The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 4178 miles, with a variance of 124,609. If he is correct, what is the probability that the mean of a sample of 40 cars would be less than 4265 miles? Round your answer to four decimal places.
Answers
Answer:
P(X' < 4265) = 0.9418
Step-by-step explanation:
Due to the fact that the population is normal, the distribution of the sample mean of 40 cars is;
X' = (x1 + x2 + x3....... + x40)/40
We are given;
Normal mean;μ = 4178 miles
Variance = 124,609
Standard deviation; σ = √variance = √124609 = 353
Formula for standard error of mean = σ/√n = 353/√40 = 55.814
So from the formula;
z = (x - μ)/(σ/√n)
So for P(X' < 4265) we have;
z-value of P(X' < 4265) = (4265 - 4178)/55.814 ≈ 1.56
From the z-table attached, we have for P(z < 1.56) = 0.94179
Approximating to 4 decimal places gives 0.9418
Related Questions
What are the vertical asymptote(s) of y= (x-6)/(x+8) (x-7)
Answers
Answer:
x = -8 and x= 7
Step-by-step explanation:
recall that for a rational expression, the vertical asymptotes occur at x-values that causes the expression to become undefined. These occur when the denominator becomes zero.
Hence the asymptototes will occur in x-locations where the denominator , i.e
(x+8)(x-7) = 0
solving this, we get
(x+8) = 0 ----> x = -8
or
(x-7) = 0 ------> x = 7
hence the asymptotes occur x = -8 and x= 7
Answer:
x = -8 and x = 7.
Step-by-step explanation:
The vertical asymptotes are lines that the function will never touch.
Since no number can be divided by 0, the function will not touch points where the denominator of the function is equal to 0.
[tex]\frac{x - 6}{(x + 8)(x - 7)}[/tex], so the vertical asymptotes will be where (x + 8) = 0 and (x - 7) = 0.
x + 8 = 0
x = -8
x - 7 = 0
x = 7
The vertical asymptotes are at x = -8 and x = 7.
Hope this helps!
(SAT Prep) In the given figure, a║b. What is the value of x? A. 70° B. 45° C. 80° D. 65° I NEED THIS FAST PLZZZZZZ!!!!!!!!!!!!
Answers
Answer:
70
Step-by-step explanation:
You have to find the vertical of x. To the right of the vertical, we see that there is an angle of 25 (since the 25 up top corresponds to that blank angle). Once you add 25 + 85 + x = 180 (since this is a straight line), we see that x is 70, and its vertical is also 70.
It has been observed that some persons who suffer acute heartburn, again suffer acute heartburn within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 55 people in the first group and this group will be administered the new drug. There are 45 people in the second group and this group will be administered a placebo. After one year, 11% of the first group has a second episode and 9% of the second group has a second episode. Conduct a hypothesis test to determine, at the significance level 0.1, whether there is reason to believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode?
Answers
Answer:
Null hypothesis :
[tex]H_o:p_1-p_2 = 0[/tex]
Alternative hypothesis:
[tex]H_1:p_1-p_2 \neq 0[/tex]
Decision Rule:
To reject the null hypothesis if z < -1.65 and z > 1.65
Conclusion:
Failed to reject null hypothesis if z > -1.65 or z < 1.65
z -value = 0.33022
P-value = 0.7414
Decision Rule:
Since the P-value is higher than the level of significance , therefore do not reject the null hypothesis at the level of significance of 0.1
Conclusion: we failed to reject null hypothesis, Therefore, the data does not believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode
Step-by-step explanation:
From the summary of the given statistical data sets.
Let consider to [tex]p_1[/tex] represent percentage of the first group ; &
[tex]p_2[/tex] represent percentage of the second group
The null and the alternative hypothesis can be stated s follows:
Null hypothesis :
[tex]H_o:p_1-p_2 = 0[/tex]
Alternative hypothesis:
[tex]H_1:p_1-p_2 \neq 0[/tex]
At the level of significance ∝ = 0.1; the two tailed critical value from the z-table
[tex]z_{\alpha/2} = 1.65[/tex]
Decision Rule:
To reject the null hypothesis if z < -1.65 and z > 1.65
Conclusion:
Failed to reject null hypothesis if z > -1.65 or z < 1.65
However; from the question:
There are 55 people in the first group and this group will be administered the new drug.
