. Find the area for the following figure.
20.3 cm
6.2 cm

Answer:

19.2 inches

Step-by-step explanation:

The arc length,s, can be calculated using the formula s=r*c, where r is the radius of the circle and c is the central angle in radians. So, for a circle with a radius of 8 inches and a central angle of 2.4 radians, the arc length would be s=8 inches*2.4 radians =19.2 inches

The arc length s cut off by an angle with a measure of 2.4 radians in a circle with a radius of 8 inches is 19.2 inches.

What is the arc length?

Arc length is a measure of the distance along a curved line segment of a circle or a curve. It represents the length of a portion of the circumference of a circle, or the distance between two points on a curved line. In mathematical terms, it is defined as the integral of the magnitude of the velocity vector along the curve. The formula for the arc length of a circle depends on the radius r and the central angle θ (measured in radians) that cuts off the arc. It is given by

s = r * θ

In this case, the radius r is 8 inches, and the central angle θ is 2.4 radians. Plugging in these values, we get:

s = 8 * 2.4 = 19.2 inches

Hence, the arc length s cut off by an angle with a measure of 2.4 radians in a circle with a radius of 8 inches is 19.2 inches.

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Answer: 15.5^2 - 7.2^2 = 240.25 - 51.84= 188.41

188.41 square root is 13.7262522197 or 13.7

Step-by-step explanation: Hope this helps!! :))

Using a standard normal distribution table or a z-table gives us

P(¯Z≤0.8181)≈0.20662

Let us write down some of the parameters and statistics that are given in the question.

Population mean thickness

μ=4mm.

Population standard deviation

σ=1.1mm.

Random sample size

n=100.

Let the random normal variable

¯X denote the average thickness of the sample.

Then according to the Central Limit Theorem,

¯X

follows a normal distribution with mean

μ¯X=μ=4

and standard deviation

σ¯X=σ√n=1.1√100=1.110=0.11.

Then we can convert ¯X

into its standard normal form ¯Z

using the following transformation:

¯Z=¯X−μ¯Xσ¯X=¯X−40.11(1)

Now the question reads that we need the probability that the average thickness of the 100 sheets is less than 3.91 mm. In other words, we need

P(¯X<3.91).

Using (2) we get

P(¯X<3.91)=P(¯Z<3.91−40.11)=P(¯Z≤0.8181)(3)

Using a standard normal distribution table or a z-table gives us

P(¯Z≤0.8181)≈0.20662

which is our answer.

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Using a standard normal distribution table or a z-table gives us

P(¯Z≤0.8181)≈0.20662

Let us write down some of the parameters and statistics that are given in the question.

Population mean thickness

μ=4mm.

Population standard deviation

σ=1.1mm.

Random sample size

n=100.

Let the random normal variable

¯X denotes the average thickness of the sample.

Then according to the Central Limit Theorem,

¯X

follows a normal distribution with mean

μ¯X=μ=4

and standard deviation

σ¯X=σ√n=1.1√100=1.110=0.11.

Then we can convert ¯X

into its standard normal form ¯Z

using the following transformation:

¯Z=¯X−μ¯Xσ¯X=¯X−40.11(1)

Now the question reads that we need the probability that the average thickness of the 100 sheets is less than 3.91 mm. In other words, we need

P(¯X<3.91).

Using (2) we get

P(¯X<3.91)=P(¯Z<3.91−40.11)=P(¯Z≤0.8181)(3)

Using a standard normal distribution table or a z-table gives us

P(¯Z≤0.8181)≈0.20662

which is our answer.

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The ratio of red to green to blue to yellow marbles is, 3 : 5 : 2 : 6

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Give that,

A jar contains,

three red, five green, two blue, and six yellow marbles

the ratio of red to green to blue to yellow marbles = ?

The ratio can be written as,

⇒ 3 : 5 : 2 : 6

Hence, the ratio of balls is 3 : 5 : 2 : 6

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When comparing sets, a higher mean absolute deviation denotes a greater degree of dispersion of the data points from the mean and vice-versa.

What is mean absolute deviation?

The ratio of the sum of all absolute values of deviation from the central measure to the total number of observations is known as the mean absolute deviation.

We find the mean of the data set first, then use that value to calculate the mean absolute deviation of the data.

The mean absolute deviation reveals how dispersed or concentrated a group of data is around the mean. This is the data's variation.

When comparing sets, a higher mean absolute deviation denotes a greater degree of dispersion of the data points from the mean. Data points are more closely packed around the mean when the mean absolute deviation is lower.

Hence, this way the mean absolute deviation is used to compare data sets.

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Answer:

26/9 or 2 8/9

The number of pies made by 1 peck of apples is 5.25.

What is the Unitary method?

A quantity's unit value must first be determined in order to solve a problem for two different quantities of the quantity. The unitary approach is the name of this technique.

Due to that,

One bushel of apples weighs 42 pounds.

There are four pecks in a bushel.

Additionally, two pounds of apples are needed to produce one pie.

The following unitary method can be used to tackle the provided problem:

One peck weighs 42/4, or 10.5 pounds.

Since one pie only requires two pounds.

Pie can be made from 1 pound.

Therefore, 10.5 pounds or one peck can yield 5.25 pies (10.5 0.5).

Thus, 5.25 pies can be made from one peck of apples.

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If 500 grams of flour are used, 166.66666 grams of sugar must be added, followed by 200 grams of sugar.

When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage.

A ratio is a tool for comparing like-kind quantities or illustrating relationships between them. To compare similar items, we employ ratios.

Two numbers or measurements are compared to form a ratio. The quantities being compared are referred to as the terms of the ratio. A ratio divides two amounts into equal parts, with the dividend or antecedent serving as the unit of comparison and the divisor or unit of comparison serving as the unit of comparison.

To make a cake, I combined 750g of flour, 250g of butter, and 300g of sugar.

a) 250/750 = 1/3 = 1 : 3

b) 750/300 = 15/6 = 5/2 = 5 : 2

c) 250/300 = 5/6 = 5 : 6

If 500 grams of flour are used, 166.66666 grams of sugar must be added, followed by 200 grams of sugar.

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Step-by-step explanation:

when multiplying factors of the same base, we can simply add the exponents.

when dividing, we subtract.

so,

z⁹xz⁶/z⁷ = xz^(9+6-7) = xz⁸

Number of seconds it takes the object to travel the entire length of the path is 15 seconds.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Given that, the object travels 1/20 of the length of the path in 3/4 seconds.

1/20 is a tiny portion of the length that needs to be traveled.  

20/20 is the whole length.  

If 1/20 gets traveled in 3/4 of a second, multiply 3/4 by 20.

That is, 20(3/4) = 15 seconds

Therefore, number of seconds it takes the object to travel the entire length of the path is 15 seconds.

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The probability that the sample mean is between 39.75 and 41.25 is approximately 0.5987.

The probability that the sample mean is between 39.75 and 41.25 can be calculated using the Central Limit Theorem. This theorem states that the distribution of the sample means will be normally distributed with a mean equal to the population mean (μ = 40) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (σ = 8/√32).

Using this information, we can calculate the probability that the sample mean is between 39.75 and 41.25, which will be the area under the normal curve between those two points. This area can be calculated using the z-score formula, which is (x-μ)/σ = (41.25-40)/(8/√32). This gives us a z-score of 0.25. The probability can then be calculated using a z-table, which is approximately 0.5987. Therefore, the probability that the sample mean is between 39.75 and 41.25 is approximately 0.5987.

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Answer: 10

Step-by-step explanation:

a2 + b2 =c2

(5 x 5) + (9 x 9) = c2

25 + 81 = 106

Root of 106 = 10.295630141

Round to the nearest tenth

Answer: n= -48 and h=6

Step-by-step explanation:

For the first one,

-36=3/4 n.

So, divide both sides by 3/4.

-36/(3/4)= -48.

Plug into original equation to double check the answer is -48.

3/4(-48)= -36

For the second one, 2/3h +14= 18

subtract 14 from both sides.

2/3h= 4

Now, divide both sides by 2/3 to get you h=6.

Same as the first one, plug into the original equation. h is in fact 6! yay!

The mass in grams of 0. 450 moles of magnesium sulfate, MgSO4 in grams is 54.2.

The mole, which is 6.0221023 molecular entities, is the basic unit of a substance. One mole of a substance is equivalent to that substance's molecular weight.

The link between moles and molar mass means that the quantity of moles in a material is equal to the product of its mass and molecular mass.

The molar mass of magnesium sulphate is:

Magnesium = 24

Oxygen = 16 x 4 = 64

Sulphate = 32

Thus, the mass of magnesium sulphate is = 24 + 64 + 32 = 120 grams.

Now, moles is equal to:

Moles = given mass/molecular mass

Putting the values:

moles = given mass / 120

0.450 x 120 = given mass

Given mass = 54g.

Thus, the given mass of the magnesium sulphate is 54 g.

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The true mean study time is likely between 19.6 and 21.6 hours per week .The higher the confidence level, meaning that we can be more sure that the true mean study time is within the given range.

The margin of error is an important statistic that helps measure the accuracy of a survey. It is calculated by multiplying the standard deviation by the z-score for the given confidence level. A 90% confidence level has a z-score of 1.645, a 96% confidence level has a z-score of 1.96, and a 99% confidence level has a z-score of 2.58. Using this information, the margin of error for a survey of 225 students with a mean study time of 20.6 and a standard deviation of 2.7 is approximately 1.0. This means that the true mean study time is likely between 19.6 and 21.6 hours per week. The higher the confidence level, the higher the margin of error, meaning that we can be more sure that the true mean study time is within the given range.

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Answer: 66.2°F

Step-by-step explanation: (19°C × 9/5) + 32 = 66.2°F

Answer is 66.2°F.

How to calculate 19 °C in °F?

The base formula for this c to f converter is

Fahrenheit = (19 °C x 9/5) + 32

                 = 66.2°F

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The total growth of the plant in 2 weeks is 7/6 inches.

A fraction is defined as a piece of a whole. The complete could be a single thing or a group of objects. The component reflects the percentage of the cake when we really cut a slice of cake from the whole cake. Latin is where the word "fraction" originates.

Given plant grew in the first week = 1/3 inch

the plant grew in the second week = 5/6 inch

total growth in 2 weeks = 1/3 + 5/6

1/3 is equivalent to 2/6 with same diameter,

total growth in 2 weeks = 2/6 + 5/6

total growth in 2 weeks = 7/6 inches

Hence the total growth is 7/6 inches.

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The correct question is,

Katya measured the growth of a plant seedling. The seedling grew 1/3 inch by the end of the first week and another 5 / 6 inch by the end of the second week. About how much did the seedling grow in the first 2 weeks? Explain how you made your estimate.

The timeline which correctly organizes the founding of important world religions are;

Judaism, Buddhism, Christianity, and Islam

The correct answer choice is option B.

Chronological order is the order of events from the first to the last.

Christianity was founded about 2,000 years ago.

Islam was founded about 1,400 years ago.

Hinduism was founded about 3,500 years ago.

Buddhism was founded about 2,500 years ago.

Judaism was founded about 4,000 years ago

Arrangements from the first to the last;

Therefore, the important world religions are in the order; Judaism, Hinduism, Buddhism, Christianity and Islam.

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Answer:  Decreasing, if it "Halves (cuts in half)". If it was increasing, it would probably say double.

Step-by-step explanation:

So, if it was being cut in half every two days, we would only be counting days 2, 4, and 6.

So days 2, it would be cut in half, and go from 500 to 250. Day 4, it would go from 250 to 125. The day 6, it would go from 125 to 62.5.

In 6 days, the investment will be worth $62.50

It is used the observational study. A survey of high school students was conducted to see if students who take advanced classes are offered more scholarship money than students who do not take advanced classes

Now, According to the question:

"Information available from the question"

A survey of high school students was conducted to see if students who take advanced classes are offered more scholarship money than students who do not take advanced classes

Statisticians often refer to the "levels of measurement" of a variable, a measure, or a scale to distinguish between measured variables that have different properties. There are four basic levels: nominal, ordinal, interval, and ratio.

In an observational study, we measure or survey members of a sample without trying to affect them. In a controlled experiment, we assign people or things to groups and apply some treatment to one of the groups, while the other group does not receive the treatment.

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a) The  hiked 8 miles on first day.

b) The Equation is [tex]S_7 = a_1(r^7 -1)[/tex]/(r -1)

c) 127.49 miles the hiker will travel in 10 days

A sequence is defined as an arrangement of numbers in a particular order. On the other hand, a series is defined as the sum of the elements of a sequence.

Given:

The sequence of distances is a geometric sequence with first term a1 and common ratio (1 +10%) = 1.10.

and, The sum of 7 terms of the sequence is ...

So,

[tex]S_7 = a_1(r^7 -1)[/tex]/(r -1)

75.897= [tex]a_1(1.1^7 -1)[/tex]/(1.1 -1)

[tex]a_1[/tex]= 7.99999

[tex]a_1[/tex]= 8

So, hiker hiked 8 miles on first day.

b) The Equation is of the form of Geometric Sequence

[tex]S_7 = a_1(r^7 -1)[/tex]/(r -1)

c) For n= 10 days

[tex]S_{10}= a_1(r^{10} -1)[/tex]/(r -1)

     = [tex]8(1.1^{10} -1)[/tex]/(1.1 -1)

      = 127.49 miles

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To calculate the measures of spread for Mrs. Hampton's class data, you need to calculate the range, interquartile range (IQR), variance, and standard deviation.

The range is the difference between the highest and lowest values. To calculate the IQR, you must first find the quartiles of the data set.

The variance is the sum of the squared difference between each data value and the mean, divided by the number of data values. Finally, the standard deviation is the square root of the variance. To justify your response, you can explain how each of these measures of spread can provide insight into the data set, such as showing the spread of values or the degree of variation.

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45 divided by 3 is 15. The solution has been obtained by using long division.

What is long division?

When splitting huge numbers, the task is divided into several sequential steps using the long division approach. The dividend is divided by the divisor, just like in conventional division problems, and the result is known as the quotient; occasionally, it also produces a remainder.

Using long division, we get    

   1 5  

3 | 45

-  3              (Multiplying 3 by 1, we get 3)

    1 5            (Bringing down the next number of the dividend)

-  1 5            (Multiplying 3 by 5, we get 15)

    0  

Hence, 45 divided by 3 is 15.

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Answer:

(3y-2)(y+4)Ω

Step-by-step explanation:

real simple

The coordinates of A= are also (-3,4). The answer to the query is determined by the coordinates of the second endpoint B. (x, y). The midpoint's coordinates can be calculated using the formula below:

The following are b's coordinates: B= (-7,-8) (-7,-8)

We are given the midpoint's coordinates as M= (-5,-2).

Furthermore, A='s coordinates are (-3,4). The solution to the question depends on the coordinates of the second endpoint B.

the coordinates of B (x, y). The following formula can be used to determine the midpoint's coordinates:

[tex]$& x_m=\frac{x_a+x_b}{2} \\[/tex]

[tex]$& y_m=\frac{y_a+y_b}{2}[/tex]

We know xa = -3 and xm = -5. Solve the first equation for x b :

[tex]$2 x_m=x_a+x_b \Rightarrow x_b=2 x_m-x_a[/tex]

Substituting:

[tex]$& x_b=2 \cdot(-5)-(-3)=-10+3 \\[/tex]

[tex]$& x_b=-7[/tex]

We can solve the second equation for xb and get:

[tex]$y_b=2 y_m-y_a[/tex]

Since ya = 4 and ym = -2, then:

[tex]$& y_b=2 \cdot(-2)-(4)=-4-4 \\[/tex]

[tex]$& y_b=-8[/tex]

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The derivative of the natural log of y is (1/y)(dy/dx). The derivative is performed with respect to x.

What is a natural logarithm?

A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equal to 2.718281828459.

Given function is log y.

The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's fundamental tool is the derivative.

Generally derivative or the changes of the function is found with respect to x.

Assume that

z = log y

Differentiate with respect to x:

dz/dx = d(log y)/dx

Applying the formula of drivative d(ogx)/dx = 1/x:

dz/dx = (1/y)(dy/dx)

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The total number of unique keys after the distribution will be 48.

When the package containing 12 electrical locks is delivered to 16 job site superintendents, each superintendent will receive 3 locks. This means that the total number of locks will be 16 * 3 = 48

When the locks are distributed, each superintendent will receive 12/16 = 3/4 of a lock. This means that each superintendent will receive 3 locks.

Since each lock comes with a unique key, the total number of unique keys after the distribution will also be 48.

It is important to note that each lock is unique and comes with its own key, so even though the locks are being distributed among 16 superintendents, the number of unique keys will remain the same, which is 48.

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Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence.

Given data :

a )

There are 7 people from the CS department and 5 people from the math (M) department who could serve on the committee, so there are a total of 12 people.

department that could serve on a 4-person committee

b) probability that the only people serving on the committee are from the cs department :

The general probability formula can be expressed as: Probability = Number of Favorable Outcomes / Total Number of Outcomes. or. P(A) = f / N

 = 5 / 7

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