The number of large box is 12 and small box is 8.
What is cube?
The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. It is also asserted to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent example in daily life and can help to increase brain capacity. Similar to this, you'll run into a lot of real-world examples, like 6 sided dice, etc. Solid geometry is the study of three-dimensional objects with surface areas and volumes. Cube, cylinder, cone, and sphere are some of the other solid shapes. Here, we'll talk about its definition, attributes, and relevance to mathematics.
Given :
The volume of small box is 9 cubic feet
The volume of the large box is 12 cubic feet
The volume of all box is 216 cubic feet
There are 20 boxes of paper shipped.
Total Volume covered by small box will be 9x
Total Volume covered by large box will be 24x
Total volume shipped = 216
9x + 24x = 216
33x = 216
x = 6
So The number of large box is 12 and small box is 8.
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Eliminiation Please!
0.5x + 0.5y = -2
x - 0.25y = 6
Answer:
x = 4; y = -8
Step-by-step explanation:
0.5x + 0.5y = -2
x - 0.25y = 6
Rewrite the first equation. Multiply both sides of the second equation by 2 and write below the first equation. then add the equations.
0.5x + 0.5y = -2
+ 2x - 0.5y = 12
---------------------------
2.5x = 10
x = 4
x - 0.25y = 6
4 - 0.25y = 6
-0.25y = 2
y = -2/0.25
y = -8
x = 4; y = -8
Differentiate the given function.
y=x² √4x-3
Answer: I hope this helps you
Step-by-step explanation:
[tex]y=x^2\sqrt{4x-3}\implies \cfrac{dy}{dx}=\stackrel{\textit{\LARGE product rule}}{2x\sqrt{4x-3}~~ + ~~x^2\cdot \stackrel{\textit{chain rule}}{\cfrac{1}{2}(4x-3)^{-\frac{1}{2}}(4)}} \\\\\\ \cfrac{dy}{dx}=2x\sqrt{4x-3}~~ + ~~\cfrac{2x^2}{\sqrt{4x-3}}\implies \cfrac{dy}{dx}=\cfrac{8x^2-6x+2x^2}{\sqrt{4x-3}} \\\\\\ \cfrac{dy}{dx}=\cfrac{6x^2-6x}{\sqrt{4x-3}}\implies \cfrac{dy}{dx}=\cfrac{6x(x-6)}{\sqrt{4x-3}}[/tex]
Find the area of the figure.
Answer:
1) 143 square inches
2) 32 square inches
3)152 square yards
4) 150 square inches
Step-by-step explanation:
Finding the area:1) Parallelogram:base= 11 in ;height = 13 in
[tex]\sf \boxed{\text{Area of parallelogram = base * height}}[/tex]
= 11 * 13
= 143 square inches
2) Triangle:base = 8 cm ; height = 8 cm
[tex]\sf \boxed{\text {Area of triangle = } \dfrac{1}{2}*base * height}[/tex]
[tex]\sf =\dfrac{1}{2}*8 * 8\\\\= 4 * 8\\\\= 32 \ in^2[/tex]
3) Kite:diagonal = p = 7 + 12 = 19 yd
diagonal 2 = q = 8 + 8 = 16 yd
[tex]\sf \boxed{\text{Area of kite =} \dfrac{pq}{2}}[/tex]
[tex]\sf =\dfrac{19*16}{2}\\\\= 19*8\\\\= 152 \ yd^2[/tex]
4)Trapezium:a = 13 in ; b = 12 ; h = 12 in
a,b are the parallel sides of the trapezium.
[tex]\sf \boxed{\text{Area of trapezium = }\dfrac{(a + b)*h}{2}}[/tex]
[tex]\sf = \dfrac{(13+12)*12}{2}\\\\\\=\dfrac{25*12}{2}\\\\=25*6\\\\= 150 \ in^2[/tex]
Fred is a weightlifter who can lift 800 pounds on 45% of his attempts. Which of these expressions represents the probability Fred will make 30 lifts out of 60? A. B(30,.45,60)B. B(30,800,60)C. N(30, 800,60) D. N(60, 45, 30)E. B(60, 45, 30)
Expression represents the probability of the given number of attempts and the success rate is given by option E. B( 60 , 45 , 30 ).
