Answer:
167688 ways
Step-by-step explanation:
Given that:
Number of boys = 17 &;
Number of girls = 19
The number of ways that five students can be chosen such that more boys than girls are selected are:
The ways of choosing = 5 boys 0 girls + 4 boys 1 girl + 3 boys 2 girls
The ways of choosing = [tex]^{17}C_5 +( ^{17}C_4 \times ^{19}C_1} )+( ^{17}C_3 + ^{19}C_2})[/tex]
The ways of choosing = [tex]\dfrac{17!}{5!(17-5)!} + \begin {pmatrix} \dfrac{17!}{4!(17-4)!} \times \dfrac{19!}{1!(19-1)!} \end {pmatrix} + \begin {pmatrix} \dfrac{17!}{3!(17-3)!} \times \dfrac{19!}{2!(19-2)!} \end {pmatrix}[/tex]
[tex]=\dfrac{17!}{5!(12)!} + \begin {pmatrix} \dfrac{17!}{4!(13)!} \times \dfrac{19!}{1!(18)!} \end {pmatrix} + \begin {pmatrix} \dfrac{17!}{3!(14)!} \times \dfrac{19!}{2!(17)!} \end {pmatrix}[/tex]
[tex]=\dfrac{17*16*15*14*13*12!}{5!(12)!} + ( \dfrac{17*16*15*14*13!}{4!(13)!} \times \dfrac{19*18!}{1!(18)!} ) + ( \dfrac{17*16*15*14!}{3!(14)!} \times \dfrac{19*18*17!}{2!(17)!} )[/tex][tex]=6188 + ( 2380\times19 ) + (680 \times171)[/tex]
= 167688 ways
Using the combination principle, the number of ways of selecting 5 students such that the number of boys is greater the number of girls selected ls 167688 ways.
Number of boys = 17Number of girls = 19Number of selections to be made = 5
In other to choose more boys than girls :
5 boys and 0 girls4 boys and 1 girl3 boys and 2 girlsUsing the combination relation :
(17C5 × 19C0) + (17C4 × 19C1) + (17C3 × 19C2)
(6188 × 1) + (2380 × 19) + (680 × 171)
(6188 + 45220 + 116280)
= 167688 ways
Therefore, the Number of ways of making the selection is 167688 ways
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You need a 40% alcohol solution. On hand, you have a 350 mL of a 15% alcohol mixture. You also have 90%
alcohol mixture. How much of the 90% mixture will you need to add to obtain the desired solution?
You will need
mL of the 90% solution
Submit Question
Let x be the amount of 90% solution you will use.
You have 350 mL of a 15% alcohol solution, so it contains 0.15 • 350 mL = 52.5 mL.
For each mL of the 90% solution that you use, you would add 0.9 mL of alcohol. So in the new mixture, the volume would be (350 + x) mL, and its concentration needs to be 40% so that
((52.5 + 0.9x) mL) / ((350 + x) mL) = 0.4
Solve for x :
(52.5 + 0.9x) / (350 + x) = 0.4
(52.5 + 0.9x) / 0.4 = 350 + x
131.25 + 2.25x = 350 + x
1.25x = 218.75
x = 175
so you will need to use 175 mL of the 90% solution.
Which of the following numbers can be expressed as repeating decimals 4/7, 2/5, 7/8, 4/9. I will mark brainliest
Answer:
4/9
Step-by-step explanation:
Put it in a calculator and you get .4 but there's a lot of 4's. That's the repeating decimal.
Answer:4/9 and 4/7
Step-by-step explanation: Trust
I need help with this question.
The sum of three numbers is 1349 the greatest number is three times the least number the third number is 133 less than twice the least number what are the three numbers?
Answer:
1,216 131,784 130,435
Step-by-step explanation:
you have observed that the average size of a particular goldfish is 1.5 inches long. the standard deviation of the size of the goldfish is 0.25 inches. approximately what is the size of a goldfish such that only 16 percent of the goldfish are smaller from such size
Answer:
The 16 percent of the goldfish are smaller from 1.25 inches.
Step-by-step explanation:
Let X denote the size of a particular goldfish.
It is provided that the mean size is, μ = 1.5 inches and standard deviation of the size is, σ = 0.25 inches.
Assume that X is normally distributed.
Compute the size of a goldfish such that only 16 percent of the goldfish are smaller from such size as follows:
P (X < x) = 0.16
⇒ P (Z < z) = 0.16
The z-value for such a probability is:
z = -0.99
*Use a z-table.
