Given that the fraction is 1/36
And we need to find the equivalent ones.
Explanation-
So first we will solve all the options and then we will get the required answer.
If we shift power from the numerator to the denominator then the sign of the number n the power gets changed and vice-versa.
Then,
\(3^{-6}=\frac{1}{3^6}=\frac{1}{729}\ne\frac{1}{36}\)\(6^{-2}=\frac{1}{6^2}=\frac{1}{36}\)\(\frac{6^3}{6^5}=\frac{1}{6^5\times6^{-3}}=\frac{1}{6^{5-3}}=\frac{1}{6^2}=\frac{1}{36}\)\(\frac{6^2}{6^{-1}}=6^2\times6=6^3=216\ne\frac{1}{36}\)\(6\times6^{-2}=\frac{6}{6^2}=\frac{1}{6}\ne\frac{1}{36}\)\(6^{-9}\times6^7=\frac{6^7}{6^9}=\frac{1}{6^9\times6^{-7}}=\frac{1}{6^{9-7}}=\frac{1}{6^2}=\frac{1}{36}\)Hence,
The final answer is option 2, 3, and6
juan rode his bicycle at a rate of 22 feet per second. what is his rate in feet per hour?
Juan rode his bicycle at a rate of 22 feet per second. 79200 is his rate in feet per hour.
How to convert feet per second to feet per hour?Since the International Yard and Pound Agreement of 1959, one foot is precisely equal to 0.3048 meters. One foot equals 12 inches in both customary and imperial measures, whereas one yard equals three feet.
To calculate the rate we have a conversion type:
1 feet per second = 3600 feet per hour
1 feet per second=(exactly)0.3048/(0.3048/36001)
1 feet per second=3600 ft/hr
The SI units are 0.3048 meters per second, for 1 feet per second.
And SI units approximately 8.4666667 × 10⁻⁵ meters per second, for 1 feet per hour.
This shows, that feet per second are bigger units than feet per hour.
Given feet per second=22
Now, for 22 feet per second contain how many feet per hour for this we need to multiply by 3600.
rate=22 × 3600
rate=79200 ft/hr
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what is the area of a circle with a radius of 5m?
Circle
Solve for area
A≈78.54m²
r Radius
5
m
d
r
r
r
d
d
C
A
Solution
A=πr2=π·52≈78.53982m²
Answer:
25π or 78.54m²
Step-by-step explanation:
the area of a circle with a radius of 5m=πr²=π×5²=25π or 78.54m²
An item is regularly priced at $55 . It is on sale for $40 off the regular price. What is the sale price?
$15
$15 because they are asking you to do a subtraction the initial amount used to be $55then you have to substract $40 because they are saying $40 OFF
$15 because they are asking you to do a subtraction the initial amount used to be $55then you have to substract $40 because they are saying $40 OFF55 - 40= 15don't forget to add the $ sign
$15 because they are asking you to do a subtraction the initial amount used to be $55then you have to substract $40 because they are saying $40 OFF55 - 40= 15don't forget to add the $ sign !Hope I helped you
5. The table below shows the participation in a school's debate club
during the last four years,
Year
1
2
3
4
Students
14
19
25
33
Between which two years did the club see the greatest growth?
By what percent did it grow? Round to the nearest whole number.
Q3-4
lol
Answer:
8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
40/50
Let A be a diagonalizable matrix whose eigen values satisfy that A2 = A + 1. Then A satisfies A) A² = A +1 B) A² = A + 2 C) A² = A D) A² = A + 1
D) A^2 = A + 1 this equation represents diagonal matrices with the same eigenvalues on the diagonal.
Let λ be an eigenvalue of the matrix A, and let v be the corresponding eigenvector. Since A is diagonalizable, we can write A = PDP^(-1), where D is the diagonal matrix containing the eigenvalues on the diagonal, and P is the matrix whose columns are the eigenvectors.
We know that A^2 = A + 1, so we can substitute A with its diagonalizable form:
(PDP^(-1))^2 = PDP^(-1) + 1.
Expanding the square and applying the matrix multiplication rules, we get:
PD^2P^(-1) = PDP^(-1) + 1.
Since D is a diagonal matrix, D^2 will have the eigenvalues squared on the diagonal. Therefore, we have:
P(D^2)P^(-1) = PDP^(-1) + 1.
Multiplying both sides by P^(-1) on the right, and by P on the left, we obtain:
D^2 = D + 1.
This equation holds because P^(-1)P = I (the identity matrix), and D and D^2 are diagonal matrices with the same eigenvalues on the diagonal.
Therefore, the correct answer is D) A^2 = A + 1.
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Help, will rate brainlist if correct!!
y = x4 - 5x2
A.) What is the y-intercept of this graph? How do you know? (1 point)
B.) What are the x-intercepts/roots/zeros? Show your work. (4 points)
C.) Describe the end behavior of this function (2 points)
D.) Draw a graph of this function, carefully labeling your intercepts and showing the end behavior.
A. The y-intercept is at the point (0, 0).
B. The zeros are x = 0 or x = ±√5
C.
How to solve the expressionA) The y-intercept of this graph is the point where x = 0.
When x = 0, the value of y
= 0^4 - 5*0^2
= 0.
Therefore, the y-intercept is at the point (0, 0).
B) The x-intercepts/roots of the function are the values of x that make y = 0.
To find these values, we need to set y = 0 and solve for x:
x⁴ - 5x² = 0
x⁴ = 5x²
x² = x⁴/5
x = ±√(x⁴/5)
We can simplify this expression by factoring x² out of both sides:
x²(x² - 5) = 0
x² = 0 or x² - 5 = 0
x = 0 or x = ±√5
hence the x-intercepts are at x = 0 and x = ±√5.
C) The end behavior of this function refers to how the graph of the function approaches the x-axis as x approaches positive infinity and negative infinity.
x → ∞ f(x) → ∞
x → -∞ f(x) → -∞
D) The graph is attached
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A certain kind of bacteria moves at a distance of 0.0000004 meters per step. Howmany steps would the bacteria have to take to move a distance of 1 meter?
Let's review the information given to us to answer this exercise correctly:
Distance a certain kind of bacteria moves per step = 0.0000004 meters
Let's answer the question, as follows:
Number of steps to move 1 meter = 1/Distance a certain kind of bacteria moves per step
Replacing with the values we know:
Number of steps to move 1 meter = 1/ 0.0000004
Number of steps to move 1 meter = 2'500,000
The bacteria will need 2'500,000 steps to move a distance of 1 meter
Solve 2(x + 1) = 2x + 2. (1 point)
♡
0
O
All real numbers
No solution
1
Answer:
B. All real numbers
Step-by-step explanation:
2(x + 1) = 2x + 2
Distribute the 2 inside the parenthesis.
2x + 2 = 2x + 2
Since the two expressions are equal and will stay equal with any value, the answer to this question is All real numbers.
Example:
2(x + 1) = 2x + 2
2(5 + 1) = 2(5) + 2
2(6) = 10 + 2
12 = 12
2(x + 1) = 2x + 2
2(150 + 1) = 2(150) + 2
2(151) = 300 + 2
302 = 302
The expression is equal for any value put in x.
What is the answer to y=-6x-3, -8x-3y=-1.
Answer:
x=−y/6− 1/2
x= 1−3y/8
hope it helps
Express the confidence interval 15.8% ± 5.4% in interval form.Answer using decimals rounded to three places, not as percentages
Okay, here we have this:
Considering the provided confidence interval we are going to express it in interval form, so we obtain the following:
So let's first convert the interval from percent to decimals:
Confidence interval=15.8% ± 5.4%
Confidence interval=0.158 ± 0.054
And the interval form will be obtained by leaving the result using the lesser on the left side, and the result using the more on the right side:
Confidence interval=[0.158-0.054, 0.158+0.054]
Confidence interval=[0.104, 0.212]
Finally we obtain that the confidence interval in interval form is equal to [0.104, 0.212].
A store began selling its line of fall sweaters. On the first day, 6 cotton, 4 orlon, and 5 wool sweaters were sold. On the second day, 3 cotton, 5 orlon, and 8 wool sweaters were sold. On the third day, 4 cotton, 1 orlon and 4 wool sweaters were sold. Total sales for the three days were $395, $505, and $260, respectively. What was the sale price for each sweater?
The given data in this problem allows for the creation of a system with three variables, that represent the earnings from the sales in the three days, by solving this system we can obtain these following sale prices:
Cotton: $15.Orlon: $20.Wool: $45.How to obtain the sale price for each sweater?The sale price for each sweater is obtained solving a system of equations.
The variables of the system of equations are given as follows:
Variable x: cost of a cotton sweater.Variable y: cost of an orlon sweater.Variable z: cost of a wool sweater.Considering the profits for each day, along with the amounts of each sweater sold, the equations that compose the system are given as follows:
6x + 4y + 5z = 395.3x + 5y + 8z = 505.4x + y + 4z = 260.Inserting these three equations into a calculator, the solution to the system of equations is given as follows:
x = 15, y = 20, z = 45.
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1, Which of the following is NOT an example of independent events? (1
point) *
a.rolling a die and spinning a spinner
b.tossing a coin two times
c.picking two cards from a deck with replacement of first card
O selecting two marbles one at a time without replacement
Answer:
The last choice: selecting two marbles one at a time without replacement.
Step-by-step explanation:
Independant events means that the second action is not dependant or does not get influenced by the first action. Lets look at our options...
a) There is no correlation between rolling a die and spinning a spinner
b) Whatever result you get (heads or tails) the first time of tossing the coin will not effect your next result since you always have a 50% chance of both sides.
c) Because you put back the first card you choose, the probability of choosing a certain card is the same.
d) Because you don't put back the marble after the first time, you end up changing up the probability of choosing a certain marble, meaning that it is NOT a independant event.
5 bananas cost 2.95 how much would 27 bananas cost
Answer:
78 dollars and 3 cents
Step-by-step explanation: use a calculator
Answer:
15.93
Step-by-step explanation:
each banana costs 0.59 so you multiply 27 times 0.59 = 15.93
Find the volume of a cone with a diameter of 5 inches and a height of 12 inches.
Quick please!!
Answer:
78.54 in
Step-by-step explanation:
\(\pi r^2\frac{h}{3}\) = v (volume)
r = diameter / 2
h = 12
\(\pi\) = 3.14159...
plug in values
\(\pi\) * \(2.5^2\) * \(\frac{12}{3}\) = 78.54
your answer is 78.54 in
hope this helps:)
Alex had $3.63 more than Rick. Together they had $27.93. How much money did both Alex and Rick have?
Alex has $15.78 and Rick has $12.15 money.
According to the question,
We have the following information:
Alex had $3.63 more than Rick. Together they had $27.93.
Let's take the money Rick has to be $x.
Now, we have the following expression for the money Alex has:
3.63+x
Now, we have:
x+3.63+x = 27.93
2x+3.63 = 27.93
Subtracting 3.63 from both the sides:
2x = 27.93-3.63
2x = 24.3
Dividing by 2 on both the sides:
x = 24.3/2
x = $12.15
So, Rick has $12.15.
Now, the money Alex has:
3.63+12.15
$15.78
Hence, Alex has $15.78 and Rick has $12.15 money.
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Lin and Diego both ran for 10 seconds, each at their own constant speed. Lin ran 40 meters and Diego ran 55 meters. How far did each person move in 1 second
Answer:Lin 4 and Diego 5.5
Step-by-step explanation: Lin 40÷10=4 and Diego 55÷10=5.5
Choose the equation that shows a step in the
process of completing the square on the given
quadratic.
y=x2 + 8x - 3
O y=x2 + 8x + 8 - 3-8
Oy=x2 + 8x + 8-3 +8
O y = x2 + 8x + 16 - 3 - 16
O y = x2 + 8x +16 - 3+16
Answer: y = x2 + 8x + 16 – 3 – 16
Step-by-step explanation:
Can someone check to see if I got this right?!??
Answer:
yes!
Step-by-step explanation:
hi, that is correct. 3800 is a constant, meaning it is consistent and the initial height of the plane before it starts its descent.
If a reader wants to evaluate a text, which is the best question to ask while reading it?
A. What are the goals of the text, and what elements help achieve those goals?
B. When did the author of this text decide on its goals, and when did he write it?
C. How long is this text, and how quickly does it get to the point?
D. Where else is there a text with similar goals that used different elements?
D.
Its the answer.
Im sure it is.
Answer: D. Where else is there a text with similar goals that used different elements?
Step-by-step explanation: correct answer
each of two persons tosses three gair coincs. what is the probability that they obtain the same numbre of heads
The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.
1/8
The probability of getting a head or a tail when flipping a coin is 1/2.
Therefore, the probability of getting two heads when tossing two coins is 1/2 x 1/2 = 1/4.
The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.
Since each person is tossing three coins, the probability that they both obtain the same number of heads is 1/8.
The probability of getting n heads when tossing n coins is 1/2^n. Therefore, the probability of getting the same number of heads when two people toss n coins is 1/2^n. This means that if two people each toss a coin, the probability that they both get heads is 1/4; if they each toss two coins, the probability that they both get two heads is 1/16; if they each toss three coins, the probability that they both get three heads is 1/64; and so on.
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If g(x) = 8-2 (3x-4) what is the value of g(-5)
Answer: 46
Step-by-step explanation: g(-5)= 8-2 (3(-5)-4), equals 46! Hope this helps :)
A company is trying to introduce a new product to as many
people as possible through television advertising in a large metropolitan area
with 2 million possible viewers. A model for the number of people N (in
millions) who are aware of the product after t days of advertising was found to
be
� = 2(1 − �9<.
Approximately 1.33 million people will be aware of the product after 20 days.
The model for the number of people N (in millions) who are aware of the product after t days of advertising was found to be N = 2(1 - e^(-0.09t)).
the model for the number of people N (in millions) who are aware of the product after t days of advertising was found to be N = 2(1 - e^(-0.09t))
To find: The number of people who will be aware of the product after 20 days can be found by replacing t by 20 in the given model of N
N = 2(1 - e^(-0.09t))
N = 2(1 - e^(-0.09×20))
Evaluate `e^(-0.09×20)
as follows e^(-0.09×20) = 0.335
Hence, the number of people N (in millions) who are aware of the product after 20 days of advertising will be
N = 2(1 - e^(-0.09t))
N = 2(1 - e^(-0.09×20))
N = 2(1 - 0.335)`=> N = 2(0.665)`=> `N = 1.33
Therefore, approximately 1.33 million people will be aware of the product after 20 days.
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What is the length of the unlabeled side of this triangle ?
A) 2
B) 44
C) 134
D) 4
Answer:
b is the answer should be
Step-by-step explanation:
2 is too long fo dat
44 is too long
134 like rlly rlly dawg way too long
4 should be it ight
Asap pls help I need help
Answer:
\(a_{n}=2+3(n-1)\)
Step-by-step explanation:
Step 1. To find the equation that describes the pattern, we use the arithmetic sequence formula:
\(a_{n}=a_{1}+d(n-1)\)
Where a_n is the n'th terms and d is the common ratio between the numbers.
Step 2. The sequence we have is:
2 5 8 11
The first term is:
\(a_{1}=2\)
And the common ratio or the difference between consecutive numbers is:
3 2+3=8 5+3=8 8+3=11
This will be the value of d:
d=3
Step 3. Substituting a_1 and d into the formula:
\(a_{n} =a_{1}+d(n-1)\\a_{n}=2+3(n-1)\)
This is the equation that represents the number pattern, it represents that we add three each time to the previous number in the sequence.
Hence, the correct answer is \(a_{n}=2+3(n-1)\)
sketch the area represented by g(x). g(x) = x t2 dt 1
The area represented by g(x) is a triangular region with base 1 and height (7/3) x, where x is the variable along the horizontal axis. The resulting shape will be a right triangle with vertices at (0,0), (1,0), and (0, (7/3) x).
It seems like you are asking to sketch the area represented by the function g(x) given as the integral of x with respect to t from 1 to 2. However, there seems to be a typo in your question. I will assume that you meant g(x) = ∫[1 to x] t^2 dt. Please follow these steps to sketch the area represented by g(x):
1. Draw the function y = t^2 on the coordinate plane (x-axis: t, y-axis: t^2).
To sketch the area represented by g(x) = x t2 dt 1, we first need to evaluate the definite integral. Integrating x t2 with respect to t gives us (1/3) x t3 + C, where C is the constant of integration. Evaluating this expression from t=1 to t=2 gives us (1/3) x (2^3 - 1^3) = (7/3) x.
2. Choose an arbitrary x-value between 1 and 2 (e.g., x = 1.5).
3. Draw a vertical line from the x-axis to the curve of y = t^2 at x = 1.5. This line represents the upper limit of the integral.
4. Draw another horizontal axis from the x-axis to the curve of y = t^2 at x = 1. This line represents the lower limit of the integral.
5. The area enclosed by the curve y = t^2, the x-axis, and the vertical lines at x = 1 and x = 1.5 represents the area for the given value of x.
In conclusion, the area represented by g(x) = ∫[1 to x] t^2 dt can be sketched by plotting the curve y = t^2, choosing a specific x-value between 1 and 2, and then finding the enclosed area between the curve, x-axis, and the vertical lines at x = 1 and x = chosen x-value.
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When constructing a perpendicular bisector why must the compass opening be greater than 1/2.
It is critical to open a compass with over half the way in order for the arcs formed to meet for perpendicular bisector.
What is perpendicular bisector?A perpendicular bisector would be a line that cuts a line segment in half and forms a 90-degree angle at the intersection point. In other words, a perpendicular bisector separates a line segment now at midpoint, forming a 90-degree angle.
Now, consider an example;
When you wish to build a perpendicular line on a line segment, like line AB, you do the following;
Set the compass on a radius more than half the length of the line AB.Using A as your center, draw an arc above and below line AB.With the same radius and B as our center, draw additional arcs on top or below line AB to join a first arcs on the both side of the line.Join the two arc intersections to cut line AB at M.A line AB appears to be bisected perpendicularly as a result. The arcs would not have met if the compass is opened less than half way down line AB.
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The image shows a portion of a bridge supported by two vertical pillars built from the points B and C on the slope below.
The length of the bridge between pillar B and pillar C is
feet.
The length of the bridge between pillar B and pillar C is 56 feet.
How to calculate the length of the bridge?In order to determine the length of the bridge between pillar B and pillar C, we would determine the magnitude of the angle subtended by applying cosine ratio because the given side lengths represent the adjacent side and hypotenuse of a right-angled triangle.
cos(θ) = Adj/Hyp
Where:
Adj represents the adjacent side of a right-angled triangle.Hyp represents the hypotenuse of a right-angled triangle.θ represents the angle.By substituting the given side lengths cosine ratio formula, we have the following;
cos(θ) = Adj/Hyp
cos(A) = 40/50
cos(A) = 0.8
For the length of AD, we have:
Cos(A) = AD/(50 + 70)
0.8 = AD/(120)
AD = 96 feet.
Now, we can determine the length of the bridge as follows;
x + 40 = 96
x = 96 - 40
x = 56 feet.
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A cable hanging from the top of a building is 15m long and has a mass of 40kg. A 10kg weight is attached to the end of the rope. How much work is required to pull 5m of the cable up to the top? Give your answer as an exact number (assume acceleration due to gravity is 9.8ms−2).
It would require 490 joules of work to pull 5m of the cable up to the top.
To solve this problem, we need to use the formula for work:
Work = force x distance x cos(theta)
where force is the tension in the cable, distance is the distance moved, and theta is the angle between the force and the distance.
First, let's find the tension in the cable. The weight of the cable itself is negligible compared to the weight of the weight, so we can assume that the tension is equal to the weight of the weight:
Tension = weight of weight = 10kg x 9.8m/s² = 98N
Next, let's find the angle between the force and the distance. Since we are pulling the cable straight up, the angle is 0 degrees, so cos(theta) = 1.
Now we can plug in the values and solve for work:
Work = 98N x 5m x 1
Work = 490J
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Solve: 7×-4=-8×+8
hurry!
Answer:
x = 4/5
FILLER FILLER FILLER
The scale drawing of the tennis court shown below is drawn using a scale of 1 inch = 12 feet.
(image)
The net would have to be ________ to stretch from one side of the court to the other, as shown by the center line.
fill in the blank
A. 7.05 ft
B. 20.4 ft
C. 30 ft
D. 51 ft
The net would be 51 feet long to stretch from one side of the court to the other.
What are scaled drawings?Scale drawings are drawings that shows a diagram with another proportional dimensions
The scale ratio of the diagram is given as:
Scale = 1 inch = 12 feet
The length of the net is given as:
Length = 4.25 inches
So, the actual length of the net is:
\(Length=4.25*12\)
Evaluate the product
\(Length=51\)
Hence, the net would be 51 feet long, if stretched across the court
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