The probability distribution for the number of automobiles lined up at a Lakeside Olds dealer at opening time (7:30 AM) for service is:


Number Probability

10 .05

20 .30

30 .40

40 .25


On a typical day, how many automobiles should Lakeside Olds expect to be lined up at opening time?

Step-by-step explanation:

240 miles = 9 gallons of gas

1 mile = 9/240

= 3/80 (0.0375) gallons of gas

216 miles = 3/80 (0.0375) × 216

= 8.1 gallons of gas

(a) The z-score corresponding to x = 25 is -1. (b)The z-score corresponding to x = 42 is 2.4.(c) The raw score corresponding to z = -3 is 15. (d)  The raw score corresponding to z = 1.5 is 37.5.

For a normal distribution with mean μ = 30 and standard deviation σ = 5:

(a) To find the z-score corresponding to x = 25, we use the formula:

z = (x - μ) / σ

Substituting the values, we get:

z = (25 - 30) / 5 = -1

Therefore, the z-score corresponding to x = 25 is -1.

(b) To find the z-score corresponding to x = 42, we again use the formula:

z = (x - μ) / σ

Substituting the values, we get:

z = (42 - 30) / 5 = 2.4

Therefore, the z-score corresponding to x = 42 is 2.4.

(c) To find the raw score (x) corresponding to z = -3, we use the formula:

z = (x - μ) / σ

Rearranging the formula, we get:

x = μ + zσ

Substituting the values, we get:

x = 30 + (-3) x 5 = 15

Therefore, the raw score corresponding to z = -3 is 15.

(d) To find the raw score (x) corresponding to z = 1.5, we use the same formula:

x = μ + zσ

Substituting the values, we get:

x = 30 + 1.5 x 5 = 37.5

Therefore, the raw score corresponding to z = 1.5 is 37.5.

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The solution to x' = jx using exp(jt) is x(t) = ce^(jt), where c is a constant.

We start by assuming that x(t) = ce^(jt), then taking its derivative we get x'(t) = c(j)e^(jt). We substitute these values into the equation x' = jx and get c(j)e^(jt) = jce^(jt). We can then divide both sides by ce^(jt) to get j = j, which is true. This means that our assumption of x(t) = ce^(jt) is valid, and the solution is x(t) = ce^(jt).

The exponential function e^(jt) is a complex-valued function that can be used to represent sinusoidal functions with angular frequency t. In this case, we use it to represent the solution to the differential equation x' = jx. By assuming that x(t) is of the form ce^(jt), we are essentially saying that the function x(t) is a sinusoidal function with angular frequency t, and that its amplitude is a constant c.

The solution to x' = jx using exp(jt) is x(t) = ce^(jt), where c is a constant. This solution represents a sinusoidal function with angular frequency t, and its amplitude is a constant c.

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the first one ((x+8, y+2), r x-axis)

The missing values for the exponential function are x = 1 and y = 12, which corresponds to option b. (12, 8) in the given answer choices.

From the given table, we can observe that the values of y are increasing as x increases. This indicates an exponential growth pattern. To find the missing values for the exponential function, we can use the general form of an exponential function, which is y = a * b^x, where a represents the initial value and b represents the growth factor.

To find the initial value (a), we can substitute one of the points (0, 18) into the equation and solve for a:

18 = a * b^0

18 = a * 1

a = 18

Next, we can use another point (-2, 8) to find the growth factor (b):

8 = 18 * b^(-2)

b^(-2) = 8/18

b^(-2) = 4/9

Taking the square root of both sides:

b = √(4/9) = 2/3

Finally, we can substitute the values of a and b into the equation to find the missing values for x = 1:

y = 18 * (2/3)^1

y = 18 * 2/3

y = 12

Therefore, the missing values for the exponential function are x = 1 and y = 12, which corresponds to option b. (12, 8) in the given answer choices.

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Answer:

Step-by-step explanation:

2.b=90

1.30

Answer:

Step-by-step explanation:

6. You're gonna use Cos to find Y

Cos = adj/hyp

Cos 27 = 10/y

10/cos27 = y

11.2 = y

7. It'll help immensily if you draw this one out.

You're gonna use Sin to find the angle.

Sin = opp/hyp

Sin 65 = 14/x

14/sin65 = x

15.4 = x

Answer:

7/50

Step-by-step explanation:

The tangency condition becomes8L^-0.5 = 4K^-0.5Squaring both sides of the equation, we get:L = 2K Thus, the cost-minimizing bundle is given by L = 2K. The optimal combination of labor and capital is 2 times the amount of labor used.

The cost-minimizing bundles of labor and capital for a Japanese synthetic rubber firm's production function, 9-10.5 0.5 (Flath, 2011), where w

= $20 and r

= $10 is given by the tangency rule.The production function of the Japanese synthetic rubber firm is given by:Q = 9KL^0.5The equation for the cost function isC

= wL + rKWhere w is the cost of labor, r is the cost of capital, L is labor, and K is capital.The cost of producing the synthetic rubber is minimized by selecting the appropriate combination of labor and capital. The cost-minimizing bundle of labor and capital is the one for which the cost function is tangent to the isoquant of the production function at the desired level of output.The tangency condition for the cost-minimizing bundle of labor and capital is given by the following equation:MPL/ w

= MPK / rWhere MPL is the marginal product of labor and MPK is the marginal product of capital.Substituting the production function Q

= 9KL^0.5 in the above equation,MPL/ w

= 9L^-0.5 / 20

= 0.45L^-0.5MPK / r

= 4.5K^-0.5 / 10

= 0.45K^-0.5The cost-minimizing bundle is given by K

= 2L,Therefore, the tangency condition becomes 0.45L^-0.5

= 0.45(2L)^-0.5Squaring both sides of the equation, we get:L

= 4K Thus, the cost-minimizing bundle is given by L

= 4K. The optimal combination of labor and capital is 4 times the amount of labor used.How does your answer change if w

= $40 and r

= $5?At the cost-minimizing bundle as a function of L, K

= 2L.The tangency condition for the cost-minimizing bundle of labor and capital is given by the following equation:MPL/ w

= MPK / r Substituting the values of w and r,MPL/40

= MPK/5MPL

= 8MPK The cost-minimizing bundle is given by K

= 2L.The tangency condition becomes 8L^-0.5

= 4K^-0.5Squaring both sides of the equation, we get:L

= 2K Thus, the cost-minimizing bundle is given by L

= 2K. The optimal combination of labor and capital is 2 times the amount of labor used.

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Work Shown:

\(5t +2r = 3t+10\\\\5t = 3t+10-2r\\\\5t-3t = 10-2r\\\\2t = 10-2r\\\\t = \frac{10-2r}{2}\\\\t = \frac{10}{2}-\frac{2r}{2}\\\\t = 5-r\\\\\)

Suppose Dee invests "x" dollars in 9.5% interest paying account and "y" dollars in 4% interest paying account.

Total Invested = $ 10,125

Thus, we can write:

Simple Interest earned is given by the formula

Where

i is the interest earned,

P is the amount invested in the account,

r is the rate of interest in decimal

t is the time in years

• For 9.5% account, we can say that the interest earned is:

• For 4% account, we can say that the interest earned is:

The total interest earned is 1580, thus we can form the second equation:

Solving the first equation for x gives us:

Now, we substitute this into the second equation and solve for y first:

Using this value of y, we can easily figure out the value of x.

So,

Dee invested $7000 in 9.5% account and $3125 in 4% account.

Hello,

\(sin(45^o)=\dfrac{\sqrt{2} }{2} \\\\sin(45^o)=\dfrac{a}{c} \\\\\dfrac{\sqrt{2} }{2}=\dfrac{a}{6} \\\\a=6*\dfrac{\sqrt{2} }{2}=3\sqrt{2}\\\)

Answer A

The cost of Green fees for each person is $16.

As per the question statement, Sergio went golfing with 3 other friends and two of them rented clubs for $6 each, the total cost of the rented clubs and the green fees  being $76.

We are required to calculate the cost of Green fees for each person.

Let us assume that the cost of Green fees for each person is "x".

We will now form a linear equation of single variable "x" based on the conditions mentioned in the question statement, and solving for x, we will obtain our desired answer.

\([4x+(2*6)]=76\\or,4x+12=76\\or, 4x=76-12\\or, 4x=64\\or, x=\frac{64}{4}=16\)

That is, the cost of Green fees for each person is $16.

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Answer:

  b.  4.0 cm

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the ratio of the adjacent side to the hypotenuse is given by the cosine of the angle:

  Cos = Adjacent/Hypotenuse

  cos(35°) = NL/NK

  NL = NK·cos(35°)

__

Similarly, it reminds you that the ratio of the opposite side to the hypotenuse is given by the sine function:

  Sin = Opposite/Hypotenuse

  sin(53°) = NM/NL

  NM = NL·sin(53°)

Substituting from the first triangle, we have ...

