Find the volume of the triangular prism.

Following are the numbers correct to 3 significant figures

Answers to the following questions:

(1) Round to the needed significant figure: 37400;

(2) Round to the required significant figure: 84600;

(3) Round to the required significant figure: 261;

(4) Round to the needed significant figure: 0.00262

(5) Round to the required significant figure: 0.368

(6), round to the needed significant figure: 0.00257

The most significant number in the number is rounded up. Check the first non-zero digit if you want to round to one significant figure while doing so. If rounding to two significant numbers, have a look at the digit that comes after the first non-zero digit.

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Answer:

5) 3x = 135° and x = 45°

6) (8x + 5) = 61° and (3x + 8) = 29°

Step-by-step explanation:

5) supplementary of two angles whose sum is 180°

3x + x = 180 → 4x = 180

4x / 4 = 180 / 4

x = 45

3x = 3(45)

135°

6) complimentary of two angles whose sum is 90°

(8x + 5) + (3x + 8) = 90 → 11x + 13 = 90

11x + 13 - 13 = 90 - 13

11x = 77

11x / 11 = 77 / 11

x = 7

(8x + 5) = 8(7) + 5

56 + 5 = 61

(3x + 8) = 3(7) + 8

21 + 8 = 29

Answer:

191

Step-by-step explanation:

All you have to do is 127+64 to get the total before the withdrawal.

The relationship that represents a function with a greater rate of change than the function graphed is given as follows:

A. y = 4x - 3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b.

The slope represents the average rate of change of a linear function.

From the graph, when x increases by one, y decreases by two, hence the slope m is given as follows:

m = -2.

For function A, the function is defined as follows:

y = 4x + 3.

Hence the rate of change is given as follows:

m = 4, which is greater than -2.

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Answer:

Step-by-step explanation:

The perimeter of a rhomboid: The perimeter of a rhomboid is the sum of all sides of the figure i.e. P= (a +b + a +b) = 2(a + b).

B is the base of the rhomboid and a is the length of the side of the rhomboid.

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The equation of the parallel line will be y = (2/3)x - 8/3.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.

The equation of the line is given below.

y - 4 = 2/3 (x - 3)

The equation of the line that is parallel to the given line will be written as,

y = (2/3)x + c

The equation of the line that passes through (1, -2), then we have

- 2= (2/3)(1) + c

- 2 = 2 /3 + c

c = - 8 / 3

Then the equation of the parallel line will be y = (2/3)x - 8/3.

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Answer:

x = -16

Step-by-step explanation:

The angles are corresponding angles and when the lines are parallel, corresponding angles are equal.

8x+260 = 132

Subtract 260 from each side.

8x+260-260 = 132-260

8x = -128

Divide each side by 8.

8x/8= -128/8

x = -16

Answer:

x = -16

Step-by-step explanation:

We know that, corresponding angles in parallel lines are equal.

Accordingly,

8x + 260 = 132

Subtract 260 from each side.

8x = 132 - 260

8x = -128

Divide both sides by 8.

x = -16

Answer:

Rounded to the nearest hundredths, the volume of the cylinder is approximately 58.91 cm^3.

Step-by-step explanation:

To find the volume of a cylinder, you need to know its radius (r) and height (h). In this case, the radius is given as 5 cm and the height is 0.75 cm.

The formula for the volume of a cylinder is:

V = π * r^2 * h

where π is a mathematical constant approximately equal to 3.14159.

Let's substitute the given values into the formula:

V = π * (5 cm)^2 * 0.75 cm

V ≈ 3.14159 * (25 cm^2) * 0.75 cm

V ≈ 58.909 cm^3

Using linear approximation, the expression √125.2 can be approximated as approximately 10.02.

To find the equation of the tangent line to the function f(x) = √x at x = 125, determine the slope (m) and the y-intercept (b) of the tangent line.

First, find the slope (m) using the derivative of the function f(x) = √x:

f'(x) = 1 / (2√x)

Evaluate the derivative at x = 125:

f'(125) = 1 / (2√125) = 1 / (2 × 5) = 1/10

Now, find the y-coordinate of the point on the function f(x) at x = 125:

f(125) = √125 = 5

So, the tangent line at x = 125 passes through the point (125, 5) and has a slope of 1/10.

Using the point-slope form of a linear equation, the equation of the tangent line can be written as:

y - 5 = (1/10)(x - 125)

To simplify, multiply through by 10:

10y - 50 = x - 125

Rearranging the equation, express it in the form y = mx + b:

y = (1/10)x - 75/10 + 5

Simplifying further:

y = (1/10)x - 75/10 + 50/10

Combining the terms:

y = (1/10)x - 25/10

Therefore, the equation of the tangent line to f(x) = √x at x = 125 is y = (1/10)x - 25/10.

Now, use this tangent line to approximate the value of √125.2:

Substitute x = 125.2 into the equation:

y = (1/10)(125.2) - 25/10

y = 12.52 - 2.5

y ≈ 10.02

So, using linear approximation, approximate √125.2 as approximately 10.02.

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Answer:

-57.6=x

Step-by-step explanation:

-22.3= x/3-3.1
-19.2=x/3
-57.6=x

Answer:

c

Step-by-step explanation:

Answer:

-0.5

Step-by-step explanation:

Answer:

a. 0.4364 = 43.64% probability that the total of their scores is above 260.

b. 0.0351 = 3.51% probability that Jeff's score is higher.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Sum/Subtraction between normal variables:

When two normal variables are added/subtracted, the mean is the sum/subtraction of the means, while the standard deviation is the square root of the sum of the variances.

a. the total of their scores is above 260.

Mean is the sum of the means, so:

\(\mu = 100 + 155 = 255\)

Standard deviation is the square root of the sum of the variances. So

\(\sigma = \sqrt{21^2+22^2} = 30.4\)

The probability is 1 subtracted by the p-value of Z when X = 260. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{260 - 255}{30.4}\)

\(Z = 0.16\)

\(Z = 0.16\) has a p-value of 0.5636

1 - 0.5636 = 0.4364

0.4364 = 43.64% probability that the total of their scores is above 260.

b. Jeff's score is higher.

Jeff's mean is of 100, while Pam's is of 155. The probability of Jeff's score being higher is the probability that the subtraction is above 0. The mean is:

\(\mu = 100 - 155 = -55\)

The probability is 1 subtracted by the p-value of Z when X = 0. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{0 - (-55)}{30.4}\)

\(Z = 1.81\)

\(Z = 1.81\) has a p-value of 0.9649.

1 - 0.9649 = 0.0351

0.0351 = 3.51% probability that Jeff's score is higher.

Answer:

2

Step-by-step explanation:

so if you take away 14 by 2 =12 and 12 divided by 6= 2

Answer:

each candy bar cost 2 dollars

Step-by-step explanation:

Answer:

500 markers

Step-by-step explanation:

Multiply 5000 by 1/10

\(5000*\frac{1}{10} \\\\= \frac{5000}{10}\\\)

Simplify (dividing the numerator and denominator by 10)

\(\frac{5000}{10} \\= \frac{500}{1}\\= 500\)

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Answer:

70%

Step-by-step explanation:

First find the ones that still need to be installed

270-81

189

Percent to be done = number to be installed / total

                                   =189/270 =.7

Change to percent form = .7 *100% = 70%

Answer:

Game #1B is the correct answer i guess so

Answer:

0.8358 = 83.58% probability of reaching into the box and randomly drawing a chip number that is smaller than 627

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

\(P(X < x) = \frac{x - a}{b - a}\)

There are 750 identical plastic chips numbered 1 through 750 in a box

This means that \(a = 1, b = 750\)

What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 627?

\(P(X < x) = \frac{627 - 1}{750 - 1} = 0.8358\)

0.8358 = 83.58% probability of reaching into the box and randomly drawing a chip number that is smaller than 627

Answer:

y = 4\(\sqrt{5}\) , ? = 10

Step-by-step explanation:

using Pythagoras' identity on the smallest right triangle

x² = 4² + 2² = 16 + 4 = 20 ( take square root of both sides )

x = \(\sqrt{20}\) = \(\sqrt{4(5)}\) = \(\sqrt{4}\) × \(\sqrt{5}\) = 2\(\sqrt{5}\)

using Pythagoras' identity on the middle right triangle

y² = 8² + 4² = 64 + 16 = 80 ( take square root of both sides )

y = \(\sqrt{80}\) = \(\sqrt{16(5)}\) = \(\sqrt{16}\) × \(\sqrt{5}\) = 4\(\sqrt{5}\)

using Pythagoras' identity on the largest right triangle

?² = x² + y² = (2\(\sqrt{5}\) )² + (4\(\sqrt{5}\) )² = 20 + 80 = 100

Take square root of both sides

? = \(\sqrt{100}\) = 10

Answer:

Chemical Energy

Step-by-step explanation:

According to the Law of Conservation of Energy, energy is neither created nor destroyed. It is an entity that's always existing in the environment. It takes different forms of energy. Among the choices, the best answer would be letter B. Chemical energy. The chemical energy originates from the energy within the muscles that are dormant. Once used, this chemical energy is transformed into mechanical energy by the action of pushing his foot on the ground.

Answer:

Chemical energy

Step-by-step explanation:

Law of conversation says energy cannot be created or destroyed. Chemical energy is made from the muscles and transformed into mechanical energy when he pushes down.

Probability that the person is in the air force or the marines is 5/13.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Given, in bar graph

Number of persons in marines = 170 + 10 = 180

Number of persons in air force = 300 + 70 = 370

Total Military personnel

= 300 + 70 + 420 + 80 + 170 + 10 + 320 + 60

= 1430

Probability that the person is in the Air Force or the marines.

= 180+370/1430

= 550/1430

= 5/13

Hence, 5/13 is probability of a person is in air force or marines.

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We should add 25 both side by method of completing the square.

We have to given that;

A student is solving the problem

x² + 10x + _ = 16 + _

Now, We can completing the square as;

⇒ x² + 10x + 5² = 16 + 5²

⇒ x² + 10x + 25 = 16 + 25

⇒ (x + 5)² = 16 + 25

Hence, We should add 25 both side by method of completing the square.

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Answer:

The scanning electron microscope

Step-by-step explanation:

The scanning electron microscope can determine the proximity to a discharging firearm and/or the contact with a surface exposed to GSR

Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.

Heron of Alexandria (c. 62 ce) is credited with developing the Heron's formula, which determines the area of a triangle in regards of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: √s(s - a)(s - b)(s - c)

where s = half the perimeter,

s = (a + b + c)/2.

given data:

In ΔHIJ,

semi -perimeter s = (i + j + h) / 2

s = (33 + 61 + 39) / 2

s = 66.5

Now,

s - h = 66.5 - 33 = 33.5

s - i = 66.5 - 61 = 5.5

s - j = 66.5 - 39 = 27.5

area of ΔHIJ = √s(s - h)(s - i)(s - j)

area of ΔHIJ = √66.5*33.5*5.5*27.5

area of ΔHIJ = √336947.1875

area of ΔHIJ = 580.47

Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.

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Answer:

Ellen have left 56 glasses to wash.

Step-by-step explanation:

Given that:

Number of glasses to be washed = 175

Percentage of glasses Ellen washed = 68%

Number of glasses Ellen washed = \(\frac{68}{100}*175\)

Number of glasses Ellen washed = 119

Number of glasses left = Total glasses - Number of glasses washed

Number of glasses left = 175 - 119 = 56

Hence,

Ellen have left 56 glasses to wash.

120 many combinations are possible.

The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the process of choosing items or things from a bigger group where order is irrelevant.

Consider a collection of three integers P, Q, and R. The number of ways that we may choose two numbers from each group is thus determined by combination.

It is represented as: \(^nC_r\)

where, n = total number of objects in the set

r = number of choosing objects from the set

Given that,

Cell Phone Models A particular cell phone company offers:

4 models of phones

each in 6 different colors

each available with any one of 5 calling plans

Thus, possible combination numbers are:

= (No. of models) × (No. of colors) × (No. of calling plans)

= (4)× (6)× (5)

= 120 possibilities

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Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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Answer:

Key Feature: - decreasing, As x approaches -(infinite), y approaches (infinite), As x approaches (infinite), y approaches a constant.

Not a Key feature: increasing, As x approaches (infinite) y approaches (infinite), As x approaches -(infinite) y approaches -(infinite), & As x approaches -(infinite) y approaches a constant.

Step-by-step explanation:

The amount saved by repaying the loan early is $831.25

The amount of discount received by purchasing supplies is $3,500

The net amount saved by purchasing supplies rather than repaying loan is $2,668.75

What is ordinary interest?

Ordinary interest is the interest computation that is based on 360-day a  year count rather than 365-day year count, hence, in determining the amount saved by paying $35,000 out of the amount due to Citizens Bank, we time-apportion the interest for 90 days with respect to 360 days not 365 days.

Amount saved in interest=$35,000*9.5%*90/360

Amount saved in interest=$831.25

Using the $35,000 to purchase serving supplies, 10% discount is given off the normal cost of $35,000

Amount saved with discount=10%*$35,000

Amount saved with discount=$3,500

The difference between discount on supplies and interest saved=$3,500-$831.25

The difference between discount on supplies and interest saved=$ 2,668.75

The other factors to consider before making the final decisions include, the fact the loan is more important than the supplies because the loan relates to the firm's financing rather than operational needs of supplies

Secondly, the amount saved in interest may be more if another loan of $35,000 can be borrowed elsewhere with significant lower interest rates

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