Answer:
[tex]f^{-1}(x) = \sqrt[3]{x+5}[/tex]
Step-by-step explanation:
A function [tex]f^{-1}[/tex] is the inverse of f if whenever y =f(x) and [tex]x =f^{-1}[/tex]
To find the inverse of f(x) = [tex]x^{3}[/tex] - 5, we use the following steps:
Step 1 : Put y for f(x) and solve for xy = [tex]x^{3}[/tex] - 5
<=> [tex]x^{3}[/tex] = y + 5
<=> x = [tex]\sqrt[3]{y+ 5}[/tex]
Step 2: Put [tex]f^{-1}(y)[/tex] for x, we have:[tex]f^{-1}(y) =\sqrt[3]{y+5}[/tex]
Step 3: Interchange y =x, we have[tex]f^{-1}(x) = \sqrt[3]{x+5}[/tex]
Let Calculate 3 points on f(x)
x = 0 => y = -5
x = 1 => y = -4
x = 2 => y = 3
Let Calculate 3 points on [tex]f^{-1}[/tex] (x)
x = -5 => y = 0
x = -4 => y = 1
x = 3 => y = 2
Yes, the inverse is correct because:
the domain of the inverse function is the range of the original function the range of the inverse function is the domain of the original functionJasmine thinks that the images are the same because they are both isosceles triangles. Do you agree with Jasmine why or why not?
Answer:
No, images are not same as their dimensions are different although two sides in each of the two triangles are equal.
Step-by-step explanation:
Given: images of two isosceles triangles.
To check: if images are the same
Solution:
A triangle is a polygon made up of three sides.
An isosceles triangle is a triangle in which two sides are equal. Also, in an isosceles triangle, angles opposite to equal sides are equal.
The given images of two isosceles triangles A and B are not the same as their dimensions are different although two sides in each of the two triangles are equal.
5 red flowers 10 yellow 75 total how many red
Answer
25 are red
Step-by-step explanation:
red I blue
5 I 10
10 I 20
15 I 30
20 I 40
25 I 50
Four fifths of 30 students finished the test early .How may students finished the test early?
Answer:
24
Step-by-step explanation:
count by sixes. Good luck
Answer:
24
Step-by-step explanation:
(4/5)*30=24
4/5=.8
(.8)*30=24
A bag contains 40 tickets, each numbered between 1-40. If a ticket is drawn at random, find the probability of it being odd or less than 26
Answer:
you have a 50% chance of getting an odd number and a 60% chance of getting a number less than 26.
Step-by-step explanation:
Between 1 and 40 there are 20 odd numbers
20÷ 40 x 100=50, This means you have a 50% (20:20) chance of getting an odd number.
Between 1 and 40 there 25 numbers less than 26
15÷25 x 100=60, This means you have a 60% (25:15) chance of getting a number under 26.
Final answer:
The probability of drawing an odd ticket or a ticket numbered less than 26 from a bag containing 40 numbered tickets is 4/5 or 0.8, meaning there is an 80% chance to draw such a ticket.
Explanation:
To find the probability of drawing an odd ticket or a ticket numbered less than 26 from a bag containing tickets numbered 1-40, we need to consider the total number of favorable outcomes for each separate event and be careful not to double-count any outcomes that satisfy both conditions.
Firstly, there are 20 odd numbered tickets (1, 3, 5, ..., 39) which satisfy the first condition. For the second condition, there are 25 tickets that are numbered less than 26 (1, 2, 3, ..., 25).
However, half of the tickets less than 26 are odd (1, 3, 5, ..., 25), which we've already counted. So, we should only add the even numbered tickets that are less than 26 to get the total number of favorable outcomes. There are 12 even numbered tickets less than 26 (2, 4, 6, ..., 24).
Adding the odd numbered tickets (20) to the unique even numbered tickets less than 26 (12), we get a total of 32 favorable outcomes.
Since there are 40 tickets in total, the probability of drawing a ticket that is either odd or less than 26 is 32/40.
To simplify, divide both numerator and denominator by their greatest common divisor which is 8, giving us 4/5 or 0.8, which means there's an 80% chance of drawing a ticket that meets the criteria.
Your credit card limit is $5,000, and your current balance is $4,500. Your credit score will increase by 10 points for every $250 decrease in your balance. At the end of the year you have paid down your balance to $2,500. By how many points has your credit score increased?
Answer:
80
Step-by-step explanation:
4500-2500 is 2000 dollars reduction, or money paid off.
For every 250 dollars, there is a 10 points increase. 2000 divided by 250 is 8. There are 8 sets of 250 dollars. So, for every 250 dollars (you have 8 of them), 10 points increase. Therefore, you multiply 10 by 8.
10x8 = 80. Your credit score has increased by 80 points.
At the end of the year, my credit score would have increased by 80 points.
If my current balance is $4500 and at the end of the year, my balance is $2500. It means that the total decrease in my credit balance is $2000 ($4500 - $2500).
In order to determine the total increase in the number of points, the first step is to determine the amount of 250 that is in 2000. In order to do this, the first step would be to divide 2000 by 250.
2000 / 250 = 8
The second step is to multiply 8 by 10
8 x 10 = 80 points.
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The city aquarium got a new tank for their dolphins. The tank is 16 feet high with a radius of 28 feet. Answer these
questions about the new dolphin tank.
Approximately how much water will it take to fill the tank?
The aquarium needs to purchase a plastic cover for the tank. What should the approximate size of the cover be?
Answer:
I know the answer to the last one. Its D
Step-by-step explanation:
Approximately, the quantity of water it will take to fill this tank is equal to 39,413 cubic feet.
Given the following data:
Radius of cylinder = 28 feet.
Height of cylinder = 16 feet.
How to calculate the volume of this cylinder?Mathematically, the volume of a cylinder is calculated by using this formula:
V = πr²h
Where:
h is the height.r is the radius.Substituting the given parameters into the formula, we have;
V = 3.142 × 28² × 16
V = 39,413.248 ≈ 39,413 cubic feet.
For the cover size, we have:
Area = πr²
Area = 3.142 × 28²
Area = 2,463.328 ≈ 2,463 ft².
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help me plz and thank you!!!!
Answer: A is the answer
Step-by-step explanation:
Ryan and Matt are playing a game by rolling two number cubes, with faces numbered 1 through 6, one after the other. Ryan gets a point when the number on the first cube is an odd number and the number on the second cube is an even number. Matt gets a point when the number on the first cube is 5. The table below shows all possible combinations of numbers on the cubes.
Who is more likely to get a point on the first roll of both the cubes?
A.
Ryan is more likely to get a point, because 13/36>9/36
B.
Matt is more likely to get a point, because 13/36 > 6/36
C.
Both are equally likely to get a point, because 6/36 = 6/36
D.
Ryan is more likely to get a point, because 9/36>6/36
Ryan is more likely to get a point than Matt on the first roll of both cubes.
The fraction of outcomes in which Ryan gets a point is 9/36, which simplifies to 1/4.
The fraction of outcomes in which Matt gets a point is 1/36.
Option A is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
To determine who is more likely to get a point, we need to count the number of outcomes that satisfy each condition and then compare the fractions.
Ryan gets a point if the first cube shows an odd number and the second cube shows an even number.
There are three odd numbers and three even numbers,
So there are 3 x 3 = 9 outcomes that satisfy this condition.
Matt gets a point if the first cube shows a 5.
There is only one outcome that satisfies this condition.
Therefore,
Ryan is more likely to get a point than Matt on the first roll of both cubes.
The fraction of outcomes in which Ryan gets a point is 9/36, which simplifies to 1/4.
The fraction of outcomes in which Matt gets a point is 1/36.
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A gift box has the shape of a rectangular prism how much wrapping paper do you need to cover the box
2
You need _ in. Of a paper to cover the box
Answer:
654in squared
Step-by-step explanation:
Determine the sine of
Answer:
The sine of the angle = the length of the opposite side. the length of the hypotenuse.
The cosine of the angle = the length of the adjacent side. the length of the hypotenuse.
The tangent of the angle = the length of the opposite side. the length of the adjacent side.
I'm not sure if this answers your question.
A CD is shaped like a circle wit a diameter of 12 cm. to the nearest centimeter what is the circumference of the CD
Answer:
The answer is that the circumference of the CD is 37.7 cm.
Answer:
38cm
Step-by-step explanation:
Find the area of the triangle below.
Answer:
90
Step-by-step explanation:
The formula for a triangle is base times height then dividing it by 2
So 15 times 12 is 180 and dividing it by 2 gets you 90.
Hope this helps!
Answer:
72 :)Step-by-step explanation:
To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles. For example, in the diagram to the left, the area of each triangle is equal to one-half the area of the parallelogram.Hope this helps
Which of the following is a solution of y> |x| - 5?
(4,-1)
(-1,-4)
(-4, 1)
Answer:
(-4,1)
Step-by-step explanation:
Let us check the choices.
y > |x| - 5
- 1 > |4| - 5 = -1 NO (4,-1);
-4 > |-1| - 5 = -4 NO not(-1,-4)
1 > |-4| - 5 = -1 TRUE, yes (-4,1)
Which expression is equivalent to 8g+2+4g-2-2g
Answer:
10g
Step-by-step explanation:
add 8g,4g and -2g to get 10g
add 2 and -2 to receive 0
the simplified expression would be 10g
The equivalent expression for 8g + 2 + 4g - 2 -2g after combining like terms is 10g.
The original expression given is 8g + 2 + 4g - 2 -2g. To find an equivalent expression, we need to combine like terms. We do this by adding or subtracting the coefficients of identical variables and also combining any constant terms.
In this case, we combine the coefficients of g:
8g + 4g - 2g = (8 + 4 - 2)g = 10g.
Next, we combine the constant terms: 2 - 2 = 0. Since adding or subtracting 0 does not change the value, we can ignore this part.
Thus, the equivalent expression is simply 10g.
Which of the following is a statistical question?
A. How many books did Matt read?
B. How many jars are kept on the shelf?
C. How many pieces of candy does Rachel have?
D. How many runs did the baseball team score in each game this season?
Answer:
D
Step-by-step explanation:
It is asking overall
Find the linear equation that represents the scenario.
y= 235x + 15
y= 4x + 955
y= 15x + 235
y= 3x + 705
Answer: y=235x+15
Step-by-step explanation:
Answer:
y=235x+15
Step-by-step explanation:
Your water bill lists a previous reading of 5,520 ccf and a present reading of 5,981 ccf. The water company charges $0.93 per ccf of water. How much will you be charged on the current bill?
Answer:
$428.73
Step-by-step explanation:
The previous reading of the water bill is 5,520 ccf and a present reading of 5,981 ccf.
The number of units used is given as the present reading minus the previous reading.
This means that the number of units used is:
5981 - 5520 = 461 ccf
The water company charges $0.93 per ccf of water.
Therefore, the charges on the current bill will be:
0.93 * 461 = $428.73
convert 64 km to miles
Answer:
39.68 miles
Step-by-step explanation:
1 km is roughly 0.62 miles
Multiply 0.62 by 64 to get the answer of 39.68
Answer:
39.768 miles
Step-by-step explanation:
1.60934 Km equals 1 miles so 64 divide by 1.60934 to get the answer, 39.768.
If the length of the 45° region of
this circle is 10 inches, what is the
radius of the circle?
Answer:
Your answer is 1.6 inches.
Step-by-step explanation:
please leave explanation thank you also brainliest
Answer:
x=-2
Step-by-step explanation:
1. Convert base
(1/64) to (4^-3)
2.Apply exponent rule
4^-3(2x+10)
3. 4x-10=-3(2x+10)
4.Expand
4x-10=-6x-30
4x-10+10=-6x-30+10 (add 10 to both sides)
4x=-6x-20 (simplify)
4x+6x=-6x-20+6x (add 6 to both sides)
5. 10x=-20 (divide both side by 10)
6. Then you get x= -2.
Evaluate 4x-8 for x=3 and for x=4
Answer:
a) 4 ; b) 8
Step-by-step explanation:
4×3-8 = 12-8 = 4
4×4-8 = 16-8 = 8
Answer:
a) 4 ; b) 8
Step-by-step explanation:
The Great Pyramid of Giza is an example of a square pyramid and is the last surviving structure considered a wonder of the ancient world. The builders of the pyramid used a measure called a cubit, which represents the length of the forearm from the elbow to the tip of the middle finger. One cubit is about 20 inches in length. The height of the great pyramid is?
Answer:
The height of the great pyramid is:
303.6 cubits approximately.Or:
5464.6 inches approximately.Step-by-step explanation:
The Great Pyramid of Giza could be said to have two heights: one at the time of being built and the other that can be currently measured, however, to answer the question, the current height has been used, which is 303.6 cubits (I give the answer in this unit because it was the one used by its builders).
There is a slight discrepancy with the values given in the exercise: one cubit equals 18 inches, not 20.
Answer: 3560 in
Step-by-step explanation: algebra nation told me so
pls help! will give brainlist!
which triangle is possible?
Answer:
The top triangle.
Step-by-step explanation:
The top triangles numbers are 3,4,5, which is known as a pythagorean triple, which makes a proportionate triangle. There you go! :D
4. Factor (2a - b)2 - 4a2
The answer is b(-4a+b)
Use the following compound interest formula to complete the problem. A = P (1 + StartFraction r over n EndFraction) superscript n superscript t Currently you have two credit cards, H and I. Card H has a balance of $1,186.44 and an interest rate of 14.74%, compounded annually. Card I has a balance of $1,522.16 and an interest rate of 12.05%, compounded monthly. Assuming that you make no purchases and no payments with either card, after three years, which card’s balance will have increased by more, and how much greater will that increase be? a. Card I’s balance increased by $53.16 more than Card H’s balance. b. Card I’s balance increased by $13.45 more than Card H’s balance. c. Card H’s balance increased by $35.61 more than Card I’s balance. d. Card H’s balance increased by $49.06 more than Card I’s balance. Please select the best answer from the choices provided A B C D
Answer:
ANSWER
A.Card I’s balance increased by $53.16 more than Card H’s balance.
Step-by-step explanation:
Currently you have two credit cards, H and I. Card H has a balance of $1,186.44 and an interest rate of 14.74%, compounded annually. Card I has a balance of $1,522.16 and an interest rate of 12.05%, compounded monthly. Assuming that you make no purchases and no payments with either card, after three years, which card’s balance will have increased by more, and how much greater will that increase be? And so the total amount would be $53.16.
Card H's balance is decreased by $1579.3 than a card I.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
Principal(P) = $1,186.44
Interest Rate(r) = 14.74%
Number of time period(n) = 3 years.
Applying the above values in the formula given in the question:
[tex]A=P(1+\frac{r}{n}) ^{nt}[/tex]
A=$1792.2
Amount of Card I after 3 years:
Principal(P) = $1,522
Interest Rate(r) = 12.05%
A number of the time periods (n):
12 months × 3 years=36 months
A=3351.8
Now we take the difference between both the credit cards, we have:
Amount of credit card I - Amount of credit card H
$1579.38
Therefore, card H's balance is decreased by $1579.3 than a card I.
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Suppose that an urn contains 3 black marbles, 7 yellow marbles, and 10 green marbles. If one marble is selected, determine the probability that it is green. The answer should be an integer or a simplified fraction.
Answer:
1/2
Step-by-step explanation:
Simple probability is a ratio of the number of ways the thing we want to happen can to the total possible outcomes.
(For example, we flip a coin and want heads, but it can land on heads or tails. Our probability of getting heads is 1/2, one way to get heads over the 2 possible outcomes)
So for this problem, there's 20 possible things that CAN happen (3 + 7 + 10) and 10 ways we get what we want (a green marble).
Our probability of getting a green marble is [tex]\frac{10}{20\\}[/tex], which simplifies to [tex]\frac{1}{2}[/tex]
A blanket is 4 feet wide. It is 3 times as long as it is wide. Find the perimeter and area of the blanket.
Answer:
P: 32
A: 48
Step-by-step explanation:
(4+(4*3))*2=32
4*(4*3)=48
The blanket is 4 feet wide and 12 feet long. The perimeter of the blanket is 32 feet and the area is 48 square feet.
Explanation:The blanket is given to be 4 feet wide, and its length is 3 times its width, which means the length is 3 x 4 = 12 feet. Therefore, the blanket is 4 feet wide and 12 feet long.
For a rectangle, the formula for perimeter is 2*(length + width). Plugging in our values gives us 2*(12 + 4) = 32 feet.
The formula for the area of a rectangle is length * width. Using our dimensions, the area is 12 * 4 = 48 square feet.
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Help Me Out With This Question Plz!!
Gio is standing at the base of his house. He measures the angle of elevation to the top of a nearby high rise to be
50°. He decides to go to the roof of his house standing in the same position and measures the elevation to the top
of the same high rise to be 25°. If the height of the high rise is 150 meters tall, how tall is the house? How much
taller is the high riser than the house? Draw a diagram
Answer:
the apartment building is 31.2 meters
Step-by-step explanation:
Evaluate 5+ (-11) - (-11)
Answer:
5
Step-by-step explanation:
To solve a problem with negatives, we use the following rule.
If it is like
x+(-y), it is equivalent to x-y
If the equation is like
(-x)-(-y), it is equivalent to (-x)+y
So,
5+(-11)=5-11=-6
(-6)-(-11)=(-6)+11=5
Your answer is 5.