Fill in the blanks with NUMERICAL ANSWERS ONLY. Round all decimals to the nearest hundredth.

Find the hemisphere’s diameter if its radius is 6 cm.
centimeters

Find the hemisphere’s diameter if its radius is 9.008 ft.
feet

Find the hemisphere’s radius if its diameter is 6 cm.
centimeters

Find the hemisphere’s radius if its diameter is 9.008 ft.

Insect population growth in January by 40% and again by 40% in February is the scenario that describes a process of exponential growth. The correct choice is C.

Quantity rises over time through a process called exponential growth. When a quantity's instantaneous rate of change with regard to time is proportionate to the quantity itself it happens.

From the given option, it is observed that an insect population growth in January by 40% and again by 40% in February is the scenario that describes a process of exponential growth.

Because the growth is continuous and exponential.

Hence an insect population growth in January by 40% and again by 40% in February is the scenario that describes a process of exponential growth. The correct choice is C.

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Answer:

More than half of the people surveyed in each sample chose oranges as their favorite fruit. Since most people in each sample chose oranges, it is likely that oranges are the favorite fruit of the entire population.

I hope this helps you

Step-by-step explanation:

For the binomial distribution, √npq formula finds the standard deviation.

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Answer:

(i) 9

(ii) 12

Step-by-step explanation:

Comedy is 90 degrees out of 360 degrees or 1/4 of the circle.

36 students took the survey.

1/4 × 36 = 9

Horror is 120 degrees out of 360 degrees or 1/3 of the circle.

1/3 × 36 = 12

Answer:

9 comedy

12 horror

Step-by-step explanation:

First, there are 360 degrees in a circle.

Comedy = 90 degrees

Action and romance = 90 degrees combined

Horror = 120 degree

Science fiction = 60 degrees

To find sci fi : 90 +90 +120 = 300 - 360 = 60 degrees

36 students took the survey.

1/4 × 36 = 9

Horror is 120 degrees out of 360 degrees or 1/3 of the circle.

1/3 × 36 = 12

The statement that shows equivalent measurements is "52 meters = 520 decimeters." Option C.

To determine the equivalent measurements, we need to understand the relationship between different metric units.

In the metric system, each unit is related to others by factors of 10, where prefixes indicate the magnitude. For example, "deci-" represents one-tenth (1/10), "centi-" represents one-hundredth (1/100), and "kilo-" represents one thousand (1,000).

Let's analyze each statement:

5.2 meters = 0.52 centimeters: This statement is incorrect. One meter is equal to 100 centimeters, so 5.2 meters would be equal to 520 centimeters, not 0.52 centimeters.

5.2 meters = 52 decameters: This statement is incorrect. "Deca-" represents ten, so 52 decameters would be equal to 520 meters, not 5.2 meters.

52 meters = 520 decimeters: This statement is correct. "Deci-" represents one-tenth, so 520 decimeters is equal to 52 meters.

5.2 meters = 5,200 kilometers: This statement is incorrect. "Kilo-" represents one thousand, so 5.2 kilometers would be equal to 5,200 meters, not 5.2 meters.

Based on the analysis, the statement "52 meters = 520 decimeters" shows equivalent measurements. So Option C is correct.

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Note the correct and the complete question is

Select the statement that shows equivalent measurements.

A.) 5.2 meters = 0.52 centimeters

B.) 5.2 meters = 52 decameters

C.) 52 meters = 520 decimeters

D.) 5.2 meters = 5,200 kilometers

Answer:

557.51

Step-by-step explanation:

TOOK ONE FOR THE TEAM

A plane in r3 is defined parametrically as the set of points is n · u * b + n · v * c = n · (P - a).

To give an implicit description of a plane in R3, we need to find a single equation that describes all the points in the plane.

Let's assume that the plane is defined parametrically as the set of points:

P(u,v) = a + u * b + v * c

where a, b, and c are vectors in R3 and u and v are parameters.

To find the implicit equation, we can start by taking the cross product of the vectors b and c, which gives us a normal vector to the plane. Let's call this vector n.

n = b x c

Next, we can take the dot product of the normal vector n with the vector (P - a), where P is any point on the plane. This will give us an equation that describes all the points in the plane:

n · (P - a) = 0

Expanding this equation, we get:

n · (u * b + v * c) = n · (P - a)

Simplifying further, we get:

n · u * b + n · v * c = n · (P - a)

This is the implicit equation of the plane in R3.

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The answer is (a) $10,000.

The total cost of producing 200 units of output can be found by multiplying the output (200 units) by the average total cost (ATC) per unit, which is given as $50. Therefore, the total cost is:

Total Cost = Output x ATC

Total Cost = 200 x $50

Total Cost = $10,000

Therefore, the answer is (a) $10,000.

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In 286 ways are there to distribute seven identical apples and six identical pears to three distinct people.

There are 7 identical apples and 6 identical pears.

So total number of fruits here = 7+6 = 13 identical fruits

The number of ways to distribute 13 fruits in three distinct people is given by \(=^{13}C_3=286\) ways.

Hence the number of ways is 286.

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The probability that exactly one of the coins is a 10p piece is 1/2.

To find the probability that exactly one of the coins is a 10p piece, we can consider the possible outcomes.

There are two coins, and each coin can be either a 10p piece or a non-10p piece. Let's consider the four possible outcomes:

1. Erin's coin is a 10p piece, and Jack's coin is a non-10p piece.

2. Erin's coin is a non-10p piece, and Jack's coin is a 10p piece.

3. Both Erin's and Jack's coins are 10p pieces.

4. Both Erin's and Jack's coins are non-10p pieces.

Since the total amount of the two coins is less than 50p, we can eliminate the third possibility (both coins being 10p pieces).

Now, let's calculate the probability for each of the remaining possibilities:

1. Erin's coin is a 10p piece, and Jack's coin is a non-10p piece:

The probability of Erin having a 10p piece is 1/2, and the probability of Jack having a non-10p piece is also 1/2. Therefore, the probability of this outcome is (1/2) * (1/2) = 1/4.

2. Erin's coin is a non-10p piece, and Jack's coin is a 10p piece:

This is the same as the previous case, so the probability is also 1/4.

3. Both Erin's and Jack's coins are non-10p pieces:

The probability of Erin having a non-10p piece is 1/2, and the probability of Jack having a non-10p piece is also 1/2. Therefore, the probability of this outcome is (1/2) * (1/2) = 1/4.

Now, we sum up the probabilities of the two cases where exactly one of the coins is a 10p piece:

1/4 + 1/4 = 2/4 = 1/2.

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Step-by-step explanation:

the slope (m) of a line is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.

so, going from (-8, 19) to (4, -2)

x changes by +12 (from -8 to 4).

y changes by -21 (from 19 to -2).

the slope (m) is therefore

-21/+12 = -7/4

and by using (4, -2) as the point, we get

-2 = -7/4 × 4 + b = -7 + b

5 = b

and the full equation is

y = (-7/4)x + 5

Step-by-step explanation:

I am not fully sure what your teacher is aiming for. it friends very much on what you were just discussing in class (which I don't know).

but the first thing coming to mind is a minus sign ("-"). squaring a negative number removed the minus and makes the result equal to squaring the same positive number.

just for the undoing the 1/2 :

that is, because a fraction as exponent specifies in its denominator the root to be calculated for the basic value or expression.

so, 1/2 means square root. and yes, square is the inverse function of a square root, and it "undoes" the square root.

in exponent calculation it just means that for exponent 1 to the power of exponent 2 we simply multiply both exponents. and so, 1/2 × 2 = 1

FYI - the numerator still represents an original "to the power of" operation.

so, e.g. 3/2 would mean put the basis to the power of 3 and then do the square root of that result. or the other way around. these operations are commutative (the sequence does not matter).

This inference procedure allows you to compare the sample mean to the recommended minimum and determine if there is a statistically significant difference.

To answer this question, we would use a hypothesis test. Specifically, we would set up a null hypothesis that the average math achievement score for eighth-graders in Maryland is equal to or less than 76%, and an alternative hypothesis that the average score exceeds 76%.

We would then collect a sample of math achievement scores from eighth-graders in Maryland and use a t-test or z-test to determine if the sample mean is significantly different from 76%.

To answer the question of whether eighth-graders in Maryland exceed the recommended minimum of 76% on a test of math achievement, you should use a one-sample t-test. This inference procedure allows you to compare the sample mean to the recommended minimum and determine if there is a statistically significant difference.

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Shock advertisement are a type of advertising strategy that aims to provoke strong emotional responses from viewers by presenting controversial, shocking, or disturbing content.

An example of a shock add is Poking fun at events

By displaying content that is debatable, surprising, or upsetting, shock advertisement try to elicit strong emotional reactions from their target audience.

The goals of shock advertisements are to draw attention, leave a lasting impression, and elicit conversation about the good or message they are promoting.

These commercials frequently defy accepted norms, step outside of the box, and employ vivid imagery or provocative storytelling approaches.

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Step-by-step explanation:

since both points are on the same horizontal line (same y coordinate), we can save the detour via the Pythagoras approach. we only need to look at the difference of the x coordinates to get the distance :

10.8 - -15.6 = 10.8 + 15.6 = 26.4

Answer:

Arithmetic sequence

Step-by-step explanation:

An list of numbers whereby the difference between each consecutive number is constant is called an arithmetic sequence. Given thelistvif numbers:

–8, –4, 0, 4, 8, 12 ;

We can see that each consecutive number in the list has a constant difference of 4. Hence x this is called an arithmetic sequence.

Answer:

1

Step-by-step explanation:

2-1 = 1

Answer:

2 cookies - 1 cookie = 1 cookie

Answer.

Acute and Obtuse

Step-by-step explanation:

This is because the triangle has two different angles and the one on the left is acute because the angle is smaller than 90 degrees. While the other is obtuse because it is larger than 90 degrees.

Hope this helps! Enjoy your day and your assignments! :)

:p

~sunny~

Sam drove the truck for 247 miles. The solution has been obtained by using the arithmetic operations.

Let's assume that Sam drove the truck for "x" miles. According to the given information, there was a base fee of $16.95 and an additional charge of 98 cents for each mile driven. Therefore, the total cost for renting the truck can be calculated by adding all which gives us the following:

Total cost = Base fee + (Additional charge per mile * Number of miles driven)

From the information given, we know that Sam had to pay $259.01 when he returned the truck. By substituting the values into the equation, we can solve for the number of miles driven:

$259.01 = $16.95 + (0.98 * x)

Rearranging the equation, we have:

0.98x = $259.01 - $16.95

0.98x = $242.06

Dividing both sides of the equation by 0.98, we get:

x = $242.06 / 0.98

x ≈ 247.02

Therefore, Sam drove the truck for approximately 247 miles.

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The length of A + B is approximately 20.35 units and its direction is approximately 76.53 degrees.

Given vectors: Vector A has a length of 10 units and is at a direction of 30 degrees.

Vector B has a length of 15 units and is at a direction of 100 degrees.

We are required to calculate the sum of vectors A and B, i.e., A + B.

Using the component method, we can write the vector A as:

A = 10 cos 30 i + 10 sin 30 j

= 5√3 i + 5 j

And, the vector B as:

B = 15 cos 100 i + 15 sin 100 j

= -5.34 i + 14.52 j

Now, adding the two vectors, we get:

A + B = (5√3 - 5.34) i + (5 + 14.52) j

= (5√3 - 5.34) i + 19.52 j

We can use the Pythagorean theorem to calculate the magnitude of the vector A + B:

Magnitude = √[(5√3 - 5.34)² + 19.52²]

≈ 20.35 units

To determine the direction of the vector, we use the inverse tangent function (tan⁻¹):

Angle = tan⁻¹ [(19.52)/(5√3 - 5.34)]

≈ 76.53°

Therefore, the length of A + B is approximately 20.35 units and its direction is approximately 76.53 degrees.

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Answer:

3. 7

4. 9

5. 19

6. 15

7. 40

8. 32

9. 100

10. 18

11. 500

12. 125

Step-by-step explanation:

Given:

The number is \(\sqrt{125}\).

To find:

The estimate value of given number.

Solution:

We have,

\(\sqrt{125}=\sqrt{5\times 5\times 5}\)

It can be written as

\(\sqrt{125}=5\sqrt{5}\)

We know that, \(\sqrt{5}\approx 2.236\). So,

\(\sqrt{125}=5(2.236)\)

\(\sqrt{125}=11.18\)

Approx the value to the nearest integer.

\(\sqrt{125}\approx 11\)

Therefore, the required integer is 11.

Answer:

1/2 cup of lemonade per lemon

Step-by-step explanation:

2 cups of lemonade use 4 lemons

(2 cups of lemonade)/(4 lemons) =

= 2/4 cup of lemonade per lemon

= 1/2 cup of lemonade per lemon

Answer:

k+15

Step-by-step explanation:

The word "increased" indicates that there will be addition and the word "product" indicates there will be multiplication. Since it's asking for the product of 5 and 3, we can solve by multiplying those two numbers to get 15. Our variable k will then add 15. So, the final answer we get is: k+15

A circle is a curve sketched out by a point moving in a plane. The length of wx is 18 cm.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

Given the length of the circle's diameter, z is 72 cm, therefore, the length of zx(Radius) is 36cm. Since the length of yz is 30 cm, the length of xy is 6 cm.

Also, the length of the circle's diameter, w is 48 cm, therefore, the length of wy(Radius) is 24 cm. Since the length of xy is 6 cm, the length of wx will be equal to,

Length of wx = wy-xy = 24cm - 6cm = 18 cm

Hence, the length of wx is 18 cm.

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The indefinite integral of x/7 √\((49+x^2)\) dx using the substitution x = 7 tan(θ) is -7√(1 + \((x/7)^2\)) + C.

Let x = 7 tan(θ), then dx/dθ =\(7 sec^2(\theta )\), or dx = \(7 sec^2(\theta)\)dθ.

Substituting into the integral, we get:

∫x/7 √(49+\(x^2\)) dx = ∫tan(θ) √(49 + 49 \(tan^2(\theta)\)) * 7 s\(ec^2\)(θ) dθ

= 7∫tan(θ) sec(θ) sec(θ) dθ

= 7∫sin(θ) dθ

= -7cos(θ) + C, where C is the constant of integration.

Substituting back x = 7 tan(θ), we get:

-7cos(θ) + C = -7cos(arctan(x/7)) + C

= -7√(1 + \((x/7)^2\)) + C.

Therefore, the indefinite integral of x/7 √\((49+x^2)\) dx using the substitution x = 7 tan(θ) is:

-7√(1 + \((x/7)^2\)) + C.

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The percent of decrease in the cost of tuition is 11.11%

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

Last year = 9390

This year = 8451

The percent of decrease in the cost of tuition is calculated as

Percent = (Last year - This year)/Last year * 100%

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

Percent = (9390 - 8451)/8451 * 100%

Evaluate

Percent = 11.11%

Hence, the percent of decrease in the cost of tuition is 11.11%

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The diameter of the circular clarifier required to treat 3.2 mgd with a detention time of 2 hours and a depth of 8 feet is approximately 51.2 feet. This is assuming that the overflow rate is 233.14 gpm/sq.ft.

To find the diameter of a circular clarifier designed to treat 3.2 mgd, with a detention time of 2 hours and a depth of 8 feet, we can use the following formula:Q = 3.1416 x D²/4 x Vwhere Q = flow rate in million gallons per day (mgd), D = diameter of the clarifier in feet, V = overflow rate in gallons per minute per square foot (gpm/sq.ft.).

We can rearrange this formula to solve for the diameter D: D = √(4 x Q / 3.1416 x V)Since we are given Q = 3.2 mgd and detention time = 2 hours, we can convert detention time to overflow rate V:V = Q / (60 x 24 x D x H)where H = depth of the clarifier = 8 feet.

Substituting the given values, we get:V = 3.2 mgd / (60 x 24 x D x 8 ft)V = 233.14 / (D x H)Now we can substitute V into the previous formula for D:D = √(4 x Q / 3.1416 x V)D = √(4 x 3.2 mgd / (3.1416 x 233.14 gpm/sq.ft.))D = 51.2 feet (rounded to one decimal place)

Therefore, the diameter of the circular clarifier required to treat 3.2 mgd with a detention time of 2 hours and a depth of 8 feet is approximately 51.2 feet. This is assuming that the overflow rate is 233.14 gpm/sq.ft.

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