Answer:
168 ways
Step-by-step explanation:
Given
[tex]Junior = 7[/tex]
[tex]Senior = 3[/tex]
Required
Number of ways 3 project can be assigned
Starting with the second project.
This can be assigned to only senior coders
So:
[tex]n_1 = 3[/tex]
Then, the third project.
This can be assigned to only junior coders
So:
[tex]n_2 = 7[/tex]
At this point, we are left with 2 senior coders and 6 junior coders
Since the first can be assigned to anybody.
[tex]n_3 =2+ 6[/tex]
[tex]n_3 =8[/tex]
The number of selection is then calculated as:
[tex]n = n_1 * n_2 * n_3[/tex]
[tex]n = 3 * 7 * 8[/tex]
[tex]n = 168[/tex]
if cos 25°=K , determine cos50°
Answer:
cos 50⁰ = cos 2.25⁰ = 2cos²25⁰ - 1 = 2K² - 1
what is the number 21.0384 rounded to the nearest hundredth?
Answer:
21.04
Step-by-step explanation:
the 8 is closest to 10 so that would make the 3 a 4.
There are 4 oranges, 7 bananas, and 5 apples in a fruit basket.
Ignacio selects a piece of fruit at random and then Terrance
selects a piece of fruit at random.
probability of two bananas
p( two bananas )
Please help meh out wit this :>
Answer:
Goodluck
Step-by-step explanation:
if m 1 =7x and m 4 =3x +20 what is the value of x
Answer:
this is a wild guess but 10.
Step-by-step explanation:
Not sure if you're allowed to do this but i added the x's
7x+3x= 10x
10x+20.
I then subtracted 10 by both sides. That leaves me with 10.
x =10
this is a guess i apologize if it's wrong
Find y' if y= In (x2 +6)^3/2
y'=
Answer:
[tex]\displaystyle y' = \frac{3xln(x^2 + 6)^{\frac{1}{2}}}{x^2 + 6}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FactoringCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
ln Derivative: [tex]\displaystyle \frac{d}{dx} [lnu] = \frac{u'}{u}[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle y = ln(x^2 + 6)^{\frac{3}{2}}[/tex]
Step 2: Differentiate
[Derivative] Chain Rule: [tex]\displaystyle y' = \frac{d}{dx}[ln(x^2 + 6)^{\frac{3}{2}}] \cdot \frac{d}{dx}[ln(x^2 + 6)] \cdot \frac{d}{dx}[x^2 + 6][/tex][Derivative] Chain Rule [Basic Power Rule]: [tex]\displaystyle y' = \frac{3}{2}ln(x^2 + 6)^{\frac{3}{2} - 1} \cdot \frac{d}{dx}[ln(x^2 + 6)] \cdot \frac{d}{dx}[x^2 + 6][/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{3}{2}ln(x^2 + 6)^{\frac{1}{2}} \cdot \frac{d}{dx}[ln(x^2 + 6)] \cdot \frac{d}{dx}[x^2 + 6][/tex][Derivative] ln Derivative: [tex]\displaystyle y' = \frac{3}{2}ln(x^2 + 6)^{\frac{1}{2}} \cdot \frac{1}{x^2 + 6} \cdot \frac{d}{dx}[x^2 + 6][/tex][Derivative] Basic Power Rule: [tex]\displaystyle y' = \frac{3}{2}ln(x^2 + 6)^{\frac{1}{2}} \cdot \frac{1}{x^2 + 6} \cdot (2 \cdot x^{2 - 1} + 0)[/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{3}{2}ln(x^2 + 6)^{\frac{1}{2}} \cdot \frac{1}{x^2 + 6} \cdot (2x)[/tex][Derivative] Multiply: [tex]\displaystyle y' = \frac{3ln(x^2 + 6)^{\frac{1}{2}}}{2} \cdot \frac{1}{x^2 + 6} \cdot (2x)[/tex][Derivative] Multiply: [tex]\displaystyle y' = \frac{3ln(x^2 + 6)^{\frac{1}{2}}}{2(x^2 + 6)} \cdot (2x)[/tex][Derivative] Multiply: [tex]\displaystyle y' = \frac{3(2x)ln(x^2 + 6)^{\frac{1}{2}}}{2(x^2 + 6)}[/tex][Derivative] Multiply: [tex]\displaystyle y' = \frac{6xln(x^2 + 6)^{\frac{1}{2}}}{2(x^2 + 6)}[/tex][Derivative] Factor: [tex]\displaystyle y' = \frac{2(3x)ln(x^2 + 6)^{\frac{1}{2}}}{2(x^2 + 6)}[/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{3xln(x^2 + 6)^{\frac{1}{2}}}{x^2 + 6}[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
PLS HELP ME NOW!! pls pls pls
Answer:
x/300=24/100
Step-by-step explanation:
24/100 is the same as 24% and by cross multiplying you can find 24% of 300
Answer:
24 percent just means "24 for every hundred" 300 is literally three hundreds, so 24 percent of it three 24s, or 72.
Solve the system of equations.
8x + 16y = -42
- 2x + 3y = 7
A. (-4,1)
B. (0.5, -2.69)
C. (4.3, 0.5)
D. (-4.25, -0.5)
The width of a casing for a door is normally distributed with a mean of 24 in and a standard deviation of 0.14 in. The width of a door is normally distributed with a mean of 23.87 in and a standard deviation of 0.08 in. Assume independence of the two widths. Find the probability that the width of the casing exceeds the width of the door by more than 0.25 in.
Answer:
0.2296 = 22.96% probability that the width of the casing exceeds the width of the door by more than 0.25 in.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Subtraction of normal variables:
When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
The width of a casing for a door is normally distributed with a mean of 24 in and a standard deviation of 0.14 in.
This means that [tex]\mu_{C} = 24, \sigma_{C} = 0.14[/tex]
The width of a door is normally distributed with a mean of 23.87 in and a standard deviation of 0.08 in.
This means that [tex]\mu_{D} = 23.87, \sigma_{D} = 0.08[/tex].
Find the probability that the width of the casing exceeds the width of the door by more than 0.25 in?
This is P(C - D > 0.25).
Distribution C - D:
The mean is:
[tex]\mu = \mu_{C} - \mu_{D} = 24 - 23.87 = 0.13[/tex]
The standard deviation is:
[tex]\sigma = \sqrt{\sigma_{C}^2+\sigma_{D}^2} = \sqrt{0.14^2+0.08^2} = 0.1612[/tex]
Probability:
This probability is 1 subtracted by the pvalue of Z when X = 0.25. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.25 - 0.13}{0.1612}[/tex]
[tex]Z = 0.74[/tex]
[tex]Z = 0.74[/tex] has a pvalue of 0.7704
1 - 0.7704 = 0.2296
0.2296 = 22.96% probability that the width of the casing exceeds the width of the door by more than 0.25 in.
Write an emergency that could happen that would have a financial cost
Answer:
Your house burning down.
Step-by-step explanation:
You would have to pay to repair it.
Answer:
Earthquake will make the building crash and people will lost their things and money. And the building need to rebuild.
The building fire will make people lost their things and the building need to rebuild.
Tsunami will make the things near beach all destroy, all the things will lost and more people will die in disaster. All the building need to rebuild in this disaster.
Bank robbery will lost money, sometimes people will kill by the gun of the thief, and the building do not need to rebuild, maybe the window need to rebuild.
Rob the shop will make the boss of the shop lose all the money in the store, the door or window might need to rebuild.
Blasting vehicle will make the things in the car lose. the car need to put the windows on again.
Terrorist attacks will lost lives more than lost money or other things.
Volcanic eruptions will make the building near burn, and so plant and many other things. The building might need to rebuild.
That is all I can think of.
I NEED THE ANSWER NOW! PLEASE! THE QUESTION IS DUE TOMMOROW. Find the area of the shaded polygon:
The bottom of a swimming pool is 10 feet below the surface of the water in the pool. The surface of the water is represented by the number 0, and the bottom of the pool is represented by the number -10. The pool's diving board is the same distance above the surface of the water as the bottom of the pool is below the surface of the water. What integer represents the location of the diving board?
Answer:
10
Step-by-step explanation:
If the bottom of the swimming pool is 10 feet below 0, that makes it -10. If the diving board is the same distance above the swimming pool, that would make the integar 10. Both integers have a distance of 10ft away from 0.
I hope that helped. :)
The diving board is represented by the integer 10.
What are Integers?Integers are defined as the collection of Whole Numbers and the negative values of Natural Numbers make up an integer. Fractional numbers are not included in integers. Integers are represented by the symbol Z.
The location of the diving board is the same distance above the surface of the water as the bottom of the pool is below the surface of the water.
Since the surface of the water is represented by the number 0 and the bottom of the pool is represented by the number -10, this means that the diving board must be represented by the number 10, which is the opposite of -10. The diving board is indicated by the integer 10.
Therefore, the diving board is represented by the integer 10.
Learn more about the number system here:
https://brainly.com/question/21751836
#SPJ2
What is the measure of ∠B?
A is 28 degrees
C is 36 degrees
Answer:
The measure of angle B is 116
Step-by-step explanation:
Answer:
B=118 degrees
Step-by-step explanation:
All triangles are meant to be exactly 180 degrees. So 180 - (28 +36) =B =118 degrees
A bag contains colored tiles.
33 tiles are red
66 tiles are green
33 tiles are blue
A tile will be randomly selected from the bag. What is the on
probability in decimal form that the tile selected will be green?
Answer:
0.5
Step-by-step explanation:
Add everything together 33+66+33 = 132
Then 66/132, = 1/2 or 0.5
A machine used to fill beverage cans is supposed to supply exactly 16 ounces toeach can, but the actualamount supplied varies randomly from can to can. The machine is calibrated so that the population standard deviation is 0.04 ounces. How many filled cans must be sampled so that we estimate the mean fill volume within 0.015 ounces with 99% confidence
Answer:
48 cans must be sampled.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The machine is calibrated so that the population standard deviation is 0.04 ounces.
This means that [tex]\sigma = 0.04[/tex]
How many filled cans must be sampled so that we estimate the mean fill volume within 0.015 ounces with 99% confidence?
n cans must be sampled, and n is found when M = 0.015. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.015 = 2.575\frac{0.04}{\sqrt{n}}[/tex]
[tex]0.015\sqrt{n} = 2.575*0.04[/tex]
[tex]\sqrt{n} = \frac{2.575*0.04}{0.015}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.575*0.04}{0.015})^2[/tex]
[tex]n = 47.2[/tex]
Rounding up, 48 cans must be sampled.
Help please I give brainliest serious plz
Answer:
brainlisdt pplease
Step-by-step explanation:
Does the mapping diagram represent a function? Why or why not?
х
y
-6
10
2
Answer:
use mathwy
Step-by-step explanation:
its better for a. expansion
What is 5+5? Please help the lol
Answer:
10
Step-by-step explanation:
5+5=10
your answer is 10
Answer:
10
Step-by-step explanation:
1+1= 2
1+1 = 2
2+2= 4
4 + 1 = 5
5 + 5 = 10
Two angle measures of a triangle are 35° and 50° . What is the measure, in degrees, of the other angle?
The measure of the third angle of the triangle is 95°
According to the triangle theorem :
The sum of the angles in a triangle is 180° ; i.e Given a triangle A, B and C ; the sum of it's angles :
A + B + C = 180°
Hence, for a triangle with two of it's sides being ; 35° and 50°
Let the third angle = x
The third angle will be :
180° = (35° + 50° + x)
180° = 85° + x
x = 180° - 85°
x = 95°
Hence, the measure of the third angle is 95°
Learn more : https://brainly.com/question/14780489
A novelist can write 3 1/2 pages in 1/3 of an hour. How many pages can she write in one hour?
Answer:
LG sjsjsjdjdbvebsjsuwknsnsbbskoejenndnd
Answer:
12 pages
Step-by-step explanation:
3 1/2 pages = 1/3 hour
? pages = 1 hr
; Cross multiply. Multiply 1 times 3 1/2 which is 4. Then, divide 4 by 1/3.
4/1 times 3/1 which equals 12 pages.
How many zeros does the equation
7x^4 - 63x^3 -29x^2+10x+15 have?
