Consider the following function:
f(x) = 2x/3x^2-3 What is the domain of the function?

The price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit is 62.13

y = -14x² + 1035x - 10266

-14x² + 1035x - 10266 = 0

x = -b ± √b² - 4ac / 2a

= -1035 ± √1035² -4(-14)(-10266) / 2(-14)

= -1035 ± √1071225 - 574896 / -28

= -1035 ± √496329 / -28

x = 1035 / 28 ± √496329 / 28

x = 11.80 or 62.13

The maximum value of x is 62.13

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Answer: step by step

Step-by-step explanation:

not totally sure what you're asking but in this equation p=2

Answer: f(n) = 2n - 2

Therefore, we can use this formula to find the value of f(n) for any positive integer n.

Step-by-step explanation: Using the given recursive formula:

f(1) = 0

f(n) = f(n-1) + 2

We can find the values of f(n) for different values of n:

f(1) = 0

f(2) = f(1) + 2 = 0 + 2 = 2

f(3) = f(2) + 2 = 2 + 2 = 4

f(4) = f(3) + 2 = 4 + 2 = 6

f(5) = f(4) + 2 = 6 + 2 = 8

And so on.

We can see that each term in the sequence is 2 more than the previous term. So, we can write the general formula for f(n) as:

f(n) = 2n - 2

Therefore, we can use this formula to find the value of f(n) for any positive integer n.

Answer:

-42

Step-by-step explanation:

\((7)( - 6) \\ = 7( - 6) \\ = - 42\)

Totally correct about the mentioned before is 2.5%. This is because the z-score for this situation is (494 - 686) / 96 = -2. According to the Empirical Rule, approximately 95% of observations will fall within 2 standard deviations of the mean. In this case, the question is asking for the percent of students who scored less than 494, which is below 2 standard deviations, so the answer is 2.5%.

The Empirical Rule states that for a normal distribution, approximately 68% of the data will fall within one standard deviation of the mean, approximately 95% of the data will fall within two standard deviations of the mean, and approximately 99.7% of the data would get fall within 3 standard deviations of the mean. So if we know the mean and standard deviation of a normal distribution, we can use this rule to estimate the percentage of data that falls within a certain range.

In this specific question, the mean of Math Level 2 SAT subject test score was 686 with a standard deviation of 96. We were asked to find the percent of students who scored less than 494. To find this we first calculated the z-score which is (494 - 686) / 96 = -2.

Since the z-score is -2 it means that it's 2 standard deviation below the mean, and according to the Empirical rule 95% of observations will fall within 2 standard deviations of mean. This means that 2.5% of observations will fall above 2 standard deviations and 2.5% of observations will fall below 2 standard deviations. So the answer is 2.5%.

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Answer:

A. Relation

B. Relation

C. Function

D. Function

E. Relation

The Length of the rod is 3/5 meters.

The civil engineer wants to find the length of a rod that stretches for 1 meter and can be given by the function x=2y^(3/2).

To find the length of the rod, we need to integrate the function x=2y^(3/2) with respect to y. Integrating both sides of the equation,

we have:'int dx = int 2y^(3/2) evaluating the left-hand side gives x = 2/5 y^(5/2) + C, where C is the constant of integration. To find the value of C,

we use the given information that the rod stretches for 1 meter. At y = 0, x = 0 since the rod has no length when it is not stretched. At y = 1, x = 1 since the rod stretches for 1 meter.

Therefore, we have:1 = 2/5 (1)^(5/2) + C1 = 2/5 + CC = 3/5 Substituting C = 3/5 back into the equation for x,

we have:x = 2/5 y^(5/2) + 3/5

The length of the rod is given by the value of x when y = 1. Substituting y = 1,

we have:x = 2/5 (1)^(5/2) + 3/5 = 3/5

The length of the rod is 3/5 meters.

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Answer:

To calculate Karl Pearson's coefficient of skewness, we need to use the formula:

Skewness = 3 * (Mean - Mode) / Standard Deviation

Given the Mean = 73.19, Mode = 79.56, and Variance = 16, we need to find the Standard Deviation first.

Standard Deviation = √Variance = √16 = 4

Now we can substitute the values into the formula:

Skewness = 3 * (73.19 - 79.56) / 4

Skewness = -6.37 / 4

Skewness = -1.5925

Rounded to four decimal places, the Karl Pearson's coefficient of skewness for the given values is approximately -1.5925.

The straight-line distance between Akira's house and Cooper's house is 6.13 kilometers (rounded to the nearest tenth)

Given that,To get from home to his friend Akira's house, Jaden would have to walk 2.8 kilometers due east.The straight-line distance between Akira's house and Cooper's house is given by the distance between two points in a coordinate plane. Let the home be the origin (0, 0) of the coordinate plane and Akira's house be represented by the point (2.8, 4.7). Similarly, let Cooper's house be represented by the point (8.3, 7.4).The distance formula between the two points (2.8, 4.7) and (8.3, 7.4) is given by:distance = √[(8.3 - 2.8)² + (7.4 - 4.7)²]= √[5.5² + 2.7²]= √(30.25 + 7.29)= √37.54= 6.13 km (rounded to the nearest tenth)

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For the probability of rain on julty 4h of 0.5 his expected profit is  8885.5 dollars.

The probability is occurrence of a certain event out of the total number f events that can happen.

Given in the question the probability of rain is 0.5 therefore the probability of not raining is also 0.5.

If it does not rain he makes a profit of 30427 dollars and if it rains he suffers a loss of 12656 dollars.

We know, the expected profit is,

= 0.5(30427) - 0.5(12656).

= 15213.5 - 6328.

= 8885.5 dollars.

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Solution:

perimeter of rectangle = 2 ( Length + Width )

Find length/width:

2 (length + length) = 48

2(length) = 24

length = 12 cm

width = 12 cm

⇒ The dimensions of square: 12 x 12

If the square cut into half, the dimensions of either length or width will half.

Therefore, the perimeter of rectangle:

→ 2 (length + width)

→ 2 ( 12 + 6 )

→ 2 ( 18 )

→ 36 cm

Answer:

            4  to  1

Step-by-step explanation:

                                                Tablespoon of cocoa   to Tablespoon of sugar

                                                                          8             :                2

                                                                          \(\frac{8}{2}\)              :                \(\frac{2}{2}\)

                                                                          4             to                1

When recipe is doubled:                             ( 8 x 2)         to        (2 x 2)

                                                                         16             :              4

                                                                         \(\frac{16}{4}\)             :               \(\frac{4}{4}\)

                                                                          4           to              1

It can be observed that the ratio remains the same

Answer: $252

Step-by-step explanation:

21$ an hour x 12 hours = $252 total :)

Answer:

She earned $252 thsi month.

Step-by-step explanation:

1  hour = $21

12 hours = $?

21*12 = 252

Answer:

x = 136

Step-by-step explanation:

This one is quite simple

The shape formed inside of the circle is a quadrilateral.

when a quadrilateral is formed inside of a circle opposite angles of the quadrilateral will add up to 180

we are given x's opposite angle so we can find x by subtracting the given angle's measure (44) from 180

so x = 180 - 44

180 - 44 = 136

hence, x = 136

The y-intercept of the linear model is 211,400, which represents the estimated number of automobiles in the town in the year 2015 (when the independent variable is zero).

To find the y-intercept of the linear model, we need to determine the value of the dependent variable (the number of automobiles) when the independent variable (the number of years since 2015) is equal to zero.

Let's first find the slope of the line, which represents the rate of change of the number of automobiles per year:

slope = (change in number of automobiles) / (change in number of years)

slope = (2420 - 1890) / (2020 - 2015) = 106 automobiles per year

Now we can use the point-slope form of a linear equation to find the y-intercept:

y - y1 = m(x - x1)

where y1 is the value of the dependent variable when the independent variable is x1. In this case, x1 = 2015, y1 = 1890, and m = 106 (the slope we just calculated).

y - 1890 = 106(x - 2015)

To find the y-intercept, we can set x = 0:

y - 1890 = 106(0 - 2015)

y - 1890 = -213,290

y = 211,400

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12x'6(4x'4)_5y'2(7y'2)

_________________

60x'6y'2

Step-by-step explanation:

48x'10_35y4. ___________. 60x6y2

The amount in year 6 is $1282.5.

What is simple interest?

Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

Given,

rate of interest = 7%

time = 1 year

Amount on first year = $950

First we will calculate simple interest for 5 years, because amount is available for 1 year.

SI =PRT

SI = 950(7/100)1

SI = $332.5

Therefore, the amount after 6 years = 950+332.5

=$1282.5

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3)

Given that the line passes through (-5, -5) and (-5, 3).

We have to find the slope form of the equation.

The equation passes through (x1, y1) and (x2, y2) is given by:

So, the required equation is:

Thus, the equation of the line passes through (-5, -5) and (-5, 3) is x = -5.

the surface area of the cylinder is approximately 471 dm².

Now, For the surface area of the cylinder, we need to find the lateral area  and the area of the two circular bases.

Since, The formula for the lateral area of a cylinder is

L = 2πrh,

where r is the radius of the cylinder and h is the height.

In this case, the diameter is 10 dm,

So the radius is 5 dm.

And the height is also 10 dm.

Therefore, the lateral area is:

L = 2πrh

L = 2π(5 dm)(10 dm)

L = 100π dm²

The formula for the area of a circle is

A = πr²,

where r is the radius.

In this case, the radius is 5 dm,

So the area of each base is:

A = πr²

A = π(5 dm)²

A = 25π dm²

To find the total surface area, we add the lateral area and the area of the two bases:

SA = 2(Area of Base) + Lateral Area

SA = 2(25π dm²) + 100π dm²

SA = 50π dm² + 100π dm²

SA = 150π dm²

Substitute pi as 3.14, we can calculate:

SA ≈ 150(3.14) dm²

SA ≈ 471 dm²

Therefore, the surface area of the cylinder is approximately 471 dm².

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Answer:

  D. Square

Step-by-step explanation:

You want the best name for the quadrilateral with vertices (-3, 0), (-3, -3), (0, -3), and (0, 0).

A graph of the points is shown in the attachment. We notice the vertices are aligned with the grid, so the corner angles are all right angles.

The differences of x-coordinates and y-coordinates are both 3, so the side lengths of this rectangle are all 3 units.

The figure is all of a rectangle, rhombus, and square.

The most specific name for the figure is Square.

__

Additional comment

A trapezoid has one pair of parallel sides. This figure has two pairs of parallel sides, so is not a trapezoid.

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Answer:

It has infinite length, but no width and no thickness (It describes a Line )

Hope it helps...

Have a great day :P

The height of the sand in the display container is 12 inches when the display container is right triangular prism.

What is right triangular prism ?

A right triangular prism is a three-dimensional geometric shape with two parallel triangular bases and three rectangular faces. The rectangular faces connect the corresponding vertices of the triangular bases.

To find the height of the sand in the display container, we need to use the fact that the volume of sand in the storage container is equal to the volume of sand in the display container.

The storage container has a length, width, and height of 6 inch, 6 inch, and 6inche, respectively. Then, the volume of the storage container is:

\(V_{storage} = L * W * H = 6 * 6 * 6 = 216 inch^3\)

Similarly, let's assume that the display container has a base of length 4 inch and height 9 inches and height of sand be H.

Then, the volume of the display container is:

\(V_{display} = (1/2) * b * h * H = (1/2) * 4 * 9 * H = 18H\)

where (1/2) is the area of the triangle base of the display container.

Since the volumes of sand in both containers are equal, we can set these expressions equal to each other and solve for h:

216 = 18H

H = 12 inches

Therefore, the height of the sand in the display container is 12 inches.

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Answer:

two solutions work: x = 5 + \(\sqrt{19}\) and x = 5 - \(\sqrt{19}\)

Step-by-step explanation:

x + 6 ( 1/x ) = 10

x^2 + 6 = 10x

x^2 - 10x + 6 = 0

x = 5 + \(\sqrt{19}\), 5 - \(\sqrt{19}\)

Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

Answer:

61%

Step-by-step explanation:

16/26 x 100 = 61.538461

You have to round it up if the question tells you to round it up.

hope it helps! :)

Answer:

62%

Step-by-step explanation:

42 x 62% = 26.04

I am sorry if you get this wrong. I really hope this helps.

On solving the provided question we can say that ordinary number the answer is  1.495 x 10^0

An ordinary number, also known as a standard form number or a decimal number, is a number that is written in the familiar base-10 format, with a whole number part and a fractional part separated by a decimal point.

A) 5.1 x 10¹ as an ordinary number is 51.

B) To work out the value of (1.7 x 10¹) × (8.5 x 10-²), we first need to multiply the two numbers:

(1.7 x 10¹) × (8.5 x 10-²) = 1.7 x 8.5 x 10¹ x 10-² = 14.95 x 10-1

To express the answer in standard form, we need to move the decimal point to the left so that there is only one non-zero digit to the left of it. 14.95 x 10-1 is 1.495 x 10^0. So the answer is 1.495 x 10^0

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Answer:

4 is D, 5 is D, 6 is A, 7 is C

Step-by-step explanation:

just do da math

To solve the savings plan balance, we have to calculate the interest for 19 months. The formula for calculating interest for compound interest is given below:$$A = P \left(1 + \frac{r}{n} \right)^{nt}$$where A is the amount, P is the principal, r is the rate of interest, t is the time period and n is the number of times interest compounded in a year.

The given interest rate is 11% per annum, which will be converted into monthly rate and then used in the above formula. Therefore, the monthly rate is $r = \frac{11\%}{12} = 0.0091667$.

The monthly payment is $PMT = $250. We need to find out the amount after 19 months. Therefore, we will use the formula of annuity.

$$A = PMT \frac{(1+r)^t - 1}{r}$$where t is the number of months of the plan and PMT is the monthly payment. Putting all the values in the above equation, we get:

$$A = 250 \times \frac{(1 + 0.0091667)^{19} - 1}{0.0091667}$$$$\Rightarrow

A = 250 \times \frac{1.0091667^{19} - 1}{0.0091667}$$$$\Rightarrow

A =250 \times 14.398$$$$\Rightarrow A = 3599.99$$

Therefore, the savings plan balance after 19 months with an APR of 11% and monthly payments of $250 is $3599.99 (approx).

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