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A college professor asked every student in his statistics class to flip a coin 100 times and report how many times the coin landed on heads. The results followed a normal distribution, with a mean of 50 and a standard deviation of 5.



If there were 70 students in the class, how many of the students most likely got heads between 45 times and 60 times?


Round your answer to the nearest whole number of students

Answer:

a. g(x) = (1/3)√(x + 4)

b. g(x) = 4√x + 3

c. g(x) = √(x + 2) - 6

Step-by-step explanation:

(a) To shift the graph of f(x) = √x left 4 units, we need to replace x with (x + 4). To vertically compress the graph by a factor of 1/3, we need to multiply the entire function by 1/3. Therefore, the transformed equation is:

g(x) = (1/3)√(x + 4)

(b) To vertically stretch the graph of f(x) = √x by a factor of 4, we need to multiply the entire function by 4. To shift the graph 3 units up, we need to add 3 to the function. Therefore, the transformed equation is:

g(x) = 4√x + 3

(c) To shift the graph of f(x) = √x left 2 units, we need to replace x with (x + 2). To shift the graph 6 units down, we need to subtract 6 from the function. Therefore, the transformed equation is:

g(x) = √(x + 2) - 6

The product for the given multiplication numerical -36.01 x 7.2 is -259.272. The negative sign is due to the product of positive and negative is negative.

-36.01 x 7.2, find the product.

Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes. Multiplication is represented by the signs cross (×), asterisk (*), or dot (·). While writing in your notebooks, you are most likely to use the cross. The asterisk and dot are used in computer languages and algebra (higher mathematics). Multiplication is not just an arithmetic tool. It is a life skill that students must master at a very early age to solve real life problems.

-36.01 * 7.2 = -259.272.

The negative sign is due to the product of positive and negative is negative.

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Answer:

25/18

Step-by-step explanation:

5/6 / 6/10

K    C    F

5/6 * 10/6

50/36 = 25/18

The convolution integral y(t) = x(t) * h(t) for the given pair of signals x(t) and h(t) can be computed as follows:

y(t) = ∫[x(τ) * h(t - τ)] dτ

1) x(t) = δ(t) and h(t) = δ(t - 2) * (t - 1)

The convolution integral becomes:

y(t) = ∫[δ(τ) * δ(t - τ - 2) * (τ - 1)] dτ

To evaluate this integral, we consider the properties of the Dirac delta function. When the argument of the Dirac delta function is not zero, the integral evaluates to zero. Therefore, the integral simplifies to:

y(t) = δ(t - 2) * (t - 1)

The convolution result y(t) is equal to the shifted impulse response h(t - 2) scaled by the factor of (t - 1). This means that the output y(t) will be a shifted and scaled version of the impulse response h(t) at t = 2, delayed by 1 unit.

In summary, for x(t) = δ(t) and h(t) = δ(t - 2) * (t - 1), the convolution integral y(t) = x(t) * h(t) simplifies to y(t) = δ(t - 2) * (t - 1).

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Answer:

44-4i

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

Answer:

3(2+x)=0

Step-by-step explanation:

Here are some vocab words:

Product: Multiplication

Sum: Addition

"A number": x

3(2+x)=0

Answer: 3 / 8 of the puppies have red collars

The required 2 properties to describe the relationship between DE and AC are  1. DE || AC and 2. DC = AC / 2.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
From the figure,
AD = BD and BE = EC

It implies that D and E are the midpoints of the side AB and BC,
So, 1. for the given triangle line joining the midpoints of the triangle always parallel to the third side of the triangle.
DE || AC

And when DE || AC then the measure of DE is equal to half of the measure of AC.
DC = AC / 2

Thus, the required 2 properties are 1. DE || AC and 2. DC = AC / 2.

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Answer:

\(\frac{1}{27}\) and \(\frac{16}{625}\)... or \(\frac{1}{27}\) and \(\frac{2}{625}\)... read below!

Step-by-step explanation:

The first set of answers (\(\frac{1}{27}\) and \(\frac{16}{625}\)) were assuming that the problem was \((\frac{1}{3})^3\) and \((\frac{2}{5})^4\).

The second set of answers ( \(\frac{1}{27}\) and \(\frac{2}{625}\)) were assuming that the problem was \(\frac{1}{3^3}\) and \(\frac{2}{5^4}\) .

Please be clear in your notation next time!

None of the given options is correct for the length of the path described by the given parametric equations.

To find the length of the path described by the parametric equations x = sin(t^3) and y = e^(5t) from t = 0 to t = π, we can use the arc length formula for parametric curves:

L = ∫√(dx/dt)^2 + (dy/dt)^2 dt

Let's differentiate the given equations to find dx/dt and dy/dt:

dx/dt = d(sin(t^3))/dt

= 3t^2cos(t^3)

dy/dt = d(e^(5t))/dt

= 5e^(5t)

Now we can substitute these derivatives into the arc length formula:

L = ∫√[(3t^2cos(t^3))^2 + (5e^(5t))^2] dt

L = ∫√[9t^4cos^2(t^3) + 25e^(10t)] dt

None of the provided answer choices matches this integral. Therefore, none of the given options is correct for the length of the path described by the given parametric equations.

