Step-by-step explanation:

[tex]\frac{-8.8}{x}[/tex] = [tex]\frac{1.5}{10}[/tex]

Cross multiply

1.5x = (-8.8)(10)

1.5x = -88

Divide, solve for x

x = -88/1.5 = -58.6666667 = around -58.67

Answer:

3

Step-by-step explanation:

12/4=3

The matrix multiplication is possible for option (b) 1 × 3 by 3 × 3, and option (c) 2 × 1 by 1 × 2.

What is a matrix?

A matrix is a rectangular array or table with numbers or other objects arranged in rows and columns. Matrices is the plural version of matrix. The number of columns and rows is unlimited. Matrix operations include addition, scalar multiplication, multiplication, transposition, and many others.

It is known that if the number of columns of a matrix A be equal to the number of rows of another matrix B then the product of matrix A and matrix B i.e. AB is defined.

a)  In this option no of columns in first matrix is 1 and the no of rows in second matrix is 2.

That means no of columns in first matrix is not equal to no of rows in second matrix.

Hence, in this case matrix multiplication is not possible.

Therefore, option (a) is incorrect.

b)  In this option no of columns in first matrix is 3 and the no of rows in second matrix is also 3.

That means no of columns in first matrix is equal to no of rows in second matrix.

Hence, in this case matrix multiplication is possible.

Therefore, option (b) is correct.

c)  In this option no of columns in first matrix is 1 and the no of rows in second matrix is 1.

That means no of columns in first matrix is equal to no of rows in second matrix.

Hence, in this case matrix multiplication is possible.

Therefore, option (c) is correct.

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Mallory is further from the surface than Eva. So, Mallory > Eva. Therefore, option D is the correct answer.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, Mallory is exploring at an elevation of -25 feet.

So, distance between Mallory and the surface of water is 25 feet

Jacob is standing on the boat, at an elevation of 15 feet.

Distance between Jacob and the surface of water is 15 feet

Eva just jumped in and is 5 feet below the surface of the water.

Distance between Eva and the surface of water is 5 feet

In this case, the person closest to the surface is Eva, who is 5 feet from the surface.

So, the inequality is Mallory > Eva

Therefore, option D is the correct answer.

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Write each vector in component form and add the components separately. This new vector will represent the sum of the two original vectors. This is the most straightforward way to add two vectors.

1. Write each vector in component form. This means breaking down each vector into its x- and y-components.

2. Add the x-components of each vector together and the y-components of each vector together.

3. The result will be a single vector with both x- and y-components.

To add two vectors, I should write each vector in component form, breaking them down into their x and y components. Then, I should add the components together, resulting in a new vector with components that are the sum of the two original vectors' components. This new vector will represent the sum of the two original vectors. This is the most way to add two vectors.

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The probability of x successes in the n independent trials of the experiment is 0.1640625

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, n=9​, p=0.5​, x≤3 we need to find probability of x successes in the n independent trials of the experiment.

We know that,

P(X=x) = ⁿCₓpˣq⁽ⁿ⁻ˣ⁾

q = 1-p = 1-0.5

q = 0.5

P(X=x) = ⁹C₃(0.5)³(0.5)⁹⁻³

P(X=3) = ⁹C₃ (0.5)³(0.5)⁶

⁹C₃ = 9! / 3!(9-3)! = 9!/3! × 6!

⁹C₃ = 84

P(X=3) = 84×0.125×0.015625

= 0.1640625

Hence, the probability of x successes in the n independent trials of the experiment is 0.1640625

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