Here is a correlation, does it also represent causation? Explain you answer.

The number of additional calories consumed and the amount of weight gained.

A person must have a score of 126.26 to qualify Mensa.

it is given that,

Mean [tex](\mu) = 100,[/tex]

Standard deviation [tex](\sigma) = 15[/tex].

A person must score in the upper 4% of the population,

100% - 4% = 96% = 0.96

P(X < Xo) = 96% = 0.96

P(X < 1.7507) = 0.96          ....................................using the Normal distribution table,

Or, when the Invnorm function is used, Invnorm(0.96) = 1.7507

Therefore, The required value of X is,

[tex]Z = \frac{(X - \mu )}{ \sigma }[/tex]

1.7507 = (X - 100) / 15

X - 100 = 26.26

X = 100 + 26.26

X = 126.26

thus, the score a person must have to qualify Mensa is 126.26.

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Answer:

The length = 5x + 25

Step-by-step explanation:

A = l x w

The equation of the linear function is represented by the table given in the slope-intercept form is y = x -1.

What is an equation of a line?

A line's equation is a single representation of all of the line's points. The general form of a line equation is ax + by + c = 0, and each point on the line satisfies this equation. The slope of the line and a point on the line are the two necessary components to create the equation of a line.

The equation of a line, in the slope-intercept formula:

y = mx + b

In which,

           m is the slope, that is, how much y changes when x changes by 1.

           b is the y-intercept, that is, the value of y when x = 0.

           Given two points (x,y), the slope is the change in y divided by the change in x.

We have points (-1, -2) and (1, -4).

[tex]m = \frac{(-2 - (-4))}{1 - (-1)}[/tex]

m = 1;

Then,

y = 1x + b

Point (-1,-2) means that when x = -1 and y = -2, we use this to find b.

y = 1x + b

-2 = 1(-1) + b

b = -2 + 1

b = -1

Thus,

y = x -1.

Hence, the equation of the linear function is represented by the table given in the slope-intercept form is y = x -1.

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Answer: 14=2x

Step-by-step explanation:

the answer is 14=2x7=14

The equation of the given line written in the slope-intercept form is: y = 21x + 10.25.

The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.

Note that the general slope equation is:

y = mx + b

Where

m is the slope of the line and

b is the y-intercept.

In this specific instance, m is the change in the price of the ticket

b is the additional fee value that needs to be included for each ticket

Hence, the cost of the ticket (y) is given as:

y = (change rate of x) + added fee to every order

Where rate of change = 21; and

The fee added to each order is 10.25

Given the above, the general equation becomes:

y = 21x + 10.25

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Answer:

Domain = { -2 , 0 , 2 , 4 }

Range = { 3 }

Step-by-step explanation:

Domain is the x-values that the Function have and Range is the y-values that the Function have corresponding to these x-values

Since the x-values for the Function attached are -2 , 0 , 2 , 4

and the y-values for the Function is 3

Then the Domain = { -2 , 0 , 2 , 4 }

and the Range = { 3 }

Glad to Help

Answer:

B No solution

Step-by-step explanation:

3(x+ 4) = 3x + 4  Distribute the 3

3(x) + 3( 12) = 3x + 4

3x + 12 = 3x + 4   There is not number that I can multiply by 3 and then add to 12 on one side and add to 4 on the other side of the equal sign to make a true statement, so the answer is no solution.

3x + 12 = 3x +4  Subtract 3x from both sides

12≠4.  A false statement means no solution.

When the equation is simplified and the coefficient of the variable (the number before the letter) is the same on both sides of the equation and the constraints (the numbers without letters) are different, this will result in no solution.

The length of TS, using similar triangles, is given as follows:

TS = x = 25.

Similar triangles are two triangles that share these two features:

In the context of this problem, the similar triangles are given as follows:

STU and SQR.

The proportional side lengths from these two similar triangles are given as follows:

Hence the proportional relationship that relates these lengths on the similar triangles is given as follows:

x/45 = x - 5/36

Applying cross multiplication, the length of TS, equals to x, is obtained as follows:

45(x - 5) = 36x

45x - 225 = 36x

9x = 225

x = 225/9

x = 25.

The diagram is given by the image shown at the end of the answer.

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For 0 < a < b <  1,  a^x < b^x, for x < 0.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given,  0 < a < b < 1.

Assuming a = 0.25 and b = 0.5.

∴ (0.25)^x < (0.5)^x for x > 0, again assuming x to be 2.

∴ (0.25)^2 = 0.625 and (0.5)^2 = 0.25.

Now, 0.625 > 0.25 which is not satisfying a^x < b^x, for x > 0.

Therefore, if 0 < a < b <  1, then a^x < b^x, for x < 0.

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Answer:a. 24

b. 14

Step-by-step explanation:

a. 3ab=

3*a*b=

3*4*2=

12*2=24

b. a+5b=

a+5*b=

4+5*2=

4+10=14

Answer: a) 24

              b) 14

Step-by-step explanation:

step1: We have to substitute the numbers.

step2: Then finish the answer.

a) 3ab = 3 x 4 x 2 = 24

b) a+5b = 4 + 5 x 2 = 4 + 10 = 14

The value of expression -23 +-15+|-17| + -35 is -56

In this question, we have been given a numerical expression.

-23 +-15+|-17| + -35

We need to find the value of given numerical expression.

Consider given numerical expression,

-23 +-15+|-17| + -35

= -23 + (-15) + |-17| + (-35)

= -23 - 15 + |-17| - 35

We know that for any real number a, |±a| = a

So, |-17| = 17

= -38 + 17 - 35

= -56

Therefore, the value of expression -23 +-15+|-17| + -35 is -56

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The number of wrapped present with 20 centimeters of tape is given as 5 presents.

In this question, we have the following values

12 centimeters of tape was used to wrap 3 presents

hence we would have

12 = 3 presents - - - - 1

Then we are to know the presents that would be wrapped with the use of 20 centimeters of tape.

we would have

20 = ? presents - - - 2

We have to bring the equations together

12 = 3 presents

20 = ? presents

? is the presents that is to be wrapped with 20 centimeters of tape. It is our unknown.

We would have to cross multiply

12 x ? = 3 x 20

12? = 60

We would have to divide through by 12 in order to get the unknown

? = 60 / 12

? = 5

Hence the number of presents that she wrapped is given as 5

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The correct option is c. that is observation is set of recorded values of variables associated with a single entity.

What is observation?

An observation is a case of the data being collected.

For example, if we were collecting data on students in the class, the observations would be each individual student in the class. It could be the student's height, weight, marks scored, etc.

A variable is an attribute or characteristic of the observation we record in our data.

Also an observation in statistics is a value of something of interest measured or counted during a study or experiment: a person’s height, a bank account value at a certain point in time, or number of animals.

Therefore from the given option c is correct.

Observation is set of recorded values of variables associated with a single entity.

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The total cost of his order of DVDs will be $32.23.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Samuel orders four DVDs from an internet-based music store. Every DVD costs $9.97. He has a 25% markdown code, and the deal charge is 7.75%.

The cost of DVDs after discount will be given as,

⇒ 4 x $9.97 x (1 - 0.25)

⇒ $29.91

The cost of DVDs after tax will be given as,

⇒ $29.91 x (1 + 0.0775)

⇒ $32.23

The total cost of his order of DVDs will be $32.23.

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Answer:

The answer is (1, 6)

Step-by-step explanation:

The density of the planet is 4.81 g/cm^3, and with this in mind, we assume that the planet is made of titanium or yttrium.

Density is defined as the quotient between mass and volume.

Here we know that the mass is:

9.43*10²⁷g

And the radius is 7.6x10^8cm, remember that the volume of a sphere of radius R is:

V = 3.14*(3/4)*R³

Then in this case the volume is:

V = 3.14*(3/4)*(9.43*10⁸ cm)³ = 1.96*10²⁷ cm³

Then the density is:

D = (9.43*10²⁷g)/(1.96*10²⁷ cm³) = 4.81 g/cm^3

For this density, we can assume that the planet is made of Titanium or Yttrium (or a combination of a lot of elements like most planets)

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The equation, y = 3x - 15, written in standard form is 3x - y = 15

From the question, we are to write the given equation is standard form.

The given equation is

y = 3x - 15

The standard form of a linear equation is

Ax + By = C

Where A, B, and C are constants

x and y are variables

Now, we will write the given equation is the standard form of a linear equation.

y = 3x - 15

Substract y from both sides

y - y = 3x - y - 15

0 = 3x - y - 15

That is,

3x - y - 15 = 0

Add 15 to both sides of the equation

3x - y -15 + 15 = 0 + 15

3x - y = 15

Hence, the standard form is 3x - y = 15

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The time that It would take  for the value of the account to reach $2,860 is; 21.6 years

We are told that a person invested $440 in an account growing at a rate allowing the money to double every 8 years. Thus, the account balance can be modeled by the equation;

A = 440(2)^(t/8)

where;

A is final amount

t is in years

We want to find t when A = 2860. Thus;

2860 = 440(2^(t/8))

divide both sides by 440 to get;

6.5 = 2^(t/8)

log(6.5) = (t/8)log(2)

t = 8 * log(6.5)/log(2)

t ≈ 21.604

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The two triangles are congruent by SAS criterion.

