A circle with a radius of 7 ft is cut into 6 equal pieces. How many sq ft are 2 of the pieces? Use 22/7 for pi

1. 7 1/3 sq ft

2. 14 2/3 sq ft

3. 51 1/3 sq ft

4. 205 1/3 sq ft

Completed table is shown below. With this h number, we can calculate the cone's volume as V = (1/3)(72)h[tex]\pi[/tex] = 49/3h[tex]\pi[/tex] = 6[tex]\pi[/tex]h = 131.88.

To complete the table relating the height and volume of cones with a radius of 7 units using the equation[tex]v = 6\pi h[/tex], we need to substitute the radius value of 7 units into the formula for volume and then solve for height.

Height (h) Volume (V)

1                  131.88

2                  263.76

3                  395.64

4                  527.52

5                  659.4

To obtain volume for each height, we plug in radius value of 7 units into the formula for the volume of a cone, which is given by [tex]V = (1/3)\pi r^{2} h[/tex]. This gives us [tex]V = (1/3)\pi (7^{2} )h = 49/3\pi h[/tex],

which simplifies to V = 16.33h. Then we substitute this expression for V into given equation [tex]v = 6\pi h[/tex] to obtain [tex]16.33h = 6\pi h[/tex], and solve for h to obtain h = 6.56.

Using this value of h, we can obtain the volume of the cone as [tex]V = (1/3)\pi (7x^{2} )h = \\49/3\pi h = \\6\pi h = \\131.88[/tex]

After that, by multiplying the value of h by 16.33 and rounding to two decimal places, we can determine the volumes for the other heights in the table.

Therefore, the completed table is as shown above.

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Answer:

Therefore, -8(2x-4) simplifies to -16x + 32.

Step-by-step explanation:

-8 * 2x - (-8 * 4)

Simplifying this expression further gives:

-16x + 32

Therefore, -8(2x-4) simplifies to -16x + 32.

Answer:

Step-by-step explanation:

The half-life of Potassium-42 can be calculated using the following formula:

t1/2 = (ln 2) / λ

where t1/2 is the half-life, ln is the natural logarithm, and λ is the decay rate.

Substituting the values given, we get:

t1/2 = (ln 2) / 0.055

t1/2 ≈ 12.6 hours

Therefore, the original quantity of Potassium-42 will be halved in approximately 12.6 hours.

It will take approximately 13.51 hours for the original quantity of potassium 42 to be halved with a decay rate of 5.5% per hour.

To find the number of hours it takes for potassium 42 to be halved with a decay rate of 5.5% per hour, we can use the formula:

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There are 56 ways to select a group of five employees from the eight employees in the company for advanced training.

To select a group of five employees from a company that employs eight people, you can use the concept of combinations.
A combination is the selection of items from a larger set, where the order of items does not matter.

In this case, we want to choose 5 employees from a group of 8.

The formula for calculating combinations is:
C(n, k) = n! / (k!(n-k)!)
Where n is the total number of items, k is the number of items you want to select, and ! denotes the factorial.
So, for this problem:
n = 8 (total employees)
k = 5 (employees to be selected)
Now, we can plug these values into the formula:
C(8, 5) = 8! / (5!(8-5)!)
C(8, 5) = 8! / (5!3!)
C(8, 5) = (8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / ((5 × 4 × 3 × 2 × 1)(3 × 2 × 1))
C(8, 5) = (8 × 7 × 6) / (3 × 2 × 1)
C(8, 5) = (336) / (6)
C(8, 5) = 56

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19 is the range and 14 is the IQR. So, "The range is 19, and the IQR is 14" is the appropriate response.

The range in statistics is the distinction between the greatest and lowest values within a set of data. It is a gauge of variation that reveals the degree to which values within a dataset are dispersed.

You simply take the difference between the two values to determine the range. The range is given by: When the dataset, for instance, has the values 2, 3, 5, 8, et 10, the lowest value is 2, and the highest is 10.

Range = Highest value – Lowest value = 10 – 2 = 8 .The range in this instance is hence 8.

given

The range is the discrepancy between the data set's maximum and minimum values.

The box plot shows that the range is between 40 and 59, with 40 being the smallest value and 59 being the maximum.

Maximum value - Minimum value equals 59 - 40, which equals 19.

You may determine the values of Q1 and Q3 to be roughly 45 and 59, respectively, using the box plot.

