A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
y=-x^2+51x-201

Answer:

area=½×base×height

=½×10×70

=½×700

=350cm²

Answer:

40,924.79

Step-by-step explanation:

To calculate the approximate user base 13 months from now, we need to apply a 4.1% growth rate to the current user base of 25,220 for each month.

First, let's convert the growth rate to decimal form: 4.1% = 0.041.

To find the user base after one month, we can multiply the current user base by the growth rate:

User base after one month = 25,220 + (25,220 * 0.041)

User base after one month ≈ 25,220 + 1,034.02 ≈ 26,254.02

Next, we repeat this process for the subsequent months, compounding the growth each time. After two months:

User base after two months ≈ 26,254.02 + (26,254.02 * 0.041) ≈ 27,309.36

We continue this calculation for a total of 13 months:

User base after three months ≈ 27,309.36 + (27,309.36 * 0.041) ≈ 28,391.16

User base after four months ≈ 28,391.16 + (28,391.16 * 0.041) ≈ 29,500.57

User base after five months ≈ 29,500.57 + (29,500.57 * 0.041) ≈ 30,638.69

User base after six months ≈ 30,638.69 + (30,638.69 * 0.041) ≈ 31,806.89

User base after seven months ≈ 31,806.89 + (31,806.89 * 0.041) ≈ 33,006.55

User base after eight months ≈ 33,006.55 + (33,006.55 * 0.041) ≈ 34,238.09

User base after nine months ≈ 34,238.09 + (34,238.09 * 0.041) ≈ 35,502.95

User base after ten months ≈ 35,502.95 + (35,502.95 * 0.041) ≈ 36,802.57

User base after eleven months ≈ 36,802.57 + (36,802.57 * 0.041) ≈ 38,138.42

User base after twelve months ≈ 38,138.42 + (38,138.42 * 0.041) ≈ 39,511.98

User base after thirteen months ≈ 39,511.98 + (39,511.98 * 0.041) ≈ 40,924.79

The point on the line which is closes to the point ( -, ) would be (49/9, -10/7).

Having obtained the minimum distance between (-3, 4) and the line, we now seek to locate the precise point on that line. Achieving this requires a comprehension of the perpendicular line concept. Identifying where the line encountering the pivot point in question and intersecting the reference line perpendicularly is crucial for determining the closest point present on the line.

At present, the slope of the perpendicular line as well as its passing point (-3, 4) have been successfully determined. Employing the point-slope method we can obtain the equation representing the aforementioned perpendicular line:

-2x + 4 - 28 = 7x + 21

-9x = -49

x = 49/9

We can then use x to find y:

y = ( - 2 ( 49 / 9 ) + 4 ) / 7

y = (4 - 98 / 9 ) / 7

y = ( - 90 / 9) / 7

y = -10 / 7

So, the point on the line closest to the point (-3, 4) is ( 49 / 9, -10 / 7 ).

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Answer:

2 1/3

Step-by-step explanation:

7/3 = 2 1/3 or 2.33333333333333333333333333333333333333333333333333333333333333....

The given expression can be written as a Riemann sum with Δx = 1/n and xi = i/n, where i = 1, 2, ..., n. Thus, we have:
lim n→∞ ∑i=1n (2+i/n)² (1/n) = lim n→∞ ∑i=1n [(2/n)² + 4i/n³ + (i/n)²] = lim n→∞ [(2/n)² ∑i=1n 1 + 4/n³ ∑i=1n i + (1/n²) ∑i=1n i²]

Using the formulas for the sum of the first n natural numbers and the sum of the squares of the first n natural numbers, we can simplify this expression to:
lim n→∞ [(2/n)²n + 4/n³(n(n+1)/2) + (1/n²)(n(n+1)(2n+1)/6)]
Taking the limit as n approaches infinity, we see that the first term goes to 0, the second term goes to 0, and the third term goes to 1/3. Therefore, we have:
lim n→∞ ∑i=1n (2+i/n)² (1/n) = 1/3
Thus, the definite integral that is equal to this limit is:
∫₀¹ (2+x)² dx = [x³/3 + 4x²/2 + 4x]₀¹ = (1/3) + 4 + 8 = 28/3
Therefore, the definite integral that is equal to the given limit is 28/3.

