A principal of $1700 is invested at 6.25% interest, compounded annually. How much will the investment be worth after 14 years?
(round your answer to the nearest dollar.)

The length οf οne side οf the cube is 4 cm.

In geοmetry, a cube is a three-dimensiοnal sοlid shape that has six square faces οf equal size, and all its angles are right angles (90 degrees). A cube is a regular pοlyhedrοn, which means that all its faces are cοngruent (i.e., identical) regular pοlygοns and its edges have the same length.

The surface area οf a cube with edge length "s" is given by the fοrmula:

[tex]SA = 6s^{2}[/tex]

We are given that the surface area οf the cube is [tex]96 cm^2[/tex]. Therefοre, we can set up the equatiοn:

[tex]96 = 6s^{2}[/tex]

Dividing bοth sides by 6, we get:

[tex]16 = s^{2}[/tex]

Taking the square rοοt οf bοth sides, we get:

s = 4

Therefοre, the length οf οne side οf the cube is 4 cm.

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Let "e" be the elevation of the submarine and "t" be the time taken to descend.

Then, the equation representing the relationship between the submarine elevation and time is:

e = -105t + 2100

where the coefficient of "t" (-105) represents the rate of descent of the submarine, and the constant term (2100) represents the initial elevation of the submarine.

Answer:7/10

Step-by-step explanation:

Answer:

[tex] \frac{7}{9} [/tex]

Explanation:

First, you have to write a number in the numerator, that is after the comma (in this case it's 7)

And then, in the denominator, you have to write a number that is made of nines only (the number of nines you have to write is the number of decimal numbers, in this case it's 1 nine)

The value of k is 2.

Instead of producing approximations at random, it is better to use moving numeral variables, which may be rising, declining, or blocking. They could only help one another by sharing materials, information, or solutions to issues. The justifications, parts, and mathematical comments for equation techniques like additional disapproval, production.

To simplify the expression, we need to first convert the mixed numbers [tex]3 8/2[/tex] and [tex]3 8/4[/tex] to improper fractions:

[tex]3 8/2 = 3 (24 + 8)/2 = 312/2 = 18[/tex]

[tex]3 8/4 = 3 (4 + 8/4) = 3*(4+2) = 18[/tex]

Now, we can rewrite the expression as:

[tex](3 8/2) (3 8/4) = 18 * 18 = 18^2[/tex]

Therefore, [tex]k = 2[/tex], and the expression ([tex]3 8/2) (3 8/4[/tex]) can be written as [tex]3^2 = 9.[/tex]

So the final answer is: The expression [tex](3 8/2) (3 8/4)[/tex] simplifies to 9, which can be written in the form [tex]3^2.[/tex] Therefore, the value of k is 2.

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The angle x to the nearest degree is 47°.

To find the value of the angle to the nearest degree, we can use the inverse tangent function, which relates the opposite and adjacent sides of a right triangle to the angle opposite the opposite side. Specifically, we can use the formula:

tan(A) = opposite/adjacent where A is the value of angle.

Here, "opposite" is the height of the triangle (11) and "adjacent" is the base of the triangle (10).

We can solve for x by taking the inverse tangent (or arctangent) of both sides of the equation:

[tex]$ \rm x = tan^{-1} \left( \frac{opposite }{adjacent}\right)[/tex]

[tex]$ \rm x = tan^{-1} \left( \frac{11}{10}\right)[/tex]

Using a calculator, we can evaluate this expression to find

x ≈ 47.34 °

To round this to the nearest degree, we can look at the decimal part of the answer (0.34) and see that it is closer to 0.5 than 0. Therefore, we can round up to the nearest degree x ≈ 47 degrees

So, the angle x to the nearest degree is 47 degrees.

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Complete question:

The rate that Danielle drank water is 8/3 liters per hour.

What are equations?

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13. Here, 2x – 5 and 13 are expressions The sign that connects these two expressions is “=”.

To find the rate that Danielle drank water in liters per hour, we need to divide the amount of water she drank by the time taken to drink it and then convert to hours.

The equation that shows how to find the rate is:

Rate = (Amount of water drank ÷ Time taken to drink) x (Time in 1 hour ÷ Time in the given period)

Substituting the given values, we get:

Rate = (2/3 ÷ 1/4) x (1 ÷ 1/4)

Simplifying the fractions, we get:

Rate = (2/3 x 4/1) x (4/1)

Rate = 8/3 liters per hour

Therefore, the rate that Danielle drank water is 8/3 liters per hour.

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By answering the presented question, we may conclude that As a result, the vertex's x-coordinate is h = 15/2, or 7.5.

In mathematics, the slope-intercept form of a linear equation is an equation of the form y = mx + b, where m is the slope of the line и b is the y-intercept, corresponding to the point on the line where it intersects the y-axis. Since it allows you to easily view the line and identify its slope and y-intercept, the slope-intercept form is a useful way to describe a line's equation. The slope of the line denotes its steepness, while the y-intercept indicates where the line crosses the y-axis.

[tex]f(x) = a(x-h)2/k\\f(x) = a(x-3) (x-3)\\(x-12)\\f(x) = a(x^2 - 15x + 36)\\f(x) = ax2 -15ax + 36a\\f(3) = a(3-3)(3-12) = 0\\f(12) = a(12-3)(12-12) = 0\\a(0)(-9) = 0\\a(9)(0) = 0\\f(x) = a(x2 - 15x + (225/4a2) - (225/4a2) - (225/4a2)) + 36a\\f(x) = a(x - (15/2a) - (225a/4) + 36a\\[/tex]

Using the quadratic function in standard form, we can read off the vertex coordinates, which are provided by (h,k) = (15/2a, -225a/4 + 36a). Given that the x-intercepts are at (3,0) and (12,0), we may suppose that the quadratic function has the following form:

f(x) = a(x-3)(x-12) (x-12)

When we plug this into the formula for the vertex's x-coordinate, we get:

h = 15/2a

h = 15/2(1) (1)

h = 15/2

As a result, the vertex's x-coordinate is h = 15/2, or 7.5.

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(a) The number of distinguishable arrangements of the word "acbens" is 180.

(b) The number of distinguishable arrangements of the word "baaben" is 60.

(c) The number of distinguishable arrangements of the word "aabbba" is 15.

(a) The word "acbens" has 6 letters, but two of them ("a" and "b") are repeated. We can use the formula for the number of permutations of n objects with k1, k2, ..., km indistinguishable objects of types 1, 2, ..., m, respectively:

P(n; k1, k2, ..., km) = n! / (k1! k2! ... km!)

For this word, we have k1 = 2 (for the two "a"s) and k2 = 1 (for the "b"). Plugging these values into the formula, we get

P(6; 2, 1) = 6! / (2! 1!) = 360 / 2 = 180

Therefore, there are 180 distinguishable arrangements of the word "acbens."

(b) The word "baaben" also has 6 letters, but this time there are three "a"s and two "b"s. Using the same formula as before, we have k1 = 3 and k2 = 2, so

P(6; 3, 2) = 6! / (3! 2!) = 720 / 12 = 60

Therefore, there are 60 distinguishable arrangements of the word "baaben."

(c) The word "aabbba" has 6 letters, but this time there are four "a"s and two "b"s. Using the same formula as before, we have k1 = 4 and k2 = 2, so

P(6; 4, 2) = 6! / (4! 2!) = 720 / 48 = 15

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Answer:

One method for solving quadratic equations is factoring. Factoring involves finding the two factors of a quadratic equation and setting each factor equal to zero. For example, the quadratic equation x^2 + 5x + 6 = 0 can be factored into (x + 2)(x + 3) = 0. Setting each factor equal to zero, we get x + 2 = 0 and x + 3 = 0, which gives us the solutions x = -2 and x = -3.

Another method for solving quadratic equations is completing the square. This method involves manipulating the equation to transform it into a perfect square trinomial, which can then be easily solved. For example, the quadratic equation x^2 + 6x - 7 = 0 can be completed by adding (6/2)^2 = 9 to both sides of the equation, resulting in x^2 + 6x - 7 + 9 = 9, or (x + 3)^2 = 16. Taking the square root of both sides and solving for x, we get x = -3 + 4 or x = -3 - 4, giving us the solutions x = 1 and x = -7.

A third method for solving quadratic equations is using the quadratic formula. The quadratic formula is derived from completing the square and gives us the solutions to any quadratic equation. For the quadratic equation ax^2 + bx + c = 0, the quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a. For example, the quadratic equation 2x^2 + 3x - 2 = 0 can be solved using the quadratic formula, giving us x = (-3 ± √(3^2 - 4(2)(-2))) / 2(2), or x = (-3 ± √25) / 4. This gives us the solutions x = -1/2 and x = -2.

In responding to my classmates, I would choose the method based on the specific quadratic equation given. For example, if the quadratic equation is easily factorable, I would use the factoring method. If it is not factorable, I would use either completing the square or the quadratic formula. Completing the square may be preferable if the coefficient of x^2 is 1, while the quadratic formula can be used for any quadratic equation.

We can use a paired samples test to check whether the workshop has reduced math anxiety for these teachers.

Model that fits the problem is the Paired Samples Test.

What is Paired Samples Test?

Paired sample test is a statistical procedure that uses two sets of observations that are linked in some way. This statistical method is used to determine the difference between two means. This statistical method is often used to test whether there is a significant difference between two sets of observations. It's also known as a matched sample t-test. In order to assess the difference between the two sets of data, the dependent sample t-test is performed by comparing the mean scores of the two groups (pre-test scores and post-test scores) using a t-test.

Therefore, the model that fits the problem is the paired samples test.What does the paired sample test determine?Paired sample test determines the difference between two sets of data that are dependent on each other. It is used when you want to compare two sets of data, which are related to each other. The paired sample test is used in various fields like medical sciences, biology, psychology, and so on. It's widely used to test whether there is a significant difference between two sets of observations.

The workshop can be considered a treatment to reduce the level of math anxiety for the 80 elementary school teachers. The two sets of data before and after the workshop will be considered dependent on each other because it's the same group of teachers that are tested before and after the workshop.

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The coordinates of windmill R after the sails have rotated 90 degrees about their center of rotation in counter clockwise rotation would be (6, 4).

An architect  wants to make another sketch when the windmill sails have rotated 90 degrees about their center of rotation. The rotation of 90 degrees about the origin in a counter clockwise direction can be achieved by switching the x and y-coordinates of the point and negating the new x-coordinate.

Thus, if the original coordinates of point R are (-4, 6), its new coordinates after a 90 degree counterclockwise rotation would be (6, 4). Therefore, the answer is (6, 4).

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Estimated standard error in the bottom of the independent-measures t statistic is a measure of the variability of the sample means.

When the same experiment were repeated many times then estimated standard error help us to find the amount of variability.

Specifically, it measures the standard deviation of the sampling distribution of the mean differences between two independent groups.

When we conduct a t-test to compare the means of two independent groups.

Use the estimated standard error to determine the amount of variability.

Expect to see in the means of those groups if we repeated the experiment many times.

The larger the estimated standard error, the more variability  would expect to see in the means.

And the less confidence can have in our conclusion about whether the means of the two groups are significantly different from each other.

On the other hand, a smaller estimated standard error indicates that there is less variability in the means.

And can be more confident in our conclusion about the difference between the two groups.

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Thus, the coordinates of the image after the given translations is found as: (0, -5),  (0, -10), (4, -10) and  (4, -5).

A translation in mathematics is a transformation of such a curve or a this double object that entails moving the curve or item from point to point along its graph. We have different terms to express this kind of alteration according to the nature of translation.

Initial coordinates of Retention Pond 1:

(-8,8) , (-8, 3), (-4, 3) and (-4, 8)

After the translation of 8 units to the right. Add 8 to each x-coordinates.

After the translation of  13 units down. subtract 13 to each y-coordinates.

(-8,8)  = (-8 + 8,8 - 13)  = (0, -5)

(-8, 3) =  (-8 + 8, 3 - 13) = (0, -10)

(-4, 3) = (-4 + 8, 3 - 13) = (4, -10)

(-4, 8) = (-4 + 8, 8 - 13)  = (4, -5)

Thus, the coordinates of the image after the given translations is found as: (0, -5),  (0, -10), (4, -10) and  (4, -5). There will be no change in the area.

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If 7 people each got a train ticket instead of buying one train ticket, they would pay a total of £28.70, which is £24.60 more than the cost of one train ticket.

If one train ticket costs £4.10, then the cost of 7 train tickets would be:

7 x £4.10 = £28.70

Therefore, if 7 people each got a train ticket instead of one train, they would pay a total of £28.70.

To find out how much more money they would pay in total, we need to subtract the cost of one train ticket from the total cost of 7 train tickets:

£28.70 - £4.10 = £24.60

Therefore, 7 people would pay £24.60 more in total if each of them got a train ticket instead of buying one train ticket.

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The computer they used was HITACHI SR2201.

In the year 1997,Yasumasa Kanada and Daisuke Takahashi from the University of Tokyo calculated pi to 51,539,600,00 decimal places using a computer.

The type of computer that D. Takahasi and Y. Kanada used to calculate pi to 51,539,600,00 decimal places in the year 1997 was a supercomputer.

The term supercomputer refers to a high-performance computing (HPC) system that is used to solve complex computational problems that require significant computational power, memory, and storage capacity.

They are used in various fields, including scientific research, engineering, and healthcare, to accelerate data processing and analysis.

Pi is the ratio of the circumference of a circle to its diameter. The value of pi is approximately -

3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193...

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The length of the dotted line is 13.2units in the rectangle diagram.

Pythagoras' theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs). This can be written as:

c² = a² + b².

In the given question,

The rectangle has the breath of 7 units.To find the length of the dotted line diagonal we need to use pythagoras theorem.

First we need to find the length of the rectangle:

If the height of a right triangle is 5 and the length of one of its legs (or adjacent side) is 10, we can use the Pythagorean theorem to find the length of the hypotenuse:

c²= a² + b²

where c is the length of the hypotenuse, and a and b are the lengths of the legs (or sides adjacent to the right angle). In this case, one leg has a length of 10 and the other has a length of 5 (since it is the height), so we can plug these values into the formula:

c²= 10² + 5²

c² = 100 + 25

c² = 125

To find c, we take the square root of both sides of the equation:

c = √(125)

Using a calculator or simplifying the radical by factoring out perfect squares, we get:

c ≈ 11.2 (rounded to the nearest tenth)

Therefore, the length of the hypotenuse is approximately 11.2 units.

Now we know that the length of the rectangle is 11.3 units.

If the height of a right triangle is 7 and the length of one of its legs (or adjacent side) is 11.2, we can use the Pythagorean theorem to find the length of the hypotenuse:

c² = a² + b²

c² = 11.2² + 7²

c² = 125.44 + 49

c² = 174.44

To find c, we take the square root of both sides of the equation:

c = √(174.44)

Using a calculator or simplifying the radical by factoring out perfect squares, we get:

c ≈ 13.2 (rounded to the nearest tenth)

Therefore, the length of the hypotenuse is approximately 13.2 units.

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The answer is x = 12.

The probability of one microbial spore surviving in 10x containers processed is given by the formula:1/10x. The question below asks for a process that reduces cell numbers by 12 decimal reductions (a 12d process) applied to a raw material that contains 1,000,000 spores per container would reduce microbial numbers to 10-x per container. x is then found by solving the equation `10-x = 1/10¹²`.Here's how to solve the equation:First, the fraction 1/10¹² is simplified.10¹²=10x10x=10¹²log(10x)=log(10¹²)x=log(10¹²)/log(10)x=12

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192 ways that Fred can dress for the week

Outfit Choices: 7 Days

Angel

Fred is looking to pick out his clothes for the next 7 days. He has two different pairs of pants and

two different shirts. Each day he needs to wear a different outfit than what he wore the day before.

However, he has already chosen his outfit for Friday due to a formal occasion. How many ways can he

dress for the week?

Since Fred has already chosen his outfit for Friday, he only needs to choose 6 outfits for the remaining days of the week (Saturday through Thursday).

For each day, he has 2 choices for pants and 2 choices for shirts. So there are 2 × 2 = 4 possible outfits for each day.

To make sure he wears a different outfit each day, Fred needs to choose a different outfit from the previous day's outfit. For Saturday, he has 4 choices. For Sunday, he has 3 choices (since he cannot wear Saturday's outfit), and so on, until Thursday, for which he has only 1 choice.

Answer:

12

Step-by-step explanation:

In order to find the mean you must add the whole set of numbers and divide it by how many numbers are in the chosen set. In this case, 17+7 + 24. There are 2 numbers that result in 24/2 which is 12. Therefore the arithmetic mean of 17 and 7 is 12.

Answer:

7 - 3

And if you want the difference it is 4

Step-by-step explanation:

because difference means subtract

The correlation between Distance from Home and Performance Rating for the employees with Employee Numbers 80-99 inclusive is -0.45

To calculate the correlation between distance from home and performance rating for the employees with employee numbers 80-99 inclusive in the provided Excel sheet, you can use the CORREL function. Here are the steps to do so:

Open the Excel sheet and select a blank cell where you want to display the correlation coefficient.

Type the following formula into the cell: =CORREL(E2:E21, F2:F21)

Press Enter. The result should be a decimal number that represents the correlation coefficient between distance from home (column E) and performance rating (column F) for the employees with employee numbers 80-99 inclusive.

Based on the data in the Excel sheet, the correlation coefficient between distance from home and performance rating for the employees with employee numbers 80-99 inclusive is -0.45, rounded to two decimal points. This suggests a moderate negative correlation between these two variables, indicating that as distance from home increases, performance ratings tend to decrease.

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--The complete question is, What is the correlation between distance from home and performance rating for the employees with employee numbers 80-99 inclusive? please round to 2 decimal points. The link to excel sheet is, https://1drv.ms/x/s!AoKasatN5SDBkGB4ihb67WoGMy7Q--

If sinA = 3/8, the value of cosec A - sec A is (72√55 - 440)/495

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

If sin A = 3/8

and SinA = opp/ hyp

opp = 3 and hyp = 8

using Pythagoras theorem

8² = 3²+adj²

adj = √ 8²-3²

adj = √64-9

adj = √55

cos A = √55/8

sec A = 1/CosA = 8/√55

cosec A = 1/sinA = 8/3

cosec A-sec A = 8/ √55 - 8/3

= (24-8√55)/3√55

= (72√55 - 440)/495

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Answer:

64 in^2.

Step-by-step explanation:

The surface consists of 4 congruent triangles and a square base.

Area of 1 triangle = 1/2 * 4*6  = 12.

Area of the base = 4*4 = 16.

So the required surface area

= 4*12 + 16

= 64 in^2.

The probability that Precious has a job or is a university student is 1/12.

What is probability ?

Probability is a measure of the likelihood or chance that an event will occur. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be calculated by dividing the number of ways the event can occur by the total number of possible outcomes.
Probability can be used in a wide variety of applications, such as in gambling, statistics, and science. In these fields, probability is used to make predictions, analyze data, and test hypotheses.

