Answer:
[tex] (x_1 =2, y_1 = 6), (x_2 = 2, y_2 = 4)[/tex]
[tex] m =\frac{y_2 -y_1}{x_2 -x_1}[/tex]
And replacing we got:
[tex] m=\frac{4-6}{8-3}= -\frac{2}{5}[/tex]
And for this case we can use the first point to find the intercept like this:
[tex] 6 = -\frac{2}{5}(3) +b[/tex]
And solving we got:
[tex] b = 6 +\frac{6}{5}= \frac{36}{5}[/tex]
And then the line equation would be given by:
[tex] y = -\frac{2}{5}x +\frac{36}{5}[/tex]
Step-by-step explanation:
For this case we have the following two points given:
[tex] (x_1 =2, y_1 = 6), (x_2 = 2, y_2 = 4)[/tex]
And for this case we want an equation for a line with the two points given by:
[tex] y = mx+b[/tex]
Wher m is the slope and b the y intercept. We can find the slope with this formula:
[tex] m =\frac{y_2 -y_1}{x_2 -x_1}[/tex]
And replacing we got:
[tex] m=\frac{4-6}{8-3}= -\frac{2}{5}[/tex]
And for this case we can use the first point to find the intercept like this:
[tex] 6 = -\frac{2}{5}(3) +b[/tex]
And solving we got:
[tex] b = 6 +\frac{6}{5}= \frac{36}{5}[/tex]
And then the line equation would be given by:
[tex] y = -\frac{2}{5}x +\frac{36}{5}[/tex]
Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write all numbers as integers or simplified fractions.
7x + 6y + 4z = 10
3x + 3y + 3z - 1
4x + 4y + 4z = 2
Part: 0/2
Part 1 of 2
Evaluate the determinants D, Dx Dy and Dz.
D=
Dx=
Dy=
Dz=
Answer:
D = 0 , Dx = 4 , Dy = -6 , Dz = 2
Step-by-step explanation:
As per cramer's rule,
D = | 7 6 4 | = 0
| 3 3 3 |
| 4 4 4 |
Dx = | 10 6 4 | = 4
| 1 3 3 |
| 2 4 4 |
Dy = | 7 10 4 | = -6
| 3 1 3 |
| 4 2 4 |
Dz = | 7 6 10 | = 2
| 3 3 1 |
| 4 4 2 |
Luggage checked-in at Airline A arrives on time to its intended destination with a probability of 0.63. In a random sample of 2000 bags, what would be the mean number of bags (out of the 2000) that arrive on time to its intended destination. Also find the standard deviation. Group of answer choices
Answer:
The mean number of bags that arrive on time to its intended destination is 1260 with a standard deviation of 21.59.
Step-by-step explanation:
For each bag, there are only two possible outcomes. Either it arrives on time to it's intended destination, or it does not. The probability of a bag arriving on time is independent of other bags. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Luggage checked-in at Airline A arrives on time to its intended destination with a probability of 0.63.
This means that [tex]p = 0.63[/tex]
In a random sample of 2000 bags
This means that [tex]n = 2000[/tex]
Mean and standard deviation of the number of bags that arrive on time to its intended destination:
[tex]E(X) = np = 2000*0.63 = 1260[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{2000*0.63*0.37} = 21.59[/tex]
The mean number of bags that arrive on time to its intended destination is 1260 with a standard deviation of 21.59.
HELPPPPPPWhich is the simplified form of -7 +5-12?
1
12
S
O M - 512
12
S
o
1
12
S
Answer:
Step-by-step explanation:
[tex]r^{-7} +s^{-12} \\Use Negative Power Rule: x^{-a} =\frac{1}{x^{a} } \\r^{\frac{1}{7} } +s^{\frac{1}{12} } \\[/tex]
I hope i am correct
A sample of carbon-12 has a mass of 6.00 g. How many atoms of carbon-12 are in the sample?
3.01 x 10^23
6.02 x 10^23
1.20 x 10^24
3.60 x 10^24
Answer:
The answer is 3.01 x 10’23
Step-by-step explanation:
I got the answer to wrong and guessed the first one and it was correct
A gas company president for a particular city is interested in the proportion of homes heated by gas. Historically, the proportion of homes heated by gas has been 0.72. A sample of 75 homes was selected and it was found that 45 of them heat with gas. Perform the appropriate test of hypothesis, at level .05, to determine whether the proportion of home heated by gas has changed. Group of answer choices
Answer:
p-value (0.0208) is less than alpha = 0.05 reject H0.
Step-by-step explanation:
we have the following data:
sample size = n = 75
x, the number to evaluate is 45
the sample proportion would be: x / n = 45/75
p * = 0.6
Now, the null and alternative hypotheses are:
H0: P = 0.72
Ha: P no 72
two tailed test
statistic tes = z = (p * - p) / [(p * (1-p) / n)] ^ (1/2)
replacing we have:
z = (0.6 - 0.72) / [(0.72 * (1-0.72) / 75)] ^ (1/2)
z = -2.31
p-vaule = 2 * p (z <-2.31)
using z table, we get:
p-vaule = 2 * (0.0104)
p-vaule = 0.0208
Therefore, p-value (0.0208) is less than alpha = 0.05 reject H0.
Which is the correct classification of StartFraction 3 Over 8 EndFraction?
Answer:
Classifications would include
Rational; Fraction; Can be turned into Decimal; Positive
Those would be classifications
Answer: rational number, 0.375
Step-by-step explanation:
help!! Algebra 1!!
sorry if the picture is bad
Answer:
The first one matches with f(x)√x because a square root cannot be negative
The second one matches with f(x)=√(x-5) because the square root would be negative if it were less than five.
The third one matches with f(x)=8x because there is nothing that makes it a not possible answer
The last one matches with 7/(x-8) because there cannot be a denominator of zero.
find the LCM
of
75, 5,3
Answer:
LCM = 75
Step-by-step explanation:
1: Multiply the factor by the greatest number
Description:
The least common multiple for 75,5,3 is 75.
LCM= Least common Multiple
Please mark brainliest
Hope this helps.
Answer:
75
Step-by-step explanation:
Break each number into prime factors
75 = 25*3 = 5*5*3
5 = 5*1
3 = 3*1
Multiply by the greatest number of each factor
3 = 1 time
5 = =2 times
The least common multiple = 3 * 5*5 = 75
What is the quotient of (x3-x2-17x-15) / (x-5)
Answer:
Step-by-step explanation:
x
2
+
4
x
+
3
x
2
+
4
x
+
3
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
B. (f + g)(x) = x - 7
Step-by-step explanation:
→Set it up, like so:
-3x - 5 + 4x - 2
→Add like terms (-3x and 4x, -5 and -2):
x - 7
What are the zeroes of the polynomial x(x²+4x-12)
Answer:
x= 0, 2, -6
Hope this helps!
• Write the number that is 10 more than 178.25:
Step-by-step explanation:
10 more than 178.25 is add so
178.25 + 10 = 188.25
Solve the inequality for x
Answer:
see below
Step-by-step explanation:
[tex]\frac{x-c}{d} > y[/tex]
x - c > dy
x > dy + c
In a completely randomized design involving three treatments, the following information is provided: Treatment 1 Treatment 2 Treatment 3 Sample Size 5 10 5 Sample Mean 4 8 9 The overall mean for all the treatments is a. 7.00 b. 6.67 c. 7.25 d. 4.89
Answer:
c. 7.25
Step-by-step explanation:
Given the following information from an experiment:
[tex]\left\begin{array}{ccc}&$Sample Size&$Sample Mean \\$Treatment 1&5&4\\$Treatment 2&10&8\\$Treatment 3&5&9\end{array}\right[/tex]
Total Sample Size =5+10+5=20
Therefore, the overall mean
[tex]=\dfrac{(5 \times 4)+ (10 \times 8) + (5 \times 9)}{20} \\=\dfrac{145}{20}\\\\=7.25[/tex]
m is directly proportional to r squared when r=2 m=14 work out the value of r when m = 224
Answer:
32
Step-by-step explanation:
r:m
2:14
1:7
m=224
r=224 divided by 7
224/7=32
Edit: unless it is proportional to r^2 in which case it is a different answer
Answer:
m=504
Step-by-step explanation:
Mr Chan flies from London to Los Angeles, a distance of 8800 km.
The flight takes 11 hours and 10 minutes.
His plane leaves London at 09 35 local time.
The local time in Los Angeles is 8 hours behind the time in London.
Calculate the local time when the plane arrives in Los Angeles.
Answer:
12 45
Step-by-step explanation:
plane leaves London at 09 35
plane arrives in Los Angeles after 11 hrs and 10 min
considering time difference:
11 10 - 8 00= 03 10local arrival time:
09 35 + 03 10= 12 45 local timeNoah has a t-shirt collection. Three-eighths of the t-shirts are blue. Of the blue t-shirts,two-ninths of them have a pocket. What fraction represents the numbers of t-shirts that are blue and have a pocket?
Answer:
1/12
Step-by-step explanation:
blue = (3/8)collection
blue&pocket = (2/9)blue = (2/9)(3/8)collection
blue&pocket = (6/72)collection = (1/12)collection
1/12 of Noah's collection is blue and has a pocket.
Determine whether the numerical value in braces is a parameter or a statistic. Explain your reasoning. In a certain soccer league (43%) of the 14 teams had won more games than they had lost.
Choose the correct answer below.
a. Statistic, because the data set of a sample of teams in a league is a sample.
b. Statistic, because the data set of a sample of teams in a league is a population.
c. Parameter, because the data set of all 14 teams is a population.
d. Statistic, because the data set of all 14 teams is a sample.
e. Parameter, because the data set of all 14 teams is a sample.
f. Parameter, because the data set of a sample of teams in a league is a population.
g. Parameter, because the data set of a sample of teams in a league is a sample.
h. Statistic, because the data set of all 14 teams is a population.
Answer:
C. Parameter since the data set of all 14 teams is a population.
Explanation:
Find the attachment
:4. In the Department of Natural Sciences, 14 faculty members have a PhD, and 30 faculty members do not have a PhD. In the Department, the number of female faculty who do not have a PhD is 10 more than the number of females who have a PhD. If a third of the male faculty in the Department have a PhD, then what is the number of female faculty in the Department with a PhD?
Answer:
The number of female faculty in the Department with a PhD is 8.
Step-by-step explanation:
There are 14 + 30 = 44 faculty members.
Of those, x are male and y are female.
Then
x + y = 44.
The number of female faculty who do not have a PhD is 10 more than the number of females who have a PhD.
y = z + w
z is the number of females with PhD.
w is the number of females without PhD.
w = z + 10
If a third of the male faculty in the Department have a PhD
[tex]\frac{x}{3} + z = 14[/tex]
Now, we can write all variables as functions of z, which is the number of female faculty in the Department with PhD.
The objective is:
To find z from the first equation, that is:
[tex]x + y = 44[/tex]
To do this, we have to write x and y as functions of z.
Writing x and y as functions z.
[tex]\frac{x}{3} + z = 14[/tex]
[tex]\frac{x}{3} = 14 - x[/tex]
[tex]x = 3(14 - z)[/tex]
[tex]x = 42 - 3z[/tex]
And
[tex]y = z + w[/tex]
In which
[tex]w = 10 + z[/tex]
So
[tex]y = z + 10 + z[/tex]
[tex]y = 2z + 10[/tex]
Replacing:
[tex]x + y = 44[/tex]
[tex]42 - 3z + 2z + 10 = 44[/tex]
[tex]-z + 52 = 44[/tex]
[tex]z = 52 - 44[/tex]
[tex]z = 8[/tex]
The number of female faculty in the Department with a PhD is 8.
what is the solution? X - 7 > -6
Answer:
x > 1
Step-by-step explanation:
Add 7 to both sides
x > 1
(TEKS 2A.) EF has endpoints E (8,3) and F(-4,9). What is the distance of the given segment?
A 8.544
C 11.250
B 10.345
D 13.416
The Toylot company makes an electric train with a motor that it claims will draw an average of only 0.8 ampere (A) under a normal load. A sample of nine motors was tested, and it was found that the mean current was x= 1.22 A, with a sample standard deviation of s = 0.44 A. Do the data indicate that the Toylot claim of 0.8 A is too low? (Use a 1% level of significance.)
1. What are we testing in this problem?
a. single proportion
b. single mean
2. What is the level of significance?
3. State the null and alternate hypotheses.
4. What sampling distribution will you use? What assumptions are you making?
a. The Student's t, since we assume that x has a normal distribution with known σ
b. The standard normal, since we assume that x has a normal distribution with known σ.
c. The standard normal, since we assume that x has a normal distribution with unknown σ.
d. The Student's t, since we assume that x has a normal distribution with unknown σ.