As given in the question,
In the given situation,
Let us consider 'n' represents the number of trials attempt by the weightlifter.
'p' represents the probability of success in his number of trials.
And 'r' represents the number of success out of his total number of attempts.
Here n = 60
p = 45%
r = 30
Using binomial distribution method we can represents the expression of the probability for the given condition :
B( n , p , r )
Substitute the values we get,
= B( 60, 45, 30 )
Therefore, for the given total number of lifts , success rate the expression represents the probability is given by option E . B ( 60, 45 , 30 ).
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Maria clothing store sold $5230 worth of items last week. She invested half of her income
from the week in new items to sell. Then she paid herself $300 salary for the week. A
manufacturer gave her a rebate of $500 for items that were reduced at the factory. What was
her ending balance?
Write the expression and find the balance.
(5230-300+500)/2; $2715
(5230/2)-300 + 500; $2815.
(5230/2) +500 - 300; $2815
Answer:
Step-by-step explanation:
Maria clothing store sold $5230 worth of items last week. She invested half of her income from the week in new items to sell.Then she paid herself $300 salary for the week. A manufacturer gave her a rebate of $500 for items that were reduced at the factory. What was her ending balance? Write the expression and find the balance.
Approximately how much principal would need to be placed into an account earning 3.575% interest compounded
quarterly so that it has an accumulated value of $68,000 at the end of 30 years?
a. $23,706
b. $23,377
c. $52,069.
d. $58,944
Please select the best answer from the choices provided
The compound interest the answer is b)$23377.
What is compound interest?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
We know that for compound interest, A = [tex]P(1+\frac{r}{n})^n[/tex]
Where,
A = Future amount = $68,000
P = ??
r = 3.575% annual = 0.03575
n = 4 as interest is compounded quarterly
t = time in year = 30 years
Putting the values,
=> 68000 = P [tex](1+\frac{0.03575}{4})^{4*30}[/tex]
=> 68000 = P[tex](1+\frac{0.03575}{4})^{120}[/tex]
=> 68000 = P (1.0089375)[tex]^{120}[/tex]
=> P = $23377.5
Hence the correct option is b)$23377.
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Write an equation (any form) for the quadratic graphed below:
I added the photo of the graph
Check the picture below.
so we are really looking for the equation of a parabola whose vertex is at (2 , 3) and it passes through (4 , 1)
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=2\\ k=3\\ \end{cases}\implies y=a(~~x-2~~)^2 + 3\hspace{4em}\textit{we also know that} \begin{cases} x=4\\ y=1 \end{cases}[/tex]
[tex]1=a(4-2)^2+3\implies -2=a(2)^2\implies -2=4a \\\\\\ \cfrac{-2}{4}=a\implies -\cfrac{1}{2}=a~\hfill \boxed{y=-\cfrac{1}{2}(x-2)^2 + 3}[/tex]
80% of 40 please help me
Answer:
32
Step-by-step explanation:
0.8 x
Answer:
32
Step-by-step explanation:
the quotient of 2 and 9
Answer: The quotient of 2 and 9 is 0.2222 (approximately) or 2/9
Step-by-step explanation:
Quotient is a mathematical term that refers to the result of dividing one number by another. In this case, the quotient of 2 and 9 is found by dividing 2 by 9, which results in 0.2222 (approximately) or 2/9.
It's important to note that the quotient is a decimal number because 9 doesn't divide into 2 exactly, so there is a remainder of 0.2222. The quotient represents the number of times 9 can be divided into 2, which is a fraction of a time. In this case, 9 can be divided into 2 only 0.2222 times.
I hope this helps :)
The quotient of 2 and 9 is the result of the division of 2 by 9 which is approximately 0.2222.
Explanation:The question is asking for the quotient of 2 and 9. The quotient is the result of division. So, to find the quotient of 2 and 9, you need to divide two by nine.
The calculation is as follows: 2 ÷ 9 = 0.2222 (rounded to the fourth decimal place).
So, the quotient of 2 and 9 is approximately 0.2222.
Always remember, that when the divider (the number we divide by) is larger than the dividend (the number to be divided), we get a quotient less than one.
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If Bob is driving along a toll road and passes the first toll reader at 12:00 and is traveling 50 miles an hour, he then passes the second reader 12 miles later at 12:10.
Using the Mean Value Theorem, can you prove that Bob was driving faster than 55 miles per hour at some point?
Responses
Bob’s average speed was 60 miles/hr and the Mean Value Theorem can be used to prove that he was traveling faster than 55 miles per hour at some point between the two toll readers.
Bob’s average speed was 60 miles/hr and the , Mean Value Theorem, can be used to prove that he was traveling faster than 55 miles per hour at some point between the two toll readers.
Bob’s average speed was 72 miles/hr and the Mean Value Theorem cannot be used to prove that he was traveling faster than 55 miles per hour at some point between the two toll readers.
Bob’s average speed was 72 miles/hr and the , Mean Value Theorem, cannot be used to prove that he was traveling faster than 55 miles per hour at some point between the two toll readers.
Bob’s average speed was 72 miles/hr and the Mean Value Theorem can be used to prove that he was traveling faster than 55 miles per hour at some point between the two toll readers.
Bob’s average speed was 72 miles/hr and the Mean Value Theorem can be used to prove that he was traveling faster than 55 miles per hour at some point between the two toll readers.
Bob’s average speed was 60 miles/hr and the Mean Value Theorem cannot be used to prove that he was traveling faster than 55 miles per hour at some point between the two toll readers.
Bob’s average speed was 72 miles/hr and the Mean Value Theorem can be used to prove that he was traveling faster than 55 miles per hour at some point between the two toll readers.
How to determine the true statementWe have the following parameters
Rate = 50 miles per hour
Time = 12:00 to 12:10 where he passed the second reader after 12 miles
This means that he drove 12 miles in 10 minutes or 1/6 hour
The speed within this interval is calculated as
Speed = 12/(1/6)
Evaluate
Speed = 72 miles
So, at a point t, Bob was driving at an instantaneous speed of 72 miles per hour, which is faster than 55 miles per hour.
Therefore, Bob was traveling faster than 55 miles per hour at some point between the two toll readers.
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find the values of x and y.
Answer:
how if there are no numbers or anything to find
Step-by-step explanation:
The student government snack shop sold 32 items this week.
For each snack type, what percentage of all snacks sold were of that type? Do not round your answers.
The percentages of each snack type that were sold are given as follows:
Fruit cup: 25%.Veggie sticks: 18.75%.Chips: 43.75%.Water: 12.5%.How to obtain the percentage?A percentage is one example of a proportion, as it is obtained by the number of desired outcomes divided by the number of total outcomes, and then multiplied by 100%.
Hence the percentages for each type are obtained as follows:
Fruit cup: 8/32 x 100% = 25%.Veggie sticks: 6/32 = 18.75%.Chips: 14/32 = 43.75%.Water: 4/32 = 12.5%.More can be learned about proportions at https://brainly.com/question/24372153
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In a survey of 653 randomly chosen workers from a manufacturing plant, 68 said that they prefer to work the night shift. The manufacturing plant employees a total of 2,700 workers. Based on this in formations,about how many plant workers refer the night shift?
Answer:
Approximately 281 workers prefer working the night shift
Step-by-step explanation:
68/653 = 0.104134
2700 * 0.104134
281.16
Determine the amount of semi-annual coupon paid for a 3% bond with a
face value of P100,000 which matures after 8 years. How many coupons
A semi-annual coupon bond is a bond that pays interest twice a year at a fixed rate.
To determine the amount of semi-annual coupon paid, you can use the following formula:
C = (r * FV) / n
Where:
C = coupon payment (semi-annual)
r = annual coupon rate (3% in this case)
FV = face value (100,000 in this case)
n = number of coupon payments per year (2 for semi-annual)
So, the semi-annual coupon payment for the bond is:
C = (0.03 * 100,000) / 2
C = 1500
The bond matures after 8 years, so the bond will pay 8*2 = 16 semi-annual coupons.
Dinesh is a mason and he takes Rs 3,250 for 5 days working everyday. If he received only Rs 7,800 in two weeks, how many days was he absent in his work?
Given Dinesh earns Rs 3,250 for 5 days working everyday, we can divide the total by 5 to find that he earns Rs 650 daily. Because there are 14 days in two weeks, we can set up an equation:
650 • 14 = Rs 9,100
This means if Dinesh worked every day for two weeks, he would earn Rs 9,100; however, we are told he earns 7,800 in the two weeks. Upon subtraction of 9,100 and 7,800, we will find that Dinesh earned Rs 1,300 less than he would have for a full two weeks.
We know Dinesh earns Rs 650 daily, so we can divide 1,300 by 650 to find that he was absent for 2 days out of the two weeks.
Trapezoid ABCD has parallel sides AB and CD, of lengths 12 and 18, respectively. Diagonals AC and BD intersect at E. Draw the line through E that is parallel to AB and CD, and let P and Q be its intersections with DA and BC, respectively. Find PQ.
PQ is the length of the line segment that is parallel to AB and CD, which intersects DA at P and BC at Q. The length of PQ can be found using the Pythagorean Theorem.
Let PQ = x.
Since the line is parallel to AB and CD, the triangles APE, PQC, and BQD are all right triangles.
Using the Pythagorean Theorem,
12^2 + x^2 = 18^2
x^2 = 18^2 - 12^2
x^2 = 324 - 144
x^2 = 180
x = √180
Therefore, PQ = √180
Since the line through E is parallel to AB and CD, the triangles APE, PQC, and BQD are all right triangles. Using the Pythagorean Theorem, we can calculate the length of PQ. We let PQ = x and set up the equation 12^2 + x^2 = 18^2. After solving for x^2, we get x^2 = 180, and x = √180. Therefore, PQ = √180. This is the length of the line segment that is parallel to AB and CD which intersects DA at P and BC at Q.
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Julie is rolling two trick number cubes she got with a magic set she purchased. Both of her number cubes have the number 5 on three of the faces, 10 on two of the faces, and 15 on one of the faces. Which of the following tables is a probability model for the sum of the two number cubes?
A 2-column table with 3 rows. Column 1 is labeled Sum with entries 5, 10, 15. Column 2 is labeled probability with entries one-third, one-third, one-third.
A 2-column table with 3 rows. Column 1 is labeled Sum with entries 5, 10, 15. Column 2 is labeled probability with entries one-half, one-third, one-sixth.
A 2-column table with 3 rows. Column 1 is labeled Sum with entries 10, 20, 30. Column 2 is labeled probability with entries one-half, one-third, one-sixth.
A 2-column table with 3 rows. Column 1 is labeled Sum with entries 10, 15, 20. Column 2 is labeled probability with entries one-fourth, one-third, StartFraction 5 Over 18 EndFraction.
A 2-column table with 3 rows. Column 1 is labeled Sum with entries 10, 15, 20. Column 2 is labeled probability with entries one-fifth, one-fifth, one-fifth.
The probability of rolling two trick number cubes with the numbers 5, 10, and 15 on them can be calculated using the formula P(A) = n(A) / n(S), where P(A) is the probability of event A, n(A) is the number of favorable outcomes, and n(S) is the total number of possible outcomes.
In this case, the total number of possible outcomes is 6, since there are six possible combinations of two number cubes. The number of favorable outcomes for a sum of 10 is 2, since there are two possible combinations (5 and 5, and 10 and 15). Therefore, the probability of rolling a sum of 10 is 2/6, or one-third. The probability of rolling a sum of 15 is also one-third, since there is only one possible combination (10 and 5). The probability of rolling a sum of 20 is one-sixth, since there is only one possible combination (10 and 10). Therefore, the probability model for the sum of the two number cubes is a 2-column table with 3 rows. Column 1 is labeled Sum with entries 5, 10, 15. Column 2 is labeled probability with entries one-half, one-third, one-sixth.
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you run an experiment in which you flip 3 coins, and each one lands heads or tails. your sample space can be written: {hhh, hht, hth, htt, thh, tht, tth, ttt}. assume all outcomes have equal probability.
The sample space consists of 8 possible outcomes, each with an equal probability of 1/8. The outcomes are the combinations of heads (h) and tails (t) when flipping 3 coins.
1. Determine how many possible outcomes there are in the sample space.
There are 8 possible outcomes in the sample space: hhh, hht, hth, htt, thh, tht, tth, and ttt.
2. Determine the likelihood of each result.
Since all outcomes have equal probability, the probability of each outcome is 1/8.
In this experiment, we are flipping three coins, and each one lands either heads (h) or tails (t). Our sample space consists of all the possible combinations of heads and tails that can occur when flipping the coins. Therefore, our sample space is {hhh, hht, hth, htt, thh, tht, tth, ttt}. Since all outcomes have equal probability, the probability of each outcome is 1/8. This means that the probability of each combination of heads and tails is the same. For example, the probability of getting 3 heads is 1/8 and the probability of getting 2 heads and 1 tail is also 1/8.
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Chantelle works at Mattresses R Us. She had $60,000 in sales and made $1200 in commission. What percent commission does she get?
Answer =
I got 2 i did math wrong... please help
The percentage of commissions is obtained as follows:
2%.
How to obtain the percentage of commission?The percentage of commission is obtained applying the proportions in the context of this problem.
A proportion is applied as the sales commission percentage is given by the sales commission divided by the total number of sales, and then multiplied by 100%.
The parameters for this problem are given as follows:
$60,000 in sales.Commission of $1,200.Hence the percentage can be then obtained as follows:
1200/60000 x 100% = 2%.
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We want to know how a student’s level of education and their gender impacts both their annual income and amount of student loan debt. However, we want to account for the annual income of the student’s parents as well. So which Statistical Test are you going to use?
The statistical tests that van be used to analyze the relationship include multiple regression analysis and ANOVA.
How to explain the statistical test?There are several statistical tests that could be used to analyze the relationship between a student's level of education, gender, annual income, student loan debt, and the annual income of their parents.
One possibility is to use a multiple regression analysis, which would allow you to simultaneously examine the impact of all of these variables on annual income and student loan debt.
Another option could be to use a two-way ANOVA (Analysis of Variance) which would allow you to examine the interaction effects of the student's level of education and gender on annual income and student loan debt. And also, you can use chi-square test for categorical variables like gender. It ultimately depends on the specific research question and the type of data you have.
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The area of a circle is 27 square meters. Determine the radius. Use 3 for pi
The radius of a circle with area of 27 square meters is 3 meters.
What is area of a circle?
The area of a circle is the space encircled or encompassed by its circumference. It is represented in the form of square units.
Area of circle(A)= πr^2
where 'r' represents the radius of the circle
We are given that area of a circle is 27 square meters i.e.
⇒πr^2 = 27
The value of π is 3
So, we get
⇒3r^2 = 27
⇒r^2 = 9
⇒r = 3
Hence, the radius of a circle with area of 27 square meters is 3 meters.
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In 2010, the population of a city was 144,000. From 2010 to 2015, the population grew by 8%. From 2015 to 2020, it fell by 7%. How much did the population decrease from 2015 to 2020, to the nearest 100 people?
Answer:
144600
Step-by-step explanation:
In 2010, pop'n 144,000.
From 2010 to 2015, the population grew by 8%.
so by 2015 = 144000*1.08 = 155520
From 2015 to 2020, it fell by 7%.
so 155520 * (1-7%) = 155520 * 0.93 = 144634
round to the nearest 100 = 144600
the perimeter of an athletic field is 352 m. if the width is 68 m, find the length. write your answer as an integer or simplified fraction
Answer:
108
Step-by-step explanation:
p=2(l+w)
352=2(l+68)
352=2l+136
2l=352-136
2l=216
l=108
Formula of Perimeter of rectangle( P ) = 2 ( l + b )
Perimeter = 352m
Width = 68m
Length = ?
Now
Perimeter ( P ) = 2 ( l + b )
352m = 2 ( l + 68m )
352m = 2l + 136m
352m - 136m = 2l
216m = 2l
[tex]l \: = \frac{216m}{2} \\ [/tex]
l = 108m
hence the length is 108m...
video rental company offers a plan that includes a membership fee of $10 and charges $2 for every DVD borrowed. They also offer a second plan, that costs $42 per month for unlimited DVD rentals. If a customer borrows enough DVDs in a month, the two plans cost the same amount. How many DVDs is that? What is that total cost of either plan?
The number of DVDs will be 19 for the first plan.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the video rental company offers a plan that includes a membership fee of $10 and charges $2 for every DVD borrowed. They also offer a second plan, that costs $42 per month for unlimited DVD rentals.
The number of the DVDs will be calculated as:-
C₁ = 2D + 10
The cost for the second plan is,
48 = 2D + 10
2D = 38
D = 38 / 2
D = 19
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140/297 write as simplest Fraction form
Answer:
is already in the simplest form. It can be written as 0.47138 in decimal form (rounded to 6 decimal places).
Find the GCD of numerator and denominator
GCD of 140 and 297 is 1
When you divide both the numerator and denominator by 1
The answer will remain the same
Ellie had 15 candies , after opening it she found out that 13 were not green, if she opens 3 or more packs , how many green candies should she expect
Answer:
She should expect 8 candies
Step-by-step explanation:
If 13 were not green that would leave 2 that were green which means that ( hoping that the same amount is in each one) if you count by 2's 3 more times you would get 8 and if there is more just continue counting by 2's
Please answer it asap, it's missing
To find the value of ( f ∘ g ) (4), we need to first substitute 4 into the definition of g(x) and then substitute the result into the definition of f(x).
First we substitute 4 into g(x):
g(4) = -2(4) + 15 = -8 + 15 = 7
Now we substitute 7 into f(x):
f(g(4)) = f(7) = 7^2 - 5(7) - 2 = 49 - 35 - 2 = 12
So the value of ( f ∘ g ) (4) is 12.
List all possible rational zeros of the function f(x) = 3x^3 + 2x^2 – 3x + 2
Answer:
j
Step-by-step explanation:
l
A monopolistic firm's marginal revenue function is
dr 100q+43
dq q² +4q+3
=
where output (=demand) is measured in 100s of units/week and revenue is measured in
$1000s/week. The firm's marginal cost function is constant, de/dq= 3, and cost is also
measured in $1000s/week.
If the demand (= output) for the firm's good increases from 2000 units/week to 2500
units/week, then their weekly revenue increases by [Select]
and their
weekly profit changes by [Select]
Comment: pay attention to the units.
The weekly profit changes by $1000s/week.
What is profit?
The profit is defined as the amount gained by selling a product, and it should be more than the cost price of the product. In other words, the profit is a gain obtained from any business activities.
To find the increase in weekly revenue, we need to find the difference in revenue at the two output levels:
2500 units/week: Revenue = 100(2500) + 43 = 2543
2000 units/week: Revenue = 100(2000) + 43 = 2043
So the increase in weekly revenue is 2543 - 2043 = $500s/week.
To find the change in weekly profit, we need to subtract the change in cost from the change in revenue:
Change in cost: 2500 units/week - 2000 units/week = 500 units/week * 3 $1000s/week/unit = 1500 $1000s/week
Change in profit: $500s/week - $1500s/week = -1000
Hence, the weekly profit changes by $1000s/week.
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Determine the longest interval in which the given initial value problem is certain to have a unique twice differentiable solution. Do not attempt to find the solution.
the longest interval in which the initial value problem is certain to have a unique twice differentiable solution is (-∞, ∞).
Initial value problem:
y'' + 4y' + 4y = 0, y(0)=1, y'(0)=2
The longest interval in which the initial value problem is certain to have a unique twice differentiable solution is the interval (-∞, ∞).
The given initial value problem is a second order linear homogeneous differential equation. This type of equation is known to have a unique twice differentiable solution on the interval (-∞, ∞). Therefore, the longest interval in which the initial value problem is certain to have a unique twice differentiable solution is (-∞, ∞).
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