The point-slope form of the equation of the line that passes through (-9, -2) and (1, 3) is y – 3 = {(x - 1). What is the
slope-intercept form of the equation for this line?
Oy=1x+2
Oy={x-4
O y = x + 3/2
Oy=2x-
2.

The volume of the solid whose base is the region bounded between the curve y=x^3 and the y-axis from y=0 to y=1 and whose cross section taken perpendicular to the y-axis are squares is 2.4 cubic units.

for given question,

We need to find the volume of the solid whose base is the region bounded between the curve y = x³ and the y-axis from y = 0 to y = 1 and whose cross section taken perpendicular to the y-axis are squares.

Now we rewrite given curve y = x³ in terms of x.

\(x=\sqrt[3]{y}\)

Since the length of the side of each cross sectional square is \(2\sqrt[3]{y}\), the cross sectional area A(y) can be given by

A(y) = \((2\sqrt[3]{y})^2\)

A(y) = \(4y^{\frac{2}{3} }\)

The region is bounded from y = 0 to y = 1

so, the volume V can be found by,

\(V=\int\limits^1_04y^{\frac{2}{3} }~dy\\\\V=4\int\limits^1_0 y^{\frac{2}{3} }~dy\\\\V=4\times \frac{3}{5} \\\\V=\frac{12}{5}\\\\V=2.4\)

Therefore, the volume of the solid whose base is the region bounded between the curve y=x^3 and the y-axis from y=0 to y=1 and whose cross section taken perpendicular to the y-axis are squares is 2.4 cubic units.

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Answer:

500, 500, 50, 10.

Step-by-step explanation:

5000 ÷ 500 = 10,

500 ÷ 50 = 10

50 ÷ 5 = 10

Answer:

5,000/500 = 10

50 /5 = 10

500/50 = 10

Method:

Calculator ;)

If nominal GDP increased by 5 percent and the GDP deflator increased by 3 percent, then real GDP increase by 2 % percent.

The change in real GDP can be found by the formula :

Real GDP = (Nominal GDP / GDP deflator) x 100

This can be changed to account for the change in real GDP to become :

Change in Real GDP = [(Nominal GDP x 1.05) / (GDP deflator x 1.03) x 100 - Nominal GDP / GDP deflator x 100] / (Nominal GDP / GDP deflator x 100) x 100

However, a simpler way of finding the real GDP would be :

= Increase in nominal GDP - Increase in GDP delfator

= 5 % - 3 %

= 2 %

Real GDP will therefore increase by 2 %.

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Farmer Ed has 3,000 meters of fencing and wants to enclose a rectangular plot that borders on a river.The largest area that can be enclosed is 750,000 square meters.

To get the largest area that can be enclosed, we have to find the dimensions of the rectangular plot. Let's assume that the width of the rectangle is x meters.The length of the rectangle can be found by subtracting the width from the total length of fencing available:L = 3000 - x. The area of the rectangle can be found by multiplying the length and width:Area = L × W = (3000 - x) × x = 3000x - x²To find the maximum value of the area, we can differentiate the area equation with respect to x and set it equal to zero.

Then we can solve for x: dA/dx = 3000 - 2x = 0x = 1500. This means that the width of the rectangle is 1500 meters and the length is 3000 - 1500 = 1500 meters.The area of the rectangle is therefore: Area = L × W = (3000 - 1500) × 1500 = 750,000 square meters. So the largest area that can be enclosed is 750,000 square meters.

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The amount of sales tax is $3,

The total amount the group paid, including tax and tip is $47.79.

A percentage is a figure or ratio that can be stated as a fraction of 100.

If we need to determine the percentage of the given number, we divide the number by its whole number and multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." It is represented by the symbol "%".

Given The bill, before sales tax and tip,

amount of the bill before sales tax and tip = $37.50

sales tax is 8% on bill

sales tax = 8% of 37.50

sales tax = 37.50*8/100

sales tax = 37.50*0.08

sales tax = $3

amount after sales tax = $37.50 + $3

amount after sales tax = $40.5

the tip is 18% of the amount after the sales tax

tip = 18% of 40.5

tip = 40.5*18/100

tip = 40.5*0.18

tip = $7.29

total bill amount = $37.50 + $3 + $7.29

total bill amount = $47.79

Hence the sales tax is of $3 and the total amount is $47.79.

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Answer:

81 inches^3

Step-by-step explanation:

The empty space at the top is

3 inches wide by 9 inches long by (12-9) inches tall

3*9*3 = 81 inches^3

Taxation is done on the discounted price. The equation representing the final price of a tablet for this condition is : Option A: c[p(t)] = 0. 918t

Functions which are formed by composing two or more functions in a way that one's input is another's output unless its the last and first function is called composite functions.

For given case, it is given that

Discounted price for original 't' price of a tablet is

\(p(t) = 0.85t\)

This discounted price is then passed as input to the tax calculating function as taxation is specified to be done on the discounted price and not on the original price.

The total cost calculating function is \(c(p) = 1. 08p\)

Thus, for original price t, the total cost is given as:

\(c(p(t)) = 1.08(p(t)) = 1.08 \times 0.85t = 0.918t\)

We composed the two available function to get the direct final cost from value of t.

Thus,

The equation representing the final price of a tablet for this condition is Option A: c[p(t)] = 0. 918t

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The rewritten expression as a sum or difference is \(y = 8x + 2x^{2} + 8x^{1/4}\), and the derivative of y with respect to x is \(y' = 8 + 4x + 2x^{-3/4}.\)

To rewrite the expression \(y = x^{1/4}(8x^{3/4} + 2x^{7/4} + 8)\) as a sum or difference, we can distribute the x^(1/4) term to each term inside the parentheses:

\(y = 8x^{3/4 + 1/4} + 2x^{7/4 + 1/4} + 8x^{1/4}\\= 8x + 2x^(2) + 8x^{1/4}\)

Now, to find y', the derivative of y with respect to x, we can differentiate each term individually using the power rule:

\(y' = d/dx (8x) + d/dx (2x^2) + d/dx (8x^{1/4})\\= 8 + 4x + 2x^{-3/4}\)

Therefore, the rewritten expression as a sum or difference is \(y = 8x + 2x^{2} + 8x^{1/4}\), and the derivative of y with respect to x is \(y' = 8 + 4x + 2x^{-3/4}.\)

The complete question is:

Use algebraic techniques to rewrite \(y= x^{1/4}(8x^{3/4} +2x^{7/4} +8)\) as a sum or difference; then find y'

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Answer:

48.0 m

Step-by-step explanation:

12.0*4 = 48.0m

The Paired samples t-test is the most suitable statistical technique for comparing the mean span of the dominant and non-dominant hands in this study.

To investigate whether the span of a person's dominant hand is greater than that of their non-dominant hand, the most appropriate statistical technique would be the Paired samples t-test.

The Paired samples t-test is used when comparing the means of two related groups or conditions. In this case, the dominant and non-dominant hands are related because they belong to the same individuals in the study. By comparing the means of the dominant and non-dominant hand spans, we can determine if there is a significant difference between the two.

The other options listed, ANOVA (Analysis of Variance), Independent samples t-test, Wilcoxon's matched-pairs signed rank test, and Mann-Whitney U test, are not suitable for this scenario because they are designed for different types of comparisons:

- ANOVA is used when comparing the means of three or more independent groups, which is not the case here.

- Independent samples t-test is used when comparing the means of two independent groups, which is not the case here as the measurements are paired.

- Wilcoxon's matched-pairs signed rank test and Mann-Whitney U test are non-parametric tests that are used when the data do not meet the assumptions of parametric tests. However, in this case, we have paired measurements, and the paired samples t-test is the appropriate parametric test.

Therefore, the Paired samples t-test is the most suitable statistical technique for comparing the mean span of the dominant and non-dominant hands in this study.

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Answer:

I don't know how to convert it but the answer as to how many hours is 36.

Answer:

you go down 5 to get to H from G

The AP United States History (APUSH) exam consists of two sections, the multiple-choice/short-answer section and the free-response section.

The AP United States History (APUSH) exam consists of two sections, the multiple-choice/short-answer section and the free-response section. The free-response section includes a document-based question (DBQ) and two other long essay questions. The DBQ is worth 25% of the total exam score, and it is scored using a rubric that evaluates students' abilities to analyze and synthesize historical documents to construct an argument.

The DBQ is scored on a scale of 0 to 7 points, with a total of 9 possible points. The rubric evaluates the following areas:

The scores for each of the five areas are added up to determine the overall score for the DBQ, which ranges from 0 to 7 points. The scores are then converted to a scale of 0 to 9 points, with 9 being the highest score.

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The three (3) possible combinations are

Alex should 20 hats and 20 scarves

Let the number of scarves be x and y be the number of hats

He can make at most 20 hats and 30 scarves, but no more than 40 items altogether

x ≤ 20

y ≤ 30

x + y ≤ 40 (in time of market)

x + y ≥ 25

The possible combinations are

He should choose the third option x = 20, y = 20 this allows him to take more products to the show

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Answer:

a = 11

Step-by-step explanation:

a + 8 = 19

=> a = 19 - 8

=> a = 11

Answer:

2

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

The leading coefficient will always be the number multiplied to the highest degree variable.

Our highest degree term is 2x. Our leading coefficient would then be 2.

The percentage by which the price increased is 150% on re-selling the car on revised prices.

The percentage increase in price will be calculated by the formula -

Percentage increase = change in price/previous price × 100

Previous price = $12

New price = $30

Change in price = 30 - 12

Change in price = $18

Keep the values in percentage increase formula to find the value

Percentage increase = 18/12 ×100

Performing multiplication and division on Right Hand Side of the equation

Percentage increase = 150%

Hence, the percentage increase is 150%.

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Answer:

0

Step-by-step explanation:

This is prob wrong

1068/4=

267*20=

5,340

The difference in volume between the two pyramids is 12,371,740 cubic feet.

To find the volume of a square pyramid, you use the formula :

V = (1/3)Bh, where B is the area of the base and h is the height.

Using the dimensions given in the table, we can calculate the volumes of the two pyramids:

- Volume of Bent Pyramid = (1/3)(619 feet * 619 feet)(332 feet) = 26,384,053.33 cubic feet
- Volume of Red Pyramid = (1/3)(722 feet * 722 feet)(341 feet) = 38,755,793.33 cubic feet

To find the difference in volume between the two pyramids, we subtract the smaller volume from the larger volume:

38,755,793.33 - 26,384,053.33 = 12,371,740 cubic feet.

Rounding to the nearest cubic foot, the difference in volume between the two pyramids is 12,371,740 cubic feet.

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Answer:

$ 30

$ 20

Step-by-step explanation:

Sea el costo fijo xy el costo por km sea y suponiendo que es el mismo para ambos taxis.

De la pregunta obtenemos las dos ecuaciones

\(x+8y=190\quad ...(i)\)

\(x+5y=130\quad ...(ii)\)

Aplicando \((i)-(ii)\)

\(8y-5y=190-130\\\Rightarrow 3y=60\\\Rightarrow y=\dfrac{60}{3}\\\Rightarrow y=20\)

Sustituyendo en \((ii)\)

\(x+5y=130\\\Rightarrow x+5\times 20=130\\\Rightarrow x=130-100\\\Rightarrow x=30\)

Entonces, el costo fijo es de $ 30 y el costo por km es de $ 20.

Given that x and y are two non-negative numbers such that x+y=2. The expression is \(x²y²/30\), which represents the area of a rectangle with dimensions x/√30 and y/√30.

To calculate its maximum and minimum values, we must analyze the limits of the function as x and y vary within their possible ranges. To do so, we must first examine the boundary conditions.

Boundary conditionsThe domain of the function is the square defined by the points (0,2), (2,0), (0,0), and (2,2).

By applying the constraints \(x≥0 and y≥0\), we see that this region is reduced to the triangle bounded by points (0,2), (2,0), and (0,0).

In this triangular region, the maximum and minimum values of x and y are limited to the endpoints of the line x+y=2.

The graph of the function is a paraboloid of revolution with its apex located at the origin of the coordinate system.

As a result, the maximum and minimum values of the function correspond to its points of intersection with the boundary of the triangular region.

The minimum value of the function is 0, which is attained at the origin of the coordinate system.

The maximum value of the function is 4/15, which is attained at the two points (2,0) and (0,2).

\(The difference between the maximum and minimum of the quantity x²y²/30,\) where x and y are two non-negative numbers such that\(x+y=2 is 4/15 - 0 = 4/15\)

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Answer:

1) x= 20

2) x= 75

Step-by-step explanation:

In the first problem, we see vertical angles. This means that both angles equal each other: 50= 2x+10

Step 1- Subtract 10 to both sides.

50= 2x+10

-10         -10

40= 2x

Step 2- Divide both sides by 2.

40= 2x

2     2

x= 20

In the next problem we see a straight line and an intersecting point. Now, both of these angles sum up to 180 degrees. So the equation would be:

x-10+2x-35= 180

Step 1- Add common variables.

(x+2x)+(-10-35)= 180

3x-45= 180

Step 2- Add 45 to both sides.

3x-45= 180

   +45  +45

3x= 225

Step 3- Divide both sides by 3.

3x= 225

3      3

x= 75

Input the value of x into the equations.

75-10= 65

2(75)-35= 115

Hope this helps!

The distance that Ann drove last weekend is 144 miles.

The first step is to determine the rate of Ann's car. Rate is the distance traveled per gallon. It is determined by dividing the total miles traveled by the total gas used.

Rate = distance/gallons

= 252/ 7 = 36 miles per gallon

The next step is to multiply the rate by the gallons she used last weekend. Multiplication is the process of determining the product of two or more numbers. The sign that represents multiplication is x.

