Write the ratios for sin M, and tan M

sin M =

Answer:

2880 km

Step-by-step explanation:

(distance) = (rate)*(time).

Here we have:

(distance traveled) = (720 km/hr)(4 hrs) = 2880 km

Answer:

3.5 kilometers per/hour

Step-by-step explanation:

6/4= 1.5

1.5+2=3.5

Answer:

The answer is 90

The value of the 10!/(10 - 2)! is 90 after simplification of the factorial option (C) 90 is correct.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have given an expression:

10!/(10 - 2)!

The sign '!' represents the factorial of the number.

As we know,

If factorial of any number can be evaluated:

n! = n(n - 1)(n - 2)(n - 3)(n - 4).......1

10! = 10×9×8×7×6×5×4×3×2×1

or

10! = 90(8!)

(10 - 2)! = 8!

= 90(8!)/(8)!

90

8! is canceled out from the numerator and denominator

Thus, the value of the 10!/(10 - 2)! is 90 after simplification of the factorial option (C) 90 is correct.

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Answer:

False

Step-by-step explanation:

Answer:

answer is A

Step-by-step explanation:

To calculate the total cost for a 660 feet fence by Company 2, subtract the initial 550 feet covered by the flat fee from the total length, multiply the additional feet by the per-foot cost, and add the flat fee to get the final cost, which is $7790.

The student is asking about calculating the total cost for installing fencing, which involves initial fees and additional per unit costs. In this case, Company 2 charges a flat fee for the first 550 feet of fence and then an additional fee for each foot beyond that.

To find the total cost when Company 2 installs a fence of 660 feet, we first calculate the number of feet beyond the initial 550 feet. This is 660 - 550 = 110 feet. Then, we multiply the additional feet by the cost per additional foot: 110 feet x $29/foot = $3190.

Lastly, we add the initial flat fee of $4600 to the cost for the additional feet to get the total cost: $4600 + $3190 = $7790.

Answer:

  8/12 yard or 2/3 yard

Step-by-step explanation:

The sum of the two lengths is ...

  5/12 yd + 3/12 yd = (5+3)/12 yd = 8/12 yd

This fraction can be reduced by removing a factor of 4 from numerator and denominator.

  8/12 yd = 2/3 yd

If the arm portions are end-to-end, the total length is 2/3 yard.

Answer:

Step-by-step explanation:

15Answer:

Step-by-step explanation:

Answer: x = -14/5

Step-by-step explanation: We shall begin by expanding the brackets for both sides of the equation

-2/3 (x + 2) = 1/6 (x + 6)

(-2x/3) -4/3 = (x/6) + 1

By collecting like terms we now have

(-2x/3) - (x/6) = 1 + 4/3

(-4x - x)/6 = 7/3

-5x/6 = 7/3

By cross multiplication we now have

-5x (3) = 7 (6)

-15x = 42

x = -(42/15) {simplify further by dividing the RHS by 3}

x = -14/5

Therefore x equals, minus fourteen over five (-14/5)

Answer:

1

Step-by-step explanation:

The cone is sliced by a plane, which produces a smaller cone on top.  This cone is similar to the original cone.  Therefore:

R / H = r / h

2 / 8 = r / 4

r = 1

The radius of the circle at the intersection of the plane and the cone is 1.

To find the radius of the circle at the intersection of the plane and the cone, we start by understanding the geometry of the cone and the slicing plane.

Given:

- Cone height ( h = 8 )

- Cone radius ( r = 2 )

- The plane slices the cone halfway along its height, so the distance from the vertex to the plane is  [tex]\( \frac{8}{2} = 4 \)[/tex].

Let's denote:

- ( R ): Radius of the circle at the intersection of the plane and the cone.

At height ( h ) from the vertex of the cone, the radius ( R ) of the circle formed by the intersection with the plane is related to the similar triangles formed by the cone and the slice plane.

The ratio of corresponding sides of similar triangles gives us:

[tex]\[ \frac{R}{r} = \frac{h - 4}{h} \][/tex]

Substitute the given values:

[tex]\[ \frac{R}{2} = \frac{8 - 4}{8} = \frac{4}{8} = \frac{1}{2} \][/tex]

Now, solve for ( R ):

[tex]\[ R = 2 \cdot \frac{1}{2} = 1 \][/tex]

Therefore, the radius of the circle at the intersection of the plane and the cone is [tex]\( \boxed{1} \).[/tex]

Answer:

AB = [tex]4\sqrt{3}[/tex]

Step-by-step explanation:

30-60-90 theorem, usually x is used to explain but I will use y since x is in your problem, just substitute any variable for y

in a 30 -60 -90 triangle

the length opposite the 30 degrees is y

the length opposite the 60 degrees is y[tex]\sqrt{3}[/tex]

the length opposite the 90 degrees is 2y

since y[tex]\sqrt{3}[/tex] = 6

y = 6/[tex]\sqrt{3}[/tex]

rationalizing the denominator

[tex]\frac{6}{\sqrt{3} } *\frac{\sqrt{3}}{\sqrt{3}}[/tex] = [tex]\frac{6\sqrt{3} }{3} = 2\sqrt{3}[/tex]

if y = [tex]2\sqrt{3}[/tex], 2y = [tex]4\sqrt{3}[/tex]

The width of the rectangle, given its perimeter and length, is calculated using the formula for the perimeter of a rectangle. By reorganizing the terms and isolating the width, we find that the width is 4x + 3/2y, which is Answer Choice A.

The perimeter of a rectangle is given as 15x + 17y. The length is provided as 7/2x + 7y. To find the width, we need to remember that the perimeter of a rectangle is twice the sum of its length and width (P = 2l + 2w). Let's denote the width of the rectangle as 'w'.

So, the equation representing the perimeter is:

15x + 17y = 2(7/2x + 7y) + 2w

Now let's multiply out the factors on the right side:

15x + 17y = 2(7/2x) + 2(7y) + 2w

15x + 17y = 7x + 14y + 2w

To find 'w', we need to move all terms involving 'w' to one side of the equation and all other terms to the other side:

2w = 15x + 17y - (7x + 14y)

2w = 15x - 7x + 17y - 14y

2w = 8x + 3y

Divide throughout by 2 to find 'w':

w = 4x + 3/2y

The width of the rectangle is 4x + 3/2y, which corresponds to Answer Choice A.

Answer:

The correct answer is B. $ 29,555.50

Step-by-step explanation:

Let's calculate A, using the formula provided, this way:

A = P * [(1 + r)ⁿ - 1]/r * (1 + r)ⁿ, where:

P is the month payment = 725

r is the monthly interest rate = 0.0825/12 = 0.006875

n is  the the number of months to pay = 4 * 12 = 48

Replacing with the values we know, we have:

A = P * [(1 + r)ⁿ - 1]/r * (1 + r)ⁿ

A = 725 * [(1 +0.006875 )⁴⁸ - 1]/0.006875 * (1 +0.006875 )⁴⁸

A = 725 * 0.38939833/0.006875 * 1.38939833

A = 282.313789/0.009552114

A = 29,555.50

The correct answer is B. $ 29,555.50

The correct option is B. [tex]\$29555.50[/tex]. The maximum loan Chase can afford, while making monthly payments of [tex]\$725[/tex] for [tex]4[/tex] years at an [tex]8.25\%[/tex] annual interest rate.

Given:

Monthly payment [tex]\( P = $725 \)[/tex]

Annual interest rate [tex]\( r = 8.25\% \)[/tex] or [tex]\( 0.0825 \)[/tex] as a decimal

Number of payments per year [tex]\( n = 12 \)[/tex] (since monthly payments)

Number of years [tex]\( t = 4 \)[/tex]

The formula to calculate the present value [tex]\( A \)[/tex] of the loan is:

[tex]\[ A = P \times \frac{1 - (1 + \frac{r}{n})^{-nt}}{\frac{r}{n}} \][/tex]

Now, substitute the given values

[tex]\[ A = 725 \times \frac{1 - (1 + \frac{0.0825}{12})^{-12 \times 4}}{\frac{0.0825}{12}} \][/tex]

First, calculate [tex]\( \frac{r}{n} \)[/tex]

[tex]\[ \frac{0.0825}{12} = 0.006875 \][/tex]

Next, calculate [tex]\( (1 + \frac{r}{n})^{-nt} \)[/tex]

[tex]\[ (1 + 0.006875)^{-48} = 0.7221 \][/tex]

Now substitute these values into the formula for [tex]\( A \)[/tex]

[tex]\[ A = 725 \times \frac{1 - 0.7221}{0.006875} \][/tex]

[tex]\[ A = 725 \times \frac{0.2779}{0.006875} \][/tex]

[tex]\[ A = 725 \times 40.4218 \][/tex]

[tex]\[ A = 29555.50 \][/tex]

Answer:

$75 x .20=$15

75-15=$60

To find out how much Gena's outfit cost after the 20% discount, subtract the discount amount from the original price.

To find out how much Gena's outfit cost after the 20% discount, we can use the formula:

The discount amount = original price x discount percentage

In this case, the discount amount = $75 x 0.20 = $15.

Therefore, Gena's outfit cost after the discount is:

Original price - discount amount = $75 - $15 = $60.

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Answer: x =750

Step-by-step explanation:

Well you just make 3 and 400 a fraction 3/400 and 100,000 and the unknown number a fraction x/100,000. Now you do :

3/400=x/100,000

and figure that out :

3/400=x/100,000

3/400=x/100,000

(3)*(100000)=x*(400)

300000=400x

400x=300000

400x/400=300000/400

x=750 is your answer.

3/400=750/100,000.

Hoped I helped!

Answer:

m=3/4

Step-by-step explanation:

Slope is equal to the change in y over the change in x, or rise over run.

m=change in y/change in x

The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).

m=y2−y1/x2−x1

Substitute in the values of x and y into the equation to find the slope.

m=9−(3)/5−(−3)

Simplify.

m=3/4

The slope of the line passing through the points (-3,3) and (5,9) is 3/4

The formula for calculating the slope of a line is expressed as:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\[/tex]

Given the coordinate (-3,3) and (5,9), substitute the coordinates into the formula as shown below;

[tex]m=\frac{9-3}{5-(-3)}\\m=\frac{6}{5+3} \\m=\frac{6}{8}\\m=\frac{3}{4}[/tex]

Hence the slope of the line passing through the points (-3,3) and (5,9) is 3/4

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Solution:

Given that,

[tex]y = 4.50x[/tex]

We have to find the constant of proportionality in the equation

We know that,

When y varies directly with x, then

[tex]y \propto x\\\\y = kx ---- eqn\ 1[/tex]

Where, "k" is constant of proportionality

From given,

y = 4.50x

Compare the above equation with eqn 1,

Thus, constant of proportionality in the equation y = 4.50x is 4.50

Step-by-step explanation:

[tex]5 \: hours \: = 5 \times 60 = 300 \: min \\ minutes \: per \: episode = \frac{300}{6} \\ = 50 \\ [/tex]

Hence, each episode lasted for 50 minutes on an average.

On average, each episode of the TV series lasts 50 minutes, calculated by converting the total viewing time of five hours to 300 minutes and dividing that by the number of episodes, which is six.

To calculate the average duration of an episode, we need to convert the total time of all episodes from hours to minutes and then divide by the number of episodes.

There are 60 minutes in one hour, so five hours equates to 300 minutes (5 hours × 60 minutes/hour = 300 minutes). With six episodes in total, we divide the total minutes by the number of episodes to find the average length of one episode.

300 minutes / 6 episodes = 50 minutes per episode.

Therefore, on average, each episode of the TV series lasts 50 minutes.

The expression 30 divided by (3+x) is already presented in its simplest form which is 30 / (3 + x).

The question which expression is equivalent to 30 divided by (3+x) pertains to the simplification of algebraic expressions, a basic concept in algebra. To solve or simplify this expression directly, it remains 30 / (3 + x), as there is no further simplification that can be done without additional context or constraints on the variable x. In algebra, expressions are simplified or manipulated using algebraic rules, but in this case, the expression is already in its most simplified form unless specific values are provided for x.

i dont wanna just give away the answer so heres a hint

#x stands for # X x  or # times x

x is a vairable so the x+13 part will be #+13

figure out what the number is then if you still need help ask me again

Answer: B) 1 second

Step-by-step explanation:

plug 16 (final height) into the equation given:

16=-16t^2+8t+24, and solve for t.

x will equal -1/2 or 1

disregard the negative because you can’t have time.

To reach 16 feet above the water, you would reach that height after approximately 1/2 second. Option C

To find when you would reach 16 feet above the water, set the function h(t) equal to 16 and solve for t:

-16t2 + 8t + 24 = 16

Combine like terms to get:

-16t2 + 8t + 8 = 0

Now, you can use the quadratic formula to solve for t:

t = (-b ± √(b2 - 4ac)) / (2a)

Plug in the values of a, b, and c from the equation:

t = (-8 ± √(82 - 4(-16)(8))) / (2(-16))

Simplify the expression inside the square root and solve for t to get the answer:

t ≈ 1/2 second

Option C

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Answer: p = 0.23

Step-by-step explanation:

-10 + 20p + 6p =-16

To find the value of p

Step 1: combine like terms

20p + 6p = -16 + 10

26p = 6

Divide both sides by 26

p = 6/26

P= 0.23

I hope this helps.

Answer:

p = -3/13

Explanation:

1. add 10 onto right side

2. combine like terms

3. divide by 26 to get p by itself

4. simplify

Answer:

20.4

Step-by-step explanation:

20.35185185185185

You have to round it because in the hundredth place #5 is over 5 so, it rounds so the answer is 20.4.

Anything more than 5, 6, 7, 8, 9 ^ rounds.

Answer: 20x + 15k

Step-by-step explanation:

Lose the parentheses and add the like terms. Add 18x and 2x, then add 9k and 6k. That's all there is to it.

The equivalent expression of (18x + 9k) + (2x + 6k) is 20x + 15k.

The correct option is A.

Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

We have an expression,

(18x + 9k) + (2x + 6k).

To find the equivalent expressions:

Simplifying,

(18x + 9k) + (2x + 6k),

= 20x + 15k

This is the equivalent expression.

Therefore,  20x + 15k is the equivalent expression.

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To divide the number in the thousands place by itself and then multiply the answer by 0, we can follow a simple process. Let's consider an example where the number in the thousands place is 5. Dividing 5 by 5 gives us 1. Multiplying 1 by 0 gives us 0, which is the answer in the tenths place.

To divide the number in the thousands place by itself, we can consider a specific number for better understanding. Let's say the number in the thousands place is 5. Dividing 5 by 5 gives us 1. To find the answer in the tenths place, we need to multiply 1 by 0. The product of 1 and 0 is 0. Therefore, the answer in the tenths place is 0.

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a) Net result of Tamiko's transactions = $143.75

b) Total amount she can save = $86.25

Step-by-step explanation:

Step 1 :

Given,

Amount Tamiko got in her first check =  $109.60

Amount of the bonus check = $34.15

Fraction of the amount she wants to save = [tex]\frac{3}{5}[/tex]

We need to find the net results of her transactions and the amount she will save

Step 2 :

The new result of her transactions can be computed by adding the amount she has received through both the check.

Total amount she received  = 109.60 + 34.15 = 143.75

Total amount she can save =   [tex]\frac{3}{5}[/tex] × 143.75 = 86.25

Step 3 :

Answer :

a) Net result of Tamiko's transactions = $143.75

b) Total amount she can save = $86.25

Answer:

Step-by-step explanation:

A net is a drawing that shows the edges and faces of a solid in two dimensions. You can think of a net as what you would get if you “unfolded” a solid. ... The net is made of three congruent rectangles and two congruent equilateral triangles. The surface area is the sum of the areas of the five shapes.

Answer:

three-dimensional figure that represents a cylinder

Step-by-step explanation:

The total cost of a cake that serves 20 people is $35.

Step-by-step explanation:

The equation can be formed as:

Therefore, the total cost of a cake that serves 20 people is $35.