9514 1404 393
Answer:
1/2 + 1/6
Step-by-step explanation:
2/3 = 1/2 + 1/6
__
The sum of unit fractions is called an Egyptian Fraction. There are several different algorithms for finding such a sum. Here, we are starting with the form ...
2/p
where p is a small prime. Then the sum can be written as ...
1/((p+1)/2) +1/(p(p+1)/2) = 1/(4/2) +1/(3(4/2)) = 1/2 + 1/6
A different algorithm is used when p is a composite number.
__
Using the "greedy" algorithm, we can find the largest unit fraction less than 2/3 to be ...
1/ceil(3/2) = 1/2
Then the largest unit fraction in the remainder is similarly found. The remainder is ...
2/3 -1/2 = 1/6 . . . . already a unit fraction
So, the sum is ...
2/3 = 1/2 + 1/6
A screening test for a disease shows a positive result in 91% of all cases when the disease is actually present and in 7% of all cases when it is not. Assume that the prevalence of the disease is 1 in 650. If the test is administered to a randomly chosen individual, what is the probability that the result is positive
Answer:
0.0713 = 7.13% probability that the result is positive.
Step-by-step explanation:
Probability of a positive test:
91% of 1/650(has the disease).
7% of 1 - 1/650 = 649/650(does not have the disease). So
[tex]p = 0.91\frac{1}{650} + 0.07\frac{649}{650} = \frac{0.91 + 0.07*649}{650} = 0.0713[/tex]
0.0713 = 7.13% probability that the result is positive.
HELP ME PLEASE (pre algebra)
Answer:
30
Step-by-step explanation:
5ab -2c
Let a = 2 b=3 c=0
5*2*3 - 2*0
30 - 0
30
Solving a word problem involving rates and time conversion
A car travels at an average speed of 52 miles per hour. How long does it take to travel 247 miles?
Answer:
It takes 4.75 hours(4 hours and 45 minutes) to travel 247 miles.
Step-by-step explanation:
This question is solved by rates, using a rule of three.
52 miles in one hour. How many hours for 247 miles?
1 hour - 52 miles
x hours - 247 miles
Applying cross multiplication:
[tex]52x = 247[/tex]
[tex]x = \frac{247}{52}[/tex]
[tex]x = 4.75[/tex]
It takes 4.75 hours = 4 hours and 3/4*60 = 45 minutes to travel 247 miles.
What percentage of the individuals rode the Ferris wheel and did not ride the roller coaster?
Answer:
B and D
Step-by-step explanation:
they both make srnse to me
The required percentage of individuals is 66.07%.
What is percentage?
A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
The required data from the given table is as follows,
The total number of individuals is 112.
The number of individuals who ride Ferris wheel but not roller coaster is 74.
As per the question the percentage can be found as below,
Required percent = (The required number ÷ Total number) × 100
= (74 ÷ 112) × 100%
= 66.07%
Hence, the percentage of the individuals rode the Ferris wheel and did not ride the roller coaster is 66.07%.
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Simplify the following fraction 4½-2⅝
Answer:
Step-by-step explanation:
4 1/2 - 2 5/8
4 4/8 - 2 5/8 = 1 and 7/8
i mean i guess you could also do this witho ut sol ving
4 4/8 - 21/8 --> 36/8 - 21/8
i dk it's si mplify not solve so here?
Describe the relationship of the formula.
y = kx
If two variables (x and y) are directly proportional to each other, their relationship can be described as y=kx, where k is how they change relative to one another
What is the slope intercept form of this line?
Answer:
y = 1/4 x - 2
Step-by-step explanation:
y = mx + b
m = 1/4 *rise/run --> rises 1 square then runs 4 squares to the left indicating it's positive
x = x
b = y-intercept --> (0,-2) --> -2
Which equation has no solution?
A. x + 3 = 5(x+3)
B. 3x + 4 = 3(x - 5)
C. X+ 6 = 6x
D. 5x + 2 = 4x - 3
Answer: B: 3x + 4 = 3(x - 5) (has no solution)
Step-by-step explanation: (these have solutions)
C: X+ 6 = 6x = 6/5
A: x + 3 = 5(x+3) = −3
D: 5x + 2 = 4x - 3 = −5
Anyone good at 8th grade math please help out
Answer:
It should be y = -x + r or y = r - x. To solve for y you would have to isolate y by removing all other variables from y's side of the equation.
pls help anyone!! i don’t know the answers :(
Answer:
36 Times
Step-by-step explanation:
If there is 10 fruits and 3 of them are pears
10x 12= 120
3x12 = 36
Answer:
Step-by-step explanation:
all the fruits are 10
the pears are 3
probability of picking a pear is 3/10
out of 120 times the pear may be picked 120*(3/10) = 36 times
Find the value of a in this isosceles trapezoid. D. 11 A. 7 B. 15 C. 4
Answer:
B
Step-by-step explanation:
Because 15-4=11
and both angles are equal
Pls help 10 pts
X =
1
3
7
Answer:
3
Step-by-step explanation:
Answer:
x=3
Step-by-step explanation:
Secant-Secant Formula:(whole secant) x (external part) =
(whole secant) x (external part)
4 *(9) = x *(12)
36 =12x
Divide each side by 12
36/12 = 12x/12
3 =x
Elena is conducting an experiment to determine if the high school students are more relaxed when the lights are off or when music is played during an exam. She selects 10 of her friends to take an exam with the lights off and another 10 of her friends to take an exam with music playing.
Required:
What is problematic about the way that Elena selected her groups?
Answer:
Problematic is that - only one factor should be analysed at a time. However she has considered both.
Step-by-step explanation:
Groups for any experimental study should be selected on the basis of one variable, other factor(s) remaining constant.
In this case, here are two variables - lights on or off, music playing or not playing - effecting relax level during exams.
She selects 10 students for exam with lights off , 10 for exam without music. This is problematic, as at once only lights or only music factor should be considered.
If one group is with light on , other should be with light off. If one group is with music, other should be without music. This mix up of one light off aspect & one music without music is inapt.
give me question about equation of a circle question with real life situation.
. In this exercise, you will conduct regression analysis with binary and categorical variables. (a) Use the command tabulate to show the categories of the variable occupation and their frequencies. What is the relative frequency of the category Sales
which is the best estimate of 5 5/6 - (1 1/4 + 3 7/8)
Answer:
Step-by-step explanation:
"Best estimate' doesn't happen automaticallly, because you have to define "best" in this context. We could merely round all numbers and work with the results:
For example, starting with the work inside parentheses, we have:
5 5/6 - (1 + 4) = 5 5/6 - 5. We must round 5 5/6 up to 6. Then the "best estimate' is 6 - 5, or just 1.
The solution of the given expression is 17 / 24.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the expression is 5⁵/₆ - (1¹/₄ + 3⁷/₈). The value of the expression will be calculated as:-
E = 5⁵/₆ - (1¹/₄ + 3⁷/₈)
E = 35 / 6 - [ 5 / 4 - 34 / 8 ]
E = 35 / 6 - [ ( 10 + 31 ) / 8 ]
E = 35 / 6 - 41 / 8
E = ( 140 - 123 ) / 8
E = 17 / 21
Hence, the solution of the expression is 17 / 21.
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True or false diagonals of rectangle are equal
Answer: A rectangle is a quadrilateral in which all angles are right angles. A rectangle is a parallelogram, so its opposite sides are equal. The diagonals of a rectangle are equal and bisect each other.
Step-by-step explanation:
are these correct???
Answer:
yes
Step-by-step explanation:
Assume that the GMAT scores across the U.S. follow a bell shaped distribution (symmetric and unimodal) with mean 549 and standard deviation 76. Use the Empirical Rule (68-95-99.7 rule) to answer the following question: What is the GMAT score corresponding to the 16th percentile
Answer:
The GMAT score corresponding to the 16th percentile is 473.
Step-by-step explanation:
Empirical Rule.
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.
68% of the measures within 1 standard deviation of the mean.
This means that they are between the 50 - (68/2) = 50 - 34 = 16th percentile(one standard deviation below the mean) and the 50 + (68/2) = 50 + 34 = 84th percentile(one standard deviation above the mean).
In this question:
Mean of 549, standard deviation of 76.
16th percentile:
One standard deviation below the mean, so 549 - 76 = 473.
The GMAT score corresponding to the 16th percentile is 473.
in a group of 35 children, 10 have blonde hair, 14 have brown eyes, and 4 have both blonde hair and brown eyes. if a child is selected at random, find the probability that the child has blonde hair or brown eyes
[tex] \frac{14}{35} + \frac{10}{35} - \frac{4}{35} = \frac{4}{7} [/tex]
The solution is, 4/7 is the probability that the child has blonde hair or brown eyes.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
given that,
in a group of 35 children, 10 have blonde hair, 14 have brown eyes, and 4 have both blonde hair and brown eyes.
let, the event be A,
i.e. A = if a child is selected at random, that child has blonde hair or brown eyes.
now, we have,
total no of sample space = 35
probability of blonde hair = 10/ 35
probability of brown eyes = 14/35
probability of both blonde hair and brown eyes = 4/35
so, we get,
probability of blonde hair or brown eyes = 14/ 35 + 10/ 35 - 4/35
= 20 / 35
= 4/7
Hence, The solution is, 4/7 is the probability that the child has blonde hair or brown eyes.
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Write the equation of the line that passes through
the points (-1,2) and (6, 3) in slope-intercept form
A defense company working for the government claims that at most 6% of its missiles are defective. A sample of 160 missiles is taken and 16 are defective. Test their claim at 1% level.
Required:
State clearly the null and the alternative hypothesis
Answer:
Null Hypothesis: H0: Defective defense missiles not more than 6%
Alternate hypothesis: Ha: Defective defense missiles are greater than 6%
Step-by-step explanation:
The null hypothesis is the problem statement and the alternate hypothesis is a contradiction of null hypothesis
Hence,
Null Hypothesis: H0: Defective defense missiles not more than 6%
Alternate hypothesis: Ha: Defective defense missiles are greater than 6%
Given Limit of f (x) = 6 as x approaches 1. What is Limit of left-bracket 5 f (x) right-bracket as x approaches 1? 5 6 11 30
Answer: D. 30
Step-by-step explanation:
Edge 100%
Answer:
the answer is d on edge
Step-by-step explanation:
Fimd the medium.of given data ? 5,19,8,11,7,6,17,11,6,10
If pis inversely proportional to the square of q, and p is 23 when q is 4, determine p
when q is equal to 2.
Answer:
[tex]p\ =\ 92[/tex]
Step-by-step explanation:
Given
[tex]p\ \alpha\ \frac{1}{q^2}[/tex]
[tex]p =23; q=4[/tex]
Required
Find p, when [tex]q = 2[/tex]
We have:
[tex]p\ \alpha\ \frac{1}{q^2}[/tex]
Express as equation
[tex]p\ =\ \frac{k}{q^2}[/tex]
Make k the subject
[tex]k =pq^2[/tex]
When: [tex]p =23; q=4[/tex]
[tex]k =23 * 4^2[/tex]
[tex]k =368[/tex]
When [tex]q = 2[/tex], we have:
[tex]p\ =\ \frac{k}{q^2}[/tex]
[tex]p\ =\ \frac{368}{2^2}[/tex]
[tex]p\ =\ \frac{368}{4}[/tex]
[tex]p\ =\ 92[/tex]
Consider f(x) = 2x^2 + 1 and g(x) = 3x - 6. Which statement about f + g is true?
A.It is a linear function.
B.It is a quadratic function.
C. The domain is x 2-3.
D. The range is all real numbers.
Answer:
Vertex of a quadratic function (formula)
Step-by-step explanation:
The average number of employees that call in sick for the day over the course of a year is 25. The number of employees that call in sick on 12 days are 25, 10, 16, 39, 27, 25, 32, 25, 25, 22, 28, and 14. Enter the sample mean and the population mean in the boxes
Answer:
sample mean (x with the bar on top) =24
Step-by-step explanation:
Take the mean of all the number of employees but divide by the number of days size: (25+10+16...)/12=25
population mean (mu) =11.52
The same goes for the other one but divide by the population which is 25
What is the area of the figure below?
:8 in.
21 in.
A 84 in2
B 160 in?
C 168 in2
D 336 in?
Answer:
The answer is C. 168 in^2
Step-by-step explanation:
(Area = Base x Height)
21 * 8 = 168
Help me PLEASEEEEEEEEEEEEE
Answer:
D. 44.55
Step-by-step explanation:
if you multiply 4.95x9 you get D
Answer:
the answer is D
Step-by-step explanation:
Since each is 4.95 multiply 4.95 x 9 = 44.55
hope this helps
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FIND P VALUE A medical school claims that more than 28% of its students plan to go into general practice. It is found that among a random sample of 120 of the school's students, 30% of them plan to go into general practice. Find the P -value for a test of the school's claim.
Answer:
0.3128
Step-by-step explanation:
H0 : p ≤ 0.28
H0 : μ > 0.28
The test statistic :
(phat - p) ÷ √(pq / n)
q = 1 -p = 1 - 0.28 = 0.72
phat = 0.30
(0.30 -0.28) ÷ √((0.28*0.72) / 120)
0.02 ÷ 0.0409878
Test statistic = 0.48795
Using the Pvalue from test statistic calculator :
Pvalue(0.05, right tailed) = 0.3128