Gabriel’s father has a garden in the back yard. The dimension of the garden are shown here 7 3/4 and 2 2/3

Therefore , the solution of the given problem of volume comes out to be a) 30 cubic inches , b)rectangular prism  and c) cylinder volume is 108.6 cubic inches.

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The digits cm3 and in3 are two examples of cubic units. However, one can gauge an object's size using its bulk. Usually, the weight of an item is converted into mass measurements like kilogrammes or kilos.

Here,

a. By multiplying the rectangular prism toy's length, breadth, and height together, one can determine its volume:

Capacity is calculated using the formula LWH.

5 in. × 3 in. x 2 in.

thirty cubic inches of volume

Consequently, the rectangular prism toy has a capacity of 30 cubic inches.

b. I calculated the capacity of a rectangular prism using the following formula:

Capacity is calculated using the formula LWH.

c. The equation for a cylinder's volume is:

=> V = π x radius² x height

We can determine the radius using the following formula given that the cylindrical toy's height is 4 inches and its width, which is twice the radius, is 5.2 inches:

=> radius = circumference / 2.

=> radius=5.2 inches/two

=> radius: 2.6 inches

When we enter the numbers, we obtain:

Dimensions = 2.6 in x 2 in x 4 in

108.6 cubic inches of volume

Consequently, the cylindrical toy has a capacity of roughly 108.6 cubic inches.

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Answer:

Step-by-step explanation:

Since PQR is a triangle with QR = PQ, we have:

∠PQR = ∠QPR (since the angles opposite to equal sides are equal)

Let x be the measure of ∠QPR. Then:

∠PQR + ∠QPR + ∠R = 180° (sum of angles in a triangle)

x + x + 50° = 180°

2x = 130°

x = 65°

Therefore, the measure of ∠QPR is 65°.

Answer: B

Step-by-step explanation:

The length of the bar is doubled because it was stretched to twice the length of the original bar.

A multiplication equation that shows how the length is scaled is 2 × 8 = 16.

The length of the bar is halved because it was compressed to one-half the length of the original bar.

A multiplication equation that shows how the length is scaled is 1/2 × 8 = 4.

In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the length of the image (new figure) by the length of the pre-image (original figure):

Since the original bar has a length of 8 units, we can logically deduce that its length became doubled because it was expanded to twice the length of the original bar. Therefore, a multiplication equation to model this expansion is given by:

2 × 8 = 16.

Conversely, the original bar has a length of 4 units, we can logically deduce that its length was halved because it was shrunk to one-half the length of the original bar. Therefore, a multiplication equation to model this compression is given by:

1/2 × 8 = 4.

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Answer:

It's 5

Step-by-step explanation:

i tootk the test

Step-by-step explanation:

To solve the system of equations:

3x - 4y = 16

2x + 3y = 5

We can use either substitution or elimination method. Here, we will use the elimination method:

Multiply the second equation by 4 to get:

8x + 12y = 20

Now we can add this equation to the first equation:

3x - 4y + 8x + 12y = 16 + 20

Simplifying the left side and adding the right side, we get:

11x = 36

Dividing both sides by 11, we get:

x = 36/11

Substituting this value of x into the second equation, we get:

2(36/11) + 3y = 5

Multiplying through by 11 to eliminate the fraction, we get:

72/11 + 3y = 55/11

Subtracting 72/11 from both sides, we get:

3y = -17/11

Dividing both sides by 3, we get:

y = -17/33

Therefore, the solution to the system of equations is:

x = 36/11, y = -17/33

or in decimal form,

x ≈ 3.27, y ≈ -0.52

Answer:

18.8

Step-by-step explanation:

consider rounding off 7 that becomes 8

Answer:

18.8

Step-by-step explanation:

Yes...Thats the ans...

Therefore , the solution of the given problem of unitary method comes out to be P and R are separated by 5 units.

One may use this common convenience, already-existing variables, or all important elements from the original Bishop customizable question that adhered to a particular method to achieve the goal. If so, there will be another chance to get in touch with the object. If it doesn't, all of the crucial elements that make up an expression proof outcome will be lost.

Here,

The triangle formed by the points P, Q, and R in the provided diagram is right-angled.

