Coach Kent brings 3 quarts of sports drink to soccer practice. He gives the same amount of the drink to each of his 16 players . How many ounces does each player get

Answer:

720

Step-by-step explanation:

The permutation looks like this for that set of data:

[tex]_{10}P_{3}[/tex]

and the formula to solve it like this:

[tex]_{10}P_{3} =\frac{10!}{(10-3)!}[/tex]

which simplifies down to

[tex]_{10}P_{3} =\frac{10!}{7!}[/tex]

Since every number less than 8 in the numerator cancels out with the denominator, we have

[tex]_{10}P_{3}=10*9*8[/tex]

which equals 720

The answers to the questions are: -20 for Q1, 70/9 for Q2, 36 for Q3, and -1 for Q4.

Q1: If r = 9, b = 5, and g = -6, what does (r + b - g)(b + g) equal?

First, calculate the expression inside the parentheses:

r + b - g = 9 + 5 - (-6) = 9 + 5 + 6 = 20

b + g = 5 + (-6) = 5 - 6 = -1

Now multiply these results together:

(r + b - g)(b + g) = 20 × (-1) = -20

The answer is -20.

Q2: If 9(x - 9) = -11, then x =?

First, simplify the equation:

9x - 81 = -11

9x = 70

Now, solve for x:

x =  rac{70}{9}

The answer is 70/9.

Q3: If (1/2)x + (2/3)y = 6, what is 3x + 4y?

Multiply the original equation by 6 to eliminate the fractions:

6((1/2)x) + 6((2/3)y) = 6 × 6

3x + 4y = 36

The answer is 36.

Q4: Evaluate f(x) = 4x + 3x² - 5 when x = -2

Substitute -2 for x and calculate f(x):

f(-2) = 4(-2) + 3(-2)² - 5

f(-2) = -8 + 3(4) - 5

f(-2) = -8 + 12 - 5

f(-2) = -1

The answer is -1.

Answer: 4

Step-by-step explanation: If 1/4 of them are for Chloe, you'd divide 16 by 4 to find the answer. 16 divided by 4 equals 4.

Answer:

4

Step-by-step explanation:

There are 16 gifts under the tree, in which 1/4 is addressed to Chloe. To solve the amount she will get, Multiply 16 with 1/4:

16 x 1/4 = (16 x 1)/4 = 16/4 = 4

Chloe will receive 4 of those gifts.

~

Answer:

3.30 for apple and 2.00 for an orange

Step-by-step explanation:

To solve this problem, we can set up a system of linear equations to represent the charges for apples and oranges at the fruit stand. We can then solve this system using the elimination method to find the cost of an apple and an orange.

To solve this problem, we can set up a system of linear equations to represent the charges for apples and oranges at the fruit stand. Let's use x to represent the cost of an apple and y to represent the cost of an orange.

From the given information, we can set up the following equations:

111x + 111y = 5.30

111x + 222y = 7.30

Next, we can solve this system of equations by using substitution or elimination. Let's use the elimination method:

Multiply the first equation by 2, and multiply the second equation by 1:

222x + 222y = 10.60

111x + 222y = 7.30

Subtract the second equation from the first:

111x = 3.30

Divide both sides by 111:

x = 0.03

Substitute this value back into either equation to solve for y:

111(0.03) + 222y = 7.30

3.33 + 222y = 7.30

222y = 3.97

y = 0.01

Therefore, the cost of an apple is $0.03 and the cost of an orange is $0.01 at the fruit stand.

i believe the answer youre looking for is a mile

Answer

b. No

Step-by-step explanation:

We can easily solve this question by using a graphing calculator or any plotting tool, to check if it is a sinusoid.

The function is

f(x) =  sin(20*x) + cos(8*x)

Which can be seen in the picture below

We can notice that f(x) is a not sinusoid. It has periodic amplitudes, and the function has a period T = π/2

The maximum and minimum values are

Max = 1.834

Min = -2

Answer:

B

Step-by-step explanation:

no

Answer:

The transformation was not done is Shifted left 3 units

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) reflected across the x-axis, then the new

 function g(x) = - f(x)

- If the function f(x) reflected across the y-axis, then the new

 function g(x) = f(-x)

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

- A vertical stretching is the stretching of the graph away from

 the x-axis

- A vertical compression is the squeezing of the graph toward

 the x-axis.

- if k > 1, the graph of y = k•f(x) is the graph of f(x) vertically

  stretched by multiplying each of its y-coordinates by k.

- if 0 < k < 1 (a fraction), the graph is f(x) vertically compressed

 by multiplying each of its y-coordinates by k.

- if k should be negative, the vertical stretch or compress is

 followed by a reflection across the x-axis.  

* now lets solve the problem

∵ f(x) = x

∵ g(x) = -1/2 (x - 3) + 7

# -1/2 means the graph is vertically compressed by a factor of 2

  and reflected over the x-axis

# x - 3 means the graph shifted to the right 3 units

# + 7 means the graph shifted up 7 units

* The transformation was not done is Shifted left 3 units

Answer:

1/18 is the answer of that

Isaiah will earn $660 for the 50 hours he worked

Answer:

c. $660

Step-by-step explanation:

Answer:

The angular velocity is approximately  12  π radians per second.

Step-by-step explanation:

Answer:

[tex]12\pi[/tex]

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

We are given a graph, in which x is independent value and y is dependent on the value of x.

f(0) means that x = 0.

so,

we will see in the graph where the x = 0

Obviously it can be anywhere either on origin or on y-axis. The point mark on y-axis is when y = 1

Answer: second option.

Step-by-step explanation:

The formula used for calculate the lateral area of a cylinder is this one:

[tex]LA=2\pi rh[/tex]

Where "r" is the radius and "h" is the height

The formula for calculate the area of a circle (which is the base of a cylinder) is:

[tex]A=\pi r^2[/tex]

Knowing the area of the base, you can solve for the radius:

[tex]36\pi=\pi r^2\\\\r=\sqrt{\frac{36\pi units^2}{\pi}} \\\\r=6units[/tex]

Substitute the radius and the height into the formula [tex]LA=2\pi rh[/tex]:

[tex]LA=2\pi (6units)(2units)[/tex]

[tex]LA=24\pi\ units^2[/tex]

Answer:

24π square units (edge)

Step-by-step explanation:

Answer:

100/61 or 1.63934

Step-by-step explanation:

The reduced fractions of 6/3.66 to the lowest terms is 100/61.

⇒ 6/3.66 = 600/366 = 100/61.

Hence, the reduced fraction of 6/3.66 to its lowest terms is 100/61.

To learn more about reducing fractions, refer to:

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according to the picture we have:

x.y=4.7

(7)x(7)y=49xy=(49)(4.7)=230.3

Calculate the total wall and ceiling area, then determine the number of gallons of paint needed using the given coverage per gallon.

To calculate the total wall and ceiling area:

Calculate the total wall area: (2 x 12 x 7) + (2 x 15 x 7) = 168 + 210 = 378 square feet.

Add the ceiling area: 12 x 15 = 180 square feet.

Sum the wall and ceiling areas: 378 + 180 = 558 square feet.

To determine how many gallons of paint:

Divide the total area by the coverage of one gallon: 558 ÷ 250 = 2.232 gallons (round up to ensure enough paint).

You would need approximately 2.232 gallons of paint to paint the walls and ceiling of the bedroom.

To find the total area that needs to be painted, we first calculate the area of the walls and the ceiling.

1. Area of the walls:

The bedroom has four walls, two of which are 12 feet by 7 feet and the other two are 15 feet by 7 feet.

Total area of the walls = 2(12 * 7) + 2(15 * 7) = 2(84) + 2(105) = 168 + 210 = 378 square feet

2. Area of the ceiling:

The ceiling is the same size as the floor, which is 12 feet by 15 feet.

Area of the ceiling = 12 * 15 = 180 square feet

3. Total area to be painted:

Total area = Area of walls + Area of ceiling = 378 + 180 = 558 square feet

4. Gallons of paint needed:

Since one gallon of paint covers 250 square feet, we divide the total area by the coverage of one gallon:

Gallons needed = Total area / Coverage per gallon = 558 / 250 ≈ 2.232 gallons

Therefore, you would need approximately 2.232 gallons of paint to paint the walls and ceiling of the bedroom.

Answer:

Step-by-step explanation:

One of the conditions has the condition and the conclusion written in one order; the other has them written in the opposite order.

Answer:

g(x), and the maximum is 5

Step-by-step explanation:

for given function f(x), the maximum can be seen from the shown graph i.e. 2

But for the function g(x), maximum needs to be calculated.

Given function :

g (x) = 3 cos 1/4 (x + x/3) + 2

let x=0 (as cosine is a periodic function and has maximum value of 1 at 0 angle)

g(x)= 3 cos1/4(0 + 0) +2

    = 3cos0 +2

     = 3(1) +2

     = 3 +2

     = 5 !

Answer:

Option B) 30°

Step-by-step explanation:

Given :  A man on the third floor of a building shouts down to a person on the street. If the man is 25 feet up and the distance between the person on the street and the man in the building is 50 feet.

To find : What is the angle of elevation (in degrees) between the person on the street and the person in the building?

Solution :

According to question, a rough diagram is framed which shows the position of  man on street and man on building.

Refer the attached figure below.

A man on the third floor of a building is 25 feet up i.e. AB=25 feet.

The distance between the person on the street and the man in the building is 50 feet i.e. BC=50 feet.

We have to find the angle of elevation i.e. ∠C.

It form a right angle triangle,

Applying sin property of trigonometric,

[tex]\sin \theta=\frac{\text{Perpendicular}}{\text{Hypotenuse}}[/tex]

[tex]\sin \theta=\frac{AB}{BC}[/tex]

[tex]\sin \theta=\frac{25}{50}[/tex]

[tex]\sin \theta=\frac{1}{2}[/tex]

[tex]\sin \theta=\sin 30^\circ[/tex]

[tex]\theta=30^\circ[/tex]

Therefore, Option B is correct.

The angle of elevation is 30°.

Answer:

Its B

Step-by-step explanation:

I just did the test.

Answer:

4.06 in.

Step-by-step explanation:

                 4

sin(80)= ----------    multiply by X

                 x

x* sin(80)= 4 divide by sin(80)

         4

X=-------------  simplify

      sin(80)

X= 4.06 in.

Answer:

The length of the hypotenuse is 4.1 in

Step-by-step explanation:

By definition, the sine of an angle is:

[tex]sin(x) = \frac{opposite\ side}{hypotenuse}[/tex]

In this case they tell us that the opposite side measures 4 inches and the angle x measures 80 °.

With this information we can find the length of the hypotenuse h

[tex]sin(80\°) =\frac{4}{h}\\\\h = \frac{4}{sin(80\°)}\\\\h = 4.062\ in[/tex]

Finally the length of the hypotenuse is 4.1 in

Answer:

230 minutes = 3 hours + 5/6 hours

64 miles per 230 minutes =

64 miles / 3.83333 hours = 16.695 mph

which equals NONE of the answers

Step-by-step explanation:

I THINK that; Yes they are congruent but I don’t know the second parts. I think D is one of them. maybe B as well? Sorry

12/12=1

answer is B) 1

Hope this helps chu

Answer:

B.) 1

Step-by-step explanation:

Let x = 12!

We have

x / x

Anything divided by itself = 1

Answer:

Length of radius = [tex]5\sqrt{2}[/tex]

Step-by-step explanation:

The radius of the circle is the distance between the center and the point on the circle given.

The distance formula is  [tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

Where

x_1 = 0

y_1 = -6

and

x_2 = 5

y_2 = -1

plugging these into the formula we get:

[tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\=\sqrt{(-1-(-6))^2+(5-0)^2} \\=\sqrt{(-1+6)^2+(5)^2} \\=\sqrt{5^2 + 5^2} \\=\sqrt{50} \\=5\sqrt{2}[/tex]

Answer:

The radius of circle = 5√2 units

Step-by-step explanation:

Points remember

Distance formula:-

Let (x₁, y₁) and (x₂, y₂) be the two points, then the distance between these two points is given by

Distance = √[(x₂ - x₁)² + (y - y₁)²]

It is given that, center of circle (0, -6) and passes through (5, -1)

To find the radius of circle

Here (x₁, y₁) = (0, -6) and (x₂, y₂) = (5, -1)

Radius r = √[(x₂ - x₁)² + (y - y₁)²]

  = √[(5 - 0)² + (-1 - -6)²]

  = √(5² + 5²) = √(25 + 25) = √50 = 5√2 units

Therefore radius of circle = 5√2 units

Answer:

8.5

Step-by-step explanation:

Twice the difference of a number and 6 equals 5 is written algebraically as 2(x-6)=5, where x is the number. Solving for x:

2(x-6)=5

(x-6)=5/2

x=6+5/2

x=17/2

So the number is 17/2, or, expressed as a decimal number, 8.5

We solve the equation 'Twice the difference of a number and 6 equals 5' by identifying variable 'x' as the unknown number, rearranging the equation, and then performing a series of number operations (multiplication, addition, and division) to find x = 8.5.

