Data were collected from a typing class with 45 students. The class had an average of 56 words per minute (WPM)
with a standard deviation of 7 WPM. The teacher realized that the data from one student who typed 55 WPM was
not entered. If this student's results were included in the data set, what effect would it have on the standard
deviation?
O The standard deviation would be noticeably larger.
O The standard deviation would be noticeably smaller.
O The standard deviation would be about the same, perhaps a little larger.
O The standard deviation would be about the same, perhaps a little smaller.

Answer:

x = 34

Step-by-step explanation:

Pytago:

x\(30^{2} + 16^{2} = x^2\\x = \sqrt{30^2 + 16^2} \\x = 34\)

Evaluating the limit of f(x) as it approaches 0 on both sides, the function is continuous at x = 0 which makes a = 0

To check if f(x) is continuous at x = 0, we need to evaluate the limit of f(x) as x approaches 0 from both the left and right sides and see if it is equal to f(0).

As x approaches 0, x^2cos(1/x^2) oscillates between -x^2 and x^2. This means that the limit of f(x) as x approaches 0 does not exist because the oscillations do not approach any single value.

Therefore, for f(x) to be continuous at 0, the value of a must be such that f(0) exists and is equal to the limit of f(x) as x approaches 0. The only way for this to happen is if a = 0 because the function value at 0 is defined to be a. In this case, the limit of f(x) as x approaches 0 exists and is equal to 0, which is the same as the value of f(0). Hence, a = 0 is the only value that ensures f(x) is continuous at x = 0.

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Answer:

Isolate one of the variables. Substitute the expression from Step 1 into the other equation. The resulting equation should have only one variable, not both x and y.: Solve the new equation.

                    Hope this helps!

Answer:

A = 530.929158457

Answer:

Area = 706.8583471

Explanation:

The used law to measure the surface area of the sphere is

\(area \: = 4\pi \: {r}^{2} \)

Where (r) is the radius. The radius is half the diameter, so it will be half 13 which is equal to 7.5. By using this law:

\(4\pi \: {7.5}^{2} = 706.8583471\)

Answer:

Step-by-step explanation:

The sides are x and x - 1

The area is:

The value of the function f(-1) is 1/3. Option D

A function can be defined as a law, an expression or rule that is used to show the relationship between two variables.

These variables are listed as;

From the information given, we have the function written as;

f(x) = 3ˣ

To determine the function f(-1), we need to substitute the value of the variable x as -1 in the function f(x)

Substitute the values, we have;

f(-1) = 3⁻¹

Take the inverse of the value, we get;

f(-1) = 1/3

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Area of the patio is -6x² + x + 2 square yards and perimeter of the patio is 6 - 2x yards.

A yard is a unit of measurement used to measure length or distance in both the US customary system and the British imperial system. One yard is equal to 3 feet or 36 inches. In the US customary system, a yard is equal to 0.9144 meters, while in the British imperial system, it is equal to 0.9144 meters or 3 feet. Yards are commonly used for measuring larger distances, such as in construction or landscaping, as well as in some sports like American football and cricket.

The area of the rectangular patio is given by multiplying its length by its width, so the area is:

A = (1 + 2x)(2 - 3x)

Now using distributive property we get,

A = 2 - 3x + 4x - 6x²

Simplifying further, we get:

A = -6x² + x + 2

Therefore, the area of the patio is described by the quadratic equation -6x² + x + 2.

To find the perimeter of the patio, we add up the lengths of all four sides. The length and width are given as (1 + 2x) and (2 - 3x), respectively, so the perimeter is:

P = 2(1 + 2x) + 2(2 - 3x)

Simplifying this expression, we get:

P = 2 + 4x + 4 - 6x

P = 6 - 2x

Therefore, the perimeter of the patio is described by the linear equation 6 - 2x.

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Answer:

6n+2

Step-by-step explanation:

Answer:

\(a_{n} = -64(-\frac{1}{4})^{n-1}\)

it seems like the first term is -64, so lets write the formula accordingly:

a_n = a1(r)^(n-1)

where 'n' is the number of terms

a1 is the first term of the sequence

'r' is the ratio

the ratio is \(-\frac{1}{4}\) because -64 * \(-\frac{1}{4}\) = 16 and so on...

the explicit formula is :

\(a_{n}\) = \(-64(-\frac{1}{4} )^{n-1}\)

Answer: Will continue to rise

Step-by-step explanation:

Looking at the graph one notices that after a slight dip in the unemployment rate from August 2010 to January 2011, the unemployment rate began to rise and by November 2011 was still rising.

