=========================================================
Explanation:
We have 3 slots, which I'll call slot 1, slot 2, slot 3.
For slot 1, we have 4 choices to pick fromThen slot 2 has 3 choices since we can't reuse a letterFinally, slot 3 has 2 choices. We count our way down each time we move to the next slot.Once all the slots are accounted for, we multiply the values mentioned: 4*3*2 = 12*2 = 24.
There are 24 different three-letter "words" that can be formed where any letter selected cannot be reused.
--------------
A slightly different approach:
Order matters because a "word" like BON is different from a "word" like BNO.
Since order matters, we'll use a permutation
We have n = 4 letters to pick from and r = 3 slots to fill.
Apply those values into the nPr permutation formula
[tex]_{n} P_{r} = \frac{n!}{(n-r)!}\\\\_{4} P_{3} = \frac{4!}{(4-3)!}\\\\_{4} P_{3} = \frac{4!}{1!}\\\\_{4} P_{3} = \frac{4*3*2*1}{1}\\\\_{4} P_{3} = \frac{24}{1}\\\\_{4} P_{3} = 24\\\\[/tex]
We end up with the same result as before.
Researchers interested in lead exposure due to car exhaust sampled the blood of 52 police officers subjected to constant inhalation of automobile exhaust fumes while working traffic enforcement in a primarily urban environment. The blood samples of these officers had an average lead concentration of 122.31 µg/l and a SD of 38.75 µg/l; a previous study of individuals from a nearby suburb, with no history of exposure, found an average blood level concentration of 35 µg/l.
Required:
a. Write down the hypotheses that would be appropriate for testing if the police officers appear to have been exposed to a higher concentration of lead.
b. Explicitly state and check all conditions necessary for inference on these data.
c. Test the hypothesis that the downtown police officers have a higher lead exposure than the group in the previous study. Interpret your results in context.
d. Based on your preceding result, without performing a calculation, would a 99% confidence interval for the average blood concentration level of police officers contain 35 ug/l?
Step-by-step explanation:
n = 52
x bar = 122.31
standard deviation sd = 38.75
1. the hypothesis:
null hypothesis
h0: μ ≤ 35
alternative hypothesis
h1: μ > 35
2.
we have been given the sd of the sample but not that of the population. so what we are supposed to use here is the t test and not the z test. the following conditions have to be met.
population has to be normalsample size has to be more than 30. we have sample size = 52 in this question.3.
= [tex]\frac{122.31-35}{38.75/\sqrt{52} }[/tex]
= 87.31/5.37
= 16.26
using the T distribution function in excel, the p value was calculated and found to be approximately equal to 0.
TDIST(16.26, 51, 1)
since p value is very small we reject the null and accept the alternate hypothesis.
4. from the result above the answer to this question is yes
HEEEEEEEEEELLLLLLLLLLP
Oil costs $4 per gallon and diesel costs 5.24 per gallon. If the price of oil rises at 10% per month, how many months will it take before a gallon of oil costs more than a gallon of diesel?
Answer:
It would take 31 Months for oil to get the same price as diesel.
write the number pattern by writing the next number of 100, 90, 80, 70
Answer:
60
Step-by-step explanation:
Goes down by ten everytime.
Answer: 60
Step-by-step explanation:
You are taking away 10 each time.
Please help! It’s super easy and I’ll reward you brainiest
Find the area of the composite figure.
If you answer I'll give you branliest :)))(
Answer:
252cm²
Step-by-step explanation:
This figure consists of 2 trapeziums.
Area of a trapezium= (The sum of the parallel side/2)× height
Explanation:
[(16+20)÷2]×7
[36÷2]×7
18×7
126cm²
Since the 2 trapezium have the same value we will just multiply the answer by 2.
126×2
252cm²
Hope this helps:)
Elizabeth has a book collection. Her biographies are 42 pages each. Her fiction books are 50 pages each. She has 3 biographies and 6 fiction books. How many pages do the books have altogether?
WALLAI HELP ME THIS IS HARD HELP ME PLEASE
Answer:
3,-1 I hope it is a right answers
Step-by-step explanation:
( 3,1 )
please mark as brilliant
Solve the problem:
Kiram has 5 ziploc bags. He puts an equal number of marbles (X).Then he realized that he
needed to add 2 more marbles for each bag. If the total number of marbles is 30 how many
marbles in each bag?
Answer:
6?
Step-by-step explanation:
I guessed dont trust the answer
[tex] \sqrt{x - 1} (x - 6) {}^{2} [/tex]
inflection points?
Answer:
1 and 6
Step-by-step explanation:
it is just like the roots of a polynomial, since [tex]\sqrt{x-1}[/tex](x-6)^2=0
we can separate the two pieces of the problem
\sqrt{x-1} =0
square both sides to get
x-1=0. x=1
(x-6)^2=0
square root both sides and get
x-6=0
x=6
so the two inflection points of the equation are 6 and 1
Hope that helps :)
wn
he quantity
8. 25% of 32.4
Step-by-step explanation:
25 percent of 32.4 is 8.1
Answer:
8.1
Step-by-step explanation:
.25x32.4=8.1
Angela began studying at 3:17 P.M. She studied until 4:22 P.M.
How long did Angela study?
Answer:
1hr 5mins
Step-by-step explanation:
thanks. for the free points
3 17 to 4 17 one HR
4 17 to 4 22 5 mins
total is one hour plus five mins
so 1 hr 5 mins
Answer:
1 hour and 5 minutes
Step-by-step explanation:
Between 4:22 pm and 3:17 pm, 1 hour has passed.
3:17 + 1 hour = 4:17
Between 4:17 pm and 4:22 pm, 5 minutes has passed.
4:17 + 5 minutes = 4:22
Therefore, Angela has studied for 1 hour and 5 minutes.
I hope this helps!
I really need help with this. Can anyone help me please?
Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.
3,-2+2i
Thank you!
Answer:
f(x) = x³ + x² - 4x - 24Step-by-step explanation:
Since one of zero's is complex number, its conjugate should also be a zero of the given polynomial.
The conjugate of -2 + 2i is -2 - 2iThe polynomial is going to be:
f(x) = (x - a)(x - b)(x - c) with minimum of degree 3, with zero's a, b and c.Substitute zero's:
f(x) = (x - 3)(x - (-2 + 2i))(x - (-2 - 2i)) = (x - 3)(x² - x (-2 + 2i -2 - 2i) + (-2 + 2i)(-2 - 2i)) = (x - 3)(x² + 4x + 8) = x³ + x² - 4x - 2425. Which equation is not proportional? *
Oy=2x-3
Oy=150x
Oy=1/2x
YE 7
Hi there! Your answer is y = 2x-3
Please see an explanation for a better and clear understanding to your problem.
Any questions about my answer and explanation can be asked through comments! :)
Step-by-step explanation:
For an easy understanding to "proportional equation", It is basically an equation that is in form of y = mx + b where b = 0. Therefore, when b = 0 - Our new equation would be y = mx.
Other choices are in form of y = mx while the first choice isn't in the form of y = mx.
To be a proportional function or equation, the equation must be in the form of y = mx only.
The question asks which equation Is not proportional. Hence, the answer is the first choice.
Hope this helps!
Fruit-O-Rama sells dried pineapple for $0.25 per ounce. Mags spent a total of $2.65 on pineapple. How many ounces did she buy
Answer:
2.65/.25= 10.6oz
............
Answer:
10.6 Ounces
Step-by-step explanation:
Each ounce of dried pineapple costs $0.25
Divide $2.65 by $0.25
2.65/0.25=10.6
Mags bought 10.6 oz.
Find m∠ABC in the picture. (it's not solving for x.)
Answer:
The answer would be 6º
Step-by-step explanation:
first we know that a straight lin is always 180º
so since we know that the angle outside of the triangle is 110º we can do 180º -110º
then we get the measuerment for angle C :70º
since we dont know the measurements of the other angles but know that a full triangle is equal to 180º we make this equation
2+6x+12x+70=180
then we solve
72+18x=180
-72 -72
18x=108
/18 /18
x=6
then we plug in the x value to find the angle measurement
2+6(6)
2+36
38º
your answer is m<CAB is 38º
the farmer has a field of 300m.he want to fence it with 4 rounded barbed wire . what is the total length of wire he requires
Answer:
1,200 meters.
Step-by-step explanation:
Given that the farmer has a field of 300 meters and he wants to fence it with 4 rounded barbed wire, to determine what is the total length of wire he requires, the following calculation must be performed:
300 x 4 = X
1,200 = X
Thus, the farmer needs 1,200 meters of barbed wire to be able to fence his entire field.
find the value of expression when b=9, c=5, d=1/2; expression is 1/2d + c^3 - b
Answer:
115 3/4
Step-by-step explanation:
[tex]\frac{1}{2} * \frac{1}{2}[/tex] Because d=1/2. 1/2*1/2=1/4
C=5 so, C^3=5x5x5
C=125
Next, b=9
Then, you put everything together.
1/4+125-9=125 1/4-9
115 3/4
115 3/4+9 1/4
Original amount: 27
End amount: 38.61
Increase or decrease
Answer:
increase
Step-by-step explanation:
11.61 was added to 27
You can sell 60 pet chias per week if they are marked as $1 each, but only 50 per week if they are marked $2 per chia. Your chia supplier is prepared to sell you 10 chias per week if they are marked $1 per chia, and 20 per week if they are marked $2 per chia. At what price should the chias be marked so that there is neither surplus nor a shortage of chias
Answer:
$1 for 60
Step-by-step explanation:
60$ is a better deal.
Find the solution set to 2x-1<7 and 3x-5>16
Answer:
2
Step-by-step explanation:
express 75 as a product of three factors
what is the value of a?
Answer:
9\sqrt{2}
Step-by-step explanation:
this is a 30-60-90 triangle so
the side opposite of 30 is x and the opposite side of 60 is x[tex]\sqrt{2}[/tex]. then the side opposite 90 is 2x.
so if 9=x then a=x\sqrt{2}
9\sqrt{2} is the side length of a
Hope that helps :)
factor 3a^5-18a^3+6a^2, I know the answer is 3a^2(a^3-6a+2) but I am so lost on how to get the factor of 3a^2..How in the world do you get the exponent for the factor
Answer:
[tex]\huge\boxed{3a^2(a^3-6a+2)}[/tex]
Step-by-step explanation:
[tex]\sf 3a^5-18a^3+6a^2\\\\HCF = 3a^2\\\\Take \ 3a^2 \ common\\\\= 3a^2(a^3-6a+2)\\\\\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Given the function f(x) = 4x + 1, EXPLAIN and show how to find the average rate of change between x = 1 and x = 3.
The average rate of change is calculated as the slope of the line between the two points on the graph. Since at x = 1, y = -3, and at x = 3, y = 1, these are the two points which we calculate the slope from. Using the formula
m = (y2 - y1)/(x2 - x1)
m = (1 - (-3))/(3 - 1)
m = 4/2
m = 2
Therefore the slope, or the average rate of change, between these points is 2.
You invested $23,000 in two accounts paying 6% and 7% annual interest, respectively. If the total interest earned for the year was $1560, how much was invested at each rate?
Answer:
$ 18,000 was invested at 7%, and $ 5,000 was invested at 6%.
Step-by-step explanation:
Given that I invested $ 23,000 in two accounts paying 6% and 7% annual interest, respectively, and the total interest earned for the year was $ 1,560, to determine how much was invested at each rate, the following calculation must be performed:
23,000 x 0.07 + 0 x 0.06 = 1,610
22,000 x 0.07 x 1,000 x 0.06 = 1,600
21,000 x 0.07 x 2,000 x 0.06 = 1,590
20,000 x 0.07 x 3,000 x 0.06 = 1,580
19,000 x 0.07 x 4,000 x 0.06 = 1,570
18,000 x 0.07 x 5,000 x 0.06 = 1,560
Thus, $ 18,000 was invested at 7%, and $ 5,000 was invested at 6%.
If a day of the week is randomly selected, what's the probability that the day contains the letter "a" in its name?
Round your answer to four decimal places (if necessary).
Answer:
1
Step-by-step explanation:
monday, tuesday, wednesday, thursday, friday, saturday, and sunday all have "a" in it so it has a 100% probability
Answer:
There would be a 100% chance.
Step-by-step explanation:
All the days of the week end with -day. The word day has an 'a' in it.
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Therefore, it will be certain that you will pick a day that has an 'a' in it's name.
Hope this helps!
Solve. Remember to insert units when writing your answer. A carpenter needs to cut a board into fourths. If the board is 32 ft 8 in. long originally, how long will each cut be?
Answer:
[tex]Each\ cut = 8ft\ 2in[/tex]
Step-by-step explanation:
Given
[tex]Length = 32ft\ 8in[/tex]
[tex]Cuts = 4[/tex]
Required
Determine the length of each cut
This is calculated by dividing the total length by the number of cuts.
So, we have:
[tex]Each\ cut = \frac{Length}{Cuts}[/tex]
[tex]Each\ cut = \frac{32ft\ 8in}{4}[/tex]
Split:
[tex]Each\ cut = \frac{32ft}{4} + \frac{8in}{4}[/tex]
[tex]Each\ cut = 8ft+ 2in[/tex]
[tex]Each\ cut = 8ft\ 2in[/tex]
Simplify the expression:
6(20 + 1)
=
Answer:
120+6
Step-by-step explanation:
Using distributive property 6times 20 is 120 and 6 times 1 is 6 so 120+6
pls help the teacher said it’s not 14 I don’t know
Answer:
let no be x
by the question
2x-5=9
2x=9+5
x=14/2=7
the secret no is 7.