Question 5(Multiple Choice Worth 2 points)
(Surface Area of Cylinders MC)

Ice cream is packaged in cylindrical gallon tubs. A tub of ice cream has a total surface area of 232. 36 square inches. If the diameter of the tub is 8 inches, what is its height? Use π = 3. 14. 6. 75 inches
5. 25 inches
3. 375 inches
2. 625 inches

Answer:

3.44 is the area of the shaded region between the square and circle

Area:

The size of a surface that can be calculated by multiplying the length by the width.

Area of square = [tex]x^{2}[/tex] , where 'x' is the side of square

Area of circle = π[tex]r^{2}[/tex] , where 'r' is the radius of circle

According to the given information:

Let the side of the square be 'A'

the radius of the circle intercepts the side of square equally

which gives us radius = A/2

so if radius is 2 , side of square will be 4

So the area of shaded region = Area of square - Area of circle

Area of shaded region = [tex]A^{2}[/tex] - π[tex][A/2]^{2}[/tex]

Area of shaded region = [tex]A^{2}[/tex]-π[tex]A^{2}[/tex]/4

Area of shaded region = [4[tex]A^{2}[/tex] - π[tex]A^{2}[/tex]]/4

Area of shaded region =[4*16 - 3.14*16]/4

Area of shaded region = 3.44[tex]unit^{2}[/tex]

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Answer:

The area of the shaded region is 3.4 square units, rounded to the nearest tenth.

Step-by-step explanation:

To calculate the area of the shaded region, we need to subtract the area of circle N from the area of the square JKLM.

The formula for the area of a circle with radius, r, is A = πr².

Given that circle N has a radius of 2 units, the area of circle N is:

[tex]\begin{aligned}\sf Area\;of\;circle\;N&=\pi \cdot 2^2\\&=4 \pi\\&=12.5663706... \; \sf square\;units \end{aligned}[/tex]

The diameter of a circle is the distance across the widest part of the circle, passing through the center, and is equal to twice the radius.

Therefore, the diameter of circle N is:

[tex]\begin{aligned}\sf Diameter\;of\;circle\;N&=2r\\&=2 \times 2\\&=4\; \sf units\end{aligned}[/tex]

The side length of square JKLM is equal to the diameter of circle N, since each side of the square is tangent to the circle.

Therefore, the side length of square JKLM is 4 units.

The formula for the area of a square with side length, s, is A = s².

Therefore:

[tex]\begin{aligned}\sf Area\;of\;square\;JKLM&=4^2\\&=4 \times 4\\&=16\; \sf square\;units\end{aligned}[/tex]

Finally, we can calculate the area of the shaded region:

[tex]\begin{aligned}\sf Area\;of\;shaded\;region&=\sf Area\;of\;square\;JKLM-Area\;of\;circle\;N\\&=16-12.5663706...\\&=3.4336293...\\&=3.4\;\sf square\;units\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, the area of the shaded region is 3.4 square units, rounded to the nearest tenth.

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)

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.

Thus, the total length of lap covered to get the seven different obstacles is found as: 52 units.

the Pythagorean theorem is used to calculate the distance between two locations using the distance formula. The Pythagorean theorem can be rewritten as d = √((x2 - x1)²+(y2 - y1)²)  to calculate the separation between any two locations.

Given data:

Points on  y-axis and an x-axis are given,

M(-3,5), F(8,5), G(8,2), H(3,2), I(3,-5), J(-8,-5), K(-8,-2), and L(-3,-2).

Starting and ending point is F.

Points lies between the starting and ending are-

F ,G, H, I, J, K, L, M, F

Total length = sum of all length

d = √((x2 - x1)²+(y2 - y1)²)

FG =  √((8 - 8)²+(2 - 5)²)

FG =  √9

FG =  3

GH =  √((8 - 3)²+(2 - 2)²)

GH  =  √25

GH =  5

HI =  √((3 - 3)²+(2 + 5)²)

HI  =  √49

HI  =  7

IJ =  √((3 + 8)²+(-5 + 5)²)

IJ =  √121

IJ =  11

JK =  √((-8 + 8)²+(-2 - 5)²)

JK =  √9

JK =  3

KL =  √((-8 + 3)²+(-2 + 2)²)

KL =  √25

KL =  5

LM =  √((-3 + 3)²+(-2 - 5)²)

LM =  √49

LM =  7

MF =  √((8 + 3)²+(+5 - 5)²)

MF =  √121

MF =  11

Total length = 3 + 5 + 7 + 11 + 3 + 5 + 7 + 11

Total length = 52 units

Thus, the total length of the lap covered to get the seven different obstacles is found as: 52 units.

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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

Answer:

2

Step-by-step explanation:

Answer:

Step-by-step explanation:

The total surface area includes:

The area is:

Answer: it should be 17.5

15+20 = 35

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

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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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:

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.

Answer:

We know that there were three large tables with an equal number of guests seated at each table. Let's represent the number of guests at each of these large tables with the variable N.

So, the total number of guests seated at the large tables is 3N.

In addition to these guests, there were 7 late arriving guests seated at a smaller table.

Therefore, the total number of guests in all is:

3N + 7

We also know that the total number of guests in all is 37. So we can set up an equation to represent this:

3N + 7 = 37

Simplifying this equation, we get:

3N = 30

Dividing both sides by 3, we get:

N = 10

So, there were 10 guests seated at each of the 3 large tables.

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.

Rounded to two decimal places, the value of the test statistic is 0.41.

The value of the test statistic to compare the publisher's reported percentage of 75% and the marketing executive's claim that the actual percentage is different can be found by using the formula z = (p1 - p2)/(sqrt[p*(1-p)*((1/n1)+(1/n2))]), where p is the pooled proportion, p1 is the proportion of the publisher's readers owning the particular make of car, p2 is the proportion of the random sample owning the particular make of car, n1 is the total number of the publisher's readers, and n2 is the total number of the random sample.

In this case, p = [tex](75% + 69%)/2 = 72%, p1 = 75%, p2 = 69%, n1[/tex]is unknown, n2 = 250. Thus, the test statistic is z =[tex](75%-69%)/(sqrt[72%(1-72%)((1/n1)+(1/250))]) = 0.41.[/tex]

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

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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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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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 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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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%.

The following factors work to reduce conflict and promote positive interaction between grieving couples who have lost a child by death is open and honest communication, expressing emotions in each other's company, and the ability of partners to reframe each other's behavior in a positive way. The correct option is B. 1, 2, and 4

When grieving couples lose a child due to death, it can lead to tension in their relationship, leading to conflicts between the couple. However, some factors work to reduce conflicts and promote positive interaction between grieving couples who have lost a child by death.

These factors include the following:

:Open and honest communication: Open communication is essential when it comes to expressing emotions, needs, and expectations from one another. It helps to build understanding, trust, and positive interaction between the couples. Honest communication provides room for clarification and better comprehension of each other's feelings and needs

Reframing each other's behavior in a positive way helps to build a healthy relationship and reduce conflicts.Crying separately to minimize the open grief and pain: Crying separately does not help reduce conflicts between the couple as it promotes distance and an unhealthy way of dealing with grief. It is important to grieve together and find support from each other to heal and move forward.

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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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The common difference of the arithmetic sequence is d = 3.

What is an Arithmetic sequence?

An arithmetic progression, also referred to as an arithmetic sequence, is a set of numbers where each term following the first is derived by adding a fixed constant number to the term before it.

To solve this problem, we can use the formula for the nth term of an arithmetic sequence. The formula is as follows:

an = a1 + (n - 1)d

Where an is the sequence's nth term, a1 is the first term, d is a common difference, and n is the number of terms we want to discover:

We know that a1 = 10 and a4 = 19. By entering these numbers into the formula, we obtain:

          a4 = a1 + (4 - 1)d

          19 = 10 + 3d

In order to find d, we can divide by 3 after subtracting 10 from both sides:

          9 = 3d

          d = 3

Therefore, the common difference of the arithmetic sequence is d = 3.

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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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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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Answer: It is 160

Step-by-step explanation:

I just completed the test

Therefore , the solution of the given problem of surface area comes out to be the right response is option c 160 in².

Calculating how much space would be needed to fully cover the outside will reveal its overall size. The surroundings are considered when determining the same surface with a rectangular form. The surface area of something determines its overall dimensions. The amount of edges present in the space between a cuboid's four trapezoidal corners determines how much water it can hold inside.

Here,

the base's outermost boundary is:

=> Perimeter = 4s

To locate s,

=> Base  Area = s² = 64 in².

To solve for s, we obtain:

=> √(64 in²) = 8 in

We can now determine the perimeter:

=> perimeter: 4s

=> (4 * 8 inches)/(32 inches)

Finally, we can enter the numbers into the surface area formula as follows:

=>  Base Area + (1/2) x Perimeter x Slant Height

=> Surface Area Surface Area = 64 in² + (1/2) x 32 in x 6 in

=> Surface area = 64 in² + 96 in².

160 in² is the surface area.

Consequently, the cone has a surface area of 160 in².

The right response is (c) 160 in².

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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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