if b = -3, what is the value of b³?​

Answer:

54ft squared

Step-by-step explanation:

All faces:

Front: 2*3/2=4.5f squared * 2 (other side)= 9ft squared

Sides: 10*3/2= 15ft squared * 2 (other side)= 30ft squared

Bottom: 3*10/2= 30/2= 15ft squared

=54 ft squared

Surface area of the triangular prism is 96 feet.

The area of a three dimensional object on it's outer surface is called the surface area of the object.

A triangular prism has 2 triangular bases and 3 rectangular lateral faces.

Area of a triangle = \(\frac{1}{2}\) × base × height

There are 2 triangles at the top and bottom.

Here base = 3 feet and height = 2 feet

Total surface area on the top and bottom = 2 × \(\frac{1}{2}\) × base × height

                                                                     = base × height

                                                                     = 3 × 2

                                                                     = 6 feet

There are 3 rectangular faces.

Area of the rectangle = Length × width

Here, length = 10 feet and width = 3 feet

Area of the rectangular face = 10 × 3 = 30 feet

Since there are 3 rectangular faces,

Total lateral surface area = 3 × 30 = 90 feet

Total surface area of the triangular prism = 90 + 6 = 96 feet

Hence the total surface area of the given triangular prism is 96 feet.

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Answer:

the answer is 32,768 hopes this helps

Step-by-step explanation:

8^5 = 8x8x8x8x8 = 64x8x8x8= 64x64x8 = 4096x8= 32,768

Answer:

\( 18 \%\: of \: x = 63 \\ \frac{18}{100} x = 63 \\ x = \frac{63 \times 100}{18} \\ x = 350\)

Answer:

350

Step-by-step explanation:

To figure out the number, divide 63 by 18%

63/0.18 = 350

You can check by doing the opposite operation with your answer:

350 · 0.18 = 63

the total decrease in value of the machine in the second 5 years after it was bought is $35000. option B is correct.

To find the total decrease in value of the machine in the second 5 years after it was bought, we need to integrate the rate of change of value over that time period.

Given that the rate at which the value changes is 500(t - 12) dollars per year, we can integrate this expression over the interval t = 12 to t = 17 (second 5 years).

The integral of 500(t - 12) with respect to t is:

∫[0 to 10] 500(t - 12) dt

= 500 ∫[0 to 10] (t - 12) dt

= 500 [(t²/2 - 12t) | [0 to 10]

= 500 [(10²/2 - 12*10) - (0²/2 - 12*0)]

= 500 [(50 - 120) - 0]

= 500 [-70]

= - 350000

Therefore, the total decrease in value of the machine in the second 5 years after it was bought is $35000. option B is correct.

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Answer:

30%

Step-by-step explanation:

\(\boxed{percentage \: discount = \frac{discount}{original \: price} \times 100\%}\)

Discount

= original price -sale price

= $86 -60.20

= $25.80

Percentage discount

\( = \frac{25.80}{86} \times 100\% \\ = 30\%\)

Answer:

y = (3/2)x + 8

Step-by-step explanation:

You rewrite the original expression in the form of y = mx + b.

Answer:

Y = \(\frac{3}{2} x+8\)

Step-by-step explanation:

First, you must isolate 2y

In order to complete that, subtract 3x from both sides

Now you should have...

\(-2y=-3x-16\)

Now, you are able to make everything positive since everything is negative (it makes calculations easier.

\(2y = 3x + 16\)

Now, divide by the coefficient of y on both sides, which should result in...

\(y=\frac{3}{2} x + 8\)

Hope this helps!

Check the picture below.

so from the picture below, we can see that the rock reach its maximum at the vertex of the parabolic path, now , let's get the x-coordinate then

\(\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-8}x^2\stackrel{\stackrel{b}{\downarrow }}{+16}x\stackrel{\stackrel{c}{\downarrow }}{+2} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)\)

\(\left(-\cfrac{ 16}{2(-8)}~~~~ ,~~~~ 2-\cfrac{ (16)^2}{4(-8)}\right) \implies \left( - \cfrac{ 16 }{ -16 }~~,~~2 - \cfrac{ 256 }{ -32 } \right) \\\\\\ \left( 1 ~~~~ ,~~~~ 2 +8 \right)\implies \stackrel{ seconds ~~ meters }{(\text{\LARGE 1}~~,~~10)}\)

The number of miles in 4 weeks is 20 mules

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

Stone runs 1 mile five times a week

This means that the rate is

Rate = 1 mile * 5 per week

So, we have

Rate = 5 miles per week

For 4 weeks, we have

Distance = 5 * 4

Evaluate

Distance = 20 miles

Hence, the distance is 20 miles

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The decimal number that lies between 0.7 and 0.8, has three digits to the right of the decimal point, and whose sum of the digits is 24 is 7.98.

A decimal number is a number that has a fractional part represented by a decimal point. The digits to the right of the decimal point represent values that are smaller than 1.

In this problem, we are given that the decimal number has three digits to the right of the decimal point and that its sum of the digits is 24. Let's call the decimal number x. We can write an equation to represent the sum of the digits:

x = a + b/10 + c/100

Where a, b, and c are the digits of x.

We know that 0.7 < x < 0.8 and that the sum of the digits of x is 24, so we can write two more equations:

0.7 < a + b/10 + c/100 < 0.8

a + b + c = 24

By solving these three equations, we can find the decimal number x.

We know that a must be 7 because 0.7 < x < 0.8, so a = 7. We also know that b + c = 24 - 7 = 17. Now we need to find two digits b and c such that b + c = 17 and b/10 + c/100 is between 0 and 0.1.

The largest value of b that still satisfies this condition is 9. This means that

=> c = 17 - 9 = 8.

Therefore, the decimal number

=> x = 7 + 9/10 + 8/100 = 7.98.

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Answer:

325 miles. If one inch is 65 miles and the two locations are 5 inches apart, 65 x 5 is 325.

Fun fact: Minneapolis to St. Cloud in reality is only 70 miles. ;)

I hope this helps you

take both of sides paranthesis square

(2a+7b)^2=(11)^2

4a^2+2.4a.7b+49b^2=121

4a^2+49b^2+56.2=121

4a^2+49b^2=9

Answer:

65

Step-by-step explanation:

Please see the attached picture for full solution.

3.9979(depends on what place you need to round to

The equation is V=πr2h. First plug in what you know, 314=π5^2h. 5x5=25 and its multiplied with π. It would look like 314=25πh. Divide the 25π by both sides, leaving your h. Plug it into your calculator.

Check answer:

(I rounded the 4 to the nearest whole number) 4*25*π is approximately 314

Answer:

4 ft

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

Volume of cylinder formula:

Given:

Find h:

Dr. Brown used a randomized controlled trial (RCT) research design.

A randomized controlled trial (RCT) is a type of scientific experiment in which two or more groups of patients are subjected to various clinical treatments, interventions, or exposures. In an RCT, subjects are randomly allocated to either a treatment group or a control group, and the treatment group receives the new intervention being tested, while the control group receives the standard intervention or placebo.

Therefore, Dr. Brown used a randomized controlled trial (RCT) research design in which participants were randomly assigned to either the treatment condition or a comparison treatment condition, and their symptoms were measured before treatment, during treatment, and now 3-months post-treatment.

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Answer:

all the answers are correct

Step-by-step explanation:

2 times 2 times 3 times 3 =36

2 times 3 times 2 times 3 = 36

2 times 9 times 2 = 36

2 times 2 times 9 = 36

A reasonable price for X would be $ 2.

Since a class of 30 students visits an art museum and a special exhibit while there, and the prices were as follows:

To estimate a reasonable value for x, the following logical reasoning must be made:  

Therefore, a reasonable price for X would be $ 2.

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First, lets find the numbers 8 2/3 and 1 3/5, as follows:

And:

Now we can find our division, as follows:

Answer:

Option B

The directrix of the parabola is parallel to the axis of symmetry

Step-by-step explanation:

The directrix of the parabola is not parallel to the axis of symmetry. It is as a matter of fact, perpendicular to it.

A parabola is actually a set of points that are equidistant from a given point, the focus, and a given line the directrix.

The axis of symmetry is a line that divides the parabola into two equal halves and it always passes through the focus.

The directrix of the parabola is always perpendicular to this axis of symmetry as they always intersect at right angles.

We want to see which one of the given statements is false. We will see that the false one is B: "The directrix of the parabola is parallel to the axis of symmetry"

So in a parabola, we define the axis of symmetry as the vertical line that divides the parabola in two equal parts.

For a general parabola:

y = a*x^2 + b*x + c

The line of symmetry is at:

x = -b/2a

While we know that in a parabola the directrix is a horizontal line.

So the axis of symmetry and the directrix are perpendicular lines.

Then the statement that is false is B: "The directrix of the parabola is parallel to the axis of symmetry"

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the answer is 360 Hope it helps you

Among the three options provided, the cross-sectional data set is the demographic data. Correct option is B).

