How do you partition the segment (-3, 4) (7, 6) 1:1 ?

The function f(x1, x2) = 2x1 + 3x2  defined from Real Number to Real Number is both one-to-one and onto.  

Let's assume we have two input pairs (x1, x2) and (y1, y2) such that f(x1, x2) = f(y1, y2). Then, we have 2x1 + 3x2 = 2y1 + 3y2. To show that f is one-to-one, we need to prove that if the equation 2x1 + 3x2 = 2y1 + 3y2 holds, then it implies x1 = y1 and x2 = y2. we can see that the equation holds only if x1 = y1 and x2 = y2. Therefore, f is one-to-one.

For any real number y in R, we need to find input pairs (x1, x2) such that f(x1, x2) = y. Rewriting the function equation, we have 2x1 + 3x2 = y. By solving this equation, we can express x1 and x2 in terms of y: x1 = (y - 3x2)/2. This shows that for any given y, we can choose x2 freely and calculate x1 accordingly.

Therefore, every real number y in the codomain R has a preimage in the domain RxR, indicating that f is onto.

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The p-value represents the probability of obtaining a test statistic at least as extreme as the observed value, assuming the null hypothesis is true. In exercise 9.1.3, the p-value is calculated for three different values of the test statistic, x=11.25, x=11.0, and x=11.75.

The p-value is calculated using the standard normal distribution and the formula for a one-tailed test. For x=11.25, the z-score is (11.25 - 11) / (0.5/\(\sqrt{16}\)) = 1.5, and the p-value is the area to the right of 1.5 under the standard normal curve, which is 0.0668. For x=11.0, the z-score is (11 - 11) / (0.5/√(16)) = 0, and the p-value is the area to the right of 0, which is 0.5. For x=11.75, the z-score is (11.75 - 11) / (0.5/√(16)) = 3, and the p-value is the area to the right of 3, which is 0.0013. Therefore, the p-values for x=11.25, x=11.0, and x=11.75 are 0.0668, 0.5, and 0.0013, respectively.

The p-value is a key concept in hypothesis testing. It is a measure of the evidence against the null hypothesis provided by the data. If the p-value is small, it means that the observed data are unlikely to have occurred by chance if the null hypothesis is true, and we may reject the null hypothesis in favor of the alternative hypothesis. If the p-value is large, it means that the observed data are likely to have occurred by chance if the null hypothesis is true, and we fail to reject the null hypothesis.

In this exercise, we are given three values of the test statistic, x=11.25, x=11.0, and x=11.75, and we need to calculate the corresponding p-values. To do this, we need to first calculate the z-score, which is the number of standard deviations that x is away from the mean under the null hypothesis. In this case, the null hypothesis is that the population mean is 11, and the standard deviation is 0.5. We also assume that the sample size is 16 and the distribution of the sample mean is approximately normal. Once we have the z-score, we can use the standard normal distribution to calculate the p-value. For a one-tailed test, the p-value is the area to the right of the z-score under the standard normal curve. We can use a table of the standard normal distribution or a calculator to find this area.

In conclusion, the p-values for x=11.25, x=11.0, and x=11.75 are 0.0668, 0.5, and 0.0013, respectively. These p-values represent the evidence against the null hypothesis provided by the data and can be used to make a decision about whether to reject or fail to reject the null hypothesis.

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The exponent of a number is the number of times it is multiplied by itself. Product of Powers and Power to a Power are examples of exponent characteristics.

In algebra, the seven exponent properties are as follows:

1. A byproduct of power.

2. The power quotient is in charge.

3. The power's reign.

4. The product power rule.

5. The efficacy of a quotient rule.

6. The zero-power rule.

7. The negative exponent rule.

For example, 2 to the third (written as 2³) is equivalent to 2 x 2 x 2 = 8. 2 × 3 = 6 is not equivalent to 2³. Remember that a number multiplied by one equals itself.

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Answer:

The common for the second question is 30

Answer:

39/30 Here 30 will be common in denominators

Step-by-step explanation:

6/15×2/2=12/30

3/10×3/3=9/30

3/5×6/6=18/30

= 12/30+9/30+18/30

39/30

{ 0,2,4,6,8} is  the complement of the set.

What is natural number in math?

Is zero a natural number?

u = {0, 1, 2, 3, 4, 5, 6, 7, 8}

Odd number less than 8  = { 1,3,5,7 }

complement =  {0, 1, 2, 3, 4, 5, 6, 7, 8} -  { 1,3,5,7 }

                     = { 0,2,4,6,8}

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The following values are as follows: a) Mean = 0.6, b) standard deviation = 0.073 and c) Probability is 0.0855

a) As the number of samples is large enough which is up to 30 then the mean of the average number of moths in 30 traps is given as 0.6, given from the central limit theorem.

b) The population deviation divided by the square root of the sample size gives the standard deviation value.

standard derivation = σ/ \(\sqrt{n}\) = 0.4 / \(\sqrt{30}\) = 0.4/ 5.477 = 0.073

c) The probability that an approximately normally distributed data with the standard deviation, σ, with a sample size of n is greater than a number, x, and a mean, μ, is given by

1 - P (X < x)= P (X > x)

= 1 - P(z< x- µ/ σ/\(\sqrt{n}\))

Thus, given that the mean is 0.6 and the standard deviation is 0.4, the probability that the average number of moths in 30 traps is greater than 0.7 is given by:

1 -P (X - 0.7) = P (X > 0.7)

= 1 - P(z < \(\frac{0.7-0.6}{0.073}\)) = 1 - P(z < 1.369)

= 1 - 0.91455 = 0.0855

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The interest rate your friend is charging you for the $20,000 loan is 20% per year.

The simple interest is expressed as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is the interest rate and t is time.

Given that;

The Principal P = $20,000

Accrued amount A = $40,000

Elapsed time t = 5 years

Interest rate r =?

Plug these values into the above formula and solve for the interest rate r:

\(A = P( 1 + rt )\\\\r = \frac{1}{t}( \frac{A}{P} -1 ) \\\\r = \frac{1}{5}( \frac{40000}{20000} -1 ) \\\\r = \frac{1}{5}( 2 -1 ) \\\\r = \frac{1}{5}\\\\r = 0.2 \\\\\)

Converting r decimal to R a percentage

Rate R = 0.2 × 100%

Rate r = 20% per year

Therefore, the interest rate is 20% per year.

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f(0)=3

Explanation

Step 1

when x= 0

the function is defined

by

Step 2

replace x= 0

Answer: 45 minutes for BOTH workouts

Step-by-step explanation:

Let time for plan a be x

Let time for plan b be y

On Wednesday

# of clients for plan a are 5

# clients for plan b are 3

On Thursday

# of clients for plan a are 7

# of clients for plan b are 9

Wednesday eqn --> 5x+3y=6

Thursday eqn --> 7x+9y=12

Multiply Wednesday equation by -3 and use elimination to solve

-15x-9y=-18

7x+9y=12

-8x=-6

x=6/8

Reduce: x=3/4 hour

Substitute x=3/4 into Thursday equation

7(3/4)+9y=12

9y=27/4

y=3/4

Therefore, the length of BOTH the plan a and plan b workouts were 45 minutes

Answer:

565.9.

Step-by-step explanation:

The second decimal place is 4 so the first one stays at 9.

There are three defects, and two pencils can be considered defectives.  a crack with broken lead, being broken in half, and a missing eraser. Each defect represents a unique issue or imperfection in the respective pencil.

Examining the three pencils, we can identify three distinct defects: a crack with broken lead, being broken in half, and a missing eraser. Each defect represents a unique issue or imperfection in the respective pencil.

Now, considering the term "defectives," it refers to the number of pencils that have defects. In this case, two out of the three pencils exhibit defects. The pencil with the crack and broken lead, as well as the pencil broken in half, can be categorized as defectives since they possess flaws affecting their functionality or appearance.

there are three defects present among the three pencils, representing the specific issues each pencil has. Additionally, two pencils can be classified as defectives, indicating the number of pencils that possess one or more defects.

