Question 1
Find the volume of the prism, Round your answer to the nearest tenth, if necessary.
13 m
3m
5m
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Step-by-step explanation:

ab = 72    then  a = 72/b     sub into first equation

72/b  * b^4 = 48

72 b^3 = 48

b^3 = 48/ 72

b = .87358

then a = 72/b = 82.4194

The value of 'b' in the ordered pair that satisfies the equations ab^4 = 48 and ab = 72 can be found by expressing 'a' in terms of 'b' from the second equation, substituting into the first and solving for 'b'. The final answer is b = cuberoot(2/3).

The subject of this problem is about finding the value of b in an ordered pair (a, b) that satisfies the given equations ab^4 = 48 and ab = 72.

From the second equation, we could express 'a' as a = 72/b. Now, let's substitute 'a' into the first equation, the new equation becomes (72/b) * b^4 = 48. Simplifying this gives b^3 = 48/72 = 2/3, taking the cube root of both sides obtains the value of b which is cuberoot(2/3).

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The height of the TV is approximately 52.3 inches when rounded to the nearest tenth of an inch.Hence, the TV is approximately 52.3 inches tall.

To find the height of the TV, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the diagonal) of a right triangle is equal to the sum of the squares of the other two sides.

In this case, the width and height of the TV form the legs of a right triangle, with the diagonal as the hypotenuse.

Let's denote the height of the TV as h. According to the Pythagorean theorem:

h² + 67² = 85²

Simplifying the equation, we have:

h² + 4489 = 7225

Subtracting 4489 from both sides, we get:

h² = 2736

Taking the square root of both sides, we find:

h ≈ 52.3.

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Answer:

The circumference of the circle is 12pi cm.

Answer:

The circumference of the circle is 12π cm.

that's the answer

The sum of the exterior angles of the heptagon in the given diagram is 51.43 degrees.

To find the sum of the exterior angles of a heptagon, we can use the formula:

Sum of exterior angles = 360 degrees

Since a heptagon has 7 sides, it also has 7 exterior angles.

Therefore, each exterior angle of a heptagon is equal to:

= 360 degrees / 7

= 51.43 degrees (rounded to two decimal places)

Hence, the sum of the exterior angles of the heptagon in the given diagram is 51.43 degrees.

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The final price of the textbook for an English literature course, which is 12% more than the listed price of $130 when tax and shipping costs are included, is $145.60.

The final price of the textbook includes the costs of tax and shipping of 12%, which is added to the listed price.

The final price of the textbook can be computed, using the increase factor, as follows:

The listed price = $130

The increase in the final price = 12%

12% = 0.12 (12/100)

Increase factor = 1.12%

The final price = $145.60 ($130 x 1.12)

Thus, when adding 12%, which represents the tax and shipping costs, to the listed price, the final price is $145.60.

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The smallest size that will allow this confidence interval to be built is given as follows:

n = 75.

The bounds of the confidence interval are given by the rule presented as follows:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

The margin of error is calculated as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The desired margin of error is of M = 0.5, as we have the time in hours, with [tex]\sigma = 2.2[/tex], hence the sample size is obtained as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.5 = 1.96\frac{2.2}{\sqrt{n}}[/tex]

[tex]0.5\sqrt{n} = 1.96 \times 2.2[/tex]

[tex]\sqrt{n} = \frac{1.96 \times 2.2}{0.5}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 2.2}{0.5}\right)^2[/tex]

n = 75 -> rounded up.

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K is a maximal subgroup of G, and we have[tex]H ⊆ K[/tex] since H is a proper subgroup of G and thus H is in M.

Let G be a finite group and let H be a subgroup of G. We want to show that H is contained in a maximal subgroup of G.

First, we note that if H is already a maximal subgroup of G, then we are done. So assume that H is not maximal.

Let M be the set of all subgroups of G that contain H. Note that M is non-empty, since G is itself in M. Since G is finite, M has a maximal element, say K. Then K is a maximal subgroup of G, and we have [tex]H ⊆ K[/tex] since H is in M.

To show that every subgroup H of G, where H is not equal to G itself, is contained in a maximal subgroup of G, we can use the same argument as above.

Let M be the set of all proper subgroups of G (i.e., subgroups that are not equal to G itself). Note that M is non-empty, since {e}, the subgroup consisting only of the identity element, is in M. Since G is finite, M has a maximal element, say K. Then K is a maximal subgroup of G, and we have[tex]H ⊆ K[/tex] since H is a proper subgroup of G and thus H is in M.

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Answer:

Total Increase in Population of India from 1961 to 2001 = 1028-439 million = 659 million

Answer:1.5

Step-by-step explanation:

Y=1/2 of x

Answer and Explanation:

We can check if these triangles are similar by comparing the ratios of their corresponding side lengths:

[tex]\dfrac{QP}{LK} \stackrel{?}{=} \dfrac{RP}{MK}[/tex]

[tex]\dfrac{6}{16} \ne \dfrac{11}{36}[/tex]

These triangles are not similar because the ratios of their corresponding side lengths is not the same.

Answer:

Step-by-step explanation:

you have to find the mean of the two fractions, adding and then dividing by two

(1/5 + 1/9) : 2 =

14/45 : 2 =

7/45

Answer:

Step-by-step explanation:

There are 72 students in the school.

The number for Igbo language = 54

The number for Igbo language = 40

The Venn diagram is attached

Assuming that the total number of students in the school is x.

Information from the problem

3/4 of students credited Igbo language and

5/9 credited Agriculture.

every student in the school credited at least one of the two subjects. hence we have that

3/4x + 5/9x - 22 = x

Simplifying this equation gives

3/4x + 5/9x - x = 22

11x / 36 = 22

11x = 36 * 22

x = (36 * 22) / 11

x = 72

The number for Igbo language

= 3/4 * 72 = 54

The number for Igbo language

= 5/9* 72 = 40

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The function of the area of the figure is M(x) = (x + 2)(3/2x - 2)

From the question, we have the following parameters that can be used in our computation:

The composite figure

The total area of the composite figure is the sum of the areas of the individual shapes

So, we have

Area = Rectangle + Triangle

Using the area formula, we have

M(x) = (x + 2)(x - 2) * 1/2 * x * (x + 2)

Factorize

M(x) = (x + 2)(x - 2 + x/2)

So, we have

M(x) = (x + 2)(3/2x - 2)

Hence, the function of the area of the figure is M(x) = (x + 2)(3/2x - 2)

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The value of the given fraction is 18.

Given is fraction, [tex]\frac{2+\sqrt{5} }{2-\sqrt{5}} +\frac{2-\sqrt{5} }{2+\sqrt{5}}[/tex], we need to show it in a+b√5 form,

So,

[tex]\frac{2+\sqrt{5} }{2-\sqrt{5}} +\frac{2-\sqrt{5} }{2+\sqrt{5}}\\\\\\= \frac{(2+\sqrt{5})^2+(2-\sqrt{5} )^2 }{(2+\sqrt{5})(2+\sqrt{5} ) } \\\\\\= \frac{4+5+4\sqrt{5}+4+5-4\sqrt{5} }{2^2-\sqrt{5}^2 } \\\\\\= 18[/tex]

Hence the value of the given fraction is 18.

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Answer:

-------------------

Original price is $66 and the sale price is 50% off, so the sale price is:

Janelle will pay $33 for the ticket.

The volume of the rectangular prism is 168.7 cubic units.

The volume of a rectangular prism can be calculated using the following formula:

V = base area x height

A prism is a polyhedron in three dimensions with two identical ends.

In this case, the base area is 24.1 units² and the height is 7 units.
Let the base area can be represented as B and the height be described as H,

then volume can be rearranged as,

V = BH

Here:

B = 24.1 units²

H = 7 units

When these values are entered into the formula, we get:

V = 24.1 x 7

V = 168.7

Therefore, the volume of the rectangular prism is 168.7 cubic units.

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The complete polynomial is f(x) = 2x⁴ - 3x² - 6 and the values are n = 4 and a = -3

From the question, we have the following parameters that can be used in our computation:

This means that

f(1) = 7

f(-3) = 129

So, we have

f(1) = 2(1)ⁿ + a(1)² - 6

f(-3) = 2(-3)ⁿ + a(-3)² - 6

Evaluate

f(1) = 2 + a - 6

f(-3) = 2(-3)ⁿ + a(-3)² - 6

Recall that

f(1) = -7 and f(-3) = 129

So, we have

2 + a - 6 = -7

2(-3)ⁿ + 9a - 6 = 129

This gives

a = -3

Recall that

2(-3)ⁿ + 9a - 6 = 129

So, we have

2(-3)ⁿ + 9(-3) - 6 = 129

2(-3)ⁿ = 162

Divide by 2

(-3)ⁿ = 81

Solve for n

n = 4

So, the complete polynomial is f(x) = 2x⁴ - 3x² - 6

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The mean mass per bag is 99 kilograms.

The mode is the value that appears most frequently in a dataset. In the given dataset of bag masses, the mode would be the mass value that occurs most often. Let's find the mode.

The masses of the bags are:

90, 94, 96, 98, 99, 102, 105, 91, 102, 99, 105, 94, 99, 90, 94, 99, 98, 96, 102, and 105.

To find the mode, we can simply count the frequency of each mass value and identify the one that appears most often:

90 appears twice

94 appears three times

96 appears two times

98 appears two times

99 appears four times

102 appears three times

105 appears three times

91 appears once

Therefore, the mode in this dataset is 99, as it appears most frequently.

To calculate the mean mass per bag, we need to sum up all the masses and divide by the number of bags. Let's calculate it:

Sum of masses = 90 + 94 + 96 + 98 + 99 + 102 + 105 + 91 + 102 + 99 + 105 + 94 + 99 + 90 + 94 + 99 + 98 + 96 + 102 + 105

Sum of masses = 1980

Number of bags = 20

Mean mass per bag = Sum of masses / Number of bags

Mean mass per bag = 1980 / 20

Mean mass per bag = 99 kilograms

Therefore, the mean mass per bag is 99 kilograms.

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Here is the table for the function f(x) = 3 * (3/4) ˣ:

x f(x)

-3 16.000

-1 4.000

0 3.000

1 2.250

3 1.688

The function is an exponential decay function

f(x) = 3 * (3/4) ˣ, in the given exponential function the starting function is

3. The base is 3/4.

The base is what determines exponential decay or growth. The condition for determining exponential growth or exponential decay is

The base function here is a factor which is 3/4 = 0.75 and less than one and hence a decay function

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From the origin, move 3 units to the right, and then move 9 units up is the intersection of the graphs of the two equations be located on a coordinate grid

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Given that solution to a system of two linear equations is x = 3: y = 9.

We need to find how the intersection of the graphs of the two equations be located on a coordinate grid

As we know that the numbers on right side of zero are positive and number of upside of zero on y axis are positive.

As x=3 which is positive

y=9 which is positive.

So From the origin, move 3 units to the right, and then move 9 units up is the intersection of two equations

Hence, From the origin, move 3 units to the right, and then move 9 units up is the intersection of the graphs of the two equations be located on a coordinate grid

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[tex]A[/tex] — at least one of the children is a girl

[tex]A'[/tex] — none of the children is a girl

[tex]P(A)=1-P(A')\\\\|\Omega|=2^5=32\\|A'|=1\\\\P(A')=\dfrac{1}{32}\\\\P(A)=1-\dfrac{1}{32}=\dfrac{31}{32}\approx96.9\%[/tex]

Answer:

The probability that when a couple has five children, at least one of them is a girl is 31/32 or approximately  [tex]0.96875.[/tex]

Explanation:

We can determine the probability of having at least one girl by using the complement rule, which states that the probability of an event occurring is equal to one minus the probability of the event not occurring. In this case, the event of interest is having at least one girl among five children and the complement is having only boys among five children.

Since there are two equally likely outcomes (boy or girl) for each child and the events are independent, we can find the probability of having all boys by multiplying the probabilities of each individual event together: (1/2)^5 = 1/32.

So, the probability of having at least one girl is 1 - 1/32 = 31/32 or approximately 0.96875.

Step-by-step explanation:

70 x 68 = 4760 marks

# mrks / 70  papers =  68 marks/paper

# marks   =   70 papers * 68 marks/paper

The critical point in the solution of the equation -5x + 7y > 2 and 2x - 5y < -7 using graph is

(3.5, 2.8)

The solution of the inequality equation s given as

A) -5x + 7y > 2

B) 2x - 5y < -7

would be solved by graphical method

Using the graph the point of the intersection of the two lines is the critical points of the solution. The critical point from the graph is (3.5, 2.8)

The solution also entails the areas or points covered in the areas where the two shades superimpose.

The graph showing the solution is attached

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The length of each leg is 14.69  in the triangle

In an isosceles triangle, the median drawn from the vertex angle also acts as an altitude, dividing the triangle into two congruent right triangles.

Let the length of one of the legs of the triangle "x".

Using the Pythagorean theorem, we can write:

x²+ (15)² = (21)²

x² + 225 = 441

x² = 441 - 225

x² = 216

Taking the square root of both sides, we find:

x = √216

x =14.69

Therefore, the length of each leg is 14.69 in the triangle

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Step-by-step explanation:

Future Value = Present Value ( 1 + i)^n  

                                    i = decimal interest per PERIOD (.0712/12)

                                    n = periods = 25 * 12 = 300 months

Future value = 8000 ( 1 + .0712/12)^300 = $ 47189.98

Answer:

Step-by-step explanation: Take the amount he started with, 8,000, our coefficient, and since it is being increased by 7.12 percent, therefore, we put it all together, and that will be 8000(1.712) to the power of five which is.. 117,654.56 dollars (you're welcome)

Based on the information, the town will run out of water in 1 hour.

The town has a total water consumption of 500 people * 10 liters/day = 5000 liters/day.

The town has a water supply of 5000 liters/day / 1000 liters/m³ = 5 m³

The town will run out of water in 5 m³/ 5000 liters/day = 0.01 days = 1 hour.

Time to run out of water = Total water supply / Total water consumption per day = 5000 liters / 5000 liters/day

= 1 hour

Therefore, the town will run out of water in 1 hour.

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The measure of angle C is  13. 94 degrees

To determine the value of the angle, we need to know the six different trigonometric identities.

These identities are;

From the information given, we have that;

The Hypotenuse side of the triangle ABC =  34

the adjacent side of the triangle = 33

Using the cosine identity, we have that;

cos C= adjacent/hypotenuse

cos C = 33/34

Divide the values

cos C = 0. 9706

Find the inverse

C = 13. 94 degrees

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Answer: Congruent and Perpendicular

Step-by-step explanation:

If diagonals of a quadrilateral bisect each other then it is a rectangle and if they are perpendicular as well then it is a square.