The pentagonal prism below has a height of 13.4 units and a volume of 321.6 units ^3 . Find the area of one of its bases.

Answer: 5.625 Cubed

Step-by-step explanation: First you will times 3.75 and 1.5. Which should get you 5.625 squared. Next you will just times 5.625 squared by 1. Which will get you 5.625 cubed.

Answer: The sum of all the data values divided by the number of data values is 7.

Answer:

Step-by-step explanation:

Let's use a Venn diagram to help us visualize the information given in the problem. We can start with three overlapping circles representing Physics (P), Chemistry (C), and Biology (B), and then fill in the numbers given:

                  P

                /   \

               /     \

              /       \

             CP        BP

              \       /

               \     /

                \   /

                  B

We know that 6 students study pure Chemistry, so we can write this number in the circle for Chemistry (C). We also know that 10 students study pure Physics and 8 students study pure Biology, so we can write these numbers in the circles for Physics (P) and Biology (B), respectively:

                  P (10)

                /   \

               /     \

              /       \

        CP (18)       BP (21)

              \       /

               \     /

                \   /

                  B (8)

               C (6)

Now we can use the information given in the problem to fill in the remaining numbers:

22 students study Physics and Biology, so this number goes in the overlap between P and B: PB = 22

21 students study Chemistry and Biology, so this number goes in the overlap between C and B: CB = 21

We don't know the number of students who study Physics and Chemistry only, but we can use the fact that 6 students study pure Chemistry to figure it out. Since 18 students study Chemistry and Physics in total, and 6 of them study pure Chemistry, the remaining 18 - 6 = 12 students must study both Chemistry and Physics but not Biology. We can write this number in the overlap between C and P: CP = 12.

                  P (10)

                /   \

               /     \

              /       \

        CP (12)       BP (21)

              \       /

               \     /

                \   /

                  B (8)

               C (6)

Now we can find the total number of students by adding up all the numbers in the Venn diagram:

Total = P + C + B - (CP + CB + PB) + (CPB)

Total = 10 + 6 + 8 - (12 + 21 + 22) + 0

Total = 19

Therefore, the total number of students in the class is 19.

Answer:

22 × 100

(which is 2200)

Step-by-step explanation:

44 × 50 may not look like a problem you can do in your head. But if you notice that there is a 2 in the 44 that you can "move over" to the 50 instead, you totally can do this multiplication in your head.

44 × 50

= 22 × 2 × 50

= 22 × 100

= 2200

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2100\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 2100\left(1+\frac{0.02}{1}\right)^{1\cdot 5}\implies A=2100(1.02)^5 \implies A \approx 2318.57[/tex]

Answer:

Step-by-step explanation:

-5

The answer is right angle with leg 3 and 8.

To use the box method to find the area of the parallelogram, we need to divide it into two triangles. One possible way to do this is by drawing a diagonal from (5, 17) to (18, 9), and creating two triangles with vertices (5, 17), (10, 20), and (18, 9), and (5, 17), (13, 6), and (18, 9).

The length of the diagonal can be found using the distance formula:

d = √[(18 - 5)^2 + (9 - 17)^2]

d = √[(13)^2 + (-8)^2]

d = √(169 + 64)

d = √233

Now, the area of the parallelogram is equal to the product of the length of the diagonal and half the height of the parallelogram. One of the cutouts from the box method will be a right triangle with legs equal to half the height and half the length of the diagonal.

Half the height can be found by taking the difference in y-coordinates between (5, 17) and (18, 9) and dividing by 2:

h = (17 - 9)/2

h = 4

Half the length of the diagonal is:

l = √233/2

Using these values, we can check each of the given right triangles to see which one matches the dimensions of the cutout:

A right triangle with legs 5 and 17 does not match, since the legs should be half the diagonal and half the height.

A right triangle with legs 5 and 8 does not match, since the legs should be half the diagonal and half the height.

A right triangle with legs 8 and 11 does not match, since the legs are not proportional to the dimensions of the parallelogram.

A right triangle with legs 3 and 8 matches, since half the diagonal is approximately 7.66 and half the height is 4, and 3 and 8 are proportional to these values.

Therefore, the correct answer is the right triangle with legs of 3 and 8.

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Answer:

its the middle one ( 8,11)

Step-by-step explanation:

Answer:

He has 68.8% of his drink left

Step-by-step explanation:

do 32 oz - 10 oz = 22 oz to get how much of his drink is left

To get the percentage, just do what left divided by original amount

so 22/32 = 0.6875 and in percent, that is about 68.8%

Answer:

60°

Step-by-step explanation:

it's one half of an equilateral triangle, all sides equal and angles congruent, sum is 180°, divide by three and you have 60° which is your answer.

