Answer:
a) 80
b) 56
Step-by-step explanation:
a) Calculate the volume of the the cup using volume of cylinder equation: [tex]V = \pi r^{2} h[/tex]
Where V = Volume, r=radius, and h=height. Your answer should be in cubic inches ([tex]in^3[/tex]).
You're given diameter, so use equation [tex]d/2 = r[/tex] to find radius.
Substituting these equations will give you: [tex]V = \pi (d/2)^2 h[/tex]
However, the given volume of the sink is 3000[tex]\pi[/tex], meaning that you should modify your results to match this value. Do not substitute [tex]\pi[/tex] for 3.14..., leave it as a symbolic value. Your final V of the cup should = 37.5 [tex]\pi[/tex]
Divide the volume of the sink by the volume of the cup. This number will be the amount of cups needed to empty it. In equation form:
[tex]Vsink / V cup =[/tex] # of cups.
Note the the [tex]\pi[/tex] will cancel each other out, so there's not need to factor that in.
b) Repeat the steps above with the new d (diameter) value.
In a story, a tortoise and a hare take part in a race.
They have to run up and down the same hill.
The distance from the foot to the top of the hill is 996 meters.
The hare takes a nap after rrunning 578 meters.
How much further must the hare run to complete the race?
Give your answer in kilometers and meters.
Answer:
418 meters
Step-by-step explanation:
The total distance is 996 meters, hare completed 578 meters. The question asked how much further hare has to run which indicates that this is a subtraction problem.
Equation to solve :996-578=x
x=418
Hope this helps, let me know if I am wrong. Have a good day:)
Bonus: The probability that our administrators are athletic is .79. The probability that they are
intelligent is .89. The probability that they are both athletic and intelligent is.83. What is the
probability that if we choose an administrator, randomly, that he/she is not athletic?
Answer:
79
Step-by-step explanation:
Steve hade 17 pencils in his backpack. this represents 5 more than 6/7 the number of pencils that Clyde has in his backpack
Answer:
Clyde has 14 pencils in his backpack
Step-by-step explanation:
Let x be the number of pencils that Clyde has in his backpack.
We can translate this statement “Steve hade 17 pencils in his backpack. this represents 5 more than 6/7 the number of pencils that Clyde has in his backpack” mathematically like this :
[tex]17=5+\frac{6}{7} x \\\\ \Longleftrightarrow 17-5=\frac{6}{7} x \\\\ \Longleftrightarrow 12=\frac{6}{7} x \\ \\\Longleftrightarrow x=\frac{12\times 7}{6} =14[/tex]
Let he has n pencils
So
[tex]\\ \rm\hookrightarrow \dfrac{6n}{7}+5=17[/tex]
[tex]\\ \rm\hookrightarrow \dfrac{6n}{7}=12[/tex]
[tex]\\ \rm\hookrightarrow 6n=84[/tex]
[tex]\\ \rm\hookrightarrow n=14[/tex]
Before a renovation, a movie theater had 120 seats. After the renovation, the theater has 162 seats. What is the approximate percentage increase of the number of seats in the theater? If necessary, round to the nearest tenth of a percent.
Answer:
35%
Step-by-step explanation:
Percent increase is (new number - old number) / old number
(162 - 120) / 120 = 42 / 120 = 0.35 = 35%
What is the algebraic rule?? And how do you find out what algebraic rule on a graph is (x,y)to (x,y+10)??? I know how to find basic rules according to the degree rotation but I don’t understand what does + 10 mean how am I supposed to find that on a graph based on rotation degrees???
The teacher never taught me please help me
Thank you!
Answer:
(x, y) ⇒ (-x, y)
Step-by-step explanation:
When you're looking for a rule that transforms one figure to the other, the first step is to look at the figures. You want to identify their orientation (order of vertices) and the relative locations of corresponding vertices.
Here, vertices VWX are in clockwise order. The corresponding vertices V'W'X' are in counterclockwise order. For that to happen, there must be a reflection involved.
The y-axis goes through the midpoints of VV', WW' and XX'. This means the y-axis is the line of reflection. The coordinates of V'W'X' have the same y-values as their originals, but their x-values have changed sign.
The algebraic rule for these two figures is ...
(x, y) ⇒ (-x, y) . . . . . . reflection over y-axis; sign of x changes
__
Additional comment
No rotation is involved here.
The rule (x, y) ⇒ (x, y+10) means the y-coordinate has had 10 added to it. That causes a translation upward by 10 units. This is the algebraic rule.
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is 15 more than the second.
Answer:
Angle #1 is 45 degrees
Angle #2 is 60 degrees
Angle #3 is 75 degrees
Step-by-step explanation:
x- angle #1
y- angle #2
(180-x-y)- angle #3
3x=180-x
4x=180
x=45
180-x-y=y+15
y=60
180-60-45=
180-105= 75
Solve equation by using the quadratic formula.
2x² - 5x = 7
Answer:
c
Step-by-step explanation:
trust
In the figure, A ABC is similar to ADEF.
What is mZ1?
B
77
F1
O 103
E
62
O 118°
D
O 139°
O 167
Answer:
need pictures of questions
Step-by-step explanation:
please
When are two angles complementary?
Answer:
90 degree's
Step-by-step explanation:
Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees
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[tex]\blue\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
When are two angles complementary?
[tex]\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]
Two angles are complementary when they add up to [tex]\tt{90\textdegree}[/tex].
For example:-
Angles whose measures are 60º and 30º are complementary because they add up to 90º.
Now, supplementary angles add up to [tex]\tt{180\textdegree}[/tex].
For example, angles whose measures are 140º and 40º are supplementary because they add up to 180º.
Good luck.
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Find the area.
2 in
9 in
2 in
11 in
WHOEVER GIVES RIGHT ANSWER I GIVE BRAINLIEST
Answer:
See the photo above
Step-by-step explanation:
Hope this helps and have a nice day
What cosine function represents an amplitude of 2, a period of 2π, a horizontal shift of π, and a vertical shift of −1? (6 points) a f(x) = −1 cos πx + 2 b f(x) = −1 cos (x − π) + 2 c f(x) = 2 cos (x − π) − 1 d f(x) = 2 cos πx − 1
Answer:
c. f(x) = 2 cos(x − π) − 1
Step-by-step explanation:
The amplitude is the multiplier of the cosine function. The vertical shift is a constant added to the cosine function. The horizontal shift is a value subtracted from x in the argument of the cosine function.
For amplitude 2, vertical shift -1, and horizontal shift π, the function will look like ...
f(x) = 2·cos(x -π) -1
The graph of the Function F(x) is shown below. What is the value of f^-1(1)
Answer: [tex]f^-1(1)=-1[/tex]
Step-by-step explanation:
From the graph given we can derive the function [tex]f(x)[/tex]
[tex]f(x) = .5x + 1.5[/tex]
To solve [tex]f^-1(1)[/tex] we need to find the inverse function of [tex]f(x)[/tex].
Inverse functions are functions that essentially "reverse" the mapping of the domain ([tex]x[/tex]) and range ([tex]y[/tex]) of the parent function.
To find the inverse function [tex]f(x)[/tex] we need to solve for x in terms of y.
[tex]y = .5x + 1.5[/tex]
[tex]y - 1.5 = .5x[/tex]
[tex]\frac{y - 1.5}{.5} = \frac{.5x}{.5}[/tex]
[tex]x=2y-3[/tex]
from this, we can derive that
[tex]f(y)^-1=2y-3[/tex]
this can also be written as a function of x
[tex]f(x)^-1 = 2x-3[/tex]
both functions are identical.
take one of these functions and you can find that
[tex]f^-1(1) = 2(1) - 3[/tex]
[tex]f^-1(1) = -1[/tex]
What is the volume of the figure composed of two congruent triangular prisms if a = 5 units, b = 3 units, and c = 6 units?
A.
60 cubic units
B.
45 cubic units
C.
90 cubic units
D.
180 cubic units
Finding π (optional)
You need:
• Six or fewer objects that have a round surface
• Yard or meter stick
• Ruler
• String (must be long enough to go around each of the round surfaces)
Directions:
1. List each object in the chart below.
2. Take your string and measure the distance around the circular object. Write that measurement
in the chart under Circumference.
3. Use your ruler to measure the diameter of the circular object. Write that measurement in the
chart under Diameter.
4. Divide the circumference by the diameter. Write that answer in the chart under Ratio. Was your
answer close to π
The circumference of the ball will be 43.988cm and dividing the circumference by the diameter equals pie.
How to calculate the circumference?The object that's chosen in this scenario is a circular ball. The diameter of the ball is 14cm.
The circumference of the ball will be:
= 2πr
= 2 × 3.142 ×(14/2)
= 2 × 3.142 × 7
= 43.988cm
Dividing the circumference by the diameter will be:
= 43.988cm/14cm
= 3.142
The answer is close to pi.
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A _____ has to be paid in full on the due date.
A credit card has to be paid in full on the due date. The correct option among all the options that are given in the question is the first option. The other choices are incorrect and can be easily neglected. The amount of money that the credit card company bills for a month has to be paid in full within the due date or additional fine would be added to the next bill.
50 POINTS WILL MARK BRAINLIEST
A cable television company has 8000 subscribers in a suburban community. The company offers two premium channels, A and B. If 2350 subscribers receive channel A, 1860 receive channel B, and 5220 do not receive any premium channel, how many subscribers receive both channel A and channel B?
Answer:
The answer is 4,530
Step-by-step explanation:
2550 + 1980 = 4,530
f (x) = 7x + 2. Find the inverse of f(x).
O A. f-1(2)= 4
O B. f-1(r)=Tx-2
O c. f-(t) =%á
O D. f (x) = 2- 7x
Answer:
[tex] \frac{x - 2}{7} [/tex]
Step-by-step explanation:
[tex]f(x) = 7x + 2[/tex]
[tex]let \: \: f(x) = y[/tex]
[tex]7x + 2 = y[/tex]
[tex]7x = y - 2[/tex]
[tex]x = \frac{y - 2}{7} [/tex]
[tex] {f}^{ - 1} (x) = \frac{x - 2}{7} [/tex]
[tex]\large\text{view\:explanation\:for\:more\:details}[/tex]
Calculations ↓Remember , inverse functions do the opposite things in the opposite order.
Here's what happened to x here :
First , it's been multiplied by 7 .Then , 2 has been added to it .We can easily find the inverse of any function by following these steps :
Set the function equal to y as follows :f(x)=7x+2
y=7x+2
2. Now , switch y and x places :
x=7y+2
3. Solve for y .
First , subtract 2 on both sides :
x-2=7y
Divide by 7 on both sides :
[tex]\text{y=$\displaystyle\frac{x-2}{7}$}}[/tex]
We've found the inverse function of f(x)=7x+2.[tex]\tiny\text{hope\:helpful}[/tex]
Please solve with explanation (high points)
The value of ∠AKL and ∠AKC are both 45° each. The justification is that lines AK and KC both split the regular polygons BKLC (rectangle) and ABCD in two. The sum of angles in a right angle is 90°, hence half of that is 45°
What is a regular polygon?A regular polygon is one that is two-dimensional and can be created at least three lines together.
Because, the sum of angles in a right angle is 90°, hence half of that is 45°. Therefore, the values of ∠AKL and ∠AKC are both 45° each.
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PLEASE HELP
Log,3 7=x is equivalent to which of the following (choose all correct answers)
Answer:
should be 3^X = 7 and X = log7/log3
Step-by-step explanation:
Answer:
[tex]3^x = 7\\x = \frac{log7}{log3}[/tex]
what is the reference angle for a 240 degree angle?
Which steps could be part of the process in algebraically solving the system of equations, y + 5x = x + 10 and y = 4x – 10?
Select two options.
y=x2 + 5x + 10
y + 5x = x2 + 10 + 4x - 10
0 = x2-9x 0 = x2 - 9x + 20
One x-value of a solution to the system is 4.
y=x2 + 5x + 10
y + 5x = x2 + 10 + 4x - 10
0 = x2-9x 0 = x2 - 9x + 20
A raffle at a local fair has tickets for purchase for $10 each. There are 100 total tickets in the raffle. The tickets are shuffled, then 3 are selected to win a $100 prize. Use the table below to help you calculate the expected value of this raffle.
If the probability of success is 0.03. Then the expected value of the raffle will be 3.
What is binomial distribution?Binomial distributions consist of n independent Bernoulli trials.
The expected value X will be given below.
E(X) = np
A raffle at a local fair has tickets for purchase for $10 each.
There are 100 total tickets in the raffle.
The tickets are shuffled, then 3 are selected to win a $100 prize.
Then the probability of success will be
p = 3/100
p = 0.03
Then the expected value of the raffle will be
n = 100
Then we have
E(X) = np
E(X) = 100 x 0.03
E(X) = 3
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How do I find the perimeter of a regular triangular pyramid?
Answer:Triangular Pyramid Solved Examples Example 1: Find the surface area of a triangular pyramid with the base area is 28cm.sq., the perimeter is 20cm, slant length is 5cm. Solution: Surface area = [Base area] + ½ × Perimeter × [Slant length] = 28 + ½ × 20 × 5 = 28 + 50 = 78 cm.sq.
Step-by-step explanation:
A class of 30 swim team members took a life saving test 18 of the members had an average of 92 points the remaining members had an average score of 84 points what was the average for the entire swim team
Answer:
88.8
Step-by-step explanation:
Write down two different expressions that are equivalent to 5x + 2 – 4y.
Answer:
2 + 5x - 4y
OR
-4y + 5x + 2
Step-by-step explanation:
The order of arrangement doesn't matter, what matters are the signs
)) What is 2.1 x 3.2?
the answer is 6.72.
2.1 x 3.2 = 6.72
Answer:
6.72 is the answer
100 POINTS TO WHOEVER IS CORRECT!!
SHOW ALL WORK. PLEASE HELP.
ALSO SHOW WHERE YOU CONNECTED THE DOTS
QUESTION -
WHAT IS THE AREA OF THIS IRREGULAR POLYGON
Answer:
25 unit²
Step-by-step explanation:
NEED ANSWERS TO 25 APSPSLANDEBEB PLEASE
What is the common denominator for 4 3/8 + 5 7/8?
Answer:
The common denominator is 8
Step-by-step explanation:
It depends on what you mean. The denominator is 8 in both of the fractions that is being added together