let a and b be two possible events when a random number generator is used once. suppose you are told that a and b are mutually exclusive. this implies that the probability that either A. A happens or B happens is equal to theproduct of the probabilities of A and B B. the probability that A and B both happen is equal to the sum ofthe probabilities of A and B C. the probability that either A happens or B happens is equal to thesum of the probabilities of A and B D. the probability that A happens given that B happens is equal tothe probability that A happens E. the probability that A and B both happen is equal to the productof the probabilities of A and B

The transformation that is needed in order to obtain the graph of​ h(x) from the graph of​ f(x) is D. Vertical translation

From the question, we have the following parameters that can be used in our computation:

f(x) = |x|

h(x) = |x| + 3

Using the above as a guide, we have the following:

h(x) = f(x) + 3

This means that the function f(x) is translated 3 units up to get the function h(x)

See attachnent for the graph

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To find the sum of the digits of all possible values of 'a', we need to add the sum of the digits of each value of abc. The sum of the digits for all possible values of a would be 8 + 7 + 15 + ... + 27, which can be calculated further.

The divisibility rule for 125 states that a number is divisible by 125 if the last three digits are divisible by 125. In the case of 24687abc, we know that the last three digits (abc) must be divisible by 125. This means that abc must be a multiple of 125. The smallest multiple of 125 is 125, and the largest is 999, so the possible values of abc are 125, 250, 375, 500, ..., 999.

The sum of the digits of each possible value of a can be calculated by adding the individual digits of each value of abc. For example, for the value 125, the sum of the digits is 1 + 2 + 5 = 8. For the value 250, the sum of the digits is 2 + 5 + 0 = 7. For the value 375, the sum of the digits is 3 + 7 + 5 = 15.

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The simplified answer as a single exponent is (122)¹¹.

Given is the expression as follows -

(122)⁴ . (122)⁷

The given expression is -

(122)⁴ . (122)⁷

(122)⁴ ⁺ ⁷

(122)¹¹

Therefore, the simplified answer as a single exponent is (122)¹¹.

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{Complete question -

simplify. Express your answer as a single term exponents -

(122)⁴ . (122)⁷}

The algebraic expression is (x² - 4x - 21)/4(x - 7) , we need to find the simplified value of it . Therefore , the simplified form is (x + 3)/4 .

What is simplification?

Rules are typically rewritten to achieve this simplicity. Systems for computer algebra use them in a methodical way. Associative operations, such as addition and multiplication, can be challenging. It is common practice to approach associativity by assuming that addition and multiplication can have any number of operands, such that the symbol for a + b + c is "+." (a, b, c). It follows that a + (b + c) and (a + b) + c are both condensed to "+"(a, b, c), which is shown as a + b + c.

In the question ,it is given that ,

the algebraic expression is (x² - 4x - 21)/4(x - 7) ,

we need to find the simplified value of it .

we first simplify the

numerator

that is x² - 4x - 21 ,

By using the split the

middle term method ,

we get ,

= x² - 7x  3x - 21

= x(x - 7)  3(x - 7)

= (x  3)(x - 7)

Writing the simplified numerator in the expression ,

we get ,

= (x  3)(x - 7)/4(x - 7)

cancelling out the common term (x-7) , we get

= (x  3)/4

Therefore , the simplified form is (x + 3)/4  . It is important to take into account different classes of rewriting rules. The easiest are formulas like E E 0 or sin(0) 0 that always make the expression smaller.

Complete question

What is the simplified form of the expression  

(x² - 4x - 21)/4(x - 7) ?

(a) (x+3)/4

(b) (x-3)/4

(c) (x+3)/(x-7)

       (d) (x-3)/(x-7)

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The quotient of the given division expression is 183.25

The division is multiplying one number by any other number to produce a different number. Consequently, the dividend is the number that is divided in this instance. A number's divisor is the one that divides the given number. The quotient is the sum of the two numbers we arrive at as a result. A number is called a "remainder" when a divisor produces a result that does not divide a given number entirely.

formula for dividing

Dividend Divisor = Quotient is how division is performed.

