According to the Bureau of Labor Statistics, 7.1% of the labor force in Wenatchee, Washington was unemployed in February 2019. A random sample of 100 employable adults in Wenatchee, Washington was selected. Using the normal approximation to the binomial distribution, what is the probability that 6 or more people from this sample are unemployed
Answer:
73.24% probability that 6 or more people from this sample are unemployed
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
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]
Normal probability distribution
Problems of normally distributed samples can be 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.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 100, p = 0.071[/tex]
So
[tex]\mu = E(X) = np = 10*0.071 = 7.1[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.071*0.929} = 2.5682[/tex]
What is the probability that 6 or more people from this sample are unemployed
Using continuity correction, this is [tex]P(X \geq 6 - 0.5) = P(X \geq 5.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 5.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5.5 - 7.1}{2.5682}[/tex]
[tex]Z = -0.62[/tex]
[tex]Z = -0.62[/tex] has a pvalue of 0.2676
1 - 0.2676 = 0.7324
73.24% probability that 6 or more people from this sample are unemployed
At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain a mean of 519 ml. The filling process follows a normal distribution with a known process standard deviation of 6 ml.
1) The normal distribution should be used for the sample mean because:_____.
a) the sample population has a large mean.
b) the population distribution is known to be normal.
c) the population standard deviation is known.
d) the standard deviation is very small.
2) Set up hypotheses and a two-tailed decision rule for the correct mean using the 5 percent level of significance. The hypothesis for a two-tailed decision is:_______.
A. H0: mu not equal to 519, H1: mu = 519, reject if z < -1.96 or z > 1.96.
B. H0: mu not equal to 519, H1: mu = 519, reject if z > 1.96 or z < -1.96.
C. H0: mu = 519, mu not equal to 519, reject if z> 1.96 or z< -1.96.
D. H0: mu = 519, H_1: mu not equal to 519, reject if z > -1.96 or z< 1.96.
a. a.
b. b.
c. c.
d. d.
3) If a sample of 16 bottles shows a mean fill of 522 ml, does this contradict the hypothesis that the true mean is 519 ml?
A) Yes.
B) No
Answer:
1) The normal distribution should be used for the sample mean because the population distribution is known to be normal (answer b).
2) C. H0: mu = 519, H_1: mu not equal to 519, reject if z> 1.96 or z< -1.96.
3) Yes. There is enough evidence to support the claim that the true mean is not 519 ml.
Step-by-step explanation:
1) When the population follows a normal distribution, it is correct to assume a normal distribution for the sample mean.
2) As it is a two-tailed decision rule, we are interested in detecting a significant difference below and above the mean. This is why we use the unequal sign in the alternative hypothesis.
The null hypothesis state that there is not significant difference from 519.
The critical value for a significance level of 5% is z=1.96.
[tex]H_0: \mu=519\\\\H_a:\mu\neq 519[/tex]
3) The claim is that the true mean is not 519 ml.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=519\\\\H_a:\mu\neq 519[/tex]
The significance level is 0.05.
The sample has a size n=16.
The sample mean is M=522.
The standard deviation of the population is known and has a value of σ=6.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{6}{\sqrt{16}}=1.5[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{522-519}{1.5}=\dfrac{3}{1.5}=2[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=2\cdot P(z>2)=0.046[/tex]
As the P-value (0.046) 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 true mean is not 519 ml.
What is the value of x?
Answer:
x = 22
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the interior angles
6x+1 = 79+ 2x+10
Combine like terms
6x+1 = 2x+89
Subtract 2x from each side
4x+1 = 89
Subtract 1 from each side
4x = 88
Divide by 4
4x/4 = 88/4
x = 22
Answer:
The answer is
Step-by-step explanation:
We can cross out A. So it has to be either B, C, or D.
Please answer this correctly
Answer:
Look at the money bags below!!! (but I'll give you the answer)
Step-by-step explanation:
John F: 7 full bags - 1 half
Juan A: 9 full bags
Jason A: 3 full bags
Nick J: 3 full bags- 1 half
Alfonso S: 8 full bags
Hope this helped and wasn't confusing!!! xx - Asia
Simplify: 5y + 2p – 4y – 6P
Answer:
[tex]y-4p[/tex]
Step-by-step explanation:
Add/subtract like terms.
[tex]5y+2p-4y-6p\\5y-4y+2p-6p\\y-4p[/tex]
Please answer this correctly
Answer:
50 inches
Step-by-step explanation:
Since the formula for the area of a triangle is bh/2, where b is the base and h is the height, you can set up the following equation:
30b/2=750
30b=1500
b=1500/30=50
Hope this helps!
The right answer is 50 inches.
Please see the attached picture for full solution
Hope it helps...
good luck on your assignment..
If the captain has a 3/4 probability of hitting the ship and the pirate has a 1/4 probably what is the probability the pirate hits and the captain misses
Answer:
9/16
Step-by-step explanation:
captain has a 3/4 probability of hitting the ship
pirate has a 1/4 probability of hitting the ship
This means he has a 3/4 probability of missing the ship
P (captain hitting and pirate missing) = 3/4*3/4 = 9/16
During the worst periods of inflation in America, the price of food increased at a rate of 12 % per month. If your food bill was $300 one month during this period, what was it two months later?
Exponential; $337.08
Linear; $672.00
Exponential; $376.32
Linear; $372.00
Answer:
Exponential; $376.32
Step-by-step explanation:
Generally, an increase of 12% in a month means the prices are 12% more than they were in the previous month. That is, the value has been multiplied by 1.12.
The same would be true for the second month, so the overall multiplier for the two months is ...
(1.12)(1.12) = 1.12^2 = 1.2544
This makes the food bill for the second month amount to ...
1.2544 × $300 = $376.32
_____
As with all percentages, you need to be clear about what base is being used. Here, we have assumed the base for a monthly increase is the value at the beginning of the month.
If, instead, it is the value at the beginning of the year, then the increase is linear, not exponential. 12% of the value at the beginning of the year is the same throughout the year.
Consider the function y=f(x)=3x. The values of f(1/2) and f(1/4), rounded to the nearest hundredth, are_______ and__________ , respectively.
Answer:
f(1/2)=1.5
f(1/4)=0.75
Mr. Azu invested an amount at rate of 12% per annum and invested another amount, GH¢ 580.00 more than the first at 14%. If Mr. Azu had total accumulated amount of GH¢2,358.60, how much was his total investment?
Answer:
GH¢2082.12
Step-by-step explanation:
Let "a" represent the amount invested at 12%. Then (a+580) is the amount invested at 14%. The total amount invested (t) is ...
t = (a) +(a +580) = 2a+580
Solving for a, we get
a = (t -580)/2
__
The accumulated amount from the investment at 12% is 1.12a. And the accumulated amount from the investment at 14% is 1.14(a+580). Together, these accumulated amounts total GH¢2358.60.
1.12(t -580)/2 +1.14((t -580/2 +580) = 2358.60
0.56t -0.56(580) +0.57t -0.57(580) +1.14(580) = 2358.60 . . . remove parens
1.13t + 5.8 = 2358.60 . . . . . . . . . simplify
1.13t = 2352.80 . . . . . . . . . . . . . . subtract 5.8
t = 2352.80/1.13 = 2082.12 . . . . divide by the coefficient of t
Mr. Azu's total investment was GH¢2082.12.
Choose the equation for the graph
below.
a. y =
1
X-2
2
b.y =
x²–4
3
c. y =
x+2
-3
d.y=
e. y =
2x+4
1
x2+2x+1
Answer:
C
Step-by-step explanation:
Plugged into calculator
Vertical asymptotes: x=-2
Horizontal asymptotes: y=0
No oblique asymptotes
(2)/(5) and (1)/(x)common denominator =10 find the value of x
Answer:
[tex]x=5/48[/tex]
Step-by-step explanation:
[tex]2/5 + 1/x =10[/tex]
[tex]1/x=10-2/5[/tex]
[tex]1/x=48/5[/tex]
[tex]48x=5[/tex]
[tex]x=5/48[/tex]
Answer:
[tex]x = \frac{5}{48} [/tex]
Step-by-step explanation:
[tex]\frac{2}{5} + \frac{1}{x} = 10 \\ \frac{1}{x} = 10 - \frac{2}{5} \\ \frac{1}{x} = \frac{50 - 2}{5} \\ \frac{1}{ x } = \frac{48}{5} \\
use \: \: \: \: cross \: \: \: multiply
\\ 5 = 48x \\ \frac{5}{48} = \frac{48x}{48} \\ x = \frac{5}{48} \\ [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Playbill magazine reported that the mean annual household income of its readers is $119,155 (Playbill, January 2006). Assume this estimate of the mean annual household in- come is based on a sample of 80 households, and based on past studies, the population standard deviation is known to be a = $30,000. a. Develop a 90% confidence interval estimate of the population mean. b. Develop a 95% confidence interval estimate of the population mean. c. Develop a 99% confidence interval estimate of the population mean. d. Discuss what happens to the width of the confidence interval as the confidence level is increased. Does this result seem reasonable? Explain.
Answer:
a) CI = (113,637.5 , 124,672.5)
b) CI = (112,581 , 125,729)
c) CI = (110,501.4 , 127,808.6)
Step-by-step explanation:
You have the following information:
[tex]\overline{x}[/tex]: mean annual household income = 119,155
σ: standard deviation = 30,000
n: sample = 80
The interval of confidence is given by the following expression:
[tex]\overline{x}\pm Z_{\alpha/s}(\frac{\sigma}{\sqrt{n}})[/tex]
Z_α/2: distribution density factor
where α and Z_α/2 are given by the range of the confidence interval.
a) For a 90% confidence interval you have:
α = 1 - 0.9 = 0.1
Z_0.1/2 = Z_0.05 = 1.645 (found in a table of normal distribution)
You replace in the equation (1) to obtain the confidence interval:
[tex]119,155\pm (1.645)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm5,517.5[/tex]
Then, the confidence interval is (119,155 + 5,517.5 , 119,155 - 5,517.5 )
= (113,637.5 , 124,672.5)
b) For a 95% confidence interval you have:
α = 1 - 0.95 = 0.05
Z_0.05/2 = Z_0.025 = 1.96
[tex]119,155\pm (1.96)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm 6,574.0[/tex]
The confidence interval is (112,581 , 125,729)
c) For a 99% confidence interval:
α = 1 - 0.99 = 0.01
Z_0.01/2 = Z_0.005 = 2.58
[tex]119,155\pm (2.58)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm 8,653.6[/tex]
The confidence interval is (110,501.4 , 127,808.6)
d) When the confidence level increases the width of the confidence increases too. This can be noticed in the normal distribution, when the confidence level is higher, the area of the tails is reduced, and so, the confidence interval is higher.
Which of the following is an arithmetic sequence?
Answer:
D
Step-by-step explanation:
An arithmetic sequence is a series of numbers that increases or decreases by a certain quantity every step. A is not an arithmetic sequence, since it alternates between 2 and -2. B is not an arithmetic sequence, since it does not grow constantly in one direction. C is not an arithmetic sequence, but rather a geometric one. D is an arithmetic sequence, decreasing by 3 with each step. Hope this helps!
Solve: x - 1 < 3 help me plssss
Answer:
x =2
Step-by-step explanation:
becaue 2-1 is smaller than 3
Answer:
Hello!
I believe your answer is:
x=2
If this is not correct, please let me know and I will try again!
Step-by-step explanation:
8. Mr. Azu invested an amount at rate of 12% per annum and invested another amount. GHe
580.00 more than the first at 14%. IN Mr. Azu had total accumulated amount of
GH42.358.60. how much was his total investment?
Ans:
Answer:
GH¢.37480.36
Step-by-step explanation:
Let the amount invested at 12% per annum =GH¢.x
He invested 580.00 more than the first at 14%.
