A graduate student wanted to estimate the average time spent studying among graduate students at her school. She randomly sampled graduate students from her school and obtained a hours/week. In the context of the problem, which of the following interpretation is correct?
A. There is a 99% chance that the average amount of time spent studying for all graduate students at this student's school is between 173 and 22.5 hours per week OH
b. Graduate Mudents at this student's school study between 173 and 22 5 hours per week 99% of all weeks during the year
C. At this student's school 99% of all graduate students study between 17 3 and 22.5 hours per week, on average
D. Approximately 99% of all random samples of graduate students from this school will give a mean number of hours studied per week between 172 and 225
E. We are 99% sure that the average amount of time spent studying among graduate students at this student's school is between 17.3 and 22 5 hours per week

Answer:

  3

Step-by-step explanation:

You want to know the number of roots of x^3+4x^2-9x-36.

The degree of the given polynomial is the highest exponent of x: 3. That is the number of roots the polynomial has.

There are 3 roots.

The number of sign changes among the coefficients tells you the number of positive real roots. The signs go from + to - one time, so there is one positive real root.

When the signs of odd-degree terms are switched, the signs become ...

  - + + -

There are two sign changes here, meaning that there may be 2 or 0 negative real roots. (If there are 0 real roots, the two roots are complex.)

You can see that successive pairs of terms have coefficients with the same ratio. That means you can factor this by grouping terms:

  x^3+4x^2-9x-36

  = (x^3+4x^2) -(9x+36)

  = x^2(x +4) -9(x +4)

  = (x^2 -9)(x +4)

  = (x -3)(x +3)(x +4) . . . . . roots -4, -3, and +3

__

Additional comment

The graph shows you the polynomial has 3 real roots.

A square and a rectangle have the same perimeter, then the area of the square and the rectangle are the same.

An object's area is how much space it takes up in two dimensions. It is the measurement of the amount of unit squares which completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

Let x be the side of the square,

The length of the rectangle, l = 2x - 4,

The width of the rectangle, w = x - 6,

So, we have: (2x - 4) × (x -6) = x²,

x = 2 (4 + √10)

= 14.32455 cm, it is the side of the square

14.32455 × 2 -4

=24.6491cm, it is the length of the rectangle.

14.32455 - 6

=8.32455cm, it is the width of the rectangle.

24.6481 × 8.32455 = 14.32455²

= 205.19 cm²

Thus, it means that the areas of square and rectangles are similar.

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The equation of the line is x is -6

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

A line's steepness is indicated by its slope. Any line's slope is constant along its length. The direction of the line on the coordinate plane can also be determined by the slope. A line's graph can be used to determine slope, or the coordinates of any two points on a line can be used.

Given ,

m=(y2-y1)/(x2-x1)

Using the points given, we have:

m=(3 - 3)/(-5 - 3) = 0

These would be the vertical lines, and vertical lines have an equation with only x.

So the equation of the line is x = -6.

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Answer: f(x) = -3(x + 3)² + 8

Step-by-step explanation:

(h, k) are the coordinates to the vertex of the graph, which in this case would be (-3, 8), so the function for now would be:

[tex]f(x)=a(x+3)^2+8[/tex]

Plug in the coordinates (0, -19) to find the value of a:

[tex]-19=a(0+3)^2+8\\-19=9a+8\\9a=-19-8\\9a=-27\\a=-3[/tex]

So, the function is f(x) = -3(x + 3)² + 8.

Answer:

Step-by-step explanation:

Answer:

24663.9!

Step-by-step explanation:

The required cost of the loan is given as $100,966.80.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

here,
Bought a new house for $195,000.
Financed the house and the monthly payments are $822.13 a month for 30 years.

Total money paid against the loan = 822.13 × 30 × 12
                                                    = $295,966.8

Cost of the loan = 295,966.8 - 195,000
                         = $100,966.8

Thus, the required cost of the loan is given as $100,966.80.

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yes its a skill related mostly to math

Matrix A is invertible such that A⁻¹ = - A - 3I. This is solved using the Calely Hamilton Theorem.

This theorem says that every square matrix satisfies its own characteristic equation. In other words, the scalar polynomial

p(λ) = det(λI − σ) also holds for the stress polynomial p(σ).

It also states that The roots λ₁, λ₂........λₙ of a typical equation (aₙλₙ + aₙ₋₁ λⁿ⁻¹ + ...... a₁ λ + a₀)  will indicate the nature of the Matrix A. If either of the roots of the attributes equation is 0, the matrix's determinant becomes zero. As a result, the matrix is non-invertible.

Based on the above, we know that Matrix A fulfills the qualities below::

A²+3A + I = 0

Since every square matrix fulfills its own characteristic

λ₁ + λ₂ = -3

λ₁ x λ₂ = 1 ≠ 0

This is true for any order of a square matrix. That is:
λ₁ x λ₂ x λ₃ x........ x λₙ ≠ 0

Thus

|A| = λ₁ x λ₂ x λ₃ x........ x λₙ

|A| ≠ 0 → Invertibel Matrix

A² + 3A + I = 0
I = -A² - 3A
A⁻¹ x I = A⁻¹ (-A - 3A); hence

A⁻¹ = - A - 3I

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first multiple of 5 is 5

15 th multiple is 75

now lets use arithmetic progression

common difference d is 5

first term a=5

formula:

sum=n/2[first term + last term]

n=15

sum=15/2[75+5]

=15 x 40

=600

check it

5+10+15+20+25+30+35+40+45+50+55+60+65+70+75=600

The linear equation in the list of equations is y = [tex]\frac{1}{2}x + 3[/tex]

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

A linear equation must have the highest power of the independent variable as 1.

option A and C, the independent variable x has degree 2

option D the x variable there stands for absolute values.

So only B is a linear equation since variable x has degree 1

In conclusion, the linear equation is y = [tex]\frac{1}{2}x + 3[/tex]

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Answer:

90 books

Step-by-step explanation:

B:C

3:7

X:210

210÷7=30

3*30=90

Answer:

3:7

x:210

=210(3) ÷7

=90

Answer:

X Y

1. 2

2. 3

3. 4

This is the answer to your question

The program is an illustration of loops and conditional statements and the part of the complete program is

n = int(input())

for i in range(1,n+1):

  if not(i%3 == 0 or i%5==0):

The program written in Python where comments are used to explain each line is as follows:

#This gets input for n

n = int(input())

#This iterates through n

for i in range(1,n+1):

  #If the current number is not a multiple of 3 and 5

  if not(i%3 == 0 or i%5==0):

      #This prints the number

      print(i,end="")

  else:

      #This prints "Fizz", if the current number is a multiple of 3

      if i%3 == 0:

          print("Fizz",end="")

      #This prints "Buzz", if the current number is a multiple of 5

      if i%5==0:

          print("Buzz",end="")

  #This prints a new line

  print()

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8.00 - 3.50 = 4.50

4.50 / .75 = 6

Nataly can travel 6 miles

The distance between the two points in the line segment A_F is 6.3 units

Distance between two points is the length of the line segment that connects the two given points. Distance between two points in coordinate geometry can be calculated by finding the length of the line segment joining the given coordinates. Let us understand the formula to find the distance between two points in a two-dimensional and three-dimensional plane.

The distance between any two points is the length of the line segment joining the points. There is only one line passing through two points. So, the distance between two points can be calculated by finding the length of this line segment connecting the two points.

The data points are;

Distance between points A and F 6.3 units

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Answer:

1410 = 2:10PM

0515 = 5:15AM

Step-by-step explanation:

That’s The Translation

The value of test statistic t is -2.39 and P-value is P(t₈< -2.39).

The mean and the standard deviation can be calculated from the below formulae:

Sample mean (X)= (∑xi)/n

Sample standard deviation (s)= √(∑xi- X)²/(n-1)

where, n is sample size = 9

xi= elements in sample

On calculation we get X as,

X = (3.5+6.5+6.5+5.5+19.5+7+12.5+20+10.5)/9 = 10.17

s = √(∑xi- X)²/(n-1)

= √(44.49+13.47+13.47+21.81+87.05+10.05+5.43+96.63+0.11)/8

= √36.57 = 6.04

t would represent the static, it is given by the formula,

t = (X-μ₀)/(s/√n)

where μ₀ = 15 from the data (the value we want to test)

t = (X-μ₀)/(s/√n) = (10.17-15)/(6.04/√9) = -2.39

The formula to find out P value is pv = P(t₈< -2.39)

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The median of the wages is class 2,001-3,000 and the modal of the wages is 2,001-3,000

The table of values is given as

Wage                  Number of Employees

1,001-2,000           5

2,001-3,000           9

3,001-4,000          4

4,000-5,000         2

The total frequency is

Total = 5 + 9 + 4 + 2

Evaluate

Total = 20

So, the median position is

Median = (20 + 1)/2 th

Evaluate

Median = 11.5 th

This position is located at class 2,001-3,000

So, the median is wages 2,001-3,000

The table of values is given as

Wage                  Number of Employees

1,001-2,000           5

2,001-3,000           9

3,001-4,000          4

4,000-5,000         2

The mode is the highest frequency of the class

The highest frequency above is 9

So, the modal is wages 2,001-3,000

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the equation straight line y = -1/5 x + 4. of the line drawn in the picture is attached below.

