Answer:
d(A,B)=100
Step-by-step explanation:
The distance between two points A([tex]x_A,y_A[/tex]) and B=([tex]x_B,y_B[/tex]) is:
d(A,B)=[tex]\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}[/tex]
In this case:
[tex]x_B = - 93\\x_A = 3\\y_B = -37\\y_A = -9[/tex]
In this case:
[tex]d(A,B)=\sqrt{( - 93 -3)^2+( - 37 - (-9))^2} =\\=\sqrt{( - 96)^2+(-28)^2} =\\=\sqrt{9.216+784} \\=\sqrt{10000}=\\=\sqrt{10^4} =\\=100[/tex]
Coliform bacteria are randomly distributed in a river at an average concentration of 1 per 20cc of water. What is the variance of the number of Coliform bacteria in a sample of 40cc of water
Answer:
[tex]Var = 1.9[/tex]
Step-by-step explanation:
Given
[tex]p = \frac{1}{20}[/tex] i.e. 1 per 20cc of water
[tex]n = 40[/tex] -- sample size
Required
The variance
This is calculated using:
[tex]Var = np(1 - p)[/tex]
So, we have:
[tex]Var = 40 * \frac{1}{20} * (1 - \frac{1}{20})[/tex]
[tex]Var = 40 * \frac{1}{20} * \frac{19}{20}[/tex]
[tex]Var = 2 * \frac{19}{20}[/tex]
[tex]Var = \frac{38}{20}[/tex]
[tex]Var = 1.9[/tex]
The slope of diagonal OA IS__,
and its equation is__
Answer:
[tex](a)\ m = \frac{4}{3}[/tex] --- slope of OA
[tex](b)\ y = \frac{4}{3}x[/tex] --- the equation
Step-by-step explanation:
Given
The attached graph
Solving (a): Slope of OA
First, we identify two points on OA
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (3,4)[/tex]
So, the slope (m) is:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
This gives:
[tex]m = \frac{4-0}{3-0}[/tex]
[tex]m = \frac{4}{3}[/tex]
Solving (b): The equation
This is calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
Recall that:
[tex](x_1,y_1) = (0,0)[/tex]
[tex]m = \frac{4}{3}[/tex]
So, we have:
[tex]y = \frac{4}{3}(x - 0) + 0[/tex]
[tex]y = \frac{4}{3}(x)[/tex]
[tex]y = \frac{4}{3}x[/tex]
Solve by graphing. Round each answer to the nearest tenth.
6x2 = −19x − 15
a: −2, 1.7
b: −1.7, −1.5
c: −1.5, 1.5
d: −1.5, 1.7
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Answer:
b: -1.7, -1.5
Step-by-step explanation:
The graph is shown below. We have annotated the x-intercepts for the equivalent equation ...
6x^2 +19x +15 = 0
The probability that a person will develop the flu after getting a flu shot is 0.04. In a random sample of 100 people in a community who got a flu shot, what is the probability that 5 or more of the 100 people will get the flu
Answer:
0.3711 = 37.11% probability that 5 or more of the 100 people will get the flu
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they will develop the flu after getting the shot, or they will not. The probability of a person developing the flu after getting the shot is independent of any other person, which means that the binomial probability distribution is used 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.
The probability that a person will develop the flu after getting a flu shot is 0.04.
This means that [tex]p = 0.04[/tex]
Random sample of 100 people:
This means that [tex]n = 100[/tex]
What is the probability that 5 or more of the 100 people will get the flu?
This is:
[tex]P(X \geq 5) = 1 - P(X < 5)[/tex]
In which
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{100,0}.(0.04)^{0}.(0.96)^{100} = 0.0169[/tex]
[tex]P(X = 1) = C_{100,1}.(0.04)^{1}.(0.96)^{99} = 0.0703[/tex]
[tex]P(X = 2) = C_{100,2}.(0.04)^{2}.(0.96)^{98} = 0.1450[/tex]
[tex]P(X = 3) = C_{100,3}.(0.04)^{3}.(0.96)^{97} = 0.1973[/tex]
[tex]P(X = 4) = C_{100,4}.(0.04)^{4}.(0.96)^{96} = 0.1994[/tex]
Then
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0169 + 0.0703 + 0.1450 + 0.1973 + 0.1994 = 0.6289[/tex]
[tex]P(X \geq 5) = 1 - P(X < 5) = 1 - 0.6289 = 0.3711[/tex]
0.3711 = 37.11% probability that 5 or more of the 100 people will get the flu
PLEASE HELPP ITS AN EMERGENCY
Find the measure of angle A.
a. 23 = -11 - 4x
b. 23 = -11 + (-4x)
C. 23 + 11 = -11 + (-4x) + 11
d. 23 + 11 = -11 + 11 +(-4x)
e. 34 = - 4x
f. 34/-4 = -4x/ -4
g. -8.5 = x
Which properties of equality justify steps c and f?
A.) addition property of equality; subtraction property of equality B.) addition property of equality; division property of equality C.) subtraction property of equality; multiplication property of equality D.) multiplication property of equality; division property of equality
Answer:
B.) addition property of equality; division property of equality
If the angles (4x + 4)° and (6x – 4)° are the supplementary angles, find the value of x.
Answer:
18
Step-by-step explanation:
Supplementary angles means sum of angles is 180.
4x + 4 + 6x - 4 = 180
4x + 6x + 4 - 4 = 180
10x = 180
x = 180 / 10
x = 18
Answer:
x=18 degree
Step-by-step explanation:
If they are supplementary angles, then their sum = 180 degree
4x+4 + 6x-4 =180
4x+6x + 4-4 = 180
10x = 180
x=180/10
x=18
What is 2225 rounded to the nearest thousand? Hurry please
Answer:
2000
Step-by-step explanation:
2225 to the nearest 100 is 2300 but 3
<5 so it is 2000
Solve the system of equations using the elimination method. 5x + 10y = 3 10x + 20y = 8
Answer:
Can not be solved
Step-by-step explanation:
5x+10y = 3............. Equation 1
10x+20y = 8 ............ Equation 2
From the equation above,
both equations can not be solved by elimination method, because both variables will be eliminated
Tom swims a 1/2 kilometers every 1/4 hour. How far will he swim in one hour.
Answer:
2 kilometers
Step-by-step explanation:
every 1 kilometer is a 1/2 hour. double that and you get 2
The time spent waiting in the line is approximately normally distributed. The mean waiting time is 6 minutes and the variance of the waiting time is 9. Find the probability that a person will wait for more than 9 minutes.
Answer:
0.1587 = 15.87% probability that a person will wait for more than 9 minutes.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The mean waiting time is 6 minutes and the variance of the waiting time is 9.
This means that [tex]\mu = 6, \sigma = \sqrt{9} = 3[/tex]
Find the probability that a person will wait for more than 9 minutes.
This is 1 subtracted by the p-value of Z when X = 9. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{9 - 6}{3}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.8413.
1 - 0.8413 = 0.1587
0.1587 = 15.87% probability that a person will wait for more than 9 minutes.
I’ll mark u plz help
Answer:
D is the answer
Step-by-step explanation:
all sides and angles are equal
hope it helps!! let me know if it does
Which equation can be simplified to find the inverse of
Answer:
x=y²-7hope it helps.
stay safe healthy and happy...What is the length of my
?
M
3x
X + 8
7639
630
N
¿
O
A. 8
B. 4
C. 16
a
D. 12
Answer:
The length of MN is 4
Choose B
write the following statement in symbolic mongo are delicious but expensive .
Step-by-step explanation:
let a=mangoes are delicious
b=mangoes are expensive
the symbolic form is a^b
Find the volume of the figure. Express answers in terms of , then round to the nearest
whole number
Please help :)
Answer:
26244π in³
Step-by-step explanation:
Applying,
Voluem of a sphere
V = 4/3(πr³).......... Equation 1
Where r = radius of the sphere, π = pie
From the diagram,
Given: r = 54/2 = 27 in
Substitute these value in equation 1
V = 4/3(27³)(π)
V = 26244π in³
Hence the volume of the figure expressed in terms of π is 26244π in³
8-6•4+10divided by 2 =
Solve the system using elimination. x – y = –5 3x + y = 1
(–1, 4)
(–1, 2)
(2, –2)
(–3, 4)
Answer:
(–1,4)
Step-by-step explanation:
x – y = –5
3x + y = 1
You omit Ys due to their positive and negative signs and you got
4x = –4===> x= –1
and now place –1 inside the upper linear equation and there you have the Y, look
–1 – Y= –5===> –Y= –4===> Y = 4
(–1,4)
Please help !!!! will mark brainliest !!
Answer:
the first one
Step-by-step explanation:
Which of the following is equivalent to the product below?
Square root 3 square root 21
I NEED HELP ILL GIVE BRAINLIEST
The equivalent of the products given = 3√7
Simplifying square rootsA perfect square root is said to be a number that gives rise to an integer when it's square root is carried out. Examples are √16, √9 which is 4 and 3 respectively.
√3 × √21
But √a ×√b = √ a×b
Find the prime factors which when multiplied would give 21 = 3 and 7.
Therefore,
[tex] \sqrt{3 \times 3 \times 7} [/tex]
[tex] \sqrt{9 \times 7} [/tex]
[tex] 3 \sqrt{7} [/tex]
Therefore, the equivalent of the products of √3 × √21 =
3√7
Learn more about perfect square roots here:
https://brainly.com/question/3617398
Is 237405 divisible by 11 Correct Answer = Brainliest
Answer:
Yes.
Step-by-step explanation:
.
Log(4) 5 + log (4) ? =log(4) 35
Answer:
7
Log(4) 5 + log (4) 7 =log(4) 35
Step-by-step explanation:
Which division problem does the diagram below best illustrate?
A diagram with 8 ovals containing 4 squares each.
O 16 divided by 4 = 4
O 32 divided by 4 = 8
O 36 divided by 4 = 9
O 8 divided by 2 = 4
Answer:
The answer is 32 divided by 4
Step-by-step explanation:
Because in each box there is 4. There are 8 ovals all together. So 8×4, you get 32 and divide it by the number of squares in an oval which is 4
Answer:
the answer is 32 divided by 4=8
Step-by-step explanation:
because when you look at the ovals there's eight ovals and in side there's four squares..
HOPE THIS HELPS!!!!!
The sum of four consecutive odd integers is –72. Write an equation to model this situation, and find the values of the four integers.
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Answer:
(x -3) +(x -1) +(x +1) +(x +3) = -72-21, -19, -17, -15Step-by-step explanation:
Let x represent the even integer between the middle two odd integers. Then the sum of the four odd integers is ...
(x -3) +(x -1) +(x +1) +(x +3) = -72
4x = -72
x = -18
The four integers are -21, -19, -17, -15.
_____
Additional comment
You could let x represent one of the integers. Often, people choose to let it represent the least of them. Then the equation becomes x +(x+2) +(x+4) +(x+6) = -72, so 4x = -84 and x = -21. This introduces a "subtract 12" step in the solution process that is unnecessary if x is chosen to be the average of the integers.
As the average, x is the sum divided by the number of them, so you know x=-72/4 = -18 immediately. Then you just have to find the nearest two odd integers below and above -18. You can do the whole problem mentally.
Divide the following quantities in the following ratios £100 1:3
Geometry please someone help i cant fail this class
Test the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats at the 0.2 significance level.
Answer:
Test the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats at the 0.2 significance level.
The null and alternative hypothesis would be: H 0 : μ M = μ F H 1 : μ M < μ F H 0 : μ M = μ F H 1 : μ M > μ F H 0 : p M = p F H 1 : p M ≠ p F H 0 : p M = p F H 1 : p M < p F H 0 : p M = p F H 1 : p M > p F H 0 : μ M = μ F H 1 : μ M ≠ μ F
The test is:
right-tailed
left-tailed
two-tailed
Based on a sample of 40 men, 25%Based on a sample of 40 men, 25% owned cats
Based on a sample of 40 women, 40% owned cats
The test statistic is:
The p-value is:
Based on this we:
Reject the null hypothesis
Fail to reject the null hypothesis
if side of square is 4.05 find its area
Answer:
A
≈
16.4
please give brain list2•^4= ?
A) 1/16
B) 1/8
C) 1
Answer:
1/16.
Step-by-step explanation:
2^-4 = 1/2^4
= 1/16.
The police department in Madison, Connecticut, released the following numbers of calls for the different days of the week during a February that had 28 days: Monday (114); Tuesday (152); Wednesday (160); Thursday (164); Friday (179); Saturday (196); Sunday (130). Use a 0.01 significance level to test the claim that the different days of the week have the same frequencies of police calls. Is there anything notable about the observed frequencies
Answer:
different days of the week Do not have the same frequency.
Step-by-step explanation:
Given the data:
Observed values :
Monday (114); Tuesday (152); Wednesday (160); Thursday (164); Friday (179); Saturday (196); Sunday (130).
H0 : frequency are the same
H1 : frequency is not the same
Expected value is the same for all days:
Σ (observed values) * 1/ n
n = number of days in a week. = 7
Expected value = (114+152+160+164+179+196+130) / 7 = 156.428
χ² = Σ (observed - Expected)²/Expected
χ² = (11.508 + 0.125 + 0.082 + 0.366 + 3.257 + 10.01 + 4.465)
χ² = 29.813
The Pvalue(29.813, 6) ;
df = 7 - 1 = 6
The Pvalue(29.813, 6) = 0.000043
α = 0.01
Since, Pvalue < α ; Reject H0 ; and conclude that, different days of the week Do not have the same frequency.
