Shen started cleaning at 11:51 AM.
He finished at 1:29 PM.
How long did he clean?
hour(s) and minute(s)

Answer:

The answer is below

Step-by-step explanation:

The time until recharge for a battery in a laptop computer under common conditions is normally distributed with mean of 270 minutes and a standard deviation of 50 minutes. a) What is the probability that a battery lasts more than four hours b) What are the quartiles (the 25% and 75% values) of batterylife? c) c) What value of life in minutes is exceeded with 95% probability? (Roundthe answer to the nearest integer.)

Solution:

The z score is used to determine by how many standard deviations the mean is above or below the raw score. If the z score is positive then the raw score is above the mean while if the z score is negative then the raw score is below the mean. The z score is given by:

\(z=\frac{x-\mu}{\sigma}\\ \\\mu=mean, \sigma=standard\ deviation\)

Given μ = 270 minutes, σ = 50 minutes

a)

P(x > 4 hours) = P(x > 240 minutes)

\(z=\frac{x-\mu}{\sigma}\\ \\z=\frac{240-270}{50} =-0.6\)

From the distribution table, P(x > 240) = P(z > -0.6) = 1- P(z < 0.6) = 1 - 0.2743 = 0.7257

c)  P(z > z*) = 0.95

1 - P(z < z*) = 0.95

P(z < z*) = 0.05

This corresponds to a z score of -1.645

\(z=\frac{x-\mu}{\sigma}\\ \\-1.645=\frac{x-270}{50} \\\\x=187.75 \ minutes\)

For 75%, P(z < z*) = 0.75

This corresponds to a z score of 0.68

\(z=\frac{x-\mu}{\sigma}\\ \\0.68=\frac{x-270}{50} \\\\x=304 \ minutes\)

c) For 25%, P(z < z*) = 0.25

This corresponds to a z score of -0.67

\(z=\frac{x-\mu}{\sigma}\\ \\-0.67=\frac{x-270}{50} \\\\x=236.5 \ minutes\)

Answer:

undefined

Step-by-step explanation:

slope = (y_2 - y_1)/(x_2  x_1)

slope = (-3 - 4)/(6 - 6)

slope = -7/0

Since division by zero is undefined, this line has undefined slope.

Answer:

∠F = 80

Step-by-step explanation:

Let's find inner ∠D first, as you can see, it's a straight line but a line is in between, the outer angle is 120, and a straight line is 180, so 180 - 120 = 60. The inner ∠D is 60, now we can find ∠F, a triangle is 180:

40 + 60 + ∠F = 180

100 +∠D = 180

subtract 100 from both sides

∠F = 80

The expression that is always equivalent to sin x when 0° < x < 90° is (1) cos (90° - x). Option 1

To understand why, let's analyze the trigonometric functions involved. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Since we are considering angles between 0° and 90°, we can guarantee that the side opposite the angle will always be the shortest side of the triangle, and the hypotenuse will be the longest side.

Now let's examine the expression cos (90° - x). The cosine of an angle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. In a right triangle, when we subtract an angle x from 90°, we are left with the complementary angle to x. This means that the remaining angle in the triangle is 90° - x.

Since the side adjacent to the angle 90° - x is the same as the side opposite the angle x, and the hypotenuse is the same, the ratio of the adjacent side to the hypotenuse remains the same. Therefore, cos (90° - x) is equivalent to sin x for angles between 0° and 90°.

On the other hand, options (2) cos (45° - x) and (3) cos (2x) do not always yield the same value as sin x for all angles between 0° and 90°. The expression cos x (option 4) is equivalent to sin (90° - x), not sin x.

Option 1 is correct.

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Answer:

Correct option: D

Step-by-step explanation:

In the figure we have a right triangle, that is, one of the angles is a 90° angle. Therefore, we can use the Pythagoras' theorem to find the relation between the sides of the triangle:

\(a^2 = b^2 + c^2\)

Where b and c are cathetus of the triangle (sides adjacent to the 90° angle) and a is the hypotenuse (opposite side to the 90° angle).

So in our case, we have that x is the hypotenuse, and 40 and 42 are cathetus, so we have:

\(x^2 = 40^2 + 42^2\)

\(x^2 = 1600 + 1764\)

\(x^2 = 3364\)

\(x = 58\)

So the correct option is D.

Answer:

B) 4,700

Step-by-step explanation:

6000 - 4000 = 2000

2000 in 15 year, find how much for each year

2000/ 15 = 133.3333333

133.3333333 estimated = 133

133 approximately for each year

1975 to 1980 is five years

133 x 5 = 665

4000 + 665 = 4665

4665 rounded the the nearest hundred

4700

The approximate difference in the circumferences of the two circles is: C. 61 cm.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

Substituting the given parameters into the circumference of a circle formula, the circumference of the small circle is;

Circumference of circle, C = πD

Circumference of circle, C = 3.14 × 4.5

Circumference of circle, C = 14.13 cm.

For the larger circle, we have:

Circumference of circle, C = 3.14 × 24

Circumference of circle, C = 75.36 cm.

Difference = 75.36 cm - 14.13 cm.

Difference = 61.23 ≈ 61 cm.

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Answer:

1286.8

Step-by-step explanation:

Volume of a cylinder is pi(r²)(h)

The radius is 6.4 and the height is 10

Answer:

1286.1 units³

Step-by-step explanation:

V = πr²h

= 3.14 x 6.4 x 6.4 x 10

= 3.14 x 409.6

= 1286.144 units³

= 1286.1 units³

Answer:  $2 or $9

Step-by-step explanation:

Revenue (R) = $1800 , x = 1100 - 100p

R = xp

1800 = (1100 - 100p)p             substituted x with 1100 - 100p

1800 = 1100p - 100p²             distributed p into 1100 - 100p

100p² - 1100p + 1800 = 0       added 100p² & subtracted 1100p on both sides

     p² - 11p + 18 = 0                divided both sides by 100

(p - 2) (p - 9) = 0                     factored quadratic equation

p = 2  p = 9                         applied Zero Product Property to solve for p

The odd one out in the set is "FOQZ." It deviates from the pattern  by the other sets, where the letters are arranged in Alphabetical order.

The set of letters "BCDEGPTV AJK FOQZ IY" seems to follow a specific pattern. If we examine the letters in each group, we can identify a difference that sets "FOQZ" apart from the others.

In the first group "BCDEGPTV," the letters are arranged in alphabetical order. Similarly, in the second group "AJK," the letters are also in alphabetical order. However, when we look at the third group "FOQZ," the letters do not follow alphabetical order.

Based on this pattern, we can conclude that the odd one out in the set is "FOQZ." It deviates from the pattern followed by the other sets, where the letters are arranged in alphabetical order.

It's worth noting that the pattern could be based on different criteria, such as the position of the letters in the alphabet or some other sequence. Without additional information or context, it is difficult to determine the exact pattern or reason for the deviation.

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For the first question, we can see that g(x) = f(kx). To find k, we can compare the x values of f(x) and g(x). We can see that when x = -8 for g(x), x = -2 for f(x). This means that k(-8) = -2. Solving for k gives us k = -2/-8 = 1/4. Therefore, k is equal to one fourth.

For the second question, we can see that g(x) is f(x) shifted to the right by 4 units. Therefore, f(x) should be shifted to the left by 4 units to match g(x). The answer is left by 4 units.

Received message. For the first question, we can see that g(x) = f(kx). To find k, we can compare the x values of f(x) and g(x). We can see that when x = -8 for g(x), x = -2 for f(x). This means that k(-8) = -2. Solving for k gives us k = -2/-8 = 1/4. Therefore, k is equal to one fourth. For the second question, we can see that g(x) is f(x) shifted to the right by 4 units. Therefore, f(x) should be shifted to the left by 4 units to match g(x). The answer is left by 4 units.

hopes thats help thank you

Answer:

\(\frac{612}{999}\)

Step-by-step explanation:

To convert repeating decimals to fractions, you take the numbers that are repeating, in this case 612, and you see how many numbers are repeating. Here we have 3 numbers repeating and so you would divide 612 by 3 9's meaning 999. So 0.612 repeating is equal to \(\frac{612}{999}\). To make sure the answer is right, you can divide the numbers in a calculator to make sure you get the correct decimal.

Answer:

k = 20

Step-by-step explanation:

310-(30x7) = 5k

310-210=5k

100=5k

 /5   /5

20=k

Answer:225 jeans.

Step-by-step explanation: What we need to do here is convert the number of jeans to a percentage. There were 25 jeans when 50 customers were surveyed and 25 is half of 50 or 50%. This means that if 450 pairs of pants are ordered half of them should be jeans. 450/2 = 225.

The amount of Bruno's yearly pay deducted for FICA is approximately

A. $4,524.15. The closest option provided is A. $4521.15.

To calculate the amount of FICA deducted from Bruno's yearly pay, we need to consider the specific FICA tax rates for Social Security and Medicare.

As of 2021, the Social Security tax rate is 6.2% on income up to a certain threshold, and the Medicare tax rate is 1.45% on all income.

Given that Bruno's gross income per pay period is $4925 and he is paid monthly, we can calculate the yearly gross income as follows:

Yearly gross income = $4925 * 12 = $59,100

To calculate the FICA deduction, we need to find the sum of the Social Security and Medicare taxes. Using the respective tax rates mentioned earlier:

Social Security deduction = $59,100 * 6.2% = $3,667.20

Medicare deduction = $59,100 * 1.45% = $856.95

Adding these two deductions together:

FICA deduction = $3,667.20 + $856.95 = $4,524.15

Therefore, the amount of Bruno's yearly pay deducted for FICA is approximately $4,524.15.

The closest option provided is A. $4521.15.

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Answer:

A

Hope This Helps! :)

Answer:

B. 4 inches

Step-by-step explanation:

(24)(1) / 6 = 4

Mrs. Wu initially had $1062.40.

Let's break down the given information step by step:

1. Mrs. Wu spent 1/6 of her money on a dress and 2 blouses.

  Let's assume Mrs. Wu's total money is represented by the variable M. She spent 1/6 of M on the dress, which means she spent (1/6)M on the dress and the same amount on two blouses.

2. The dress cost 3 times as much as each blouse.

  Let's assume the cost of each blouse is represented by the variable B. Therefore, the cost of the dress would be 3B.

3. Mrs. Wu spent 3/4 of her remaining money on a watch.

  After spending on the dress and blouses, Mrs. Wu has (M - (1/6)M) = (5/6)M remaining. She spent 3/4 of this remaining money on a watch, which is (3/4) * (5/6)M = (15/24)M.

4. She spent $220.50 more on the watch than on the dress.

  The amount spent on the watch is (15/24)M, and the amount spent on the dress is (1/6)M. The difference between these amounts is $220.50.

To find the value of M, we can set up an equation:

(15/24)M - (1/6)M = $220.50

Simplifying the equation:

(15/24 - 1/6)M = $220.50

(5/24)M = $220.50

Multiplying both sides by (24/5):

M = $220.50 * (24/5)

M = $1062.40

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Answer:

Step-by-step explanation:

570.675

The formula for the 'B' variable is V/MK

To solve for the variable B is to make it the subject of formula.

Subject of formula is the variable that is expressed in terms of the other variables in a given formula, expression, function or equation.

Example;

In the equation,  2x + y = 4, let's make 'y' the subject of formula

y = 4 - 2x

Given the expression;

V=BMK

To make 'B' the subject, we need to divide both sides by the coefficients of B, we have;

V/MK = BMK/MK

B = V/MK

Thus, the formula for the 'B' variable is V/MK

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Answer:

8x - 2

Step-by-step explanation:

2x + 3 - (5 - 6x) ← distribute parenthesis by - 1

= 2x + 3 - 5 + 6x ← collect like terms

= (2x + 6x) + (3 - 5)

= 8x + (- 2)

= 8x - 2

Answer:

(a) The area of the sheet is (9x² - 12x + 4).

(b) The total surface area of the box is x (5x - 4) inches².

Step-by-step explanation:

It is provided that the width and the length of the box are x inches and the height of the box is (x - 1) inches

Then the width of the sheet is:

Width of sheet = (x - 1) + x + (x - 1)

                         = x - 1 + x + x - 1

                         = 3x - 2

(1)

The area of the sheet is:

Area of sheet = (3x - 2)² =

                       = (3x)² - 2 · 3x · 2 + (2)²

                       = 9x² - 12x + 4

Thus, the area of the sheet is (9x² - 12x + 4).

(2)

The central area, i.e. the base of the box = x²

Each arm folded up = x by (x - 1)

Then the areas of the 4 arms = 4 · x · (x - 1) = 4x² - 4x

Then the total surface area is:

Total Surface Area = Central Area + Areas of the 4 arms

                                = (x²) + (4x² - 4x )

                                 = 5x² - 4x

                                = x (5x - 4) inches²

Thus, the total surface area of the box is x (5x - 4) inches².

The quantity of red blood cell that is in the sample would be = 42 × 10⁵

Blood cells are those vascular cells that makes up the circulating blood of living organism which includes the white blood cells and the red blood cells.

The amount of white blood cells = a

The amount of red blood cells = 6 x 10² (a)

The amount of white blood cells in the sample = 7 × 10³

Therefore the amount of red blood cell in that sample =

6× 10² × 7 × 10³ = 42 × 10⁵

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Answer:

D

Step-by-step explanation:

solution is the points where the two graphs intersect.

they intersect at (-3,-3) and (0,6)

Answer:

10-15 mins

Step-by-step explanation:

Answer:

10-15 minutes

Step-by-step explanation:

im not sure though because you didn't give me enough information

Step-by-step explanation:

try the suggested solution; the lines and their inequalities are shown with the same colours. Points A[0;-1] and B[0;-3] are interception points, according to them to define equations of the lines.

Answer:

(x-8.5)2=81.25

Answer:

\(x = \frac{y}{3} - \frac{5}{3}\)

Step-by-step explanation:

Given

\(y = 5 + 3x\)

Required

Solve for x

Subtract 5 from both sides

\(y-5 = 5 -5+ 3x\)

\(y-5 = 3x\)

Divide through by 3

\(\frac{y}{3} - \frac{5}{3} = x\)

\(x = \frac{y}{3} - \frac{5}{3}\)

Answer:

events at A and B are independent because P(A)(B)≠P(A)