Marcus charges 130$ per week to pet sit. Next week he is offering an 18% discount. What is the amount of the discount?

The slope of the graph is the same positive value that is 0.75.

Hence the correct option is (1).

We know that the equation of a straight line with slope 'm' and y intercept 'c' is given by,

y = mx + c

Here the model equation

c = 0.75h, where c is the total cost to buy hotdogs

h is the number of hotdogs bought

And 0.75 is the price of one hotdog

Now we can clearly say that c = 0.75h will make a straight line coordinate plane.

Now comparing the equation with slope intercept equation of straight line we get,

m = 0.75 and c = 0

So the slope of the line represented by model equation = 0.75 which is a positive number.

y intercept  = 0.

We know that the slope of one particular straight line on cartesian plane is unique.

So, the slope of the graph is the same positive value.

Hence the correct option is (1).

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Answer:

h = 15 cm

Step-by-step explanation:

Given:

C (base's circumstance) = 48π cm

V (volume) = 8640π cm^3

Find: h (height) - ?

[tex]c = 2\pi \times r[/tex]

[tex]2\pi \times r = 48π[/tex]

[tex]r = 24[/tex]

We found the radius

[tex]v = \frac{1}{3} \times \pi {r}^{2} \times h[/tex]

[tex] \frac{1}{3} \times \pi \times {24}^{2} \times h = 8640π[/tex]

Multiply the whole equation by 3 to eliminate the fraction:

[tex]1728\pi \times h = 25920\pi[/tex]

[tex]h = 15[/tex]

The real-world problem is modeled by the proportion 66/100 = x/2,500, where 66 is the sample proportion and 2,500 represents the population size.

To find the value of x, which represents the number of individuals with a specific characteristic in the population, follow these steps:

1. Cross-multiply the terms in the proportion:
  66 * 2,500 = 100 * x
2. Simplify the equation:
  165,000 = 100x
3. Divide both sides by 100 to isolate x:
  x = 1,650

Thus, 1,650 individuals in the population share the specific characteristic represented by the sample proportion. This proportion helps us understand and predict the prevalence of a certain characteristic or behavior within a larger population, based on the information gathered from a smaller sample.

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The distance that shows how much farther (in km) from the sun is Saturn than Venus is: [tex]1.2 * 10^9[/tex] km.

According to the table, the distance of Saturn from the Sun is [tex]1.4 * 10^{9}[/tex] and the distance of Venus from the Sun is [tex]1.1 * 10^{8}[/tex] .

Now to determine how much further from the Sun is Saturn than Venus, we will subtract the distance of the planet with the higher distance span from the one with the lower distance.

So our calculation will go thus:

[tex]1.4 * 10^9 - 1.1 * 10^8 = \\140000000 - 11000000 = 1290000000\\= 1.29 * 10^9[/tex]

From the calculation above, we can see how much further from the sun, is Saturn than Venus.

Complete Question:

The table shown below gives the approximate distance from the sun for a few different planets. How much farther (in km) from the sun is Saturn than Venus? Express your answer in scientific notation.

_______km

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Answer:

Step-by-step explanation:

EX.  in function f(x) = 2 cos x -2  

The first 2 is your amplitute, how high from middle line it goes

the last 2 is the shift in y direction.  

For f(x) = 2 cos x -2   (see image for this function)

it has been shifted down 2 and has a period

At [tex]\pi[/tex] your function has a solution of -4

The first blank is  f(x) = cos x+2

Second blank is f(x) =  cos x -2

Answer:

when the diameter of a spherical balloon shrinks to one-half of its original size, the surface area of the balloon will decrease to one-fourth of its original size, while the volume will decrease to one-eighth of its original size.

Step-by-step explanation:

When the diameter of a spherical balloon shrinks to one-half of its original size, it means the new diameter is half of the original diameter.

Let's assume the original diameter of the balloon was "d," then the new diameter will be "d/2."

Surface Area:

The surface area of a sphere is given by the formula 4πr², where "r" is the radius of the sphere. Since the diameter of the sphere is halved, the radius will also be halved. Therefore, the new surface area (SA') of the balloon will be:

SA' = 4π (d/4)² = πd²/4

Thus, the new surface area of the balloon will be one-fourth (1/4) of the original surface area.

Volume:

The volume of a sphere is given by the formula (4/3)πr³. Again, since the diameter of the sphere is halved, the radius will also be halved. Therefore, the new volume (V') of the balloon will be:

V' = (4/3)π (d/4)³ = πd³/24

Thus, the new volume of the balloon will be one-eighth (1/8) of the original volume.

Answer: 6

Step-by-step explanation:42/7=6

Calculated test statistic of 2.08 is greater than the critical value of 1.645, we reject the null hypothesis and conclude that there is convincing evidence at the 0.05 level that more than 55% of California residents use Netflix.

We can use a hypothesis testing approach to answer this question. The null hypothesis is that the true proportion of California residents who use Netflix is the same as the national proportion, or p = 0.55. The alternative hypothesis is that the true proportion of California residents who use Netflix is greater than 0.55, or p > 0.55.

We can use the sample proportion of Netflix users in California, which is 360/600 = 0.6, as an estimate of the true proportion p. The standard error of the sample proportion is:

SE = √[(p*(1-p))/n] = √[(0.55*(1-0.55))/600] = 0.024

The test statistic is:

z = (p - 0.55)/SE = (0.6 - 0.55)/0.024 = 2.08

Assuming a significance level of 0.05 and a one-tailed test (since the alternative hypothesis is one-sided), the critical z-value is 1.645.

Since our calculated test statistic of 2.08 is greater than the critical value of 1.645, we reject the null hypothesis and conclude that there is convincing evidence at the 0.05 level that more than 55% of California residents use Netflix. However, we should keep in mind that this conclusion is based on a sample of 600 adults from California, and there is always some degree of uncertainty involved in statistical inference based on samples.

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A circular plate fragment is found by an archaeologist. The plate is 13.9 inches in diameter.

A chord in mathematics is a piece of a straight line that joins two points on a curve. A chord is a line segment with its endpoints on the curve, to be more precise.

The word "chord" is most frequently used in relation to the geometry of circles, where a chord is a line segment that joins two points on a circle's circumference. Given the lengths of the circle's radii and the separation between the chord's ends, the Pythagorean theorem can be used to determine the chord's length in this situation.

The relationship between two notes in music can also be represented by chords. A chord is, in this context, a grouping of three or more notes performed simultaneously to produce a harmonic sound. The structure of musical compositions can be analysed and understood using the mathematical concepts of chord progressions.

The equidistant chords theorem states that two chords are congruent in the same circle or a congruent circle if and only if they are equidistant from the centre.

Additionally, as depicted in the illustration, the supplied chords are equally spaced apart; as a result, they must meet in the circle's centre.

LHE is formed by connecting the points L and E to make a right-angled triangle ΔLHE.

The perpendicular chord bisector theorem states that if a circle's diameter is perpendicular to a chord, the diameter will also bisect the chord's arc HE≅ HD.

and  IF≅IG

hence , HE=7/2

HD=7/2

IF=7/2

And IG=7/2

Applying the Pythagorean theorem, simplifying by addition, and substituting 6 for the perpendicular P, LE for the hypotenuse H, and 7/2 for the base B in the equation P²+B²=H².

P²+B²=H²

6²+7/2²=LE²

LE²= 36+ 12.25

LE²= 48.25

Since LE represents the radius of a circle, it is impossible for it to be negative, hence the negative value LE=6.94 is disregarded.

Since LE is the circle's radius, the circle's radius is 6.94. As a result, the circle has a 13.88 diameter.

The diameter should be rounded out to the closest tenth.

d≈13.9.