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The required chances to win the game is more than 50% no matter what two are.

The  probability is the proportion of the likelihood of an occasion to occur. It estimates the conviction of the occasion. The recipe for likelihood is given by; P(E) = Number of Ideal Results/Number of all out results.

Allow the two numbers to be an and b, with a<b. Look at an acknowledgment of X (free of your decision of an or b) with the worth of the main number you see. Assuming that X is greater, switch, in any case keep the number.

The likelihood of winning can be registered as follows:

In the event that you pick a (with 12 possibility), you win assuming you switch, ie if X>a. This has prob. P(X>a).

Comparably assuming you pick b (with 12 possibility), you win on the off chance that you don't switch, ie if X≤b. This has prob. P(X≤b).

So the general likelihood of winning is 1/2+1/2P(a<X≤b), which is marginally bigger than 1/2 in view of our presumptions on X.

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Answer:

the number is 20

Step-by-step explanation:

Denote the number as "x",

write out the problem:

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

inverse operations

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

           +6        +6

(1/2(x)) + 10 = x

-(1/2(x))           -(1/2(x))

10 = ((1/2)x)

*2       *2

20 = x

Reduced sample size is a result of a fall in predicted rate, an increase in the tolerated rate, and a rise in the allowable risk of estimating control risk too low.

Given that,

We have to find what impact does a larger acceptable risk of estimating control risk too low have on sample size in characteristics sampling.

The term "risk of over-reliance" refers to the "risk of estimating control risk too low" in characteristics sampling, and it relates with the so-called 

Reduced sample size is a result of a fall in predicted rate, an increase in the tolerated rate, and a rise in the allowable risk of estimating control risk too low.

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Answer:

The cost of 7 pens is RS 70

Step-by-step explanation:

Let c=the cost of one book and p=the cost of one pen

5b+4p=115

b=15

5(15)+4p=115

75+4p=115

4p=115-75

4p=40

p=40/4

p=10

7p=7*10

7p=70

The cost of 7 pens is RS 70

Answer:

$6000.00

Step-by-step explanation:

1. Create an Equation

y/100x(20-10)=600

2. Solve

y/100x(20-10)=600

y/100x10=600

y/100x100x10=600x100

y x 10=60000

10y/10=60000/10

y=6000

3. Check

6000/100x(20-10)=600

60x(20-10)=600

60x10=600

600=600

Correct!

4. Answer

$6000.00

A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.

z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)

Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.

B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.

The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm

Now we can calculate the z-score for a mean length of 122 cm:

z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)

Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.

C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.

Probability = (0.9999)^3 ≈ 0.9997

Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.

Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.

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Answer:

25.5 dollars

Step-by-step explanation:

Answer:

25.5

Step-by-step explanation:

you go 85 x 0.3 and get that as your answer

The given exponential function equation is A = P(1+r)t, where P represents the principal amount, A represents the final amount, r represents the annual interest rate, and t represents the time in years.a.

The independent variable is t (time in years) while the dependent variable is A (final amount).b. The growth factor can be obtained by dividing A by P. Therefore, Growth factor = A/PLet us assume P=100, r=20%, and t=1. Then we can find A as follows:A = P(1+r)tA = 100(1+0.2)1A = 100(1.2)A = 120Therefore, the growth factor is:A/P = 120/100 = 1.2If we assume P=150, r=5%, and t=2, thenA = P(1+r)t = 150(1+0.05)2= 150(1.1025)= 165.375The growth factor is:A/P = 165.375/150 = 1.1025

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The correct answer is Option B. There'll be 70 kg/ha organic carbon would be saved annually by using reduced tillage.

Reduced tillage, also known as conservation tillage, is a practice that minimizes the disturbance of the soil and helps to maintain organic carbon in the soil. This practice can help to improve soil health, reduce erosion, and increase water retention.
One study found that reduced tillage can increase organic carbon levels in the soil by 70 kg/ha (kilograms per hectare) per year. This is equivalent to 70,000 g/ha (grams per hectare) per year. Therefore, the correct answer is option B. 70 kg/ha.
In conclusion, reduced tillage can help to increase organic carbon levels in the soil, leading to improved soil health and other benefits. The amount of organic carbon saved annually by using reduced tillage is 70 kg/ha.

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The car will travel a distance of 33.34 meter in 2 sec.

The definition of velocity is a vector estimate of the rate & direction of motion.

Some features abut the velocity are-

Now according to the question-

A car is driving at 60 kilometers per hour.

That means car is travelling 60 km in 1 hour.

Velocity of the car = 60km/hr

convert the velocity in m/s

1 km = 1000 m

1 hour = 3600 second.

velocity = (60×1000m)/3600s

velocity = 100/6  m/s

Now, the distance covered by the car in 2 seconds

Distance = velocity×time

Distance = (100/6)×2

Distance = 100/3

Distance = 33.24 (approx)

Therefore, distance covered by the car in 2 second is 33.34 meters.

