Simplify, (Write each expression without using the absolute value symbol)
x-(-12) if x<-12

Step-by-step explanation:

If x < 0, we consider the absolute value of x/3.

The absolute value is always positive or zero, which means when x < 0, the expression becomes -x/3. This is because we remove the negative sign from negative numbers when finding the absolute value.

So, |x/3| = (-x)/3 when x < 0.

Answer:

-x/3

Step-by-step explanation:

because x < 0 , so lets take x = -3

Then | -3/3 |

    = | -1 | = -(-1) = 1

There fore , | x/3 | for x < 0 = -x/3

The figures that are translations of A are C and D

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

The figure A

Also, we have the possible figures B to F

The figures that are translations of A are the figures that have the following properties

using the above as a guide, we have the following

The figures that are translations of A are C and D

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1.) For the triangle with sides 9 and 5, the third side must satisfy the inequality:

9 - 5 < x < 9 + 5

which simplifies to:

4 < x < 14

So the range of possible measures for the third side is 4 < x < 14.

2.) For the triangle with sides 5 and 8, the third side must satisfy the inequality:

8 - 5 < x < 8 + 5

which simplifies to:

3 < x < 13

So the range of possible measures for the third side is 3 < x < 13.

3.) For the triangle with sides 6 and 10, the third side must satisfy the inequality:

10 - 6 < x < 10 + 6

which simplifies to:

4 < x < 16

So the range of possible measures for the third side is 4 < x < 16.

4.) For the triangle with sides 6 and 9, the third side must satisfy the inequality:

9 - 6 < x < 9 + 6

which simplifies to:

3 < x < 15

So the range of possible measures for the third side is 3 < x < 15.

5.) For the triangle with sides 11 and 8, the third side must satisfy the inequality:

11 - 8 < x < 11 + 8

which simplifies to:

3 < x < 19

So the range of possible measures for the third side is 3 < x < 19.

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Step-by-step explanation:

y = x^3 + 1     switch x and y....then solve for y

x = y^3 + 1

x-1 = y^3

y = cubrt ( x-1)     <====this is the inverse function

The probability that the randomly selected patient had a blood test requested during their visit is approximately 0.120

In this case:

We can calculate the overall probability as the weighted average of the probabilities from each doctor:

Probability = (Probability from Dr. Sarabia) * (Percentage of patients seen by Dr. Sarabia) + (Probability from Dr. Tran) * (Percentage of patients seen by Dr. Tran) + (Probability from Dr. Jackson) * (Percentage of patients seen by Dr. Jackson)

Probability = (0.10 * 0.27) + (0.10 * 0.32) + (0.15 * 0.41)

Probability ≈ 0.027 + 0.032 + 0.061

Probability ≈ 0.12

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The line represents the graph of the equation y = -x - 1. It has a negative slope (-1) and passes through the y-axis at -1. The line extends infinitely in both directions.

To graph the function described by the equation y = -x - 1, we can create a table of values and plot the corresponding points on a graph. Here is a table of values for x and y:

x y

-3 -2

-2 -1

-1 0

0 -1

1 -2

2 -3

3 -4

Now, let's plot these points on a graph:

Each point on the graph represents an (x, y) pair from the table. We can then connect the points to create a line

Drawing a line that passes through all the points, we get:

The line represents the graph of the equation y = -x - 1. It has a negative slope (-1) and passes through the y-axis at -1. The line extends infinitely in both directions.

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Answer: 18300/29

Step-by-step explanation:

The statement that represents the equation (x – 3)2 + y2 = 16 is On a coordinate plane, a circle has a center at (3, 0) and radius 4.

The given equation is (x – 3)^2 + y^2 = 16

We solve to obtain:

(x – 3)^2 + (y - 0)^2 = 16

(x – 3)^2 + (y - 0)^2 = 4^2

This is an equation of a circle

Therefore, we can conclude that On a coordinate plane, a circle has a center at (3, 0) and radius 4.

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(1) The potential function for conservative vector field F=4yzi+4xzj+4xyk is f=4xyz+C. (2) The potential function for F=8xyi+(4x^2+8yz)j+4y^2k is f=4x^2y+4y^3/3+C.

To find a potential function f for a conservative vector field F, we need to find a scalar function whose gradient is equal to F. That is, we need to find a function f(x, y, z) such that:

∇f = F

where ∇ is the gradient operator. To do this, we can find the potential function by integrating each component of F with respect to its corresponding variable.

(1) F = 4yz i + 4xz j + 4xy k

∂f/∂x = 4yz

∂f/∂y = 4xz

∂f/∂z = 4xy

Integrating the first equation with respect to x, we get:

f = ∫4yz dx = 4xyz + C1(y, z)

where C1(y, z) is an arbitrary constant of integration that depends on y and z.

Taking the partial derivative of this expression with respect to y, we get:

∂f/∂y = 4xz + ∂C1/∂y

Comparing this with the second component of F, we see that ∂C1/∂y = 0, so C1(y, z) must be a constant with respect to y.

Similarly, taking the partial derivative of the expression for f with respect to z, we get:

∂f/∂z = 4xy + ∂C1/∂z

Comparing this with the third component of F, we see that ∂C1/∂z = 0, so C1(y, z) must be a constant with respect to z as well.

Therefore, the potential function for F is:

f = 4xyz + C

where C is a constant.

(2) F = 8xy i + (4x^2 + 8yz) j + 4y^2 k

∂f/∂x = 8xy

∂f/∂y = 4y^2

∂f/∂z = 8yz

Integrating the first equation with respect to x, we get:

f = ∫8xy dx = 4x^2y + C1(y, z)

where C1(y, z) is an arbitrary constant of integration that depends on y and z.

Taking the partial derivative of this expression with respect to y, we get:

∂f/∂y = 4x^2 + ∂C1/∂y

Comparing this with the second component of F, we see that ∂C1/∂y = 4y^2, so we integrate this with respect to y:

C1(y, z) = 4y^3/3 + C2(z)

where C2(z) is an arbitrary constant of integration that depends on z.

Similarly, taking the partial derivative of the expression for f with respect to z, we get:

∂f/∂z = 8yz + ∂C1/∂z

Comparing this with the third component of F, we see that ∂C1/∂z = 0, so C2(z) must be a constant with respect to z.

Therefore, the potential function for F is:

f = 4x^2y + 4y^3/3 + C

where C is a constant.

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The surface area of the given right rectangular prism is 288 square inches.

The given dimensions of the right rectangular prism are:

Length = 6 inches

Width = 4 inches

Height = 12 inches

The surface area of a rectangular prism can be calculated using the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values into the formula:

Surface Area = 2(6)(4) + 2(6)(12) + 2(4)(12)

Surface Area = 48 + 144 + 96

Surface Area = 288 square inches

Therefore, the surface area of the given right rectangular prism is 288 square inches.

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The value of y where it crosses the y-axis is (0, 4).

Given is an equation of line y+7 = 3x+11, we need to find the value of y where it crosses the y-axis,

So this mean we need to find the y-intercept,

To find the same put x = 0,
y+7 = 3(0) + 11

y+7 = 11

y = 4

Therefore, the y-intercept is (0, 4)

Hence the value of y where it crosses the y-axis is (0, 4).

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Answer: 50

Step-by-step explanation:

Greatest common factor of 200 and 150 is 50

200/50=4

150/50=3

Answer:

No.

Step-by-step explanation:

No, because 10 of her close friends are not the entire school. A school doesn't have 10 students, it has way more students, so that survey would not represent all students at her school.

Message:
Hope this helps! <3

(0, 0) is the y-intercept of the given line.

To detect the y-intercept of a line in a graph, you need to find the point where the line intersects the y-axis. In other words, it's the point where the value of x is zero.

To find the y-intercept of a line on a graph:

If the equation of the line is in slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept, then the value of b is the y-coordinate of the point where the line intersects the y-axis.

In the given graph line is paasing through origin (0, 0).

Thus, the value of y where the value of x will be zero is zero.

So the y-intercept is 0.

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The solution of the function is as follows:

(f + g)(3) = 9

(f.g)(-1) = -8

(f o g)(2)  = 8

(g o f)(0) = 2

(g o g)(3) = - 1

A function relates input and output. In other words, a function is an expression that defines a relationship between one variable (the independent variable) and another variable(dependent variable).

Therefore, let's solve the function as follows:

(f + g)(3) = f(3) + g(3) = 8 + 1 = 9

(f.g)(-1) = f(-1) × g(-1) = -2 × 4 = -8

(f o g)(2) = ƒ(g(2)) = f(3) = 8

(g o f)(0) = g(f(0)) = g(0) = 2

(g o g)(3) = g(g(3)) = g(1) = - 1

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Answer:

Step-by-step explanation:

You would divide 244.40 by 26%

You would get  63.544.... Now times the 63.544 to the remainder of the 26 from 100...which is 74.  63.544 times 74 equals 4702.256.

Now add the 244.40 to that and u get the answer of 4946.656.

Answer:

Good Luck

Step-by-step explanation:

Let the regular price be "x".

According to the problem, the sofa is being sold for 26% of the regular price, which means the sale price is:

Sale price = 0.26x

The problem also states that the sale price is $244.40, so we can write:

0.26x = 244.40

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides by 0.26:

x = 244.40 ÷ 0.26

x = 940

Therefore, the regular price of the sofa is $940.

The probability that none of the three products is successful is calculated by multiplying the probabilities of failure (1 - probability of success) for each product. Assuming independence, the calculation is as follows:

Product 1 failure probability: 1 - 1/9 = 8/9
Product 2 failure probability: 1 - 2/3 = 1/3
Product 3 failure probability: 1 - 1/5 = 4/5

Probability of all products failing: (8/9) × (1/3) × (4/5) = 32/135


Since the probabilities of success for each product are independent, we can simply multiply the probabilities of failure for each product to find the overall probability of none of the products being successful. This is a basic principle of probability when dealing with independent events.


The probability that none of the three products is successful in the market is 32/135.

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Answer: Leah

Step-by-step explanation: Leah cleaned more rooms as the fraction 4 11/18 shows that Leah cleaned more rooms.

The surface area of the prism is 520 in².

The area of the prism is 750 in³.

We have,

The given figure is a rectangular prism.

The surface area can be calculated by adding all the areas of the surfaces.

Now,

There are two types of surfaces.

Top and bottom surfaces and the side surfaces

So,

Top surface = Bottom surface

Area = 2 x (8 x 7(1/2)) = 8 x 15 = 120

Side surface.

Area = 4 x (8 x 12(1/2)) = 4 x (8 x 25/2) = 4 x 4 x 25 = 16 x 25 = 400

The surface area.

= 120 + 400

= 520 in²

And,

The area of the prism.

= 8 x 7(1/2) x 12(1/2)

= 8 x 15/2 x 25/2

= 2 x 15 x 25
= 30 x 25

= 750 in³

Thus,

The surface area of the prism is 520 in².

The area of the prism is 750 in³.

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To determine how many confidence intervals from the samples contain the population mean, you would need to know the specific confidence level, sample size, and data for each interval.

Generally, the higher the confidence level (e.g., 95% or 99%), the greater the likelihood that the intervals contain the true population mean.The same information is required for this question as in part (a).

The number of confidence intervals containing the population mean depends on the confidence level, sample size, and data of each interval.

With this information, you can evaluate which intervals contain the population mean.

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The solution is: 5 in hours did Ben work that Saturday​.

The number of hours that Ben worked at the restaurant can be calculated by the expression, Xpm - Xam.

The number of hours that Ben worked can be represented as:

= Time he finished working - Time he started working

= X pm - X am

If for instance, he started work at 7 am and finished at 12 pm, he would have worked:

= 12 - 7

= 5 hours

The expression that shows the length of time he worked can therefore be concluded to Xpm - Xam.

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complete question:

Ben is a waiter at a restaurant. on Saturday, Ben got up at 6:30am, started work at X.am and finished work at X.pm. how long in hours did Ben work that Saturday​

Therefore, the sample variance is approximately 65 using 95% confidence interval.

To find the sample variance, we need to use the formula for the confidence interval of the mean:

X ± tα/2 (s/√n)

Where:

X is the sample mean

tα/2 is the critical value for the t-distribution at the desired confidence level (with n-1 degrees of freedom)

s is the sample standard deviation

n is the sample size

From the given information, we know that the sample size n = 13, and the confidence interval is (3.5990, 19.0736) with a 95% confidence level. This means that the critical value for the t-distribution at α/2 = 0.025 and 11 degrees of freedom is approximately 2.201.

Using the formula for the confidence interval and the upper and lower bounds of the interval, we can solve for s:

19.0736 = X + 2.201(s/√13)

3.5990 = X - 2.201(s/√13)

Adding the two equations gives:

22.6726 = 2X

Therefore, X = 11.3363

Substituting this value of X into one of the original equations gives:

19.0736 = 11.3363 + 2.201(s/√13)

Solving for s, we get:

s ≈ 8.0587

Rounding to the nearest integer, the sample variance is:

s^2 ≈ 65

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Answer:

  0.16

Step-by-step explanation:

You want the probability that team b will win 2 games in a row, given that the probability of team a winning is 0.6, and the probability of team b winning is 0.4.

After one win for team A, the series can have the possible outcomes ...

  A – team a wins with probability 0.6

  BA – team a wins with probability (0.4)(0.6) = 0.24

  BB – team b wins with probability (0.4)(0.4) = 0.16

The probability of team b winning the series is 0.16.

__

Additional comment

The probability team a wins the series after winning the first game is 0.6 +0.24 = 0.84 (= 1 -0.16). At the beginning of the series, the probability b wins is 0.352, dropping dramatically after a wins the first game.

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The probability that Team B wins the series after Team A wins the first game is 0.4 or 40%.

What is probability?

Probability is a measure or quantification of the likelihood of an event occurring. It is a numerical value assigned to an event, indicating the degree of uncertainty or chance associated with that event. Probability is commonly expressed as a number between 0 and 1, where 0 represents an impossible event, 1 represents a certain event, and values in between indicate varying degrees of likelihood.

To determine the probability that Team B wins the series after Team A wins the first game, we need to consider the different possible outcomes of the remaining games.

Since the series continues until one team wins two games, there are three possible scenarios:

Team A wins the next game (Team A wins the series)

Team B wins the next game, followed by Team A winning the third game (Series tied at 1-1)

Team B wins both the next and third games (Team B wins the series)

We'll calculate the probabilities of these scenarios and then determine the probability of Team B winning the series.

Scenario 1: Team A wins the next game (Team A wins the series):

The probability of Team A winning the next game is 0.6.

Scenario 2: Team B wins the next game, followed by Team A winning the third game (Series tied at 1-1):

The probability of Team B winning the next game is 0.4.

The probability of Team A winning the third game is 0.6.

To calculate the probability of this scenario, we multiply the individual probabilities:

Probability = 0.4 * 0.6 = 0.24

Scenario 3: Team B wins both the next and third games (Team B wins the series):

The probability of Team B winning the next game is 0.4.

The probability of Team B winning the third game is 0.4.

To calculate the probability of this scenario, we multiply the individual probabilities:

Probability = 0.4 * 0.4 = 0.16

To find the probability of Team B winning the series, we add the probabilities of Scenario 2 and Scenario 3 since both outcomes result in Team B winning the series:

Probability = 0.24 + 0.16 = 0.4

Therefore, the probability that Team B wins the series after Team A wins the first game is 0.4 or 40%.

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A ball thrown by a(n) person travels an average speed of 29 feet per second.

The average speed is the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity. It is represented by the magnitude and does not have direction.

The word "person" fills the blank in the sentence. This suggests that the sentence is referring to a human individual who throws the ball. By specifying that a person throws the ball, it provides context and clarifies who is responsible for the ball's movement. The sentence implies that the average speed of the ball is 29 feet per second when thrown by a person.

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The expression that is equivalent to 42x - 48 is: 6(7x - 8)

An algebraic expression is defined as a mathematical phrase that includes both variables, constants, coefficients, and algebraic operations.

An algebraic expression is also considered as a variable expression described using its terms, and operations on the terms. For example, x + 3 can be described as "3 more than x".

We want to factorize the expression 42x - 48

The number that is common to both numbers is 6 and as such we have the expression factorized as:

6(7x - 8)

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From the hypothesis test conducted, the calculated t-statistic of -3.57 is less than the lower critical t-value of -2.064. This tells us that the observed sample mean of 87% is significantly different from the claimed population mean of 92% at the 0.05 significance level. Therefore, the null hypothesis can be rejected and conclusions can be made that that there is enough evidence to suggest that the average grade of the students in the Algebra 2 class this year is not equal to the average grade of the same students in the Algebra 1 class two years ago.

To determine whether there is enough evidence to reject the teacher's claim, we can conduct a hypothesis test. A one-sample t-test will be us to compare sample mean.

Here are the sample statistics:

Sample size (n) = 25

Sample mean (X) = 87%

Sample standard deviation (s) = 7%

A significance level (α) of 0.05, wil be used

We first calculate the t-statistic, with  (X - μ) / (s/√n),

t = (87 - 92) / (7/√25) = -5 / (7/5) = -3.57

Then, we check this value against the critical t-value for a two-tailed test with 24 degrees of freedom (n-1), and α = 0.05.

The critical t-values for a two-tailed test at α = 0.05 and df = 24 are approximately -2.064 and +2.064.

-3.57 t-test is less than the lower critical t-value of -2.064. This means that the observed sample mean of 87% is significantly different from the claimed population mean of 92% at the 0.05 significance level.

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Answer:

Sure, here are the answers:

2/7 + 5/3 - 4/5 - 1/3 = (2/7 + 5/3) - (4/5 + 1/3)

= (6/21 + 15/21) - (9/15 + 7/15)

= 21/21 - 16/15 = 5/15 = 1/3

3/7 - 4/7 - 11/9 + 7/9 + 9/7 + 7/7 = (3/7 - 4/7) + (-11/9 + 7/9) + (9/7 + 7/7)

= (-1/7) + (-4/9) + (16/7) = -1/7 - 4/9 + 16/7 = 16/7 - 1/7 - 4/9 = 15/7 - 4/9 = (45/63) - (28/63) = 17/63

2/5 + 8/3 - 11/4 - 2/5 + 15/5 + 3/15 = (2/5 + 8/3) - (11/4 + 2/5) + (15/5 + 3/15)

= (6/15 + 40/15) - (27/20 + 4/5) + (3/1 + 1/5)

= 46/15 - 31/20 + 8/5 = (230/60) - (31/20) + (40/20) = (230 - 31 + 40)/60 = 179/60 = 13/20

-8/9 - 13/7 + 17/9 + 7/7 + 21/7 = (-8/9 - 13/7) + (17/9 + 7/7) + 21/7

= (-59/63 + 126/63) + (147/63) = 67/63 + 147/63 = 214/63 = 22/9

Step-by-step explanation:

Answer:The circle has a center at (5,5) and a radius of 2. Therefore, the equation is (x-5)2+(y-5)2=22, or (x-5)2+(y-5)2=4.

Step-by-step explanation:

i did the qestion on my test

Answer:

22,338

Hence, the smallest number which is divisible by both 306 and 657 is 22,338. Given that HCF (306, 657) = 9, find LCM (306, 657).

Step-by-step explanation:

have a nice day.

Therefore, the smallest number that is divisible by both 306 and 657 is 1581378.

To find the smallest number which is divisible by both 306 and 657, we need to find their least common multiple (LCM).

We can start by finding the prime factorization of each number:

306 = 2 x 3 x 3 x 17

657 = 3 x 3 x 73

To find the LCM, we need to take the highest power of each prime factor that appears in either factorization. That means we need to include the factors 2, 3, 17, and 73, and for each factor we need to take the highest power that appears in either factorization:

2^1 x 3^2 x 17^1 x 73^1 = 1581378