The arrow on the graph serves to indicate the direction the unemployment rate is going and as it is pointing upwards, this means that the Unemployment rate will continue to rise.

This was down to the fact that in 2011 the US was still yet to recover from the Great Recession of 2008 - 2009.

Answer:

EDGE 2021

Step-by-step explanation:

1) 4%

2) Increase

If m∠A > 30, an inequality which must be true include the following: 1. m∠B < 20°

In Mathematics, the exterior angle theorem or postulate can be defined as a theorem which states that the measure of an exterior angle in a triangle is always equal in magnitude (size) to the sum of the measures of the two remote or opposite interior angles of that triangle.

By applying the exterior angle theorem, we can reasonably infer and logically deduce that the sum of the measure of the two interior remote or opposite angles in the given triangle is equal to the measure of angle C (∠C);

m∠A + m∠B = B∠C

m∠B = B∠C - m∠A

m∠B = 50° - 40°

m∠B = 10°

Therefore, m∠B < 20°

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The graph that represents the function y= tanx is Option A.

The graph of y =tan (x) is a periodic function that has vertical asymptotes at x = (n + 1/2)π, where n is an integer.

It oscillates between positive and   negative infinity, creating a wave-  like pattern.

It has a repeating pattern of sharp peaks and valleys, exhibiting both positive and negative slopes.

Thus, option A is the correct answer.

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Michael drove 1125 miles and paid $295 for renting the truck for 3 days

Rental company charges per day = $70

Rental company charges per mile = $0.20

Number of days truck is rented by Michael = 3 days

The total amount paid by Michael for the truck = $295

Let x be the number of miles Michael drives the truck

Formulating the equation using the information given in the question:

295 = 70 + 0.20(x)

295-70 = 0.20(x)

225 = 0.20(x)

x = 1125 miles

Therefore, the total miles driven by Michael is 1125 miles.

Michael paid $295 for driving the truck for 1125 miles and renting it for 3 days.

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Answer:

1187.49

Step-by-step explanation:

\(P(40)=0.023(40)^3-0.289(40)^2+3.068(40)+55.170=1187.49\)

True because all properties are preserved under dilation from triangle ABC to A'B'C'.

We have given a triangle ABC is dilated by a factor of 2/3 , result triangle A'B'C'

We have to determine after dilation,  the properties of triangle ABC and A'B'C' is true or false.

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

Dilation of a triangle are results in either decreases or increases in the corresponding length of the triangle, it depends on by which scale factor triangle is dilated ,and dilation does not affect the angle measures of the triangle.

here scale factor is 2/3 so the corresponding sides of the triangle A'B'C' decreases.

So, the dilation of the triangle is not congruent but similar to the original triangle ABC

Therefore, the basic properties of triangles are preserved under the dilation of triangle by a scale factor.

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Answer:

Step-by-step explanation:

The answer is FALSE for the first one AB and A'B' are on the same line.

and TRUE for the second one The measures of B and B' are equal.

Answer:

S₂₇ = 1188

Step-by-step explanation:

using the given formula for \(S_{n}\) , that is

\(S_{n}\) = \(\frac{n}{2}\) (a₁ + \(a_{n}\) )

with a₁ = 5 and \(a_{n}\) = a₂₇ = 83 , then

S₂₇ = \(\frac{27}{2}\) (5 + 83) = 13.5 × 88 = 1188

Answer:

casidy from fanf ?!?!

Step-by-step explanation:

Answer:

<4  (D)

Step-by-step explanation:

it is the same angle :D

also can you please help me??

Answer: The answer is D. the last option

Step-by-step explanation:

The correct answer is option d) The graph is the radical function, y = √x shifted right 1 unit and up 4 units.

The original function is y = √(x - 1) + 4, which represents a radical function.

This function involves taking the square root of the quantity (x - 1) and then adding 4 to the result.

By shifting the function right 1 unit, we are replacing x with (x - 1). This means that the graph will be shifted horizontally by 1 unit to the right compared to the standard square root function.

By shifting the function up 4 units, we are adding 4 to the output of the square root function.

This means that the graph will be shifted vertically by 4 units compared to the standard square root function.

Therefore, the graph of the function y = √(x - 1) + 4 is the radical function y = √x shifted right 1 unit and up 4 units.

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Answer: 172 ounces

Step-by-step explanation:

We are given 10 pounds and 12 ounces to convert to ounces.

There are 16 ounces in 1 pound.

We can create a proportion to find out how much ounces 10 pounds is.

10 pounds / x ounces = 1 pound / 16 ounces

We need to solve for x by isolating the variable x.

10/x = 1/16

10 = x/16

10 * 16 = x

160 ounces = x

so 10 pounds is equivalent to 160 ounces. But we are not done yet.

We were asked to convert 10 pounds and 12 ounces.

So add together the ounces to find the total ounces:

160 ounces + 12 ounces = 172 ounces.

Answer:

15 19/20

Step-by-step explanation:

95 cents means 95/100 then reduce that and you get 19/20 and then on the end you still have the $15

Answer:

damien starts with 4 bacteria in a petri dish

f(x) = 5x + 1

table

graph

The graph of the function y = 2x⁴ - 5x³ + x² - 2x + 4 is plotted and attached.

Polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s). For example -

y = 4x⁴ + 3x³ + 2x² + 6x + 7

We have the 4 functions as shown in the image attached.

The y - intercept is the point where the graph intercepts the y - axis.

Function [1] -

y = 4 + 2x

y - intercept is 4

Function [2] -

y = 5ˣ + 1

y - intercept is 2.

Function [3] -

the y - intercept is 1.

Function [4] -

the y - intercept is at -1.

Therefore, the greatest y - intercept is of function -

f(x) = 2x + 4

and the least y - intercept is of function shown in graph [4] or function [4].

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The Multiplicative inverse of 1/16 ÷ 1/81 +-1/8​ is 16/79

1/16 ÷ 1/81   +    -1/8

1/16 ÷ 1/81   = 81/16

+    -1/8  = - 1/8

81/16  - 1/8

Then,

= 81/16  - 2/16

= (81 - 2)/16

= 79/16

Multiplicative inverse = 16/79

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Answer:

B.

y = –2x – 1

Step-by-step explanation:

Find the slope of the original line and use the point-slope formula  y − y 1 = m ( x − x 1 )  to find the line parallel to  y = − 2 x + 3 .

y = − 2 x − 1

...............................................................................................................................................

Find the negative reciprocal of the slope of the original line and use the point-slope formula  y − y 1 = m ( x − x 1 )  to find the line perpendicular to  y = − 2 x + 3 .

y = 1 /2 x + 13 /2

Answer:

8 hours and 26 minutes

Step-by-step explanation:

To convert 506 minutes to hours and minutes, we can use the fact that there are 60 minutes in one hour.

First, we can divide 506 by 60 to find the number of hours:

506 ÷ 60 = 8 with a remainder of 26

This means that 506 minutes is equal to 8 hours and 26 minutes.

Therefore, the conversion of 506 minutes to hours and minutes is:

8 hours and 26 minutes

From the resulting solution, the correct linear inequality graph is Graph C.

Given the inequality equation below:

2(2x-1)+7< 13 or -2x+5 ≤ -10.​

Simplify the expression

2(2x-1)+7< 13

Expand

4x - 2 + 7 < 13

4x + 5 < 13

4x < 13 - 5

4x < 8

x < 2

For the inequality -2x+5 ≤ -10.

-2x+5 ≤ -10

-2x  ≤ -15

x  ≥ 7.5

Hence the solution to the given system of inequalities are x < 2 and x  ≥ 7.5

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Answer:

there is no pic

Step-by-step explanation:

Answer:

The amount of income tax in dollars and cents is $4,695.75

Step-by-step explanation:

To find the amount of income tax that should be paid, we simply use the percentage said to be for the income tax

Mathematically;

income tax = 9% of 52,175

= 9/100 * 52175

= $4695.75

The income tax to be paid on the income is $52,175

Answer:4695.75

Step-by-step explanation:

Well if u made 52175 a whole then put 9 as a percentage you would cross multiply 52175 with 9 then divided with the whole percentage (100)