  NM = NK·cos(35°)·sin(53°)

  NM = (6.1 cm)(0.81915)(0.79864)

  NM ≈ 3.991 cm

  MN ≈ 4.0 cm

Answer:

5 miles

Step-by-step explanation:

We will use the method of cross multiplying and dividing.

You will multiply 60 x 3

Then, take the answer (180) and divide it by 36.

That will give you 5 and your answer.

The unit of measure that represents a metric unit dosage of strength is the gram (a).

In the metric system, the gram is the standard unit for measuring mass or weight. It is commonly used in the healthcare field to quantify the amount or dosage of medication or drug strength.

Medications are often prescribed and administered in specific gram amounts, indicating the quantity of the active ingredient in the medication. For example, a doctor may prescribe a medication dosage of 500 milligrams (mg), which is equivalent to 0.5 grams.

On the other hand, grains (b), ounces (c), and tablespoons (d) are not typically used as metric units of measure for medication dosage strength. Grains are more commonly used in the imperial system, especially in the United States, to measure the weight of medications. Ounces and tablespoons are used to measure volume or liquid medications rather than dosage strength.

In the context of metric unit dosage strength, the gram is the most appropriate and commonly used unit of measure.

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Answer:

I don't know (-_-)  HAHAHAHA

Step-by-step explanation:

The distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

We can use the distance formula to find the distance between two points in a coordinate plane. The distance formula is:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the coordinates of M(6, 16) and Z(-1, 14), we get:

d = √((-1 - 6)² + (14 - 16)²) = √(49 + 4) = √53 ≈ 7.1

Therefore, the distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

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Answer:

150 cm

Step-by-step explanation:

So the scale is 2 cm on the blueprint = 3.5 meters in real life.

Basically you can just divide the height of the building by 3.5 meters:

259/3.5=75

There are 75, 3.5 meters in 259 meters

Since 3.5 meters on the print is 2 cm

You need to multiply the number of 3.5 meters by 2:

75*2=150

150 cm

32. Solving integral equation using the convolution theoremThe convolution theorem states that the convolution of two signals in the time domain is equivalent to multiplication in the frequency domain.

Therefore, to solve the given integral equation using the convolution theorem, we need to take the Fourier transform of both sides of the equation.

y(t) = ∫_{-∞}^{∞} sinh(−)g() + ∫_{-∞}^{∞} sinh(−−)g()Taking the Fourier transform of both sides, we haveY() = 2π[G()sinh() + G()sinh(−)]where Y() and G() are the Fourier transforms of y(t) and g(t), respectively.Rearranging for y(t), we gety(t) = (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]e^(j) d= (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)](cos()+j sin())d= (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]cos()d+ j(1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]sin()dTherefore, the solution to the integral equation is given by:y(t) = (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]cos()d + (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]sin()d

It is always important to understand the principles that govern an integral equation before attempting to solve them. In this case, we used the convolution theorem to solve the equation by taking the Fourier transform of both sides of the equation and rearranging for the unknown signal. The steps outlined above provide a comprehensive solution to the equation.  33. Fourier series representation of f(x)

The Fourier series representation of a periodic signal is an expansion of the signal into an infinite sum of sines and cosines. To find the Fourier series representation of the given signal, we need to first compute the Fourier coefficients, which are given by:an = (1/T) ∫_{-T/2}^{T/2} f(x)cos(nx/T) dxbn = (1/T) ∫_{-T/2}^{T/2} f(x)sin(nx/T) dxFurthermore, the Fourier series representation is given by:f(x) = a_0/2 + Σ_{n=1}^{∞} a_n cos(nx/T) + b_n sin(nx/T)where a_0, a_n, and b_n are the DC and Fourier coefficients, respectively. In this case, the signal is given as:f(x) = -1, -π

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Answer:

answer is 120 for the first one

30.8 for the second one

Step-by-step explanation:

First one:

Going diaganally is 305.16389 feet

going along the fence is 425 feet

answer is 119.838611

Answer:

-the lines should be straight

-there is no 9.5 thousand number of visitors given on the y axis

Step-by-step explanation:

The two faults are the x axis has 2, 3 and 4 and the year is 2017, 2018 etc. However we do not know the relationship between 2 and 2017. and the line is not smooth.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given that Sam has drawn a time series graph to show the numbers, in thousands, of visitors to a theme park.

Jayne, Sam's friend, tells him it is the worst graph she has ever seen

and she can see quite a few things about the graph that are wrong

or misleading.

The x axis has 2, 3 and 4 and the year is 2017, 2018 etc. However we do not know the relationship between 2 and 2017.

The line is not correct when drawing the graph the line used to connect the point should be smooth but the given graph is not smooth.

Hence, the two faults are the x axis has 2, 3 and 4 and the year is 2017, 2018 etc. However we do not know the relationship between 2 and 2017. and the line is not smooth.

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Answer:

The area of the shaded region is the difference between the area of the entire polygon and the area of the unshaded part inside the polygon. The area of the shaded part can occur in two ways in polygons.

Step-by-step explanation:

Observe that the area of the unshaded region is equal to the area of the shaded region subtracted from the area of the rectangle, i.e. . ar(Unshaded) = ar(ABCD) – ar(Shaded).

please give me brainlist!

Answer:

This is what I got! Hope it helps! :)

The zeroes are (2, 0) and (8, 0),Vertex is (5, 9), remaining points plotted on the graph are (4,8) and (6,8).

The graph is not a line. This figure is called a parabola. Every quadratic equation has a graph that looks like this.

All parabolas of the form y = \(a{x}^{2}+bx+c\) open upwards or downwards.

When the \({x}^{2}\) term is positive, the parabola opens upward, and when the \({x}^{2}\) term is negative, the parabola opens downward.

After plotting the equation \(y=-x^{2} +10x-16\)

From the graph i have labelled 5 points, they are

As per the graph the zeroes are (2, 0) and (8, 0),Vertex is (5, 9), remaining points plotted on the graph are (4,8) and (6,8).

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Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.

Given solution of a question done by two people.

Jenna's method

5(30+4)

(5)(30)+(5)(4)

150+20=170

Mia's method

5(30+4)

5(34)=170

We are required to find why they have achieved at the same answer.

Jenna and Mia have achieved at the same answer because they both have adopted the right method.Jenna's method is the equation in its simplest form. Addition of that is easily understood. While Mia's method is just valid as Jenna's some people may have trouble remembering the steps of multiplication within parantheses as well as being able to look at large multiplication problem and automatically knowing the answer or being able to get the answer as fast as simple addition.

Hence Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.

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Answer:

No

Step-by-step explanation:

Hope this helps :)

The one-sample z-statistic for evaluating the hypothesis that unvaccinated people get COVID-19 is not 0.03 is -85.7. This statistic tested the hypothesis that unvaccinated people do not get COVID-19 at 0.03%.

In order to compute the one-sample z-statistic, we must first do a comparison between the observed proportion of COVID-19 instances in the placebo group and the expected proportion of 0.03. (p - p0) / [(p0(1-p0)) / n is the formula for the one-sample z-statistic. In this formula, p represents the actual proportion, p0 represents the predicted proportion, and n represents the sample size.

The observed proportion of COVID-19 instances among those who received the placebo is 162/18325 less than 0.0088. According to the received wisdom, the proportion that should be anticipated is 0.03. The total number of people sampled is 18325. After entering these numbers into the formula, we receive the following results:

z = (0.0088 - 0.03) / √[(0.03(1-0.03)) / 18325] ≈ (-0.0212) / √[(0.0291) / 18325] ≈ -85.7

As a result, the value of the z-statistic for just one sample is about -85.7. This demonstrates that the observed proportion of COVID-19 cases in the unvaccinated population is significantly different from the expected proportion of COVID-19 cases in that population.

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Answer:

2.3 hours

Step-by-step explanation:

✓In Each year; malcom earns total of 120 hrs of vaction

✓But we are given that 52 weeks = 1 year

✓The number of hours of vaction time malcome earns in week= (120 hrs/52 weeks)

= 2.3 hours

The system is inconsistent.

The two lines are parallel and never intersect.

====================================================

Work Shown:

Solving the 1st equation for y.

3x-y=18

-y=18-3x

y = -(18-3x)

y = -18+3x

y = 3x-18

Plugging that into the other equation to solve for x.

-2y=-6x-120

-2(y)=-6x-120

-2(3x-18)=-6x-120

-6x+36=-6x-120

-6x+6x=-120-36

0x = -156

0 = -156

We arrive at a false statement.

Therefore, this system has no solutions

The system is inconsistent.

If you were to use a graphing tool like Desmos or GeoGebra, then you'll see the two lines are parallel. They never intersect to form a solution.