You are mowing lawns to earn money to buy a new video game system which costs at least $500. You plan to save every dollar you earn. In addition, you want to be able to to afford the accessories for the video game (i.e. controllers, games, etc). You already have $150. you charge 9.50 per hour. Write an inequality equation to show how many hours you need to work before you have enough money to purchase the video game and its accessories.

a) Inequality equation:

b) How many hours must you work? (Hint: solve for x):​

Answer:

Interquartile Range: 8

Step-by-step explanation:

25th Percentile: 13

50th Percentile: 17

75th Percentile: 21

So the answer must be 8

Hope this helps :)

Answer:

the area is 207

Step-by-step explanation:

The equation to solve the area of a cylinder is A=2πrh+2πr^2

The radius is the length from the outside to the center, 6 is the diameter so we could half that to get the radius, 3 and height is 8

A=2*3.14*3*8+2*3.14*3^2

A=6.28*3*8+6.28*9

A=18.84*8+56.52

A=150.72+56.52

A=207.24

207.24 rounded to the nearest whole number is 207 so your area is 207

Answer:

15

Step-by-step explanation:

Pretend a is the number.

We have: 31 + 3a = 76

=> 3a = 76 - 31 = 45

=> a = 45/3

=> a = 15

Answer: 3 cm

Step-by-step explanation:

The formula for the area of a circle is A = πr², where A is the area and r is the radius. We are given that the area of the circle is 28½ cm².

So, 28½ = πr²

We need to solve for r. Dividing both sides by π, we get:

r² = 28½/π

r² = 9

Taking the square root of both sides, we get:

r = 3√1 = 3 cm

Therefore, the radius of the circle is 3 cm.

The function that has a range of y < 3 is \(y = -2^x+3\).

Using a graphing tool

Let's graph each of the cases to determine the solution of the problem

case A) \(y = 3(2^x)\)  

The range is the interval--------> (0,∞)

y > 0

therefore

the function \(y = 3(2^x)\) is not the solution

case B) \(y = 2(3^x)\)

The range is the interval--------> (0,∞)

y > 0

therefore

the function \(y = 2(3^x)\) is not the solution

case C)  \(y = -2^x+3\)

The range is the interval--------> (-∞,3)  

y < 3

therefore

the function \(y = -2^x+3\) is the solution

case D)  \(y = 2^x-3\)

The range is the interval--------> (-3,∞)  

y > -3

therefore

the function \(y = 2^x-3\) is not the solution

Hence the answer is the function that has a range of y < 3 is \(y = -2^x+3\).

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Answer:

79-83= 2

84-88 =4

89-93= 5

94-98=2

Step-by-step explanation:

put in order then you can just count them

Answer:

Step-by-step explanation:

Maggie made the following quilt from 64 square pieces of fabric, what is the side length of each square piece

Answer:

huh

Step-by-step explanation:

Answer: 1.6

Step-by-step explanation:

each golf is 1.6 ounces and you 20 golf balls in order to reach 32 ounces

Answer:

shown below

Step-by-step explanation:

golf balls per ounce = 5/8 or 0.625

ounces per gold ball = 8/5 or 1.6

Answer:

$6,872.05

Explanation:

The maturity value of the loan can be calculated as:

Where P is the initial amount, r is the interest rate as a decimal and t is the time in years.

4.25% is equivalent to: 4.25/100 = 0.0425

91 days are equivalent to 91/365 = 0.25 years

Then, the maturity value is equal to:

So, the maturity value of the loan is $6,872.05

a. The value of c in the probability mass function when x is a discrete random variable is 0.15

b. The value of P(x > 3)  is 0.25

c. The value of P(3 ≤ x ≤ 5) is 0.15

d.  the probability that x is less than 6 given that it is greater than or equal to 1 is approximately 0.353.

In probability mass function, sum of the probabilities for all possible values of x must be equal to 1

Thus,

0.2 + 2c + 0.2 + c + 0.1 = 1

Solve for c

c = 0.15

Hence, the probability mass function for x can be rewritten as;

x:      0     1     2   4     10

p(x): 0.2 0.3 0.2 0.15 0.1

To find P(x > 3), add the probabilities for all values of x that are greater than 3. The values greater than 3 are 4 and 10

sum of their  probabilities

P(x > 3) = P(x = 4) + P(x = 10)

= 0.15 + 0.1

= 0.25

To find P(3 ≤ x ≤ 5),sum the probabilities for all values of x between 3 and 5, inclusive:

P(3 ≤ x ≤ 5) = P(x = 4)

= 0.15

To find P(x < 6 | x ≥ 1), use the formula for conditional probability:

P(x < 6 | x ≥ 1) = P(x < 6 and x ≥ 1) / P(x ≥ 1)

To find the numerator, we sum the probabilities for all values of x between 1 and 5, inclusive

P(x < 6 and x ≥ 1) = P(x = 1) + P(x = 2) + P(x = 4)

= 0.3

To find the denominator, we sum the probabilities for all values of x greater than or equal to 1:

P(x ≥ 1) = P(x = 1) + P(x = 2) + P(x = 4) + P(x = 10)

= 0.85

Therefore, we have

P(x < 6 | x ≥ 1) = (0.3 / 0.85) ≈ 0.353

Thus, the probability that x is less than 6 given that it is greater than or equal to 1 is approximately 0.353.

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If there are 95 families to feed then each family will receive 11 cans of assorted tins.

Assorted tins typically refer to cans or containers of food items that come in different varieties or flavors.

To calculate the number of cans each family will receive, we need to first determine the total number of cans in the 19 boxes.

19 boxes × 55 cans per box = 1045 cans

Now we can divide the total number of cans by the number of families to determine the number of cans each family will receive:

1045 cans ÷ 95 families = 11 cans per family (rounded to the nearest whole number)

Therefore, each family will receive 11 cans of assorted tins.

For example, a box of assorted tins may contain cans of different types of vegetables, fruits, soups, or other food items. The specific assortment may vary depending on the context and the supplier. In the context of the given question, the 19 boxes of assorted tins likely contain cans of different types of food that will be packed into food parcels for the poor.

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The surface area of the triangular base pyramid is 19.75 mm².

The surface area of a triangular pyramid is the sum of the area of the whole sides of the triangular pyramid.

Therefore,

Surface area of a triangular pyramid = base area + 1 / 2 (perimeter × slant height)

The base of the triangular pyramid is an equilateral triangle. An equilateral triangle has congruent sides.

Therefore,

base area = 1 / 2 × 5 × 4.3

base area = 10.75 mm²

Hence,

perimeter of the base = 5 + 5 + 5 = 15 mm

Surface area of a triangular pyramid = 10.75 + 1 / 2 (15 × 3)

Surface area of a triangular pyramid = 10.75 + 1 / 2(18)

Surface area of a triangular pyramid = 10.75 + 9

Surface area of a triangular pyramid = 19.75 mm²

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Answer:

n = 10

Step-by-step explanation:

6(3n - 11) = n + 104

18n - 66 = n + 104

17n = 170

n = 10

Using the Green's Theorem, the one along which the work done by the force is 11π/16.

In the given question we have to find the one along which the work done by the force is the greatest.

The given closed curves in the plane is

\(F(x,y)=\left(\frac{x^{2}y}{4} + \frac{y^3}{3}\right)\hat{i}+x\hat{j}\)

Suppose C be a simple smooth closed curve in the plane. It is also oriented counterclockwise.

Let S be the interior of C.

Let P = \(\frac{x^{2}y}{4} + \frac{y^3}{3}\) and Q = x

So the partial differentiation is

\(\frac{\partial P}{\partial y}=\frac{x^2}{4}+y^2\) and  \(\frac{\partial Q}{\partial x}\) = 1

By the Green's Theorem, work done by F is given as

W= \(\oint \vec{F}d\vec{r}\)

W= \(\iint_{S}\left ( \frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y} \right )dxdy\)

W= \(\iint_{S}\left ( 1-\frac{x^2}{y}-y^2 \right )dxdy\)

Let C = x^2+y^2 = 1 and

x = rcosθ, y = rsinθ

0≤r≤1; 0≤θ≤2π

There;

W = \(\int_{r=0}^{1}\int_{\theta=0}^{2\pi}\left ( 1-\frac{r^2\cos^2\theta}{4}-r^2\sin^2\theta \right )\left|\frac{\partial(x,y)}{\partial{r,\theta}}\right|d\theta dr\)

and \(\frac{\partial (x,y)}{\partial(r, \theta)}=\left|\begin{matrix}\cos\theta &-r\sin\theta \\ \sin\theta & r\cos\theta\end{matrix} \right |\) = r

Thus;

W = \(\int_{r=0}^{1}\int_{\theta=0}^{2\pi}\left ( 1-\frac{r^2\cos^2\theta}{4}-r^2\sin^2\theta \right )rd\theta dr\)

After solving

W = 11π/16

Hence, the one along which the work done by the force is 11π/16.

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The right question is:

Among all simple smooth closed curves in the plane, oriented counterclockwise, find the one along which the work done by the force:

\(F(x,y)=\left(\frac{x^{2}y}{4} + \frac{y^3}{3}\right)\hat{i}+x\hat{j}\)

is the greatest. (Hint: First, use Green’s theorem to obtain an area integral—you will get partial credit if you only manage to complete this step.)

Answer:

311.3 feet

Step-by-step explanation:

1 yard = 3 feet

Therefore, 103.76 yards = 311.28 feet (by multiplying 103.76 by 3)

Rounding to the nearest tenth gives us 311.3 feet.

Answer:

\(\mathbf{g(x) = \sum \limits^{\infty}_{n=0} (-1 + (\dfrac{-1}{6})^n)x^n }\)

and the interval of the convergence is (-1, 1)

Step-by-step explanation:

To find a power series for the function, centered at c.

\(g(x) = \dfrac{7x}{x^2 +5x-6} ,\ c = 0\)

If we factorize the denominator, we have:

\(g(x) = \dfrac{7x}{(x +6)(x-1)}\)

\(g(x)= \dfrac{1}{x-1}+\dfrac{6}{x+6}\)

Thus;

\(g(x)= \dfrac{-1}{1-x}+\dfrac{1}{1+\dfrac{x}{6}}\)

\(g(x)= \dfrac{-1}{1-x}+\dfrac{1}{1-(-\dfrac{x}{6})}\)

\(g(x) = - \sum \limits^{\infty}_{n=0} x^n + \sum \limits^{\infty}_{n=0} x^n(\dfrac{-x}{6})^n \ \ if \ \ |x| < 1 \ \ and \ \ |\dfrac{x}{6}< 1\)

\(g(x) = \sum \limits^{\infty}_{n=0} (-1 + (\dfrac{-1}{6})^n)x^n , \ if |x|<1\)

\(\mathbf{g(x) = \sum \limits^{\infty}_{n=0} (-1 + (\dfrac{-1}{6})^n)x^n }\)

and the interval of the convergence is (-1, 1)

Answer:

answer a

a.

x = -11 or x = -1

Answer:

20 mph

Step-by-step explanation:

If it took the car originally 12 minutes to travel the road with an average speed of 60 mph. Than you would just divide the average speed by three because it is taking 3 times the amount of time than it would originally.

36/12=3

60/3=20

20 mph

In this problem, we have different expressions involving products, by applying the distributive law for the multiplication we can generate equivalent expressions.

The distributive law for multiplication says that:

Example

14. 8 (4x + 9)

By applying the distributive law, we have:

Which is an equivalent expression, and it is the answer.

Answer

For point 14, 8 (4x + 9), the answer is 32x + 72.

Answer:

Step-by-step explanation:

Given the sample data 2 6 15 9 11 22 1 4 8 19, before we can get the standard deviation, we need to first calculate the mean.

mean = 2 +6 +15 +9 +11 +22 +1 +4 +8 +19/10

mean = 97/10

mean = 9.7

Standard deviation for ungrouped data is expressed using the formula;

\(S = \sqrt{ \dfrac{\sum(x-\overline x)^2}{n-1} }\)

\(\overline x \ is\ the \ mean\\n \ is \ sample \ size\)

\(S = \sqrt{\frac{(2-9.7)^2+(6-9.7)^2+(15-9.7)^2+(9-9.7)^2+(11-9.7)^2+(22-9.7)^2+(1-9.7)^2+(4-9.7)^2+(8-9.7)^2+(19-9.7)^2}{10-1} }\\ S = \sqrt{\frac{(-7.7)^2+(-3.7)^2+(5.3)^2+(-0.7)^2+(1.3)^2+(12.3)^2+(-8.7)^2+(-5.7)^2+(-1.7)^2+(9.3)^2}{10-1} }\\\\S = \sqrt{\dfrac{59.29+13.69+28.09+0.49+1.69+151.29+75.69+32.49+2.89+86.49}{10-1} }\\\\\\S = \sqrt{\dfrac{452.1}{9} }\\\\S = \sqrt{50.23}\\ \\S = 7.08\\\\S \approx 7.1\)

Hence the standard deviation of the sample data is 7.1

Answer:

We have 300 edges and 200 vertices

Step-by-step explanation:

A prism is basically a 2D shape which extends into three dimensions. Thus, it has two end faces, and one face for each side on the original shape.

In addition to the two 100-sided polygons at top and bottom, the prism will also have 100 rectangular faces.

We will solve this by Euler’s formula which ks:

V - E + F = 2

where;

V is the number of vertices (corners),

E is the number of edges

F is the number of faces (of any polyhedron).

Number of vertices is 100 surrounding the top while it's 100 at the bottom. So total V = 100 + 100 = 200 .

The number of edges is 100 at the top, and 100 at the bottom. Also an additional 100 separating the hundred vertical faces.

Total number of edges is;

E = 100 + 100 + 100 = 300.

Thus, we have 300 edges and 200 vertices

Answer:

Isosceles

Step-by-step explanation:

Answer: It is an Isosceles triangle because two sides are equal. Hope this helps!

Answer:

3:5

Step-by-step explanation:

To find the simplest ratio, divide each number by 2:

6/2

= 3

10/2

= 5

So, the simplest ratio of triangles to squares is 3:5

Answer:

Step-by-step explanation:

\(hope \: it \: helps\)

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The variance of a distribution is the square of the standard deviation

The variance of the data is 9

The given parameters are:

Mean = 9 cars

Distribution type = Poisson distribution

The variance and the mean of a Poisson distribution are equal.

So, we have:

Variance = 9 cars

Hence, the variance of the data is 9

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Answer:

Please find attached pdf

Step-by-step explanation:

The requried measure of the ARC(WVY) is 250°. Option C is correct.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
We know that the tangent subtended to the circle from a common point then,
larger arc - smaller arc / 2 = angle between the tangent
10a - 4a -10 / 2 = 70
6a = 140 + 10
a = 150/6
a = 25

Now,

arc(WVY) = 10a = 10*25
                         = 250°

The requried, measure of the ARC(WVY) is 250°. Option C is correct.

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