Find the value of x.

Answer:

[tex]|x-8|=6[/tex]

Step-by-step explanation:

Let's begin by finding the midpoint of 2 and 14. To do this, we'll add the numbers and then divide by 2.

2+14=16

16/2=8

The number that is the same distance between 2 and 14 is 8.

Now, let's find how far away each number is from 8.

8-2=6

14-8=6

2 and 14 are 6 away from 8.

Let's set up the absolute value equation using these two values.

Since 8 is the midpoint, this will be what the absolute value expression is equal to.

Since each number is 6 away from 8, this is the number (6) we will be taking away from 2 and 14.

Remember that absolute value is just distance.

In other words, 2 is 6 away from 8, and 14 is also 6 away from 8.

Or, the distance between a number x and 8 is 6.

Using this knowledge, we have:

[tex]|x-8|=6[/tex]

Answer:

|x-8|=6

Step-by-step explanation:

i checked rsm its correct :3

If a hypothesis test is conducted to see if there is evidence that the average wait time is 5 minutes, the p-value is 0.040.

To calculate the p-value for the hypothesis test, we need to perform the following steps:

Step 1: State the null and alternative hypotheses.

In this case, the null hypothesis (H0) is that the average wait time for customers during the lunch hour is 5 minutes. The alternative hypothesis (Ha) is that the average wait time is not 5 minutes.

Step 2: Determine the test statistic.

We can use a t-test since we do not know the population standard deviation. We calculate the t-value using the formula:

t = (x' - μ) / (s / √n)

where x' is the sample mean, μ is the population mean (5 minutes), s is the sample standard deviation, and n is the sample size (15).

Step 3: Calculate the p-value.

We can use a t-distribution table or software to find the p-value associated with our calculated t-value. Alternatively, we can use the t-test function in Excel or other statistical software to calculate the p-value directly.

Assuming a two-tailed test and a significance level of 0.05, if the p-value is less than 0.05, we reject the null hypothesis in favor of the alternative hypothesis. If the p-value is greater than 0.05, we fail to reject the null hypothesis.

Suppose the sample mean is 6.2 minutes, the sample standard deviation is 1.3 minutes, and the sample size is 15. Then the t-value is:

t = (6.2 - 5) / (1.3 / √15) = 2.22

Using a t-distribution table or software with 14 degrees of freedom (15 - 1), we find the p-value to be approximately 0.040, which is less than 0.05. Therefore, we reject the null hypothesis and conclude that there is evidence to suggest that the average wait time for customers during the lunch hour is not 5 minutes.

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$90m + $500 is the correct expression for the given data.

Troy's grandpa gave him a one-time gift of $700, so let's start there.

Next, let's think about Troy's monthly salary. He receives $40 a month from his grandfather, so in m months he would have gotten 40 million dollars.

He gets $50 a month from his mother, but she just started doing so 4 months after his grandfather, so he would have gotten that amount for (m-4) months. The entire sum he received from his mother would be as follows:

50(m-4)

We can add up the three sums to make the statement for Troy's overall payment after m months simpler:

Total amount = $700 + $40m + $50(m-4)

Condensing the phrase:

Total amount = $700 + $40m + $50m - $200

Total amount = $90m + $500

Therefore, the simplified expression for the amount of money Troy received m months after his mother started giving him money is $90m + $500.

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Answer: there's a 50-50 chance of at least two people having the same birthday.

In a group of 50 people, the expected number of days of the year which are one of their birthdays can be determined using the concept of probability which are one of their birthdays is approximately 194 days.

The expected number of days of the year which are one of their birthdays in a group of 50 people can be calculated using the formula E(X) = np, where n is the number of trials and p is the probability of success in each trial. In this case, there are 50 people and 365 days in a year, so each person has a probability of 1/365 of having their birthday on a particular day. Therefore, the expected number of people with a birthday on any given day is 50*(1/365) = 0.137. Since there are 365 possible days, we can multiply this by 365 to get the expected number of days with at least one birthday, which is approximately 50.034 days. So, the expected number of days of the year which are one of their birthdays in a group of 50 people is around 50.034.
In a group of 50 people, the expected number of days of the year which are one of their birthdays can be determined using the concept of probability.
Assuming that each person's birthday is equally likely to fall on any of the 365 days in a year (ignoring leap years), the probability of any particular day being a birthday is 1/365.
Now, the probability of a day not being a birthday for a single person is (364/365). For 50 people, the probability of a day not being any of their birthdays would be (364/365)^50.
To find the expected number of days with at least one birthday, we can calculate the probability of a day having at least one birthday, which is the complement of no birthdays on that day. This probability is:
1 - (364/365)^50
Now, we multiply this probability by the total number of days in a year to find the expected number of days with at least one birthday:
365 * (1 - (364/365)^50) ≈ 194.03
So, in a group of 50 people, the expected number of days of the year which are one of their birthdays is approximately 194 days.

