Mathematics College

The minimum sustained wind speed of a category 1 hurricane is 74 miles per hour. The maximum sustained wind speed is 95 miles per hour. Write an absolute value equation that represents the minimum and maximum speeds. Let V represent the wind speed.

Answers

Answer 1
Final answer:

The absolute value equation that represents the range of a category 1 hurricane's wind speed is |V - 84.5| ≤ 10.5. 84.5 is the average of the range and 10.5 is the difference from the range's center to the end.

Explanation:

The absolute value equation that represents the minimum and maximum sustained wind speeds of a category 1 hurricane can be written as |V - 84.5| ≤ 10.5. Here, V stands for the wind speed. The middle value of 74 and 95 is 84.5 (the average of 74 and 95). And the distance from 84.5 to either end of the range (74 or 95) is 10.5. So, the range of speeds is represented by the absolute difference from the center of the range is less than or equal to 10.5.

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Related Questions

Which of the following is the inverse of the statement "If I like math, then I like science"? A. If I do not like science, then I do not like math. B. If I do not like math, then I like science. C. If I do not like math, then I do not like science. D. If I like science, then I like math

Answers

Original Conditional: If P, then Q

Inverse: If not P, then not Q

Using that template, the inverse would be "If I do not like math, then I do not like science" (simply insert those two "not" words keeping the order the same)

so the answer is choice C

Answer:

Option C If I do not like math, then I do not like science

Step-by-step explanation:

we know that

To find the inverse of a conditional, negating both the hypothesis and conclusion of a conditional statement

In this problem we have

"If I like math, then I like science"

therefore

the inverse is

If I do not like math, then I do not like science

An important part of customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first 5 troubles reported on a given day, what is the probability that fewer than 2 troubles will be repaired on the same day?

Answers

The answer to your question is
D.  .2373


Hope this helps

Answer:

The probability that fewer than 2 troubles will be repaired on the same day is:

0.015576

Step-by-step explanation:

We have to use the Binomial function is n=order to calculate the probability of r successes out of the n-events.

We know that the probability of r success out of the n-events is given by:

[tex]P(X=r\ successes)=n_C_r\cdot p^r\cdot (1-p)^{n-r}[/tex]

where p is the probability of an success.

Here we have:

n=5 and r=0,1.

since we are asked to find the probability that fewer than 2 troubles will be repaired on the same day.

i.e we have to find:

[tex]P(X<2)=P(X=0)+P(X=1)[/tex]

Also p=0.75 ( since, likelihood is 0.75 that troubles in a residential service can be repaired on the same day )

Hence,

[tex]P(X=0)=5_C_0\cdot (0.75)^{0}\cdot (1-0.75)^{5-0}\\\\P(X=0)=1\cdot 1\cdot (0.25)^5\\\\P(X=0)=0.000976[/tex]

and

[tex]P(X=1)=5_C_1\cdot (0.75)^{1}\cdot (0.25)^{5-1}\\\\P(X=1)=5\cdot (0.75)\cdot (0.25)^4\\\\P(X=1)=0.0146[/tex]

Hence,

[tex]P(X<2)=0.000976+0.0146\\\\P(X<2)=0.015576[/tex]

Hence,  the probability that fewer than 2 troubles will be repaired on the same day is:

0.015576

The distance that light travels in 1 second is 186,000 miles. How far will light travel in 1 year? (There are approximately 31,500,00 seconds in 1 year. ) change the numbers to scientific notation and then perform the appropriate operations.

Answers

light travels 186,000 miles per second.....1.86 x 10^5
31,500,000 seconds per yr....3.15 x 10^7

how far will light travel in 1 yr...
(1.86 x 10^5)(3.15 x 10^7) =
(1.86 * 3.15)(10^5 * 10^7) =
5.859 x 10^12 miles in 1 yr <===
(5,859,000,000,000 miles)....whoa....a lot of traveling...thats like 5 trillion + miles

michael wittry has been investing inhis roth IRA retirement account for 20 years. Two years ago his account was worth $215,658. after losing 1/3 of its origional value, it then gained 1/2 of its new value back, what is the current value of his roth IRA?

Answers

let's say

a = 215,658

ok... so.. he first lost 1/3 of that

[tex]\bf \textit{\underline{lost} }\frac{1}{3}a\qquad \qquad a-\cfrac{1}{3}a\implies a-\cfrac{a}{3}\implies \cfrac{3a-a}{3}\implies \cfrac{2a}{3} \\\\\\ \textit{then he \underline{gained} }\frac{1}{2}\textit{ of }\frac{2a}{3}\qquad \qquad \cfrac{2a}{3}+\cfrac{\frac{2a}{3}}{2}\implies \cfrac{\frac{2a}{3}}{\frac{2}{1}} \\\\\\ \cfrac{2a}{3}+\cfrac{2a}{3}\cdot \cfrac{1}{2}\implies \cfrac{2a}{3}+\cfrac{2a}{6}\implies \cfrac{4a+2a}{6} \\\\\\ \cfrac{6a}{6}\implies \boxed{a}\implies 215,658[/tex]


so, his nickname might just be even steven, because, he ended up with the same original amount after the 1/2 bump.

His current value is 215658 dollars.

How to calculate a fraction of amount of a total amount ?

To calculate a fraction of amount of a total amount just multiply the given fraction to the total amount.

According to the given question

Michael  wittry has been investing in his roth IRA retirement account for 20 years.

Two years ago his account was worth $215,658.

1/3rd of it's original value is

= (1/3) × 215658

= 71886 dollars.

∴ Remaining value is

=(215658 - 71886)

=143772 dollars.

After some time it gained half of it's new value back

∴ Half of this new value is

(1/2) × 143772

= 71886 dollars.

So , the current value is

(143772 + 71886)

=215658 dollars.

Actually his currect value of roth IRA is same as it was two years ago.

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round 2,412 to the nearest thousands

Answers

2,000 since you're rounding to the nearest thousands.
The answer is 2,000 because 2,412 is closer to 2,000 than 3,000. Hope I helped!

Harry estimates that the dinner will have 48 g of fat. if the recommended daily allowances is 70 g What percentage of her total daily allowance of fat will the dinner be

Answers

divide 48 by 70

48 / 70 = 0.6857 = 68.6%

Banks pay interest on savings accounts because

A. they can get more customers that way.

B. they want to encourage you to save.

C. they invest your money.

D. they're just very nice.

Answers

I'm gonna go with C or B cause(based on Google)Banks use the money deposited on savings accounts to lend to borrowers, who pay interest on their loans. After paying for various costs, the banks pay money on savings deposits to attract new savers and keep the ones they have. 
Hey there!

Banks aren't in the business of being nice and actually get most of their revenue from their relentless overdraft fees. While it may seem like they're doing something nice or encouraging you to save your money, they're really just encouraging you to become a customer. They don't invest your money, since it needs to be present for you if you want to withdraw it. 

Interest on your savings is simply a method for getting new customers. 

Hope this helped you out! :-)

Nia is three years older than half Jordans age , if Jordan is eight years old , how old is Nia?

Answers

Hello! 

If Nia is three years older than half of Jordan's age, we must divide Jordan's age by 2 (to find half of his age).

Jordan is eight years old:
8 divided by 2 equals 4

4 years old is half of Jordan's age. Now, to find Nia's age, we must add 3 to half of Jordan's age (4).

4+3= 7
Nia is 7 years old. 

I hope this helps answer your question! Have a great day!

Answer:

7

Step-by-step explanation:

A segment has endpoints ar (-2,3) and (7,9) how long is the segment

Answers

[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -2}}\quad ,&{{ 3}})\quad % (c,d) &({{ 7}}\quad ,&{{ 9}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ d=\sqrt{[7-(2)]^2+[9-3]^2}\implies d=\sqrt{(7+2)^2+(9-3)^2} \\\\\\ d=\sqrt{9^2+6^2}\implies d=\sqrt{81+36}\implies d=\sqrt{117} \\\\\\ \boxed{117=3^2\cdot 13}\qquad \qquad d=\sqrt{3^2\cdot 13}\implies d=3\sqrt{13}[/tex]

A rectangular plot of land has an area of 1/8 square mile. Its width is 3/20 mile.What is the length of the plot of land?

Answers

A = L * W
A = 1/8
W = 3/20

1/8 = 3/20L
(1/8) / (3/20) = L
1/8 * 20/3 = L
20/24 reduces to 5/6 miles = L <===

The outside diameter of a pipe is 5 and 7/32 inches. The walls of the pipe are 5/32 inches thick. What is the inside diameter?

Answers

check the picture below

thus

[tex]\bf 5\frac{7}{32}-\cfrac{5}{32}\implies \cfrac{5\cdot 32+7}{32}-\cfrac{5}{32}\implies \cfrac{167}{32}-\cfrac{5}{32}\implies \cfrac{162}{32} \\\\\\ \cfrac{81}{16}\implies 5\frac{1}{16}''[/tex]

50 POINTS!!! DO NOT ANSWER JUST FOR THE POINTS!!! IF YOU DO, ALL OF YOUR EARNED POINTS WILL BE TAKEN~~~~~~~~~~~~~~~

Refer to the graph.

The function is increasing on the interval(s):

The function is decreasing on the interval(s):

The function is constant on the interval(s):

Please explain the steps you used.

Answers

A) [-7,-4] U [4,7]; B) [-4,-1]; C) [1,4]


A) [-7,-4] U [4,7]; B) [-4,-1]; C) [1,4]

solve (6-5x)/10-(2x+1)/5+x/3=2x/15

Answers

multiply2 * x/15 to 2x/15

multiply both sides by 30 which is the LCM of 10, 5, 3, and 15

expand it

simplify 18 - 15x - 12x - 6 + 10x to 12 - 17x

add 17x to both sides

add 4x + 17x to = 21x

divide both sides by 21

simplify 12/21 to 4/7

now simplify

Answer: x = 4/7.

3a/(a+1)^2
Give the equivalent numerator if the denominator is (a + 1)³.

Answers

Given 3a/(a+1)^2
To make the denominator a cube, you would have to multiply by 1 or (a+1)/(a+1)
yielding 3a(a+1)/(a+1)^3
(3a^2 + 3a) is the equivalent numerator

Answer:

3a(a+1)

Step-by-step explanation: for those who were confused on the other asnwer he gave a different veriation of this answer. however it is correct.



Brainliest plsss


Is y=2x-8 and 2x-y=8 a dependent independent or inconsistent

Answers

Note that 2x-y=8 can be solved for y:  y=2x-8.  This is identical to the first equation.  The graph of one is exactly the same as the graph of the other.  Thus, the two equations are dependent.

Answer:

dependent

Step-by-step explanation:

[tex]y=2x-8[/tex] and [tex]2x-y=8[/tex]

First equation is already solve for y

LEts solve the second equation for y

[tex]2x-y=8[/tex]

Subtract 2x on both sides

[tex]-y=-2x+8[/tex]

Divide the whole equation by -1

[tex]y=2x-8[/tex]

After solving for y, both equation are same

When both the system of equation are same then  it has infinite solutions.

They are said to be dependent.

Prove that if an converges to a nonzero constant then 1/an is bounded

Answers

Assume [tex]\dfrac1{a_n}[/tex] is not bounded, i.e. there are no [tex]u,\ell[/tex] for which [tex]\ell\le\dfrac1{a_n}\le u[/tex] for all [tex]n[/tex].

Now, [tex]a_n\to k\neq0[/tex] is to say that for any [tex]\varepsilon>0[/tex], we can find a large enough [tex]N[/tex] such that [tex]|a_n-k|<\varepsilon[/tex] whenever [tex]n\ge N[/tex]. Simultaneously, this means that [tex]a_n[/tex] is bounded.

Let's suppose without loss of generality that [tex]a_n\neq0[/tex] for any [tex]n[/tex]. (Note that if [tex]a_n=0[/tex] for some finite number of values of [tex]n[/tex], we can simply remove them from consideration.)

So we have

[tex]|a_n-k|=\left|a_n\left(1-\dfrac k{a_n}\right)\right|=|a_n|\left|1-\dfrac k{a_n}\right|<\varepsilon[/tex]

Because [tex]a_n[/tex] is bounded, we know there is some [tex]\alpha[/tex] such that [tex]|a_n|\le\alpha[/tex] for all [tex]n[/tex]. Now,

[tex]|a_n|\left|1-\dfrac k{a_n}\right|\le\alpha\left|1-\dfrac k{a_n}\right|<\varepsilon[/tex]
[tex]\left|1-\dfrac k{a_n}\right|<\dfrac\varepsilon\alpha[/tex]
[tex]-\dfrac\varepsilon\alpha<1-\dfrac k{a_n}<\dfrac\varepsilon\alpha[/tex]
[tex]-1-\dfrac\varepsilon\alpha<-\dfrac k{a_n}<-1+\dfrac\varepsilon\alpha[/tex]
[tex]1-\dfrac\varepsilon\alpha<\dfrac k{a_n}<1+\dfrac\varepsilon\alpha[/tex]
[tex]\dfrac1k-\dfrac\varepsilon{\alpha k}<\dfrac 1{a_n}<\dfrac1k+\dfrac\varepsilon{\alpha k}[/tex]

But we initially assumed that [tex]\dfrac1{a_n}[/tex] is unbounded, so the above is impossible. Thus [tex]\dfrac1{a_n}[/tex] must be bounded.

Suppose a line has slope 4 and passes through the point (-2, 5). Which other point must also be on the graph?

A) (2, 6) B) (-1, 9) C) (-1, 1) D) (-6, 4)

Answers

D) -6,4. because if it has a slope of 4 which is positive it has to have an uphill slope which passes through -2,5, in order for that to happen you plot it and make the line and count the rise over run till you have the slope of 4.

[tex]\bf slope = {{ m}}= \cfrac{rise}{run}\implies 4\implies \cfrac{4}{1}[/tex]

so the rise is 4 units and the run is 1 unit, ok.

now, from point -2, 5, if we move 4/1, that is, "1  unit over the x-axis, and 4 units over the y-axis", we'll find another point, now, a fraction can be positive so long both top and bottom are the same sign, so -4/-1 is the same as 4/1 and therefore, if we move +4 and +1 over the axes we get a point, or if we move -4 and -1 we also get another point, and any other subsequent points from there on.

so, hmm let's check    [tex]\bf (\stackrel{x+1}{-2}~,~\stackrel{y+4}{5})\implies (-1~,~9)[/tex]

Using only definition 2.2.3, prove that if (x

Answers

you can use Google or a calculated but to check it but it's : 6

The sum of three numbers is 99. The first number is 9 more than the third. The second number is 4 times the third. What are the numbers?

Answers

first number=x+9
second number=4x
third number=x
4x+x+x+9=99
6x=90
x=15
 first number=24
second number=60
third number=15


Final answer:

The first number is 24, the second number is 60, and the third number is 15.

Explanation:

Let's assign variables to represent the three numbers. Let x represent the third number. Since the first number is 9 more than the third, we can write the equation:

First number = x + 9

Since the second number is 4 times the third, we can write the equation:

Second number = 4x

Now, we can add the three numbers together, according to the given information:

(x + 9) + 4x + x = 99

Simplifying this equation, we get:

6x + 9 = 99

Subtracting 9 from both sides, we have:

6x = 90

Dividing both sides by 6, we find:

x = 15

So the third number is 15. Plugging this value back into the two other equations, we find that the first number is 24 and the second number is 60. Therefore, the three numbers are 24, 60, and 15.

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Shelia mixed 3 ounces of blue paint with 2 ounces of yellow paint. She decided to create 20 ounces of the same mixture. How many ounces of yellow paint does Sheila need for the new mixture?

Please explain!!

Answers

Yellow:blue is a ratio of 2:3, meaning that 2/5 of the desired mixture is yellow. From this, you need to find how much yellow is necessary for 20 ounces. Well, 2/5 of the 20 ounces will be yellow paint, while the other 3/5 will be blue. So she will need 8 ounces of yellow paint to get 20 ounces of the desired mixture. Hope this helps! :)
3 ounces of blue paint added with 2 ounces of yellow you would get 5 onces

Then you divide 20 by 5 you get 4
Then multiply 4 by 2 ounces you get 8

Sheila will need 8 ounces of of yellow paint for the new mixture.

12 tenths plus 9 tenths =21 tenths = ____ ones _____ tenths

Answers

2100 ones if I am thinking about this right. hope it helps

Which of the following statements is true? 0.74 < 0.80 0.61 > 0.93 0.83 < 0.94 1.548 < 0.698

Answers

0.74 < 0.80
0.83 < 0.94

Among the given statements, the only true statements are

0.74 < 0.80 and 0.83 < 0.94.

How is this so?

In both cases, the number on the left is less than the one on the right. Which  makes the expression and or use of the less than symbol correct.

The greater than symbol (>) and the less than symbol (<) are used to compare two numbers or expressions to determine their relationship.

The greater than symbol (>) represents "greater than" and indicates that the number on the left side is larger than the number on the right side.

The less than symbol (<) represents "less than" and indicates that the number on the left side is smaller than the number on the right side.

For example, 5 > 3 means "5 is greater than 3," and 2 < 7 means "2 is less than 7."

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386-123= estimate then find the difference

Answers

390-125= 265
Round 386 to 390 and 123 to 125
you estimate 386 to 400 and 123 to 100 so you will get 
400-100=300

kim has 3/4 pound servings of grapes. how many 1/8 pound servings can Kim make from his grapes

Answers

he can make 6 servings

(3/4) / (1/8) =
3/4 * 8/1 =
24/4 =
6 <=== there are 6 one-eighth pound servings

The length of a rectangle is 11 m greater than the width. The area is 42 m^2. Find the length and width.

Answers

the answer is that the width is 3 m and the length will be 14 m because 3•14 = 42m² and 3+11=14
Hello friends my name is blank I'm sorry but I need to ask a question so buy

A book had a length of 5 inches and a width of 8 inches. What is the perimeter of the book

Answers

26 inches hope this helps

the perimeter is 26in

Using place value how to increase 2384598 by six million

Answers

6 million = 6,000,000

2,384,598 + 6,000,000 = 8,384,598

your answer is 8,384,598

hope this helps

The 1998 team payroll of the Baltimore orioles was $68,988,134

Answers

what is the rest of the question

The arctic lion's Mane Jellyfish is one of the largest known animals. Its tentacles can be as long as 120 feet. Find how this length compares to your height. Round your height to the nearest foot. 120 feet is time as long as feet.

Answers

To solve this problem, we must first know your height. So assuming that your height is 5 feet. Therefore we can divide:

120 feet / 5 feet = 24

 

So that the answers in the blanks are:

120 feet is 24 times as long as 5 feet

If you drive for 2 hours, at 60 miles per hour, you will have traveled 120 miles. this is a very common type of calculation, involving three quantities: distance, rate and time. if you know just two of these three quantities, you can always calculate the third. thus, if you want to know how much time it is going to take you to get somewhere, and you know that the distance is 120 miles and you will drive at a rate of 60 miles per hour, you can divide the 120 miles by the 60 miles per hour and obtain a time of 2 hours.

Answers

do u still need the answer

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