Final answer:
To determine how Eva can arrange 24 photos in an album so that each page has the same number of photos, we need to find the factors of 24. With factors of 1, 2, 3, 4, 6, 8, 12, and 24, there are 8 distinct ways to arrange the photos across the album's pages with each page having the same number of photos.
Explanation:
The student's question is about determining the different ways Eva can arrange 24 photos in an album so that each page contains the same number of photos. To solve this, we need to consider the factors of 24, as the number of photos on each page must be a factor of the total number. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. This means Eva has 8 different page arrangements where each page has the same number of photos.
Now, for each of these arrangements, the order of the photos on each page and the order of the pages themselves can change. If we assume all photos are distinct, the number of ways to arrange the photos on a single page is the factorial of the number of photos per page. However, since Eva is concerned only with the arrangement of the number of photos per page being the same, not the order within the pages, we only need to consider the 8 different page arrangements.
What is the acceleration of a wagon of mass 20 kg if a horizontal force of 64 N is applied to it? (Ignore friction)
The acceleration of the wagon is 3.2 m/s².
Explanation:To find the acceleration of the wagon, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force applied to it divided by its mass. In this case, the net force is 64 N (the horizontal force applied) and the mass of the wagon is 20 kg. So the acceleration can be calculated as follows:
A = F/M = 64 N / 20 kg = 3.2 m/s²
Therefore, the acceleration of the wagon is 3.2 m/s².
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what is the momentum of a 20-kg dog running at a speed of 8 m/s
The momentum of a 20-kg dog running at a speed of 8 m/s is 160 kg.m/s. This is calculated using the formula for momentum, which is the product of mass and velocity.
Explanation:To calculate the momentum of an object, you need to multiply its mass by its velocity. This is due to the fact that momentum is directly proportional to the object's mass and its velocity. Hence, a 20-kg dog running at a speed of 8 m/s would have a momentum of 160 kg.m/s.
Momentum (p) is represented as the product of mass (m) and velocity (v), hence expressed as p = m*v. Momentum is a vector quantity, which means it has both magnitude (amount) and direction. In this case, we're only concerned with its magnitude.
So, for the 20-kg dog running at 8 m/s, we substitute these values into the momentum formula to find its momentum:
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A hiker is walking down a mountain. She walked 5,978 feet in 17 minutes. In that time, she descended 1,024 feet from the top of the mountain. She then walked 3,972 feet in 7 minutes. In that time, she descended 500 more feet. Express the average rate of change in altitude of the hiker from her starting point to her ending point as a unit rate.
The average rate of change in altitude of the hiker from her starting point to her ending point is -63.5 feet per minute.
The following can be deduced based on the information provided in the question:
During the first walk, she descended 1024 feet and during the second walk, she descended 500 feet. Therefore, the total will be:
= 1024 feet + 500 feet = 1524 feet
During the first walk, the time taken was 17 minutes while for the second walk, the time taken was 7 minutes. Therefore, the total time taken will be:
= 17 minutes + 7 minutes
= 24 minutes.
Therefore, the average rate will be:
= 1524 / 24
= 63.5 feet per minute
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Find the difference. 632
-274
Two events, X and Y, are independent of each other. P(Y) = 5/6 and P(X and Y) =1/3 . What is P(X) written as a decimal?
Mark put his dog on a diet. The dog's total weight change for the first 2 weeks was −3/4 pound. The dog lost the same amount of weight each week. What was the change in the dog's weight after the first week of the diet? Enter your answer in the box.
Which of the following measurements could be the side lengths of a right triangle? A. 66 in, 88 in, 110 in
B. 66 in, 88 in, 132 in
C. 66 in, 99 in, 110 in
D. 55 in, 88 in, 110 in
please dont answer if not 100 % sure.
Answer:
Step-by-step explanation:
The cable is 50 yards long, viewing post is 40 yard high , how far is the bottom cable from the base of the viewing post
Dave has a 32-ounce energy drink. He drinks 10 ounces. Enter the percentage of ounces Dave had left from his energy drink. Round your answer to the nearest hundredth
Answer:
Step-by-step explanation:
Dave has a 32-ounce energy drink and he drinks 10 ounces then 68.75% of the energy drink has been left by Dave.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Dave has a 32-ounce energy drink.
Dave drinks 10 ounces of energy drink.
We need to find the percentage of ounces Dave had left from his energy drink.
To find this first we have to subtract 10 from 32
32-10 = 22.
Now let us find 22 is what percentage of 32.
x/100 × 32 = 22
0.32x=22
Divide both sides by 0.32
x=22/0.32
x=68.75 %
Hence, 68.75% of the energy drink has been left by Dave.
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12x+28y=84 how do I graph it
What is 763 thousandths in scientific notation?
I can't figure this out... Can someone please help me?
A spinner is separated into 3 equal pieces, as shown below: A spinner is shown with three colors, red, yellow, and purple, marked on it. The arrow points towards the red color. Mary spins the spinner 6 times. What is the theoretical probability that it stops on the red sector on the last spin?
The theoretical probability that it stops on the red sector on the last spin is 1 by 3.
Calculation of the theoretical probability:Since A spinner is separated into 3 equal pieces. A spinner is shown with three colors, red, yellow, and purple, marked on it. Mary spins the spinner 6 times.
So, the theoretical probability is
Probability= Successful outcome ÷ Possible outcome
= 1÷3
Therefore, The theoretical probability that it stops on the red sector on the last spin is 1 by 3.
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going down the river a boat went 13 km/h. going up the river it only 1 km/h. Find the speed of the boat in still water and the speed of the current.
The speed of boat is 7 km/h and speed of stream is 6 km/h.
What is speed ?
In unit time the distance covered by any object is called speed.
In mathematical term, Speed is express as S=D/T,
where S=speed, D=distance, T= time .
Let the speed of boat in N, and the speed of current is D,
Given that,
The speed in downward stream of a boat N+D= 13 km/h, (1)
And the speed in upward stream of a boat N-D= 1 km/h. (2)
To Find speed of boat in still water, add equation (1) and (2),
2N=14 ⇒ N=7 km/h
To Find speed of current, substract equation (1) and (2),
2D=12 ⇒ D=6 km/h.
The speed of boat is 7 km/h and speed of stream is 6 km/h.
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Solve for S.
3s + 2 = 12 - 2s
3s+2=12-2s
(3s-3s)+2=12(-2s-3s)
2=12-5s
2-12=(12-12)-5s
-10=-5s
-10/-5=-5s/-5
2=s
Check
(3*2)+2=12-(2*20
6+2=12-4
8=8
S=2
What is the fraction of 35%
The bus driver made 6 stops on his way into town. No passengers exited the bus. By stop 3, there were 9 passengers on the bus. This graph shows this information.
How many stops did it take to have 13 passengers on the bus?
A:2
B:3
C:4
D:5
The number of bus stops is 4 if the bus driver made 6 stops on his way into town option (C) 4 is correct.
What is a dot plot?A dot plot also referred to as a dot chart or stripe graph, is a sort of simple histogram-like figure used in statistics for little data sets with values falling into a number of discrete bins.
It is given that:
The bus driver made 6 stops on his way into town. No passengers exited the bus. By stop 3, there were 9 passengers on the bus
The graph is shown in the picture.
The x-axis represents the bus stops
The y-axis represents the number of passengers
From the graph point to the 13 on the y-axis and locate the related value of x on the x-axis.
The number of bus stops corresponds to 13 = 4
Thus, the number of bus stops is 4 if the bus driver made 6 stops on his way into town option (C) 4 is correct.
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a group of 4 people go out to eat. they decide to split the bill so each person pays 1/4 of the total price. appetizers are $6 and main dishes are $9. write an expression to show how many each person pays.
Please help!
Prove that opposite sides of a parallelogram are congruent. Be sure to create and name the appropriate geometric figures.
a football team gains 8 yards in one play, then loses 5 yards in the next.How many yards did the team gain in these two plays
47% of $118 estimate
a table is 6 feet long and 3 feet wide. You extend the table by inserting two identical table leaves. The longest side length of each rectangular leaf is 3 feet. The extended table is rectangular with an area of (18+6x) square feet. a) write an algebraic expression that represents the length of the extended table b) what does your variable represent?
a. The algebraic expression that represents the length of the extended table is 6 + 2x
b. The variable 'x' represents the length added by inserting each identical table leaf.
How to write an algebraic expression
a) To write an algebraic expression representing the length of the extended table, consider the original length of the table (6 feet) and the length added by inserting two identical table leaves (each with a longest side length of 3 feet).
Let's denote the length added by inserting the table leaves as 'x'.
Since we're inserting two identical leaves, the total length added would be 2x.
The length of the extended table can be expressed as the sum of the original length (6 feet) and the length added by the table leaves (2x):
Length of the extended table = 6 + 2x
b) The variable 'x' represents the length added by inserting each identical table leaf. It quantifies the extra length that extends the original table when the leaves are inserted.
Write a problem involving how much more Than and solve it. Explain how drawing a diagram helped you solve the problem
An MP3 player can hold 350 hours of music. Each song on an MP3 player is about 2.5 minutes in lenght. Abut how many songs can the MP4 player store?
PLEASE YOU CAN ANSWER NUMBER 1 OR 2 OR BOTH PLEASE I JUST NEED HELP WITH BOTH AND NO ONE WILL ANSWER MY QUESTIONS!!!!!!!! :(
1.)In two or more complete sentences, explain how to find the time it takes for a rocket following the path, h(x) = -4x 2 + 16x, to hit the ground.
2.)A ball is thrown straight up from the top of a building that is 280ft high with an initial velocity of 48ft/s. The height of the object can be modeled by the equation s(t) = -16t 2 + 48t + 280.
In two or more complete sentences explain how to determine the time(s) the ball is higher than the building in interval notation.
1.) You plug a number into the variable x. Then you will solve the equation for h(x) to find the time it takes for the rocket to travel the path given.
Answer:
Step-by-step explanation:
Given that a rocket path is given by
[tex]h(x) = -4x^2 + 16x[/tex]
When it hits the ground h(x) =0
Hence we get
[tex]-4x^2 + 16x=0\\x=0, 4[/tex]
i.e. after 4 minutes the rocket hits the ground
2) Given that
[tex]s(t) = -16t^2 + 48t + 280.[/tex]
We have to find time t when height >280
[tex]s(t) = -16t^2 + 48t + 280>280\\\\t=0, 3[/tex]
Between 0 and 3 seconds the object would be above the building.
You have $ 2 0 $20dollar sign, 20 to spend on taxi fare. The ride costs $ 5 $5dollar sign, 5 plus $ 2 . 5 0 $2.50dollar sign, 2, point, 50 per mile. Let m mm represent the number of miles ridden. Write an inequality to determine how many miles you can ride for $ 2 0 $20dollar sign, 20.
Answer:
6 x $2.5 = $15
$15 + $5 = $20
on a tour of an old gold mine, you find a gold nugget containing .82 ounces of gold. gold is worth $1566.80 per ounce. how much is your gold worth?
The value of a gold nugget containing 0.82 ounces of gold at $1566.80 per ounce is $1284.776.
The value of a gold nugget containing 0.82 ounces of gold, given that gold is worth $1566.80 per ounce, can be calculated through a simple multiplication. The value of the gold nugget is found by multiplying the amount of gold in the nugget by the price per ounce of gold.
To calculate:
Multiply the weight of the gold nugget (0.82 ounces) by the value per ounce ($1566.80).0.82 ounces imes $1566.80/ounce = $1284.776Therefore, the gold nugget is worth $1284.776.
What is the value of the underlined digit 53
The Ortiz family will travel round-trip from Indianapolis to Denver this summer. The driving distance between the two cities is 1,058 miles. They need to find out about how much the gas will cost round trip. Their car gets about 20 miles per gallon. They usually spend about $2.89 per gallon.
Write words to match the expression of 4x(10 -2)
Are the expressions below equivalent 3(4x+8) 12x+24