Suppose you have a population with mean 25 and standard deviation 20. You take samples of size 100 and consider the distribution of the means of those samples. What is the mean of the sample means?.

Answer: The arrow is pointing to 76.5.

Step-by-step explanation: It's pointing to 76.5 because there are 10 spaces between 75 and 80 so in that case, each line is .5, and since it's on the third line that means it is 1.5 more than 75 so 76.5.

Answer:

C) The arrow points to 76.5.

Step-by-step explanation:

The number line is divided into 10 parts equally.

We can find out the distance between each point by taking the difference between the largest and smallest number on the number line and dividing the difference by 10.

80 - 75 = 5

5/10 = .5

So, the distance between each number/mark on the line is .5

Now, we can label each point by adding .5 to each mark as we go. Then, we'd get this.

*see attachment below

Since the number line constructed here has all the values, we can now tell which value the arrow is pointing to.

The answer is therefore 76.5.

The probability that at least five spots will be showing up on the die is 1/3.

It is given that a professor rolls a fair, six-sided die.

We need to find the probability that at least five spots will be showing up on the die.

Total possible outcomes = {1,2,3,4,5,6}

Number of total outcomes = 6

At least five spots will be showing up on the die. So,

Favorable outcomes = {5,6}

Number of favorable outcomes = 2

Formula for probability:

Probability = [tex]\frac{Number of Favorable Outcomes}{Number of Total Outcomes}[/tex]

On substituting Number of favorable outcomes and Number of total outcomes in the formula of Probability, we get

Probability = 2/6

Probability = 1/3

Therefore, the required probability is 1/3.

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Answer:25.8184143223

1+1+278*67/782

1+1+18626/782

2+23.8184143223

25.8184143223

The equation of the circle with the centre (5,7) and containing the point p (1,9) is [tex]\sqrt{20} =(x-5){2}+(y-7){2}[/tex]

The equation for a circle in standard form is [tex](x-x1){2}[/tex]+ [tex](y-y1){2}[/tex]  = [tex]r{2}[/tex], where (x, y) denotes arbitrary coordinates on the circle's perimeter, r denotes the circle's radius, and (x1, y1) denotes the coordinates of the circle's centre.

The equation of a circle with centre (x1,y1)

[tex](x-x1){2}[/tex]+ [tex](y-y1){2}[/tex]  = [tex]r{2}[/tex]

we know the centre , which is (5,7) so the equation changes to:

[tex](x-5){2}[/tex]+ [tex](y-7){2}[/tex]  = [tex]r{2}[/tex]

putting the values of the point p we get

[tex](1-5){2}[/tex] [tex]+ (9-7){2}[/tex][tex]= r{2}[/tex]

r=[tex]\sqrt{20}[/tex]

so the equation of the circle will be:

[tex]\sqrt{20} =(x-5){2}+(y-7){2}[/tex]

Therefore the equation that satisfies the given condition of a circle with centre (5,7) and containing point p (1,9) is [tex]\sqrt{20} =(x-5){2}+(y-7){2}[/tex]

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Part 1

[tex)400+30x=4900[/tex]

Part 2

[tex]30x=4500 \\ \\ x=150[/tex]

So, the answer is 150 ft².

The resultant matrix after elementary row operation is:

[tex]A = \left[\begin{array}{ccc}-12&20&8\\-24&3&-9\end{array}\right][/tex]

What is elementary row operation?

In mathematics, the elementary row operation is a method in which the two rows exchanged. In this, the rows are either multiplied, added or division. Sometimes, single row is multiplied by some constant.

According to the question, the given matrix A is written below:

[tex]A = \left[\begin{array}{ccc}-3&5&2\\8&-1&3\end{array}\right][/tex]

Now, performing elementary row operations represented by [tex]-3R_{2} +4R_{1}[/tex]

The given matrix becomes after elementary row operations:

[tex]A = -3R_{2} + 4R_{1} = \left[\begin{array}{ccc}-12&20&8\\-24&3&-9\end{array}\right][/tex]

Hence, the resultant matrix after elementary row operation is::

[tex]A = \left[\begin{array}{ccc}-12&20&8\\-24&3&-9\end{array}\right][/tex]

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Answer: [tex]y=\frac{1}{7}x+19[/tex]

Step-by-step explanation:

Perpendicular lines have slope that are negative reciprocals, so the slope of the line we want to find is 1/7.

The equation in point-slope form is [tex]y-21=\frac{1}{7}(x-14)[/tex].

Rearranging into slope-intercept form,

[tex]y-21=\frac{1}{7}x-2 \\ \\ y=\frac{1}{7}x+19[/tex]

The correct option is D) g(x) = |x - 2| for the shifting of graph of f (x) = |x| is shifted to the left 2 units.

For the given question, the function is given as;

f(x) = |x|

There is a shifting of 2 units towards the left, it means there is shift on the x-axis toward the negative x-axis.

Then, value of x will be reduced by 2 units, which is given by function.

g(x) = |x - 2|.

Thus, the function which correctly described shifting of 2 units left is g(x) = |x - 2|.

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Answer:The correct option is D) g(x) = |x - 2| for the shifting of graph of f (x) = |x| is shifted to the left 2 units.

Step-by-step explanation: I did it on plato.

The circumference of the given circle will be 18.84cm and its area will be 28.26cm²

the center of the given circle is A with coordinates (2,3)

we are given that each block on the graph represents 1cm,

on observing the graph we can conclude that the radius of the circle is 3cm.

circumference of the circle is given by  the formula,

2πr

taking pi as 3.14 and substituting r=3 in the above formula we get,

2*3.14*3

=18.84cm

thus the circumference of the circle will be 18.84 units.

Similarly, area of a circle can be calculated using the formula,

πr²

taking π as 3.14 and substituting r=3 in the above formula,

3.14*3²

=28.26cm²

What is the difference between area and perimeter?

Perimeter is - "distance around the outside of a shape" while area is - "measures of the space inside a shape."

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Step-by-step explanation:

0 20 40 60 80 100.................

Using mathematical operations, the maximum whole number of gigabytes of data Genesis can use while staying within her budget is 2GB.

Mathematical operations are used in mathematical functions to produce a defined output.

Some of the mathematical operations include addition, subtraction, multiplication, division, exponentiation, and modulus operations.

In this situation, we used the mathematical operations of subtraction, division, addition, and multiplication to determine Genesis's data maximum usage that does not exceed her budget.

Fixed cost per month = $40.50

Usage rate per gigabyte or part thereof = $5

Budgeted bill = $55 per month

Maximum gigabyte usage per month = 2.9 {($55 - $40.50) ÷ $5}

But Genesis cannot use 3GB but only 2GB because 3GB will make her total bill exceed her budget.

Check:

Cost of using 3GB = $55.50 ($40.50 + $5 x 3)

Cost of using 2GB = $50.50 ($40.50 + $5 x 2)

Thus, for Genesis to maintain her data plan within budget, the maximum she can spend is 2GB.

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Answer:

B) To make a right triangle in the center, the area of the smaller two square must add to equal the area of the largest square

Step-by-step explanation:

1) add the area of the two smaller squares together

f^2= 9

g^2 = 16

9+16=25

2) compare the sum of the two squares to the larger square (the hypotonus)

h^2= 25 so, f^2 + g^2 = h^2

3) The area of the smaller squares is equal to the area of the larger square, therefore b is the correct answer.

The layer of dirt would be between 3 and 4 yards and precisely 3.6458 yards.

Given the volume of the lot is 7000 cubic yards.

After spreading to an even layer

The dimension is 30 yards and 64 yards

The volume of the lot can be given as Length x Width x Depth

Let us say the depth of the lot is x

Which means

30 x 64 x X = 7000

1920 x X = 7000

X = 3.6458

Hence the depth of the lot is 3.6458 which is between 3 and 4.

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In a case whereby the area of a trapezoid is given by the formula A=12(b1+b2)h then the equation for b2 is b2= (A - 12hb1)/12h.

The formula for the  trapezoidis given as A=12(b1+b2)h , where the value of term b2 is been exdpected to be found.

firstly, we need to open the bracket as :

A=12(b1+b2)h

A= 12hb1 + 12hb2

Then this can be simplified as  12hb2= (A - 12hb1)

Then we can try to make the b2 the subject of the formula as

b2= (A - 12hb1)/12h.

Therefore, the value of the term b2 can be written as b2= (A - 12hb1)/12h.

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The experimental probability of an odd number other than 9 being generated is 0.38.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

According to the probability formula, the probability of an event occurring, or P(E), is equal to the proportion of positive outcomes to all outcomes. P(E) is defined mathematically as favorable outcomes divided by total outcomes.

Given Data

A random number generator is used to create a list of 150 single-digit numbers. Of those 150 numbers, 72 are odd and 78 are even. The number 9 was generated 15 times.

Total numbers generated = 150

Odd numbers = 72

Even numbers = 78

Generation of number 9 = 15

Number of odd numbers except 9 itself

= 72 -15

= 57

Probability = [tex]\frac{Odd numbers except 9 itself}{total munbers}[/tex]

Probability = [tex]\frac{57}{150}[/tex]

Probability = 0.38

The experimental probability of an odd number other than 9 being generated is 0.38.

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Answer:

Step-by-step explanation:a-t457 =e36_0uh

If Caleb worked his 40 regular hours last week, plus 6 overtime hours at the time-and-a-half rate. His gross pay was $1,063. His hourly rate is : $21.69.

Hourly rate can simply be defined as the wages earn per hour.

Given data :

Regular hours = 40

Over time = 6 ( 1.5 ) = 9

Gross pay = $1,063

Hence,

let h represent the hourly rate

So,

1.5h = overtime rate

Now let determine the hourly rate

40h + 6(1.5h) = 1,063

40h + 9h = 1,063

49h = 1,063

Divide both side by 49h

h = 1,063/ 49

h = $21.69

Therefore the hourly rate is the amount of $21.69.

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The error Julius made in his explanation is using the area of a rectangle as the longest side instead of area of a square.

Pythagorean theorem is the sum of the square of opposite and adjacent sides which result in the sum of the square of the hypotenuse of a triangle.

c² = a² + b²

Where,

The error Julius made in his explanation is using the area of a square as the hypotenuse. The figure he used to represent the longest side (hypotenuse) is a rectangle.

The correct working should be:

c² = area of square a + area of square b

c² = 25 + 16

c² = 41

c = √41

c = 6.40312423743

Approximately,

c = 6.4

In conclusion, Julius made the mistake of representing the longest side with area of a rectangle instead of a triangle.

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If each digit can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9, giving a total of 10 possible numbers for each digit. if a pin is 4 digits, each digit can be any one of the 10 possible numbers, The different possible combinations are there is : 10,000.

Given :

Digit = 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9

Possible number  = 10

Pin = 4 digits

Now let determine the different possible number

Possible number combination = 10 x 10 x 10 x 10

Possible number combination = 10,000

Therefore the combination is 10,000.

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The value of k that will make the quadratic equation kx² - 4x + 1 = 0 to have two equal roots is; k = 4

The general form of representing a quadratic equation is;

ax² + bx + c = 0

Now, we are given the quadratic equation which is;

kx² - 4x + 1 = 0

Now, for a quadratic equation to have 2 equal roots, it means that;

b²  = 4ac

Thus, applying that to our given quadratic equation gives us;

(-4)² = 4(k * 1)

4k = 16

k = 4

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By using the method subtraction, Jackson's height is 1.25m.

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.

Given that,

Grace's height is 1.45 m.

Jackson is 0.2 m shorter than Grace.

Jackson's height is 1.45 -0.2 = 1.25

Therefore, Jackson's height is 1.25m.

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The approximate value of x(t), which indicates the location of coordinate the ladder's foot at time t seconds, is 6.85. 7

Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ). Mathematicses, scientists, and engineers frequently employ a variety of coordinate systems.

The location in the cartesian plane will be determined by the coordinate points. A point's distance from the y axis is known as the x-coordinate, also known as the abscissa, and its distance from the x-axis is known as the y-coordinate, also known as the ordinate.

based on the information provided,

x = the distance between the wall and the bottom of the ladder

y = distance of the top of the ladder from the ground

x² + y² = 25²

x² + 7² = 25²

x² = 625 -49 = 429

y = √576

Differentiating the equation with respect to time t gives

2x dx/dt + 2y dy/dt = 0

dx/dt = -y dy/dt / x

 = -√576 * (2) / 7

= 6.85 feet per second approximately.

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This is a Metric conversion problem. Note that it will take 38.4 minutes to create a 2-foot by 4-foot pattern drive. See the explanation below.

There are several ways to do this. Let's use the area of the times and that of the pattern drive.

Note that the area of the 3inch by 5-inch tile =

Area of a rectangle

L x B =

3 x 5

= 15inches

Applying the same rule to the pattern drive, we have
2 x 4

= 8 foot

Note that 1 foot = 12 inches

For convenience, thus, we convert the area of the pattern drives into inches. This gives us:
8 x 12

= 96 inches

To get how many minutes it will take to create a 2 by 4-foot pattern drive, we have

Recall that it takes 6 minutes to lay a 3x5 which is 12 inches in area.
Hence,

96/15
= 6.4
6.4 x 6
= 38.4 minutes.
Hence, it will take Rachel 38.4 minutes to lay a 2 by 4-foot pattern drive given the parameters above.

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The principal of account A is $20.83 and the principal of account B is $58.33. Account 2 earned the most interest rate in the first​ month.

The formula to calculate Simple interest, Simple interest = Principal × rate of interest × time.

The principle for Account A would be,

2 = Principal × 3.2% × 3

So, the principal is $20.83

The principle for account B would be,

38.50 = Principal × 2.2% × 30

So, the principal is $58.33,

The interest rate for both accounts is now as follows:

For account 1

= $20.83 × 3.2%

= $0.67

And, for account 2

= $58.33 × 2.2%

= $1.28

Account 2 has the greatest interest rate, thus it is taken into account.

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Answer:

subtract 2x from 3x thats x so 50=x

Step-by-step explanation:

Answer:x=50

Step-by-step explanation:bring 3x over on one side with 2x and bring 50 over on the other side by itself.

The equation becomes 2x-3x=-50

2x-3x is -x

so the equation is -x=-50

there are two negatives in the equation so you make the equation positive because a negative and a negative equals a positive

Therefore the answer is x=50

The cost of the polishing, £C, is given by C = 6πr² + 300/r​.

The volume of the solid cylinder is 75 m³.

Formula for volume of cylinder = πr²h.

Where R is rhe radius of cylinder and h is the height of the cylinder.

So we can write,

πr²h = 75

h = 75/πr².

So the height of the cylinder is 75/πr² centimeters.

Curved surface area of the cylinder is 2πrh m².

Cost of polishing the curved surface area is £2/cm².

Total cost of polishing the curved surface area = £2×2πrh

Area of the base and the top is 2(πr²).

Cost of polishing base and top is £3/cm².

Cost of polishing 1m² of the base and top,

Cost of area of base and top = £3/cm².

Total Cost of polishing base and top area = £3×2(πr²)

The total cost C of polishing the whole glass,

C = 4πrh + 6πr²

Puting the value of h = 75/πr²

C = 4πr(75/πr²) + 6πr²

C = 6πr² + 300/r.

Hence it is proved that the total cost of polishing is,

C = 6πr² + 300/r.

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there are no restrictions other than 2 x + 1 > 81 on the radical inequality.

We are given the radical inequality as:

⁴√ 2 x + 1 > 3

We need to find the restriction on this inequality.

For this we will first put x on one side and other constant on the other side.

So, we get that:

2 x + 1 > 3⁴

2 x + 1 > 81

So, the restriction is not from the given options.

But, the value of 2 x + 1 should be greater than 81 for the inequality to be true.

Therefore, we get that, there are no restrictions other than 2 x + 1 > 81 on the radical inequality.

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Answer:

4⅜ or 4.375 inches.

Step-by-step explanation:

35 ribbon into 8 pieces is:

35/8 = 4⅜ or 4.375 inches.

Answer:2479

Step-by-step explanation: subtract 2,994 and 515 and you would get 2479

Answer: 3509 treats

Step-by-step explanation:

If I'm understanding correctly, we need to add the desserts together right?

[tex]2994+515\\=3509[/tex]treats in total