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Answer:

57 cm^2/s

Step-by-step explanation:

The area of a rectangle is the length times the width of the rectangle

A =lw

Where l is the length while w is the width of the rectangle respectively

This equation can be found by taking the derivative of the previous equation

dA/dt = dl/dt.w + l.dw/dt

Given that the length = 7cm and the width = 4cm

The increasing rate for the length = 9cm/s while the increasing rate for the width is = 3cm/s

We can solve for the unknown variable by using the given numbers.

dA/dt = 9(4 )+ 7(3)

= 36 + 21

= 57 cm^2/s

Given :

The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of 3 cm/s.

When the length is 7 cm and the width is 4 cm .

To find :-

how fast is the area of the rectangle increasing?

Solution :-

As we know that :-

A = lb

To find the rate :-

d(A)/dt = d(lb)/dt .

Differenciate :-

dA/dt = l (db/dt ) + b (dl/dt )

Substitute :-

dA/dt = 9*4 + 7*3

dA/dt = 36 + 21 cm²/s

dA/dt = 57 cm²/s

Answer:

Step-by-step explanation:

15% of 20 is 3

Answer:0.8p+1 and 1+0.8p

Step-by-step explanation:

0.5p+0.3p=0.8p

7-6=+1

0.8p+1

and

Swap both numbers

(0.5p+7)+(0.3p-6)=1+0.8p

Answer:

i think its -17

Julia needs to buy 42 packets of patties to make 500 hamburgers for the school function

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

Hamburger patties are sold in packets of 12. Let x represent the number of packet of patties to be bought to make 500 hamburgers. Hence:

12x = 500

x = 500/12

x = 41.67

x≅ 42

Julia needs to buy 42 packets

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Answer: 12.5 cm or 125 mm

Explanation:

Given: \(\frac{5}{8}\ of\:20\)

\(\frac{5}{8}\cdot \:20\)

\(\frac{5\cdot \:20}{8\cdot \:1}\)

\(\frac{100}{8}\)

\(\frac{50}{4}\)

\(\frac{25}{2}\)

\(12.5 cm\)

Conversion:

1 cm --> 10 mm

12.5 cm --> ( 12.5 * 10 ) mm

12.5 cm --> 125 mm

The nth term of the given sequence is 1/n².

An arithmetic progression (AP) is a sequence of numbers in which each term, starting from the second term, is obtained by adding a fixed constant value to the previous term. This constant value is called the common difference, and it remains the same throughout the sequence.

A geometric progression (GP) is a sequence of numbers in which each term, starting from the second term, is obtained by multiplying the previous term by a fixed constant value. This constant value is called the common ratio, and it remains the same throughout the sequence.

In the given question,

The given sequence is of the form:

1, 1/2², 1/3², 1/4², ...

So, the nth term can be written as:

1/n²

Therefore, the nth term of the given sequence is 1/n².

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Answer:

The mean and standard deviation of Y is $6.56 and $2.77 respectively.

Step-by-step explanation:

Consider the provided information.

Let Y represent their profit on a randomly selected pizza with this promotion.

The company is going to run a promotion where customers get $2 off any size pizza.

Therefore, \(Y=\text{Profit}-\$2\)

\(Y=X-\$2\)

So the mean will be reduced by 2.

\(\mu_Y=\mu_X-\$2\)

\(\mu_Y =\$ 8.56 - \$2\)

\(\mu_Y =\$6.56\)

If we add or subtract any constant number from a given distribution, then the mean is changed by the same number(i.e constant number) but the standard deviation will remain the same.

Therefore \(\sigma_Y=\sigma_X=2.77\)

Hence, the mean and standard deviation of Y is $6.56 and $2.77 respectively.

Answer:

14/x = 1/7.

Step-by-step explanation:

Let x be the number:

14/x = 1/7

Answer:

1

Step-by-step explanation:

Hope this helps! Have a great day ahead. Please tell me if I'm wrong :) Stay safe <3

Answer:

1

Step-by-step explanation:

2/3 + 1/12 + 1/4

First, we need a common denominator of 12

2/3 *4/4 =8/12

1/12

1/4 *3/3 = 3/12

8/12 + 1/12 + 3/12

add

12/12

1

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Step-by-step explanation:

The ONE  solution to this system of two lines is the point where the two lines cross   at   (1,4)

the difference of of equations in the system 1. Equation (1) for system 1 is similar to the equation (4) of the system 2.

Lx + My = N ---------(1)

Ax + By = C ---------(2)

System 2 :

(L - A)x + (M - B)y = N - C -------(3)

Lx + My = N ---------(4)

If we subtract equation (2) from equation (1),

(Lx + My) - (Ax + By) = N - C

Lx - Ax + My - By = N - C

(L - A)x + (M - B)y = N - C

Which is similar to equation (3) of the system 2.

And equation (1) of the system (1) is similar to the equation (4) of the system (2)

Therefore, equation (3) of the system 2 is the difference of of equations in the system 1. Equation (1) for system 1 is similar to the equation (4) of the system 2.

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Answer:

resizing by the factor of 5/7

x = 3.5 * 5/7

= 17.5/7

= 2.5

The roots of the equation \((x^2 + 1)(x^3 + 2x)(x^2 - 64)\) = 0 are x = ±i, ±√(-2), 0, 8, -8.

To find the roots of the equation \((x^2 + 1)(x^3 + 2x)(x^2 - 64)\) = 0, we can use the zero-product property, which states that if a product of factors equals zero, then at least one of the factors must be equal to zero.

So, we'll set each factor equal to zero and solve for 'x':

1. \(x^2 + 1\) = 0

  Subtracting 1 from both sides:

 \(x^2\) = -1

  Taking the square root of both sides:

  x = ±√(-1)

  Since the square root of a negative number is not defined in the real number system, the solutions to this equation are complex numbers.

  Therefore, the roots for this factor are:

  x = ±i (where i represents the imaginary unit)

2. \(x^3 + 2x\) = 0

  Factoring out 'x':

\(x(x^2 + 2)\) = 0

  Applying the zero-product property:

  x = 0 (one root)

  Also, \(x^2 + 2\) = 0

  Subtracting 2 from both sides:

  \(x^2\) = -2

  Taking the square root of both sides:

  x = ±√(-2)

  Again, the solutions to this equation are complex numbers.

  Therefore, the roots for this factor are:

  x = ±√(-2)

3.\(x^2 - 64\) = 0

  This is a quadratic equation, so we can solve it by factoring:

  (x - 8)(x + 8) = 0

  Applying the zero-product property:

  x - 8 = 0  or  x + 8 = 0

  x = 8  or  x = -8

Combining all the roots from each factor, we have:

x = ±i, √(-2), 0, 8, -8

The solutions to the equation \((x^2 + 1)(x^3 + 2x)(x^2 - 64)\) = 0, including all real and complex numbers are x = ±i, √(-2), 0, 8, -8.

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Answer:

Step-by-step explanation:

Therefore, the height of the tower is approximately 121.4 meters.

Answer:

1995 => 22°

2005 => 36°

Step-by-step explanation:

Central angle of the sector representing nuclear energy in 1995 = percentage of nuclear energy in 1995 ÷ 100 × 360°

Nuclear energy is approximately 6% (rounded to whole number) in 1995.

Central angle = \( \frac{6}{100}*360 = \frac{6}{10}*36 \)

\( = \frac{216}{10} = 21.6 \)

Central angle representing nuclear energy in 1995 ≈ 22° (nearest whole number).

Central angle of the sector representing nuclear energy in 2005 = percentage of nuclear energy in 2005 ÷ 100 × 360°

Nuclear energy is approximately 10% (rounded to whole number) in 1995.

Central angle = \( \frac{10}{100}*360 = \frac{1}{1}*36 \)

\( = \frac{36} = 36 \)

Central angle representing nuclear energy in 2005 = 36°.

a) Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. b) Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.

a) In the context of Scooter's business, the slope of the function f(x) = 200 + 15x represents the rate at which the total money earned increases with each additional sale. Each unit increase in x (number of sales) results in an increase of $15 in total money earned. The y-intercept of 200 represents the initial amount of money Scooter already had before making any sales.

In the context of Karissa's business, the slope of the function f(x) = 80 + 35x represents the rate at which the total money earned increases with each additional repair job. Each unit increase in x (number of repairs) results in an increase of $35 in total money earned. The y-intercept of 80 represents the initial amount of money Karissa already had before doing any repair jobs.

Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. This means that Karissa's business earns more money per repair job compared to Scooter's business per t-shirt sale.

b) To determine who had the better month, we need to calculate the total money earned by each individual based on the given sales/repairs.

For Scooter, with x = 20 (number of shirts sold):

f(x) = 200 + 15x

f(20) = 200 + 15 * 20

f(20) = 200 + 300

f(20) = 500

For Karissa, with x = 12 (number of repairs):

f(x) = 80 + 35x

f(12) = 80 + 35 * 12

f(12) = 80 + 420

f(12) = 500

Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.

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Explanation:

A = set of odd numbers = {1,3,5}

B = set of factors of 12 = {1,2,3,4,6}

A U B = union of set A and set B

A U B = {1,3,5} union {1,2,3,4,6}

A U B = {1,3,5,       1,2,3,4,6}

A U B = {1,2,3,4,5,6}

The set union operation combines two sets into one bigger set. Duplicates are tossed out.

There are 6 elements in the set A U B = {1,2,3,4,5,6} out of 6 faces of the number cube.

Therefore, the probability event  A U B happens is 6/6 = 1 = 100%; i.e. it is guaranteed to happen. Each face of the number cube is either odd, a factor of 12, or both.

Side notes:

The total number of equally-sized tiles on a circular floor.

Here, we are covering the region or the total space occupied by all the tiles on the floor.

Hence, the area is calculated.

Answer:

9.80

Step-by-step explanation:

U can get 9.80 manually by using fractions.

Answer:

yes this option is correct

Answer:

A. The stepwise selection procedure uses Adjusted R-square as the "best" model criterion.

Step-by-step explanation:

Stepwise regression is a model which uses variables in step by step manner. The procedure involves removal or inclusion of independent variables one by one. It adds the most significant independent variable and removes the less significant independent variable. Usually stepwise selection uses R-square or Mallows Cp for picking the best fit.

Answer:

A) If it is a triange, the figure has 3 sides.

Step-by-step explanation:

The first half or in this case, the thing is the conclusion statement

Answer:

B: A figure has three sides.

Step-by-step explanation:

The hypothesis is the first part of the conditional statement.

The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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Answer: (51ab^2)/(20c)

STEP

1

:

Equation at the end of step 1

 ((17•(a3))•(b2)) ((18•(b4))•(c3))

 ————————————————•————————————————

 ((15•(b3))•(c2))  ((23a2•b)•c2)  

STEP

2

:

Equation at the end of step

2

:

 ((17•(a3))•(b2)) ((2•32b4)•c3)

 ————————————————•—————————————

 ((15•(b3))•(c2))    23a2bc2  

STEP

3

:

           (2•32b4c3)

Simplify   ——————————

            23a2bc2  

Dividing exponential expressions :

3.1    b4 divided by b1 = b(4 - 1) = b3

Dividing exponential expressions :

3.2    c3 divided by c2 = c(3 - 2) = c1 = c

Dividing exponents:

3.3    21   divided by   23   = 2(1 - 3) = 2(-2) = 1/22

Equation at the end of step

3

:

 ((17•(a3))•(b2)) 9b3c

 ————————————————•————

 ((15•(b3))•(c2)) 4a2

STEP

4

:

Equation at the end of step

4

:

 ((17•(a3))•(b2)) 9b3c

 ————————————————•————

   ((3•5b3)•c2)   4a2

STEP

5

:

Equation at the end of step

5

:

 (17a3 • b2)   9b3c

 ——————————— • ————

  (3•5b3c2)    4a2

STEP

6

:

             17a3b2

Simplify   —————————

           (3•5b3c2)

Dividing exponential expressions :

6.1    b2 divided by b3 = b(2 - 3) = b(-1) = 1/b1 = 1/b

Equation at the end of step

6

:

  17a3   9b3c

 ————— • ————

 15bc2   4a2

STEP

7

:

Dividing exponential expressions :

7.1    a3 divided by a2 = a(3 - 2) = a1 = a

Dividing exponential expressions :

7.2    b3 divided by b1 = b(3 - 1) = b2

Dividing exponential expressions :

7.3    c1 divided by c2 = c(1 - 2) = c(-1) = 1/c1 = 1/c

Final result :

 51ab2

 —————

  20c

A) The algebraic expression will be 12d + 7 = 91

B) He drives 7 miles per day to work.

For 11 days straight, Ms. Chung drove the same distance every day going to and coming from work.

The distance she drove on Saturday was; 0.9 miles.

The number of miles she drives per day:

84 miles/12

= 7 miles per day

Let the number of miles she travels be day = d

12d + 7 = 91 miles

12d + 7 = 91

12d = 91 - 7

12d = 84

d = 84/12

d = 7 miles per day

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Answer:

Y = 4

Step-by-step explanation:

5x-y=54

50-y=54

circle y and subtract 50 from itself then subtract 50 from 54.

after subtracting you should have y=4