There are 45 people in the second group and this group will be administered a placebo.
After one year, 11% of the first group has a second episode and 9% of the second group has a second episode.
The test statistic for the for the first group who suffered from the second episode can be denoted as :
[tex]\hat p_1 = \dfrac{\overline x_1}{n_1}=0.11[/tex]
The test statistic for the for the second group who suffered from the second episode can be denoted as :
[tex]\hat p_2 = \dfrac{\overline x_2}{n_2}=0.09[/tex]
where;
[tex]n_1[/tex] = sample size of group 1 = 55
[tex]n_2[/tex] = sample size of group 2 = 45
The total probability of both group is :
[tex]\hat p = \dfrac{n_1 \hat p_1 + n_2 \hat p_2}{n_1 + n_2}[/tex]
[tex]\hat p = \dfrac{55*0.11+ 45 * 0.09}{55+45}[/tex]
[tex]\hat p = \dfrac{6.05+ 4.05}{100}[/tex]
[tex]\hat p = \dfrac{10.1}{100}[/tex]
[tex]\hat p = 0.101[/tex]
The standard error of the statistic [tex]\hat p_1 - \hat p_2[/tex] an be computed as follows:
[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{ p_1 (1 - \hat p)( \dfrac{1}{n_1}+\dfrac{1}{n_2})}[/tex]
[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.101 (1 - 0.101)( \dfrac{1}{55}+\dfrac{1}{45})}[/tex]
[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.101(0.899)(0.0404)}[/tex]
[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.0036682796}[/tex]
[tex]S.E(\hat p_1 - \hat p_2)=0.060566[/tex]
Now; The test statistics is determined to be :
[tex]z = \dfrac{(\hat p_1 - \hat p_2 ) - (p_1-p_2)}{SE(\hat p_1 - \hat p_2)}[/tex]
[tex]z = \dfrac{(0.11-0.09) - 0}{0.060566}[/tex]
z = 0.33022
Hence; the value for the test statistics = 0.33022
the value for the test statistics = 0.33
From the z value; The P-value for the test statistics can be computed as:
P-value = 2P(Z ≥ |z|)
P-value = 2P(Z ≥ 0.33022)
P-value = 2 × P (Z ≤ - 0.33022)
From the z table Z ≤ - 0.33022 = 0.3707
P-value = 2 × 0.3707
P-value = 0.7414
Decision Rule:
Since the P-value is higher than the level of significance , therefore do not reject the null hypothesis at the level of significance of 0.1
Conclusion: we failed to reject null hypothesis, Therefore, the data does not believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode
If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. Consider the cost function C(x) given below. C(x) = 54,000 + 130x + 4x3/2 (a) Find the total cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ (b) Find the average cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ per unit (c) Find the marginal cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ per unit (d) Find the production level that will minimize the average cost. (Round your answer to the nearest whole number.) units (e) What is the minimum average cost? (Round your answer to the nearest dollar.) $ per unit
Answers
Answer:
Step-by-step explanation:
Given that:
If C(x) = the cost of producing x units of a commodity
Then;
then the average cost per unit is c(x) = [tex]\dfrac{C(x)}{x}[/tex]
We are to consider a given function:
[tex]C(x) = 54,000 + 130x + 4x^{3/2}[/tex]
And the objectives are to determine the following:
a) the total cost at a production level of 1000 units.
So;
If C(1000) = the cost of producing 1000 units of a commodity
[tex]C(1000) = 54,000 + 130(1000) + 4(1000)^{3/2}[/tex]
[tex]C(1000) = 54,000 + 130000 + 4( \sqrt[2]{1000^3} )[/tex]
[tex]C(1000) = 54,000 + 130000 + 4(31622.7766)[/tex]
[tex]C(1000) = 54,000 + 130000 + 126491.1064[/tex]
[tex]C(1000) = $310491.1064[/tex]
[tex]\mathbf{C(1000) \approx $310491.11 }[/tex]
(b) Find the average cost at a production level of 1000 units.