We can determine the length of PR, the hypotenuse of this triangle, using the Pythagorean Theorem.

PQ² + QR² = PR²

The illustration shows that PQ and QR each equal four units.

By replacing these numbers, we obtain:

=> PR² = 4² + 3²

=> PR² = 16 + 9

=> PR² = 25

When we square the two edges, we obtain:

=> PR = √25

=> PR = 5

As a result, P and R are separated by 5 units.

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The solution of the arithmetic expression is 4 2/5.

option C.

An arithmetic expression is a combination of numbers, operators (such as addition, subtraction, multiplication, and division), and parentheses, which are used to indicate the order of operations. Arithmetic expressions can be evaluated or simplified using the rules of arithmetic, which specify how the various operations should be performed.

We can solve this arithmetic expression by performing the multiplication operation first and then adding the results.

(2 x 2) + (2 x 1/5)

= 4 + 2/5

= 20/5 + 2/5

= (20 + 2) / 5

= 22/5

= 4 2/5

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The complete question is below:

Find 2 × 2  +  2 1/5 = ?

A. 2 2/5

B. 4 1/5

C. 4 2/5

D. 5​

A line passing through the coordinates (2, 8) & (-2, k) does have a 34 slope. As a result, k has a value of 5.

The slope of a line governs its steepness. Rise over fall is a mathematical formula that describes slope.

We can construct an equation & solve for k using the slope formula:

if (x1, y1) & (x2, y2) are indeed the provided locations, slope is defined as (y2 – y1)/(x2 - x1).

Inputting the specified values results in:

¾ = (k - 8)/(-2 - 2) (-2 - 2)

By condensing this equation, we obtain:

3/4 = (k - 8)/(-4) (-4)

The result of multiplying all sides by -4 is:

-3 = k - 8

5 Equals k when we add 8 to both sides.

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Answer: 2.5 hours

Step-by-step explanation:

Let's call the number of signatures that Steve needs to collect "x". We know that Dirk has 20 signatures, so he needs to collect "x - 20" more signatures to have the same number as Steve.

We can set up an equation to represent this:

6h + 20 = 10h + x - 20

Simplifying this equation, we get:

x = 4h + 40

So, Steve needs to collect 4 signatures more per hour than Dirk to eventually collect the same number of signatures. We can solve for "h", the number of hours it will take for them to have the same number of signatures:

6h + 20 = 10h + (4h + 40)

6h + 20 = 14h + 40

8h = 20

h = 2.5

So, it will take 2.5 hours for Dirk and Steve to have collected the same number of signatures.

Answer:

There are 64 (4/ (1/16)) 1/16 of an inch in 4 inches.

The slope of the image of the original line y = 2x - 4 after the transformation (x,y) (-x, -y) is -2.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of the original line y = 2x - 4 is 2.

To find the slope of the image after the transformation, we can apply the transformation rule to two points on the original line, and then find the slope of the line passing through the images of those two points.

Let's choose two points on the original line:

Point 1: (0, -4)

Point 2: (1, -2)

Now we apply the transformation rule to each of these points:

Point 1 image: (-0, -(-4)) = (0, 4)

Point 2 image: (-1, -(-2)) = (1, 2)

The images of these two points lie on the line y = -2x + 4. The slope of this line is -2.

Therefore, the slope of the image of the original line y = 2x - 4 after the transformation (x,y) (-x, -y) is -2.

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The required graph is attached.

An organized representation of the data is all that the graph is. It facilitates our understanding of the facts. Data is the term used to describe the numerical information obtained through observation.

The modification looks like this.

Combining two transformations results in the transformation of

h(x) to -h(x) -4.

1. An X-axis-centered reflection. Every point (x, y) in h(x) is transformed into (x', y'), where x' = x and y' = -y. Hence, (x, y) (x, -y)

2. A 4-unit translation of each reflected point, where the x value remains constant, but the y value is translated downward to become y'-4 = -y -4

Every coordinate (x, y) in h(x) will be transformed to the following as a result of both transformations: (x, -y -4)

Given that the graph is made up of two straight lines that intersect at the origin, all we need to do is select any three points in h(x), determine their transformed coordinates, and then connect them using straight lines: h(x0 -h(X) - 4 (-2, 4) (-2, -4-4) =(-2, -8) (0, 0) (0, -0 - 4) =(0, -4) (4, 2) (4, (4, -6)

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Answer:

From what I remember, words like "at least" mean that that's the minimum, so it can be more than that, but not less than. So I believe the inequality that would best represent this is n ≥ 4.

