Simplify.
(4x’y - 9xy + 4) + (-7r’y+ 4xy? + 8)

Answer: Top right, a rectangle has all the properties of a square

Step-by-step explanation: A rectangle does not have all the properties of a square.

Answer:

  10.2

Step-by-step explanation:

Apparently, you want to find the solution for ...

  132.2 = 23.2√(5 +2.7t)

  132.2/23.2 = √(5 +2.7t) . . . . divide by 23.2

  (132.2/23.2)² = 5 +2.7t . . . . . square both sides

  (132.2/23.2)² -5 = 2.7t . . . . . subtract 5

  ((132.2/23.2)² -5)/2.7 = t . . . . divide by the coefficient of t

  10.2 ≈ t

It will take about 10.2 years for the demand for computers to reach 132.2 million.

Answer:

[tex]33.6\ cm^{2}[/tex]

Step-by-step explanation:

Given that

The Base of a rhombus = 8 centimetres

Height of a rhombus = 4.2 centimetres

Based on the above information, the area of a rhombus is

[tex]Area\ of\ rhombus = Base \times height[/tex]

[tex]= 8 \times 4.2[/tex]

[tex]= 33.6\ cm^{2}[/tex]

By multiplying the base of a rhombus with the height of a rhombus we can get the area of the rhombus and the same is applied & shown in the computation part i.e to be shown above

Answer:

For a duration of 5 years, Monthly Payment =$600.42

For a duration of 6 years, Monthly Payment =$508.83

Step-by-step explanation:

[tex]P=\dfrac{ar (1+r)^n}{(1+r)^n-1} \\[/tex]

where a= Amount to Finance=$33,000

Annual interest rate = 3.5%=0.035

r=Monthly Interest Rate= 0.035 ÷ 12 =[tex]\frac{7}{2400}[/tex]

n=number of months to pay

For a duration of 5 years

n=5X12=60 months

[tex]P=\dfrac{ar (1+r)^n}{(1+r)^n-1} \\\\P=\dfrac{33000 X\frac{7}{2400} (1+\frac{7}{2400} )^{60}}{(1+\frac{7}{2400})^{60}-1} \\=\dfrac{96.25 (1.1909)}{1.1909-1}\\=\dfrac{96.25 (1.1909)}{0.1909}\\=\dfrac{114.62}{0.1909}=\$600.42[/tex]

For a duration of 6 years

n=6X12=72 months

[tex]P=\dfrac{ar (1+r)^n}{(1+r)^n-1} \\\\P=\dfrac{33000 X\frac{7}{2400} (1+\frac{7}{2400} )^{72}}{(1+\frac{7}{2400})^{72}-1} \\=\dfrac{96.25 (1.2333)}{1.2333-1}\\=\dfrac{96.25 (1.2333)}{0.2333}\\=\dfrac{118.71}{0.2333}=\$508.83[/tex]

Answer:

The z-score (value of z) for an income of $1,100 is 1.

Step-by-step explanation:

We are given that the mean of a normally distributed group of weekly incomes of a large group of executives is $1,000 and the standard deviation is $100.

Let X = group of weekly incomes of a large group of executives

So, X ~ N([tex]\mu=1,000 ,\sigma^{2} = 100^{2}[/tex])

The z-score probability distribution for a normal distribution is given by;

               Z = [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean income = $1,000

            [tex]\sigma[/tex] = standard deviation = $100

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, we are given an income of $1,100 for which we have to find the z-score (value of z);

So, z-score is given by = [tex]\frac{X-\mu}{\sigma}[/tex] = [tex]\frac{1,100-1,000}{100}[/tex] = 1

Hence, the z-score (value of z) for an income of $1,100 is 1.

The z-score for an income of $1,100 is 1.0.

The z-score is a measure of how many standard deviations a particular value, in this case, income, is from the mean of a normally distributed dataset. The formula to calculate the z-score is:

z = (x - μ) / σ

Where:

Given the mean (μ) is $1,000 and the standard deviation (σ) is $100, we can substitute these values into the formula to find the z-score of an income of $1,100.

z = ($1,100 - $1,000) / $100

z = $100 / $100

z = 1

Therefore, the z-score for an income of $1,100 is 1.0. This means the income of $1,100 is one standard deviation above the mean.

Answer:

A.

Its the simplkified version of the question and they both have the same out come which is 22.4

The equivalent expression for 10√5 is √500.

An equivalent expression is an expression that has the same value but does not look the same. When you simplify an expression, you're basically trying to write it in the simplest way possible.

For the given situation,

The expression is 10√5.

If a square number lies inside the square root, then we write that number outside the square root. So,

⇒ [tex]10\sqrt{5}[/tex]

⇒ [tex]\sqrt{10^{2}(5) }[/tex]

⇒ [tex]\sqrt{(100)(5)}[/tex]

⇒ [tex]\sqrt{500}[/tex]

Hence we can conclude that the equivalent expression for 10√5 is √500.

Learn more about equivalent expression here

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This problem can be approached as a binomial distribution. The probability of a particular number of flights on time is calculated using the binomial probability formula. Determining 'unusual' can be subjective but normally a probability less than 0.05 is considered unusual.

This problem is a binomial probability problem because we have a binary circumstance (flight is either on time or it isn't) and a fixed number of trials (14 flights). The binomial probability formula is P(X=k) = C(n, k) * (p^k) * ((1 - p)^(n - k)) where n is the number of trials, k is the number of successful trials, p is the probability of success on a single trial, and C(n, k) represents the number of combinations of n items taken k at a time.

(a) For all 12 flights on time, it seems there's a typo; there are 14 flights in the sample. We can't calculate for 12 out of 14 flights without the rest of the information.

(b) For exactly 10 flights, we use n=14, k=10, p=0.85: P(X=10) = C(14, 10) * (0.85^10) * ((1 - 0.85)^(14 - 10)).

(c) For 10 or more flights on time, it's the sum of the probabilities for 10, 11, 12, 13, and 14 flights on time.

(d) For determining whether 11 or more on-time flights is unusual, it depends on the specific context, but we could consider it unusual if the probability is less than 0.05.

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Analyzing a sample of 14 flights at Denver International Airport, the probability of 10 or more flights arriving on time is 0.3783, and the probability of 11 or more flights arriving on time is 0.2142, which is not considered unusual.

(a) All 12 of the flights were on time.

(b) Exactly 10 of the flights were on time.

(c) 10 or more of the flights were on time.

(d) Would it be unusual for 11 or more of the flights to be on time?

We can use the binomial probability formula to solve this problem. The binomial probability formula is:

P(k successes in n trials) = (n choose k) *[tex](p)^k[/tex] * [tex](q)^(^n^-^k^)[/tex]

where:

n is the number of trials

k is the number of successes

p is the probability of success

q is the probability of failure

In this case, n = 14, p = 0.85, and q = 0.15.

(a) To find the probability that all 12 of the flights were on time, we can plug k = 12 into the binomial probability formula:

P(12 successes in 14 trials) = (14 choose 12) * [tex](0.85)^1^2[/tex]*[tex](0.15)^2[/tex]

Using a calculator, we can find that this probability is approximately 0.0032.

(b) To find the probability that exactly 10 of the flights were on time, we can plug k = 10 into the binomial probability formula:

P(10 successes in 14 trials) = (14 choose 10) *[tex](0.85)^1^0[/tex] *[tex](0.15)^4[/tex]

Using a calculator, we can find that this probability is approximately 0.1022.

(c) To find the probability that 10 or more of the flights were on time, we can add up the probabilities of 10, 11, 12, 13, and 14 successes:

P(10 or more successes) = P(10 successes) + P(11 successes) + P(12 successes) + P(13 successes) + P(14 successes)

Using a calculator, we can find that this probability is approximately 0.3783.

(d) To determine whether it would be unusual for 11 or more of the flights to be on time, we can find the probability of this event and compare it to a common threshold for unusualness, such as 0.05.

P(11 or more successes) = P(11 successes) + P(12 successes) + P(13 successes) + P(14 successes)

Using a calculator, we can find that this probability is approximately 0.2142. This probability is greater than 0.05, so it would not be considered unusual for 11 or more of the flights to be on time.

Answer:

97.73% of bags weigh more than 14.8 ounces.

Step-by-step explanation:

We are given that the weight of potato chip bags filled by a machine at a packaging plant is normally distributed with a mean of 15.0 ounces and a standard deviation of 0.1 ounces.

Let X = weight of potato chip bags filled by a machine

So, X ~ N([tex]\mu=15.0,\sigma^{2} =0.1^{2}[/tex])

The z-score probability distribution for normal distribution is given by;

               Z = [tex]\frac{ X -\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean weight = 15.0 ounces

            [tex]\sigma[/tex] = standard deviation = 0.1 ounces

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, percentage of bags that weigh more than 14.8 ounces is given by = P(X > 14.8 ounces)

  P(X > 14.8 ounces) = P( [tex]\frac{ X -\mu}{\sigma}[/tex] > [tex]\frac{14.8-15.0}{0.1}[/tex] ) = P(Z > -2) = P(Z < 2)

                                                                   = 0.9773 or 97.73%

Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 2 in the z table which has an area of 0.9773.

Hence, 97.73% of bags weigh more than 14.8 ounces.

To find the percentage of bags weighing more than 14.8 ounces, we calculate the z-score for 14.8 ounces and use the normal distribution properties. A z-score of -2 corresponds to 2.28% of bags weighing less, so about 97.72% weigh more.

To determine what percentage of potato chip bags weigh more than 14.8 ounces when the mean weight is 15.0 ounces with a standard deviation of 0.1 ounces, we use the properties of the normal distribution. First, we calculate the z-score for 14.8 ounces:

Z = (X - μ) / σ = (14.8 - 15.0) / 0.1 = -2

The z-score tells us how many standard deviations away 14.8 ounces is from the mean. A z-score of -2 indicates that 14.8 ounces is 2 standard deviations below the mean. Using the z-score table or a calculator with normal distribution functions, we find the area to the left of z = -2. This area represents the percentage of bags weighing less than 14.8 ounces. Since we're interested in bags weighing more than 14.8 ounces, we subtract this value from 1 (or 100% if we're working with percentages).

For z = -2, the area to the left is approximately 0.0228 (or 2.28%). Therefore, the percentage of bags that weigh more than 14.8 ounces is about 100% - 2.28% = 97.72%.

Answer:

(a) The least-square regression line is: [tex]y=4.662+2.709x[/tex].

(b) The number of households using online banking at the beginning of 2007 is 31.8.

Step-by-step explanation:

The general form of a least square regression line is:

[tex]y=\alpha +\beta x[/tex]

Here,

y = dependent variable

x = independent variable

α = intercept

β = slope

(a)

The formula to compute intercept and slope is:

[tex]\begin{aligned} \alpha &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \\\beta &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \end{aligned}[/tex]

The values of ∑X, ∑Y, ∑XY and ∑X² are computed in the table below.

Compute the value of intercept and slope as follows:

[tex]\begin{aligned} \alpha &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 68.6 \cdot 55 - 15 \cdot 218.9}{ 6 \cdot 55 - 15^2} \approx 4.662 \\ \\\beta &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 6 \cdot 218.9 - 15 \cdot 68.6 }{ 6 \cdot 55 - \left( 15 \right)^2} \approx 2.709\end{aligned}[/tex]

The least-square regression line is:

[tex]y=4.662+2.709x[/tex]

(b)

For the year 2007 the value of x is 10.

Compute the value of y for x = 10 as follows:

[tex]y=4.662+2.709x[/tex]

  [tex]=4.662+(2.709\times10)\\=4.662+27.09\\=31.752\\\approx 31.8[/tex]

Thus, the number of households using online banking at the beginning of 2007 is 31.8.

Answer:

Please see attachment

Question:

The options are;

(a) (9 - 2s1, 3 + 3s1, s1)

solution

not a solution

(b) (-4 - 5s1, s1,  -(3 + s1)/2)

solution

not a solution

(c) (11 + 10s1, -3 - 2s1, s1)

solution

not a solution

(d) ((6 - 4s1)/3, s1, -(7 - s1)/4)

solution

not a solution

Answer:

The options that form a solution of the given system are;

(b) and (c)

Step-by-step explanation:

Here we have

3·x₁ + 8·x₂ − 14·x₃ = 9

x₁ + 3·x₂ − 4·x₃ = 1

(a) (9 - 2·s₁, 3 + 3·s₁,s₁)

3·(9 - 2·s₁) + 8·(3 + 3·s₁) − 14·s₁ = 4s₁+51

Not a solution

(b) (-4 - 5s₁, s₁, -(3 + s1)/2)

3·(-4 - 5s₁) + 8·(s₁) − 14·-(3 + s1)/2 = 9

(-4 - 5s₁) + 3·(s₁) − 4·-(3 + s1)/2 = 2

Solution

(c) (11 + 10s₁, -3 - 2s₁, s₁ )

3·(11 + 10s₁) + 8·(-3 - 2s₁) − 14·s₁  = 9

(11 + 10s₁) + 3·(-3 - 2s₁) − 4·s₁ = 2

Solution

(d) ((6 - 4s1)/3, s1, -(7 - s1)/4)

3·(6 - 4s1)/3+ 8·s1− 14·-(7 - s1)/4 = 0.5s₁ +30.5  

Not a solution

Answer:

1/2

Step-by-step explanation:

Answer:

11/12

Step-by-step explanation:

If you convert 3/4 and 1/6,

you will get 9/12+2/12.

If you add both of them, you will get your answer.

Answer:

Step-by-step explanation:

Hi there,

To get started, recall the area of a bound circle formula:

[tex]A = \pi r^{2}[/tex]    where r is radius of the circle. However, Juan used an approximate value of π, 3.14. So for our purposes, the formula becomes:

[tex]A=[/tex] [tex](3.14)r^{2}[/tex]

Juan measured the circle's diameter, so we can find radius from diameter first. Radius is simply twice the length of the diameter; from one circle endpoint to the center, to the endpoint across, making a straight line:

[tex]d=2r[/tex] ⇒ [tex]r=\frac{d}{2} = \frac{5 \ cm}{2} = 2.5 \ cm[/tex]

Now plug in to obtain area:

[tex]A = (3.14)(2.5 cm)^{2} =19.625 \ cm^{2}[/tex]

The area is 19.265 centimetres squared.

Cross-sections are the area shapes when you cut through a 3D volume; if you cut through a pipe perpendicular to where it flows, you can see it is a circle! If you cut straight through a cube, it would be a square, etc.

If you liked this solution, hit Thanks or give a Rating!

thanks,

Answer:

[tex]y=x-2[/tex]

Step-by-step explanation:

So we are given the formula for the slope of a hyperbola in this form:

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex].

That formula for the slope is [tex]m=\frac{b^2x}{a^2y}[/tex]

If we compare the following two equations, we will be able to find [tex]a^2[/tex] and [tex]b^2[/tex]:

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]

[tex]\frac{x^2}{8}-\frac{y^2}{4}=1[/tex]

We see that [tex]a^2=8[/tex] while [tex]b^2=4[/tex].

So the slope at [tex](x,y)=(4,2)[/tex] is:

[tex]m=\frac{b^2x}{a^2y}=\frac{4(4)}{8(2)}=\frac{16}{16}=1[/tex].

Recall: Slope-intercept form of a linear equation is [tex]y=mx+b[/tex].

We just found [tex]m=1[/tex]. Let's plug that in.

[tex]y=1x+b[/tex]

[tex]y=x+b[/tex]

To find [tex]b[/tex], the [tex]y[/tex]-intercept, we will need to use a point on our tangent line. We know that it is going through [tex](4,2)[/tex].

Let's enter this point in to find [tex]b[/tex].

[tex]2=4+b[/tex]

Subtract 4 on both sides:

[tex]2-4=b[/tex]

Simplify:

[tex]-2=b[/tex]

The equation for the tangent line at [tex](4,2)[/tex] on the given equation is:

[tex]y=x-2[/tex]

Answer: y = x - 2

Step-by-step explanation:

First you take the derivative of each term. d/dx(x²/8) - d/dx(y²/4) = d/dx(1)

x/4 - (y/2)dy/dx = 0

Then you solve for dy/dx: dy/dx = x/2y

Plug in the values: dy/dx = 1

To find the y-intercept, plug in values for y = mx+ b. 2 = 4 + b, b = -2

The equation is y = x - 2

Answer:

[tex]t_{1/2} \approx 9.6\,days[/tex]

Step-by-step explanation:

The time constant of the radioactive constant is:

[tex]\tau = \frac{1}{0.072}\,days[/tex]

[tex]\tau = 13.889\,days[/tex]

The half-life of the substance is:

[tex]t_{1/2} = \tau \cdot \ln 2[/tex]

[tex]t_{1/2} = (13.889\,days)\cdot \ln 2[/tex]

[tex]t_{1/2} \approx 9.6\,days[/tex]

Answer:

0.124 = 12.4% probability that exactly 9 small aircraft arrive during a 1-hour period.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given time interval.

Rate of 8 per hour

This means that [tex]\mu = 8[/tex]

(a) What is the probability that exactly 9 small aircraft arrive during a 1-hour period?

This is P(X = 9).

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 9) = \frac{e^{-8}*8^{9}}{(9)!} = 0.124[/tex]

0.124 = 12.4% probability that exactly 9 small aircraft arrive during a 1-hour period.

Answer:

pls I can't see any diagram anywhere

Answer:

A:0.055

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 2.5, \sigma = 0.25[/tex]

Which of the following is closest to the probability that the selected battery will have a life span of at most 2.1 hours?

This is the pvalue of Z when X = 2.1. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.1 - 2.5}{0.25}[/tex]

[tex]Z = -1.6[/tex]

[tex]Z = -1.6[/tex] has a pvalue of 0.0548

So the correct answer is:

A:0.055

Final answer:

The probability that all three students were born on Wednesday is 1/343.

Explanation:

To find the probability that all three students were born on Wednesday, we need to consider the total number of possible outcomes and the number of favorable outcomes.

There are 7 days in a week, so each student has a 1/7 chance of being born on Wednesday. Since the students are chosen at random and the choices are independent, we can multiply the probabilities together to find the probability that all three students were born on Wednesday:

P(all three born on Wednesday) = (1/7) * (1/7) * (1/7) = 1/343.

Answer:

F (x) = -3x+5x^2+8 has complex roots.

Step-by-step explanation:

number of roots?

ok.

f(x) =   5xx - 3x + 8  =   5xx + 5x  - 8x  + 8   ( I was guessing what numbers would sum to -3)

nope.

ok try discriminant:    (-3)^2 - 4*5 * 8 =   9 - 160  < 0

2 complex roots

Answer:

2/4

Step-by-step explanation:

2+2=4 so 2/4

50%

Answer:

50% chance

Step-by-step explanation:

since half of the balls are red and half are black there will be a 50%chance of picking a black one from the bag

Answer: I think it’s B and D on eduinuity 2021

Step-by-step explanation:

The required 5m²2n² is the greatest common factor of (b) 5m⁴n₃ and (d) 15m²n².

The greatest common factor (GCF) is the largest positive integer that divides two or more numbers without leaving a remainder. In other words, it is the largest number that is a factor of all the given numbers.

For example, the GCF of 12 and 18 is 6, because 6 is the largest positive integer that divides both 12 and 18 without leaving a remainder.

here,
The terms that could have the greatest common factor of 5m²n² are:
5m⁴n₃, since 5m²n² is a factor of both 5m⁴n³ and 5m²n².
15m²n², since 5m²n² is a factor of both 15m²n² and 5m²2n².

Therefore, the correct options are (b) 5m⁴n₃ and (d) 15m²n².

Learn more about the greatest common factors here: https://brainly.com/question/11221202
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The complete question is given in the attachment below,

Answer: x=  −6 /5  is the answer

Answer:

x= -1 1/5 or x= -1.2

Step-by-step explanation:

-4x+-3=x+3

-5x-3=3

-5x=6

-x=6/5

x=-6/5

x=-1 1/5

or x=-1.2

Hope this helps! Pls rate brainliest

Answer:

18.86 feet

Step-by-step explanation:

The circumference of the inner circle is 88 ft.

Circumference of a Circle[tex]=2\pi r[/tex]

Therefore:

[tex]2\pi r =88\\r=88 \div (2*\frac{22}{7})=14 ft[/tex]

Radius of the inner circle=14 feet

If the distance between the inner circle and the outer circle is 3 ft, the radius of the outer circle=14+3 =17 feet.

Therefore. circumference of the outer Circle[tex]=2\pi r[/tex]

[tex]=2*\frac{22}{7}*17=106.86 ft[/tex]

Difference in Circumference=106.86-88 =18.86 feet

The circumference of the outer circle is greater than that of the inner circle by 18.86 feet.

18.9

Step-by-step explanation:

Answer:

Increasing:

[tex](\frac{\pi}{3},\frac{5\pi}{3})[/tex]

Decreasing

[tex](0,\frac{\pi}{3})[/tex] U [tex](\frac{5\pi}{3},2\pi)[/tex]  

Step-by-step explanation:

Increasing and Decreasing Intervals

To find if a function is increasing in a point x=a, we evaluate the first derivative in x=a and if:

For continuous functions, we can safely assume between a given critical point and the next one, the function keeps its behavior, i.e. it's increasing or decreasing in the interval formed by both points.

So, we find the critital points of  

[tex]f(x)=x-2sinx[/tex]

Taking the derivative

[tex]f'(x)=1-2cosx[/tex]

Equating to 0

[tex]1-2cosx=0[/tex]

Solving

[tex]\displaystyle cosx=\frac{1}{2}[/tex]

There are two solutions in the interval  [tex](0,2\pi)[/tex]

[tex]\displaystyle x=\frac{\pi}{3},\ x=\frac{5\pi}{3}[/tex]

Now we compute the second derivative

[tex]f''(x)=2sinx[/tex]

Evaluating for both critical points

[tex]\displaystyle f''(\frac{\pi}{3})=2sin\frac{\pi}{3}=\sqrt{3}[/tex]

Since it's positive, the point is a minimum

[tex]\displaystyle f''(\frac{5\pi}{3})=2sin\frac{5\pi}{3}=-\sqrt{3}[/tex]

Since it's negative, the point is a maximum

In the interval  

[tex](0,\frac{\pi}{3})[/tex]

the function is decreasing

In the interval  

[tex](\frac{\pi}{3},\frac{5\pi}{3})[/tex]

the function is increasing

In the interval  

[tex](\frac{5\pi}{3},2\pi)[/tex]  

the function is decreasing

First, you need to find the derivative of the function f(x) = x - 2sin(x).

Using the rules of calculus, the derivative of x is 1 and the derivative of -2sin(x) is -2cos(x). Therefore, the derivative of the function, denoted as f'(x), is given by:

f'(x) = 1 - 2cos(x).

To determine where the function is increasing or decreasing, we need to find the critical points, the x-values where the derivative of the function is equal to zero or undefined.

Setting the derivative equal to zero and solving:

1 - 2cos(x) = 0.

2cos(x) = 1.

cos(x) = 1/2.

The solutions to this equation on the interval 0 to 2π are x = π/3 and x = 5π/3.

With these critical points, we have divided the entire interval into three subintervals:

(0, π/3), (π/3, 5π/3), and (5π/3, 2π).

We now determine the sign of the derivative on each of these intervals. We pick a "test point" from each interval and substitute it into the derivative.

From (0, π/3), we pick x = π/6, and find that f'(π/6) is positive.
From (π/3, 5π/3), we pick x = π, and find that f'(π) is negative.
From (5π/3, 2π), we pick x = 3π/2, and find that f'(3π/2) is positive.

By the First Derivative Test, a positive derivative indicates that the function is increasing on that interval and a negative derivative indicates that the function is decreasing on that interval.

Therefore, the function increases on the intervals (0, π/3) and (5π/3, 2π),
and decreases on the interval (π/3, 5π/3).

#SPJ3

Answer:

  about 100 cm²

Step-by-step explanation:

The side length of the rhombus is 1/4 of the perimeter so is 10 cm. The length of half of the other diagonal will be the length of the leg of a right triangle with hypotenuse 10 and leg 7 (half the given diagonal).

  d= √(10² -7²) = √51

Then the area of the rhombus is the product of this and the given diagonal:

  A = (14 cm)(√51 cm) ≈ 99.98 cm²

The area of the rhombus is about 100 cm².

Answer:

At 95% confidence level, the difference between the proportion of freshmen using steroids in Illinois and the proportion of seniors using steroids in Illinois is -7.01135×10⁻³ < [tex]\hat{p}_1-\hat{p}_2[/tex] < 1.237

Step-by-step explanation:

Here we are required to construct the 95% confidence interval of the difference between two proportions

The formula for the confidence interval of the difference between two proportions is as follows;

[tex]\hat{p}_1-\hat{p}_2\pm z^{*}\sqrt{\frac{\hat{p}_1\left (1-\hat{p}_1 \right )}{n_{1}}+\frac{\hat{p}_2\left (1-\hat{p}_2 \right )}{n_{2}}}[/tex]

Where:

[tex]\hat{p}_1 = \frac{34}{1679}[/tex]

[tex]\hat{p}_2 = \frac{24}{1366}[/tex]

n₁ = 1679

n₂ = 1366

[tex]z_{\alpha /2}[/tex] at 95% confidence level = 1.96

Plugging in the values, we have;

[tex]\frac{34}{1679}- \frac{24}{1366} \pm 1.96 \times \sqrt{\frac{ \frac{34}{1679}\left (1- \frac{34}{1679}\right )}{1679}+\frac{\frac{24}{1366} \left (1-\frac{24}{1366} \right )}{1366}}[/tex]

Which gives;

-7.01135×10⁻³ < [tex]\hat{p}_1-\hat{p}_2[/tex] < 1.237.

At 95% confidence level, the difference between the proportion of freshmen using steroids in Illinois and the proportion of seniors using steroids in Illinois = -7.01135×10⁻³ < [tex]\hat{p}_1-\hat{p}_2[/tex] < 1.237.

Answer:

6 minutes

Step-by-step explanation:

Since it's you have 10 dollars in one hour, and you want to find 1/10th of the dollar value, you'd multiply 1/10th, or 0.1 by the time as well. I converted it into minutes because we're finding a smaller unit of time than 1 hour.

60 min x 1/10 (or 60 min/10)=  6 minutes

I hope this helped!

6 minutes

If it takes 1 hour to earn $10, we convert that 1 hour to 60 minutes. Now we will divide 60 by 10, and that gives you 6. Therefore every 6 minutes you earn $1.

Hope this helps!

The input units of the function f(t) are students multiplied by dollars per student.

The function[tex]\( f(t) = s(t) \cdot c(t) \)[/tex] represents the total cost to educate all the students in the elementary school t years after 2002. To determine the input units of this function, we need to analyze the units of its individual components.

s(t) is the number of students at time t. Its unit is "students."

c(t) is the cost to educate one student at time t. Its unit is "dollars per student."

When you multiply s(t)  by c(t), the units combine as follows:

[tex]\[ f(t) = s(t) \cdot c(t) = \text{"students"} \times \left(\frac{\text{"dollars"}}{\text{"student"}}\right) = \text{"students"} \cdot \text{"dollars per student"} \][/tex]

Therefore, the input units of the function f(t) are students multiplied by dollars per student.

The student must sell at least 70 glasses of lemonade at $0.25 each, considering the initial costs of $16.00 and the additional $0.02 cost per glass for sugar, to begin to make a profit.

To calculate the minimum number of glasses of lemonade that must be sold to start making a profit, we need to consider the total costs and the revenue per glass. The student spent $12.00 on lemons and $4.00 on glasses, totaling $16.00 in costs. Additionally, each glass of lemonade has an added cost of $0.02 for sugar. The revenue from selling one glass of lemonade is $0.25.

To break even, the total revenue must equal the total costs. As costs are fixed at $16.00 and the variable cost is $0.02 per glass, we can set up the equation: (Number of glasses × $0.25) - (Number of glasses × $0.02) = $16.00. This simplifies to (Number of glasses × $0.23) = $16.00, and solving for Number of glasses gives us Number of glasses = $16.00 / $0.23, which is approximately 69.57 glasses. Since you can't sell a fraction of a glass, rounding up means the student needs to sell at least 70 glasses to begin to make a profit.

Answer:

a) 10.34% probability​ that, in a​ year, there will be 4 hurricanes.

b) 3.62 years are expected to have 4 ​hurricanes

c) Either 3 or 4 hurricanes(discrete number) are close to the mean of 3.62, which means that the Poisson distribution works well in this case.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

6.7 per year.

This means that [tex]\mu = 6.7[/tex]

a. Find the probability​ that, in a​ year, there will be 4 hurricanes.

This is P(X = 4).

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 4) = \frac{e^{-6.7}*(6.7)^{4}}{(4)!} = 0.1034[/tex]

10.34% probability​ that, in a​ year, there will be 4 hurricanes.

b. In a 35​-year ​period, how many years are expected to have 4 ​hurricanes?

Each year, 0.1034 probability of 10 hurricanes.

In 35 years

35*0.1034 = 3.62

3.62 years are expected to have 4 ​hurricanes

c. How does the result from part​ (b) compare to a recent period of 35 years in which 3 years had 4 ​hurricanes? Does the Poisson distribution work well​ here?

Either 3 or 4 hurricanes(discrete number) are close to the mean of 3.62, which means that the Poisson distribution works well in this case.

Final answer:

Using the Poisson distribution with a mean of 6.7 hurricanes per year, the probability of exactly 4 hurricanes occurring in one year is calculated. Multiplying this probability by 35 provides the expected number of years with 4 hurricanes in a 35-year period, which is then compared to an actual historical period to evaluate the fit of the Poisson distribution to the data.

Explanation:

The student's question pertains to the application of the Poisson distribution to determine the probability of certain events. Given that the mean number of hurricanes in a certain area is 6.7 per year, we can use the Poisson formula to calculate the probabilities:

To find the probability that there will be 4 hurricanes in a year, we use the formula:

P(x; μ) = ( × e^-μ) / x!

To determine how many years are expected to have 4 hurricanes in a 35-year period, we multiply the probability found in part a by 35.

When comparing the expected number of years with 4 hurricanes to an actual 35-year period where 3 years had 4 hurricanes, it can be seen whether the Poisson distribution provides a good fit for the actual data.