Answer:
Step-by-step explanation:
A sector is a portion of the circle that is bounded by 2 radii forming an angle at the center of the circle. If it is folded into a cone, the radius of the sector becomes the slant height of the cone. The length of the arc formed by the sector becomes the circumference of the circular base of the cone. Therefore, to calculate the
1) Base radius, we would apply the formula,
Circumference = 2πr
Circumference = length of arc = 125/360 × 2 × 3.14 × 18
= 39.25
Radius, r = 39.25/2 × 3.14 = 6.25 cm
2) Semi vertical height, we would apply Pythagoras Theorem with the slant height of the cone being the hypotenuse, the radius being the adjacent side and the slant height being the opposite side.
h² = 18² - 6.25² = 284.9375
h = √284.9375 = 16.88 cm
3) Volume = 1/3πr²h where h represents the vertical height
Volume = 1/3 × 3.14 × 6.25² × 16.88 = 690.15 cm³
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
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
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
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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.
Determine the infinite limit.
lim (x + 6) / (x + 7)
xââ7â
Answer:
[tex]\lim_{x \to \infty} \frac{x+6}{x+7}[/tex] = 1
Step-by-step explanation:
You have to calculate the following limit:
[tex]\lim_{x \to \infty} \frac{x+6}{x+7}[/tex]
To solve the previous limit, you can factor x from numerator and denominator of the function, and use the fact that c/∞ = 0 with c a constant.
[tex]\lim_{x \to \infty} \frac{x+6}{x+7}= \lim_{x \to \infty}\frac{x(1+\frac{6}{x})}{x(1+\frac{7}{x})}=\lim_{x \to \infty}\frac{1+6/x}{1+7/x}=\frac{1+0}{1+0}=1[/tex]
Hence, the limit is 1, L = 1
. A coin is tossed three times, and the sequence of heads and tails is recorded.(a) Determine the sample space, Ω.(b) List the elements that make up the following events: i.A= exactly two tails, ii.B= at least twotails, iii.C= the last two tosses are heads(c) List the elements of the following events: i.A, ii.A∪B, iii.A∩B, iv.A∩C
Answer:
See explanation below
Step-by-step explanation:
Here a coin was tossed three times.
Let H = head & T = tail
Find the following:
a) The sample space:
Since a coin is tossed thrice, all possible outcome would be:
S = { HHH, HHT, HTH, HTT, TTT, TTH, THH, THT}
b) i) A = Exactly 2 tails: Here exactly 2 tails were recorded.
A = {HTT, TTH, THT}
ii) B = at least two tails: Here 2 or more tails were recorded.
B = {HTT, TTT, TTH, THT}
iii) C = the last two tosses are heads:
C = { HHH, THH}
c) List the elements of the following events:
i) A. This means all outcomes in A
= {HTT, TTH, THT}
ii) A∪B. A union B, means all possible outcomes present in A or B or in both
= {HTT, TTH, THT, TTT}
iii) A∩B. This means all possible outcomes of A that are present in B.
= {HTT, TTH, THT}
iv) A∩C. All outcomes A that are present in B
= {∅}
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
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.
A person tosses a coin 9 times. In how many ways can he get 3 heads?
The equation is up above I’m not sure how to use it
Answer: if he/she tosses the coin 9 times i am pretty sure he/she out of 5/9 he/she will get heads
Step-by-step explanation:
1 if he flips the coin 9 times and it spins and it flips i am pretty sure a couple times he/she will get tails or heads 2 but there is a way for him/her to get heads it flips and spins he/she is most likey to get heads 3 if he/she flips the coin and the coin keeps going the coin will flip and he/she will get heads hope this helps you :)
Construct an inscribed circle in triangle PQR by finding the incenter of the triangle.
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Explanation:
You need to know these construction techniques:
bisect an anglecreate a perpendicular through a point not on a line1. Bisect vertex angle P (as the problem statement tells you)
2. Bisect vertex angle R. This angle is chosen because it is the largest angle in the triangle. Any angle can be used, but the construction is likely to be more accurately done for larger angles.
3. The point where the angle bisectors cross is the incenter. Label that point A. It will be used as the "off-line point" for the next step.
4. Create a perpendicular to line PQ through the point A. PQ is chosen because it is the segment opposite the largest angle. This gives you the most room for the construction, so it can be done with best accuracy. Mark the the point of intersection of the perpendicular with PQ as point B.
5. Using AB as the radius, draw the incircle centered at A.
It would look something like this. I don't know if this helps or not.
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.
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!
The Bayley Scales of Infant Development yield scores on two indices--the Psychomotor Development Index (PDI) and the Mental Development Index (MDI)--which can be use to assess a child's level of functioning in each of these areas at approximately one year of age. Among normal healthy infants, both indices have a mean value of 100. As part of a study assessing the development and neurologic status of children who have undergone reparative heart surgery during the first three months of life, the Bayley Scales were administered to a sample of one-year-old infants with congenital heart disease. The data contained in the data set heart. PDI scores are saved under the variable name pdi while MDI scores are saved under mdi. Use the treatment=1 group
a. At the 0.05 level of significance, test the null hypothesis that the mean PDI score for children born with congenital heart disease who undergo reparative heart surgery during the first three months of life is equal to 100, the mean score for healthy children. Use a two-sided test. What is the p-value? What do you conclude?
b. Conduct the analogous test of hypothesis for the mean MDI score. What do you conclude?
c. Construct 95% confidence intervals for the true mean PDI score and the true mean MDI score for this population of children with congenital heart disease. Does either of these intervals contain 100? Would you have expected that they would?
Answer:
Step-by-step explanation:
Hello!
The Psychomotor Development Index (PDI) has an average value of μ= 100
The Mental Development Index (MDI) has an average value of μ= 100
At an approximate age of 1 year of normal healthy infants.
Using the group data set heart = 1 for all calculations (see attachment for complete table), you can define two variables of interest and obtain the descriptive statistics:
X₁: PDI of an infant with congenital heart disease who had to undergo reparative heart surgery during the first three months of life.
n₁= 69
X[bar]₁= 97.61
S₁= 14.73
X₂: MDI of an infant with congenital heart disease who had to undergo reparative heart surgery during the first three months of life.
n₂= 69
X[bar]₂= 106.33
S₂= 14.67
a)
You have to test the hypothesis that the average PDI for kids with congenital heart disease who have to undergo reparative heart surgery during the first three months of life is equal to 100.
H₀: μ₁ = 100
H₁: μ₁ ≠ 100
α: 0.05
[tex]Z= \frac{X[bar]_1-Mu_1}{\frac{S_1}{\sqrt{n_1} } }[/tex]≈N(0;1)
[tex]Z_{H_0}= \frac{97.61-100}{\frac{14.73}{\sqrt{69} } } = -1.347[/tex]
p-value: 0.17798
Using this approach the decision rule is:
If p-value ≤ α, reject the null hypothesis.If p-value > α, do not reject the null hypothesis.The p-value is greater than the level of significance, the decision is to not reject the null hypothesis. Then the average PDI of the kids with congenital heart disease who have to undergo reparative heart surgery during the first three months of life is equal to 100.
b)
H₀: μ₂ = 100
H₁: μ₂ ≠ 100
α: 0.05
[tex]Z= \frac{X[bar]_2-Mu_2}{\frac{S_2}{\sqrt{n_2} } }[/tex]≈N(0;1)
[tex]Z_{H_0}= \frac{106.33-100}{\frac{14.67}{\sqrt{69} } } = 3.584[/tex]
p-value: 0.000338
Using this approach the decision rule is:
If p-value ≤ α, reject the null hypothesis.If p-value > α, do not reject the null hypothesis.The p-value is less than the level of significance, the decision is to reject the null hypothesis. Then the average MDI of the kids with congenital heart disease who have to undergo reparative heart surgery during the first three months of life is different from 100.
c)
[tex]Z_{1-\alpha /2}= Z_{0.975}= 1.96[/tex]
95% CI for PDI
X[bar]₁ ± [tex]Z_{1-\alpha /2}[/tex] * [tex]\frac{S_1}{\sqrt{n_1} }[/tex]
97.61 ± 1.96 * [tex]\frac{14.73}{\sqrt{69} }[/tex]
[94.134; 101.086]
95% CI for MDI
X[bar]₂ ± [tex]Z_{1-\alpha /2}[/tex] * [tex]\frac{S_2}{\sqrt{n_2} }[/tex]
106.33 ± 1.96 * [tex]\frac{14.67}{\sqrt{69} }[/tex]
[102.869; 109.791]
The CI for the mean PDI of the kids with congenital heart disease who have to undergo reparative heart surgery during the first three months of life contains 100, this is to be expected since the null hypothesis in the hypothesis test made at complementary confidence level, was not rejected.
I hope this helps!
Let x stand for the number of calories in each individual snack. 25 snacks are sampled at a time. The population mean is 95 calories and the population standard deviation is 2.5 calories. What is the mean and standard deviation of the sampling distribution of sample means?
a. mean = 19. standard deviation = 2.5
b. mean = 95, standard deviation = 0.5
c. mean = 95, standard deviation = 2.5
d. mean = 19. standard deviation = 0.5
Answer:
b)
Mean of the sample μₓ = 95
Standard deviation of the sample (S) = 0.5
Step-by-step explanation:
Step(i):-
Given sample size 'n' = 25
Mean of the Population μ = 95 calories
Standard deviation of the Population = 2.5 calories
Step(ii):-
Mean of the sample μₓ = μ
Mean of the sample μₓ = 95
Standard deviation of the sample
[tex]= \frac{S.D}{\sqrt{n} } = \frac{2.5}{\sqrt{25} } =0.5[/tex]
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.
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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PLEASE HELP MEH please :
Answer:
2 degrees celcius
Step-by-step explanation:
If its halway between 2pm (7 deg) and 8pm (-3 Deg) then the midpoint is 2
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]
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.
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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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
The pie chart shows the age distribution in a village of 120 a) how many people are older than 60 = 120 B) What percentage of the villagers are under 25? I KNOW A I NEED TO KNOW B
Answer:
5%
Step-by-step explanation:
Plz rate thanks
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
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.
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...
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.
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”.
Suppose it takes 18 hours for a pipe to fill a tank of water, if the tank
had no leak. However, our tank has a crack that will cause a full tank to
leak out in 30 hours. If the tank starts off empty, how long will it take to
fill the leaky tank?
Answer:
Step-by-step explanation:
Let the volume of tank be x
In 18 hours volume of tank filled = x
we have to find the volume of tank which is filled in 1 hours.
For that we divide LHS and RHS by 18
In 18/18 hours volume of tank filled = x/18
In 1 hours volume of tank filled = x/18
In 30 hours volume of tank emptied = x
we have to find the volume of tank which is emptied in 1 hours.
For that we divide LHS and RHS by 30
in 30/30 hours volume of tank filled = x/30
In 1 hours volume of tank filled = x/30
If tank is empty and one starts to fill it, two things will happen
it will start filling at rate of x/18 hours
But there is leak which will start to empty the tank at x/30 hours
So , at any given time rate if filling of water will be rate of filling the tank- rate of emptying the tank
In 1 hour volume of tank filled if both filling and leaking takes place simultaneously = x/18 -x/30 = (30-18)x/18*30 = 12x/18*30 = x/3*15 = x/45
In 1 hour volume of tank filled = x/45
in 1*45 hour volume of tank filled = x/45*45 = x
Thus, it will take 45 hours to fill the leaky tank .
Which quantity is proportional to 40⁄8?
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.
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)