what is the area of square HIJK

Final answer:

The volume of a cylinder with a radius of 4 units and a height of 8 units is 401.92 cubic units, calculated using the formula V = πr²h and rounding to the nearest hundredth.

Explanation:

Calculating the Volume of a Cylinder

To find the volume of a cylinder, we can use the formula V = πr²h, where 'V' represents the volume, 'r' is the radius, and 'h' is the height of the cylinder. Since you have provided that the radius (r) is 4 units and the height (x) is 8 units, we can substitute these values into the formula as follows:

V = 3.14 × (4 units)² × 8 units

First, we calculate the radius squared (4 units)²:

(4 units)² = 16 units²

Now we multiply this by the height and π as given:

V = 3.14 × 16 units² × 8 units

V = 3.14 × 128 units³

V = 401.92 units³

Therefore, the volume of the cylinder is 401.92 cubic units, rounded to the nearest hundredth.

The area of Dominic's trapezoid-shaped bench seat is 11.25 square feet. This is calculated using the trapezoid area formula with given bases of 5 and 4 feet and a height of 2.5 feet.

To find the area of the seat of Dominic's bench, which is in the shape of a trapezoid, we use the formula for the area of a trapezoid:

Area = 1/2 × (Base1 + Base2) × Height

In this case:

Substitute these values into the formula:

Area = 1/2 × (5 + 4) × 2.5

Area = 1/2 × 9 × 2.5

Area = 4.5 × 2.5

Area = 11.25 square feet

Thus, the area of the trapezoid-shaped seat is 11.25 square feet.

Here are the steps to follow:

The LCD of [tex]\( \frac{4}{6} \)[/tex] and [tex]\( \frac{5}{7} \)[/tex] is [tex]42[/tex]. This is because [tex]42[/tex] is the smallest number that both [tex]6[/tex] and [tex]7[/tex] divide into evenly, ensuring that [tex]\( \frac{25}{6} \)[/tex] and [tex]\( \frac{39}{7} \)[/tex] can be expressed with a common denominator of [tex]42.[/tex]

1. Convert [tex]\( 4 \frac{1}{6}[/tex]  to an improper fraction:

[tex]\[ 4 \frac{1}{6} = \frac{4 \times 6 + 1}{6} = \frac{24 + 1}{6} = \frac{25}{6} \][/tex]

2. Convert [tex]\( 5 \frac{4}{7} \)[/tex] to an improper fraction:

[tex]\[ 5 \frac{4}{7} = \frac{5 \times 7 + 4}{7} = \frac{35 + 4}{7} = \frac{39}{7} \][/tex]

Now, the fractions [tex]\( \frac{25}{6} \)[/tex] and [tex]\( \frac{39}{7} \)[/tex] need to have a common denominator to find the LCD.

Finding the Least Common Denominator (LCD)

To find the LCD, we need to determine the least common multiple (LCM) of the denominators [tex]6[/tex] and [tex]7[/tex]

The prime factorization of [tex]6[/tex] is [tex]\( 2 \times 3 \).[/tex]

The prime factorization of [tex]7[/tex] is [tex]\( 7 \).[/tex]

The LCM of [tex]6[/tex] and [tex]7[/tex] is [tex]\( 6 \times 7 = 42 \).[/tex]

Verify and Convert to Common Denominator:

Convert both fractions to have a denominator of [tex]42[/tex]

[tex]\[ \frac{25}{6} \times \frac{7}{7} = \frac{175}{42} \][/tex]

[tex]\[ \frac{39}{7} \times \frac{6}{6} = \frac{234}{42} \][/tex]

Now, [tex]\( \frac{25}{6} \) converts to \( \frac{175}{42} \) and \( \frac{39}{7} \) converts to \( \frac{234}{42} \).[/tex]

The Putri turned 36 degrees to her left should she turn before walking home if Putri is searching for a secret cave that she knows is 3.72 kilometers from her home. Starting from her home, she walks 2.60 kilometers in a straight line before coming upon a large rock.

The triangle can be defined as a three-sided polygon in geometry and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

We have:

The total distance between cave to home AC = 3.72 km

The distance she walks AB = 2.60 km

The angle of turn = 58°

As we can see in the triangle ABC we can apply the sin law:

[tex]\rm \frac{AB}{sinx} = \frac{AC}{sin58\°}[/tex]

[tex]\rm \frac{2.6}{sinx} = \frac{3.72}{sin58\°}[/tex]

sinx = 0.5927

x = 36.35 ≈ 36°

Thus, the Putri turned 36 degrees to her left should she turn before walking home if Putri is searching for a secret cave that she knows is 3.72 kilometers from her home. Starting from her home, she walks 2.60 kilometers in a straight line before coming upon a large rock.