Therefore:
The amount invested at 14% =GH¢.(x+580)
For each investment option:
Amount Accrued =Principal + Simple Interest
Amount Accrued at 12%
[tex]=x+x*0.12\\=1.12x[/tex]
Amount Accrued at 14%
[tex]=(x+580)+0.14(x+580)\\=x+580+0.14x+81.2\\=1.14x+661.2[/tex]
Mr. Azu had total accumulated amount of GH42,358.60
Therefore:
1.12x+1.14x+661.2=42,358.60
2.26x=42,358.60-661.2
2.26x=41697.4
x=GH¢.18450.18
Therefore:
The amount invested at 12% per annum= GH¢.18450.18
The amount invested at 14% per annum= GH¢.18450.18+580
=GH¢.19030.18
Mr Azu's Total Investment = 18450.18 +19030.18
=GH¢.37480.36
Find the point of diminishing returns (x comma y )for the function R(x), where R(x) represents revenue (in thousands of dollars) and x represents the amount spent on advertising (in thousands of dollars).
Complete Question
The complete question is shown on the first uploaded image
Answer:
The point of diminishing returns (x , y ) is (11, 21462)
Step-by-step explanation:
From the question we are told that
The function is [tex]R(x) = 10,000 -x^3 - 33x^2 + 800x , \ \ 0 \le x \le 20[/tex]
Here R(x) represents revenue (in thousands of dollars) and x represents the amount spent on advertising (in thousands of dollars).
Now differentiating R(x) we have
[tex]R'(x) = -3x^2 +66x + 800[/tex]
Finding the second derivative of R(x)
[tex]R''(x) = -6x +66[/tex]
at inflection point [tex]R''(x) = 0[/tex]
So [tex]-6x +66 = 0[/tex]
=> [tex]x= 11[/tex]
substituting value of x into R(x)
[tex]R(x) = 10,000 -(11)^3 - 33(11)^2 + 800(11) ,[/tex]
[tex]R(x) = 21462[/tex]
Now the point of diminishing returns (x , y ) i.e (x , R(x) ) is
(11, 21462)
the ratio of the ages of Kissi and Esinam is 3:5 and that of Esinam and Lariba is 3:5 and
the sum of the ages of all 3 is 147 years, what is the age difference between oldest the youngest
Answer:
The age difference between oldest the youngest is of 48 years.
Step-by-step explanation:
We can solve this question using a system of equations.
I am going to say that:
Kissi's age is x.
Esinam's age is y.
Lariba's age is z.
The ratio of the ages of Kissi and Esinam is 3:5
This means that [tex]\frac{x}{y} = \frac{3}{5}[/tex], so [tex]5x = 3y[/tex]
That of Esinam and Lariba is 3:5
This means that [tex]\frac{y}{z} = \frac{3}{5}[/tex], so[tex]5y = 3z[/tex]
The sum of the ages of all 3 is 147 years
This means that [tex]x + y + z = 147[/tex]
What is the age difference between oldest the youngest
z is the oldest
x is the youngest.
First i will find y.
We have that, from the equations above: [tex]x = \frac{3y}{5}[/tex] and [tex]z = \frac{5y}{3}[/tex]
So
[tex]x + y + z = 147[/tex]
[tex]\frac{3y}{5} + y + \frac{5y}{3} = 147[/tex]
The lesser common multiple between 5 and 3 is 15. So
[tex]\frac{3*3y + 15*y + 5*5y}{15} = 147[/tex]
[tex]49y = 147*15[/tex]
[tex]y = \frac{147*15}{49}[/tex]
[tex]y = 45[/tex]
Youngest:
[tex]x = \frac{3y}{5} = \frac{3*45}{5} = 27[/tex]
Oldest:
[tex]z = \frac{5y}{3} = \frac{5*45}{3} = 75[/tex]
Difference:
75 - 27 = 48
The age difference between oldest the youngest is of 48 years.
A marine biologist is preparing a deep-sea submersible for a dive. The sub stores breathing air under high pressure in a spherical air tank that measures wide. The biologist estimates she will need of air for the dive. Calculate the pressure to which this volume of air must be compressed in order to fit into the air tank. Write your answer in atmospheres. Round your answer to significant digits.
The complete question is;
A marine biologist is preparing a deep-sea submersible for a dive. The sub stores breathing air under high pressure in a spherical air tank that measures 78.0 cm wide. The biologist estimates she will need 2600 L of air for the dive. Calculate the pressure to which this volume of air must be compressed in order to fit in to the air tank. Write you answer in atmospheres
Answer:
10.5 atm
Step-by-step explanation:
Formula for Volume of a sphere is;
V = (4/3)πr³
r = 78/2 = 39 cm
V = (4/3)π(39)³
V = (4/3)*π*59319
V = 248475 cm³
Now, from conversions, 1000 cm³ = 1L
So,
V = 248475/1000
V = 248.5 L
This is the volume of the storage tank
If we assume that the 2600 L of air is measured at 1 atmosphere pressure, then we will obtain the following relationship:
From Boyles law,
P1 × V1 = P2 × V2
Thus;
(1 atm) × (2600 L) = (P2) × (248.5 L)
P2 = 2600/248.5
P2 = 10.463 atmospheres
Approximating to 3 significant figures is; P2 = 10.5 atm
Assume a simple random sample of 10 BMIs with a standard deviation of 1.186 is selected from a normally distributed population of recent Miss America winners. Use 0.01 significance level to test the claim that the BMI for recent Miss America winners are from a population with standard deviation of 1.34.
A. Identify the null hypothesis and the alternative hypothesis.
B. Find the critical value or values.
C. Find the test statistic.
D. State the conclusion that addresses the original claim.
Answer:
a) H0: [tex]\sigma = 1.34[/tex]
H1: [tex]\sigma \neq 1.34[/tex]
b) [tex] df = n-1= 10-1=9[/tex]
And the critical values with [tex]\alpha/2=0.005[/tex] on each tail are:
[tex] \chi_{\alpha/2}= 1.735, \chi_{1-\alpha/2}= 23.589[/tex]
c) [tex] t=(10-1) [\frac{1.186}{1.34}]^2 =7.05[/tex]
d) For this case since the critical value is not higher or lower than the critical values we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not significantly different from 1.34
Step-by-step explanation:
Information provided
n = 10 sample size
s= 1.186 the sample deviation
[tex]\sigma_o =1.34[/tex] the value that we want to test
[tex]p_v [/tex] represent the p value for the test
t represent the statistic (chi square test)
[tex]\alpha=0.01[/tex] significance level
Part a
On this case we want to test if the true deviation is 1,34 or no, so the system of hypothesis are:
H0: [tex]\sigma = 1.34[/tex]
H1: [tex]\sigma \neq 1.34[/tex]
The statistic is given by:
[tex] t=(n-1) [\frac{s}{\sigma_o}]^2 [/tex]
Part b
The degrees of freedom are given by:
[tex] df = n-1= 10-1=9[/tex]
And the critical values with [tex]\alpha/2=0.005[/tex] on each tail are:
[tex] \chi_{\alpha/2}= 1.735, \chi_{1-\alpha/2}= 23.589[/tex]
Part c
Replacing the info we got:
[tex] t=(10-1) [\frac{1.186}{1.34}]^2 =7.05[/tex]
Part d
For this case since the critical value is not higher or lower than the critical values we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not significantly different from 1.34
Simple regression was employed to establish the effects of childhood exposure to lead. THe effective sample size was about 122 subjects. THe independent variable was the level of dentin lead (parts per million). Below are regressions using various dependent variables.
Calculate the t statistic for each slope, at significance level = 0.01.
Dependent Variable R2 Estimated Std. t calculated p-value Differ from 0?
Slope Error
Highest grade achieved .061 −0.027 0.009 .008 No / Yes
Reading grade equivalent .121 −0.070 0.018 .000 No / Yes
Class standing .039 −0.006 0.003 .048 No / Yes
Absence from school .071 4.8 1.7 .006 No / Yes
Grammatical reasoning .051 0.159 0.062 .012 Yes / No
Vocabulary .108 −0.124 0.032 .000 No / Yes
Hand-eye coordination .043 0.041 0.018 .020 No / Yes
Reaction time .025 11.8 6.66 .080 No / Yes
Minor antisocial behavior .025 −0.639 0.36 .082 Yes / No
B) It would be inappropriate to assume cause and effect without a better understanding of how the study was conducted.
1. No
2. Yes
Answer:
Step-by-step explanation:
Simple regression was employed to establish the effects of childhood exposure to lead. THe effective sample size was about 122 subjects. THe independent variable was the level of dentin lead (parts per million). Below are regressions using various dependent variables.
Calculate the t statistic for each slope, at significance level = 0.01.
Dependent Variable R2 Estimated Std. t calculated p-value Differ from 0?
Slope Error
Highest grade achieved .061 −0.027 0.009 .008 No / Yes
Reading grade equivalent .121 −0.070 0.018 .000 No / Yes
Class standing .039 −0.006 0.003 .048 No / Yes
Absence from school .071 4.8 1.7 .006 No / Yes
Grammatical reasoning .051 0.159 0.062 .012 Yes / No
Vocabulary .108 −0.124 0.032 .000 No / Yes
Hand-eye coordination .043 0.041 0.018 .020 No / Yes
Reaction time .025 11.8 6.66 .080 No / Yes
Minor antisocial behavior .025 −0.639 0.36 .082 Yes / No
B) It would be inappropriate to assume cause and effect without a better understanding of how the study was conducted.
1. No
2. Yes
solution[tex]t=\frac{\text {estimated slope}}{\text {std error}}[/tex]
a)
Estimated Slope Std error t - calculated
-0.027 0.009 -3
-0.070 0.018 -3.89
-0.006 0.003 -2
4.8 1.7 2.82
0.159 0.062 2.56
-0.124 0.032 -3.87
0.041 0.018 2.28
11.8 6.66 1.77
-0.639 0.36 -1.78
b) Yes, It would be inappropriate to assume cause and effect without a better understanding of how the study was conducted.
If the mean of 5 positive integers is 15, what is the maximum possible difference between the largest and the smallest of these 5 numbers?
Answer:
The maximum possible difference between the largest and the smallest of these 5 numbers is 65( if numbers aren't repeated )
Which product represents the fraction of the circle that is shaded?
A
B
C
D
Answer:
B
Step-by-step explanation:
What’s the correct answer for this question?
Answer:
C.
Step-by-step explanation:
First finding height using Pythagoras theorem
(H)²=(B)²+(P)²
8.2²=5.4²+P²
P² = 67.24 - 29.16
P² = 38.08
P = 6.2
Now
Volume of cone = (1/3)πr²h
= (1/3)(3.14)(5.4)²(6.2)
= (1/3)(567.9)
= 189.2 cm³
The given line segment passes through the points (0, -3) and (-5, -4).
What is the equation of the line that is parallel to the given line and passes through the point (-2, 2)?
Answer:
y= 1/5x + 12/5
Step-by-step explanation:
Points: (0, -3) and (-5, -4)Line: y= mx+bSlope: m=(y2-y1)/(x2-x1)= (-4+3)/(-5-0)= -1/-5= 1/5Y-intercept: -3= 0*1/5+b ⇒ b= -3So the line is: y= 1/5x - 3Parallel line to this has same slope and passes through the point (-2, 2)
Its y- intercept is: 2= 1/5(-2)+b ⇒ b= 2+2/5= 12/5The required equation in slope- intercept form is:
y= 1/5x + 12/5Which of the options is the response variable?
A. The number of adults.
B. The type of training exercises performed by each participant.
C. The size of the physiological blind spot.
D. The number of times an adult performed training exercises.
Question:
The physiological blind spot refers to a very small zone of functional blindness in the eye where the optic nerve passes through the retina. We do not notice it because our nervous system compensates for it. Can eye training reduce the size of a person's physiological blind spot? Researchers recruited a representative sample of 10 adults with normal vision. Each participant performed training exereises with one eye for three weeks. The size of the physiological blind spot was measured (in degrees of visual angle squared) with a motion detection task both prior to training and again after the training was completed. Which of the options is the response variable?
A) The size of the physiological blind spot
B) The number of adults.
C) The type of training exercises performed by each participant.
D) The size of the physiological blind spot.
E) The number of times an adult performed training exercises.
Answer:
The correct answer is A)
Explanation:
The response variable (when experimenting) is the variable or factor about which the researcher is concerned. It can also be (as the name entails) the variable which respond to changes in the experiment.
The changes in the experiment is the training. The variable which the researcher is concerned about and which may or may not change with the introduction of training is the size of the physiological blind spot.
Cheers!
6x – 2y = 10 2x + 3y = 51 Solving the first equation above for y gives: y = x – 5
Answer:
x =6y =13Step-by-step explanation:
This is the method I am familiar with.
I Hope It helps :)
[tex]METHOD- 1 : Elimination\\6x - 2y=10------(1)\\2x+3y =51------(2)\\Multiply -eq-(1)- by -the-coefficient-of-x-in-equation (2)\\Multiply-eq-(2) -by -the-coefficient-of-x-in-equation (1)\\6x - 2y=10------(1) *2\\2x+3y =51------(2)*6\\\\12x-4y=20 ------(3)\\12x+18y=306 ------(4)\\Subtract -eq- (4)- from- eq -(3)\\-22y =-286\\\frac{-22y}{-22} =\frac{-286}{-22} \\y =13\\[/tex]
[tex]Substitute- 13- for y -in-equation -(1)-or-(2)\\6x - 2y=10------(1)\\6x -2(13)=10\\6x -26=10\\6x =10+26\\6x =36\\\frac{6x}{6} =\frac{36}{6} \\x =6[/tex]
Answer:
Correct answers is
Step-by-step explanation:
1. 3
2. B
3. 6
4. (6,13)
A $210 suit is marked down by 10%. Find the sale price.
Answer:
sale prices = $252
Step-by-step explanation: 280 - (280 x 10%) = 280 - 28 = $252
Answer:
$189
Step-by-step explanation:
10% of 210 = 21
210 - 21 = 189
Describe the difference between a probability derived from the analytic view (logical analysis), the Relative Frequency view (sampling from a distribution with known characteristics), and the Subjective (feeling) view. Describe situations in which each view of probability could be useful.
Answer:
See the explanation
Step-by-step explanation:
Analytic View:If and event can occur in A number of way and fail in B number of ways, then probability of its occurrence is:
[tex]P(A)= \frac{A}{A+B}[/tex]
or probability of its failing is:
[tex]P(B)=\frac{B}{A+B}[/tex]
Example:Rolling a number smaller than 3 in a dice.
A= 2 (1,2)
B = 4 (3,4,5,6)
[tex]P(A)= \frac{2}{2+4}=\frac{1}{3}[/tex]
Relative Frequency View:Definition of Probability in terms of past performances (data). It can be taken as how often things happens divided by all outcomes.
Example:A batter has 50 safe hits at 200 bats, which makes his batting average [tex]\frac{50}{200}= 0.25[/tex] which is the probability.
Subjective View:When you define a probability due to personel beleif in the likelihood of an outcome. It involve no formal calculations and varies from person to person, depending on their past experience.
Example:A person beleives that probability that the batter will hit safely in the next bat is 0.75
WILL GIVE BRAINLIEST! HURRY
Answer:
-1/2 =x
Step-by-step explanation:
4x - 6 = 10x -3
Subtract 4x from each side
4x-4x - 6 = 10x-4x -3
-6 = 6x-3
Add 3 to each side
-6+3 = 6x
-3 = 6x
Divide each side by 6
-3/6 = 6x/6
-1/2 =x
[tex]answer \\ - \frac{1}{2} \\ solution \\ 4x - 6 = 10x - 3 \\ or \: 4x - 10x = - 3 + 6 \\ or \: - 6x = 3 \\ or \: x = \frac{3}{ - 6} \\ x = - \frac{1}{2} \\ hope \: it \: helps[/tex]