Recall that :
the average cost per unit is c(x) = [tex]\dfrac{C(x)}{x}[/tex]
SO;
[tex]c(x) =\dfrac{(54,000 + 130x + 4x^{3/2})}{x}[/tex]
Using the law of indices
[tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex]
[tex]c(1000) = \dfrac{54000}{1000}+ 130 + {4(1000)^{1/2}}[/tex]
c(1000) =$ 310.49 per unit
(c) Find the marginal cost at a production level of 1000 units.
The marginal cost is C'(x)
Differentiating C(x) = 54,000 + 130x + 4x^{3/2} to get C'(x) ; we Have:
[tex]C'(x) = 0 + 130 + 4 \times \dfrac{3}{2} \ x^{\dfrac{3}{2}-1}[/tex]
[tex]C'(x) = 0 + 130 + 2 \times \ {3} \ x^{\frac{1}{2}}[/tex]
[tex]C'(x) = 0 + 130 + \ {6}\ x^{\frac{1}{2}}[/tex]
[tex]C'(1000) = 0 + 130 + \ {6} \ (1000)^{\frac{1}{2}}[/tex]
[tex]C'(1000) = 319.7366596[/tex]
[tex]\mathbf{C'(1000) = \$319.74 \ per \ unit}[/tex]
(d) Find the production level that will minimize the average cost.
the average cost per unit is c(x) = [tex]\dfrac{C(x)}{x}[/tex]
[tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex]
the production level that will minimize the average cost is c'(x)
differentiating [tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex] to get c'(x); we have
[tex]c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{4}{2 \sqrt{x} }[/tex]
[tex]c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{2}{ \sqrt{x} }[/tex]
Also
[tex]c''(x)= \dfrac{108000}{x^3} -x^{-3/2}[/tex]
[tex]c'(x)= \dfrac{54000}{x^2} + \dfrac{4}{2 \sqrt{x} } = 0[/tex]
[tex]x^2 = 27000\sqrt{x}[/tex]
[tex]\sqrt{x} (x^{3/2} - 27000) =0[/tex]
x= 0; or [tex]x= (27000)^{2/3}[/tex] = [tex]\sqrt[3]{27000^2}[/tex] = 30² = 900
Since production cost can never be zero; then the production cost = 900 units
(e) What is the minimum average cost?
the minimum average cost of c(900) is
[tex]c(900) =\dfrac{54000}{900} + 130 + 4(900)^{1/2}[/tex]
c(900) = 60 + 130 + 4(30)
c(900) = 60 +130 + 120
c(900) = $310 per unit
An architect needs to consider the pitch, or steepness, of a roof in order to ensure precipitation runoff. The graph below shows
the vertical height, y, versus the horizontal distance, x, as measured from the roof peak's support beam.
Roof Steepness
y
14
12
10
8
Vertical Height (feet)
4
2
+X
10 12 14
0
2
4
6
8
Horizontal Distance (feet)
Determine the equation that could be used to represent this situation.
Answers
Answer:
The third answer (C).
Step-by-step explanation:
This graph starts at 10. So it needs the +10 at the end.
Also the slope is -1/2 because the graph goes down one, right two. Rise/run.
Answer:
y= -1/2x+10
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
For the the given graph, the y-intercept is 10. The slope can be determined by finding the rate of change between any two points on the graph, such as (2,9) and (8,6).
The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the probability that a flight is between 125 and 140 minutes
Answers
Answer: 0.5
Step-by-step explanation:
If the probability of the time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. Therefore, the probability that a flight is between 125 and 140 minutes is 0.5
2 x - 3 + 3x equals -28 what is the value of x
Answers
Answer:
[tex]x = -5[/tex]
Step-by-step explanation:
We can simplify this equation down until x is isolated.
[tex]2x - 3 + 3x = -28[/tex]
We can combine the like terms of x.
[tex]5x - 3 = -28[/tex]
Add 3 to both sides.
[tex]5x = -25[/tex]
Now we can divide both sides by 5.
[tex]x = -5[/tex].
So x = -5.
Hope this helped!
