Which table of values represents a linear function?
A
xx yy
-3−3 00
00 22
33 44
66 77
B
xx yy
-1−1 44
22 11
55 -2−2
88 -5−5
C
xx yy
-1−1 22
00 44
22 66
33 88
D
xx yy
00 88
22 44
33 00
55 -4−4

Answer:

x/-5

Step-by-step explanation:

Just divide by 5 and the denominator will be 5 meaning x would have to be 4.

Make sure your 5 is negative so the whole equation also ends up negative. x/-5=-4/5

Answer: She used 4 sides.

Step-by-step explanation:

2.4 ÷ 0.6 = 4

Answer:

difference is the same as subtracting a number from another. so, the difference of six and two would look like (6-2). considering we are dividing we take those two numbers and divide them by four. so your numerical equation would look like:  (6-2)/4

Answer:

\(\boxed{\sf n= \dfrac{2}{5} ,\: n=1}\)

Step-by-step explanation:

\(\rightarrow 5n^2 = 7n -2\)

\(\rightarrow 5n^2 - 7n +2=0\)

\(\rightarrow 5n^2 - 5n -2n+2=0\)

\(\rightarrow 5n(n - 1) -2(n-1)=0\)

\(\rightarrow (5n-2)(n-1)=0\)

\(\rightarrow 5n-2= 0,\: n-1=0\)

\(\rightarrow 5n= 2,\: n=1\)

\(\rightarrow n= \dfrac{2}{5} ,\: n=1\)

Step-by-step explanation:

\(\hookrightarrow\sf{5n^2 = 7n -2}\\\\\hookrightarrow\sf{5n^2 - 7n +2=0}\\\\\hookrightarrow\sf{5n^2 - (5+2)n +2=0}\\\\\hookrightarrow\sf{5n^2 - 5n -2n+2=0}\\\\\hookrightarrow\sf{ 5n(n - 1) -2(n-1)=0}\\\\\hookrightarrow\sf{ (5n-2)(n-1)=0}\\\\\hookrightarrow\sf{ 5n-2= 0\:or~ n-1=0}\\\\\hookrightarrow\sf{ 5n= 2\:or~n=1}\\\\\hookrightarrow\bold{ n= \dfrac{2}{5} \:or~ n=1}\)

3.14 is the answer aaaa

Answer:

3.14

Step-by-step explanation:

Answer:

$111.5699. Round to hundredths $111.57

Step-by-step explanation:

First identify the %

20% =.20 20/100= .20

3.5% = .035 3.5/100= .035

Then Find the tax rate and tip

Tax Rate .035 × 90.34

= $3.1619 (tax rate)

Tip. is .20× 90.34

= $18.068 (tip)

Final Add all it up tax rate+ tip + original price

$90.34. Don't forget to line up your demicals

$3.1619. or use a calculator

+ $18.068

Total = $111.5699

round to the nearest hundredth

$111.57 is your total

Answer:

I think its $1000

Step-by-step explanation:

if she earned $12 the 1012-12=1000

Answer:

I really don't know much but this is what I know

If she has $12 dollars in interest and a year later she has $1012 making it so she earned EXACTLY $1,000 in the time being.

Answer:

A= 1/2 x bace x hight

Step-by-step explanation:

A= 1/2 x 20 x 40 =400

A= 400

Answer:

24 cm

Step-by-step explanation:

Let the length of other base be x cm

Therefore, by mid segment formula of a trapezoid, we have:

\(23 = \frac{1}{2} (x + 22) \\ \\ 23 \times 2 = x + 22 \\ 46 = x + 22 \\ 46 - 22 = x \\ x = 24 \: cm\)

If an atlas beetle is about 0.15 meters long then the length of the atlas beetle is 10 times the length of a leafcutting bee which is 0.015.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Length of atlas beetle = 0.15 meter

Length of leafcutting bee = 0.015 meter

Now,

0.015 x 10 = 0.15

This means,

The length of the atlas beetle is 10 times the length of a leafcutting bee

Thus,

The length of the atlas beetle is 10 times the length of a leafcutting bee.

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In school suspension

Answer:

250 smaller boxes

Step-by-step explanation:

Find the volume of the 2 cuboids.

Formula = Length x width x height

Big cuboid = 50 x 30 x 20 = 30000

Small cuboid = 10 x 3 x 4 = 120

Now divide them.

30000 ÷ 120 = 250 small boxes

To determine whether a critical point is a relative minimum or maximum using concavity, we need to examine the second derivative of the function at the critical point.

If the second derivative is positive, then the function is concave up, meaning it is shaped like a bowl opening upwards. At a critical point where the first derivative is zero, this indicates a relative minimum, as the function is increasing on either side of the critical point.

On the other hand, if the second derivative is negative, then the function is concave down, meaning it is shaped like a bowl opening downwards. At a critical point where the first derivative is zero, this indicates a relative maximum, as the function is decreasing on either side of the critical point.

If the second derivative is zero, then the test is inconclusive and further analysis is needed, such as examining higher order derivatives or using other methods such as the first derivative test.

Therefore, the concavity test is a useful method for determining the nature of critical points and whether they represent a relative minimum or maximum.

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Complete question is:

What we need to examine for a method for determining whether a critical point is a relative minimum or maximum using concavity.

Answer:

The function can have its own inverse, that is, \($f^{-1}(x)=f(x)$\) and this type of function is called an involution. Example f(x)=6-x.

Step-by-step explanation:

A statement that a function can be its own inverse is given.

It is required to explain whether a function has its own inverse. Then explain whether the given statement satisfies the condition.

Step 1 of 3

Consider a function is f(x)=6-x.

This function is a continuous function for all values of x. This function is also a linear function. So, every continuous linear function is a one-to-one function.

So, this function is one-to-one.

Step 2 of 3

Consider f(x) as y and rewrite the equation.

The equation becomes \($y=6-x$\)

Solve the rewritten equation.

Add -6 on both sides of the equation.

\($$\begin{aligned}&y=6-x \\&y-6=6-x-6 \\&y-6=-x\end{aligned}$$\)

Step 3 of 3

Multiply by -1 on both sides.

\($$\begin{aligned}&y-6=-x \\&(-1)(y-6)=(-x)(-1) \\&-y+6=x \\&x=6-y\end{aligned}$$\)

Interchange x and y in solved equation.

\($$\begin{aligned}&x=6-y \\&y=6-x\end{aligned}$$\)

So, the inverse of the given function is \($f^{-1}(x)=6-x$\).

The function and inverse of the function are the same, that is, \($f^{-1}(x)=f(x)$\)

So, a function can have its own inverse. This type of function is called an involution.

Answer:

2b+9

Step-by-step explanation:

Step-by-step explanation:

2x+13x-15=180 since a linear pair is a pair of consecutive angles that adds up to 180 degrees.

15x-15=180 because we combine like terms.

15x=165 because of the subtraction property of equality.

x=11 by the division property of equality.

abc=22 by substitution and multiplication

cbd=143-15 by substitution and multiplication

cde=128 by subtraction

Based on the given information, person C would take 600 minutes to finish the job by himself.

Let's break down the steps to find out how long it would take person C to finish the job by himself.

1. Determine the rate at which person A completes the job. We can find this by dividing the total job by the time it takes person A to complete it: 1 job / 100 minutes = 1/100 job per minute.

2. Similarly, determine the rate at which person B completes the job: 1 job / 120 minutes = 1/120 job per minute.

3. When person A and person B work together, we can add their rates to find the combined rate: (1/100 job per minute) + (1/120 job per minute) = (12/1200 + 10/1200) = 22/1200 job per minute.

4. After 40 minutes of working together, person C joins them, and together they finish the job in an additional 10 minutes. So the total time they take together is 40 minutes + 10 minutes = 50 minutes.

5. Calculate the total job done by person A and person B working together: (22/1200 job per minute) * (50 minutes) = 22/24 = 11/12 of the job.

6. Since person C helped complete 11/12 of the job in 50 minutes, we can calculate the rate at which person C works alone by dividing the remaining 1/12 of the job by the time taken: (1/12 job) / (50 minutes) = 1/600 job per minute.

7. Now we can find how long it would take person C to finish the job by himself by dividing the total job (1 job) by the rate at which person C works alone: 1 job / (1/600 job per minute) = 600 minutes.

Therefore, it would take person C 600 minutes to finish the job by himself.


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It would take c approximately 3.75 minutes to finish the job by himself. To find out how long it would take c to finish the job by himself, we need to first calculate how much work a and b can do together in 40 minutes.

Since a can finish the job in 100 minutes, we can say that a completes \(\frac{1}{100}\)th of the job in 1 minute. Similarly, b completes \(\frac{1}{120}\)th of the job in 1 minute.

So, in 40 minutes, a completes \(\frac{40}{100}\) = \(\frac{2}{5}\)th of the job, and b completes \(\frac{40}{120}\) = \(\frac{1}{3}\)rd of the job.

Together, a and b complete 2/5 + 1/3 = 6/15 + 5/15 = 11/15th of the job in 40 minutes.

Since a, b, and c complete the entire job in an additional 10 minutes, we can subtract 11/15th of the job from 1 to find out how much work c did in those 10 minutes. This comes out to be 1 - 11/15 = 4/15th of the job.

Therefore, c can complete 4/15th of the job in 10 minutes.

To find out how long it would take c to complete the whole job by himself, we can set up a proportion:

    (4/15) / x = 1 / 1

Cross-multiplying gives us:

    4x = 15

=> x = 15/4 = 3.75 minutes.

Therefore, it would take c approximately 3.75 minutes to finish the job by himself.

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The solution to the integral is ∫ (16x-130) / (x²-16x+63) dx = -ln|x-9| + 41ln|x-7| + C

Now, let's get into the details of the problem. We are given the integral:

∫ (16x-130) / (x²-16x+63) dx

To solve this integral, we first need to factor the denominator. We can factor it using the quadratic formula, which gives us:

x²-16x+63 = (x-9)(x-7)

Therefore, we can rewrite the integral as:

∫ (16x-130) / [(x-9)(x-7)] dx

To apply this technique, we need to first write the fraction as:

(16x-130) / [(x-9)(x-7)] = A/(x-9) + B/(x-7)

where A and B are constants that we need to find. We can find A and B by multiplying both sides by the common denominator and then equating the numerators. This gives us:

16x - 130 = A(x-7) + B(x-9)

Now, we can solve for A and B by substituting values of x that make one of the terms zero. For example, if we substitute x=9, we get:

16(9) - 130 = A(9-7) + B(9-9)

Simplifying this expression gives us:

2A = -2

Therefore, A = -1.

Similarly, if we substitute x=7, we get:

16(7) - 130 = A(7-7) + B(7-9)

Simplifying this expression gives us:

-2B = -82

Therefore, B = 41.

Now that we have found A and B, we can rewrite the original fraction as:

(16x-130) / [(x-9)(x-7)] = -1/(x-9) + 41/(x-7)

Using this decomposition, we can integrate the original function by integrating each term separately. This gives us:

∫ (16x-130) / [(x-9)(x-7)] dx = ∫ [-1/(x-9) + 41/(x-7)] dx

= -ln|x-9| + 41ln|x-7| + C

where C is the constant of integration.

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Answer:

Step-by-step explanation:

1) Understand the formula for volume

The formula to find volume is: area of cross section x height

In this case the cross section is the area of the triangular side and the height is 2 inches

2) Work out the volume

Area of cross section: \(\frac{8x4}{2}\) = 16

16 x 2 = 32 inches

This means our answer is 32 inches³

Hope this helps, have a lovely day! :)

The volume of the prism shown is equal to 145.89 cubic inches.

In Mathematics and Geometry, the volume of a triangular prism can be determined or calculated by using the following formula:

Volume of triangular prism, V = 1/2 × b × h.

Where:

By substituting the given dimensions (side lengths) into the formula for the volume of a triangular prism, we have;

Volume of triangular prism, V =  1/2 × 5.27 × 8.13 × 6.81

Volume of triangular prism, V = 291.775131/2

Volume of triangular prism, V = 145.89 cubic inches.

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The volume of the prism is 145.89 cubic inches.

To find the volume of a prism, multiply the area of the base by the height of the prism.

We know the formula for the volume of a triangular prism is:

\(V = \frac{1}{2}\times b \times h\)

Where:

b represent the base area of a triangular prism.

h represent the height of a triangular prism.

Therefore, we can calculate the volume of the prism by cubing the length of one of its sides:

\(V = \frac{1}{2}\times 5.27\times 8.13 \times 6.81\)

\(V= \frac{291.775131}{2}\)

\(V = 145.89\) cubic inches.

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Answer:

Triangle KLM

Step-by-step explanation:

Firstly, we need to write the coordinates of triangle NPQ

We have this as;

(-7,-6) for N

(-4,-3) for P

(-4,-6) for Q

Now, we are going to use the given translation formula;

(x + 8, y + 1)

N’ will be (-7+ 8, -6 + 1) = (1,-5)

P’ will be (-4+ 8, -3+1) = (4,-2)

Q’ will be (-4+ 8, -6+1) = (4,-5)

Now, we need to find the triangle with the exact given transformation coordinates calculated above;

We have the triangle as;

KLM

With K as (1,-5) ; L as (4,-2) and ; M as (4,-5)

The general solution to the differential equation y' - 2y + 3e^t = 0 is: y = Ce^(2t) - e^t.  As t approaches infinity, the solution approaches infinity because the dominant term in the solution is e^(2t).

The given differential equation is:

y' - 2y + 3e^t = 0

We can first find the homogeneous solution by setting the right-hand side equal to zero:

y' - 2y = 0

This is a separable differential equation that can be solved by separating variables:

dy/y = 2dt

Integrating both sides, we get:

ln|y| = 2t + C

where C is an arbitrary constant. Solving for y, we get:

y = Ce^(2t)

This is the general solution to the homogeneous equation.

Now, we need to find a particular solution to the non-homogeneous equation. Since the non-homogeneous term is a constant times e^t, we can guess a particular solution of the form:

y_p = Ae^t

where A is a constant. Substituting this into the original equation, we get:

Ae^t - 2Ae^t + 3e^t = 0

Simplifying, we get:

A = -1

Therefore, the particular solution is:

y_p = -e^t

The general solution to the non-homogeneous equation is the sum of the homogeneous solution and the particular solution:

y = Ce^(2t) - e^t

To determine how solutions behave as t approaches infinity, we can analyze the behavior of the exponential terms. Since e^(2t) grows much faster than e^t, the dominant term as t approaches infinity is e^(2t). Therefore, the solution approaches infinity as t approaches infinity.

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Answer:

-9/3

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

2x+3=6x-5

2x-6x=-5-3

-4x=-8

X=8/4

X=2

So the final answer is 2

a) The probability that all 3 of your answers are incorrect is 27/64.

b) The probability that all 3 of your answers are correct is 1/64.

c) The probability that exactly 1 of your answers are correct is 9/16.

(a) The probability of guessing the incorrect answer for a single question is 3/4. Since each question is independent of the others, the probability of guessing all 3 questions incorrectly is:

(3/4) x (3/4) x (3/4) = 27/64

(b) Similarly, the probability of guessing all 3 questions correctly is:

(1/4) x (1/4) x (1/4) = 1/64

(c) To calculate the probability that exactly 1 of your answers are correct, we need to consider all possible ways in which this could happen. There are three questions and each question has four possible answers, so there are a total of 4 x 4 x 4 = 64 possible ways to answer all three questions.

The number of ways to answer exactly one question correctly is:

3 x (1/4) x (3/4) x (3/4) = 27/64

(We are multiplying by 3 because there are three ways to choose which question to answer correctly.)

Similarly, the number of ways to answer exactly two questions correctly is:

3 x (1/4) x (1/4) x (3/4) = 9/64

(The factor of 3 comes from the three ways to choose which questions to answer correctly.)

Finally, the number of ways to answer all three questions incorrectly is:

(3/4) x (3/4) x (3/4) = 27/64

So the probability of answering exactly one question correctly is:

27/64 + 9/64 = 36/64 = 9/16

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The probability that exactly 3 of the 7 people selected at random have obtained their flu shot is approximately 0.315 or 31.5%.

This problem can be solved using the binomial distribution, which models the probability of getting a certain number of successes (in this case, people who received their flu shot) in a fixed number of trials (in this case, selecting 7 people at random) when each trial has the same probability of success (in this case, 60%).

The probability of getting exactly 3 people who received their flu shot is given by the formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where n is the total number of trials (7), k is the number of successes (3), p is the probability of success (0.6), and (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.

Plugging in the values, we get:

P(X = 3) = (7 choose 3) * (0.6)^3 * (1-0.6)^(7-3)

= 35 * 0.216 * 0.4096

= 0.315

Therefore, the probability that exactly 3 of the 7 people selected at random have obtained their flu shot is approximately 0.315 or 31.5%.

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Answer:

75 students

Step-by-step explanation:

500 students x 0.25 (25%) = 125 play baseball

500 students x 0.10 (10%) = 50 play soccer

125 who play baseball - 50 who play soccer  = 75 more students who play baseball

Answer:

75 students because

since there are 500 students..

10% of 500 is 50

25% of 500 is 125

125-50=75

Step-by-step explanation: