Against the Wind a small plane flew 858 miles in 2 hours and 10 minutes the return trip only took 1 hour and 50 minutes what was the speed of the wind?what was the speed of the plane in still air?​

Answer:

8.433 to the power of 4

Step-by-step explanation:

The reason is because the nukber written in scientific notation always has to be between 1-10. It can't be 84.33 or 843.3. The number has to be between 1 and 10.

Answer:

it would take 3,000 neyland stadiums to take 300milion people is rounded i hope this helps

Step-by-step explanation:

The coin is flipped at least 52 times in order to obtain a 99% confidence interval of width of at most . 18 for the probability of flipping a head.

Hence, Option F is correct answer.

In a sample with a number n of people surveyed with a probability of a success of π , and a confidence level of (1-α), we have the following confidence interval of proportions.

[tex]\pi[/tex] ± z[tex]\sqrt{\frac{\pi \p(1-\pi )}{n} }[/tex]

z is the z-score that has a pvalue of [tex]1-\frac{\alpha }{2}[/tex]

Since, the coin is fair, so [tex]\pi =0.5[/tex].

The margin of error is:

[tex]M=z\sqrt{(\frac{\pi (1-\pi )}{n} )}[/tex]

99% confidence level:

So [tex]\alpha =0.01[/tex] ,z is the value of Z that has a p value of 1-[tex]\frac{0.01}{2}[/tex]=0.995,

so Z= 2.575

We have to flip the coin in order to obtain a 99% confidence interval of width of at most 18 for the probability of flipping a head at least n times.

n is found when M=0.18 .

So

M=[tex]z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex]

[tex]0.18=2.575\sqrt{\frac{0.5*0.5}{n} }[/tex]

[tex]0.18\sqrt{n} =2.575*0.5[/tex]

[tex]\sqrt{n}=\frac{2.575*0.5}{0.18}[/tex]

[tex]\sqrt{n} ^{2} =(\frac{2.575*0.5}{0.18} )^{2}[/tex]

n = 51.16

Thus, we have to flip the coin at least 52 times.

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The remaining credit after 81 minutes of calls is $17.04.

Given that, the remaining credit after 44 minutes of calls is $22.96, and the remaining credit after 68 minutes of calls is $19.12.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Let x be the number of minutes and y be the number of dollars.

According to question, the ordered pair is

(44, 22.96) and (68, 19.12)

The point slope form is (y-y1)=m(x-x1)

Slope = (y2-y1)/(x2-x1)

= (19.12-22.96)/(68-44)

= -3.84/24

m= -0.16

Put m= -0.16 and (x1, y1)=(44, 22.96), we get

(y-22.96)=-0.16(x-44)

When x=81

y-22.96=-0.16(81-44)

⇒ y-22.96=-0.16×37

⇒ y-22.96=-0.16×37

⇒ y-22.96=-5.92

⇒ y=-5.92+22.96

⇒ y=17.04

Therefore, the remaining credit after 81 minutes of calls is $17.04.

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The number that represents the location of the penguin in relation to the surface 2 minutes after beginning his dive is 440.

An emperor penguin dives down into the ocean at a constant rate. From the surface, he dives 1,760 feet in 8 minutes. The number 1,760 represents the location of the penguin in relation to the surface. We need to find out the number that represents the location of the penguin in relation to the surface two minutes after he begins his dive.

First, we will calculate the speed of the penguin. The speed is represented by the variable "s".

s = 1,760/8

s = 220 feet per minute

The location of the penguin after 2 minutes is calculated below.

d = 2×s

d = 2×220

d = 440

Hence, the number that represents the location of the penguin in relation to the surface 2 minutes after beginning his dive is 440.

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For the given equation 9(x-4) -5x = __x -30 has no solution when it is written as 9(x - 4) -5x = 4x -30.

As given in the question,

Given equation is equal to :

9 ( x - 4) - 5x = _ x - 30

Simplify Left hand side of the given equation we get,

9 ( x - 4) -5x

= 9x - 36 - 5x

Collect the like terms we have,

9x - 5x - 36

= 4x - 36

Now compare left hand side and right hand side to get no solution of the equation,

4x -36 = _x -30

Blank should be filled by 4

Therefore, for the given equation 9(x-4) -5x = __x -30 has no solution when it is written as 9(x - 4) -5x = 4x -30.

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Answer:

2/5

Step-by-step explanation:

flip 5/6 to become 6/5 then cross reduce then cross multiply

The slope is m = 5.

What is slope?

The change in y coordinate relative to the change in x coordinate is referred to as a line's slope in mathematics. The symbols Δy and Δx stand for the net change in the y-coordinate and the net change in the x-coordinate, respectively. where "m" denotes a line's gradient. tanθ then represents the slope of a line.

We have to find the slope of the points given.

First to find the change between each y - value.

16 - 11 = 5

21 - 16 = 5

26 - 21 = 5

31 - 26 = 5

So the change between each y - value is 5.

Now, to find the slope of the points.

Since,

Slope = m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m_1=\frac{16-11}{6-5}= \frac{5}{1} =5\\ m_2=\frac{21-16}{7-6}=\frac{5}{1} =5\\ m_3=\frac{26-21}{8-7}=\frac{5}{1}=5\\m_4=\frac{31-26}{9-8}=\frac{5}{1} =5[/tex]

Hence, the slope of the given points is 5.

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Answer:

The answer is 5

Step-by-step explanation:

Though there is also a bottom number, just put a 1 in the bottom number

Answer:2380 minutes. By saying how many more minutes does an infant sleep than an adult in one week impies that you have to subtract how long an adult sleeps taken away from the amount of time an infinte sleeps. Once you get the answer you multiply it by seven.

Step-by-step explanation:

Answer:340 minutes

Step-by-step explanation:you subtract the amount an infant sleeps (820 minutes) by the amount an adult sleeps (480 minutes)

820-480=340

Yes, it is reasonable for her to use a normal model for the sampling distribution of the sample​ proportion. In this case, less than ten efforts have been successful. Since 5 is a lot less than 10, this is the case.

Because the data don't fit the success and failure criteria, it is not appropriate to adopt a normal model for a sampling of the sample distribution.

50 students make up the sample. The probability that she assumes 10% of the group will attend is 10%.

It will be demonstrated by:

1 - p = 1 - 10% = 1 - 0.10 = 0.90

np = 50 × 0.1 = 5. This suggests the number of victories.

Less than 10 attempts have succeeded in this instance. 5 is much less than 10, hence this case. As a result, the data does not satisfy the requirement.

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The question is -

For her final project, Stacy plans on surveying a random sample of 50 students on whether they plan to go to Florida for spring break. from past years, she guesses that about 10% of the class goes. is it reasonable for her to use a normal model for the sampling distribution of the sample proportion? why or why not?

The domain and the range of a function have the concepts given as follows:

The domain of a function or of a relation is the set that contains all possible input values. Hence, among possible representations, we have that:

The range of a function or of a relation is the set that contains all possible output values. Hence, among possible representations, we have that:

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The p-value is higher than 0.05, so we are unable to rule out the null hypothesis. There is little proof to back up the director's claim.

Hypothesis:

H₀ : μ = 3000

H₁ : μ > 3000

The t-test should be employed when the population mean and standard deviation are unknown. Since the sample size is high, we can infer that the sample mean's sampling distribution is normal.

The following information is provided:

s = 450

x = 3200

n = 14

Therefore, test statistics will be:

t = (x - μ) / (s / √n) = (3200 - 3000) / (250 / √14) = 1.66

The test in this instance is right-tailed, and its degree of freedom is df=n-1=14-1=13.

0.0601 is the p-value.

We are unable to reject the null hypothesis since the p-value is higher than 0.05. The director's allegation is not supported by a lot of evidence.

Since p =.0601, the director's assertion cannot be supported by the available data.

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The probability that it has a hairline crack is 19/27.

Given that;

In a shipment of 54 vials, only 16 do not have hairline cracks.

Let shipment of 54 Vials;

x(s) = 54

Let,' A ' be the event that selects 16

x(A) = 16

P(A) = x(A) / x(s)

       = 16/54

But only 16 don't have hairline Crakes;

To solve a given case;

The probability that it has a hairline crack is:

P(A') = 1 - P(A)

       = 1- 16/54

P(A') = 19/27

Hence, the probability that it has a hairline crack is 19/27.