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The correct term to fill in the blank is "a) sequestered."

Fossilized carbon, which is found in ancient plant and animal remains, is said to be sequestered.

This means that the carbon is trapped or stored within these remains over long periods of time. Fossilization occurs when organic material undergoes a process called carbonization, where the carbon in the remains is preserved. This carbon then becomes fossilized and is no longer part of the carbon cycle.

It is important to note that fossilized carbon is different from carbon that is transferred, eroded, or absorbed.

These terms refer to processes that involve the movement or interaction of carbon in various forms, whereas sequestering specifically refers to the trapping and preservation of carbon within fossils.

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Answer:

rewrite: (x-10)^2=81

solution: x=10±9

Step-by-step explanation:

took the quiz.

After solving the equation the value of x is -12. So the option b is correct.

The first step to solving an equation is to identify the unknown variable(s). Once the unknown variable(s) is identified, the next step is to isolate the variable(s) on one side of the equation. After isolating the variable(s), you can then use inverse operations to solve the equation. Finally, check your answer to make sure it makes sense in the context of the equation.

The equation is −10x + 1 + 7x = 37.

To solve that equation we first simplify the equation.

After simplifying the equation we isolate the variable of x.

−10x + 1 + 7x = 37

-3x + 1 = 37

Subtract 1 on both side, we get

-3x = 36

Divide by -3 on both side, we get

x = -12

So the option b is correct.

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The complete question is:

Solve the equation.

−10x + 1 + 7x = 37

a. x = -15

b. x = -12

c. x = 12

d. x = 15

Tthe width of the strip that needs to be taken along the two sides to widen the roads while maintaining the desired remaining lot area of 844 square yards.

To determine the width of the strip that needs to be taken along the two sides of a corner lot to widen the roads while maintaining a remaining lot area of 844 square yards, we can solve an equation based on the given dimensions of the lot.

Let's assume the width of the strip is "w" yards. After taking the strip along the two sides, the dimensions of the remaining lot will be reduced by 2w yards. The length of the remaining lot will be (40 - 2w) yards and the width will be (25 - 2w) yards.

To find the area of the remaining lot, we multiply the length and width:

Area = (40 - 2w)(25 - 2w) = 844

Expanding and rearranging the equation, we get:

100w^2 - 130w + 384 = 0

We can solve this quadratic equation to find the value of "w" using factoring, completing the square, or the quadratic formula. After finding the value of "w", we can determine the width of the strip that needs to be taken along the two sides to widen the roads while maintaining the desired remaining lot area of 844 square yards.

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Answer:

2 months

Step-by-step explanation:

To solve this equation create an expression for the cost of each club. Use the slope-intercept form of y=mx+b where m is the monthly fee and b is the flat fee. So the 2 expressions would be A) 29x+14 and B) 22x+28. Since we want to find when these are equal, set the expressions equal to each other. This gives the equation 29x+14=22x+28. Then, solve for x.

When solved, x=2. This means that after 2 months the cost of each will be the same.

Manipulating temperature in a room to study its impact on task performance involves categorizing the various temperature conditions as the "levels" of the variable.

In experimental research, when investigating the influence of temperature on task performance, researchers manipulate and control the temperature to create different conditions or levels. These temperature levels serve as the independent variable in the study. By systematically altering the temperature, researchers can observe and analyze how variations in temperature affect participants' performance on the given tasks. This experimental design allows researchers to identify patterns, trends, and potential causal relationships between temperature and task performance. Understanding the different temperature conditions or levels in such studies helps researchers learn about the nuanced impact of temperature on human performance and potentially inform practical applications in various settings, such as optimizing work environments or designing effective learning spaces.

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For conducting experiment based on effect of a net force , to apply net force on the object two other quantities should be measured in each trial of the experiment is given by velocity and time.

As given in the question,

To conduct a experiment based on the effect of net force applied to an object the dependable quantities are as follow:

Force = mass × acceleration

As object remain same ⇒ mass is constant as object remain same.

And there is change in the acceleration.

Acceleration depends change in velocity over total time taken.

Acceleration depends on velocity and time.

Net force also depends on velocity and time.

Two measurements need to know  while conducting trail experiments are velocity and time.

Therefore, to conduct experiment based on effect of a net force , to apply net force on the object two other quantities should be measured in each trial of the experiment is given by velocity and time.

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The three-point technique, also known as the three-point estimation or the PERT (Program Evaluation and Review Technique), is a project management tool used to estimate the duration or effort required for completing a task or project.

It involves estimating three values for a specific task - the optimistic estimate (O), the most likely estimate (M), and the pessimistic estimate (P).

These   three estimates are thenused to calculate the expected estimate (E) using the formula: E = (O + 4M + P) / 6.

The three-point technique   is important because it provides a more realistic andreliable estimate by considering both best-case and worst-case scenarios, leading to better planning and decision-making in project management.

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Answer:

4

Step-by-step explanation:

all the details can be found in the attachment.