rectangle has a perimeter of 64.8 millimeters and a base of 15.8 millimeters. What is the height?

Rectangular prism is also called cuboid.

Formula :

\(\bigstar \: \boxed{\sf {Volume_{(Cuboid)} = \ell \times b \times h}} \\ \)

\( \longmapsto \) Volume = (3 × 6 × 2) feet\(\sf ^3 \)

\( \longmapsto \) Volume = (18 × 2) feet\(\sf ^3 \)

\( \longmapsto \) Volume = 36 feet\(\sf ^3 \)

Therefore,

Answer:

All are true

Step-by-step explanation:

You’re welcome

Answer from left to right: 48, 80, 4.5, 160

Step-by-step explanation:

(a) FALSE: The statement Z12≅A4 is false. Z12 represents the additive group of integers modulo 12 under addition, and A4 represents the alternating group of permutations on 4 elements. These two groups are not isomorphic. Z12 is a cyclic group of order 12, while A4 is a non-abelian group of order 12.

(b) TRUE: The statement Z18*≅Z6 is true. Z18* represents the multiplicative group of integers modulo 18 under multiplication, and Z6 represents the additive group of integers modulo 6 under addition. Both of these groups are cyclic of order 6 and are isomorphic to each other.

(c) FALSE: The statement R≅R* is false. R represents the additive group of real numbers under addition, and R* represents the multiplicative group of non-zero real numbers under multiplication. These two groups are not isomorphic. R is an infinite group, while R* is not even a group as it lacks the identity element (0).

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Using differentials to estimate the relative error in the calculated area of the disk of disk with radius 15 cm is equals to the 3.192%.

We have, a disk with radius of 15 cm.

Maximum error = 0.25

We have to determine the area of the disk. Area is a two dimensional quantity. It is defined as the space occupied by figure or any two dimensional shape. Here, formula for area of disk, A = πr² --(1)

here, r = 15 cm , dr = 0.25

Relative error is defined as the ratio of absolute error in measurement to the oringnal measurement. Differentating the equation (1) with respect to r, dA = d( πr²)

=> dA = 2πr dr

Substitutes the known values, in above formula, dA = 2× π × 15 ×0.25

=> dA = 7.50 × π = 23.55

So, absoulte error in area = 22.55

Original value of area = π(15)² = 706.5 cm²

Now, relative error % = (∆A/A)×100

= (22.55/706.5)×100

= 0.031917 × 100

= 3.1917 ~ 3.192 %

Hence, required value is 3.192%.

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Complete question:

the radius of a disk is given 15 cm as with a maximum error of 0.25 . use differentials to estimate the relative error in the calculated area of the disk. please enter your answer in decimal format with three significant digits after the decimal point.

The formula 180(n - 2), where n is the number of sides in the polygon, is used to calculate the sum of the interior angles in a regular polygon.

A polygon (/pln/) is a closed polygonal chain made up of a finite number of straight line segments that are joined to form a planar figure in geometry (or polygonal circuit).

A polygon is a region that is bounded by a bounding circuit, a bounding plane, or both.

A polygonal circuit's segments are referred to as its edges or sides.

The polygon's vertices (plural: vertices) or corners are the places where two edges converge.

A solid polygon's body is another name for its inside.

A polygon with n sides is referred to as a "n-gon"; a triangle is an example of one.

Simple polygons do not overlap one another.

Mathematicians frequently focus on small polygons' bounding polygonal chains, and they frequently define.

Hence, The formula 180(n - 2), where n is the number of sides in the polygon.

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Answer:

the answer is 1.4N/kg

Answer:

D.) -3

Step-by-step explanation:

N is greater than -4 and less than -2.

Therefore, -3 is N since it is between -4 and -2.

Answer:

No, it does not.

Step-by-step explanation:

As if we attempted to solve for x, 5x & 5x will both cross each other out. There are no values of x that make the equation true.

According to the question 42% of investment managers were bullish on the stock market, and the average expected return for equities was 11.8%.

1. The average expected return over the next 12 months for equities was 11.8%.

The average expected return for equities, based on the responses of the investment managers surveyed, was found to be 11.8%. This indicates the average anticipated profitability of investments in equities over the next year.

