a cuboid has length 4.2 m breadth 1.4 m and height 1.2 m . find the number of cubes each of lengh 20cm ,which canbe cut from the cuboid.

a. The normal model for IQ scores would be a bell-shaped curve, also known as a Gaussian distribution, centered at a mean of 100 and with a standard deviation of 16. The curve should be labeled "IQ Scores" and include tick marks at the mean (100) and at one standard deviation above and below the mean (84 and 116, respectively).

Using the 68-95-99.7 rule, the area under the curve between each pair of tick marks represents the percentage of scores falling within those ranges. b. According to the 68-95-99.7 rule, the central 95% of IQ scores should be found within two standard deviations of the mean. Since the standard deviation is 16, we can calculate the interval by adding and subtracting two standard deviations from the mean: 100 - (2 * 16) to 100 + (2 * 16). This gives us the range of 68 to 132, meaning that we should expect the central 95% of IQ scores to fall within this interval.

c. To determine the percentage of people with IQ scores above 116, we can calculate the area under the curve to the right of the IQ score 116. We can use statistical tables or software to find the corresponding z-score for 116 and then look up the percentage associated with that z-score. Based on the standard normal distribution, the percentage of people with IQ scores above 116 would be the complement of the percentage below 116.

d. To calculate the percentage of people with IQ scores between 84 and 116, we can find the area under the curve between these two values. Similar to the previous calculation, we can convert the IQ scores to z-scores, look up the corresponding percentages, and subtract the lower percentage from the higher percentage to obtain the desired percentage.

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The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

where c is a constant.

The solution to the question is shown below.

Step 1: We have given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

We have to find the number of words we have to write to express this function in words.

Step 2: Solution

f(t) = et5+4t + ln(t²+3c)⁷ +te-1+5e⁶

Where,

et5+4t = exponential function

ln(t²+3c)⁷ = natural logarithmic function

te-1 = linear function

e⁶ = exponential function

Therefore, f(t) can be expressed in words as:

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Step 3: Conclusion

Hence, the function f(t) can be expressed in words with:The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

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for a typical person, the average number of breath cycles per minute during a very relaxed state is 12 to 16 breaths per minute.

The Respiratory rate and pattern can be observed when the frequency of the inspiratory phase is noted because this phase is active and very easy to count. Also, taking into account the number of breaths taken per minute, is referred to as the Respiratory rate. Lymph flow which occurs during hyperventilation has stopped. A venule is a small blood vessel which is in the microcirculation that accepts deoxygenated blood to return from capillary beds to veins. Venous pooling which is the Venous return of blood and lymph.

for a typical person, the average number of breath cycles per minute during a very relaxed state is 12 to 16 breaths per minute.

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Answer:

Exponential decay

Step-by-step explanation:

The general form of an exponential function is

\(P=P_{0}a^t\), where P0 is the initial value, a is the base, and t is the exponent.

In your example, P0 is 1 and a is 4/5.

A function is experiencing exponential growth when a > 1.

A function is experiencing exponential decay when 0 < a < 1.

4/5 lies between 0 and 1, so the function is experiencing exponential decay.

Answer:

Step-by-step explanation:

Denominators of the fractions are 7 and 3, which are mutually prime numbers.

The LCD is the product of 7 and 3:

Simplify into mixed fraction

\(\\ \sf\longmapsto 6\dfrac{5}{7}=\dfrac{47}{7}\)

\(\\ \sf\longmapsto 6\dfrac{1}{3}=\dfrac{19}{3}\)

Find LCD

\(\\ \sf\longmapsto 7(3)\)

\(\\ \sf\longmapsto 21\)

Answer:

x=36° (180/5x because 2x+3x)

Step-by-step explanation:

Answer:

162

=12h+30w

=12(6)+30(3)

=72+90

=162

​

Answer:

About 80 pounds

Step-by-step explanation:

25 / 4 = 6.25

500 / 6.25

Answer:

80 pounds

Step-by-step explanation:

Step-by-step explanation:

2904/4 = 726 miles per hour (against wind)

3504/4 = 876 miles per hour (with wind)

Assuming the wind stayed constant, the rate of the wind would be the difference between these two values halved

876-726=150

150/2=75 miles per hour (wind speed)

Therefore the rate in still air would be the middle value of the two:

726+75=801 miles per hour

Answer:

The indifference point is 3 days.

Step-by-step explanation:

Company A:

Total cost= 40*x

Company B:

Total cost= 60 + 20*x

x= number of days

To calculate the indifference point, we need to equal both formulas. and isolate x:

40x = 60 + 20x

20x= 60

x= 60/20

x= 3

The indifference point is 3 days.

Prove:

Company A:

Total cost= 40*3= $120

Company B:

Total cost= 60 + 20*3= $120

To compare the proportional relationships, the amount earned by walking per mile should be used to find the unit rate. By comparing the three people, we conclude that Beth>Manuel=Petra.

Given that the equation y = 20x. This equation represents the amount of money raised by Beth for walking x miles.

In order to compute for Manuel, we must first divide the money raised by miles walked. Then, $45÷3=$15. From this, we can conclude that Manuel raises about $15 per mile of walking. This is the same as Petra.

So we have to compare both Manuel and Petra with Beth. Rewriting the equation with respect to Manuel and Petra, we get y=15x. Now compare this equation with the given equation, then,15x < 20x. Therefore, Beth earns more money while walking than Manuel and Petra.

The complete question is -

Beth, Manuel, and Petra are collecting sponsors for a walkathon. The equation y=20x  represents the amount of money Beth raises for walking x miles. The table shows the relationship between the number of miles Manuel walks and the amount of money he will raise. Petra will earn $15 for each mile that she walks. a. In order to compare the proportional relationships, what quantities should you use to find the unit rate? b. Compare the amount of money raised per mile by the three people.

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I picked two points in the graph, (-1, 0) and (1, 1).

Find the rate by solving for the slope (rise / run).

Rise = x₂ - x₁ = 1 - (-1) = 2

Run = y₂ - y₁ = 1 - 0 = 1

Slope = 2 / 1 = 2

The rate is m = 2

Answer:

there is the answer to your question

Answer:

Scalene Right Triangle

Step-by-step explanation:

A possible type of triangle that has no equal sides and one right angle is a right triangle.

Right triangles have just one angle that is equal to 90°, and they can be either isosceles or scalene triangles.

Hope this helped!

The initial value problem (IVP) that models the process can be written as follows.

dQ/dt = (29/1) * (4 1/min) - Q(t) * (4 1/min)

Q(0) = 0

where:

- Q(t) represents the amount of salt in the tank at time t,

- dQ/dt is the rate of change of salt in the tank with respect to time,

- (29/1) * (4 1/min) represents the rate at which the salt solution enters the tank,

- Q(t) * (4 1/min) represents the rate at which the salt solution flows out of the tank,

- Q(0) is the initial amount of salt in the tank (at time t=0), given as 0 since the tank initially contains pure water.

(b) To solve the IVP, we can separate variables and integrate both sides:

dQ / (Q(t) * (4 1/min) - (29/1) * (4 1/min)) = dt

Integrating both sides:

∫ dQ / (Q(t) * (4 1/min) - (29/1) * (4 1/min)) = ∫ dt

Applying the integral on the left side:

ln(|Q(t) * (4 1/min) - (29/1) * (4 1/min)|) = t + C

where C is the constant of integration.

Using the initial condition Q(0) = 0, we can solve for C:

ln(|0 * (4 1/min) - (29/1) * (4 1/min)|) = 0 + C

ln(116 1/min) = C

Substituting the value of C back into the equation:

ln(|Q(t) * (4 1/min) - (29/1) * (4 1/min)|) = t + ln(116 1/min)

Taking the exponential of both sides:

|Q(t) * (4 1/min) - (29/1) * (4 1/min)| = e^(t + ln(116 1/min))

Since the expression inside the absolute value can be positive or negative, we have two cases:

Case 1: Q(t) * (4 1/min) - (29/1) * (4 1/min) ≥ 0

Simplifying the expression:

Q(t) * (4 1/min) ≥ (29/1) * (4 1/min)

Q(t) ≥ 29/1

Case 2: Q(t) * (4 1/min) - (29/1) * (4 1/min) < 0

Simplifying the expression:

-(Q(t) * (4 1/min) - (29/1) * (4 1/min)) < 0

Q(t) * (4 1/min) < (29/1) * (4 1/min)

Q(t) < 29/1

Combining the two cases, the expression for the amount of salt Q(t) in the tank at any time t is:

Q(t) =

29/1, if t ≥ 0

0, if t < 0

(c) The limiting amount of salt in the tank Q after a very long time can be determined by taking the limit as t approaches infinity:

lim(Q(t)) as t → ∞ = 29/1

Therefore, the limiting amount of salt in the tank after a very long time is 29 liters.

(d) To find the time T needed for the salt to reach half the limiting amount, we set Q(t) = 29/2 and solve for t:

Q(t) = 29/2

29/2 = 29/1 * e^(t + ln(116 1/min))

Canceling out the common factor:

1/2 = e^(t + ln(116 1/min))

Taking the natural logarithm of both sides:

ln(1/2) = t + ln(116 1/min)

Simplifying:

- ln(2) = t + ln(116 1/min)

Rearranging the equation:

t = -ln(2) - ln(116 1/min)

Calculating the value:

t ≈ -0.693 - 4.753 = -5.446

Since time cannot be negative, we disregard the negative solution.

Therefore, the time T needed for the salt to reach half the limiting amount is approximately 5.446 minutes.

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The area left for children for playing 114464 sq. m

As per the given data inside a park:

The length of the park is 400 m

The breadth of the park is 300 m

The formula for the area of the park = Length × Breadth

= (400 × 300) sq. m

= 120000 sq. m

The width of the walking track inside the park is 4 m

The length of the park without the walking track

= 400 − (4 + 4) m

= 400 − 8 m

= 392 m

The breadth of the park without the walking track

= 300 − (4 + 2) m

= 300 − 8 m

=292 m

Area of the park without the walking track:

= 392 × 292

= 114464 sq. m

Therefore the area left for children for playing other than the walking track is 114464 sq. m.

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A major disadvantage of electron microscopes compared to light microscopes is that they cannot be used to view live specimens. Therefore, option B is the correct answer.

A major disadvantage of electron microscopes compared to light microscopes is that they cannot be used to view live specimens. This is because the electron microscope requires a vacuum environment to function properly, which would kill any live specimen. Additionally, electron microscopes can only see surface details and do not have a very high power of resolution. Lastly, electron microscopes can only be used by doctors or trained technicians, so they are not as widely available as light microscopes.

Therefore, option B is the correct answer.

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A disadvantage of electron microscopes compared to light microscopes is that they cannot be used to view live specimens (option b). Electron microscopes use a beam of electrons to create an image, which requires a vacuum environment. This means that living organisms cannot survive in the vacuum and therefore cannot be observed with electron microscopes.

I hope this helped! :)

In the given statement is:

You conduct a survey of your small town about having a town wide gargae sale. of those surveyed, 56% are in favor and 44% are opposed. the actual percent could be 5% more or 5% less than the acquired results.

Using the absolute value function, we have that:

A. The least percentage is of 39% and the greatest is of 49%.

B. Since the greatest percentage is below 50%, the statement conflicts with the survey data.

What is the absolute value function?

The absolute function is defined by:

It measures the distance of a point x to the origin.

For this problem, the difference between the percentage of opposed and 44% can be of at most 5%, hence the absolute value equation is:

|x - 44| = 5.

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Answer:

Inconsistent

Step-by-step explanation:

A system of linear equations that has at least one solution is called consistent, whereas a system of linear equations that has no solutions is called inconsistent.

A system of linear equations that has no solution is a set of inconsistent equations.

The correct answer is an option (B)

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

"It is a set of equations for which we find a common solution."

"A system of equations is consistent if there is at least one set of values that satisfies each equation in the system."

"A system of equations is inconsistent if there is no solution to the given system of equations."

From the definition, we can see that the system of equations is inconsistent if a system of equations has no solution.

Therefore, A system of linear equations that has no solution is a set of inconsistent equations.

The correct answer is an option (B)

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The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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The feasible region is the region that comes from intersecting the different regions described by the equations that constrain the problem.

Let's take a look:

From this, we can conclude that the vertices of the feasible region are:

A 1% error in r will lead to a larger error in the volume.

A 1% error in r will cause a larger error in the volume, since the percentage increase in volume is proportional to the square of r.

The volume of a cylinder of radius r and height h is V = πr2h. The linear approximation to the volume of a cylinder is given by V ≈ πr2(h + r).

Thus, the percentage increase in volume when r and h are each increased by c is given by 100% × (Vnew - Vold) / Vold = 100% × (π(r + c)2(h + c + r) - πr2h) / πr2h = 200c/r + 100c/h.

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Answer:

x=10

Step-by-step explanation:

We know that the sum of all these angles is 180°, so, we solve for \(x\) using this information:

\((9x-16)+(3x+11)+(7x-5)=180\\19x-10=180\\19x=190\\x=10\)

We can now use x to find the value of each angle:

\(9(10)-16=\\90-16\\=74\\\\\)

\(3(10)+11\\30+11\\41\)

\(7(10)-5\\=70-5\\=65\)

Hope this helped! Have a good day.

Answer:

\(total \: angle \: for \: a \: triangle = 180 \\ then \: \\ 3x + 11 + 9x - 16 + 7x - 5 = 180 \\ 19x - 10 = 180 \\ 19x = 180 + 10 \\ 19x = 190 \\ x = \frac{190}{19} = 10 \\ thank \: yo\)

Using the given information, the unit rate is 0.0645 miles/minute

From the question, we are to determine the unit rate

From the given information,

Daniel runs 40/5 miles in 124 minutes

That is,

Distance = 40/5 miles = 8 miles  

Time = 124 minutes

Using the formula,

Rate = Distance / Time

Rate = 8 miles / 124 minutes

Rate = 0.0645 miles/minute

Hence, the unit rate is 0.0645 miles/minute

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The unit rate is 0.0645 miles/minute

We have calculated the rate

From the question, we are to determine the unit rate

From the given information,

Daniel runs 40/5 miles in 124 minutes

Distance = 40/5 miles

Distance = 8 miles  

Time = 124 minutes

Rate = Distance / Time

Rate = 8 miles / 124 minutes

Rate = 0.0645 miles/minute

Hence, the unit rate is 0.0645 miles/minute

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Answer:

Step-by-step explanation:

68 degree F to C.

9/5c+32=68

C=20

Answer:

The answer is C=20

because 9/5c+32=68

Answer:

25

Step-by-step explanation:

Answer: 180 minutes

Step-by-step explanation:

300/60

5-2=3

3x60=180

GD DAY AND NIGHT EMMANUEL MUDIAY

Answer:

\(26\,\sqrt{5} +2\,\sqrt{10}\)

Step-by-step explanation:

We start by using distributive property multiplying the constant term outside the parenthesis times each of the terms inside the parenthesis:

\(2\,\sqrt{5} \,(13+\sqrt{2} )=2*13\,\sqrt{5} +2\,\sqrt{5} \,\sqrt{2} = 26\,\sqrt{5} +2\,\sqrt{5\,*\,2} =26\,\sqrt{5} +2\,\sqrt{10}\)