Let x be the age in years of a licensed automobile driver. Let y be the percentage of all fatal accidents (for a given age) due to speeding. For example, the first data pair indicates that 34% of all fatal accidents of 17-year-olds are due to speeding. x 17 27 37 47 57 67 77 y 34 24 17 12 10 7 5 A button hyperlink to the SALT program that reads: Use SALT. Complete parts (a) through (e), given Σx = 329, Σy = 109, Σx2 = 18,263, Σy2 = 2339, Σxy = 3843, and r ≈ −0.9549. (a) Draw a scatter diagram displaying the data. (b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r = (c) Find x, and y. Then find the equation of the least-squares line y hat = a + bx. (Round your answer to four decimal places.) x = y = y hat = + x (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to four decimal places. Round your answers for the percentages to two decimal place.) r2 = explained % unexplained % (f) Predict the percentage of all fatal accidents due to speeding for 40-year-olds. (Round your answer to two decimal places.)

Answer:

14.2°

Step-by-step explanation:

We solve this using the Cosine rule formula

​From the question we have

Side a = 5

Side b = 11

Side c = ?

We are given Angle C = 120°

Hence,

c² = a² + b²− 2ab cos(C)

Hence,

c² = 5² + 11² - 2(5 × 11) × cos (120°)

c =√[ 5² + 11² - 110 × cos (120°)]

c = 14.18 °

Approximately to the nearest tenth

c = 14.2°

Lines have a larger m value, that is, m > 1 have steeper slope and lines having an m value between 0 and 1, usually in the form of a fraction have a flatter slope .

Slope is the rate of change in the dependent variable with respect to the independent variable.

For an equation of line of the type - y= mx +c , the slope is given by the m value.

Now, if the value of m > 1 like m=1,2,3, ... , the lines have a steeper slope and have a steep nature.

Similarly, if the value of m < 1 i.e. 0 < m < 1 like m=1/2,2/3, ... fractional values,  the lines have a flatter slope and do not have a steep nature.

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Answer:

1. The area is found by using the formula for a rectangle

The area is 150 cm²

2. The area is found by the definite integral for the area between two points under a curve

3. The methods are different

The methods are different because the area of figure A is found by the multiplication between the dimensions, while the area of figure B is found by the difference between the values of the integral of the function between the points

Step-by-step explanation:

1. The area of the shaded figure A is found by multiplying the dimensions of the figure, which is the length multiplied by the breadth of the figure

From the question, we have;

The area of the rectangular figure, A = Length × Breadth

The length of the figure = 15 cm

The breadth of the rectangular figure = 10 cm

Therefore, we have;

A = 15 cm × 10 cm = 150 cm²

The area of the rectangular figure, A = 150 cm²

2. The bell shape of the figure B is obtained from a function f(x) as obtained from MIT mathematics website as follows;

\(f(x) = e^{-t^2}\)

Therefore the area of the shaded region in the bell shaped figure between the points 0 and 1 on the x-axis is found by integration as follows;

\(A = \int\limits^1_0 {e^{-t^2}} \, dt = \dfrac{1}{2} \cdot \sqrt{\pi} \times erf(t)\)

Using a graphing calculator, we have;

\(A = \int\limits^1_0 {e^{-t^2}} \, dt \approx 0.746824\)

3. The method of finding the area of figure A is different from the method of finding the area of the figure B

The methods are different because the area of figure A is the area of the whole figure of a geometric shape with known formula for area while the area of of the shaded region has no predefined formula but is calculated using the calculus for the area under a curve.

The like terms to the Linear expression: 4a-4+6a-11 is 10a - 15

A Linear equations are the equations of degree 1. It is the equation for the straight line.

Collect the like terms of the expression

4a +6a -4 -11

Add the like terms

10a -15

Therefore the like terms in the linear expression is 10a -15

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Answer:

\( \boxed{\sf b. \ 8(2a + 9)} \)

Step-by-step explanation:

\( \sf Factor \: the \: following: \\ \sf \implies 16a + 72 \\ \\ \sf Factor \: 8 \: out \: of \: 16a + 72: \\ \sf \implies 8 \times 2a + 8 \times 9 \\ \\ \sf \implies 8(2a + 9)\)

Answer:

55

Step-by-step explanation:

m angle A and m angle C are equal sine two of those sides are equal. You would do 3x + 40 = x +50

You subtract x, leaving it to be 2x + 40 = 50

Subtract the 40, leaving it be 2x = 10

Divide both sides by 2, which leaves x = 5

and then you would do 3(5) + 40, which is 55

Answer:

Read it carefully below

Step-by-step explanation:

Based on the formula you provided, the function appears to model exponential decay. In general, exponential decay occurs when the growth rate of a quantity is proportional to its current value, and the growth rate is a fixed constant less than 1.

In this case, the growth rate is given by the constant factor 7/3 (which is less than 1), and the function uses the variable t as the exponent. As t increases, the value of the function decreases exponentially.

The simplest form is:

Answer: One Half

Step-by-step explanation: 3 is half of 6 and  I took the test ;)

The midpoint of the line segment is (1.5, 0).

To determine the midpoint of the line segment, we need to find the average of the x-coordinates and the average of the y-coordinates of the two endpoints.

Given the endpoints (1.5, -2) and (1.5, 2), we can find the midpoint as follows:

Average of x-coordinates: (1.5 + 1.5) / 2 = 3 / 2 = 1.5

Average of y-coordinates: (-2 + 2) / 2 = 0 / 2 = 0

The midpoint of a line segment is found by averaging the x-coordinates and the y-coordinates of the two endpoints. In this case, the given endpoints are (1.5, -2) and (1.5, 2). To find the x-coordinate of the midpoint, we add the x-coordinates of the endpoints and divide by 2: (1.5 + 1.5) / 2 = 3 / 2 = 1.5. Similarly, for the y-coordinate, we add the y-coordinates of the endpoints and divide by 2: (-2 + 2) / 2 = 0 / 2 = 0. Therefore, the midpoint of the line segment is located at (1.5, 0). This means that the midpoint is 1.5 units to the right of the y-axis and lies on the x-axis.

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1. (f∘g)(2): We evaluate g(2) first, which gives us 2³ + 8 = 16. Then we evaluate f(16) by taking the square root of 16, which equals 4.

2. (f∘f)(25): We evaluate f(25) first, which gives us √25 = 5. Then we evaluate f(5) by taking the square root of 5.

3. (g∘f)(x): We evaluate f(x) first, which gives us √x. Then we substitute this into g(x), which gives us (√x)³ + 8.

4. (f∘g)(x): We evaluate g(x) first, which gives us x³ + 8. Then we substitute this into f(x), which gives us √(x³ + 8).

In summary, we simplified the compositions as follows: (f∘g)(2) = 4, (f∘f)(25) = √5, (g∘f)(x) = x^(3/2) + 8, and (f∘g)(x) = √(x³ + 8).

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Probability that -2.51 < z < -1.53 = 0.057

Given that z is a standard normal random variable. Then the z - values are given by the area under standard normal curve. It can be found from the standard normal tables.

Now probability that  -2.51 < z < -1.53  = P( -2.51 < z < -1.53 )

                                                               = P( -2.51 < z < 0 ) - P( -1.53 < z < 0 )

                                                               = P( 0 < z < 2.51) - P( 0 < z < 1.53 ) [Since areas are equal for same positive and negative values]

P( 0 < z < 2.51) = 0.4940

P( 0 < z < 1.53) = 0.4370  

[From the normal tables]

Therefore, Probability that -2.51 < z < -1.53 = 0.4940 - 0.4370  = 0.057

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Look at the picture.

<, > - dotted line

≤, ≥ - solid line

x > a, x ≥ a - to the right of a

x < a, x ≤ a - to the left of a

y > a, y ≥ a - up from a

y < a, y ≤ a - down from a

Answer:

the unit of length ,mass , and time are same in both the system , thus, the SI system is the extended from of MKS system.

and why is the subject math lol

Answer:

Step-by-step explanation:

the answer is (6m+1). Hope i helped :)

The domain of r(t) is (-INF, INF). a) The domain of r(t) = [ln(6t), -t + 16, 1/(10t)] is t > 0. a) The domain of the vector function r(t) = [ln(6t), -t + 16, 1/(10t)] can be determined by considering the individual components.

The natural logarithm, ln(6t), is defined only for positive values of 6t, so we need 6t > 0. This implies that t > 0.

The second component, -t + 16, is defined for all real values of t.

The third component, 1/(10t), is defined as long as 10t ≠ 0, which means t ≠ 0.

Putting these conditions together, we find that the domain of r(t) is t > 0.

b) The vector function r(t) = [t - 9, sin(6t), t^2] does not have any explicit restrictions on its domain.

The first component, t - 9, is defined for all real values of t.

The second component, sin(6t), is also defined for all real values of t.

The third component, t^2, is defined for all real values of t.

Therefore, the domain of r(t) is (-INF, INF). a) The domain of r(t) = [ln(6t), -t + 16, 1/(10t)] is t > 0.

b) The domain of r(t) = [t - 9, sin(6t), t^2] is (-INF, INF).

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The domains of the vector functions r(t) are respectively: for the first one t > 0, for the second one t >= 9 and for the third one it is a union of intervals, t < -6 U t > 6.

The domain of a vector function r(t) is defined as the set of all t-values for which the function is defined.

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Answer: the answer is ..

Step-by-step explanation: fec r/sm mkdnjervc

The coefficient in the expression is 25.

Given is the following expression -

f(p, q) = 25pq

The coefficient in the expression is 25.

Therefore, the coefficient in the expression is 25.

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Answer:

25

Step-by-step explanation:

Using sampling concepts, it is found that the most representative sample of the population of interest is given by:

50 randomly selected employees at the company.

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which has to involve all groups in the population.