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The surface area and volume of the cylindrical can are resepctively:

849.49 cm² and 1898.07 mL

The formula for the surface area of a can or cylinder is:

SA = 2πr (h + r)

we are given:

r = 6.5 cm

h = 14.3 cm

Thus:

SA = 2π(6.5(14.3 + 6.5)

SA = 849.49 cm²

The volume of the can is given by the formula:

V = πr²h

V = π * 6.5² * 14.3

V = 1898.07 cm³

Converting to mL is:

V = 1898.07 mL

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Answer:

The answer is d: (x+2)(x-6)

Step-by-step explanation:

[tex]x^{2} - 4x - 12[/tex]

[tex]x^{2}[/tex] being a, [tex]- 4x[/tex] being b, and [tex]-12[/tex] being c

Step 1 is to figure out what two numbers can add to b while also multiplying to c

Those two numbers for this equation are [tex]-6[/tex] and [tex]2[/tex]

[tex]x^{2} + 2x - 6x - 12[/tex]

Then we factor it down

[tex]x(x+2)[/tex] and [tex]-6(x+2)[/tex]

The outside properties go in their own parenthesis

[tex](x - 6)[/tex]

and the Inside ones are already one object

[tex](x+2)[/tex]

Therefore the final product is

[tex](x+2)(x-6)[/tex]

Answer:

61

Step-by-step explanation:

Quick maths

The volume of the cone is  37. 68 cubic units

The surface area is  75. 36 square units.

The formula for calculating the volume of a cone is expressed as;

Volume = πr²h/3

From the information given, we have that;

radius = 3 units

h = 4 units

Substitute the values, we get;

Volume = 3.14 × 3² × 4/3

Divide the values

Volume = 37. 68 cubic units

The formula for surface area is expressed as;

Surface area = πrl + πr²

Substitute the values

Surface area = 3.14 × 3 × 5 + 3.14 × 3²

Surface area = 47. 1 + 28. 26 = 75. 36 square units.

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The volume of the prism is 792 cubic feet.

To find the volume of a rectangular prism, we need to multiply its length, width, and height.

The three-dimensional solid object known as a prism has identical ends and flat sides. The shape of its ends—a rectangular prism or a triangular prism—gives the object its name.

The volume of a prism may be estimated by dividing the area of the base by the height.

Given the dimensions of the prism:

Length = 9 ft

Width = 8 ft

Height = 11 ft

Volume = Length x Width x Height

Volume = 9 ft x 8 ft x 11 ft

Volume = 792 cubic feet

Therefore, the required volume is 792 cubic feet.

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The scale factor of the drawing is 1/24.

We can set up a proportion to find the scale factor

(scale length)/(actual length) = scale factor

We are given that the length of the tent in the drawing is 5 inches, and

the actual length of the tent is 10 feet, which is equivalent to 120 inches. Substituting these values into the proportion, we get:

5/120 = scale factor

Simplifying the fraction on the left-hand side, we get:

1/24 = scale factor

Therefore, the scale factor of the drawing is 1/24.

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The distance that the tip of the base ball travels is 214 inches.

Given that Kyle is practicing his baseball swing

He made an arc with radius of 48 inches

We have to find the distance the tip of the base ball travels

Radius = 48 in and θ = 255 degrees

Arc length = θ/360 × 2πr

=255/360 ×2×3.14×48

=76867.2/360

=213.52 inches

=214 inches

Hence, the distance that the tip of the base ball travels is 214 inches.

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The perimeter of the cross-section of the rectangular prism is 42 meters.

The cross-section formed by the plane that contains points D, E, K, and L is a trapezoid with bases DE and KL and height 5.

The length of DE can be found using the Pythagorean theorem: DE = √((EK - DK)² + (EL - DL)²) = √((12 - 4)² + (0 - 0)²) = 8 meters.

Similarly, the length of KL is also 8 meters.

Therefore, the perimeter of the cross-section is the sum of the lengths of the sides of the trapezoid, which is given by

perimeter = DE + KL + 2√((EK - DL)² + 5²)

perimeter = 8 + 8 + 2√((12 - 0)² + 5²)

perimeter = 16 + 2*√(169)

perimeter = 16 + 26

perimeter = 42 meters (rounded to the nearest tenth)

Hence, the perimeter of the cross-section is 42 meters.

