Eight less than the product of six and the difference of a number and two is twice the number. What is the number?

Answer:

  7 boxes

Step-by-step explanation:

The area of a rectangular prism is given by the formula ...

  A = 2(LW +H(L+W))

The amount of wallpaper Carmen needs for one box is found by computing the area of the box.

__

  A = 2(5·6 +7(5+6)) = 2(30 +7·11) = 2(107) = 214 . . . square feet

  Carmen will be using a total of 214x square feet of wallpaper to cover x boxes. She has 1498 ft² available, so can cover ...

  1498 ft²/(214 ft²/box) = 7 boxes

Carmen has enough wallpaper to cover 7 storage boxes.

Answer:

a) 513775.5 m^3  ≈ 51.38 * 10^4 m^3

b)  256887.75 m^3 ≈ 25.69 * 10^4 m^3

Step-by-step explanation:

Given data :

Depth of pond = 2m

flow in the stream = 20 cfs = 4.8931 * 10^4 m^3/day

settling rate = 0.2 m/day

rate constant ( k )= 0.2 / 2 = 0.1 / day

steady-state removal of the solids required = 65%

A) determine size of a single CSTR to achieve 65%

First determine the time required to achieve this using the relation below

C = \(c_{o} e^{-kt}\)

∴ t = \(\frac{-1}{k}* ln( 1 - 0.65 )\)

     = ( -1 / 0.1 ) * (- 1.05 ) = 10.5 day

The size of a single CSTR required = ( 4.8931*10^4 ) * (10.5 ) = 513775.5 m^3

B) determine the sizes of a pair of identical CSTRs in series needed to achieve the desired removal

sizes of a pair = 513775.5 / 2 = 256887.75 m^3

The value of the missing side lengths x and y are 5√2 and 5 respectively.

The figure in the image is a right triangle.

Angle θ = 45 degree

Hypotenuse = x

Opposite to angle θ = y

Adjacent to angle θ = 5

To solve for side x and side y, we use the trigonometric ratio.

Note that:

Cosine = adjacent / hypotenuse

tangent = opposite / adjacent

Solving for x:

Cosine = adjacent / hypotenuse

Plug in the values

cos( 45 ) = 5/x

x = 5 / cos( 45 )

x = 5√2

Solving for side y:

tangent = opposite / adjacent

Plug in the values

tan( 45 ) = y/5

y = tan( 45 ) × 5

y = 5

Therefore, the value of side length x is 5 units.

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The selling price of the house is approximately $110,516.97.

To calculate the selling price of the house, we need to consider the down payment and the monthly mortgage payments. We can use the formula for the present value of an ordinary annuity to calculate the mortgage payments and then add the down payment.

The formula for the present value of an ordinary annuity is:

PV = \(PMT × (1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value (selling price)

PMT = Monthly payment

r = Interest rate per period (monthly interest rate)

n = Total number of periods (number of months)

Given:

Down payment = $25,000

Monthly payment = $525

Interest rate = 7.8% per year (monthly interest rate = 7.8% / 12 / 100)

Number of periods = 30 years (30 years × 12 months per year)

Calculating the monthly interest rate:

Monthly interest rate = 7.8% / 12 / 100 = 0.0065

Calculating the number of periods:

Number of periods = 30 years × 12 months per year = 360 months

Calculating the present value (selling price):

PV = \(PMT × (1 - (1 + r)^(-n)) / r\)

PV = \(525 × (1 - (1 + 0.0065)^(-360)) / 0.0065\)

Now let's calculate the selling price:

PV = \(525 × (1 - (1 + 0.0065)^(-360)) / 0.0065\)

PV ≈ $110,516.97

Therefore, the selling price of the house is approximately $110,516.97.

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The two other positive angles of rotation that take A to B are 19π/6 and 31π/6.

The unit circle is rotationally symmetric, meaning that any angle of rotation on the unit circle will take a point to another point on the unit circle with the same distance from the origin. This means that if we rotate point A by 7π/6 radians, we can also rotate it by 19π/6 or 31π/6 radians and end up at the same point B.

The point A has polar coordinates (1, 0). This means that it is located at a distance of 1 unit from the origin and has an angle of 0 radians with the positive x-axis.

The point B has polar coordinates (√3/2, 1/2). This means that it is located at a distance of √3/2 units from the origin and has an angle of 7π/6 radians with the positive x-axis.

If we rotate point A by 19π/6 radians, we get a point with polar coordinates (√3/2, -1/2). This point is located at the same distance from the origin as point B and has the same angle with the positive x-axis.

Therefore, the two other positive angles of rotation that take A to B are 19π/6 and 31π/6.

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The Area of Composite figure is 131cm² we can find it by dividing the figure in two parts.

Rectangle is a plane which one side is long and other side is short and and all angle between these sides are 90° and opposite sides are parallel to each other.

We can divide this figure in two part Rectangle and Triangle.

The Rectangle having length = 10 cm and breadth = 5 cm.

Whereas, Triangle have sides having length 6cm (Base) and 3 cm (Perpendicular).

\(Area\ of\ Rectangle = Length (l) * Breadth (b)\)

= 10 x 5 cm²

= 50 cm².

\(Area\ of\ Triangle =\frac{1}{2} *b*h\)

For this we have to find third side,

\(Third\ Side = \sqrt{(First\ Side)^{2} +(Second\ Side)^{2} }\) ( Using Pythagoras Theorem)

\(Third\ Side = \sqrt{(6)^{2} +(3)^{2} }\)

Third Side = 6.7 cm

\(s= \frac{a + b + c}{2}\) , where a, b, c are three sides

\(= \frac{6.7 + 6 +3}{2}\)

= 7.85 cm.

Now we use Heron's formula to find the area of triangle,

Area of Triangle = \(\sqrt{s\ (s-a)\ (s-b)(\ s-c)}\)\(=\sqrt{7.85\ (7.85-6.7)\ (7.85-6)\ (7.86-3)}\)

= 81 cm²

So the Area of Composite figure = (50 + 81) cm²

= 131 cm²

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A. The solution to the system of equations is x = 1/2, y = -1.

B. The solution to the system of equations is x = 1/2, y = -1.

C. The solution to the system of equations is x = 215/81, y = -175/81.

D. The solution to the system of equations is x = 215/81, y = -175/81.

A. To solve the system of linear equations:

3x - y = -11 ... (1)

-x + y = 5 ... (2)

Add equations (1) and (2) to eliminate y:

2x = -6

x = -3

Substitute x = -3 into equation (2) to solve for y:

-(-3) + y = 5

y = 8

Therefore, the solution to the system of equations is x = -3, y = 8.

To check the solution, substitute x = -3 and y = 8 into both equations and verify that they are true:

3(-3) - 8 = -11

-(-3) + 8 = 5

Both equations are true, so the solution is correct.

B. To solve the system of linear equations:

-2y + 3 = 4x + 2 ... (1)

6x + 4y = 1 ... (2)

Simplify equation (1) by subtracting 3 from both sides and dividing by 4:

-2y = 4x - 1

y = -2x + 1/2

Substitute y = -2x + 1/2 into equation (2) and solve for x:

6x + 4(-2x + 1/2) = 1

-2x + 2 = 1

-2x = -1

x = 1/2

Substitute x = 1/2 into equation (1) to solve for y:

-2y + 3 = 4(1/2) + 2

-2y + 3 = 5

-2y = 2

y = -1

Therefore, the solution to the system of equations is x = 1/2, y = -1.

To check the solution, substitute x = 1/2 and y = -1 into both equations and verify that they are true:

-2(-1) + 3 = 4(1/2) + 2

6(1/2) + 4(-1) = 1

Both equations are true, so the solution is correct.

C. To solve the system of linear equations:

32y - x = -25 ... (1)

5x = 100 + x - 8y ... (2)

Simplify equation (2) by combining like terms:

4x + 8y = 100

Divide both sides of equation (1) by -1:

x - 32y = 25

Add equations (1) and (2) to eliminate x:

5x - 32y = 75

Substitute the simplified equation (2) into the above equation to solve for y:

5(4x + 8y) - 32y = 75

20x + 8y = 75

y = (75 - 20x)/8

Substitute the above value of y into equation (1) to solve for x:

32[(75 - 20x)/8] - x = -25

240 - 80x - x = -25

-81x = -215

x = 215/81

Substitute x = 215/81 into the equation for y:

y = (75 - 20(215/81))/8

y = -175/81

Therefore, the solution to the system of equations is x = 215/81,

y = -175/81.

To check the solution, substitute x = 215/81 and y = -175/81 into both equations.

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Answer:

yea we can't click on the link

Step-by-step explanation:

you need to put it on again

A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.

In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.

A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.

Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.

Option A: 200 respondents

This represents only 1% of the population.

While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.

Option B: 20 respondents

This represents only 0.1% of the population.

With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.

Option C: 2000 respondents

This represents 10% of the population.

While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.

The study may provide reasonably reliable results, but there is room for potential sampling error.

Option D: 2 respondents

This represents an extremely small sample size, accounting for only 0.01% of the population.

With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.

Based on the options provided, option C with 2000 respondents would be the most reliable study.

Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.

However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.

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Answer:

∠ W = 53°

Step-by-step explanation:

the measure of the secant- secant angle W is half the difference of the measures of the intercepted arcs , that is

∠ W = \(\frac{1}{2}\) (YC - GT) = \(\frac{1}{2}\) (160 - 54)° = \(\frac{1}{2}\) × 106° = 53°

Answer:

inequality form: u≥−5

Interval Notation: [−5,∞)

Answer:

False

Step-by-step explanation:

The linear function can assume a constant value (where slope is 0), meaning it is neither increasing nor decreasing.

Answer:

0.85083 ; 0.83147 ; 0.6823 ; 0.015386

Step-by-step explanation:

Given that:

σ = 25

μ = 86

(a) x is more than 60

P(x > 60)

obtain standardized score (Zscore)

Zscore = (x - μ) / σ

Z = (60 - 86) /25

Z = - 1.04

P(Z > - 1.04) = 0.85083 (Z probability calculator)

(b) x is less than 110

P(x < 110)

obtain standardized score (Zscore)

Zscore = (x - μ) / σ

Z = (110 - 86) /25

Z = 0.96

P(Z < 0.96) = 0.83147 (Z probability calculator)

(c) x is between 60 and 110

P(x < 110) - P(x < 60)

P(Z < 0.96) - P(Z < - 1.04)

0.83147 - 0.14917

= 0.6823

(d) x is greater than 140

P(x > 140)

obtain standardized score (Zscore)

Zscore = (x - μ) / σ

Z = (140 - 86) /25

Z = 2.16

P(Z > 2.16) = 0.015386 (Z probability calculator)

The truck driver would deliver 105 packages in a 7 hours day

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Let y represent the number of packages delivered by the truck driver in x hours. Using the point (1, 15) and (4, 60). Hence, the equation is:

y - 15 = [(60-15)/(4-1)](x - 1)

y = 15x

For a 7 hour day (x = 7):

y = 15(7) = 105

The driver would deliver 105 packages in 7 hours

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Answer: The probability of Anita Bath getting a purple tulip on the first pick is 7/28 (since there are 7 purple tulips out of 28 total flowers in the bouquet). After the first pick, there are 27 flowers left in the bouquet, including 6 purple tulips.

The probability of Lois Price getting a purple tulip on the second pick, given that Anita Bath has already received a purple tulip, is 6/27. This is because there are 6 purple tulips left in the bouquet out of 27 flowers in total (since one purple tulip has already been removed).

Therefore, the probability of both Anita Bath and Lois Price getting a purple tulip is:

(7/28) * (6/27) = 42/756 = 7/126

So the probability that both Anita and Lois get a purple tulip is 7/126.

The approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

To solve the equation 1/x-1 = |x-2| using three iterations of successive approximation, we will start with an initial guess and refine it using an iterative process.

Given that the equation involves absolute value, we will consider two cases:

Case 1: x - 2 ≥ 0

In this case, |x-2| simplifies to x-2, and the equation becomes 1/(x-1) = x-2.

Case 2: x - 2 < 0

In this case, |x-2| simplifies to -(x-2), and the equation becomes 1/(x-1) = -(x-2).

Now, let's perform the successive approximation:

Iteration 1:

Let's start with an initial guess, x = 2.

Case 1: When x - 2 ≥ 0,

1/(2-1) = 2-2,

1/1 = 0,

which is not true.

Case 2: When x - 2 < 0,

1/(2-1) = -(2-2),

1/1 = 0,

which is not true.

Since our initial guess did not satisfy the equation in either case, we need to choose a different initial guess.

Iteration 2:

Let's try x = 3.

Case 1: When x - 2 ≥ 0,

1/(3-1) = 3-2,

1/2 = 1,

which is not true.

Case 2: When x - 2 < 0,

1/(3-1) = -(3-2),

1/2 = -1,

which is not true.

Again, our guess did not satisfy the equation in either case.

Iteration 3:

Let's try x = 2.5.

Case 1: When x - 2 ≥ 0,

1/(2.5-1) = 2.5-2,

1/1.5 = 0.5,

which is true.

Case 2: When x - 2 < 0,

1/(2.5-1) = -(2.5-2),

1/1.5 = -0.5,

which is not true.

Our guess of x = 2.5 satisfies the equation in Case 1.

Therefore, the approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

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Answer:

1.6726

Step-by-step explanation:

square each standard deviation, add them then squareroot.

\(\rm SD = 1.6726\)

Step-by-step explanation:

Given :

Stroke Category                  Time                    Standard Deviation

   Backstroke                    55.6 sec                         0.70 sec

   Breaststroke                  63.3 sec                         0.92 sec

   Butterfly                         54.4 sec                         0.94 sec

   Freestyle                        50.2 sec                         0.76 sec

Calculation :

To find the standard deviation of the sum of the 4 random variables we need to square each of the standard deviation and add them and then take the square root.

\(\rm SD = \sqrt{(0.70^2)+(0.92^2)+(0.94^2)+(0.76^2)}\)

\(\rm SD = \sqrt{2.7976}\)

\(\rm SD = 1.6726\)

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The ratio of the sides EF/LM after the transformation is 1/8

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Dilation is the increase or decrease in size of a figure by a factor while translation is the movement of a point up, down, left or right.

Given the tansformation:

Hence:

LM = 8 * EF

EF/LM = 1/8

The ratio of the sides EF/LM after the transformation is 1/8

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Based on the information, it should be noted that the reduced ratio of trucks to motorcycles is 9:4.

For the ratio of trucks to cars:

Multiply both sides of the ratio by 9 to make the denominator 36.

9 × 9: 4 × 9

81:36

For the ratio of cars to motorcycles:

Multiply both sides of the ratio by 4 to make the denominator 36.

7 × 4: 9 × 4

28:36

Now we have the ratios as follows:

Trucks to cars: 81:36

Cars to motorcycles: 28:36

Finally, to find the reduced ratio of trucks to motorcycles, we can directly compare the number of trucks to the number of motorcycles.

Trucks to motorcycles: 81:36

Dividing both sides by 9, we get:

81 ÷ 9: 36 ÷ 9

9:4

Therefore, the reduced ratio of trucks to motorcycles is 9:4.

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The ratio of trucks to cars is 9:4. The ratio of cars to motorcycles is 7:9. What is the reduced ratio of trucks to motorcycles?

Answer:

300-20w=?

150+10w=?

Step-by-step explanation:

Answer:

Step-by-step explanation:

320

The probability of Miguel selecting a tile number less than 3 from each bag -1 is 1/5 and bag-2 is 2/5.

The given tiles in bag-1 = {2, 4, 5, 8, 9}

Total number of tiles in bag-1 = 5

The number of tiles less than number 3 in the bag - 1 = 1

The probability of Miguel selecting a tile number less than 3 =

number of tiles less than 3 / total number of tiles = 1/3

The given tiles in bag-2 = {0, 1, 3, 6, 7}

Total number of tiles in bag-2 = 5

The number of tiles less than number 3 in the bag-2 = 2

The probability of Miguel selecting a tile number less than 3 =

number of tiles less than 3 / total number of tiles = 2/3

From the above analysis, we solved the problem.

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The probability of getting at least 6 heads is3/256 or 0.0117

Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution.

Probability is a measure of how likely something is to occur. Calculating probability involves dividing the total number of outcomes by the number of possible ways an event may occur.

Given that,

A fair coin is tossed = 8 time.

We have to find the probability of getting at least 6 heads.

Since, the probability of getting head, when one coin is tossed = 1/2

And the probability of getting tale = 1/2  

The probability of getting head at least  6 times when coin is tossed 8 times can be given as,

The head can come 6 times, then probability = \((1/2)\x^{6} (1/2)\x^{2}\) =  (1/2)⁸

The head can come 7 times, then probability = (1/2)⁷(1/2) = (1/2)⁸

The head can come 8 times, then probability = (1/2)⁸

The probability of getting head at least 6 times

= (1/2)⁸ + (1/2)⁸ +  (1/2)⁸ = 3(1/2)⁸ = 3/256 = 0.0117

The probability of getting at least 6 heads is3/256 or 0.0117

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Answer:

2.5 components but if you need to round 2

Answer:  

150 per 60 mins would be 2.5 per 1 min

Step-by-step explanation:

150/60 = 2.5

Answer:

z = 7.5

Step-by-step explanation:

Polygon ABCD and polygon EFGH are similar, therefore, their sides would be proportional to each other. This means the ratio of their corresponding sides would be equal to each other.

BC corresponds to FG

CD corresponds to GH

Therefore:

8/6 = 10/z

4/3 = 10/z

Cross multiply

4*z = 10*3

4z = 30

4z/4 = 30/4

z = 7.5

Answer:

3 in 730500

tens of thousands

3 in 73050

thousands

Answer:

10 times

Step-by-step explanation:

the value of the digit 3 in 730,500 is 10 times the value of the digit 3 in 73,050

730,500 (digit 3) = 30,000

73,050 (digit 3) = 3,000

30,000/3,000 = 10

Answer:

26

Step-by-step explanation: