of the 10 people attending a seminar, 5 have gray hair.
What is the probability that a randomly selected person will have gray hair?

Step-by-step explanation:

[tex]y' + y = y^2[/tex]

We can rewrite the differential equation above as

[tex]\dfrac{dy}{dx} + y = y^2[/tex]

[tex]dy = (y^2 - y)dx[/tex]

or

[tex]\dfrac{dy}{y^2 -y} = dx[/tex]

We can rewrite the left side of the equation above as

[tex]\dfrac{dy}{y^2-y}=\dfrac{dy}{y(y-1)}= \left(\dfrac{1}{y-1} - \dfrac{1}{y} \right)dy[/tex]

We can the easily integrate this as

[tex]\displaystyle \int \left(\dfrac{1}{y-1} - \dfrac{1}{y} \right)dy = \int dx[/tex]

or

[tex]\displaystyle \int \dfrac{dy}{y-1} - \int \dfrac{dy}{y} = \int dx[/tex]

This will then give us

[tex]\ln |y-1| - \ln |y| + \ln |k| = x[/tex]

where k is the constant of integration. Combining the terms on the left hand side, we get

[tex]\ln \left|\dfrac{k(y-1)}{y} \right| = x[/tex]

or

[tex]\dfrac{y-1}{y} = \frac{1}{k}e^x[/tex]

Solving for y, we get

[tex]y= \dfrac{1}{1- \frac{1}{k} e^x}=\dfrac{k}{k-e^x}[/tex]

We know that [tex]y(0)= \frac{1}{3}[/tex], so when we substitute [tex]x=0[/tex], we find that [tex]k = -\frac{1}{2}[/tex].

Therefore, the final form of the solution to the differential equation above is

[tex]y = \dfrac{1}{1+2e^x}[/tex]

Answer:

221

Step-by-step explanation:

5(3)2-4

Answer:

221

Step-by-step explanation:

Answer: Part A: Find a rational number that is between 9.5 and 9.7. Explain why it is rational.

Step-by-step explanation:

Part B: Find an irrational number that is between 9.5 and 9.7. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth

Answer:

x = 17

Step-by-step explanation:

in such a constellation (two beams from the same point of origin cut through the same circle) the relative relation between the segments of these beams to the overall length of the beam have to be the same :

7 × (7+x) = 8 × (8+13)

49 + 7x = 8 × 21 = 168

7x = 119

x = 17

Answer:

1. positive

2. No

(for number 3, I'm not sure if my answer to it is going to be correct)

Step-by-step explanation:

1. the dots look like they are going up

2. there are no outlying dots that look unusual

Step-by-step explanation:

SA=

[tex]2\pi \gamma {2} + 2\pi \gamma h[/tex]

[tex]2\pi(7){2} + 2\pi(7)(20)[/tex]

[tex]2\pi(49) + 2\pi(140)[/tex]

[tex]98\pi + 280\pi[/tex]

[tex]378\pi[/tex]

[tex]1187.52cm[/tex]

Answer:

A

Step-by-step explanation:

Answer:

A. f(x) = -0.5(x+3) (x-5)

Answer:

2.5 hours is the time it will take.

Step-by-step explanation:

50t + 55t-30 = 235

105t = 265

T = 2.5 hours (rounded to one d.p)

Answer:

5814

Step-by-step explanation:

V= width x height x length

V=17·19·18=5814

Answer:

The values of [tex]m[/tex] and [tex]n[/tex] are 0 and 2, respectively.

Step-by-step explanation:

If [tex]\vec {c} = m\,\hat{i} + n\,\hat{j} + \hat{k}[/tex] is perpendicular to [tex]\vec {a} = 5\,\hat{i} + \hat{j} -2\,\hat{k}[/tex] and [tex]\vec {b} = 3\,\hat{i} - 3\,\hat{j} + 6\,\hat{k}[/tex], then the following relationships must be observed:

[tex]\vec {c}\,\bullet\,\vec {a} = 0[/tex] (1)

[tex]\vec{c}\,\bullet \,\vec{a} = 0[/tex] (2)

Then, we expand the previous expressions:

[tex](m, n, 1)\,\bullet\,(5, 1, -2) = 0[/tex]

[tex]5\cdot m + n = 2[/tex] (1b)

[tex](m, n, 1)\,\bullet\,(3, -3, 6) = 0[/tex]

[tex]3\cdot m - 3\cdot n = -6[/tex] (2b)

Then, we solve for [tex]m[/tex] and [tex]n[/tex]:

[tex]m = 0, n = 2[/tex]

The values of [tex]m[/tex] and [tex]n[/tex] are 0 and 2, respectively.

Answer:

82% of what number is 369

82% of 450 is 369

Answer:

number is 450

Step-by-step explanation:

let the number be x

82% of x=369

[tex]\frac{82}{100}[/tex]x = 369

82x=369*100

x=36900/82

x=450

Answer:

10x ÷ 5x=2x

10x ÷ 5x = 2x

10x÷ 5x = 2x

Answer:

[tex]e^{2x}=5[/tex]

Step-by-step explanation:

Recall that [tex]\log_b a=c\implies b^c=a[/tex].

In this case, we need to find the base of the logarithm. The logarithm [tex]\ln[/tex] denotes natural [tex]\log[/tex] with a base of [tex]e[/tex], a mathematical constant.

Therefore, we can re-write the equation as:

[tex]\log_e5=2x[/tex]

To write the equation as an exponential equation, recall the definition of log (first sentence of explanation):

[tex]\boxed{e^{2x}=5}[/tex]

Answer:

Answer:

11n + 19

Step-by-step explanation:

The parentheses can be removed immediately without affecting the clarity of this expression:

4n + 13 + 6 + 7n

Next we combine like terms, obtaining:

11n + 19

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\textsf{(4n + 13) + (6 + 7n)}\\\\\large\textsf{ = 4n + 13 + 6 + 7n}\\\\\large\textsf{COMBINE the LIKE TERMS}\\\\\large\textsf{(4n + 7n) + (13 + 6)}\\\\\large\textsf{4n + 7n = \boxed{\large\textsf{\bf 11n}}}\\\\\large\textsf{13 + 6 = \boxed{\large\textsf{\bf 19}}}\\\\\\\boxed{\huge\textsf{= 11n + 19}}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Answer: \bf 11n + 19}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

(6,6)

You can use the midpoint formula.

Answer:

24x+2

Step-by-step explanation:

Answer:

answer is B 38-18

Step-by-step explanation:

38 + (-18)

38-18

Answer:

Step-by-step explanation:

588000-540000=48000

48000/540000=8.8%

8.8%/2 years =4.4%

Answer:

The interval that would represent the middle 68% of the scores of all the games that Riley bowls is (147, 173).

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 160, standard deviation of 13.

Middle 68% of the scores of all the games that Riley bowls.

Within 1 standard deviation of the mean, so:

160 - 13 = 147.

160 + 13 = 173.

The interval that would represent the middle 68% of the scores of all the games that Riley bowls is (147, 173).

Answer:

The upper bound of the interval is below 0.5, which means that it can be claimed that a majority of people are not in favor of legalized abortion

Step-by-step explanation:

Confidence interval:

Sample proportion plus/minus margin of error.

In this question:

Sample proportion of 0.45, margin of error of 0.04. So

0.45 - 0.04 = 0.41

0.45 + 0.04 = 0.49

The confidence interval is of (0.41,0.49). The upper bound of the interval is below 0.5, which means that it can be claimed that a majority of people are not in favor of legalized abortion

Answer:

[tex]\text{C. }1[/tex]

Step-by-step explanation:

In the question, we're given that the notation [tex]\#\#(a,b,c)[/tex] produces a number [tex]a[/tex] less than the product of [tex]b[/tex] and [tex]c[/tex] raised to the [tex]a[/tex] power. Let the number produced be [tex]n[/tex]. As a mathematical equation, we can write this production as [tex]n=(bc)^a-a[/tex]

For [tex]\#\#(2, 5, x)[/tex], we can assign:

Substituting these values into [tex]n=(bc)^a-a[/tex], we get:

[tex]23=(5x)^2-2[/tex]

Add 2 to both sides:

[tex]25=(5x)^2[/tex]

Take the square root of both sides:

[tex]5=|5x|[/tex]

For [tex]y=|z|[/tex], there are two cases:

[tex]\begin{cases}y=z,\\y=-z\end{cases}[/tex]

Therefore, we have:

[tex]\begin{cases}5=5x, x=\boxed{1}\\5=-(5x), 5=-5x, x=\boxed{-1}}\end{cases}[/tex]

The only answer choice applicable is [tex]\boxed{\text{C. }1}[/tex].

Answer:

19 billion dollars

Step-by-step explanation:

Given the equation :

S - 1.3x = 6

Where, S = amount of sale of statin in billions of dollars ; x = number of years after 1998

Amount spend in 2008

x = 2008 - 1998 = 10

Put x = 10 in the equation ;

S - 1.3x = 6

S - 1.3(10) = 6

S - 13 = 6

S = 6 + 13

S = 19

People will spend about 19 billion dollars on statin in 2008

Answer:

0.3745 = 37.45% probability that a single randomly selected value is less than 962 dollars.

0.0037 = 0.37% probability that a sample of size 72 is randomly selected with a mean less than 962 dollars.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

CNNBC recently reported that the mean annual cost of auto insurance is 1049 dollars. Assume the standard deviation is 275 dollars.

This means that [tex]\mu = 1049, \sigma = 275[/tex]

Find the probability that a single randomly selected value is less than 962 dollars.

This is the p-value of Z when X = 962. So

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

[tex]Z = \frac{962 - 1049}{275}[/tex]

[tex]Z = -0.32[/tex]

[tex]Z = -0.32[/tex] has a p-value of 0.3745

0.3745 = 37.45% probability that a single randomly selected value is less than 962 dollars.

Sample of 72

This means that [tex]n = 72, s = \frac{275}{\sqrt{72}}[/tex]

Probability that the sample mean is les than 962.

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

By the Central Limit Theorem

[tex]Z = \frac{962 - 1049}{\frac{275}{\sqrt{72}}}[/tex]

[tex]Z = -2.68[/tex]

[tex]Z = -2.68[/tex] has a p-value of 0.0037

0.0037 = 0.37% probability that a sample of size 72 is randomly selected with a mean less than 962 dollars.

Answer:

a) The initial quantity is 2.9.

b) The initial quantity is 2.9.

c) The multiplier is 1.05 > 1, and thus, the quantity is growing.

Step-by-step explanation:

Exponential equations:

Have the following format:

[tex]A(t) = A(0)(k)^t[/tex]

In which A(0) is the initial amount and k is the multiplier.

If k > 0, the quantity is growing.

If k < 0, the quintity is decaying.

In this question:

[tex]P(t) = 2.9(1.05)^t[/tex]

a, b. The initial quantity is

P(0). So

[tex]P(0) = 2.9(1.05)^0 = 2.9*1 = 2.9[/tex]

The initial quantity is 2.9.

c. Is the quantity growing or decaying?

The multiplier is 1.05 > 1, and thus, the quantity is growing.

9514 1404 393

Answer:

  -7x -3

Step-by-step explanation:

(f -g)(x) = f(x) -g(x) = (-3x -5) -(4x -2)

(f -g)(x) = -3x -5 -4x +2 = (-3-4)x +(-5+2)

(f -g)(x) = -7x -3

Answer:

10/13

Step-by-step explanation:

The chance that you pick an apple is 5/13 and the chance it's a peach is 5/13 because in total there's 13 fruits.

Since it says what's the chance it's either an apple OR peach you add these two fractions: 5/13+5/13 = 10/13

If the question said what's the probability you pick an apple AND a peach then you'd mutiply not add.

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the dimension of the dam is not given.

However, a general way of calculating volume is to calculate the base area and the multiply by height.

Take for instance,the dam has a rectangular base of 20m by 30m.

The base area will be

Area = 20m * 30m = 600m²

If the height of the water in the dam is 40m, then the volume is:

Volume = 600m² * 40m

Volume = 24000m³

Answer:

n=3.5, n=0

Step-by-step explanation:

Open the parenthesis

2n(-4n)-7(-4n)=0

-8n^2+28n=0

Factor:

n(-8n+28)=0

Solve:

n=0, or -8n+28=0

-8n=-28

8n=28

n=28/8

n=3.5

n can be either 3.5 or 0

Answer:

0, 7/2

Step-by-step explanation:

See image below:)

Answer:

5pi

is answer

Step-by-step explanation:

hear is your answer in attachment