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The dimension of the rectangle is 40 inches by 64 inches. Then the area of the rectangle is 2,560 square inches.

Assume L is the length and W is the width. Then the area is given as,

A = L × W

And the perimeter is given as,

P = 2(L + W)

A rectangle has a width-to-height ratio of 8:5. The perimeter of the rectangle is 208 inches. Then the equations are given as,

208 = 2(W + H)

H + W = 104                ...1

H / W = 8 / 5              ....2

From equations 1 and 2, then we have

(8/5)W + W = 104

(13/5)W = 104

W = 40 inches

Then the height is given as,

H = (8/5) x 40

H = 64 inches

Then the area of the rectangle is given as,

A = 40 x 64

A = 2,560 square inches

The dimension of the rectangle is 40 inches by 64 inches. Then the area of the rectangle is 2,560 square inches.

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Answer:

Step-by-step explanation:

Basically, we want to use the formula for the area of a sphere: V = 4/3πr^3

And plug-in our radius, 4 for r.

We get an answer around 67 sooooooo

The volume of the ball is about__67__cubic centimeters. The density of the ball is__1.343__grams per cubic centimeter. Based on its density, the ball will__sink__.

Answer:

The base should be sink

Calculation of the volume, density:

Since the density of water is 1 gram per cm^3.

The volume is

Here a = base area and h = height of the pyramid

So,

Now

Density is

Since The mass of the pyramid is 1.17 g.

So, the density is

Density

Since its density is more than that of water, so it will sink.

Hence, we can conclude that The base should be sink.

Step-by-step explanation:

Hope this helped!

Answer:

To calculate the total amount of carbon dioxide emitted over the course of 15 years, we can start with the initial amount of 92,000 kilotons and multiply by 0.95 (the reduction factor) each year.

Step-by-step explanation:

Year 1: 92,000 kilotons

Year 2: 92,000 * 0.95 = 87,400 kilotons

Year 3: 87,400 * 0.95 = 82,990 kilotons

and so on, until year 15.

To find the total amount of carbon dioxide emitted over the course of 15 years, we need to sum up the emissions for each year:

92,000 + 87,400 + 82,990 + ... + (92,000 * 0.95^14) = 92,000 * (1 + 0.95 + 0.95^2 + ... + 0.95^14)

This is a finite geometric series and can be calculated using the formula for the sum of a finite geometric series:

S = a * (1 - r^n) / (1 - r),

where S is the sum, a is the first term, r is the common ratio, and n is the number of terms.

For this series, a = 92,000, r = 0.95, and n = 15. Plugging these values into the formula, we get:

S = 92,000 * (1 - 0.95^15) / (1 - 0.95)

S = 92,000 * (1 - 0.556774) / 0.05

S = 92,000 * 0.443226 / 0.05

S = 92,000 * 8.86452

S = 814,178.24 kilotons

Rounding to the nearest whole number, the country would emit 814,178 kilotons of carbon dioxide over the course of 15 years.

The area and the angle are matched as below.

Area        Angle

25/8 π in² = 45°

25/18 π in² = 20°

25/36 π in² = 10°

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

Diameter = 10 in

Radius = 5 in

Area of the circle in sector = 360°

πr² = 360

π x 5² = 360

25π in² = 360° _____(1)

Now,

From (1),

25π in² = 360°

Divide both sides with 8.

25/8 π in² = 45°

From (1),

25π in² = 360°

Divide both sides with 18.

25/18 π in² = 20°

From (1),

25π in² = 360°

Divide both sides with 36.

25/36 π in² = 10°

Thus,

Area        Angle

25/8 π in² = 45°

25/18 π in² = 20°

25/36 π in² = 10°

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A bar chart or a histogram might be suitable if all the sample sizes are the same and the team is worried about the amount of flaws.

Consider comparing the quantity of defects across several production lines, departments, or time periods.

The number of faults would be the continuous variable in this instance, and the bars would represent the number of samples that included a particular number of defects.

When illustrating the distribution of a count variable, such as the number of defects, bar charts and histograms can be used to visually spot patterns and trends in the data.

Therefore, the number faults would be the continuous variable in this instance, and the bars would represent the number of samples that included a particular number of defects.

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The cost of an apple is $1 and the cost of an orange is $2

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

x = apples

y = oranges

Using the above as a guide, we have the following:

5x + 2y = 9

7x + 3y = 13

Multiply (1) by 3 and (2) by 2

15x + 6y = 27

14x + 6y = 26

Subtract

x = 1

So, we have

5(1) + 2y = 9

This gives

y = 2

Hence, the cost of orange is $2

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Step-by-step explanation:

This is a trick question I think.

It says he managed to only travel 3 7/8. So wouldn't that mean the fraction of his planned trip that he travel would be... 3 7/8? Unless they want it as 31/8? Something is odd with the question

Answer:

the answer is c

Step-by-step explanation:

Divide 198.00 by 100, multiply 1.98 by 40, 198.00 minus 79.20, 118.80

The Z score associated with our observation is 2.45. This means that our observed value is 2.45 standard deviations away from the expected value.

