Isaac has 21 green marbles and 7 blue marbles. He wants to place them in identical groups without any marbles left over. What is the greatest number of groups Isaac can make? PLEASE ANSWER WITH WORK!!!
Answer:
7 groups.
Step-by-step explanation:
We have been given that Isaac has 21 green marbles and 7 blue marbles. He wants to place them in identical groups without any marbles left over.
To find the greatest number of groups Issac can make we will find the GCF of 7 and 21.
Factors of 7 are: 1, 7.
Factors of 21 are: 1, 7, 3, 21.
We can see that 7 is the greatest common factor of 7 and 21, therefore, Issac can make 7 groups from 21 green marbles and 7 blue marbles.
Let us find number of each type of marble is each group.
[tex]\text{Number of green marbles in each group}=\frac{21}{7}[/tex]
[tex]\text{Number of green marbles in each group}=3[/tex]
Therefore, there will be 3 green marbles in each group.
[tex]\text{Number of blue marbles in each group}=\frac{7}{7}[/tex]
[tex]\text{Number of blue marbles in each group}=1[/tex]
Therefore, there will be 1 blue marble in each group.
What is mass measured in?
The Ferris wheel at the Comal County Fair is a three minute ride that takes its riders on a thrilling ride up to a maximum height of 105 feet and a low point of 5 feet. Assuming that the Ferris wheel rotates at 6 revolutions per minute and a rider starts his stopwatch immediately as his ride starts at its low point,
Final answer:
In a Ferris wheel, gravity and normal forces act on riders, affecting circular motion and contributing to centripetal force. Redistribution of mass affects the moment of inertia and could change angular velocity, assuming conservation of angular momentum without external torques.
Explanation:
Understanding the forces acting on people in a Ferris wheel and the effects on angular velocity and angular momentum involves comprehending basic physics concepts of circular motion and rotational dynamics.
Angular velocity is affected by how fast the Ferris wheel rotates. If the wheel accelerates, angular velocity increases. The total angular momentum of the system, a product of moment of inertia and angular velocity, can change due to external torques, like the motor driving the Ferris wheel or resistance due to air. However, in the absence of external torques, the system's angular momentum remains constant.
Considering the positions of people on the Ferris wheel (4 o'clock, 1 o'clock, 9 o'clock, and 6 o'clock), gravity acts downwards on each person, and the normal force acts perpendicular to the wheel's surface. These forces contribute to the centripetal force that keeps the people in circular motion. The redistribution of mass as people move or as the wheel turns can change the wheel's moment of inertia, potentially altering its angular velocity assuming angular momentum is conserved in the absence of external torques.
Find the area of a circle with a radius of 1.
There is a line whose y-intercept is 7 and whose slope is 8. What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
y = x +
The figure shows the letter M and four of its transformed images—A, B, C, and D:
Which of the four images was formed by a reflection of the letter M?
Answer:
Figure D is the answer.
Step-by-step explanation:
The reflection transformation is a type of transformation, where the new image is the mirror image of the original image. Here, the x-coordinate and y-coordinate change places.
So, out of all the new figure, figure D is the answer.
Rest figures B and C are translations (simply moving aside) and A is rotation and translation both.
A tennis Racquet costs $100 and is 30% off right now. Sales tax is 5.5%.
can you please explain how to do it?
The table shows the number of students in a school who like rap and/or hip-hop:
Like Rap Do Not Like Rap Total
Like Hip-Hop 35 8 43
Do Not Like Hip-Hop 10 21 31
Total 45 29 74
What is the relative frequency, by row, of students who do not like rap or hip-hop?
0.17
0.68
0.72
0.81
Answer:
The correct answer would be 0.68. I just took the test, your welcome :)
Step-by-step explanation:
The relative frequency, by row, of students who do not like rap or hip-hop is:
0.68
Step-by-step explanation:Like Rap Do Not Like Rap Total
Like Hip-Hop 35 8 43
Do Not Like Hip-Hop 10 21 31
Total 45 29 74
The relative frequency by row of an outcome is calculated as the ratio of the frequency corresponding to the outcome to the total of the row.
Total of a row is: 31
The number of students who did not like Rap or Hip-Hop is: 21
Hence, the relative frequency is: 21/31=0.6777
which is approximately equal to 0.68
HELP ME PLZZZZ WILL GIVE BRAINLIEST
Match the Polynomials with their names.
The freshman class is selling T-shirts to raise money for a field trip cost of each costume design T-shirt is eight dollars there is a $45 fee to create the design the class plans to sell the search for $12 what is the cost and revenue function
Which of the following represents the number of subsets of five elements can be formed from a set of six elements?
5!
C(6, 5)
P(6, 5)
Three brothers, Justin, Jared, and Jonathan decided to buy a present for their mom's birthday. Justin gave decided to spend 1/4 of his savings on the present, Jared said he will contribute 1/3 of his money, and Jonathan was willing to put in 2/5 of all he had. Each brother invested exactly the same amount of money and they bought a vase that costed $33.00. How much money did each boy have before the purchase?
Final answer:
Each brother spent $11 on the gift. To find their original savings, we calculate 4 * $11 for Justin, which is $44, 3 * $11 for Jared, which is $33, and 5/2 * $11 for Jonathan, which is $27.50.
Explanation:
The question is asking us to find out how much money each of the three brothers, Justin, Jared, and Jonathan, had before they each spent an equal amount on a present for their mom's birthday. They bought a vase for $33, and Justin spent 1/4 of his savings, Jared contributed 1/3 of his, and Jonathan gave 2/5 of his. We can set up an equation for each brother using the fact that they all spent the same amount, which we'll call 'x'. So for Justin, (1/4) * Justin's savings = x, for Jared, (1/3) * Jared's savings = x, and for Jonathan, (2/5) * Jonathan's savings = x. Since the total cost of the vase is $33, we know that 3x = $33 or x = $11. This means each brother spent $11.
Now, we can find out how much each had originally:
Justin's original savings: (1/4) of his savings is $11, so Justin had 4 * $11 = $44 before the purchase.Jared's original savings: (1/3) of his savings is $11, so Jared had 3 * $11 = $33 before the purchase.Jonathan's original savings: (2/5) of his savings is $11, so Jonathan had 5/2 * $11 = $27.50 before the purchase.If the triangle ABC is similar to the triangle DEF, estimate the area of triangle ABC if the area of the triangle DEF is 90
The area of triangle ABC, given that it is similar to triangle DEF with an area of 90, cannot be estimated without the ratio of corresponding sides. Areas of similar triangles are proportional to the square of the ratio of their corresponding sides.
Explanation:To estimate the area of triangle ABC given that triangle ABC is similar to triangle DEF, and the area of triangle DEF is 90, we first need to understand that the areas of similar triangles are proportional to the square of the ratio of their corresponding sides. However, without knowing the specific ratio of the corresponding sides of triangles ABC and DEF, we cannot calculate the exact area of triangle ABC.
For example, if we knew that every side of triangle ABC was twice as long as the corresponding sides of triangle DEF, the area of triangle ABC would be 4 times the area of triangle DEF, because the area is proportional to the square of the side lengths (2 squared is 4). In this case, if the area of DEF is 90, then the area of ABC would be 90 × 4 = 360.
Without the ratio of the sides, we can't directly calculate the area of triangle ABC from the area of triangle DEF. The relationship between similar triangles and their areas illustrates an important geometric principle, but requires specific information about the ratio of corresponding linear dimensions to make an estimation.
A rectangular prism has a length of 212 meters, a width of 4 meters, and a height of 214 meters. What is the volume of the prism? Enter your answer in the box as a simplified mixed number or a decimal.
Answer:
22 1/2
I got that answer when I reviewed the test
Parker is single and paying off his graduate student loan. The monthly payment is $679.34. He is hoping to receive an income tax refund that is large enough to make at least one monthly payment. His taxable income is $77,911 and his employer withheld $19,458 in federal taxes. a. How much of a refund will Tony receive? b. How many loan payments will Parker be able to make with this refund?
Parker will receive a tax refund of $2,318. With this refund, he can make approximately 3 loan payments.
Explanation:To determine Parker's tax refund and the number of loan payments he can make with this refund, we should consider his income and his withholdings. Since his taxable income is $77,911 and he has had $19,458 in federal taxes withheld, we can calculate his tax liability using the federal tax rates. In the U.S, the marginal tax rates for a single taxpayer range from 10% to 35%, depending on income.
For someone earning $77,911, they would be in the 22% tax bracket according to the 2020 tax tables from the Internal Revenue Service. The tax on income from $80,251 to $171,050 is 22%. Therefore, Parker's expected tax liability is $77,911 * 22% = $17,140.
However, the amount his employer withheld was $19,458. This means Parker has overpaid and is eligible for a refund of $19,458 - $17,140 = $2,318.
In terms of how many loan payments Parker can make with this refund, since his monthly loan payment is $679.34, he can make approximately $2,318/$679.34 = 3.41 payments.
Therefore, Parker will receive a tax refund of $2,318 and will be able to make approximately 3 loan payments with this refund.
Learn more about Tax refund and loan payment here:https://brainly.com/question/12811169
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Liv and Ira are throwing balls in the air and catching them. Liv has caught 41 balls. Ira has caught 12 more balls than Liv.
How many balls has Ira caught?
Final answer:
Ira has caught 53 balls, which is found by adding 12 to Liv's total of 41 balls.
Explanation:
The question asks to find out how many balls Ira has caught if Liv has caught 41 balls and Ira has caught 12 more balls than Liv. To solve this, we start with the number of balls Liv has caught, which is 41. Since Ira has caught 12 more balls than Liv, we add 12 to Liv's total. Therefore, the number of balls caught by Ira is calculated as follows:
Liv's total = 41 balls
Ira's total = Liv's total + 12
Ira's total = 41 + 12 = 53 balls
Thus, Ira has caught 53 balls.
A batch of muffins needs to bake in the oven for 22 minutes. They need to cool for at least 15 minutes before they should be eaten. Wade puts the muffins in the oven at 10:17 am. Select true or false for each statement.
a) Wade can eat muffins at 10;39 pm
b) wade can eat muffins at 10:44 am
c)Wade should take the muffins out of the oven at 10:39 pm
d) Wade should take the muffins out of the oven at 10:39 am
Wade placed the muffins in the oven at 10:17 AM; they will be ready to eat after baking and cooling at around 10:54 AM. The statements about eating the muffins at 10:39 PM and taking them out at 10:39 PM are false, while the statement about taking them out at 10:39 AM is true.
Explanation:To calculate when Wade can eat the muffins we must add the baking time and cooling time to the time he put the muffins in the oven. Wade puts the muffins in at 10:17 am and the muffins need to bake for 22 minutes. After baking, they need 15 minutes to cool.
First, the muffins would be done baking at 10:39 am (10:17 am + 22 minutes). Then, after cooling for at least 15 minutes, Wade can eat the muffins at 10:54 am (10:39 am + 15 minutes).
a) False: Wade cannot eat muffins at 10:39 pm because this time is 12 hours after the correct time.b) False: Wade cannot eat muffins at 10:44 am because they will only have cooled for 5 minutes, which is not enough.c) False: Wade should take the muffins out at 10:39 am, not pm.d) True: This is the correct time for Wade to take the muffins out of the oven.A deli makes potato, macaroni, three bean, Caesar, 7-layer, and Greek Salads. The deli randomly makes only four salads each day. What is the probability that the four salads made in one day are 7-layer, macaroni, Greek, and potato?
What is the correct answer for number 6
Write a function in terms of t that represents the situation.
Your starting annual salary of $35,000 increases by
4% each year.
With instructions on how you did it please!!!
To represent the situation, the function can be written as f(t) = 35000 × (1 + 0.04)^t, where t represents the number of years into the future.
Explanation:To write a function in terms of t that represents the situation, we can start with the initial salary of $35,000 and then calculate the annual increase using the 4% growth rate.
We need to multiply the current salary by (1 + 0.04) to get the new salary for each year. The function can be written as:
f(t) = 35000 × (1 + 0.04)^t
Here, t represents the number of years into the future from the initial starting point.
For example, if you want to find the salary after 3 years, you can plug in t = 3 into the function.
A function that represents your annual salary starting at $35,000 and increasing by 4% each year,
[tex]S(t) = 35000 * (1 + 0.04)^t[/tex], where t is the number of years.
To create a function that represents your annual salary starting at $35,000 and increasing by 4% each year,
we use the formula for exponential growth,
[tex]final amount = initial amount * (1 + growth rate)^t^i^m^e.[/tex]
Given that your initial salary is $35,000 and the growth rate is 4% (or 0.04),
let's define the function S(t) where S represents your salary and t represents the number of years:
[tex]S(t) = 35000 * (1 + 0.04)^t[/tex]
the initial salary=$35,000.
Convert the percentage increase to a decimal,
4% becomes 0.04.
Set up the function using the formula for exponential growth,
which is initial amount multiplied by [tex](1 + growth rate) ^t[/tex]
Thus, for any year t, the function [tex]S(t) = 35000 * (1 + 0.04)^t[/tex] calculates your annual salary.
farid takes 7/8 teaspoon of allergy medicine everyday how much medicine will he take in one week
A sign in front of a roller coaster says ''you must be 40 inches tall to ride" what percentage of this height is A 34 inches and B 54 inches please answer both if you can thank you.
The percentage of height of A is 85% and the percentage of height of B is 135% and it can be evaluated by using unitary method.
Given :
To ride on roller coaster you must be 40 inches tall.
Unitary method is used to find the percentage of height of A and percentage of height of B. Single unit is determined first in the unitary method and than multiply the single unit to find the necessary value.
Applying unitary method to determined the percentage of height of A.
Divide 34 by 40.[tex]=\dfrac{34}{40}[/tex]
Multiply the above value by 100.[tex]=\dfrac{34}{40}\times 100[/tex]
= 85%
Again applying unitary method to determined the percentage of height of B.
Divide 54 by 40.[tex]=\dfrac{54}{40}[/tex]
Multiply the above value by 100.[tex]=\dfrac{54}{40}\times 100[/tex]
= 135%
The percentage of height of A is 85% and the percentage of height of B is 135% and it can be evaluated by using unitary method.
For more information, refer the link given below:
https://brainly.com/question/20196352
100 POINTSS!!!!!
Which expression is equivalent to 1/3(4−5x−1) ?
−5x+3
−5/3x−1
−5/3x+1
−5x+1/3
Big points+ brainliest
Enter the missing numbers in the box to complete the table of equivalent ratios of length to widths. PLEASE HELP
How would 6,000,000,000 + 70,000,000 + 40,000 + 700 + 8 be written in standard form?
A. 67,478
B. 670,478
C. 677,040,708
D. 6,070,040,708
The area of a quarter circle is 0.785 square kilometers. What is the quarter circle's perimeter?
To find the perimeter of the quarter circle, the radius is first calculated using the area, and then the perimeter formula for a circle is applied, adjusting the final calculation to include the straight edges of the quarter circle.
The student has provided the area of a quarter circle and is seeking to find its perimeter. The area of the full circle can be found by multiplying the quarter circle area by 4, yielding an area of 3.14 square kilometers (since the area of a quarter circle is 0.785 square kilometers). Using the formula for the area of a circle, A = πr², we can solve for the radius (r).
Let's calculate the radius of the circle:
A = πr² = 3.14 km²r² = A/πr² = (3.14)/(3.1415927)r = 1 km (Here we're considering π to be approximately 3.1415927)Now, the perimeter (or circumference) of the full circle is given by the formula P = 2πr. For a quarter circle, the perimeter includes the arc of the quarter circle and the two radii.
The perimeter of the quarter circle is thus:
P = (1/4) × 2πr + 2rP = (1/4) × 2 × 3.1415927 × 1 km + 2 × 1 kmP = 1.57079635 km + 2 kmP = 3.57079635 kmBut since we know the measurements are to a certain precision, we must adjust our answer accordingly:
The final perimeter of the quarter circle, rounded to an appropriate number of significant figures based on the original measurement given, is approximately 3.57 km.
Recipes are written using mixed numbers. Would it matter if they were written by using improper fraction? Explain.
What is the constant of variation?