Answer: [tex]\dfrac{665}{1496}[/tex]
Step-by-step explanation:
Given : In a group , there are 20 boys and 14 girls.
Total people = 20+14=34
Number of ways to choose 3 people out of 34 = [tex]^{34}C_3[/tex]
Number of ways to choose 1 girl and 2 boys = [tex]^{14}C_1\times^{20}C_2[/tex]
The probability that 1 girl and 2 boys are selected = [tex]\dfrac{^{14}C_1\times ^{20}C_2}{^{34}C_3}[/tex]
[tex]\dfrac{14\times\dfrac{20!}{2!18!}}{\dfrac{34!}{3!31!}}\ \ \ [^nC_r=\dfrac{n!}{r!(n-r)!}]\\\\=\dfrac{14\times\dfrac{20\times19}{2}}{\dfrac{34\times33\times32\times31!}{3\times2\tims3!}}\\\\=\dfrac{665}{1496}[/tex]
Hence, required probability = [tex]\dfrac{665}{1496}[/tex]
10 POINTS.. ILL GIVE BRAINLIEST
Solve for x:
a) x = 18
b) x = 19
c) X = 20
d) x = 21
Answer:
D. x = 21
Step-by-step explanation:
So a straight line is equal to 180º and that's what we're trying to figure out here. Set both equations to equal 180, it should look like:
5x + 4x - 9 = 180
Now we just solve!
5x + 4x - 9 = 180
5x + 4x = 9x
9x - 9 = 180
+9 +9
------------------
9x = 189
Divide both sides by 9 to get x by itself.
189/9 = 21
x = 21
A normal distribution has a mean of 10 and a standard deviation of 1. What is the probability of selecting a number that is at most 10
Answer:
15.87% probability of selecting a number that is at most 9
Step-by-step explanation:
the fastest man in the world can run 100 metres in 9 seconds how far can He run in 1 minute and 2 seconds
With steps plz......
(Its not usain)
Answer:
Step-by-step explanation:
Rate per sec = 100 ÷ 9 = 11.111
1 min and 2 sec = 3600 + 2sec = 3602 sec
Metre = 324.21 metre
Shaniqua brings home $250 per week working 25 hours. She is able to save $30 of her earnings each week.
Shaniqua wants to have $750 saved at the end of 15 weeks. She is allowed to work up to 30 hours per week if she
wants. She can save all the money earned working extra hours. How many hours (as a whole number) each week
must Shaniqua work to save $750 at the end of 15 weeks? Show your work.
Answer: She'd have to work 27 hours a Week because by her working 2 more hours shed be able to save up 50 a week.
Explanation: 750 divided by 15 (the weeks) is 50. Shed need to save 50 a week instead of 30 to reach her goal and the amount 50 divided by the number of hours she works (25) is 2. Add the 2 to 25 and you get 27 weeks.
X
-3
1
3
y
10
2
2
10
Function? Yes or No?
Justify your answer:
Answer:
Yes.
Step-by-step explanation:
The x's are all different, so the set of numbers is indeed a function. Although two y's are the same, it doesn't matter.
Hope this helped you!! Have an amazing day :D
How many kilometers are in 60 miles? Note: There are 1.609kms in 1mi.
Answer:
Your answer is 96.5606 Kilometers.
Step-by-step explanation:
1.609 x 60 = 96.5606
Mark as brainliest if it's correct!
Answer:
96.5606kms
Step-by-step explanation:
25 percent of ____ is 6
Answer:
24
Step-by-step explanation:
1/4 of x is 6 so you multiply 6 by 4
Help please! I’ll give brainliest!
Answer:
the first
Step-by-step explanation:
becasue you have -4 and it drops by 5 each hour so your timing it by 5 so 5h then sinv=ce it drops its -5h.
Answer:
The answer should be B
Step-by-step explanation:
A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is 19 feet more than the length of the shortest side. Find
the dimensions if the perimeter is 163 feet.
What is the length of the shortest side?
The length of the shortest side is
This is simple as the perimeter is given. All you have to do is make an expression and then equate it to the perimeter.
Side lengths:
Shortest Side: [tex]x[/tex]
1st side: [tex]2x[/tex] (Given that it's twice the length of the shortest of twice of [tex]x[/tex])
3rd side: [tex]x + 19[/tex] (Given that it's 19 more than the length of the shortest side or [tex]x[/tex])
Since the perimeter is just the addition of all the sides of the shape, the perimeter is going to be the addition of all the expression we made.
