Suppose that the number of gallons of milk sold per day at a local supermarket are normally distributed with mean and standard deviation of 436.6 and 23.23, respectively. What is the probability that on a given day the supermarket will sell below 449 gallons of milk?

Answer: 248mL

Step-by-step explanation:

Given:

Concentration of buffer solution Cs = 1.24%w/v of boric acid

Concentration of boric acid solution Cb = 5 % w/v boric acid

For 1 liter of buffer solution, the weight of boric acid needed is:

mb = 1 × 1.24 = 1.24 unit weight

mb = Cb × Vb .....1

Cb = concentration of boric acid solution.

Vb = volume of boric acid solution needed.

mb = weight of boric acid needed.

From equation 1.

Vb = mb/Cb

Vb = 1.24/5

Vb = 0.248L

Vb = 248mL

248 milli-liters of a 5% w / v boric acid solution should be used to obtain the boric acid needed.

Since the formula for a buffer solution contains 1.24% w / v of boric acid, to determine how many milli-liters of a 5% w / v boric acid solution should be used to obtain the boric acid needed in preparing 1 liter of the buffer solution, the following calculation must be performed:

Therefore, 248 milli-liters of a 5% w / v boric acid solution should be used to obtain the boric acid needed.

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Answer:

The answer to your question is See the picture below

Step-by-step explanation:

Analysis of the graphs

a) In the first graph, we observe that Natasha is running after 1 h and 1/4, the comeback for to her origin, finally she continues running forward. This option is incorrect.

b) In the second graph, Natasha runs for 1 1/4 hours, after this time, she comes back to her origin, takes a rest and continues running forward. This answer is incorrect.

c) In the third graph, Natasha runs for 1 1/4 hour, takes a rest and comes back to the origin. This option is incorrect.

d) In the forth graph, Natasha runs for 1 1/4 hour, takes a rest and continues running upwards. This is the right option.

Answer:

the last one to the far right at the bottom

Step-by-step explanation:

Answer:

1) ∭(z−2) dV  negative.

2) ∭e^{−xyz} dV  positive.

3) ∭( z-\sqrt{x²+y²})  positive.

Step-by-step explanation:

From Exercise we have:

z=\sqrt{x²+y²}

z=2

⇒2=\sqrt{x²+y²}

4=x²+y²

Therefore, we get that  the solid bounded by:

\sqrt{x²+y²}≤z≤2

4=x²+y²

1) From initial condition we have that

\sqrt{x²+y²}≤z≤2

⇒ 2-z≤0

Therefore, we get that the triple integral is

∭(z−2) dV  negative.

2) We know that e^{-xyz} is always positive number.

Therefore, we get that the triple integral is

∭e^{−xyz} dV  positive.

3) From initial condition we have that

\sqrt{x²+y²}≤z≤2

⇒ z-\sqrt{x²+y²}>0

Therefore, we get that the triple integral is

∭( z-\sqrt{x²+y²})  positive.

The given triple integrals, when evaluated over the defined region, result in the first integral being zero, while the second and third integrals yield positive values. This determination is made based on the properties of the integrand over the given region, without resorting to complete calculation.

The question involves the evaluation of triple integrals over a given region W bounded by the surfaces z = sqrt(x^2 + y^2) and z = 2.1. Without explicit calculations, we can determine the sign of the integrals by assessing the integrand function over the specified region.

Therefore, the first integral would yield zero, while the second and third integrals would yield positive values.

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Answer:

D. 6.3 in^3

Step-by-step explanation:

V= 1/3 (3.14)(r^2)(h)

V= 1/3 (3.14) (1^2)(6)

V=6.3 in^3

Answer:

c

Step-by-step explanation: it was on usa test prep and the answer that was there was wrong.

To reach a $8000 down payment in 4 years with an account that compounds quarterly at an APR of 6%, you would need to make an initial deposit of approximately $6304.05 today.

To calculate the initial deposit needed to save for a $8000 down payment in 4 years with an account that offers quarterly compounding at an APR of 6%, we use the compound interest formula:

[tex]P = A / (1 + r/n)^{(nt)[/tex]

Where:

Given:

Now we can calculate the initial deposit:

[tex]P = $8000 / (1 + 0.06/4)^(4*4)P = $8000 / (1 + 0.015)^(16)P = $8000 / (1.015)^16P \approx $8000 / 1.26824179P \approx $6304.05[/tex]

Therefore, you would need to deposit approximately $6304.05 today to have $8000 in 4 years in the account with the given interest rate and compounding frequency.

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To reach an $8000 goal in 4 years with a 6% APR compounded quarterly, you need to deposit approximately $6307.17 now.

To determine how much to deposit now to reach your $8000 goal in 4 years with quarterly compounding and an APR of 6%, you can use the formula for compound interest:

[tex]P = A / (1 + r/n)^(nt)[/tex]

Where:

Now, substitute the given values into the formula:

P = [tex]$8000 / (1 + 0.06/4)^(4*4)[/tex]

P = $8000 / [tex](1 + 0.015)^(16)[/tex]

P = $8000 / [tex](1.015)^(16)[/tex]

P = $8000 / 1.2682 (approximately)

P = $6307.17 (approximately)

So, you would need to deposit approximately $6307.17 now to reach your $8000 goal in 4 years with quarterly compounding at a 6% APR.

Answer:

inverse f-1 (x) = x/18

Step-by-step explanation:

To find the inverse of a function f-1 (x), we represent f(x) by y or let f(x) = y

then make x the subject of the formula,

f(x) = 18x

Let f(x) = y

hence Y = 18x, make x the subject of the formula, do that by dividing both sides by 18,

Y/18 = x or x = Y/18

Interchanging or swapping x and y, therefore f-1 (x) = x/18

therefore, F(x) = 18x, the inverse f-1 (x) = x/18

Answer:

a) True

Step-by-step explanation:

The given statement is true.

[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]  

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.  

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

The standard deviation express the variation of data from the mean and therefore, have the same unit as the data like lbs, inches, dollars, etc.

Coefficient of variation on the other hand is the ratio of standard deviation and mean. It is also a measure of dispersion but since it is a ratio, the units cancel each other.

[tex]C.V = \dfrac{s}{\bar{x}}[/tex]

Thus, coefficient of variation is dimensionless.

Thus, it is a relative measure.

Answer:

a)  sample mean = 2.63 inches

     sample standard deviation = [tex]\frac{standard \hspace{0.15cm} deviation}{\sqrt{n} } = \frac{0.03}{\sqrt{9} } = \frac{0.03}{3} = 0.01[/tex]

b)  P(X < 2.61) = 0.0228

c.) P(2.62 < X < 2.64)  = 0.6827

d.)  Therefore 0.06 = P(2.6292 < X < 2.6307)

Step-by-step explanation:

i) the diameter of a brand of tennis balls is approximately normally distributed.

ii) mean  = 2.63 inches

iii) standard deviation = 0.03 inches

iv) random sample of 9 tennis balls

v) sample mean = 2.63 inches

vi) sample standard deviation = [tex]\frac{standard \hspace{0.15cm} deviation}{\sqrt{n} } = \frac{0.03}{\sqrt{9} } = \frac{0.03}{3} = 0.01[/tex]

vii) the sample mean is less than 2.61 inches = P(X < 2.61) = 0.0228

viii)the probability that the sample mean is between 2.62 and 2.64 inches

     P(2.62 < X < 2.64)  = 0.6827

ix) The probability is 6-% that the sample mean will be between what two values symmetrically distributed around the population measure

  Therefore 0.06 = P(2.6292 < X < 2.6307)

a) The sampling distribution of the mean is 2.63 inches and sample standard deviation = 0.01

b)  P(X < 2.61) = 0.0228

c) P(2.62 < X < 2.64)  = 0.6827

d)  0.06 = P(2.6292 < X < 2.6307)

Let's solve this step by step:

Step 1: The diameter of a brand of tennis balls is approximately normally distributed.