Learn more about the triangle here:

brainly.com/question/25813512

#SPJ3

Putri should turn 122 degrees to her left when facing the big rock to head back to her home. This direction aligns her with the original path she took to reach the cave.

To determine the number of degrees to her left Putri should turn, we need to analyze her movements using the angles involved.

When Putri is in the cave facing the large rock, to get back to her home, she needs to turn in the opposite direction of her initial right turn:

Putri should turn 122 degrees to her left when facing the big rock to head back to her home.

If buying a dozen bagels for $2.39 also gets an additional bagel for free, the cost per bagel when rounded to the nearest cent is $0.18.

The subject of your question is on the topic of unit cost. In this case, we will be calculating the cost per bagel when you buy a dozen bagels for $2.39 and get an additional bagel for free.

https://brainly.com/question/29355214

#SPJ12

Answer:

Answer X = 67

Step-by-step explanation:

so what you do is

180 - 46 = 134

then you devide 134 by 2 which is

134/2 = 67

Answer X = 67

please give me Brainliest  if this was helpful, or a thankyou

Answer:

Out of the options given prior to the question, the graph that is wider than the graph y = 3x^2 + 2 would be B) y = 0.5x^2 + 1. Hope we helped! :D

Answer:

Circumference of the circle to the nearest hundredth is, 69.08 cm

Step-by-step explanation:

Circumference(C) of the circle is given by:

[tex]C = 2\pi r[/tex]            .....[1]

where,

r is the radius of the circle.

As per the statement:

middle of circle is 11 cm

⇒[tex]r = 11 cm[/tex]

use [tex]\pi = 3.14[/tex]

Substitute these in [1] we have;

[tex]C = 2 \cdot 3.14 \cdot 11 = 69.08 cm[/tex]

Therefore, the circumference of the circle to the nearest hundredth is, 69.08 cm

The circumference of a circle with a radius of 11cm is 69.08cm, rounded to the nearest hundredth.

To estimate the circumference of a circle using π (Pi), you need to know the diameter of the circle which is twice the radius. Since you've mentioned the circle has a middle (radius) of 11cm, the diameter is 22cm. The formula for the circumference of a circle is C = πd, where d is the diameter.

Using the given approximation of Pi (π = 3.14), you can calculate:

C = 3.14 × 22cm

C = 69.08cm

Therefore, the estimated circumference is 69.08cm, which can be rounded to the nearest hundredth as 69.08cm.

We are given:  The cost of one flower bouquet =$ b.

The cost of one vase = $ v.

First florist bought: 2 flower bouquets and 2 vases.

2 *  cost of one flower bouquet + 2*cost of one vase = Total cost.

2b +2v = 12.50   ------------------------equation (1).

Second florist bought: 8 flower bouquets and 2 vases.

8 *  cost of one flower bouquet + 2*cost of one vase = Total cost.

8b +2v = 29.00    ------------------------equation (2).

Therefore, system of equations  we got is 2b +2v = 12.50  and 8b +2v = 29.00.

Subtracting first equation from second equation.

8b +2v = 29.00

-(2b +2v = 12.50)

____________________

6b = 16.50.

Dividing both sides by 6, we get.

b= 2.75.

Plugging b=2.75 in first equation we get

2(2.75) +2v = 12.50

5.50 +2v = 12.50

Subtracting 5.50 from both sides, we get

5.50-5.50 +2v = 12.50-5.50

2v = 7

Dividing both sides by 2, we get

v =3.50.

Therefore, cost of one flower bouquet is $2.75 and cost of one vase is $3.50.

If a rectangular prism has a lenght of 8 inches and a width of 7 inches. The lateral area is 150 square inches then the height of the rectangular prism is 5 inches.

To find the height of the rectangular prism, we'll first find the formula for the lateral area of a rectangular prism and then solve for the height using the given lateral area.

The lateral area of a rectangular prism is given by the formula:

[tex]\[ \text{Lateral Area} = 2 \times (\text{Length} \times \text{Height} + \text{Width} \times \text{Height}) \][/tex]

Given that the length is 8 inches, the width is 7 inches, and the lateral area is 150 square inches, we can substitute these values into the formula and solve for the height:

[tex]\[ 150 = 2 \times (8 \times \text{Height} + 7 \times \text{Height}) \][/tex]

[tex]\[ 150 = 2 \times (8\text{Height} + 7\text{Height}) \][/tex]

[tex]\[ 150 = 2 \times 15\text{Height} \][/tex]

Divide both sides by 2:

[tex]\[ 75 = 15\text{Height} \][/tex]

Now, solve for the height:

[tex]\[ \text{Height} = \frac{75}{15} \][/tex]

[tex]\[ \text{Height} = 5 \text{ inches} \][/tex]

So, the height of the rectangular prism is 5 inches.

