A potter is designing a large ceramic planter to grow herbs in. He wants to spin it on his potter’s wheel and fire it in his kiln. Before he begins, he needs to determine the dimensions of his pot so that he knows it will have enough volume to hold a bag of potting soil. The potter has drawn a 2-D view of the planter. Assume the base of the pot has a radius of inches in all directions.

The length of side x in simplest radical form is √128/1 with a rational denominator of 1.

The triangle is given in the question which is a right triangle.

As per the given figure, we can determine the length of side x by the Pythagoras theorem.

According to Pythagoras's theorem,

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

perpendicular²+base² = hypotenuse²

8² + 8² = (x)²

64 + 64 = (x)²

(x)² = 128

x = √128

Hence, the required length of side x of the triangle is √128.

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The probability that a student is a sophomore and does not exercise is 42/600, or 7/100.

This probability can be calculated by dividing the number of sophomores who do not exercise (42) by the total number of students in the survey (600).

The contingency table provided in the question shows that there are 150 sophomores in the survey, and 42 of them do not exercise. This means that the probability of being a sophomore and not exercising is 42/150, or 7/25. However, the question asks for the probability as a simplified fraction, so the fraction can be simplified further to 7/100.

Overall, this means that the probability of being a sophomore and not exercising is relatively low, as it represents just 7% of the total number of students in the survey.

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Population standard deviation, level of significance are same.

Margin of error increased.

With increase in margin of error sample size decreases.

By dividing the population's standard deviation by the sample size and then multiplying the resulting number by the crucial factor, the margin of error—a statistical expression used to estimate how much a result will deviate from the value of the full population—can be determined.

The standard deviation of the sample statistics, if we could take several samples of the same size, is the standard error.

Population standard deviation, level of significance are same.

Margin of error increased.

Margin of error increases leads to decrease in the sample size

as the margin of error is in denominator position in sample size formula. Hence with increase in margin of error sample size decreases.

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Answer:

Base = 10 cm

Height = 6 cm

Step-by-step explanation:

Here is the formula for the area of a triangle.

 [tex]A=\frac{bh}{2}[/tex]

We are given

[tex]A=30[/tex]

[tex]b=h+4[/tex]

Replace all occurrences of [tex]b[/tex] with [tex]h+4[/tex] in each equation.

[tex](h+4)*\frac{h}{2} =30[/tex]

Apply the distributive property.

[tex]h(\frac{h}{2})+4(\frac{h}{2})=30[/tex]

[tex]\frac{h*h}{2}+4(\frac{h}{2})=30[/tex]

Use the power rule to combine exponents.

[tex]\frac{h^2}{2}+4(\frac{h}{2})=30[/tex]

Factor 2 out of 4 .

[tex]\frac{h^2}{2}+2(2)(\frac{h}{2})=30[/tex]

Cancel the common factor.

[tex]\frac{h^2}{2}+2h=30[/tex]

Solve for h.

Multiply each term in  [tex]\frac{h^2}{2}+2h=30[/tex]  by 2 to eliminate the fractions.

[tex]\frac{h^2}{2}*2+2h*2=30*2[/tex]

Simplify each term.

Cancel the common factor of 2.

[tex]h^2+2h*2=30*2[/tex]

[tex]h^2+4h=60[/tex]

Subtract 60 from both sides of the equation.

[tex]h^2+4h-60=0[/tex]

Factor using the AC method.

Consider the form [tex]x^2+bx+c[/tex] . Find a pair of integers whose product is [tex]c[/tex] and whose sum is [tex]b[/tex] . In this case, whose product is − 60 and whose sum is 4 .

−6, 10

Write the factored form using these integers.

[tex](h-6)(h+10)=0[/tex]

Set [tex]h-6[/tex] equal to 0 and solve for h.

Then add 6 to both sides of the equation.

[tex]h-6=0\\h=6[/tex]

Set [tex]h+10[/tex] equal to 0 and solve for h.

Then subtract 10 from both sides of the equation.

[tex]h+10=0\\h=-10[/tex]

The final solution is all the values that make [tex](h-6)(h+10)=0[/tex] true.

[tex]h=6,-10[/tex]

Given [tex]b=h+4[/tex]

Replace all occurrences of h with 6 in each equation.

[tex]b=6+4\\b=10\\h=6[/tex]

Answer:

The number of minutes should be 68.

A cell phone plan costs $23.70 monthly for 700 minutes of talk time. It costs an additional $0.06 per minute for each minute over 700 minutes.

Getting e-mail access costs 20% of the price for 700 minutes of talk time. The total cost for all 6 months is $195.12.Equation and number of minutes:The equation is 195.12=6(0.06m+23.70+0.20(23.70))195.12 = 0.36m + 142.2 + 28.4424.48 = 0.36mm = 68 minutes

The probability that the sample mean is greater than 18 as calculated  is 0.8413.

Given data,

n = 36, sample size

μ = 17, population mean

σ = 6, population standard deviation

when x = 18

z = (18 - 17)/1 = 1

P(x <18) = 0.8413

Therefore , the probability = 0.8413

A population's standard deviation serves as a gauge for how widely distributed its individual data points are. It's a way to express how dispersed from the mean the data is.

While a large standard deviation indicates that the data is more spread, a small standard deviation indicates that the data points are often close to the mean.

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Answer:

It is better to buy 8 eggs for 12 rupees.

Step-by-step explanation:

21/12 = 1.75

It cost 1.75 rupees per egg.

12/8 = 1.5

It costs 1.5 rupees per egg.

The large percentage obtained above will still not be a cause for celebration, because the observations demand a higher precision in the calculation results being obtained after running a logistic reg-session.

A precise calculation can be referred to or considered as a type of calculation, wherein the final results obtained are completely true and correct. Unlike approximate results, there is no scope of true and fair results in a precise calculation. Usually, rounding-off shall be avoided to obtained precise solutions at the end.

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Answer:

9

Step-by-step explanation:

a.) cube root of 729

³√729

= 9

b.) look for a number that you will multiply thrice to get 729

which is 9 or u will use your calculator

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54 cents cost for 9 inches of wire.

Cost rate is the amount that a worker costs the business. For instance, Zack bills $100 per hour and makes $25 per hour in costs. In other words, the corporation pays him $25 for every hour he bills. The profitability of your workers, projects, and employment is determined by cost rates.

The smallest unit of length is the inch (plural: inches). One foot is made up of 12 inches. An inch is equivalent to 2.54 cm in the metric system. For shorter measurements like measuring a pencil's length or an eraser's breadth, inches are utilized.

Wire measuring 16 inches costs 96 cents,

thus the price is 96/16 = 6 cents.

6cents is the cost per inch of wire

so for 9inch the cost will be

9*6 = 54cents will be the cost of 9inch of wire

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The formula for the cumulative probability of a Poisson distribution can be used to calculate the likelihood that there will be at most 2 reported car accidents over the course of a month:

Cumulative probability is equal to (number of events * e)/(average number of events per time period).

(Number of events / (-average number of events per time period)!)

In this instance, there are typically 0.05 events per time period (the likelihood that a car accident is reported at the intersection on any given day), and there are typically between 0 and 2 events per time period (at most 2 car accidents). With these values entered into the formula, we obtain:

Cumulative probability is equal to (0.05 * e(-0.05)) / 0, (0.05 * e(-0.05)) / 1, and (0.05 * e(-0.05)) / 2, respectively.

That amounts to:

Probability total = 1 + 0.05 + 0.0025

which translates to 1.0525 percent, or 105.25%. It's crucial to keep in mind that this probability exceeds 1, which is impossible. This is because the formula for cumulative probability makes the assumption that each event is independent, which means that the occurrence of one event has no bearing on the probability of the occurrence of another. The cumulative probability calculated using this formula may not accurately reflect the probability of at most 2 car accidents occurring throughout a month because in reality, the probability of a car accident occurring on a given day may be influenced by the number of car accidents that have already occurred. You would need to account for the dependencies between the events in order to calculate this probability precisely.

according to the central limit theorem, as sample size increases, the population from which the sample was taken approaches the normal distribution is a True.

The Central Limit Theorem states that when the sample size of a population increases, the sampling distribution of the mean of that population will become normally distributed, regardless of the distribution of the population from which it was taken.The Central Limit Theorem states that, as sample size increases, the distribution of the sample mean will approach a normal distribution, regardless of the shape of the data’s original population distribution. The larger the sample size, the more closely the sample mean will approximate a normal distribution. This means that, regardless of the distribution of the population from which the sample is taken, the sampling distribution of the mean will approach a normal distribution as the sample size increases.

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Answer:

10

Step-by-step explanation:

Using this equation,

l × w × h = v

We can simply substitute the numbers into the equation.

2 × 2 × 2 1/2 =?

(We know that the width is equal to 2 because it is a square.)

2 × 2 = 4,

4 × 2 1/2 = 10

The volume of the storage box is equal to 10.

The true inequality in the list of options is (a) 6π > 2

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

6π > 2, 7π > 30, 8 - π > 5 and π + 4 < 7

The value of the constant π is 3.142

So, we solve for π in the inequality expressions

A.6π > 2

This gives

π > 2/6

Divide

π > 0.33 -- true

B. 7π > 30

Divide

π > 4.29 -- false

C. 8 - π > 5

This gives

π < 3 -- false

D. π + 4 < 7

This gives

π < 3 -- false

Hence, the true inequality is 6π > 2

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Complete question

Which inequality is true?

A. 6π > 2

B. 7π > 30

C. 8 - π > 5

D. π + 4 < 7

To estimate the distance across the river, Delma can multiply the number of paces she takes by the length of each pace to find the total distance she walks.

For example, if Delma takes 27 paces and each of her paces is 14 inches long, she can estimate the distance she walks by performing the following calculation:

27 paces * 14 inches/pace = 378 inches

This means that Delma estimates the distance across the river to be 378 inches, or about 31.5 feet.

It's important to note that this is just an estimate, and the actual distance across the river may be slightly different due to factors such as the terrain or the accuracy of Delma's pacing.

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Measure of other angle is 133 if Two angles form a linear pair. One angle measure is 47° more than the other.

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. A linear pair is a pair of neighboring angles created by the intersection of two lines. 1 and 2 create a linear pair in the illustration. The same holds true for pairs 1, 2, 3, and 4. A linear pair's two angles are always supplementary, which means that the sum of their measurements is 180 degrees.

Given

Two angles form a linear pair.

One angle measure is 47° more than the other.

Other angle be x.

Sum of linear pair is 180.

x + 47 = 180

x = 180 - 47

x = 133

Measure of other angle is 133 if two angles form a linear pair. One angle measure is 47° more than the other.

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Answer:

Linear function:  y = x + 7.75

Step-by-step explanation:

A store sells packages of comic books with a poster. We are told that:

Let p be the cost of one poster.

Let c be the cost of one comic book.

Write a system of equations using the given information and the defined variables:

[tex]\begin{cases}p + 4c = 11.75\\p + 11c = 18.75\end{cases}[/tex]

Subtract the first equation from the second equation to eliminate p:

[tex]\begin{array}{crcrcl}&p&+&11c&=&18.75\\-&(p&+&4c&=&11.75)\\\cline{2-6}&&&7c&=&\;\;7.00\\\cline{2-6}\end{array}[/tex]

Solve for c:

[tex]7c=7.00[/tex]

 [tex]c=1.00[/tex]

Therefore, the cost of one comic book is $1.00.

Substitute the found value of c into one of the equations and solve for p:

[tex]\begin{aligned}p+4(1.00)&=11.75\\p+4.00&=11.75\\p&=7.75\end{aligned}[/tex]

Therefore, the cost of one poster is $7.75.

Now we know the cost of one poster and one comic, we can write a linear function that models the cost y of a package containing x number of comic books:

[tex]y = 1.00x + 7.75[/tex]

[tex]y =x + 7.75[/tex]

We are told that another store sells a similar package modeled by a linear function rule with initial value $6.99.  The initial value is the y-intercept of each function, i.e. the cost of the package when zero comics are sold. So the linear function for this package is:

[tex]y = x + 6.99[/tex]

To determine which store has the better deal, we need to compare the y-intercepts (the initial values). The store with the lower initial value provides a better deal because it charges less for the basic package (when the number of comic books is zero).

Since 6.99 is less than 7.75, the other store offers a better deal, as it has a lower initial cost for the basic package.