So the final expression is going to be: [tex]x + 2x + x + 19[/tex]
This is nothing but the perimeter so we can therefore equate it to [tex]163[/tex]
[tex]x + 2x + x + 19 = 163[/tex]
Now we solve the equation. Here it goes!:
[tex]4x + 19 = 163\\4x = 163 - 19\\4x = 144\\x = 144/4 = 36[/tex]
Therefore, [tex]x = 36[/tex]
So now we plug them into the previous expressions we made for the sides and you get:
Shortest side: [tex]36[/tex]
1st side: [tex]72[/tex]
3rd side: [tex]55[/tex]
And also, the length of the shortest side is [tex]36[/tex] as mentioned previously :D
A picture is 3 in. wide by 5 in. high was enlarged so that the width was 15 inches. How high is the enlarged picture?
Answer:
25
Step-by-step explanation:
trust me
Maths questions
X+1/x-6 times 7x/x+2
Answer:
7x^2+7x/x^2-4x-12
Step-by-step explanation:
Given the expression
X+1/x-6 times 7x/x+2
Rewrite
X+1/x-6 * 7x/x+2
= 7x(x+1)/(x-6)(x+2)
= 7x^2+7x/x^2+2x-6x-12
= 7x^2+7x/x^2-4x-12
Hence the product of both function is expressed as 7x^2+7x/x^2-4x-12
A recipe that serves 8 people requires 4 1/2 cup of flour how much do you need to serve for 24 people
Answer:
You would need thirteen and a half( [tex]13\frac{1}{2}[/tex]) cups of flour.
Step-by-step explanation:
You can find this by taking [tex]4\frac{1}{2}[/tex] and multiplying it by 3, since 24/8=3. This gives you [tex]13\frac{1}{2}[/tex] .
How many milliliters of full-strength Sustacal are needed to prepare 240ml of half-strength sustacal?
The question is incomplete, the complete question is;
How many milliliters of full-strength Sustacal are needed to prepare 240 mL of half-strength Sustacal?
1. 120 mL
2. 240 mL
3. 360 mL
4. 480 mL
Answer:
120 mL
Step-by-step explanation:
From the question, we can see that the full strength solution is supposed to contain 240 ml of Sustacal .
If that is so, we can get a half strength solution by using only 120 ml of full strength solution and making up the remaining volume with water. This solution now has half the strength of a 240 ml full strength solution.
Consider the function f(x)=xln(x). Let Tn be the nth degree Taylor approximation of f(2) about x=1. Find: T1, T2, T3. find |R3| <= ?
Answer:
R3 <= 0.083
Step-by-step explanation:
f(x)=xlnx,
The derivatives are as follows:
f'(x)=1+lnx,
f"(x)=1/x,
f"'(x)=-1/x²
f^(4)(x)=2/x³
Simialrly;
f(1) = 0,
f'(1) = 1,
f"(1) = 1,
f"'(1) = -1,
f^(4)(1) = 2
As such;
T1 = f(1) + f'(1)(x-1)
T1 = 0+1(x-1)
T1 = x - 1
T2 = f(1)+f'(1)(x-1)+f"(1)/2(x-1)^2
T2 = 0+1(x-1)+1(x-1)^2
T2 = x-1+(x²-2x+1)/2
T2 = x²/2 - 1/2
T3 = f(1)+f'(1)(x-1)+f"(1)/2(x-1)^2+f"'(1)/6(x-1)^3
T3 = 0+1(x-1)+1/2(x-1)^2-1/6(x-1)^3
T3 = 1/6 (-x^3 + 6 x^2 - 3 x - 2)
Thus, T1(2) = 2 - 1
T1(2) = 1
T2 (2) = 2²/2 - 1/2
T2 (2) = 3/2
T2 (2) = 1.5
T3(2) = 1/6 (-2^3 + 6 *2^2 - 3 *2 - 2)
T3(2) = 4/3
T3(2) = 1.333
Since;
f(2) = 2 × ln(2)
f(2) = 2×0.693147 =
f(2) = 1.386294
Since;
f(2) >T3; it is significant to posit that T3 is an underestimate of f(2).
Then; we have, R3 <= | f^(4)(c)/(4!)(x-1)^4 |,
Since;
f^(4)(x)=2/x^3, we have, |f^(4)(c)| <= 2
Finally;
R3 <= |2/(4!)(2-1)^4|
R3 <= | 2 / 24× 1 |
R3 <= 1/12
R3 <= 0.083
A car is sold for $18,000. After one year, the value of the car is $9,900. Write an exponential function y to determine the value of
the car after x years if the rate of decrease is the same each year.
y =
Estimate the value of the car after 6 years. Round the answer to the nearest dollar.
Answer:
temperature and kinctic energy are related
If you brainliest me I will friend you and text you everyday and most of all this game is called: What's In The Box? Here are some things for you to guess
1: it has a paper over it
2: you can eat it
3: it starts with and H
Comment below to find out What's In The Box?
Answer:
Is it hershey
Step-by-step explanation:
Which steps show how to use the distributive property to evaluate 5. 58?
A. 5(58) = 5(50 + 8) = 5.50 – 5.8 = 250 – 40 = 210
B. 5(58) = 5(50 + 8) = 5.50 +8 = 250 + 8 = 258
C. 5(58) = 5(50 + 8) = 5.50 + 50 8 = 250 + 400 = 650
D. 5(58) = 5(50 + 8) = 5.50 +5.8 = 250 + 40 = 290
Answer:
D.
Step-by-step explanation:
You are splitting the equation up. (I don't really know how to explain it sorry)
The correct steps to evaluate 5 · 58 using the distributive property following are: 5(58) = 5(50 + 8) = 5 · 50 +5 · 8 = 250 + 40 = 290.
What is the distributive property of multiplication?The product of a number by addition is equal to the total of the products of that number by each of the addends, according to the distribution property of multiplication.
The correct steps to evaluate 5 · 58 using the distributive property are:
Start with the expression 5 · 58.
Use the distributive property to rewrite the expression as 5(50 + 8).
Use the distributive property again to rewrite the expression as 5 · 50 + 5 · 8.
Calculate the value of each term in the resulting expression:
5 · 50 = 250 and 5 · 8 = 40.
Add the values of the two terms to get the final result:
250 + 40 = 290.
Therefore, the correct answer is D. 5(58) = 5(50 + 8) = 5 · 50 + 5 · 8 = 250 + 40 = 290.
To learn about the distributive property of multiplication here:
brainly.com/question/20754996
#SPJ5
Which of the following statements best describes the modulus of a complex number? Select all that apply.
the absolute value of a complex number
the distance that a complex number is from the pole
the distance that a complex number is from the origin
the complex number squared
Answer:
Step-by-step explanation:
i beleive its the 1st or 3rd option
what is 5/ 16 expressed as a percentage
Answer:
31.25%Step-by-step explanation:
To express a number as a percent we will first divide the top number by the bottom number.
5/16 = 0.3125
A percent is expressed by moving the decimal two places to the left.
31.25%You start at (0, 8). You move up 1 unit and right 3 units. Where do you end?
Answer:
1.11
Step-by-step explanation:
Given the function f(x) = 5(x+4) − 6, solve for the inverse function when x = 19.
Answer:
5.74
Step-by-step explanation:
fx=5(x+4)-6
f(19)=5(19+4)-6
19f=5(23)-6
19f=115-6
19f=109
f=109÷19
f=5.74 or 19 14/19
Test the claim that the mean GPA of night students is larger than 2 at the .025 significance level. The null and alternative hypothesis would be: H 0 : μ = 2 H 0 : μ = 2 H 1 : μ > 2 H 1 : μ > 2 H 0 : p = 0.5 H 0 : p = 0.5 H 1 : p ≠ 0.5 H 1 : p ≠ 0.5 H 0 : p = 0.5 H 0 : p = 0.5 H 1 : p > 0.5 H 1 : p > 0.5 H 0 : μ = 2 H 0 : μ = 2 H 1 : μ < 2 H 1 : μ < 2 H 0 : p = 0.5 H 0 : p = 0.5 H 1 : p < 0.5 H 1 : p < 0.5 H 0 : μ = 2 H 0 : μ = 2 H 1 : μ ≠ 2 H 1 : μ ≠ 2 Based on a sample of 60 people, the sample mean GPA was 2.02 with a standard deviation of 0.06 The test statistic is (to 3 decimals) The critical value is (to 3 decimals) Based on this we fail to reject the null hypothesis reject the null hypothesis
Answer:
[tex]H_0: \, \mu = 2[/tex].
[tex]H_1:\, \mu > 2[/tex].
Test statistics: [tex]z \approx 2.582[/tex].
Critical value: [tex]z_{1 - 0.025} \approx 1.960[/tex].
Conclusion: reject the null hypothesis.
Step-by-step explanation:
The claim is that the mean [tex]\mu[/tex] is greater than [tex]2[/tex]. This claim should be reflected in the alternative hypothesis:
[tex]H_1:\, \mu > 2[/tex].
The corresponding null hypothesis would be:
[tex]H_0:\, \mu = 2[/tex].
In this setup, the null hypothesis [tex]H_0:\, \mu = 2[/tex] suggests that [tex]\mu_0 = 2[/tex] should be the true population mean of GPA.
However, the alternative hypothesis [tex]H_1:\, \mu > 2[/tex] does not agree; this hypothesis suggests that the real population mean should be greater than [tex]\mu_0= 2[/tex].
One way to test this pair of hypotheses is to sample the population. Assume that the population mean is indeed [tex]\mu_0 = 2[/tex] (i.e., the null hypothesis is true.) How likely would the sample (sample mean [tex]\overline{X} = 2.02[/tex] with sample standard deviation [tex]s = 0.06[/tex]) be observed in this hypothetical population?
Let [tex]\sigma[/tex] denote the population standard deviation.
Given the large sample size [tex]n = 60[/tex], the population standard deviation should be approximately equal to that of the sample:
[tex]\sigma \approx s = 0.06[/tex].
Also because of the large sample size, the central limit theorem implies that [tex]Z= \displaystyle \frac{\overline{X} - \mu_0}{\sigma / \sqrt{n}}[/tex] should be close to a standard normal random variable. Use a [tex]Z[/tex]-test.
Given the observation of [tex]\overline{X} = 2.02[/tex] with sample standard deviation [tex]s = 0.06[/tex]:
[tex]\begin{aligned}z_\text{observed}&= \frac{\overline{X} - \mu_0}{\sigma / \sqrt{n}} \\ &\approx \frac{\overline{X} - \mu_0}{s / \sqrt{n}} = \frac{2.02 - 2}{0.06 / \sqrt{60}} \approx 2.582\end{aligned}[/tex].
Because the alternative hypothesis suggests that the population mean is greater than [tex]\mu_0 = 2[/tex], the null hypothesis should be rejected only if the sample mean is too big- not too small. Apply a one-sided right-tailed [tex]z[/tex]-test. The question requested a significant level of [tex]0.025[/tex]. Therefore, the critical value [tex]z_{1 - 0.025}[/tex] should ensure that [tex]P( Z > z_{1 - 0.025}) = 0.025[/tex].
Look up an inverse [tex]Z[/tex] table. The [tex]z_{1 - 0.025}[/tex] that meets this requirement is [tex]z_{1 - 0.025} \approx 1.960[/tex].
The [tex]z[/tex]-value observed from the sample is [tex]z_\text{observed}\approx 2.582[/tex], which is greater than the critical value. In other words, the deviation of the sample from the mean in the null hypothesis is sufficient large, such that the null hypothesis needs to be rejected at this [tex]0.025[/tex] confidence level in favor of the alternative hypothesis.
Stefan sells Jin a bicycle for $163 and a helmet for $17. The total cost for Jin is 150% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin? Stefan originally spent $
Answer:
44$
Step-by-step explanation:
Answer:
Answer
5.0/5
7
PiaDeveau
Ace
5K answers
22.1M people helped
The selling cost for Stefan bicycle = $114 and
the selling cost of a helmet = $18.
The total cost for Jin is 120% of the money spent.
Let us assume purchasing cost of a bicycle = $x.
Purchasing cost of a halmet = $y.
For bicycle
120% of x is $114
=> 1.20 × x = 114
Dividing both sides by 1.20, we get
x=$95.
For helmet.
120% of y is $18.
=> 1.20 × y = 18.
Dividing both sides by 1.20, we get
y = $15.
Therefore, Stefan spent originally to buy a bike $95 and $15 to buy a helmet.
$114 - 95 = $19
$18 - 15 = $3.
Therefore, he made $19 by selling the bicycle and $3 by selling the helmet to Jin.
Step-by-step explanation:
if f(x) = x^4+7, g(x) = x-9, h(x) = sqrt x, then
f*g(x) =
g*f(x) =
h*g(x) =
Answer:
ejeqf
Step-by-step explanation:
kmd
A coach shows the following ratio table to a team. The table shows the average amount of calories burned for a certain number of minutes of running.
Practice
Minutes of running
Calories burned
4
20
8
40
?
100
Based on the table, how many minutes does a person need to run to burn 100 calories?
Answer:
20 Minutes
Step-by-step explanation:
Answer:
20 minutes
From the given information, we can see that:
4 minutes burns 20 calories, and
8 minutes burns 40 calories.
Step-by-step explanation:
ok
PLEEEEEEEEEEEAAAAAAAAASEEEEEEE HELPPPPPP ME
f(x)=-x^3 find the end behavior of function
Answer:
What is X its fiesty
Step-by-step explanation:
fdsfa
6/3=22/x (i really need help
2,5,9,12,7,10,6,3,6
a) find the mean of the above data
Answer:
Step-by-step explanation:
2,5,9,12,7,10,6,3,6
mean=(2+5+9+12+7+10+6+3+6)/9
=60/9
=6.67(approx)
Find the slope of the line given the pair of points.
(-9,5), (10, 4)
Answer:
-1/19
Step-by-step explanation:
