The distribution of IQ (Intelligence 100 and a standard deviation of 13 . Type numbers in the boxes. 10 points According to the standard deviation rule, \% of people have an IQ between 87 and 113. Do not round. Question 13 The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of Type numbers in the boxes. 100 and a standard deviation of 18. According to the standard deviation rule, only % of people have an IQ over 118.

An expression for which subtracting 5 from an expression would isolate the variable is -9x + 5 = x + 2

Algebraic expressions are described as expressions that consists of coefficients, terms, variables, factors and constants.

These expressions are also known to consist of arithmetic operators, which includes;

From the information given, we have to subtract five from an expression to isolate the variable

Now, let's us the algebraic expression;

-9x + 5 = x + 2

Let's subtract 5 from both sides of the equation, we get;

-9x + 5 - 5 = x + 2 - 5

add and subtract the like terms

-9x + x = -3

-8x = -3

x = 3/8

Hence, the expression is -9x + 5 = x + 2

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For given direct variation with points (2,6) and (n,3), n will be 1.

What is direct variation?

The relationship between two variables in which one is a constant multiple of the other is referred to as direct variation. For example, they are said to be in proportion when one variable influences the other. If b is directly proportional to a, the equation is b = ka (where k is a constant). When two variables are coupled in such a way that the ratio of their values always remains the same, they are said to be in direct variation. Direct variation can be stated mathematically in a variety of ways. Because the ratio of y to x never changes in equation form, y and x fluctuate directly.

Formula for direct variation is

                            y=kx, where k is a constant.

Now,

Given Coordinates are (2,6) and (n,3)

So putting point 1 in formula y=kx

6=2k

k=3

Using k=3 in pont 2

3=3n

n=1

Hence,

         For given direct variation with points (2,6) and (n,3), n will be 1.

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The equation of the circle is 4x² + 4y² - 64y + 207 = 0

Given data ,

To write the equation in standard form for the circle with center (0,8) passing through (0,7/2), we can use the standard form equation of a circle:

(x - h)² + (y - k)² = r²

where (h,k) is the center of the circle and r is the radius. Substituting the given values, we have:

(x - 0)² + (y - 8)² = r²

Now, we need to find the value of r. We know that the circle passes through the point (0,7/2), so we can substitute these values and solve for r:

(0 - 0)² + (7/2 - 8)² = r²

(-7/2)² = r²

49/4 = r²

r = ± 7/2

We take the positive value of r since radius can't be negative. So, the equation of the circle in standard form is:

x² + (y - 8)² = (7/2)²

Expanding and simplifying, we get:

x^2 + y^2 - 16y + 64 = 49/4

Multiplying by 4 to get rid of the fraction, we get:

4x² + 4y² - 64y + 256 = 49

Hence , equation of the circle in standard form 4x² + 4y² - 64y + 207 = 0

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From the figures and the properties of the parallelogram was possible to find that: UT=27, ST=18, RV=7 and US=14.

There are different quadrilaterals, for example: square, rectangle, rhombus, trapezoid and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example,  the opposite sides are equal and parallel, for a parallelogram. In a parallelogram is noted too that the opposite angles and the diagonals are equal.

From the properties: the opposite sides are equal and parallel for a parallelogram. It is possible to find:

UT=RS=27

ST=RU=18

Considering that UV=7, then VS= 7 since V is the midpoint of the diagonal US. Therefore, US=14.

From the property: the diagonals are equal for a parallelogram. It is possible to find:

US=RT=14

RV=RT/2=14/2=7

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There are approximately 3.64 x 10¹⁸ liters of water available for human and plant use in the entire world. We can calculate it in the following manner.

To find how many liters of water are available for human and plant use, we need to multiply the total amount of water in the world (1.4 x 10²¹ liters) by the percentage available for human and plant use (0.26% or 0.0026).

The calculation is:

1.4 x 10²¹ liters x 0.0026 = 3.64 x 10¹⁸ liters

Therefore, there are approximately 3.64 x 10¹⁸ liters of water available for human and plant use in the entire world.

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Answer:

t1/2=1m => 30days

A0=500g =0.5kg

t=8m = 240days

A=?

λ=ln2÷t1/2

λ=0.6931÷30

λ=0.0231033333

A=A0×e^-λ×t

A=0.5×e^-0.0231033333×240

A=1.953125grams

The standard deviation is 6.

What a standard deviation means?

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Standard deviation in statistics is a measure of dispersion of a set of data relative to the mean of the data set.

The square root of the variance of the data set gives the standard deviation of the data set.

In this case, the variance,

s²=36 ( as given, variance of the set of values is 36 )

The standard deviation,

s=√36 =6

Therefore, the standard deviation is 6.