You may alternatively write the expression above as:

Dividends times quotients is a divisor.

In this instance, the divisional symbol is "." However, sometimes, the symbol "/" is used instead, as in

Divisor / Dividend = Quotient

733 ÷  4= 183.25

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Answer:

(y-8)(y-8)

(y + 8)^2

Step-by-step explanation:

To factor the perfect square trinomial "y^2-16y+64" into two binomials, we need to find two binomials that multiply to give the trinomial.

Let's use the formula (y + n)(y + m), where n and m are integers.

If we set n = 8 and m = 8, we get:

(y + 8)(y + 8) = y^2 + 16y + 64

So, the perfect square trinomial y^2 - 16y + 64 can be factored into the binomials (y + 8)^2.

This hypothesis test can be set up as a one-tailed test, where the null hypothesis is that the mean is equal to $23,000 and the alternative hypothesis is that the mean is greater than $23,000.

The p-value, which is the probability of obtaining a test statistic as extreme or more extreme than the one observed, given that the null hypothesis is true, can then be used to determine whether to reject or fail to reject the null hypothesis.

In this case, if the p-value is very small, it indicates strong evidence against the null hypothesis and in favor of the alternative hypothesis.

This means that it is highly unlikely that the mean subscription cost per customer is equal to $23,000, given the sample data and the assumptions of the test.

Therefore, it is appropriate for the software company to make the conclusion that the mean is greater than $23,000. However, it is important to note that the conclusion should be based on the assumptions of the test being met and the sample being representative of the population of customers.

Additionally, it is always good practice to report the results of the test, including the p-value, the sample mean, the sample standard deviation, and the sample size, to provide context for the conclusion.

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Span{V1, V2} is the set of all vector linear combinations V1 and V2, which contains every vector that can be represented as a vector linear combination of V1 and V2. The five vectors in SpanV1, V2 are as follows:

[7, 3, 8] (V1)

[-7, 4, 0] (V2)

[0, 0, 0] (the zero vector)

[7, 7, 8] (V1 + V2)

[-14, 10, 16] (2V1)

A vector is a matrix that has only one row or one column. A row vector is a matrix with only one row. Example Because it only contains one row, the matrix is a row vector. A column vector is a matrix with only one column. If all of the scalars in a matrix are real-valued, it is indicated using uppercase boldface letters, such as A R m n. That is, the matrix exists in a real-valued vector space with m n dimensions. As a result, matrices are just vectors expressed in a two-dimensional table-like format.

Here,

Span{V1, V2} is the set of all linear combinations of vectors V1 and V2, which includes any vector that can be expressed as a linear combination of V1 and V2. The five vectors in Span{V1, V2} are:

[7, 3, 8] (V1)

[-7, 4, 0] (V2)

[0, 0, 0] (the zero vector)

[7, 7, 8] (V1 + V2)

[-14, 10, 16] (2V1)

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The exponential equation of ln x = 3 is: x = e^3.

The formula for an exponential function is f (x) = axe, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

The logarithmic function can be written in exponential form as follows:

x = logb(a) ⇔ a = b^x

The two functions can be written in an equivalent form.

The given logarithmic function is ln x = 3.

The exponential equation of ln x = 3 is:

x = e^3

Hence, The exponential equation of ln x = 3 is: x = e^3.

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Answer:

9x+15

Step-by-step explanation:

The value of the expression (1 - 1/2) × (1 - 1/3) × (1 - 1/4)...(1 - 1/20) will be 1/20.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ (1 - 1/2) × (1 - 1/3) × (1 - 1/4)...(1 - 1/20)

Simplify the expression, then we have

⇒ (1 - 1/2) × (1 - 1/3) × (1 - 1/4)...(1 - 1/20)

⇒ (1/2) × (2/3) × (3/4)...(19/20)

⇒ 1 / 20

The value of the expression (1 - 1/2) × (1 - 1/3) × (1 - 1/4)...(1 - 1/20) will be 1/20.

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Yessica and Zoe's average speeds are equal to 63 miles/90 minutes, or 0.7 miles/minute.

To solve this problem, we need to use the formula for average speed, which is distance divided by time. We are given the combined distance traveled by both women, which is 63 miles, and the total time they took, which is 90 minutes. We can divide the distance (63 miles) by the time (90 minutes) to get the average speed: 63/90 = 0.7. This means that their average speed was 0.7 miles per minute. This can also be expressed as 42 mph, which is the same as 0.7 miles per minute. To summarize, Yessica and Zoe's average speeds were 0.7 miles per minute or 42 mph.

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Therefore , the solution of the given problem of function comes out to be  the graph of option D and c(x)=3x+200 match.

If the function under consideration whose graph needs to be drawn is

Typically, the output values are represented on the vertical axis while the values of "x" (also known as the input variable, independent

variable, and independent variable) are plotted on the horizontal axis.

Here,

Given: They are plotted together on this point.

=> (x,y) = (x,f(x))

The functions are typically written as:

=> y = f (x) because of this (x)

In this instance, the cost of taxi ride is determined by the number of minutes that are used.

For this reason, we design the graph so that the horizontal axis receives values for x (the amount of minutes elapsed) and the vertical scale receives values for c(x), which is the cost.

The number of mins can be any amount over zero but cannot be lower than zero.

The required graph will be produced by calculating c(x) for the at least one or two values and combining the line segment that does not extend below x= 0.

=> x c(x) = 2x + 2

=> 0   = 0  + 2 =  2

=> 1    = 2 + 2 = 4

Plot the two points (0,2) and (1,4), link them, and go on to the left, not back behind x = 0.

Using the notions discussed above, we arrive at the graph shown below:

As a result, the graph of option D and c(x)=3x+200 match.

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The complete question is " The cost, c(x), for a taxi ride is given by c(x) = 2x + 2.00, where is the

number of minutes.

On a piece of paper, graph c(x) = 2x + 2.00. Then determine which answer

matches the graph you drew, including the correct axis labels."

Answer:

Below

Step-by-step explanation:

x + 2y = 10        given

2x + y = 14         given      multiply this equation by -2 to get :

-4x - 2y = - 28     add to top equation to get

-3x = -18        so   x = 6

x + 2y = 10     so y = 2

Answer:

Andre has more money in his savings account.

Step-by-step explanation:

  We need to have equations for both Andre and Elena. Andre starts with $100 in his savings and adds $5 per week.  Based on this, Andre's equation will be y = 5x + 100. Elena starts with $10 and adds $20 per week. Based on this, Elena's equation will be y = 20x + 10.

Andre: y = 5x + 100

Elena: y = 20x + 10

We have to figure out who will have more money in their account after 4 weeks. To do that, we plug in 4 into x because x is the number of weeks.

Andre: y = 5(4) + 100

          y = 20 + 100

          y = 120

Andre has $120 after 4 weeks.

Elena: y = 20(4) + 10

         y = 80 + 10

         y = 90

Elena has $90 after 4 weeks.

Which is greater? $120 or $90? That's right, its $120. Andre has more money in his savings account. I hope this helps!  

Carpentry frequently employs 3-4-5 triangles to verify that angles are 90°

What is the 3-4-5 triangle rule?

The 3-4-5 triangle rule states that you must multiply 3, 4, and 5 by the same amount in order to accomplish this.

The theorem demonstrates the effectiveness of the 3-4-5 approach and the fact that multiplying the 3-4-5 triangle, as opposed to using the formula to determine the length, will yield the missing side.

A ratio can be conceived of as the lengths 3, 4, and 5. To obtain triangles with varying lengths but the same proportion, this ratio can be scaled.

A real life example of the 3-4-5 triangle rule is carpentry, where it is frequently employed to verify that angles are 90°.

Hence, carpentry employs 3-4-5 Triangles in Real Life.

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The symbol for the common normal CDF is. The function represents the CDF of the standard normal distribution.

What is CDF?

The probability function that X will have a value less than or equal to x is known as the Cumulative Distribution Function (CDF) of a real-valued random variable X, evaluated at x. It is employed to describe a table's random variables' probability distribution. And using these data, we can quickly make a CDF plot in an Excel spreadsheet.

So, CDF determines the cumulative probability for the specified value. Under specific circumstances, it is used to compare the probability between values and to ascertain the probability of a random variable. For continuous distribution functions, CDF provides the area under the probability density function up to the specified value, and for discrete distribution functions, it provides the probability values up to what we specify.

F(x)=P(X≤x)=x∫−∞f(t)dt, for x∈R, In other words, integrating the pdf yields the cdf for a continuous random variable. It should be noted that the Fundamental Theorem of Calculus implies that cdf differentiation can be used to determine the pdf of a continuous random variable.

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Answer:

Step-by-step explanation: (3 sqrt 2x^3)(sqrt 8x^3) when simplified is 12x^8

Michael's opportunity cost of a sculpture is 2 paintings per sculpture.

According to the table, Michael can produce either 3 sculptures or 6 paintings in a day. Therefore, the opportunity cost of producing one sculpture for Michael is 2 paintings, as he could have produced 2 additional paintings instead of the sculpture.

Opportunity cost represents the trade-off between two options and helps decision makers understand the benefits and drawbacks of different choices. In this case, by choosing to produce a sculpture, Michael is forgoing the opportunity to produce 2 paintings.

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The inequality to determine the height of Great Dane can be expressed as [tex]b-6\frac{1}{4}\geq 25 inches[/tex] and according to that the height of the dog should atleast be 31.25 inches

Let us assume the height of Great Dane as b

if the height of Yorkshire Terrier is 6.25 inches and is atleast 25 inches smaller than Great Dane then the inequality can be represented as

[tex]b-6\frac{1}{4}\geq 25 inches[/tex]

now, on solving this inequality the height of great dane comes out to be atleast 31.25 inches

[tex]b\geq 25+6\frac{1}{4}[/tex] = 31.25 inches

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Answer:

68%

Step-by-step explanation:

So we had 34 filets and 16 steaks.

We can add these two together to find the total amount of items sold.

[tex]34 + 16 = 50[/tex]

So 50 total, but we're dealing with filets which is at 34

A percentage can be found by dividing 50 and 34

[tex]34\div 50[/tex]

Giving us 0.68, also known as 68%

The statement that is true about the graphs include the following: D. both graphs have the same horizontal asymptotes.

In Mathematics, a horizontal asymptote can be defined as a horizontal line (y = b) where the graph of a function approaches the line as the input values (domain or independent value) approach negative infinity (-∞) to positive infinity (∞).

In this context, the line passing through the ordered pair (0, 3) on the graph of this exponential decay function represents a horizontal asymptote and it has an equation of y = -4, as shown in the image attached above.

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The x-axis is the horizontal center line on the coordinate plane (left to right). The y-axis is the vertical center line on the coordinate plane. The point where the x and y axis interact, identified by 0, is called the origin.

This point is located at coordinates (0,0). The x-axis is usually associated with the horizontal axis in a two-dimensional graph and is typically used to represent different categories of data. The y-axis is associated with the vertical axis and is used to represent a range of values from high to low.

The formula for determining the coordinates of a point is (x,y). The x-coordinate is the distance from the origin on the x-axis and the y-coordinate is the distance from the origin on the y-axis. For example, if a point has an x-coordinate of 4 and a y-coordinate of -3, the coordinates of the point would be (4,-3). To calculate the distance between two points, you can use the distance formula, which is the square root of the sum of the squares of the differences between the x-coordinates and the y-coordinates. For example, if the coordinates of point A are (2,3) and the coordinates+ of point B are (7,1), the distance between A and B would be calculated by taking the square root of (5-2)^2+(1-3)^2, which would equal 5.

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The estimated volume of the given cuboid is 736 inch³

In geometry, a cuboid is a three-dimensional figure or geometrical shape that has 6 faces, 12 edges, and 8 vertices. The space occupied by the cuboid is known as the Volume of the cuboid.  

The dimensions of the cuboid are Length, Width, and Height. The formula for the volume of the cuboid is given by

Volume of cuboid = Length × Width × Height  

Here we have

Measurements cuboid are

Length = 22.8 inches  

On rounding to a whole number, Lenght = 23 inches

Width = 1.8 inches

On rounding to a whole number, Width = 2 inches

Height = 15.8 inches

On rounding to a whole number, height = 16 inches  

As we know

The volume of a cuboid = Length × Width × Height  

= 23 inch × 2 inch × 16 inch  

= 736 inch³

Therefore,

The estimated volume of the given cuboid is 736 inch³

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The gateway arch in st. Louis, MO is approximately 630 ft tall, the same height of the Nickels would be in a stack is 98474.

Height of Gateway Arch in St. Louis, MO = 630ft tall

We are asked, how many nickels would be in a stack of the same

height when 1 nickel is 1.95 mm thick.

Convert height in ft to mm

1 ft = 304.8 mm

630ft = X

After Cross Multiply,

630ft × 304.8mm/1ft

= 192024 mm.

To find how many nickel would be in a stack of the same height

= Total thickness/ Thickness of 1 US dime

= 192024 mm/1.95mm

= 98473.8

≈98474 nickels

Therefore, the number of nickel that would be in a stack of the same height is 98474.

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A statement which best describes how the graph of h is different from the graph of g include the following: A. The graph of h is the graph of g vertically shifted up 1 unit.

In Mathematics, the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image or function.

In Mathematics, a horizontal translation to the left is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

In this scenario, the function g(x) = x² is translated upward by 1 units to produce h(x) = g(x) + 1.

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The value of x is given as follows:

x = 14.

Similar triangles are triangles that share these two features presented as follows:

Due to the bisection, the two triangles in this problem are similar, hence the equivalent side lengths are given as follows:

The proportional relationship is then given as follows:

(x + 2)/12 = 24/18

Applying cross multiplication, the value of x is obtained as follows:

18(x + 2) = 24 x 12

18x + 36 = 288

x = (288 - 36)/18

x = 14.

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Kareem make muffin using a ratio of 3. 5 cup of flour for every 1. 75 cup of sugar. If he ha 3. 5 cup of sugar, flour doe he need to make the muffin is 7 cups.

The ratio that Kareem uses to make the muffin is 3.5 cups of flour for every 1.75 cups of sugar .

let the number of cups of flour be "y" and

the number of cups of sugar be "x" .

So , y ∝ x ,

y = k*x , where k is the constant of proportionality .

From the given data ,

3.5 = k*1.75

k = 3.5/1.75

k = 2 .

we have to find the cups of flour that Kareem needs , if he has 3.5 cups of sugar .

the equation becomes ,

y = 2*3.5

y = 7

Therefore , Kareem needs 7 cups of flour .

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other.

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The perimeter of the rectangle is P = 27n + 1.

The whole distance encircling a shape is referred to as its perimeter. It is the length of any two-dimensional geometric shape's boundary or outline. Depending on the size, the perimeter of several figures can be the same. Consider a triangle built of an L-length wire, for instance. If all the sides are the same length, the same wire can be used to create a square.

The length of the rectangle is: l = 9.5n+10.

The width of the rectangle is: w = 4n-9.5.

The perimeter of the rectangle is given as:

P = 2(l + w)

P = 2(9.5n + 10 + 4n-9.5)

P = 2(13.5n + 0.5)

P = 27n + 1

Hence, the perimeter of the rectangle is P = 27n + 1.

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