Verification:

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Step-by-step explanation:

2x - 27 + 3x + 27 = 180

5x = 180

x = 36

Let x denote the score. Assuming x follows normal distribution with

mean m = 70 and SD = 5 ,

we first calculate P( x < or = 80)

The SNV is z = (x — m) /SD

When x = 80, Z = ( 80 — 70)/5 = 2

So, P( x < or= 80)

Given that total number of students is

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The equation of the graph represented by the figure is f(x) = |x - 3| + 5

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

The graph is an absolute value graph

As a general rule, an absolute value is expressed as

y = |x - h| + k

In this case, the vertex is

Vertex = (h, k)

As a general rule, the vertex of a function is the minimum point on the graph

On the given graph, the minimum point is (3, 5)

This means that

(h, k) = (3, 5)

Substitute the values (h, k) = (3, 5) in the equation y = |x - h| + k

So, we have the following representation

y = |x - 3| + 5

Rewrite the equation as a function

f(x) = |x - 3| + 5

Hence, the equation is f(x) = |x - 3| + 5

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The required equation will be y = -1/3x + 21/4 in slope-intercept form.

The general equation of a line is y = mx + c

where m is the slope of the line and c is the intercept.

First, we need to determine the slope of the given line.

y = 4/9x - 6

Here the slope of the given line is 4/9.

The required line is perpendicular to a given line

So the  required line's slope will be m₂ = -1 / (4/9) = -9/4

The line passes through the point (5, -6) which is given in the question,

Now we can use the point-slope form of a line to create the equation of the new line:

(y + 6) = (-9/4) (x - 5)

y = (-9/4)x + 45/4  - 6

y = -1/3x + 21/4

Hence, the required equation will be y = -1/3x + 21/4 in slope-intercept form.

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Answer:

-2.475

Step-by-step explanation:

The number of months till Dan and Sydney would have paid the same amount for the high-speed Internet service is 6.12 months

Assuming the number of months is denoted as x, the total cost equation for Dan's provider would be:

= Installation cost + internet charge per month x number of months

= 60 + 42.95x

The total cost equation for Sydney's provider is:

= Installation cost + internet charge per month x number of months

= 0 + 52.75x

= 52.75x

To find the number of months till Dan and Sydney pay the same amount, equate the equations:
60 + 42.95x = 52.75x

52.75x - 42.95x = 60

9.8x = 60

x = 60 / 9.8

x = 6.12 months

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If 100 sixth grade students prefer hip hop music, the number of sixth graders at the school is 250.

Percentage is a measure of frequency that is used to express a number as as a fraction of 100. In order to change a value to percentage, multiply the number by 100. The sign that represents percentage is %.

In order to determine the number of sixth graders, divide the number of sixth graders that prefer hip hop music by the percentage.

Number of sixth graders = number that prefer hip hop / percentage

100 / 40%

100 / 0.4 = 250

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The quotient is x²+x+1 - 14/(x-1) after divide x³-15 by x-1.

What is synthetic division?

In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.

The divisor is x - 1.The dividend is (x³-15).

Step 1:Take the constant term of the divisor with the opposite sign and write it to the left.

Write the coefficients of the dividend to the right (missed terms are written with zero coefficients).

Step 2:Write down the first coefficient without changes:

Step 3:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

Step 4:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).Add the obtained result to the next coefficient of the dividend, and write down the sum

Step 5:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).Add the obtained result to the next coefficient of the dividend, and write down the sum.

We have completed the table and have obtained the following resulting coefficients: 1,1,1,−14.

All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.

The quotient is x²+x+1 and the remainder is -14.Therefore (x³-15)÷(x-1) = x²+x+1 - 14/(x-1)

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The expression that is equivalent to the given expression is 6y³ + 8y⁵

From the question, we are to determine the expression that is equivalent to the given expression

The given expression is

2y (3y^2 + 4y^4)

This can be properly written as

2y (3y² + 4y⁴)

Now, to determine the expression that is equivalent to this expression, we will expand the expression by applying the distributive property.

2y(3y² + 4y⁴)

2y(3y²) + 2y(4y⁴)

Multiplying

6y³ + 8y⁵

Hence,

The expression is 6y³ + 8y⁵

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Answer:

(-4,-1) and (3,1), respectively.

Step-by-step explanation:

I am not quite sure if the question is necessarily asking for this, but the x and y values are switched to get the points of the inverse. (-1,-4) --> (-4,-1) and (1,3) --> (3,1). I hope that makes sense!