Answer:
1. B
Step-by-step explanation:
1. We are testing against the null hypothesis which is a single mean that sauce the average load is 0.8A
2. The level of significance is 1% (99% confidence interval)
3. The null hypothesis: u = 0.8
Alternative hypothesis: u =/ 0.8
4. a. The Student's t, since we assume that x has a normal distribution with known σ
5. Using the formula t = (x - u) / σ√n
Where x = 1.22 u = 0.8 σ = 0.44 n = 9
t = (1.22-0.8) / 0.44√9
t = 0.42/(0.44x3)
t = 0.42/1.32
t = 0.318
P value for 0.318 at 1% level of significance at 8 degree of freedom is 0.7586. Since our p value here is greater than 0.01, we can convince that there is not enough statistical evidence that indicate that the Toylot claim of 0.8 A is too low.
Leila runs each lap in 6 minutes. She will run less than 9 laps today. What are the possible numbers of minutes she will run today? Use t for the number of minutes she will run today. Write your answer as an inequality solved for t.
Answer:
I'm not sure if Leila is allowed to run 0 laps.
6 ≤ t ≤ 48
Step-by-step explanation:
To find the number of possible laps, you just find the smallest possible number and the largest.
1 = smallest
8 = largest
But, you have to multiply by 6 to find the time.
6 ≤ t ≤ 48
Find the function value. tan495°
Answer: -1
Step-by-step explanation:
You want to find an angle that is coterminal to 495. So, subtract 360 degrees until youre in the range of 0-360. I got 495 - 360 = 135°
Tangent is equal to [tex]\frac{sin(theta)}{cos(theta)}[/tex], we already solved theta which was 135°
This next part is hard to explain to someone who doesnt know their trig circle, idk if you do. The angle 135 is apart of the pi/4 gang. So we know this is going to be some variant of √2/2. Sine of quadrant 1 and 2 is gonna be positive:
[tex]sin135=\frac{\sqrt{2} }{2}[/tex]
Now lets do cosine of 135°, which again is apart of the pi/4 gang because its divisible by 45°. Its in quadrant 2 so the cosine will be negative.
[tex]cos135=-\frac{\sqrt{2} }{2}[/tex]
The final step is to divide them. They are both fractions so you should multiply by the reciprocal.
[tex]\frac{\sqrt{2} }{2} *-\frac{2}{\sqrt{2} } =-\frac{2\sqrt{2} }{2\sqrt{2} } =-1[/tex]
(X+3)/6=5/4 what is x
Answer:
x = 9/2
Step-by-step explanation:
(x+3)/6=5/4
(x+3)/6*6=5/4*6
x+3=30/4
x+3-3=30/4-3
x=9/2
which products have the same sign as (-2 3/7) (-6/11) check all that apply
A.) 3/8(-6/7)
B.) 1 2/9(2 16/17)
C.) -9/20(3 4/5)
D.) -1/3 (-2/3
hurry answer pls
Answer: Options B and D.
Step-by-step explanation:
We start with the equation:
(-2 3/7)*(-6/11)
now, you need to recall the signs relations:
(+)*(+) = +
(-)*(+) = -
(-)*(-) = +
Then our initial equation has a positive sign.
a) (3/8)*(-6/7) here we have (+)*(-), so this is negative, this option is not correct.
b) (1 2/9)*(2 16/17) here we have (+)*(+), so this is positive, this option is correct.
c) (-9/20)*(3 4/5) here we have (-)*(+), so this is negative, this option is not correct.
d) (-1/3)*(-2/3) here we have (-)*(-), so this is positive, then this option is correct.
Answer:
The awnser is B and D
Step-by-step explanation:
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Answer:
1
Step-by-step explanation:
divide vertical drop by horizontal drop
or vertical increase by horizontal increase
for example, in the graph when y increases by 1 x increases by 1
1/1=1 and thus the gradient is 1
the whole equation is y=x+3
Answer:
The slope = 1.
Step-by-step explanation:
If we count squares down for the top arrow then left to the point where the line cuts the horizontal axis we get 10 and 10.
So the slope = 10/10 = 1.
PLEASE HELP QUICKLY AS POSSIBLE THANK YOU :)
Answer:
Option (B).
Step-by-step explanation:
From the table shown in the figure attached,
There is a common difference of 5 in every successive and previous term, so the relation is a linear relation.
Let the equation representing the relation is,
y - y' = m(x - x')
where m = slope of the line
Now we choose two ordered pairs from the table,
Let the points are (10, 54) and (11, 59)
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
m = [tex]\frac{59-54}{11-10}[/tex]
m = 5
Now the equation of of the line passing through (10, 54) and slope = 5
y - 54 = 5(x - 10)
y - 54 = 5x - 50
y = 5x - 50 + 54
y = 5x + 4
By substituting the values of x and y from the ordered pairs given in the options we find option B satisfies the equation.
For (2, 14),
14 = 5×2 + 4
14 = 14 [True]
For (3, 19),
19 = 5×3 + 4
19 = 19 [True]
Therefore, option (B) will be the answer.
The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9 ppm and standard deviation 1.5 ppm. 38 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.
1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. What is the probability that one randomly selected city's waterway will have more than 9.6 ppm pollutants?
4. For the 37 cities, find the probability that the average amount of pollutants is more than 9.6 ppm.
5. For part d), is the assumption that the distribution is normal necessary? YesNo
6. Find the IQR for the average of 37 cities.
Q1 = ppm
Q3 = ppm
IQR: ppm
Answer:
Step-by-step explanation:
Hello!
There are two values of n in the text, I'll use the one that appears in all the questions.
The variable of interest is
X: pollutants found in waterways near large cities. (ppm)
This variable has a normal distribution with parameters μ= 9ppm and σ= 1.5ppm
1) X~N(μ;σ²)
X~N(9;2.25)
2) The distribution of the sample mean is X~N(μ;σ²/n)
σ²/n= 2.25/37= 0.06
X~N(9;0.06)
3) P(X>9.6)
To calculate this probability you have to use the standard normal distribution. Using the population parameters, you can calculate the corresponding Z value:
Z= (X-μ)/σ= (9.6-9)/1.5= 0.4
P(Z>0.4)= 1-P(Z≤0.4)= 1 - 0.65542= 0.34458
The probability of selecting a city at random and finding 9.6ppm pollutants.
4) In this item, instead of calculating the probability of one value of the variable you have to calculate the probability of the sample average taking a determined value. Because of this, you have to work using the distribution of the sample mean, instead of the distribution of the variable.
P(X[bar]>9.6)
Z= (X[bar]-μ)/(σ/√n)= (9.6-9)/√0.06= 2.45
P(Z>2.45)= 1 - P(Z≤2.45)= 1 - 0.99286= 0.00714
5) The assumption of a normal distribution is not necessary for item 4. Since the sample size is large enough (greater than 30) you can apply the central limit theorem and approximate the distribution of the sample mean to normal, regarding the distribution of the original variable.
6)
In this case, you have to work starting with the standard normal distribution and then "translate" the Z values into values of the average amount of pollutants.
The first quartile divides the bottom 25% of the distribution from the top 75%, symbolically:
P(Z≤z₁)= 0.25
z₁= -0.674
z₁= (X[bar]-μ)/(σ/√n)
z₁*(√n/σ)=X[bar]-μ
X[bar]=z₁*(√n/σ)+μ
X[bar]=(-0.674)*(√37/1.5)+9= 6.27ppm
The third quartile divides the bottom 75% of the distribution from the top 25%, symbolically:
P(Z≤z₂)= 0.75
z₂= 0.674
z₂= (X[bar]-μ)/(σ/√n)
z₂*(√n/σ)=X[bar]-μ
X[bar]=z₂*(√n/σ)+μ
X[bar]=(0.674)*(√37/1.5)+9= 11.7.3ppm
IQR= Q₃-Q₁= 11.73-6.27= 5.46ppm
I hope this helps!
The altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 4 and 12. Find the length of the shorter leg of the right triangle.
Answer:
8 units.
Step-by-step explanation:
The smaller of the right triangles formed is similar to the whole triangle so
4/x = x/16 where x = the shorter leg
x^2 = 64
x = 8.
The length of the shorter leg of the right triangle is 3 units.
Let's denote the length of the shorter leg of the right triangle as "x." Since the altitude drawn to the hypotenuse divides it into segments of lengths 4 and 12, we can set up a proportion between the two triangles formed.
According to the similarity of triangles, the length of the shorter leg to the length of the segment of the hypotenuse it divides is the same as the length of the longer leg to the length of the other segment of the hypotenuse.
So, we can set up the proportion:
x / 4 = 12 / (hypotenuse length).
Now, we know that the hypotenuse length is equal to the sum of the two segments (4 + 12 = 16). We can substitute it into the proportion:
x / 4 = 12 / 16.
Now, cross-multiply and solve for x:
16x = 4 * 12,
16x = 48,
x = 48 / 16,
x = 3.
To learn more about triangle click on,
https://brainly.com/question/30847435
#SPJ2