Answer:
1
Step-by-step explanation:
How much money will the movie theater make if a birthday party of 12 kids each buys a box of candy and a soda but does not go see a movie?
candy $3.75
soda is $4.00
Answer:
$93
Step-by-step explanation:
12(3.75+4.00)
= 93
At a Beirut market, oranges are priced at $1.29/KG. Ms. X buys 10 oranges that have a total weight of 4.82 kgs. What is the average price per orange that she pays?
Answer:
The average price of each orange is $0.62.
Step-by-step explanation:
Given that at a Beirut market, oranges are priced at $ 1.29 per kilo, and Ms. X buys 10 oranges that have a total weight of 4.82 kilograms, to determine what is the average price per orange that she pays must perform the following calculation:
(4.82 x 1.29) / 10 = X
6.21 / 10 = X
0.62 = X
Thus, the average price of each orange is $ 0.62.
)
Which recursive definition could be used to generate the sequence {1, 5, 11, 19, 29...)?
A)
ay = 1 and a, = a -1 + 2n
B)
a = 1 and an = an-1 + 4n
ay = 1 and an = an-1 + 5n
D)
a1 - 1 and an = an-1 +6n
Answer:
d
Step-by-step explanation:
just trying to help but i don;t know if isss right so sorryy
Answer:
A
Step-by-step explanation:
I did the prep
which expressions are equivalent to 2 In a +2In b- In a?
what does 2 1/4 round to?
A) 2
B) 3
C) 1
D) 2 3/4
WHO EVER GETS IT CORRECT FIRST WILL BE BRAINLEST
Answer:
2 is the answer
Step-by-step explanation:
The answer would be A) 2 Because when rounding you go to the nearest whole number. 2 is only 1/4 from 2 1/4 while 3 is 3/4 away and C) 1 is lower than answer A) 2, And Option D) 2 3/4 isnt even a valid option because its not a whole number/
Answer: A) 2
Please help!!!!!!!!!!!!!!!!!!!!!!
y=mx+b
?????????????
Answer:
??
Step-by-step explanation:
thats the slope equation, m is your slope, x is your variable, and b is your y interger or whatever's (0,y)
The following data are the daily number of minutes of smartphone use for a random sample of 8 students at your institution:
117, 156, 89, 72, 116, 125, 101, 100.
Required:
a. Test the null hypothesis according to which the true mean is greater or equal to 100 min against the alternative that it is less than 100. Use a significance level of 5% (state the null and the alternative hypothesis, the test statistic and the conclusion).
b. Compute a 90% confidence interval for the true mean number of minutes per day a student uses his or her smartphone. Is your finding consistent with your answer in (a) (Explain why or why not)
Answer:
We fail to reject the Null ;
(88.323, 130.677)
Step-by-step explanation:
Given the data :
117, 156, 89, 72, 116, 125, 101, 100
H0 : μ ≥ 100
H1: μ < 100
From the data: using calculator :
Mean, x = 109.5
Standard deviation, s = 25.33
The test statistic:
(x - μ) ÷ s/Sqrt(n)
(109.5 - 100) ÷ 25.33/sqrt(8)
Test statistic = 1.06
Since, same size is small, we use t test ;
Using the Pvalue calculator :
T at df = 8 - 1 = 7, α = 0.05
Pvalue = 0.161
Pvalue > α
0.161 > 0.05 ; Hence, we fail to reject H0.
B.)
C. I = mean ± Tcritical *s/√n
Tcritical = 2.365 at 95% and df = 7
109.5 ± 2.365(25.3264/√8)
109.5 ± 2.365(8.9542)
(109.5-21.1768 ; 109.5+21.1768)
(88.323, 130.677)
In conclusion true mean is in the confidence interval, so it is consistent.
The chart shows the temperatures at noon during a week in January. HELP
Day
Monday
Tuesday
Wednesday
Thursday
Friday
Temperature
-6°F
0°F
5°F
-3°F
3°F
Which day was the coldest?
A. Monday
B. Tuesday
C. Thursday
D. Friday
Monday was the coldest day of the week, at -6 degrees Fahrenheit.