Answer:

n>=4

Step-by-step explanation:

False. The value of money does not reside solely in the physical materials (paper or metal) from which it is made.

In modern economies, money has value because it is widely accepted as a means of exchange for goods and services. The value of money is derived from the trust people have in its ability to facilitate transactions and store value over time.

The physical materials used to make money (paper or metal) are simply a medium of exchange that represent the value of the currency. The value of a currency can fluctuate based on a variety of factors such as inflation, interest rates, and global economic conditions.

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The value of x is found by using the similarity theorem to create a proportion of the sides of the similar triangle, such that: x = 6 cm.

Both triangles in the image above are similar to each other based on the AA similarity theorem, which states if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. This means that the corresponding sides of the triangles are proportional.

Therefore, we will have:

x/42 = 4/28

Cross multiply:

28x = 168

x = 168/28

x = 6 cm

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Willka would need 6 liters of paint to cover an area of 27 square meters according to the ratio.

A ratio is a comparison of two or more values or quantities. It is a way of expressing the relationship between two or more quantities in a mathematical form. A ratio is typically expressed in the form of "a:b" or "a to b", where a and b are two values being compared.

According to question:

To find the coverage per liter of paint, we can divide the total area covered by the amount of paint used.

In this case, we can divide 13.5 m² by 3 L:

Coverage per liter = 13.5 m² / 3 L = 4.5 m²/L

This means that with 1 liter of paint, Willka can cover an area of 4.5 square meters.

If we know the area to be painted, we can use this ratio to determine how much paint is needed.

For example, if we want to paint an area of 27 square meters, we can calculate:

Paint needed = area to be painted / coverage per liter = 27 m² / 4.5 m²/L = 6 L

So Willka would need 6 liters of paint to cover an area of 27 square meters.

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The distance between the points z₁ = 3+7i and z₂ = -5-2i is 12.04.

Distance is the total movement of an object without any regard to direction.

To calculate the distance between the two complex expression, we use the

formula below

Formula:

From the question,

Given the question

Where:

Substitute these values into equation 1

Hence, the distance is 12.04.

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The possible ways of possibilities might refer to the different interpretations or perspectives that could be applied to a particular idea or concept. For instance, a philosopher might consider the different ways in which free will could be defined or understood.

The possible ways of possibilities might refer to the different ways in which a particular artistic vision could be realized. For instance, a filmmaker might consider the different ways in which a particular scene could be shot or edited to convey a certain emotion or message.

There are three possible ways to show off:

Cigar only

Watch only

Cigar and watch

To show off a cigar only, you have six options. To show off a watch only, you have four options. To show off both, you have six options for the cigar and four options for the watch, giving a total of  [tex]6 \times 4 = 24[/tex] options.

Therefore, So the total number of possibilities to show off is: 6 (cigar only) + 4 (watch only) + 24 (cigar and watch) =  [tex]34[/tex] Possibilities.

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Answer:

Step-by-step explanation:

We know that the area of the plane shape is given by A = (10x - 2) cm^2, and we also know that:

A is not greater than or equal to 12 cm^2 (i.e., A < 12), and

A is not less than 2 cm^2 (i.e., A > 2).

To find the smallest possible area of the shape, we need to find the smallest possible value of x that satisfies these conditions.

From the given conditions, we have:

10x - 2 < 12

10x < 14

x < 1.4

and

10x - 2 > 2

10x > 4

x > 0.4

Therefore, the smallest possible value of x that satisfies both conditions is:

0.4 < x < 1.4

To find the smallest possible area, we can substitute the lower bound of x into the area formula:

A = (10x - 2) cm^2

A = (10 × 0.4 - 2) cm^2

A = 2 cm^2

Therefore, the smallest possible area of the shape is 2 cm^2.

Answer:

First, we need to calculate the total number of payments Ryan will make over 10 years, which is 10 years x 12 months/year = 120 months.