Answer:
x=-5
Step-by-step explanation:
first combine like terms
5x-3=-28
add on both sides
5x=-25
divide
x==-5
I need answers for 1 , 2, 4
Answers
Answer:
(3) x ≥ -3
(4) 2.5 gallons
(4) -12x + 36
Step-by-step explanation:
Hey there!
1)
Well its a solid dot meaning it will be equal to.
So we can cross out 1 and 2.
And it's going to the right meaning x is greater than or equal to -3.
(3) x ≥ -3
2)
Well if each milk container has 1 quart then there is 10 quarts.
And there is 4 quarts in a gallon, meaning there is 2.5 gallons of milk.
(4) 2.5 gallons
4)
16 - 4(3x - 5)
16 - 12x + 20
-12x + 36
(4) -12x + 36
Hope this helps :)
What is the y-intercept of the line described by the equation below? Y=3x - 6
Answers
We are given the equation y = 3x - 6
The slope-intercept form of a line is y = mx + b where m is the slope and b is the y-intercept.
The b value in this equation is -6, thus the y-intercept is -6.
Let me know if you need any clarifications, thanks!
What are the expressions for length, width, and height?
Volume = length width height
V = _____ _____ _____
For odyyseyware
Answers
Answer:
[tex]\boxed{V=lwh}[/tex]
Step-by-step explanation:
The formula for volume of a cuboid is:
[tex]V=lwh[/tex]
[tex]volume = length \times width \times height[/tex]
Answer:
V = l w h
Step-by-step explanation:
Volume of a Cuboid = Length × Width × Height
Where l = length, w = width and h = height
Explain the relationship between variance and standard deviation. Can either of these measures be negative? Explain. Choose the correct answer below. A. The variance is the positive square root of the standard deviation. The standard deviation and variance can never be negative. Squared deviations can never be negative. B. The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative. Squared deviations can never be negative. C. The variance is the negative square root of the standard deviation. The variance can be negative but the standard deviation can never be negative. D. The standard deviation is the negative square root of the variance. The standard deviation can be negative but the variance can never be negative.
Answers
Answer:
A. The variance is the positive square root of the standard deviation. The standard deviation and variance can never be negative. Squared deviations can never be negative.
Step-by-step explanation:
As we know that
The standard deviation is the square root of the variance and on the other side the variance is the square of the standard deviation
In mathematically
[tex]\sigma = \sqrt{variance}[/tex]
And,
[tex]variance = \sigma^2[/tex]
Moreover, the standard deviation and the variance could never by negative neither the squared deviation is negative. All three are always positive
Hence, the correct option is a.
Answer:
B. The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative. Squared deviations can never be negative.
The length of time, in hours, it takes a group of people, 40 years and older, to play one soccer match is normally distributed with a mean of 2 hours and a standard deviation of 0.5 hours. A sample of size 50 is drawn randomly from the population. Find the probability that the sample mean is less than 2.3 hours. g
Answers
Answer:
[tex]P(\overline X < 2.3) = 0.9999[/tex]
Step-by-step explanation:
Given that:
mean = 2
standard deviation = 0.5
sample size = 50
The probability that the sample mean is less than 2.3 hours is :
[tex]P(\overline X < 2.3) = P(Z \leq \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt{n}}})[/tex]
[tex]P(\overline X < 2.3) = P(Z \leq \dfrac{2.3 - 2.0}{\dfrac{0.5}{\sqrt{50}}})[/tex]
[tex]P(\overline X < 2.3) = P(Z \leq \dfrac{0.3}{0.07071})[/tex]
[tex]P(\overline X < 2.3) = P(Z \leq 4.24268)[/tex]
[tex]P(\overline X < 2.3) = P(Z \leq 4.24)[/tex]
From z tables;
[tex]P(\overline X < 2.3) = 0.9999[/tex]
Write these as normal numbers
Answers
Hi there!! (✿◕‿◕)
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A.) 7.2 x 10^-5 = 0.000000072
B.) 6.3 x 10^-9 = 0.0000000063
C.) 4.54 x 10^-5 = 0.0000454
D.) 7.041 x 10^-10 = 0.0000000007041
Hope this helped!! ٩(◕‿◕｡)۶
The numbers can be written as;
A.) 7.2 x 10^{-5} = 0.000000072
B.) 6.3 x 10^{-9} = 0.0000000063
C.) 4.54 x 10^{-5} = 0.0000454
D.) 7.041 x 10^{-10} = 0.0000000007041
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We are given the parameters
We need to Write these as normal numbers
A.) 7.2 x 10^{-5} = 0.000000072
B.) 6.3 x 10^{-9} = 0.0000000063
C.) 4.54 x 10^{-5} = 0.0000454
D.) 7.041 x 10^{-10} = 0.0000000007041
Learn more about multiplications;
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Imagine a man in the Chicago suburbs went outside to shovel his driveway after the Feb 10, 2018 snowstorm and had a heart attack while shoveling. When the police discovered the body later that day at 4PM, his body temperature had dropped from 98.6°F to 42°F. The environmental air temperature was 10°F. What time did he die from the heart attack?