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\-0.99=\frac{x-1.5}{0.25}\\\\x=1.5-(0.99\times 0.25)\\\\x=1.2525\\\\x\approx 1.25[/tex]
Thus, the 16 percent of the goldfish are smaller from 1.25 inches.
Help me, pleeassee?
I'm dyyiinnnggg
Answer:
The function is an x exponential function.
The domain is infinite
The range is y<2
Find the distance from point A (-1/4,5) to the line -x+2y=14. Round your answer to the nearest tenth.
Answer:
1.7
Step-by-step explanation:
That was the correct answer trust me
A grocery store clerk can scan 1 product every
1
2
of a second. At what rate can she scan products?
Answer:
2 products a second.
Step-by-step explanation:
Solve -9x-3x+4 = -10x - (2x- 4)
Answer:
−
9
x
−
3
x
+
4
, then set it equal to
−
10
x
−
(
2
x
−
4
)
.
Always true
Step-by-step explanation:
Answer:
All real numbers
Step-by-step explanation:
-9x-3x+4 = -10x - (2x- 4)
-12x+4=-10x-2+4
-12x+4=-12x+4
Please help ASAP
In the diagram, line a and b are parallel. Line is the transversal.
Given that the measure of angle POQ is 114° determine the measure of angle QON
In your explanation be sure to include the key terms corresponding angles ,supplementary Angles, parallel lines ,and transversal computational slep in complete sentences
Answer:
66 not parallel or transversal I believe its supplementary
Step-by-step explanation:
PLSSS HELPPPP RIGHT NOWWW I NEED THISSSSS PLSS ANYBODY
Answer:
You cant see the picture its glitched send another one
Step-by-step explanation:
A bag contains 5 blue 3 red 6 green 9 orange and 20 black marbles. What is the ratio of the number of blue marbles to the number of marbles that are orange or green
Answer: 5 to 9
Step-by-step explanation:
you just add them all together! (:
Two number cubes are rolled. What is the probability that the sum is 5?
Answer:
2.2
Step-by-step explanation:
In a small city, approximately 15% of those eligible are called for jury duty in any one calendar year. People are selected for jury duty at random from those eligible, and the same individual cannot be called more than once in the same year. (a) What is the probability that a particular eligible person in this city is selected in both of the next 2 years
Answer:
0.0225
Step-by-step explanation:
Probability that an eligible individual is called for jury duty in any one calendar year = 15/100 = 0.15
a) What is the probability that a particular eligible person in this city is selected in both of the next 2 years
Probability that an eligible person is chosen in each of the next 2years:
P(being chosen in first year) * P(being chosen in second year)
Since the probability of being chosen is the same in any one year with a probability of 0.15
Hence,
P(being chosen in first year) * P(being chosen in second year)
0.15 * 0.15 = 0.0225
a. the probability that a particular eligible person in this city is selected in both of the next 2 years is 0.0225
Calculation of the probability:Since In a small city, approximately 15% of those eligible are called for jury duty in any one calendar year and there is two years.
So, the probability is
= 0.15 (0.15)
= 0.0225
Learn more about probability here: https://brainly.com/question/10695144
Does anyone know how to find the measure of this missing angle ?
Answer:
x=57
Step-by-step explanation:
x+28+x+38=180
Step 1: Simplify both sides of the equation.
x+28+x+38=180
(x+x)+(28+38)=180(Combine Like Terms)
2x+66=180
2x+66=180
Step 2: Subtract 66 from both sides.
2x+66−66=180−66
2x=114
Step 3: Divide both sides by 2.
2x/2=114/2
Answer:
x=57
Answer:
57
Step-by-step explanation:
x+28+x+38=180
2x+66=180
-66 -66
2x=114
/2 /2
x=57
I think
What is the degree of x5 - 4x + 2?
A. 5
B. 3
C. 4
D. 6
Answer:
c-5Step-by-step explanation:
.......
...................
The degree of the given polynomial x⁵ - 4x + 2 is 5. The correct answer is option A. 5.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The degree of a polynomial is the highest power of the variable with a non-zero coefficient.
As per the question,
Here, 5 is the highest power of x with a non-zero coefficient.
Therefore, the degree of x⁵ - 4x + 2 is 5.
Hence, the correct answer is option A. 5.
Learn more about the polynomial here:
brainly.com/question/11536910
#SPJ7
Line d has a slope of -9/7. Line e is parallel to line d  what is the slope of line E
Answer: -9/7
Step-by-step explanation: The slope of parallel lines are the same/equal. Only the y intercept is different
Look at this table, X W 11 1 10 3 13 -17 17 Is this relation a function? yes or no
The solution to -2x/3 + 7< 15 is the set ? A x>-12 B x<-12 C x>33 D x<-10
Answer:
A. x>-12
Step-by-step explanation:
-2x/3+7<15 Subtract 7 on both sides.
-7 -7
-2x/3<8 -2x/3 is equal to -2/3x, so you can simplify to that.
-2/3x<8 Because you have to isolate x, multiply by the reciprocal of the
*-3/2 *-3/2 fraction. This will divide by -2/3 on both sides.
x>-12 Remember, because you multiplied by a negative, you have to flip the inequality sign.
Hope this helps you! Have a nice day c:
a box has a square base of side x and height h find the dimensions x, h for which the volume is 14 and the surface area is as small as possible
Volume of cuboid :
[tex]14 = x^2h\\\\h = \dfrac{14}{x^2}[/tex]
Surface area of this cuboid :
[tex]A = 2( x^2 + xh + xh )\\\\A = 2( x^2 + 2xh)[/tex]
Putting [tex]h = \dfrac{14}{x^2}[/tex] in above equation, we get :
[tex]A=2(x^2 + 2x\times \dfrac{14}{x^2})\\\\A = 2( x^2 + \dfrac{28}{x} )[/tex]
For minimum area, [tex]\dfrac{dA}{dx}=0[/tex] :
[tex]\dfrac{dA}{dx}=2( 2x -\dfrac{28}{x^2})\\\\\dfrac{dA}{dx }= 4(x - \dfrac{14}{x^2})\\\\x - \dfrac{14}{x^2}=0\\\\x=\sqrt[3] {14} = 2.41[/tex]
Therefore, value of x is 2.14 .
Hence, this is the required solution.
The dimension for which the volume is 14 and the surface area is as small as possible are 2.41 by 2.41 by 2.41
The formula for calculating the volume of the square box is expressed as:
[tex]V = x^2h[/tex]
Given that the volume of the box is 14, on substituting the value we will have:
[tex]14 =x^2h\\h=\frac{14}{x^2}[/tex]
The surface area of the box is expressed as:
[tex]S = 2(x^2+xh+xh)\\S=2(x^2+2xh)\\S = 2(x^2+2x(\frac{14}{x^2} ))\\S = 2(x^2+\frac{28}{x} )\\S=2x^2+\frac{56}{x}[/tex]
To get the surface area is as small as possible, then dS/dx = 0
[tex]\frac{dS}{dx} = 4x-\frac{56}{x^2}\\0 = 4x-\frac{56}{x^2}\\4x = \frac{56}{x^2}\\4x^3 = 56\\ x^3=14\\x=\sqrt[3]{14}\\x= 2.41[/tex]
Get the height of the box. Recall that;
[tex]h=\frac{14}{x^2}\\h=\frac{14}{(2.41)^2}\\h=\frac{14}{5.8081}\\h= 2.41[/tex]
Hence the dimension for which the volume is 14 and the surface area is as small as possible are 2.41 by 2.41 by 2.41
Learn more here: https://brainly.com/question/18761821
Which answer choice shows the numbers in correct order from least to greatest?
(3)
A 1-3.5], -3.65, 37, 3.85
B 3.85, 3, 1-3.51, -3.65
C -3.65, 1-3.51, 32, 3.85
D 33,1-3.5), 3.65, 3.85
please answer this asap
What is the probability of spinning a C
Slope intercept (-2,5) and (2,1)
Answer:
y=-1x+3
Step-by-step explanation:
1-5=-4
2--2=4
-4/4= -1
In a survey of 2,100 people who owned a certain type of car, 420 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Consider versus A random sample of 35 observations taken from this population produced a sample mean of 40.27. The population is normally distributed with Calculate the p-value. Round your answer to four decimal places.
Complete Question
Consider H0: μ=38 versus H1: μ>38. A random sample of 35 observations taken from this population produced a sample mean of 40.27. The population is normally distributed with σ=7.2.
Calculate the p-value. Round your answer to four decimal places.
Answer:
The [tex]p-value = 0.030742[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 38[/tex]
The sample size is n = 35
The sample mean is [tex]\= x = 40.27[/tex]
The standard deviation is [tex]\sigma = 7.2[/tex]
The null hypothesis is [tex]H_o[/tex]: μ=38
The alternative hypothesis is H1: μ>38
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \= x -\mu }{\frac{\sigma }{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{ 40.27 - 38 }{\frac{ 7.2 }{ \sqrt{ 35} } }[/tex]
=> [tex]t =1.87[/tex]
Generally from the z table the p-value of [tex](Z > 1.87 )[/tex] is
[tex]p-value = P(Z > 1.87) = 0.030742[/tex]
some tv sets show 25 images called frames each second what is the time interval between each frame and the next?
Answer:
0.04
Step-by-step explanation:
25 images / 1 second
pls mark brainlist :)
Is the number a multiple of 3? Write yes or no.
11. 8
10 4
12. 24
13. 38
Answer:
10: No
11: No
12: Yes
13: No
Step-by-step explanation:
8 / 3 = 2.66
4 / 3 = 1.33
24 / 3 = 8
38 / 3 = 12.66
Hope this help and have a great day!
solve for X SOMEONE PLSSSSS
x+53+65+70=180
Answer:
Ok so the answer is x = -8
Step-by-step explanation:
Have a nice day!!!
A researcher is interested in determining the average number of years employees of a company stay with the company. If past information shows a standard deviation of 7 months, what size sample should be selected so that at 95% confidence the margin of error will be 2 months or less?
Answer:
48
Step-by-step explanation:
The significance level is 95%
Z-alpha/2 = 1.96 at 0.05 from the standard normal distribution table.
The standard deviation has been given to be 7
Margin of error is 2
We solve further using the formula:
n = (z-alpha/2 * sd/ME)²
n = (1.96 * 7/2)²
n = (1.96x3.5)²
= 6.86²
= 47.0596
This is approximately
n = 48
So the sample size they should be selected should be 48 for at 95% confidence level.
calculate the rate of change in your neighborhood population of squirrels based on the data from a june 2015
The question is incomplete. Here is the complete question.
Scenario: You are bored during quarantine. However, you have been observing a bird feeder in your backyard and wow... do there seem to be a lot of squirrels in your neighbourhood. You begin to wonder how many squirrels are actually in your neighbourhood and devise an experiment to track their population.
Part 1. Using the data below, estimate the population of squirrels in your neighbourhood as if you employed the Mark-and-Recapture method. Please be sure to include any units in your final answer.
#captured on 06/01/20 10
#captured on 06/30/20 6
#recaptured on 06/30 from 06/01 3
Part 2. Calculate the rate of change in your neighbourhood population of squirrels based on the data from a June 2015 report that indicated a population of 40 squirrels.
Part 3. Calculate the intrinsic growth rate (r) for this population of squirrels based on the data you have acquired so far.
Part 4. Interpretations: In 1-2 sentences, summarize what's happening here (e.g. is the population growing or shrinking or staying the same?) and propose one plausible explanation for this change.
Answer: Part 1: Population of 20 squirrels
Part 2: Rate of change 50%
Part 3: r = -0.1386 anos
Step-by-step explanation: The Mark-and-Recapture method is a method to estimate a population when counting each individual is impractical. The method consists in capture a small population of individuals, mark them and released them back to the population. After a while, you catch another group and record the ones with the mark.
The calculations are made following this formula:
[tex]N=\frac{M*C}{R}[/tex]
N is the estimated population
M is marked individuals
C is total number of captured individuals (with and without the mark) the second time
R is recaptured individuals with the mark.
Part 1: Population of squirrels will be:
[tex]N=\frac{10*6}{3}[/tex]
N = 20
Population of squirrels in 2020 is 20 squirrels.
Part 2: Rate of change is calculated by the change in the population divided by the original population:
rate = [tex]\frac{20-40}{40}[/tex]
rate = - 0.5 or 50%
Part 3: The model for a population growth is exponential:
[tex]N=N_{0}e^{rt}[/tex]
N is population at that moment
N₀ is initial population
r is growth rate
t is period of time
Growth rate will be:
[tex]N=N_{0}e^{rt}[/tex]
[tex]20=40e^{5r}[/tex]
[tex]e^{5r}=0.5[/tex]
[tex]5r=ln(0.5)[/tex]
[tex]r=\frac{ln0.5}{5}[/tex]
[tex]r=-0.1386[/tex]
Growth rate (r) for the population of squirrels after 5 years is [tex]r=-0.1386[/tex] years.
Part 4: The growth rate has a negative sign, which means population is decreasing along the 5 years, so population is shrinking.
One possible explanation is the environment the population are in is lacking the squirrels primary need, i.e., squirrels' food source is diminishing, causing the population to decrease.
