The diagram represents a right rectangular prism with dimensions labeled as algebraic expressions.


Determine the volume for the figure below.

Select all that apply.


A.
7
x
B.
4
x
2
−
25
C.
12
x
3
−
75
x
D.
3
x
(
4
x
2
−
25
)
E.
(
2
x
+
5
)
(
6
x
2
−
15
x
)
F.
12
x
3
+
60
x
3
+
75
x
G.
12
x
3
+
30
x
+
10
x
−
25

Answer:

2,968

Step-by-step explanation:

you would do the inside of the parentheses so -5 + 61 is 56 and 2 + 51 is 53. then you would multiply 56 and 53 and get 2,968. you multiplied these numbers because they are in parentheses still and when parentheses are next to each other that means you multiply. Whats in the parentheses together.

Answer: 2968

Step-by-step explanation:

1. Do what is in the parentheses

(-5+61)=56

(2+51)=53

2. Then multiply both of those answers

(56)(53) =2968

Answer:

  3/2   (see comment)

Step-by-step explanation:

You want the scale factor relating image triangle B to original triangle A.

Triangle B is an isosceles right triangle with sides of 3 units. Triangle A is an isosceles right triangle with sides of 2 units. The scale factor of the two triangles is ...

  (B size)/(A size) = 3/2

The scale factor is 3/2.

__

Additional comment

Triangle B can be obtained from triangle A by dilation about the point (1, 1) using a scale factor of -3/2. The negative scale factor reflects the image across the center of dilation, in addition to changing its size.

The same effect can be achieved by dilation by a factor of 3/2, then rotating the figure 180° (or reflecting it across the x- and y-axes), and translating it to its final position.

Whether you call the scale factor 3/2 or -3/2 depends on how it fits into the transformation of ∆A to ∆B.

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Answer:

 you would  have 84-.10 I think

Step-by-step explanation:

The angle of elevation of the ladder is approximately 78.7 degrees. The ladder reaches approximately 22.2 ft high on the building.

To find the angle of elevation of the ladder, we can use trigonometry. The angle of elevation is the angle between the ladder and the ground.

Given:

Length of the ladder (hypotenuse) = 23 ft

Distance of the base of the ladder from the base of the building (adjacent side) = 6 ft

To find the angle of elevation (θ), we can use the inverse tangent function (arctan) with the ratio of the opposite side to the adjacent side:

\(\theta = tan^{-1}(opposite/adjacent)\)

In this case, the opposite side is the height the ladder reaches on the building.

Using the Pythagorean theorem, we can find the height (opposite side):

\(Height^2 = Length of the ladder^2 - Distance of the base^2\\Height^2 = 23^2 - 6^2\\Height^2 = 529 - 36\\Height^2 = 493\\Height = \sqrt{493}\)

Now, we can calculate the angle of elevation:

\(\theta = tan^{-1}(opposite/adjacent)\\\theta = tan^{-1}(\sqrt{493} / 6)\)

Calculating this value, we find:

θ ≈ 78.7 degrees (rounded to one decimal place)

Therefore, the angle of elevation of the ladder is approximately 78.7 degrees.

To find how high the ladder reaches on the building, we substitute the calculated value of the height:

Height = \(\sqrt{493}\)

Height ≈ 22.2 ft (rounded to one decimal place)

Therefore, the ladder reaches approximately 22.2 ft high on the building.

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Answer:

up

Step-by-step explanation:

a is positive

Answer:

Hope this helps!! :)

Given expression is  \(x⁵/⁹\).

Recall to write the nth root of a number, we have to type root(n).

For example, to get\(³√4x\), type "\(root(3)(4x)\)".

We can write the expression x⁵/⁹ as follows:

\($$\frac{x^5}{9}$$\)

Let's rewrite the expression as:

\($$\frac{x}{\sqrt[9]{9}}^5$$\)

Let's write the nth root of a number by typing root(n).

Therefore, the final answer becomes:

\($$\frac{x}{root(9)(9)}^5$$\)

Therefore, the given expression in radical form is   \(\frac{x}{root(9)(9)}^5\)

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The answer is 18 ounces of salt in 20% solution should be mixed with 27 ounces of 10% solution to produce 45 ounces of 14% salt solution.

let x and y be the amount of 20% and 10% solutions respectively:

x + y = 45 ____eq.1

20%x + 10%y = 14% (45)

20/100x + 10/100 y = 14/100 (45)

0.2x + 0.1y = 0.14 (45)____eq.2

Rewrite eq.1 to (x=45-y) and plug that value into that of eq.2

0.2(45-y) + 0.1y = 6.3

9 - 0.2y + 0.1y = 6.3

-0.1y = -2.7

y = (-2.7) ÷ (-0.1)

y = 27

put the value of y in eq. 1

x + y = 45

x + 27 = 45

x = 45 - 27

x = 18

Therefore, 18 ounces of salt in 20% solution should be mixed with 27 ounces of 10% solution to produce 45 ounces of 14% salt solution.

Full Question:

How many ounces of a 20% salt solution should be mixed with a 10% salt solution to produce 45 ounces of a 14% salt solution?

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Number which produces an irrational number when multiplied by 1/2 is 2/3.

Any real number that cannot be written as the quotient of two integers, p/q, where p and q are both integers, is referred to as an irrational number. For instance, the square root of 2 cannot be expressed as an integer or a fraction. Additionally, if the value of the square root of 7 yields a value after the decimal point that neither terminates nor repeats, it will be an irrational number. The number 7 is an irrational number because its value, 2.64575131106, is non-terminating and non-repeating.

Given,

Number which produces an irrational number when multiplied by 1/2

We multiply 2/3 by 1/2

2/3 × 1/2

1/3

0.3333

which is an irrational number.

Number which produces an irrational number when multiplied by 1/2 is 2/3.

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To find two numbers whose sum is 11 and whose product is maximum, we can use a mathematical approach.

Let's denote the two numbers as x and 11 - x, where x represents the first number. The sum of these numbers is 11, so we can write the equation x + (11 - x) = 11. Simplifying this equation gives us 2x = 11, and solving for x results in x = 11/2 or 5.5. Therefore, the two numbers are 5.5 and 5.5.

To explain this answer, we can consider the properties of quadratic functions. When we multiply two numbers, their product is maximized when the numbers are equal. By representing one number as x and the other as 11 - x, we ensure that their sum is 11. We then set up an equation using the sum constraint and solve for x. In this case, we find that x = 5.5, indicating that both numbers are 5.5. As a result, their product is maximized at 30.25.

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Scalar projection of vector u onto v is 5 / √14 and vector projection of vector u onto v is (15i - 5j + 10k) / 14.

Given vectors u = i + 2j + 3k and v = 3i - j + 2k.

Scalar projection:

compvU = u.v / |v|

Vector projection:

projvU = (u.v / |v|²).v = ((u.v / v.v).v)

u = i + 2j + 3k and v = 3i - j + 2k.

The dot product of vectors u and v is given by,u.v = (1*3) + (2*(-1)) + (3*2) = 3 - 4 + 6 = 5

Magnitude of vector v is,|v| = √(3² + (-1)² + 2²) = √14

Scalar projection of vector u onto v is compvU = u.v / |v|= 5 / √14

Vector projection of vector u onto v is projvU = (u.v / |v|²).v = ((u.v / v.v).v)= ((5 / 14).(3i - j + 2k))= (15i - 5j + 10k) / 14

The scalar projection of u onto v is (7 / sqrt(14)), and the vector projection of u onto v is (3/2)i - (1/2)j + k. These calculations can be used to understand the relationship between the vectors u and v and to perform further computations involving these vectors.

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Answer:

Step-by-step explanation:

Sorry I can't explain how it is done. It is very difficult to explain on paper.

Answer:

O hrs and 30 minutes is the answer

Step-by-step explanation:

want proof?

Answer:

  about 0.04878 hours ≈ 2 minutes 56 seconds

Step-by-step explanation:

You want the time until a whale-watching boat and a whale meet if the boat is traveling south at 83 km/h and the whale is traveling north at 40 km/h when they start 6 km apart.

The speed at which the gap between the boat and the whale is closed is the sum of their respective speeds:

  closing speed = 83 km/h + 40 km/h = 123 km/h

The time it takes to close the 6 km gap is ...

  time = distance/speed

  time = (6 km)/(123 km/h) ≈ 0.04878 h

Converted to minutes and seconds, that is about ...

  0.04878 h ≈ 2 minutes 55.6 seconds

It will be about 2 minutes 56 seconds before the boat and whale meet.

__

Additional comment

NOAA recommends a distance of at least 100 yards be maintained between a boat and a whale. In some areas, the recommended distance is 400 yards when approaching head-on. The recommended boat speed is 15 knots or less, about 28 km/h.

Answer:

Not 100% sure, but I think it is #2

Step-by-step explanation:

Answer:

The fourth one

Step-by-step explanation: sorry if wrong

The total cost of the stethoscope, including sales tax, is $172.80.

To calculate the total cost of the stethoscope including sales tax, we need to add the sales tax amount to the original cost of the stethoscope.

Given that the cost of the stethoscope is $160.00 and the sales tax rate is 8% (or 0.08), we can calculate the sales tax amount as follows:

Sales tax amount = Cost of stethoscope * Sales tax rate

= $160.00 * 0.08

= $12.80

To find the total cost, we add the sales tax amount to the original cost of the stethoscope:

Total cost = Cost of stethoscope + Sales tax amount

= $160.00 + $12.80

= $172.80

Therefore, the total cost of the stethoscope, including sales tax, is $172.80.

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Answer: $0.95

Step-by-step explanation:

7.90 - 1.25 = 6.65

6.65 divided by 7 = 0.95

Answer:

6 work out sessions

Step-by-step explanation:

From the above question, we know that:

Jasmine has a goal to workout a total of at least 6 hours this week.

Her workout sessions are always 3/4 an hour long.

Hence: Her total workout sessions

3/4 hour = 1 workout session

6 hours = x

Cross Multiply

3/4 × x = 6 × 1

x = 6/3/4

x = 6 ÷ 3/4

x = 6 × 4/3

x = 8 work out sessions

We are told that:

She already worked out for 1 1/2 hours.

Hence: if :

3/4 hour = 1 workout session

1 1/2 hours = x

Cross Multiply

3/4 × x = 1 1/2

x = 1 1/2 ÷ 3/4

x = 3/2 ÷ 3/4

x = 3/2 × 4/3

x = 2 work out sessions

Therefore:

the minimum number of workout sessions she would need to complete in order to achieve her weekly goal is calculated as:

8 work out sessions - 2 work out sessions

= 6 work out sessions

Converting this to workout sessions

Step-by-step explanation:

my instagram account bdq.frk follow please

Part (c) is the correct option i.e. The total dealer's cost is $16588.36.

What is Percentage ?

Percentage, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolised as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

Given, Cost paid for car's options = 82 % $3,098 = $2540.36

           Cost paid for base price = 85 % $15,480 = $13158.

           Destination charge = $890

∴ The total dealer's cost will be :

 = Cost paid for car's options +  Cost paid for base price +  Destination charge

=  $2540.36 + $13158 + $890

= $16588.36.

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Step-by-step explanation:

The diagonal is the hypotenuse of a right triangle with legs 40 in and ? inches.    Use Pythagorean Theorem

54^2 = 40^2 + ? ^2

?^2 = 54^2 - 40^2

?^2 = 1316

? = 36.3 in

Answer: 36.3

Step-by-step explanation:

Answer:  641/2x 10-2 it is 3203

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

\(147 \times 4 \div 42 = 14\)

It would take 14 days  to build a similar house with 42 workers

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that  the number of days required to build is inversely proportional to with the number of workers.

One house was built in 147 days by 4 workers.

So,

147 x 4 = 588

Now the days to build a similar house with 42 workers

588/ 42 = 14

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Answer:

13.9 ft

Step-by-step explanation:

use Pythagoras theorem

surface²=7²+12²

surface²=193

surface=√193=13.89 ft≈13.9 ft

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Answer:

Tessa receives £60

Step-by-step explanation:

The ratio is 5:3 so 5+3=8 which is then what you use to divide 96

96/8=12

12x5(the 5 comes from the ratio for Tess) is 60 therefore she receives £60

Answer:

Step-by-step explanation:

Tesa and Vivienne share £96 in the ratio 5:3. How much does Tesa receive?​

96 : (5 + 3) = 12

12 * 5 = 60

Answer:

C x=40, y=30

Step-by-step explanation:

Remember the opposite side of parallelogram is the same

so angle C and angle A is the same.

3x=120

divide both sides by 3 and you get 40

All parallelogram equal to 180 degrees so to find y

180=2y+120

-2y=120-180

-2y=-60                   negative divide negative is positive.

y=30

To find the series solution for the differential equation y'' + 2xy' + 2y = 0, we can assume a power series solution of the form:

Now, substitute y(x), y'(x), and y''(x) into the differential equation:

∑(n=0 to ∞) aₙn(n-1) xⁿ⁻² + 2x ∑(n=0 to ∞) aₙn xⁿ⁻¹ + 2 ∑(n=0 to ∞) aₙxⁿ = 0

We can simplify this equation by combining the terms with the same powers of x. Let's manipulate the equation step by step:

We can combine the three summations into a single summation:

∑(n=0 to ∞) (aₙ₊₂(n+1)n + 2aₙ₊₁ + 2aₙ) xⁿ = 0

Since this equation holds for all values of x, the coefficients of the terms must be zero. Therefore, we have:

This is the recurrence relation that determines the coefficients of the power series solution To find the series solution, we can start with initial conditions. Let's assume that y(0) = y₀ and y'(0) = y'₀. This gives us the following initial terms:

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The word "and" in probability implies that we use the Multiplication rule.

The correct option is Option D.

The likelihood of both events A and B occurring, in accordance with the probability multiplication rule, is equal to the product of the probability of B occurring and the conditional probability of event A occurring given that event B occurs.

The relationship between two events is explained by the probability multiplication rule.

Set A∩B represents the events in which both events A and B have occurred for two events A and B related to a sample space S. Consequently, (A∩B) indicates that occurrences A and B happened at the same time. You can write the event A∩B as AB. Using the characteristics of conditional probability, the likelihood of event AB is calculated.

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The probability that a given student is called upon j times during the term

b(32,j,1/80) = (32/j)∗(1/80)j∗(79/80)(32−j)

Probability:

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).

given that

In a class of 80 students, the professor calls on 1 at random for a recitation in each class period

there are 32 class periods in a term

the probability that a given student is called upon j times during the term

b(32,j,1/80) = (32/j)∗(1/80)j∗(79/80)(32−j)

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