Answers
Answer:
I did my best with the information! The Man died at around 11:20 am.
Step-by-step explanation:
So due to the algus mortis process, after death, a body can stay at its regulated temperature for up to 2 to 3 hours postmortem. But after that, the body soon drops at about 1 degrees celsius each hour. 1 degrees celsius is about -33 . So he was found at 42 degrees fahrenheit, which means he died somewhere around 11 o-clock. We do not know how long the postmortem process had his temperature delayed, so it would be roughly I say around 11: 20 am.
Please answer this correctly without making mistakes
Answers
Explanation:
There are 11 equal parts
He did 3 on Saturday
Which mean he did 3/11 of the total parts
Answer:
3/11
Step-by-step explanation:
There are eleven equal parts.
So the denominator is 11.
He copies 8 parts on Sunday.
11-8=3.
He copied 3 parts on Saturday.
Hope this helps ;) ❤❤❤
About 9% of the population has a particular genetic mutation. 600 people are randomly selected.
Find the standard deviation for the number of people with the genetic mutation in such groups of 600.
Answers
Answer:
The mean for all such groups randomly selected is 0.09*800=72.
Step-by-step explanation:
The value of the standard deviation is 7.
What is the standard deviation?Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.
The standard deviation is calculated by using the formula,
[tex]\sigma = \sqrt{Npq}[/tex]
N = 600
p = 9%= 0.09
q = 1 - p= 1 - 0.09= 0.91
Put the values in the formulas.
[tex]\sigma = \sqrt{Npq}[/tex]
[tex]\sigma = \sqrt{600 \times 0.09\times 0.91}[/tex]
[tex]\sigma[/tex] = 7
Therefore, the value of the standard deviation is 7.
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Find the value of a A.130 B.86 C.58 D.65
Answers
Answer:
Option (B)
Step-by-step explanation:
If two chords intersect inside a circle, measure of angle formed is one half the sum of the arcs intercepted by the vertical angles.
Therefore, 86° = [tex]\frac{1}{2}(a+c)[/tex]
a + c = 172°
Since the chords intercepting arcs a and c are of the same length, measures of the intercepted arcs by these chords will be same.
Therefore, a = c
⇒ a = c = 86°
Therefore, a = 86°
Option (B) will be the answer.
Tanya's car will go 45 meters on 7 gallons. Tanya wants to know how fuel efficient the car is. Please help by computing the ratio. (round to 2 decimal places)
Answers
Answer:
5 meters : 1 gallon
fuel efficiency of Car is 7 meters per gallons
Step-by-step explanation:
Given Tanya car goes 45 meters on 7 gallons.
In terms of ratio of distance traveled and fuel consumed
45 meters : 7 gallons
since both 45 and 7 are multiple of 7 dividing both side by 7
45/7 meters : 7/7 gallons
5 meters : 1 gallon
Thus, fuel efficiency of Car is 7 meters per gallons.
Is the test below left-, right-, or two-tailed? H0:p=0.39, Ha:p≠0.39 Select the correct answer below: The hypothesis test is two-tailed. The hypothesis test is left-tailed. The hypothesis test is right-tailed.
Answers
Answer:
The hypothesis test is a two-tail test
Step-by-step explanation:
The test hypothesis:
Null hypothesis H₀ p = 0,39 or p = p₀
Where p₀ is a nominal proportion (established proportion) and
Alternate hypothesis Hₐ p ≠ 0,39 or p ≠ p₀
Is a two-tail test, (≠) means different, we have to understand that different implies bigger and smaller than something.
For a test to be one tail-test, it is necessary an evaluation only in one sense in relation to the pattern ( in this case the proportion )
A catering service offers 11 appetizers, 12 main courses, and 8 desserts. A customer is to select 9 appetizers, 2 main courses, and 3 desserts for a banquet. In how many ways can this be done?
Answers
Answer: 203,280
Step-by-step explanation:
Given: A catering service offers 11 appetizers, 12 main courses, and 8 desserts.
Number of combinations of choosing r things out of n = [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
A customer is to select 9 appetizers, 2 main courses, and 3 desserts for a banquet.
Total number of ways to do this: [tex]^{11}C_9\times ^{12}C_2\times^{8}C_3[/tex]
[tex]=\dfrac{11!}{9!2!}\times\dfrac{12!}{2!10!}\times\dfrac{8!}{3!5!}\\\\=\dfrac{11\times10}{2}\times\dfrac{12\times11}{2}\times\dfrac{8\times7\times6}{3\times2}\\\\= 203280[/tex]
hence , this can be done in 203,280 ways.
Perform the indicated operation. kyz * 1/kyz answer choices is 0 1 and k^2 y^2 z^2
Answers
Answer:
1
Step-by-step explanation:
[tex]\frac{kyz}{1}*\frac{1}{kyz} =\frac{kyz}{kyz}=1[/tex]
Consider two consecutive positive integers such that the square of the second integer added to 3 times the first is equal to 105
Answers
Answer:
8 and 9
Step-by-step explanation:
If x is the smaller integer, and x + 1 is the larger integer, then:
(x + 1)² + 3x = 105
x² + 2x + 1 + 3x = 105
x² + 5x − 104 = 0
(x + 13) (x − 8) = 0
x = -13 or 8
Since x is positive, x = 8. So the two integers are 8 and 9.
17. What is the most likely outcome of decreasing the wavelength of incident light on a diffraction grating? A. lines become narrower B. distance between lines increases C. lines become thicker D. distance between lines decreases
Answers
When the wavelength of a diffraction grating is decreased, the distance between lines decreases.
What is a diffraction grating?The diffraction grating is used to carry out interference experiments. It consists of a number of small lines that are constructed to be close to each other and produce an interference pattern.
The outcome of decreasing the wavelength of incident light on a diffraction grating is that the distance between lines decreases.
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Gamal spent $12.50 at the book store. The difference between the amount he spent at the video game store and the amount he spent at the book store was $17. The equation d minus 12.50 = 17 can be used to represent this situation, where d is the amount Gamal spent at the video game store. Which equation is an equivalent equation that can be used to find the amount Gamal spent at the video game store?
Answers
Answer:
d - 12.50 = 17
add 12.50 to both sides to get d alone.
d = 12.50 + 17
Answer:
It's B d= 17 + 12.50
Step-by-step explanation:
Got it right on edg
Please explain what this means! (no math needs to be done as I got the answers but I don't understand the explanation...)
Answers
you can imagine this as a venn diagram. the "or" event would consist of everything in both sides and the middle of the venn diagram because you can choose form either event x or event y.
the "and" event would consist of everything in the middle of the venn diagram because you choice must be a part of both event x and event y.
the complement of an event is just everything that is not included in the event. for example, in a coin flip, the complement of heads is tails. in a dice roll, the complement of {1,2} is {3,4,5,6}
so if you come across these just think "either or" or "both and." and remember that the complement is everything excluding what is listed.
i apologize if this does not help, im not that great at explaining things
Evan wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn, so he needs no fence on that side. The other three sides will be enclosed with wire fencing. If Evan has 1000 feet of fencing, you can find the dimensions that maximize the area of the enclosure. a) Let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn). Write an function for the area A of the enclosure in terms of w . (HINT first write two equations with w and l and A . Solve for l in one equation and substitute for l in the other). A(w) = ___________ b) What width would maximize the area? w = __________ c) What is the maximum area? A = _________ square feet
Answers
Answer: A. A=(1000-2w)*w B. 250 feet
C. 125 000 square feet
Step-by-step explanation:
The area of rectangular is A=l*w (1)
From another hand the length of the fence is 2*w+l=1000 (2)
L is not multiplied by 2, because the opposite side of the l is the barn,- we don't need in fence on that side.
