Answer:
HCF means Highest common factor
there's no formula dear....
Find the length of KC
Answer:
54
give me brainliest please please please and follow my page
Step-by-step explanation:
To find length of KC...we need to find the length of HM and MU first ...
so....HM= 96- 78 = 14
JU = 96 + HM = 96 + 14 = 110
....
KU = 110 - JK = 110 - 82 = 28
....
UN = 105+ 82 -( 96 + 14 )
187 - 110
= 77
UC = 77 - 51 = 26
KC = UC + KU = 26 + 28 = 54
The length of [tex]\overline{KC}[/tex] along line [tex]\overline{JN}[/tex] is given as 54 (Option A) See the computation below.
How do you compute the length of [tex]\overline{KC}[/tex]?To determine the length of [tex]\overline{KC}[/tex], the length of [tex]\overline{HM}[/tex] and [tex]\overline{MU}[/tex]must first be derived.
[tex]\overline{HM}[/tex] = 96 - 78
[tex]\overline{HM}[/tex] = 14
[tex]\overline{JU}[/tex] = 96 + [tex]\overline{HM}[/tex]
= 96 + 14
[tex]\overline{JU}[/tex]= 110
[tex]\overline{KU}[/tex] = 110 - [tex]\overline{JK}[/tex]
= 110 - 82
[tex]\overline{KU}[/tex]= 28
[tex]\overline{UN}[/tex] = 105+ 82 -( 96 + 14 )
=187 - 110
[tex]\overline{UN}[/tex]= 77
[tex]\overline{UC}[/tex] = 77 - 51
[tex]\overline{UC}[/tex]= 26
Thus,
[tex]\overline{KC}[/tex] = [tex]\overline{UC}[/tex] + [tex]\overline{KU}[/tex]
[tex]\overline{KC}[/tex]= 26 + 28
[tex]\overline{KC}[/tex]= 54
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A sample of size 42 college students produced a 95% confidence interval of (3.1, 5.2) for the mean number of coats owned. Then there is a 95% chance that these 42 students own on average between 3.1 and 5.2 coats.
a. True
b. False
Answer:
b. False.
Step-by-step explanation:
According to the presented information, at the 95% confidence level, the mean number of coats owned will be between 3.1 and 5.2. That does not mean that there is a 95% chance that they will own that many coats; just that you are 95% confident that they will own the coats.
Hope this helps!
Galina had two boxes with pieces of paper in each. In the first box, each piece of paper had one possible outcome from flipping a coin 4 times (e.g. HHTH). There was one piece of paper for every possible outcome.
How many pieces of paper were in the first box?
Answer:
B
Step-by-step explanation:
Create a unique equation using the graphic above with the solution (answer) of 36.
Travis bought $9.45 worth of 49-cent stamps and 21-cent stamps. The number of 21-cent stamps was 5 fewer than the number of 49-cent stamps. Solve the equation 0.49s+0.21(s−5)=9.45 for s to find the number of 49-cent stamps Travis bought.
Answer:
15 49-cent stamps
Step-by-step explanation:
We can solve this problem with the equations 0.49(x) + 0.21(y) = 9.45 and x - 5 = y. Well, 0.49(15) + 0.21(10) = 9.45, so we know that there are 15 49-cent stamps and 10 21-cent stamps. The question is asking for the number of 49-cent stamps, so we can tell Travis bought 15 49-cent stamps.
Hope this helps! Plz give me brainliest, it will help me achieve my next rank.
The number of 49-cent stamps that Travis bought given the equation is 15.
What he number of 49-cent stamps Travis bought?Given this equation: 0.49s+0.21(s−5)=9.45 take the following steps to determine the value of s
Expand the bracket: 0.49s + 0.21s - 1.05 = 9.45Combine similar terms : 0.49s + 0.21s = 9.45 + 1.05Add similar terms: 10.50 = 0.70sDivide both sides of the equation by 0.70: s = 15To learn more about mathematical equations, please check: https://brainly.com/question/26427570
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Please help me ASAP I need this done D,: and it’s confusing me
Answer:
D.
Step-by-step explanation:
A) ∠V and ∠Y is not the alternate interior angles.
B)∠W and ∠Z is not the alternate interior angles.
C) Not this one because the reflexive property of congruence means that an angle, line segment, or shape is always congruent to itself.
D)∠VXW ≅∠ZXY because they are vertical. ∠W≅∠Y because they are right angles. So, triangles are similar by AA.
Do the table and the equation represent the
same function?
y = 390 + 11(x)
Answer:
NO
Step-by-step explanation:
Try to replace x by -50 y= 390 + 11*(-50) = -160 in the table we have -210 so the table doesn't represent the equationwhich one doesn't belong? anything helps thx!!
Answer:
in 1,2 options they r in exponential form
in 4,option also, we can write it as xpower1/2 so this also in exponential form
but in third option y=x there is no exponential form
The sum of 9 distinct positive integers is 2009. Find the maximum possible value of the greatest common divisor of these 9 numbers.
Answer:
49
Step-by-step explanation:
The greatest common divisor of the addends must also be a divisor of 2009. That number can be factored as ...
2009 = 1×2009 = 7×287 = 41×49
The largest possible factor such that the other factor can be a sum of 9 positive integers is 49.
The maximum value of the GCD is 49.
Periodically, customers of a financial services company are asked to evaluate the company's financial consultants and services. Higher ratings on the client satisfaction survey indicate better service, with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use
α = 0.05
and test to see whether the consultant with more experience has the higher population mean service rating.
Consultant A Consultant B
n1 = 16
n2 = 10
x1 = 6.82
x2 = 6.28
s1 = 0.65
s2 = 0.75
(a)
State the null and alternative hypotheses.
H0:
μ1 − μ2 ≤ 0
Ha:
μ1 − μ2 = 0
H0:
μ1 − μ2 > 0
Ha:
μ1 − μ2 ≤ 0
H0:
μ1 − μ2 ≠ 0
Ha:
μ1 − μ2 = 0
H0:
μ1 − μ2 ≤ 0
Ha:
μ1 − μ2 > 0
H0:
μ1 − μ2 = 0
Ha:
μ1 − μ2 ≠ 0
(b)
Compute the value of the test statistic. (Round your answer to three decimal places.)
(c)
What is the p-value? (Round your answer to four decimal places.)
p-value =
(d)
What is your conclusion?
Reject H0. There is sufficient evidence to conclude that the consultant with more experience has a higher population mean rating.Do not reject H0. There is insufficient evidence to conclude that the consultant with more experience has a higher population mean rating. Do not Reject H0. There is sufficient evidence to conclude that the consultant with more experience has a higher population mean rating.Reject H0. There is insufficient evidence to conclude that the consultant with more experience has a higher population mean rating.
Answer:
A) Null hypothesis; H0: μ1 − μ2 ≤ 0
Alternative hypothesis; Ha: μ1 − μ2 > 0
B) Test statistic = t = 1.878
C) p-value is 0.038823.
D) Reject the Null hypothesis H0
Step-by-step explanation:
We are given;
α = 0.05
n1 = 16
n2 = 10
bar x1 = 6.82
bar x2 = 6.28
s1 = 0.65
s2 = 0.75
A) The hypothesis is as follows;
Null hypothesis; H0: μ1 − μ2 ≤ 0
Alternative hypothesis; Ha: μ1 − μ2 > 0
B) Formula yo determine the test statistic is;
t = ((bar x1) - (bar x))/√((s1)²/n1) + (s2)²/n2))
Plugging in the relevant values, we have;
t = (6.82 - 6.28)/√((0.65)²/16) + (0.75)²/10))
t = 0.54/√(0.02640625 + 0.05625)
t = 0.54/0.2875
t = 1.878
C) The formula for the degree of freedom is;
Δ = [(s1)²/n1) + (s2)²/n2))]²/[((s1²/n1)²/(n1 - 1)) + ((s2²/n2)²/(n1 - 1))
Plugging in the relevant values, we have;
Δ = [(0.65)²/16) + (0.75)²/10))]²/[((0.65²/16)²/(16 - 1)) + ((0.75²/10)²/(10 - 1))
Δ = 0.00683205566/(0.000046486 + 0.0003515625)
Δ ≈ 17
Thus, the P-value;
From online p-value calculator from t-score and DF which i attached, we have the p-value as;
The p-value is 0.038823.
D) The p-value result is significant at p < 0.05
Thus, we reject the Null hypothesis H0
A) Null hypothesis: μ1 − μ2 ≤ 0
B) Test statistic = t = 1.878
C) The p-value is 0.038823.
D) Reject the Null hypothesis H0.
HypothesisWhat all information we have ?
α = 0.05
n1 = 16
n2 = 10
bar x1 = 6.82
bar x2 = 6.28
s1 = 0.65
s2 = 0.75
Part A)
The hypothesis is as follows;
Null hypothesis; H0: μ1 − μ2 ≤ 0
Alternative hypothesis; Ha: μ1 − μ2 > 0
Part B)
The formula to determine the test statistic is :
t = ((bar x1) - (bar x))/√((s1)²/n1) + (s2)²/n2))
t = (6.82 - 6.28)/√((0.65)²/16) + (0.75)²/10))
t = 0.54/√(0.02640625 + 0.05625)
t = 0.54/0.2875
t = 1.878
The formula to determine the test statistic is t = 1.878.
Part C)
The formula for the degree of freedom is;
Δ = [(s1)²/n1) + (s2)²/n2))]²/[((s1²/n1)²/(n1 - 1)) + ((s2²/n2)²/(n1 - 1))
Δ = [(0.65)²/16) + (0.75)²/10))]²/[((0.65²/16)²/(16 - 1)) + ((0.75²/10)²/(10 - 1))
Δ = 0.00683205566/(0.000046486 + 0.0003515625)
Δ ≈ 17
Thus, the P-value is 0.038823.
Part D)
The p-value result is significant at p < 0.05 is :
Thus, we reject the Null hypothesis H0.
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U is the set of letters of the English alphabet. X is the set of letters in the word 'triangle'. Y is the set of letters in the word 'trapezoid'. Z is the set of letters in the word 'hyperbola'. What is (Y ∩ Z)’ ∩ X? *
Answer:
(Y∩Z)∩X = {r,a,e}
Step-by-step explanation:
U = {a,b,c,d,e,f,............,z)
X = { t,r,i,a,n,g,l,e}
Y = {t,r,a,p,e,z,o,i,d}
Z = {h,y,p,e,r,b,o,l,a}
Firstly,
Y∩Z = {t,r,a,p,e,z,o,i,d} ∩ {h,y,p,e,r,b,o,l,a} [Intersection : Common Elements]
=> Y∩Z = {r,a,p,e,o}
Now,
(Y∩Z)∩X = {r,a,p,e,o} ∩ { t,r,i,a,n,g,l,e}
=> (Y∩Z)∩X = {r,a,e}
Scott has eight CDs, and he picks two to take to work each day. How many different ways can Scott choose two CDs?
Answer:
The total number of ways to select 2 CDs from 8 CDs is 28.
is -17 a natural number
━━━━━━━☆☆━━━━━━━
▹ Answer
-17 isn't a natural number
▹ Step-by-Step Explanation
Positive integers are only natural numbers, meaning negative numbers aren't natural numbers.
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
adam had used 84 wihite squares 20 more white than yellow and 15 more red than yellow. what is the number of red squares adam used.
Answer:
Number of red squares used are 79.
Step-by-step explanation:
Given that Adam had used 84 white squares.
White squares used are 20 more than that of yellow.
Let yellow squares used = [tex]x[/tex]
([tex]x[/tex] + 20) is the number of white squares used.
Also given that 15 more red than yellow
So, Number of red squares used = [tex]x+15[/tex]
To find:
Number of red squares that Adam used.
Solution:
As per given statement:
White squares used =
[tex]x+20=84\\\Rightarrow x=64[/tex]
[tex]\therefore[/tex] Number of yellow squares used, [tex]x[/tex] = 64
Number of red squares = [tex]x + 15 = 64+15 =79[/tex]
So, Number of red squares used are 79.
This is not an incomplete question, it has come from a very reliable source, please dont delete. If 60% of the students in Mr. Bobby's class are bio majors, which of the following could be the total number of students in his class? 28 32 35 39 PLZHELPTHANKS
Answer:
35 students
Step-by-step explanation:
Take the number of students in the class and multiply by 60% and see if you get an integer number
28 * .60 =16.8 not an integer
32 * .6 =19.2
35 * .6 =21 yes
39*.6 =23.4
The table shows claims and their probabilities for an insurance company.
O A. (a)
O B. (a)
Amount of Claim
$0
$50,000
$100,000
$150,000
$200,000
$250,000
Probability
0.60
0.25
0.09
0.04
0.01
0.01
O c. (a) $
OD. (a) $
(a) Calculate the expected value.
(b) How much should the company charge as an average premium so that it breaks even on its claim
costs?
(c) How much should the company charge to make a profit of $60 per policy?
Answer:
a) Expected Value of Claims = $32,000
b) Average premium per claim, in order to break-even on claim costs
= $5,333.33
c) To make a profit of $60 per policy (i.e. a total profit of $360 ($60 x 6), it must charge:
= $5,393.33 per policy
Step-by-step explanation:
a) Data and Calculations:
Amount of Claim Probability Expected Value
$0 0.60 $0
$50,000 0.25 $12,500
$100,000 0.09 9,000
$150,000 0.04 6,000
$200,000 0.01 2,000
$250,000 0.01 2,500
Expected Cost of claims = $32,000
b) Average premium per claim, in order to break-even on claim costs
= Total Claim cost divided by number of policies
= $32,000/6 = $5,333.33
c) To make a profit of $60 per policy (i.e. a total profit of $360 ($60 x 6), it must charge:
Total Claim cost + Total profit / 6 or Average Premium plus Profit per policy =
= ($32,000 + $360)/6 or $5,333.33 + $60
= $32,360/6 or $5,393.33
= $5,393.33
The total expected value is $32000, the average premium so that it breaks even on its claim costs are $5333.33 and the company charge to make a profit of $60 per policy is $5393.33.
Given :
The table shows claims and their probabilities for an insurance company.
Amount of Claim Probability Expected Value
$0 0.60 0
$50000 0.25 $12500
$100000 0.09 $9000
$150000 0.04 $6000
$200000 0.01 $2000
$250000 0.01 $2500
A) So, the total expected value is = 12500 + 9000 + 6000 + 2000 + 2500
= $32000
B) The average premium is given by:
[tex]=\dfrac{32000}{6}[/tex]
= $5333.33
C) The company charge to make a profit of $60 per policy is:
[tex]= \dfrac{32000+360}{6}[/tex]
[tex]=\dfrac{32360}{6}[/tex]
= $5393.33
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A random variable X follows the uniform distribution with a lower limit of 720 and an upper limit of 920. a. Calculate the mean and the standard deviation of this distribution. (Round intermediate calculation for standard deviation to 4 decimal places and final answer to 2 decimal places.) Mean Standard deviation b. What is the probability that X is less than 870? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Probability
(a) The support has length 920 - 720 = 200, so X has probability density
[tex]f_X(x)=\begin{cases}\frac1{200}&\text{for }720\le x\le920\\0&\text{otherwise}\end{cases}[/tex]
X has mean
[tex]E[X]=\displaystyle\int_{-\infty}^\infty xf_X(x)\,\mathrm dx=\frac1{200}\int_{720}^{920}x\,\mathrm dx=\boxed{820}[/tex]
and variance
[tex]V[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2[/tex]
The second moment is
[tex]E[X^2]=\displaystyle\int_{-\infty}^\infty x^2f_X(x)\,\mathrm dx=\frac1{200}\int_{720}^{920}x^2\,\mathrm dx=\frac{2,027,200}3[/tex]
and so
[tex]V[X]=\dfrac{2,027,200}3-820^2=\dfrac{10,000}3[/tex]
The standard deviation is the square root of the variance, so
[tex]SD[X]=\sqrt{V[X]}=\sqrt{\dfrac{10,000}3}\approx\boxed{57.73}[/tex]
(b)
[tex]P(X<870)=\displaystyle\int_{-\infty}^{870}f_X(x)\,\mathrm dx=\frac1{200}\int_{720}^{870}\mathrm dx=\frac{870-720}{200}=\boxed{0.75}[/tex]
A taxi company charges $2.25 per ride plus $0.30 per mile. Enter a linear model represents the cost, C, as a function of d, the number of miles of the ride.
Answer:
C(d) = d(2.25) + m(0.3)
Step-by-step explanation:
A taxi company charges $2.25 per ride plus $0.30 per mile.
Let d represent number of rides..
Let m represent number of Miles...
Then let C represent the total cost for each ride at a specific number of Miles.
The linear model representing the cost as a function of d the total ride
C(d) = d(2.25) + m(0.3)
The values stand independently because the customer can choose a different right and a different mile.
Charlotte is running at a rate of 9 (km)/(h) what is charlotte speed in (m)/(s)
Answer:
2.5 meters per second
Step-by-step explanation:
9x1000=9000m/h
9000/60/60=2.5m/s
Answer:
2.5 m/s
Step-by-step explanation:
convert kilometers to meters and then use a conversion calc to do the rest
a patient is taking 65 grams of medicine if it is increased by 20% how many grams are they taking
Answer:
78 grams
Step-by-step explanation:
20% is 1/5
1/5 of 65 is 13
65 + 13 = 78
brainliest?
perform the indicated operations a. 3/10+6/10. b. 1/3+2/4+1/6. c. 5/6-3/6 d. 2/3-6/10 e. 4/10×3/7 f. 1/6x6/15 g. 1/8÷4/9 h. 1/5÷3/4
Answer:
A. [tex]\frac{9}{10}[/tex]
B. 1
C. [tex]\frac{2}{6}[/tex] or [tex]\frac{1}{3}[/tex]
D. [tex]\frac{2}{30}[/tex] or [tex]\frac{1}{15}[/tex]
E. [tex]\frac{12}{70}[/tex] or [tex]\frac{6}{35}[/tex]
F. [tex]\frac{6}{90}[/tex] or [tex]\frac{1}{15}[/tex]
G. [tex]\frac{9}{32}[/tex]
H. [tex]\frac{4}{15}[/tex]
Answer:
Step-by-step explanation:
Reducing the given expressions to the lowest terms:
A. 3/10 + 6/10:
B. 1/3 + 1/4 + 1/6:
C. 5/6-3/6:
D. 2/3-6/10:
E. 4/10*3/7:
F. 1/6*6/15:
G. 1/8 divided by 4/9:
H. 1/5 divided by 3/4:
A particular fruit's weights are normally distributed, with a mean of 476 grams and a standard deviation of 36 grams. The heaviest 19% of fruits weigh more than how many grams? Give your answer to the nearest gram.
Answer:
Step-by-step explanation:
Given that:
mean (μ) = 476 grams, standard deviation (σ) = 36 grams. P(z) = 19%
The z score shows by how many standard deviation the raw score is above or below the mean. It is given by the equation:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Since the 19% weigh more, therefore 81% (100% - 19%) weigh less.
From the normal distribution table, the z score that corresponds to a probability of 81%(0.81) = 0.87
We substitute z = 0.88 in the z score equation to find the raw score. Therefore:
[tex]z=\frac{x-\mu}{\sigma}\\0.87=\frac{x-476}{36}\\ x-476=31.32\\x=31.32+476\\x=507.32\\[/tex]
x ≅ 507 grams
Therefore 19% of fruits weigh more than 507 grams
The paint used to make lines on roads must reflect enough light to be clearly visible at night. Let mu denote the true average reflectometer reading for a new type of paint under consideration. A test of
H0:μ=20 versus Ha:μ is greater than 20 will be based on a random sample of size n from a normal population distribution. What conclusion is appropriate in each of the following situations? (Round your P-values to three decimal places.)
a. n = 17, t = 3.1, α=0.05
State the conclusion in the problem context.
A. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
B. Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
C. Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
D. Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
b. n = 10, t = 1.8, α=0.01
State the conclusion in the problem context.
A. Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
B. Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
C. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
D. Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
c. n = 24, t = -0.4, p-value =
Answer:
a) D. Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
b) C. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
Step-by-step explanation:
a) We have a hypothesis test with the following hypothesis:
[tex]H_0: \mu=20\\\\H_a:\mu> 20[/tex]
The significance level is 0.05 for this right-tailed test.
The sample size is n=17.
This means we have 16 degrees of freedom.
[tex]df=n-1=17-1=16[/tex]
The test statistic has already been calculated and has a value of t=3.1.
This test is a right-tailed test, with 16 degrees of freedom and t=3.1, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>3.1)=0.0034[/tex]
As the P-value (0.0034) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that the new paint has a reflectometer reading higher than 20.
b. The hypothesis are the same as point a:
[tex]H_0: \mu=20\\\\H_a:\mu> 20[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=10-1=9[/tex]
The significance level is 0.01.
The test statistic has already been calculated and has a value of t=1.8.
This test is a right-tailed test, with 9 degrees of freedom and t=1.8, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>1.8)=0.0527[/tex]
As the P-value (0.0527) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.01, there is not enough evidence to support the claim that the new paint has a reflectometer reading higher than 20.
Which of the following are congruent? ΔSTV and ΔTVU ST and TV ∠STV and ∠SVT UV and SV ∠U and ∠S ∠TVU and ∠SVT
Answer:
ΔSTV and ΔUTV
UV and SV
∠U and ∠S
∠TVU and ∠SVT
Step-by-step explanation:
A D E F
ΔSTV And Δ UTV , UV and SV , ∠ U and ∠ S , ∠ TVU and ∠ SVT are congruent .
What is congruency?Two figures are said to be congruent if we can superimpose them on each other. For congruency there are three criteria:
three corresponding sides are equaltwo pair of corresponding sides and corresponding angles are equalTwo corresponding pairs of angles and the corresponding sides are equal.How to check congruency?For congruency firstly check first part of question which is STV and TVU triangles because two corresponding sides TS and TU and SV and UV and angle TSV and angle TUV are equal so these two triangles are congruent.
ST and TV are not congruent
angle STV AND SVT are also non congruent
UV and SV are congruent because these are shown in the figure that these are equal.
Angle U and S are congruent as these are the alternate angles of the two triangles.
Angle TVU and SVT are also congruent because these are also alternate angles.
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ABC trucking company realized that on an annual basis that distance traveled is normally distrubuted with a mean of 50,000 miles and a standard deviation of 12,000 HOw many miles will be traveled by at least 80% of the trucks
Answer:
39896 miles will be traveled by at least 80% of the trucks
Step-by-step explanation:
Given that :
the mean [tex]\mu[/tex] = 50000
standard deviation [tex]\sigma[/tex] = 12000
we are to calculate how many miles will be traveled by at least 80% of the trucks.
This implies that :
[tex]P(X > x_o) = 0.8[/tex]
Likewise;
[tex]P(X < x_o) = 1- P(X > x_o)[/tex]
[tex]P(X < x_o) = 1-0.8[/tex]
[tex]P(X < x_o) = 0.2[/tex]
We all know that
[tex]z = \dfrac{X- \mu}{\sigma}[/tex]
[tex]P(\dfrac{X- \mu}{\sigma}< \dfrac{x_o - \mu }{\sigma}) = 0.2[/tex]
[tex]P({z < \dfrac{x_o - \mu }{\sigma}) = 0.2[/tex]
Using the z table to determine the value for (invNorm (0.2)); we have ;
[tex]\dfrac{x_o - \mu }{\sigma} = invNorm (0.2)[/tex]
[tex]{x_o - \mu } = {\sigma} \times invNorm (0.2)[/tex]
[tex]{x_o } = \mu + {\sigma} \times invNorm (0.2)[/tex]
From z tables; [tex]invNorm (0.2)= -0.842[/tex]
[tex]{x_o } = 50000 + 12000 \times(-0.842)[/tex]
[tex]{x_o } = 50000 -10104[/tex]
[tex]\mathbf{{x_o } =39896}[/tex]
Thus; 39896 miles will be traveled by at least 80% of the trucks
Susan's friends Vicki, Luis, Maddy, Todd, Ron, and Geri have volunteered to help with the preparations for a party. How many ways can Susan assign someone to buy beverages
someone to arrange for food, and someone to send the invitations? Assume that no person does two jobs.
How many ways can Susan assign her volunteers?
ways
Answer:
120 ways
Step-by-step explanation:
She has 6 friends and needs 3 people to do jobs. This means that for the first job, she has 6 options for someone to buy beverages, but for the second job, she will now only have 5 options, as somebody is already buying beverages. After she assigns someone to the second job, she now has 4 people to pick from for the third job, as 2 are already doing a job. This means she has 6*5*4 ways to assign her volunteers, or 120 ways.
Which are the roots of the quadratic function f(b) = 62 – 75? Select two options.
b=573
Ob= -573
b=35
b= -35
Ob= 253
Answer:
[tex]b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}[/tex]
Step-by-step explanation:
Given
[tex]f(b) = b^2 - 75[/tex]
Required
Determine the roots
To get the root of the function, then f(b) must be 0;
i.e. f(b) = 0
So, the expression becomes
[tex]0 = b^2 - 75[/tex]
Add 75 to both sides
[tex]75 + 0 = b^2 - 75 + 75[/tex]
[tex]75 = b^2[/tex]
Take square roots of both sides
[tex]\sqrt{75} = \sqrt{b^2}[/tex]
[tex]\sqrt{75} = b[/tex]
Reorder
[tex]b = \sqrt{75}[/tex]
Expand 75 as a product of 25 and 3
[tex]b = \sqrt{25*3}[/tex]
Split the expression
[tex]b = \sqrt{25} *\sqrt{3}[/tex]
[tex]b = \±5 *\sqrt{3}[/tex]
[tex]b = \±5 \sqrt{3}[/tex]
[tex]b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}[/tex]
The options are not clear enough; however the roots of the equation are [tex]b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}[/tex]
A trough of water is 8 meters deep and its ends are in the shape of isosceles triangles whose width is 5 meters and height is 2 meters. If water is being pumped in at a constant rate of 6 m3Isec. At what rate is the height of the water changing when the water has a height of 120 cm?
Answer:
0.3 m/s
Step-by-step explanation:
The first thing is to attach the allusive graphic to the question. Now yes, let's move on to the solution that would be:
If the through is completely filtered the its volume will:
V = l * [1/2 w * h] = 1/2 l * w * h
Now we derive with respect to time and we are left with:
dV / dt = 1/2 * l * w * dh / dt
We solve by dh / dt and we have:
dh / dt = (2 / (l * w)) * (dV / dt)
We know that l = 8 and w = 5, in addition to dV / dt = 6, we replace:
dh / dt = (2 / (8 * 5)) * (6)
dh / dt = 0.3
Therefore the rate at which the height of the water changes is 0.3 m / s
The probability that an automobile being filled with gasoline also needs an
oil change is 0.25; the probability that it needs a new oil filter is 0.40; and
the probability that both the oil and the filter need changing is 0.14.
(a) If the oil has to be changed, what is the probability that a new oil
filter is needed?
(b) If a new oil filter is needed, what is the probability that the oil has to
be changed?
P(B | A) = probability of B given A
P(B | A) = P(B and A) / P(A)
thus
P(new oil filter | oil change) = P(both) / P(oil change)
= 0.14 / 0.25
(b) = 0.14 / 0.4
According to the Stack Overflow Developers Survey of 20184 , 25.8% of developers are students. The probability that a developer is a woman given that the developer is a student is 7.4%, and the probability that a developer is a woman given that the developer is not a student is 76.4%. If we encounter a woman developer, what is the probability that she is a student
Answer:
3.26%
Step-by-step explanation:
The computation of the probability that she is a student is shown below:
Percentage of student developers = 25.8% = SD
The Percentage of the developer is student = 7.4% = DS
The percentage of the developer is not student = 76.4% = ND
Based on this, the probability is
[tex]= \frac{SD \times DS}{SD \times DS + DS \times ND}[/tex]
[tex]= \frac{25.8\% \times 7.4\%}{25.8\% \times 7.4\% + 7.4\% \times 76.4\%}[/tex]
=3.26%
we simply considered all the elements