For what angles c in [0, 2pi) does the cos(x) have the same value as sin (3pi/4)?

Answer:

Part a) The volume of the pill is [tex]603\ mm^{3}[/tex]

Part b) [tex]1.7\frac{mg}{mm^{3}}[/tex]

Part c) [tex]215\ mg[/tex]

Step-by-step explanation:

Part a) Find the volume of the pill in cubic millimeters

we know that

The volume of the pill is equal to the volume of the cylinder plus the volume of a sphere (two hemisphere is equal to one sphere)

so

[tex]V=\frac{4}{3}\pi r^{3}  +\pi r^{2}h[/tex]

we have

[tex]r= (18-11)/2=3.5\ mm[/tex]

[tex]h=11\ mm[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]V=\frac{4}{3}(3.14)(3.5)^{3}  +(3.14)(3.5)^{2}(11)[/tex]

[tex]V=603\ mm^{3}[/tex]

Part b) If the pill is to contain 1,000 milligrams of vitamin C, then how much vitamin C does the pill contain per  cubic millimeter?

Divide 1,000 milligrams by the volume

[tex]1,000/603=1.7\frac{mg}{mm^{3}}[/tex]

Part c) Another pill that is entirely spherical has a diameter of 10 millimeters and contains 1.5 milligrams of  vitamin C per cubic millimeter. How much less vitamin C does this second pill contain, rounded to the

nearest milligram, than the one pictured?​

step 1

Find the volume of the sphere

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=10/2=5\ mm[/tex] ----> the radius is half the diameter

assume

[tex]\pi =3.14[/tex]

substitute

[tex]V=\frac{4}{3}(3.14)(5)^{3}[/tex]

[tex]V=523.33\ mm^{3}[/tex]

step 2

Multiply the volume by 1.5 milligrams of  vitamin C per cubic millimeter

so

[tex]523.33*1.5=785\ mg[/tex]

step 3

Find the difference

[tex]1,000-785=215\ mg[/tex]

Answer:

B.   3x^2 - 2x - 1.

Step-by-step explanation:

(f + g)x = f(x) + g(x)

= -4x + 3 + 3x^2 + 2x - 4

Adding like terms we get the answer:

= 3x^2 - 2x - 1.

The answer is:

B. [tex](f+g)(x)=3x^{2} -2x-1[/tex]

To solve the problem, we need to add/subtract like terms. The like terms are the terms that share the same variable and the same exponent.

For example:

[tex]x^{2} +3x^{2} +5x^{3}=4x^{2}+5x^{3}[/tex]

We were able to add the terms that were squared since both shares the same variable and the same exponent.

So, we are given the functions:

[tex]f(x)=-4x+3\\g(x)=3x^{2} +2x-4[/tex]

Now, we are asked to calculate (f+g)(x) which is also equal to f(x) + g(x).

Then, calculating we have:

[tex](f+g)(x)=(-4x+3)+(3x^{2} +2x-4)\\\\(f+g)(x)=3x^{2} -4x+2x+3-4\\\\(f+g)(x)=3x^{2} -2x-1[/tex]

Hence, the answer is:

B. [tex](f+g)(x)=3x^{2} -2x-1[/tex]

Have a nice day!

Answer: 42

Step-by-step explanation:

The different types of one-topping pizzas that they serve are 196.

The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

where,

n is the number of choices available,

r is the choices to be made.

As the size of the pizzas that are available is of 3 different types, therefore, the number of choices for the size of the pizza is 3, which can be written as,

[tex]\text{Choices of Pizza}=^3C_1[/tex]

The number of toppings that are available is 14, therefore, the number of choices for pizza toppings can be written as,

[tex]\text{Choices of Toppings}=^{14}C_1[/tex]

Now, the different types of one-topping pizzas that they serve are,

[tex]= \text{Choices of Pizza} \times \text{Choices of Toppings}\\\\= ^3C_1 \times ^{14}C_1\\\\=3 \times 14\\\\= 196[/tex]

Hence, the different types of one-topping pizzas that they serve are 196.

Learn more about Combination:

https://brainly.com/question/11732255

Answer:

97.6

Step-by-step explanation:

test

The amount of three-dimensional space enclosed by a closed surface. The volume of the object is 97.6 in³.

The amount of three-dimensional space enclosed by a closed surface is expressed as a scalar quantity called volume.

The volume of the object is the difference between the volume of the cylinder and the volume of the cone. Therefore, the volume of the object can be written as,

The Volume of object =  Volume of cone - Volume of cylinder

[tex]\text{Volume of Object} = \pi r^2h_{cylinder} - \dfrac13 \pi r^2h_{cone}[/tex]

Since π and radius of the cone and cylinder are common, therefore the equation can be written as,

[tex]\text{Volume of Object} = \pi r^2h_{cylinder} - \dfrac13 \pi r^2h_{cone}\\\\\\\text{Volume of Object} = \pi r^2(h_{cylinder} - \dfrac13 h_{cone})[/tex]

As it is given that the radius of the figure is 2 inches, and the height of the cylinder is 8 inches while the height of the cone is 0.7 inches, therefore, the volume can be written as,

[tex]\text{Volume of Object} = \pi \times (2^2) \times (8 - \dfrac{0.7}{3} ) = 97.6\rm\ in^3[/tex]

Thus, the volume of the object is 97.6 in³.

Learn more about Volume:

https://brainly.com/question/13338592

Answer:

XY = 5[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Calculate the coordinates of X and Y using the midpoint formula

[ [tex]\frac{1}{2}[/tex](x₁ + x₂), [tex]\frac{1}{2}[/tex](y₁ + y₂) ]

with (x₁, y₁ ) = A(- 3, 9) and (x₂, y₂ ) = B(- 5, - 3)

X = [[tex]\frac{1}{2}[/tex](- 3 - 5), [tex]\frac{1}{2}[/tex](9 - 3) ] = (- 4, 3)

Repeat with

(x₁, y₁ ) = B(- 5, - 3) and (x₂, y₂ ) = C(7, - 1)

Y = [ [tex]\frac{1}{2}[/tex](- 5 + 7), [tex]\frac{1}{2}[/tex](- 3 - 1) ] = (1, - 2)

---------------------------------------------------------------------------------------------

Calculate the length of XY using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = X(- 4, 3) and (x₂, y₂ ) = Y(1, - 2)

XY = [tex]\sqrt{(1 +4)^2+(-2-3)^2}[/tex]

     = [tex]\sqrt{5^2+(-5)^2}[/tex]

     = [tex]\sqrt{25+25}[/tex] = [tex]\sqrt{50}[/tex] = 5[tex]\sqrt{2}[/tex]

Answer:

[tex]y=11.5466(1.8484)^x[/tex]

Step-by-step explanation:

Given :

x       y

0      14  

1       23  

2      30  

3      58  

4     137  

5     310

To Find: What is the exponential regression equation to best fit the data?

Solution:

General form of exponential regression equation : [tex]y=ab^x[/tex]

So, using calculator

Regression Equation:  [tex]y=11.5466(1.8484)^x[/tex]

Hence  the exponential regression equation to best fit the data is  [tex]y=11.5466(1.8484)^x[/tex]

Answer:

I have the correct answer for you people on the quiz

Step-by-step explanation:

Answer:

The vertex is the point (4,3)

Step-by-step explanation:

we have

[tex]y=\frac{3}{4}x^{2}-6x+15[/tex]

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]y-15=\frac{3}{4}x^{2}-6x[/tex]

Factor the leading coefficient

[tex]y-15=\frac{3}{4}(x^{2}-8x)[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side.

[tex]y-15+12=\frac{3}{4}(x^{2}-8x+16)[/tex]

[tex]y-3=\frac{3}{4}(x^{2}-8x+16)[/tex]

Rewrite as perfect squares

[tex]y-3=\frac{3}{4}(x-4)^{2}[/tex]

[tex]y=\frac{3}{4}(x-4)^{2}+3[/tex] ----> equation in vertex form

The vertex is the point (4,3)

180-88=92 becuase supplementary angles add up to 180 and 88 plus 92 equal 180

angle 4=92

Answer:

92 degrees

Step-by-step explanation:

YOUR WELCOME

PLEASE MARK ME BRAINLIEST

The radius is 3.

Because the diameter is 3•2=6

Hope this helps.

Answer:

3

Step-by-step explanation:

The diameter of the circle is 2 times the radius

d = 2r

6 = 2r

Divide each side by 2

6/2 =2r/2

3=r

The radius is 3

hey buddy how's it going?

Answer:

Step-by-step explanation:

Because 25% is the same as 1/4. We can do the same thing as if we were changing 1/4 into a whole 1/4·4=1. So 25%·4=1. So 150·4 is our answer. So 150·4=600. There are 600 gumballs in the machine. :D

Answer:

600 Gumballs in total

Step-by-step explanation:

Write it as a proportion.

25/100 = 150/x

25x = 15000

x = 600 gumballs

OR

You could multiply 150 by 4 because 25% equals 1/4.

Answer:

w = 21

x = 13

y = -11

z = -16

Step-by-step explanation:

Matrix subtraction is simply subtracting "corresponding" values e.g. row 1 column 1 value of one matrix and row 1 column 1 value of another matrix, and so on...

Thus, w = 17 - (-4) = 17 + 4 = 21

x = 12 - (-1) = 12 + 1 = 13

y = -3 -8 = -11

z = -2 -14 = -16

These are the values of w, x, y and z , respectively.

Answer:

2/3

Step-by-step explanation:

Divide both the numerator and denominator by the GCD

4 ÷ 2 = 2

6 ÷ 2 = 3

Answer:

2/3

Step-by-step explanation:

4/6 reduces to 2/3.

[tex]53 + x \leq 60[/tex]

53 is what he's driving at, x is how much faster he can go, 60 is the speed limit.

If we solve it, we can see that Mr.Erikson can go 7 miles per hour faster.

2 units between (-3,-2) and (-1,-2)

The distance between the points (-3, -2) and (- 1, - 2) is 2 units.

The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by

[tex]D = \sqrt{x_2 - x_1)^2 + (y_2 - y_1)^2[/tex].

Given, Are two points (-3, -2) and (- 1, - 2).

Therefore the distance between these two points can be obtained by the distance formula,

[tex]D = \sqrt{x_2 - x_1)^2 + (y_2 - y_1)^2[/tex].

Therefore,

[tex]D = \sqrt{-1 + 3)^2 + (-2 + 2)^2[/tex].

[tex]D = \sqrt{2)^2 + (0)^2[/tex].

[tex]D = \sqrt{4[/tex].

D = 2units.

So, The distance between the points (-3, -2) and (- 1, - 2) is 2 units.

learn more about the distance between two points here :

https://brainly.com/question/15958176

#SPJ2

The population consists of volunteers in a certain state.

The problem mentions that volunteers took the survey, as well that the survey is meant to find the opinions of people in a certain state.

Answer:

f(x) = x^3 - x^2 -2x

Step-by-step explanation:

If x = a is a zero of a polynomial, then x-a is a factor of the polynomial. Given the factors of a polynomial, the polynomial can be obtained by multiplying the factors.

The factors of the given polynomial are;

x - 2

x + 1

x

Multiplying the first two factors;

(x-2)(x+1) = x^2 + x -2x -2

              = x^2 -x -2

We finally multiply this result by x to obtain our polynomial;

f(x) = x ( x^2 -x -2)

      = x^3 - x^2 -2x

which is a cubic polynomial since it has 3 roots.

Answer:

f(x) = x³ - x² - 2x

Step-by-step explanation:

given a polynomial with zeros x = a, x = b, x = c

Then the factors are (x - a), (x - b) and (x - c)

and the polynomial is the product of the factors, that is

f(x) = k(x - a)(x - b)(x - c) ← where k is a multiplier

--------------------------------------------------------------------

Here the zeros are x = 2, x = - 1 and x = 0, thus the factors are

(x - 2), (x + 1) and (x - 0) , thus

y = kx(x - 2)(x + 1) ← let k = 1 and expand factors

 = x(x² - x - 2) = x³ - x² - 2x

Hence a possible polynomial is

f(x) = x³ - x² - 2x

Answer:

4 and 5

Step-by-step explanation:

The mode is the value or values which occur most in the data set.

Here 4 occurs 3 times and 5 occurs 3 times, while 7 and 8 only occur once.

Hence there are 2 modes, that is 4 and 5

4 and 5

That’s your answer

Answer:

15

Step-by-step explanation:

Well first I found the area of the big rectangle which is lxw which will be equal to 12. while the small rectangle the area will be equal to 3. Finally, I added the 2 areas and I got 15. I hope this helped you.

Answer:

b

Step-by-step explanation:

Answer:D

Step-by-step explanation:

-9+9=0

First find the probability of each color being drawn.

We need to find the total number of marbles first.

4 + 3 + 6 = 13

So everything will be over 13.

Probability of a white marble being drawn --> [tex]\frac{4}{13}[/tex]

Probability of a blue marble being drawn --> [tex]\frac{3}{13}[/tex]

Probability of a red marble being drawn --> [tex]\frac{6}{13}[/tex]

Now to find the probabilities of more than one being drawn, we can multiply.

Part a :

[tex]\frac{6}{13}*\frac{6}{13}=\frac{36}{169}[/tex]

Part b :

[tex]\frac{3}{13}*\frac{3}{13}=\frac{9}{169}[/tex]

Part c :

[tex]\frac{6}{13}*\frac{3}{13}=\frac{18}{169}[/tex]

Part d :

[tex]\frac{7}{13}*\frac{7}{13}=\frac{49}{169}[/tex]

Final answer:

The probability of drawing a marble of a specific color remains the same after each draw when a marble is replaced in the bag. For a bag of 13 marbles, the probability of drawing a blue marble twice in a row is 3/13 for each draw, assuming replacement after the first draw.

Explanation:

The question asks to calculate the probability of certain outcomes when drawing marbles from a bag with replacement. Considering a bag with a total of 13 marbles (4 white, 3 blue, and 6 red), the probability of drawing a marble of a specific color is calculated by dividing the number of marbles of that color by the total number of marbles in the bag. Since each marble is replaced after it is drawn, the probabilities for the second draw remain the same as the first.

For example, the probability of drawing a blue marble is 3 out of 13. If we replace the marble and draw again, the probability of drawing a blue marble for the second time is still 3 out of 13. The events are independent, and the probabilities do not change after each draw because of the replacement.

you change the y to have it y=3x+16 and same with the other one i think

She profited $110 because $10 per dozen equals to $150. Then, you subtract $40 then you have $110. Hope my answer helped. (:

10x15=150

150-40=110

110 is the profit!

hope this helped!

Answer: 1 and 1/5 pounds

Step by step explanation:

Find a common denominator.

In this particular equation we’ll use 15. Take 4/5 and multiply that by 3/3 and you get 12/15. Then take 2/3 and multiple that by 5/5, you then get 10/15. (That step was simply so we can compare the data easier, it is a crucial step to this question). So now you know that you have 12/15 cherries in the bucket and you need get 3/15 more to fill the bucket. And if 2/3=6/15 than you would need another 1/3 so, you would add 6/15 to 12/15 and get 18/15= 1 3/15. Im not complete sure if this is correct, but I tried :(.

Answer:

(1/6)π(7²) = (49/6)π square inches

= about 25.66 square inches

Answer:

The area of the right triangle is [tex]43.88\ cm^{2}[/tex]

Step-by-step explanation:

The question in English is

From a right triangle it is known that its hypotenuse measures 20 cm and the sum of the legs measures 24 cm. How much does its area measure?

Let

x-----> the measure of one leg

y----> the measure of the other leg

Assume x is less than y

we know that

Applying Pythagoras Theorem

[tex]20^{2}=x^{2}+y^{2}[/tex] -----> equation A

[tex]x+y=24[/tex]

[tex]y=24-x[/tex] -----> equation B

Substitute equation B in equation A and solve for x

[tex]20^{2}=x^{2}+(24-x)^{2}\\ \\400=x^{2} + 576-48x+x^{2}\\ \\ 2x^{2} -48x+576-400=0\\ \\2x^{2} -48x+176=0[/tex]

Solve the quadratic equation by graphing

The solution is  [tex]x=4.5\ cm[/tex]  

see the attached figure

[tex]x=4.5\ cm[/tex]

[tex]y=24-4.5=19.5\ cm[/tex]

The area is equal to

[tex]A=xy/2=(4.5)(19.5)/2=43.88\ cm^{2}[/tex]

Answer:

c=15.50+0.08t

Step-by-step explanation:

Sandra's total monthly cost for her cell phone, represented by C, consists of a fixed rate of $15.50 for unlimited minutes and an additional $0.08 per text message. The formula to calculate her total cost is C = 15.50 + 0.08t, where t is the number of text messages.

The total monthly cost, C, for Sandra's cell phone is composed of a fixed monthly charge plus a variable charge that depends on the number of text messages she sends.

The fixed charge is her unlimited minutes plan which costs $15.50 per month.

On top of that, each text message costs $0.08, so if we let t represent the number of texts she sends, the variable cost will be 0.08t.

Therefore, the equation to model Sandra's total monthly cost would be:

C = 15.50 + 0.08t

We can confidently state that this equation represents how Sandra's monthly expenses on her cell phone will add up depending on the number of texts, t, she sends in a month.

Answer:

the definition is two of the same kind

An ordered pair is a set of coordinates or points on a graph. In order, they would be the x coordinate and the y coordinate. The ordered pair would look like this (x, y). For example, on a graph, the ordered pair of a point that is 3 over and 4 up would look like this: (3, 4), as the x value is 3 and y value is 4. The x value always comes before the y value in an ordered pair.

There is 1 17-year-old player on the varsity basketball team whose height is 74 inches or less. The correct option is B.

In a scatter plot, each dot represents one player, with the x-axis typically representing age and the y-axis representing height. By examining the data points corresponding to 17-year-olds, we find only one dot where the height is 74 inches or less.

This analysis involves visually inspecting the scatter plot and identifying the specific data points that satisfy the criteria mentioned in the question. The correct answer, therefore, reflects the count of such data points, and in this case, it is one.

Answer:

2

Step-by-step explanation:

IF YOU LOOK AT THE CHART, YOU WILL SEE THATTHE NUMBER OF 17 YEAR OLDS THAT ARE 74 INCHES AND UNDER ARE 2