What is equation straight line?

There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1).

The given equation y = -1/5 x + 4.

Here m = -1/5

and c= 4

So the plot on the graph will be as fallow.

Hence the equation of the line drawn in the picture attached below

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Answer: b=14

Step-by-step explanation:

we can use three steps

isolate the variable, use inverse operation and do everything on both sides of the equation to keep the equation in balance

if we had 5 back on both sides of the equation:

b-5=9

b= 14

B-5=9

b=9+5

b=14

To get variable b by itself , you add 5 to both sides of the equation.

The coordinate of the quadratic function at the intersection with the y-axis is (0, 1).

Given that,

A quadratic function is graphed with a y-intercept of 1.

What are functions?

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,

The graph of a quadratic function is shown, whose y-intercept is 1,

by this, we can conclude that when the quadratic function interset the y axis the coordinate of the intersection point is (0, 1).

Thus, the coordinate of the quadratic function at the intersection with the y-axis is (0, 1).

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As per the concept of transformation, there is a single rigid motion that would map triangle WXY to triangle W"X"Y"' is reflection.

Single rigid motion:

Basically, the single rigid motions are also called congruence transformations. Translations, reflections, rotations, and glide reflections are rigid motions.

Given,

Here we have the graph.

And we need to find is there a single rigid motion that would map triangle WXY to triangle W"X"Y"'.

While we looking into the graph, we have identified that, the image of the triangle is moved from one position to another position.

Here we need to identify the Single rigid motion that would map triangle WXY to triangle W"X"Y"',

For that, we have to carefully looking on the image,

So, we have identified that the triangle X"Y"Z" is the mirror reflection of the triangle XYZ.

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Answer:

-----------------------------

When the ball is punted the value of x is zero, therefore f(0) is:

Answer:

1.5 feet

Step-by-step explanation:

Given function,

→ f(x) = (-16/1225)x² + (7/5)x + 1.5

Required function,

→ f(x) = f(0)

→ f(0) = (-16/1225)x² + (7/5)x + 1.5

Now the needed height is,

→ (-16/1225)x² + (7/5)x + 1.5

→ (-16/1225)(0)² + (7/5)(0) + 1.5

→ 0 + 0 + 1.5

→ 1.5 feet

Hence, the height is 1.5 feet.

Answer:

x= 67

Step-by-step explanation:

x = 21+2×(90-x)

x= 21+180-2x

x= 201-2x

3x=201

x= 67

The perimeter of triangle ABC = 60 + 20√3  cm

What is perimeter?

The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet.

In triangle ADB,

sin (30°) = AD/AB

1/2 = ( 10 √3 ) /AB

AB  = 20√3

In triangle ABC,

cos (30°) = AB/BC

√3 /2 =  20√3 / BC

BC = 40

tan (30°) = AC/AB

1/√3 =  AC/ 20√3

AC = 20

Perimeter of triangle ABC =  AB +BC  + AC

                                           = 20√3  +  40  + 20

                                           = 60 + 20√3

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Answer:

1.728 m^3

Step-by-step explanation:

120 cm = 1.20 m

V = 1.20^ 3 = 1.728 m^3

Answer:

[tex]\huge\boxed{\sf Volume = 1.728 \ m\³}[/tex]

Step-by-step explanation:

Length = l = 120 cm = 1.2 m

We know that,

Volume = 1.2³

Volume = 1.728 m³

[tex]\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

Remove any grouping symbol such as brackets and parentheses by multiplying factors.

Use the exponent rule to remove grouping if the terms are containing exponents.

Combine the like terms by addition or subtraction

Combine the constants

Simplify 3x2 + 5x2

Solution

Since both terms in the expression are have same exponents, we combine them;

3x2 + 5x2 = (3 + 5) x2 = 8x2

Answer:

  y = x³ +x² -20x

Step-by-step explanation:

You want a polynomial with roots x ∈ {0, -5, 4}.

When a polynomial has a root p, it has a factor (x -p). The three given roots mean the polynomial you want can be factored as ...

  y = (x -0)(x -(-5))(x -4) = x(x+5)(x-4)

When this product is expanded, the result is ...

  y = x³ +x² -20x . . . . polynomial with roots {0, -5, 4}