Given:

Mean  = 2.63 inches

Standard deviation = 0.03 inches

For random sample of 9 tennis balls

Step 2: Sample mean = 2.63 inches

Sample standard deviation = [tex]\frac{\text{standard deviation}}{\sqrt{n} } =\frac{0.03}{\sqrt{9} } =\frac{0.03}{3} =0.01[/tex]

Step 3: The sample mean is less than 2.61 inches = P(X < 2.61) = 0.0228

Step 4: The probability that the sample mean is between 2.62 and 2.64 inches = P(2.62 < X < 2.64)  = 0.6827

Step 5: The probability is 6-% that the sample mean will be between what two values symmetrically distributed around the population measure

Therefore 0.06 = P(2.6292 < X < 2.6307)

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The correct answer is: False.

As the sample size increases, the variation of the sample mean from the population mean typically becomes smaller. This is known as the Central Limit Theorem, which states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution with a mean equal to the population mean and a standard deviation that decreases as the sample size increases. Therefore, with larger sample sizes, the sample mean tends to be a more accurate estimate of the population mean, and the variation around the population mean decreases.

Answer:

Explanation:

The problem requires that you find how far the shape was moved horizontally.

To find the horizontal translation of the shape, you must subtract the x-coordinate of the original corner (the pre-image) from the x-coordinate of the final corner (the image)

Final corner (image):

Original corner (preimage):

Translation:

Thus, the horizontal move of the shape was 10 units to the right.

Answer:

No. it's not enough

Step-by-step explanation:

1) No. it's not enough

2) To compute the area of a parallelogram it's necessary the height of the parallelogram, i.e. a perpendicular line segment from the base up to its parallel side.

3) Because a parallelogram is made up by two triangles and the area of it is calculated using the height. Then to cover the area of a parallelogram it's mandatory to calculate the height, the perpendicular distance between their horizontal sides.

No, the lengths of the sides of a parallelogram alone are not enough to compute its area. Additional information, such as the length of the perpendicular distance between the sides, is needed to calculate the area.

No, the lengths of the sides of a parallelogram alone are not enough to compute its area. To calculate the area of a parallelogram, you need two pieces of information: the length of one of its sides and the length of the corresponding altitude (or height), which is the perpendicular distance between the side and the opposite side. With just the lengths of a and b, we don't know the height, so we can't calculate the area.

To find the area of a parallelogram, you can use the formula: Area = base x height. The base is one of the side lengths, and the height is the length of the perpendicular from the base to the opposite side.

For example, if side a is the base, the height is the distance between side a and the opposite side, which can be found by drawing a perpendicular line. Once you know the height, you can calculate the area using the formula: Area = a x height.

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Answer:

a. Quantitative

b. Quantitative

c. Qualitative

d. Qualitative

e. Qualitative

Step-by-step explanation:

a. The temperature readings can be quantify and can be represented numerically so, it is quantitative variable.

b. The scores in English test can be quantify and can be represented numerically so, it is quantitative variable.

c. The blood type can be categorized as O plus, O negative, A plus, A negative, AB plus, Ab negative, B plus, B negative and cannot be represented numerically so, it is qualitative variable.

d. The last four digit of social security number take numerical values, yet they are qualitative because these are used as identifiers and mathematical operations of social security don't have meaningful interpretation.

e. The number on the jerseys of 53 football players also takes numerical values yet they are qualitative because these are used as identifiers for players and mathematical operations of number on the jerseys of football players don't have meaningful interpretation.

The measures in question are classified as either quantitative or qualitative.

a. The 30 high-temperature readings of the last 30 days - Quantitative. These temperatures are numerical values that can be measured and compared.

b. The scores of 40 students on an English test - Quantitative. The scores represent numerical values that can be added, averaged, and compared.

c. The blood types of 120 teachers in a middle school - Qualitative. Blood types are descriptive categories or labels that cannot be measured numerically.

d. The last four digits of social security numbers of all students in a class - Qualitative. The last four digits are specific identifiers that cannot be measured or compared numerically.

e. The numbers on the jerseys of 53 football players on a team - Qualitative. The numbers are labels or identifiers, not measurable quantities.

