John paid $280 for a new mountain bicycle to sell in his shop. He wants to price it so that he can offer a 30% discount but still make 10% of the price he paid for it. At what price should the bike be marked?

Answer: 15

Step-by-step explanation:

casue

Answer:

x = 1

Lemme know if you need the steps.

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The area of the sector in terms of π is 35.6π inches squared.

The area of the sector is approximately  111.6 inches square

The area of sector of a circle is the amount of space enclosed within the boundary of the sector.

Therefore,

area of a sector = ∅ / 360 × πr²

where

Therefore,

∅ = 200 degrees

r = 8 inches

area of the sector = 200 / 360 × 8²π

area of the sector = 200 / 360 × 64π

area of the sector =12800π/  360

area of a sector = 35.6π inches squared

Let's find the area of the sector with π = 3.14

area of a sector = 35.6 × 3.14 = 111.6 inches square

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Answer:

D. Two hours exercising and eight hours cleaning

Step-by-step explanation:

Rob works part time at the Fallbrook Riding Stable. He makes $5 an hour exercising horses and $10 an hour cleaning stalls. Because Rob is a full-time student, he can work no more than 12 hours per week. However, he must make at least $60 per week.

x = hrs. exercising horses

y = hrs. cleaning stalls

Equations:

Hours he can work per week:

x + y ≤ 12

Amount of money he can make per week:

5x + 10y ≥ 60

Now, graph your equations into desmos.

As you can see in the graph, the correct answer is D (2, 8)

Check your answer by hand:

x + y ≤ 12

2 + 8 ≤ 12

10 ≤ 12

This statement is correct

5x + 10y ≥ 60

5(2) + 10(8) ≥ 60

10 + 80 ≥ 60

90 ≥ 60

This statement is correct

Therefore, the correct answer is D

Hope this helps!

Answer: C

Step-by-step explanation:

Point D is at -14 on the number line.

In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).

Since E is the midpoint of line segment CD, we can logically deduce the following relationship:

Line segment CD = Line segment C + Line segment D

Midpoint E = (point C + point D)/2

By substituting the given points into the equation above, we have the following:

-3 = (8 + D)/2

-6 = 8 + D

D = -6 - 8

D = -14

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Answer:

x = b - 2

Step-by-step explanation:

Given :

3x + 6 - 3b = 0

Subtract (6 - 3b) on both sides :

3x + 6 - 3b - (6 - 3b) = 0 - (6 - 3b)

3x + 6 - 6 + 3b - 3b = -6 + 3b

3x = 3b - 6

Divide throughout by 3 :

1/3 x 3x = 1/3 x (3b - 6)

x = b - 2

Done!

Answer:

The maximum profit the florist will earn from selling celebration bouquets is $725.

The florist will break-even after one-dollar decreases when her profit is zero. From the graph, this occurs at x = 10. So the florist will break-even after 10 one-dollar decreases.

The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is (0, 10). This is because the profit is positive for values of x between 0 and 10, and becomes negative after 10.

Step-by-step explanation:

The dimensions of the island on the blueprint are 14 inches by 3.5 inches.

We have,

The actual dimensions of the island are 3 1/2 feet by 1 3/4 feet.

We need to find the dimensions of the island on the blueprint, given that the scale of the blueprint is 1 inch = 2 feet.

To convert the actual dimensions to the dimensions on the blueprint, we need to use the scale factor of 1 inch = 2 feet.

We can set up a proportion to relate the actual dimensions to the dimensions on the blueprint:

Actual dimension/blueprint dimension = scale factor

Let x be the length of the island on the blueprint.

Then we can set up the following proportion:

3.5 feet / (1.75 feet)

= x inches / 7 inches

Simplifying,

2 = x / 7

Multiplying both sides by 7, we get:

x = 14 inches

The length of the island on the blueprint is 14 inches.

Similarly, we can find the width of the island on the blueprint:

1.75 feet / 3.5 feet

= y inches / 7 inches

Simplifying, we have:

0.5 = y / 7

Multiplying both sides by 7, we get:

y = 3.5 inches

The width of the island on the blueprint is 3.5 inches.

Thus,

The dimensions of the island on the blueprint are 14 inches by 3.5 inches.

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Answer:

\(\huge\boxed{-0.001a^{n+1}}\)

Step-by-step explanation:

\(-0.001a^{3n+3}=-0.001a^{3(n+1)}=(-0.001a^{n+1})^3\\\\\text{Used}\\\\a(b+c)=ab+ac\qquad\text{distributive property}\\\\(a^n)^m=a^{n\cdot m}\)

Answer:

Step-by-step explanation:

Answer:

z = 41

Step-by-step explanation:

TU = z + 41

SV = z

SV = ½(TU) => Based on the triangle midsegment theorem

Substitute

z = ½(z + 41)

Multiply both side by 2

2*z = z + 41

2z = z + 41

Subtract both sides by z

2z - z = 41

z = 41

Answer:

The probability of getting a 2, 4, or 6 when a dice is rolled is 1/2, or 50%. This is because there are six possible outcomes when a dice is rolled, and three of them are favorable outcomes (2, 4, or 6). Therefore, the probability of getting a 2, 4, or 6 is 3/6, which simplifies to 1/2 or 50%.

The two types of figures are open and closed, geometric figures respectively. Figures that don't end where they begin are said to be open figures.

Closed geometric shapes are made up of points, line segments, circles, and curves. All around us, we can observe these types of shapes. Circle, rectangle, triangle, and other geometric shapes are a few examples. The triangle-shaped slices of a pizza are round.

Straight lines have been drawn on the floor, the door, the window, and the zebra crossing by the roadside in the classrooms. Even though angles are used in building construction, they also have connections to disciplines like physics and chemistry.

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Answer:

(22;-3)

Step-by-step explanation:

if to calculate the coordinates of the given midpoint it needed to use:

\(x_{midpoint}=\frac{x_{endpoint1}+x_{endpoint2}}{2};\)

\(y_{midpoint}=\frac{y_{endpoint1}+y_{endpoint2}}{2};\)

then to calculate the coordinates of endpoint2, it needed to perform the substitution:

\(\frac{-10+x_{endpoint2}}{2}=6,\)

\(2=\frac{7+y_{endpoint2}}{2},\)

finally:

\(x_{endpoint2}=22;\)

\(y_{endpoint2}=-3.\)

Step-by-step explanation:

Let x be the miles Kenyon ran on tuesday

Let y be the miles Kenyon ran on thursday

Given,

Mon + Tues + Wed + Thu = 8mi

\(1.2 + x + 1.6 + y = 8 \\ 2.8 + x + y = 8 \\ x + y = 8 - 2.8 \\ x + y = 5.2\)

also given,

\(y = x + 0.4 \\ - x + y = 0.4\)

Now we have x + y = 5.2 as equation 1 and -x + y = 0.4 as equation 2

Using equation 1,

\(x + y = 5.2 \\ x = 5.2 - y\)

Substitute this equation into equation 2.

\( - (5.2 - y) + y = 0.4 \\ - 5.2 + y + y = 0.4 \\ - 5.2 + 2y = 0.4 \\ 2y = 0.4 + 5.2 \\ 2y = 5.6 \\ y = 5.6 \div 2 \\ = 2.8mi\)

Substitute y = 2.8 into equation 1.

\(x + 2.8 = 5.2 \\ x = 5.2 - 2.8 \\ = 2.4mi\)

Therefore Kenyon ran 2.4 miles on tuesday, and ran 2.8 miles on thursday.

Answer:

5x - 9

Step-by-step explanation:

2x -(-3x + 9)                

2x + 3x - 9)                  DISTRIBUTE -1

5x - 9                           COMBINE LIKE TERMS

The depth of the aquarium is approximately 4 feet when rounded to the nearest whole number (since 3.64 is closer to 4 than it is to 3 when rounded to the nearest whole number).

To calculate the depth of the aquarium, we need to use the formula for volume of a rectangular prism,

which is V = lwh where V is the volume, l is the length, w is the width, and h is the height (or depth, in this case).

Given that the aquarium holds 11.35 cubic feet of water, the volume of the aquarium can be represented by V = 11.35 cubic feet.We are also given that the length of the aquarium is 2.6 feet and the width is 1.1 feet.

Substituting these values into the formula for volume,

we get:11.35 = 2.6 × 1.1 × h

Simplifying this expression:

11.35 = 2.86h

Dividing both sides by 2.6 × 1.1,

we get:h ≈ 3.64 feet (rounded to two decimal places)

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Answer:

It's C. g(x) = (1.6)x − 9 + 5

Step-by-step explanation: hope it helps ^w^

The first three non zero terms in the Taylor polynomial approximation to the given DE is y(t) = t + t²/2 -(3/2)t³ .

In the question ,

it is given that ,

the differential equation is

y'' + 9y + 5y³ = Cos(10t)   ...equation(1)

y(0) = 0, y'(0) = 1

for y = 0 , the differential equation is

y''(0) + 9y(0) + 5{y(0)}³ = Cos90)

y''(0) + 9 + 5 = 1 ;

y''(0) = 1.

differentiating equation(1) with respect to "t" , we have

y''' + 9y' + 15y²y' = -10Sin(10t)

y'''(0) + 9y'(0) + 15{y(0)}².y'(0) = -10Sin(0)

y'''(0) + 9 + 0 = 0

y'''(0) = -9

The Taylor series is given by

y(t) = y(0) + y'(0)t + 1/2.y''(0)t² + 1/3!.y'''(0)t³ + ....

Now substituting the values of y(0) , y'(0) , y''(0) , y'''(0) , we have

y(t) = 0 + 1.t + 1/2.t² + 1/6.(-9)t³ + ....

= t + t²/2 - 3/2.t³ + ...

Therefore , the first three terms are t , t²/2 , -3/2.t³   .

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The expression that is the same as sin⁻¹ x is (b) arcsin x

From the question, we have the following sine expression that can be used in our computation:

sin^-1 x

When this expression is rewritten, we have the following representation

sin⁻¹ x

The above expression is pronounced as arc-sin of x

And it can be represented as

arcsin x

This means that the equivalent expression of the given expression is (b) arcsin x

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Answer:

Step-by-step explanation:

174

Answer:

i believe its 26

Step-by-step explanation:

please mark brainliest if right

The actual base of the building is 1890 square feet.

A rectangle is a two-dimensional figure with length and width.

The area of a rectangle is Length x width.

We have,

1 inch = 15 feet

Rectangular base:

Length = 4.2 in

Width = 2 in

So,

4.2 in = 4.2 x 15 feet = 63 feet

2 in = 2 x 15 = 30 feet

Now,

The actual base of the building.

= 63 x 30

= 1890 square feet

Thus,

1890 square feet.

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Step-by-step explanation:

divide each of the following: using the two methods

Using the lowest common factor of the shuttles' run times, they will depart again for the campus simultaneously at 10.25 A.M.

We can use the lowest common factor (LCM) of their run time to determine when they depart again for the campus.

The lowest common factor of 30 and 20 is 60 because both 30 and 20 can divide 60 evenly without a remainder, showing that it takes 60 minutes for the two shuttles to depart for the campus at the same time.

We can conclude that every 60 minutes or hour, the two shuttles simultaneously depart for the campus.  Every hour, the shuttle departing from Ball Hall completes 2 runs, while the shuttle departing from Lot A completes 3 runs.

Thus, using the lowest common factor, the next time both shuttles will depart for the campus at the same time is 10:25 A.M.

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Using generating function number of different selections of r hot dogs when there are four types of hot dogs are g(x) = ( 1/(1-x) )⁴.

For a sequence a₀,a₁,...,aₙ,... the corresponding generating function f(x) is the sequence

f(x)=a₀+a₁x+...+aₙxₙ+...= ∑aᵢxᵢ , 0 ≤ i ≤ ∞

Since here we have 4 types of hot dogs, from which we need to select "r" hot dogs, we would use a generating function as follows:

There can be any number of selections from any pile of hot dogs ( repitions is allowed). therefore, from each pile, you could pick up 1 or 2 or 3 or ... hot dogs. The same would go for all types of hot dogs. Therefore ,the generating function for the same would be,

g(x) = (1 + x + x² + x³ + x⁴ + ...)(1 + x + x² + x³ + x⁴ + ...)(1 + x + x² + x³+ x⁴ + ...)(1 + x + x² + x³+ x⁴+ ...)

Therefore, g(x) = (1 + x + x² + x³ + x⁴ + ...)⁴

This is an infinite geometric series, which can be solved to give the sum: g(x) = ( 1/(1-x) )⁴. Therefore, our required the coefficient of xʳ in (1/ (1-x) )⁴.

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Answer:

x = 28

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

7 divided by 1/4

then you get you answer

=28

hoped this helped, have a good day! c:

Answer:

Let a be the larger number

Let b be the smaller number

A= b+7

Step-by-step explanation:

Hope this helps :) Have a great day!!!

Answer:

4 hours

Step-by-step explanation:

36/9