The LCD of the given rational function is option B (x²-25)(6x + 30)(6x).

An equation containing one or more rational expressions is referred to as a rational equation. A fraction with polynomials as the numerator and denominator is known as a rational expression. A rational expression is, in other words, the ratio of two polynomials. Finding the LCD (Least Common Denominator) of the fractions, removing the denominators, and then simplifying the resultant equation can be used to solve rational equations. By resolving the resultant equation, which may require factoring, simplification, or the use of other algebraic strategies, the solutions of rational equations can be discovered. In order to simulate complicated systems and events, rational equations are frequently employed in physics, engineering, and other disciplines.

For the given rational equation the LCD will be the multiplication of all the denominators in the given rational equation.

Thus,

(x²-25)(6x + 30)(6x)

Hence, the LCD of the given rational function is option B (x²-25)(6x + 30)(6x).

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Answer:

22.8 Inches

Step-by-step explanation:

To find the hypotenuse, the formula is √c=√a^2+b^2

Lets input our values now:

c=√14^2+18^2

Now, let's solve:

c=√196+324

c=√520

The square root of 520 equals about 22.8, so our answer would be 22.8 inches.

Maker spent $48,000 on a brand-new rolling press. Its value has decreased at a pace of 18% per two years. Seven years after the initial purchase, the rolling press is worth $18,687.53.

We can solve this problem by using the formula for exponential decay:

V = [tex]P * (1 - r)^n[/tex]

where V is the value of the rolling press after n years, P is the initial purchase price, r is the depreciation rate per period, and n is the number of periods.

In this case, we have:

P = $48,000 (the initial purchase price)

r = 18% every 2 years = 0.09 per year (since there are 2 two-year periods in 1 year)

n = 7 years (the number of years that have passed)

These values are entered into the formula to produce the following results:

V = [tex]$48,000 * (1 - 0.09)^7[/tex]

V ≈ $18,687.53

Hence, seven years after the original purchase, the rolling press is now worth roughly $18,687.53.

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The area of the sector rounding to the nearest tenth is C. 8377.6 [tex]cm^2[/tex].

The law of cosines is a formula used to find the length of a side or the measure of an angle in a non-right triangle (a triangle that does not have a 90-degree angle).

According to given information:

To find the area of the windshield swept by the wiper blade, we can consider it as a sector of a circle with radius equal to the length of the segment swept by the wiper blade. The length of this segment can be found using the law of cosines:

[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]

where a and b are the lengths of the sides adjacent to the angle C, and c is the length of the side opposite to the angle C.

In this case, we have:

a = 80 cm (length of the wiper blade)

b = 90 cm (length of the swing arm)

C = 120 degrees (angle swept by the swing arm)

Substituting these values, we get:

[tex]c^2 = 80^2 + 90^2 - 2(80)(90)cos(120)[/tex]

[tex]c^2[/tex] ≈ [tex]20418[/tex]

[tex]c[/tex] ≈ [tex]142.8 cm[/tex]

So the radius of the circle is approximately 142.8 cm. The central angle of the sector is 120 degrees, so its measure in radians is 2π/3. Therefore, the area of the sector is:

A = (1/2) * [tex]r^2[/tex] * θ

A = (1/2) * [tex](142.8)^2[/tex] *[tex](2\pi /3)[/tex]

A ≈ 8377.6 [tex]cm^2[/tex]

Rounding to the nearest tenth, we get the answer as C. 8377.6 [tex]cm^2[/tex].

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Answer:

a) To find the probability that the length of the croaker fish is less than 7 inches, we need to calculate the z-score of 7 inches using the formula:

z = (x - mu) / sigma

where x is the length of the fish we are interested in, mu is the mean length of the population, and sigma is the standard deviation of the population.

In this case, x = 7, mu = 10, and sigma = 2. So the z-score is:

z = (7 - 10) / 2 = -1.5

We can look up the probability of a z-score less than -1.5 in a standard normal distribution table or use a calculator. The probability is approximately 0.0668 or 6.68%.

Therefore, the probability that the length of the croaker fish is less than 7 inches is 0.0668 or 6.68%.

b) To find the probability that the length of the fish is between 7 and 15 inches, we need to calculate the z-scores of 7 inches and 15 inches using the same formula as above:

z1 = (7 - 10) / 2 = -1.5

z2 = (15 - 10) / 2 = 2.5

We can look up the probability of a z-score between -1.5 and 2.5 in a standard normal distribution table or use a calculator. The probability is approximately 0.9332 or 93.32%.

Therefore, the probability that the length of the fish is between 7 and 15 inches is 0.9332 or 93.32%.

Answer:

  19.2

Step-by-step explanation:

You want the solution to 38.4 = 2x.

When you divide both sides of the equation by 2, you will have your answer.

  38.4/2 = (2x)/2

  19.2 = x

The solution to the equation is x = 19.2.

__

Additional comment

When you learned multiplication and division, you learned that each multiplication fact corresponds to two division facts:

  A = B×C . . . . . . . 6 = 2×3

  A/B = C . . . . . . . . 6/2 = 3

  A/C = B . . . . . . . . 6/3 = 2

We use that relationship here to find the value of one of the factors in the product:

  38.4 = 2·x

  38.4/2 = x

The other division fact is still true, but isn't useful here for finding the value of x.

  38.4/x = 2

Answer:

your answer is the second one.

The value of k, considering the numeric value of the derivative at x = 0, is given as follows:

b) k = -2 or k = 2.

The function in the context of this problem is defined as follows:

y = (x + k)³.

Applying the power of x rule followed by the chain rule, the derivative of the function is given as follows:

y' = 3(x + k)².

When x = 0, the numeric value of the derivative is of 12, hence the value of k is obtained as follows:

3k² = 12

k² = 4

k = -2 or k = 2.

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After answering the presented question, we can conclude that As a equation result, the turkey's temperature after 45 minutes is roughly 134.43 Fahrenheit.

In mathematics, an equation is a statement that states the equality of two expressions. An equation consists of two sides separated by an algebraic equation (=). The argument "[tex]2x + 3 = 9,[/tex]" for example, states that the sentence "[tex]2x + 3[/tex]" equals the value "9." The goal of solving equations is to find the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, linear or nonlinear, and contain one or more parts. In the equation "[tex]x2 + 2x - 3 = 0[/tex]," the variable x is raised to the second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.

a. [tex]dT/dt=-k(T-Ts)[/tex]

  [tex]-kdt=(DT/(T-Ts)[/tex][tex])[/tex]

When both sides are combined, the following results:

[tex]-kt + C = ln|T - Ts|[/tex]

where C is the integration constant. To calculate C, we can start with the assumption that the turkey is 185 degrees Fahrenheit when it comes out of the oven:

[tex]ln|185 - 75| = -k(0) + C[/tex]

[tex]C = ln(110) (110)[/tex]

As a result, the equation relating the temperature of the turkey to time is:

[tex]-kt+In|T-75|=-kt+In(110)[/tex]

[tex]T=e(-ktIn(110)+75[/tex]

[tex]T=110e(-0.5k)+75[/tex]

[tex]T=110e(-0.75k+75 T134.43[/tex] degrees Fahrenheit

As a result, the turkey's temperature after 45 minutes is roughly 134.43 Fahrenheit.

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The arc length of the each arc are 14π cm, 95π/6 ft, 7π cm, 39π/4 ft.

What is arc length of a circle?

The arc length formula for a circle is given by L = rθ, where L is the arc length, r is the radius, and θ is the central angle measured in radians.

9) Here angle= 315° and radius= 8cm.

First, we need to convert the angle to radians: 315° × (π/180°) = 7π/4.

Then we can use the arc length formula,

L = 8 × 7π/4 = 14π cm.

10) Here angle = 150° and radius= 19 ft.

First, we need to convert the angle to radians: 150° × (π/180°) = 5π/6.

Then we can use the arc length formula,

L = 19 × 5π/6 = 95π/6 ft

11) Here angle = π/2 and radius= 14 cm.

According to the arc length formula,

L = 14 × π/2 = 7π cm .

12) Here angle= 3π/4 and radius= 13 ft.

According to the arc length formula,

L = 13 × 3π/4 = 39π/4 ft.

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Answer: x=-((y-2)^2)/12 +5

Step-by-step explanation:

Since the directrix is vertical, use the equation of a parabola that opens up or down. Find the vertex.

The interest rate would a corporate bond have to offer for Lavonia to be indifferent between the two bonds is 6.35%.

What is an interest rate?

The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.

Here, we have

Given: Assume that Lavonia's marginal tax rate is 20%. If a city of Tampa bond pays 8% interest.

We have to find the interest rate would a corporate bond have to offer for Lavonia to be indifferent between the two bonds.

= Interest rate/(1-Tax rate)

= 5%/(1-0.20)

= 6.25%

Hence, the interest rate would a corporate bond have to offer for Lavonia to be indifferent between the two bonds is 6.35%.

