Answer:
The probability is [tex]P(X > x) = 0.0013499[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 25[/tex]
The standard deviation is [tex]\sigma = 5 \ minutes[/tex]
The random number [tex]x = 40[/tex]
Given that the time taken is normally distributed the probability is mathematically represented as
[tex]P(X > x) = P[\frac{X -\mu}{\sigma } > \frac{x -\mu}{\sigma } ][/tex]
Generally the z-score for the normally distributed data set is mathematically represented as
[tex]z = \frac{X - \mu}{\sigma }[/tex]
So
[tex]P(X > x) = P[Z > \frac{40 -25}{5 } ][/tex]
[tex]P(X > x) = 0.0013499[/tex]
This value is obtained from the z-table
Please help
ASAP
ANSWERS
A-48.21
B-66.35
C-53.68
D-28.34
Answer:
B
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos54° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{39}{AB}[/tex] ( multiply both sides by AB )
AB × cos54° = 39 ( divide both sides by cos54° )
AB = [tex]\frac{39}{cos54}[/tex] ≈ 66.35 → B
what is the average when you add 122.99%, 108.46% and 102.65%? I don't know how to add percentages.
Answer:
111.33667
Step-by-step explanation:
You add percentages just like you would any other number.
122.9% + 108.46% + 102.65% = 334.01%
334.01%/3 = 111.33667
Adam is going to cook a turkey for 14 people
Answer:
they divied the turkey into 14 pices
Step-by-step explanation:
If ABC~DEF and the scale factor from ABC to DEF is 3/4, what is the length of DF?
Answer:
the length of DF = 3/4 AC
see below for explanation
Step-by-step explanation:
ABC is said to be approximately equal to DEF
The scale factor from ABC to DEF = 3/4
From the question, we can tell the original and new shape is a triangle because the lettering to indicate the vertices for both are 3.
We can deduce from the question, ΔABC was dilated to form ΔDEF
In dilation, the length of each of the corresponding side of the new figure is equal to the multiplication of each of the corresponding sides of the old figure and thee scale factor.
In the absence of cordinates for each vertices and length of each sides, ΔABC has 3 sides :
AB, BC and AC
ΔDEF has 3 sides : DE, EF and DF
If AB corresponds to DE
BC corresponds to EF
AC corresponds to DF
Then:
length DE = scale factor × AB = 3/4 AB
length EF = scale factor × BC = 3/4 BC
length DF = scale factor × AC = 3/4 AC
Therefore, the length of DF = 3/4 AC
The soldering iron’s highest temperature setting is 400 °F. What is the soldering iron’s temperature in Centigrade?
Answer:
204.4(repeating) degrees
Step-by-step explanation:
The equation to go from F to C, is (F-32)×5/9. So 400-32 is 368.
368×5=1840
Than 1840/9=204.44 degrees. The 4 is repeating at the end.
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Third-degree, with zeros of −3, −1, and 2, and passes through the point (1,10).
Answer:
[tex]\Large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}[/tex]
Step-by-step explanation:
Hello,
Based on the indication, we can write this polynomial as below, k being a real number that we will have to identify (degree = 3 and we have three zeroes -3, -1, and 2).
[tex]\Large \boxed{k(x+3)(x+1)(x-2)}[/tex]
We know that the point (1,10) is on the graph of this function, so we can say.
[tex]k(1+3)(1+1)(1-2)=10}\\\\4*2*(-1)*k=10\\\\-8k=10\\\\k=\dfrac{10}{-8}=-\dfrac{5}{4}[/tex]
Then the solution is:
[tex]\large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Which is the recommended method for reading your math textbook most effectively? a. read, question, summarize, practice b. highlight, skim, ask, and review c. preview, read, summarize, and review
Answer: a. read, question, summarize, practice
Step-by-step explanation:
This may be subjective, but the most efficient method usually is:
> Read:
Obviously the first step is read, if there is something that you do not understand, keep reading (but take note of all the things that you don't understand), is important that you have a complete overview on the topic that you are studying
> Question:
Now is time to ask about the things that you did not understand in the first read, always when you do not fully understand something, is a good habit to ask about it, this is the best and easiest way to learn.
> Summarize:
Now that you understand all the text (or at least most of it) is the moment to summarize your new knowledge: Write all the new equations that you learned, also write for what they are for, when they can be useful, etc.
This is what you will use to solve exercises, so you should be clear when writing.
> Practice:
This is one of the most important parts, here is where you put in practice your new knowledge. Here you may find some problematic situations where you need to be inventive with your equations, which will allow you to learn new ways to use your equations, so this is a really important step.
So the correct option is A.
what is the world smallest number that is divisible by all the numbers 1,2,3,4,5,6,7,8,9,10?
Answer:
1
Step-by-step explanation:
1 ÷ 1 = 1
2 ÷ 1 = 2
3 ÷ 1 = 3
4 ÷ 1 = 4
5 ÷ 1 = 5
6 ÷ 1 = 6
7 ÷ 1 = 7
8 ÷ 1 = 8
9 ÷ 1 = 9
10 ÷ 1 = 10
Answer:
The world smallest number that is divisible by all the numbers 1,2,3,4,5,6,7,8,9,10 means that all the above numbers can divide that number without a remainder.
From the question the world smallest number that is divisible by the above numbers is
2520Hope this helps you
A study reports the mean change in HDL (high-density lipoprotein, or "good" cholesterol) of adults eating raw garlic six days a week for six months. The margin of error for a 95% confidence interval is given as plus or minus 7 milligrams per deciliter of blood (mg/dl). This means tha:_________a) There is a 95% probability that the true population mean is within 7 mg/dl. b) The study used a method that gives a results within 7 mg/dl of the truth about the population in 95% of all samples. c) 95% percent of the population has changed their HDL after eating raw garlic six days a week for six months. d) We can be certain that the study results is within 7 mg/dl of the truth about the population. e) We could be certain that the study result is within 7 mg/dl of the truth about the population if the conditions for inferences were satisfied.
Answer:
Option B
Step-by-step explanation:
The margin of error describes how many percentage points the results will differ from the real population value, thus 'the margin of error for a 95% confidence interval is given as plus or minus 7 milligrams per deciliter of blood (mg/dl)' can be interpreted as 'The study used a method that gives a results within 7 mg/dl of the truth about the population in 95% of all samples.'
Could someone answer the question with the photo linked below? Then explain how to solve it?
Answer:
Hey there!
Pythagorean Theorem:
[tex]a^2+b^2=c^2\\[/tex]
Let 6 be a, and 11 be b.
[tex]6^2+11^2=c^2\\[/tex]
[tex]36+121=c^2\\[/tex]
[tex]157=c^2[/tex]
[tex]\sqrt{157} =c[/tex]
Hope this helps :)
Answer:
[tex]12.529[/tex]
Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {6}^{2} + {11}^{2} = {c}^{2} \\ 36 + 121 = {c}^{2} \\ 157 = {c}^{2} \\ \sqrt{157} = {c}^{2} \\ c = 12.529[/tex]
[tex]hope \: it \: helps \: < 3[/tex]
Luke is organising a camping trip for the youth club. He is looking at the temperature and rainfall charts for Brighton and Newquay. What is the probability of it raining in July in Brighton? Give your answer as a fraction.
Answer:
The answer is 15.6/31 or 1/2
Step-by-step explanation:
The data in the question is sufficient to find an answer for it.
1. I look at the temperature and rainfall chart for Brighton, United Kingdom.
2. Check for rainy season and dry season.
3. The rainy season lasts approximately 5 months while the dry season (which still has some rainfall) lasts approximately 7 months. All together, 12 months of the calendar year.
4. July happens to fall within the dry season. The temperature and rainfall statistics are observed.
The number of rainfall days is 15.6 and we know there are 31 days in July.
If the approximate number of days it rains in Brighton, in July, is 15.6 then the probability of rainfall in the month is 15.6/31 which is = 0.503 or 0.5
Therefore, there's a 50% chance of having rainfall in Brighton, on any day in the month of July.
In fraction, 0.5 = 1/2
helppppppppppppp pleaseeeeeeeeeeeeee
Answer:
work is shown and pictured
Over the last three evenings, Melissa received a total of 126 phone calls at the call center. The first evening, she received 6 more calls than the third evening. The second evening, she received 4 times as many calls as the third evening. How many phone calls did she receive each evening? Number of phone calls the first evening: Number of phone calls the second evening: Number of phone calls the third evening:
Answer:
calls first evening = 26
calls second evening = 80
calls third evening = 20
Step-by-step explanation:
Let x = calls third evening
x+6 = calls first evening
4x = calls second evening
x+6 + 4x + x = total calls = 126
Combine like terms
6x+6 = 126
Subtract 6 from each side
6x =120
Divide by 6
6x/6 =120/6
x = 20
x+6 = calls first evening = 20+6 = 26
4x = calls second evening = 4*20 = 80
Let x = calls third evening = 20
if ade has 23hand bag and he sells one for 409$ and he sells 22 for toby what will be the amount
Step-by-step explanation:
Hello there!
Its simple,
Given that, Ade had 23 hand bags.
selling price of each bag=$409
total sold bags= 22.
now, total amount he got was = no.of sold bag×sp of each bag.
so, total amount = 22×$409
=$8998.
Therefore, he has $ 8998 now.
Hope it helps...
Factor d^2-10d+10 by grouping
Answer:
(d-5-√15)(d-5+√15)
Step-by-step explanation:
What is the measure of o?
Answer:
2π radians
Step-by-step explanation:
The distance S that a certain object falls from a height of 350 ft in T seconds is given by the following formula.
S = 350 - 16t^2 + vt
Find S when T = 2 and V = -4
S = ??ft
Answer:
278 feet.
Step-by-step explanation:
S = 350 - 16t^2 + vt
t =2; v = -4.
S = 350 - 16 * (2)^2 + 2 * (-4)
S = 350 - 16 * 4 - 8
S = 350 - 64 - 8
S = 350 - 72
S = 278 feet.
Hope this helps!
The assistant principal set up chairs in the auditorum for graduation. She placed
the chairs in 24 rows with 28 chairs in each row. How many chairs are set up in
the auditorium
Answer:
672 chairs
Step-by-step explanation:
24 × 28 = 672
hope this helps
Which equations represent the asymptotes of the hyperbola?
Answer:
see below
Step-by-step explanation:
The equation of the hyperbola can be written as ...
((x -h)/a)² -((y -k)/b)² = 1
This has asymptotes ...
(x -h)/a ± (y -k)/b = 0
Solving for y, we have ...
y = ±(b/a)(x -h) +k
Filling in the given values a=6, b=8, h=1, k=2, we have ...
y = ±8/6(x -1) +2
[tex]y=\dfrac{\pm4x\mp4+6}{3}\\\\\boxed{y=\dfrac{4x+2}{3}\ \text{and }y=\dfrac{10-4x}{3}}[/tex]
Answer:
A. y = 4x+2/3 and y = 10-4x/3
Step-by-step explanation:
this is the correct answer for the question on edmentum and Plato
Simplify 3 (2x + 1) - 2 (x + 1)
Let's simplify step-by-step.
3(2x+1)−2(x+1)
Distribute:
=(3)(2x)+(3)(1)+(−2)(x)+(−2)(1)
=6x+3+−2x+−2
Combine Like Terms:
=6x+3+−2x+−2
=(6x+−2x)+(3+−2)
=4x+1
4x+1 is the answer to the question
Karen has 6 more than twice as many newspaper customers as when she started selling newspapers. She now has 98 customers. How many did she have when she started?
Answer:
46 customers
Step-by-step explanation:
If the number of original customers is n, we can write the following equation:
98 = 2n + 6
92 = 2n
46 = n
Solve for y: 3(2y + 4) = 4(2y – 1/2).
The solution is y =
Answer:
Answer y=7
Step-by-step explanation:
Please help! Find the perimeter and total area of the composite shape below!
Answer:
Perimeter = 19.42 in and area = 26.13 in^2.
Step-by-step explanation:
The perimeter = 2 * 5 + length of the semicircle
= 10 * 3.14 * 3
= 19.42 in.
Total area = area of the semicircle + area of the triangle
= 1/2 * 3.14 * 3^2 + 3 * 4
= 26.13 in^2.
A positive integer is 2 less than another. If the sum of the reciprocal of the smaller and twice
the reciprocal of the larger is 11/15,
then find the two integers.
Answer:
Step-by-step explanation:
Let x represent the smaller integer.
Let y represent the larger integer.
A positive integer is 2 less than another. It means that
y = x + 2
If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 11/15, it means that
1/x + 2/y = 11/15- - - - - - - - - - 1
Substituting y = x + 2 into equation 1, it becomes
1/x + 2/(x + 2) = 11/15
Considering the left hand side of the equation, it becomes
(x + 2 + 2x)/x(x + 2)
Therefore,
(3x + 2)/(x² + 2x) = 11/15
Cross multiplying, it becomes
15(3x + 2) = 11(x² + 2x)
45x + 30 = 11x² + 22x
11x² + 22x - 45x - 30 = 0
11x² - 23x - 30 = 0
11x² + 10x - 33x - 30 = 0
x(11x + 10) - 3(11 + 10) =℅0
(x - 3)(11x + 10) = 0
x - 3 = 0 or 11x + 10 = 0
x = 3 or x = - 10/11
Since it us a positive integer, the smaller integer is 3 and the larger integer is 3 + 2 = 5
Answer: Let x represent the smaller integer.Let y represent the larger integer.A positive integer is 2 less than another. It means that y = x + 2 If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 11/15, it means that 1/x + 2/y = 11/15- - - - - - - - - - 1Substituting y = x + 2 into equation 1, it becomes 1/x + 2/(x + 2) = 11/15Considering the left hand side of the equation, it becomes(x + 2 + 2x)/x(x + 2) Therefore,(3x + 2)/(x² + 2x) = 11/15Cross multiplying, it becomes15(3x + 2) = 11(x² + 2x)45x + 30 = 11x² + 22x11x² + 22x - 45x - 30 = 011x² - 23x - 30 = 011x² + 10x - 33x - 30 = 0x(11x + 10) - 3(11 + 10) =℅0(x - 3)(11x + 10) = 0x - 3 = 0 or 11x + 10 = 0x = 3 or x = - 10/11Since it us a positive integer, the smaller integer is 3 and the larger integer is 3 + 2 = 5
Step-by-step explanation:
A city council consists of eight Democrats and eight Republicans. If a committee of six people is selected, find the probability of selecting two Democrats and four Republicans.
(Type answer a fraction Simplify your answer.)
Answer:
The probability is [tex]P[ D n R] = 0.196[/tex]
Step-by-step explanation:
From the question we are told that
The number of Democrats is [tex]D = 8[/tex]
The number of republicans is [tex]R = 8[/tex]
The number of ways of selecting selecting two Democrats and four Republicans.
[tex]N = \left {D} \atop {}} \right. C_2 * \left {R} \atop {}} \right. C_1[/tex]
Where C represents combination
substituting values
[tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1[/tex]
[tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8!}{(8-2)! 2!} * \frac{8! }{(8-4)! 1 !}[/tex]
=> [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8!}{(6)! 2!} * \frac{8! }{(6)! 1 !}[/tex]
=> [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8 * 7 * 6!}{(6)! 2!} * \frac{8*7 *6! }{(6)! 1 !}[/tex]
=> [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8 * 7 }{ 2*1 } * \frac{8*7 }{ 1 *1 }[/tex]
=> [tex]N = 1568[/tex]
The total number of ways of selecting the committee of six people is
[tex]Z = \left {D+R} \atop {}} \right. C_6[/tex]
substituting values
[tex]Z = \left {8+8} \atop {}} \right. C_6[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6[/tex]
substituting values
[tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16! }{(16-6) ! 6!}[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16 *15 *14 * 13 * 12 * 11 * 10! }{10 ! 6!}[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16 *15 *14 * 13 * 12 * 11 }{6* 5 * 4 * 3 * 2 * 1}[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6 = 8008[/tex]
The probability of selecting two Democrats and four Republicans is mathematically represented as
[tex]P[ D n R] = \frac{N}{Z}[/tex]
substituting values
[tex]P[ D n R] = \frac{1568}{8008}[/tex]
[tex]P[ D n R] = 0.196[/tex]
If the 2nd and 5th terms of a
G.P are 6 and 48 respectively,
find the sum of the first four
terms
Answer:
45
Step-by-step explanation:
The n th term of a GP is
[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
where a is the first term and r the common ratio
Given a₂ = 6 and a₅ = 48, then
ar = 6 → (1)
a[tex]r^{4}[/tex] = 48 → (2)
Divide (2) by (1)
[tex]\frac{ar^4}{ar}[/tex] = [tex]\frac{48}{6}[/tex] , that is
r³ = 8 ( take the cube root of both sides )
r = [tex]\sqrt[3]{8}[/tex] = 2
Substitute r = 2 into (1)
2a = 6 ( divide both sides by 2 )
a = 3
Thus
3, 6, 12, 24 ← are the first 4 terms
3 + 6 + 12 + 24 = 45 ← sum of first 4 terms
FIRST ANSWER GETS BRAINLIEST!!!
How do you write 0.00696 in scientific notation?
Answer:
6.96x10^-3
Step-by-step explanation:
0.00696
We move the decimal point to between 6 and 9
since the number with the decimal point should be between 0 and 9.
Then we count the numbers.
6.96x10^-3.
Hope this helps. ❤❤❤
Answer: 6.96 * 10^(-3)
Step-by-step explanation:
In scientific notation, you multiply a number that has a value in the ones place and no value in the tens place by 10 raised to an exponent.
Hope it helps <3
a.Find the L.C.M of 18, 40, and 75.
Answer:
1800
Step-by-step explanation:
Hello,
First of all we need to find the prime factorisation of the numbers.
18 = 2 * 3 * 3
40 = 2 * 2 * 2 * 5
75 = 3 * 5 * 5
It means that the LCM should have 5 * 5 , 2 * 2 * 2 and 3 * 3
Then LCM = 3 * 3 * 2 * 2 * 2 * 5 * 5 = 1800
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
1800
Step-by-step explanation:
→ First of all we need to find the prime factorisation of the numbers.
18 = 2 × 3 × 3 or 2 × 3²
40 = 2 × 2 × 2 × 5 or 2³ × 5
75 = 3 × 5 × 5 or 5² × 3
→ Now find the number that appear twice or more and write them down
3 and 3 from 18
2, 2 and 2 from 40
5 and 5 from 75
→ Now multiply all of these numbers together
3 × 3 × 2 × 2 × 2 × 5 × 5 = 3² × 2³ × 5² = 1800
Values for relation g are given in the table. Which ordered pair would be found in the inverse of g? X Y 2 2 3 5 4 9 5 13 A: (4,9) B:(-3.-5) C:(13,5) D:(-2,-2)
Answer:
D (13,5)
Step-by-step explanation:
X 2 3 4 5
Y 2 5 9 13
So the ordered pairs are (2,2),(3,5), (4,9), (5,13)
and the ordered pairs for the inverse are
(2,2),(5,3), (9,4), (13,5)
from which D (13,5) is found among the options.
Answer:
b
Step-by-step explanation:
what is the measure of SR?
Answer:
RS = 8
Step-by-step explanation:
Given:
Secant QU = internal secant segment PU + external secant segment PQ = 7 + 9 = 16
Secant QS = internal secant segment RS + external secant segment RQ = (3x - 5) + 8
To find the measure of RS, we need to find the value of x.
Thus, recall the "Two Secant Theorem"
According to the theorem,
(RS + RQ)*RQ = (PU + PQ)*PQ
Thus,
[tex] (3x - 5 + 8)*8 = (7 + 9)*9 [/tex]
[tex] (3x + 3)*8 = (16)*9 [/tex]
[tex] 24x + 24 = 144 [/tex]
Subtract 24 from both sides
[tex] 24x + 24 - 24 = 144 - 24 [/tex]
[tex] 24x = 120 [/tex]
Divide both sides by 24
[tex] \frac{24x}{24} = \frac{120}{24} [/tex]
[tex] x = 5 [/tex]
Plug in the value of x into (3x - 5) to find the measure of RS
RS = 3(5) - 5 = 15 - 7
RS = 8