Using the normal distribution, the probabilities are given as follows:
a) 0.6517 = 65.17%
b) 0.0823 = 8.23%.
c) 0.6109 = 61.09%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 8.9, \sigma = 2.8[/tex]
Item a:
The probability is the p-value of Z when X = 10, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{10 - 8.9}{2.8}[/tex]
Z = 0.39
Z = 0.39 has a p-value of 0.6517.
0.6517 = 65.17% probability that the time is less than 10 minutes.
Item b:
The probability is the one subtracted by the p-value of Z when X = 5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5 - 8.9}{2.8}[/tex]
Z = -1.39
Z = -1.39 has a p-value of 0.0823.
0.0823 = 8.23% probability that the time is more than 5 minutes.
Item c:
The probability is the p-value of Z when X = 15 subtracted by the p-value of Z when X = 8, hence:
X = 15:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15 - 8.9}{2.8}[/tex]
Z = 2.18
Z = 2.18 has a p-value of 0.9854.
X = 8:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{8 - 8.9}{2.8}[/tex]
Z = -0.32
Z = -0.32 has a p-value of 0.3745.
0.9854 - 0.3745 = 0.6109 = 61.09%.
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3) Which letter has a perpendicular line segment?
A. Y
B. L
C. R
D. U
Answer: L
Step-by-step explanation:
The two segments that form L meet at a 90 degree angle.
The graph is of a function in the form p(t) = a*b^t. What is the function?
Answer:
p(t) = 5*2^t
Step-by-step explanation:
We can solve for 'a' and 'b' using the point coordinates shown on the graph.
SetupSubstituting for (t, p(t)), the two equations we can make from the given points are ...
p(t) = a*b^t
5 = a*b^0 . . . . . . . (t, p(t)) = (0, 5)
10 = a*b^1 . . . . . . . (t, p(t)) = (1, 10)
SolutionThe first equation tells you ...
5 = a
The second equation tells you ...
10 = 5*b
2 = b
EquationThe function is ...
p(t) = a*b^t
p(t) = 5*2^t
Problem
A prime trio is a collection of three prime numbers [tex]\{p,q,r\}[/tex] in arithemtic progression, with common difference [tex]q-p=r-q[/tex]. For example, the prime trio [tex]\{3,5,7\}[/tex]has common difference 2.
(a) Find a prime trio with common difference 50.
(b) Find two prime trios with common difference 60.
(c) Prove that there is no prime trio with common difference 70.
Answer:
(a) 50:
3 53 103
(b) 60:
7 67 127
11 71 131
Step-by-step explanation:
OK, I think you can prove this with the theorem that any prime greater than 3 is 6n-1 or 6n+1, for integer n. In other words, any prime is near a multiple of 6; it is either one less or one more. The proof for this is very easy, look it up.
Given this fact, if two primes (p,q) are 70 a part, this means the first one has to be a case of 6n+1 and the second one has to be a case of 6n-1. Why? Because the nearest multiple of 6 is 72 and with +1 on one end and -1 on the other end, you can reach a "gap" of 70.
Now for the next two primes (q,r) the same must hold. Only, it can't because this requires q to be both 6n-1 and 6n+1.
Which statements are true? Select three options.
You can use for reference ;)
At a restaurant levys total bill is 46 bucks, if he wants to tip 15 percent how much should he leave as a tip?
Evaluate the following expression.
(5x)^0
Hello,
Answer:
1
Step-by-step explanation:
(5x)⁰ = 1
Rule : a⁰ = 1
Answer:
1
Step-by-step explanation:
(5x)^0
Any base raised to the zero power is 1
a^0 = 1
5^0 =1
(5x)^0 =1
Silva the formula I=Prt, in general, to find the principal, p.
Dividing both sides by rt,
[tex]\boxed{P=\frac{I}{rt}}[/tex]
Choose the lowest common denominator.
03 04 05 06 08 010 012
Find the sum:
Alw
The sum is
and
colch
The expression written in equivalent form with a
common denominator is
Done
1) 8
2) [tex]-\frac{3}{4}=-\frac{6}{8}[/tex], so it is equal to [tex]-\frac{6}{8}+\frac{5}{8}[/tex]
3) 1/8
does 6(2x-6)=-7(-2x+4) have no solution or infinite solution
Answer:
It does not.
Step-by-step explanation:
[tex]6(2x - 6) = -7(-2x + 4); \\ 6 * 2x - 6 * 6 = -7 * (-2x) + (-7) * 4; \\ 12x - 36 = 14x - 28; \\ 14x - 12x = -36 + 28; \\ 2x = -8; \\ x = -4.[/tex]
[tex]\{-4\}[/tex] is our set of solutions. Answering your question, it does not.
Whats the correct answer answer asap for brainlist
Answer:
B
Step-by-step explanation:
Given that a bag of m&ms has 21 brown candies, 15 orange candies, 10 yellow candies, 14 red candies, and 5 green candies, find the probabilities
The probability of drawing brown candies , orange candies, yellow candies, red candies, green candies is 0.323 , 0.231 , 0.154 , 0.215 ,0.077
What is Probability ?Probability is the study of likeliness of an event to happen.
It is given that a bag of candies that have
21 brown candies
15 orange candies,
10 yellow candies,
14 red candies,
5 green candies,
probabilities of drawing each candy =?
Total Candies = 21 +15+10+14+5 = 65
Probability = No. of chances / Total outcomes
Probability of drawing Brown candies = P(B) = 21 /65 = 0.323
Probability of drawing Yellow candies = P(Y)= 10/65= 0.154
Probability of drawing Orange candies = P(O) = 15/65= 0.231
Probability of drawing Red candies =P( R) = 14/65= 0.215
Probability of drawing Green candies = P(G) = 5/65= 0.077
Therefore the probability of drawing brown candies , orange candies, yellow candies, red candies, green candies is 0.323 , 0.231 , 0.154 , 0.215 ,0.077.
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Giving brainliest to first accurate answer
Answer:
x<3
Step-by-step explanation:
There isn't a question that I can see for the first image, and I cannot see the yellow part, so I am not 100% sure if this is an accurate answer to the question you were asking.
how would i explain my students proportional reasoning
Answer:
proportional reasoning involved thinking about relationship and making comparisons of countries are values in the words of John went Diwali portion reasoning is difficulty find it is not something that you can or not to but is diploma over 3 reasoning
what mixed number is equivalent to the fraction 28/5
The mixed number equivalent to the fraction 28 / 5 is 5 3 / 5
What is mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction.
Therefore, it is a combination of a whole number and a proper fraction.
Hence,
The fraction is in improper fraction, let's convert it to mixed fraction.
Therefore,
28 / 5 = 5 3 / 5
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Define coefficiend, base and index of an algebraic term with an example
Step-by-step explanation:
a number used multiplier variable
example 6z menas 6 times z and z is a variable so sixes coefficient variable with no number have a question of one example X is a really 1x
Find the angle between the vectors A = <2,-3> asnd B = <-2, -5> to the nearest tenth of a degree.
Answer:
55.5
Step-by-step explanation:
answer is 55.491477012331599 which rounded to the nearest tenth is 55.5
when you said to the nearest tenth of degree i assume that meant like rounding to the nearest tenth
sari ran for class president. each student in her class voted one time. sari won 25% of the student votes. if sari recived 60 votes, how many students voted altogether
The number of students who voted is 240.
How many students voted?Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.
The number of students who voted = number of votes Sari received / percentage number
60 / 0.25 = 240
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how long would it take to drive 18 miles while going 18 mph
Answer:
1 hour
Step-by-step explanation:
18 miles because if u go 18 miles per hour it takes a hour
9029
2066
10
4
-6-54-3-2-12- 2 3 4 5 6 x
-f(x)
-6
-8
-10
-12+
Which functions have a maximum and are transformed to the left and down of the parent function, f(x)=x2? Check
all that apply.
p(x) = 14(x + 7)² + 1
g(x) = -5(x + 10)² - 1
s(x) = –(x − 1)? +0.5
g(x) = 2x² + 10x-35
t(x) = -2x² - 4x - 3
Using translation concepts, the functions that have a maximum and are transformed to the left and down of the parent function are given by:
g(x) = -5(x + 10)² - 1t(x) = -2x² - 4x - 3What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
For the translations, we have that:
Shift left, hence x -> x + a, a > 0.Shift down, hence y -> y - a, a > 0.Having a maximum means that the leading coefficient is negative.The functions that respect these conditions are:
g(x) = -5(x + 10)² - 1t(x) = -2x² - 4x - 3 = -2(x² + 2x) - 3 = -2(x + 1)² - 1More can be learned about translation concepts at https://brainly.com/question/4521517
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Work out the surface area of the triangular prism below. Give your answer in cm cm². 17 cm 14 cm 15 cm 8 cm
Answer:
Step-by-step explanation:
A= 2AB+(a+b+c)h
AB= s (s﹣a) ( s﹣b) (s﹣c)
s = a+b+c
2
Solving for A
A= ah +bh+ch+1
2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=17·8+14·8+15·8+1
2·﹣174+2·(17·14)2+2·(17·15)2﹣144+2·(14·15)2﹣154≈ 567.35897
X. y.
-1. 1/10
0. 1/2
1. 5/2
2. 25/2
3. 125/2
What is the rate of change of the function described in the table?
a. 12/5
b. 5
c. 25/2
d. 25
Answer: B
Step-by-step explanation:
Each time x increases by 1, y is multiplied by 5.
What is the slope of a line parallel to the line with equation 2x−5y=9?
25
−25
−95
−52
Answer:
For this one the parallel slope is going to be 2/5
Step-by-step explanation:
Please help me....trying to get my HS diploma, i did not graduate :(
Kevin wants to buy an area rug for his living room. He would like the area rug to be no smaller that 48 square feet and no bigger than 80 square feet. If the length is 2 feet more than the width, what are the range of possible values for the length?
Answer:
It would be B.
Step-by-step explanation:
[tex]area = l \times w \\ but \: w = l - 2[/tex]
[tex]area = l(l - 2) = l {}^{2} - 2l[/tex]
[tex]l {}^{2} - 2l \geqslant 48 \\ l {}^{2} - 2l - 48 \geqslant 0 \\ (l + 6)(l - 8) \geqslant 0[/tex]
[tex]l {}^{2} - 2l \leqslant 80 \\ l {}^{2} - 2l - 80 \leqslant 0 \\ (l + 8)(l - 10) \leqslant 0[/tex]
Sol 1: L in ]-∞,-6]U[8,∞[Sol 2: L in [-8,10]Intersection:L belongs [-8,-6[U[8,10]But Length cannot be negativeL belongs [8,10] or 8≤L≤10Describe the transformation of the function, y=1/7 x from y = x.
The transformation of the function, y=1/7 x from y = x is y = 7x
How to determine the transformation?The function is given as:
y = 1/7x
The transformation rule is given as:
y = x
This means that we swap x and y.
So, we have:
x = 1/7 y
Multiply through by 7
y = 7x
Hence, the transformation of the function, y=1/7 x from y = x is y = 7x
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ANSWERS QUCIK PLS AND THINK U
Answer:
50.3cm²
Step-by-step explanation:
Formula: The area of a circle is found by A = πr²
Given:
radius is 4cmπ = 3.142Plug in:
A = πr² → A = (3.142)(4)²
→ A = (3.142)(16)
→ A = 50.272
"1 decimal places", round up to 50.3
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324 divided into 6.846
324 divided into 6.846 is 47.33
How to evaluate the division?The statement is given as:
324 divided into 6.846
This is represented as:
324/6.846
Using a calculator, we have:
47.3269062226
Approximate
47.33
Hence, 324 divided into 6.846 is 47.33
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Find the missing value of the ordered triple that will make the solution to the equation x + 2y – 3z = 8 true.
7. (4, , 0)
8. ( , -2, -2)
9. (2, 3, )
10. (-3, -2, )
The missing value of the ordered triple for questions 7,8,9 and 10 will be y=2,x=6,z=0, and z=-5 respectively.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
The given equation in the problem is;
7) (4, ,0)
Substitute the values in the equation;
⇒x+2y-3z = 8,
⇒4+2y-3(0) = 8
⇒2y=8-4
⇒2y=4,
⇒y=4/2
⇒y=2
8) (, -2, -2)
Substitute the values in the equation;
x+2(-2) -3(-2)= 8
x-4+6 =8
x= 8-6+4
x=8-6+4
x=6
9)(2, 3, )
Substitute the values in the equation;
⇒2+2(3)-3z = 8
⇒8-3z = 8
⇒-3z = 0
⇒z = 0/-3
⇒z= 0
10) (-3, -2, )
Substitute the values in the equation;
⇒-3+2(-2) -3z = 8
⇒-7 -3z = 8
⇒-3z = 15
⇒z = 15/-3
⇒z = -5
Hence, the missing value of the ordered triple for questions 7,8,9, and 10 will be y=2,x=6,z=0, and z=-5 respectively.
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Two friends, Olivia and Melanie, took summer jobs. The equation y=22.2xy=22.2x represents Melanie's earnings in dollars and cents, yy, for working xx hours. Olivia earned $1156 in 40 hours. How much less per hour does Melanie earn than Olivia?
Answer:
$6.70 per hour
Step-by-step explanation:
We want to compare the pay for 1 hour's work.
Melanie's payThe equation tells us that her pay for working 1 hour can be found from the equation using x=1.
y = 22.2x
y = 22.2×1 = 22.2 . . . . pay for 1 hour
Melanie earns $22.20 per hour.
Olivia's payWe assume that Olivia's pay is proportional to hours worked, so pay for 40 hours will be 40 times 1 hour's pay.
pay per hour = $1156/(40 h) = $28.90/h
Olivia earns $28.90 per hour.
Pay differenceThe difference in their rates of pay is ...
$28.90 -22.20 = $6.70
Melanie earns $6.70 less per hour than Olivia.
The coordinates of the points P, Q and R are given by (-2, 1), (1, 4) and (4, k) respectively. Find the value(s) of k if
(b) PQ=QR(clue:distance).
There are two values of k based on the assumption that PQ = QR and the definition of distance and the Pythagorean theorem, k₁ = 7 and k₂ = 1.
How to find the missing value of a coordinate
Herein we can find the value of the missing coordinate of point by the Pythagorean theorem, which is described below:
PQ = QR (1)
[tex](Q_{x}-P_{x})^{2} + (Q_{y}-P_{y})^{2} = (R_{x}-Q_{x})^{2} + (R_{y}-Q_{y})^{2}[/tex]
If we know that P(x, y) = (- 2, 1), Q(x, y) = (1, 4) and R(x, y) = (4, k), then the missing value of the point R is:
[1 - (- 2)]² + (4 - 1)² = (4 - 1)² + (k - 4)²
(k - 4)² = 9
k - 4 = ± 3
k = 4 ± 3
There are two values of k based on the assumption that PQ = QR and the definition of distance and the Pythagorean theorem, k₁ = 7 and k₂ = 1.
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