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Answer:

22 problems

Step-by-step explanation:

50% is half of 100, so if 100 divided by 2 is 50, then 11 x 2 is 22. 22 is the answer

Answer:

Step-by-step explanation:

1●area of shaded region = area of big rectangle -area of small rectangle

=(12×7)-(8×3)

=84-24

=60ft²

2● Area of shaded region =sum of area of all three rectangle

=9×3.5+9×3.5+16×7

=63+112

=175ft²

Answer:

Step-by-step explanation:

Formula of a square Area=[tex]x^{2}[/tex]

1)Area of a Rectangle =l*w

area=(12)(7)

=84 ft

solution for the area non shaded=(8)(3)

= 24 ft

solution for area shaded=84-64

=60 ft

The vertex of the parabola is (h, k) = (3, -8), The graph in red has vertex (3, -8), thus, the red parabola is correct.

A quadratic function is a polynomial function of the form f(x) = ax² + bx + c, where a, b, and c are constants and a is not equal to 0.

We know that the standard form of the parabola is y=ax²+bx+c. Thus, the vertex form of a parabola is y = a(x-h)² + k, and the vertex is given by (h, k)

here,  y = −(x − (3))² (−8) is already in vertex form.

Then,

h = 3

k = -8

Thus, the vertex of the parabola is (h, k) = (3, -8), The graph in red has vertex (3, -8), thus, the red parabola is correct.

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Complete question:

Which line describes the graph of y = −(x − 3)2 − 8?

The sequence of the function is -34,-34 -8

In mathematics, the common difference is a term used in arithmetic sequences to refer to the fixed difference between any two consecutive terms in the sequence.

An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a fixed value, called the common difference, to the preceding term.

-34 -21 -8 5 ...

f(1) = -34

f(n) = f(n-1) + [n-2]*13 for n = 2, 3, 4, ...

The common difference between consecutive terms of the sequence is 13.

The first term of the sequence is -34, which is f(1).

To get the nth term of the sequence, we add (n-2)*13 to the (n-1)th term of the sequence.

For example, to get the 2nd term of the sequence, we add (2-2)*13 = 0 to the 1st term, -34, which gives us -34.

To get the 3rd term, we add (3-2)*13 = 13 to the 2nd term, which gives us -21+13 = -8.

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The Volume of Silo is. V= 13886 ft cube

A grain Silo is cylindrical in shape.

Height  (h) = 49 ft.

Diameter (d) = 19 ft.

We need to find the Volume of silo.

We will first find the radius.

Radius can be given as half of the diameter.

hence Radius (r) = 9.5

Since Silo is in Cylindrical Shape we will find the volume of a cylinder.

Now We know that the Volume of a cylinder can be calculated by multiplying π with the square of the radius and height.

Volume of Cylinder = πr²h

            V= 3.14×9.5×9.5×49

            v=13885.865 ft cube

Rounding to the nearest whole number we get;

Hence, the Volume of the Silo is. V= 13886 ft cube

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Graph the two inequalities,

The region shaded in black satisfies both inequalities

Buying a car for $2,500 in 1960 would be like buying a car for $539.23 in 2004 dollars .we can solve by using formula by substituting all details along with consumer price index

what is consumer price index ?

The Consumer Price Index (CPI) is a measure of the average change over time in the prices paid by urban consumers for a basket of goods and services. The CPI is often used as an indicator of inflation

In the given question,

To compare the dollar amounts over time, we can use the formula V = (A/S) x (C/C'), where:

V = the current value of the old dollar amount

A = the old dollar amount ($2,500 in this case)

S = the starting year's consumer price index (CPI) for the old dollar amount (1960 CPI)

C = the converting year's CPI (2004 CPI)

C' = the starting year's CPI for the converting year (1960 CPI)

Using the formula, we can calculate the current value of $2,500 in 1960 dollars as:

V = (A/S) x (C/C')

V = (2,500/29.6) x (188.9/29.6)

V = 84.46 x 6.380

V = $539.23

Therefore, buying a car for $2,500 in 1960 would be like buying a car for $539.23 in 2004 dollars.

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Answer:

Step-by-step explanation:

Equation of a circle:  [tex](x-a)^2+(y-b)^2=r^2[/tex]    with centre [tex](a,b)[/tex], radius [tex]r[/tex].

[tex](x-0)^2+(y+1)^2=4^2[/tex]

[tex]x^2+(y+1)^2=16[/tex]

Answer: The teacher is incorrect

Step-by-step explanation: 20x3=60 4x12=48 60+48=108 108/24=4.5

4.5 does not equal 6.    5 packs of battery's will be needed and there will be 12 battery's left over.