Answer:
y = 54/25
Step-by-step explanation:
y = p×q^(x-1)
when x = 1 then y = 10
so,
10 = p×q^(1-1)
or, 10 = p×1
or, p = 10
when x = 6 then y = 0.7776
0.7776=p×q^(6-1)
or, 0.7776=p×q^5
or, 0.7776=10×q⁵
[0.7776 = 7776/10000 = 486/625]
or, 486/625 = 10×q⁵
or, 486/6250=q⁵
or, [tex] \frac{ \sqrt[5]{486} }{ \sqrt[5]{6250} } = q[/tex]
or, [tex]q = \frac{3 \sqrt[5]{2} }{5 \sqrt[5]{2} } [/tex]
or, q = 3/5
so, when x = 4
y = p×q^(x-1)
y = 10×(3/5)^(4-1)
y = 10×(3/5)^3
y = 10×27/125
y = 54/25
P(A) = 1/2
P(B) = 1/3
PIAN B) = 1/6
Find P(AUB)
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
so that P(A U B) = 1/2 + 1/3 - 1/6 = 2/3
help me with this please! I don’t understand
Answer:
40/41
Step-by-step explanation:
tanB=opposite length/adjacent length
tanB=40/41
The FDA regulates that fish that is consumed is allowed to contain 1.0 mg/kg of mercury. In Florida, bass fish were collected in 53 different lakes to measure the amount of mercury in the fish. The data for the average amount of mercury in each lake is in the given table ("Multi-disciplinary niser activity," 2013). Do the data provide enough evidence to show that the fish in Florida lakes has more mercury than the allowable amount? Test at the 10% level. Use the framework below to guide your work. Hypotheses:
H0 : u = 1.0 mg/kg
HA: ul > 1.0 mg/kg
Test statistic = -10.09 p-value is approximately 1, would report 0.9999. Since this is not less than or equal to 0.10, we do not favor Ha. We would conclude that there is not enough evidence to show that the mean amount of mercury in fish in Florida lakes is more than the allowable amount Why is the p-value so high when the test statistic seems extreme?
A. The alternative is > so the p-value matches the area to the left. Since the TS is negative, this results in shading most of the curve.
B. The TS is negative so the p-value matches the area to the left and results in a very small area. This p-value reported is not correct.
C. The alternative is > so the p-value matches the area to the right. Since the TS is negative, this results in shading most of the curve.
D. The TS should be positive so the p-value matches the area to the left and results in shading most of the curve.
Answer:
Step-by-step explanation:
H0 : u = 1.0 mg/kg
HA: u > 1.0 mg/kg
Test statistic = -10.09
p-value is approximately 1, would report 0.9999
α = 10% ; 0.1
Using the Pvalue, we can make a decision pattern ;
Recall ; H0 is rejected If Pvalue < α
Here,
Pvalue Given is ' 0.99999 α = 0.1
Pvalue > α ; Hence, we fail to reject the Null ;
The actual Pvalue calculated using the test statistic will be :
Pvalue(-10.09) with test statistic value using a Pvalue calculator
Pvalue < 0.00001
Exhibit 9-2 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minute. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. Refer to Exhibit 9-2. At a .05 level of significance, it can be concluded that the mean of the population is _____.
Answer:
At a .05 level of significance, it can be concluded that the mean of the population is significantly more than 3 minutes.
Step-by-step explanation:
We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes.
At the null hypothesis, we test if the mean is of at most 3 minutes, that is:
[tex]H_0: \mu \leq 3[/tex]
At the alternative hypothesis, we test if the mean is of more than 3 minutes, that is:
[tex]H_1: \mu > 3[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
3 is tested at the null hypothesis:
This means that [tex]\mu = 3[/tex]
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minute.
This means that [tex]n = 100, X = 3.1, \sigma = 0.5[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{3.1 - 3}{\frac{0.5}{\sqrt{100}}}[/tex]
[tex]z = 2[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample mean above 3.1, which is 1 subtracted by the p-value of z = 2.
Looking at the z-table, z = 2 has a p-value of 0.9772.
1 - 0.9772 = 0.0228
The p-value of the test is of 0.0228 < 0.05, meaning that the is significant evidence to conclude that the mean of the population is significantly more than 3 minutes.
what is the vertex of the quadratic function below? y=x^2-8+1
9514 1404 393
Answer:
(4, -15)
Step-by-step explanation:
We assume you want the vertex of ...
y = x² -8x +1
We can add and subtract 16 to complete the square.
y = x² -8x +16 +1 -16
y = (x -4)² -15
Compare to the vertex form ...
y = (x -h)² +k . . . . . . . quadratic with vertex (h, k)
We see that the vertex of the given function is ...
(h, k) = (4, -15)
When two balanced dice are rolled, find the probability that either doubles or the sum of 6.
We know, the probability of an event = Favorable outcomes / Total outcomes.
In a case of two dices,
Total outcomes = 6 × 6 = 36
A.T. Q favorable outcome is a sum of 6,
Ways of obtaining a sum of 6
(1,5), (5,1), (2,4),(4,2) and (3,3). Total 5 ways in which 6 can be obtained using two dices.
Therefore, required probability (P),
P = 5/ 36
Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of kg. Interpret your answer in terms of sampling error
Answer:
The result indicates that the percentage of all samples of three men that have mean brain weights within (1.24 * sampling error) of the mean is 78.50%.
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
According to one study, brain weights of men are normally distributed with mean = 1.20 kg and a standard deviation = 0.14 kg.
Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg. Interpret your answer in terms of sampling error.
The explanation of the answers is now provided as follows:
Based on the Central limit theorem, it possible to say that the mean of sampling distribution (μₓ) is approximately equal to the population mean (μ) as follows:
μₓ = μ = 1.20 kg …………………………. (1)
Also, the standard deviation of the sampling distribution can be written as follows:
σₓ = (σ/√N) ……………………….. (2)
Where:
σ = population standard deviation = 0.14 kg
N = Sample size = 3
Substituting the values into equation (2), we have:
σₓ = 0.14 / √3 = 0.0808
Since we are to determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg, this implies that we have:
P(1.10 ≤ x ≤ 1.30)
Therefore, 1.10 and 1.30 have to be first normalized or standardized as follows:
For 1.10 kg
z = (x - μₓ) / σₓ = (1.10 - 1.20) / 0.0808 = -1.24
For 1.30 kg
z = (x - μₓ)/σₓ = (1.30 - 1.20) / 0.0808 = 1.24
The required probability can be determined when P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24).
From the normal distribution table, the following can be obtained for these probabilities:
P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24) = P(z ≤ 1.24) - P(z ≤ -1.24) = 0.89251 - 0.10749 = 0.7850, or 78.50%
Therefore, the sampling error is equal to 0.0808 which is the standard deviation of the sampling distribution.
In terms of the sampling error, the result indicates that the percentage of all samples of three men that have mean brain weights within (1.24 * sampling error) of the mean is 78.50%.
You can model that you expect a 1.25% raise each year that you work for a certain company. If you currently make $40,000, how many years should go by until you are making $120,000? (Round to the closest year.
Which equation would find the distance between the
two points show on the coordinate plane?
Answer: The third one or C
Step-by-step explanation: That is the correct distance formula.
Answer:
the last equation.
Step-by-step explanation:
you would subtract the x values, square them, and add it to the subtracted and squared y values. then take the square root of the remaining value.
please do asaaaaapppp
Answer:
D. y ≤ 2 and y ≤ x
Calculus 3 Problem:
5. The velocity field of a fluid flowing through a region in space is
F=-4 xy i+ 8y j +2 k
Find the flow along the curve r(t) = ti+t^2 j+k,
[tex]0 \leqslant t \leqslant 2[/tex]
Answer:
हेहेवोफेन्वोश्व्भ्जेहेहेहेहेहीहेह्सुउआअन्ब्य्हपन्स्न्द्कह्ध्फ्फ्ज्बिफ्न्व्मौएएएकेनेह्फिग्ग्तिर
Step-by-step explanation:
ddhxuxhdheuejeuejeiejejwoqoooeurrttqoyuxj न्क्क्द्सिइएर्रिरिर्क्जेव्व्व्द!दर्फ्ज्र्ज्द्ज74848491$=:/%*$*73829238%77-%7:8/:="829192=/:
Write in words 127075
Answer:
one lakh twenty seven thousand and seventy five
I hope this will help you
A number is chosen at random from 1 to 50. What is the probability of selecting
multiples of 10.
Answer: 25
Step-by-step explanation:
Frank sold 6,859 books in one year and 8,541 books in the next year. How many books did she sell altogether?
Answer:
15400 books
Step-by-step explanation:
in the first year he sold =6859 books
in the second year he sold =8541 books
therefore, to find the book he sold altogether
6859+8541
= 15400 books altogether
Answer:
15400 books altogether.
Explanation:
Books sold in 1st year: 6859
Books sold in 2nd year: 8541
Total books sold:
6859 + 8541 = 15400.
So for this problem I have completed most of it however, I am just missing the last box. Can someone help me on the last box please? Thank you for your help!
Let X be the random variable representing the weight of a randomly selected widget. You're given that the mean and standard deviation of X (which is normally distributed) are 41 oz and 11 oz, respectively.
Then
Pr[X > 19] = Pr[(X - 41)/11 > (19 - 41)/11] = Pr[Z > -2]
where Z follows the standard normal distribution with mean 0 and s.d. 1.
I assume you're familiar with the 68-95-99.7 rule, the important part of which says that approximately 95% of any normal distribution lies within 2 standard deviations of the mean. Mathematically, this is to say
Pr[-2σ < X < 2σ] ≈ 0.95
where σ is the s.d. of X, or in terms of Z,
Pr[-2 < Z < 2] ≈ 0.95
This means that roughly 5% of the distribution falls outside this range:
Pr[(Z < -2) or (Z > 2)] = 1 - Pr[-2 < Z < 2] ≈ 0.05
and because the distribution is symmetric about its mean, the probability of falling within either tail of the distribution is half of this, or roughly 2.5%
Pr[Z < -2] ≈ 0.05/2 ≈ 0.025
Then the probability of the complement is
Pr[Z > -2] = 1 - Pr[Z < -2] ≈ 1 - 0.025 ≈ 0.975
so that Pr[X > 19] ≈ 97.5%.
(3.5 x 10 ^ -4) ÷ (5 x 10 ^ 5) in standard form
Answer:
0.7 x 10 ^ -9
Step-by-step explanation:
(3.5 x 10 ^ -4) ÷ (5 x 10 ^ 5)
3.5 / 5 x 10 ^ -4/ 10 ^ 5
=> 0.7 x 10 ^ -9
20 POINTS please explain well
The difference of course is the symbol between the f and g letters.
The circle [tex]\circ[/tex] notation means we're doing a function composition.
Writing [tex](f \circ g)(x)[/tex] is the same as saying [tex]f(g(x))[/tex] where g is the inner function.
Here's an example
f(x) = x^2
g(x) = 3x
f( g(x) ) = ( g(x) )^2 ... note how x is replaced with g(x)
f( g(x) ) = ( 3x )^2
f( g(x) ) = 9x^2
-------------------
On the other hand, the dot notation means we multiply the f(x) and g(x) functions.
Going back to the previous example, we could say
[tex]f(x) = x^2\\\\g(x) = 3x\\\\(f \cdot g)(x) = f(x)*g(x)\\\\(f \cdot g)(x) = x^2*3x\\\\(f \cdot g)(x) = 3x^3\\\\[/tex]
Find the minimum and maximum value of the function on the given interval by comparing values at the critical points and endpoints.
y= √1+x^2 −2x, [0, 1]
Answer:
maximum: y = 1
minimum: y = 0.
Step-by-step explanation:
Here we have the function:
y = f(x) = √(1 + x^2 - 2x)
we want to find the minimum and maximum in the segment [0, 1]
First, we evaluate in the endpoints, which are 0 and 1.
f(0) =√(1 + 0^2 - 2*0) = 1
f(1) = √(1 + 1^2 - 2*1) = 0
Now let's look at the critical points (the zeros of the first derivate)
To derivate our function, we can use the chain rule:
f(x) = h(g(x))
then
f'(x) = h'(g(x))*g(x)
Here we can define:
h(x) = √x
g(x) = 1 + x^2 - 2x
Then:
f(x) = h(g(x))
f'(x) = 1/2*( 1 + x^2 - 2x)*(2x - 2)
f'(x) = (1 + x^2 - 2x)*(x - 1)
f'(x) = x^3 - 3x^2 + x - 1
this function does not have any zero in the segment [0, 1] (you can look it in the image below)
Thus, the function does not have critical points in the segment.
Then the maximum and minimum are given by the endpoints.
The maximum is 1 (when x = 0)
the minimum is 0 (when x = 1)
Find 356*27+537*373-235*73=
Answer:
Using PEMDAS the answer would be 192758
Step-by-step explanation:
(356*27)+(537*373)-(235*73)=
9612+200301-17155=
Solve
192758
Happy learning!
--Applepi101
In one year, profit fell from $1.73 billion to $1.18 billion. What was the percent decrease in profit?
Answer:
31.7919075 % decrease
Step-by-step explanation:
To find the percent decrease
Take the original amount and subtract the new amount
1.73 billion - 1.18 billion =.55 billion
Divide by the original amount
.55 billion / 1.73 billion
.317919075
Change to percent form
31.7919075 % decrease
Find a fraction equivalent to
that has a denominator of 10.
Answer:
1/10
Step-by-step explanation:
any number (1-9) as the number above the fraction line (numerator) with the number 10 below the fraction line is a fraction with a denominator of 10.
if it was 10/10, it will = 1
Find the value of x that will make A||B
Answer:
x = 4
Step-by-step explanation:
If A is parallel to B, therefore,
9x + 4 = 5x + 20 (alternate interior angles are congruent)
9x + 4 - 5x = 5x + 20 - 5x (subtraction property of equality)
4x + 4 = 20
4x + 4 - 4 = 20 - 4 (subtraction property of equality)
4x = 16
4x/4 = 16/4 (division property of equality)
x = 4
If 3^2x+1 =3^x+5, what is the value of x?
Answer:
x = 4
Step-by-step explanation:
[tex]3^{2x+1} = 3^{x+5}[/tex]
if the bases are equal then the powers must be equal as well
2x+ 1 = x+5 export like terms to same side of equation
2x - x = 5 - 1 add/subtract like terms
x = 4
What is the range of this graph ?
Answer:
D. 6
Step-by-step explanation:
Range of any data set is the difference between the maximum value and the minimum value.
From the graph given above, the least data value plotted on the graph is 1.
Minimum value = 1
The maximum data value = 7
The range of the data set = max - min
Range = 7 - 1
Range = 6
HELP ASAP PLEASE!!!!!!!!
Answer:
1
Step-by-step explanation:
1 : 1 :sqrt(2)
The legs are in the ratio of 1 to 1
tan 45 = opp side / adj side
tan 45 = 1/1
tan 45 =1
Answer:
Step-by-step explanation:
The number of bacteria in a second study is modeled by the function b_2(t)=800(1.6)^t.
What is the growth rate, r, for this equation?
Answer:
1.6 = 1 + .6 = 60% growth rate
Step-by-step explanation:
Assume that the Poisson distribution applies to the number of births at a particular hospital during a randomly selected day. Assume that the mean number of births per day at this hospital is 13.4224. Find the probability that in a day, there will be at least 1 birth.
Answer:
0.9999985 = 99.99985% probability that in a day, there will be at least 1 birth.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Assume that the mean number of births per day at this hospital is 13.4224.
This means that [tex]\mu = 13.4224[/tex]
Find the probability that in a day, there will be at least 1 birth.
This is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-13.4224}*13.4224^{0}}{(0)!} = 0.0000015[/tex]
Then
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0000015 = 0.9999985 [/tex]
0.9999985 = 99.99985% probability that in a day, there will be at least 1 birth.
Based on experience, the Ball Corporation’s aluminum can manufacturing facility in Ft. Atkinson, Wisconsin, knows that the metal thickness of incoming shipments has a mean of 0.2935 mm with a standard deviation of 0.000924 mm.
(a) A certain shipment has a diameter of 0.2963. Find the standardized z-score for this shipment.
Answer:
Step-by-step explanation:
the formula attached
which statement is true about the y- intercept of a quadratic function
a. a quadratic function can only have one y - intercept
b. a quadratic function can have up to two y-intercepts
c. the y-intercepts is also called a zero of the function
d. the y-intercept is located at the point where the value is y is 0
Answer:
A. a quadratic function can only have one y-intercep
PLz help!!
What is the degree of the polynomial
Answer:
3 maybe I'm just guessing.
now thats room for an answer again: yeah, 3 is right. its the x³ that defines the degree, its just the biggest power.