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Answer:

10=n/5+6

Step-by-step explanation:

Answer:

s+a= 556

5s+8a=3797

a=339; s=217

Step-by-step explanation:

s= student tickets a= adult tickets

s=556-a

5s= 2780-5a

2780-5a+8a=3797

3a=1017

a=339

s=217

The solution of the equation given as -13x + x = 8x - 20x is infinite many solutions

From the question, the equation is given as

-13x + x = 8x - 20x

To start with, we need to rewrite the expression

So, we have the following representation

x - 13x = 8x - 20x

Solving further, we need to evaluate the like terms

So, we have the following equation

-12x = 8x - 20x

Evaluate the like terms again

So, the equation becomes

-12x = -12x

Both sides of the above equation are the same

i.e. -12x is on both sides of the equation

When we have a solution that all sides of the equation have the same value, then the solution is that the equation has infinite many solutions

Hence, -13x + x = 8x - 20x has infinite solutions

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Answer: 26 cards

Step-by-step explanation:

Suppose there are x cards initially

Min gave half to bill i.e. 0.5x

Bill gives one-third of those cards to Sam i.e. \(\frac{1}{3}\times 0.5x\)

Sam gave 2 cards back to min and kept 6 i.e. Sam gets 8 cards from Bill

\(\Rightarrow 8=\dfrac{1}{3}\times 0.5x\\\\\Rightarrow 0.5x=24\\\Rightarrow x=48\)

So, min has 0.5x+2 cards i.e.

\(\Rightarrow 0.5\times 48+2\\\Rightarrow 26\ \text{cards}\)

The value of the integral ∫^3_1 (5e^x - 2) dx is 5e^3 - 5e - 4. To evaluate the integral ∫^3_1(5e^x − 2) dx, we can use the properties of integrals, specifically the linearity property.

The linearity property states that the integral of a sum or difference of functions is equal to the sum or difference of their individual integrals.

The antiderivative of e^x is e^x itself. Therefore, we can evaluate this integral by taking the difference of the exponential function evaluated at the upper and lower limits of integration:

First, let's break down the integral into two separate integrals:

∫^3_1 (5e^x - 2) dx = ∫^3_1 5e^x dx - ∫^3_1 2 dx

Now, we can evaluate each integral separately using the given result:

∫^3_1 5e^x dx = [5e^x]_1^3 = 5e^3 - 5e^1

∫^3_1 2 dx = [2x]_1^3 = 2(3) - 2(1)

Combining the results:

∫^3_1 (5e^x - 2) dx = (5e^3 - 5e^1) - (2(3) - 2(1))

= 5e^3 - 5e - 6 + 2

= 5e^3 - 5e - 4

Therefore, the value of the integral ∫^3_1 (5e^x - 2) dx is 5e^3 - 5e - 4.

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Answer:b

Step-by-step explanation:

Answer:

5x

Step-by-step explanation:

Answer:

10.5 units^2

Step-by-step explanation:

The formula for a triangle is 1/2 * b * h

Count the units for the base of the triangle - 7

Count the units for the height - 3

Use formula: 1/2 * 7 * 3

= 10.5

Note: When countung the units, count the sides you definitely know the units for. If you use any other areas of the triangle as the base, you'll end up getting a height that isn't very exact.

Gursoy's purchase level should be 0.3.

According to the given data, we have the following:

Mean demand, μ = 100

Standard deviation, σ = 30

Purchase price = $10

Selling price = $25

Hence, Cost of under-ordering, Cu = $25 - $10 =$15

Cost of over-ordering, Co = $10 + $25 =$35

Therefore, the calculation of optimal purchase level is calculated as follows:

purchase level = Cu / (Cu + Co)

purchase level = $15 / ($15 + $35)

purchase level = $15 / $50

purchase level = 0.3

The purchase level would be 0.3.