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This is the derivative of the given function f(x) = (3x + 1)^5(3x - 1)^6 using the Generalized Power Rule.

To find the derivative of the function f(x) = (3x + 1)^5(3x - 1)^6 using the Generalized Power Rule, we will need to apply both the Product Rule and the Chain Rule.

The Product Rule states that if you have a function f(x) = g(x)h(x), then f'(x) = g'(x)h(x) + g(x)h'(x).

First, let's identify g(x) and h(x) in your function:
g(x) = (3x + 1)^5
h(x) = (3x - 1)^6

Next, we'll find the derivatives g'(x) and h'(x) using the Chain Rule, which states that if you have a function y = [u(x)]^n, then y' = n[u(x)]^(n-1) * u'(x).

For g'(x):
u(x) = 3x + 1
n = 5
u'(x) = 3
g'(x) = 5(3x + 1)^(5-1) * 3 = 15(3x + 1)^4

For h'(x):
u(x) = 3x - 1
n = 6
u'(x) = 3
h'(x) = 6(3x - 1)^(6-1) * 3 = 18(3x - 1)^5

Now, we apply the Product Rule:
f'(x) = g'(x)h(x) + g(x)h'(x) = 15(3x + 1)^4(3x - 1)^6 + (3x + 1)^5 * 18(3x - 1)^5

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If 4 buses carrying 150 football fans from same school arrive at a football stadium, then the expected-value, "E(X)" is 41 and variance "Var(X)" is 99.

To find the expected value of X, we use the formula E(X) = ∑x P(X=x), where x is = possible values of X and P(X=x) = probability of X taking the value x.

Four buses have a total of 150 students, the probability that the randomly selected person is from a bus with x students is the proportion of students on that bus divided by the total number of students:

P(X=x) = (number of students on bus with x students)/(total number of students);

So, We have:

P(X=20) = 20/150 = 2/15

P(X=35) = 35/150 = 7/30

P(X=45) = 45/150 = 3/10

P(X=50) = 50/150 = 1/3

The expected-value of X is : E(X) = 20(2/15) + 35(7/30) + 45(3/10) + 50(1/3) = 41

To find the variance of X, we use the formula Var(X) = E(X²) - [E(X)]².

We already know E(X), so we need to find E(X²).

E(X²) = ∑ x² P(X=x);

So, We have:

E(X²) = 20²(2/15) + 35²(7/30) + 45²(3/10) + 50²(1/3) = 1780;

So, variance of X is : Var(X) = E(X²) - [E(X)]² = 1780 - 41² = 99.

Therefore, the expected value of X is 41 and the variance of X is 99.

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A) The amount of interest he will earn in a year is $3,000.

B) The amount he spent on furniture is $600.

Part A: To calculate the interest Alex will earn in one year, use the formula for simple interest:

Interest = Principal × Rate × Time.

In this case, Principal = $30,000, Rate = 10% (0.10), and Time = 1 year. So,

Interest = $30,000 × 0.10 × 1 = $3,000.

Part B: Alex spends 20% of the interest on furniture. To calculate this amount, multiply the interest by 20% (0.20): $3,000 × 0.20 = $600.

Therefore, in one year, Alex will earn $3,000 in interest. He will spend $600 on furniture for his new house.

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Answer:

D

Step-by-step explanation:

Because the opposite of 37 is -37, III must be true.

Given that absolute values can never be negative, II must be untrue.

Remember the definition of absolute value:

If |x| = x if x >= 0 and |x| = -x if x 0 then IV must be true.

The value of angle HCI is determined as 244⁰.

The value of angle HCI is calculated by applying intersecting chord theorem as follows;

The intersecting chord theorem, also known as the secant-secant theorem, states that when two chords intersect inside a circle, the products of the segments of one chord are equal to the products of the segments of the other chord.

From the diagram, the value arc CUH is equal to the value of angle HCI.

Thus, angle HCI = 244⁰

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Answer: Diffusion

Step-by-step explanation:

The area of S is:

[tex]A(S) = 16\pi \sqrt{(500/11)}= 128.8[/tex]

The surface S can be described in terms of cylindrical coordinates by setting:

x = r cos(θ)

y = r sin(θ)

z = z

Using these coordinates, we can rewrite the equation for C as:

r² = 22/100(x² + y²) = 22/100r²

Simplifying this equation, we get:

[tex]r = \sqrt{(500/11)}[/tex]

Thus, the surface S is the portion of the cylinder of radius [tex]\sqrt{(500/11)}[/tex] between z = 1 and z = 5.

To calculate the area of S, we can use the formula:

A(S) = ∫∫∂S ||n|| [tex]dA[/tex]

where ||n|| is the magnitude of the normal vector to the surface, and [tex]dA[/tex] is the area element on the surface.

For the cylinder, the normal vector is simply the radial unit vector pointing outward from the origin:

n = (cos(θ), sin(θ), 0)

The magnitude of the normal vector is ||n|| = 1, so we can simplify the formula for the area to:

A(S) = ∫∫∂S [tex]dA[/tex]

To evaluate this integral, we need to parameterize the surface S. We can use the cylindrical coordinates we defined earlier:

x = r cos(θ)

y = r sin(θ)

z = z

with 0 ≤ θ ≤ 2π and 1 ≤ z ≤ 5.

The area element in cylindrical coordinates is given by:

[tex]dA = r \ dz\ d\theta[/tex]

Substituting in our parameterization of S, we get:

A(S) = ∫∫∂S r [tex]dz[/tex] dθ

[tex]= \int\limits^{2\pi }_0 \int\limits^5_1 {\sqrt{(500/11)} dz d\theta}\\= \sqrt{(500/11)} \int\limits^{2\pi }_0 {(5 - 1) d\theta}\\= 16\pi \sqrt{(500/11)[/tex]

Therefore, the area of S is:

[tex]A(S) = 16\pi \sqrt{(500/11)}= 128.8[/tex]

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The triangle above has the following measures. The length of sider is 13.3 inches.

q = 8 inches

m ∠Q = 37°

sin (Q) = q/r

r = q / sin(Q)

= 8 / sin (37°)

= 13.3 inches

In Math, a triangle is a three-sided polygon that comprises of three edges and three vertices. The main property of a triangle is that the amount of the inward points of a triangle is equivalent to 180 degrees. This property is called point total property of triangle.

There are three points in a triangle. These points are framed by different sides of the triangle, which meets at a typical point, known as the vertex. The amount of every one of the three inside points is equivalent to 180 degrees.

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The area of the object is 40 square centimeters

The correct answer is an option (B)

We know that the formula for the area of trapezoid is,

A = ((a + b)/2) × h

where a and b are the two parallel bases

h is the height of the trapezoid

From the attached figure, first we determine the length of the two parallel bases.

Let us assume that 'a' represents the length of the upper base and 'b' represents the length of the bottom side of the trapezoid

We can observe that a = 2x

so the length of a = 6 centimeters

And b = 2z

So, the length of b = 2(5)

                              = 10 cm

Here, the height h of the trapezoid is given by y = 5 cm

Using above formula for the area of trapezoid, the area of the object would be,

A = ((a + b)/2) × h

A = ((6 + 10)/2) × 5

A = (16/2)  × 5

A = 40 cm²

Therefore, the correct answer is an option (B)

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Find the complete question below.

La proportion de boules vertes dans cette boîte est de 2/3.

Pour déterminer la proportion de boules vertes dans cette boîte, nous devons comparer le nombre de boules vertes au nombre total de boules dans la boîte.

Le nombre total de boules dans la boîte est la somme des boules vertes et des boules bleues, soit 12 + 6 = 18 boules.

Maintenant, pour calculer la proportion de boules vertes, nous divisons le nombre de boules vertes par le nombre total de boules.

Proportion de boules vertes = Nombre de boules vertes / Nombre total de boules

Proportion de boules vertes = 12 / 18

Simplifiant cette fraction, nous obtenons :

Proportion de boules vertes = 2/3

La proportion de boules vertes dans cette boîte est donc de 2/3 ou environ 66.67%.

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(a) The three different trigonometric ratios that could have been used to find the distance x between Emma and the base of the tree are sin(60°) = 43.3/50, cos(60°) = x / 50, and tan(60°) = 43.3 / x. The distance is 25 ft.

(b) Using the Pythagorean theorem, the distance x between Emma and the base of the tree is 25 ft.

(a) We can use sine, cosine, and tangent trigonometric ratios to find the distance x between Emma and the base of the tree.

1. Sine:
sin(60°) = opposite/hypotenuse = (tree height) / 50
tree height = 50 * sin(60°) = 43.3 ft (since it's given that the tree is 43.3 ft tall)

2. Cosine:
cos(60°) = adjacent/hypotenuse = x / 50
x = 50 * cos(60°) = 25 ft

3. Tangent:
tan(60°) = opposite/adjacent = (tree height) / x
x = (tree height) / tan(60°) = 43.3 / tan(60°) ≈ 25 ft

(b) To find the distance x between Emma and the base of the tree using the Pythagorean theorem, we can consider the triangle formed by Emma, the base of the tree, and the top of the tree.

Let's call the distance from the base of the tree to the top of the tree (tree height) y.

Emma's distance to the cat (50 ft) is the hypotenuse, the distance x is one leg, and the tree height y (43.3 ft) is the other leg of the right triangle.

Using the Pythagorean theorem: x² + y² = hypotenuse²
x² + 43.3² = 50²
x² + 1874.89 = 2500
x² = 625.11
x ≈ 25 ft

So, the distance between Emma and the base of the tree is approximately 25 ft.

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The critical numbers of f(x) = -2x^3 + 39x^2 - 240x + 2 are A = 5 and B = 8.

To find the critical numbers of a function, we need to find the values of x where the derivative of the function is zero or undefined.

For the function f(x) = 5x^2 + 7x - 10, the derivative is:

f'(x) = 10x + 7

To find the critical numbers, we need to set f'(x) = 0 and solve for x:

10x + 7 = 0

10x = -7

x = -7/10

So the critical number of f(x) = 5x^2 + 7x - 10 is x = -7/10.

For the function f(x) = -2x^3 + 39x^2 - 240x + 2, the derivative is:

f'(x) = -6x^2 + 78x - 240

To find the critical numbers, we need to set f'(x) = 0 and solve for x:

-6x^2 + 78x - 240 = 0

We can simplify this equation by dividing both sides by -6:

x^2 - 13x + 40 = 0

Now we can factor the quadratic:

(x - 5)(x - 8) = 0

So the solutions are x = 5 and x = 8.

To determine which critical point is A and which is B, we need to check the sign of the second derivative of f(x) at each critical point.

The second derivative of f(x) is:

f''(x) = -12x + 78

Plugging in x = 5, we get:

f''(5) = -12(5) + 78 = 18

Since f''(5) is positive, we know that f(x) has a local minimum at x = 5. Therefore, x = 5 is the critical point A.

Plugging in x = 8, we get:

f''(8) = -12(8) + 78 = -6

Since f''(8) is negative, we know that f(x) has a local maximum at x = 8. Therefore, x = 8 is the critical point B.

Therefore, the critical numbers of f(x) = -2x^3 + 39x^2 - 240x + 2 are A = 5 and B = 8.

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The dimensions of the pasture that require the least amount of fence are approximately 600 meters by 300 meters.

To minimize the amount of fence needed, we want to maximize the length of the side next to the canal. Let's call this side x and the other two sides y.

