The middle 99.7% is within 60 seconds to 63 seconds.
The empirical rule states that for a normal distribution, 68% are within one standard deviation from the mean, 95% are within two standard deviations from the mean and 99.7% are within three standard deviations from the mean.
Given that:
mean (μ) = 60 seconds, standard deviation (σ) = 1 second
99.7% are within three standard deviations = μ ± 3σ = 60 ± 3(1) = (57, 63)
The middle 99.7% is within 60 seconds to 63 seconds.
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Use the formula Sn =a (1 - rn ) ÷ (1 – r) to find the sum Sn for each of the infinite and finite geometric series.
9. The first 9 terms of 12, – 6 ,+ 3, - …
10. The first 15 terms of -1, + 1, -…
11. The first 6 terms of 1, + 3, + …
12. The first 10 terms of 2, – 4, + …
Answer: 11
Step-by-step explanation:
9. The Sum of 9 terms is 513/64.
10. The sum of 15 terms is -1.
11. The sum of 6 terms is 364
12. The sum of 10 terms is -682.
We have,
Sn =a (1 - [tex]r^n[/tex] ) ÷ (1 – r)
9. 12, -6, 3, .....
Here, r= -6/ 12= -1/2
So, S(9)
= 12 (1- [tex](-1/2)^9[/tex])/ (1 - (-1/2))
= 513/ 64
10.-1, +1, -.....
Here, r= 1/ (-1)= -1
So, S(15) = 1 (1- [tex](-1)^{15[/tex])/ (1 - (-1))
= -1
11. 1, 3, .....
Here, r = 3/1 = 3
So, S(6) = 1 (1- [tex](3)^{6[/tex])/ (1 - 3)
= 364
12. 2, -4, ...
Here, r= (-4)/ 2= -2
So, S(10) = -682
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log x √x + log √c c² = ?
[tex] log_{x}\sqrt{x} + log_{ \sqrt{c} } {c}^{2} = \\ [/tex]
please help me!!!!?;
Given that
log √x (x) + log c² (c)
⇛ log x^1/2 (x) + log c² (c)
We know that
log a^m (b^n) = m/n log a (b)
⇛ 1/2 log x (x) + 2 log c (c)
We know that
log a ( a) = 1
⇛ (1/2)(1) + 2(1)
⇛ (1/2)+2
⇛ (1+4)/2
⇛ 5/2
Answer:- log √x (x) + log c² (c) = 5/2
[(x) ,(c) , (a) represents the bases ]
Additional comment:
(a+b)(a-b) = a²-b²log a^m (b^n) = m/n log a (b)log a ( a) = 1also read similar questions: if log^2(x)=log^2(a)+log^2(b)-log^2(c) then x is....
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simplify the following expression. log(x2) - log(x) A. log(x^2+x) B. log(x^3) C. log(x^2-x) D. log(x)....
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JoAnn is making jewelry. Set an expression that shows how much it will cost Joanne for the long length chain bracelet and for b beads that cost $0.30 each. Then find the total cost of the jewelry lol JoAnn uses 34 beads
Answer:
$0.30 x b
$10.20
Step-by-step explanation:
The equation is
$0.30 x b
Since we know JoAnn uses 34 beads, we can replace b with 34
$0.30 x 34 = $10.20
A movie theater charges $8.00 for adults and $5.00 for children. If there were 40 people altogether and the theater collected $272.00 at the end of the day, how many
of them were adults?
A. 29 adults
B. 16 adults
C. 24 adults
D.10 adults
Answer:
C.24
Step-by-step explanation:
First multiply 8 by 24 this is so you know how much 24 adults would be. You will get 192 so next you need to subtract 192 from the total money 272 to get 80 and 80 should be how much all of the kids cost now to check and make sure there are 40 people divide 80 by 5 to get 16 which is the total number of kids no just add 16 and 24 together to get 40
pls help. Have tried this problem a couple times but my answers didnt work
Answer:
infinite solutions...
Step-by-step explanation:
Is there more information to this problem? It can be pretty much anything.
N=3M
Nina can be 30 and Maryna 10, Nina can be 3 and Maryna 1, Nina can be 15 and Maryna 5...
Answer:
N - 4 = 3(M - 4). Simplified further, N - 4 = 3(M - 4)
Given,
Nina is N years old now and;
Maryna is M years old now
If four years ago, Nina was three times as old as Maryna was, then
Four years ago, Nina's age was N - 4
Four years ago, Maryna's age was M - 4
Given that Nina was three times as old as Maryna was four years ago, it means that
N - 4 = 3(M - 4)
To solve further
N = 3m - 12 + 4
N = 3M - 8
Step-by-step explanation:
what is the value of x?
Answer:
132
Step-by-step explanation:
corresponding angles are the same
Sara has $65 and wants to buy the following items from a store. Board game: $14.95 Building blocks: $25.49 Art kit: $35.79 At the store, all items are one-fourth off of the original price and there is a 5% sales tax. Sara wants to know if she can buy all of these items. Which statement is TRUE?
The correct statement is Sara can afford to purchase the items because the final price of the items is $60.
The first step is to determine the total cost of the items Sara wants to buy. The total cost can be determined by adding the cost of the items together.
Total cost = $14.95 + $25.49 + $35.79 = $76.23
The second step is to determine the cost of the items after the discount.
Price of the items = total cost x (1 - discount)
= total cost x (1 - 1/4)
total cost x 3/4
$76.23 x 3/4 = $57.17
The third step is to determine the cost of the items after tax.
Cost = (1.05) x $57.17 =$60.03
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HELP!! I'm not sure what goes in the blank.
Answer:
10[tex]sin^{2} ([/tex]β[tex])[/tex]
Step-by-step explanation:
We can find this two ways, first by seeing in the step after it, cosines are canceled out. Since you already have 10[tex]sin^{2} ([/tex]β[tex])[/tex] on the next step, you can assume that (since only the cosines changed and the cosine next ot the blank was removed), the value is 10[tex]sin^{2} ([/tex]β[tex])[/tex].
You can also use double angle formulas from the previous step:
(sin(2β) = 2 sin(β) cos(β))and find that:
5 sin (2β) sin(β) = 5 * (2 sin(β) cos(β)) sin(β)) = (10 sin(β) sin(β)) cos(β) =
10[tex]sin^{2} ([/tex]β[tex])[/tex] cos(β)
But since cos(β) is already present, we can see that the answer is 10[tex]sin^{2} ([/tex]β[tex])[/tex]
A wall map of the United States has a distance of 8.5 in. between Memphis and Denver, two cities that are actually 1040 mi apart. The actual distance between St. Louis and Des Moines is 333 mi. How far apart are St. Louis and Des Moines on the map?
Answer:
2.72 inches
Step-by-step explanation:
1040/8.5=122.35
1 inch on the map = 122.35 miles actual distance
333/122.35=2.72
Find the equation of the line passing through the point (−5,−9) and parallel to the line y=3x+2 .
Answer:
Root:(-⅗,0)
vertical intercept:(0,5)
Step-by-step explanation:
Mai makes her favorite shade of green paint by using 5 cups of blue paint for every 3 cups of yellow paint. Priya makes her favorite shade of green paint by using 7 cups of blue paint for every 5 cups of yellow paint. Whose favorite shade of green paint has more of a blue tint? Explain how you know.
Answer:
Priya
Step-by-step explanation:
Mai= 5:3 Priya=7:5
Mai= 15:15 Priya=21:15
The ratios above are blue:yellow so Priya's shade has more of a blue tint because it is 21:15 and Mai's is 15:15 so it is evenly spread.
round 3,817,453 to the nearest 100
Answer:
The nearest hundredth would be 3,817,500
Step-by-step explanation:
The hundreds place is the four and the five behind it rounds the number to a up to a 5
find the answer given below
Answer:
Surface area = 6l^2
Volume = l^3
If total surface area increased by 2, then the length increased by [tex]\sqrt{2}[/tex]
Volume then is increased by ([tex]\sqrt{2}[/tex]l)^3 = 2[tex]\sqrt{2}[/tex]l^3
1 :2 [tex]\sqrt{2}[/tex]
Which is not an option in the question so this question clearly has a problem.
First of all It's supposed to be "then" not "than," so I'm not sure who teaches math without even knowing this basic grammar.
Second of all, if the answer is 8:1 the question should be "If each sides of a cube is doubled" not "the lateral surface area." Come to think of it what even is lateral surface area of a cube if all sides of the cube is supposed to be same.
Or, if the answer is 2:1 then, it should be If height lateral surface area of a cube is doubled by doubling the height and without changing the length and width" But, then the the shape would no longer be a cube.
Who even wrote this garbage question what.
Please look at picture for question
Answer:
a=0.62
b=7/9
c=10/9
Determine the area of the yellow sector
Answer:
146 is the answer im positive
PLEASE HELP I WILL MARK YOU BRAINLEST!!!
please read the question on the photo and these are the choices bellow!!
A-translation, reflection
B- rotation, reflection
C-reflection, rotation
D-rotation, translation
help me pleas, I need the energy.
Answer:
negative
Step-by-step explanation:
Answer:
negative
Step-by-step explanation:
as it goes further right, it goes further down, so it is a negative slope
please help!! easy but i don't understand <3
in essence it's just asking on getting the equation of that line in more or less slope-intercept form, hmmm well, it's a line, so all we need is two points to get it, hmmm let's see let's use the starting point and terminal point, so we know it goes through the origin, (0,0) and also goes through (1, 0.7), let's change 0.7 to a fraction, so its 7/10, ok, let's use those two points from it.
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{\frac{7}{10}}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{\frac{7}{10}}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{0}}}\implies \cfrac{~~ \frac{7}{10}~~}{1}\implies \cfrac{7}{10}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{\cfrac{7}{10}}(x-\stackrel{x_1}{0})\implies y = \cfrac{7}{10}x[/tex]
What is the equation of the line: * parallel to the line y = -¼x + 5 and * passing through the point (2, -1)
y = -¼x - 1/2
y = ¼x + 2
y = -¼x + 4
y = ¼x - 1
Answer:
last one
Step-by-step explanation:
GUYS PLEASE HELP ME ON THIS ONE!, i will give brainliest to the right answers
Aisha has $40 to spend for her ornithology club. She spends some of it buying birdseed and saves the rest. Her savings is given by f(x)=40−1.25x, where x is the number of pounds of birdseed she buys at $1.25 per pound.
Answer:
Step-by-step explanation:
Given f(x)=40-1.25x, where x=pounds of birdseed and 40=her saved amount, and birdseed costs 1.25/lb.
f(3)=40-1.25(3)
f(3)40-3.75
f(3)=36.25
If she buys (3 pounds) of birdseed, she saves ($36.25).
f(18)=40-1.25(18)
f(18)=40-22.5
f(18)=17.5
If she buys (18 pounds) of birdseed, she saves ($17.5)
f(36)=40-1.25(36)
f(36)=40-45
f(36)=-5
If she buys (36 pounds) of birdseed, she will need an extra $5 to pay off her debt.
If she buys (36 pounds) of birdseed, she will need an extra $5 to pay off her debt.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given function f(x)=40-1.25x,
where x=pounds of birdseed and 40 is her saved amount, and birdseed costs is 1.25/lb.
f(3)=40-1.25(3)
f(3)40-3.75
f(3)=36.25
If she buys (3 pounds) of birdseed, she saves ($36.25) then;
f(18)=40-1.25(18)
f(18)=40-22.5
f(18)=17.5
If she buys (18 pounds) of birdseed, she saves ($17.5) then;
f(36)=40-1.25(36)
f(36)=40-45
f(36)=-5
If she buys (36 pounds) of birdseed, she will need an extra $5 to pay off her debt.
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Suppose Bella wanted to make a gift basket worth $25 instead the gift basket must also have more wheat loaves than muffins show one way Bella can make the gift basket
PLEASE ANSWER FOR 30 POINTS
Answer:
One Solution
Step-by-step explanation:
x + 3y = 3
x - y = -3
4y = 6 Subtract to solve by elimination.
y = [tex]\frac{3}{2}[/tex] Divide by 4.
x - [tex]\frac{3}{2}[/tex] = -3 Substitute [tex]\frac{3}{2}[/tex] for y in the original equation.
x = -[tex]\frac{3}{2}[/tex] Add [tex]\frac{3}{2}[/tex].
HELP ME. NO LINKS!! PLEASE
Answer: 99% sure its b
Step-by-step explanation:
a. How much higher is 500 than 400 m?
b. How much higher is 500 than -400 m?
C. What is the change in elevation from 8,500 m to 3,400 m?
d. What is the change in elevation between 8,500 m and -300 m?
Line j has an equation of y = 1/5x + 7. Perpendicular to line j is line k, which passes through
the point (-1, -3). What is the equation of line k?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]\begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \impliedby y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{5}}x+7 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{1}{5}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{5}{1}}\qquad \stackrel{negative~reciprocal}{-\cfrac{5}{1}\implies -5}}[/tex]
so then line K has a slope of -5 and pass through (-1, -3)
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{-3})\qquad \qquad slope=m=-5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{-5}[x-\stackrel{x_1}{(-1)}] \\\\\\ y+3=-5(x+1)\implies y+3=-5x-5\implies y=-5x-8[/tex]
From a sample of 45 students exam scores, it was found that there was a mean score was 75 and a standard deviation of 5. Assume the distribution of exam scores is normal.
construct and interpret a 95% confidence interval for the true mean score.
Answer:
The 95% confidence interval for the true mean score is [tex][73.539,76.461][/tex]
Step-by-step explanation:
Note that [tex]CI=\bar x\pm z\frac{s}{\sqrt{n}}[/tex] where [tex]\bar x[/tex] is the sample mean, [tex]z[/tex] is the upper critical value for the desired confidence level, [tex]s[/tex] is the sample standard deviation, and [tex]n[/tex] is the sample size.
Therefore, [tex]CI=75\pm 1.96\frac{5}{\sqrt{45}}\approx[73.539,76.461][/tex]
Omar deposited $4000 into an account with 4.4% interest, compounded quarterly. Assuming that no withdrawals are made, how much will he have in the account after 10 years?
Do not round any intermediate computations, and round your answer to the nearest cent.
Find the perimeter and area of this polygon. (Geometry)
Answer:
rectangle= 22*9 = 198ft
triangle=11*10 = 110 ft
110+ 198 = 308 polygon
What is 18x4=9xn? Just tell me the answer.
Answer:
Step-by-step explanation:
x=0
Answer:
8
Step-by-step explanation:
18×4 = 72
And 72 ÷ 9 = 8
So 9×8 would be 72
Women comprise 83.3% of all elementary school teachers. In a random sample of 300 elementary school teachers, what is the probability that fewer than 260 are women?
Using the normal approximation to the binomial, it is found that there is a 0.9319 = 93.19% probability that fewer than 260 are women.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].In this problem:
Women comprise 83.3% of all elementary school teachers, hence [tex]p = 0.833[/tex]A sample of 300 teachers is taken, hence [tex]n = 300[/tex]The mean and the standard deviation for the approximation are given by:
[tex]\mu = np = 300(0.833) = 249.9[/tex]
[tex]\sigma = \sqrt{np(1 - p)} = \sqrt{300(0.833)(0.167)} = 6.46[/tex]
Using continuity correction, as the binomial distribution is discrete and the normal distribution is continuous, the probability that fewer than 260 are women is P(X < 260 - 0.5) = P(X < 259.5), which is the p-value of Z when X = 259.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{259.5 - 249.9}{6.46}[/tex]
[tex]Z = 1.49[/tex]
[tex]Z = 1.49[/tex] has a p-value of 0.9319.
0.9319 = 93.19% probability that fewer than 260 are women.
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