Distance Ann traveled = rate x gallons of gas used

= 36 x 4 = 144 miles

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The distance Ann's car travelled using 4 gallons is 144 miles.

The first step is to determine how many miles Ann's car can go using one gallon. To do this, calculate the rate of Ann's car. Rate is the total distance divided by the total gallons.

Miles travelled on one gallon = 252 / 7 = 36 gallons per mile

Now, multiply the rate by the gallons she has. Multiplication is the process that is used to determine the product of two or more numbers.

Total distance travelled = 36 x 4 = 144 miles.

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Answer: 106 km/h,2.5 hr

Step-by-step explanation:

Given

The train travels 315 km in the same time car travels 265 km

The average speed of the train is 20 kmph faster than car

Suppose, speed of the car is v and it travels 265 km in t hours

\(\therefore \dfrac{315}{v+20}=\dfrac{265}{v}\\\\\Rightarrow 315v=265\left (v+20\right)\\\\\Rightarrow 315v=265v+5300\\\Rightarrow 50v=5300\\\Rightarrow v=106\ km/h\)

Time taken to travel is

\(\Rightarrow t=\dfrac{265}{106}}\\\\\Rightarrow t=2.5\ h\)

The point estimate of the population standard deviation for the given data set (13, 15, 14, 16, 12) is 1.581. Therefore, the correct option is A.

The data is collected from a simple random sample from an infinite population. In order to calculate the point estimate of the population standard deviation for the given data:

1. Calculate the mean (average) of the data set:

(13+15+14+16+12) / 5 = 70 / 5 = 14.

2. Subtract the mean from each data point and square the result:

(13-14)^2=1, (15-14)^2=1, (14-14)^2=0, (16-14)^2=4, (12-14)^2=4.

3. Find the sum of these squared differences:

1+1+0+4+4 = 10.

4. Divide the sum by the number of data points minus 1 (this is the degrees of freedom):

10 / (5-1) = 10 / 4 = 2.5.

5. Take the square root of the result to find the point estimate of the population standard deviation:

√2.5 = 1.581.

Hence the point estimate of the population standard deviation is 1.581. Hence, option A is the correct answer.

Note: The question is incomplete. The complete question probably is: The following data were collected from a simple random sample from an infinite population. 13 15 14 16 12 The point estimate of the population standard deviation is _____. a. 1.581 b. 2.500 c. 2.000 d. 1.414

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To begin with, let's recall the definition of a one-to-one function. A function f: A → B is one-to-one if every element in A is mapped to a unique element in B. In other words, no two distinct elements in A are mapped to the same element in B.
Now, let's assume that f is one-to-one and even. This means that f(-x) = f(x) for all x in R. To prove that f cannot be both one-to-one and even, we will use a proof by contradiction. Suppose f is both one-to-one and even. Then, for any x and y in R, if f(x) = f(y), we must have x = y. Now, let's consider the case when x and y are negative numbers such that x ≠ y. Since f is even, we have f(-x) = f(x) and f(-y) = f(y). However, since f is one-to-one, we cannot have f(-x) = f(-y) because x and y are distinct.Therefore, f cannot be both one-to-one and even. Alternatively, we could use the contrapositive of the statement. The contrapositive of "f one-to-one => f not even" is "f even => f not one-to-one". This means that if f is even, then it cannot be one-to-one. This is true because, as we showed earlier, if f is even, there exist distinct negative numbers that are mapped to the same value, which violates the one-to-one property. In conclusion, we have shown that if a function f is one-to-one, then it cannot be even, using either a proof by contradiction or the contrapositive of the statement.

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Answer:

(-2, 3)

Step-by-step explanation:

Point (2, -3) becomes:

The choice between a 50-day and a 200-day moving average depends on the specific trading strategy and time horizon.

Moving averages are commonly used technical indicators that smooth out price data over a specified period to identify trends and potential buy or sell signals. The choice between a 50-day and a 200-day moving average primarily depends on the trader's objective and time horizon.

A 50-day moving average is more sensitive to short-term price fluctuations and can provide quicker signals for shorter-term trading strategies. It reacts more swiftly to price changes and may generate more frequent trading signals. However, it can also be more prone to false signals or whipsaws due to its sensitivity to short-term market noise.

On the other hand, a 200-day moving average is slower to react to price changes and is considered a longer-term trend indicator. It smooths out short-term fluctuations and is often used by traders with longer time horizons, such as swing traders or investors. The signals generated by a 200-day moving average tend to be more reliable but may come with a lag in response to recent price movements.

Ultimately, the choice between a 50-day and a 200-day moving average depends on the trader's preferred trading style, time horizon, and the level of sensitivity they seek in their trading signals.

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