sam wants to build a toy box in the shape of a rectangular prism that will hold 36 cubic feet. if the height needs to be 1 foot less than the width and the length is twice the width, find the height of the toy box.

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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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%.

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

The volume of the softball is estimated to be 9π, so the correct option is C.

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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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)

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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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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Answer:

Step-by-step explanation:

The total surface area includes:

The area is:

The value of the side of the triangles are;

18. 17. 89

19. y = 9. 43, x = 5. 67

Using 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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Answer: There is one unique solution: (-3,1)

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.

The expense of 1.5 lbs of bananas and 1 gallon of apple juice, according to the provided statement, is $7.45.

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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Answer: x = 24

Step-by-step explanation:

21 + 3= 24

Answer: it should be 17.5

15+20 = 35

35/2 = 17.5 -----> mean of the two numbers

The height of the trapeziod is 7 feet

The 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;

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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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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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.

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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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

In Mathematics, a proportional relationship produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

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.

Answer:

Step-by-step explanation:

9to12

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

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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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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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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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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