Which of these points is closest to the point (7,1)?
A
(4,1)
B
(7,-1)
C.
(7,4)
D
(11,1)

Area of a square:

We have s = 6⁴, then the area is:

Or, apply the power of the power rule (xᵃ)ᵇ=xᵃᵇ to get:

If the base length of the triangle is 10 units. Then the area of the triangle will be 35 square units.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The region of a right triangle is straightforwardly relative to the foundation of the triangle. The region of a triangle is 42 square units for a base length of 12 units.

The proportionality is given below.

A ∝ b

A = kb

Where A is the area, b is the base length, and k is the constant.

The ratio of Area to base length remains constant.

If the base length of the triangle is 10 units. Then the equation is given as,

A / 10 = 42 / 12

Simplify the equation, then we have

A / 10 = 42 / 12

A = 35 square units

If the base length of the triangle is 10 units. Then the area of the triangle will be 35 square units.

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The linear equation for their total combined age in 5 years is 2x + 17 = 31.

Let the age of Alex be x years old.

Let the age of June be 'y'.

June is exactly 7 years older than Alex.

y = x+7

In next 5 years, combined  total age will be of 31 years.

(x+5) + (y+5) = 31

Now, the linear equation that models total combined age in 5 years

Replace y with (x+7)

x + 5 + (x+7) + 5 = 31

2x + 17 = 31

Thus, linear equation for their total combined age in 5 years is 2x + 17 = 31.

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Answer:

B

Step-by-step explanation:

The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. It is calculated using a formula that takes into account the values of the two variables and their relationship to each other. This formula is not affected by changes in the units of measurement of either variable. Therefore, changing the units of time from minutes to seconds in this scenario would not affect the value of the correlation coefficient, so it would remain the same.

Option A, "The correlation and time measurement would change proportionally to one another," is incorrect because the correlation coefficient is not affected by changes in the units of measurement of either variable.

Option C, "The correlation would increase because changing the units for time would result in an increase in time values," is also incorrect because the correlation coefficient is not affected by changes in the actual values of the variables, only by the strength and direction of the relationship between them.

Option D, "It is impossible to determine the amount of change experienced by the correlation," is incorrect because, as explained above, the correlation coefficient is not affected by changes in the units of measurement of either variable.

Option E, "The correlation would decrease because only the units for one of the variables changed," is also incorrect because, as explained above, the correlation coefficient is not affected by changes in the units of measurement of either variable.

The right response is C. Only X-values inside the original data's range give meaning to the prediction values.

A statistical model that depicts the relationship between two variables is a regression line. It is utilized to forecast the value of a dependent variable depending on the value of an independent variable (independent variable).

The degree to which the regression line matches the data determines how accurate these forecasts are. For values of the independent variable that are similar to the values used to fit the model, the regression line will typically offer the most precise predictions. Prediction values therefore typically only have significance for X-values that fall within or very near the range of the original data set.

The predictions might not be correct if you use the regression line to construct them for independent variable values that are far outside the original data range. This is because, outside of the range of the data that was used to construct the model, the model may not effectively represent the connection between the two variables.

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Answer:

∠M ≅ ∠G

Step-by-step explanation:

Given:

This means that triangle MTD is congruent to triangle GLS.

Two triangles are said to be congruent if:

Therefore:

Similarly:

Therefore, the true statement is ∠M ≅ ∠G.

Answer:

x = 4.5

Step-by-step explanation:

2x = 9 ( isolate x by dividing both sides by 2 )

x = [tex]\frac{9}{2}[/tex] = 4.5

The simplest expression is x³ - x² - 17x + 20.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(x - 4) (x² + 3x - 5)

x³ + 3x² - 5x - 4x² - 12x + 20

x³ - x² - 17x + 20

Thus,

The final expression is

x³ - x² - 17x + 20

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Answer:3.33%

Step-by-step explanation:

Her annual income will be 3.33%

IQ is normally distributed with a mean and Standards deviations .

a) The probability that this person has an iq greater than 95 is 0.6306 or 63.1%

b) The probability that this person has an IQ less than 125 is 0.9522 or 95.2 %.

c) In a sample of 700 people, the number of people would have an IQ less than 110 is 598 people.

d)In a sample of 700 people, how many people would have an IQ greater than 140 is three in count.

We have normal distribution here with

Mean , u = 100

Standard deviations, s = 15

let X be random variable, X~ N(15, 100)

a) P(X > 95)

From Z- statistic, Z = (X - u) /s

Converting to standard normal variable,

P( X- u/sd <( 95 - u)/s)

P(Z > (95 - 100) / 15)

= P(Z > -0.3333)

Using standard normal tables, value of P(Z > -0.3333) = 0.6306

Therefore 63.1% is the required percentage here.

b) P(X < 125)

= P(Z < (125 - 100) / 15)

= P(Z < 1.6667)

Using standard normal tables,

= 0.9522

Therefore 95.2% is the required percentage here.

c) The probability here is computed as:

P(X < 110)

= P(Z < (110 - 100) / 15)

= P(Z < 0.6667 )

Using the standard normal tables,P(Z < 0.6667 ) = 0.7475

Therefore expected number of people:

= 800×0.7475

= 598

Therefore 598 is the required expected number of people here.

d) P(X > 140)

= P(Z > (140 - 100) / 15)

= P(Z > 2.6667)

Getting from standard normal tables,

= 0.0038

Therefore expected number of people here:

= 800×0.0038

= 3.04

Therefore 3 is the expected number of people here. Hence, we get the required probability for each case

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Complete question:

IQ is normally distributed with a mean of 100 and a standard deviation of 15. a) Suppose one individual is randomly chosen. Find the probability that this person has an IQ greater than 95. Write your answer in percent form. Round to the nearest tenth of a percent. P (IQ greater than 95) = % b) Suppose one individual is randomly chosen. Find the probability that this person has an IQ less than 125. Write your answer in percent form. Round to the nearest tenth of a percent. P (IQ less than 125) = % c) In a sample of 700 people, how many people would have an IQ less than 110? people d) In a sample of 700 people, how many people would have an IQ greater than 140? people

Yes, the starting position of these players form a perpendicular line.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Using Trigonometry

sin [tex]\theta[/tex] = 33.33/100

sin [tex]\theta[/tex] = 0.3333

[tex]\theta[/tex] = [tex]sin^{-1}[/tex] (0.3333)

[tex]\theta[/tex] = 19.469

cos 19.469 = B/ 100

0.9428 = B/ 100

B= 94.28

tan  [tex]\theta[/tex] = P/B

tan  [tex]\theta[/tex] = 94.28/ 33.33

[tex]\theta[/tex] = 70.5

Using Angle Sum property

< 3= 180 - (70.5 + 19.5)

<3 = 180 - 90

<3 = 90

Hence, they form perpendicular line.

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Answer:

7

Step-by-step explanation:

The lines q and t are, perpendicular to each other.

If two lines are perpendicular to each other, then their slopes are negative reciprocal of each other. That means, if one line's slope is 'a', then its perpendicular line's slope would be -1/a

Noted that Parallel lines have the same slope, the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.

Given that Lines q, r, s, and t are distinct lines in the same plane.

IF the lines are;

q is perpendicular to r,

r is perpendicular to s

s is perpendicular to t

Then we can conclude that q is perpendicular to t

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When data records are not in any desired sequence for processing or viewing the appropriate task is to sort the contents in different fields.

Depending on the method employed, the data collection process may include several stages. Here are a couple such examples:

Data generation is the process of discovering and organizing facts in an orderly manner. This could be a manually generated document or data gathered from a source and easily fed into a computer using a data capture device such as a barcode scanner.

Data preparation is the process of converting data from a source document to a machine-readable format. This may not apply to all input devices. Data obtained by devices that take data directly in digital form do not require transcription.

Data transmission will determine whether or not data must be delivered to the central server using communication means.

Manual labor is time-consuming and dull, especially when doing repetitive tasks. Mechanical devices were developed to help in the automation of manual tasks. Typewriters, printing presses, and weaving looms are examples of mechanical devices. Initially, these devices were devoid of electronic intelligence.

Scientists have spent a long time investigating methods to build devices or technologies that would stimulate some type of human intellect during information and data processing. This was made feasible in part by the development of electronic programmable devices such as computers.

The development of microprocessor technology substantially boosted the efficiency and capability of data processing. Examples include computers, cellular (mobile) phones, calculators, petroleum pumps, modern television sets, washing machines, and other microprocessor-controlled devices.

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The given geometric series [tex]$\quad 8+7+\frac{49}{8}+\frac{343}{64}+\cdots$[/tex] is convergent in nature.

[tex]$\quad 8+7+\frac{49}{8}+\frac{343}{64}+\cdots$[/tex]

Since it is geometric series. (As it is given in the question)

A series is considered to be convergent if the partial sums gravitate to a certain value, also known as a limit. In contrast, a divergent series is one whose partial sums do not reach a limit. Divergent series typically go to ∞, go to −∞, or don't approach one specific number.

Here the value of a=8, while the value of the common ratio [tex](r)=\frac{a_2}{a_1}=\frac{7}{8}=\frac{7}{8}[/tex]

since [tex]$|r|=\frac{7}{8} < 1$[/tex]

So the given series is convergent.

The sum of geometric series with infinite terms is equal to [tex]$\frac{a}{1-r}$$$[/tex]

Sum[tex]=\frac{8}{1-\frac{7}{8}}=\frac{8}{\frac{1}{8}}=64[/tex]

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Answer: 0 = 2

Step-by-step explanation:

First you need to multiply the numbers:

2x + 2(-x) = 2

2x - 2x = 2

Combine the like terms:

2x-2x = 2

So, 0 = 2

The given Commutative Property is 8y - 0.2y + 0.5y + 2.2 + 1.3 - 0.4 by solving this property we get the answer as (8.3y + 3.1).

The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer.

According to the associative property of addition, the sum of three or more numbers remains the same regardless of how the numbers are grouped. According to the question,

Steps involved are:-

So,

8y - 0.2y + 0.5y + 2.2 + 1.3 - 0.4

= (8 - 0.2 + 0.5) y + (2.2 + 1.3 - 0.4)

= (8 + 0.5 - 0.2) y + (2.2 + 1.3 - 0.4)    

= (8.5 - 0.2) y + (3.5 - 0.4)    

= (8.3) y + 3.1    

= (8.3y + 3.1)

Thus , by following all the steps and properties we get the obtained result.

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Answer:b

Step-by-step explanation:

Answer:

[tex] \sf \: t = 19[/tex]

Step-by-step explanation:

Given equation,

→ t - 6 = 13

Now the value of t will be,

→ t - 6 = 13

→ t = 13 + 6

→ [ t = 19 ]

Hence, the value of t is 19.

The graph of x = 3et cos(t), y = 3et sin(t), 0 ≤ t ≤ π is shown below.

In this question we have been given two curves  x = 3e^t cos(t), y = 3e^t sin(t), 0 ≤ t ≤ π

We need to graph the given curves.

First we find find few coordinates.

For t = 0,

x = 3e^0 cos(0)

x = 3 * 1 * 1

x = 3

and y = 3 * e^0 * sin(0)

y = 3 * 1 * 0

y = 0

For t = π,

x = 3 * e^π * cos(π)

x = 3 * 23.14 * (-1)

x = -69.42

and y = 3 * e^π * sin(π)

y = 3 * 23.14 * 0

y = 0

For x = π/2

x = 3 * e^π/2 * cos(π/2)

x = 3 * 4.81 * 0

x = 0

and y = 3 * e^π/2 * sin(π/2)

y = 3 * 4.81 * 1

y = 14.43

So, we have the coordinates (3, 0), (-69.42, 0) and (0, 14.43)

The graph of x = 3et cos(t), y = 3et sin(t) is as shown below.

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Answer:

Step-by-step explanation:c because I’m in college and Ik trust me

The probability that exactly two people out of a group of five have responded to a telephone poll is approximately 26%.

The probability that exactly two people out of a group of five have responded to a telephone poll can be calculated using the binomial distribution. The probability of a single person responding to a call in a poll is 15%, and the probability of a single person not responding to a call in a poll is 85%.

The probability of two people out of a group of five responding to a call in a poll can be calculated using the formula for the binomial probability mass function:

[tex]P(X=2) = (5 choose 2) * (0.15)^2 * (0.85)^3[/tex]

where (5 choose 2) is the binomial coefficient, which represents the number of ways to choose 2 people out of a group of 5.

Plugging in the values, we get:

[tex]P(X=2) = (10) * (0.15)^2 * (0.85)^3 = 0.2574[/tex]

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Answer: x = 9

Step-by-step explanation:

Let's start with what we know. We know that the sum of all angles is 180 so:

13x + 2 + 3x - 4+ 5x - 7 = 180

21x - 9 = 180

21x = 189

Divide by 21 on both sides:

x = 9

If we are rolling a six-sided dice, where. a = get a roll that is even, then the value of [tex]$P\left(A^c\right)^$[/tex]  will be 1/2

Option (c) is the correct choice.

As we know,

A dice has 6 faces on which 6 different numbers (1,2,3,4,5 and 6) are printed on each of the six faces of the dice.

Now, considering an unbiased die the probability of any of the faces appearing in a single roll is 1/6.

So, we can write it as:

P(1)=P(2)=P(3)=P(4)=P(5)=P(6)=1/6

Now that number to be even is 2,4,6

And for each individual number, the probability will be 1/6

So, the value of P(A) =P(2) + P(4)+ P(6)

= 1/6 + 1/6 +1/6 =3/6

P(Ac) = 1 - P(A) = 1 - ( 3/6 ) = 1/2.

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The complete question may be:

Suppose that you are rolling a six sided dice.

Let A= get a roll that is even

What is [tex]$P\left(A^c\right)^$[/tex] ?

(a) 1 / 3

(b) 1 / 4

(c) 1 / 2

(d) 1 / 6

Step-by-step explanation:

45° is an alternate angle with 5y+10. All alternate angles are equal. opposite sides of a parallelogram are equal, we equate to find x.

source: A tutor on another math app. (Brainly doesn't recognize the name)

The price of the microwave before sales is 350 dollars.

Javier bought a microwave for $105. The cost was 30% off the original price.  Therefore, the price of the microwave before sales can be calculated as follows:

let

x = price before sales(original price)

Therefore,

105 = 30% of x

105 = 30 / 100 × x

105 = 30x / 100

cross multiply

10500 = 30x

divide both sides by 30

10500 / 30 = 30x / 30

x = 350 dollars

Therefore, the original price is 350 dollars.

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The z-score for that condition is 0.38. To be exact, the z-score is 0.38461538461.

First we have to extract mean and standard deviation from x~n(145, 13) where mean (μ) = 145 and standard deviation(б) = 13. As per given corresponding to an observation(x) is directly given = 150 we can start to find the z-score with formula z-score = (x - μ) :  б. So

z = (x - μ) :  б.

z = [tex]\frac{150-145}{13}[/tex]

z = [tex]\frac{5}{13}[/tex]

z = 0.38461538461

Normally z written in 2 to 4 digit after decimal, so z-score = 0.38

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Answer:

all of them are true except the last one ( no. e)

The probability that all three will be in box 1 will be  [tex]\frac{1}{8}[/tex] or 0.125.

As per the given data the three balls which are labeled as A, B, C are placed into two different boxes of box 1 and box 2.

Box 1 has 10 balls and box two has 5, if all the arrangements are equally likely we have to determine the probability that all the three will be in box 1.

Formula for finding the probability:

Probability = The total number of outcomes ÷ The favorable number of outcomes.

The total number of outcomes:

= [tex]$${ }^3 C_3+{ }^3 C_2+{ }^3 C_1+{ }^3 C_0$$[/tex]

= 1+3+3+1

=8

The favorable number of outcomes:

= [tex]{ }^3 C_3[/tex]

=1

The probability that all the three will be in box 1:

= [tex]\frac{1}{8}[/tex]

= 0.125

Therefore the probability is  [tex]\frac{1}{8}[/tex] or 0.125.

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a. The solution to the system is shown in the graph given below, which is (3, 8).

b. Plugging in the values of x and y into each equation, both sides of each equation are balanced.

To find the solution to a system of equations, plot both equations on a coordinate plane, then find the coordinates of the point where the two lines intersect, which is the solution.

a. Given the system, 3y = x + 21 and y + 2/3x = 10, the image below show each line where 3y = x + 21 is represented as the blue line, and y + 2/3x = 10 is represented as the red line.

The lines of both equations intersect at point (3, 8) which shows that the solution of the system is solved graphically as (3, 8).

b. 3y = x + 21 --> eqn. 1

y + 2/3x = 10 --> eqn. 2

Substitute x = 3 and y = 8 into equation 1:

3(8) = 3 + 21

24 = 24 [true]

Substitute x = 3 and y = 8 into equation 2:

8 + 2/3(3) = 10

8 + 2 = 10

10 = 10 [true]

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