Define the relation O on Z as follows: ᵾm, n € z, m O n <----> ⱻk € z |(m – n) = 2k +1 Which one of the following statements about the relation O is true? a. The relation is reflexive, symmetric, and transitive. b. The relation is not reflexive, not symmetric, and transitive. c. The relation is not reflexive, symmetric, and not transitive. d. The relation is reflexive, not symmetric, and transitive.

Answer:

17 meters

Step-by-step explanation:

I did 16^2 and 7^2 to get, 256 + 49 = 305. 305 squared is 17.4... Once you round it you should get the answer 17 meters.

Hope this helps :)

Answer:

The answer is 17 meter

Step-by-step explanation:

So the formula for this is a^2 + b^2 = c^

The two legs are a and b

So plug those into the equation

It should look something like this 7^2 + 16^2 = c^2

Then solve the exponents and you get 49 + 256 = c^2

After that just add the two integers and you have 305

Finally take the square root of 305 and you get 17

pls mark brainliest because i didnt waste your time Lol

This is the number 80 thousand

==========================================================

Explanation:

1/2, aka 2/4, of the original fund was given to his wife and 1/4 was given to his son. That totals 3/4 since 2/4+1/4 = (2+1)/4 = 3/4.

In short, 3/4 of the fund is distributed between the wife and son. That leaves 1/4 of the fund for the two brothers to share equally.

Imagine a cake cut into quarters. Then cut each slice in half to get eighths, i.e. there are 8 equal slices. This means each brother gets 1/8 of the fund.

Since each brother got Rs 10000, this must mean the original fund is worth 8*10000 = 80000

Taking 1/8 of Rs 80000 will get us Rs 10000 for each brother.

----------------------------------

Checking the answer:

original fund amount = 80000

1/2 of 80000 = 40000 is the amount the wife gets

1/4 of 80000 = 20000 is the amount the son gets

That totals 40000+20000 = 60000 leaving 80000-60000 = 20000 leftover for the two brothers to share. Cut that 20 thousand figure in half to arrive at Rs 10000 for each brother. These steps help confirm the answer.

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Another method using algebra:

x = original amount of the fund

W = x/2 = 2x/4 = half of the fund = amount wife gets

S = x/4 = quarter of the fund = amount the son gets

W+S = (2x/4) + (x/4) = (2x+x)/4 = 3x/4

W+S represents the sum of the wife's and son's amounts.

We'll subtract this from the original amount x to find out what's left

x - (W+S) = x - (3x/4) = (4x/4) - (3x/4) = (4x-3x)/4 = x/4

This shows that 1/4 of the fund is left over after distributing to the wife and son.

The amount x/4 is then cut in half to get x/8 to represent the amount each brother gets. We're told that amount is Rs 10000

So,

x/8 = 10000

x = 8*10000

x = 80000

The original fund is worth Rs 80000

The 95% confidence interval is 0.4046 < p < 0.4063.

Given,

The sample size is 1127.

The number that America is getting roughly correctly is k = 457.

In general, the sample fraction of the number that indicates America is doing approximately the proper amount is expressed mathematically as

p = k ÷ n

p = 457 ÷ 1127

p = 0.4055

According to the question, the confidence level is 95%, hence the degree of importance is,

\(\alpha\) = (100 - 95)%

\(\alpha\) = 5%

\(\alpha\) = 0.05

According to the normal distribution table, the critical value of is \(\alpha\) ÷ 2 is,

Z(\(\alpha\)/2) = 1.96

In general, the margin of error is expressed numerically as

E = Z × √(p(1 - p)) ÷ n

E = 1.96 × √(0.4055(1 - 0.4055)) ÷ 1127

E = (1.96 × √(0.4055(1 - 0.4055))) ÷ 1127

E = 0.000853

A 95% confidence interval is typically expressed mathematically as

p - E < p < p + E

0.4055 - 0.000853 < p < 0.4055 + 0.000853

0.4046 < p < 0.4063

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The question is -

In 2015 as part of the General Social Survey, 1127 randomly selected American adults responded to this question: “Some countries are doing more to protect the environment than other countries. In general, do you think that America is doing more than enough, about the right amount, or too little?” Of the respondents, 457 replied that America is doing about the right amount. What is the 95 % confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment?

Answer:

Step-by-step explanation:

When dilating quadrilateral ABCD using P as the center and a scale factor of 1/2, the image is A'B'C'D'.

To dilate the quadrilateral, we multiply the coordinates of each vertex by the scale factor. With a scale factor of 1/2, we can determine the new coordinates as follows:

A' = (1/2) * A

B' = (1/2) * B

C' = (1/2) * C

D' = (1/2) * D

Labeling the new vertices, we have A'B'C'D' as the image of quadrilateral ABCD under the dilation with a scale factor of 1/2.

Similarly, if we dilate quadrilateral ABCD using P as the center and a scale factor of 2, the image is A"B"C"D".

Using the same process as before, we determine the new coordinates:

A" = 2 * A

B" = 2 * B

C" = 2 * C

D" = 2 * D

Labeling the new vertices, we have A"B"C"D" as the image of quadrilateral ABCD under the dilation with a scale factor of 2.

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The  transformation of \(\(y= \frac{x^{4} }{6x+6}\)\) graph is compressed by a factor of 2.

The function is a rational function in which the numerator is a degree 4 polynomial, and the denominator is a degree 1 polynomial.

Rational functions are in the form of \(\(f(x) = \frac{p(x)}{q(x)}\)\), where p(x) and q(x) are polynomial functions and the degree of p(x) is less than the degree of q(x).

To transform a graph of a function, one can translate, stretch, or reflect it.

Here are some of the transformations of the function \(\(y= \frac{x^{4} }{6x+6}\)\)

Vertical Shift: To get the new graph, we add or subtract a constant from the function.

When f(x) is replaced with f(x) + k, we get a graph that is k units above the graph of f(x). In this case, if we subtract 2 from the equation, we get the following equation:

\(y = (x^4) / (6x+6) - 2\)

This means that the graph of the function is shifted 2 units downwards.

Horizontal Shift: To get the new graph, we add or subtract a constant to the variable.

When f(x+c) is replaced with f(x), the graph is shifted c units to the left.

When f(x-c) is replaced with f(x), the graph is shifted c units to the right.

In this case, we can shift the graph by substituting x-2 for x in the function.

The new function is: \(y = ((x-2)^4) / (6(x-2)+6)\)

This means that the graph is shifted 2 units to the right.

Vertical Stretch/Compression: When a constant is multiplied to the function, the graph is vertically stretched or compressed.

In this case, if the function is multiplied by 2, we get the following function:

\(y = 2(x^4) / (6x+6)\)

This means that the graph is compressed by a factor of 2.

It can also be stretched by dividing the function by a constant.

Horizontal Stretch/Compression:

When a constant is multiplied to the variable of the function, the graph is horizontally stretched or compressed. In this case, if the variable is divided by 2, we get the following function:

\(y = (x^4) / (3x+3)\)

This means that the graph is compressed by a factor of 2.

It can also be stretched by multiplying the variable by a constant.

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well, the tax is clearly $35.20 - $32 = $3.20.

now, if we take 32(origin amount) to be the 100%, what is 3.20 off of it in percentage?

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 32 & 100\\ 3.20& x \end{array} \implies \cfrac{32}{3.20}~~=~~\cfrac{100}{x} \\\\\\ 32x=320\implies x=\cfrac{320}{32}\implies x=10\)

Answer:

y=-9x+5

Step-by-step explanation:

Answer:

y=2x

Step-by-step explanation:

slope = rise/run = 2/1 = 2

The solution is, y = -1/3 x + 5 this equation represents the given graph.

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

The horizontal axis is called the x-axis.

And the vertical one is the y-axis.

Points are written as xy pairs in parentheses, like so: (x, y).

Now, just locate the position on x-axis as well as in y-axis and finally plot where these points meet.

Proof :

(0, 5) and ( 15, 0) these are the points where the graph is plotted.

y = -1/3 x + 5

put x= 0 and find y

y = 0 + 5

y = 5

put y = 0 and find x

0 = -1/3 x + 5

-5 = -1/3 x

x = 15

So, now we get the same points i.e, (0, 5) and ( 15, 0) as plotted in the given graph.

Hence, we can say that  y = -1/3 x + 5 this equation represents the given graph.

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Answer:

Domain

Step-by-step explanation:

Answer: the x values

Step-by-step explanation:

Answer:

152.6 hours

Step-by-step explanation:

Distance = Speed × Time

Time = Distance/Speed

Santa's sleigh covered a total distance of 5797 kilometres averaging a speed of 38 km/h in snow storm conditions

Hence: Time Santa spent in snow storms is calculated as:

5797km ÷ 38 km/h

= 152.55263158 hours

Approximately = 152.6 hours

Answer:

\(x=61^{\circ}\)

Step-by-step explanation:

The sum of the interior angles of a triangle add up to 180 degrees. Therefore, we have the following equation:

\(x+67+52=180,\\x=180-67-52=\boxed{61^{\circ}}\)

Answer:

A

Step-by-step explanation:

In an expression with variables, the constants are the numbers that are not multiplied by variables, in other words, plain numbers.

Answer: A

The yield of CaO in terms of kg of CaO per kg of CO2 produced is:Yield = mass of CaO produced / mass of CO2 produced= 49 / 21= 2.33 kg CaO/kg CO2.

(a) The decomposition of limestone (pure CaCO3) to form calcium oxide (CaO) is represented by the following chemical equation: CaCO3 (s) → CaO (s) + CO2 (g)Given that the reaction goes to 70% completion.

Therefore, the maximum amount of CaO that can be produced from 100 kg of limestone is 70 kg. The mass of CO2 produced from the decomposition of 100 kg of limestone is 30 kg, assuming that the process goes to completion.

The total mass of the product withdrawn from the kiln is 70% of the maximum theoretical yield (70 kg).Therefore, the mass of CaO produced is 0.70 x 70 = 49 kg and the mass of CO2 produced is 0.70 x 30 = 21 kg.

The percentage composition of the solid product is, by definition:Mass percent of CaO = (mass of CaO / mass of product) x 100 = (49 / 70) x 100 = 70.0%Mass percent of CaCO3 = (mass of CaCO3 / mass of product) x 100 = [(70 – 49) / 70] x 100 = 30.0%(b) In 1 kg of CO2, there are 12/44 kg of C. Therefore, the amount of carbon in 21 kg of CO2 is:Mass of carbon = (12/44) x 21 = 5.72 kg

The yield of CaO in terms of kg of CaO per kg of CO2 produced is:Yield = mass of CaO produced / mass of CO2 produced= 49 / 21= 2.33 kg CaO/kg CO2.

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Answer:

$135 each

Step-by-step explanation:

Since they plan to pay in 4 equal payments and the total is $540, you'd divide 540 ÷ 4 and it will give you $135

Answer:

135

Step-by-step explanation:

540/4=135

hope this helps :3

if it did pls mark brainliest

Answer:

2 dollars.

Step-by-step explanation:

1 meter costs 3 dollars

2/3 meter costs 2/3 * 3

2/3 * 3 = 2

So you would pay 2 dollars for 2/3 of a meter.

Answer:

452.39

Step-by-step explanation:

to find the surface area of a sphere all you need is the radius (half the diameter) and assuming the sphere touches both top and bottom that makes the radius 6 so your equation is

SA=4πr^2

SA=4*π*6^2

SA=4*π*36

SA=4*113.09

SA=452.389

then rounded up to 452.39, that is your answer

Answer:

12x6+2(6-1)

72+2x5

72+10

82

82 is the answer.

Step-by-step explanation:

Just replace the X's in the problem with 6.

The expression is equivalent to the given expression is 5x²+12x-7: Option C

You should understand that  simplification means making an expression more simpler for better understanding

The given expression is

-2x²+8x-9+4x+7x²+2

The first thing to do is to rearrange the expression in the following ways by collecting the like terms

7x²-2x²+8x+4x-9+2

This implies that

5x²+12x-7

Conclusively the simplest form of the expression is 5x²+12x-7

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Δy=v-0.32 and dy = -0.32 .Δy and dy are both used to represent changes in the dependent variable y based on changes in the independent variable x.

Δy represents the change in y (the dependent variable) resulting from a specific change in x (the independent variable). In this case, y = x^4 + 7, x = -2, and Δx = dx = 0.01. Therefore, we need to calculate Δy and dy based on these values.

To calculate Δy, we substitute the given values into the derivative of the function and multiply it by Δx. The derivative of y = x^4 + 7 is dy/dx = 4x^3. Plugging in x = -2, we have dy/dx = 4(-2)^3 = -32. Now, we can calculate Δy by multiplying dy/dx with Δx: Δy = dy/dx * Δx = -32 * 0.01 = -0.32.

On the other hand, dy represents an infinitesimally small change in y due to an infinitesimally small change in x. It is calculated using the derivative of the function with respect to x. In this case, dy = dy/dx * dx = 4x^3 * dx = 4(-2)^3 * 0.01 = -0.32.

Therefore, both Δy and dy in this context have the same value of -0.32. They represent the change in y corresponding to the change in x, but Δy considers a specific change (Δx), while dy represents an infinitesimally small change (dx) based on the derivative of the function.

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However, we need to substitute a with s since that is the value we have calculated. Therefore, we get \(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

Let's consider that s be the length of a side of the regular pentagon.

The perimeter of the regular pentagon will be 5s. Therefore, we have the equation:5s = 140s = 28 cm

Also,

we have the formula for the area of a regular pentagon as:

\($A=\frac{1}{4}(5 +\sqrt{5})a^{2}$,\)

where a is the length of a side of the pentagon.

In order to represent the area of a regular pentagon whose perimeter is 140 cm, we need to substitute a with s, which we have already calculated.

Therefore, we have:\(A(s) = $\frac{1}{{4}(5 +\sqrt{5})s^{2}}$\)

Now, we have successfully used function notation (with the appropriate functions above) to represent the area of a regular pentagon whose perimeter is 140 cm.

The area of a regular pentagon can be represented using function notation (with the appropriate functions above). The first step is to calculate the length of a side of the regular pentagon by dividing the perimeter by 5, since there are 5 sides in a pentagon.

In this case, we are given that the perimeter is 140 cm, so we get 5s = 140, which simplifies to s = 28 cm. We can now use the formula for the area of a regular pentagon, which is\(A = (1/4)(5 + sqrt(5))a^2\), where a is the length of a side of the pentagon.

However, we need to substitute a with s since that is the value we have calculated. Therefore, we get\(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

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Answer:

\(\huge\boxed{\sf 8 + 4\sqrt{2} \ cm }\)

Step-by-step explanation:

\(\theta = 45 \textdegree\)

opposite = 4 cm

Using tan first to find the adjacent side:

\(\displaystyle tan \theta = \frac{opposite}{adjacent} \\\\tan \ 45 = \frac{4}{adjacent}\\\\1 = \frac{4}{adjacent} \\\\Multiply \ 'adjacent' \ to \ both \ sides\\\\adjacent = 4 \ cm\)

Finding Hypotenuse now by using Pythagorean theorem:

\((Hyp)^2 = (base)^2 + (perp)^2\)

where base = 4, hyp = 4

(Hyp)² = (4)² + (4)²

(Hyp)² = 16 + 16

(Hyp)² = 32

Take sqrt on both sides

\(Hyp = 4\sqrt{2}\) cm

Exact perimeter of triangle:

= base + perpendicular + hypotenuse

= 4 + 4 + 4√2

= \(8 + 4\sqrt{2}\) cm

\(\rule[225]{225}{2}\)

We know that 1 gallon = 3.785 L,Therefore, 24.1364 L = 24.1364/3.785 gallons= 6.3781 gallons (rounded to four decimal places)Therefore, the car will use approximately 6.3781 gallons of gas on this trip.

The car travels for 3.0 hours at a velocity of 55 miles per hour. The gas mileage of the car is 11 km/L. We have to find how many gallons of gas will be used on this trip. We can solve this problem by using the following steps:Step 1: Convert the velocity from miles per hour to km/hourWe know that 1 mile

= 1.609 km Therefore, 55 miles per hour

= 55 × 1.609 km per hour

= 88.5 km per hour Step 2: Calculate the distance traveled by the car We know that distance = velocity × time Therefore, distance traveled by the car

= 88.5 km/hour × 3.0 hours

= 265.5 km

Step 3: Convert the distance from kilometers to miles We know that 1 mile

= 1.609 km Therefore, 265.5 km

= 265.5/1.609 miles

= 165.1287 miles (rounded to four decimal places)Step 4: Calculate the fuel consumption in liters We know that fuel consumption

= distance traveled/gas mileage Therefore, fuel consumption

= 265.5 km/11 km/L

= 24.1364 L (rounded to four decimal places)Step 5: Convert the fuel consumption from liters to gallons.We know that 1 gallon

= 3.785 L,Therefore, 24.1364 L

= 24.1364/3.785 gallon

s= 6.3781 gallons (rounded to four decimal places)Therefore, the car will use approximately 6.3781 gallons of gas on this trip.

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Answer:

Using the law of sines ,measure of a is 66 m.

The correct statement is :David started at 0 instead of 2

A number line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, for example, plotting a point.

Given here: In a number line the interval (-5,5) is marked and 2 to 5 is 3

The right steps are

Add 3 to 2 to obtain the required number as there are 3 spaces between 2 and 5

Thus 2+3=5 which is the required answer

but David addes 2-3=-1 which is incorrect.

Hence, David started at 0 instead of 2

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Answer:

Answer is: 8 2/3 but improper is 26/3

Answer:

f^-1(x) = _x__

               5

Step-by-step explanation:

Answer:

\( {f}^{ - 1} (x) = \frac{x}{5} \)

Step-by-step explanation:

f(x) = 5x

To find f^-1(x) equate f(x) to y

That's f(x) = y

y = 5x

Interchange the variables

x = 5y

Make y the subject by dividing both sides by 5

y = x/5

The final answer is

f^-1(x) = x/5

Hope this helps you.

Answer:

Andre     Noah     Weeks

 20           10             1

 25         17.50         2

 30           25            3

Step-by-step explanation:

Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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The standard deviation is $42.96.

The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation. As the formula shows, the z-score is simply the raw score minus the population mean, divided by the population standard deviation. There are three ways to find the z-score that corresponds to a given area under a normal distribution curve 1. Use the z-table. 2. Use the Percentile to Z-Score Calculator.

Given : 75% of all families spend more than $75 weekly for food,

Mean = μ = $104

We have to find standard deviation σ.

75% of all families spend more than $75 weekly for food

For 100 - 75 = 25%, z = -0.675

Now, z = (x - μ) / σ

∴ σ =  (x - μ) / z

σ = (75 - 104)/-0.675

= -29/-0.675

= 42.96

Thus, the standard deviation is $42.96.

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