Next, we can use the formula for the present value of an annuity to calculate the maximum price of the boat:

PV = PMT x [1 - (1 + r/n)^(-nt)] / (r/n)

where PV is the present value, PMT is the monthly payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

Plugging in the values we have:

PMT = $500

r = 0.13

n = 12 (since the loan is monthly)

t = 10

PV = $500 x [1 - (1 + 0.13/12)^(-12x10)] / (0.13/12)

PV = $44,484.72

Therefore, the maximum price for a boat that Ryan's budget can afford, rounded to the nearest hundred dollars, is $44,500.

The area of the triangles are

1. 105.84 cm²

2. 210 in²

3. 126 ft²

How to find the area of the triangles

The formula for the area of a triangle is:

Area = (1/2) * base * height

where

Using the formula we have that

1)

base = 16.8 and height = 12.6

= 0.5 * 16.8 * 12.6

= 105.84 cm²

2)

base = 20 in + 8 in = 28 in and height = 15

= 0.5 * 28 * 15

= 210 in²

3)

base = 12 ft and height = 21 ft

= 0.5 * 12 * 21

= 126 ft²

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Work Shown:

1 ft = 12 inches

3 ft = 3*12 = 36 inches

1 yard = 3 ft = 36 inches

8 yards = 8*36 = 288 inches

x = number of presents

9x = amount of ribbon

9x = 288

x = 288/9

x = 32

Taking the quantities by volume of each potion into consideration, we can respectively answer 250ml (A), 40 mL of red and 60 mL of blue potion (B), and no (C).

For question A: Let x be the amount of red potion (in mL) that must be added to 500 mL of blue potion to produce a potion that is 40% magical syrup by volume. The amount of magical syrup in the red potion is 0.6x, and the amount of magical syrup in the blue potion is 0.3(500) = 150. The total amount of syrup in the final mixture is 0.4(500 + x), and the amount of magical syrup in the final mixture is 0.4x + 150. We can set up the equation:

0.4x + 150 = 0.4(500 + x)

Solving for x, we get x = 250 mL. Therefore, 250 mL of red potion must be added to 500 mL of blue potion to produce a potion that is 40% magical syrup by volume.

For question B: Let x be the amount of red potion (in mL) and y be the amount of blue potion (in mL) that must be combined to produce 100 mL of a potion that is 54% magical syrup by volume. The amount of magical syrup in the red potion is 0.6x, and the amount of magical syrup in the blue potion is 0.3y. The total amount of syrup in the final mixture is x + y, and the amount of magical syrup in the final mixture is 0.6x + 0.3y. We can set up the equations:

x + y = 100 (equation 1)

0.6x + 0.3y = 0.54(100) (equation 2)

Solving for x and y, we get x = 40 mL and y = 60 mL. Therefore, 40 mL of red potion and 60 mL of blue potion must be combined to produce 100 mL of a potion that is 54% magical syrup by volume.

For question C: No, there does not exist a combination of red potion and blue potion that can produce a potion that is 75% magical syrup by volume. The amount of magical syrup in the red potion is 60%, which is more than twice the amount of magical syrup in the blue potion (30%). Therefore, any combination of the two potions will always have less than 60% magical syrup by volume.

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Answer: 120

Step-by-step explanation: When 50 is divided by half, which is 100, and added 20 to it, it is 120

Answer:

45

step by step explaination:

Think about what same 2 numbers that, when added together make fifty. 25! so when you divide 50 by half, if equals 25. Then, add 25+20 to equal 45 :)

Answer:

n=5

Step-by-step explanation:

First cross multiply to get:

36n = 180

Divide both sides by 36

36n/36 = 180/36

n=5

Answer: The height of Nasim's kite above the ground is 51.79 feet

Step-by-step explanation

Let h represent the height from Nasim hand to the kite, hence:

sin(28) = h / 105

h = 49.29

Kite height above the ground = 2.5 + 49.29 = 51.79 feet

The height of Nasim's kite above the ground is 51.79 feet

Answer:

The height of Nasim kite above the ground is 51.79 feet

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let h represent the height from Nasim hand to the kite, hence:

sin(28) = h / 105

h = 49.29

Kite height above the ground = 2.5 + 49.29 = 51.79 feet

The height of Nasim kite above the ground is 51.79 feet