A simple random sample of 40 items resulted in a sample mean of 25. The population standard deviation is 5.a. What is the standard error of the mean? round answer to 2 decimal place.b. At 95% confidence, what is the margin of error? round answer to 2 decimal place

One is not considered a prime factor.

One has only a single element, which is itself, hence it is not regarded as a prime number. A prime number is a positive integer greater than 1 with just itself and the number one as its other positive divisors. Since there is only one divisor of one, one is not regarded as a prime number. Additionally, 1 does not adhere to the conventional characteristics of prime numbers and is regarded as a unit in mathematics.

For instance, a number's value is unaffected by division or multiplication by one, and it is always one when raised to any power. Since one does not meet the criteria for primes and does not share their characteristics, it is likewise excluded from the set of prime numbers.

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Using the formula of volume of a cone, the diameter of the cone is 5cm

The volume of a cone is a measure of the amount of space inside the cone. It can be calculated using the formula:

Volume = (1/3) * π * r^2 * h

Where:

The formula for the volume of a cone is a product of 1/3 and the product of π, radius square and height. The unit of measurement of the volume will be the cube of the unit of measurement of the radius and height.

It's important to note that a cone has a circular base, the radius of which is the distance from the center of the base to its edge. The height of the cone is the distance from the tip of the cone to the center of the base.

In this problem, we can simply find the diameter by calculating the radius.

V = 1/3(πr²h)

Substituting the values into the formula

42.5 = 1/3(3.14 * r² * 6.5)

42.5 * 3 = 20.41 r²

127.5 = 20.41r²

r² = 6.2469

r = 2.5

But the radius of a circular body is always half the length of it's diameter

d = 2 * r

d = 2 * 2.5

d = 5

The diameter is 5cm

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Answer:

1

Step-by-step explanation:

use Pythagoras as shown

The equation y = 3x describes the relationship between x and y in the table.

What is the slope intercept?

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b.

A relationship that when graphed produces a straight line. Equation. A mathematical sentence that sets 2 expressions equal to each other.

This equation shows that for every increase of 1 in the value of x, y increases by 3.

This is consistent with the values in the table, where for each increment of 1 in x, y also increases by 3.

Hence, The equation y = 3x describes the relationship between x and y in the table.

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The total number of different arrangements is 36 * 1 = 36

Permutation and Combination:

Permutation and combination are the ways to represent a group of objects by selecting them in a set and forming subsets. It defines the various ways to arrange a certain group of data. When we select the data or objects from a certain group, it is said to be permutations, whereas the order in which they are represented is called a combination.

There are 9 types of flowers and you are choosing 2 of them, so the number of ways to choose the flowers is 9 choose 2 which is equal to (98)/(21)=36.

There is 1 vase and you are choosing 1 of them, so the number of ways to choose the vase is 1 choose 1 which is equal to 1.

The total number of different arrangements is 36 * 1 = 36.

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Answer

a=3/2

b=1/2

Step-by-step explanation:

let f(x)=ax+b

f(2x-3)=a(2x-3)+b

f(2x-3)=2ax-3a+b

3x-4=2ax-3a+b

3x=2ax

3=2a

a=3/2

b-3a=-4

b-3(3/2)=-4

b=1/2

Answer:

π /5

Step-by-step explanation:

Use the form a * cos(bx−c) + d

The  expression that shows how many minutes it will take to complete an order, assuming there are x parts in an order is 2x+10y = x

The statement states that  it takes 2 minutes to manufacture each part and 10 minutes to pack all the parts for an order.

Also, it is stated that there are  x parts in an order

This implies that  2(x) + 10(y) = x

Opening the brackets to have

2x + 10y = x

This is to say that 2 minutes of manufacture and 10 minutes of packing will give all the parts.

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the area of the shaded regions of all circles in terms of pi is a = 253.42 in², a = 215.98 yd², a = 25.13 ft², a = 201.06 yd² and a = 64.14 ft² respectively.

What is the shaded region?

The area of the shaded region is the difference between the area of the entire polygon and the area of the unshaded part inside the polygon. The area of the shaded part can occur in two ways in polygons. The shaded region can be located at the center of a polygon or the sides of the polygon.

The formula for calculating the area of a shaded segment of a circle is:

a = π ∗ r² ∗ angle/360

The area of the sector depends on the radius of the circle r and the measure of the angle t.

The area of a sector for angle t is  A = t/360 ⋅ π ⋅ r²

We have given the figures with their radius and shaded region angles,

In the first figure:

radius r =  11 in and  shaded region angle = 260°

so, a = π ∗ r² ∗ angle/360

a = π ∗ (11)² ∗ 260/360

a =  π ∗ 121 ∗ 2/3

a = 253.42 in²

In the second figure:

radius r =  15 yd and  shaded region angle = 110°

so, a = π ∗ r² ∗ 110/360

a = π ∗ (15)² ∗ 110/360

a =  π ∗ 225 ∗ 11/36

a = 215.98 yd²

In the third figure:

radius r =  6 ft  and  shaded region angle = 80°

so, a = π ∗ r² ∗ 80/360

a = π ∗ (6)² ∗ 80/360

a =  π ∗ 36 ∗ 2/9

a = 25.13 ft²

In the fourth figure:

radius r =  16 yd  and  shaded region angle = 90°

so, a = π ∗ r² ∗ 90/360

a = π ∗ (16)² ∗ 90/360

a =  π ∗ 256 ∗ 1/4

a = 201.06 yd²

In the fifth figure:

radius r =  7 ft  and  shaded region angle = 150°

so, a = π ∗ r² ∗ 150/360

a = π ∗ (7)² ∗ 150/360

a =  π ∗ 49 ∗ 5/12

a = 64.14 ft²

Hence, the area of the shaded regions of all circles in terms of pi is a = 253.42 in², a = 215.98 yd², a = 25.13 ft², a = 201.06 yd² and a = 64.14 ft² respectively.

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Answer:

Below in bold.

Step-by-step explanation:

m < DAC  = 360 -15 - 155 - 166

                = 24⁰

The bearing of D from A

                = 180 + 15 + 24

                 =  219⁰

or S 39⁰ W.

So, 216° is the largest angle among the heptagon.

A heptagon has 7 sides and 7 angles. We know that two of the angles are (3x – 17)° and one angle is (4x – 36)°. The remaining four angles are all (2x – 13)°.

We can find the total measure of all the angles in the heptagon by using the formula for the sum of the angles in a polygon:

(n-2) * 180 = (7-2) * 180 = 5 * 180 = 900°

We can set up an equation to find the measure of the remaining angles by subtracting the measure of the known angles from the total measure:

900 = 2(3x – 17) + (4x – 36) + 4(2x – 13)

Expanding and simplifying the equation:

900 = 6x – 34 + 4x – 36 + 8x – 52

900 = 18x – 122

Now we can solve for x:

18x = 1022

x = 57

Now we know that one of the angle is (4x – 36) = (4*57 - 36) = 216°

That is the largest angle among the heptagon.

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x axis described as the independent variable

What is horizontal line?

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x-axis is the horizontal line dividing the plane into parts. The x-axis is also described as  the abscissa and it used for independent variable.

A horizontal line is any straight path that runs from left to right or from right to left. In coordinate geometry, a line is said to be horizontal if two points on it have the same Y-coordinates. Its origins are in the term "horizon." In other words, the horizontal lines and the horizon, or x-axis, are always parallel.

A line that moves from left to right is said to be horizontally oriented. When you look beyond the horizon, you are seeing the dawn over a horizontal line. The x-axis serves as a representation of a horizontal line.

A horizontal line is one that extends from left to right across the full page. This is explained by the fact that horizontal lines are parallel to the horizon. By considering this fact, children can maintain the meaning of horizontal lines. Its root word, "horizon," refers to the line that may be seen separating the earth from the sky.

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Answer:

All I know is:

Step-by-step explanation:

You have to Graph

Then Find the Empirical/Simplest Formula

After you have to Calculate the Formula Weights

Then Find the Derivative - d/dx

Last, Find the Derivative - d/dy

Sorry I don't know the real answer.

Answer:

Step-by-step explanation:

Density is a measure of how much mass is contained in a given volume. It is calculated by dividing the mass of an object by its volume.

To find the density of the cow's leg bone, we can use the following formula:

Density = mass / volume

In this case, the mass of the bone is 18 g, and the volume is 10 cm3. So we can plug in these values into the formula:

Density = 18 g / 10 cm3

The density of the bone is 1.8 g/cm3.

It's important to note that this is the density of the bone, but it's not the same density as a whole cow. Also, density can also change depending on the bone and the species.

Therefore , the solution of GCD problem comes out to be the greatest common factor of 252 and 60 is 223 = 12.

The number that divides two or more numbers most precisely by itself is said to be the largest common denominator (GCD) of those numbers. It is also known as the highest common denominator (HCF). Since both 15 and 10 can be divided by 5, for instance, the highest common factor of these two numbers is 5.

Here,

The highest common factor (hcf), greatest common factor, and the greatest common divisor (gcd) are other names for it (gcf).

The highest integer which divides both numbers is known as the largest common series of 2 numbers.

We must choose the number that divides 252 and 60 most equally.

252's prime factorization is as follows:

252 = 2×2×3×3×7

the prime factors that make up 60 are.

60 = 2×2×3×5

These common elements are: 2 2 3

Therefore, the greatest common factor of 252 and 60 is 223 = 12.

Therefore , the solution of GCD problem comes out to be the greatest common factor of 252 and 60 is 223 = 12.

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Answer:

obviously 16 meters to the west

The correct system of equations to determine the number of nickels and dimes that Luis has is: n + d = 30 and 0.5n + 0.1d = 2.20.
What is Equation?
In mathematics, an equation is a statement that two expressions are equal. It consists of two expressions connected by an equal sign (=). For example, the equation "2 + 2 = 4" states that the sum of two and two is equal to four. Equations are used to describe relationships between different variables, as well as to solve unknown values.

This system of equations can be used to solve for n and d. The first equation states that the total number of coins is equal to 30, while the second equation states that the total value of the coins is equal to $2.20. By solving these two equations, it can be determined how many nickels and dimes Luis has.

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Step-by-step explanation:

since we got a point and actually the slope, we can start with the point-slope form and transform.

you know that the slope-intercept form is

y = ax + b

"a" is the slope, "b" is the y-intercept.

we see therefore, that the slope of the given line is 1/4.

a perpendicular slope (90°) turns the slope fraction upside-down and flips the sign.

so, the perpendicular slope is -4/1 = -4.

the point-slope form is

y - y1 = a(x - x1)

"a" is again the slope (for the new line this is -4), (x1, y1) is a given point. in our case (1, 1).

so, we get

y - 1 = -4(x - 1)

we transform by simplifying :

y - 1 = -4x + 4

y = -4x + 5

y = -4x + 5

is the perpendicular line in slope-intercept form that passes through (1, 1).

The Partitions occur on the line segments that Partitions are referred or called  as directed line segments .

What are Directed Line Segments  ?

The Directed Line Segments are defined as the line segments that has distance (length) and direction .

A line segment can be partitioned into many smaller segments which are compared/called as ratios and the Partitions that occur on line segments  are referred to as Directed segments .

The Simple Definition of Partition means to separate or to divide .

let AB be any line segment and we Partition the line AB in the ratio a:b , it means that we are dividing it into (a + b) equal parts and then we find a  point C which is "a" equal parts from A and "b" equal parts from B .

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Answer:

16 ounces of $400 alloy

Step-by-step explanation:

If JK has endpoints (-10, 1) and K(2, -2). Point L divides JK into two parts with lengths in a ratio of 2:1 then the possible locations of L is at (-7, 0.25)

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0

L divides JK into two parts with lengths in a ratio of 2:1

so JL:LK is either 2:1 or 1:2

Let us solve the midpoint of JK

Midpoint=(-10+2/2, 1-2/2)

M=(-4,-1/2)

Midpoint of JM is (-10-4/2, 1-1/2/2)

L: (-7, 1/4)

Hence, the possible locations of L is at (-7, 0.25)

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There are 15 ways to put 4 indistinguishable balls in 3 indistinguishable boxes.

Since the balls and boxes are indistinguishable, we only need to count the number of ways to distribute the 4 balls among the 3 boxes.

We can use the concept of stars and bars. The number of ways to distribute n indistinguishable items into r distinguishable boxes is given by (n+r-1) choose (r-1).

Here, the number of ways to distribute 4 indistinguishable balls into 3 distinguishable boxes is (4+3-1) choose (3-1) = 6 choose 2 = 15

So, there are 15 ways to put 4 indistinguishable balls in 3 indistinguishable boxes.

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You can get a number between two numbers by adding the two numbers together and then dividing by two.

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On solving the provided question, we can say that there are 66 ways , on counting .

Calculating the number of components in a limited collection of objects is the process of counting. H. Calculate the set's size. Calculating the quantity or overall number of items in a collection or group is the definition of counting in mathematics. In other words, counting something entails reciting the number in order and individually valuing each item in the group. To count objects, use the count number. 1, 2, 3, 4, 5, and so forth are examples of counting numbers. In daily life, people employ the numbers required to count items, items, money, etc. Because of this, count numbers cannot be fractions, integers, negative numbers, or decimals.

here in question,

there are 66 ways.

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The equation has one extraneous solution which is n is approximately 2.38

Here we have the following equation

=> 9/n²+1 = n+3/4

Now, we have to find the value of n by simplifying the given equation,

In order to so the simplification we have to do the cross multiplication on then, then we get the resulting expression as,

=> n²+1(n + 3) = 36

When we expand it then we get,

=> n²+1(n) + n²+1(3) = 36

=> n³ + n + 3n² +3 - 36 = 0

=> n³ + 3n² +  n - 33 =  0

Here we have to find the roots are the  x  values where the graph intersects the x-axis.

And then we have to find the roots replace y with  0  and solve for  x.

Then the value of n is obtained as

=> n  ≈  2.38

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The possible values of x are values greater than 0.67

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

0.6 < x > 67%

Express 67% as a decimal

So, we have the following representation

0.6 < x > 0.67

The above statement means that 0.6 is less than x and x is greater than 0.67

This implies that x is greater than 0.6 and x is greater than 0.67

The possible values in this case are values greater than 0.67

Take for instance, 0.7 is greater than 0.6 and 0.67

Hence, the value of x is 0.7

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Answer:

Step-by-step explanation:

3a-7=-4b+1

3a=-4b+1-7

simplify:

3a=-4b-6

divide by 3:

a=-4b-6/3

Answer:

.10d + .05n  ≤ 1.00

Step-by-step explanation:

a dine with worth 10 cents and a nickel is worth 5 cents.  Together this amount cannot be over 1 dollar.

The 40 randomly selected teachers: sample.

The list of all teachers in the school district: frame.

The 245 teachers in the school district: population.

A sample is a subset of a population that is selected for research purposes. In this case, the school board has randomly selected 40 teachers out of the 245 teachers in the district as a sample to survey their opinions on the new professional development plan.

A population is the entire group of individuals or objects that researchers are interested in studying. In this case, the population is all 245 teachers in the school district.

A frame is the list or method used to define the population. In this case, the frame is the list of all 245 teachers in the school district that was used as the basis for selecting the random sample of 40 teachers.

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