In this problem, all employees have to be considered, no matter their department or experience on the company, hence the most representative sample of the population of interest is given by:

50 randomly selected employees at the company.

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Answer:

-25 ,B

Step-by-step explanation:

y = 3x - 4 is the equation of the line in slope intercept form. Option C is correct

The formula for calculating the equation of a line in point slope form is expressed as:

y - y0 = m(x - x0)

where:

m is the slope

(x0, y0) is the point on the line

Using the coordinate points (2, 2) and (0, -4). The slope is calculated as:

Slope = -4-2/0-(2)
Slope = -6/-2
Slope = 3

The required equation will therefore be expressed as:

y + 4 = 3(x - 0)

y + 4 = 3x

y = 3x - 4

Hence the slope-intercept form of the equation is y = 3x - 4

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The total possible number of outcomes for the season record is 3¹⁸, or 387,420,489. This is because there are three possible outcomes for each of the 18 games: win, loss, or tie.

To find the total number of outcomes, you can use the fundamental counting principle, which states that the total number of outcomes is equal to the product of the number of outcomes for each event. For example, if you flip a coin twice, there are two possible outcomes for each flip: heads or tails. Using the fundamental counting principle, you can find the total number of outcomes by multiplying the number of outcomes for each event:2 x 2 = 4So there are four possible outcomes for flipping a coin twice: heads-heads, heads-tails, tails-heads, or tails-tails. Using the same logic, you can find the total number of outcomes for the soccer team's season record by multiplying the number of outcomes for each game:3 x 3 x 3 x ... (18 times)= 3¹⁸= 387,420,489So there are 387,420,489 possible outcomes for the soccer team's season record.

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Answer:

Step-by-step explanation:

Let the number of student tickets is s and general admission tickets - g.

Set equations and solve:

Double the first equation and subtract from the second to eliminate s:

Find s:

Let the student tickerts and general tickets be x and y respectively

From (1) put in (2)

And

Answer:

a. False

b. False

c. False

d. True

Step-by-step explanation:

a. 4.25 x 10⁶ = 425,000 (false) should be 4,250,000

b. 6.38 x 10⁹ = 638,000,000,000 (false) should be 6,380,000,000

c. 5.11 x 10⁻² = 511 (false) should be 0.0511

d. 2.79 x 10⁻⁴ =  0.000279  (true)

Answer:

True

False

False

True

Step-by-step explanation:

The simplified form of the expression is 6^(-3)

From the question, we are to simplify the given expression

The given expression is

6^2/6 • 6^12 / 6^8

Simplifying

6^2/6 • 6^12 / 6^8

Applying the division law of indices

6^(2 -1 ) • 6^(12 - 8)

6^(1) • 6^(4)

Applying the multiplication law of indices

6^(1 - 4)

6^(-3)

Hence, the simplified form of the expression is 6^(-3)

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Answer:

$960

Step-by-step explanation:

Quarterly Dividend Per Share = $0.12

Quarterly Dividend For 2000 shares = 0.12 x 2000 = $240

Since there are 4 quarters in a year, yearly dividend for 2000 shares at $0.12 per share

= $240 x 4 = $960

Answer:

6 > 2x + y

To find the slope and y-intercept for this linear inequality, we need to write it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Rearranging the given inequality, we get:

y > -2x + 6

Comparing this with y = mx + b, we can see that the slope is -2 and the y-intercept is 6.

So, the slope is m = -2 and the y-intercept is b = 6.

To graph this linear inequality, we can draw the line y = -2x + 6 (which has a slope of -2 and y-intercept of 6) as a dashed line (since y > -2x + 6, not y = -2x + 6). Then we shade the region above the line, since all the points in that region satisfy the inequality y > -2x + 6.

x < 3y - 6

Again, we need to write this inequality in slope-intercept form to find the slope and y-intercept. Rearranging, we get:

3y > x + 6

Dividing both sides by 3, we get:

y > (1/3)x + 2

So, the slope is m = 1/3 and the y-intercept is b = 2.

To graph this linear inequality, we draw the line y = (1/3)x + 2 (which has a slope of 1/3 and y-intercept of 2) as a dashed line (since x < 3y - 6, not x = 3y - 6). Then we shade the region below the line, since all the points in that region satisfy the inequality x < 3y - 6.

The wavelength of an atom is 3.28× 10−11 m when it is travelling at its root-mean-square speed at 20 °C. Decide on the atom. Consequently, M = 2 and the gas's molar mass is 2 kgmol−1 .

Radio waves, light waves, and infrared (heat) waves are examples of electromagnetic radiation that flow through space in distinct patterns. Every wave is a specific size and shape.

calculation

urms=  \(\sqrt{\frac{3RT}{M} }\)

and

λ=h/murms

⟹urms=h/mλ⟹

 \(\sqrt{\frac{3RT}{M} }\)=h/mλ

72.2 = 148.17 / M

M = 148.17/72 ≈ 2

Consequently, M = 2 and the gas's molar mass is 2  kgmol−1. A gas with a molecular mass of 2 kgmol-1, however, does not exist.

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