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--The given question is incomplete, the complete question is given

" The rectangular prism is intersected by a plane that contains points D, E, K, and L.

What is the perimeter of the cross section?

Enter your answer in the box. Round only your final answer to the nearest tenth.

m

A rectangular prism with height 5 meters, length 12 meters, and width 4 meters. The vertices are labeled as G, D, H, L, E, F, J, and K."--

Answer: $8.64.

Step-by-step explanation:

P = price of the pizza

R = radius of the pizza

We know that the price of the pizza varies directly as the square of its radius. This means that we can write the following equation:

P = kR^2

where k is a constant of proportionality.

We are given that a pizza with a diameter of 20 cm costs $6.00. This means that the radius of the pizza is 10 cm. We can use this information to find the value of k.

6 = k(10)^2

6 = 100k

k = 0.06

Now that we know the value of k, we can find the price of a pizza with a radius of 12 cm.

P = 0.06(12)^2

P = 0.06(144)

P = 8.64

Therefore, a pizza with a radius of 12 cm would cost $8.64.

The solution set for the given inequality is:

8/3 > x > 14/9  or in interval form, (14/9, 8/3)

Here we have the compound inequality:

1/3> (x - 1)/5 >1/9

To solve it, we need to isolate the variable x, so let's do that:

First we can multiply all the inequality by 5, then we will get:

1/3> (x - 1)/5 >1/9

5/3 > x - 1 > 5/9

Now add 1.

5/3 + 1 > x > 5/9 + 1

Now simplify it to get:

8/3 > x > 14/9

Thus, the solution set is (14/9, 8/3)

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From Bayes' Theorem, an event, the probability that the blue cab involved in accident as well as witness also identified it as blue cab is equals to the 0.41 or 41%.

Bayes' Theorem states that the conditional probability of an event, is based on the occurrence of another event, is equal to the like of the second event the first event multiplied by the probability of the first event. According to scenario, it is found that a cab was involved in a hit and run accident at night. Number of cab companies operates in city = 2 (blue and green)

Probability that green cab involved in accident, P(G) = 85% = 0.85

Probability that blue cab involved in accident, P(B) = 15% = 0.15

Now, the cab which is identified by witness was a blue cab. Here, probability that witness is correct to identification a blue cab = P(W/B) = 0.80

Probability that witness is wrong to identify the blue cab = P(W/G) = 0.20

Using the Baye's theorem, Probability that accident was caused by blue cab provided witness identifies is written as [tex]P(B/W) = \frac{ P(B ∩W) }{P(W)} = \frac{ P(B) P( W/B)}{W}[/tex]

Total Probability, [tex]P(W) = \frac{P(B)}{P(W/B)}+ \frac{P(G)}{P(W/G)}[/tex]

= 0.15 x 0.8 + 0.85 x 0.2 = 1.2 + 1.7 =0.29

[tex]P(B/W) = \frac{ P(0.15×0.8}{0.29}[/tex]

= 0.12/0.29 = 0.413 = 41%

Hence, required probability value is 41%.

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Answer:

75°/360° = 5/24

Area of sector = (5/24)(π)(10^2)

= 125π/6 square inches

= 65.4 square inches

Length of arc = (5/24)(2π)(10)

= 25π/6 inches

= 13.1 inches

The mean of the data set A is 6.5

And the mean of the data set B is 3

We know that the mean of the data set is nothing but the ratio of the sum of all data values to the total number of data values in the data set.

From the attached line plot, the data values of data set A would be,

4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9

Using above definition of mean, the mean of data set A would be,

m₁ = (4 + 5 + 5 + 5 + 6 + 6 + 7 + 7 + 8 + 8 + 8 + 9) / 12

m₁ = 78/12

m₁ = 6.5

And the data values of data set B would be,

1,2, 2, 2, 3, 3,3, 4, 4, 4, 5

m₂ = 1 + 2 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 5

m₂ = 33/11

m₂ = 3

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The minimum amount that the person should be ready to accept today is Rs. 28258.86, as this is the present value of the future cash flows discounted at a rate of 14%.

To determine the minimum amount that a person should be ready to accept today from a debtor who has to pay Rs. 5000 today and a series of future payments, we need to calculate the present value of these future cash flows. The present value of a future cash flow is the value of that cash flow in today's terms, given a certain interest rate.