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Answer:

15x - 52

Step-by-step explanation:

Hi,

All you have to do is combine like terms. 4x + 11x is 15x. 9 + (-61) is simply -52.

Hope this helps :)

Answer:

15x-52

Step-by-step explanation:

The estimated crop yield from the simulation is 443 (option b).

To estimate the crop yield from the given random numbers, we need to assign a specific meaning to each random number. Let's assume that each random number represents the crop yield for a particular year.

Given random numbers: 37, 23, 92, 01, 69, 50, 72, 12, 46, 81

To find the estimated crop yield, we sum up all the random numbers:

37 + 23 + 92 + 01 + 69 + 50 + 72 + 12 + 46 + 81 = 443

Therefore, the estimated crop yield from the simulation is 443. The correct option is b.

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Answer:

34.1%, D

Step-by-step explanation:

To convert a number into a percent, you multiply it by 1, or more precisely, 100%. 100% can be thought of as 100 * 1%
0.341 * 100 * 1 %   = 34.1%

Answer:

Step-by-step explanat

Answer: The answer is 3

Step-by-step explanation:

Answer:

A and D

Step-by-step explanation:

> means larger than. 11.436 is larger than 11.422 and 11.286, but not 11.484 or 11.621.

The value of S, which represents the length of each side of the square, is 4 miles.

To find the value of S, we need to determine the length of each side of the square. Given that the perimeter of the square is 16 miles, we can use the formula for the perimeter of a square, which is 4 times the length of a side.

Perimeter = 4 × S

Given that the perimeter is 16 miles, we can substitute this value into the equation:

16 = 4 × S

To solve for S, we divide both sides of the equation by 4:

16 ÷ 4 = S

4 = S

Therefore, S, which stands for the square's side lengths, has a value of 4 miles.

So, S = 4 miles.

This means that each side of the square measures 4 miles, and the square has equal sides and right angles at each corner.

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a) TI = 7√3 in

b) IR = 7 in

Using cosine rule:

\(\sf cos(x) = \dfrac{adjacent}{hypotenuse}\)

\(\hookrightarrow \sf cos(30) = \dfrac{TI}{14}\)

\(\hookrightarrow \sf TI = 14cos(30)\)

\(\hookrightarrow \sf TI = 7\sqrt{3}\)

Using sine rule:

\(\sf sin(x) = \dfrac{opposite}{hypotenuse}\)

\(\hookrightarrow \sf sin(30) = \dfrac{IR}{14}\)

\(\hookrightarrow \sf IR = 14sin(30)\)

\(\hookrightarrow \sf IR = 7\)

Answer:

See explanation

Step-by-step explanation:

So what you would need to do is take 300/10

300/10 which is 1/10 of 300, would be 30

You can also check your work by doing 30 x 10

This equals 300, so its correct.

Answer:

7

Step-by-step explanation:

the x-coordinates are -1 and 6. there's a distance of 7 between those two.

the y-coordinates are -5 and -5. there's a distance of 0 between those two.

(distance between points)² = 7² + 0² = 49 + 0 = 49.

take the square root of both sides:

distance between points = √49 = 7.

this would also have worked if the y-coordinates were different.

Work Shown:

30% of 470 = 0.30*470 = 141

The value goes up by $141, so the answer would be 470+141 = $611

A slight shortcut would be to say

1.30*470 = 611

This works because 1.30 = 1 + 0.30 = 100% + 30%

Answer:

$141

Percentage increase = 30% × 470

New value = 470 + Percentage increase

New value =

470 + Percentage increase =

470 + (30% × 470) =

470 + 30% × 470 =

(1 + 30%) × 470 =

(100% + 30%) × 470 =

130% × 470 =

130 ÷ 100 × 470 =

130 × 470 ÷ 100 =

61,100 ÷ 100 =

611

Calculate absolute change (actual difference)

Absolute change (actual difference) =

New value - 470 =

611 - 470 =

141