The greatest number of containers is 2⁴ = 16 containers.
How to find the greatest number of containers he can make?Since Mr. Pinello has 80 colored pencils and 64 markers to divide into containers for his class. He wants each container to have the same number of items. To find the number of containers, we need to find the highest common factor (H.C.F) of both numbers.
So, writing both numbers in prime factorization, we have
For the 80 colored pencils,
80 = 2 × 2 × 2 × 2 × 5
= 2⁴ × 5
Also, the prime factorization for the 64 markers, we have
64 = 2 × 2 × 2 × 2 × 2 × 2
= 2⁶
So, the highest common factor is 2⁴
So, the greatest number of containers is 2⁴ = 16 containers.
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If you borrowed $646 at an interest rate of 5% for 6 years, how much interest will you pay? Round to the nearest tenth if necessary.
Answer:
P=646
R=5%
T=2yrs
I=?
I=PRT/100
I= 646*5*2/100
I= 64.6
Step-by-step explanation:
Answer:
the answer is 100
Step-by-step explanation:
646 X 5 IS 3000
3000/5 is 600
and then round tenth so its 10
600/10 is 60
60 + 40 = 100 and there you go bravo
A square patio has a side length of (x − 8) feet. It is surrounded by a flower garden with a uniform width. The side length of the entire square area including the patio and the flower garden is (x + 8) feet. Enter an expression for the area of the flower garden.
9514 1404 393
Answer:
32x ft²
Step-by-step explanation:
The area of the garden plus patio is ...
(x +8)² = x² +16x +64
The area of the patio is ...
(x -8)² = x² -16x +64
The area of the flower garden is the total area less the patio area:
(x² +16x +64) -(x² -16x +64) = 32x . . . area of the flower garden
Please give me the correct answer.Only answer if you're very good at math.Please use the Pythagorean Theorem formula which is a^2 + b^2 = c^2.
Answer:
c = 8.7 inches
Step-by-step explanation:
a^2 + b^2 = c^2
Substitute in the known values for a and b (the order doesn't matter):
(4.8)^2 + (7.3)^2 = c^2
multiply 4.8 times itself, 7.3 times itself:
23.04 + 53.29 = c^2
76.33 = c^2
Now find the square root of both sides of the equation (square root of c^2 = c):
8.736= c
It says round to the nearest tenth, so c = 8.7 inches
The length of a rectangle is 5 centimeters less than twice its width. Its area is 63 square centimeters.
Find the dimensions of rectangle
Answer:
I think the Length is 5 cm and the width is 7 cm
Step-by-step explanation:
What is y in this equation
Answer:
y = 88
Step-by-step explanation:
y + 53 + 39 = 180
y + 92 = 180
y = 88
Animals were trapped in a city and later released into the wild. A random sample of the data is provided in the table below.
Animal type Raccoon Skunk Fox
Number of animal 230 140 120
If a random sample of 5,000 animals are trapped in the city, how many skunks would be estimated to be included? (3 points)
a
2,500
b
280
c
1,400
d
380
Answer:
c
1,400
Step-by-step explanation:
We take the sample proportion of skunks and estimate for the entire population.
Sample:
140 skunks out of 230 + 140 + 120 = 490 animals.
140/490 = 0.28571428571
If a random sample of 5,000 animals are trapped in the city, how many skunks would be estimated to be included?
0.28571428571 out of 5000. So
0.28571428571*5000 = 1429
Close to 1400, which means that the answer is given by option C.
Jason jumped off a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t) = -16t^2 +16t+480
How long did it take Jason to reach his maximum height?
Answer:
5 seconds
Step-by-step explanation:
I did the same question a while ago.
Find a fraction with a demominator of 30 that is equivalent to 1/3
Answer:
10/30
Step-by-step explanation:
First, multiply the denominator by 10 to make 30.
Then, since we multiplied the denominator, we multiply the numerator. 1 x 10= 10
Therefore the answer is 10/30.
Can someone pls help me with this question
Vladimir hit a home run at the ballpark. A computer tracked the ball's trajectory in feet and modeled its flight path as a
parabola with the equation, y = -0.003(x – 210)2 + 138. Use the equation to complete the statements describing the
path of the ball.
Answer:
The vertex of the parabola is
✔ (210, 138)
The highest the ball traveled was
✔ 138
feet.
Step-by-step explanation:
Edge 2022
A parabola is a mirror-symmetrical planar curve that is nearly U-shaped. The highest the ball has travelled is 138 feet.
What is an equation of a parabola?A parabola is a mirror-symmetrical planar curve that is nearly U-shaped.
y = a(x-h)² + k
where,
(h, k) are the coordinates of the vertex of the parabola in form (x, y);
a defines how narrower the parabola is, and the "-" or "+" that the parabola will open up or down.
A.) In the given quadratic equation, the vertex of the equation is y=-0.003(x-210)² + 138 is (210,138).
B.) Since the vertex is the highest point, therefore, The highest the ball has travelled is 138 feet.
The complete question is,
Vladimir hit a home run at the ballpark. A computer tracked the ball's trajectory in feet and modelled its flight path as a parabola with the equation, y = -0.003(x – 210)2 + 138. Use the equation to complete the statements describing the
path of the ball.
The vertex of the parabola is ?
The highest the ball travelled was? Feet
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If 2 tacos and 3 drinks cost $14, and 3 tacos and 2 drinks cost $16, how much does a taco cost?
Answer:
1 taco is $4
Step-by-step explanation:
2t + 3d = 14 4t + 6d = 28
3t + 2d = 16 -9t -6d = -48
-5t = -20
t = 4
A tacos would cost $4.00.
Let the cost of tacos be T.Let the cost of drinks be D.Translating the word problem into an algebraic equation, we have;
[tex]2T \; + \; 3D = 14[/tex] ......equation 1
[tex]3T \; + \; 2D = 16[/tex] ......equation 2
To find how much a tacos cost, we would solve the above system of equations by using the substitution method.
From eqn 1, we would make D the subject of formula;
[tex]D = \frac {14 \; - 2T}{3}[/tex] .....equation 3
Substituting eqn 3 into eqn 2, we have;
[tex]3T \; + \; 2(\frac {14 \; - 2T}{3}) = 16\\\\3T \; + \; \frac {28 \; - 4T}{3} = 16\\\\[/tex]
Lowest common multiple (LCM) = 3
[tex]\frac {9T \; + \; 28 \;- \; 4T}{3} = 16\\\\\\[/tex]
Cross-multiplying, we have;
[tex]9T \; + \; 28 \;- \; 4T = 16 \; * \; 3\\\\5T \; + 28 = 48\\\\5T = 48 \; - 28\\\\5T = 20\\\\T = \frac{20}{5} \\[/tex]
Tacos, T = $4.00
Therefore, the cost of a tacos is $4.00.
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Two groups of school children had their forearm lengths measured. Dot plots are provided showing these results.
a
Group Y. There were 6 children who had a forearm length that measured longer than 12 inches.
b
Group X. There were 4 children who had the lowest forearm length of 10 inches in this group.
c
Group X. None of the children in this group had a forearm length longer than 12 inches.
d
Group Y. One child in this group had the smallest forearm length of 10 inches.
Answer:
Stament a, b, and c are correct.
Statement d is INCORRECT.
Step-by-step explanation:
Based on the dot plots given, the following statements are true and correct:
✔️Statement A is correct
Rationale: in the dot plot representing group Y, there are 6 dots on number 13. These shows that 6 children have an arm length of 13 inches. This means that there are actually 6 children who had a forearm length that measured longer than 12 inches.
✔️Statement b is correct:
Rationale: the lowest forearm length displayed on the dot plot for group X is 10 inches, represented by 4 dots.
✔️Statement c is correct:
Rationale: the dot plot for group X shows that the maximum arm length recorded for group X was 12 inches. Therefore no child in group X has a forearm length that is longer than 12 inches.
❌Statement d is NOT CORRECT
Rationale: the dot plot for group Y shows that 2 children had the smallest forearm length of 11 inches.
Accountants often use the median when studying salaries for various businesses. What is the median of the following salary list: $32,019; $21,971; $27,596; $43,715, $38,850, $25,963?
Answer
40.5
Step-by-step explanation
Are these ratios equivalent?
28 hot dogs to 50 hamburgers
15 hot dogs to 30 hamburgers
Answer:
Step-by-step explanation:
28 : 50 and 15 : 30
14 : 25 and 1 : 2 are not equivalent
subtract and simplify 1/6m - (-5/8 m +1/3)
show full work
Answer:
11/24
Step-by-step explanation:
first we work out the bracket -5/8+1/3= -7/24. then 1/6 - -7/24 two negatives means you will add to get the answer
Evaluate the expression: 12 x (3+2)² ÷ 2 -10
Answer:
140
Step-by-step explanation:
Here, we use BODMAS
12 x (3+2)² ÷ 2 - 10
12 x (5)² ÷ 2 - 10
12 x (5)² ÷ 2 - 10
12 × 25 ÷ 2 - 10
12 × 12.5 - 10
150 - 10 = 140
Thus, The answer is 140
-TheUnknownScientist
Two hockey teams, the Winnipeg Jets (yay!) and the Toronto Maple Leafs (boo!), miraculously make it to
the Stanley Cup finals. As soon as a team wins 3 games, the championship is over.
The schedule for the playoffs (for home games) is: Jets - Leafs - Jets - Leafs - Jets
If the Jets are playing at home, there is a 60% chance they'll win. If they are playing on the road, there is
a 45% chance they'll win.
Find the probability that the Jets win the Stanley Cup. Round answers to at least 4 decimal places.
Can anyone help me please. No links please
Answer: 58 .23
Step-by-step explanation:
Jets are playing at home, there is a 60% chance they'll win. If they are playing on the road, there is
a 45% chance they'll win.
HELP PLEASE! I WILL GIVE BRAINLIEST
Answer:
13.89
Step-by-step explanation:
A^2+B^2=C^2
7^2+12^2=C^2
193 = C^2
193 square root = 13.89
Ceasar opens a bank account and makes an initial deposit of $800. The banker tells Ceasar that he is going to receive an annual rate of 10% compounded continuously on his investment. Find the bank balance assuming Ceasar leaves the account untouched for 8 years.
Can you please do the problem using the formula A(t)=pe^(rt).
Find the median: 12, 5, 9, 18, 22, 25, 6, 15, 28, 14, 8, 24
Answer:
14.5
Step-by-step explanation:
20% of _____ is 18
what is the blank
Answer:
90
Step-by-step explanation:
In 2012, the world population was 7.02 billion. The birth rate had stabilized to 134 million per year and is projected to remain constant. The death rate is projected to increase from 56 million per year in 2012 to 80 million per year in 2040 and to continue increasing at the same rate.
(a) Assuming the death rate increases linearly, write a differential equation for P(t), the world population in billions t years from 2012.
(b) Solve the differential equation.
(c) Find the population predicted for 2050.
Answer:
[tex](a)\ \frac{dP}{dt} = 0.078- 0.000857t[/tex]
[tex](b)\ P = 0.078t- 0.0004285t^2 + 7.02[/tex]
[tex](c)\ 9.37\ billion[/tex]
Step-by-step explanation:
Given
In 2012
[tex]P(t) = 7.02\ billion[/tex]
[tex]R_1 = 134\ million/year[/tex] --- Birth rate
[tex]R_2 = 56\ to\ 80[/tex] -- Death rate from '12 to '40
Solving (a): Equation for population from 2012
In 2012, we have the addition in population to be:
[tex]\triangle P= Birth - Death[/tex]
[tex]\triangle P= 134 - 56[/tex]
[tex]\triangle P = 78[/tex] million
From 2012 to 2040, we have the death rate per year to be:
[tex]Rate/yr = \frac{80 - 56}{2040 - 2012}[/tex]
[tex]Rate/yr = \frac{24}{28}[/tex]
[tex]Rate/yr = \frac{6}{7}[/tex] million/year
So, the differential equation is:
[tex]\frac{dP}{dt} = \triangle P - Rate/yr * t[/tex] where t represents time
[tex]\frac{dP}{dt} = 78 - \frac{6}{7} * t[/tex]
[tex]\frac{dP}{dt} = 78 - \frac{6t}{7}[/tex]
Express in millions
[tex]\frac{dP}{dt} = \frac{78}{1000} - \frac{6t}{7000}[/tex]
[tex]\frac{dP}{dt} = 0.078- 0.000857t[/tex]
Solving (b): The solution to the equation in (a)
[tex]\frac{dP}{dt} = 0.078- 0.000857t[/tex]
Make dP the subject
[tex]dP = (0.078- 0.000857t)dt[/tex]
Integrate both sides
[tex]\int dP = \int (0.078- 0.000857t)dt[/tex]
[tex]P = \int (0.078- 0.000857t)dt[/tex]
This gives:
[tex]P = 0.078t- \frac{0.000857t^2}{2} + c[/tex]
[tex]P = 0.078t- 0.0004285t^2 + c[/tex]
Solve for c.
When t = 0; P = 7.02
So, we have:
[tex]7.02 = 0.078*0- 0.0004285*0^2 + c[/tex]
[tex]7.02 =0-0 + c[/tex]
[tex]7.02 =c[/tex]
[tex]c = 7.02[/tex]
So:
[tex]P = 0.078t- 0.0004285t^2 + c[/tex]
[tex]P = 0.078t- 0.0004285t^2 + 7.02[/tex]
Solving (c): The population in 2050
We have:
[tex]P = 0.078t- 0.0004285t^2 + 7.02[/tex]
In 2050, the value of t is:
[tex]t = 2050 - 2012[/tex]
[tex]t = 38[/tex]
So, the expression becomes
[tex]P = 0.078*38- 0.0004285*38^2 + 7.02[/tex]
[tex]P \approx 9.37\ billion[/tex]
Ceasar opens a bank account and makes an initial deposit of $800. The banker tells Ceasar that he is going to receive an annual rate of 10% compounded continuously on his investment. Find the bank balance assuming Ceasar leaves the account untouched for 8 years.
Can you please do the problem using the formula A(t)=pe^(rt).
Answer:
1780.43
Step-by-step explanation:
Given:
P = 800
r = 10% or 0.1
t = 8
Work:
[tex]A=Pe^{rt}\\\\A=800e^{0.1*8}\\\\A=800e^{0.8}\\\\A=1780.43[/tex]
Pls help,
Type the answers and leave each part as abcd so I don’t type it in wrong
I WILL MARK BRANLIST IF U GIVE ME AN ACTAUL ANSWER
Answer:
a
If they are vertical angles, they are equal.
5x - 24 = 3x + 24 Add 24 to both sides
5x -24 +24 = 3x + 24 + 24 Combine
5x = 3x + 48 Subtract 3x
5x - 3x = 3x-3x + 48 Combine
2x = 48 Divide by 2
x = 24
<A =5*24 - 24
<A = 96
Step-by-step explanation:
FREE BRAINLIST NEED HELP ASAP
Answer:
The answer is C
Step-by-step explanation:
Trust me I made a graph to organize the numbers
Ava read 126 books in 12 months. How many books per month did she read? Show your work
Help please will mark brainliest
Answer:
SA = 638 mi²Steps:
SA = 2L² + 4(LH)
SA = 2×11² + 4(11×9)
SA = 2×121 + 4×99
SA = 242 + 396
SA = 638 mi²
WALLAHI HELP ME PLEASE
9514 1404 393
Answer:
(a) yes
Step-by-step explanation:
Put the numbers in for x and y and see if you get a true statement.
5 ≤ 2(4) +1
5 ≤ 9 . . . . . . true
The point is a solution.
6 8ths -2 8ths thanks please explain to
Answer:
0.5 or [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Sheldon spent $42 on cookies. If each box cost $6, which equation will tell you how many boxes of cookies Sheldon bought?
Answer:
42 multpliy by 6
Step-by-step explanation:
Sheldon bought 7 boxes of cookies if he spent $42 on cookies.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Cost of one box of cookies = $6.
And total amount spent by Sheldon on cookies = $42.
Let Sheldon bough x boxes of cookies.
To find the number of boxes of cookies x,
Use ratio property,
Cost of one box of cookies = $6
Cost of x boxes of cookies = $6x
Total price = 42
6x = 42
x = 7
The required number of boxes of cookies is 7.
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