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The graph represents the system of equations -3x + y = 3 and -x + 2y = -4 is option (b) On a coordinate plane, 2 lines intersect at (negative 2, negative 3).

The system of equation are

-3x + y = 3

-x + 2y = -4

Here we have to use the substitution method

-3x + y = 3

y = 3 + 3x

Substitute the value of y in the second equation

-x + 2(3 + 3x) = -4

-x + 6 + 6x = -4

-x + 6x = -4-6

5x = -10

x = -10/5

x = -2

Substitute the value of x in the first equation

-3x + y = 3

-3(-2) + y = 3

6 + y = 3

y = 3 - 6

y = -3

Hence, the graph represents the system of equations -3x + y = 3 and -x + 2y = -4 is option (b) On a coordinate plane, 2 lines intersect at (negative 2, negative 3).

The complete question is:

Which graph represents the system of equations –3x + y = 3 and –x + 2y = –4?

a) On a coordinate plane, 2 lines intersect at (3, 0).

b) On a coordinate plane, 2 lines intersect at (negative 2, negative 3).

c) On a coordinate plane, 2 lines intersect at (negative 1.5, 1).

d) On a coordinate plane, 2 lines intersect at (1.5, 2.5).

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Answer:

B

Step-by-step explanation:

both point intersect at ( -2, -3)

The following are the equations which matches the given word problems:

a. Skate rental charges an additional $3 :

y = x+3

b. Jeff is 3 years less than Tony's age:

y=x-3

c. Marie buys balloons for a party that are $3.00 each:

y = 3x

Given, we have the word problems:

a. Skate rental charges an additional $3 :

here, based on the fixed charge, additional charge is taken as $3.

let the total charge be represented as y and

x represent the fixed charge,

hence the equation we get is:

y = x+3

b. Jeff is 3 years less than Tony's age.

let y represent the age of Jeff

and x represent the age of Tony.

hence we frame the equation as:

y = x - 3

c. Marie buys balloons for a party that are $3.00 each:

let the cost of the balloon be represented as y

and x represent the number of balloons Marie wants to buy for $3 each.

hence the equation we frame is:

y = 3x

Hence we get the required equations.

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The equations that are quadratic in form include:

A. x⁴ – 6x²– 27 = 0

D. 6x⁴ = -x² + 5

E. 8x⁴ + 2x² – 4x = 0

A quadratic equation simply refers to the equation which is in an algebraic equation that is of the second degree.

It should be noted that a quadratic equation is in the form of ax² + bx + c = 0.

In this situation, a and b are the coefficients while c is the constant in the equation.

Therefore, based in the information given, the correct options are A, D, abd E.

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Answer:

The equations that are quadratic in form include:

A. x⁴ – 6x²– 27 = 0

D. 6x⁴ = -x² + 5

E. 8x⁴ + 2x² – 4x = 0

Step-by-step explanation:

a) The derivative of the composite function is F'(x) = [2 · [(1 / 3) · x³ + 7] + 6] · x².

b) The standard form of the polynomial is F'(x) = (2 / 3) · x⁵ + 7 · x².

Chain rule is a differentiation rule use to find the derivative of a composite function of the form f(u(x)), whose operation is defined below:

df / dx = (df / du) · (du / dx)

a) Let be f(x) = x² + 6 · x - 40 and g(x) = (1 / 3) · x³ + 7, such that F(x) = f(g(x)). Then, the resulting expression for the derivative of the function is obtained below:

F'(x) = [2 · g(x) + 6] · g'(x)

F'(x) = [2 · [(1 / 3) · x³ + 7] + 6] · x²

b) Now we proceed to expand the polynomial in its standard form:

F'(x) = [(2 / 3) · x³ + 7] · x²

F'(x) = (2 / 3) · x⁵ + 7 · x²

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With the help of binomial distribution we can conclude our answer.

acc to our question-

The confidence interval can be found out using,

Hence, the confidence interval for the mean load required to pull the wood apart is (29,485.192 , 32,114.8).

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Answer is (a) The solution set is {x | (-∞,-7)∪(5,12)}.

Given equation,

[tex]\frac{(x-5)(x+7)}{x-12} < 0[/tex]

For values (-∞,-7)

equation stands true

For values (-7,5)

equation stands false

For values (5,12)

equation stands true

For values (12,∞)

equation stands false

Hence, x ∈ (-∞,-7)∪(5,12).

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Answer:

y=6x+2

Step-by-step explanation:

y=mx+c

8=6(1)+c

8=6+c

c=2

y=6x+2

The solution to the inequality is y < -12 ( y less than negative 12).

Given inequality is;

y + 15 less-than 3

y+15<3

For solving the inequality, we will subtract 15 from both sides in order to find y.

Subtracting 15 from both sides of inequality

The solution to the inequality is y < -12 ( y less than negative 12).

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Answer: y = -.06x + 0.2

Step-by-step explanation: Find the slope by plugging in the given values to the slope formula to find that the slope is -0.6. Next, determine the y-intercept is b=y1−m⋅x1: b = 2 - (-0.6) ⋅ (-3) = 0.2 Finally, the equation of the line can be written in standard form y= -0.6x + 0.2.

Answer:

No solution (0 = 1)

Step-by-step explanation:

Given equation,

→ 5 + 2x = 2x + 6

Then the value of x will be,

→ 5 + 2x = 2x + 6

→ 2x = 2x + 6 - 5

→ 2x - 2x = 1

→ 0 = 1

Hence, there is no solution.

[tex]\boxed{\begin{array}r \large{ \tt solution \: : } \: \: \: \: \: \\ \\ { \longrightarrow5 + 2x = 2x + 6}  \\ \\ \\ ( \sf 2x \: \: present \: \: on \sf\: \: both \: \: \\ \sf sides \: \: of \: \: equality \: \: \: \\ \sf \: \: gets \: \: \sf canceled\: \: out) \\ \\ \sf \longrightarrow5 \neq6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \tt \: \: therefore \: \: there \: \: is \\ \tt no \: \:solution \: \: for \: \: x \: \: \\ \\ \tt that \: \: is \: \: no \: \: value \: \: \: \: \\ \tt \: of \: \: x \: \: that \: \: satisfies \\ \tt the \: \: given \: \: equation\end{array} }[/tex]

Given function:

y = |x − 3| + 1

Table:

x     y  

1     3

2    2

3    1

4    2

5    3

Here the vertex is (3,1).

Graph is in the image uploaded.

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The total quantity of diesel fuel is 15.75 gallons.

The total quantity of diesel fuel can be calculated by summing up all the values. But, firstly converting quarts and pint into gallons.

1 quart = 0.25 gallon

For first container, 3 quarts = 0.25 × 3

3 quarts = 0.75 gallon

For second container, 2 quarts = 0.25 × 2

2 quarts = 0.5 gallon

For third container, it has 0.25 gallon

1 pint = 0.125 gallon

For first and third container, it has 0.125 gallon

So, amount of diesel fuel in first container = 3 + 0.75 + 0.125

Amount of diesel fuel in first container = 3.875 gallons

Amount of diesel in second container = 5 + 0.5

Amount of diesel in second container = 5.5 gallons

Amount of diesel in third container = 6 + 0.25 + 0.125

Amount of diesel in third container = 6.375 gallons

So, the total quantity of diesel fuel = 3.875 + 5.5 + 6.375

The total quantity of diesel fuel = 15.75 gallons

Hence, the total quantity is 15.75 gallons.

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Answer: 55.56%

Step-by-step explanation:

To find the percentage, we need to do part over whole. Part being the females and the total marathon runners being the total. So that would be 95/95+125, then 95/225, then 55.555555 and repeating. Then we would round that to 55.56%.

Answer: Ethiopia has a population growth rate above 2.5% and a life expectancy of 61 years old

Answer:

Step-by-step explanation:

The Cathy's Clothmart job had a profit comprises of pairings of the form (x,y), where the two integers are paired because of some relation.

In this instance, the relation is effectively "in month x it truly had a profit y" The ordered pairs are then, in a really significant sense, (April, 3000), (May, 4000), and (June, 5000). The ordered pairs can be written as follows if the month's number is used to identify them: (4,3000), (5,4000), They generally believed that both kinds of ordered pairings are generally correct.

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May, 4,000

The only correct pair is may and 4,000 because the other options don't have the proper profit to represent the corresponding months.