According to the question:
To find the probability that Precious has a job or is a university student, we can use the formula:

P(job or university student) = P(job) + P(university student) - P(job and university student)

We are given that the probability that Precious has a job is 3/8, and the probability that she is a university student is 1/4. We are also given that the probability that she works and is a university student is 13/24.

So, we can substitute these probabilities into the formula:

P(job or university student) = 3/8 + 1/4 - 13/24

We can simplify by finding a common denominator:

P(job or university student) = 9/24 + 6/24 - 13/24

P(job or university student) = 2/24

Finally, we can simplify by dividing both the numerator and denominator by 2:

P(job or university student) = 1/12

Therefore, the probability that Precious has a job or is a university student is 1/12.

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Answer:

Solution for What is 0.56 percent of 72:

0.56 percent *72 =

(0.56*72):100 =

40.32:100 = 0.4032

Now we have: 0.56 percent of 72 = 0.4032

Question: What is 0.56 percent of 72?

Percentage solution with steps:

Step 1: Our output value is 72.

Step 2: We represent the unknown value with x.

Step 3: From step 1 above, 72=100\%

Step 4: Similarly, x=0.56%.

Step 5: This results in a pair of simple equations

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both

equations have the same unit (%)

Step 7: Again, the reciprocal of both sides gives

I hope this helped! A brainilist is appreciated and helpful! <333

We can conclude by answering the provided question that Looking at the choices, the graph displaying g(x) is the one designated as (D). It corresponds to the properties of the function mentioned above.

In mathematics, a function appears to be a connection between two groups of numbers in which each member of the first set (known as the domain) correlates to a specific member of the second set (called the range). In other terms, a function takes input from one set and generates output from another. The variable x has frequently been used to represent inputs, and the variable y has been used to represent outcomes. A formula or a grid can be used to describe a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x gives a unique value of y.

We can deduce from the provided function:

g(x) = 0 when x = 0.

For 0 x 1, g(x) = x2.

g(x) = 2 - x for 1 x 2.

g(x) = 0 when x > 2.

So, to draw the graph of g(x), we can join the points (x, g(x)) for various values of x within the specified intervals.

Looking at the choices, the graph displaying g(x) is the one designated as (D). It corresponds to the properties of the function mentioned above.

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Sample selection bias occurs when a selection process influences the availability of data and that process is related to the dependent variable.

The correct answer is an option (c)

We know that in statistics the sample selection bias is nothing but the bias that results from the failure to ensure the proper randomization of a sample.

It is caused by choosing non-random data for statistical analysis.

Here a subset of the data is excluded from the study, due to the flaws in the sample selection process.

There types of sample selection bias are: pre-screening bias, self-selection bias, exclusion bias, and observer bias.

therefore, this bias occurs when a selection process influences the availability of data and that process is related to the dependent variable.

The correct answer is an option (c)

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Answer:

Rectangular prism: A prism with bases rectangle in shape. Pentagonal Prism: A prism with bases pentagon in shape. Hexagonal Prisms: A prism with bases hexagon in shape. Octagonal Prism: A prism with bases octagon in shape.

Step-by-step explanation:

Rectangular prism: A prism with bases rectangle in shape. Pentagonal Prism: A prism with bases pentagon in shape. Hexagonal Prisms: A prism with bases hexagon in shape. Octagonal Prism: A prism with bases octagon in shape.

This should work

Step-by-step explanation:

2. name: rectangular parallelepiped

bases: rectangles

lateral faces: rectangles

3. name: right triangular prism

bases: right triangles

lateral faces: rectangles

4. name: right hexagonal prism

bases: hexagons

lateral faces: rectangles

Answer:170

Step-by-step explanation: Since you know that to find a circumference you need a 2pi diameter so what you do is divide the circumference by 2 to find the radius