2. 42% of managers classified themselves as bullish or very bullish on the stock market.

Out of the investment managers surveyed, 42% expressed a bullish or very bullish outlook on the stock market. This suggests that a significant portion of the surveyed managers held an optimistic view of the stock market's performance.

In conclusion, the descriptive statistics gathered from the survey of investment managers indicate that the average expected return for equities is 11.8%, and 42% of managers classified themselves as bullish or very bullish on the stock market.

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Answer:

11/1024.

Step-by-step explanation:

Binomial Probability distribution.

This is the probability of 9 tails or 10 tails being flipped.

Prob ( 10 tails) = (1/2)^10 = 1/1024

Prob ( 9 tails) = 10C9 * 1/2^9* 1/2 = 5/512

Required probability =  1/1024 + 5/512

= 11/1024.

Given:

Blue car travels \(44\dfrac{1}{2}\) miles on \(1\dfrac{1}{4}\) gallons of gasoline.

Red car travels \(20\dfrac{4}{5}\) miles on \(\dfrac{4}{5}\) gallons of gasoline.

To find:

The unit rate for miles per gallon for each car and find which car could travel the greatest distance on one gallon of gasoline.

Solution:

We know that,

\(\text{Unit rate}=\dfrac{\text{Total distance covered by the car}}{\text{Number of gallons of gasoline}}\)

Using this formula, the unit rate of blue car is

\(\text{Unit rate of blue car}=\dfrac{44\dfrac{1}{2}}{1\dfrac{1}{4}}\)

\(\text{Unit rate of blue car}=\dfrac{\dfrac{88+1}{2}}{\dfrac{4+1}{4}}\)

\(\text{Unit rate of blue car}=\dfrac{89}{2}\times \dfrac{4}{5}\)

\(\text{Unit rate of blue car}=\dfrac{178}{5}\)

\(\text{Unit rate of blue car}=35.6\)

Unit rate of red car is

\(\text{Unit rate of red car}=\dfrac{20\dfrac{4}{5}}{\dfrac{4}{5}}\)

\(\text{Unit rate of red car}=\dfrac{\dfrac{100+4}{5}}{\dfrac{4}{5}}\)

\(\text{Unit rate of red car}=\dfrac{104}{5}\times \dfrac{5}{4}\)

\(\text{Unit rate of red car}=26\)

Therefore, the unit rate of blue car is 35.6 miles per gallon of gasoline and  unit rate of red car is 26 miles per gallon of gasoline.

Since, unit rate of blue car is greater than the red car, therefore blue car travel the greatest distance on one gallon of gasoline.

Answer:

x=55  (i think)

Step-by-step explanation:

190=(2x-10)+90

(subtract 90 from 190)

100=(2x-10)

(add 10 to 100)

110=2x

(divide by 2)

55=x

The net of a triangular prism consists of two triangles and three rectangles.

In the net of a triangular prism, we can observe two types of polygons: triangles and rectangles.

First, let's discuss the triangles.

A triangular prism has two triangular faces, which are congruent to each other.

These triangles are equilateral triangles, meaning they have three equal sides and three equal angles.

Each of these triangles contributes two polygons to the net, one for each face.

Next, we have the rectangles.

A triangular prism has three rectangular faces that connect the corresponding sides of the triangular bases.

These rectangles have opposite sides that are parallel and equal in length.

Each rectangle contributes one polygon to the net, resulting in a total of three rectangles.

To summarize, the net of a triangular prism consists of two equilateral triangles and three rectangles.

The triangles represent the bases of the prism, while the rectangles form the lateral faces connecting the bases.

Altogether, there are five polygons in the net of a triangular prism.

It's important to note that the dimensions of the polygons may vary depending on the specific size and proportions of the triangular prism, but the basic shape and number of polygons remain the same.

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Answer:

30 students: $346.5

1 student: $11.55

Step-by-step explanation:

It would cost a total of $57.75 every 5 student so just multiply by 6 to get your amount for 30 students. Then divide by 30 to get the amount per student.

Answer:

volume of the sphere

=4/3π × r³

=4/3π × 3 × 3 × 3

=4/3π × 27

=36π ( c )

The value of volume of the sphere shown with a radius of 3 is,

⇒ 36π units³

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Since, We know that;

volume of the sphere is,

V = 4/3π × r³

Here, We have;

r = 3

Hence, We get;

V = 4/3π × 3 × 3 × 3

= 4/3π × 27

=36π

Thus, The value of volume of the sphere shown with a radius of 3 is,

⇒ 36π units³

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The car was driven 105 miles.

What is rent?

An agreement where a fee is paid for the temporary use of a good, service, or property owned by another is known as renting, sometimes known as hiring, or letting.

In the given example the cost function is, c = 15 + 2m

Where, c is the total cost and m is the number of miles car driven.

The total cost was $225.

So, plug c = $225 in the above equation.

225 = 15 + 2m

210 = 2m

   m = 105

Therefore, the car was driven 105 miles.

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68.18% is the right answer

Answer:

the answer is $12 per hour

Step-by-step explanation:

just took the quiz

Answer:

its A $12 per hour

Step-by-step explanation:

just took the test

You should remember the formula: Interest = P * R * T /100

Apply it in every part.

A) I = 624 * 5 * 3 / 100

I = 9360/100

I = 93.60

So, Total amount = 93.60 + 624 = $717.60

B) I = 4120 * 7 * 3 / 2*100

I = 86520 / 200

I = 432.60

So, Total amount = 432.60 + 4120 = $4552.60

C) I = 900 * 3.1 * 1 / 2 * 100

I = 2790 / 200

I = 13.95

So, Total Amount = 13.95 + 900 = $913.95

D) I = 275 * 4.8 * 8 /100

I = 10560 / 100

I = 105.60

So, Total amount = 105.60 + 275 = $380.60

Hope this helps

Based on the given data, the professors' grading procedures have different variances. To determine if the difference is statistically significant at the 2% level of significance, we can use a two-sample F-test. The F-statistic is calculated by dividing the larger variance by the smaller variance. In this case, the F-statistic is 2.97. Using a critical value of 5.05, we can reject the null hypothesis that the variances are equal. Thus, the decision is that there is a statistically significant difference in the variance of the professors' grading procedures.

In statistics, variance is a measure of the spread of a distribution. When comparing two variances, we can use a two-sample F-test to determine if they are statistically different. The F-statistic is calculated by dividing the larger variance by the smaller variance. If the calculated F-value is greater than the critical value, we reject the null hypothesis that the variances are equal.

In this case, the professors' grading procedures have different variances, with Professor 1 having a larger variance than Professor 2. Using a two-sample F-test, we determined that the difference in variances is statistically significant at the 2% level of significance. This means that there is strong evidence to suggest that the professors' grading procedures differ in their spread of grades.

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Answer:

$50

Step-by-step explanation:

To get previous prices, divide by what you would have multiplied to get the next price. X*.70 (that’s 30% off)=21. So... 21/.70=X. Repeat for each price change... (((21/.7)/.75)/.8)=$50.

Answer:

$50 is the answer

Answer:

x≈12.6

Step-by-step explanation:

We have the equation:

19(1.12^x) = 8(1.18^x)

Divide both sides by 8:

19/8 (1.12^x) = (1.18^x)

Take the natural logarithm of both sides:

ln[19/8 (1.12^x)] = ln[1.18^x]

Using the properties of logarithms, we can simplify the left side:

ln(19/8) + ln(1.12^x) = x ln(1.18)

Substituting y = 1.12^x, we get:

ln(19/8) + ln(y) = ln(1.18) y

Now we can solve for y:

ln(y) = ln(1.18) y - ln(19/8)

Using a numerical method or a graphing calculator, we can find that y ≈ 10.584.

Substituting back to solve for x:

1.12^x ≈ 10.584

Taking the logarithm base 1.12 of both sides:

x ≈ ln(10.584)/ln(1.12)

x ≈ 12.6

Therefore, the solution to the equation is x ≈ 12.6.

Hi there!  

»»————-　★　————-««

I believe your answer is:  

Distribution property

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

From the first step to the next step, the 5 gets distributed into the 'x-2'. The distribution property is getting used.

