which expression is equivalent to the given expression? \(6ab (a0b2)4\)

A person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.

How to determine the amount of carpet needed for a rectangular room?

To determine the amount of carpet needed for a rectangular room, you need to convert the measurements to the same unit of measurement. Since the carpet is sold in square yards, we need to convert the dimensions of the room to yards.

The length of the room is given in yards, so we don't need to make any conversions for that dimension. However, the width of the room is given in feet, so we need to convert it to yards by dividing by 3 (since there are 3 feet in a yard),

18 feet ÷ 3 feet/yard = 6 yards

So the dimensions of the room in yards are 10 yards by 6 yards.

To find the total area of the room, we need to multiply the length and width,

10 yards × 6 yards = 60 square yards

Therefore, a person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.

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Answer: a) To find the number of working days on which under 18,000 bottles are filled, we need to calculate the z-score for this value:

z = (18,000 - 20,000) / 2000 = -1

Using a standard normal distribution table or calculator, we find that the probability of a value being less than -1 standard deviation is approximately 0.1587. Therefore, the approximate number of working days on which under 18,000 bottles are filled is:

0.1587 x 260 ≈ 41

b) To find the number of working days on which over 16,000 bottles are filled, we need to calculate the z-score for this value:

z = (16,000 - 20,000) / 2000 = -2

Using a standard normal distribution table or calculator, we find that the probability of a value being less than -2 standard deviations is approximately 0.0228. Therefore, the approximate number of working days on which over 16,000 bottles are filled is:

0.0228 x 260 ≈ 6

c) To find the number of working days on which between 18,000 and 24,000 bottles are filled, we need to calculate the z-scores for these values:

z1 = (18,000 - 20,000) / 2000 = -1

z2 = (24,000 - 20,000) / 2000 = 2

Using a standard normal distribution table or calculator, we find that the probability of a value being less than -1 standard deviation is approximately 0.1587, and the probability of a value being less than 2 standard deviations is approximately 0.9772. Therefore, the approximate number of working days on which between 18,000 and 24,000 bottles are filled is:

(0.9772 - 0.1587) x 260 ≈ 236

Step-by-step explanation:

Answer:

x = -18

Step-by-step explanation:

Distribute: 3*5x = 15x ; 3*-6 = -18 ; 6*2x = 12x ; 6*-12 = -72

15x - 18 = 12x - 72

Add 18 to both sides: 15x = 12x - 54

Subtract 12x from both sides: 3x = -54

Divide both sides by 3: x = -18

Answer:

x= 17.666666...

Step-by-step explanation:

3(5x - 6) = 6(2x - 12)

(3 times 5x , 3 times  -6)             (6 times 2x, 6 times - 12)

15x-18 = 12x -72           (multiply insides)

-12x       -12x              (remove 12x from right side)

3x-19 = -72                (product)

   +19 = +19                (add 19 left side to remove it)

3x = 53                        (product)

x = \(\frac{53}{3}\)                              (divide)

x= 17.666666...                (answer)

x = 17.67                     (if simplify)

Answer:

6

Step-by-step explanation:

8x + 2 + 70 + 60 = 180 ( sum of all angles of a triangle = 180 degree )

8x + 132 = 180

8x = 180 - 132

8x = 48

x = 48 / 8

x = 6

Therefore 3 rd option is correct.

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Answer: D

Step-by-step explanation:

Hope it helps

Answer:

(71.28, 78.72)

Step-by-step explanation:

We have the following information from the statement:

mean (m) = 75

sample standard deviation (sd) = 5

Sample size (n) = 13

Significance level (alpha) = 1 - 0.98 = 0.02

Degrees of freedom for t-d (df) = n - 1 = 13 - 1 = 12

The critical value would be:

t (alpha / 2) / df = T (0.01) / 12 = 2,681 (this for the table)

Margin of error equals:

E = t (alpha / 2) / df * sd / n ^ (1/2), replacing:

E = 2,681 * 5/13 ^ (1/2)

E = 3.72

Therefore, the interval of 98% confidence interval would be:

75 + 3.72 = 78.72

75 - 3.72 = 71.28

(71.28, 78.72)

The value of the given problem by using box method is 2546.

Multiplication computations involving numbers greater than ten can be simplified using the grid method, sometimes referred to as the box method, which is also known as the method of boxes. Making a table with the first factor's place values along the top and the second factor's place values down the left is how you multiply two numbers using the box approach. Place values are multiplied, and their products are added to the table. Clear up the table. In arithmetic, there is an alternative to the lengthy, error-prone classical multiplication approach: the box method. Multiplication of two or more digits is made easier with the use of the box approach.

X       60        7

30    1800    210

8       480      56

Therefore, 1800+480+210+56=2546

Therefore, the value of the given problem by using box method is 2546.

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Jim did not buy any tickets (n_Jim = 0).

Larry bought 7 more tickets than Jim.

To determine the number of tickets Larry bought more than Jim, we need to find the values of n for Larry and Jim's ticket purchases.

For Larry:

Let's substitute C = $170 into the equation C = 24n + 2 and solve for n:

$170 = 24n + 2

Subtracting 2 from both sides:

$168 = 24n

Dividing both sides by 24:

n = 7

For Jim:

We can calculate the number of tickets Jim bought by subtracting 12 from Larry's number of tickets:

n_Jim = n_Larry - 12

n_Jim = 7 - 12

n_Jim = -5

Since we cannot have a negative number of tickets, we can conclude that Jim did not buy any tickets (n_Jim = 0).

To find the difference in the number of tickets bought, we subtract the number of tickets Jim bought from the number of tickets Larry bought:

n_difference = n_Larry - n_Jim

n_difference = 7 - 0

n_difference = 7

Therefore, Larry bought 7 more tickets than Jim.

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Question

The equation C=24n+2 represents the cost, C, in dollars, of buying n tickets to a play. J $170. How many more tickets did Larry buy than Jim? 12

Answer:

We use the rule,

\((a^b)^c = a^{bc}\)

a. (10^7)²

\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)

10^14

b. (10^9)³

\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)

10^27

c. (10^6)³

\(10^{(6)(3)}= 10^{18}\)

10^18

d. (10^2)³

\(10^{(2)(3)} = 10^{6}\)

10^6

e. (10³)²

\(10^{(3)(2)}=10^{6}\)

10^6

f. (10^5)^7

\(10^{(5)(7)} = 10^{35}\)

10^35

Step-by-step explanation:

Answer:

sorry :/ im not sureee but they would have sold 20  

Step-by-step explanation:

They sold 20 guitars that month.

Step-by-step explanation:

\( \frac{12 \times 100}{60} = total\)

\( \frac{1200}{60} = 20\)

Answer:

42

Step-by-step explanation:

14 = /3

3 ⋅ 14 = 3⋅ /3

x = 42

Answer:

Step-by-step explanation:

first one -2-(-9) is 7

Second one for -2-9 is -11

And last one for -2-(-9)-(-2) is 9

Answer:

-2-(-9) = 7

-2-9 = -11

-2-(-9)-(-2) = 9

Answer:

A,d,e not sur tho

Step-by-step explanation:

Answer:

\(r^{2}+6r+9=(r+3)^{2} \\m^{2}-10m+25=(m-5)^{2}\)

Step-by-step explanation:

Only !

Answer: 165 miles

Step-by-step explanation: In order to figure out the answer, you must do 55 x 3 because he drove for 3 hours at 55 mph so you could break it up and go 50 x 3 to equal 150 and 5 x 3 to equal 15 and add those to get 165.

Answer:

The answer is 165miles

Step-by-step explanation:

\(distance = speed \times time\)

d=55×3

d=165 miles

Answer: D

Step-by-step explanation:

set the functions to subtract

Given statement solution is :- It  would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

To find the cost of installing tile in the dining room and carpet in the bedroom, we need to calculate the areas of both rooms first.

Given:

Every 2 centimeters on the floor plan represents 1 meter of the house.

Dining Room:

On the floor plan, the dining room is 8 cm by 10 cm.

Converting this to meters, the dimensions of the dining room are 8 cm / 2 = 4 meters by 10 cm / 2 = 5 meters.

The area of the dining room is 4 meters * 5 meters = 20 square meters.

Bedroom:

On the floor plan, the bedroom is 6 cm by 10 cm.

Converting this to meters, the dimensions of the bedroom are 6 cm / 2 = 3 meters by 10 cm / 2 = 5 meters.

The area of the bedroom is 3 meters * 5 meters = 15 square meters.

Now, let's calculate the costs.

Cost of Tile:

The cost of installing tile is $34 per square meter.

The area of the dining room is 20 square meters.

Therefore, the cost of installing tile in the dining room is 20 square meters * $34/square meter = $680.

Cost of Carpet:

The cost of installing carpet is $21 per square meter.

The area of the bedroom is 15 square meters.

Therefore, the cost of installing carpet in the bedroom is 15 square meters * $21/square meter = $315.

Therefore, it would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

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Answer:

the answer is (4,7).

Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4 using trigonometric ratio.

We know that the point (-3, 4) is on the terminal side of the angle θ, and we can use the Pythagorean theorem to find the value of the hypotenuse:

r² = x² + y²

r² = (-3)² + 4²

r² = 9 + 16

r² = 25

r = 5

Now we can find the values of sin θ, csc θ, and cot θ:

sin θ = y/r = 4/5

csc θ = r/y = 5/4

cot θ = x/y = -3/4

Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4.

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to subtract 7

then

To subtract 6

then

To subtract 5

then

To subtract 4

Evertime you subtract go down 1 number.

The total number of workers that were studied can be found to be 139,340,000.

The percent of workers unemployed would be 5. 4 %.

Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.

Number of employed workers :

= 74,624,000 + 64, 716, 000

= 139,340,000

Percentage unemployed :

= ( 4, 209,000 + 3,314,000 ) / 139,340,000

= 5. 4 %

Percentage of unemployed men :

= 4,209,000 / 74,624,000

= 5.6 %

Percentage of unemployed women:

= 3,314,000 / 64, 716, 000

= 5. 1 %

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The full question is:

a. How many workers were studied?

b. What percent of the workers were unemployed?

c. Compare the percent unemployed for the men and the women.

Answer:

1) both

2) Yes. It is appropriate to conclude that the health of the student affects ability to taste.

Step-by-step explanation:

Random Sampling  is done when each element of the sample has equal probability of being chosen. In both the samples of healthy and runny nose students each student has equal probability of being tested.

Random Assignment is one in which there is a control group and experimental group. The control group contains all the participants and each participant has the equal probability of being placed in the experimental group. For example in this experiment each student has equal probability of being tested with the given chocolate bar.

2) Yes. It is appropriate to conclude that the health of the student affects ability to taste.

the probability of success in healthy student is 78/154= 0.5065 = 50.65%

the probability of success in runny nose student is 44/118= 0.3729 = 37.29%

From this we see the probability of success is more in healthy students as compared to runny nose students

50.65> 37.29

Therefore it is appropriate to conclude that the health of the student affects ability to taste.

Answer:

2.75 m²  

Step-by-step explanation:

From the information given:

the thickness of the paint = 0.07 cm = (0.07/100) m

= 0.0007 m thick

the diameter hemispherical dome = 50 m

∴

radius of the dome = 50m /2 = 25 m

The volume of a hemispherical dome is expressed as:

\(V = \dfrac{2}{3}\pi r^3\)

Thus, the change in the volume now is:

\(\dfrac{dV}{dr} = \dfrac{2}{3}\pi *3 r^2\)

\({dV} = \dfrac{2}{3}\pi *3 r^2 (dr)\)

\({dV} = 2 \pi r^2 (dr)\)

∴

dV = 2π × (25)² (0.0007)

where;

dr = 0.0007

dV = 2π × (25)² (0.0007)

dV = 2.75 m²  

The value of y' by implicit differentiation, the value of y is \(y = \sqrt{5x +c}\)

We differentiate each side of an equation with two variables by taking one as a variable and the rest are constant.

Given

The function is \(y^2 + 5 = 5x\)

where x and y are variables..

On differentiating the equation, we have;

\(2yy' + 0 = 5\)

on simplifying, we have

2yy' = 5

Now solve the equation explicitly for y and differentiate to get y' in terms of x.

2yy' = 5

Separate the variables

\(y^2 = 5x + c\)

Taking square root on both the side

\(y = \sqrt{5x +c}\)

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Number of words: 252

Time: 4.5 minutes

To find the unit rate r in words per minute, we use the formula:

Where W is the number of words, and t is the time elapsed. Using the information of the problem:

Answer:

no and no

Step-by-step explanation:

2/6 is not a whole number and 2/2 is exactly a whole number.

its the same thing as 4/6 and 2/2

Answer: neither are equal to 2/2

Step-by-step explanation:

to figure this out, you have to divide the numerator by the denominator

in this case, you would need to divide 2 from 2, which is 1.

_ _

since 4/6 is 0.6 and 2/6 is 0.3, neither are equal to 1

Solution:

Give that

The AAS Theorem. If two angles and a nonincluded side of one triangle are congruent to two angles and a nonincluded side of a second triangle, then the triangles are congruent.

Hence,

The final answer is OPTION A