Answer:
[tex]\dfrac{18(3\sqrt2-1)}{17}[/tex]
Step-by-step explanation:
The given expression is :
[tex]x=\dfrac{18}{3\sqrt2+1}[/tex]
We need to rationalize the denominator.
Multiplying and dividing both sides by [tex]3\sqrt2+1[/tex] as follows :
[tex]x=\dfrac{18}{3\sqrt2+1}\times \dfrac{3\sqrt2-1}{3\sqrt2-1}\\\\=\dfrac{18(3\sqrt2-1)}{(3\sqrt2)^2-1}\\\\=\dfrac{18(3\sqrt2-1)}{(18-1}\\\\=\dfrac{18(3\sqrt2-1)}{17}[/tex]
So, the answer is [tex]\dfrac{18(3\sqrt2-1)}{17}[/tex].
The physical plant at the main campus of a large state university receives daily requests to replace fluorescent light bulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 47 and a standard deviation of 7. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 47 and 68
Answer:
The approximate percentage of lightbulb replacement requests numbering between 47 and 68 is 49.85%.
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 47
Standard deviation of 7
What is the approximate percentage of lightbulb replacement requests numbering between 47 and 68?
The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% of the above.
Between 47 and 68:
68 = 47 + 7*3
So 68 is three standard deviations of the mean.
Of the 50% above the mean, approximately 99.7% are between the mean of 47 and 3 standard deviations above the mean, which is 68. So
0.5*0.997 = 0.4985
0.4985*100 = 49.85%
The approximate percentage of lightbulb replacement requests numbering between 47 and 68 is 49.85%.
convert 576,904,320 using scientific notation
Answer:
5.76904320x 10^8
Step-by-step explanation:
5.76904320x 10^8
bill js a builder. On Monday he msde mortar mix. he used 24kg of sand and 5kg of cement. on tuesday bill will make the same type of mortar mix. he will use 36kg of sand. how much cement does he need to make the same type of mortar mix?
Answer: 7.5kg
Step-by-step explanation:
Since Bill made mortar mix and he used 24kg of sand and 5kg of cement. This means that for 1 kg of cement, (24/5) = 4.8 kg of sand is used.
Therefore, when he uses 36kg of sand, the kg of cement used will be:
= 36 / 4.8
= 7.5 kg
Therefore, he'll use 7.5kg of cement and 36kg of sand.
is going to plant y vegetable seeds in one garden and 3y+8 vegetable seeds in another. How many seeds is Frank going to plant?
Answer:
4y + 8 vegetable seeds
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsStep-by-step explanation:
We know that Frank has 2 gardens, one with y vegetable seeds and another with 3y + 8 vegetable seeds. If we are trying to find the total amount of seeds planted, we must add the 2 gardens together:
Garden 1: y
Garden 2: 3y + 8
Garden 1 + Garden 2 = Total veggie seeds
y + 3y + 8 = Total veggie seeds
Total veggie seeds = 4y + 8
A mouse is moving through a maze and must make four turns where it can go either left or
right. The mouse will escape the maze if it makes three lefts and one right, in any order.
(a) To the right, draw a tree diagram
of all possible routes the mouse
could take.
(b) Using your tree diagram, create
an organized list of the routes. For
example, a route of right, left, left,
right could be listed as RLLR.
(C) What is the probability the mouse
escapes the maze if all turns are
randomly made?
I WILL GIVE BRAINLIEST :)
A car repair shop charges an hourly rate plus a pickup and delivery fee. The graph below represents the relationship between the total cost of the repair, including pickup and delivery fee, and the number of hours it takes the shop to complete the repairs.
Answer: I got 50x+$75 but I’m not too sure for the last step
Step-by-step explanation:
Answer:
y=50x+75
Step-by-step explanation:
y=125=225-125 Divide 3-1 (x-1)
y-125=50(x-1)
y=50x-50+125
y=50x+75
Please give me the correct answers
Answer:
x = 25°
y = 25°
Step-by-step explanation:
✔️(x + 35)° + 30° + 90° = 180° (sum of triangle)
x + 35 + 30 + 90 = 180
Add like terms
x + 155 = 180
x + 155 - 155 = 180 - 155
x = 25°
✔️(y + 30)° + 35° + 90° = 180° (sum of triangles)
y + 155 = 180
y = 180 - 155
y = 25°
If the opposite of g(x) is –g(x),
then –g(x) =
Answer:
g(x) not negitive
Step-by-step explanation:
The Enormous State University's Business School is buying computers. The school has two models to choose from, the Pomegranate and the iZac. Each Pomegranate comes with 400 GB of memory and 80 TB of disk space, while each iZac has 300 GB of memory and 100 TB of disk space. For reasons related to its accreditation, the school would like to be able to say that it has a total of at least 52,500 GB of memory and at least 12,700 TB of disk space. If both the Pomegranate and the iZac cost $2,200 each, how many of each should the school buy to keep the cost as low as possible?
Answer:
90 Pomegranate and 55 iZac
Step-by-step explanation:
Represent Pomegranate with p and iZac with i
The data can be represented in the following table.
[tex]\begin{array}{cccc}{} & {Pomegranate} & {iZac} & {Total} & {Memory} & {400} & {300} & {52500} & {Disk\ Space} & {80} & {100} & {12700} \ \end{array}[/tex]
The table can be represented as follows:
[tex]400p + 300i = 52500[/tex] --- (1)
[tex]80p + 100i = 12700[/tex] ---- (2)
Multiply equation (2) by 3
[tex]3 *\ ([/tex][tex]80p + 100i = 12700[/tex][tex])[/tex]
[tex]240p + 300i = 38100[/tex] ---- (3)
Subtract (3) from (1)
[tex]400p - 240p + 300i - 300i = 52500 - 38100[/tex]
[tex]160p = 14400[/tex]
Divide both sides by 160
[tex]p = 90[/tex]
Substitute [tex]p = 90[/tex] in (2)
[tex]80p + 100i = 12700[/tex]
[tex]80 * 90 + 100i = 12700[/tex]
[tex]7200 + 100i = 12700[/tex]
Collect like terms
[tex]100i = 12700 - 7200[/tex]
[tex]100i = 5500[/tex]
Divide by 100
[tex]i = 55[/tex]
So;
[tex]p = 90[/tex] and [tex]i = 55[/tex]
What is (3 x 20) + 9 and what is (4 x 100) + 20?
Answer:
(3 x 20) + 9 = 69
4 x 100) + 20 = 420
Answer:
(3x20) + 9 is 69
(4x100) + 20 is 420
Please answer this correctly without making mistakes I want ace expert and genius people to answer this correctly without making mistakes my homework is due today I have to finish this today
Answer:
24 i think
Step-by-step explanation:
I evaluated using he given value
what is 4/5÷3 explain
Answer:
4/15
Step-by-step explanation:
4/5 ÷ 3 =
4/5 x 1/3 = 4/15
Answer:
4/15 = 0.2667
The answer is rounded to the nearest four decimal points if necessary.
Step-by-step explanation:
Here we will show you how to calculate 4/5 divided by 3. We will give you the answer in fraction form and in decimal form.
Here is 4/5 divided by 3 displayed mathematically in colors:
4/5 divided by 3
The numbers in 4/5 divided by 3 are labeled below:
4 = numerator
5 = denominator
3 = whole number
To make it a fraction form answer, you keep the numerator and multiply the denominator by the whole number to make a new denominator:
4/5x3=4/15
Thus, the answer to 4/5 divided by 3 in fraction form is:
4/15
To make the answer to 4/5 divided by 3 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:
4/15 = 0.2667
The answer is rounded to the nearest four decimal points if necessary.
The ratio of the number of apples to oranges is 5:4. If there is a total of 135 apples and oranges, how many apples are there?
Answer:
The number of appleis 108
Round 1688 to the nearest hundred
1688 to the nearest hundred would be 1700
Answer:
The answer is 1700
Step-by-step explanation:
Have a great day.
how do you find the area of a circle?
Answer:
The formula to find the area of a circle is pi times the radius squared (A = π r²).
Step-by-step explanation:
A group of people signed up for a bus tour that costs a total of $1120. If they can increase the size of their group by 7 people, the amount each person has to pay decreases by $8. How many people are currently signed up?
Answer: 160
Step-by-step explanation:
which of the following is a true statement?
3/12>3/8
3/8<7/16
3/8<8/24
5/16>3/8
Answer:
3/8 is less than 7/16. 3/8 is equal to 6/16.
Judy bought a hat for $44.67 and sunglasses for $110.76 with her credit card. Judy has $89.35 in her checking account. How much money does she need to put in her checking account so she can pay her credit card at the end of the month?
Answer:
$66.08
Step-by-step explanation:
Judy bought two things, a hat and sunglasses. So, the total money spent is:
$44.67 + $110.76 = $155.43
She has $89.35 in her checking account and spent $155.43 on the two items.
So that means she spent more than she has in the account. To find how much she needs to put in her checking account, we're going to subtract how much money she spent and how much she has in her account.
$89.35 - $155.43 = -$66.08
Therefore, she needs to put in $66.08 into her account to pay off her debt at the end of the month.
Suppose we want to choose 2 letter, without replacement, from the 3 lettersA, B, C.
How many ways can this be done, if the order of the choices is not relevant
Answer:
3
Step-by-step explanation:
We can choose three ways:AB, AC, BC, as the order is not important.
Or you can calculate 3C2=(3×2)/(1×2)=3
Answer:
only 3, A with B B with C and A with C, but if you can use the same 2 if reversed it would be 6, for it would be A with B, B with A, C with B, B with C, A with C, and C with A.
Step-by-step explanation:
Brianliest? :/
Hope I Helped.
Have a nice day.
what is the sum of 4 and the product of 9 and 5
Answer:
49
Step-by-step explanation:
sum of 4 and the product of 9 and 5
= 4 + ( 9 x 5 )
= 4 + 45
= 49
35% of best buy customers buy a computer, 25% buy a warranty, and 5% buy a computer and a warranty. Find the probability that a Best Buy customer buys a computer given that the customer bought a warranty
Answer:
.2
Step-by-step explanation:
(.35((.05)).25)
.05/.25 = .2
Mark was watching a movie that was 124 minutes long. He fell asleep 75% of the way through. How many minutes of the movie did Mark actually watch?
Answer:
93 minutes
Step-by-step explanation:
Since 75 percent is just .75, multiply 124 by .75 to find out how much was watched. 124 * .75 = 93
Hopefully this helps- let me know if you have any questions
What is the minimum value of the cube root parent function on -8≤x≤8?
Minimum means smallest, so what is the smallest number possible for this set?
-8
---
hope it helps
Answer:
-2
Step-by-step explanation:
B
What does a single point on the plot represent?
(Need help) (ASAP)
Point: 18
Answer:
10
Step-by-step explanation:
On the Fahrenheit scale, at what temperature does water boil?
A.451°F
b. 264°F
C.212°E
d. 100°F
What is the area of the composite figure?
3 cm
7 cm
7 cm
o 54.25 cm2
o 49 cm?
70 cm
o 59.5 cm?
Answer: (D) 59.5
Step-by-step explanation:
Cos Milky said it. Trust Milky. Milky Smart.
Help this is for my sister
Answer:
i have to go with B...?
Step-by-step explanation:
i mean more than is greater than and its no sign of equal to so that's the only option
Students recruited at the cafeteria at Hope College were blindly given a single Skittles® candy to put in their mouth. They were told the five possible flavors and then were asked which flavor they had. Of the 154 healthy students tested, 78 gave the correct answer. Of the 118 students tested who had stuffy or runny noses, 44 gave the correct answer.
1. Did the study involve random sampling, random assignment, both, or neither?
2. An appropriate analysis of the data shows that there is strong evidence that healthy students were more likely to give the correct answer. Is it appropriate to conclude that the health of the student affects ability to taste? Why or why not?
Answer:
1) both
2) Yes. It is appropriate to conclude that the health of the student affects ability to taste.
Step-by-step explanation:
Random Sampling is done when each element of the sample has equal probability of being chosen. In both the samples of healthy and runny nose students each student has equal probability of being tested.
Random Assignment is one in which there is a control group and experimental group. The control group contains all the participants and each participant has the equal probability of being placed in the experimental group. For example in this experiment each student has equal probability of being tested with the given chocolate bar.
2) Yes. It is appropriate to conclude that the health of the student affects ability to taste.
the probability of success in healthy student is 78/154= 0.5065 = 50.65%
the probability of success in runny nose student is 44/118= 0.3729 = 37.29%
From this we see the probability of success is more in healthy students as compared to runny nose students
50.65> 37.29
Therefore it is appropriate to conclude that the health of the student affects ability to taste.
21n over 9n in lowest terms
Answer:
21n/9n
= 7n/3n
21n/9n in the lowest terms is 7n/3n