graph each function and give its domain
f(x) = √x - 2

Answer:

See below!

Step-by-step explanation:

254, 202, 284, 269, 151, 258, 202

Mean of the data:

\(\displaystyle Mean= \frac{Sum \ of \ data}{number \ of \ data} \\\\Mean = \frac{254+202+284+269+151+258+202}{7} \\\\Mean=\frac{1620}{7} \\\\\boxed{Mean = 231.4}\)

Median of data:

Arrange the data in increasing order.

151, 202, 202, 254, 258, 269, 284

The middle value = 254

So,

Mode in data:

The mode, here, is 202. (occurring 2 times.)

So,

\(\rule[225]{225}{2}\)

Answer:

what

Step-by-step explanation:

Answer:

2/7=1.5/x (similar shapes)

2x=1.5 x 7

x= 1.5x7/2

The solution is

The value of x = 5.25

The value of y = 7.5

What are Congruent Triangles?

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same ( angle, side, angle)

Two sides are equal and the angle between the two sides is equal

( side, angle, side)

A right angle, the hypotenuse and a corresponding side are equal (right angle, hypotenuse, side)

Given data ,

Let the triangles be ΔABC , ΔADE , ΔAXZ where the triangles are congruent

The sides of the triangles are given

Now , from the congruent theorem ,

The 2 angles are the same , the corresponding side is the same

A right angle, the hypotenuse and a corresponding side are equal

So , from the congruent theorem , we get

2 / 7 = 1.5 / x

Multiply by 7 on both sides , we get

10.5 / x = 2

Multiply on both sides , we get

2x = 10.5

Divide by 2 on both sides , we get

x = 5.25

Therefore , the value of x = 5.25

7 / 10 = 5.25 / y

Multiply on both sides of the equation , we get

7y / 10 = 5.25

Multiply by 10 on both sides , we get

7y = 52.5

Divide by 7 on both sides of the equation , we get

y = 7.5

Therefore , the value of y is 7.5

Hence ,

The value of x = 5.25

The value of y = 7.5

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Using the same-side interior angles theorem,

\(8x+30+6x+24=180 \\ \\ 14x+54=180 \\ \\ 14x=126 \\ \\ \boxed{x=9}\)

Using vertical angles,

\(6(9)+24=10y+2 \\ \\ 78=10y+2 \\ \\ 10y=76 \\ \\ \boxed{y=7.6}\)

The length of the side of the square in simplest form is 2sqrt(14).

The area of a square is given by the formula \(A = s^2\), where A is the area and s is the length of a side.

We are given that the area of the square is 56 units, so we can set up the equation:

\(56 = s^2\)

To solve for s, we can take the square root of both sides of the equation:

sqrt(56) = \(sqrt(s^2)\)

We can simplify the square root of 56 by factoring it:

sqrt(56) = sqrt(222*7) = 2sqrt(14)

So, we have:

2sqrt(14) = s

This is an improper fraction because the numerator is larger than the denominator. Therefore, the length of the side of the square in simplest form is 2sqrt(14).

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Answer:

Step-by-step explanation:

Solution:

We can simplify the ratio 305 : 60 by dividing both terms by the greatest common factor (GCF).

The GCF of 305 and 60 is 5.

Divide both terms by 5.

305 ÷ 5 = 61

60 ÷ 5 = 12

Therefore:

305 : 60 = 61 : 12

Answer:

AB = 5√55

Step-by-step explanation:

Part 1 = AD = 25

Hypotenuse = AC = 55

Leg 1 = AB = x

To find AB, apply the leg rule which is:

Hypotenuse/leg 1 = leg 1/part 1

Plug in the values

55/x = x/25

Cross multiply

x*x = 55*25

x² = 1,375

x = √1,375

x = 5√55

AB = 5√55

The p-values of the test is given by p = -0.533

Given data ,

A random sample of 16 ATM transactions shows a mean transaction time of 2.8 minutes with a standard deviation of 1.2 minutes

Now , alternate hypothesis is mu < 2.96

where test statistic for a one-sample t-test is calculated as:

t = (x - μ) / (s / √n)

Where:

x = sample mean (2.8 minutes)

μ = hypothesized population mean (2.96 minutes)

s = sample standard deviation (1.2 minutes)

n = sample size (16)

Substituting the given values into the formula, we have:

t = (2.8 - 2.96) / (1.2 / √16)

t = (-0.16) / (1.2 / 4)

t = (-0.16) / (0.3)

t ≈ -0.533

And , we need to find the p-value associated with this test statistic. Since the alternative hypothesis is mu < 2.96, we are performing a one-tailed test

The p-value of the test is the probability of observing a test statistic as extreme as -0.533, assuming the null hypothesis is true

Hence , the p-value of the hypothesis is solved

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Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

Therefore , the solution of the given problem of matrix comes out to be matrix A's (3,4)th place is -1.

A matrix is a group of numbers arranged in rows and columns to form a rectangular array. The numbers make up the matrix's constituents or parts. Matrix algebra is widely used in many branches of mathematics, as well as in the sciences of architecture, physics, economics, and statistics.

Here,

Given that matrix A has 4 rows and 5 columns,

=> it has a dimension of 4 x 6.

=> -1, 2, 3, 4, and 5 are the values in the fourth row of matrix A.

=> 2, 0, 6, and -3 are the values in matrix A's third column.

The entry in matrix A's (3,4)th place is -1.

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Answer: I agree

Step-by-step explanation:

Im in 11th grade and its pretty hard ngl.

Answer:

The measure of CD is 46

Step-by-step explanation:

From the midpoint theorem, we have,

FG = (1/2)CD

so,

\(13+5x=(1/2)(-3x+52)\\So,\\2(13+5x)=-3x+52\\26+10x=-3x+52\\13x=52-26\\13x=26\\x=26/13\\x=2\)

Now,

\(CD = -3x+52\\since \ x=2\\we \ get\\CD=-3(2) +52\\CD=-6+52\\CD=46\)

Answer:

B. Distributive property

Step-by-step explanation:

Because (2 times 7) times 3 is the same as 2 times (7 times 3)

The numbers are just put different, and makes a different answer.

So, just because the answers are the same, doesn't make them commutative property,

Answer:

252 is your answer

Step-by-step explanation:

Your Welcome! :)

Answer:

The mean is of 45.

The standard deviation is 2.28.

Step-by-step explanation:

The mean is the sum of all values divided by the number of values.

The standard deviation is the square root of the sum of the difference squared between each value and the mean, and divided by the number of values.

Mean:

\(M = \frac{45 + 48 + 42 + 47 + 43}{5} = 45\)

The mean is of 45.

Standard deviation:

\(M = \sqrt{\frac{(45-45)^2 + (48-45)^2 + (42-45)^2 + (47-45)^2 + (43-45)^2}{5}} = 2.28\)

The standard deviation is 2.28.

Answer:

slope is 1/6

Step-by-step explanation:

Answer:

its c

Step-by-step explanation:

i took the test and got 100 percent

Answer:

B

Step-by-step explanation:

Answer:

52.5 inch square

Step-by-step explanation:

Area of pentagon: A = 1/2 × p × a;

where 'p' is the perimeter of the pentagon and 'a' is the apothem of the pentagon.

A = 1/2 x (6 x 5) x 3.5 = 1/2 x 30 x 3.5 = 15 x 3.5 = 52.5

The area of the regular pentagon with apothem 3.5 and side 6 is 52.5

In Mathematics, a pentagon is a polygon with 5 sides. A pentagon can be classified as a regular pentagon and irregular pentagon. When all the sides and the angles of a pentagon are of equal measure, then it is called a regular pentagon.

Given the question, we need to find the area of the regular pentagon with apothem 3.5 and side 6.

In order to find the area, the formula to calculate the area of the regular pentagon is given by:

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)

Now,

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times 6 \times 3.5\)

\(\text{Area of pentagon} =52.5\)

Therefore, the area of the regular pentagon with apothem 3.5 and side 6 is 52.5

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The sample space for rolling a fair 12-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

Sample space is a set of all possible outcomes of an experiment or random event. It is the collection of all possible results or outcomes that can occur when a particular event is performed.

In the given question,

The sample space is the set of all possible outcomes of an experiment. In this case, the experiment is rolling a fair 12-sided die. The sample space would include all possible values that the die can land on when rolled.

Since a 12-sided die has 12 equally likely outcomes, the sample space would consist of the numbers 1 through 12. However, only one of the options presented in the question includes all 12 numbers in the sample space, which is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

Option S = {1, 2, 3, 4, 5, 6} represents the sample space of a regular 6-sided die, while options S = {1} and S = {12} only include one possible outcome, which is not applicable for a 12-sided die.

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Step-by-step explanation:

3x × 8x- 3x×16

24x -48x

-24x

The result of engaging in the row multiplication operation in a matrix would be [ 1 /2   0 | 3 / 4 ]

[ -1   5 | 4 ].

First, you should multiply the first row by the value given of 1 / 4 to be:

( 1 / 4 ) x 2 = 1 / 2

( 1 / 4 ) x 0 = 0

( 1 / 4 ) x 3 = 3 / 4

Then you can replace the values found by the values in the matrix to be :

[ 1 / 2   0 | 3 / 4 ]

[   - 1     5 | 4      ]

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Answer:

\(\displaystyle (f - g)(x) = -x^2 + 2x + 8\)

Step-by-step explanation:

We are given the two functions:

\(\displaystyle f(x) = 2x + 1 \text{ and } g(x) = x^2 - 7\)

And we want to find:

\(\displaystyle (f- g)(x)\)

Recall that:

\(\displaystyle (f - g)(x) = f(x) - g(x)\)

Substitute and simplify:

\(\displaystyle \begin{aligned}(f-g)(x) &= f(x) - g(x) \\ \\ &= (2x + 1) - (x^2 - 7) \\ \\ &= (2x +1 )+ (-x^2 + 7) \\ \\ &= -x^2 +2x + 8\end{aligned}\)

In conclusion:

\(\displaystyle (f - g)(x) = -x^2 + 2x + 8\)

Answer:

\(→(f - g)(x) \\ = f(x) - g(x) \\ = (2x + 1) - ( {x}^{2} - 7) \\ = 2x + 1 - {x}^{2} + 7 \\ = \boxed{ - {x}^{2} + 2x + 8}✓\)

The correct answer is D. Elements are randomly selected from equal-sized blocks of the total population is NOT true regarding a randomized block design experiment

From the question we are told that one statement is NOT true regarding a randomized block design experiment.

Where

D) Elements are randomly selected from equal-sized blocks of the total population is Not True

In conclusion

The all other Options are true except option D which states that Elements are randomly selected from equal-sized blocks of the total population.

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The new dimension of the rectangular field are 45 ft by 120ft.

If the field has originally dimensions length L and width W, and we apply a scale factor K, then the new dimensions of the rectangle are:

lenght = K*L

width = K*W

In this case the original dimensions are:

L = 30ft

W = 80ft

And the scale factor is K = 1.5, then the new dimensions are:

L' = 1.5*30ft = 45ft

W' = 1.5*80ft = 120ft

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Answer:

∠ ABC = 49°

Step-by-step explanation:

the chord- tangent angle ABC is half the measure of the intercepted arc AB

∠ ABC = \(\frac{1}{2}\) AB = \(\frac{1}{2}\) × 98° = 49°

Answer:

$27

Step-by-step explanation:

Answer:

Step-by-step explanation:

"Tamara runs 5 miles each week"

Let Tamara runs 'x' weeks then equation that represents the total distance covered by Tamara will be,

1). y = 5x

2). Here 'y' is directly proportional to the number of weeks 'x'.

3). And the graph when plotted will start from 0. Therefore, graph (1) will be the graph for the given equation.

"Tamara runs 5 minutes more than she walks each day."

1). If Tamara walks 'x' minutes daily and she runs for y minutes then relation between x and y will be,

y = x + 5

2). y and x are non proportional.

3). Graph will have y-intercept = 5

Answer:

ik somebody answer already n stuff

Step-by-step explanation:

Answer:

  t ≈ 0.0664731

Step-by-step explanation:

Use the inverse sine function.

  sin(12t) = 141/197

  12t = arcsin(141/197)

  t = arcsin(141/197)/12

  t ≈ 0.0664731 . . . . . . . radians

__

This is the principal value. There are other solutions at values of t that have integer multiples of π/6 added to this. There are also solutions where any of those values is subtracted from π.

_____

In general, angles in math are assumed to be in radians, unless specified otherwise. This angle corresponds to about 3.81°. (In geometry, the usual assumption is that angles are measured in degrees.)