Cross-sectional data refers to a type of data that captures information about different individuals, entities, or units at a specific point in time. It provides a snapshot of a population or sample at a particular moment, allowing for comparisons and analysis of various characteristics or variables. In the case of demographic data, it typically includes information about individuals' age, gender, education level, income, and other demographic attributes. This data set does not capture changes or trends over time but rather provides a snapshot of the population's characteristics at a specific time.

On the other hand, the BCAD data and links could refer to data related to building codes, regulations, and their corresponding references, while code cases may refer to specific instances or examples of code violations or compliance. These data sets may be specific to certain incidents or cases and do not necessarily capture information about a population or sample at a particular point in time, making them less likely to be considered cross-sectional data.

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The maximum interest rate that can be charged during the fifth year is 6.75%. The correct option is the third option c. 6.75%

From the question, we are to determine the maximum interest rate that can be charged during the fifth year

A 2/1 ARM means that the interest rate is fixed for the first two years and then adjusts annually based on a specified index plus a margin. The "2/10 cap" means that the interest rate can only increase or decrease by a maximum of 2 percentage points each year, and can never be more than 10 percentage points higher than the initial rate.

Since the initial rate is 2.75%, the maximum rate that can be charged during the fifth year is:

2.75% + (2 x 2%) = 6.75%

Hence, the maximum interest rate that can be charged during the fifth year is 6.75%.

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Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

The y-intercept of a linear equation represents the value of the dependent variable when the independent variable is equal to zero.

What is linear equation?

A linear equation is a mathematical equation of the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept.

What is y-intercept?

In a linear equation of the form y = mx + b, the y-intercept (b) is the point where the line intersects the y-axis.

The y-intercept of a linear equation represents the value of the dependent variable when the independent variable is equal to zero. In the context of Justine's race, the y-intercept would represent her starting distance from the finish line.

It would be the distance from the finish line when she began the race, or the distance she would have to run to reach the finish line if she started at the beginning. The slope of the line would tell you how much the distance decreases as she runs.

Together, the y-intercept and slope of the line can provide useful information for understanding and analyzing Justine's race.

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The answer of the given question based on the linear relationship is , the y-intercept gives information about Justine's initial position or starting point before she started running the race.

A linear relationship is a type of relationship between two variables where their relationship can be described by a straight line. In other words, the change in one variable is directly proportional to the change in the other variable. This means that as one variable increases or decreases, the other variable also changes in a consistent and predictable way. Linear relationships are commonly studied in mathematics, statistics, and other fields as they provide a useful framework for understanding the relationship between two variables and making predictions based on that relationship.

In the context of this linear relationship, the y-intercept represents the starting point of Justine's race. It is the point where her distance from the finish line is zero, which is the beginning of the race. Therefore, the y-intercept gives information about Justine's initial position or starting point before she started running the race.

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The two numbers that add up to 158 are 99 and 59.

The equation of variables that have a maximum power of 1 is known as a linear equation.

Let the lesser number be x.

So, the greater number will be x+40.

And the sum of both the numbers is 158.

So, the resulting linear equation based on given conditions is,

x + x + 40 = 158

2x = 158 - 40

2x = 118

x = 118/2

x = 59

So, the lesser number is 59.

And the greater number is 59 + 40 = 99.

Hence, the two numbers that add up to 158 are 99 and 59.

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Answer:

19.43

Step-by-step explanation:

This is a trick for you.

Make the numbers to become whole numbers(1474+469)

After adding the whole numbers,the decimal point were 2 so,move 2jumps from the right to the left which will give you 19.43 as your answer.

The measure of angle 3 based on the information is 142°.

We are given that L and M are parallel. Use all the condition or properties of parallel lines.

Here use vertically opposite angle. Also, coointerior angles sum is 180°.

Now, angle 6= 38° { Vertically opposite angle}.

angle 6 + angle 5 = 180° { as sum of coointerior angles are equal to 180°}

38°+angle 5 = 180°

or, angle 5 = 180°-38°

Therefore, angle 5 = 142°

Now, angle 3 = angle 5 { Vertically opposite angle}

Therefore, the measure of angle 3 is 142°.

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The sum of w and its additive inverse is 0

The number is given as:

Number = 0.8

The number w is the additive inverse.

This means that

w = -0.8

The sum of 0.8 and w is

w + 0.8 = -0.8 + 0.8

w + 0.8 = 0

So, we have:

Sum = 0

Hence, the sum of w and its additive inverse is 0

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