A librarian sorts 500 books at a constant rate. After 6 days, the librarian still has 200 books to sort. How much time does it take to sort the books from start to finish?
Answer: 10 days
Step-by-step explanation: So if the librarian sorted at a constant rate, then they sorted the same amount of books all 6 days. If they still have 200 books left to sort, then they sorted 300 books over 6 days. This means that they sorted 50 books per day. 200 divided by 50 is 4. So it will take 4 more days to finish sorting all the books. So altogether, it will take 10 days to sort all of the books.
The total number of required days is 10.
What is Unitary method ?In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.
The total number of books is 500.
The books left after 6 days is 200.
The number books read per day is given as,
(500 - 200)/6
= 300/6
= 50
Now, number of days the remaining number of books to be read is,
200/50 = 4
Thus, the total number of days is 6 + 4 = 10.
Hence, it will take 10 days from the start to finish all the books.
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Express into slope form
Answer: y= 3/2x+1
Step-by-step explanation:
What is 2052 divided by 76
Answer:
27
Step-by-step explanation:
Answer:
Yes, by 27 times
Step-by-step explanation:
I hope it helps you
Select the correct answer.
Brianna created a scatter plot and drew a line of best fit, as shown.
What is the equation of the line of best fit that Brianna drew?
The equation of the line of best fit that Brianna drew is: c. y = 2x + 5
Recall:
Line of best of fit of the line shown in the scatter plot can be found by finding the slope (m) and the y-intercept (b) of the line then substituting each value into y = mx + b.Thus:
Slope of a line (m) = change in y/change in x
From the scatter plot given,Change in y = 2 units
Change in x = 1 unit
Slope = 2/1 = 2
The y-intercept is the point where the line of best fit intercepts the y-axis which is at y = 5.
y-intercept (b) = 5
Substitute b = 5 and m = 2 into y = mx + b
y = 2x + 5
Therefore, the equation of the line of best fit that Brianna drew is: c. y = 2x + 5Learn more about line of best fit on:
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Answer:
c ..)
Step-by-step explanation:
The life expectancy (M) in the United States is 85 with a standard deviation of 6 years. A random sample of 36 individuals is selected. What is the probability that the sample mean will be between 82.5 and 86 years?
Answer:
The probability that the sample mean will be between 82.5 and 86 years is 0.8351.
Step-by-step explanation:
According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\mu\\[/tex]
And the standard deviation of the sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
[tex]\mu=85\\\sigma=6\\n=36[/tex]
As the sample size is large enough the Central Limit Theorem can be used to approximate the sampling distribution of sample mean life expectancy (M) in the United States.
Compute the probability that the sample mean will be between 82.5 and 86 years as follows:
[tex]P(82.5<\bar X<86)=P(\frac{82.5-85}{6/\sqrt{36}}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{86-85}{6/\sqrt{36}})\\\\=P(-2.5<Z<1)\\\\=P(Z<1)-P(Z<-2.5)\\\\=0.84134-0.00621\\\\=0.83513\\\\\approx 0.8351[/tex]
Thus, the probability that the sample mean will be between 82.5 and 86 years is 0.8351.
The probability that the sample mean will be between 82.5 and 86 years is 0.8351.
Standard deviation σ = 6
Sample size n =36
What is the central limit theorem?The central limit theorem (CLT) states that the distribution of sample means approximates a normal distribution as the sample size gets larger, regardless of the population's distribution.
Since the sample size is significant i.e. large, so the given scenario can be treated as normally distributed as per the central limit theorem.
So, the standard deviation of sample means = σ/√n
The probability that the sample mean will be between 82.5 and 86 years:
[tex]P(82.5 < X < 86) = P(\frac{82.5-85}{\frac{6}{\sqrt{36} } } < Z < \frac{86-85}{\frac{6}{\sqrt{36} } } )[/tex]
[tex]P(-2.5 < Z < 1)=P(Z < 1)-P(Z < 2.5)[/tex]
[tex]P(-2.5 < Z < 1) =0.8413-0.0062=0.8351[/tex]
Therefore, the probability that the sample mean will be between 82.5 and 86 years is 0.8351.
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What is the missing value in ___x 1/10=0.27
Find an equation of the plane through the point (1, -4, 0) and perpendicular to the vector (5, 1, -4). Do this problem in the standard way or WebWork may not recognize a correct answer.
Answer:
x = = -5 ; y = -1 ; z = 4 [tex]\bigg | = 3 \bigg |[/tex]
Step-by-step explanation:
The equation of the plane through (1,-4,0) is,
a(x-1) + b(y+4) + c(z+0) = 0 ....... (1)
Again the plane is perpendicular to the vector (5,1,-4)
So, the direction ratios of the normal to the plane is proportional to the direction ratios of the vector (5,1,-4)
So, a/(5) = b/(1) = c/(-4 )
Let,a/(5) = b/(1) = c/(-4 ) = k
So, a = 5k, b = k and c = -4k
So, from (1) we have,
(5k)(x-1) + (k)(y+4) + (-4k)(z+0) = 0
Thus;
-5(x-1) -(y+4) +4(z+0) = 0
So,
-5x +1 -y-4+4z+0 =0
-5x - y +4z -3 = 0
-5x - y +4z = 3
x = = -5 ; y = -1 ; z = 4 [tex]\bigg | = 3 \bigg |[/tex]
Estimate the squrae root to rhe nearest hundredth.
1. 138
2. 405
3. 800
4. 1150
5. 6500
6. 580
7. 300
8. 250
9. 284
10. 794
Salamt....
Answer:
1.11.83
2. 20.12
3. 28.28
4. 33.91
5.80.62
6.24.08
7.17.32
8. 15.81
9. 16.85
10. 28.18
Step-by-step explanation:
pls make me brainliest
In which pair do both decimals represent rational numbers?
O A. 0.296 and 0.9888...
B. 4.462837305718274... and 0.9888
O C. 6.32891237302554... and 0.9888...
D. 6.32891237302554... and 0.296
Answer:
Step-by-step explanation:
Option A. 0.296 and 0.9888 is correct because rational no are terminating and repeating ..
There are 20 squares and 16 triangles. What is the simplest ratio of triangles to total shapes?
Answer:
4/9
Step-by-step explanation:
20+16= 36 total shapes. 16/36 simplifys to 4/9.
The simplest ratio of triangles to total shapes is 4:7.
Given that the number of squares=20 and the number of triangles=15.
The total number of shapes=20+15=35.
We need to find the simplest ratio of triangles to total shapes.
What is the ratio?The quantitative relation between two amounts shows the number of times one value contains or is contained within the other.
Now, triangles: total shape=20:35
=4:7
Therefore, the simplest ratio of triangles to total shapes is 4:7.
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how do i solve this help
Answer is : A .. Hope it helped
A hot air balloon is descending at a rate of 6.75 feet per second.
What is the change in the balloon's height after 3 1/3 seconds?
The hot air balloon descends 22.498 feet after 3.333 seconds.
How much does a hot air balloon's height decreases?
The situation indicates that the height decrease is directly proportional to time. The distance is equal to the product of speed (v), in feet per second, and time (t), in seconds.
s ∝ t
s = v · t (1)
If we know that v= 6.75 ft / s and t = 3.333 ft, then the change in the height of the hot air balloon is:
s = (6.75 ft / s) · (3.333 s)
s = 22.498 ft
The hot air balloon descends 22.498 feet after 3.333 seconds.
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Assume the table gives data on field goal shooting for two members of the Benedict College 2014-2020 men's basketball team. Seth Fitzgerald Roberto Mantovani Made Missed Made Missed Two-pointers 123 118 87 84 Three-pointers 31 6 2 17 NOTE: The numerical values in this problem have been modified for testing purposes. (a) What percent of all field goal attempts did Seth Fiqzgerald make? (Enter your answers rounded to two decimal places.) Seth Fitzgerald's overall field goal percentage:_______ What percent of all field goal attempts did Roberto Mantovani make? (Enter your answers rounded to two decimal places.) What percent of all field goal attempts did Roberto Mantovani make? (Enter your answers rounded to two decimal places.) Roberto Mantovani's overall field goal percentage:______________. (b) Find the percent of all two-point field goals and all three-point field goals that both Seth and Roberto made. (Enter your answers rounded to two decimal places.) Seth Fitzgerald's two-pointers: ______________% Roberto Mantovani's two-pointers:___________ % Seth Fitzgerald's three-pointers:____________ Roberto Mantovani's three-pointers:__________ (c) Roberto had a lower percent than Seth for both types of field goals, but had a better overall percent. That sounds impossible, select the correct statement concerning the situation. i) This is an example of Simpson's paradox. The comparison that holds for both field goal groups is reversed when the groups are combined into one group. ii) The sample size is too small and this explains why the results seem contradictory. iii) You should never compare percentages for two different groups. iv) This is an example of correlation. The comparison that holds for both field goal groups is reversed when the groups are combined into one group.
Answer:
(a) What percent of all field goal attempts did Seth Fitzgerald make? (Enter your answers rounded to two decimal places.)
Seth Fitzgerald's overall field goal percentage:__59.69%_____
What percent of all field goal attempts did Roberto Mantovani make? (Enter your answers rounded to two decimal places.)
Roberto Mantovani's overall field goal percentage: ______40.31%________.
(b) Find the percent of all two-point field goals and all three-point field goals that both Seth and Roberto made. (Enter your answers rounded to two decimal places.)
Seth Fitzgerald's two-pointers: _____58.57%_________%
Roberto Mantovani's two-pointers:_____41.43%______ %
Seth Fitzgerald's three-pointers:_____64.58%_______
Roberto Mantovani's three-pointers:_____35.42%_____
(c) Roberto had a lower percent than Seth for both types of field goals, but had a better overall percent. That sounds impossible, select the correct statement concerning the situation.
i) This is an example of Simpson's paradox. The comparison that holds for both field goal groups is reversed when the groups are combined into one group
Step-by-step explanation:
a) Data and Calculations:
Benedict College 2014-2020 men's basketball team:
Seth Fitzgerald Roberto Mantovani Total
Made Missed Made Missed Made Missed
Two-pointers 123 118 87 84 210 205
Three-pointers 31 6 17 2 48 8
Total 154 124 104 86 258 210
a) All field goal attempts = 258 (154 + 104)
Field goal attempts by Seth Fitzgerald = 154/258 * 100 = 59.69%
Goal 154 - 124 = 30/258 * 100 = 11.63%
Roberto Mantovani = 104/258*100 = 40.31%
Goal 104 - 86 = 18/258 *100 = 6.98%
Percent of all two-point field goals and all three-point field goals that both Seth and Roberto made:
Goals by both = 48 (30 + 18) = 48/258*100 = 18.61 (11.63 + 6.98)
Seth Fitzgerald's two-pointers = 123/210*100 = 58.57%
Roberto Mantovani's two-pointers = 87/210*100 = 41.43%
Seth Fitzgerald's three-pointers = 31/48*100 = 64.58%
Roberto Mantovani's three-pointers = 17/48*100 = 35.42%
b) Simpson's paradox, also called Yule-Simpson effect, says that when we combine all of the groups together (e.g. two-pointer and three-pointer games played by Seth and Roberto respectively) and look at the data in total form, the correlation that we noticed before may reverse itself. The cause of this reversion is lurking variables or numerical values of the data.
What is 9x for x = 4
Answer:
36
Step-by-step explanation:
9x is equal to 9 multiplied by x.
x=4 so it is 9 x 4
9 x 4=36
What function represents the amount of change given from a $10 bill, f(x), based on x, the number of bagels purchased? f(x) = 4x + O f(x) = -x + 10 Of(x) = x + 10 O f(x) = -x + 10
Answer:
the answer is c
Step-by-step explanation:hope this helps
Answer:
C or the third option, 3/4 x + 10
Step-by-step explanation:
100% correct please mark brainlist. HAVE A GREAT DAY
Joan planted 150 tulip bulbs, but only 20% of them bloomed. How many tulips
bloomed?
