If the equation of the regression line that relates hours per week spent in the lab, x, to GPA, y, is y = 2.1 + 0.28x, then the best prediction for the GPA of students who never go to the lab 2.1.TrueFalse

Answer:

.923 goals per game

Step-by-step explanation:

All you have to do is divide the number of goals by the number of games.

767/831 = .923

According to the given data the length of a \(90^{0}\) arc is \(\pi /2\) or approximately \(1.57\) feet.

In geometry, the length of an arc is the distance along the curved line that makes up the arc. It is a measure of the "length" of a portion of a circle's circumference, and it is usually expressed in the same units as the circle's radius.

According to the given information:

The length of a \(90^{0}\) arc in a circle with radius \(1\) foot can be calculated using the formula:

Length of arc = (angle/\(360\)) x \(2\pi r\)

where angle is the central angle of the arc in degrees, r is the radius of the circle, and \(\pi\) is a mathematical constant approximately equal to \(3.14159\).

Substituting the given values, we have:

Length of arc = (\(90/360\)) x \(2\pi(1 ft)\)

Length of arc = \((1/4)\) x \(2\pi ft\)

Length of arc = \(\pi /2 ft\)

Therefore, the length of the \(90^{0}\) arc is \(\pi /2 feet\) or approximately \(1.57 feet\)

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the length of the 90° arc is π/4 feet or approximately 0.785 feet

What is arc of circle?

In geometry, an arc of a circle is a portion of the circle's circumference. It is defined by two endpoints and all points along the circle between those endpoints. The measure of an arc is typically given in degrees or radians and can be used to calculate various properties of the circle, such as its length, area, and sector angles.

The formula for the length of an arc is:

L = (θ/360) × 2πr

where L is the length of the arc, θ is the central angle of the arc in degrees, and r is the radius of the circle.

In this case, θ = 90° and r = 1 ft, so we have:

L = (90/360) × 2π(1) = (1/4) × π = π/4

Therefore, the length of the 90° arc is π/4 feet or approximately 0.785 feet (rounded to 3 decimal places).

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Answer: the transformation of ABC to MNO preserves both side lengths and angle measures of the triangle.

Step-by-step explanation:

Answer:

B - The transformation of triangle ABC to triangle MNO preserves both the side lengths and angle measures of the triangle.

Answer:

-2.4

Step-by-step explanation:

Set the expressions equal to each other and solve.

.5x-2=3x+4

.5x-3x=6

-2.5x=6

x=-2.4

Plug in -2.4 into each expression and solve to check your work. You should end up with the same answer from both expressions.

Answer:

x = 33.5 °

Step-by-step explanation:

The two angle add to a straight 180 degree angle

so

4x+5     + 41 = 180

4x = 134

x = 33.5 °

The true statement about the system of equations is the fourth one:

"(8, 2) is a solution to one equation but not the other one, so it is not a solution to the system."

The system of equations is:

x - 3y = 2

y = x + 6

We want to see which statement is true, all of them refer to the point (8, 2), so let's see if it is a solution of the system.

Replacing the values in the first equation we will get:

8 - 3*2 = 2

8 - 6  =2

2 = 2

For the second equation:

2 =8 + 6

2 = 14

This is false, so (8, 2) is not a solution of the second equation.

Then the true statement is:

" (8, 2) is a solution to one equation but not the other one, so it is not a solution to the system."

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The width of the rectangle is 1/9 cm.

The perimeter of the rectangle is 3.2 cm.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Rectangle:

Area = 1/6 cm²

Length = 1.5 cm

Width = w

Now,

Area = length x width

Perimeter = 2 (length + width)

So,

1/6 = 1.5 x w

w = 1/(6 x 1.5)

w = 1/9 cm

And,

Perimeter.

= 2 (1.5 + 1/9)

= 2 x (13.5 + 1)/9

= 29/9

= 3.2 cm

Thus,

The width of the rectangle is 1/9 cm.

The perimeter of the rectangle is 3.2 cm.

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The volume of the rectangular prism is 208cm³

Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m3, cm3, in3 etc. Sometimes, volume is also termed capacity.

The volume of a rectangular a prism is expressed as base area × height. The base area is a rectangle and the area of a rectangle is Length × width

length = 2cm

width = 13 cm

height = 8cm

base area = 13× 2 = 26cm²

Volume of the prism = 26× 8 = 208cm³

Therefore the volume of the rectangular prism is 208cm³.

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Using the margin of error, it is found that he must survey 601 adults in order to be 95% confidence that his estimate is within 4 percentage points of the true population percentage.

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the z-score that has a p-value of \(\frac{1+\alpha}{2}\).

The margin of error is:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

95% confident, hence:

\(\alpha = 0.95\), z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so \(z = 1.96\).

We have no estimate, hence, \(\pi = 0.5\) is used.

Within 4%, hence, it is needed to find n for which M = 0.04.

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.04\sqrt{n} = 1.96(0.5)\)

\(\sqrt{n} = \frac{1.96(0.5)}{0.04}\)

\((\sqrt{n})^2 = \left(\frac{1.96(0.5)}{0.04}\right)^2\)

\(n = 600.25\)

Rounding up, 601 adults must be sampled.

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Answer:

See Explanation

Step-by-step explanation:

The question is incomplete but a possibility is that the given parameters are points  on a straight line.

I'll answer base on that assumption.

\(RS = 6y + 2\)

\(ST =2y + 7\)

\(RT =13y -21\)

To solve for y, we have that:

\(RT = RS + ST\)

This gives:

\(13y - 21 = 6y + 2 + 2y + 7\)

Collect Like Terms

\(13y - 6y - 2y = 21 +2+7\)

\(5y = 30\)

Divide both sides by 5

\(y = 6\)

To get the measure of each line. Substitute 6 for y in

\(RS = 6y + 2\)

\(ST =2y + 7\)

\(RT =13y -21\)

\(RS = 6 * 6 + 2 = 36 + 2 = 38\)

\(ST = 2*6 + 7 = 12 +7 = 19\)

\(RT = 13*6 - 21 = 78 - 21 = 57\)

Answer: Survey

Step-by-step explanation:

Survey can be employed as a means of data collection to aid them know the amount of books student bring to into the media center during the final week. This can be achieved by the use of questioners which are handed to each and every student. The questionier must be simple and easy to understand to as to get an accurate result. Example close ended where options are provided.

The required simplified expression is: x² - 9/ 9x⁴ + 9x² for all x ≠ 0 or 3.

The given expression below is:

x² - 9 / (3x²)(3x²) + 9x²

To simplify the given expression, we must first distribute the terms on the numerator and denominator.

The numerator becomes x² - 9 and the denominator becomes (3x²)(3x²) + 9x².

Next, we must simplify the denominator by combining like terms. The denominator becomes 9x⁴ + 9x².

Finally, we can simplify the entire expression by dividing the numerator by the denominator.

This gives us the simplified expression: x² - 9/ 9x⁴ + 9x².

Note that this expression is not defined when x = 0 or x = 3, as it would result in a division by zero.

Thus, the final simplified expression is x² - 9/ 9x⁴ + 9x² for all x ≠ 0 or 3.

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Answer:

The equation of the line parallel to 2y = x – 3 and passing through point (-4,3) in slope-intercept form is y = (1/2)x + 5.

Step-by-step explanation:

To find the equation of a line that is parallel to 2y = x – 3, we need to determine the slope of the given line.

2y = x - 3 can be written in slope-intercept form y = (1/2)x - 3/2.

The slope of this line is 1/2.

Since we want a line parallel to this line, the slope of the new line will also be 1/2.

Next, we can use the point-slope form of a line to write the equation of the new line.

Point-slope form: y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope of the line.

Substituting the values, we get:

y - 3 = (1/2)(x - (-4))

Simplifying, we get:

y - 3 = (1/2)x + 2

Adding 3 to both sides, we get the final equation in slope-intercept form:

y = (1/2)x + 5

Therefore, the equation of the line parallel to 2y = x – 3 and passing through point (-4,3) in slope-intercept form is y = (1/2)x + 5.

The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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The inequality on the graph is the third option:

(2/5)*x - 3/2 ≥ y

Let's analyse the graph if the inequality.

We can see that there is a solid linear equation with a positive slope, and the shaded area is below that line, then the inequality is of the form:

y ≤ linear equation.

We know that the symbol "≤" must be used because of the solid line.

We also can see that when x = 0, y takes a velue between -1 and -2.

With that in mind the correct option is the third one:

(4/5)*x - 2y ≥ 3

Isolating y we get:

(4/5)*x - 3 ≥ 2y

(2/5)*x - 3/2 ≥ y

Changing the order:

y ≤ (2/5)*x - 3/2

That is the graphed inequality.

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Answer:

y=45x+150

its a function but not a linear function

Step-by-step explanation:

hope this helps

Answer:

10 ways

Step-by-step explanation:

The number of ways in which five basketball players could be placed in three positions is:

5\(C_{3}\) = \(\frac{5!}{(5-3)!3!}\)

      = \(\frac{5!}{3!2!}\)

      = \(\frac{5*4*3*2!}{3*2*2!}\)

      = 5 × 2

     = 10

The basketball players can be arranged in 10 ways.

Answer: 15 ways

the guy who answered before me is wrong the way you measure probability is multiplying the outcomes 3x5=15 not 10

Pls mark brainliest

Answer:

if x=0than 3×0×(6×0)_< 9

The number that belongs in the green box using sine rule is 13.96.

The rule of sine or the sine rule states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

To calculate the number that belongs in the green box, we use the formula below

Formula:

From the diagram,

Given:

Substitute these values into equation 1

Solve for x

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Answer:

d. 10, 24, 26

Explanation:

To identify the side lengths that form a right triangle, we check if it satisfies the Pythagorean theorem.

By the theorem:

a. 12, 13, 16

These side lengths do not form a right triangle.

b. 15, 20, 21

These side lengths do not form a right triangle.

c. 9,40,42

These side lengths do not form a right triangle.

d. 10, 24, 26

These side lengths form a right triangle since both sides of the equation are the same.

Answer:

4 points

Step-by-step explanation:

if you look its only 4, 1 on top, and 3 around.

Answer:

radius=diameter/2

=9/2

=4.5 in.

diameter=radius*2

=3m*2

=6m

Step-by-step explanation:

Step-by-step explanation:

1) r=d/2

r=9in/2

r=4.5in

2) d= r×2

d=3m×2

d=6m

1. The possible amounts of time for which the chemistry club could rent the meeting room are 1 to 5 hours.

2. Solving the inequality for t is 39 + 6.80t ≤ 73, where the maximum time is 5 hours.

Inequality is a mathematical statement that two or more mathematical expressions are unequal.

Inequalities are depicted using the following symbols:

The total budget of the chemistry club for renting a meeting room = $73.60

The reservation fee charged by the college = $39

The additional fee (variable cost) per hour = $6.80

The number of hours the club can rent the meeting room = t

The inequality representing the situation is:

39 + 6.80t ≤ 73.

39 + 6.80t ≤ 73

6.8t ≤ 73 - 39

6.8t ≤ 34

t ≤ 5 (34/6.8)

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Answer:

1.2

Step-by-step explanation:

1.Arrange the numbers in order by size.

15,20,25,30,35,41

2.If there is an odd number of terms, the median is the center term.

with these numbers they are even (6 numbers total)

3.If there is an even number of terms, add the two middle terms and divide by 2.

30 ÷ 25=1.2

Answer:  

1) 260 degrees

2) 73 degrees

3) 1.518 rad

4) 3.805 rad

5) 320 degrees

6) 160 degrees

7) 45 degrees

8) 150 degrees

9) 5.498 rad

The price of the couch after the markup gotten during a sale, a store offered a 30% discount on a couch that originally sold for $870 is $791.70.

The concept that will be used here is the discounted price . The discount is represented in the advertisement as a percentage off the list price. As a result, a sale price of $70 will be achieved with a 30% discount on a $100 list price. Another way to understand the phrase is to say that it simply refers to the selling price of an item.

The  price of the couch after the markup can be determine as :

$870 * (1 + 30% ) *  (1 - 30% )

Then this can be simplifIed as :

= $870  *1.3 * 0.7

=$ 791.7

Then Rounding up to the nearest cent will give $ 791.70

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Answer:

The answer is :

Step-by-step explanation:

Axis of symmetry is the equation where it cuts the middle of the quadratic graph.

For quadratic equation in the form of (x+a)² + b, the axis of symmetry will be (x+a) = 0 which is x = -a :

Question 1,

\((x + 3) = 0\)

\(x = - 3\)

Question 2,

\((y - 4 )= 0\)

\(y = 4\)

Answer:

\(\boxed{x=-3} \\ \boxed{y=4}\)

Step-by-step explanation:

Axis of symmetry is a line that cuts the parabola in half touching the vertex.

Quadratic forms ⇒ y = ax² + bx + c or x = ay² + by + c

Axis of symmetry ⇒ x = \(\frac{-b}{2a}\) or y = \(\frac{-b}{2a}\)

First problem:

y = -3(x+3)²-2

Write in quadratic form ⇒ y = ax² + bx + c

y = -3(x² + 6x + 9) - 2

y = -3x² -18x - 27 - 2

y = -3x² -18x - 29

a = -3, b = -18

Find axis of symmetry.

\(x= \frac{-b}{2a}\)

\(x=\frac{--18}{2(-3)}\)

\(x=\frac{18}{-6}=-3\)

Second problem:

x = -4(y -4)² +6

Write in quadratic form ⇒ x = ay² + by + c

x = -4(y² - 18y + 16) + 6

x = -4y² + 32y - 64 + 6

x = -4y² + 32y - 58

a = -4, b = 32

Find axis of symmetry.

\(y= \frac{-b}{2a}\)

\(y=\frac{-32}{2(-4)}\)

\(y=\frac{-32}{-8}=4\)

The domain are the possible input while the range are the possible output

of a function.

Reasons:

The given functions can be expressed by the equation; (-x + 1)·(x + 1) = -x² + 1

Therefore, we have;

(a) y = f(x) + 1 = -x² + 1 + 1 = -x² + 2

The x-intercept of the above function are, x = √2, and x = -√2

Which gives;

The domain = [-√2, √2]

The range = [0, 2]

(b) y = 3·f(x) = 3 × (-x² + 1) = -3·x² + 3

At the x–intercepts, we have;

-3·x² + 3 = 0

x = ±1

The domain = [-1, 1]

The maximum value of y is given at x = 0, therefore;

= -3 × 0² + 3 = 3

The range = [0, 1]

(c) y = -f(x) = -(-x² + 1) = x² - 1

At the x–intercepts, x² - 1 = 0

x = ± 1

The domain = [-1, 1]

The minimum value of y is given at x = 0, which is y = -1

The range = [0, -1]

(d) y = f(x - 1) = -(x - 1)² + 1 = -x² + 2·x

At the x–intercepts, we have;  -x² + 2·x = 0, which gives;

(-x + 2)·x = 0

Which gives, x = 0, or x = 2

The domain = [0, 2]

The maximum value of y is given when x = -b/(2·a) = -2/(2×(-1)) = 1

y = f(1) =  -1² + 2×1 = 1

Therefore;

The range = [0, 1]

(e) y = f(x + 2) + 1 = (-(x + 2)² + 1) + 1 = -x² - 4·x - 2

At the x–intercepts, we have;  -x² - 4·x - 2 = 0, which gives;

x = -(2 + √2) or x = x = √2 - 2

The domain = [-(2 + √2), (√2 - 2)]

The maximum value of y is given when x = -4/(2)) = -2

Which gives;

-(-2)² - 4·(-2) - 2 = 2

The range = [0, 2]

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