Answer:
[tex]tan(\frac{11\pi}{6}) =-\frac{\sqrt{3} }{3}[/tex]
Step-by-step explanation:
Notice that [tex]\frac{11\pi}{6}[/tex] is an angle in the fourth quadrant (where the tangent is negative), and the angle is in fact equivalent to [tex]-\frac{\pi}{6}[/tex]. This is one of the special angles for which the sine and cosine functions, as well as the tangent function have well know values:
Recall that the tangent is defined as
[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]
and for this angle ( [tex]\frac{11\pi}{6}[/tex] ) the value of the sine and cosine functions are well known:
[tex]sin (\frac{11\pi}{6}) =-\frac{1}{2} \\cos( \frac{11\pi}{6}) =\frac{\sqrt{3} }{2}[/tex]
Then, the tangent would be:
[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}\\tan(\frac{11\pi}{6}) = \frac{-\frac{1}{2} }{\frac{\sqrt{3} }{2} } \\tan(\frac{11\pi}{6}) =-\frac{1}{\sqrt{3} } \\tan(\frac{11\pi}{6}) =-\frac{\sqrt{3} }{3}[/tex]
Based on the following construction which statement below must NOT be true?
Answer:
see below
Step-by-step explanation:
The construction makes ray BF a bisector of angle ABC. That bisector divides ABC into the two congruent angles DBF and EBF. As a consequence, angle EBF will be half of ABC, not equal to ABC.
Describe and explain the difference between the mean, median, and mode.
Make up an example (not in the book or in your lectures) in which the median would be the preferred measure of central tendency.
Answer:
Mean, median and mode are measures of central tendency. The median is a better measure of central tendency when the given data contains outliers.
Step-by-step explanation:
Mean, median and mode are all measures of central tendency. These are statistical information that gives the middle or centre of a set of data. Since the values are central, they usually represent the entire distribution.
The mean is the obtained by dividing the sum of all the scores by the number of scores. The median is the middle value when numbers are arranged in increasing or decreasing order of magnitude. The mode is the most frequently occurring score in a distribution.
Let us see an example of the median as a measure of central tendency. Given the set of values; 4, 10, 12, and 26, the median is obtained from the average of the two middle numbers in the set of values which are 10 and 12 as seen from the set of values above. Hence the median of this set of values is 11.
The median can be a very good measure of central tendency, even better than the mean mostly in situations where there are outliers, or extreme values.
aisha places 6 counters into this place value chart
list all the possible numbers she could represent
Answer:
All the possible numbers she could represent using the counters are:
0.6 | 1.5 | 2.4 | 3.3 | 4.2 | 5.1 | 6
Step-by-step explanation:
Please refer to the attached diagram for this question.
We are asked to list all the possible numbers she could represent using the counters.
The possible numbers are:
When there is 0 counter in the "ones" place and 6 counters in the "tenths" place.
0.6
When there is 1 counter in the "ones" place and 5 counters in the "tenths" place.
1.5
When there are 2 counters in the "ones" place and 4 counters in the "tenths" place.
2.4
When there are 3 counters in the "ones" place and 3 counters in the "tenths" place.
3.3
When there are 4 counters in the "ones" place and 2 counters in the "tenths" place.
4.2
When there are 5 counters in the "ones" place and 1 counter in the "tenths" place.
5.1
When there are 6 counters in the "ones" place and 0 counter in the "tenths" place.
6
Therefore, all the possible numbers she could represent using the counters are:
0.6 | 1.5 | 2.4 | 3.3 | 4.2 | 5.1 | 6
A head librarian for a large city is looking at the overdue fees per user system-wide to determine if the library should extend its lending period. The average library user has $19.67 in fees, with a standard deviation of $7.02. The data is normally distributed and a sample of 72 library users is selected at random from the population. Select the expected mean and standard deviation of the sampling distribution from the options below.
a. σi= $7.02
b. σi= $0.10
c. σ = $0.83
d. µi= $0.27
e. µi= $2.80
Answer:
mean of the sample μ₁ = $0.27
Standard deviation of the sample σ₁ = $0.83
Step-by-step explanation:
Step(i):-
given mean of the population 'μ' = $19.67
Mean of the sample
[tex]= \frac{mean}{n} = \frac{19.67}{72} = 0.27[/tex]
Mean of the sample μ₁ = 0.27
Step(ii):-
Given standard deviation of the population (σ) = $7.02
Standard deviation of sample
[tex]= \frac{mean}{\sqrt{n} } = \frac{7.02}{\sqrt{72} } = 0.827[/tex]
Standard deviation of sample = 0.827≅ 0.83
Final answer:-
mean of the sample μ₁ = $0.27
Standard deviation of the sample σ₁ = $0.83
iven two dependent random samples with the following results: Population 1 70 60 72 55 69 50 55 74 Population 2 72 56 81 50 79 60 50 78 Can it be concluded, from this data, that there is a significant difference between the two population means? Let d=(Population 1 entry)−(Population 2 entry). Use a significance level of α=0.1 for the test. Assume that both populations are normally distributed. Step 3 of 5: Compute the value of the test statistic. Round your answer to three decimal places.
Answer:
The value of the test statistic is:
t = -1.112
Step-by-step explanation:
In this case a paired difference test is to be performed.
The hypothesis can be defined as follows:
H₀: There is no difference between the two population means, i.e. d = 0.
Hₐ: There is a significant difference between the two population means, i.e. d ≠ 0.
The significance level of the test is, α = 0.10.
Use MS-Excel to perform the analysis.
Consider the output attached below.
The value of the test statistic is:
t = -1.112
The p-value of the two-tailed test is:
p-value = 0.303.
Decision rule:
Reject the null hypothesis if the p-value is less than the significance level.
p-value = 0.303 > α = 0.10.
The null hypothesis was failed to be rejected at 10% level of significance.
Conclusion:
There is not enough evidence to support the claim that there is a difference between the two population means.
Which of the following is the simplified fraction that’s equivalent to 0.315? A) 35/999 B) 35/111 C) 105/333 D) 31/99
9514 1404 393
Answer:
B) 35/111
Step-by-step explanation:
[tex]0.\overline{315}=\dfrac{315}{999}=\boxed{\dfrac{35}{111}}[/tex]
The denominator of the fraction has as many 9s as the decimal has repeating digits. Here, the numerator and denominator both have factors of 9 that can be cancelled.
What's the measure of Z1 if Z CBD = 75° and ZABC = 135°?
Answer:
60°
Step-by-step explanation:
∠ABC-∠CBD=∠1
[tex]135-75[/tex]
[tex]=60[/tex]
Answer:
Brainliest goes to me!
Step-by-step explanation:
angle abc = 135 degrees
part of it is angle 1 and the other part is angle cbd
<abc (135) = cbd (75) + <1
angle 1 = 60 degrees
Determine whether the given graph is a function or not
Answer: yes is it a function
Step-by-step explanation:
A graph is a function when there is only one y value for each x value. You can also use the vertical line test. This example is a “quadratic function”.
A bag contains 70 pencils out of which 15 are green and 30 blue.how many pencils of other colours are in the bag
Answer:
25 pencils.
Step-by-step explanation:
You have 30 blue pencils and 15 green ones. To find how many pencils of other colors are in the bag, we can solve: 70-15-30=25
So, there are 25 pencils of other colors in the bag.
Please answer this correctly
Answer:
64
Step-by-step explanation:
There are only pink and yellow sections of the circle, so every spin will land on pink or yellow.
Answer: 64
Answer:
Brianliest!
Step-by-step explanation:
since there are only the colors pink and yellow and the prediction for the number of times it will land on pink or yellow, it will have a 100% probability
64
The altitude of an equalateral triangle is 6√3 units long what is the length on one side of the triangle a. 12 b. 6 c. (7√3)/2 d. 14√3
Answer:
A. 12
Step-by-step explanation:
If we split an equalateral triangle down, it will become 2 30-60-90 triangles. Remember your 30-60-90 triangle rules.
6√3 = x√3, so x = 6
2(6) (for hypotenuse) = 12
Since the hypotenuse is one side of the bigger triangle, we have our final answer of 12.
Edith is purchasing a car whose MSRP is $22,750. She has asked for an
upgrade to a premium package for which the cost is $5050. The delivery of
this vehicle is an additional $700. Edith will trade in her own car, and the
dealer has offered her $8000. If Edith agrees to this, what will be her total
price for the vehicle?
Answer:
Dear Yates
Answer to your query is provided below
Total Price for her vehicle will be $20600
Step-by-step explanation:
Edith's trading is worth $8000. So, without the package upgrade of the vehicle delivery charge, her cost is:
$22750 - $8000 = $14750.
Now, add the package upgrade ($5050) and the delivery charge ($800).
$14750 + $5050 + $800 = $20600.
The total cost price of the vehicle after all the expenses is given by the equation A = $ 20,500
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
The initial cost of the vehicle is = $ 22,750
Now , Edith has asked for an upgrade to a premium package for which the cost is $5050
So , the new cost of the vehicle = $ 22,750 + $ 5050 = $ 27,800
Now , the delivery charge of the vehicle = $ 700
And , the updated total price = $ 27,800 + $ 700 = $ 28,500
Now , the dealer has offered her $8000
So , the final price of the vehicle = updated total price - $ 8000
On simplifying the equation , we get
The final price of the vehicle A = $ 28,500 - $ 8,000
The final price of the vehicle A = $ 20,500
Hence , the final price of the vehicle is $ 20,500
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what is the median of this set of measurements? 10cm, 15cm, 15cm, 18cm, 20cm.
Answer:
15 cm
Step-by-step explanation:
Median means middle number
10,15,15,18,20
Answer:
15 cm
Step-by-step explanation:
The median is the number in the middle of a data set.
First, arrange the data from least to greatest.
10 cm, 15 cm, 15 cm, 18 cm, 20 cm
Now, take one number off each end of the data set until the middle number is reached.
10 cm, 15 cm, 15 cm, 18 cm, 20 cm
15 cm, 15 cm, 18 cm
15 cm
Therefore the median of the set of measurements is 15 cm.
A tree and a flagpole are on the same
horizontal ground A bird on top of the
tree observes the top and bottom of the
flagpole below it at angles of 45° and bo'
respectively. if the tree is 10.65 mhigh,
Calculate Correct to 3
figis
the height of the flagpole
significant
ures
Answer:
The height of the flagpole = 4.50m (3signifiant figures)
Question:
A tree and a flagpole are on the same
horizontal ground. A bird on top of the
tree observes the top and bottom of the flagpole below it at angles of 45° and 60° respectively. If the tree is 10.65 m high, Calculate Correct to 3 significant figures the height of the flagpole.
Step-by-step explanation:
First we have to represent the above information with a diagram to enable us solve the question.
Then label them for easy identification.
To determine the distance between the tree and flagpole, we would apply tangent rule.
Let their distance = x
Tan60 = opposite/adjacent
Tan60 = 10.65/y
Tan60 × y = 10.65
y = 10.65/Tan60
y = 10.65/1.7321
y = 6.15m
See attachment for the concluding part
Can someone help me solve this 6x+5=3x+14
Answer:
x=1/3 is the answer
Step-by-step explanation:
6x+15=3x+14
substracting 3x on both sides
6x-3x+15=3x-3x+14
3x+15=14
subtracting 15 on both sides
3x+15-15=14-15
3x=1
x=1/3
i hope this will help you
Answer:
X=3[tex]solution \\ 6x + 5 = 3x + 14 \\ or \: 6x - 3x = 14 - 5 \\ or \: 3x = 9 \\ or \: x = \frac{9}{3} \\ x = 3[/tex]
hope this helps ..
Good luck on your assignment...
The manager of a fast-food restaurant determines that the average time that her customers wait for service is 2.5 minutes. (a) Find the probability that a customer has to wait more than 4 minutes. (Round your answer to three decimal places.) (b) Find the probability that a customer is served within the first minute. (Round your answer to three decimal places.) (c) The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she doesn't want to give away free hamburgers to more than 1% of her customers. What number of minutes should the advertisement use
Answer:
a) 0.202 = 20.2% probability that a customer has to wait more than 4 minutes.
b) 0.33 = 33% probability that a customer is served within the first minute.
c) 11.5 minutes.
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
In this question:
[tex]m = 2.5, \mu = \frac{1}{2.5} = 0.4[/tex]
(a) Find the probability that a customer has to wait more than 4 minutes.
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
[tex]P(X > 4) = e^{-0.4*4} = 0.202[/tex]
0.202 = 20.2% probability that a customer has to wait more than 4 minutes.
(b) Find the probability that a customer is served within the first minute.
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
[tex]P(X \leq 1) = 1 - e^{-0.4*1} = 0.33[/tex]
0.33 = 33% probability that a customer is served within the first minute.
(c) The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she doesn't want to give away free hamburgers to more than 1% of her customers. What number of minutes should the advertisement use
We have to find x for which:
[tex]P(X > x) = 0.01[/tex]
So
[tex]P(X > x) = e^{-0.4x}[/tex]
Then
[tex]e^{-0.4x} = 0.01[/tex]
[tex]\ln{e^{-0.4x}} = \ln{0.01}[/tex]
[tex]-0.4x = \ln{0.01}[/tex]
[tex]x = -\frac{\ln{0.01}}{0.4}[/tex]
[tex]x = 11.5[/tex]
So 11.5 minutes.
on monday, it took 3 builders 5 1/2 hours to build a wall. an identical wall needs to be built on tuesday and 5 builders are available. each builder is paid £8.90 for each hour they work. work out how much each builder will be paid for the work completed on tuesday
Answer:
£29.37
Step-by-step explanation:
→ First step is to find the amount of hours it takes for 5 builders
[tex]\frac{3*\frac{11}{2} }{5} =\frac{33}{2} /5=\frac{33}{2} *\frac{1}{5} =\frac{33}{10} =3\frac{3}{10}[/tex]
→ Now we know how long 5 builder takes we need to multiply the hourly rate by their time worked
[tex]3\frac{3}{10} *8.90=\frac{33}{10} *8.90=3.3*8.90 = 29.37[/tex]
Answer:
Step-by-step explanation:
When the number of builders is increased, the hours worked will be reduced.
So, this is inverse proportion.
Number of hours worked by 5 builders = [tex]\frac{3*\frac{11}{2}}{5}\\\\[/tex]
[tex]=3*\frac{11}{2}*\frac{1}{5}\\\\=\frac{33}{10}\\\\=3\frac{1}{10}[/tex]
Amount received by each builder= 33/10 * 8.90
= £ 29.37
Which quantity is proportional to 40⁄8?
Who is correct? Explain. Tomas is correct; AC is opposite ∠B and BC is adjacent to ∠B. Iliana is correct; BC is opposite ∠B and AC is adjacent to ∠B. Both are correct because both AC and BC are opposite ∠B. Neither is correct because neither AC nor BC is opposite ∠B.
Answer:
A. Tomas is correct; AC is opposite ∠B and BC is adjacent to ∠B.
Step-by-step explanation:
edge2021
The description of Thomas is correct. AC is opposite ∠B and BC is adjacent to ∠B.
What is Right Angled Triangle?Right angled triangle are those triangle for which one of the angle is 90 degrees.
Hypotenuse of a right angled triangle is the longest side.
Opposite side with respect to an angle is the side opposite to that angle.
Adjacent side with respect to an angle is the side which is adjacent to the angle.
Given is a triangle ABC.
Here C is the right angle.
Then the side opposite to the right angle is the hypotenuse.
So AB is the hypotenuse.
Now we are describing the sides in relation to the ∠B.
Side opposite to ∠B is AC, which is the opposite side.
Side adjacent to ∠B is BC, which is the adjacent side.
This is the description of Thomas.
Hence Thomas is correct about describing the sides in relation to ∠B.
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The complete question is as follows :
Two students describe the sides of right triangle ABC in relation to ∠B. Triangle A B C is shown. Angle A C B is a right angle. Tomas : AB is the hypotenuse. AC is the opposite side. BC is the adjacent side. Iliana : AB is the hypotenuse. BC is the opposite side. AC is the adjacent side. Who is correct? Explain. Tomas is correct; AC is opposite ∠B and BC is adjacent to ∠B. Iliana is correct; BC is opposite ∠B and AC is adjacent to ∠B. Both are correct because both AC and BC are opposite ∠B. Neither is correct because neither AC nor BC is opposite ∠B.
The measure of the supplement of an angle is 42 more than 3 times the measure of the complement of an angle. Find the measure of the angle.
Answer:
126
Step-by-step explanation:
We multiply 42 × 3= 126
The measure of the angle is 126.
The measure of angle will be 66°.
What is Complementary angle?
The sum of two or more angle is 90 degree then the angle is called the complementary angle.
Given that;
The measure of the supplement of an angle is 42 more than 3 times the measure of the complement of an angle.
Now,
Let the measure of angle = x
So, We can formulate;
⇒ (180 - x) = 42 + 3 (90 - x)
Solve for x as;
⇒ 180 - x = 42 + 270 - 3x
⇒ 180 - x + 3x = 312
⇒ 2x = 312 - 180
⇒ 2x = 132
⇒ x = 66
Thus, The measure of angle will be 66°.
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Can someone plz help me solved this problem! I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer:
[tex]a. \quad 8\left(x+a\right)\\\\b. \quad 8\left(2x+h\right)[/tex]
Step-by-step explanation:
Best Regards!
Answer: (a) 8(x + a) --> 8x + 8a
(b) 8(2x + h) --> 16x + 8h
Step-by-step explanation:
f(x) = 8x²
f(a) = 8a²
[tex]\dfrac{f(x)-f(a)}{x-a}\quad = \quad \dfrac{8x^2-8a^2}{x-a}\quad = \quad \dfrac{8(x-a)(x+a)}{x-a}=\large\boxed{8(x+a)}[/tex]
f(x + h) = 8(x + h)²
= 8(x² + 2xh + h²)
= 8x² + 16xh + 8h²
f(x) = 8x²
[tex]\dfrac{f(x+h)-f(x)}{h} = \dfrac{(8x^2+16xh+8h^2)-8x^2}{h}\\\\\\.\qquad \qquad \qquad \quad =\dfrac{16xh + 8h^2}{h}\\\\\\.\qquad \qquad \qquad \quad =\dfrac{8h(2x + h)}{h}\\\\\\.\qquad \qquad \qquad \quad =\large\boxed{8(2x+h)}[/tex]
What is the sum of 2x^2-x and -x-2x^2-2
[tex]solution \\ {2x}^{2} - x + ( - x - {2x}^{2} - 2) \\ = {2x}^{2} - x - x - {2x}^{2} - 2 \\ = {2x}^{2} - {2x}^{2} - x - x - 2 \\ = - 2x - 2[/tex]
Hope it helps
Good luck on your assignment
Answer:
[tex] - 2x - 2[/tex]
Step-by-step explanation:
[tex]2 {x}^{2} - x + ( - x - 2 {x}^{2} - 2) \\ 2 {x}^{2} - x - x - 2 {x}^{2} - 2 \\ 2 {x}^{2} - 2 {x}^{2} - x - x - 2 \\ - 2x - 2[/tex]
hope this helps you.
brainliest appreciated
good luck!
have a nice day!
Which has the lowest value: 1/20, 1/80, or 1/100?
Answer:
1/100
Step-by-step explanation:
Since the numerators are all the same, the lowest value will depend on the denominators. The greater the denominator, the lower the value. Thus, the answer is 1/100
You have been assigned to determine whether more people prefer Coke or Pepsi. Assume that roughly half the population prefers Coke and half prefers Pepsi. How large a sample do you need to take to ensure that you can estimate, with 95% confidence, the proportion of people preferring Coke within 3% of the actual value? [Hint: proportion est. = 0.5] Round your answer to whole number
Answer:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]
And rounded up we have that n=1068
Step-by-step explanation:
For this case we have the following info given:
[tex] ME=0.03[/tex] the margin of error desired
[tex]Conf= 0.95[/tex] the level of confidence given
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
the critical value for 95% of confidence is [tex] z=1.96[/tex]
We can use as estimator for the population of interest [tex]\hat p=0.5[/tex]. And on this case we have that [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]
And rounded up we have that n=1068
What is (2a)^2 ? Help please
Answer:
4a²
Step-by-step explanation:
(2a)²
Distribute the square to all the terms in the bracket.
2²a²
Solve the powers if possible.
4a²
Answer:
4a²
Step-by-step explanation:
=> [tex](2a)^2[/tex]
=> [tex](2^2*a^2)[/tex]
=> 4 * a²
=> 4a²
Find the volume of the cone.
Please help fast
Answer:
[tex] \boxed{\sf Volume \ of \ cone = \frac{785}{3} \: {m}^{3} \: \: or \: \: 261.67 \: {m}^{2} } [/tex]
Given:
Diameter of cone (d)= 10 m
Height of cone (h) = 10 m
To find:
Volume of cone
Step-by-step explanation:
[tex] \sf Radius = \frac{Diameter}{2} \\ \\ \sf \implies Radius = \frac{10}{2} \: m \\ \\ \sf \implies Radius \: (r) = 5 \: m[/tex]
[tex] \sf Volume \ of \ cone = \frac{1}{3} \pi {r}^{2} h \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \pi {(5)}^{2} \times 10\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \pi \times 25 \times 10\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \pi \times 250\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \times 3.14 \times 250\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \times 785\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{785}{3} \: {m}^{3} \: \: \: \: or \: \: \: \: 261.67 \: {m}^{2} [/tex]
Answer:
262.
Step-by-step explanation:
w.k.t
r = 10\2
or , r = 5
h = 10
V=π r^2 h \3
hence ,
v=22\7 * 5^2 *10\3
261.8
after rounding up
262.
if it helps , please mark me as brainliest
Find the midpoint of AB when A=(1,-2) B=(1,-1)
Answer:
Midpoint Of AB = ( 1+1/2 , -2-1/2)
= (2/2 , -3/2)
= ( 1 , -1.5)
Hope this helps
Please mark Branliest.
Answer:
-2,0
Step-by-step explanation:
A committee of 15 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis, what is the probability that the final vote count is unanimous?
Answer:
0.006% probability that the final vote count is unanimous.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they vote yes, or they vote no. The probability of a person voting yes or no is independent of any other person. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Random voting:
So 50% of voting yes, 50% no, so [tex]p = 0.5[/tex]
15 members:
This means that [tex]n = 15[/tex]
What is the probability that the final vote count is unanimous?
Either all vote no(P(X = 0)) or all vote yes(P(X = 15)). So
[tex]p = P(X = 0) + P(X = 15)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{15,0}.(0.5)^{0}.(0.5)^{15} = 0.00003[/tex]
[tex]P(X = 15) = C_{15,15}.(0.5)^{15}.(0.5)^{0} = 0.00003[/tex]
So
[tex]p = P(X = 0) + P(X = 15) = 0.00003 + 0.00003 = 0.00006[/tex]
0.006% probability that the final vote count is unanimous.
For a specific location in a particularly rainy city, the time a new thunderstorm begins to produce rain (first drop time) is uniformly distributed throughout the day and independent of this first drop time for the surrounding days. Given that it will rain at some point both of the next two days, what is the probability that the first drop of rain will be felt between 8: 40 AM and 2: 35 PM on both days? a) 0.2479 Web) 0.0608 om c) 0.2465 d) 0.9385 e) 0.0615 f) None of the above.
Answer:
b) 0.0608
Step-by-step explanation:
As it is mentioned that the next two days i.e 24 hours, the probability of the rain is uniformly distributed
Therefore the rain probability is
[tex]= \frac{T}{24}[/tex]
where,
T = Length of the time interval
Plus, as we know that rain is independent
So let us assume the rain between the 8: 40 AM and 2: 35 PM on single day is P1 and the time interval is 5 hours 55 minutes
i.e
= 5.91666 hours long.
So, P1 should be
[tex]= \frac{5.91666}{24}[/tex]
= 0.2465
Now we assume the probability of rain on day 2 is P2
So it would be same i.e 0.2465
Since these events are independent
So, the total probability is
[tex]= 0.2465 \times 0.2465[/tex]
= 0.0608
Hence, the b option is correct
X squared plus 5x plus 6 in a factor of binomials
Answer:
(x + 3)(x + 2)
Step-by-step explanation:
Given
x² + 5x + 6
Consider the factors of the constant term (+ 6) which sum to give the coefficient of the x- term (+ 5)
The factors are + 3 and + 2 , since
3 × 2 = 6 and 3 + 2 = 5 , thus
x² + 5x + 6 = (x + 3)(x + 2)