Ben sells homemade cards at a craft fair. He wants to earn more than $50 at the fair. He sells his cards for $2 and he has already earned $36. How many cards foes he need to sell to reach his goal? Write and solve an inequality.​

The length of radius from the center is 17cm

What is radius?

The radius of a circle is the distance between the center of the circle to its circumference. The radius is exactly half of the diameter. The formula of the radius can be simply derived by dividing the diameter of the circle by two.

Given, the point from the center is 8+15i

The two points are (0,0) and (8,15)

The formula to find radius is

r = \(\sqrt{(x_2^2-x_1^2)+(y_2^2-y_1^2)}\)

Therefore,

r = \(\sqrt{64+225} =\sqrt{289}\)

r = 17

Therefore, radius =17

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Answer:

1)B

2)B

3)D

4)D

5)D

6)A

7)A

8)C

1.- The sum of the internal angles in a triangle equals 180°.

8x + 5x + 6x = 180°

19x = 180

x = 180/19

x = 180/19

2.- Calculate angle ABC

ABC = 8x

ABC = 8(180/19)

ABC = 1440 / 19

ABC = 75.8°

Given:

The expressions are:

\(\sqrt[3]{24},\sqrt{48},\sqrt[3]{54},\sqrt{45}\)

To find:

The simplified form of each expression.

Solution:

We have,

\(\sqrt[3]{24}\)

It can be written as:

\(\sqrt[3]{24}=\sqrt[3]{2\times 2\times 2\times 3}\)

\(\sqrt[3]{24}=2\sqrt[3]{3}\)

Similarly,

\(\sqrt{48}=\sqrt{2\times 2\times 2\times 2\times 3}\)

\(\sqrt{48}=(2\times 2)\sqrt{3}\)

\(\sqrt{48}=4\sqrt{3}\)

And,

\(\sqrt[3]{54}=\sqrt[3]{2\times 3\times 3\times 3}\)

\(\sqrt[3]{54}=3\sqrt[3]{2}\)

In the same way,

\(\sqrt{45}=\sqrt{3\times 3\times 5}\)

\(\sqrt{45}=3\sqrt{5}\)

Therefore, the required pairs are:

\(\sqrt[3]{24}\to 2\sqrt[3]{3}\)

\(\sqrt{48}\to 4\sqrt{3}\)

\(\sqrt[3]{54}\to 3\sqrt[3]{2}\)

\(\sqrt{45}\to 3\sqrt{5}\)

The arc length is D) 3.14 meters.

What is arc length?

In mathematics, an arc is a portion of a curve that can be thought of as a segment of the curve. An arc is a connected set of points on a curve, usually a portion of a circle.

It is defined by two endpoints and all the points along the curve between them. The length of an arc is the distance along the curve between its two endpoints.

The distance along the curved line that forms the arc (a section of a circle) is measured using the arc length formula.

                                      \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

Here the give circle Radius PR = 3m and θ=60°.

Now using arc length formula then,

=> Arc length \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

=> \(A_L=\frac{60}{360} \times2\times3.14\times3\)

=> \(A_L=\frac{1}{6}\times2\times3.14\times3\)

=> \(A_L\) = 3.14 m.

Hence the arc length is D) 3.14 meters.

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Answer:

2000

Step-by-step explanation:

Step-by-step explanation:

hope this help you have a great day!

the probability that the man would have done at least as well as 22 out of 30 correct predictions by chance alone is approximately 0.149 or 14.9%, which suggests that his ESP claim may not be supported by the coin flip test results alone.

To determine the probability that the man would have gotten at least 22 correct coin flip predictions if he had no ESP, we can use a statistical tool called a binomial distribution. Assuming the coin is fair, the probability of getting any single coin flip prediction correct is 0.5, since there are only two possible outcomes (heads or tails) and they are equally likely. We can use this probability to calculate the probability of getting exactly 22 correct predictions out of 30 coin flips, which is:

P(X = 22) = (30 choose 22) {multiply} 0.5^22 {multiply} 0.5{power}8 = 0.099

This means that the probability of getting exactly 22 correct predictions by chance is less than 10%. However, the question asks for the probability of getting at least 22 correct predictions, which includes the probabilities of getting 23, 24, 25, 26, 27, 28, 29, or 30 correct predictions as well.              

To calculate this cumulative probability, we can add up the probabilities of getting each of these outcomes separately:

P(X >= 22) = P(X = 22) + P(X = 23) + ... + P(X = 30)

Using a binomial distribution table or calculator, we can find that this cumulative probability is approximately 0.149.

Therefore, the probability that the man would have done at least as well as 22 out of 30 correct predictions by chance alone is approximately 0.149 or 14.9%, which suggests that his ESP claim may not be supported by the coin flip test results alone.

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Answer:

She should buy the coat and pay for shipping

Step-by-step explanation:

Set up a proportion to express the the 80 pounds to yen.

\(\frac{2}{292.82}\) = \(\frac{80}{x}\)

2 x 40 = 80

292.82 x 40 = 11,712.80

230.50 + 25.30 = 255.8

255.80 < 11,712.80

Helping in the name of Jesus.

population at 1992 = 3590

Population after Seven years (1999) = 4500

Given two points (t1, P1) and (t2, P2), the slope of the line m can be found.

p1 = (1992, 3590) and p2 = (1999, 4500)

m= ΔP/Δt

m= ((4500-3590))/((1999-1992))

m = 910/7

m=130 is the slope

The linear population function P(t) is

P(t)=130t + P0

Find the Y-Intercept P0

The population function P(t) is measured since the year 1990, year zero. The first moose population was measured in 1992, one year later. This provides an initial condition P (1) = 4500.

P (1) =130 (1) + P0 = 4500

P0 = 4370

P(t)=20t+4630

The moose population P(t) changes linearly year after year. The population function P(t) is measured in terms of t years since 1990.

t= 1990, P (0) =4370

t =1992, P (1) =130 (1) + 4370 = 4500 matches data

t=1999, P (2) = 130(2) + 4370 = 4630

t=2006, P (3) = 130(3) + 4370 = 4760

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Answer:

k = 3 or k = -4

(Anyone can correct me if I'm wrong)

Step-by-step explanation:

\(2x=ky+2\to\ eq1\\(k+1)x=6y-3\to\ eq2\\$Change to this form: $y=mx+c\\ky=2x-2\\y=\frac{2x-2}{k}\\$gradient of eq1: $\frac{2}{k}\\6y=(k+1)x+3\\y=\frac{(k+1)x+3}{6}\\y=\frac{k+1}{6} x+\frac{3}{6}\\y= \frac{k+1}{6} x+\frac{1}{2}\\$gradient of eq1: $\frac{k+1}{6}\\$Since gradient, m, is the same for both lines,$\\\frac{2}{k}=\frac{k+1}{6}\\12=k^{2}+k\\k^{2}+k-12=0\\(k-3)(k+4)=0\\k=3 $ or $ k=-4\)

Answer:

In this section we will discuss the method of graphing an equation in two variables. In other words, we will sketch a picture of an equation in two variables.

Step-by-step explanation:

Linear equations are a subset of non-linear equations, and the equation 3xy = 9 is a non-linear equation.

The equation 3xy = 9 is not a linear equation. It is a non-linear equation. Linear equations are first-degree equations, meaning that the exponent of all variables is 1. A linear equation is represented in the form y = mx + b, where m and b are constants.

The variables in linear equations are not raised to powers higher than 1, making it easier to graph them. In contrast, non-linear equations are any equations that cannot be written in the form y = mx + b. Non-linear equations have at least one variable with an exponent that is greater than or equal to 2. Non-linear equations are harder to graph than linear equations.

The answer is false, the equation 3xy = 9 is a non-linear equation, not a linear equation. Non-linear equations are any equations that cannot be written in the form y = mx + b. They have at least one variable with an exponent that is greater than or equal to 2.

Linear equations are a subset of non-linear equations, and the equation 3xy = 9 is a non-linear equation.

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(a) the series ∑(k=1 to ∞) gk/k! converges.method to determine whether the series converges.

to determine the convergence of the series, we can apply the ratio test. let's calculate the ratio of consecutive terms:

lim(k→∞) |g(k+1)/((k+1)!) / (gk/k!)|= lim(k→∞) |g(k+1)/gk * k!/(k+1)!|

= lim(k→∞) |g(k+1)/gk * 1/(k+1)|= lim(k→∞) |g(k+1)/gk| * lim(k→∞) 1/(k+1)

= |l| * 0 (assuming l is the limit of g(k+1)/gk as k approaches infinity)

if |l| < 1, the series converges. otherwise, if |l| > 1, the series diverges. if |l| = 1, the ratio test is inconclusive.

based on the given information, it is not explicitly stated what gk represents, so we cannot determine the exact limit l. however, the fact that gk appears as a factor in the ratio suggests that it might have a significant impact on the convergence. (b) the series ∑(k=1 to ∞) k⁸⁰ * eᵏ diverges.

explanation: to determine the convergence of the series, we can apply the limit test. let's calculate the limit of the general term:

lim(k→∞) k⁸⁰ * eᵏ= ∞ * ∞ (since eᵏ approaches infinity faster than any power of k)

= ∞

since the limit of the general term is infinity, the series diverges.

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To add scientific notation with different exponents, you need to adjust the exponents so that they are equal. Once the exponents are aligned, you can add or subtract the corresponding coefficients.

First, identify the numbers in scientific notation that you want to add. Let's say you have two numbers, A and B, expressed in scientific notation as A x 10^n and B x 10^m, where n and m are the exponents.

To add these numbers, you need to adjust one of them so that the exponents are the same.

Choose the number with the smaller exponent and multiply both its coefficient and exponent by the appropriate power of 10 to match the exponent of the other number.

For example, if n < m, you would multiply number A by \(10^{m-n}\), which means multiplying the coefficient of A by \(10^{m-n}\) and keeping the exponent of 10 as n.

Once the exponents are aligned, you can add or subtract the coefficients of the adjusted numbers.

This will give you the final result in scientific notation.

It's important to note that if the exponents are significantly different, adjusting the exponents may involve multiplying or dividing by large powers of 10, which can affect the precision of the final result.

Therefore, it's advisable to retain the appropriate number of significant figures in your calculations.

In summary, to add scientific notation with different exponents, you adjust one of the numbers by multiplying its coefficient and exponent by an appropriate power of 10 to match the exponent of the other number.

Then, you can add or subtract the coefficients and express the result in scientific notation.

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The definite integral for the area of the surface generated by revolving the curve y = 6x^3 + 2x about the x-axis, over the interval 1 ≤ x ≤ 2, can be set up and evaluated as follows:

∫[1 to 2] 2πy √(1 + (dy/dx)^2) dx

To calculate dy/dx, we differentiate the given equation:

dy/dx = 18x^2 + 2

Substituting this back into the integral, we have:

∫[1 to 2] 2π(6x^3 + 2x) √(1 + (18x^2 + 2)^2) dx

Evaluating this definite integral will provide the surface area generated by revolving the curve about the x-axis.

b) The definite integral for the area of the surface generated by revolving the curve x = 4y - 1 about the y-axis, over the interval 1 ≤ y ≤ 4, can be set up and evaluated as follows:

∫[1 to 4] 2πx √(1 + (dx/dy)^2) dy

To calculate dx/dy, we differentiate the given equation:

dx/dy = 4

Substituting this back into the integral, we have:

∫[1 to 4] 2π(4y - 1) √(1 + 4^2) dy

Evaluating this definite integral will provide the surface area generated by revolving the curve about the y-axis.

By setting up and evaluating the definite integrals for the given curves, we can find the surface areas generated by revolving them about the respective axes. The integration process involves finding the appropriate differentials and applying the fundamental principles of calculus.

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There would be the alcohol content from 2 drinks remaining in the body after 2 hours.

It is commonly estimated that the body can metabolize about one standard drink per hour.

Multiply the rate of metabolism (1 drink per hour) by the number of hours (2 hours).

1 drink/hour × 2 hours = 2 drinks

Subtract the number of drinks metabolized (2 drinks) from the initial number of drinks consumed (4 drinks).

The alcohol content remaining in the body:

4 drinks - 2 drinks = 2 drinks

Therefore, after 2 hours, there would be the alcohol content from 2 drinks remaining in the body.

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Since the chi-square test statistic is larger than the critical value, we may conclude that there is not enough evidence to conclude that cigarette tar level is associated with lung cancer. The correct option is b.

In a chi-square test, the null hypothesis states that there is no association between the variables being tested (in this case, cigarette tar level and lung cancer), while the alternative hypothesis suggests there is an association.

The chi-square test statistic measures the deviation between the observed and expected frequencies under the null hypothesis.

In this case, the chi-square test statistic is found to be 14.44, which is larger than the 5%-level critical value of 12.59. However, it is important to note that the critical value is used to determine the rejection region for the null hypothesis, not to directly compare with the test statistic.

The p-value, which is calculated based on the test statistic, is given as 0.025.

The correct interpretation of the results is based on the p-value. Since the p-value (0.025) is less than the significance level (0.05), there is evidence to reject the null hypothesis.

However, the chi-square test alone does not provide information about the direction or strength of the association. Therefore, it is incorrect to conclude that cigarette tar level is associated with lung cancer.

The correct conclusion is that there is not enough evidence to conclude that cigarette tar level is associated with lung cancer based on the results of the chi-square test.

Additional analysis or further studies are needed to investigate the relationship between cigarette tar level and lung cancer more thoroughly.

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The amount of border that Roberto will need to put around the edges of the platform, given the area is 16 units.

The platform is given in the figure and to find the amount of border that Roberto needs to cover it if the area is 12 square units, you need to count the number of dots all along the edges of the platforms.

Counting this would give us 16 dots. This then means that Roberto needs sixteen units of border to be able to put up a border around the edges of the platform.

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So we take 6 out of each term so it is \(6(4+3v)\) hope this helped.

Answer:

hey bby

Step-by-step explanation:

Answer:

step 2

Step-by-step explanation:

step 2 is supposed to be (-26.7 multiply by 3) since the reciprocal of 1/3 is 3 and not -3. the answer should be -80.1 instead of 80.1

Answer:

x = -12

Step-by-step explanation:

-10x+1+7x=37

Combine like terms

-3x+1 = 37

Subtract 1 from each side

-3x+1-1 = 37-1

-3x = 36

Divide by -3

-3x/-3 = 36/-3

x = -12

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

r=√−200x

r=−√−200x

Answer:

25n=I

Step-by-step explanation:

Because 25 dollars per customer, (so multiply) = the daily income.

Answer:

Step-by-step explanation:

To find the point on the line y = 2x + 3 that is closest to the origin (0,0), we can use the concept of the shortest distance between a point and a line.

The line y = 2x + 3 can be rewritten as 2x - y + 3 = 0 in standard form. The distance between a point (x, y) and the line can be calculated using the formula:

distance = |Ax + By + C| / √(A² + B²)

In this case, A = 2, B = -1**, and **C = 3. Plugging these values into the formula, we can calculate the distance between the origin and the line.

The point on the line that is closest to the origin is the one where the distance is minimized. By finding the point that satisfies the minimum distance condition, we can determine the coordinates of the point.

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Answer:

A

Step-by-step explanation:

yes, Corelise does have more than stephan

Answer:

Step-by-step explanation:

Assuming the parking lot is along both widths of the field and only once along the length:

the length is (300 - 2x)

the width is (200 -x)

the area is (300-2x)(200-x) = 30000

         60000 -300x - 400x +2x^2 = 30000

        2x^2 -700x + 30000 = 0

         x^2 - 350x + 15000 = 0

          (x    -   300    )(x   -    50    ) = 0

             x = 300 or x=50

x=300 results in negative measures.

the parking lot is x=50 wide

the length of the field is 200, the width of the field is 150

Answer:

quadratic

Step-by-step explanation:

hope you got it

Answer:

C = ( -7 , 6 )

R = 2

SO ...

The ANSWER is "A"