Answer:

[tex]\Huge \boxed{ \texttt{\bf{y = x + 7.75} }}[/tex]

Step-by-step explanation:

To find the linear function rule that models the cost [tex]\texttt{y}[/tex] of a package containing any number [tex]\texttt{x}[/tex] of comic books, we can use the given information:

Let's denote the cost of a poster as [tex]\texttt{P}[/tex] and the cost of a comic book as [tex]\texttt{C}[/tex]. Then, we can write two equations:

To solve these equations, we can use the method of elimination. Let's use this method to eliminate [tex]$$P$$[/tex]:

Now, substituting the value of [tex]\texttt{C}[/tex] back into equation 1:

Now that we have the cost of a poster (P) and a comic book (C), we can write the linear function rule as:

[tex]\Large \boxed{\texttt{y = x + 7.75}}[/tex]

Now, suppose another store sells a similar package modelled by a linear function rule with an initial value of $6.99. This means that the cost of a poster at the other store is $6.99. Since the cost of a comic book is the same at both stores ($1), the linear function rule for the other store is:

[tex]\Large \boxed{ \texttt{y = x + 6.99}}[/tex]

Comparing the two linear function rules, we can see that the second store has a better deal because the initial cost of a poster is lower ($6.99) compared to the first store ($7.75).

________________________________________________________

Answer:

y ≤ -3x - 3

Step-by-step explanation:

The graph crosses the y axis at -3.  The slope is -3.  (0, -3) .  From that point do down vertical 3 spaces and horizontally 1 space.  You will be at the point (1,-6)  Draw a line to join those 2 points.  The inequality is ≤ that means the solutions are the points on the line and below the line.  This is shown in the pink shading.

y ≤ -3x - 3

Step-by-step explanation:

The graph crosses the y-axis at -3.  The slope is -3.  (0, -3) .  From that point do down vertical 3 spaces and horizontally 1 space.  You will be at the point (1,-6) Draw a line to join those 2 points.  

The inequality is ≤ which means the solutions are the points on the line and below the line.  This is shown in the pink shading.

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The exponential function to show the growth in y years is P(1.2)^y

An exponential function is a mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

In this problem, this is an exponential growth since the rate increases.

Let;

The exponential function to represent this will be;

A = P(1 + r)^y

A = P(1 + 0.2)^y

A = P(1.2)^y

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The measures of those two angles is 30 degrees and 40 degrees.

What is angles?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.

A pair of rays (half-lines) having a shared terminal are combined to form an angle. The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its arms.

360 - (190 + 100) = sum of other two angles

360 - 290 = 70

70/(3+4) = 70/7 = `10

10 × 3 = 30 degrees, 10 × 4 = 40 degrees.

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(17) The value of x would be 20 degrees.

(18) The value of x would be 21.25 degrees.

(20) The value of x would be 6 degrees.

What is the sum of the angles of a triangle?

The sum of the angles of a triangle is 180 degrees. This is a fundamental property of triangles and is known as the triangle sum theorem.

(17)

By using the property of the sum of angles of a triangle, we get

(x+6) + (3x+9) + (4x+5) = 180

Simplifying the left side of the equation gives:

8x + 20 = 180

Subtracting 20 from both sides of the equation gives:

8x = 160

Dividing both sides of the equation by 8 gives:

x = 20°

(18) In a right triangle, one angle is a right angle, which measures 90 degrees. If we know the measures of the other two angles in the triangle, we can use the fact that the sum of the measures of the angles in a triangle is 180 degrees to find the value of x.

(2x-4) + (6x+14) + 90 = 180

Simplifying the left side of the equation gives:

8x + 10 = 180

Subtracting 10 from both sides of the equation gives:

8x = 170

Dividing both sides of the equation by 8 gives:

x = 21.25

(20) To find the value of x, we can use the fact that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. We can write an equation using this fact and the measures of the three angles given in the problem:

(2x+13) + (15x+19) = (7x+92)

Simplifying the left side of the equation gives:

17x + 32 = 7x + 92

Subtracting 7x from both sides of the equation gives:

10x + 32 = 92

Subtracting 32 from both sides of the equation gives:

10x = 60

Dividing both sides of the equation by 10 gives:

x = 6

Hence,

(17) The value of x would be 20 degrees.

(18) The value of x would be 21.25 degrees.

(20) The value of x would be 6 degrees.

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The magnitude of AB based on the information is 5.1.

To show that points A, B, and C are colinear, we need to show that they lie on the same line. One way to do this is to find the direction vector of the line passing through A and B, and then check whether point C is on the same line.

The direction vector of the line passing through A and B is given by the vector AB, which is equal to OB - OA. Substituting the given values for OA and OB, we find that AB = (3i - 2i) + (-2j + 3j) = i + j.

To check whether point C is on the same line as A and B, we can find the direction vector of the line passing through C and any one of the other two points.

We can find the direction vector of the line passing through C and A, which is given by the vector CA = OA - OC = (2i + 3j) - (i + 6j + 3k) = i + (-3j - 3k).

Since the direction vectors of the lines passing through A and C and through B and C are both in the same direction, we can conclude that points A, B, and C are colinear.

To find the magnitude of AB, we can use the distance formula:

AB = √((3 - 2)² + (-2 - 3)²) = √(1² + (-5)²) = √(26) = 5.1

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definition of trapezoid=

A trapezoid is a convex quadrilateral with two parallel sides of opposite length and two unequal sides. Dive into the world of learning and understanding the properties of trapezoids. People usually rely on different shapes to build, create, or measure something. One of the most common shapes is the trapezoid. A two-dimensional shape that represents a table drawn on paper. Trapezoidal patterns can be found on water glasses, table lamps, flower pots, boats, etc. after question

given data,

The measurement of the angle ∠B is

65° + 65° + 115° + ∠B = 360°

∠B = 115°

In that case, the correct choice is D.

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The graph of y = k/x has k = 4.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

y = k/x

The coordinates from the graph:

(1, 4) and (2, 2).

This can be considered as,

(1, 4) = (x, y) = (2, 2)

Now,

y = k/x

4 = k/1

k = 4

y = k/x

2 = k/2

k = 4

Thus,

The value of k is 4.

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The range of possible lengths for the third side be

0 ft < x < 76 ft

0 ft < x < 33 ft

Given, two sides of a triangle

we have to find the range of possible length for the third side of the triangle.

a) 24 ft and 52 ft

given first side of the triangle be, 24 ft

and second side of the triangle be, 52 ft

as we know that the third side should be less than the sum of the remaining two sides of any triangle.

So, let the third side be x

x < 24 + 52

x < 76

Therefore, the third side should be less than 76 ft and obviously greater than 0 ft.

Range of the third side be, 0 ft < x < 76 ft

b) 16 ft and 17 ft

given first side of the triangle be, 16 ft

and second side of the triangle be, 17 ft

as we know that the third side should be less than the sum of the remaining two sides of any triangle.

So, let the third side be x

x < 16 + 17

x < 33

Therefore, the third side should be less than 33 ft and obviously greater than 0 ft.

Range of the third side be, 0 ft < x < 33 ft

Hence, the range of possible lengths for the third side be

0 ft < x < 76 ft

0 ft < x < 33 ft

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The population in order to calculate the mean height will be all the students attending the college.

The population is the entire group of individuals being studied. In this case, the population is all the students who goes to the college.

Every member of a group constitutes a population. It is the inverse of a sample, which is a percentage or proportion of a group. It is sometimes possible to poll every member of a group. The U.S. Census is a quintessential example of a population, as it is required by law that every member of the U.S. population reply. In most circumstances, surveying everyone is unfeasible in statistics.

Consider how long it would take you to phone every dog owner in the United States to find out what brand of dog food they preferred. Furthermore, people may choose not to respond or may forget to respond, resulting in incomplete censuses. By definition, incomplete censuses become samples.

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-7/3 this expression can be represented on the Number Line.

Number Line:

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On solving the provided question we cans ay that  - To start, we compare the life expectancy in 2015 to that of 20 years ago. Difference = 78.8 - 75.8 = 3 years, therefore.

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often indicated by the percent sign '%', but the abbreviations 'pct.', 'pct', and 'pc' are also sometimes used. Percentages are dimensionless numbers. It has no units of measure. Percentages are essentially fractions with a denominator of 100. Use a percent sign (%) next to the number to indicate that the number is a percentage. For example, if you get 75 out of 100 questions correct on a test (75/100), you get a score of 75%.

To start, we compare the life expectancy in 2015 to that of 20 years ago. Difference = 78.8 - 75.8 = 3 years, therefore.

Then, we multiply the quotient by 100% after dividing this difference by the 1995 life expectancy. Consequently, (3/75.8) x 100% = 3.96%

As a result, the increase in life expectancy is around 3.96 percent.

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Answer:

I'ts 4%,

Step-by-step explanation: