A college student collected data from a number of his classmates. He recorded the number of hours each spent watching television and sleeping each night. The scatter plot shows the data he gathered and the line of best fit. Using technology, the student found the equation of the line of best fit is y = -x + 9. Based on the equation for the line of best fit, how many hours of nightly sleep would a classmate likely get if she spent 6 hours watching television each night? A. 7 hours B. 6 hours C. 3 hours D. 15 hours

The equation of the parabola is,

⇒ y = - 1/4x² + 4

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

If a parabola has two x-intercepts, it must be of the form;

⇒ y - k = a (x - h)²

where, (h, k) is the vertex.

Since, it is given that the vertex is (0, 4),

We have that h = 0 and k = 4.

So, the equation becomes

y - 4 = a (x - 0)²

y - 4 = ax²

For a, we use the fact that the parabola passes through point (4,0).

Putting x = 4 and y = 0, we get

y - 4 = ax²

0 - 4 = a (4)²

- 4 = 16a

a = - 1/4

Therefore, The equation of the parabola is,

⇒ y - 4 = (- 1/4)x²

⇒ y = - 1/4x² + 4

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Answer:

TRQ=47 degrees

TRS=133 degrees

Step-by-step explanation:

straight line=180

3x+5+10x-7=13x-2

180+2=13x-2+2

182=13x

x=14

3(14)+5=42+5=47 degrees

10(14)-7=140-7=133 degrees

47+133=180 yes.

Answer:

46

Step-by-step explanation:

With those problems if you are not given a picture is good we draw one.

Because an angle bisector forms 2 congruent angles and because is given that < XVY ≅ < YVW  then

m < XVY = m < YVW

      2x+7 = x+15 , subtract x and 7 from both sides to isolate the like terms

      2x-x = 15-7, combine like terms

           x = 8

From the picture and the given we see that

m < XVW = m < XVY + m < YVW

m < XVW = 2x+7 + x+15 , combine like terms

m < XVW = 3x + 22, substitute x for 8

m < XVW = 3*8 + 22

m < XVW = 46

Check our work:

m < XVY =  2x+7  = 2*8 +7 = 16 +7 = 23

m < YVW =  x+15 = 8 +15 = 23

m < XVW = m < XVY + m < YVW = 23+23 =46

Answer:

Step-by-step explanation:

Hello, please consider the following.

\(h(x)=5/2x+4 \\\\x=(h^{-1}o})(x)=(hoh^{-1})(x)=h(h^{-1}(x))=\dfrac{5}{2h^{-1}(x)+4}\\\\<=> 2h^{-1}(x)+4=\dfrac{5}{x}\\\\<=> h^{-1}=\dfrac{\dfrac{5}{x}-4}{2}\\\\<=>h^{-1}=\dfrac{5-4x}{2x}\)

Thank you.

The ages of people who own their homes are normally distributed with a mean of 42 and a standard deviation of 3.2. To find the age at which 75% of the home owners are older than this age, we can use the standard normal distribution table to find the z-score, which is approximately 0.674. The correct option is 44.2, as 75% of the home owners are older than 44.2.

Suppose ages of people who own their homes are normally distributed with a mean of 42 years and a standard deviation of 3.2 years. We need to find the age at which 75% of the home owners are older than this age.How to find the age?We can use the standard normal distribution table. The standard normal distribution is a normal distribution with a mean of 0 and standard deviation of 1. Using this table, we can find the z-score which corresponds to the area to the left of a particular value.Suppose z is the z-score such that the area to the left of z is 0.75. This means that 75% of the distribution is to the left of z. We can use this z-score to find the age at which 75% of the home owners are older than this age.What is the formula for z-score?The formula for finding the z-score for a value x in a normal distribution with mean μ and standard deviation σ is as follows

\(:$$z=\frac{x-\mu}{\sigma}$$\)

We can rearrange this formula to find the value of x. Here's how:$$x=\sigma z + \mu$$

Now, let's find the z-score which corresponds to the area to the left of 0.75. Using a standard normal distribution table

we can find that this z-score is approximately 0.674.Using the above formula, we can find the age x at which 75% of the home owners are older than this age. We know that μ = 42 and σ = 3.2. Therefore, we have:$$x = 3.2 \times 0.674 + 42 = 44.16$$

Therefore, approximately 75% of the home owners are older than 44.16. So, the correct option is 44.2.Approximately 75% of the home owners are older than 44.2.

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The fully simplified product of (b - 2c)(-3bc) has the following two true statements: The product is a polynomial expression. The product has a coefficient of 6bc.

To find the product of (b - 2c)(-3bc), we can use the distributive property. Expanding the expression, we get:

(b)(-3bc) + (-2c)(-3bc)

Simplifying further, we have:

-3b^2c - (-6c^2b)

Combining like terms, we get:

-3b^2c + 6c^2b

From the simplified product, we can observe the following:

The product is a polynomial expression since it consists of terms with variables raised to various powers and coefficients.

The coefficient of the product is 6bc, which is obtained from the term 6c^2b.

Therefore, the true statements about the fully simplified product of (b - 2c)(-3bc) are that it is a polynomial expression and it has a coefficient of 6bc.

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By using standard deviation, it can be concluded that

The given estimate of standard deviation = 3 is not true

What is Standard Deviation?

At first, it is important to know about variance.

Variance is the sum of the square of deviation from mean divided by the total number of observations. Standard Deviation is the square root of variance.

Highest number = 40 and lowest number  = 22

Range = 40 - 22 =18

Standard deviation = \(18 \div 4\)

Standard deviation = 4.5

So the above statement is false

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Based on the given graph of a linear equation between total wages and hours worked, we can find that:

The given graph demonstrate the linear relationship between total wages and hours worked.

First, we need to identify the linear equation between total wages and hours worked by finding the slope of the graph. We take 2 points:

(1, 12)

(2, 24)

We can use the slope formula where:

slope (m) = y₂ - y₁

                   x₂ - x₁

m = 24 - 12

        2 - 1

m = 12

The slope of the graph represents the rate of pay per hour is $12 per hour.

If we input the value of the slope into the linear equation of y = mx + c, by taking 1 point (1, 12) we can find the value of c:

y = mx + c

12 = (12) (1) + c

c = 0

The linear equation of the graph is: y = 12x

To earn $30, Adeline needs to work for:

y = 12x

$30 = 12x

x = 2.5 hours

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Answer:

A line is a straight path of points that has no beginning or end

A line segment is a portion of a line that has two endpoints

A ray is a portion of a line which has one endpoint and extends forever in one direction

Complementary angles are two angles whose sum adds up to 90 degrees

Supplementary angles are two angles that add up to 360 degrees

Answer:

10.95 or \(2\sqrt{30}\)

Step-by-step explanation:

The Pythagorean Theorem is as follows:

\(a^{2}+ b^{2}= c^{2}\)

A and B represent the legs of the triangle, and C represents the hypotenuse.

For this problem, it gives us the legs. So, we have to find the hypotenuse.

Plug the values of the legs into the equation:

\(6^{2} +8^{2}= c^{2}\)

Now solve the equation to find the hypotenuse:

\(36 + 64 = c^{2}\)                              Distribute the squares

\(120 = c^{2}\)                                     Add

\(\sqrt{120}= \sqrt{c^{2} }\)                              Square root both sides

c = 10.95 or \(2\sqrt{30}\)

Therefore the length of the missing leg is 10.95 or \(2\sqrt{30}\).

Hope this helps!! Ask questions if you need!

Answer:

sex kaise kare aur bata ky chal raha tha aur bata ky chal raha h

Answer:

The first one is 60 and the second one is 12

Step-by-step explanation:

5*12=60    6*12=72     72-60=12

There are 90 different outfits he can wear if he has to wear slacks and a shirt along with his 3 sport coats and 1 tie.

Here, we can use the multiplication principle of counting to determine the number of possible outfits a man can wear given that he must wear at least one pair of slacks and one shirt. Let us denote sport coats as A, B, and C; slacks as P1, P2, P3, P4, and P5; shirts as S1, S2, S3, S4, S5, and S6; and the tie as T.

Then, the number of outfits he can wear is given by the product of the number of choices for each item as follows: Total outfits = (Number of sport coats) × (Number of slacks) × (Number of shirts) × (Number of ties)= 3 × 5 × 6 × 1= 90. Differentiating between the cases where he wears only one shirt and one pair of slacks from those where he wears two or more of each is unnecessary because the problem statement requires that he wears at least one of each.

Therefore, we can calculate the total number of outfits directly using the multiplication principle of counting, which gives us the answer of 90 different outfits he can wear if he has to wear slacks and a shirt along with his 3 sport coats and 1 tie.

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Question 1a

To calculate the book value at the end of the first year using straight-line depreciation, we need to determine the annual depreciation expense first. The straight-line method assumes that the asset depreciates by an equal amount each year over its useful life. Therefore, we can use the following formula to calculate the annual depreciation:

Annual Depreciation = (Cost - Salvage Value) / Useful Life

Substituting the given values, we get:

Annual Depreciation = ($200,000 - $20,000) / 10 years = $18,000 per year

This means that the tractor will depreciate by $18,000 each year for the next 10 years.

To determine the book value at the end of the first year, we need to subtract the depreciation expense for the year from the original cost of the tractor. Since one year has passed, the depreciation expense for the first year will be:

Depreciation Expense for Year 1 = $18,000

Therefore, the book value of the tractor at the end of the first year will be:

Book Value = Cost - Depreciation Expense for Year 1

= $200,000 - $18,000

= $182,000

So the book value of the tractor at the end of the first year, December 31, 2022, using straight-line depreciation is $182,000. so the answer is D

Question 1(b)

To determine the farmer's noncurrent liabilities, we need to use the information provided to calculate the total liabilities and then subtract the current liabilities from it. Here's the step-by-step solution:

Calculate the total current liabilities using the current ratio:

Current Ratio = Current Assets / Current Liabilities

2 = $80,000 / Current Liabilities

Current Liabilities = $80,000 / 2

Current Liabilities = $40,000

Calculate the total liabilities using the debt/equity ratio:

Debt/Equity Ratio = Total Liabilities / Owner Equity

1.0 = Total Liabilities / $100,000

Total Liabilities = $100,000 * 1.0

Total Liabilities = $100,000

Subtract the current liabilities from the total liabilities to get the noncurrent liabilities:

Noncurrent Liabilities = Total Liabilities - Current Liabilities

Noncurrent Liabilities = $100,000 - $40,000

Noncurrent Liabilities = $60,000

Therefore, the farmer's noncurrent liabilities are $60,000. so the answer is B.

Solving a quadratic equation we can see that Jason will hit the water after 6 seconds.

We know that the height of Jason is modeled by the quadratic function:

h = - 16x² + 16x + 480

The water is at h = 0, so we need to solve the quadratic equation:

0 = - 16x² + 16x + 480

If we divide all the right side by 16,we will get:

0 = (- 16x² + 16x + 480)/16

0 = -x² + x + 30

Now we can use the quadratic formula to get the solutions:

\(x = \frac{-1 \pm \sqrt{1^2 - 4*(-1)*30} }{2*-1} \\\\x = \frac{-1 \pm 11 }{-2}\)

We only care for the positive solution, which is:

x  = (-1 - 11)/-2 = 6

Jason will hit the water after 6 seconds.

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This question is incomplete because it was a details in the question was not written correctly.

Complete Question:

A sundae requires 2 ice-cream scoops and 4 raspberries, and a milkshake requires 3 ice-cream scoops and 5 raspberries. Laila wants to sell sundaes and milkshakes with at most 80 ice-cream scoops and 150 raspberries. Let S denote the number of sundaes she makes and M the number of milkshakes she makes. Write an inequality that represents the condition based on the number of (ICE-CREAM SCOOPS).

Answer:

An inequality that represents the condition based on the number of (ICE-CREAM SCOOPS) is given as:

2S + 3M ≤ 80

Step-by-step explanation:

From the above question, we are told that:

Let S denote the number of sundaes Laila makes

M the number of milkshakes

a) A sundae requires 2 ice-cream scoops and 4 raspberries

A sundae = 2S and 4S

b) A milkshake requires 3 ice-cream scoops and 5 raspberries.

A milk shake = 3M and 5M

Laila wants to sell sundaes and milkshakes with at most 80 ice-cream scoops and 150 raspberries .

Therefore, an inequality that represents the condition based on the number of (ICE-CREAM SCOOPS) is given as:

2 ice cream scoops + 3 ice cream scoops ≤ 80

2S + 3M ≤ 80

Let's first draw the triangle being described to better understand the scenario:

Step 1: Applying the Sine Law, let's first determine the measure of Angle C represented by x.

Step 2: The sum of all interior angles of a triangle is equal to 180°, let's use this property to find the measure of Angle B represented by y.

Therefore, the answer is letter C : 101.23° or 14.77°

Answer:

Step-by-step explanation:

Now the state-space representation is

\([ΔθΔθ˙]=[001Ib​kIb​][ΔθΔθ˙]+[0Hω] cos(θ0​ + Δθ\)

\()≈[0Hω] cos(θ0​) + [0−Hω sin(θ0​)] Δθ + [0Hω] cos(θ0​) Δθ˙ + [001Ib​kIb​][ΔθΔθ˙]\)

This is the state space representation of the system if the input is ω(t) and the output is \(θ(t).\)

Given that the differential equation of the system is \(Iθ¨ + bθ˙ + kθ = Hω cosθ.\)

Here, I is the moment of inertia, b is the coefficient of damping, k is the spring constant, θ is the angular displacement, H is the torque constant and ω is the angular frequency.

The state-space representation of the above system is given by:

\([θθ˙]=[001Ib​kIb​] [θθ˙]+[0Hω]cosθ\).The linearization of the state equation can be obtained by taking the first order Taylor series expansion of the equation about the equilibrium point. At the equilibrium point \(θ0​=0\),

\(θ˙0​=0\) and

ω0​=0, the linearized state equation is given by

:\(Δθ¨ + bΔθ˙ + kΔθ = Hω cosθ or Δθ¨ + bΔθ˙ + kΔθ\)

= HωFor linearization,

\(Δθ = θ - θ0\)​ and

\(Δθ˙ = θ˙ - θ˙0​Δθ\)

\(= θ\)and

\(Δθ˙ = θ\)˙

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2x⁴+2x³-12x² is the correct option.

Given is an expression, 2x²(x+3)(x-2), we need to expand it,

To expand the given expression, we must multiply each term of every expression to each term of the other two expressions.

The expansion is as follows :

= 2x²(x+3)(x-2)

= 2x²(x²+3x-2x-6)

= 2x²(x²+x-6)

= 2x⁴+2x³-12x²

Thus, the required expended form is 2x⁴+2x³-12x².

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Answer:

B, because no misleading

Answer:

60%

Step-by-step explanation:

Answer:

60%

Step-by-step explanation:

The length of the of the conveyor belt is 10.7ft( nearest tenth)

Pythagoras theorem states that, in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

The length of the belt of the conveyor is the hypotenuse and the other two sides are given as 3.75 and 10 ft

c² = a² + b²

c² = 3.75² +10²

c² = 14.06 +100

c² = 114.06

c = √ 114.06

c = 10.7ft ( nearest tenth)

therefore the length of the belt of the conveyor is 10.7ft

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Answer:

91

Step-by-step explanation:

If we add all of the student's scores we get 273. Because there are 3 students we divide 273 by 3 and we get 91 as the average.

Answer:

y < 4x - 2

Step-by-step explanation:

Answer:

y < 4x - 2

Step-by-step explanation:

Determine the equation of the line:

A solid line means the signs ≤ or ≥ should be used (inclusive boundary)

A dotted line means the signs < or > should be used (non inclusive boundary).

> is points above the boundary line

< is points below the boundary line

Therefore, the grey shaded area is y < 4x - 2

By applying the definitions of rigid transformation ((x, y) → (0.5 · x, 0.5 · y)) and dilation, we conclude that the coordinates of Q'(x, y) are (0.1).

Herein we must apply a rigid transformation into a given point to determine an image. Rigid transformations are transformations applied on a geometric locus such that Euclidean distance is conserved. Dilations are a kind of rigid transformations such that:

(x, y) → (k · x, k · y), for k > 0

If we know that Q(x, y) = (0, 2) and k = 0.5, then the coordinates of Q' are:

Q'(x, y) = (0.5 · 0, 0.5 · 2)

Q'(x, y) = (0, 1)

By applying the definitions of rigid transformation ((x, y) → (0.5 · x, 0.5 · y)) and dilation, we conclude that the coordinates of Q'(x, y) are (0.1).

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Answer: Q' = (0,1)

Step-by-step explanation: just did it on edge