Using the formula for present value, we can calculate the present value of the future cash flows as follows:

PV = (5000/(1+0.14)⁰) + (6000/(1+0.14)) + (8000/(1+0.14)²) + (9000/(1+0.14)³) + (10000/(1+0.14)⁴)

Simplifying this equation, we get:

PV = 5000 + 5263.16 + 5805.37 + 6049.53 + 6139.80

Therefore, the present value of the future cash flows is Rs. 28258.86.

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Answer: 3, 12

Step-by-step explanation:

you divided by 2 to get top row so divide 6 by 2.  3 is in the first box

for bottom row you multiplied middle row by 3 so 12 is in the bottom row

Answer:

Step-by-step explanation:

graph 1 :   y = - |x +1| +1

graph 2:  y = |x+1|

The area of triangle CDE is 17.5 square units.

To find the area of triangle CDE, we can use the general formula:

Area = 1/2 * base * height where the base and height are two sides of the triangle. We can also use the distance formula to find the lengths of these sides.

First, let's find the length of side CD: CD = sqrt[(7-4)² + (8-4)²] = sqrt[3² + 4²] CD = √25 = 5

Next, let's find the length of side DE: DE = sqrt[(2-7)² + (9-8)²] = sqrt[5² + 1²] = DE = √26

Now, we need to find the height of the triangle. One way to do this is to use the formula for the area of a triangle:

Area = 1/2 * base * height

Rearranging this formula, we get: height = 2 * Area / base

We know the base is CD, which we found to be 5. We can find the area of triangle CDE using the shoelace formula, which gives:

Area = 1/2 * |(48 + 79 + 24) - (47 + 82 + 94)| = 17.5

Therefore, the height of triangle CDE is: height = 2 * Area / base = 2 * 17.5 / 5 = 7

Now we can use the formula for the area of a triangle to find the area of triangle CDE: Area = 1/2 * base * height = 1/2 * 5 * 7 = 17.5

Therefore, the area of triangle CDE is 17.5 square units.

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Using equations, we can find that the person was getting 35 as the hourly wage and the bonus was zero.

Equations are mathematical statements with the equals (=) symbol and two algebraic expressions on either side. This illustrates the equality of the relationship between the expressions printed on the left and right sides. The formula LHS = RHS (left hand side equals right hand side) is utilised in all mathematical equations. To determine the value of an unknown variable that represents an unknown quantity, you can solve equations. A statement is not regarded as an equation if it has no "equal to" symbol. It'll be regarded as a term.

The given equation is:

y = 35x

Where, x is hours worked.

And y is total pay.

From the equation, we can get:

The hourly wage for the person is 35 units.

As there are no constants in the equation, we can conclude that the bonus for the person was 0.

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Answer:

(π/8)(12^2) = 18π square units

The sequence of transformations you suggested does indeed map AUHS to A"U" H"S".

Transformation geometry is a branch of mathematics that deals with the study of geometric shapes and their transformations in space.

Apply the transformations to each vertex of polygon AUHS and see if the resulting vertices match the corresponding vertices of polygon A"U"H"S in order to evaluate whether the series of transformations you provided translates AUHS to A"U"H"S.

Let's begin by translating (x,y) (x-4, y-2). Each point is moved 2 units down and 4 units to the left by this transformation. Vertex A(-6,-6) would be changed to A"(-10,-8) in the following manner, for instance:

A'(-6,6) → A"(-10,4)

U'(-2,2) → U"(-6,0)

H'(4,2) → H"(0,0)

S'(-2,-6) → S"(-6,-8)

Let's now think about the rotation of the origin 90 degrees anticlockwise. Each point is rotated 90 degrees anticlockwise relative to the origin using this transformation. Vertex A"(-10,-8) would be rotated to A"(8,-10) in the following manner, for instance:

A"(-10,-8) → A'(8,-10)

U"(-6,0) → U'(0,-6)

H"(0,0) → H'(0,0)

S"(-6,-8) → S'(-8,6)

Therefore, the sequence of transformations you suggested does indeed map AUHS to A"U"H" S".

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The x-coordinate of the point of intersection of the two lines is 2.

To get the x-coordinate of the spot where the two lines intersect:

1. We can solve the system of equations given by the two lines simultaneously, which means we need to eliminate one of the variables (x or y) to obtain an equation in one variable that we can solve.

2. One way to eliminate a variable is to add or subtract the two equations in a way that cancels out one of the variables. In this scenario, we can combine the two equations:

(7x + 4y) + (9x - 4y) = 18 + 14

16x = 32

Dividing both sides by 16, we get:

x = 2

So the x-coordinate of the point of intersection of the two lines is 2.

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log 72 to the base 2n is equal to log 18 to the base n if n is equal to [tex]2^{1/10}[/tex].

We can use the change-of-base formula to convert both logarithms to a common base, such as base 10:

log 72 / log 2n = log 18 / log n

We can simplify log 72 as follows:

[tex]log 72 = log (2^3 * 3^2) = 3 log 2 + 2 log 3[/tex]

Similarly, we can simplify log 18 as:

[tex]log 18 = log (2 * 3^2) = log 2 + 2 log 3[/tex]

Substituting these expressions into the original equation, we get:

(3 log 2 + 2 log 3) / log 2n = (log 2 + 2 log 3) / log n

Multiplying both sides by log n * log 2n, we get:

(3 log 2 + 2 log 3) log n = (log 2 + 2 log 3) log 2n

Expanding the logarithms using the power rule, we get:

[tex]3 log (n^3) + 2 log (n^2) = log (2n) + 2 log (n^3)[/tex]

Simplifying and rearranging terms, we get:

[tex]3 log (n^3) - 2 log (n^3) = log (2n) - 2 log (n^2)[/tex]

[tex]log (n^9) = log (2n / n^2)[/tex]

[tex]log (n^9) = log (2/n)[/tex]

Taking the exponential of both sides, we get:

[tex]n^9 = 2/n[/tex]

Multiplying both sides by n, we get:

n^10 = 2

Taking the 10th root of both sides, we get:

[tex]n = 2^{1/10}[/tex]

Therefore, log 72 to the base 2n is equal to log 18 to the base n if n is equal to [tex]2^{1/10}[/tex]

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The probability that each player will have $1 after 2019 rings of the bell is: (c) 1/3.

To solve this problem, we need to think about the possible outcomes of the game. Each time the bell rings, each player has a 1/2 probability of giving $1 to one of the other two players. This means that after one ring of the bell, there are 2^3 = 8 possible outcomes, as each player can either give or not give money to each of the other players.

After two rings of the bell, there are 2^8 = 256 possible outcomes. After three rings, there are 2^12 = 4,096 possible outcomes. And so on.

To find the probability that after 2019 rings of the bell, each player will have $1, we need to find the total number of possible outcomes and the number of outcomes in which each player has $1.

The total number of possible outcomes after 2019 rings of the bell is 2^(3*2019) = 2^6057.

To count the number of outcomes in which each player has $1, we can use a combinatorial argument. We need to distribute 2019 dollars among the three players in such a way that each player ends up with exactly $1. This is equivalent to choosing two numbers between 0 and 2019, inclusive, and giving the first player the smaller amount, the second player the difference between the larger and smaller amounts, and the third player the remaining amount.

The number of ways to choose two numbers between 0 and 2019 is (2019+2) choose 2 = 2036 choose 2 = 2,066,530.

Therefore, the probability that each player will have $1 after 2019 rings of the bell is:

2,066,530 / 2^6057 = 1/3

So the answer is (c) 1/3.

In the game where Raashan, Sylvia, and Ted each start with $1 and a bell rings every 15 seconds, the probability that after the bell has rung 2019 times, each player will have $1 is (a) 1/7.

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The requried given sum 100 + 100 = 200 is true.

When we add two numbers, we unite them to get a new total value. In this case, we are adding 100 and 100, which gives us a total of 200. Therefore, the statement "100 + 100 = 200" is true based on the rules of addition in mathematics.

If the context of the question is different, for instance, if the "+" symbol represents concatenation (joining of two strings), then the answer might be different. But based on the premise that the "+" symbol represents an addition, the statement "100 + 100 = 200" is true.

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Answer: 10    C

Step-by-step explanation:

Variability is the range of numbers.

here it goes from 2-12

so

12-2=10

If the right rectangular-prism has a volume of 1.5 cubic inches, and product of length and width as 1.5, then the height of prism will be 1 inch.

In order to find the height of the "rectangular-prism", we use the formula for the volume of a rectangular prism, which is:

⇒ Volume = length × width × height;

We know that the volume is 1.5 in³ and

The product of the length and width is given to be 1.5,

So we can write : length × width × height = 1.5,  ....equation(1)

length × width = 1.5,

Substituting the product of "length" and "width" in equation(1),

We get,

⇒ 1.5 = 1.5 × height,

⇒ height = 1.5/1.5 = 1 inch.

Therefore, the height of prism will be 1 inch.

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