We know that the area of the rectangle must be 180,000 m², so we have x*y = 180,000. We want to minimize the amount of fence, which is the perimeter of the rectangle: P = x + 2y

To solve for the dimensions that require the least amount of fence, we need to eliminate one variable. We can do this by using the area equation to solve for one variable in terms of the other:
y = 180,000/x

Substituting this into the perimeter equation, we have:
[tex]P = x + 2(180,000/x)[/tex]

To find the minimum value of P, we take the derivative with respect to x and set it equal to zero:
[tex]P' = 1 - 360,000/x^2 = 0x = sqrt(360,000) ≈ 600[/tex]

Substituting this back into the area equation, we find:
[tex]y = 180,000/x ≈ 180,000/600 ≈ 300[/tex]

So, the dimensions of the pasture which require the least amount of fence are approximately 600 meters by 300 meters.

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Answer:

y = (x + 5)/3

Step-by-step explanation:

To make y the subject, you need to isolate y on one side of the equation.

x = 3y - 5

Add 5 to both sides:

x + 5 = 3y

Divide both sides by 3:

y = (x + 5)/3

Therefore, y is the subject of the formula when it is expressed as:

y = (x + 5)/3

The inequality represents the number of flowers, Truman would buy at Flowers Galore is f < 8.

Price of teddy bear = $13

Price of the flower = $0. 75

Florist charges the price of a teddy bear = $13

The florist charges the price of the flower = $1.25

Assume that number of flowers Truman buys = f

The total cost of purchasing teddy bears and flowers at Flowers Galore =

C1 = 13 + 0.75f

The total cost of purchasing teddy bears and flowers at  Famous Florist is C2 = 9 + 1.25f

The inequality for Flowers Galore can be written as:

C1 < C2

13 + 0.75f < 9 + 1.25f

0.5f < 4

Dividing on both sides by 0.5,

f < 8

Therefore, we can conclude that the inequality represents the number of flowers, Truman would buy is f < 8.

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The solution for the differential equation is y = (23/48) x + 4.

(A) Re-writing the differential equation in terms of differentials, we get:

dy = (23/48) dx

Here, dy and dx represent infinitesimal changes in the variables y and x, respectively.

(B) Integrating both sides of the equation with respect to their respective variables, we get:

∫dy = ∫(23/48)dx

On the left-hand side, the integral of dy is simply y (plus a constant of integration), while on the right-hand side, we can pull the constant factor (23/48) outside the integral:

y + C1 = (23/48) ∫dx

Integrating the right-hand side with respect to x, we get:

y + C1 = (23/48) x + C2

where C1 and C2 are constants of integration.

(C) To solve for y, we can isolate it on one side of the equation by subtracting C1 from both sides:

y = (23/48) x + (C2 - C1)

Next, we can use the initial condition y(0) = 4 to solve for the constant C2 - C1:

y(0) = (23/48) (0) + (C2 - C1) = C2 - C1

Since y(0) = 4, we have:

4 = C2 - C1

Therefore, C2 - C1 = 4, and we can substitute this back into the expression for y to get the final solution:

y = (23/48) x + 4

So the solution for the differential equation with initial condition y(0) = 4 is y = (23/48) x + 4.

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The option or options that would help make the graph less misleading are:

d. i and iii. The scale on the x-axis should be resized. The identity of the two parks should be more clearly differentiated.

Resizing the scale on the x-axis (option i) would help provide a clearer picture of the difference between the two parks, as it would make it easier to see the differences in the number of visitors between the two parks.

Differentiating the identity of the two parks more clearly (option iii) would also help reduce confusion and provide a more accurate representation of the data.

Resizing the scale on the y-axis (option ii) may not be necessary in this case, as the existing scale is appropriate and accurately represents the data.

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Answer:

The mean would decrease in value to about 17.1 inches.

Step-by-step explanation:

If we add a smaller data to the mean of a numerical data set, the mean will decrease.

Hope this helps.