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Answer:11 kids were at the party

Step-by-step explanation:24 slices in all , 22 were eaten so that means 22 divided by 11 is 2 so there was 11 kids

Answer:

11 children

Step-by-step explanation:

First you have to do 8 times 3 to get the number of slices of pizza there were.

Then you have to divided that by 2. But remember, there are 2 slices left.

So, you have to take away one child to get the answer: 11 children

I feel bad for that last child. I hope this helped ;)

The correct angle for a ladder is about 75 degrees from the ground, and you have a 15-foot ladder.

You need to determine how far from the house you should position the ladder's base if you know these fact.
Step 1: It is crucial to keep in mind that the height of the ladder is the same as the vertical distance between the base and the wall.
Step 2: Consider the height of the ladder to be the "opposite" side of the triangle, and the distance you want to find as the "adjacent" side of the triangle. In this scenario, we're looking for the distance from the house (the base of the ladder) to the wall, which will be the adjacent side.
Step 3: To figure out the length of the adjacent side, we'll need to use the tangent of the angle, which is given by the following formula:tan(θ) = opposite/adjacent
Step 4: The angle is 75 degrees, and the opposite side's length is 15 feet, so we can solve for the adjacent side as follows: tan(75) = 15/adjacent
Step 5: Rearranging the equation: adjacent = 15/tan(75)Step 6: Using a calculator, tan(75) is approximately 3.732, so: adjacent = 15/3.732 ≈ 4.01

Therefore, the base of the ladder should be approximately 4.01 feet from the wall (rounded to the hundredths place).

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If the assumptions for normality and equality of variances are badly violated, nonparametric statistics should be used to test the hypothesis.

In hypothesis testing, it is important to consider the assumptions underlying the statistical tests.

Two common assumptions are normality and equality of variances.

Normality assumes that the data follow a normal distribution, while equality of variances assumes that the variability of the groups being compared is similar.

When these assumptions are badly violated, meaning the data deviate significantly from normality or the variances are highly unequal, parametric tests that rely on these assumptions may not be appropriate.

In such cases, nonparametric statistics provide an alternative approach.

Nonparametric tests do not require the assumption of a specific distribution or equal variances.

These tests are based on ranks or orderings of the data rather than the actual numerical values. They are more robust to violations of the assumptions and can be used to analyze data that are not normally distributed or have unequal variances.

Examples of nonparametric tests include the Mann-Whitney U test for comparing two independent groups, the Kruskal-Wallis test for comparing multiple independent groups, and the Wilcoxon signed-rank test for paired samples.

By using nonparametric tests in situations where the assumptions for normality and equality of variances are badly violated, researchers can still make valid statistical inferences without relying on these assumptions.

However, it is important to note that nonparametric tests may have less statistical power compared to their parametric counterparts when the assumptions are met.

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Answer:

No it is not

Step-by-step explanation:

Answer:

y = ax2 + bx + c

Step-by-step explanation:

1) Standard form: y = ax2 + bx + c where the a,b, and c are just numbers.

2) Factored form: y = (ax + c)(bx + d) again the a,b,c, and d are just numbers.

3) Vertex form: y = a(x + b)2 + c again the a, b, and c are just numbers.

We need to take into account the prerequisites for utilising normal approximation methods in order to establish whether the sample size of 81 persons is sufficient to compute a confidence interval for the percentage of U.S. adults who spend more than 20 hours a week on a home computer.

Typically, both the sample size and the anticipated number of successes and failures need to be sizable for the normal approximation to be reliable. In cases where n is the sample size and p is the estimated proportion, a general rule of thumb is that both np and n(1-p) should be larger than or equal to 5.Out of 81 people, we have 36 successes in this situation (those who use a computer for more than 20 hours). The projected percentage is p.

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An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a fixed number to the previous term

The first term of an arithmetic sequence is denoted by 'a₁', the second term by 'a₂', and so on.

Given that;

Un = a + (n - 1)d

U50 = 4 + (50 - 1) 2

U50 = 102

Then;

Un = ar^n-1

U10 = 1000(1/2)^9

U10 = 1.95

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Answer: To estimate the number of people who want the toll road in their city, we can use the percentage range provided and calculate the interval estimate. Here's how you can do it:

Therefore, the interval estimate for the number of people who want the toll road in their city is (123,442, 225,608).

The conclusion from the equation |y + 6| = 2 is that it has two solutions , the correct option is (b) .

In the question ,

it is given that ,

the equation is given as |y \(+\) 6| \(=\) 2 ,

after removing the modulus  , we get the two equations , that are

y + 6 = 2 and y + 6 = -2

Solving y + 6 = 2 , we get

y + 6 = 2

Subtracting 6 from both LHS and RHS ,

we get

y = 2 - 6

y = -4

On Solving y + 6 = -2 ,

we get

y + 6 = -2,

Subtracting 6 from both LHS and RHS ,

we get

y = - 2 - 6

y = -8 .

the two solutions are y = -8 and y = -4 .

Therefore , The conclusion from the equation |y + 6| = 2 is that it has two solutions , the correct option is (b) .

The given question is incomplete , the complete question is

Consider this equation. |y + 6| = 2 what can be concluded of the equation? check all that apply.

(a) There will be one solution

(b) There will be two solutions.

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1. For the differential equation 3.1, the general solution is y = (C₁ + C₂e³x) + (1/2)e¹x - (1/2)cos 2x, where C₁ and C₂ are arbitrary constants.

2. For the differential equation 3.2, the general solution is y = (C₁cos(2x) + C₂sin(2x))e^(−x) + (1/5)sin 2x + (1/10)cos 2x, where C₁ and C₂ are arbitrary constants.



1. To find the general solution for equation 3.1, we first determine the characteristic equation by replacing D² with r², D with r, and solving r² - 5r + 6 = 0. The roots are r₁ = 2 and r₂ = 3. Thus, the homogeneous solution is y_h = C₁e²x + C₂e³x, where C₁ and C₂ are constants.

Next, we find the particular solution for the inhomogeneous term e¹x + sin 2x. Assuming y_p = Ae¹x + Bcos 2x + Csin 2x, we substitute it into the differential equation and equate coefficients. Solving the resulting equations, we find A = 1/2, B = -1/2, and C = 0. Therefore, the particular solution is y_p = (1/2)e¹x - (1/2)cos 2x.

Finally, the general solution is y = y_h + y_p, giving y = (C₁ + C₂e³x) + (1/2)e¹x - (1/2)cos 2x.

2. For equation 3.2, the characteristic equation is r² + 2r + 4 = 0, which has complex roots r₁ = -1 + 2i and r₂ = -1 - 2i. The homogeneous solution is y_h = (C₁cos(2x) + C₂sin(2x))e^(-x), where C₁ and C₂ are constants.

To find the particular solution for e²sin 2x, we assume y_p = (Acos 2x + Bsin 2x)e^(-x). Substituting it into the differential equation and solving the resulting equations, we obtain A = 1/10 and B = 1/5. Thus, the particular solution is y_p = (1/10)cos 2x + (1/5)sin 2x.

Combining the homogeneous and particular solutions, the general solution is y = y_h + y_p, giving y = (C₁cos(2x) + C₂sin(2x))e^(-x) + (1/5)sin 2x + (1/10)cos 2x.

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Answer:

8x^3+1

Step-by-step explanation:

power rule

d/dx (ax^b) = (abx^(b-1))

Answer:d/dx (ax^b) = (abx^(b-1))

Step-by-step explanation:

No explanation

Answer:

192

Step-by-step explanation:

12 x 8 x 4 x1/2 = 192

192

An algebraic expression which models the given context would be written as s + 0.02s = 1.05s.

Price can be define as an amount of money which is primarily set by the seller of a good (product), and it must be paid by a buyer to the seller, so as to enable the acquisition of this good (product).

An algebraic expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

Let s represent the price of a pair of shoes.

Therefore, an algebraic expression which models the given context would be written as follows:

s + 0.02s = 1.05s.

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The midpoints of the given coordinates and the distance between coordinates are calculated below.

1a) Coordinates of midpoint of (-4, 2), (3, 3) is;

Midpoint Coordinate = (-4 + 3)/2, (2 + 3)/2 = (-1/2, 5/2)

1b) Coordinates of midpoint of (-1, 0), (-3, -4) is;

Midpoint Coordinate = (-1 - 3)/2, (-4 + 0)/2 = (-2, -2)

2) One endpoint = (-5, 4)

Midpoint = (-10, -6)

Thus;

Coordinate of other endpoint is;

(-5 + x)/2, (4 + y)/2 = (-10, -6)

-5 + x = -20

x = -15

4 + y = -12

y = -16

(x, y) = (-15, -16)

3) Distance between the two coordinates (-3, 6) and (2, 1) is;

d = √[(2 + 3)² + (1 - 6)²]

d = √100

3b) Distance between the two coordinates (7, 6) and (0, 2) is;

d = √[(0 - 7)² + (2 - 6)²]

d = √64

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Answer:

After Rajesh took 493 stones, you would have 471 stones left.

Step-by-step explanation:

If you started with 964 stones and Rajesh took 493 stones, then you would have 964 - 493 = 471 stones left.

Answer:

Step-by-step explanation:

\( \frac{ {b}^{10} }{ {b}^{6} } \)

Using the rules of indices

That's

\( \frac{ {a}^{x} }{ {a}^{y} } = {a}^{x - y} \)

Since the bases are the same and are dividing we subtract the exponents

So we have

\( \frac{ {b}^{10} }{ {b}^{6} } = {b}^{10 - 6} \)

We have the final answer as

Hope this helps you

Answer:

b⁴

Step-by-step explanation:

b¹⁰ / b⁶ = b¹⁰ ⁻⁶ = b⁴

The scientific notation for the answer to 1.9×10⁷*3×10⁶ is 5.7×10¹³.

An exponent is a number or letter placed above and to the right of the base of a mathematical statement. It denotes that the base will be raised to a specific level of power. Exponents are classified into four types: positive, negative, zero, and rational. Positive exponents indicate how many times a base may be multiplied by itself. The number of times a number is multiplied by itself is referred to as its exponent. For instance, 2 to the third (written as 23) means: 2 x 2 x 2 = 8. 2 x 3 = 6 does not equal 23. Keep in mind that a number raised to the power of one is itself.

Here,

=1.9×10⁷*3×10⁶

=5.7×10⁽⁷⁺⁶⁾

=5.7×10¹³

The scientific notation for the result of 1.9×10⁷*3×10⁶ is 5.7×10¹³.

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The sum of the numerator and denominator of the decimal is found as 111.

As for the given question;

The decimal number is given as;

0.12 bar

Decimal to fraction conversion

100(0.12 bar) = 12(0.12 bar)

99.(0.12bar) = 100(0.12bar) - (0.12 bar)

99.(0.12bar) = 12 × 0.12bar - 0.12bar

99.(0.12bar) = 12

0.12 bar = 12/99 (lowest fraction)

Thus, in the result the numerator is found as 12 and the denominator is found as 99.

Add = 12 + 99

Add = 111

Thus, the sum of the numerator and denominator of the decimal is found as 111.

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Answer:

y = 2

Step-by-step explanation:

-2y + 1 = y-5

-2 - y = -5 - 1

-3y = -6

y = -6 ÷ -3

y = 2

The area of each slice of the cake is 3π  square inches

The cake is 12 inches in diameter. The cake top is circular.

Therefore, the area of a circle is as follows;

area of a circle = πr²

where

Therefore,

r = diameter / 2

r = 12 / 2

r = 6 inches

Hence,

area of a circle = π × 6²

area of a circle = 36π

area of each sliced cake = 36π / 12  

area of each sliced cake = 3π  square inches

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