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According to the given information, the probability that a student from any major is using the Library collection is 0.578.

Transition chart:

Probability of using the library for History/Social sciences students = 0.9

Probability of using the library for Science students = 0.7

Probability of using the library for Engineering students = 0.6

Probability of using the library for Business students = 0.5

Probability of being in History/Social sciences = 0.3

Probability of being in Science = 0.25

Probability of being in Engineering = 0.15

Probability of being in Business = 0.3(b)

The transition matrix is given as:  [0.9 0.7 0.6 0.5] × [0.3 0.25 0.15 0.3]

= [0.73 0.59 0.47 0.47]

Therefore, the transition matrix is as shown:

(c) Probability that a student from any major is using the Library collection:

P(L) = 0.73 × 0.3 + 0.59 × 0.25 + 0.47 × 0.15 + 0.47 × 0.3

= 0.219 + 0.1475 + 0.0705 + 0.141

= 0.578

Therefore, the probability that a student from any major is using the Library collection is 0.578.

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Answer:

False

What type of variables does linear regression use?

What is linear regression? Linear regression analysis is used to predict the value of a variable based on the value of another variable. The variable you want to predict is called the dependent variable. The variable you are using to predict the other variable's value is called the independent variable.

Can independent variable be categorical in linear regression?

The linear model used in regression analysis always involves a numeric dependent variable. However, in such analyses it is possible to use categorical independent variables.

Hope this helps :)

Pls brainliest...

Answer:true

Step-by-step explanation: In a linear regression model, the independent variable (also known as the predictor or input variable) is typically assumed to be of interval or ratio type. Interval and ratio data are both continuous data types that have equal intervals between values and can be subjected to mathematical operations, such as addition and subtraction.

The nth term of a sequence is given as

f(n) = 2 + (-3)(n-1)

To find the 10th term, Let n = 10

Substitute the value of n= 10 into the expression

f(10) = 2 + (-3) (10 - 1)

f(10) = 2 + (-3) (9)

f(10) = 2 + (-27)

F(10) = 2 - 27

f(10) = -25

The answer is -25

To construct a proof of the conclusion "-(∀x) (S(x) ∧ P(x))" from the given premises "-(3x) (P(x) ∧ M(x))" and "(3x) (M(x) ∧ S(x))," we can use a proof by contradiction.

We will assume the negation of the conclusion and derive a contradiction. Here's the proof:

Therefore, we have derived a contradiction, which allows us to conclude that the negation of the assumption is false. Thus, we can conclude:

-(∀x) (S(x) ∧ P(x))

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The total cost to operate 5 fluorescent 40w light bulbs for the months of April and May if they are on for 3 hours/day is given as follows:

$1,830.

The total cost is obtained applying the proportions in the context of the problem.

The number of kilowatt hours is given as follows:

Hence:

200 x 61 x 3 = 36,600 kwh.

The cost is of $0.05 per kwh, hence the total cost is given as follows:

0.05 x 36600 = $1,830.

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(a) False. The set {x∈R^n | Ax=b} is not necessarily convex. It depends on the matrix A and the vector b. For example, if A is a non-convex matrix, then the set of solutions {x∈R^n | Ax=b} will also be non-convex.

(b) True. The set {(x₁,x₂) | x₂ ≤ 3x₁²} is convex. The inequality defines a downward parabolic region, and any line segment connecting two points within this region will lie entirely within the region. (c) False. Not all polygons on the R² plane are convex. For example, a polygon with a concave portion, such as a crescent shape, would not be convex.

(d) True. If S⊆R² is convex, then it must enclose a region of finite area. Convex sets do not have "holes" or disjoint parts, so they form a connected and bounded region. (e) False. If S₁⊆R² and S₂⊆R², and S₁∩S₂=ϕ (empty set), then S₁∪S₂ can be convex. If S₁ and S₂ are both convex sets that do not overlap, their union can still be a convex set. (f) True. If S₁⊆R² and S₂⊆R² are both closed sets, then their union S₁∪S₂ must also be closed. However, it may or may not be convex. The convexity of the union depends on the specific sets S₁ and S₂.

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Using graphical method to solve the system of linear inequalities, the solution are (x, y) 3, 13.

A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.

To solve this, we can write out the equations as

x + y ≤ 16 ...eq(i)

650x + 150y ≥ 3900 ...eq(ii)

Solving both equations with a graph.

Kindly find the attached graph to the problem.

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Answer:

$11700

Step-by-step explanation:

comment if u need the explanantion ;D

(a)  The average number of orders in a 1-minute interval of time is 12. (b)  The probability that at most 8 orders are placed in a 1-minute interval 0.0659 (c)  The probability that no orders are placed in the next 12 seconds 0.8187. (d)  The expected value and variance for the number of orders arriving in the next 12 seconds is 0.2.

a) The total time period is 6 hours or 360 minutes. So the average number of orders placed in a 1-minute interval of time can be estimated as:

Average number of orders = Total number of orders / Total time in minutes

= 4320 / 360 = 12

Therefore, the estimated average number of orders in a 1-minute interval of time is 12.

b) The number of orders in a 1-minute interval of time follows a Poisson distribution with mean λ = 12. To find the probability that at most 8 orders are placed in a 1-minute interval, we can use the Poisson probability formula:

P(X ≤ 8) =\(\sum_{x=0}^{\infty} \frac{e^{-\lambda}\lambda^x}{x!}\), for x = 0, 1, 2, ..., 8

P(X ≤ 8) = \(\sum_{x=0}^{\infty} \frac{e^{-\ 12}\ 12^x}{x!}\), for x = 0, 1, 2, ..., 8

Using a calculator, we get:

P(X ≤ 8) = 0.0659

Therefore, the probability that at most 8 orders are placed in a 1-minute interval is approximately 0.0659.

c) The probability that no orders are placed in the next 12 seconds can be calculated using the Poisson probability formula again, but with λ = 12/60 = 0.2 (since there are 60 seconds in a minute):

P(X = 0) = (\(e^{0.2}\) 0.2⁰) / 0!

= \(e^{0.2}\)

≈ 0.8187

Therefore, the probability that no orders are placed in the next 12 seconds is approximately 0.8187.

d) The expected value and variance for the number of orders arriving in the next 12 seconds can be calculated using the Poisson distribution parameters:

Expected value = λ = 12/60 = 0.2

Variance = λ = 0.2

Therefore, the expected value and variance for the number of orders arriving in the next 12 seconds are both 0.2.

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The value of f[ -4 ] and g°f[-2] are \(\frac{14}{3}\) and 13 respectively.

Given the function;

For f[ -4 ], we substitute -4 for every variable x in the function.

\(f(x) = \frac{3x-2}{x+1}\\\\f(-4) = \frac{3(-4)-2}{(-4)+1}\\\\f(-4) = \frac{-12-2}{-4+1}\\\\f(-4) = \frac{-14}{-3}\\\\f(-4) = \frac{14}{3}\)

For g°f[-2]

g°f[-2] is expressed as g(f(-2))

\(g(\frac{3x-2}{x+1}) = (\frac{3x-2}{x+1}) + 5\\\\g(\frac{3x-2}{x+1}) = \frac{3x-2}{x+1} + \frac{5(x+1)}{x+1}\\\\g(\frac{3x-2}{x+1}) = \frac{3x-2+5(x+1)}{x+1}\\\\g(\frac{3x-2}{x+1}) = \frac{8x+3}{x+1}\\\\We\ substitute \ in \ [-2] \\\\g(\frac{3x-2}{x+1}) = \frac{8(-2)+3}{(-2)+1}\\\\g(\frac{3x-2}{x+1}) = \frac{-16+3}{-2+1}\\\\g(\frac{3x-2}{x+1}) = \frac{-13}{-1}\\\\g(\frac{3x-2}{x+1}) = 13\)

Therefore, the value of f[ -4 ] and g°f[-2] are \(\frac{14}{3}\) and 13 respectively.

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Answer:

4-sided shape

Step-by-step explanation:

A square, very basically, is a flat, four-sided shape.

Answer:

H = 3V/πr^2   V ∈ ℝ, r ∈ ℝ

Step-by-step explanation:

multiply both sides

swap the sides

and then write in parametric form

hope this helps!

The features of the function g(x) = f(x + 4) + 8 are:

To analyze the features of the function g(x) = f(x + 4) + 8, we need to consider the effects of each transformation applied to the original function f(x) = log2 x.

Translation: f(x + 4)

This transformation shifts the graph of f(x) horizontally to the left by 4 units. It means that every x-coordinate in f(x) is decreased by 4 units.

Vertical Shift: f(x + 4) + 8

After the horizontal translation, the graph is shifted vertically upward by 8 units. This means that every y-coordinate in f(x + 4) is increased by 8 units.

Based on these transformations, we can identify the features of the function g(x):

Y-intercept: The y-intercept of the function g(x) = f(x + 4) + 8 is (0, 10). This means that the graph intersects the y-axis at the point (0, 10).

Domain: The domain of the function g(x) = f(x + 4) + 8 is (4, ∞). The original function f(x) = log2 x has a domain of (0, ∞), but after the horizontal translation of 4 units to the left, the new domain starts from x = 4.

