A ball is shot out of a cannon at ground level, We know that its height H in feet after t sec given by the function H(t) 144t-16t Com is a. Find H(3), H(6), H(4), and H(5). Why are some of the outputs equal? H(3) feet

Answer: (C) 0.9104

Step-by-step explanation:

Given : The hours studied follows the normal distribution

Mean : [tex]\mu=\text{20 hours}[/tex]

Standard deviation : [tex]\sigma=6\text{ hours}[/tex]

Sample size : [tex]n=144[/tex]

The formula to calculate the z-score is given by :-

[tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

Let x be the number hours taken by randomly selected undergraduated student.

Then for x = 19.25 , we have

[tex]z=\dfrac{19.25-20}{\dfrac{6}{\sqrt{144}}}=-1.5[/tex]

for x = 21.0  , we have

[tex]z=\dfrac{20-21}{\dfrac{6}{\sqrt{144}}}=2[/tex]

The p-value : [tex]P(19.25<x<21)=P(-1.5<z<2)[/tex]

[tex]P(2)-P(-1.5)= 0.9772498- 0.0668072=0.9104426\approx0.9104[/tex]

Thus, the probability that the mean of this sample is between 19.25 hours and 21.0 hours = 0.9104.

Recall that for [tex]|z|<1[/tex], we have

[tex]\dfrac1{1-z}=\displaystyle\sum_{n\ge0}z^n[/tex]

Then

[tex]\dfrac1{1-z}=-\dfrac1z\dfrac1{1-\frac1z}=-\dfrac1z\displaystyle\sum_{n\ge0}z^{-n}=-\sum_{n\ge0}z^{-n-1}[/tex]

valid for [tex]|z|>1[/tex], so that

[tex]\dfrac1{1-z^2}=-\dfrac1{z^2}\dfrac1{1-\frac1{z^2}}=-\dfrac1{z^2}\displaystyle\sum_{n\ge0}z^{-2n}=-\sum_{n\ge0}z^{-2n-2}[/tex]

also valid for [tex]|z|>1[/tex].

Answer:

[tex]L\left(te^{2t }sin3t\right)=\frac{6s-12}{(s^2-4s+13)^2}[/tex].

Step-by-step explanation:

If F(s)= L{f(t)}

Then [tex]L\left\{(t^nf(t)\right\}=(-1)^n\frac{\mathrm{d^n}F(s)}{\mathrm{d^n}s}[/tex]

[tex]L\left\{te^{2t}sin3t\right\}[/tex]

f(t)=[tex]e^{2t}sin3t[/tex]

[tex]L\left\{e^{at}sinbt\right\}=\frac{b}{(s-a)^2+b^2}[/tex]

Therefore,[tex] L\left\{e^{2t}sin3t\right\}=\frac{3}{(s-2)^2+(3)^2}[/tex]

[tex]L\left\{e^{2t}sin3t\right\}=\frac{3}{s^2-4s+13}[/tex]

[tex]L\left\{te^{2t}sin3t\right}=-\frac{\mathrm{d}F(s)}{\mathrm{d}s}[/tex]

=-[tex]\frac{\mathrm{d}e^{2t}sin3t}{\mathrm{d}s}[/tex]

[tex]L\left\{te^{2t}sin3t\right\}[/tex]

[tex]=\frac{3(2s-4)}{(s^2-4s+13)^2}[/tex]

[tex]L\left\{te^{2t}sin3t\right\}=\frac{6s-12}{(s^2-4s+13)^2}[/tex].

The Laplace transform of te2tsin(3t) is 3(-1)(1)/(s2+9)2.

According to Theorem 7.4.1, the Laplace transform of a function tnf(t) can be calculated as (−1)n * dn/dsn * F(s), where F(s) is the Laplace transform of f(t). In this case, we need to evaluate the Laplace transform of te2tsin(3t).

First, we need to find the Laplace transform of te2t. Applying the formula F(s) = ℒ{f(t)} = ℒ{te2t}:

F(s) = -d/ds[2/(s-2)2]

Next, we need to find the Laplace transform of sin(3t). Applying the formula F(s) = ℒ{f(t)} = ℒ{sin(3t)}:

F(s) = 3/(s2+9)

Finally, we can evaluate the Laplace transform of te2tsin(3t) as the product of the Laplace transforms obtained:

F(s) = (-1)*(d1/d1s)*(-d1/d1s)[3/(s2+9)]

F(s) = 3(-1)(1)/(s2+9)2

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Answer:

The commission would be $ 920.

Step-by-step explanation:

Given,

Sales in 1997 ​= $ 9500,

Since, there is a commision of 8 % on the first $ 7500 of​ sales, 16% on the next $ 7500 of​ sales, and 20% on sales over $ 15,000,

If x represents the total sales,

Commission for x ≤ 7500 = 8% of x = 0.08x,

Commission for 7500 < x ≤ 15000 = 8% of 7500 + 16% of (x-7500)

= 600 + 0.16(x-7500),

Commission for 7500 < x ≤ 15000 = 8% of 7500 + 16% of 7500 + 20% of (x-15000)

= 600 + 1200 + 0.20(x-15000)

= 1800 + 0.20(x-15000)

Thus, the function that shows the given situation,

[tex]f(x)=\left\{\begin{matrix}0.08x & x \leq 7500\\ 600+0.16(x-7500) & 7500 < x \leq 15000\\ 1800+0.20(x-15000) & 15000 < x\end{matrix}\right.[/tex]

Since, 9500 lies between 7500 and 15000,

Therefore, the commission would be,

f(9500)= 600 + 0.16(9500 - 7500) = 600 + 320 = $ 920

Shelby's gross commission for July 1997 on sales of $9500 is calculated as  $920.

Kelly Price sells college textbooks on commission, and the structure of her commission is a tiered rate: 8% on the first $7500 of sales, 16% on the next $7500 of sales, and 20% on sales over $15,000.

For Shelby’s sales totaling $9500 in July 1997, we must calculate her gross commission for that month.

Here is the step-by-step calculation:

Therefore, Shelby’s gross commission for July 1997 is $920.

Answer: [tex]\$\ 3600[/tex]

Step-by-step explanation:

Given : A bank charges a 1% fee to process a credit card cash advance which is taken out of the cash advance amount.

The rate of fee can be also written as 0.01.

The amount of money a customer wants as a cash advance = $4,000

The amount of bank fee = [tex]0.01\times4000=40[/tex]

The amount which customer receive after cash advance has been processed = [tex]4000-40=\$3600[/tex]

Hence, the amount of money will he receive from the bank after the cash advance has been processed = [tex]\$\ 3600[/tex]

Answer:

95%

Step-by-step explanation:

We have a normal distribution with a mean of 6 students and standard deviation of 26.

To solve this problem, we're going to need the help of a calculator.

P(16<z<120) = 0.9545 ≈ 95.45%

Rounding, we can say that 95% of the students scored between 16 and 120.

Answer:

none

Step-by-step explanation:

We have three sides

Adding the two smallest sides together must be bigger than the third side

3.1+5.2 > 9.8

8.3> 9.8

This is false, so we cannot make a triangle

Answer:

1,460 hours per year.

113,880 hours in a lifetime.

Step-by-step explanation:

Great question, it is always good to ask away and get rid of any doubts that you may be having.

Let's assume that on an average day Americans drive 4 hours a day. This includes going and coming from work as well as any groceries they might need to do. Since there are 365 days in a year we can multiply this by the hours a day driven.

[tex]365*4 = 1,460[/tex]

We can "guesstimate" that on average an American drives 1,460 hours per year.

Based on my research the average lifetime of an American is 78 years old. We can now multiply this by the number of hours driven in a year to have an idea of the number of hours driven in a lifetime.

[tex]1,460*78 = 113,880[/tex]

On average we "guesstimate" that an American drives 113,880 hours in a lifetime.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer: 0.1052

Step-by-step explanation:

Given : Mean :[tex]\mu= 120[/tex]

Standard deviation : [tex]\sigma= 5.6[/tex]

We assume the variable is normally distributed.

The formula for z-score is given by :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x=120.4

[tex]z=\dfrac{120.4-120}{5.6}=0.0714285714286\approx0.07[/tex]

For x=121.9

[tex]z=\dfrac{121.9-120}{5.6}=0.339285714286\approx0.34[/tex]

The p-value =[tex]P(0.07<z<0.34)=P(0.34)-P(0.07)[/tex]

[tex]=0.6330717-0.5279031=0.1051686\approx0.1052[/tex]

The probability that the individual's pressure will be between 120.4 and 121.9 mm Hg = 0.1052

Final answer:

The repeating decimal 0.342 can be expressed as the fraction 38/111 in simplest form, by using algebraic methods to eliminate the repeating pattern and then simplifying the resulting fraction.

Explanation:

Expressing the repeating decimal 0.342 as a fraction involves using algebra to convert the decimal into a form that can be simplified into a fraction. First, we set the repeating decimal equal to a variable:

Let x = 0.342

To remove the repeating part, we multiply x by a power of 10 that corresponds to the number of digits in the repeating sequence. Since there are three digits repeating (342), we multiply by 1000:

1000x = 342.342

We now subtract the original equation (1x) from this new equation (1000x) to get rid of the decimal:

1000x - x = 342.342 - 0.342

999x = 342

Now we simplify by dividing both sides by 999:

x = 342 / 999

This fraction can be further simplified by dividing both the numerator and denominator by their greatest common divisor:

x = 38 / 111. Therefore, the fractional form of 0.342 is 38/111 in its simplest form.

To convert the repeating decimal 0.342 (with 342 repeating indefinitely) to a fraction, let's follow these steps:
1. Let x equal the repeating decimal:
  \( x = 0.342342342... \)
2. Recognize the pattern: the digits 342 repeat every three places. To isolate the repeating sequence, we need to multiply x by a power of 10 that has the same number of digits as the repeating sequence.
3. The repeating sequence has three digits, so we'll multiply x by \( 10^3 = 1000 \):
  \( 1000x = 342.342342... \)
4. Now, subtract the original number x from this new number to remove the repeating part:
  \( 1000x - x = 342.342342... - 0.342342342... \)
5. Notice that on the right-hand side, the repeating decimals cancel each other out, leaving whole numbers:
  \( 999x = 342.000000... \)
6. Now solve for x:
  \( x = \frac{342}{999} \)
7. To simplify the fraction, we find the greatest common divisor (GCD) of the numerator (342) and the denominator (999).
To find the GCD, we can list the factors of each:
Factors of 342 include: \( 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342 \).
Factors of 999 include: \( 1, 3, 9, 27, 37, 111, 333, 999 \).
The largest factor that appears in both lists is 9.
8. Divide both the numerator and the denominator by their GCD:
  \( x = \frac{342 ÷ 9}{999 ÷ 9} \)
9. Doing the division:
  \( x = \frac{38}{111} \)
Thus, the repeating decimal 0.342 (with a line over the entire decimal) can be expressed as the fraction \( \frac{38}{111} \) in its simplest form.

Answer:

  16.053 inches

Step-by-step explanation:

Many such probability questions are easily answered by a suitable calculator or spreadsheet.

Answer:

The height of tower is 322.7 feet.

Step-by-step explanation:

Given

Distance between a building and tower= 250 feet

BCDE is a rectangle .Therefore, we have  BC=ED and CD=BE=250 feet

In triangle ABE

[tex]tan\theta=\frac{perpendicula \; side }{hypotenuse}[/tex]

[tex]\theta=38^{\circ}[/tex]

[tex] tan38^{\circ}=\frac{AB}{BE}[/tex]

[tex]\frac{AB}{250}=0.781[/tex]

[tex] AB=0.781\times250[/tex]

AB=195.25 feet

In triangle EDC

[tex]\theta=27^{\circ}[/tex]

[tex]tan27^{\circ}=\frac{ED}{CD}[/tex]

[tex]\frac{ED}{250}=0.509[/tex]

[tex]ED=250\times0.509[/tex]

ED=127.25 feet

ED=BC=127.25 feet

The height of tower=AB+BC

The height of tower=195.25+127.25=322.5 feet

The distribution of X is a normal distribution with a mean of 66 inches and a standard deviation of 2.5 inches. To find the probability that a person's height is between 64 and 69 inches, we need to determine the z-scores for each height value and use a z-table or calculator to find the probabilities.

A) Give the distribution of X.
X ~ Normal(66, 2.5)
B) Find the probability that the person is between 64 and 69 inches.
P(64 ≤ X ≤ 69)

To find this probability, we need to calculate the z-score for each height value using the formula z = (X - μ) / σ. Then, we can use a z-table or a calculator to find the corresponding probabilities.

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The height X of Asian adult males follows a normal distribution with parameters X ~ N(66, 2.5). The probability that one randomly chosen male is between 64 and 69 inches tall can be found using Z-scores and the area under the normal curve.

The distribution of the height X for Asian adult males according to the given study is X ~ N(66, 2.5), where 66 is the mean height in inches and 2.5 is the standard deviation.

Probability that the height is between 64 and 69 inches

To find the probability that the height of a randomly chosen Asian adult male is between 64 and 69 inches, we can use the properties of the normal distribution. We first convert the raw scores to Z-scores using the formula Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

The probability statement is P(64 < X < 69). To calculate this probability, we find the Z-scores for 64 and 69 inches and then find the area under the normal curve between these two Z-scores using a standard normal distribution table or a calculator with normal distribution functions.

Answer:

650 milliliters.

Step-by-step explanation:

Amount in the Jug = 1.5 * 1000 = 1,500 mls.

She pours out 250 mls and 0.6 * 1000 = 600 mls

The amount left = 1500 - 250 - 600

= 650 milliliters.

The amount of chocolate milk left in the jug is; D: 650 milliliters

We are told;

Amount of chocolate milk in the jug = 1.5 litres

She fills one cup with 250 mL = 0.25 liters

She fills another cup with 0.6 liters

Thus;

Total amount used = 0.6 +  0.25 = 0.85 litres

Amount left = 1.5 - 0.85 = 0.65 Liters

Converting to mL gives; 650 milliliters

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Answer:

314.16 in²

Step-by-step explanation:

If the diameter is 20", then the radius is 10" (1/2 the diameter).

Area of a circle is [tex]\pi r[/tex]²

So, π 10² = 100π = 314.16 in²

Answer: 1.49

Step-by-step explanation:

We know that the standard deviation in a binomial distribution is given by :-

[tex]\sigma=\sqrt{n\cdot p\cdot (1-p)}[/tex], where n is the number of trials and p is the probability of success.

Given : The number of trials : [tex]n=10[/tex]

The probability of success = [tex]p=\dfrac{1}{3}[/tex]

Then , the standard deviation will be :-

[tex]\sigma=\sqrt{10\cdot \dfrac{1}{3}\cdot (1-\dfrac{1}{3})}\\\\\Rightarrow\ \sigma=1.490711985\approx1.49[/tex]

The standard deviation of a given binomial distribution with 10 trials and a probability of success of 1/3 is calculated using the formula σ = √npq, resulting in approximately 1.49. This value helps us understand the spread of successes in the experiment.

To compute the standard deviation of a given binomial distribution with 10 trials and a probability of success p=1/3, we first identify the probability of failure, which is q=1-p=2/3. The formula for the standard deviation (σ) of a binomial distribution is σ = √npq, where n is the number of trials, p is the probability of success, and q is the probability of failure.

By substituting the given values into the formula:

We get σ = √(10)(1/3)(2/3) = √(20/9) ≈ 1.49. Therefore, the standard deviation of the binomial distribution is approximately 1.49.

This calculation helps us understand the dispersion or spread of the distribution of successes in our binomial experiment, indicating how far the number of successes can deviate from the expected value on average.

Answer:

Step-by-step explanation:

The x-intercept exists when y = 0; the coordinate takes on the form (    , 0)

The y-intercept exists when x = 0; the coordinate takes on the form (0,   ).

We will fill in the blanks in a sec.

If the x-intercept exists when y = 0, then we fill in 0 for y and solve for x:

-3(0) - x = -9 so

-x = -9 and

x = 9

The coordinate is (9, 0) for the x-intercept.

If the y-intercept exists when x = 0, then we fill in 0 for x and solve for y:

-3y - 0 = -9 so

-3y = -9 and

y = 3

The coordinate is (0, 3) for the y-intercept.

Answer:

The answer is Parallel-forms reliability.

Parallel-forms reliability describes a measure used to compare two different tests with the same group of participants to see how closely correlated the two sets of scores are with each other.

Test-retest reliability is a measure used to compare the results of two instances of the same test taken by the same group of participants to establish how closely correlated the two sets of scores are.

The measure used to compare two different tests with the same group of participants to see how closely correlated the two sets of scores are with each other is called test-retest reliability.

In essence, test-retest reliability measures the consistency of results when a test is administered more than once. The higher the correlation between the two sets of scores, the higher the test’s reliability. For example, if a group of students were to take a vocabulary test one week, and then the same test a week later, a high correlation between the results would suggest that the test is reliable.

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Answer:

open fb and search ravi verma

Step-by-step explanation:

send friend request

one rupee coin be z

50 paisa coins=2z

25 paisa coins=4z

50/25=2 2z*2=4z

z+2x+4x=175

7z=175

7z/7=175/7

z=25

one rupee coin=25 value

50 paisa rupee coins=50 value

25 rupee coin=100 value

50/25=2 50*2=100

25+50+100=175

Answer is b) Rs 175. I think this is the answer.

Answer:$500

Step-by-step explanation:

Answer: 0.5507

Step-by-step explanation:

The cumulative distribution function for exponential distribution:-

[tex]P(X\leq x)=1-e^{-\lambda x}[/tex]

Given : The life of a light bulb is exponentially distributed with a mean of 1,000 hours.

Then , [tex]\lambda=\dfrac{1}{1000}[/tex]

Then , the probability that the bulb will last less than 800 hours is given by :-

[tex]P(X\leq 800)=1-e^{\frac{-800}{1000}}\\\\=1-e^{-0.8}=0.5506710358\approx0.5507[/tex]

Hence, the probability that the bulb will last less than 800 hours = 0.5507

The probability that the bulb will last less than 800 hours is 0.550

An incandescent light bulb is an electric light with a wire filament heated to such a high temperature that it glows with visible light. The filament of  an incandescent light bulb is protected from oxidation with a glass or fused quartz bulb that is filled with inert gas or a vacuum. The exponential distribution is the probability distribution of the time between events in a Poisson point process. It is a particular case of the gamma distribution. While the arithmetic mean is the central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values

The life of a light bulb is exponentially distributed with a mean of 1,000 hours. What is the probability that the bulb will last less than 800 hours?

What is the probability that the light bulb will have to replaced within 800 hours?

[tex]\lambda = \frac{1}{1000}[/tex]

[tex]P(x<=800) = 1 - e^{(-\lambda*x)} = 1-e^{[(-\frac{1}{1000} )*800]} = 1-e^{-0.8} = 1-0.449 = 0.550[/tex]

Grade:  5

Subject:  math

Chapter:  probability

Keywords:  mean, bulb, hours, exponential, light

Answer:

[tex]\boxed{\text{(a)}A = 100 - 99e^{-t/25}; \,\text{(b) 15 s}}[/tex]

Step-by-step explanation:

(a) Expression for mass of salt as function of time

[tex]\text{Let A = mass of salt after t min}\\\text{and }r_{i} = \text{rate of salt coming into talk}\\\text{and }r_{o}$ =\text{rate of salt going out of tank}[/tex]

i. Set up an expression for the rate of change of salt concentration.

[tex]\dfrac{\text{d}A}{\text{d}t} = r_{i} - r_{o}\\\\r_{i} = \dfrac{\text{4 gal}}{\text{1 min}} \times \dfrac{\text{1 lb}}{\text{1 gal}} = \text{4 lb/min}\\\\r_{o} = \dfrac{\text{4 gal}}{\text{1 min}} \times \dfrac {A\text{ lb}}{\text{100 gal}} =\dfrac{A}{25}\text{ lb/min}\\\\\dfrac{\text{d}A}{\text{d}t} = 4 - \dfrac{x}{25}[/tex]

ii. Integrate the expression

[tex]\dfrac{\text{d}A}{\text{d}t} = \dfrac{100 - A}{25}\\\\\dfrac{\text{d}A}{100 - A} = \dfrac{\text{d}t}{25}\\\\\int \frac{\text{d}A}{100 - A} = \int \frac{\text{d}t}{25}\\\\-\ln(100 - A) = \dfrac{t}{25} + C[/tex]

iii. Find the constant of integration

[tex]-\ln (100 - A) = \dfrac{t}{25} + C\\\\\text{At $t$ = 0, $A$ = 1, so}\\\\-\ln (100 - 1) = \dfrac{0}{25} + C\\\\C = -\ln 99[/tex]

iv. Solve for A as a function of time.

[tex]\text{The integrated rate expression is}\\\\-\ln (100-A) = \dfrac{t}{25} - \ln 99\\\\\text{Solve for } A\\\\\ln(100 - A) = \ln 99 - \dfrac{t}{25}\\\\100 - A = 99e^{-t/25}\\\\A = \boxed{\mathbf{100 - 99e^{-t/25}}}[/tex]

The diagram shows A as a function of time. The mass of salt in the tank starts at 1 lb and increases asymptotically to 100 lb.

(b) Time to 2 lb salt

[tex]A = 100 - 99e^{-t/25}\\\\2 = 100 - 99e^{-t/25}\\\\99e^{-t/25} = 98\\\\e^{-t/25} = 0.989899\\\\-t/25 = -0.01015\\\\t = 25\times 0.01015 =\text{0.25 min = 15 s}\\\\\text{The tank will contain 2 lb of salt after } \boxed{\textbf{15 s}}[/tex]

To find the amount of salt in the tank at any time t, we need to consider the rate at which the brine solution is being poured in and leaving the tank. Initially, there is 1 pound of salt in the tank. The rate at which salt is added is 1 pound per gallon, and the rate at which the mixture is being removed is 4 gallons per minute. Therefore, the amount of salt in the tank at time t can be calculated using the equation. To find the time at which the mixture in the tank contains 2 pounds of salt, we can set up the equation. Solving this equation for t will give us the time at which the mixture contains 2 pounds of salt.

To find the amount of salt in the tank at any time t, we need to consider the rate at which the brine solution is being poured in and leaving the tank. Initially, there is 1 pound of salt in the tank. The rate at which salt is added is 1 pound per gallon, and the rate at which the mixture is being removed is 4 gallons per minute. Therefore, the amount of salt in the tank at time t can be calculated using the equation:

Amount of salt at time t = 1 + (1 pound/gallon)(4 gallons/minute)(t minutes)

To find the time at which the mixture in the tank contains 2 pounds of salt, we can set up the equation:

2 = 1 + (1 pound/gallon)(4 gallons/minute)(t minutes)

Solving this equation for t will give us the time at which the mixture contains 2 pounds of salt.

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Answer:

The given function is

  f(x)=cos 3x-7 x²+ 4x

f'(x)=-3 sin 3 x-14 x+4

When you will draw the graph of the function , you will find that root of the function lie between (-1,0).

Consider initial root as,

 [tex]x_{0}=0[/tex]

Using Newton method to find the roots of the equation

 [tex]x_{n+1}=x_{n}-\frac{f{x_n}}{f'{x_{n}}}\\\\x_{1}=x_{0} - \frac{cos 3x_{0}-7 x_{0}^2+ 4x_{0}}{-3 sin 3 x_{0}-14 x_{0}+4}\\\\x_{1}=-\frac{\cos 0^{\circ}-0+0}{-3 \times 0-0+4}\\\\x_{1}=\frac{-1}{4}\\\\x_{1}= -0.25\\\\x_{2}=x_{1} - \frac{cos 3x_{1}-7 x_{1}^2+ 4x_{1}}{-3 sin 3 x_{1}-14 x_{1}+4}\\\\x_{2}=-0.25 -\frac{cos (-0.75)-7\times (0.0625)- 1}{-3 sin (-0.75)+3.50+4}\\\\x_{2}= -0.176054[/tex]

[tex]x_{3}=x_{2} - \frac{cos 3x_{2}-7 x_{2}^2+ 4x_{2}}{-3 sin 3 x_{2}-14 x_{2}+4}\\\\x_{3}=-0.176054 -\frac{cos (3\times -0.176054)-7\times (-0.176054)^2+4 \times -0.176054}{-3 sin (-0.176054)-14 \times (-0.176054)+4}\\\\x_{3}= -0.1689[/tex]

So, root of the equation is

         =0.1688878

       =0.1689(approx)

Answer: 0.7264

Explanation:

The number of independent questions (n)  = 100

Probability of answering a question (p) = 0.80

Let X be the no. of questions that need to be answered.

[tex]\therefore[/tex] random variable X follows binomial distribution

The probability function of a binomial distribution is given as

[tex]P(X=x) = \binom{n}{x}\times p^{x}(1-p)^{n-x}[/tex]

Now , we nee to find P(74 ≤ X ≤ 84)

[tex]\therefore P(74\leq X\leq 84) = P(X=74) + P(X=75).........+ P(X=84)[/tex]

P(74 ≤ X ≤ 84) = [tex]\sum_{74}^{84}\binom{100}{x}\times (0.80)^{x}(0.20)^{100-x}[/tex]

P(74 ≤ X ≤ 84) = 0.7264

Answer:

HCF(91,39) = 13 and HCF(73,21) = 1

Step-by-step explanation:

As per euclidian algorithm, a = bq + r, where a is dividend, b is divisor, q is quotient and r is remainder.

We can use euclidian algorithm to find the HCF of numbers.

To find: HCF ( 91, 39 ):

On dividing 91 by 39, we get

91=39×2+13

Here, remainder = 13 [tex]\neq 0[/tex]

So, again applying division algorithm on 39 and 13, we get

[tex]39=13\times 3+0[/tex]

As remainder = 0 and divisor at this step is equal to 13, HCF = 13 .

To find: HCF ( 73, 21 )

On dividing 73 by 21, we get

[tex]73=21\times 3+10[/tex]

Here, remainder = 10 [tex]\neq 0[/tex]

On applying division algorithm on 21 and 10, we get

[tex]21=10\times 2+1[/tex]

Here, remainder = 1 [tex]\neq 0[/tex]

On applying division algorithm on 10 and 1, we get

[tex]10=1\times 10+0[/tex]

As remainder = 0 and divisor at this step is 1, HCF = 1

Answer:

C (0, 9)

Step-by-step explanation:

First, X is reflected across the line x=2.

X(4, -7) becomes X'(0, -7).

Next, X' is reflected across the line y=1.

X'(0, -7) becomes X"(0, 9).

Answer:

Step-by-step explanation:

Infinitely many.

Infinitely many.

A non-homogeneous system of linear equations can have a unique solution, no solution, or infinitely many solutions and a homogeneous system always has at least the trivial solution, and may have infinitely many non-trivial solutions depending on the rank of A.

A non-homogeneous system of linear equations (where the vector b on the RHS is non-zero) can have three types of solutions:

In contrast, a homogeneous system of linear equations (where the vector b on the RHS is zero) always has at least the trivial solution, where all variables equal zero. Depending on the rank of matrix A:

These rules are concisely summarized by the Rouche-Capelli theorem.

Answer:

The number of adult tickets sold was 121

Step-by-step explanation:

The general equation is: S + A = T    ;where S means student tickets, A means adult tickets and T means total tickets. We know that S is two times A and T is 363. So, S will be 2x and A will be x. Then, the new equation is 2x + x = 363.

S + A = T  

2x + x = 363  

3x = 363  

x = 363 / 3

x = 121

Adult tickets: A = x = 121

Student tickets: S = 2x = 2 * 121 = 242

Final answer:

To solve for the number of adult tickets sold, set the number of adult tickets as x, the student tickets as 2x, and use the total of 363 tickets to create the equation 3x = 363. Solving for x, you find that 121 adult tickets were sold.

Explanation:

The numerical problem given is about determining the number of adult tickets and student tickets sold for a school play, with the total number of tickets sold being 363, and the number of student tickets being twice the number of adult tickets sold.

Let the number of adult tickets be x. Then the number of student tickets is 2x. The total number of tickets sold is the sum of the adult tickets and student tickets, which is x + 2x = 3x. Since we know that 363 tickets were sold in total, we can write the equation:

3x = 363

Now, solve for x:

Therefore, 121 adult tickets were sold.

Answer:

Length of B is 7.4833

Step-by-step explanation:

The vector sum of A and B vectors in 2D is

[tex]C=A+B=(a_1+b_1,a_2+b_2)[/tex]

And its magnitude is:

[tex]C=\sqrt{(a_1+b_1)^2+(a_2+b_2)^2} =9[/tex]

Where

[tex]a_1=Asinx[/tex]

[tex]a_2=Acosx[/tex]

[tex]b_1=Bsin(x+90)[/tex]

[tex]b_2=Bcos(x+90)[/tex]

Using the properties of the sum of two angles in the sin and cosine:

[tex]b_1=Bsin(x+90)=B(sinx*cos90+sin90*cosx)=Bcosx[/tex]

[tex]b_2=Bcos(x+90)=B(cosx*cos90-sinx*sin90)=-Bsinx[/tex]

Sustituying in the magnitud of the sum

[tex]C=\sqrt{(Asinx+Bcosx)^2+(Acosx-Bsinx)^2} =9[/tex]

[tex]C=\sqrt{A^2sin^2x+2ABsinxcosx+B^2cos^2x+A^2cos^2x-2ABsinxcosx+B^2sin^2x} =9[/tex]

[tex]C=\sqrt{A^2(sin^2x+cos^2x)+B^2(cos^2x+sin^2x)}[/tex]

[tex]C=\sqrt{A^2+B^2} =9[/tex]

Solving for B

[tex]A^2+B^2 =9^2[/tex]

[tex]B^2 =9^2-A^2[/tex]

Sustituying the value of the magnitud of A

[tex]B^2=81-5^2=81-25=56[/tex]

[tex]B= 7. 4833[/tex]

The calculation reveals that vector B should be approximately 7.48 in length when magnitude of A s 5.00 and magnitude of their vector sum is 9.00.

The subject question asks for the length of vector B given that it is at right angles to vector A, whose magnitude is 5.00, to ensure that the magnitude of their vector sum is 9.00. To solve this problem, we can use the Pythagorean theorem because the vectors are at right angles to each other.

Let's designate the magnitude of vector B as |B|. According to the Pythagorean theorem for right-angled triangles, we have:
|A|² + |B|² = |A + B|²
So, if |A| = 5.00 and the resultant |A + B| = 9.00, we can substitute these values to find |B|:
5.00² + |B|² = 9.00²
|B|² = 9.00² - 5.00²
|B|² = 81.00 - 25.00
|B|² = 56.00

Therefore, |B| = √(56.00)

|B| = 7.48.

So the length of B should be approximately 7.48 to get a resultant magnitude of 9.00 when added to A.