In 1927, Charles Lindburgh had his first solo flight across the Antlantic Ocean. He flew 3,610 miles in 33.5 hours. If he flew about the same number of miles each hour, how many miles did he fly each hour?

The probability that the random variable will take on a value between 31 and 35 is 0.2620 or 26.20%.

To solve this problem, we need to standardize the values of 31 and 35 using the formula:

z = (x - μ) / σ

where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

For x = 31:

z = (31 - 30) / 5 = 0.2

For x = 35:

z = (35 - 30) / 5 = 1

Now, we can use a standard normal distribution table or calculator to find the probabilities corresponding to these z-values. The probability of getting a value between 31 and 35 is the difference between the probability of getting a z-value less than 1 and the probability of getting a z-value less than 0.2:

P(31 ≤ x ≤ 35) = P(z ≤ 1) - P(z ≤ 0.2)
= 0.8413 - 0.5793
= 0.2620

Therefore, the probability that the random variable will take on a value between 31 and 35 is 0.2620 or 26.20%.

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Answer:

216*64/8=1728....

Step-by-step explanation:

12³ is the appropriate answer

Answer:

18c + 36

Step-by-step explanation:

Rearrange Terms:

9 (4 + 2c) =

9 (2c + 4) =

18c + 36

Hope this helps! :)

Answer:

1/2

Step-by-step explanation:

Convert the mixed number (1 3/8) into an improper fraction ->

8*1=8

8+3=11

11/8

Now just subtract the numerator, since the denominator is the same

11-7=4

4/8

Now simplify

1/2

Using the z-distribution, it is found that the 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).

We are given the standard deviation for the population, hence, the z-distribution is used. The parameters for the interval is:

Sample mean of  \(x = 12.7\)

Population standard deviation of  \(\sigma = 6.37\)

Sample size of .n = 50

The margin of error is:

\(M = z \frac{\sigma }{\sqrt{n} }\)

In which z is the critical value.

We have to find the critical value, which is z with a p-value of  \(\frac{1+\alpha }{2}\) , in which  \(\alpha\) is the confidence level.

In this problem, , thus, z with a p-value of , which means that it is z = 1.96.

Then:

\(M= 1.96\frac{6.37}{\sqrt{50} } = 1.77\)

The confidence interval is the sample mean plus/minutes the margin of error, hence:

x- M = 12.17 - 1.77 =10.4

x+M = 12.17 + 1.77 = 13.94

The 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).

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The probability that the mean weight of a sample of twenty freshmen will be greater than 145 pounds is 0.138.

The probability is determined using the central limit theorem and the formula for the standard error of the mean:

where;

Data given;

σ = 12.3 pounds; n = 20

SE = 12.3/√20

SE = 2.75 pounds.

The sample mean is then standardized using the z-score formula:

z = (x - μ) / SE

z = (145 - 142) / 2.75

z = 1.09

Using a calculator, the probability of a z-score greater than 1.09 is 0.138.

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Given:

The symbols \(<,>,\leq ,\geq\).

To find:

The correct name for the given group of symbols.

Solution:

We know that,

Equality symbols is \("="\).

Inequalities symbols are \("<,>,\leq ,\geq"\).

Operational signs are \(+,-,\times , \div\).

Radical signs is \(\sqrt{}\).

It means, the symbols \(<,>,\leq ,\geq\) are called inequalities symbols.

Therefore, the correct option is B.

Answer:

Step-by-step explanation:

50a³b = 2⋅5²a³b

8ab = 2³ab

GCF = 2ab

50a³b - 8ab = 2ab(5²a² - 2²)

5²a² - 2² = (5a - 2)(5a + 2)

The change in electrical potential when moving along the x-axis from x = 5.0 m to x = 1.0 m. The result depends on the values of A, B, and C, which are given as 1.5 V/m^(-3), 0.45 V/m^(-2), and -15 V/m^(-1) respectively.

To calculate the change in electrical potential, we need to integrate the electric field along the path of motion. In this case, we are moving along the x-axis, so only the x-component of the electric field is relevant.

The electric potential difference (ΔV) between two points A and B is given by the formula:

ΔV = ∫ E · dl

where E is the electric field and dl is an infinitesimal displacement along the path of motion. Since we are only concerned with the x-component of the electric field, the integral simplifies to:

ΔV = ∫ (Ax^2 + Bz) dx

Integrating with respect to x from x = 5.0 m to x = 1.0 m, we can find the change in electrical potential.

ΔV = ∫ (Ax^2 + Bz) dx = ∫ (1.5x^2 + Bz) dx

Evaluating the integral, we get the change in electrical potential when moving along the x-axis from x = 5.0 m to x = 1.0 m in the given electric field.

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\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ \left(\cfrac{1}{3}\cdot \cfrac{1}{3}\cdot \cfrac{1}{3}\cdot \cfrac{1}{3} \right)^2\implies \left[ \left( \cfrac{1}{3} \right)^4 \right]^2\implies \left( \cfrac{1^4}{3^4} \right)^2 \\\\\\ \left( \cfrac{1^{4\cdot 2}}{3^{4\cdot 2}} \right) \implies \cfrac{1}{3^8} \implies 3^{-8}\)

let's recall that  

\(\begin{array}{llll} 1^1&=&1\\ 1^{10}&=&1\\ 1^{1,000}&=&1\\ 1^{1,000,000,000}&=&1\\ 1^{1,000,000,000,000}&=&1\\ \end{array}\)

The linear representation is a proportional relationship.

What is proportional relationship?

Proportional relationships are those in which the ratios of the two variables are equal. Another way to think about them is that one variable is always a constant value multiplied by the other in a proportionate relationship. The "constant of proportionality" is the name given to this variable.

We know that in a proportional relationship the ratios are equal i.e.

\(\frac{y_{1}}{x_{1} } = \frac{y_{2} }{x_{2} } =\frac{y_{n} }{x_{n} }\)

So,

-16/4 = -12/3 = -8/2 = -4/1 = -4

Since, the ratios of the linear representation are equal, therefore, it is a  proportional relationship.

Hence, the linear representation is a proportional relationship.

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Answer: 15

Step-by-step explanation:

slow eater lol.

in one fifth of a minute, they ate 3 pieces. so add the other four fifths, 3 + 3 + 3 + 3 + 3, and youll get 15. easier to just multiply tho, 1/5 is 3, so 5/5 would be 3(5) = 15. hope this helps

We can conclude that due to the help of nurses, the survival time of patients given drugs was the highest.

The nurse takes the patient's cardiac output and makes a decision on how the patient will react to the medication.

What types of tasks does a nurse perform?

Registered nurses (RNs) administer and supervise patient care, educate the public about various ailments, and provide psychological support and counseling to patients' relatives. Most nurses collaborate to doctors in a variety of contexts.

How many years do such people live?

People who have access for informal health information as having a nurse or doctor in the parents 10% more likely to remain past the age of 80, according study released in a journal article by that of the Directorate of Economic Research.

Therefore, we can conclude that due to the help of nurses, the survival time of patients given drugs was the highest.

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The probability of selecting all bottles of the same variety is P(A) = 6/46656 = 0.00013.

The probability of selecting two bottles of each variety when randomly selecting 6 bottles can be calculated using the formula P(A) = n(A) / n(S), where n(A) is the number of possible ways to select two bottles of each variety and n(S) is the total number of possible ways to select 6 bottles. In this case, n(A) is equal to 6! / (2!2!2!) = 90 and n(S) is equal to 6^6 = 46656. So, the probability of selecting two bottles of each variety is P(A) = 90/46656 = 0.0019.

The probability of selecting all bottles of the same variety when randomly selecting 6 bottles can be calculated using the same formula. In this case, n(A) is equal to 6, which is the number of ways to select 6 bottles of the same variety, and n(S) is equal to 46656. So, the probability of selecting all bottles of the same variety is P(A) = 6/46656 = 0.00013.

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Answer:

A.32.10

Step-by-step explanation:

You have to remember to subtract the $35 then start to figure out how much he paid every month for a year.

Answer:12

Step-by-step explanation: 6 miles is traveled in 1 hour, if you multiply that by 2 you get 12.

The answer is:

12 miles

Work/explanation:

Were asked to find how far she ran. This means that we have to find the distance, given the speed and the time.

We will use the formula:

\(\boldsymbol{Distance=Speed\times Time}\)

Plug in the data

\(\boldsymbol{Distance=2\times6}\)

\(\boldsymbol{Distance=12\:miles}\)

Hence, the answer is 12 miles.

To solve the given initial-value problem, we need to find the solution for the system of differential equations x' = A * x, where x is a vector function of t, and A is the coefficient matrix.

Given:

A = [[1, 2], [0, 1]]

x(0) = [5, 9]

To find the solution, we can use the matrix exponential function.

The matrix exponential function is defined as:

e^(At) = I + At + (A^2)(t^2)/2! + (A^3)(t^3)/3! + ...

To find e^(A*t), we first need to compute the powers of A.

A^2 = [[1, 2], [0, 1]] * [[1, 2], [0, 1]] = [[1, 4], [0, 1]]

Now, we can compute e^(A*t):

e^(At) = I + At + (A^2)*(t^2)/2!

Substituting the values of A and t into the equation, we have:

e^(A*t) = [[1, 0], [0, 1]] + [[1, 2], [0, 1]]t + [[1, 4], [0, 1]](t^2)/2!

Simplifying the expression, we get:

e^(At) = [[1+t+t^2/2, 2t], [0, 1+t]]

To find the solution for the initial-value problem, we multiply e^(A*t) by the initial condition x(0):

x(t) = e^(A*t) * x(0)

Substituting the values of e^(A*t) and x(0), we have:

x(t) = [[1+t+t^2/2, 2*t], [0, 1+t]] * [5, 9]

Simplifying the expression, we get:

x(t) = [5+5t+5t^2/2, 9t]

Therefore, the solution to the given initial-value problem is:

x(t) = [5+5t+5t^2/2, 9t]

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98% sure that's corresponding angles.

Answer:

corresponding angles

Step-by-step explanation:

Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

<95141404393>

\( - \frac{4}{5} \div 2 = - \frac{4}{5} \times \frac{1}{2} = - \frac{2 }{5} \\ \)

So the second one is the correct answer.

Answer:

- 2/5

Step-by-step explanation:

divide

add - sign

hope this helps

Answer:

B) 14, 18, 5

Step-by-step explanation:

This is correct

Answer:

7

Step-by-step explanation:

because 7x7= 49

hopefully you got it right

Answer:

7

Step-by-step explanation:

The standard deviation of the distribution of weights of the dogs in the park is approximately 9.3 kilograms.

We are given that the mean weight of the dogs in the park is 15.3 kilograms. We also know that one of the dogs weighs 25.4 kilograms, which is 1.4 standard deviations above the mean.

To find the standard deviation, we can use the formula for z-score, which is given by (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. In this case, we can set up the equation as (25.4 - 15.3) / σ = 1.4.

Simplifying the equation, we have 10.1 / σ = 1.4. Rearranging, we find σ = 10.1 / 1.4 ≈ 7.214.

Therefore, the standard deviation of the distribution of weights of the dogs is approximately 7.214 kilograms, which is closest to 9.3 kilograms from the given options.

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Answer:

see explanation

Step-by-step explanation:

if the denominator of a rational expression is zero then the expression will be undefined.

the numerator is the part of the rational expression that makes it zero.

solve the numerators in each to find values of x

1

\(\frac{x+6}{x-4}\)

x + 6 = 0 ( subtract 6 from both sides )

x = - 6 ← value that makes expression equal to zero

2

\(\frac{(x+4)(x-2)}{x+6}\)

(x + 4)(x - 2) = 0

equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x - 2 = 0 ⇒ x = 2

x = - 4 and x = 2 make the expression equal to zero

3

\(\frac{2x+10}{3x-12}\)

2x + 10 = 0 ( subtract 10 from both sides )

2x = - 10 ( divide both sides by 2 )

x = - 5 ← value that makes expression equal to zero

Answer:

1)  x = -6

2)  x = -4  and  x = 2

3)  x = -5

Step-by-step explanation:

A rational expression is undefined when the denominator equals zero.

A rational expression equals zero when the numerator equals zero.

Given rational expression:

\(\dfrac{x+6}{x-4}\)

Set the numerator to zero and solve for x:

\(\implies x+6=0\)

\(\implies x=-6\)

Given rational expression:

\(\dfrac{(x+4)(x-2)}{x+6}\)

Set the numerator to zero:

\(\implies (x+4)(x-2)=0\)

Apply the zero-product property and solve for x:

\(\implies x+4=0 \implies x=-4\)

\(\implies x-2=0 \implies x=2\)

Given rational expression:

\(\dfrac{2x+10}{3x-12}\)

Factor the numerator and denominator:

\(\dfrac{2(x+5)}{3(x-4)}\)

Set the numerator to zero and solve for x:

\(\implies 2(x+5)=0\)

\(\implies x+5=0\)

\(\implies x=-5\)

Answer:

57 for the third side

Step-by-step explanation:

a = √(c² - b²)

Answer:

tenths

Step-by-step explanation:

the 2 is in the ones place and the 5 is in the hundreds meaning the 3 would be in the tenths

To compute for the 20% down,

To solve for the remaining payment,

When divided into 6 equal payments,