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Answer:

The solutions are π/4, 3π/4,5π/4,7π/4

Step-by-step explanation:

The given equation is

6sin²(x) = 3

Divide by 6 to get:

[tex] { \sin}^{2} (x) = \frac{1}{2} [/tex]

This implies that;

[tex] \sin(x) = \pm \frac{ \sqrt{2} }{2} [/tex]

If

[tex]\sin(x) = \frac{ \sqrt{2} }{2}[/tex]

[tex]x = \frac{\pi}{4} [/tex]

in the first quadrant

[tex]x = \frac{3\pi}{4} [/tex]

in the second quadrant.

If

[tex]\sin(x) = - \frac{ \sqrt{2} }{2}[/tex]

[tex]x = \frac{5\pi}{4} [/tex]

in the third quadrant

[tex]x = \frac{7\pi}{4} [/tex]

Answer:

a) [tex]\hat{p} = 0.27[/tex]    

b) All the conditions are met for constructing a confidence interval.

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 167

Number of people who had side effects, x = 45

a)  point estimate

[tex]\hat{p} = \dfrac{x}{n} = \dfrac{45}{167} = 0.27[/tex]

The point estimate for the population proportion of patients who received 10-mg doses of a drug daily and reported headache as a side effect is 0.27

b) Conditions for constructing a confidence interval

[tex]n\hat{p}>10\\167\times 0.27 = 45.09 > 10\\n(1-\hat{p})>10\\167(1-0.27) = 121.91 > 10[/tex]

Thus, all the conditions are met for constructing a confidence interval.

Answer:

y = 0

y =2x

Step-by-step explanation:

Given parametric equations:

x (t) = sin (t)

y (t) = sin (t + sin (t))

The slope of the curve at any given point is given by dy / dx we will use chain rule to find dy / dx

(dy / dx) * (dx / dt) = (dy / dt)

(dy / dx) = (dy / dt) / (dx / dt)

Evaluate dx / dt and dy / dt

dx / dt = cos (t)

dy / dt = cos (t + sin (t)) * (1+cos (t))

Hence,

dy / dx = (1+cos(t))*cos(t + sin (t))) / cos (t)

@Given point (x,y) = 0 we evaluate t

0 = sin (t)

t = 0 , pi

Input two values of t and compute dy / dx

@ t = 0

dy / dx = (1 + cos (0))*cos (0 + sin (0))) / cos (0)

dy / dx = (1+1)*(1) / (1) = 2 @ t = 0

@t = pi

dy / dx = ( 1 + cos (pi))* cos (pi + sin (pi)) / cos (pi)

dy / dx = (1-1) * (-1) / (-1) = 0 @ t = pi

The corresponding gradients are 0 and 2 in increasing order and their respective equations are:

y = 2x

y = 0

The equation of the two tangent lines at the point (x,y) = (0,0) in order of increasing slope are; y = 0 and y = 2x

We are given the parametric equations of the curve as;

x = sin(t)

y = sin(t + sin(t))

Now, since we want to find slope, the we need to find dy/dx from;

dy/dx = (dy/dt) ÷ (dx/dt)

Thus;

dx/dt = cos(t)

Using chain rule;

dy/dt = cos (t + sin(t)) × (1 + cos(t))

Thus;

dy/dx = [cos (t + sin(t)) × (1 + cos(t))]/(cos(t))

At (0, 0), we have;

0 = sin(t)   ---(1)

0 = sin(t + sin(t))   ---(2)

From eq (1), values of t that makes the function 0 are;

0 and π

Thus;

At t = 0;

dy/dx =  [cos (0 + sin(0)) × (1 + cos(0))]/(cos(0))

dy/dx = (1 + 1)/1

dy/dx = 2

At t = π;

dy/dx =  [cos (π + sin(π)) × (1 + cos(π))]/(cos(π))

dy/dx = 0

Using the point slope form; y - y₁ = m(x - x₁)

At m = 2, we have;

y - 0 = 2(x - 0)

y = 2x

At m = 0, we have;

y - 0 = 0(x - 0)

y = 0

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Answer:

  The sub rose 121 feet.

Step-by-step explanation:

The sub was less deep at 12 pm than at 10 am, so rose in the water. The amount it rose was ...

  410 -289 = 121 . . . . feet

__

If you like, you can think of the sub's elevation relative to the surface as changing from -410 feet to -289 feet. The difference is then an increase in elevation (rise) of ...

  -289 -(-410) = -289 +410 = 121 . . . feet

_____

12 am is midnight, 14 hours after 10 am. The time 2 hours after 10 am is 12 pm, noon.

Answer:

17% probability that a randomly selected student smokes.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

What is your estimate of the probability that a randomly selected student smokes?

This estiamte is the number of smoking students divided by the total number of students.

We have that:

There are 500 students.

85 smoke

So there is an 85/500 = 0.17 = 17% probability that a randomly selected student smokes.

Answer:

The best predicted pulse rate of a woman who is 74 inches tall is 80.4 (beats per minute).



Step-by-step explanation:

The best predicted pulse rate of a woman who is 74 inches tall is obtained below:

Let x denotes height (in inches) and y denotes pulse rates (in beats per minute).

From the information, the regression equation is, the total number of women is 60 and the linear correlation coefficient between height and pulse rates is 0.234 and the mean of heights is 63.4 and the mean of pulse rates is 75.6. The estimated regression line is

^y= 17.5 + 0.850x

     The required best predicted pulse rates is,

      =17.5 + (0.850×74)

=17.5 + 62.9

=   80.4  beats per minute

​

Given the exchange rate of $5 = £1 and the conversion rate of 6 pounds per ounce of gold, the equivalent amount for an ounce of gold would be $30.

In this scenario, given that the exchange rate between pounds and U.S. dollars is $5 = £1 and the conversion rate of pound to gold is six pounds per ounce, we want to find the value of an ounce of gold in U.S. dollars. Firstly, we need to establish how many pounds per ounce of gold, which is set at six pounds. With the currency exchange rate, $5 equals one pound. Therefore, to find the value in dollars, simply multiply these two rates together. That comes to 6 (pounds per ounce of gold) * 5 (dollars per pound) = $30. Hence, an ounce of gold would be worth $30.

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Answer:

The person on the ship can see the lighthouse

Step-by-step explanation:

The Circle Function

A circle centered in the point (h,k) with a radius r can be written as the equation

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Any point (x,y) can be known if it's inside of the circle if

[tex](x-h)^2+(y-k)^2\leq r^2[/tex]

The question is about a beam of a lighthouse than can be seen for up to 20 miles. If we assume the lighthouse is emitting the beam as the shape of a circle centered in (0,0), then its radius is 20 miles. Thus any person riding a ship inside the circle can see the lighthouse. This means that

[tex]x^2+y^2\leq 20^2[/tex]

[tex]x^2+y^2\leq 400[/tex]

The ship's coordinates respect to the lighthouse are (10,16). We should test the point to verify if the above inequality stands

[tex]10^2+16^2\leq 400[/tex]

[tex]356 \leq 400[/tex]

The inequality is true, so the person on the ship can see the lighthouse

The inequality is:

√(x^2 + y^2) ≤ 20 mi.

And you can see the lighthouse beam from your ship.

First, let's define our coordinate system, North will be the positive y-axis and east will be the positive x-axis. Such that the origin is the lighthouse.

The distance between a point (x, y) and the lighthouse is given by:

d = √(x^2 + y^2).

And we know that the lighthouse beam can be seen for up to 20 miles, so you can only see the lighthouse if your position (x, y) is such that the inequality is true.

√(x^2 + y^2) ≤ 20 mi.

Now, can you see the lighthouse beam from your ship?

Your ship's position is: (10 mi, 16 mi)

Replacing that in the inequality we get:

√((10mi)^2 + (16mi)^2) ≤ 20 mi

18.87 mi ≤ 20 mi

The inequality is true, then you can see the beam from the ship.

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The probability  that a sample taken from the site will have water content above 16% or below 12% is 0.3862.

Given that,

Mean = µ

= 14%

= 0.14

Standard deviation = σ

= 2.5%

= 0.025

[Using standard normal table]

16% or 12% = 0.16 or 0.12

P(X < 0.16 or X > 0.12)

Using standard normal table,    

To see the z value -0.9 in the row and 0.06 in the column of the standard normal table the cumulative probability of z = -0.96  is = 0.1685

To see the z value 0.7 in the row and 0.08 in the column of the standard normal table the cumulative probability of z = 0.78  is = 0.7823

[tex]P(X < 0.6\ or \ x > 0.12)=1-[P(0.16 < X < 0.12)][/tex]

[tex]=1-{P[\frac{0.16-0.142}{0.023} < \frac{x-\mu}{\sigma} < \frac{0.12-0.142}{0.023}]}[/tex]

[tex]= 1-[P(0.78 < z < -0.96)][/tex]

[tex]= [P(z < -0.96)-P(z < 0.78)][/tex]

[tex]=1-(0.1685-0.7823)[/tex]

[tex]= 1-0.6138[/tex]

[tex]P(X < 0.16 \ or \ X > 0.12)=0.3862[/tex]

Therefore, the probability  that a sample taken from the site will have water content above 16% or below 12% is 0.3862.

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The probability that a random sample’s water content will be higher than 16% or lower than 12% is calculated by converting the values to Z-scores and then using the standard normal distribution's cumulative probability. The values from a Z-table or calculator are used to determine this probability.

The subject of this question is Probability and Statistics, specifically related to the normal distribution. In this scenario, the water content of soil from a borrow site is normally distributed with a mean (μ) of 14% and a standard deviation (σ) of 2.5%.

To find the probability of the soil having a water content above 16% or below 12%, we first need to calculate the Z-scores for these values. The Z-score represents how many standard deviations an element is from the mean. It is calculated as (X - μ)/σ.

For X = 16%, Z = (16 - 14) / 2.5 = 0.8

For X = 12%, Z = (12 - 14) / 2.5 = -0.8

Using a Z-table or a calculator function that outputs standard normal probabilities, we would find that P(Z > 0.8) or P(Z < -0.8). By convention, Z-tables only give values as P(Z < z), for z > 0, so to find P(Z > 0.8), we can do 1 - P(Z < 0.8). Same for P(Z < -0.8).

As such, the desired probability is the sum of these two probabilities.

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By using truth tables, we can prove that given conditional statements are tautologies. The logic used in the example can also be applied to other statements. Every possible combination of truth values for the components of a tautology yields a true statement.

To show that these conditional statements are tautologies, we can generate truth tables for each one. Tautologies are logical statements that are always true regardless of the truth values of their variable components.

For example, let's examine the statement (p ∧ q) → p:

This logic can similarly be applied to the remaining statements to prove that they're tautologies.

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Answer: 117.5 seconds

Step-by-step explanation:

Given : It takes you 47 seconds to walk from the first​ (ground) floor of a building to the third floor.

Since from first floor to third , a person need to pass two levels of staircase.

We assume that the person walk at the same​ pace and the height of all floors are same.

The time taken to pass each level = (Time taken to pass 2 levels) ÷ 2

= (47 seconds)  ÷ (2) = 23.5 seconds

Also, the from first floor to sixth floor , a person need to pass 5 levels of staircase.

Then, the time taken to pass each level = 5 x (Time taken to pass one level)

= 5 x 23.5 =117.5 seconds

Hence, it will take 117.5 seconds to walk from the first floor to the sixth floor.

Answer:

y=-3x-2

Step-by-step explanation:

The slope intercept equation is y=mx+b. y2-y1/x2-x1 is the equation for the slope. 7-(-5)/-3-1 is -3. Now you have y=-3x+b, you plug in one set of cordinates so you would have 7=-3(-3)+b, 7=9+b, b=-2

y=-3x-2

Hope that helps :)

Answer:

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

The line passes through the points (1,-5) and (-3,7)

y2 = 7

y1 = - 5

x2 = - 3

x1 = 1

Slope,m = (7 - - 5)/(- 3 - 1) = 12/- 4 =

- 3

To determine the intercept, we would substitute x = - 3, y = 7 and m= - 3,

7 = - 3 × - 3 + c = 9 + c

c = 7 - 9 = - 2

The equation becomes

y = - 3x - 2

Answer:

\int\limits^7_1 {f(x)} \, dx =24

\int\limits^13_7 {f(x)} \, dx =24

Step-by-step explanation:

From Exercise we have f(x)=5-1 , we get f(x)=4.

We calculate integral, if 1≤x<7, we get

\int\limits^7_1 {f(x)} \, dx =\int\limits^7_1 {4} \, dx =4[x]\limits^7_1=4(7-1)=4·6=24

We calculate integral, if 7≤x<13, we get

\int\limits^13_7 {f(x)} \, dx =\int\limits^13_7 {4} \, dx =4[x]\limits^13_7=

=4(13-7)=4·6=24

Therefore, we conclude that the given two integrals are the same.

Answer:

Step-by-step explanation:

Hello!

You have the information about light bulbs (i believe is their lifespan in hours) And need to organize the information in a frequency table.

The first table will be with a class width of 20, starting with 800. This means that you have to organize all possible observations of X(lifespan of light bulbs) in a class interval with an amplitude of 20hs and then organize the information noting their absolute frequencies.

Example

1) [800;820) only one observation classifies for this interval x= 819, so f1: 1

2)[820; 840) only one observation classifies for this interval x= 836, so f2: 1

3)[840;860) no observations are included in this interval, so f3=0

etc... (see attachment)

[ means that the interval is closed and starts with that number

) means that the interval is open, the number is not included in it.

fi: absolute frequency

hi= fi/n: relative frequency

To graph the histogram you have to create the classmark for each interval:

x'= (Upper bond + Lower bond)/2

As you can see in the table, there are several intervals with no observed frequency, this distribution is not uniform least to say symmetric.

To check the symmetry of the distribution is it best to obtain the values of the mode, median and mean.

To see if this frequency distribution has one or more modes you have to identify the max absolute frequency and see how many intervals have it.

In this case, the maximal absolute frequency is fi=6 and only one interval has it [1000;1020)

[tex]Mo= LB + Ai (\frac{D_1}{D_1+D_2} )\\[/tex]

LB= Lower bond of the modal interval

D₁= fmax - fi of the previous interval

D₂= fmax - fi of the following interval

Ai= amplitude of the modal interval

[tex]Mo= 1000 + 20*(\frac{(6-3)}{(6-3)+(6-4)} )=1012[/tex]

This distribution is unimodal (Mo= 1012)

The Median for this frequency:

Position of the median= n/2 = 40/2= 20

The median is the 20th fi, using this information, the interval that contains the median is [1000;1020)

[tex]Me= LB + Ai*[\frac{PosMe - F_{i-1}}{f_i} ][/tex]

LB= Lower bond of the interval of the median

Ai= amplitude of the interval

F(i-1)= acumulated absolute frequency until the previous interval

fi= absolute frequency of the interval

[tex]Me= 1000+ 20*[\frac{20-16}{6} ]= 1013.33[/tex]

Mean for a frequency distribution:

[tex]X[bar]= \frac{sum x'*fi}{n}[/tex]

∑x'*fi= summatory of each class mark by the frequency of it's interval.

∑x'*fi= (810*1)+(230*1)+(870*0)+(890*2)+(910*4)+(930*0)+(950*4)+(970*1)+(990*3)+(1010*6)+(1030*4)+(1050*0)+(1070*3)+(1090*2)+(1110*4)+(1130*0)+(1150*2)+(1170*1)+(1190*1)+(1210*0)+(1230*1)= 40700

[tex]X[bar]= \frac{40700}{40} = 1017.5[/tex]

Mo= 1012 < Me= 1013.33 < X[bar]= 1017.5

Looking only at the measurements of central tendency you could wrongly conclude that the distribution is symmetrical or slightly skewed to the right since the three values are included in the same interval but not the same number.

*-*-*

Now you have to do the same but changing the class with (interval amplitude) to 100, starting at 800

Example

1) [800;900) There are 4 observations that are included in this interval: 819, 836, 888, 897 , so f1=4

2)[900;1000) There are 12 observations that are included in this interval: 903, 907, 912, 918, 942, 943, 952, 959, 962, 986, 992, 994 , so f2= 12

etc...

As you can see this distribution is more uniform, increasing the amplitude of the intervals not only decreased the number of class intervals but now we observe that there are observed frequencies for all of them.

Mode:

The largest absolute frequency is f(3)=15, so the mode interval is [1000;1100)

Using the same formula as before:

[tex]Mo= 1000 + 100*(\frac{(15-12)}{(15-12)+(15-8)} )=1030[/tex]

This distribution is unimodal.

Median:

Position of the median n/2= 40/2= 20

As before is the 20th observed frequency, this frequency is included in the interval [1000;1100)

[tex]Me= 1000+ 100*[\frac{20-16}{15} ]= 1026.67[/tex]

Mean:

∑x'*fi= (850*4)+(950*12)+(1050*15)+(1150*8)+(1250*1)= 41000

[tex]X[bar]= \frac{41000}{40} = 1025[/tex]

X[bar]= 1025 < Me= 1026.67 < Mo= 1030

The three values are included in the same interval, but seeing how the mean is less than the median and the mode, I would say this distribution is symmetrical or slightly skewed to the left.

I hope it helps!

Options A, C, and F are solutions to the differential equation.

The given differential equation is y''+4y'+4y=0.

To check which of the given functions are solutions of the differential equation, we substitute each function into the equation and check if it satisfies the equation.

By substituting each function and simplifying, we find that options A, C, and F are solutions to the differential equation.

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Answer:

Complete the following statements. In general, 50% of the values in a data set lie at or below the median. 75% of the values in a data set lie at or below the third quartile (Q3). If a sample consists of 500 test scores, of them 0.5*500 = 250 would be at or below the median. If a sample consists of 500 test scores, of them 0.75*500 = 375 would be at or above the first quartile (Q1).

Step-by-step explanation:

The median separates the upper half from the lower half of a set. So 50% of the values in a data set lie at or below the median, and 50% lie at or above the median.

The first quartile(Q1) separates the lower 25% from the upper 75% of a set. So 25% of the values in a data set lie at or below the first quartile, and 75% of the values in a data set lie at or above the first quartile.

The third quartile(Q3) separates the lower 75% from the upper 25% of a set. So 75% of the values in a data set lie at or below the third quartile, and 25% of the values in a data set lie at or the third quartile.

The answer is:

Complete the following statements. In general, 50% of the values in a data set lie at or below the median. 75% of the values in a data set lie at or below the third quartile (Q3). If a sample consists of 500 test scores, of them 0.5*500 = 250 would be at or below the median. If a sample consists of 500 test scores, of them 0.75*500 = 375 would be at or above the first quartile (Q1).

The 'Duration (amount of time)' in the study is an example of quantitative data. Quantitative data is numerical data that can be measured or counted.

The 'Duration (amount of time)' in the study is an example of quantitative data.

Quantitative data is numerical data that can be measured or counted. In this case, the duration of resident use of the local park is being measured in terms of time (amount of time).

Examples of other quantitative data include age and number of times per week.

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Answer:  52, 92 , 132, 172

Step-by-step explanation:

Given : Systematic Sampling Technique is used to select 5 numbers between 1 and 200.

⇒ Population size : N=200

Required Sample size  : n=5

Since , Sampling interval is given by :-

[tex]k=\dfrac{N}{n}[/tex]

⇒ [tex]k=\dfrac{200}{5}[=40/tex]

If the first selected number is 12, then the next four numbers would be :

(12+K) , (12+2k) , (12+3k) , (12+4k)

Put value of k , we get

(12+40) , (12+2(40)) , (12+3(40)) , (12+4(40)) =(52, 92 , 132, 172)

Hence, the  next four numbers are : 52, 92 , 132, 172