The area of a rectangle is 6x^2 + 9x, and its width is 3x. What is the length of the rectangle?

The inner surface area of the vessel, given the diameter of the hemisphere and the total height, is 133π cm².

To find the inner surface area of the vessel, we will consider the hemisphere and the cylinder separately, and then sum their inner surface areas.

Hemisphere:

The diameter of the hemisphere is 14 cm, so its radius (r1) is half of that:

r1 = 14 cm / 2 = 7 cm

Inner surface area (hemisphere) = 2 * π * r1² / 2 = π * r1² = π * (7 cm)² = 49π cm²

The radius of the cylinder is the same as the hemisphere's (r2 = r1 = 7 cm). The height (h) of the cylinder can be found by subtracting the height of the hemisphere from the total height of the vessel:

h = total height - hemisphere height = 13 cm - 7 cm = 6 cm

Inner surface area (cylinder) = 2 x π x r2 x h = 2 x π x (7 cm) x (6 cm) = 84π cm²

Total inner surface area = inner surface area (hemisphere) + inner surface area (cylinder)

Total inner surface area = 49π cm² + 84π cm² = 133π cm²

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The link between the base price and the selling price with the markup is expressed differently in both equations, but they are both true and accurately depict the same scenario using the distributive property.

A basic tenet of mathematics is the distributive property of multiplication over addition, which asserts that the product of a number and a sum is equal to the total of the products of the number and each addend. In other words, if a, b, and c are all real numbers, then a(b + c) = ab + ac. By factoring out common components, this characteristic is employed in algebra to simplify statements and resolve equations.

The link between the base price and the selling price with the markup is expressed differently in both equations, but they are both true and accurately depict the same scenario using the distributive property.

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Repeat this process for a large number of trials (e.g., 1000) and use the proportion of trials where all three-coin flips resulted in tails as an estimate of the probability that three randomly chosen people do not work out for the desired amount.

by the question.

To simulate this situation, you can use a set of three-coin flips, where heads represent the event that a person exercises for 30 minutes a day at least three times a week, and tails represent the event that a person does not exercise for that amount.

To simulate the first person, flip a coin once. If it lands heads, consider the person as exercising enough; otherwise, consider the person as not exercising enough.

Repeat this process for the second and third person as well, each time flipping the coin once to determine if the person exercises enough.

After the three-coin flips, count the number of times the coin landed tails, which represents the number of people who do not exercise for 30 minutes a day at least three times a week.

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Answer:

1. Sara has more than Martin

2. No, Jon has less money than martin

Step-by-step explanation:

[tex]\text{Martin}=0.50[/tex]

[tex]\text{Sara}: 0.50\times10 = 5[/tex]

[tex]\text{Jon}: 0.50(\dfrac{1}{10} )= 0.05[/tex]

Answer:

-17y-4

Step-by-step explanation:

we can simplify it to -17y-4 by combining like terms.

Answer:

48

Step-by-step explanation:

a² - 16                        a = 8

8² - 16

= 64 - 16

= 48

The solution of the absolute inequality is x < -9 or x > 1

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.

Absolute inequalities are inequalities  that involve algebraic expressions with absolute value symbols and inequality symbols.

Therefore, let's solve the absolute inequality as follows:

|2x + 8| > 10

2x + 8 > 10 or 2x + 8 < - 10

Let's solve them individually,

2x + 8 > 10

2x > 10 - 8

2x > 2

x > 2 / 2

x > 1

Therefore,

2x + 8 < - 10

2x < - 10 - 8

2x < -18

divide both sides of the inequality by 2

x < -18 / 2

x < - 9

Therefore,

x < -9 or x > 1

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The perimeter of the quadrilateral GHJK is 24(1+√2) which can be by using the radius of the circle, 6cm.

Perimeter is the total length of the outside boundary of any two-dimensional shape. Perimeter is calculated by adding up the length of each side of a shape.

In order to calculate the perimeter of the quadrilateral, we need to first find the length of the sides.

We can do this by using the radius of the circle, r.

The side GH is equal to r+r=2r.

The side HK is equal to (r+r)√2=2r√2.

The side JK is equal to (r+r)√2=2r√2.

And the side GJ is equal to 2r.

Now that we have the lengths of the sides, we can calculate the perimeter of the quadrilateral.

The perimeter is equal to the sum of the four sides=

2r + 2r√2 + 2r√2 + 2r

= 4r+4r√2

= 4r(1+√2)

=4*6(1+√2)

=24(1+√2)

Therefore, the perimeter of the quadrilateral GHJK is 24(1+√2).

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The perimeter of the square GHJK is 48cm which can be by using the radius of the circle, 6cm.

Perimeter is the total length of the outside boundary of any two-dimensional shape. Perimeter is calculated by adding up the length of each side of a shape.

In order to calculate the perimeter of the quadrilateral, we need to first find the diameter of the circle.

We can do this by using the radius of the circle, r=6cm.

So, diameter= 2*6

=12cm

As the quadrilateral is enclosing the circle, it must be a square.

So, now the length of the sides of the square= diameter of the circle.

which is 12cm.

A square has  4 equal sides. Thus the perimeter of the quadrilateral which is a square

=4*12cm

=48cm

Therefore, the perimeter of the quadrilateral GHJK is 48cm.

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The result will be the amount of interest earned or paid. Don't stress out too much - with a little practice, you'll become an expert at using this formula!

Sure, I'd be happy to help you with I=prt! This formula is used to calculate simple interest. "I" stands for the interest, "p" stands for the principal (the amount of money borrowed or invested), "r" stands for the interest rate (expressed as a decimal),

and "t" stands for the time period (usually expressed in years). To use the formula, simply multiply the principal by the interest rate and the time period (in years).

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The cylinder has a radius of 2 times the square root of 5 meters, or roughly 4.5 meters rounded to the nearest tenth.

The formula for the volume of a cylinder is:

V = πr²h

where V is the volume, r is the radius, and h is the height.

In this case, we have:

V = 160π m³

h = 8 m

Substituting these values into the formula, we get:

160π = πr²(8)

Simplifying the equation by canceling out π on both sides, we get:

160 = 8r²

Dividing both sides by 8, we get:

20 = r²

Taking the square root of both sides, we get:

r = √20

Simplifying the radical by factoring out 4, we get:

r = 2√5

To express the radius as a decimal rounded to the nearest tenth, we can use a calculator to get:

r ≈ 4.5

Therefore, the radius of the cylinder is 2√5 meters or approximately 4.5 meters to the nearest tenth.

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Answer:

5/12

Step-by-step explanation:

Simply times the fractions together to get the area

5/8 x 2/3 = 10/24

Now simplify 10/24 by dividing by the HCF which is 2

So, in simplest form, your final answer is 5/12

i do not know what to say its twenty words to add an answer#

Answer: Table 3

Step-by-step explanation:

exponential relationship means the y value is increasing/decreasing exponentially

In table 1: the value of y is NOT increasing/decreasing exponentially as 2 is being added continuously (linear), so not table 1

In table 2: the value of y is NOT increasing/decreasing exponentially as 4 is being subtracted continuously (linear), so not table 2

In table 3: the value of y IS increasing exponentially as the y variable is multiplied by 2, so table 3

In table 4: the value of y is NOT increasing exponentially as the y variable is only being increased by 5 constantly (linear), so not 4

The solution to this given question should be -3/14. We can find it in the following manner.

−(14w+8)+8=3

-14w - 8 + 8 = 3

-14w = 3 (+8 and -8 get cancelled)

w = -3/14

This is how one can simplify the equation and solve for w.

None of the given options match the solution we obtained. Therefore, there may have been an error in the question or the answer choices.

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

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This inequality states that the total cost of buying x gumballs and y jawbreakers must be less than or equal to $3.00.

Let x be the number of gumballs that Bob buys, and let y be the number of jawbreakers that Bob buys.

The cost of buying x gumballs is $0.50 times x, or 0.50x. The cost of buying y jawbreakers is $0.30 times y, or 0.30y.

Bob has $3.00 to spend on candy, so we can write an inequality to represent the total cost of buying both types of candy:

0.50x + 0.30y ≤ 3.00

This inequality states that the total cost of buying x gumballs and y jawbreakers must be less than or equal to $3.00.

Note that this inequality assumes that Bob spends all of his money on candy. If Bob wants to save some money or spend it on something else, the inequality would need to be modified accordingly.

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If the car's wheels revolve 10,000 times without slipping, the car will travel approximately 9.92 miles.

The circumference of a circle (which is the distance around it) is given by the formula:

C = πd, where d is the diameter of the circle.

In this case, the diameter of the car's wheels is 20 in., so the circumference of each wheel is:

C = πd

C= π(20 in.) =

C = 20π in.

If the car's wheels revolve 10,000 times without slipping, then the total distance the car travels is:

distance = number of revolutions × circumference

distance = 10,000 × (20π in.)

To convert this distance to miles, we need to divide by the number of inches in a mile, which is 63,360 in.

distance = (10,000 × 20π in.) / 63,360 in./mi

distance = 9.92 miles

Therefore, distance traveled by the car is 9.92 miles.

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Answer: q = -3, p = 6

Step-by-step explanation:

Multiply second equation by 3. 6q + 9q = 9. Equation one minus equation two which gives you p = 6. Then plug it in the second equation. 12 + 3q = 3. 3q = -9. q = -3.

Answer:

$3.45

Step-by-step explanation:

the large salad costs 1.40 more

large salad = 4.85

small salad = 4.85 - 1.40

small salad costs $3.45

Answer:

3.45$ is the price of small salad as it costs 1.40$ less than large salad

Step-by-step explanation:

i hope you find it helpful, have a nice day

Using the laws of exponents, the solution to the given problem is: 25

Some of the laws of exponents are:

1) Product of powers rule: This means that we add powers together when multiplying like bases.

2) Quotient of powers rule: This means that we subtract powers when dividing like bases.

3) Power of powers rule: This means that we multiply powers together when raising a power by another exponent.

4) Power of a product rule: This means that when any base is being multiplied by an exponent, distribute the exponent to each part of the base.

5) Negative exponent rule: This means that when there is a number being raised by a negative exponent, flip it into a reciprocal to turn the exponent into a positive

We are given the expression:

[tex]\frac{1}{5^{-2} }[/tex]

Using the negative exponent rule, we will have:

5² = 25

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After answering the provided question, we can conclude that As a result, percentage the answer is A. 27.5%.

A percentage is a ratio or number expressed as a percentage of 100 in mathematics. The abbreviations "pct.," "pct," and "pc" are also used on occasion. Despite this, the percentage symbol "%" is commonly used to represent it. The % value is dimensionally empty. In essence, percentages are fractions with a denominator of 100. To indicate that a number is a percentage, a percent sign (%) should be placed next to it. For example, you receive a 75% on an exam if you correctly respond to 75 out of 25 pages (75/100). Divide the result by 100 after dividing the amount by the total when calculating percentages. The percentage is found by multiplying (value/total) by 100%.

To calculate the percentage of Monroe Middle School seventh-graders who participate in the school band, divide the number of students who play an instrument by the total number of seventh-graders and multiply the result by 100.

There are 33 seventh-graders in the school band, and there are 120 seventh-graders in total. Therefore:

percentage = (33 / 120) x 100% % = 27.5%

As a result, the answer is A. 27.5%.

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The area of the shaded region is 19, which can be calculated by subtracting the unshaded region from the shaded region.

Area of the whole square= side *side

= 5*5

= 25

Area of the rectangle inside the square= lenght*breadth

=3*2

=6                                                                  

Now,

Area of the shaded region= Area of the square - Area of the rectangle

= 25-6

= 19.

The area of a square is the measure of the region enclosed by a square, and it is equal to the length of one side squared. The area of a rectangle is equal to its length multiplied by its width.

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Answer:

Step-by-step explanation:

Given equations,

→ x - y = 5

→ 4x + y = 10

Now we have to,

→ Find the required value of x and y.

Let's solve for the value of x,

→ (x - y) + (4x + y) = (5) + (10)

→ x + 4x - y + y = 5 + 10

→ 5x + 0 = 15

→ 5x = 15

→ x = 15/5

→ [ x = 3 ]

Then the value of y will be,

→ 4x + y = 10

→ 4(3) + y = 10

→ 12 + y = 10

→ y = 10 - 12

→ [ y = -2 ]

Hence, the value of y is -2.

California has the larger population, and it is approximately 20 times larger than Nebraska's population.

The population of California is 3.8 million, while the population of Nebraska is 1.9 million. To find the difference between the two populations, we can calculate 3.8 million minus 1.9 million, which equals 1.9 million. To find the ratio, we can divide the population of California by the population of Nebraska, which is 3.8 million divided by 1.9 million, which equals 2. Thus, California has a population that is 20 times larger than the population of Nebraska.

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Answer:

2200

Step-by-step explanation:

have a good day

Answer: They are not

Step-by-step explanation:

To be linear it needs to be a diagonal arrow across. Most of these don't follow that rule, therefore it is not linear.

The resale value of the laptop after each year is calculated by multiplying the previous value by 0.65 (100% - 35% = 65%). After 4 years the resale value will be $250.

Answer:

B) 2

Step-by-step explanation:

First, we need to find BD:

by the Pythagorean theorem, (sqrt13)^2 + (sqrt23)^2 = BD^2

we can simplify this to 13+23=BD^2, which means BD^2 = 36, and BD is 6.

Therefore to find BC, we can use the Pythagorean theorem again and create the formula:

(4sqrt2)^2 + BC^2 = 6^2

This simplifies to 32 + BC^2 = 36, which means that BC^2 = 4, and BC = 2.

As per the given commission, the sales price of the property is $405,000.

To do this, we need to break down the commission earned by the agent into two parts: the commission earned on the first $300,000 and the commission earned on the remaining amount. The commission earned on the first $300,000 can be calculated as:

Commission on first $300,000 = 6% of $300,000

Commission on first $300,000 = 0.06 x $300,000

Commission on first $300,000 = $18,000

So, the remaining commission earned by the agent on the amount that exceeds $300,000 is:

Total commission - Commission on first $300,000 = $21,150 - $18,000

Total commission - Commission on first $300,000 = $3,150

Now, we know that the commission earned on the remaining amount is 3% of the sales price that exceeds $300,000. Let's assume the sales price of the property is x. Then we can write the following equation:

3% of (x - $300,000) = $3,150

We can simplify this equation as follows:

0.03(x - $300,000) = $3,150

x - $300,000 = $3,150 / 0.03

x - $300,000 = $105,000

x = $300,000 + $105,000

x = $405,000

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Answer:

4

Step-by-step explanation:

because it median, so it number  was the middle of the total

as we know there is total of 9

and we count to 5

so it 4 letters

Answer:

4

Step-by-step explanation:

arranging the name lengths from smallest to largest we have; 3,3,3,3,4,5,7,7,9

From the set of numbers,4 appears at the middle hence the median name length.

Answer:

[tex]15x^2+4y-4z^2[/tex]

Step-by-step explanation:

Solve this question patiently.

See explanation in the attached picture.