According to a 2016 survey, 6 percent of workers arrive to work between 6:45 A.M. and 7:00 A.M. Suppose 300 workers will be selected at random from all workers in 2016. Let the random variable W represent the number of workers in the sample who arrive to work between 6:45 A.M. and 7:00 A.M. Assuming the arrival times of workers are independent, which of the following is closest to the standard deviation of W?
A. 0.24
B. 4.11
C. 4.24
D. 16.79
E. 16.92

Given:

Darcy harvests [tex]8\dfrac{3}{4}[/tex] acres of corn every [tex]\dfrac{5}{6}[/tex] of an hour.

Darcy harvests corn at a constant rate.

To find:

How many acres does she harvest per hour?

Solution:

We have,

Acres harvest in [tex]\dfrac{5}{6}[/tex] of an hours = [tex]8\dfrac{3}{4}[/tex]

Acres harvest in 1 hour = [tex]8\dfrac{3}{4}\times \dfrac{6}{5}[/tex]

                                      = [tex]\dfrac{32+3}{4}\times \dfrac{6}{5}[/tex]

                                      = [tex]\dfrac{35}{4}\times \dfrac{6}{5}[/tex]

Cancel out the common factors, we get

Acres harvest in 1 hour = [tex]\dfrac{7}{2}\times \dfrac{3}{1}[/tex]

                                      = [tex]\dfrac{21}{2}[/tex]

                                      = [tex]10\dfrac{1}{2}[/tex]

Therefore, she can harvest [tex]10\dfrac{1}{2}[/tex] acres of corn per hour.

Answer:

4th answer

Step-by-step explanation:

g(h(x)) means to put the formula for h(x) into the formula for g(  ).

[tex]g(h(x))=g(2x-2)=-3(2x-2)^3-2(2x-2)^2\\=-3(8x^3-24x^2+24x-8)-2(4x^2-8x+4)\\=-24x^3+72x^2-72x+24-8x^2+16x-8\\=-24x^3+64x^2-56x+16[/tex]

Cubing the binomial 2x - 2 can take some time!

Answer:

∅ ≈ 34º

Step-by-step explanation:

sin = opp/hyp

∅ = arcsin opp/hyp

∅ = arcsin 14/25

Use calculator

∅ = 34.055797742567906

∅ ≈ 34º

Answer:

is 55

Step-by-step explanation:

×[tex]\frac{x}{1}*\frac{14}{25}[/tex]⇒0.56

cos0.56

55

Answer:

2m+8

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

follow the proportions

Answer:

A

Step-by-step explanation:

Answer:

scale factor: 2

translation: (x+2, y+7)

Step-by-step explanation:

Refer to the attachment for complete calculation.

3²× 11^-9

Answer:

y = 6·sin(3·(x - 1)) + c

Step-by-step explanation:

The general form of an equation for a sinusoidal function is presented ad follows;

y = a·sin(b·(x - h) + c

Where;

a = The amplitude of the equation

T = The period = 2·π/b

h = The phase shift

c = The vertical shift

From the question, we have;

a = 6,

2·π/3 = 2·π/b

∴ b = 3

h = 1

We get;

y = 6·sin(3·(x - 1)) + c.

Answer:

6 sqrt(3) = x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/ hyp

sin 60 = x/12

12 sin 60 =x

12 ( sqrt(3)/2) =x

6 sqrt(3) = x

Answer:

x=6[tex]\sqrt{3}[/tex]

Step-by-step explanation:

take 60 degree as reference angle

using sin rule

sin 60=opposite/hypotenuse

[tex]\sqrt{3[/tex]/2=x/12

do cross multiplication

2*x=12*[tex]\sqrt{3}[/tex]

x=12[tex]\sqrt{3}[/tex] /2

x=6[tex]\sqrt{3}[/tex]

Answer: 4'6 2'4

Step-by-step explanation:

Answer and Step-by-step explanation:

The last answer choice is correct.

Set the product of 7 and 24 equal to the product of 8 and x, and then solve for x

The process being used in the last answer choice is called Cross multiplication, and is used to find the unknown value in fractions.

[tex]\frac{7}{8}[/tex] × [tex]\frac{x}{24}[/tex]

7 × 24 = 8x

168 = 8x

21 = x

#teamtrees #PAW (Plant And Water)

Answer:

B. [tex]^{5} P_{5}[/tex] × [tex]^{20} P_{15}[/tex]

Step-by-step explanation:

No. of students from first grade = 15

No. of students from second grade = 5

There are 5 rows of seats

Each row contains 5 seats

Total seats = 25

No. of ways for second-grade students to occupy the first row (i.e first 5 seats) = [tex]^{5} P_{5}[/tex]

Remaining seats = 20

So, now we are left with 15 first grade students  

So, No. of ways for first-grade students occupy remaining seats = [tex]^{20} P_{15}[/tex]

Using the counting rule principle,

No. of ways for the students can be seated if all of the second-grade students occupy the first row = [tex]^{5} P_{5}[/tex] × [tex]^{20} P_{15}[/tex]

So, Option B is the correct answer

Hence, no. of ways for the students can be seated if all of the second-grade students occupy the first row is ×

There are ¹⁵P₁₅ x ¹⁰P₅ possible way to seat, if all of the second-grade students occupy the first row.

A permutation in math is the number of ways in which a set of data or objects can be ordered or arranged, where the order matters.

Given that, a school bus has 25 seats, with 5 rows of 5 seats. 15 students from the first grade and 5 students from the second-grade travel in the bus.

Since you have to place all first-grade students in the first three rows,

Therefore,

For the 15 first-graders of the first three rows (15 seats), we have ¹⁵P₁₅ since all 15 places have to be occupied by all 15 first-graders.

Then we have 10 remaining seats left to be assigned to the 5 second-graders = ¹⁰P₅

We then multiply the permutation numbers of those two arrangements to get the total ways:

¹⁵P₁₅ x ¹⁰P₅

Hence there are ¹⁵P₁₅ x ¹⁰P₅ possible way to seat, if all of the second-grade students occupy the first row.

Learn more about permutation click;

https://brainly.com/question/30649574

#SPJ7

Answer:

62

Step-by-step explanation:

Draw a line from the bottom of the 4 foot line straight across (horizontally) until it hits the vertical line on your left.

The two lines (the one you drew and the left vertical line) meet at right angles.

The upper figure is a rectangle.

Area = L * W

L = 5

W = 4

Area = 5 * 4

Area = 20

Now the bottom rectangle can be found the same way.

Area = L * W

L = 14

W = 3

Area = 14 * 3

Area = 42

The total area = 42 + 20

Total area = 62.

The comment was correct.

Answer:

y = (√x)/13 for x > 0

Step-by-step explanation:

Actually, this is f(x) = 169x^2; the " ^ " indicates exponentiation.  The graph consists of the right-hand half of the parabola 169x^2.  Before we attempt to find the inverse function, we determine whether or not this function passes the vertical line test.  If x is restricted to (0, infinity), a horizontal line intersects this graph only once.  Therefore, this function has an inverse.

1.  Replace 'f(x)' with 'y:'  y = 169x^2

2.  Interchange x and y:  x = 169y^2

3.  Solve for y:  y^2 = x/169, or y = (√x)/13 for x > 0

Answer:

y-8x+7=0

Step-by-step explanation:

slope(m)=8

using slope intercept form of equation of staright line we get

y=mx+b

y=8*x+b

y-8x=b ................  eq(i)

since the line include the point (2,9) it satisfies the euation,

here x=2 and y=9

equation: y-8x=b

9-8*2=b

9-16=-b

-7=b

substituting the value of b in eq(i) we get

y-8x=-7

y-8x+7=0   is a required equation of the line.

Answer:

Aseem’s : 8.3, Stana’s : 11.6

Step-by-step explanation:

Aseem: x

Stana: 2x-5

X+2x-5=20

3x=25

X = 8.3

Answer:

-5

Step-by-step explanation:

12-7=5

7-12=-5

If this helps please mark as brainliest

Arithmetic

7-12

Meaning, 12 less than 7.

7-12=-5

Answer:

Option d) 2.1 + 2x = 7.5

Step-by-step explanation:

An isosceles triangle is a triangle with two equal sides.

Perimeter of a triangle is some of all the 3 sides.

Let the equal sides be x

Let the third side be y

Therefore,

              Perimeter = x + x + y

                         7.5 = 2x + y    

                          7.5 = 2x + 2.1                    [ given shortest side, y = 2.1m ]

Answer:

D.

Step-by-step explanation:

Standard Form (Quadratic): [tex]y=ax^2+bx+c[/tex]

Vertex Form (Quadratic): [tex]y=a(x-h)^2+k[/tex]

Intercept Form (Quadratic): [tex]y=a(x-p)(x-q)[/tex]

      p,q are x-intercepts

x-intercepts given in graph: -2,4

[tex]y=a[x-(-2)](x-4)[/tex]

eqn 1: [tex]y=a(x+2)(x-4)[/tex]

Plug in the given point to find 'a' : (3,-5)

[tex]-5=a(3+2)(3-4)[/tex]

[tex]-5=a(5)(-1)[/tex]

[tex]1=a[/tex]

Substitute 'a' in to eqn 1.

[tex]y=1(x+2)(x-4)[/tex]

eqn 2: [tex]y=(x+2)(x-4)[/tex]

Expand eqn 2. (can use FOIL)

[tex]y=x^2-2x-8[/tex]

The Answer is:

C.) (x+2)(x+3)

Answer:

(x-2)(x+3)

Step-by-step explanation:

1. Start by setting up the synthetic division. The numbers 1, -4, -11, and 30 go on the inside on the division. To get the number on the outside, set x-5 equal to 0. solve and get 5.

2. bring the one down. multiply the one and the five and place the number you get underneath the -4 in the next column. From there, add the two numbers in the column.

3. After adding those two numbers, put the number you get (which should be 1) directly below the 5. Now multiply that number and the 5 again.

4. Repeat these steps until you fill the spaces under the next two columns. If you do it correctly, the number at the bottom of the very last column should be 0. This zero is known as the remainder. The remainder is not needed to complete this problem.

 Now that you have finished synthetic division, it is time to set up the new equation you got.

5. The 1 on the bottom left will be your [tex]x^{2}[/tex] value, the next 1 will be your x value, and the -6 will be your c. You should get the equation [tex]x^{2} + x -6[/tex]

6. From here, factor the polynomial. The factors must add up to the middle value (1) and multiple to c (-6). The factors -2 and 3 add up to 1 and multiply to -6

Therefore, your answer will be (x-2)(x+3)

Answer:

x = 145

Step-by-step explanation:

The angles are same side exterior angle and same side exterior angles are supplementary

x +35 =180

Subtract 35 from each side

x = 180-35

x =145

Answer:

x=145

Step-by-step explanation:

180 -35 = 145

angle in a straight line add up to 180

x=145

F angle /corresponding angle are the same

Answer:

XY=6

Step-by-step explanation:

13-7=6

Answer:

XY = 6

Step-by-step explanation:

We know that the whole line (XZ) is equal to 13, and we know that YZ + XY is equal to XZ.

XZ = XY + YZ

13 = XY + 7

6 = XY

Hope this helped :)

Step-by-step explanation:

yes friend and your answe is wring

Answer:

Step-by-step explanation:

Complete Question

David bought a chain of fast food restaurants that operated 200 stores in 2009. The number of restaurants has grown at a rate of 12% annually.how many stores does the restaurant operate in 2020?

Answer:

[tex]N_{11} \approx 749[/tex]

Step-by-step explanation:

From the question we are told that:

Number of Fast Food Restaurants [tex]P=200[/tex]

Number of years [tex]t=11yrs[/tex]

Rate [tex]r=12%[/tex]

Generally the equation for the Number of restaurant in operation in 2020 is mathematically given by

 [tex]N(t)=Pe^{rt}[/tex]

Therefore

For t=11

 [tex]N_{11}=200*e^{0.12*11}[/tex]

 [tex]N_{11}=748.7[/tex]

 [tex]N_{11} \approx 749[/tex]