Solve the equations:
2^(3x−4) = −2
Answer:
x=NaN your welcome hehe
PLEASE HELP FAST & CORrect 50 POINTS
Answer:
105
Step-by-step explanation:
12. Sean lives 2.25 miles
from school. Write this
distance as a fraction in simplest form.
PLEASE HELP ME SIMPLIFY THIS PLEASE SHOW WORK TO! THANK YOU! 5.3x - 9 + 7.6x
Answer:
12.9x-9
Step-by-step explanation:
5.3x-9+7.6x
5.3x+7.6x = 12.9x
=12.9x-9
Write the hypothesis: If the pen is not blue then today is Friday.
a. The pen is not blue
b. If the pen is not blue
c. If today is Friday
d. today is not Friday
Mrs. Alonza ordered 4 x 10³ markers for her store. How many markers did she order?
Can anyone answer and offer a simple step by step explanation for finding the volume for this?
Answer:
x^6
Step-by-step explanation:
Volume=w times height times length
Volume=x^2 times x^2 times x^2
x^2+2+2
x^6
Answer:
x^6 is volume
Step-by-step explanation:
So a volume of a cube is lenght times width times height.
Or the cube of a side(number to the power of 3)
Let's say one of the sides is 7. Then the volume would be 7 times 7 times 7 or 7 cubed which is equal to 729.
Jim walks 6/7 of a mile every day. Russell walks 1/4 of a mile. How much farther does Jim work than Russell.
Answer:
Jim walked 17/28 for miles than Russel
Step-by-step explanation:
First you turn 6/7 and 1/4 to have the same denominators. In that case you find the least common multiple which is 28.
7: 7, 14, 21, 28
4: 4, 8, 12, 16, 20, 24, 28
Next you multiply the top and the bottom of your fraction my the factor you used to get 28 for your denominator
6/7 x 4/4 = 24/28
1/4 x 7/7 = 7/28
Lastly, you subtract the products you got.
24/28 - 7/28 = 17/28
what will be the 40th term in the sequence defined by an=-12+4(n-2)
Answer:
140
Explanation:
an=-12+4(n-2)
an=-12+4([40]-2)
an=-12+4(38)
an=-152-12
an=140
The 40th term in the sequence defined by aₙ= -12+4(n-2) is 140
using AP formula,
aₙ = a + (n - 1)d
where
a = first term
d = common difference
n = number of terms
Therefore,
aₙ = -12 + 4(n-2)
n = 40
a₄₀ = -12 + 4(40 - 2)
a₄₀ = -12 + 4(38)
a₄₀ = -12 + 152
a₄₀ = 140
The 40th term of the sequence is 140.
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10. A train to New York city leaves a station every 7 minutes. Another train to Boston leaves the
station every 6 minutes. Suppose it is 6:30 am right now. At what time will both trains leave the
station together?
Answer:
7:00
Step-by-step explanation:
Amna wants to rent a boat and spend less than 51 . The boat costs 6 per hour, and Amna has a discount coupon for 3 off What are the possible numbers of hours Amna could rent the boat?
Answer:
9 hours or less. with a $3 off coupon she could spend up to $54. divide that by $6 per hour and that gives you a possibility of nine hours of boat rental.
The graph represents f(x) = |x| + 3.
what is f(-2, 2)?
A) -2
B) 0
C) 1
D) 2
A local little league has a total of 66 players, of whom 80 % are right-handed. How many right-handed players are there?
Answer:
The amount of right-handed players is 53
Hope this Helps :)
What is the sum of -6 and 12/6
Answer:
-4
Step-by-step explanation:
Answer:
-4
Step-by-step explanation:
multiply -6 with 6 so we can have common denominator as 12/6
that's gives us -36/6+12/6
-36+12 is -24 so our answer up till now will be -24/6.... this can be simplified by 6 to get -4
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