The Height of the toy box is 7 feet.
The height of the toy box in the shape of a rectangular prism is calculated using the following formula:
Volume = Length * Width * Height.
In this case, Volume = 36 cubic feet, Length = 2 * Width, and Height = Width - 1.
Therefore, we can solve for the Width by substituting the values into the formula:
36 = (2 * Width) * (Width - 1)
36 = 2 * Width^2 - Width
2 * Width^2 - Width - 36 = 0
By using the quadratic formula, Width = 8.
Therefore, the Height of the toy box is 7 feet.
To summarize, the toy box in the shape of a rectangular prism has a Width of 8 feet, a Length of 16 feet, and a Height of 7 feet to hold a total of 36 cubic feet.
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2. The area of this trapezoid is 24.5 ft².
3 ft
4 ft
What is the height of the trapezoid? Write the formula first then SHOW YOUR WORK
Plssss I need the answer fasttttt
The height of the trapeziod is 7 feet
How to determine the height of the trapezoidThe formula used for calculating the area of a trapezoid is expressed with the equation;
A = (a + b)/2 h
Such that the parameters in the equation are;
A is the area of the trapezoid.a is the length of its base.b is the length of its base.h is the height of the trapezoid.Substitute the values, we have;
24. 5 = (3 + 4)/2 h
add the values
24. 5 = 7//2 h
Divide the values
24.5 = 2.5 h
Make 'h' the subject of formula by dividing both sides by 3.5, we get;
h = 24.5/3.5
h = 7 feet
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Please hurry
The diameter of a softball is 3.8 inches. Estimate the volume within the softball. Round answers to the nearest
whole number and leave in the answer.
a. Volume: 73
b. Volume: 14
c. Volume: 9
d. Volume: 58
The volume of the softball is estimated to be 9π, so the correct option is C.
How to estimate the volume of the softball?We know that the softball is a sphere, and we know that the volume of a sphere of diameter D is given by the formula:
V = π(4/3)*(D/2)²
Where π = 3.14
Here we know that the diameter is 3.8 inches, then we can replace that in the formula above to get the volume.
V = π*(4/3)*(3.8in/2)²
V = 9π
So the correct option is C.
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x^2+x+9=0 which number would have to be added to complete the square
diego wants to package all 48 brownies and 64 cookies so that each bag has the same combination of items. how many bags can he make, and how many of each will be in each bag? determine at least one way to package both items.
Diego can make 56 bags with each bag containing 8 brownies and 12 cookies.
To package both items, he can divide the items into groups of 8 brownies and 12 cookies. He will then make 56 of these groups, ensuring each bag contains 8 brownies and 12 cookies.
Diego has 48 brownies and 64 cookies to package. To make the same combination of items in each bag, he needs to group the items into groups of 8 brownies and 12 cookies.
This can be done by dividing the 48 brownies into 6 groups of 8, and the 64 cookies into 5 groups of 12. He then needs to combine these two groups together, making 56 total bags.
Each of these bags will contain 8 brownies and 12 cookies. This is one way of packaging both items so that each bag has the same combination.
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In need of help fast
Answer:
Step-by-step explanation:
9to12
DUE TODAY PLEASE HELP!!!!! (MARCH 11TH) A sailboat travels 3 miles in 1.5 hours the table below shows the distance traveled by the boat at various times complete the table.
The table showing the distance traveled by the boat at various times should be completed as follows;
Time (h) 0 0.5 1 1.5 2 2.5 3
Distance (mi) 0 1 2 3 4 5 6
What is a proportional relationship?In Mathematics, a proportional relationship produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
k is the constant of proportionality.y represent the distance.x represent the time.Next, we would determine the constant of proportionality (k) for the data points contained in the table as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 3/1.5
Constant of proportionality, k = 2.
When x = 0.5, the distance is given by;
y = 2x
y = 2(0.5) = 1 mile.
When x = 1, the distance is given by;
y = 2x
y = 2(1) = 2 miles.
When x = 2, the distance is given by;
y = 2x
y = 2(2) = 4 miles.
When x = 2.5, the distance is given by;
y = 2x
y = 2(2.5) = 5 miles.
When x = 3, the distance is given by;
y = 2x
y = 2(3) = 6 miles.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
the contingency table shows the results of a survey of students in two math classes. find p(more than 1 hour of tv | 6th period class). round to the nearest thousandth. did you watch more than one hour of tv last night?
The probability of P(more than 1 hour of TV | 6th period class) is option (D) 0.765
To find P(more than 1 hour of TV | 6th period class), we need to use conditional probability formula
P(more than 1 hour of TV | 6th period class) = P(more than 1 hour of TV and 6th period class) / P(6th period class)
The number of students who watched more than 1 hour of TV and were in the 6th period class is 13. Therefore, P(more than 1 hour of TV and 6th period class) = 13 / (13 + 10) = 13/23.
The total number of students in the 6th period class is 13 + 10 = 23. Therefore, P(6th period class) = 23 / (6 + 23) = 23/29.
Putting it all together
P(more than 1 hour of TV | 6th period class) = P(more than 1 hour of TV and 6th period class) / P(6th period class) = (13/23) / (23/29) = 0.765 (rounded to the nearest thousandth)
Therefore, the correct option is (D) 0.765
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The given question is incomplete, the complete question is:
The table shows the results of a survey of students in two math classes. Find P(more than 1 hour of TV | 6th period class). Round to the nearest thousandth. Did You Watch More Than One Hour of TV Last Night? Yes No 3rd period class 6 6th period class 13 10 A) 0.647 B) 0.565 C) 0.435 D) 0.765
what is the probability that a randomly selected gas station in russia charged more than the mean price in the united state
The probability that a randomly selected gas station in Russia charges more than the mean price in the United States is quite low.
This is because the prices of gas in Russia are typically much lower than the mean price of gas in the United States. The average cost of gasoline in Russia is around $0.50 per liter while in the United States, the average price of gas is around $1.78 per liter.
To explain further, the cost of living in Russia is lower than the cost of living in the United States. This means that there is more disposable income for people living in Russia and as a result, the price of gas is much lower than in the United States.
In addition, the cost of transportation and other production costs are lower in Russia than in the United States, which also keeps the prices of gas in Russia lower.
All of these factors make it unlikely that a randomly selected gas station in Russia would be charging more than the mean price in the United States.
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in a marketing study, 100 consumers were asked to select the best digital music player from the ipod touch, sony walkman, and the zune hd. to summarize the consumer responses with a frequency table, how many classes would the frequency table have?
The frequency table would have three classes, one for each digital music player option.
When summarizing the consumer responses with a frequency table, the frequency table would have 3 classes.
Frequency table:
A frequency table is a statistical tool that is used to organize raw data in a clear and concise manner.
It is a way of representing the information contained in the data so that it can be easily interpreted and analyzed.
A frequency table is often used to summarize categorical data, such as the data collected in a marketing study like the one mentioned in the question.
The marketing study in this question involved asking 100 consumers to select the best digital music player from three options:
the iPod Touch, Sony Walkman, and Zune HD.
To create a frequency table from this data, we would need to count the number of times each option was chosen by the consumers.
This can be done by grouping the data into classes, which are categories that are created based on the values in the data.
For this particular study, there are only three options to choose from, so there are only three possible classes:
iPod Touch, Sony Walkman, and Zune HD. We would simply count the number of times each option was chosen and record it in the appropriate class.
The resulting frequency table would look something like this: Digital Music Player Frequency i Pod Touch 45 Sony Walkman 28 Zune HD27
Total 100
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consider a situation in which we calculate a 95% confidence interval that ranges from 35 to 45. if we conducted a two-sided test with the null hypothesis of the population mean equaling 43, what would the likely result of our test be?
The result of the two-sided test with the null hypothesis of the population mean equaling 43, based on the 95% confidence interval that ranges from 35 to 45, would be rejecting the null hypothesis.
The 95% confidence interval that ranges from 35 to 45 suggests that we are 95% confident that the true population mean falls between those values.
To conduct a two-sided test with the null hypothesis of the population mean equaling 43, we can use the confidence interval to see if the null hypothesis falls within the range of the confidence interval or not.
Since the null hypothesis of 43 is not within the confidence interval of 35 to 45, we can reject the null hypothesis at the 0.05 level of significance, which means we have evidence to suggest that the true population mean is not 43.
Therefore, the likely result of our test would be rejecting the null hypothesis.
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Dylan has $20.00 on his gift card. After some purchases, he has $0.06 remaining on his gift card. Dylan has _____% of the original amount remaining on the gift card.
Answer:
Step-by-step explanation:
To find the percentage of the original amount that Dylan has remaining on his gift card, we can divide the remaining amount by the original amount and then multiply by 100 to express it as a percentage.
The original amount on the gift card was $20.00, and the remaining amount is $0.06, so the percentage of the original amount that Dylan has remaining on his gift card is:
($0.06 ÷ $20.00) x 100% =
0.003 x 100% =
0.3%
Therefore, Dylan has 0.3% of the original amount remaining on his gift card.
if n is the product of all multiples of 3 between 1 and 100, what is the greatest integer m for which is an integer?
The greatest integer m for which n is an integer is 40.
This is because the product of all multiples of 3 between 1 and 100 (n) is equal to the product of all integers from 3 to 99, which is equal to 3^39*2^20.
By using the prime factorization of n, we can see that the greatest integer m is equal to the sum of the exponents of the prime factors, which is 39 + 20 = 40.
To solve this problem, we must first factor n, which is the product of all multiples of 3 between 1 and 100. n can be expressed as a product of prime factors 3^39*2^20.
This can be further expressed as 3^39*2^20 = (3*2)^39*2^20 = 6^39*2^20. To find the greatest integer m for which n is an integer, we must add the exponents of the prime factors, which gives us 39 + 20 = 40. Therefore, the greatest integer m for which n is an integer is 40.
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PLEASE HELP!
Write a function that models the situation: a $4000 deposit earns a 2% annual interest compounded semiannually after t years.
A = P(1 + r/n)^(nt)
Where:
A = the amount of money after t years
P = the principal amount (in this case, $4000)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year (in this case, twice a year, so n = 2)
t = the number of years
Plugging in the given values, we get:
A = 4000(1 + 0.02/2)^(2t)
Simplifying, we get:
A = 4000(1.01)^2t
Therefore, the function that models the situation is:
A = 4000(1.01)^(2t)
A system of linear equations is shown on the graph.
The graph shows a line that passes through negative 4 comma 0, negative 3 comma 1, and 0 comma 4. The graph also shows another line that passes through negative 6 comma 0, negative 3 comma 1, and 0 comma 2.
What is the solution to the system of equations?
There are infinitely many solutions.
There is no solution.
There is one unique solution (−6, 0).
There is one unique solution (−3, 1).
Answer: There is one unique solution: (-3,1)
you have one type of chocolate that sells for $2.50/lb and another type of chocolate that sells for $3.90/lb. you would like to have 8.4 lbs of a chocolate mixture that sells for $3.60/lb. how much of each chocolate will you need to obtain the desired mixture?
You need 1.8 lbs of the type of chocolate that sells for $2.50/lb and 6.6 lbs of the type of chocolate that sells for $3.60/lb.
A set or group of equations that are solved collectively is referred to as a system of equations. Both algebraic and visual solutions are possible for these problems. The intersection of two lines represents the system of equations' solution.
let
x = lbs of the type of chocolate that sells for $2.50/lb
y = lbs of the another type of chocolate that sells for $3.90/lb
You would like to have 8.4 lbs of a chocolate mixture that sells for $3.60/lb
x + y = 8.4
2.50x + 3.90y = 8.4 x 3.60
2.50x + 3.90y = 30.24
Putting the value of x = 8.4 - y in equation 2.
2.50( 8.4 - y) + 3.90y = 30.24
21 - 2.5y + 3.9 y = 30.24
1.4y = 9.24
y = 6.6
Putting y in x equation we get,
x = 1.8
by solving the above system of equations we find:
x = 1.8 lbs
y = 6.6 lbs
Therefore, each chocolate will you need to obtain the desired mixture is 1.8 lbs and 6.6 lbs.
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Solve the triangle please help me!!
The value of the side of the triangles are;
18. 17. 89
19. y = 9. 43, x = 5. 67
How to determine the valuesUsing the Pythagorean theorem stating that the square of the hypotenuse side is equal to the sum of the squares of the other two sides of a triangle.
From the diagram shown, we have;
21² = 11² + x²
find the squares
441 = 121 + x²
collect the like terms
x² = 320
Find the square root
x = 17. 89
To determine the value of y
sin 59 = y/11
y = 11 × 0. 8571
y = 9. 43
To determine the value of x
11² - 9. 43² = x²
x = √32.096
x = 5. 67
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Tell whether the angles are complementary, supplementary, or neither.
A local store charges $1.97 per pound for bananas and $4.49 for a gallon of apple juice what is the cost of 1.5 lb of bananas and 1 gallon of apple juice
The expense of 1.5 lbs of bananas and 1 gallon of apple juice, according to the provided statement, is $7.45.
What does arithmetic multiple mean?Multiplication is one of the four basic operations in mathematics, along with adding, subtracting, and division. Multiply in mathematics refers to the continual adding of sets of identical size.
The cost of 1.5 lb of bananas can be found by multiplying the price per pound by the number of pounds:
Cost of 1.5 lb of bananas = 1.5 x $1.97 = $2.96 (rounded to the nearest cent)
The cost of 1 gallon of apple juice is $4.49.
So, the total cost of 1.5 lb of bananas and 1 gallon of apple juice is:
Total cost = Cost of bananas + Cost of apple juice
Total cost = $2.96 + $4.49
Total cost = $7.45
Therefore, the cost of 1.5 lb of bananas and 1 gallon of apple juice is $7.45.
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KLM is the midpoints of GHJ. What is the perimeter of GHJ, given GH is 12 inches, KL is 7 inches, and LJ is 4 inches
The perimeter of the given triangle are as follow,
perimeter of triangle GHJ = 34 inches.
perimeter of triangle KLM = 17inches.
Perimeter of triangle GHJ is twice of perimeter of triangle KLM.
In triangle GHJ,
K,L,M are the midpoints of GH, HJ, and JG .
GH = 12 inches
KL = 7inches
LJ = 4 inches
'L' is the midpoint of HJ.
HJ = 2(LJ)
= 2(4inches )
= 8 inches
Using midpoint theorem we have,
KL = (1/2) GJ
⇒ GJ = 2(KL)
⇒GJ = 2(7)
⇒GJ = 14inches
LM = (1/2)GH
⇒LM = (1/2) ×12 inches
LM = 6 inches
KM= (1/2)HJ
⇒KM = (1/2) ×8
⇒ KM = 4 inches
Perimeter of triangle GHJ
= GH + HJ + JG
Substitute the value we have,
⇒ Perimeter of triangle GHJ = 12 + 14 + 8
Perimeter of triangle GHJ = 34 inches
Perimeter of the triangle KLM = KL + LM + MK
Substitute the value we have,
⇒ Perimeter of the triangle KLM = 7 + 6 + 4
Perimeter of the triangle KLM = 17 inches
Relation between perimeter of triangle GHJ and KLM
34 = 2 (17)
Perimeter of triangle GHJ = 2(Perimeter of triangle KLM)
Therefore, the required perimeters are,
Perimeter of ΔGHJ = 34inches
perimeter of ΔKLM = 17inches
Perimeter of ΔGHJ =2(Perimeter of ΔKLM).
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The above question is incomplete , the complete question is:
In triangle GHJ,
K,L,M are the midpoints of GH, HJ, and JG respectively.
Given GH is 12 inches, KL is 7 inches, and LJ is 4 inches
1. What is the perimeter of triangle GHJ?
2. What is the perimeter of triangle KLM?
3. What is the relationship between the perimeter of triangle GHJ and the perimeter of triangle KLM?
Diagram is attached.
PLEASE I WILL DO ANYTHING FOR SOMEONE TO ANSWER BOHTB QUESTIONS
Answer:
see explanation
Step-by-step explanation:
(a)
to say [tex]\sqrt{32}[/tex] = 2[tex]\sqrt{16}[/tex]
is incorrect in that she has taken the 2 outside the radical, when
(b)
using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab[/tex]
then
[tex]\sqrt{32}[/tex]
= [tex]\sqrt{2(16)}[/tex] ( note 2 remains inside the radical )
= [tex]\sqrt{2}[/tex] × [tex]\sqrt{16}[/tex]
= [tex]\sqrt{2}[/tex] × 4
= 4[tex]\sqrt{2}[/tex]
≈ 4 × 1.5
= 6
Find the surface area of a square pyramid with side length 2 cm and slant height 3 cm.