Range: The range of the function g(x) = f(x + 4) + 8 is (8, ∞). The original function f(x) = log2 x has a range of (-∞, ∞), but after the vertical shift of 8 units upward, the new range starts from y = 8.

Vertical Asymptote: The vertical asymptote of the function g(x) = f(x + 4) + 8 is x = -4. This vertical asymptote is the result of the original function f(x) = log2 x having a vertical asymptote at x = 0. After the horizontal translation of 4 units to the left, the asymptote also shifts 4 units to the left and becomes x = -4.

X-intercept: The x-intercept of the function g(x) = f(x + 4) + 8 is (1, 0).

This means that the graph intersects the x-axis at the point (1, 0).

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To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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Answer:

\( \boxed{ f(x) = -2x^2 - 4x - 14 } \)

Step-by-step explanation:

f(x) = -2(x+1)²-12

f(x) = -2(x²+2x+1) - 12

f(x) = -2x² - 4x - 2 - 12

f(x) = -2x² - 4x - 14

The conversion of a fraction number with denominator 5 and numerator 2 , 2/5 in decimals is equals to the 0.4 value.

A decimal number can be defined as a number whose whole number part and fractional part are separated by a decimal point. Writing 2/5 as a decimal number by converting the denominator to powers of 10. We multiply the numerator and denominator by a number so that the denominator is a power of 10.

2/5 = (2 × 2) / (5 × 2) = 4/10

Now move the decimal point to the left as many places as there are zeros in the denominator, which is a power of 10.

The decimal moved one place to the left because the denominator was 10. Therefore, 4/10 = 0.4. Hence, required value is 0.4.

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To find the population of the city after t-5 years, we substitute t-5 into the equation P(t) = 25000e^(0.08t).

P(t-5) = 25000e^(0.08(t-5))

To simplify the expression, we can expand the exponent:

P(t-5) = 25000e^(0.08t - 0.4)

Using the properties of exponents, we can rewrite this as:

P(t-5) = 25000e^(0.08t) * e^(-0.4)

e^(-0.4) is a constant value, so we can calculate it using the base of the natural logarithm e:

e^(-0.4) ≈ 0.67032

Now we can substitute this value back into the equation:

P(t-5) ≈ 25000e^(0.08t) * 0.67032

We can simplify further:

P(t-5) ≈ 16758e^(0.08t)

Therefore, the population of the city after t-5 years is approximately 16758e^(0.08t), where t is the number of years from the present time.

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Answer:

use distance formula for the sides of the triangle

Answer:

Sarah = 3×Ross -10

11=3Ross-10

3Ross=11+10

Ross=21/3

Ross=7

Ross scored7

Answer:

27p+54

Step-by-step explanation:

Multiply 9 to all the numbers inside the parenthesis!

Hope this helps! :)

The percentage by which the price of the car went up from the original price is 60% (third option)

The first step is to determine the price of the car after the percentage increase. Percentage is the fraction of a number as a value out of 100. The sign that is used to represent percentage is %.

Price of the car after the percentage increase = (1 + percent increase/100) x original cost of the car

Price of the car after the percentage increase = (1 + 20/100) x 20,000

Price of the car after the percentage increase = (1 + 0.2) x 20,000

Price of the car after the percentage increase = 1.2 x 20,000 = $24,000

Price after the $8,000 increase = $24,000 + 8,000 = $32,000

Percentage of the original price = (32,000 / 20,000) - 1 = 0.60 = 60%

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Answer:

\(\displaystyle{P(x)=x^3-x^2}\)

Step-by-step explanation:

Given the zeros of 0, 0, 1. We can write the polynomial in form of x-intersects:

\(\displaystyle{P(x) = (x-x_1)(x-x_2)(x-x_3)}\)

Hence:

\(\displaystyle{P(x)=(x-0)(x-0)(x-1)}\)

Which can be simplified to:

\(\displaystyle{P(x)=x\cdot x \cdot (x-1)}\\\\\displaystyle{P(x)=x^2(x-1)}\)

Convert to the standard form by distributing x²:

\(\displaystyle{P(x)=x^2\cdot x - x^2 \cdot 1}\\\\\displaystyle{P(x)=x^3-x^2}\)

Performing a change of scale we will see that the actual distance is 4 miles.

We know that the scale is:

3/4 inch = 2 miles.

And the distance that Nicole found on the map is (1 + 1/2) inches.

We can rewrrite the scale as:

1 inch = (4/3)*2 miles

1 inch = (8/3) miles.

Then the actual distance will be:

distance = (1 + 1/2) inches = (1 + 1/2)*(8/3) miles = 4 miles.

The correct option is A.

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