Answer:
1/4 of his income.
Step-by-step explanation:
If Wilbur spends 2/3 of his income, 1/3 or 4/12 of it is left for other purposes (It is easier if everything has a common denominator of 12). And if he shares 1/12 of that remaining amount, there is 3/12 left. And when we simplify 3/12, we get 1/4.
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How many moles of H2 would be required to produce 9.0 grams of water? 10
2 H2 + O2 + 2 H20
Answer:
8.1 moles
Step-by-step explanation:
Given parameters: Mass of water to be decomposed = 29.2g Unknown: Number of moles of oxygen. Solution: To solve this problem, we first write the balanced reaction equation : 2H₂O → 2H₂ + O₂ Now convert the given mass of the water to number of moles; Number of moles of water = Molar mass of water = 2(1) + 16 = 18g/mol Number of moles of water = = 16.2moles From the balanced reaction equation: 2 moles of water produced 1 mole of oxygen gas; 16.2 mole of water will produce = 8.1moles of oxygen gas
Hope this helps you :3
Suppose you are constructing either a mean chart with known variation or a p-chart to monitor some process. The process will only be stopped if a sample taken falls outside your control limits. If the process is in control, management wants only 12.6% of the samples taken to fall outside of your limits. (The company does not like stopping the process "accidentally.") What Z value should you use for your chart?
Answer:
1.53
Step-by-step explanation:
Find the attachment for explanation
The z-value corresponding to the probability of 0.937 using the standard normal distribution table is 1.53 and this can be determined by using the given data.
Given :
Suppose you are constructing either a mean chart with a known variation or a p-chart to monitor some process. The process will only be stopped if a sample taken falls outside your control limits.The process is in control, management wants only 12.6% of the samples taken to fall outside of your limits.Assuming that the distribution is normal so the probability for being within the maximum limit is given by:
[tex]\rm P=1-\dfrac{6.3}{100}[/tex]
P = 0.937
Now, the z-value corresponding to the probability of 0.937 using the standard normal distribution table is 1.53.
Therefore, the correct option is D) 1.53.
For more information, refer to the link given below:
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Complete each statement in the steps to solve x2 – 4x + 3 = 0 using the process of completing the square.
Answer:
x= 3,1
Step-by-step explanation:
-b ± √b²-4(ac)/2a
4 ± √(-4)² - 4 · (1·3)/2·1
x = 2 ± 1
x = 3,1
What is the value of the expression: 4.6+(-3.2)
Answer:
1.4
Step-by-step explanation:
4.6 + (- 3.2)
A plus sign and a minus sign results in a minus sign
Re-write the expression without the parenthesis
4.6 - 3.2
Subtract
1.4
Hope this helps :)
Answer:
the answer is attached to the picture
A subtending arc on a circle with a radius of 4.5 centimeters has an arc length of 8π. The measure of the angle subtended by the arc is ?
Answer: 320°
Step-by-step explanation:
This is a circle geometry.
The arc length of the circle is given to be 8πcm and the radius is 4.5cm.
Now the length of an arc of a circle is
Arc length = πr0°/180° or 2πr0°/360°
To find the angle 0° subtend at the center we equate the arc length with the formula and solve for 0°.Now we go
πr0°/180 = 8π, convert to a simple linear equal and solve for the angle.
πr0° = 8π × 180
0°. = 8π × 180
-----------
π × r
= 8 × 180. 8 × 180
-------- or ---------
9/2. 4.5
= 8 × 180 × 2
------------
9
= 8 × 20 × 2
= 320°
or 8 × 180/4.5
= 1440/4.5
= 320°
Kate has 48 softballs. She wants to divide them evenly among b softball bags. Which expression represents how many softballs she should put into each bag? a. 48/b, b. 48b, c. b/48, d. 48-b.
Answer:
A
Step-by-step explanation:
48 softballs
Divided among b bags
Divide 48 by b
48 ÷ b
Division expressions can also be written as fractions
Rewrite
48/b
The correct answer is A, 48/b
Hope this helps :)
Final answer:
Kate should use the expression 48/b to determine how many softballs go into each bag, which means dividing 48 softballs by the number of bags she has.
Explanation:
The expression that represents how many softballs Kate should put into each bag is 48/b. This expression shows that Kate will divide her total number of 48 softballs by the variable b, which represents the number of softball bags she has. The correct choice is therefore a. 48/b, which suggests that each bag will receive an equal share of the total softballs.
A manufacturer of car batteries claims that the batteries will last, on average, 3 years with a variance of 1 year. If 5 of these batteries have lifetimes of 1.9, 2.4, 3.0, 3.5, and 4.2 years, construct a 95% confidence interval for σ2 and decide if the manufacturer’s claim that σ2 = 1 is valid. Assume the population of battery lives to be approximately normally distributed.
Answer:
[tex]\frac{(4)(0.903)^2}{11.143} \leq \sigma^2 \leq \frac{(4)(0.903)^2}{0.484}[/tex]
[tex] 0.293 \leq \sigma^2 \leq 6.736[/tex]
And in order to obtain the confidence interval for the deviation we just take the square root and we got:
[tex] 0.541 \leq \sigma \leq 2.595[/tex]
Since the confidence interval cointains the 1 we don't have enough evidence to reject the hypothesis given by the claim
Step-by-step explanation:
Data provided
1.9, 2.4, 3.0, 3.5, and 4.2
We can calculate the sample mean and deviation from this data with these formulas:
[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex] s=\frac{\sum_{i=1}^n (X_i-\bar X)^2}{n-1}[/tex]
And we got:
[tex]\bar X= 3[/tex]
s=0.903 represent the sample standard deviation
n=5 the sample size
Confidence=95% or 0.95
Confidence interval
We need to begin finding the confidence interval for the population variance is given by:
[tex]\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}[/tex]
The degrees of freedom given by:
[tex]df=n-1=5-1=4[/tex]
The Confidence level provided is 0.95 or 95%, the significance is then[tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical values for this case are:
[tex]\chi^2_{\alpha/2}=11.143[/tex]
[tex]\chi^2_{1- \alpha/2}=0.484[/tex]
And the confidence interval would be:
[tex]\frac{(4)(0.903)^2}{11.143} \leq \sigma^2 \leq \frac{(4)(0.903)^2}{0.484}[/tex]
[tex] 0.293 \leq \sigma^2 \leq 6.736[/tex]
And in order to obtain the confidence interval for the deviation we just take the square root and we got:
[tex] 0.541 \leq \sigma \leq 2.595[/tex]
Since the confidence interval cointains the 1 we don't have enough evidence to reject the hypothesis given by the claim
In a certain city, there are about one million eligible voters. A simple random sample of size 10,000 was chosen to study the relationship between gender and participation in the last election. The results were: Men Women Voted 2744 3733 Didn't Vote 1599 1924 If we are testing for a relationship between gender and participation in the last election, what is the p-value and decision at the 5% significance level? Select the [p-value, Decision to Reject (RH0) or Failure to Reject (FRH0)]
Answer:
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportion of women that vote is differs from the proportion of men that vote.
P-value=0.0036 (two tailed test).
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the proportion of women that vote is differs from the proportion of men that vote.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
Being π1: proportion of men that vote, and π2: proportion of women that vote.
The significance level is 0.05.
The sample 1 (men), of size n1=(2744+1599)=4343 has a proportion of p1=0.6318.
[tex]p_1=X_1/n_1=2744/4343=0.6318[/tex]
The sample 2 (women), of size n2=(3733+1924)=5657 has a proportion of p2=0.6599.
[tex]p_2=X_2/n_2=3733/5657=0.6599[/tex]
The difference between proportions is (p1-p2)=-0.0281.
[tex]p_d=p_1-p_2=0.6318-0.6599=-0.0281[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{2744+3733}{4343+5657}=\dfrac{6477}{10000}=0.6477[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.6477*0.3523}{4343}+\dfrac{0.6477*0.3523}{5657}}\\\\\\s_{p1-p2}=\sqrt{0.00005+0.00004}=\sqrt{0.00009}=0.0096[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.0281-0}{0.0096}=\dfrac{-0.0281}{0.0096}=-2.913[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]P-value=2\cdot P(t<-2.913)=0.0036[/tex]
As the P-value (0.0036) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportion of women that vote is differs from the proportion of men that vote.
which of the following is the inverse of f(x)=3-14x
Answer:
f(x)=-3+14x
Step-by-step explanation:
its the opposite
The inverse of the following function f(x)=3-14x will be [tex]f^-(x)[/tex] = [3 -f(x)]/14.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
A function can be regarded as a computer, which is helpful.
A function is basically a relationship between which one variable will be dependent and another will be independent.
For example, let's say y = sinx then here x will be independent but y will be dependent.
In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +9 like that.
Given that the function
f(x)=3-14x
⇒ f(x) + 14x =3
⇒ 14x = 3 -f(x)
⇒ x = [3 -f(x)]/14 hence, it will be the correct answer.
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Jimmy has 14 apples and 6 bananas. If he gives half of his fruit to Lisa, how many bananas did he give away? Please help
Answer:
3
Step-by-step explanation:
14/2=7 6/2=3 7+3=10 which is also half of 20 (20 is how many fruits he has) He gave away 3 bananas
Suppose SAT Writing scores are normally distributed with a mean of 488488 and a standard deviation of 111111. A university plans to award scholarships to students whose scores are in the top 8%8%. What is the minimum score required for the scholarship? Round your answer to the nearest whole number, if necessary.
Answer:
The minimum score required for the scholarship is 644.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 488, \sigma = 111[/tex]
What is the minimum score required for the scholarship?
Top 8%, which means that the minimum score is the 100-8 = 92th percentile, which is X when Z has a pvalue of 0.92. So it is X when Z = 1.405.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.405 = \frac{X - 488}{111}[/tex]
[tex]X - 488 = 1.405*111[/tex]
[tex]X = 644[/tex]
The minimum score required for the scholarship is 644.
Use the spinner to find the theoretical probability of spinning an even number.
25
Step-by-step explanation:
25
A newspaper reported the results of a poll concerning topics that teenagers most want to discuss with their parents. In the the poll 37% of teenagers said they would like to talk with their parents about school. These and other percentages were based on a national sampling of 536 teenagers. Estimate the proportion of all teenagers that want more discussions with their parents about school. Use a 99% confidence level. Right-click this Excel file to open a worksheet template.
Answer:
Step-by-step explanation:
Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
From the information given,
n = 536
p = 37/100 = 0.37
q = 1 - 0.37 = 0.63
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.005 = 0.995
The z score corresponding to the area on the z table is 2.53. Thus, confidence level of 99% is 2.58
Therefore, the 99% confidence interval is
0.37 ± 2.58 × √(0.37)(0.63)/536
= 0.37 ± 0.054
The lower limit of the confidence interval is
0.37 - 0.054 = 0.316
The upper limit of the confidence interval is
0.37 + 0.054 = 0.424
Therefore, with 99% confidence interval, the proportion of all teenagers that want more discussions with their parents about school is between 0.316 and 0.424
Can anyone find this area of this parallelogram
Answer:
260
Step-by-step explanation:
A = bh
Chandler has 828 millimeters of fabric.
How many centimeters of fabric does Chandler have?
Use the numbers and symbols on the tiles to enter an equation to show the
828 8.28
182.8
0.828
100 || 1.000
Chandler has
centimeters of fabric.
Answer:
82.8 centimeters
Step-by-step explanation:
Chandler has 828 millimeters of fabric.
1 centimeter =10 millimetersx centimeters = 828 millimetersExpressing as a ratio
[tex]\dfrac{1}{x}= \dfrac{10}{828}\\10x=828\\x=828\div 10\\x=82.8 cm[/tex]
Therefore, Chandler has 82.8 centimeters of fabric.
Answer:
82.8 centimeters of fabric
Step-by-step explanation:
1 centimeters= 10 millimeters;
828mm x 1cm ÷10 mm=82.8cm ;centimeters of fabric
The exercise is performed by conversion factor and a smaller unit is transferred to a larger unit that is centimeters.
The magnitude, M, of an earthquake is defined to be M=log l/s, where l is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and S is the intensity of a “standard” earthquake, which is barely detectable. Which equation represents the magnitude of an earthquake that is 10 times more intense than a standard earthquake?
Answer:
M = Log (10S/S)
Step-by-step explanation:
We are told that the magnitude, M, of an earthquake is defined to be;
M = Log l/S
Where I is intensity and S is standard earthquake.
Now, we want to find the magnitude of an earthquake that is 10 times more intense than a standard earthquake
Since 10 times more intense than standard earthquake, it means that;
I = 10S
So plugging in 10S for I in the original equation for magnitude gives;
M = Log (10S/S)
Answer:It’s C on edge
Step-by-step explanation:
Since 1936, the Gallup Organization has been asking Americans: "Are you in favor of the death penalty for a person convicted of murder?" The percentage has fluctuated significantly over the years, ranging from a low of 42% in 1966 to a high of 80% in 1994. Here are the results of the most recent survey; in a sample of 3100 females, 62% said that they were in favor of the death penalty for convicted murders. Construct a 98% confidence interval for the proportion of all American females who support the death penalty for convicted murders.
Plugging in the values and calculating, we find that the 98% confidence interval is approximately (0.5847, 0.6553).
Explanation:To construct a 98% confidence interval for the proportion of all American females who support the death penalty for convicted murders, we can use the formula:
CI = p ± z * √(p * (1-p) / n)
Where:
CI is the confidence intervalp is the sample proportion (0.62)z is the z-score corresponding to the desired confidence level (98% or 0.98)n is the sample size (3100)Using a standard normal distribution table or a calculator, we can find that the z-score for a 98% confidence level is approximately 2.33.
Plugging in the values into the formula:
CI = 0.62 ± 2.33 * √(0.62 * (1-0.62) / 3100)
Calculating the values:
CI = 0.62 ± 2.33 * √(0.62 * 0.38 / 3100)
CI = 0.62 ± 2.33 * √(0.235 / 3100)
CI = 0.62 ± 2.33 * 0.01516
CI = 0.62 ± 0.03535
CI ≈ (0.5847, 0.6553)
Therefore, the 98% confidence interval for the proportion of all American females who support the death penalty for convicted murders is approximately (0.5847, 0.6553).
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Associations In Data:Question 10
The list below show test scores for 3rd period on a
recent test. Finding the mean absolute deviation.
62 63 68 72 79 80 83 93 94 95
Select one:
7.8
101.2
78.9
10.12
Answer:
[tex] \bar X = \frac{62+63+68+72+79+80+83+93+94+95}{10}= 78.9[/tex]
[tex] |62-78.9| = 16.9[/tex]
[tex] |63-78.9| = 15.9[/tex]
[tex] |68-78.9| = 10.9[/tex]
[tex] |72-78.9| = 6.9[/tex]
[tex] |79-78.9| = 0.1[/tex]
[tex] |80-78.9| = 1.1[/tex]
[tex] |83-78.9| = 4.1[/tex]
[tex] |93-78.9| = 14.1[/tex]
[tex] |94-78.9| = 15.1[/tex]
[tex] |95-78.9| = 16.1[/tex]
[tex] MAD = \frac{\sum_{i=1}^n |X_i -\bar X|}{n}[/tex]
And replacing we got:
[tex] MAD =\frac{16.9+15.9+10.9+6.9+0.1+1.1+4.1+14.1+15.1+16.1}{10}= 10.12[/tex]
And the best anwer is
10.12
Step-by-step explanation:
We have the following data given:
62 63 68 72 79 80 83 93 94 95
And we need to begin finding the mean with the following formula:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex] \bar X = \frac{62+63+68+72+79+80+83+93+94+95}{10}= 78.9[/tex]
Now we can find the mean absolute deviation like this:
[tex] |62-78.9| = 16.9[/tex]
[tex] |63-78.9| = 15.9[/tex]
[tex] |68-78.9| = 10.9[/tex]
[tex] |72-78.9| = 6.9[/tex]
[tex] |79-78.9| = 0.1[/tex]
[tex] |80-78.9| = 1.1[/tex]
[tex] |83-78.9| = 4.1[/tex]
[tex] |93-78.9| = 14.1[/tex]
[tex] |94-78.9| = 15.1[/tex]
[tex] |95-78.9| = 16.1[/tex]
And finally we can find the mean abslute deviation with the following formula:
[tex] MAD = \frac{\sum_{i=1}^n |X_i -\bar X|}{n}[/tex]
And replacing we got:
[tex] MAD =\frac{16.9+15.9+10.9+6.9+0.1+1.1+4.1+14.1+15.1+16.1}{10}= 10.12[/tex]
And the best anwer is
10.12
Peter measures the angles in a triangle.