Answer:
16 cm²Step-by-step explanation:
The total surface area includes:
The square base with side of 2 cmFour triangle faces with base 2 cm and height 3 cmThe area is:
A = 2² + 4(1/2*2*3) = 4 + 12 = 16 cm²what is x - 3 = 21? show your wok
Answer: x = 24
Step-by-step explanation:
21 + 3= 24
There are 12 boys and 12 girls in Ms. Mooney’s homeroom class. Ms. Mooney will randomly pick 1 student to take attendance today.
Which statement explains how to find the probability that Sara, a student from Ms. Mooney’s homeroom class, will be the student picked?
PLEASE HELP
Answer:
There is a [tex]\frac{1}{24}[/tex] chance that Sara will be picked.
There is a 4.16% chance that Sara will be picked.
Step-by-step explanation:
there are 12 boys + 12 girls in Mooney's class => 24 total students
Sara is ONE out of those students
Sara is [tex]\frac{1}{24}[/tex].
[tex]\frac{1}{24}[/tex] as a percent is 4.16%.
Spencer lives 4/5 mile. In one week, he commutes a total of 16 miles to and from work. How many round trips does he make
?
To answer this problem, we must utilize the information provided to calculate the number of round trips Spencer takes every week. Spencer commutes a total of 16 miles each week,
which translates to 8 miles to work and 8 miles home. We also know that he lives around a quarter mile from his employment. the number of round trips Spencer takes every week. Spencer commutes a total of 16 miles each week, Thus we can create an equation to calculate the number of round trips he takes 8 = (4/5) * n where n is the number of trips Spencer takes. To find n, we can cross-multiply: 8 * 5 = 4 * n n = 20/4 n = 5 As a result,Spencer lives 4/5 mile. In one week, he commutes a total of 16 miles to and from work. Spencer makes five round journeys to and from work each week.
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Yooooo please help me out with this math
Geometric mean between 15 and 20
Answer: it should be 17.5
15+20 = 35
35/2 = 17.5 -----> mean of the two numbers
1 halves of a cupcake for my self 2 halves for my friend and 5 halves for our other friend
If the limit as n goes to infinity of the quotient of the absolute value of the quantity a sub n plus 1 times the n plus 1 power of the quantity x minus 7 and the absolute value of the product of a sub n and the nth power of x minus 7 for the power series the summation from n equals 1 to infinity of a sub n times the nth power of the quantity x minus 7, then what is the interval over which the power series converges absolutely? You do not need to consider the endpoints.
In conclusion, the power series converges absolutely over an interval given by [tex]\left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n\in\mathbb{N}\;\;\;\text{and}\;\;\;n>N, where N\in\mathbb{N}[/tex]is a natural number.
The interval over which the power series converges absolutely is given by [tex]\left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n\in\mathbb{N}\;\;\;\text{and}\;\;\;n>N, where N\in\mathbb{N}[/tex] is a natural number.
In other words, for any given N, the series will converge absolutely over the interval \left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n>N.
This means that the series will converge absolutely over a larger interval as N increases, since the terms \frac{\left|a_n+1\right|}{\left|a_n\right|} get closer to 1 for larger values of n.
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Let c be a positive number. A differential equation of the form
dy/dt = ky^1+c
where k is a positive constant, is called a doomsday equation because the exponent in the expression ky^1+c is larger than the exponent 1 for natural growth.
(a) Determine the solution that satisfies that initial condition y(0) = yo
y = yo/(1-cyo^c kt)^1/c
(b) Show that there is a finite time t = T (doomsday) such that lim t → T - y(t) = [infinity]
y(t) → [infinity] as 1 - cyo^c kt → 0, that is, as t → 1/cyo^c kt. Define T = 1/cyo^c kt then lim t → T - y(t) = [infinity]
(c) An especially prolific breed of rabbits has the growth term ky^1.01. If 6 such rabbits breed initially and the warren has 42 rabbits after three months, then when is doomsday? ( Round your answer to two decimal places.)
_____ months
A differential equation of the form dy/dt = ky, where y(t) is a function of time t, k is a constant, and c is a positive number.
This type of equation is known as a first-order linear differential equation and is commonly used to model exponential growth or decay processes, such as population growth, radioactive decay, or compound interest.
The general solution to this equation is y(t) = ce^(kt), where c represents the initial condition at time t = 0.
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A window is 150cm wide and 90cm high what is the area of the window in square metres