2.45

Z score = (Observed value - Expected value) / Standard Deviation

Z score = (95 - 85) / √(85*(1-85)/30)

Z score = 2.45

We can calculate the Z score associated with our observation by taking the observed value, 95%, and subtracting the expected value, 85%, and dividing this by the standard deviation. To calculate the standard deviation, we use the formula: √(expected value*(1-expected value)/sample size). In this case, 85*(1-85)/30. The Z score associated with our observation is 2.45. This means that our observed value is 2.45 standard deviations away from the expected value.

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The game with 8 minutes of time-outs is 98 minutes long.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations such as addition, subtraction, multiplication, and division.

In this case, the algebraic expression that represents the length of the soccer game would be:

m = 90 + x

where m represents the total length of the game in minutes, 90 represents the fixed length of the game, and x represents the variable length of time-outs in minutes.

To find the length of the game with 8 minutes of time-outs, we substitute x = 8 into the expression:

m = 90 + 8 = 98

Therefore, the game with 8 minutes of time-outs is 98 minutes long.

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To find out how much each ticket costs, we can use this equation:

Total cost ÷ Number of tickets = Price of each ticket

Inserting the numbers into the equation would look like this:

To check our work, we can multiply the number of tickets by the price of each ticket to see if it matches up to the correct total price.

Therefore, each ticket costs $8.

The rectangular blocks with the measure of 7 cm by 8 cm by 9 cm will not fit in the smallest cylindrical cup with the radius of 5cm.

Rectangular block with the least dimensions, 7cm by 8cm side.

Circle with radius r is x² + y² = r²

∴ x² + y² = 5² or x² + y² = 25

Draw the area of the block using the coordinates (3.5,4) ; (-3.5,4) ; (-3.5,-4) and (3.5,-4)

Its observed that the block cannot fit inside the cup. We can confirm this if

y >4 when x = 3.5

3.5² + y² = 25

12.25 + y² = 25

y² = 12.75

taking positive square root, y≈3.57

Since this is <4, the block cannot fit the 5 cm radius cup.

equation for the cup with r = 6cm,

x² + y² = 6² or x² + y² = 36

Draw the area of the block using the coordinates (3.5,4) ; (-3.5,4) ; (-3.5,-4) and (3.5,-4)

it is observed the block will fit inside the cup as y>4 when x = 3.5

3.5² + y² = 36

12.25 + y² = 36

y² = 23.75

taking positive square roots, y≈4.87

Since this is >4, the block can fit the 6 cm radius cup.

equation for the cup with r = 7cm,

x² + y² = 7² or x² + y² = 49

Draw the area of the block using the coordinates (3.5,4) ; (-3.5,4) ; (-3.5,-4) and (3.5,-4)

it is observed the block will fit inside the cup as y>4 when x = 3.5

3.5² + y² = 49

12.25 + y² = 49

y² = 36.75

taking positive square roots, y≈6.06

Since this is >4, the block can fit the 7 cm radius cup.

∴ the block will not fit the smallest cup

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Marianne's withholding tax if her monthly gross earnings are $3,270 is $305.00.

The correct option is A.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Brittany works as a medical office assistant.

She is married and claims 2 withholding allowances.

Her monthly gross earnings are $3,270.

So, 3270 - 2(666.5) = $1937.3

So,

(1937.3 x 0.15) + 14.49 = $305.00

Therefore, the value is $305.00.

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He need the 500 gram of ground chicken.

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.

We are Given that the total kilogram of chicken = 0.5 kilograms

Recall :

1000 grams = 1 kilogram

Hence,

B grams = 0.5 kg

B = (0.5 x  1000) = 500 gram.

Hence,

The 500 gram of ground chicken.

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•Mr Bradford lunged at his wedding ring as it fell into the WHIRLPOOL of the bathtub drain.

•Sarah's morher CALMED her screaming baby by giving her a teddy bear to hold.

Answer: whirlpool, calmed

Step-by-step explanation:

A vortex looks like a whirlpool

Since the baby is scream giving a teddy bear will probably calm it

To find the probability of randomly withdrawing 5 jellybeans such that at least 2 are red, we need to find the total number of ways to select 5 jellybeans from the bag and then find the number of ways to select 2 or more red jellybeans.

Let's first find the total number of ways to select 5 jellybeans from the bag:

Total number of jellybeans = 4 red + 7 green = 11 jellybeans

Number of ways to select 5 jellybeans from 11 = 11 choose 5 = 462

Next, we need to find the number of ways to select 2 or more red jellybeans:

Number of ways to select 2 red jellybeans = 4 choose 2 = 6

Number of ways to select 3 red jellybeans = 4 choose 3 = 4

Number of ways to select 4 red jellybeans = 4 choose 4 = 1

Total number of ways to select 2 or more red jellybeans = 6 + 4 + 1 = 11

The desired probability is the ratio of the number of favorable outcomes (selecting 2 or more red jellybeans) to the total number of possible outcomes (selecting 5 jellybeans):

P(at least 2 red) = 11/462 = 11/462 = 0.0239 or 2.39%

So, the probability of randomly withdrawing 5 jellybeans such that at least 2 are red is 2.39%.

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Answer:

Step-by-step explanation:

I gotchu.

sin70 = x/3.6

x = 3.6sin70

x = 3.4

Answer:

x = 3.4

Step-by-step explanation:

As the given triangle is a right triangle we can use trigonometric ratios to solve for x.

[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

From inspection of the triangle:

As we know the angle and the hypotenuse, and wish to find the side opposite the angle, substitute the values into the sine ratio and solve for x:

[tex]\implies \sin(70^{\circ})=\dfrac{x}{3.6}[/tex]

[tex]\implies x=3.6\sin(70^{\circ})[/tex]

[tex]\implies x=3.382893...[/tex]

[tex]\implies x=3.4\; \sf (nearest\;tenth)[/tex]

Therefore, x = 3.4 to the nearest tenth.

The given expression (2x^3 + 2)/(x^3 - 2) can be written as a composition of two non-identity functions as follows:

Let f(x) = 2x^3 + 2 and g(x) = x^3 - 2.

Then, the expression can be written as:

f(x)/g(x) = (2x^3 + 2)/(x^3 - 2)

So, the expression is a composition of the two non-identity functions f and g, written as:

h(x) = f(g(x)) = (2x^3 + 2)/(x^3 - 2)

Answer:

Step-by-step explanation:

The perimeter of Wendy's math certificate is 7 inches + 7 inches + 9 inches + 9 inches = 32 inches.

So, the cost to frame Wendy's math certificate would be $2.00 per inch * 32 inches = $64.00.

Answer:

“m + 5”

internet

Answer:

Genesis has 126 different outfits to choose from.

Step-by-step explanation:

To calculate the total number of different outfits Genesis can choose, we need to multiply the number of choices available for each article of clothing. So we have:

7 choices for pants

2 choices for t-shirts

3 choices for sweaters or hoodies

3 choices for shoes

To find the total number of outfits, we multiply the number of choices for each category:

7 x 2 x 3 x 3 = 126

Therefore, Genesis has 126 different outfits to choose from.

126 different combination does Genesis have to choose.

We have,

Pants = 7

T shirts = 2

Sweaters or Hoodies = 3

Shoes = 3

So, the number of different combination is

= C(7, 1) x C( 2, 1) x C(3, 1) x C(3, 1)

= 7 x 2 x 3 x 3

= 126 ways

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Answer:

The volume of one marble can be calculated as follows:

V = (4/3) * π * (r^3)

where r = 1.25 cm (diameter of 2.5 cm divided by 2)

V = (4/3) * 3.14 * (1.25^3) = 5.20 cm^3

The mass of one marble is then:

m = V * 2.6 g/cm^3 = 13.52 g

And the total mass of 66 marbles is:

m = 66 * 13.52 g = 888.32 g

Rounding to the nearest gram, the total mass of the marbles in Keisha's pouch is 888 g.

a) 720 ways 3 boys and 3 girls sit in a row.

b) 48 ways boys and the girls are each to sit together.

c) 6 ways boys must sit together.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.

Given:

Number of girls= 3

Number of boys = 3

a) Using Permutation

⁶P₆ = 6! / (6 - 6)!

⁶P₆ =  6! / (0!)

⁶P₆ = 6!

       = 6 × 5 × 4 × 3 × 2 × 1

        = 30 × 24

        = 720

b) 3 boys and 3 girls sit in a row if the boys and the girls are each to sit together

= 3! x 2³

= 3 x 2 x 2 x 2 x 2

= 48 ways

c) the number of ways boys can sit together

= 3!

= 6 ways

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Answer: 23/72

Step-by-step explanation:

180 degrees = half of circle

5 degrees = 1/72 of circle

5 degrees times 23 = 115 degrees

1/36*23 = 23/72

Answer:

23/72 of a circle

Step-by-step explanation:

4×sector=circle

90÷360=1/4

so,

115/360=23/72

Answer:

There would be 600 fish after 12 months.

Step-by-step explanation:

The number of fish on the farm increases by 10% each month, so the formula to calculate the number of fish after n months is:

F = 350 * (1 + 0.1)^n

where,

F is the number of fish after n months

We want to find the number of fish after 12 months, so:

F = 350 * (1 + 0.1)^12

F = 350 * 1.719178

F = 603.56 to the nearest 100, which is 600.

The scale factor was applied to the first diamond is 2.5

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

The diamonds

The scale factor is calclated as

scale factor = Diamond 2/Diamond 1

Substitute the known values in the above equation, so, we have the following representation

scale factor = 1.5/0.6

Evaluate

scale factor = 2.5

Hnce, the scale factor is 2.5

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Answer:

yes

Step-by-step explanation:

In maths, x and y are variables. common factor is taken only when these variables are repeatedly used.