He finds that the angles are 95°, 10° and 75º.
a)
Could he be correct?
b)
Explain your answer.
Suppose that the manager of a company has estimated the probability of a super-event sometime during the next five years that will disrupt all suppliers as 0.0023. In addition, the firm currently uses three suppliers for its main component, and the manager estimates the probability of a unique-event that would disrupt one of them sometime during the next five years to be 0.014. What is the approximate probability that all three suppliers will be disrupted at the same time at some point during the next five years?a.0.0012b.0.0140 c.0.0023 d.0.0090
Given Information:
Probability of super event = P(S) = 0.0023
Number of suppliers = n = 3
Probability of unique event = P(U) = 0.014
Required Information:
Probability that all three suppliers will be disrupted = ?
Answer:
P(3) = 0.0023
Step-by-step explanation:
We want to find out the approximate probability that all three suppliers will be disrupted at the same time at some point during the next five years.
The required probability is given by
P(n) = P(S) + (1 - P(S))*P(U)ⁿ
Where P(S) is the probability of super event that will disrupt all suppliers, P(U) is the probability of unique event that would disrupt one of the suppliers and n is the number of suppliers.
P(3) = 0.0023 + (1 - 0.0023)*(0.014)³
P(3) = 0.0023 + (0.9977)*(0.014)³
P(3) = 0.0023
The correct option is C = 0.0023
Therefore, there is 0.23% probability that all three suppliers will be disrupted at the same time at some point during the next five years.
1. 3 (x + 1)2 - 3
a. What is the "a" value?
b. What is the "h" value?
c. What is the "K" value?
Use the Ratio Test to determine whether the series is convergent or divergent.
Σ[infinity] n = 1 (-1)^n - 1 3^n/2^nn^3
Answer:
The series is absolutely convergent.
Step-by-step explanation:
By ratio test, we find the limit as n approaches infinity of
|[a_(n+1)]/a_n|
a_n = (-1)^(n - 1).(3^n)/(2^n.n^3)
a_(n+1) = (-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)
[a_(n+1)]/a_n = [(-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)] × [(2^n.n^3)/(-1)^(n - 1).(3^n)]
= |-3n³/2(n+1)³|
= 3n³/2(n+1)³
= (3/2)[1/(1 + 1/n)³]
Now, we take the limit of (3/2)[1/(1 + 1/n)³] as n approaches infinity
= (3/2)limit of [1/(1 + 1/n)³] as n approaches infinity
= 3/2 × 1
= 3/2
The series is therefore, absolutely convergent, and the limit is 3/2
A hyperbola centered at the origin has vertices at (0,±\sqrt(54) and foci at (0,±\sqrt(89)
Write the equation of this hyperbola
The equation of the hyperbola with vertices at[tex](0,±\sqrt{54}) and foci at (0,±\sqrt{89}) is \(\frac{y^2}{54} - \frac{x^2}{35} = 1\).[/tex]
To write the equation of a hyperbola, you need to know the values of a (which determines the distance from the center to the vertices) and c (which determines the distance from the center to the foci). The general equation for a hyperbola centered at the origin (h, k) with a vertical transverse axis is:
[tex]\(\frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1\)[/tex]
Since the hyperbola is centered at the origin (0,0), this simplifies the equation:
[tex]\(\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1\)[/tex]
For this hyperbola, the vertices are at [tex](0,\(\pm\sqrt{54}\)), so a is \(\sqrt{54}\)[/tex]. The foci are at [tex](0,\(\pm\sqrt{89}\))[/tex], so c is [tex]\(\sqrt{89}\)[/tex]. To find b, we use the relationship [tex]c^2 = a^2 + b^2 (since e > 1)[/tex].
Calculating b, we have:
[tex]\(c^2 = a^2 + b^2\)[/tex]
[tex]\(89 = 54 + b^2\)[/tex]
[tex]\(b^2 = 35\)[/tex]
Thus, the equation of the hyperbola is:
[tex]\(\frac{y^2}{54} - \frac{x^2}{35} = 1\)[/tex]
The equation of the hyperbola is : [tex]\[ \frac{y^2}{54} - \frac{x^2}{35} = 1 \][/tex]
To write the equation of the hyperbola given its vertices and foci, we need to determine the major axis, minor axis, and eccentricity.
The vertices of the hyperbola are at [tex]\( (0, \pm \sqrt{54}) \)[/tex] and the foci are at [tex]\( (0, \pm \sqrt{89}) \).[/tex]
The distance from the center to a vertex is [tex]\( \sqrt{54} \)[/tex], which is the length of the semi-major axis, [tex]\( a \)[/tex]. The distance from the center to a focus is [tex]\( \sqrt{89} \),[/tex] which is the length of [tex]\( c \)[/tex], the distance from the center to a focus.
The relationship between [tex]\( a \), \( b \)[/tex] (the length of the semi-minor axis), and [tex]\( c \)[/tex] for a hyperbola is given by the equation [tex]\( c^2 = a^2 + b^2 \).[/tex]
Substituting the given values, we get:
[tex]\[ 89 = 54 + b^2 \][/tex]
[tex]\[ b^2 = 89 - 54 \][/tex]
[tex]\[ b^2 = 35 \][/tex]
So, [tex]\( b = \sqrt{35} \)[/tex].
The standard form equation of a hyperbola centered at the origin with vertices on the y-axis is:
[tex]\[ \frac{y^2}{a^2} - \frac{x^2}{b^2} = 1 \][/tex]
Substituting [tex]\( a = \sqrt{54} \) and \( b = \sqrt{35} \),[/tex] we get:
[tex]\[ \frac{y^2}{54} - \frac{x^2}{35} = 1 \][/tex]
Therefore, the equation of the hyperbola is:
[tex]\[ \frac{y^2}{54} - \frac{x^2}{35} = 1 \][/tex]
This equation represents a hyperbola centered at the origin with vertices at [tex]\( (0, \pm \sqrt{54}) \) and foci at \( (0, \pm \sqrt{89}) \).[/tex]
There are two spinners containing only black and purple slices.
Spinner A has 3 black slices and 12 purple slices.
All the slices are the same size.
Spinner B has 2 black slices and 6 purple slices.
All the slices are the same size.
Each spinner is spun.
List theseſevents from least likely to most likely.
Event 1: Spinner B lands on a black slice.
Event 2: Spinner A lands on a black slice.
Event 3: Spinner B lands on a black or purple slice.
Event 4: Spinner A lands on a green slice.
Least likely
Most likely
Event |
Event |
Event |
Event []
Answer:
Event 4, Event 2, Event 1, Event 3 (least to most likely)
Step-by-step explanation:
Let's take a look at each event:
Event 1- Spinner B lands on a black slice.
2 black slices, 8 total slices
2/8=1/4=25% probability
Event 2- Spinner A lands on a black slice.
3 black slices, 15 total slices
3/15=1/5=20%
Event 3- Spinner B lands on a black or purple slice.
8 black or purple slices, 8 total slices
8/8=1=100%
Event 4- Spinner A lands on a green slice.
0 green slices, 15 total slices
0/15=0=0%
So, in order of least to most likely, we have Event 4 (0%), Event 2 (20%), Event 1 (25%), and event 3 (100%).
An aquarium at a pet store contains six fish; three yellow goldfish and three black goldfish. On Sunday, a customer came to the store and randomly selected three fish to purchase. Suppose you know the customer purchased a black goldfish. What is the probability that two yellow goldfish and a black goldfish remain in the tank after the customer has left? Please simplify your answer to a decimal value and circle your answer. Ensure you show your work.
Answer:
[tex]P=0.4737[/tex]
Step-by-step explanation:
First, we need to know that nCx give as the number of ways in which we can select x elements from a group of n. It is calculated as:
[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
Then, to select 3 fish in which at least one a them is a black goldfish we can:
1. Select one black goldfish and 2 yellow goldfish: There are 9 different ways to do this. it is calculated as:
[tex]3C1*3C2 =\frac{3!}{1!(3-1)!}* \frac{3!}{2!(3-2)!}=9[/tex]
Because we select 1 black goldfish from the 3 in aquarium and select 2 yellow goldfish from the 3 in the aquarium.
2. Select 2 black goldfish and 1 yellow goldfish: There are 9 different ways. it is calculated as:
[tex]3C2*3C1 =\frac{3!}{2!(3-2)!}* \frac{3!}{1!(3-1)!}=9[/tex]
3. Select 3 black goldfish and 0 yellow goldfish: There is 1 way. it is calculated as:
[tex]3C3*3C0 =\frac{3!}{3!(3-3)!}* \frac{3!}{0!(3-0)!}=1[/tex]
Now, we identify that just in part 2 (Select 2 black goldfish and 1 yellow goldfish), two yellow goldfish and a black goldfish remain in the tank after the customer has left.
So, the probability that two yellow goldfish and a black goldfish remain in the tank after the customer has left given that the customer purchased a black goldfish is equal to:
[tex]P=\frac{9}{9+9+1} =0.4737[/tex]
Because there are 19 ways in which the customer can select a black fish and from that 19 ways, there are 9 ways in which two yellow goldfish and a black goldfish remain in the tank.
The election of a local construction union involves 2,000 union members. Among them, 500 members are randomly selected and asked whether they planned to vote for the incumbent Union President or the challenger. Of the 500 surveyed, 350 said they would vote for the incumbent. Using the 0.99 confidence coefficient, what are the confidence limits for the proportion that plan to vote for the incumbent
Answer:
The 99% of confidence limits for the proportion that plan to vote for the incumbent.
(0.6473 ,0.7527)
Step-by-step explanation:
Explanation:-
Given data the election of a local construction union involves 2,000 union members. Among them, 500 members are randomly selected.
Given large sample size 'N' = 2000
Given sample size 'n' = 500
Given data Of the 500 surveyed, 350 said they would vote for the incumbent.
The sample Proportion
[tex]p = \frac{x}{n} = \frac{350}{500} =0.7[/tex]
q = 1-p = 1 - 0.7 = 0.3
Confidence intervals:-
The 99% of confidence intervals are determined by
[tex](p-Z_{\alpha } \sqrt{\frac{pq}{n} } , p+Z_{\alpha }\sqrt{\frac{pq}{n} } )[/tex]
The z- score of 0.99 level of significance =2.576
[tex](0.7-2.576\sqrt{\frac{0.7X0.3}{500} } , 0.7+2.576\sqrt{\frac{0.7X0.3}{500} } )[/tex]
on using calculator, we get
(0.7 - 0.0527 ,0.7+0.0527)
(0.6473 ,0.7527)
Conclusion:-
The 99% of confidence limits for the proportion that plan to vote for the incumbent.
(0.6473 ,0.7527)
According to a recent publication, the mean price of new mobile homes is $63 comma 800. Assume a standard deviation of $7900. Let x overbar denote the mean price of a sample of new mobile homes. a. For samples of size 25, find the mean and standard deviation of x overbar. Interpret your results in words. b. Repeat part (a) with nequals50. a. For ▼ the mean and standard deviation of ▼ the prices of the mobile homes all possible sample mean prices are $ nothing and $ nothing, respectively. (Round to the nearest cent as needed.) b. For ▼ samples of 50 mobile homes, the 50 mobile homes sampled, the mean and standard deviation of ▼ the prices of the mobile homes all possible sample mean prices are $ nothing and $ nothing, respectively. (Round to the nearest cent as needed.)
Answer:
a. For n=25, the mean and standard deviation of the prices of the mobile homes all possible sample mean prices are $63,800 and $1,580, respectively.
b. For n=50, the mean and standard deviation of the prices of the mobile homes all possible sample mean prices are $63,800 and $1,117, respectively.
Step-by-step explanation:
In this case, for each sample size, we have a sampling distribution (a distribution for the population of sample means), with the following parameters:
[tex]\mu_s=\mu=63,800\\\\\sigma_s=\sigma/\sqrt{n}=7,900/\sqrt{n}[/tex]
For n=25 we have:
[tex]\mu_s=\mu=63,800\\\\\sigma_s=\sigma/\sqrt{n}=7,900/\sqrt{25}=7,900/5=1,580[/tex]
The spread of the sampling distribution is always smaller than the population spread of the individuals. The spread is smaller as the sample size increase.
This has the implication that is expected to have more precision in the estimation of the population mean when we use bigger samples than smaller ones.
If n=50, we have:
[tex]\mu_s=\mu=63,800\\\\\sigma_s=\sigma/\sqrt{n}=7,900/\sqrt{50}=7,900/7.07=1,117[/tex]
For samples of size 25 and 50, the mean of x bar is $63,800. The standard deviation of x bar is $1580 for a sample size of 25 and $1117 for a sample size of 50.
a. For samples of size 25, the mean of x bar is equal to the population mean, which is $63,800. The standard deviation of x bar is equal to the population standard deviation divided by the square root of the sample size. So, the standard deviation of x bar is $7900/sqrt(25) = $1580.
b. For samples of size 50, the mean of x bar is still $63,800. The standard deviation of x bar is $7900/sqrt(50) = $1117. Note that as the sample size increases, the standard deviation of x bar decreases.
Learn more about Sample Mean and Standard Deviation here:https://brainly.com/question/14747159
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1. The midpoint of GH is (-2,3), and its endpoints are G (g,4) and H (-2,h). What are the values of g and h
Answer:[tex](g,h)=(-2,2)[/tex]
Step-by-step explanation:
Given
Midpoint is [tex](-2,3)[/tex]
Endpoints are [tex]G(g,4)[/tex] and [tex]H(-2,h)[/tex]
Mid point of any two point is given by
[tex]x=\frac{x_1+x_2}{2}[/tex]
and [tex]y=\frac{y_1+y_2}{2}[/tex]
So,[tex]-2=\frac{g+(-2)}{2}[/tex]
[tex]-4=g-2[/tex]
[tex]g=-2[/tex]
Also
[tex]3=\frac{4+h}{2}[/tex]
[tex]6=4+h[/tex]
[tex]h=2[/tex]
Therefore [tex](g,h)=(-2,2)[/tex]
The probability that it will snow on the last day of January is 85%. If the probability remains the same of the first eight day of February, what is the probability that it will snow AT LEAST five of those days in February?
Answer:
Here, we have:
P(5 days snow in this 8 days) = 8C5 x (0.85)^5 x (1 - 0.85)^3 = 0.084
P(6 days snow in this 8 days) = 8C6 x (0.85)^6 x (1 - 0.85)^2 = 0.238
P(7 days snow in this 8 days) = 8C7 x (0.85)^7 x (1 - 0.85)^1 = 0.385
P(8 days snow in this 8 days) = 8C8 x (0.85)^8 x (1 - 0.85)^0 = 0.272
Add up those above, then the probability that it will snow AT LEAST five of those days in February:
P = 0.084+ 0.238 + 0. 385 + 0.272 = 0.979
Hope this helps!
:)
Combine like terms to create an equivalent expression: -n + (-4) - (-4n) + 6
Answer:
3n + 2
Step-by-step explanation:
-n + 4n -4 + 6
3n + 2