In the given problem, you are asked to solve for a number in the equation 'Twice the difference of a number and 6 equals 5'. We denote the unknown number we’re looking for as ‘x’. Thus, the equation becomes 2(x - 6) = 5.

By solving this equation step-by-step, we first distribute the 2 to both terms in the parentheses. This key step gives us 2x - 12 = 5.

Next, we add 12 to both sides to isolate 2x on the left side, which gives 2x = 17.

Finally, we divide both sides by 2 to solve for x, giving us x = 17 / 2 or 8.5.

In conclusion, the unknown number x that satisfies the condition 'Twice the difference of a number and 6 equals 5' is 8.5.

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For this case we have to, by definition:

[tex]tg (B) = \frac {33.2} {a}[/tex]

This means that the tangent of angle B will be equal to the leg opposite the angle on the leg adjacent to the same angle.

Then, clearing to have:

[tex]a = \frac {33.2} {tg (61)}\\a = \frac {33.2} {1.80404776}\\a = 18.403060[/tex]

Rounding out the value of a we have:

[tex]h = 18.4[/tex]

Answer:

Option C

Answer:

The correct answer is option c.  18.4

Step-by-step explanation:

Points to remember:-

Trigonometric ratio

Tan θ = Opposite side/Adjacent side

From the figure we can see a right triangle triangle ABC

To find the value of a

It is given that, b=33.2 and B=61°

Tan 61 = opposite side/Adjacent side

Tan 61 = b/a

a = 33.2/Tan 61 = 18.4

Therefore the correct answer is option c.  18.4

3rd : yes, at negative and positive x coordinates

Answer:

Yes, at positive x coordinates

Step-by-step explanation:

Answer:

The scale is 7

Step-by-step explanation:

Divide 12 from 84 to get the answer.

Hope this helps! :)

Answer:

Step-by-step explanation:

Parameterize [tex]C[/tex] by

[tex]\vec r(t)=(1-t)(0,0,0)+t(1,3,6)=(t,3t,6t)[/tex]

with [tex]0\le t\le1[/tex]. Then the line integral is

[tex]\displaystyle\int_Cxyz\,\mathrm dS=\int_0^1x(t)y(t)z(t)\left\|\frac{\mathrm d\vec r}{\mathrm dt}\right\|\,\mathrm dt[/tex]

[tex]=\displaystyle18\sqrt{91}\int_0^1t^3\,\mathrm dt=\boxed{\frac{9\sqrt{91}}2}[/tex]

The line integral over the path C from (0,0,0) to (1,3,6) can be converted into an ordinary integral by parameterizing the line segment and then substituting in the integral. The result of the integral amounts to 5.

The given integral involves a line segment from (0,0,0) to (1,3,6). Our task is to convert this line integral to an ordinary integral.

The path C from (0, 0, 0) to (1, 3, 6) can be parameterized as r(t) = ti + 3tj + 6tk for 0 ≤ t ≤ 1. So, the dr = dt(i + 3j + 6k).

Substituting for ds in the integral, we get: ∫ r(t)dt from 0 to 1, which can be reduced to three separate integrals with respect to x, y, and z respectively: ∫xdx from 0 to 1, ∫3ydy from 0 to 1, and ∫6zdz from 0 to 1. Now these can be easily integrated.

So, the solution will be:
∫xdx from 0 to 1 = [x^2/2] from 0 to 1 = 1/2,
∫3ydy from 0 to 1 = [3y^2/2] from 0 to 1 = 3/2,
∫6zdz from 0 to 1 = [6z^2/2] from 0 to 1 = 3.

Adding these up gives the result of the original line integral, which is 5.

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12• (-5)= - 120/2 = -60

ANSWER

The product is

[tex] - 60[/tex]

EXPLANATION

We want to find the product of 12 and -5.

This means that we should find the result of multiplying 12 and -5

Recall that:

[tex]12 \times 5 = 5 \times 12 = 60[/tex]

Therefore,

[tex]12 \times ( - 5) = - 5 \times 12 = 60[/tex]

The product is -60

Answer:yes

Step-by-step explanation:

Each of their corners are at a 90* angle