Express l from (2):
l=1000-2w
Substitude l in (1) by 1000-2w
A=(1000-2w)*w (3) ( Part A. is done !)
Part B.
To find the width w (Wmax) that corresponds to max of area A we have to dind the roots of equation (1000-2w)w=0 ( we get it from (3))
w1=0 1000-2*w2=0
w2=500
Wmax= (w1+w2)/2=(0+500)/2=250 feet
The width that maximize area A is Wmax=250 feet
Part C. Using (3) and the value of Wmax=250 we can write the following:
A(Wmax)=250*(1000-2*250)=250*500=125 000 square feets
Kirsten has 9 syrup containers from a local cafe. There are 6 milliliters of syrup per container.
Answers
Answer: 54 mL
Step-by-step explanation:
Simply do 9(number of containers)*6(Syrup per container) to get 54 mL of syrup.
Hope it helps <3
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To clear the fractions we multiply both sides by the least common multiple of all the denominators.
1/2 x + 2/3 = 4
Denominators 2 and 3, so multiply both sides by [Answer]: 6
3/4 x + 1 = 5/6
Denoms 4 and 6, LCM=12 Answer: 12
6/7 x - 2/3 = 5/21
LCM(7,3,21)=21 Answer: 21
3/5 + x/2 = 9
LCM(5,2) Answer: 10
25/4 = 6 + 1/2 x
LCM(4,2) Answer: 4
What is the five number summary for this data set?
3, 8, 14, 19, 22, 29, 33, 37, 43, 49
Assume the numbers in each answer choice are listed in this order: min, Q1,
median, Q3, max
Answers
Answer:
see explanation
Step-by-step explanation:
The median is the middle value of the data set in ascending order. If there is no exact middle then the median is the average of the values either side of the middle.
Given
3 8 14 19 22 29 33 37 43 49
↑ middle is between 22 and 29
median = [tex]\frac{22+29}{2}[/tex] = [tex]\frac{51}{2}[/tex] = 25.5
The upper quartile [tex]Q_{3}[/tex] is the middle value of the data to the right of the median.
29 33 37 43 49
↑
[tex]Q_{3}[/tex] = 37
The lower quartile [tex]Q_{1}[/tex] is the middle value of the data to the left of the median.
3 8 14 19 22
↑
[tex]Q_{1}[/tex] = 14
The min is the smallest value in the data set, that is 3
The max is the largest value in the data set, that is 49
The 5 number summary is
3, 14, 25.5, 37, 49
Calculate the side lengths a and b to two decimal places
A. a= 10.92 b=14.52 <--- My answer
B. a= 11 b= 15
C. a=4.18 b=3.15
D. a= 11.40 b=13.38
Answers
Answer:
Option (D)
Step-by-step explanation:
In the picture attached,
An obtuse angle triangle ABC has been given.
By applying Sine rule in the triangle,
[tex]\frac{\text{SinB}}{b}=\frac{\text{SinA}}{a}=\frac{\text{SinC}}{c}[/tex]
Since, m∠A + m∠B + m∠C = 180°
45° + 110° + m∠C = 180°
m∠C = 180°- 155° = 25°
[tex]\frac{\text{Sin110}}{b}=\frac{\text{Sin45}}{a}=\frac{\text{Sin25}}{7}[/tex]
[tex]\frac{\text{Sin110}}{b}=\frac{\text{Sin45}}{a}=0.060374[/tex]
[tex]\frac{\text{Sin110}}{b}=0.060374[/tex]
b = [tex]\frac{\text{Sin110}}{0.060374}[/tex]
b = 15.56
b ≈ 15.56
[tex]\frac{\text{Sin45}}{a}=0.060374[/tex]
a = [tex]\frac{\text{Sin45}}{0.060374}[/tex]
a = 11.712
a = 11.71
Therefore, Option (D) will be the answer.