given the continuous time unit step function u(t), provide sketches for each of the following, you should show a few points on the plot to help verify your result. remember to mark the scales
a. u(t-a) a>0
b. u(t+a) a>0
c. u(-t)
d. u(-t-a) a>0
e. u(-t+a) a>0
f. g(t) = u(t) - u(t-5)

The estimated current total cost for the installed and insulated tank is $12,065.73.

The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:

surface_area = 2 * pi * r * h + 2 * pi * r^2

where:

r is the radius of the cylinder

h is the height of the cylinder

In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:

surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586

The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:

surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293

The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:

cost = 6.806032934459293 * (40 + 95) = $1,165.73

The original cost of the tank was $10,900, so the total cost of the insulated tank is:

cost = 10900 + 1165.73 = $12,065.73

Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.

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Answer:

3(13x-5)

Step-by-step explanation:

first step open your bracket,u have

=4x²+20x-3x-15-4x²+22x then collect like terms

=4x²-4x²+20x-3x+22x-15

=0x²+39x-15

=39x-15

further simplifying u have:

=3(13x-5)

The solution to each of the question takes different approach, as the questions are taken from different concepts; however, a common operation among all questions, is factorization.

\((1)\ (-xy)^3(xz)\)

Expand

\((-xy)^3(xz) = (-x)^3* y^3*(xz)\)

\((-xy)^3(xz) = -x^3* y^3*xz\)

Rewrite as:

\((-xy)^3(xz) = -x^3*x* y^3*z\)

Apply law of indices

\((-xy)^3(xz) = -x^4y^3z\)

\((2)\ (\frac{1}{3}mn^{-4})^2\)

Expand

\((\frac{1}{3}mn^{-4})^2 =(\frac{1}{3})^2m^2n^{-4*2}\)

\((\frac{1}{3}mn^{-4})^2 =\frac{1}{9}m^2n^{-8\)

\((3)\ (\frac{1}{5x^4})^{-2}\)

Apply negative power rule of indices

\((\frac{1}{5x^4})^{-2}= (5x^4)^2\)

Expand

\((\frac{1}{5x^4})^{-2}= 5^2x^{4*2}\)

\((\frac{1}{5x^4})^{-2}= 25x^{8\)

\((4)\ -x(2x^2 - 4x) - 6x^2\)

Expand

\(-x(2x^2 - 4x) - 6x^2 = -2x^3 + 4x^2 - 6x^2\)

Evaluate like terms

\(-x(2x^2 - 4x) - 6x^2 = -2x^3 -2x^2\)

Factor out x^2

\(-x(2x^2 - 4x) - 6x^2 = (-2x-2)x^2\)

Factor out -2

\(-x(2x^2 - 4x) - 6x^2 = -2(x+1)x^2\)

\((5)\ \sqrt{\frac{4y}{3y^2}}\)

Divide by y

\(\sqrt{\frac{4y}{3y^2}} = \sqrt{\frac{4}{3y}}\)

Split

\(\sqrt{\frac{4y}{3y^2}} = \frac{\sqrt{4}}{\sqrt{3y}}\)

\(\sqrt{\frac{4y}{3y^2}} = \frac{2}{\sqrt{3y}}\)

Rationalize

\(\sqrt{\frac{4y}{3y^2}} = \frac{2}{\sqrt{3y}} * \frac{\sqrt{3y}}{\sqrt{3y}}\)

\(\sqrt{\frac{4y}{3y^2}} = \frac{2\sqrt{3y}}{3y}\)

\((6)\ \frac{8}{3 + \sqrt 3}\)

Rationalize

\(\frac{8}{3 + \sqrt 3} = \frac{3 - \sqrt 3}{3 - \sqrt 3}\)

\(\frac{8}{3 + \sqrt 3} = \frac{8(3 - \sqrt 3)}{(3 + \sqrt 3)(3 - \sqrt 3)}\)

Apply difference of two squares to the denominator

\(\frac{8}{3 + \sqrt 3} = \frac{8(3 - \sqrt 3)}{3^2 - (\sqrt 3)^2}\)

\(\frac{8}{3 + \sqrt 3} = \frac{8(3 - \sqrt 3)}{9 - 3}\)

\(\frac{8}{3 + \sqrt 3} = \frac{8(3 - \sqrt 3)}{6}\)

Simplify

\(\frac{8}{3 + \sqrt 3} = \frac{4(3 - \sqrt 3)}{3}\)

\((7)\ \sqrt{40} - \sqrt{10} + \sqrt{90}\)

Expand

\(\sqrt{40} - \sqrt{10} + \sqrt{90} =\sqrt{4*10} - \sqrt{10} + \sqrt{9*10}\)

Split

\(\sqrt{40} - \sqrt{10} + \sqrt{90} =\sqrt{4}*\sqrt{10} - \sqrt{10} + \sqrt{9}*\sqrt{10}\)

Evaluate all roots

\(\sqrt{40} - \sqrt{10} + \sqrt{90} =2*\sqrt{10} - \sqrt{10} + 3*\sqrt{10}\)

\(\sqrt{40} - \sqrt{10} + \sqrt{90} =2\sqrt{10} - \sqrt{10} + 3\sqrt{10}\)

\(\sqrt{40} - \sqrt{10} + \sqrt{90} =4\sqrt{10}\)

\((8)\ \frac{r^2 + r - 6}{r^2 + 4r -12}\)

Expand

\(\frac{r^2 + r - 6}{r^2 + 4r -12}=\frac{r^2 + 3r-2r - 6}{r^2 + 6r-2r -12}\)

Factorize each

\(\frac{r^2 + r - 6}{r^2 + 4r -12}=\frac{r(r + 3)-2(r + 3)}{r(r + 6)-2(r +6)}\)

Factor out (r+3) in the numerator and (r + 6) in the denominator

\(\frac{r^2 + r - 6}{r^2 + 4r -12}=\frac{(r -2)(r + 3)}{(r - 2)(r +6)}\)

Cancel out r - 2

\(\frac{r^2 + r - 6}{r^2 + 4r -12}=\frac{r + 3}{r +6}\)

\((9)\ \frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14}\)

Cancel out x

\(\frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14} = \frac{4x + 8}{x} \cdot \frac{1}{x^2 - 5x - 14}\)

Expand the numerator of the 2nd fraction

\(\frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14} = \frac{4x + 8}{x} \cdot \frac{1}{x^2 - 7x+2x - 14}\)

Factorize

\(\frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14} = \frac{4x + 8}{x} \cdot \frac{1}{x(x - 7)+2(x - 7)}\)

Factor out x - 7

\(\frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14} = \frac{4x + 8}{x} \cdot \frac{1}{(x + 2)(x - 7)}\)

Factor out 4 from 4x + 8

\(\frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14} = \frac{4(x + 2)}{x} \cdot \frac{1}{(x + 2)(x - 7)}\)

Cancel out x + 2

\(\frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14} = \frac{4}{x} \cdot \frac{1}{(x - 7)}\)

\(\frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14} = \frac{4}{x(x - 7)}\)

\((10)\ (3x^3 + 15x^2 -21x) \div 3x\)

Factorize

\((3x^3 + 15x^2 -21x) \div 3x = 3x(x^2 + 5x -7) \div 3x\)

Cancel out 3x

\((3x^3 + 15x^2 -21x) \div 3x = x^2 + 5x -7\)

\((11)\ \frac{m}{6m + 6} - \frac{1}{m+1}\)

Take LCM

\(\frac{m}{6m + 6} - \frac{1}{m+1} = \frac{m(m + 1) - 1(6m + 6)}{(6m + 6)(m + 1)}\)

Expand

\(\frac{m}{6m + 6} - \frac{1}{m+1} = \frac{m^2 + m- 6m - 6}{(6m + 6)(m + 1)}\)

\(\frac{m}{6m + 6} - \frac{1}{m+1} = \frac{m^2 - 5m - 6}{(6m + 6)(m + 1)}\)

\((12)\ \frac{\frac{1}{y - 3}}{\frac{2}{y^2 - 9}}\)

Rewrite as:

\(\frac{\frac{1}{y - 3}}{\frac{2}{y^2 - 9}} = \frac{1}{y - 3} \div \frac{2}{y^2 - 9}\)

Express as multiplication

\(\frac{\frac{1}{y - 3}}{\frac{2}{y^2 - 9}} = \frac{1}{y - 3} * \frac{y^2 - 9}{2}\)

Express y^2 - 9 as y^2 - 3^2

\(\frac{\frac{1}{y - 3}}{\frac{2}{y^2 - 9}} = \frac{1}{y - 3} * \frac{y^2 - 3^2}{2}\)

Express as difference of two squares

\(\frac{\frac{1}{y - 3}}{\frac{2}{y^2 - 9}} = \frac{1}{y - 3} * \frac{(y - 3)(y+3)}{2}\)

\(\frac{\frac{1}{y - 3}}{\frac{2}{y^2 - 9}} = \frac{1}{1} * \frac{(y+3)}{2}\)

\(\frac{\frac{1}{y - 3}}{\frac{2}{y^2 - 9}} = \frac{y+3}{2}\)

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Answer:

58 iPads

Step-by-step explanation:

To calculate how many iPads are needed for 145 students, we can use the given ratio of 2 iPads for every 5 students.

First, find out how many groups of 5 students are in 145 students by dividing 145 by 5:

\(\sf \dfrac{145\; students}{5\; students/group} = 29\;groups\; of \;5 \;students\)

Now, for each group of 5 students, we need 2 iPads. So, multiply the number of groups of 5 students by 2 to find the total number of iPads needed:

\(\sf 29 \;groups \times2\; iPads/group = 58\; iPads\)

Therefore, 58 iPads are needed for 145 students.

solution:

1€=1.50

$x=€40

By using chain rule

1 × x =1.50×40

so,x=60

Hence,60 Australian $ can be exchanged from €1.5

The number of students whose favorite color is blue will be 40 students is the best prediction of the favorite colors by the 120 students based on the survey results given.

Here are the reasons why the other options are incorrect as follows: The number of students whose favorite color is green will be 12 more than the number of students who choose purple as their favorite color:

This statement cannot be a good prediction of the 120 students' favorite color.

It is possible that only two students chose purple, so if only two students choose purple as their favorite color, then the number of students whose favorite color is green would be 14, which does not make sense.

The number of students whose favorite color is red will be twice the number of students who choose purple as their favorite color:

This statement cannot be the best prediction of the 120 students' favorite color.

Even though 4 students chose red as their favorite color, only two students chose purple as their favorite color.

If the statement were accurate, then the number of students who chose red as their favorite color would be 4 × 2 = 8, which does not seem like a reasonable prediction.

The number of students whose favorite color is blue will be 12 less than the number of students who choose green: The statement cannot be the best prediction of the 120 students' favorite color.

Because according to the survey results, 8 students choose blue, but if this statement were accurate, the number of students who choose green would be 8 + 12 = 20.

This implies that the total number of students who choose blue is 20 - 12 = 8 students.

This is contradictory because the number of students who choose  is already given in the survey results. Therefore, this statement cannot be the best prediction.

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Answer:

42$

Step-by-step explanation:

you literally multiply 6 by 7 and it gives you 42 but i really hope this helped you

6 x 7 = 42

limx→[infinity] (√(x^3 - 5x + 2)) / ((1 + 4x) / (2 + 3x^3)) = undefined.

To evaluate the limit, we can simplify the expression and apply limit properties. Here's the step-by-step evaluation:

limx→[infinity] (√(x^3 - 5x + 2)) / ((1 + 4x) / (2 + 3x^3))

Step 1: Simplify the expression inside the square root:

limx→[infinity] (√(x^3 - 5x + 2)) / ((1 + 4x) / (2 + 3x^3))

= limx→[infinity] (√(x^3(1 - 5/x^2 + 2/x^3))) / ((1 + 4x) / (2 + 3x^3))

= limx→[infinity] (√(x^3)√(1 - 5/x^2 + 2/x^3)) / ((1 + 4x) / (2 + 3x^3))

= limx→[infinity] (x√(1 - 5/x^2 + 2/x^3)) / ((1 + 4x) / (2 + 3x^3))

Step 2: Divide every term by the highest power of x in the denominator:

limx→[infinity] (x/x^3)√(1 - 5/x^2 + 2/x^3) / ((1/x^3 + 4/x^2) / (2/x^3 + 3))

= limx→[infinity] (√(1 - 5/x^2 + 2/x^3)) / ((1/x^2 + 4/x^3) / (2/x^3 + 3))

Step 3: Take the limit individually for each part of the expression:

a. For the square root term:

limx→[infinity] √(1 - 5/x^2 + 2/x^3) = √(1 - 0 + 0) = 1

b. For the fraction term:

limx→[infinity] ((1/x^2 + 4/x^3) / (2/x^3 + 3))

= (0 + 0) / (0 + 3) = 0

Step 4: Multiply the results from Step 3:

limx→[infinity] (√(1 - 5/x^2 + 2/x^3)) / ((1/x^2 + 4/x^3) / (2/x^3 + 3))

= 1 / 0

Since the denominator approaches zero and the numerator approaches a non-zero value, the limit is undefined.

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The cubic meters of water needed to return the water level to its normal depth is 495 cubic meters or 495 000 liters or 130, 765 gallons. It will take 36 hours 20 minutes to fill the water at average of 60 gallons/minute and 46 lb the chemical is needed.

Based on the provided data, the fish hatchery is shaped like a rectangle with measurements, Length = 61 meters; Width = 35.5 meters; and Height = 4 meters. Volume of rectangle is given by:

Volume = Length*Width* Height

As 9 inches of water is added to bring the level of water up to normal level, the cubic meters of water needed to return the water level to its normal depth is the volume of water added.  The length and width is the same as for fish hatchery, and 9 inches of water is added,

Height = 9 inches = 0.2286 (1 meter = 39.37 inches)

Volume = 61*35.5*0.2286 = 495 cubic meters

This volume in liters is 495 000 liters (1 cubic meters = 1000 liter) and in gallons is 130, 765 gallons (1 cubic meters = 264.172 gallons)

The high-speed hose fills at an average of 60 gallons/minute, the hose must be run for 130, 765/60 = 2179.42 minutes = 36 hours 20 minutes.

Converting the dimensions of the pool to feet and finding the volume in cubic feet, as 1 meter = 3.28 feet, Length = 61 meters = 200.13 feet; Width = 35.5 meters = 116.47 feet; and Height = 4 meters = 13.12 feet. Hence, the volume = 200.13*116.47*13.12 = 305,815.93 cubic feet

As treatment of 1.5 lbs of chemical per 10,000 cubic feet of water is added, pounds of the chemical needed = (305,815.93/10,000)*1.5 = 45.87 lb ≈ 46 lb.

Note: The question is incomplete. The complete question probably is: The State conservation department has a constructed a large fish hatchery. It is shaped like a rectangle and measures approximately 35.5 meters wide, 61 meters long, and the water level is normally 4 meters deep. During the care of the fish, the water depth varies, and one day the manager asks you to add 9 inches of water to the depth of the hatchery to bring it up to normal level using a high-speed hose that fills at an average rate of 60 gallons/minute. After you complete that task, the manager wants you to add a treatment of 1.5 lbs of chemical per 10,000 cubic feet of water. How many cubic meters of water will you need to add to return the water level to its normal depth? How many liters is this? How many gallons is this?  How long will you need to run the hose? Express your answer in hours and minutes. Once the task is finally completed, you are to add a treatment of 1.5 pounds of chemical per 10,000 cubic feet of water. Convert the dimensions of the pool to feet and find the volume in cubic feet.. How many pounds of the chemical will you need to add to the hatchery to perform the treatment? Round to the nearest pound.

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There must be at least one student in the class with a final assessment score of 80 or higher in order to achieve an average score of exactly 80.

To prove this statement by contradiction, let's assume that no student in the class has a final assessment score of 80 or higher. This means that all 48 students have scores strictly below 80. In order for the average score to be exactly 80, the sum of all scores must be a multiple of 48.

Let's consider the worst-case scenario, where each student has a score of 79. In this case, the sum of all scores would be 48 * 79 = 3792, which is not a multiple of 48. However, since the average score is presented as an integer, the sum of scores must be a multiple of 48.

This contradiction shows that our initial assumption was incorrect. Therefore, there must be at least one student in the class with a final assessment score of 80 or higher in order to achieve an average score of exactly 80.

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Barbara's speed in nice weather is 55 mph,

and her speed in the thunderstorm is 30 mph.

Here, we have,

Let's denote Barbara's speed in clear weather as "x mph."

Given that she drives $55 {mi}$ in clear weather, the time it takes her to cover this distance is given by:

Time in clear weather = Distance / Speed = 55 / x hours

Since she encounters a thunderstorm for the last $45 {mi}$, her speed through the thunderstorm is "x - 25 mph."

The time it takes her to cover this distance is given by:

Time in thunderstorm = Distance / Speed = 45 / (x - 25) hours

The total time for the trip is given as $2.5 {hr}$:

Total time = Time in clear weather + Time in thunderstorm

2.5 = 55 / x + 45 / (x - 25)

To solve this equation, we can multiply through by x(x - 25) to eliminate the denominators:

2.5x(x - 25) = 55(x - 25) + 45x

Expanding and simplifying:

2.5x² - 62.5x = 55x - 1375 + 45x

2.5x²- 162.5x + 1375 = 0

Now we can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Plugging in the values a = 2.5, b = -162.5, and c = 1375:

x = (-(-162.5) ± √((-162.5)² - 4 * 2.5 * 1375)) / (2 * 2.5)

Simplifying:

x = (162.5 ± √(26406.25 - 13750)) / 5

x = (162.5 ± √12656.25) / 5

x = (162.5 ± 112.5) / 5

This gives us two possible values for x:

x₁ = (162.5 + 112.5) / 5 = 275 / 5 = 55 mph

x₂ = (162.5 - 112.5) / 5 = 50 / 5 = 10 mph

Since Barbara's speed cannot be 10 mph (which would imply driving at a negative speed through the thunderstorm), the only valid solution is x = 55 mph.

Therefore, Barbara's speed in nice weather is 55 mph, and her speed in the thunderstorm is 55 - 25 = 30 mph.

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Answer: 18-22

Step-by-step explanation:

I believe it is A and Yes

The bigger the price is on an item, the more tax you would have to pay, so both numbers increase. As for whether or not there is a line through the dots, you use a line when you could go inbetween the points. For example, with this question you can have 0.24, 0.86, or any other number as the price and it would make sense. If the question was sales tax on a certain number of shirts, well, you can't buy half a shirt so you don't need anywhere inbetween the dots.

Proportional in these kinds of problems means whether or not the line curves. If it doesn't and is a straight line, then it is proportional.

Answer:

15 * 15 * 15 = 3375

Step-by-step explanation:

Volume of a cube = (side) * (side)* (side)

Answer:3375

Step-by-step explanation:I was gonna give an explanation but they got to it before me..

The length of the side a = 9.43 cm and b = 12.04 cm

Consider the first triangle

The hypotenuse of the triangle = a

The base of the triangle = 5 cm

The length of the vertical side = 8 cm

Apply the Pythagorean theorem here

\(a= \sqrt{8^2+5^2}\)

Find the square of the terms

a = \(\sqrt{64+25}\)

a = \(\sqrt{89}\)

a = 9.43 cm

Consider the second triangle

The hypotenuse of the triangle = 17 cm

The base of the triangle = 12 cm

The length of vertical side = y cm

Apply the Pythagorean theorem

b = \(\sqrt{17^2-12^2}\)

b = \(\sqrt{289-144}\)

b = \(\sqrt{145}\)

b = 12.04 cm

Hence, the length of the side a = 9.43 cm and b = 12.04 cm

The complete question is

Work out the lengths of sides a and b give your answer to the 1st decimal

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Implement the bitImpl y (x, y) function using only the logical operators, i.e., | and ~. The function takes two integers as input and returns an integer. The output integer is equal to the bitwise logical IMPLY of the input integers.

Bitwise logical operations are used to perform logical operations on binary numbers. The bitwise logical IMPLY operation returns true if A implies B, i.e., A -> B. It can be calculated using the following truth table: A B | (A -> B)0 0 | 10 1 | 11 0 | 01 1 | 1The bitImply(x, y)

Function can be implemented using only the | and ~ operators as follows: `return ~x | y;` The expression `~x` flips all the bits of x and the expression `~x | y` performs the logical OR operation between the inverted x and y. The final output is the bitwise logical IMPLY of x and y. The function requires a maximum of 8 operators to perform the operation.

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Answer:

a. A testable prediction about the relationship between variables

Step-by-step explanation:

A hypothesis is the FIRST step in conducting research or experimenting. In other terms, a scientific guess based on limited knowledge. Contrary to our hypothesis, conclusion comes last in researching and states the summary of the information gathered.

The reason why it isn't letter D is because a hypothesis's provability can only be determined once you have your conclusion, which is after you have conducted a research or experiment.

The letters B and C are too unrelated to what an hypothesis is.

- 8th grade student :)) (also buried under her own mountain of assignments and activities)

1. The linear equation is T = 20 + 15W, where W is the weight of the chicken in kg.

2. The cooking time is 1 hour and 5 minutes.

3. The weight of the chicken is 6.67 kg.

1. The formula to calculate the time taken (T) to cook a full chicken would be:

T = 20 + 15W, where W is the weight of the chicken in kg.

2. If the weight of the chicken is 3kg, then the time taken to cook the chicken would be:

T = 20 + 15(3) = 65 minutes

Converting 65 minutes to hours and minutes, we have 1 hour and 5 minutes.

3. Let's say the weight of the chicken is W kg. Then, the time taken to cook the chicken would be:

T = 20 + 15W

We also know that it took 120 minutes to prepare and cook the chicken. So, we can write:

120 = 20 + 15W

15W = 100

W = 100/15 kg (rounded to two decimal places)

Therefore, the weight of the chicken is approximately 6.66666666667

kg.

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Answer:

10

Step-by-step explanation:

y intercept is found when x is zero so we set x to zero

y=3^0+9

y=1+9

y=10

hopes this helps

Answer: 10

Step-by-step explanation:

The y-intercept of a graph is when x=0 because it is on the y-axis. TO do this, we can plug x=0 Into the equation and find y.

\(y=3^0+9\)        [exponent]

\(y=1+9\)          [add]

\(y=10\)

Therefore, the y-coordinate is 10.

10. 87 is higher than 44 automatically making us round up

Answer: she can run \(6\dfrac54\) mile sin 1 hour.

Step-by-step explanation:

Given : Distance run by Jasmine in \(\dfrac23\) of an hour = \(4\dfrac56\text{ miles}=\dfrac{24+5}{6}\text{ miles}\)

\(=\dfrac{29}{6}\) miles

Distance run by Jasmine in 1 hour = \(\dfrac{29}{6}\times\dfrac{3}{2}=\dfrac{29}{4}\) miles.

\(=6\dfrac{5}{4}\)   miles.

Hence, she can run \(6\dfrac54\) mile sin 1 hour.

Answer:

No.

Step-by-step explanation:

This only applies to solids like cubes and some prisms.

It does not apply to such solids are cylinders, pyramids, cones and triangular prisms.  It will apply to a prism whose cross-section is a rectangle.

56 - 14 = 42

42/3 = 14

W = 14

Answer:

w = 14

Step-by-step explanation:

56 = 3w + 14

-14            -14

----------------------

42 = 3w

÷3       ÷3

----------------

14 = w

To evaluate the expression [2−||−23−2(−15)||]÷(−13), we need to follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).

First, let's simplify the absolute value:

||−23−2(−15)|| = ||−23+30|| = ||7|| = 7

Next, let's substitute this simplified value back into the original expression:

[2−7]÷(−13)

Now, we can simplify the expression further:

2−7 = −5

Finally, divide −5 by (−13):

−5÷(−13) = 5/13

Therefore, the value of the expression is 5/13.

The value of the expression:

[2−||−23−2(−15)||]÷(−13) is 5/13.

To evaluate the given expression [2−||−23−2(−15)||]÷(−13), we start by simplifying the absolute value within the expression. We substitute the expression inside the absolute value with its simplified form: −23+30 = 7. The absolute value of 7 is 7. Now, we substitute this value back into the original expression: [2−7]÷(−13). Simplifying further, we have 2−7 = −5. Finally, we divide −5 by (−13) to get 5/13. In conclusion, the value of the given expression is 5/13.

The value of the expression [2−||−23−2(−15)||]÷(−13) is 5/13.

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The probability that one will be green and the other red is 2/19.

The probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%.

Probability = Expected/Total outcome

We use combination because a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.

The probability of selecting green = \(^{4} C_{1}\) = 4 ( as there are 4 green marble in the jar)

The probability of selecting red = \(^{5} C_{1}\) = 5  ( as there are 5 red marble in the jar)

Expected outcome = 4 * 5

                                = 20

Total marbles in the jar = 20 (10+5+4+1)

Total outcome = \(^{20} C_{2}\)

                        = \(\frac{20!}{(20-2)!.2!}\)

                        = \(\frac{20.19.18!}{18!.2!}\)

                        = \(\frac{20.19}{2}\)

                        = 190

The probability that one will be green and the other red will be -

= 20/190 or, 2/19

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The probability of James passing the quiz is approximately 0.4933 or 49.33%.

To determine the probability of James passing the quiz, we need to know the total number of questions in the quiz and the number of questions James will be able to answer correctly. There are different formulas we can use to find the probability of James passing the quiz, but one of the simplest is the binomial probability formula. This formula is used when there are only two possible outcomes (success or failure) for each trial, the trials are independent, and the probability of success remains the same for all trials. In this case, the success is answering a question correctly, and the failure is answering a question incorrectly.

The binomial probability formula is:

P(x) = (nCx) * p^x * q^(n-x)

Where:

P(x) is equal to the probability of obtaining x successes.

n = the total number of trials

p = the probability of success

q = the probability of failure = 1 - p

p(x) = the probability of getting x successes out of n trials

The number of n-item combinations taken x at a time is given as nCx.

In this case, we have:

n = total number of questions in the quiz

p = probability of responding correctly to a question

q = probability of answering a question incorrectly = 1 - p

Let's assume that the quiz has 20 questions. Then, we have:

n = 20

p = 6/20 = 0.3

q = (20-6)/20 = 0.7

Now we can use the binomial probability formula to find the probability of James passing the quiz, which means getting at least 6 questions correct:

P(x ≥ 6) = P(x = 6) + P(x = 7) + ... + P(x = 20)

Calculating the individual probabilities for each x value, we find:

P(x = 6) = 0.2505

P(x = 7) = 0.1491

P(x = 8) = 0.0655

P(x = 9) = 0.0219

P(x = 10) = 0.0057

P(x = 11) = 0.0011

P(x = 12) = 0.0002

P(x = 13) = 0.00003

P(x = 14) = 0.000003

P(x = 15) ≈ 0

P(x = 16) ≈ 0

P(x = 17) ≈ 0

P(x = 18) ≈ 0

P(x = 19) ≈ 0

P(x = 20) ≈ 0

Now we can add all these probabilities to get the probability of James passing the quiz:

P(x ≥ 6) ≈ 0.4933

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The closest value to the total surface area of the new box is 275 cm².

To find the surface area of the new box, we need to first calculate the dimensions of the box. Since the original box is a rectangular prism, it has three dimensions - length, width, and height.  

Let's assume that the length and width of the box remain the same and only the height changes. So, the new height of the box will be 4 + 3.5 = 7.5 cm.

To calculate the surface area of the new box, we need to find the area of each face and add them up. The box has six faces - two rectangles for the front and back, two rectangles for the sides, and two rectangles for the top and bottom.

The area of each rectangle can be found by multiplying its length and width. Since we know the height and one other dimension (either length or width) of the box, we can use those dimensions to calculate the other dimension using the formula for the volume of a rectangular prism: V = lwh.

Let's assume that the length of the box is 8 cm and the width is 5 cm (these are just arbitrary numbers). Then, the area of each face is:

- Front and back: 8 cm x 7.5 cm = 60 cm² x 2 = 120 cm²
- Sides: 5 cm x 7.5 cm = 37.5 cm² x 2 = 75 cm²
- Top and bottom: 8 cm x 5 cm = 40 cm² x 2 = 80 cm²

The total surface area of the new box is the sum of these areas, which is 120 + 75 + 80 = 275 cm².

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