IQR = Q3 - Q1 = 59 - 45 = 14

When the IQR is 14 and the range is 19, the answer is:

19 is the range and 14 is the IQR. So, "The range is 19, and the IQR is 14" is the appropriate response.

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Answer:

There are 55 boys.

Step-by-step explanation:

The ratio of

girls: boys:total

4           5     4+5

4            5      9

The total is 99

To get from 9 to 99, we multiply by 11.

girls: boys:total

4*11    5*11   9*11

44      55      99

There are 55 boys.

The simplified expression for the given variables is -7x³y² + 3x²y³ + 6y³.

A set of principles called the algebraic order of operations specifies the order in which mathematical operations should be carried out in order to simplify equations. The following is the order of events:

Operation inside parentheses should come first. Simplify exponential formulas by using exponents.

Division and multiplication should be done from left to right.

Operationally, add and subtract should be done from left to right.

The given expression can be simplifies as follows:

(3x²y³ + x² - 7x³y²) - (4x³y² - 6y³ + 2x²)

= 3x²y³ + x² - 7x³y² - 4x³y² + 6y³ - 2x²

= -7x³y² + 3x²y³ + 6y³

Hence, the simplified expression is -7x³y² + 3x²y³ + 6y³.

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Answer:

1 minute and 30 seconds.

Step-by-step explanation:

200 words in 1 minute

200/2=100

1minute/2=30 seconds

100+200=300 words

1 minute+ 30 seconds= 1 minute and 30 seconds.

Answer:

Step-by-step explanation:

A = 2πrh

Find radius

Diagonal = 14 so radius 14 : 2 = 7

A = 2πrh

A = 2π×7×2

A = 2π x 14

A = 28π meters  or 87.92 meters

The volume of the given pyramid is 86 in³ respectively.

A three-dimensional shape is a pyramid.

A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base.

The bases are joined to the peak to create a pyramid.

The lateral face is a triangle face formed by the connection of each edge of the base to the apex.

A three-dimensional figure is a pyramid.

Its base is a flat polygon.

The remaining faces are all triangles and are referred to as lateral faces.

So, the formula for the volume of the pyramid is:

V = lwh/3

Now, insert values as follows:

V = lwh/3

V = 7.4*7*5/3

V = 86.33333

Rounding off: 86 in³

Therefore, the volume of the given pyramid is 86 in³ respectively.

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The statement that the f distribution is always a left-tailed test is false statement about the f distribution. So, the right choice for answer option (a).

The F distribution (Snedecor's F distribution) represents continuous probability distribution which occurs frequently as null distribution of test statistics. Let two independent

chi-square variables are x and y with n₁ and n₂ with degree of freedom respectively. So, F-distribution is defined as F = ( X/n₁)/ (Y/n₂)

Characteristics : The F random variable is non-negative variable and the distribution is skewed to the right.

The F for left tail test both right-tailed &left tailed. So, the false statement is option(a).

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Complete question:

which of the following statements about the f distribution is false? group of answer choices

a) the f distribution is always a left-tailed test.

b) the f distribution is skewed to the right.

c)the f statistic is greater than or equal to zero.

d) as the degrees of freedom of for the numerator or denominator get larger, the curves approximates the normal distribution.

Answer:

Step-by-step explanation:

[tex]f(x)=\frac{(x-1)(x+1)}{x-1}[/tex]

       [tex]=x+1[/tex]

Limit is found by substitution: Limit = 1+1 = 2

Answer:

c ik this because I took the same question as you

The product of the given algebraic expression is [tex]\frac{4}{(x-1)}[/tex].

The given expression is [tex]\frac{8x+8}{x^2-2x+1} .\frac{x-1}{2x+2}[/tex].

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

Here, [tex]\frac{4(2x+2)}{x^2-1x-1x+1} \times \frac{x-1}{2x+2}[/tex]

= [tex]\frac{4(2x+2)}{x(x-1)-1(x-1)} \times \frac{x-1}{2x+2}[/tex]

= [tex]\frac{4(2x+2)}{(x-1)(x-1)} \times \frac{x-1}{2x+2}[/tex]

Cancel the same factors, that is

= [tex]\frac{4}{(x-1)} \times \frac{1}{1}[/tex]

= [tex]\frac{4}{(x-1)}[/tex]

Therefore, the product of the given algebraic expression is [tex]\frac{4}{(x-1)}[/tex].

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Answer:

To multiply (3x - 4y) and (4x - 7y), we need to use the distributive property, which states that: a(b + c) = ab + ac Using this property, we can expand the given expression as: (3x - 4y)(4x - 7y) = 3x(4x) + 3x(-7y) - 4y(4x) - 4y(-7y) Simplifying each term, we get: = 12x^2 - 21xy - 16xy + 28y^2 = 12x^2 - 37xy + 28y^2 Therefore, the simplified answer is 12x^2 - 37xy + 28y^2.

After answering the presented question, we can conclude that Rounding this to the nearest whole number, we get a surface area of 91 sq. ft.

In geometry, the diameter of a circle is any straight line segment that has an endpoint on the circle and travels through its centre. Another way to put it is the longest chord of a circle. Either idea can be used to define the diameter of a sphere. The diameter is the length of the line that runs tangent to the two points at either end of the circle. If you take length to be the distance between two points, diameter equals length. The diameter of a circle is the distance between its two furthest points.

First, we need to find the radius of the cone:

[tex]radius = diameter/2 = 6.4/2 = 3.2 ft[/tex]

Now we can use the Pythagorean theorem to find the height of the cone:

[tex]height^2 = slant height^2 - radius^2[/tex]

[tex]height^2 = 5.8^2 - 3.2^2[/tex]

[tex]height^2 = 20.84[/tex]

height ≈ 4.56 ft

Next, we can find the surface area of the cone by adding the area of the base to the lateral surface area. The base is a circle with radius 3.2 ft, so its area is:

base area =[tex]\pi (radius)^2[/tex]

base area =[tex]\pi (3.2)^2[/tex]

base area ≈ 32.17 sq. ft.

The lateral surface area is the curved surface area of the cone, which can be found using the slant height and the radius:

lateral surface area = [tex]\pi (radius)(slant height)[/tex]

lateral surface area = [tex]\pi (3.2)(5.8)[/tex]

lateral surface area ≈ 58.92 sq. ft.

Therefore, the total surface area is:

total surface area ≈ base area + lateral surface area

total surface area ≈ [tex]32.17 + 58.92[/tex]

total surface area ≈ 91.09 sq. ft

Rounding this to the nearest whole number, we get a surface area of 91 sq. ft.

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A player would need to make a goal in approximately 18.85 minutes or faster to be sponsored by the puck company.

To determine how fast a player needs to make a goal to be sponsored by the puck company, we'll need to find the

time cutoff for the top 10% quickest goals.

Step 1: Determine the z-score for the 90th percentile (since we want the top 10%).

We can use a standard normal distribution table (or a calculator) to find that the z-score for the 90th percentile is

approximately 1.28.

Step 2: Use the z-score formula to find the time cutoff.

The formula is: Z = (X - μ) / σ

Where Z is the z-score, X is the time cutoff we're looking for, μ is the mean (12.56 minutes), and σ is the standard

deviation (4.91 minutes).

Step 3: Solve for X.

Rearrange the formula to solve for X: X = Z × σ + μ

Plug in the values: X = 1.28 × 4.91 + 12.56

X ≈ 6.29 + 12.56

X ≈ 18.85

So, a player would need to make a goal in approximately 18.85 minutes or faster to be sponsored by the puck company.

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The answer is C. (x,y) - (x - 6, y + 2)

Answer: 1264.2857%

Step-by-step explanation:

Answer:

She earned 67.29% profit

Step-by-step explanation:

First let's find how much she spent on the coats.

50 x $28

$1400

So, her expense was $1400

Now, let's find how much she earned selling these coats.

We know she sold 38 of these coats at $49 each. Let's find how much she earned for these 38 coats.

38 x $49

$1862

She earned $1862 on these 38 coats.

Now, let's find how much she earned on the rest of the coats (50-38 which is 12). We know she sold the remaining for $40 each.

12 x $40

$480

She earned $480 on the rest of the coats.

The total she earned $2342

To find the profit:

Profit= $ Earned - Expenses

Profit= 2342-1400

Profit=$942

The question is asking for the percentage.

To find the percentage, we can use the percentage formula:

[tex]\frac{Profit}{Expense}[/tex] x 100

We know that the profit is $942 and the expense is $1400

(We want to find how much profit she made out of the expense)

[tex]\frac{942}{1400}[/tex] x [tex]\frac{100}{1}[/tex]

If you round your answer, you will get 67.29

Answer: She earned 67.29% profit

The team opened 4 packs of juice.

To find out how many packs of juice the team opened, follow these steps:
1. First, find the total number of juice boxes bought by multiplying the number of packs by the number of boxes in each pack: 7 packs × 8 boxes = 56 boxes.
2. Next, subtract the remaining boxes of juice to find out how many boxes the team drank: 56 boxes - 29 boxes = 27 boxes.
3. Finally, divide the number of boxes the team drank by the number of boxes in each pack to find the number of packs they opened: 27 boxes ÷ 8 boxes = 3.375 packs.
Since they only opened each pack after they drank all the boxes from the pack before, the team opened 4 packs of juice.

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Answer:

The statement that is FALSE is b) "The area is 26ft²".

If 7 students divided by 8 sandwiches each student gets 8 pieces of sandwich.

If 7 students are divided by 8 sandwiches, we can start by calculating the total number of pieces of sandwich available:

Total number of pieces of sandwich = 7 * 8 = 56

So there are 56 pieces of sandwich available for 7 students.

To find out how many pieces of sandwich each student gets, we divide the total number of pieces of sandwich by the number of students:

Each student gets 56 / 7 = 8 pieces of sandwich.

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The percentage of measurements in a data set that are above and below each of the following percentiles are 68%, 95% and 99.7%.

We need to calculate the percentage of the measurements contained in each of the following intervals:

According to the empirical rule, approximately 68% of the measurements in a normally distributed data set will fall within one standard deviation of the mean. Therefore, approximately 68% of the measurements will fall within the interval (mean - s, mean + s).

Similarly, approximately 95% of the measurements in a normally distributed data set will fall within two standard deviations of the mean. Therefore, approximately 95% of the measurements will fall within the interval (mean - 2s, mean + 2s).

Likewise, approximately 99.7% of the measurements in a normally distributed data set will fall within three standard deviations of the mean. Therefore, approximately 99.7% of the measurements will fall within the interval (mean - 3s, mean + 3s).

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By answering the presented question, we may conclude that the value of the equation is 5/x --> x/5 or (1/5)x

In mathematics, an equation is a statement that states the equivalence of two expressions. An equation is made up of two sides separated by an algebraic equation (=).

For example, the argument contends that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to identify the value or values of the variable(s) that will make the equation true.

Simple or complicated equations, regular or nonlinear, with one or more components are all possible. For example, in the equation [tex]"x2 + 2x - 3 = 0,"[/tex] the variable x is raised to the second power. Lines are utilized in many areas of mathematics, including algebra, calculus, and geometry.

[tex](x)(2) -- > 2x[/tex]

[tex]x/2 -- > 0.5x or (1/2)x[/tex]

[tex]5+x -- > x+5[/tex]

[tex](1/5)x -- > x/5 or (x \times 0.2)[/tex]

[tex](x)/5 -- > 0.2x or (1/5)x[/tex]

2x --> same as (x)(2)

[tex](1/2)x -- > 0.5x or x/2[/tex]

Therefore,  [tex]5/x -- > x/5 or (1/5)x[/tex]

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First, we need to calculate the percentage of citizens who chose either Snakes or Dogs.

The percentage of citizens who chose Dogs is 26%, which is equivalent to 0.26 as a decimal.

The percentage of citizens who chose Snakes is 10%, which is equivalent to 0.10 as a decimal.

To find the number of citizens who chose either Snakes or Dogs, we need to multiply the total number of citizens by the combined percentage of Snakes and Dogs:

0.26 + 0.10 = 0.36

So the combined percentage of Snakes and Dogs is 36%.

To find the number of citizens who chose Snakes or Dogs, we can multiply the total number of citizens by this percentage:

0.36 x 95,000 = 34,200

The solutions for the quadratic equations ax² + bx = 0 are:

a) x=0 or x=-2 for x²+2x=0;

x=0 or x=2 for x²-2x=0;

x=0 or x=2 for -x²+2x=0;

x=0 or x=-2 for -x²-2x=0.

b) x=0 or x=-5/3 for 3x²+5x=0;

x=0 or x=5/3 for 3x²-5x=0;

x=0 or x=5/3 for -3x²+5x=0;

x=0 or x=-5/3 for -3x²-5x=0.

a) To solve the quadratic equations ax² + bx = 0, we need to factor out the common variable x, and then solve for x:

a) x²+2x=0

x(x+2)=0

x=0 or x=-2

b) x²-2x=0

x(x-2)=0

x=0 or x=2

c) -x² + 2x = 0

-x(x-2)=0

x=0 or x=2

d) -x²-2x=0

-x(x+2)=0

x=0 or x=-2

b) To solve the quadratic equations 3x²+5x=0, 3x²-5x=0, -3x²+5x=0, and -3x²-5x=0, we factor out the common variable x and then solve for x:

b) 3x²+5x=0

x(3x+5)=0

x=0 or x=-5/3

b) 3x²-5x=0

x(3x-5)=0

x=0 or x=5/3

c) -3x²+5x=0

x(-3x+5)=0

x=0 or x=5/3

d) -3x²-5x=0

x(-3x-5)=0

x=0 or x=-5/3

Therefore, the solutions for the quadratic equations ax² + bx = 0 are:

a) x=0 or x=-2 for x²+2x=0;

x=0 or x=2 for x²-2x=0;

x=0 or x=2 for -x²+2x=0;

x=0 or x=-2 for -x²-2x=0.

b) x=0 or x=-5/3 for 3x²+5x=0;

x=0 or x=5/3 for 3x²-5x=0;

x=0 or x=5/3 for -3x²+5x=0;

x=0 or x=-5/3 for -3x²-5x=0.

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The English translation of the question in the picture:

75. Solve the quadratic equations ax² + bx = 0

a) x²+2x=0,

x²-2x=0,

-x² + 2x = 0.

-x²-2x=0;

b) 3x²+5x=0,

3x²-5x=0.

-3x²+5x=0,

-3x²-5x=0;

The values of x, y, and z in the given rhombus are: x = -31, y = 20, z = -87.

An equation is a mathematical statement saying that two amounts or values are the same, for example 6 x4=12x

We know that the side of a rhombus are equal in length.therefore we can solve the given equation

4y + 8 = -3x - 5 = -z + 1 = 88

Solving each equation for the variables, we get:

4y + 8 = 88

4y = 80

y = 20

-3x - 5 = 88

-3x = 93

x = -31

-z + 1 = 88

-z = 87

z = -87

Heance , the values of x, y, and z in the given rhombus are:

x = -31, y = 20, z = -87.

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Answer:

5 units

Step-by-step explanation:

The distance from -3 to 1 is 4 and the distance from 3 to 0 is 3.  Use the Pythagorean Theorem.  

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]4^{2}[/tex] + [tex]3^{2}[/tex] = [tex]c^{2}[/tex]

16 + 9 = [tex]c^{2}[/tex]

25 = [tex]c^{2}[/tex]

[tex]\sqrt{25}[/tex] = [tex]\sqrt{c^{2} }[/tex]

5 = c

Helping in the name of Jesus.

C. Angle bisector can be constructed by drawing an angle on tracing paper and then folding the paper so that the rays forming the angle lie upon each other. When you fold the paper, the crease that is formed will be the angle bisector of the original angle.

The output of 0.7326 represents the test statistic (Z-score) computed from the 1-sample Z-test in Excel.

It tells you how many standard deviations the sample mean is from the population mean under the null hypothesis.

A test statistic (Z-score) is a numerical value used in statistical hypothesis testing to assess the evidence against the null hypothesis.

A test statistic measures the difference between a sample statistic (eg sample mean) and the corresponding population parameter (eg population mean) assuming the null hypothesis is true.

For the Z-test, the test statistic is computed as

z = (x - μ) / (σ / √n)

where x = sample mean,

μ = population mean,

σ= population standard deviation,

and n = sample size.

The resulting Z-score indicates how many standard deviations the sample mean is from the population mean, assuming the null hypothesis is true.

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The number of books that had no damage or minor damage in the sample is:

722 + 75 = 797

To estimate the number of books in the entire collection that would have no damage or minor damage, we can assume that the proportion of books with no or minor damage in the sample is approximately equal to the proportion of books with no or minor damage in the entire collection.

The proportion of books with no or minor damage in the sample is:

797 / (722 + 75 + 29) = 0.9064

So we can estimate the number of books with no damage or minor damage in the entire collection as:

0.9064 x 70,500 = 63,912.6

Rounding to the nearest whole number, we get:

63,913