Answer:

$12 per hour

Step-by-step explanation:

To solve how much did Robin earned per hour you just have to do a simple equation, we know that he worked 9 weeks, and that each week he worked 40 hours, so you equation would look like this:

[tex]Income=(wageperhour)*(hours worked)[/tex]

The hours worked is just a math done by multiplying the weeks worked by the hours worked per week that would be:

[tex]Hours worked=Hours worked per week*weeks\\Hours worked=(40 hours)*(9 weeks)\\Hours worked=360 hours[/tex]

So now we just put the data into our equation

[tex]Income=(wageperhour)*(hours worked)\\$4320=(wageperhour)*(360)\\wage per hour=4320/360\\ Wage per hour= 12[/tex]

Answer:

Here

Step-by-step explanation:

Answer:

8 - 2/x

Step-by-step explanation:

All you have to do is read the problem and then you will get your answer so as you see it say 8 - ok you get that now when it say the the quotient of two that means it’s is 2 over x so like the 2/x

eight minus the quotient of two and a number x

Hoped I Helped

Answer:

There is moderate level of overlap between the two data sets.  

Step-by-step explanation:

Overlap of data sets.

We are given two data sets in the question.

We have to find the amount of overlap in data set 1 and in data set 2.

There are 8 data points in data set 1 as shown in the image.

There are 8 data points in the data set 2 as shown in the image.

Out of the 8 data points for both data set 1 and data set 2, 5 data points overlap each other on 6, 7, 8 and 9.

Thus, we could say there is moderate level of overlap between the two data sets.

To plot points on a number line without measuring, it needs to follow various points mentioned below.

A number line is a visual representation of the real number system, where every point on the line corresponds to a unique real number.

Here,
To plot points on a number line without measuring, you can follow these steps:

Repeat steps 4 and 5 for all the points you want to plot on the number line.

Learn more about number line here:

https://brainly.com/question/11295183
#SPJ2

Volume of rectangular prism is [tex]11\frac{1}{4}[/tex] cm³

Given that:

Length of prism = [tex]2\frac{1}{2}[/tex] meter = 5/4 meter

Width of prism = 4 meter

Height of prism = [tex]2\frac{1}{4}[/tex] meter = 9/4 meter

Find:

Volume of rectangular prism = lbh

Volume of rectangular prism = [5/4][4][9/4]

Volume of rectangular prism = 45 / 4

Volume of rectangular prism = [tex]11\frac{1}{4}[/tex] cm³

Find out more information about 'Volume'.

https://brainly.com/question/21308574?referrer=searchResults

Answer:

less than 1

Step-by-step explanation:

1/8 can be translated to 0.125, multiply 0.125 by 3 to get 0.375.

What I think your assignment told you to do is calculate how many times 1/8 goes into 3 though, simply put, you just need to multiply 8 by 3 to find this result, which is 24.

John adds the outcomes of rolling two dice each showing numbers 1-6. In total, there are 36 possible outcomes when rolling two dice. The totals of the outcomes range from 2 to 12, with varying probabilities of each total.

John's activity involves the mathematical operation of adding the outcomes of two number cubes, also known as six-sided dice. Each die has six faces, numbered from 1 to 6. When you roll two dice, there are 36 possible outcomes (6 options from the first die multiplied by 6 options from the second die).

Each total has a certain probability of occurring, based on how many of the 36 possibilities will result in that total.

https://brainly.com/question/22962752

#SPJ3

Answer: I took a test, the answers C.

Step-by-step explanation:

Answer:

The correct answer is A).

Step-by-step explanation:

He have the quadratic functions f(x) = 16x²-240x+896. The first step should be to check if the coefficients 240 and 896 are divisible by 16, which is true. Then, extracting 16 as common factor we have

f(x) = 16(x²-15x+56).

Now we can use directly the formula to find the roots of a quadratic equation, or a more efficient way in terms of calculations. We must find to numbers such that their product is +56 and their addition or subtraction is -15. It is not difficult to check that -7 and -8 fulfill those conditions. Hence,

f(x) = 16(x²-15x+56)= 16(x-7)(x-8).

Therefore, the solutions are x=8 and x=7.