Find the range and the interquartile range.
57,96,72,63,88

Answer:

Thus, the pmf of the number of granite specimens selected for analysis is [tex]P(X=x)={20\choose x}0.50^{x}(1-0.50)^{20-x}[/tex].

Step-by-step explanation:

The experiment consists of collecting rocks.

The sample consisted of, 10 specimens of basaltic rock and 10 specimens of granite.

The total sample is of size, n = 20.

Let the random variable X be defined as the number of granite specimen selected.

The probability of selecting a granite specimen is:

[tex]P(Granite)=p=\frac{10}{20}=0.50[/tex]

A randomly selected rock can either be basaltic or granite, independently.

The success is defined as the selection of granite rock.

The random variable X follows a Binomial distribution with parameter n = 20 and p = 0.50.

The probability mass function of X is:

[tex]P(X=x)={20\choose x}0.50^{x}(1-0.50)^{20-x}[/tex]

Answer:

She will earn $442.89 in one week after the changes.

And this is more than her previous weekly earnings.

Step-by-step explanation:

Given:

Alondra received a 14% hourly raise, but the number of hours worked decreased by 7.5%. If her wage was $10.50 an hour and she worked 40 hours per week before the changes.

Now, to find money she will earn in one week after the changes.

Her wage was = $10.50.

She worked per week = 40 hours.

So, her salary before changes:

[tex]10.50\times 40\\\\=\$420.[/tex]

Thus, the salary per week before changes is $420.

Now, to get her salary after 14% hourly raise:

[tex]10.50+14\%\ of\ 10.50\\\\=10.50+\frac{14}{100} \times 10.50\\\\=10.50+1.47\\\\=11.97[/tex]

Salary after hourly raise = $11.97 per hour.

Then, to get the number of hours worked decreased by 7.5%:

[tex]40-7.5\%\ of\ 40\\\\=40-\frac{7.5}{100} \times 40\\\\=40-3\\\\=37.[/tex]

Number of hours per week after hours of worked decreased  = 37 hours.

Now, to get the salary after changes:

Salary after hourly raise × number of hours per week after hours of worked decreased

[tex]=11.97\times 37[/tex]

[tex]=\$442.89.[/tex]

Salary after changes in one week = $442.89.

As, the previous salary was $420 in one week.

And after changes this salary is $442.89 in one week which is more than previous.

Therefore, she will earn $442.89 in one week after the changes.

And this is more than her previous weekly earnings.

Answer:

  7

Step-by-step explanation:

5 × 7 = 35

35 cans of cola can be grouped into 7 groups of 5 cans. For each of those 7 groups, James needs to buy one orange soda.

James should buy 7 orange sodas.

Step-by-step explanation:

The cost of cashews per pound  = $7

The cost of almonds per pound  = $5

Let x represent the number of pounds of cashews.

Let y represent the number of pounds of almonds

Now, the combined weight of the mixture is less than 6 pounds.

So, Weight of (Almonds + Cashews) < 6 pounds

or,  x + y < 6   ...... (a)

Now, cost of x pounds of cashews  = x ( Cots of 1 pound of cashews)

=  x (7)  = 7 x

Cost of y pounds of almonds  = x ( Cots of 1 pound of almonds)

=  y (5)  = 5 y

So, the combined price of x pounds of cashews and y pounds of almonds

= 7 x +  5 y

Also, given the total cost of the mixture is not more than $30.

⇒ 7 x +  5 y  ≤ 30 ..... (2)

Hence, form (1) and (2), the inequalities that represent the given situation are:

x + y < 6

7 x +  5 y  ≤ 30

Answer: The inequalities that represent constraints for this situation are

x + y < 6

7x + 5y ≤ 30

Step-by-step explanation:

Let x represent the number of pounds of cashews.

Let y represent the number of pounds of almonds.

The employee wants to make less than 6 pounds of the mixture. This is expressed as

x + y < 6

Cashews cost $7 per pound, and almonds cost $5 per pound. The employee wants the total cost of the nuts used in the mixture to be not more than $30. This is expressed as

7x + 5y ≤ 30

Answer:

0.81

Step-by-step explanation:

0.45 + 0.59 - 0.23

= 0.81

The probability that a randomly selected American either enjoys cooking or shopping or both is 0.81

The probability of the union of two events (A or B) is the sum of their individual probabilities minus the probability of their intersection (A and B).

i.e.

P(A or B) = P(A) + P(B) - P(A and B)

In this case, A represents the event of enjoying cooking, and B represents the event of enjoying shopping.

So, we have

P(A) = 45% = 0.45

P(B) = 59% = 0.59

P(A and B) = 23% = 0.23

By substitution, we have

P(A or B) = 0.45 + 0.59 - 0.23 = 0.81

Hence, the probability that a randomly selected American either enjoys cooking or shopping or both is 0.81 or 81%.

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Option D: 13 units is the distance between the two points

Explanation:

Given that the points are [tex](-5,-2)[/tex] and [tex](8,-3)[/tex]

We need to find the distance between the two points.

The distance between the two points can be determined using the distance formula,

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Let us substitute the points [tex](-5,-2)[/tex] and [tex](8,-3)[/tex] in the above formula, we get,

[tex]d=\sqrt{(8-(-5))^2+(-3-(-2))^2}[/tex]

Simplifying the terms within the bracket, we have,

[tex]d=\sqrt{(8+5)^2+(-3+2)^2}[/tex]

Adding the terms within the bracket, we get,

[tex]d=\sqrt{(13)^2+(-1)^2}[/tex]

Squaring the terms, we have,

[tex]d=\sqrt{169+1}[/tex]

Adding, we get,

[tex]d=\sqrt{170}[/tex]

Simplifying, we have,

[tex]d=13.04[/tex]

Rounding off to the nearest tenth, we get,

[tex]d=13.0 \ units[/tex]

Hence, the distance between the two points is 13 units.

Therefore, Option D is the correct answer.

To determine the distance between two points, we apply the distance formula, substituting the x and y coordinates for each point into the equation. After simplifying, the resulting square root of 170 corresponds to a distance of 13.0 units when rounded to the nearest tenth. Thus, the distance between the given points is 13.0 units.

Let's apply the distance formula to the two points given: (-5, -2) and (8, -3). The distance formula, d = √[(x2 - x1)2 + (y2 - y1)2], allows us to calculate the distance between two points in a Cartesian coordinate system.

First identify the x and y coordinates for each point. For the point (-5, -2), x1= -5 and y1= -2. For the point (8, -3), x2= 8 and y2= -3.

Step 1: Substitute these values into the distance formula.

d = √[(8 - (-5))2 + ((-3) - (-2))2]

Step 2: Simplify inside the square root, which involves removing the brackets and calculating the squares of the differences of the coordinates.

d=√[(13)2 + (-1)2 ] = √[169 + 1] = √170

The final distance d is the square root of 170. Rounded to the nearest tenth, this equals 13.0 units.

Therefore, the distance between point (-5, -2) and point (8, -3) is 13.0 units.

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Answer:

The Chef planner should prepare 320 cups of soups

Step-by-step explanation:

Number of guests expected to come = 800

2 out of every 5 guest will order for soup appetizer

Hence using equivalent ratios

2:5 = X :800

X = (800 × 2) ÷ 5 = 320

Hence the Chef planner should prepare 320 cups of soups

Answer:

21y^4= B*7y^3

B=(21y^4)/(7y^3)

B=3y

Answer:

These should be the question: a) What is the average seek time = 149.995 ms, b) average rotational latency = 4.16667ms , c) transfer time for a sector = 13.88us, and d) total average time to satisfy a request = 153.1805ms.

Step-by-step explanation:

A) average seek time.

Number of tracks transversed = 299.99ms

Seek time to access  the track = 0ms

= (0+299.99)/2 ==> 149.995ms

B) average rotational latency.

Rotation speed = 7,200rpm

rotation time = 60 / 7,200 = 0.008333s/rev

Rotational latency = 0.008333/2 = 0.004166sec

= 4.16667ms

C) Transfer time for a sector

at 7200rpm, a rev = 60 / 7200 = 0.00833s :    8.33ms

transfer time one sector = 8.333/600 ms

                                         = 0.01388ms  => 13.88us

D) average time to satisfy request

149 + 4.16667 + 0.013888

153.1805ms

Answer:

C Trapezoid

Step-by-step explanation:

A trapezoid mostly has only one pair of parallel sides, not two

Answer: Trapezoid

Step-by-step explanation:

Answer:

0.6517

Step-by-step explanation:

Given that in a certain game of chance, your chances of winning are 0.3.

We know that each game is independent of the other and hence probability of winning any game = 0.3 (constant)

Also there are only two outcomes

Let X be the number of games you win when you play 4 times

Then X is binomial with p = 0.3 and n =4

Required probability

= Probability that you win at most once

= [tex]P(X\leq 1)\\=P(X=0)+P(X=1)[/tex]

We have as per binomial theorem

P(X=r) = [tex]nCr p^r (1-p)^{n-r}[/tex]

Using the above the required prob

= 0.6517

Final answer:

To calculate the probability of winning at most once over four games with a win probability of 0.3, we calculate the binomial probabilities for winning 0 times and 1 time then add them, resulting in a total probability of approximately 0.6517.

Explanation:

The question involves calculating the probability of winning at most once in a game of chance played four times, where the chances of winning each game are 0.3. We use the binomial probability formula P(x) = C(n, x) * pˣ * q⁽ⁿ⁻ˣ⁾, where C(n, x) is the number of combinations, p is the probability of winning, q is the probability of losing (1-p), and n is the total number of games. In this case, n=4, p=0.3, and q=0.7. We need to find the probability of winning 0 times (P(0)) and 1 time (P(1)) and then add these probabilities together.

Adding these probabilities gives the probability of winning at most once as P(0) + P(1) = 0.2401 + 0.4116 = 0.6517. Therefore, the probability of winning at most once in four games is approximately 0.6517.

Answer:

The weight of peanuts in the mixture   = 8  kg

The weight of corns in the given mixture = 4 kg

Step-by-step explanation:

Let us assume the weight of peanuts in the mixture   = x kg

The weight if corns in the given mixture = y kg

Total weight = (x + y) kg

The combined mixture weight = 12 kg

⇒ x  + y = 12  ..... (1)

Cost of per kg if mixture  = $ 40

So, the cost of (x + y) kg mixture  = (x+y) 40 = 40(x+ y)   ..... (2)

The cost of 1 kg of peanuts =  $ 42

So cost of x kg of peanuts  = 42 (x)  = 42 x

The cost of 1 kg of corns  = $ 36

So cost of y kg of corns  = 36 (y)  = 36 y

So, the total cost of x kg peanuts  + y kg corns =  42 x +  36 y  .... (3)

From (1) and (2), we get:

40(x+ y)  = 42 x +  36 y

x +  y = 12 ⇒ y = 12 -x

Put this in  40(x+ y)  = 42 x +  36 y

We get:

40(x+ 12 -x)  = 42 x +  36 (12 -x)

480 = 42 x + 432 - 36 x

or, 480 - 432 = 6 x

or, x  = 8

⇒ y = 12 -x = 12 - 8 = 4

⇒  y = 4

Hence, the weight of peanuts in the mixture   = 8  kg

The weight of corns in the given mixture = 4 kg

Final answer:

The weight of peanuts in the mixture is 8  kg and the weight of corns in the given mixture = 4 kg

Explanation:

A mixture of peanuts and corn sells for P40 per kilo.

Let us assume the weight of peanuts in the mixture   = x kg

The weight of corn in the given mixture = y kg

Total weight = (x + y) kg

The combined mixture weight = 12 kg

= x  + y = 12  ..... (1)

Cost of per kg if mixture  = $ 40

So, the cost of (x + y) kg mixture  = (x+y) 40 = 40(x+ y)   ..... (2)

The cost of 1 kg of peanuts =  $ 42

So cost of x kg of peanuts  = 42 (x)  = 42 x

The cost of 1 kg of corn = $ 36

So cost of y kg of corn  = 36 (y)  = 36 y

So, the total cost of x kg peanuts  + y kg corns =  42 x +  36 y  .... (3)

From (1) and (2):

40(x+ y)  = 42 x +  36 y

x +  y = 12 ⇒ y = 12 -x

Put this in  40(x+ y)  = 42 x +  36 y

We get:

40(x+ 12 -x)  = 42 x +  36 (12 -x)

480 = 42 x + 432 - 36 x

or, 480 - 432 = 6 x

or, x  = 8

= y = 12 -x = 12 - 8 = 4

= y = 4

[tex]\(3^\frac{1}{2} \cdot 3^\frac{1}{2} = 3\)[/tex].

To simplify [tex]\(3^\frac{1}{2} \cdot 3^\frac{1}{2}\)[/tex], you can use the properties of exponents.

When you multiply two powers with the same base, you add their exponents:

[tex]\[a^m \cdot a^n = a^{m+n}\][/tex]

In this case, both exponents are [tex]\(\frac{1}{2}\)[/tex], so when you multiply them together, you add the exponents:

[tex]\[3^\frac{1}{2} \cdot 3^\frac{1}{2} = 3^{\frac{1}{2} + \frac{1}{2}}\][/tex]

[tex]\[= 3^1\][/tex]

= 3

So, [tex]\(3^\frac{1}{2} \cdot 3^\frac{1}{2} = 3\)[/tex].

Answer:

40°

Step-by-step explanation:

Alternate angles

Angles BAC and ACD are equal

Answer:

(a)12cm (b)5/13 (c)12/13 (d)5/12

Step-by-step explanation:

(a) In a right triangle, the length of the sides are govered by the Pythagoras Theorem.

[tex]Hypotenuse^2=Opposite^2+Adjacent^2[/tex]

In the diagram

Hypotenuse=13cm; Opposite(With respect to angle A)=5cm

[tex]13^2=5^2+Adjacent^2\\Adjacent^2=169-25=144\\Adjacent=\sqrt{144}=12cm[/tex]

(b)sin A =[tex]\frac{opposite}{hypotenuse} =\frac{5}{13}[/tex]

(c)cos A=[tex]\frac{adjacent}{hypotenuse} =\frac{12}{13}[/tex]

(d)tan A=[tex]\frac{opposite}{adjacent} =\frac{5}{12}[/tex]

Answer:

a) 9(t - u)

Step-by-step explanation:

x = 10t + u

y = 10u + t

x - y = 10t + u - 10u - t

= 9t - 9u

= 9(t - u)

The required answer for the question is a) 9(t − u)

In mathematics , a set of simultaneous equations, also known as system of equations or an equation system, is a finite set of equations for which common solution are sought.

The given expression of x is given by,

x = 10t + u

If y be the 2-digit number formed by reversing the digits of x

then, the expression for y can be written,

y = 10u + t

Subtracting x with y we obtain,

x - y = 10t + u - 10u - t

Solving them we get

x - y = 9t - 9u

which can be written as,

x - y = 9(t - u)

Hence, the required expressions is equivalent to x − y =  9(t − u)

So the correct answer is a) 9(t − u)

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When x is greater than or equal to 0 use the equation x +2

The x value is given as 3 in f(3)

Now replace x with 3 in the equation and solve:

F(3) = 3 + 2 = 5.

The answer is 5

There are 1,296 different ways to make supreme choice pizza.

Step-by-step explanation:

Here, the total number of crusts available  = 6

The number of crust to be chosen = 1

So, the number of ways that can be done  = [tex]^6 C_1 = 6[/tex]  ways  ...... (1)

Similarly, the total number of meats available  = 4

The number of types meats to be chosen = 2

So, the number of ways that can be done  = [tex]^4 C_2 = 6[/tex]   ways ...... (2)

Similarly, the total number of vegetables available  = 9

The number of types vegetables to be chosen = 2

So, the number of ways that can be done  = [tex]^9 C_2 = 36[/tex] ways   ...... (3)

Now, combining (1), (2) and (3):

The number of ways one can choose 1 crust, 2 meat and 2 vegetables

= 6 ways x 6 ways x 36 ways  = 1,296 ways

Hence, there are 1,296 different ways to make supreme choice pizza.

To find the central angle of an arc with a length of 8/5 in a circle with a circumference of 12, we set up a proportion with the full circle's 360 degrees and solve for the angle, resulting in a central angle of 48 degrees.

You want to find the central angle of an arc in degrees for a circle with a circumference of 12 units and an arc length of 8/5 units. Since the circumference of a circle is 2π times the radius (2πr) and corresponds to a full circle or 360 degrees, the angle for the entire circle is 360°. The arc length of 8/5 is a fraction of the total circumference, so to find the corresponding angle in degrees, set up the proportion:

(arc length) / (circumference) = (angle of arc) / (360 degrees)

Plug in the known values and solve for the angle of the arc:

(8/5) / 12 = (angle) / 360

Cross-multiply to solve for the angle:

360 * (8/5) = 12 * (angle)

angle = (360 * 8) / (5 * 12)

angle = 48 degrees

Therefore, the central angle of the arc is 48 degrees.

Answer:

240π  

Step-by-step explanation:

Turbine blade that was 24 inches long is the radius of the circle the bug travels.

So the Circumference is = 2rπ = 2*24*π = 48π

The bug held on for 5 rotations. so the distance that the bug travels = 5*48π  = 240π  

Answer:

160 Chairs

Step-by-step explanation:

Convert 6 hrs to seconds, this gives you 21600 seconds. Convert 2 min and 15 sec to seconds, and this gives you 135 seconds per chair. Divide 21600 by 135. This gives you 160 Chairs produced in 6 hours.

Answer:

Step-by-step explanation:

For a. you are asked to evaluate f(0).  This is a piecewise function with different domains for each piece of the function.  You can only evaluate f(0) in the function that has a domain that allows 0 in it.  In the first domain, it says

x < -3.  0 is not less than -3, so 0 is not in that domain, so you will not use that "piece" of the function to evaluate f(0).

In the next domain, it says that x is greater than or equal to -3 and less than 0.  Again, 0 is not included in that domain, so we can't use that "piece" of the function to evaluate f(0).

The last domain says that x is greater than OR EQUAL TO 0, so this is where we evaluate f(0):

f(0) = -0 - 4 so

f(0) = -4

When we want to evaluate f(2), we follow the same rules.  Find the piece of the function that allows 2 in its domain.  That's the middle piece:

f(2) = 2(2) - 6 so

f(2) = -2

Answer:

50

Step-by-step explanation:

7+7=14

14/7=2

2+7=9..

Answer:

50

Step-by-step explanation:

not enough information

Answer:

yp = -x/8

Step-by-step explanation:

Given the differential equation: y′′−8y′=7x+1,

The solution of the DE will be the sum of the complementary solution (yc) and the particular integral (yp)

First we will calculate the complimentary solution by solving the homogenous part of the DE first i.e by equating the DE to zero and solving to have;

y′′−8y′=0

The auxiliary equation will give us;

m²-8m = 0

m(m-8) = 0

m = 0 and m-8 = 0

m1 = 0 and m2 = 8

Since the value of the roots are real and different, the complementary solution (yc) will give us

yc = Ae^m1x + Be^m2x

yc = Ae^0+Be^8x

yc = A+Be^8x

To get yp we will differentiate yc twice and substitute the answers into the original DE

yp = Ax+B (using the method of undetermined coefficients

y'p = A

y"p = 0

Substituting the differentials into the general DE to get the constants we have;

0-8A = 7x+1

Comparing coefficients

-8A = 1

A = -1/8

B = 0

yp = -1/8x+0

yp = -x/8 (particular integral)

y = yc+yp

y = A+Be^8x-x/8

Answer:

23

Step-by-step explanation:

if you have $16.10, he could buy 23 bluebarry muffins. Because if yo do

16.10 / 0.70 you woould get 23, and if you put that in the equasion you would

get this, P=$0.70(23) .  23 * 0.70 = 16.1

Step-by-step explanation:

Below is an attachment containing the solution

Answer: She would multiply the rate by the years to find the average rise in water levels, or 1.8 times 6.2 = 11.16. To find the difference between the water levels, she would subtract -13.64 from 11.16.

Step-by-step explanation:

Answer:

int i = 0; while (i < 4) { readData(); i = i + 1; }

Step-by-step explanation:

the above method is proper way to call the method readData four times because it will start from zero and will call readData until i=3, if i=4 it will stop calling readData.

double k = 0.0; while (k != 4) { readData(); k = k + 1; }

This is not the proper way to call readData four times because it will call readData only if k!=4 otherwise condition k!=4 will not be true and readData will not be called.

int i = 0; while (i <= 4) { readData(); i = i + 1; }

This is not the proper way to call readData four times because condition i<=4 will call readData five times starting from zero to 4.

int i = 0; while (i < 4) { readData(); }

This is not the proper way to call readData four times because it will call readData only one time i.e. value of is not incremented.

The proper way to call the 'readData()' method four times is by using a 'while' loop with a counter that starts at 0 and continues until it is less than 4, incrementing by 1 in each iteration.

The correct way to call the method readData() four times using a while loop is:

This loop initializes a counter variable i to 0, then enters a while loop that continues to iterate as long as i is less than 4. Inside the loop, the method readData() is called, and after each call, the counter i is incremented by 1. The loop will execute a total of four times before the condition i < 4 becomes false, thereby stopping the loop.

Japanese earthquake is 1996 times intense than the Pennsylvania earthquake.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two quantities of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol. As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

An earthquake measuring 6.4 on the Richter scale struck Japan in July 2007.

and, a minor earthquake measuring 3.1 on the Richter scale was felt in parts of Pennsylvania.

Mow,  Mj= log Ij/S and Mp = log Ip/ S

Where S is the standard earthquake intensity.

Then,

6.4 = log Ij/S and 3.1  = log Ip/ S

S x [tex]10^{6.4[/tex] = Ij  and S x [tex]10^{3.1[/tex] = Ip

So, ratio of the intensities

Ij : Ip= [tex]10^{6.4[/tex] /  [tex]10^{3.1[/tex]

      = [tex]10^{3.3[/tex]

      = 1996

Hence, Japanese earthquake is 1996 times intense than the Pennsylvania earthquake.

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Answer:

14 rows.

Step-by-step explanation:

We have been given that Jess  is planting rows of squash. To plant a row of squash Jess needs 6/7 square feet. There are 12 square feet in Jess's backyard.

To find number of rows that Jess can plant, we will divide total area of backyard by area needed to plant each row as:

[tex]\text{Number of rows that Jess can plant}=12\div\frac{6}{7}[/tex]

[tex]\text{Number of rows that Jess can plant}=\frac{12}{1}\div\frac{6}{7}[/tex]

Convert into multiplication problem by flipping the 2nd fraction:

[tex]\text{Number of rows that Jess can plant}=\frac{12}{1}\times \frac{7}{6}[/tex]

[tex]\text{Number of rows that Jess can plant}=\frac{2}{1}\times \frac{7}{1}[/tex]

[tex]\text{Number of rows that Jess can plant}=14[/tex]

Therefore, Jess can plant 14 rows of squash in her backyard.

The area of the slice is 13.0899 inch².

Explanation: