Find the volume of the rectangular prism.
7 cm
1
9 c
3 cm

Answer:

303

Step-by-step explanation:

add all of them and you get 303, hope this helps :)

Answer:

Vertical. A vertical is an alignment in which the top is always above the bottom. It is a property of two or more points in which if a point is directly below the ...

Step-by-step explanation:

A diagonal of a rectangle will intersect the same number of squares as the length of the rectangle. The rectangle has a length of 7 squares and a width of 4 squares, so the diagonal will intersect 12 squares.

A diagonal of a rectangle will always intersect the same number of squares as the length of the rectangle. In this case, the rectangle has been outlined on a grid paper with dimensions of 7x4. This means that the length of the rectangle is 7 squares and the width is 4 squares. Therefore, the diagonal of this rectangle will intersect 12 squares in total. This is because the length of the rectangle is greater than the width and so the diagonal must intersect the entire length of the rectangle and all of the squares the width intersects. As a result, the diagonal of this rectangle will intersect 12 squares.

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Answer:

2 1/6

Step-by-step explanation:

9 3/4÷ 4 1/2

9×4+3/4÷ 4 1/2

36+3/4÷ 4 1/2

39/4÷ 4 1/2

39/4÷4×2+1/2

39/4 ÷ 8+1/2

39/4÷9/2

39/4× 2/9

39×2/ 4×9

78/4×9

78/36

13/6

2 1/6

The length of the building in the scale drawing is; 31. 25 Inches

From the given, we have that Scale drawing was used 0. 25 inches represents 2 feet

The length of the building = 250 feet

Then, 0. 25 inches = 2 feet

Then, x inches = 250 feet

Now cross multiply

x × 2 = 0. 25 × 2500

Multiply through, we have;

2x = 62. 5

Make 'x' the subject by dividing both sides by 2

2x/2 = 62. 5/ 2

x = 31. 25 Inches

Thus, the length of the building in the scale drawing will be; 31. 25 Inches.

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The profit for selling 83 bumper stickers is $302.

The profit for selling 83 bumper stickers the revenue for selling x bumper stickers is given by f(x) = 5x dollars and the profit is $30 less than 80% of the revenue.

To solve this problem need to apply the formula for profit and revenue.

The revenue for selling 83 bumper stickers by substituting x = 83 in the equation f(x) = 5x:

Revenue = f(83)

= 5(83)

= 415 dollars

The profit using the formula:

Profit = 0.8 × Revenue - 30

Substituting the value of revenue, we get:

Profit = 0.8 × 415 - 30

Profit = 332 - 30

Profit = 302

The profit for selling 83 bumper stickers is $302.

The concepts of revenue and profit in business.

Revenue is the total amount of money earned from selling goods or services while profit is the amount of money earned after subtracting the costs from the revenue.

The revenue function and a formula for calculating profit allowed us to find the profit for a specific number of sales.

Understanding these concepts and their applications can help individuals and businesses make informed decisions and improve their financial performance.

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Answer:

3.36:45=0,8

4.40:32=1,25

536:45=0,8

6.48:50=0,96

Hope it helps and likes it

Step-by-step explanation:

3- sin Z = opp/hyp

  sin Z = 27/45

   Z = sin-¹(27/45)

   Z = 37

4- tan C = opp/adjacent

   tanC = 24/32

   C = tan -¹ ( 24/32)

   C = 36.87 ( or 37)

5-  cos X = adj/hyp

    cos X= 36/45

    X = cos-¹ (36/45)

   X = 37

6- sin C = opp/hyp

   sin C = 14/48

   C = sin -¹ (14/48)

   C= 17  (or 16.96)

The value of x is 44° if the given figure below are two parallel lines and

the third line is intersecting them.

Two lines in the same plane that are equally spaced apart and never cross each other are referred to in geometry as parallel lines. Both vertical and horizontal can be used. A zebra crossing, rows of notebooks, and nearby railroad tracks are just a few instances of parallel lines that we encounter every day. Coplanar, straight lines that don't intersect anywhere are considered parallel lines in geometry. Curves do not touch or intersect when they are parallel to one another and keep a predetermined minimum distance between them.

From the diagram,

x+136°=180°

x=180°-136°

x=44°

Therefore, the value of x is 44° if the given figure below are two parallel

lines and the third line is intersecting them.

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Answer:

STEP 1: Change f (x) to y.

STEP 2: Interchange x and y in the equation. x → y. y → x.

STEP 3: Isolate the exponential expression on one side (left or right) of the equation.

Step-by-step explanation:

Answer:

the negative 5 is showing that you are losing grain in the silo because you are letting some out.

Answer: 184.00

Step-by-step explanation: you have to see how many times are there 3 months in one year you divide 12 divided by 3 which equals 4 and 46 times 4

Answer: $184,00

Step-by-step explanation

Answer:

irratiional because it is repeating.  A rational number is a positive or negative whole number without fractions or decimals.

Step-by-step explanation:

7.4343 is a repeating decimal so it is irrational

Answer:

\(\bold{ 9x = (x+35)\times 5 }\)

Step-by-step explanation:

Jim completed half of the floor in 9 hours.

Let the rate of Jim = \(x\) tiles/hr

So, number of tiles that Jim lays in 9 hours = Rate of Jim multiplied by number of hours i.e. \(9 \times x\) ..... (1)

Let \(y\) tiles/hr be the rate at which Pete lays the tiles.

As per the given question, Pete can lay 35 more tiles per hour than Jim.

i.e. \(\bold{ y =x+35}\)

It is given that half of the floor is done by Jim and other half by Pete.

So, we can say that number of tiles for both of them are equal.

Number of tiles by Pete = Rate of Pete \(\times\) Number of hours = \((x+35) \times 5\)...(2)

Now, we can equate the equations (1) and (2) because the number of tiles are same.

i.e.

The equation that we can use is:

\(\bold{ 9x = (x+35)\times 5 }\)

For many hotels, including the Grand Hotel Toplice, the price of a room will fluctuate depending on  the time of year. Option B

The rates of hotel rooms tend to fluctuate depending on the demand during different seasons and times of high travel activity.

Hotels have a tendency to increase their room rates during peak tourist seasons or notable holiday periods, namely summer vacations or significant local events.

During times when there is less demand or fewer guests, prices may be decreased in order to entice visitors. The demand for hotel rooms and subsequent price changes can be impacted by factors such as climate, nearby activities, and cultural festivities specific to certain periods.

Generally, the room rates at hotels are not directly influenced by additional elements like the individual's gender, nationality, or the time of day.

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Using the set builder notation, we can write; {-6 <x < 21}.

In mathematics, we use the set builder notation to decide the condition that must be satisfied under a given provision. In this case, the condition is that the set of integers less than -6 or greater than 21 .

In effect, we are saying that the integer must lie between -6 and 21 hence using the set builder notation, we can write; {-6 <x < 21}.

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The points on the ellipse 4x^2 + y^2 = 4 that are farthest away from the point (1, 0) are (x, y) = (0, -2) with the smaller y-value and (x, y) = (0, 2) with the larger y-value.

The ellipse equation is given as 4x² + y² = 4. We are required to find the points on this ellipse that are farthest away from the point (1, 0). Solution: Given, the equation of ellipse 4x² + y² = 4Putting (1, 0) on the equation, we get; 4(1)² + (0)² = 4 ⇒ 4 + 0 = 4, which is a point on the ellipse. So, (1, 0) is on the ellipse. Hence, we are required to find the point on the ellipse that is farthest away from the point (1, 0).Let's take the equation in the form of x²/a² + y²/b² = 1.4x² + y² = 4 => x²/(4/√4) + y²/(4/1) = 1Let a = 2/1 and b = 2/√4 = 1Hence, the semi-major axis is 2 and semi-minor axis is 1.We know that the distance between two points P(x1, y1) and Q(x2, y2) is given by √[(x2 − x1)² + (y2 − y1)²].For the farthest point from the given point (1, 0), we need to find the point on the major axis that intersects with the ellipse. This point will be on the top-right and bottom-left of the ellipse, at a distance of a from the center. And, the distance between this point and (1, 0) will be a distance of c from the center. As we have the value of a, we need to find c. We know that the value of c is given by √(a² − b²).Hence, c = √(a² − b²) = √(4 − 1) = √3.Now, let's find the farthest point from (1, 0) using the formulae above.We have a = 2 and c = √3. Therefore, the coordinates of the required points are:(x, y) = (1, √(3)) and (1, −√(3))So, the required points on the ellipse are (1, √(3)) and (1, −√(3)).Hence, (x, y) = (smaller y-value) is (1, −√(3)) and (x, y) = (larger y-value) is (1, √ (3)).

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The two points on the ellipse that are farthest away from (1,0) are (-1,0) and \(( \frac{ - 1}{3} , 2 \sqrt( \frac{2}{3})) \: or \: (\frac{ - 1}{3} , - 2 \sqrt( \frac{2}{3})) \)

How to find the points on the ellipse?

To find the points on the ellipse that are farthest away from the point (1,0), we first need to find the distance between the point (1,0) and any point (x,y) on the ellipse. The distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by the formula:\(d = \sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)\)

Using this formula, we can find the distance between (1,0) and any point (x,y) on the ellipse 4x² + y² = 4 as:\(d = \sqrt((x - 1)^2 + y^2)\)

To find the points on the ellipse that are farthest away from (1,0), we need to maximize this distance function subject to the constraint 4x² + y² = 4. To do this, we can use the method of Lagrange multipliers.

Let f(x,y) = (x - 1)² + y² be the distance function and g(x,y) = 4x² + y² - 4 be the constraint function. The Lagrange function is given by:

L(x,y,λ) = f(x,y) - λ g(x,y)

Taking the partial derivatives of L with respect to x, y, and λ and setting them to zero, we get:

2(x - 1) - 8λx = 0

2y - 2λy = 0

4x² + y² - 4 = 0

From the second equation, we get y(1 - λ) = 0, which gives us two cases:

Case 1: y = 0

From the third equation, we get 4x² = 4, which gives us x = ±1. Therefore, the two points on the ellipse with y = 0 that are farthest away from (1,0) are (1,0) and (-1,0).

Case 2: λ = 1

Substituting λ = 1 into the first and third equations, we get:

2(x - 1) - 8x = 0

4x² + y² - 4 = 0

Simplifying the first equation, we get x = -1/3. Substituting this into the second equation, we get \(y = ±2 \sqrt( \frac{2}{3})\)

. Therefore, the two points on the ellipse with λ = 1 that are farthest away from (1,0) are (-1/3, 2sqrt(2)/3) and \((-1/3, -2 \sqrt \frac{2}{3})\).

Thus, the two points on the ellipse that are farthest away from (1,0) are (-1,0) and

\(( \frac{ - 1}{3} , 2 \sqrt( \frac{2}{3})) \: or \: (\frac{ - 1}{3} , - 2 \sqrt( \frac{2}{3})) \)

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Correct question is "find the points on the ellipse 4x²+ y² = 4 that are farthest away from the point (1, 0). (x, y) = (smaller y-value) (x, y) = (larger y-value)."

Answer:

Solution  = = 5

Step-by-step explanation:

1. Rearrange Terms

100 + 30x = 50x

30x + 100 = 50x

2. Subtract 100 from both sides

3. Simplify

4. Subtract 50x from both sides

5. Simplify

Please let me know if you need anymore help!

Thank You and Good Luck! :)

Answer:

36

Step-by-step explanation:

Trial and error

Two consecutive odd numbers.

I chose 17 and 19

19 + 15 = 34, which is twice the first number.

The sum of the two numbers is 17 + 19 = 36

Answer:T

Step-by-step explanation: Every Input should correspond to exactly one output. Every input should only have one output. If 2 outputs correspond to the same # for the input, then it is not a function like in this example where 4 and -4 correspond to one input # which is 3 and the same with the 5's

Option D: T

A relation is simply relating or mapping one item of domain set to any number of items of the range set.

When the number of items the domain values are mapping to is limited to only 1, then that type of relation is called  as function.

For given tables, all the first three tables are function as no single value of x has two values.

But looking at the table T,

the value of x = 3 has y = 4 and y = -4.

This tells that number x  = 3 is related to two values in the range which shows that its not a function but mere a relation.

Thus answer is T which is shown by Option D : T

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We know that y - x^2 is a parabola with a vertex at (0, 0).

So if we move it 5 units to the right and 3 units down, the vertex is at (5, -3).

Since it gives you a chart, you can plug in values for x and solve for g(x), and you will eventually get a graph that looks like a parabola with vertex at (5, -3).

The balance of the unsubsidized loan at the time of graduation is $3,691.10.

Given:

Principal amount = $2,560

Interest rate = 6.8% = 0.068

Time period = 6 months

We can use the formula for compound interest to calculate the future value:

\(Future\; Value = P (1 + \dfrac{Interest Rate}{Number of Periods}) ^{(Periods * Time )\)

Substituting the value back into the formula as

Future Value = \($2,560 (1 + \dfrac{0.068}{12} )^{(12 * 6)\)

                      = \($2,560 (1 + 0.00566667)^{(72)\)

                      = \($2,560 (1.00566667)^{(72)\)

                      = $2,560 * 1.44044291

                       = $3,691.10

Therefore, the balance is $3,691.10.

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Answer:

1. SSS

2. SAS

3. SAS

4. 1?

5. SSS

Step-by-step explanation:

Domain (from X-axis):  

Range (from Y-axis):

The range of the exponential function y based on its equation and the context of the problem is a set of positive real numbers less than the initial value of 62,150, representing the decreasing value of the car over time.

The given function represents the depreciation of Morgan's car over time, where x represents the number of months since the car was purchased. The function is y = 62,150 * (0.9999)^x.

To determine the range of the exponential function y, we need to consider the context of the problem. In this case, the range represents the possible values for the car's depreciation, or the value of y.

The base of the exponential function is 0.9999, which is less than 1. When a value between 0 and 1 is raised to a positive power, it decreases exponentially as the power increases. Therefore, as x (the number of months) increases, the value of y (the car's depreciation) decreases.

Since the base is less than 1, the range of the exponential function y is also less than the initial value of 62,150. As x approaches infinity, the value of y approaches 0, but it will never actually reach 0.

In practical terms, the range of the exponential function represents the decreasing value of the car over time. It indicates that the car's depreciation is continuous and will approach zero but will never completely reach zero.

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Answer:

300

Step-by-step explanation:

a. we can express C as C = 1000h + x(20 + 25h). b. e can express h as a function of x as h = k/x. c. the optimal number of firefighters depends on the nature of the fire and the firefighting equipment used.

A. The cost of the fire, C, can be expressed as the sum of the cost of the lost timber and the cost of the firefighters. The cost of the lost timber is given by 1000h, and the cost of the firefighters is given by the product of the number of firefighters (x), the total hours worked (h), and the cost per firefighter (20 + 25h). Therefore, we can express C as:

C = 1000h + x(20 + 25h)

B. We are given that x firefighters can stop the fire in 0 hours, which means that the rate at which the fire is extinguished is proportional to the number of firefighters. Therefore, we can express h as a function of x as follows:

h = k/x

where k is a constant of proportionality that depends on the nature of the fire and the firefighting equipment.

C. To find the number of firefighters that should be used to minimize the cost of the fire, we need to find the value of x that minimizes the function C. To do this, we can take the derivative of C with respect to x and set it equal to zero:

dC/dx = 20 + 25h - k/x^2 = 0

Substituting the expression for h in terms of x, we get:

20 + 25(k/x^2) - k/x^2 = 0

Simplifying, we get:

k/x^2 = 20/5

x^2 = k/4

This shows that x should be inversely proportional to the square root of k. Since k is a constant that depends on the nature of the fire, we cannot determine its value without additional information. However, we can conclude that as k increases, the optimal number of firefighters decreases, and as k decreases, the optimal number of firefighters increases. Therefore, the optimal number of firefighters depends on the nature of the fire and the firefighting equipment used.

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Answer:

70 - 20x = 60 - 15x

Solution:

x = 2

Step-by-step explanation:

The problem said to let x = number of pizzas purchased.

So at Josh's place 1 pizza is 20, 2 is 40, 3 is 60, etc. The mathy way to write is 20x... <<that's 20 times the number of pizzas. It tells us the dollar amount spent on pizzas. His gift card is $70. We'll subtract what he spends on pizzas from his total original amount 70.

70 - 2x

For Jessica, its the same logic, but her gift card is $60 and the pizzas are 15 each. Total spent on pizzas is 15x. Her balance will be

60 - 15x

The question wants us to find out when these to people have the same balance of their card.

70 - 20x = 60 - 15x

This is what is asked for in the question. Below is how to solve it (don't know if you need this)

minus 60 from both sides

10 - 20x = -15x

Add 20x to both sides.

10 = 5x

Divide by 5

2 = x

This means when Josh and Jess have each bought TWO pizzas, they will both have $30 left on each of their cards.

The distance between the two parallel sides of the trapezium is 8 cm.

A trapezium is a convex quadrilateral with exactly one pair of opposite sides parallel to each other.

The area of a trapezium is expressed as:

Area = 1/2 × ( a + b ) × h

Where a and b are base a and base b, h is height.

Given that:

Area of the trapezium = 36 cm²

Base a = 3 cm

Base b = 6 cm

Height h =?

Plug the given values into the above formula and solve for height:

Area = 1/2 × ( a + b ) × h

36 = 1/2 × ( 3 + 6 ) × h

36 = 1/2 × ( 9 ) × h

36 = 4.5 × h

h = 36 / 4.5

h = 8 cm

Therefore, the height of the trapezium is 8 cm.

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\(\\ \sf\longmapsto f(2+h)\)

\(\\ \sf\longmapsto 4(2+h)-3\)

\(\\ \sf\longmapsto 4h+8-3\)

\(\\ \sf\longmapsto 4h+5\)

Based on an interest rate of 8.21% and a duration of 8 years, it will be determined which Direct Benefit project will be accepted.

To determine which Direct Benefit project would be accepted, we need to compare the present value (PV) of each project. The PV represents the current value of future cash flows, taking into account the interest rate and time period.

Let's evaluate each project individually:

1. Project A: The PV of Project A can be calculated using the formula PV = FV / (1 + r)^n, where FV is the future value, r is the interest rate, and n is the number of years. If the PV of Project A is greater than zero, the project will be accepted.

2. Project B: Similarly, we calculate the PV of Project B using the same formula. If the PV of Project B is greater than zero, the project will be accepted.

3. Project C: Again, we calculate the PV of Project C using the formula. If the PV of Project C is greater than zero, the project will be accepted.

By comparing the PV values of all three projects, we can determine which project(s) will be accepted. The project(s) with a positive PV will be considered financially viable, while the one(s) with a negative PV will not be accepted.

Please provide the specific details of the cash flows or any additional information related to the projects in order to calculate the PV and provide a definitive answer on which project(s) will be accepted.

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The correct statement is :David started at 0 instead of 2

A number line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, for example, plotting a point.

Given here: In a number line the interval (-5,5) is marked and 2 to 5 is 3

The right steps are

Add 3 to 2 to obtain the required number as there are 3 spaces between 2 and 5

Thus 2+3=5 which is the required answer

but David addes 2-3=-1 which is incorrect.

Hence, David started at 0 instead of 2

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