⸻⸻⸻⸻

\(5(x-2) = 12x -39\\\\\rightarrow5(x-2)\leftarrow\\\\\left \{ {{5*x=5x} \atop {5*-2=-10}} \right. \\\\\rightarrow5(x-2)=\boxed{5x - 10}\\\\\\5(x - 2) = 12x - 39\\\\\rightarrow\boxed{5x-10}=12x-39\)

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

The radian measure of the angle at the center of the circle is approximately 1.6623 radians.

We are given that the radius of the circle is 77.0 cm and the length of the intercepted arc is 128 cm. We need to find the radian measure of the angle at the center of the circle.

To solve this problem, we use the formula relating the angle at the center of a circle, the radius of the circle, and the arc length intercepted by the angle.

The formula is given byθ = s/rwhereθ = angle at the center of the circle in radians s = arc length intercepted by the angle r = radius of the circle Substituting the given values, we getθ = 128/77.0 = 1.6623 radians (rounded to four decimal places)

Therefore, the radian measure of the angle at the center of the circle is approximately 1.6623 radians.

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Answer:

180+54sqrt3

You have to use the formula that is contained within the lessons, the answer you should have before you format it like this is: 273.530743609

Answer:

Total time = 19 minutes.

Step-by-step explanation:

Given the following data;

Time to shower = 720 seconds

Time to eat breakfast = 420 seconds

To find the total time in minutes;

Total time = 720 + 420

Total time = 1140 seconds

We know that 60 seconds equals a minute.

Total time = 1140/60

Total time = 19 minutes.

Therefore, it will take Andrew 19 minutes to take a shower and eat breakfast.

To multiply a decimal number by 10^2, you need to move the decimal point two places to the right. This is because multiplying by 10^2 is equivalent to multiplying by 100, which means shifting the decimal point two places to the right.

For example, let's say you have the decimal number 3.14 and you want to multiply it by 10^2. To do this, you move the decimal point two places to the right:

3.14 * 10^2 = 314.00

As you can see, the decimal point has been shifted two places to the right, resulting in the product of 314.00.

Similarly, if you have a decimal number with fewer digits, such as 0.25, and you want to multiply it by 10^2, you would still move the decimal point two places to the right:

0.25 * 10^2 = 25.00

Again, the decimal point has been shifted two places to the right, resulting in the product of 25.00.

Therefore, to multiply a decimal number by 10^2, you move the decimal point two places to the right.

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To calculate the Value-at-Risk (VaR) for this investment at a 99% confidence level, we need to determine the loss amount that will be exceeded with a probability of only 1% (i.e., the worst-case loss that will occur with a 1% chance).

Given that there is a 0.5% chance of a loss of $10 million and a 99.5% chance of a loss of $1 million, we can express this as:

Loss Amount | Probability

$10 million | 0.5%

$1 million | 99.5%

To calculate the VaR, we need to find the loss amount that corresponds to the 1% probability threshold. Since the loss of $10 million has a probability of 0.5%, it is less likely to occur than the 1% threshold. Therefore, we can ignore the $10 million loss in this calculation.

The loss of $1 million has a probability of 99.5%, which is higher than the 1% threshold. This means that there is a 1% chance of the loss exceeding $1 million.

Therefore, the Value-at-Risk (VaR) for this investment at a 99% confidence level is $1 million.

The Value-at-Risk (VaR) for this investment at a 99% confidence level is $1,045,000.

To calculate the Value-at-Risk (VaR) for this investment at a 99% confidence level, we need to determine the loss amount that will be exceeded with only a 1% chance.

Given that the investment has a 0.5% chance of a loss of $10 million and a 99.5% chance of a loss of $1 million, we can calculate the VaR as follows:

VaR = (Probability of Loss of $10 million * Amount of Loss of $10 million) + (Probability of Loss of $1 million * Amount of Loss of $1 million)

VaR = (0.005 * $10,000,000) + (0.995 * $1,000,000)

VaR = $50,000 + $995,000

VaR = $1,045,000

Therefore, the Value-at-Risk (VaR) for this investment at a 99% confidence level is $1,045,000.

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