Kenya worked from 2:00 pm to 11:00 pm and made $79.11. What was her rate of pay per hour?

The largest possible volume of the box is 6158.394 cm^3.

Define the dimensions of the box to be L, W, and H.

Square base, L = W

Area: A = L^2 * H

Surface Area (Base + Area of 4 sides):

1600 = L^2 + 4 (L*H) ⇒ H = (1600 - L^2) / (4L)

Area: A = 400L - (1/4)L^3

Maximum (Derivative) A' = 400 - (3/4)L^2

Solving for 0

0 = 400 - (3/4)L^2

L^2 ⇒ (40 * SQRT(3)) / 3 = 23.094 (Maximum)

Solving for dimensions, known L=23.094

L = 23.094 cm

W = 23.094 cm

H ⇒ (1600 - L^2) / (4L) = (20 * SQRT(3) / 3) = 11.547 cm

Volume ⇒ L*W*H = 6158.394 cm^3

To locate the most viable extent, add the greatest viable mistakes to every dimension, then multiply. To find the minimum viable volume, subtract the greatest feasible mistakes from each measurement, then multiply.

Volume is a scalar amount expressing the amount of 3-dimensional area enclosed by a closed surface. For example, the gap that a substance or 3-D shape occupies or consists of.

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The required expression is given by 179.2 - 10.6d.

There were 179.2 gallons of water in the barrel and 10.6 gallons are used each day

Volume, is defined as the ratio of the mass of object to its density.

the volume of water in a rain barrel after "d"days
When there were 179.2 gallons of water in the barrel and 10.6 gallons are used each day.

since the amount of water is getting consumed day by day
therefore, the expression can be given as
  =  179.2 - 10.6d

Thus, the required expression is 179.2 - 10.6d.

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Answer:

8.49 units

Step-by-step explanation:

1. The distance formula is: [tex]\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }[/tex]

2. Let's plug in the numbers: [tex]\sqrt{(-1-5)^{2} +(4--2)^{2} }[/tex]

3. [tex]\sqrt{(-6)^{2} +(6)^{2} }[/tex]

4. [tex]\sqrt{36 + 36}[/tex]

5. [tex]\sqrt{72}[/tex] ≈ 8.485

Answer:

x > -3     and     x ≤ 1

Step-by-step explanation:

   [First inequality]

Given:

 -2x + 8 < 14

Subtract 8 from both sides:

 -2x < -6

Divide both sides by -2, since it's negative we also flip the sign:

 x > 3

   [Second inequality]

Given:

 -3x - 9 ≥ -12

Add 9 to both sides:

 -3x ≥ -3

 Divide both sides by -3, since it's a negative we also flip the sign:

 x ≤ 1

Option b) [tex]x^{2} -x-\sqrt{x} +3[/tex] is not a polynomial

Polynomial equation is equation of dependent variables which is related to the independent variable.

since, the equation ,[tex]x^{2} -x-\sqrt{x} +3[/tex] contains the square root of variable that's why its not a polynomial.

Thus, Option b) [tex]x^{2} -x-\sqrt{x} +3[/tex] is not a polynomial

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Based on the game rules of randomly picking a card and multiplying it by the roll from a number cube, the following are true:

There are 6 sides to dice and 4 cards. The sample space is:

Dice             Card            Product        

1                 5                         5

1                 6                         6

1                 7                         7

1                 8                         8

2                 5                         10

2                 6                         12

2                 7                         14

2                 8                         16  

3                 5                         15

3                 6                         18

3                 7                         21

3                 8                         24

4                 5                         20

4                 6                         24

4                 7                         28

4                 8                         32

5                 5                         25

5                 6                         30

5                  7                         35

5                  8                         40

6                 5                         30                        

6                 6                         36

6                 7                         42

6                 8                         48

Frequency table

Product                     Frequency

5                                      1

6                                      1

7                                      1

8                                      1

10                                      1

12                                      1

14                                      1

16                                      1

15                                      1

18                                      1

21                                      1

24                                      2

20                                      1

28                                      1

30                                      2

32                                      1

25                                      1

35                                      1

40                                      1

36                                      1

42                                      1

48                                      1

Total                                24

The frequency table shows that to get 28 or more, a person will have a relative frequency of:

= 1 + 2 + 1 + 1 + 1 + 1 + 1 + 1

= 9

Probability is:

= 9 / 24

= 3/8

= 37.5%

The number of products required to win 25% of the time is:

= 25% x 24

= 6

To find the winning number, count down from the highest product 6 times to get 32.

The probability of getting 36 or higher is:

= ∑(Probabability of picking 36 and above numbers)

= 1 / 24 + 1/24 + 1/24 + 1/24

= 1 / 6

The probability of repeating this 4 times is:

= 1 / 6 x 1 / 6 x 1/ 6 x 1 / 6

= 1 / 1,296

= 0.0007716

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Answer:

[tex]\frac{\sqrt{7} }{4}[/tex]

Step-by-step explanation:

since sin theta = 3/4, opposite length = 3 units and hypotenuse length = 4 units

by pythagoras' theorem, adjacent length = [tex]\sqrt{7}[/tex]

thus cos theta = adjacent/hypotenuse = [tex]\frac{\sqrt{7} }{4}[/tex]

Answer:

A: y=2x+4

B. 34° Celsius

Step-by-step explanation:

A:

Since the temperature goes up at a steady rate of 2 degres per minute, we can assume that 2 is our slope. Since the graph shows us that 4 is the y-intercept, we can substitute both the slope and y-intercept into the equation of a line, or y=mx+b. (m is our slope and b is our y-intercept.)

Doing so gives you:

[tex]y = 2x + 4[/tex]

B.

Using the above formula (y=2x+4), we can substitute x with 15 (since x is the minutes that pass).

Doing so gives you y=30+4, the sum of which is 34.

Therefore, the answer should be 34° Celsius.

Answer:

Step-by-step explanation:

I had this exact question and I figured it out.

the answer is: P(police officer and chooses car)

In order to get this answer I did the P(police officer) X P(choosing car)

It ended up being 36/45 X 15/45. Which is equal to around .2666667.

Now you take the Intersection of police officer and chooses car and you divide it by 45. That value on the chart is 12.

lucky enough, the product of 36/45 and 15/45 is equal to 12/45.

So 0.8 X 0.33 = .26

.26 = .26

Answer:

answer is P(police officer and chooses car)

Step-by-step explanation:

the probability of P(policer officer) and P(choose a car) are independent probabilities ( they are not overlapping probabilities)

Answer:

9.375 miles

Step-by-step explanation:

1) Let's set up an equation.

2.60 + 1.50x = 17.60

1.50x = 17.60 - 2.60

1.60x = 15

x = 15/1.60

x = 9.375

Answer: 6

Step-by-step explanation:

The slope of ST is

[tex]\frac{-5-0}{0-(-6)}=-\frac{5}{6}[/tex]

The slope of UV is

[tex]\frac{y-1}{-9-(-3)}=\frac{y-1}{-6}[/tex]
Since parallel segments have the same slope,

[tex]-\frac{5}{6}=-\frac{y-1}{6}\\\\5=y-1\\\\y=6[/tex]

Step-by-step explanation:

no of people=2

time taken=1/60mins

no of people=10

time taken=1/x

2=1/60

10=1/x

x=12mins

The parent. function shifted down by 2 units to produce x² and to the right by 3 units to produce y = x^2 + 3

This is a way of changing the position of an object on an xy-plane.

Given the parent function expressed as  y = (x + 2^)2

From the resulting image after translation, we can see that the parent. function shifted down by 2 units to produce x² and to the right by 3 units to produce y = x^2 + 3

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The probability that he lost less than 19 pounds is 7 / 9.

According to statement

The weight loss by individual is 12 Pounds

So, by uniform distribution probability

P(c ≤ x ≤ d) = (d - c) / (b - a)

Substitute the values in it then

P(12 ≤ x ≤ 19) = (19 - 12) / (20 - 11)

P(12 ≤ x ≤ 19) = 7 / 9

So, the probability that he lost less than 19 pounds is 7 / 9.

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The list is known as the sampling frame.

To conduct a survey on current social work majors, a researcher gets a list of all students who have declared a social work major from the registrar from which a sample will be drawn.

This list is known as a sampling frame.

The sampling frame is the list from which units are drawn for the sample.

Hence, the list is known as the sampling frame.

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Answer:2.5 kg per  meter

Step-by-step explanation:since the rod is uniform i simply divided the weight of the rod(20kg), by the length of the rod(8m). 20kg/8m = 2.5kg/m

a. I and II only true statement.

b . ∠3  = 84°

c . m∠KJM = 138° and m∠KLM  = 59°

Therefore, i and ii are true for an isosceles trapezium.

∠2 ≅ ∠3

∠1 ≅ 96°

Therefore,

∠3  = 180 - 96

∠3  = 84°

m∠KJM = 180 - x - 14

5x - 2 = 180 - x - 14

5x - 2 = 180 - x  - 14

5x + x = 180 - 14 + 2

6x = 168

x = 168 /6

x = 28

m∠KJM = 5(28) - 2 = 138°

m∠KLM  = 180 - 10y + 29

3y + 14 = 180 - 10y + 29

3y + 10y = 180 + 29 - 14

13y = 195

y = 195 / 13

y = 15

m∠KLM  = 3(15) + 14

m∠KLM  = 45 + 14

m∠KLM  = 59°

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The probability that 3 separate flights will all take place is 0.531441

let A = event of scheduled flight actually take place

According to the question, P(A)=0.81

Given that 3 separate flights will all take place is an independent event.

Hence, we can use the multiplicative rule which says If the probability that one given flight takes place is 0.81 then the probability of 3 flights taking place is:

P(A∩B∩C) = P(A)*P(B)*P(C)

= 0.81*0.81*0.81

= 0.531441

so, the Probability that 3 separate flights will take place is 0.531441

The formula used for independent events:

P(A∩B∩C) = P(A)*P(B)*P(C)

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The evaluation of the algebraic fraction x+2x+1/x^2-25 is[tex]\mathbf{\implies -\dfrac{3}{5(x+5)} +\dfrac{18}{5(x-5)}}[/tex]

The division of an algebraic expression can be carried out by using the long division method or expansion of the.

Given that:

[tex]\mathbf{\dfrac{x+2x+21}{x^2-25}}[/tex]

where:

By expanding the denominator, we have:

[tex]\mathbf{\dfrac{x+2x+21}{(x+5)(x-5)}}[/tex]

[tex]\mathbf{\dfrac{3x+21}{(x+5)(x-5)}}[/tex]

Creating a partial fraction from the denominator, we have:

[tex]\mathbf{\dfrac{3x+21}{(x+5)(x-5)} = \dfrac{a_o}{x+5} +\dfrac{a_1}{x-5}}[/tex]

Multiply the equation by the denominator, and we have:

[tex]\mathbf{\dfrac{(3x+21)(x+5)+(x-5)}{(x+5)(x-5)} = \dfrac{a_o(x+5)(x-5)}{x+5} +\dfrac{a_1(x+5)(x-5)}{x-5}}[/tex]

Simplifying, we have:

3x + 21 = a₀(x-5)+a₁(x+5)

Solve for the unknown parameter by plugging the real roots of the denominator: -5, 5

[tex]\mathbf{a_o =\dfrac{-3}{5}}[/tex]

[tex]\mathbf{a_1 =\dfrac{18}{5}}[/tex]

Replacing the solutions into the partial fractions parameters to obtain the final result, we have:

[tex]\mathbf{\dfrac{-(\dfrac{3}{5})}{x+5} +\dfrac{\dfrac{18}{5}}{x-5}}[/tex]

[tex]\mathbf{\implies -\dfrac{3}{5(x+5)} +\dfrac{18}{5(x-5)}}[/tex]

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Answer:

32468.41 yards

Step-by-step explanation:

11,405.59 + 12,048.82 + 9,014 = 32468.41

32468.41 yards

△MNQ ≅ △PNQ by SAS congruence theorem.

If two triangles are congruent by the SAS congruence theorem, then they have two pairs of corresponding congruent sides and a pair of corresponding included sides that are congruent.

∠MNQ ≅ ∠PNQ [congruent angles formed by angle bisector]

Therefore, opposite sides to the angles, MQ and PQ would also be congruent.

Thus, MQ ≅ PQ

NQ ≅ NQ [reflexive property]

This means that both triangles have two pairs of corresponding congruent sides and a pair of corresponding included sides that are congruent.

Thus, △MNQ ≅ △PNQ by SAS congruence theorem.

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Answer:

Step-by-step explanation:

that is my

Answer:

Muhammad ibn Musa al-Khwarizmi

محمد بن موسی خوارزمی

Answer:

8. a , c

9. b

10. c

The correct option is D:

the curves do not intersect, so there is no solution

The area of the rectangle is given by:

f(x) = (x + 7)*(5x - 3)

f(x) = 5x² -3x + 35x - 21

f(x) = 5x² + 32x - 21

For the circle, the area is:

g(x) = 2*pi*(x + 6)^2

g(x) = 2pi*x^2  + 12pi*x + 72pi

The solution is given g(x) = f(x).

By graphing both functions (the green curve is the area of the rectangle, the orange one is the area of the circle). The two curves never do intercept, so the correct option is D.

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Answer:

Step-by-step explanation:

Solution

I'm assuming you want this simplified. If not leave a note.

a(x + 1) - b(x + 1) - x - 1                     remove the brackets

ax + a - bx - b - x - 1                        gather like terms

ax - bx - x + a - b - 1

x(a - b - 1)  + (a - b - 1)                      Use the distributive property to simplify

Answer

(x + 1)(a - b - 1)

The common factor is (a - b - 1). That can be pulled out on either side of the isolated + sign

Answer:

$1,075

Step-by-step explanation:

Simple Intereat Formula:

A = P(1+rt)

where A is the final amount,

P is the principal(original amount invested)

r = annual interest rate

t = time in years

Given P = 1000

r = 2.5/100

t = 3 (Beginning of 4th year means the 4th year is not counted)

A = 1000(1+(0.025)(3))

= 1000(1.075)

=$1,075

Answer:

2c+2b

Step-by-step explanation:

this is because standard form only applies to no. from 10 and above , furthermore, they are unlike terms

Answer:

2.7930 × [tex]10^{4}[/tex]

Step-by-step explanation:

1.9 × 105 × 140 = 27,930

Scientific notation: 2.7930 × [tex]10^{4}[/tex]