Answer:
52.63% probability that thids intial repair was made by the first technican
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Incomplete repair
Event B: Made by the first technican.
The first technican, who services 40% of the breakdowns, has 5% chance of making incomplete repair.
This means that [tex]P(B) = 0.4, P(A|B) = 0.05[/tex].
Probability of an incomplete repair:
5% of 40%(first technican) or 3% of 60%(second technican). So
[tex]P(A) = 0.05*0.4 + 0.03*0.6 = 0.038[/tex]
Given that there is a problem with the production line due to an incomplete repair, what is the probability that thids intial repair was made by the first technican
[tex]P(B|A) = \frac{0.4*0.05}{0.038} = 0.5263[/tex]
52.63% probability that thids intial repair was made by the first technican
someone help please with this question
Step-by-step explanation:
1. 180 - (36 +36)= 108
2. angle ABC = 108 angle DBC = 108-72=36
3. angle DCB=angle DBC. This is because the base angles are equal
4 therefore triangle BDC is isoscles
Answer:
Because ΔABD is isosceles, ∠ABD ≅ ∠ADB = 72° because of Base Angles Theorem which states that the base angles of an isosceles triangle are congruent. Then, ∠BDC = 180° - ∠ADB = 108° because they are supplementary angles. Because ΔABC is isosceles, ∠BAC ≅ ∠BCA = 36° because of Base Angles Theorem, which means ∠CBD = 180° - 108° - 36° = 36° because of the sum of angles in a triangle. Therefore, ΔBCD is isosceles because of the Converse of Base Angles Theorem.
HELP ASAP!!!The first picture is what each variables equal too
Answer:
Just replace the variables with the number
d5
c4 (uh oh)
a2
b-3
f-7
d-c = 5 - 4 = 1
1/3 - 4(ab+f)
2 x -3 = -6
-6 + -7 = -13
-13 x 4 = -52
1/3 - -52 = 1/3 + 52 =
52 1/3
Hope this helps
Step-by-step explanation:
A box contains 11 red chips and 4 blue chips. We perform the following two-step experiment: (1) First, a chip is selected at random from the box and is then removed from the box. (After this first step, there are 14 chips left in the box. ) (2) Then, a chip is selected at random from the box (that is, from the remaining 14 chips) . Let B 1 be the event that the chip removed from the box at the first step of the experi- ment is red. Let B 2 be the event that the chip removed from the box at the first step of the experiment is blue. Let A be the event that the chip selected from the box at the second step of the experiment is red.Find P(B1), P(B2), P(A), P(B1|A), and P(B2|A).
Answer:
P(B1) = (11/15)
P(B2) = (4/15)
P(A) = (11/15)
P(B1|A) = (5/7)
P(B2|A) = (2/7)
Step-by-step explanation:
There are 11 red chips and 4 blue chips in a box. Two chips are selected one after the other at random and without replacement from the box.
B1 is the event that the chip removed from the box at the first step of the experiment is red.
B2 is the event that the chip removed from the box at the first step of the experiment is blue. A is the event that the chip selected from the box at the second step of the experiment is red.
Note that the probability of an event is the number of elements in that event divided by the Total number of elements in the sample space.
P(E) = n(E) ÷ n(S)
P(B1) = probability that the first chip selected is a red chip = (11/15)
P(B2) = probability that the first chip selected is a blue chip = (4/15)
P(A) = probability that the second chip selected is a red chip
P(A) = P(B1 n A) + P(B2 n A) (Since events B1 and B2 are mutually exclusive)
P(B1 n A) = (11/15) × (10/14) = (11/21)
P(B2 n A) = (4/15) × (11/14) = (22/105)
P(A) = (11/21) + (22/105) = (77/105) = (11/15)
P(B1|A) = probability that the first chip selected is a red chip given that the second chip selected is a red chip
The conditional probability, P(X|Y) is given mathematically as
P(X|Y) = P(X n Y) ÷ P(Y)
So, P(B1|A) = P(B1 n A) ÷ P(A)
P(B1 n A) = (11/15) × (10/14) = (11/21)
P(A) = (11/15)
P(B1|A) = (11/21) ÷ (11/15) = (15/21) = (5/7)
P(B2|A) = probability that the first chip selected is a blue chip given that the second chip selected is a red chip
P(B2|A) = P(B2 n A) ÷ P(A)
P(B2 n A) = (4/15) × (11/14) = (22/105)
P(A) = (11/15)
P(B2|A) = (22/105) ÷ (11/15) = (2/7)
Hope this Helps!!!
The mean annual tuition and fees for a sample of 15 private colleges was with a standard deviation of . A dotplot shows that it is reasonable to assume that the population is approximately normal. You wish to test whether the mean tuition and fees for private colleges is different from 32,500 a) state the null and alternate hypotheses b) calculate the standard error c) calculate the test statistic d) find the p - value .
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
The mean annual tuition and fees for a sample of 15 private colleges was $35,500 with a standard deviation of $6500. A dotplot shows that it is reasonable to assume that the population is approximately normal. You wish to test whether the mean tuition and fees for private colleges is different from $32,500. State the null and alternate hypotheses. A) H0: 4 = 32,500, H:4=35,500 C) H: 4 = 35,500, H7:35,500 B) H: 4 = 32,500, H : 4 # 32,500 D) H0:41 # 32,500, H : 4 = 32,500
Solution
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ = 32500
For the alternative hypothesis,
Ha: µ ≠ 32500
This is a two tailed test.
Since the number of samples is small and the population standard deviation is not given, the distribution is a student's t.
Since n = 15,
Degrees of freedom, df = n - 1 = 15 - 1 = 14
t = (x - µ)/(s/√n)
Where
x = sample mean = 35500
µ = population mean = 32500
s = samples standard deviation = 6500
t = (35500 - 32500)/(6500/√15) = 1.79
We would determine the p value using the t test calculator. It becomes
p = 0.095
Assuming alpha = 0.05
Since alpha, 0.05 < than the p value, 0.095, then we would fail to reject the null hypothesis.
Which is the graph |3x-6|=21
Answer:
it should look like this
Antipsychotic drugs are widely prescribed for conditions such as schizophrenia and bipolar disease. An article reported on body composition and metabolic changes for individuals who had taken various antipsychotic drugs for short periods of time. (a) The sample of 41 individuals who had taken aripiprazole had a mean change in total cholesterol (mg/dL) of 3.55, and the estimated standard error sD n was 3.478. Calculate a confidence interval with confidence level approximately 95% for the true average increase in total cholesterol under these circumstances. (Round your answers to two decimal places.)
Answer:
95% for the true average increase in total cholesterol under these circumstances
(-2.306 , 9.406)
Step-by-step explanation:
Step(i):-
Given sample size 'n' =41
Mean of the sample(x⁻) = 3.55
The estimated standard error
[tex]S.E = \frac{S.D}{\sqrt{n} }[/tex]
Given estimated standard error ( S.E) = 3.478
Level of significance ∝=0.05
Step(ii):-
95% for the true average increase in total cholesterol under these circumstances
[tex](x^{-} - t_{0.05} S.E ,x^{-} + t_{0.05} S.E)[/tex]
Degrees of freedom
ν= n-1 = 41-1 =40
t₀.₀₅ = 1.6839
95% for the true average increase in total cholesterol under these circumstances
[tex](x^{-} - t_{0.05} S.E ,x^{-} + t_{0.05} S.E)[/tex]
( 3.55 - 1.6839 ×3.478 ,3.55 + 1.6839 ×3.478 )
(3.55 - 5.856 , 3.55 + 5.856)
(-2.306 , 9.406)
Conclusion:-
95% for the true average increase in total cholesterol under these circumstances
(-2.306 , 9.406)
A lumber company is making doors that are 2058.0 millimeters tall. If the doors are too long they must be trimmed, and if the doors are too short they cannot be used. A sample of 22 is made, and it is found that they have a mean of 2045.0 millimeters with a standard deviation of 13.0. A level of significance of 0.1 will be used to determine if the doors are either too long or too short. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.
Answer:
[tex]t=\frac{2045-2058}{\frac{13}{\sqrt{22}}}=-4.69[/tex]
The degrees of freedom are given by:
[tex]df=n-1=22-1=21[/tex]
And the p value would be given by:
[tex]p_v =2*P(t_{21}<-4.69)=0.000125[/tex]
Since the p value is a very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2058 mm at the significance level of 0.1 (10%) given
Step-by-step explanation:
Information given
[tex]\bar X=2045[/tex] represent the sample mean
[tex]s=13[/tex] represent the standard deviation
[tex]n=22[/tex] sample size
[tex]\mu_o =2058[/tex] represent the value to test
[tex]\alpha=0.1[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to cehck if the true mean for this case is equal to 2058 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 2058[/tex]
Alternative hypothesis:[tex]\mu \neq 2058[/tex]
The statistic for this case is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
[tex]t=\frac{2045-2058}{\frac{13}{\sqrt{22}}}=-4.69[/tex]
The degrees of freedom are given by:
[tex]df=n-1=22-1=21[/tex]
And the p value would be given by:
[tex]p_v =2*P(t_{21}<-4.69)=0.000125[/tex]
Since the p value is a very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2058 mm at the significance level of 0.1 (10%) given
The percentage of households that include at least one frequent gamer is 58%. A gaming magazine is interested in studying this further to see how it impacts their magazine advertisements. For what sample size, n, will the sampling distribution of sample proportions have a standard deviation of 0.02
Answer:
For a sample size of n = 609.
Step-by-step explanation:
Central limit theorem for proportions:
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
We have that p = 0.58.
We have to find n for which s = 0.02. So
[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
[tex]0.02 = \sqrt{\frac{0.58*0.42}{n}}[/tex]
[tex]0.02\sqrt{n} = \sqrt{0.58*0.42}[/tex]
[tex]\sqrt{n} = \frac{\sqrt{0.58*0.42}}{0.02}[/tex]
[tex](\sqrt{n})^{2} = (\frac{\sqrt{0.58*0.42}}{0.02})^{2}[/tex]
[tex]n = 609[/tex]
For a sample size of n = 609.
Find the equation of the line.
Use exact numbers.
Answer:
y = 2/3x + 4
Step-by-step explanation:
Step 1: Find slope
m = (4-0)/(0+6)
m = 2/3
Step 2: Write in y-int (0, 4)
y = 2/3x + 4
Kyra is using rectangular tiles of two types for a floor design. They Tyler each type is shown below:
Answer: b) the tiles are not similar because both SP:SR is 5:4 and MJ:ML is 5:2
Step-by-step explanation:
We are given that the tiles are rectangular which implies that they both have a 90° angle.
In order to prove similarity, We need to show that the lengths and widths are proportional.
P Q R S
J K L M
a) PQ : QR JK : LM
w=4 L=5 w=2 w=2
↓
We need Length (not width)
b) SP : SR MJ : ML
L=5 w=4 L=5 w=2
5 : 4 5 : 2
When comparing length to width they do not have the same ratio so the rectangles are not similar.
c) PQ : QR JK : KL
w=4 L=5 w=2 L=5
4 : 5 2 : 5
When comparing width to length they do not have the same ratio so the rectangles are not similar.
d) SR : ML PQ : JK
w=4 w=2 w=4 w=2
↓ ↓
We need Length (not width)
Terry has a number cube that is numbered from 1 to 6. She rolls the cube 50 times. Which equation can be used to predict the number of times that she will roll a number that is greater than 4? P (number greater than 4) = StartFraction 1 over 6 EndFraction (50) P (number greater than 4) = StartFraction 2 over 6 EndFraction (50) P (number greater than 4) = StartFraction 3 over 6 EndFraction (50) P (number greater than 4) = StartFraction 4 over 6 EndFraction (50)
Answer:
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Can someone please help me??
Answer : The value of x is 4.1 cm.
Step-by-step explanation :
As we know that the perpendicular dropped from the center divides the chord into two equal parts.
That means,
AB = CB = [tex]\frac{15.6cm}{2}=7.8cm[/tex]
Now we have o calculate the value of x by using Pythagoras theorem.
Using Pythagoras theorem in ΔOBA :
[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]
[tex](OA)^2=(OB)^2+(BA)^2[/tex]
Now put all the values in the above expression, we get the value of side OB.
[tex](8.8)^2=(x)^2+(7.8)^2[/tex]
[tex]x=\sqrt{(8.8)^2-(7.8)^2}[/tex]
[tex]x=\sqrt{77.44-60.84}[/tex]
[tex]x=\sqrt{16.6}[/tex]
[tex]x=4.074\approx 4.1[/tex]
Therefore, the value of x is 4.1 cm.
segment AB is dilated from the origin to create segment A prime B prime at A' (0, 6) and B' (6, 9). What scale factor was segment AB dilated by?
1/2
2
3
4
Answer:
the answer is 3
Step-by-step explanation:
i took the test
Each of the following is a confidence interval for μ = true average (i.e., population mean) resonance frequency (Hz) for all tennis rackets of a certain type:(111.6, 112.4) (111.4, 112.6)(a) What is the value of the sample mean resonance frequency?
Answer:
The value of the sample mean resonance frequency is 112Hz
Step-by-step explanation:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
In this problem, we have that:
Lower bound: 111.6
Upper bound: 112.4
Sample mean: (111.6 + 112.4)/2 = 112Hz
The value of the sample mean resonance frequency is 112Hz
The value of the sample mean resonance frequency is 112 Hz.
What is the value of the sample mean resonance frequency?The value of the sample mean resonance frequency is equivalent to the average of the upper limit and the lower limit.
The sample mean resonance frequency = (lower limit + upper limit) / 2
(111.6 +112.4) / 2
= 224 / 2
= 112 Hz
To learn more about confidence interval, please check: https://brainly.com/question/15905477
A publisher reports that 65% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 340 found that 60% of the readers owned a laptop. State the null and alternative hypotheses. Answer
Answer:
[tex]z=\frac{0.60 -0.65}{\sqrt{\frac{0.65(1-0.65)}{340}}}=-1.933[/tex]
The p value for this case can be calculated with this probability:
[tex]p_v =2*P(z<-1.933)=0.0532[/tex]
For this case is we use a significance level of 5% we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is different from 0.65 or 65%. We need to be careful since if we use a value higher than 65 for the significance the result would change
Step-by-step explanation:
Information given
n=340 represent the random sample taken
[tex]\hat p=0.60[/tex] estimated proportion of readers owned a laptop
[tex]p_o=0.65[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v{/tex} represent the p value
Hypothesis to test
We want to check if the true proportion of readers owned a laptop if different from 0.65
Null hypothesis:[tex]p=0.65[/tex]
Alternative hypothesis:[tex]p \neq 0.65[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing we got:
[tex]z=\frac{0.60 -0.65}{\sqrt{\frac{0.65(1-0.65)}{340}}}=-1.933[/tex]
The p value for this case can be calculated with this probability:
[tex]p_v =2*P(z<-1.933)=0.0532[/tex]
For this case is we use a significance level of 5% we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is different from 0.65 or 65%. We need to be careful since if we use a value higher than 65 for the significance the result would change
Show that every triangle formed by the coordinate axes and a tangent line to y = 1/x ( for x > 0)
always has an area of 2 square units.
Hint: Find the equation of the tangent line at x = a. (It will contain a’s as well as x and y.) Then find the
x-and y-intercepts for that line to find the lengths of sides of the right triangle.
Answer:
Step-by-step explanation:
given a point [tex](x_0,y_0)[/tex] the equation of a line with slope m that passes through the given point is
[tex]y-y_0 = m(x-x_0)[/tex] or equivalently
[tex] y = mx+(y_0-mx_0)[/tex].
Recall that a line of the form [tex]y=mx+b [/tex], the y intercept is b and the x intercept is [tex]\frac{-b}{m}[/tex].
So, in our case, the y intercept is [tex](y_0-mx_0)[/tex] and the x intercept is [tex]\frac{mx_0-y_0}{m}[/tex].
In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph [tex](x_0,\frac{1}{x_0})[/tex]. Which means that [tex]y_0=\frac{1}{x_0}[/tex]
The slope of the tangent line is given by the derivative of the function evaluated at [tex]x_0[/tex]. Using the properties of derivatives, we get
[tex]y' = \frac{-1}{x^2}[/tex]. So evaluated at [tex]x_0[/tex] we get [tex] m = \frac{-1}{x_0^2}[/tex]
Replacing the values in our previous findings we get that the y intercept is
[tex](y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}[/tex]
The x intercept is
[tex] \frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0[/tex]
The triangle in consideration has height [tex]\frac{2}{x_0}[/tex] and base [tex]2x_0[/tex]. So the area is
[tex] \frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2[/tex]
So regardless of the point we take on the graph, the area of the triangle is always 2.
A 2011 survey, by the Bureau of Labor Statistics, reported that 91% of Americans have paid leave. In January 2012, a random survey of 1000 workers showed that 89% had paid leave. The resulting p-value is .0271; thus, the null hypothesis is rejected. It is concluded that there has been a decrease in the proportion of people, who have paid leave from 2011 to January 2012. What type of error is possible in this situation?
Answer:
Is possible to make a Type I error, where we reject a true null hypothesis.
Step-by-step explanation:
We have a hypothesis test of a proportion. The claim is that the proportion of paid leave has significantly decrease from 2011 to january 2012. The P-value for this test is 0.0271 and the nunll hypothesis is rejected.
As the conclusion is to reject the null hypothesis, the only error that we may have comitted is rejecting a true null hypothesis.
The null hypothesis would have stated that there is no significant decrease in the proportion of paid leave.
This is a Type I error, where we reject a true null hypothesis.
Luke and skylar work at furniture store. Luke is paid $180 per week plus 5% of his total sales in dollars ,x,which can be represented by g(x)=180+0.05x. Skylar is paid $104 per week plus 7% of her total sales in dollars which can be represented by f(x)=104+0.07x. Determine the value of x in dollars that will make their weekly pay the same
Answer:
The total sales in dollars to make their pay equal is: $ 3800
Step-by-step explanation:
Since we need to find the number of sales that make both function equal in value, we equal both expressions, and solve for 'x":
[tex]180+0.05 \,x=104+0.07 \,x\\180-104=0.07\,x-0.05\,x\\76=0.02x\\x=\frac{76}{0.02} \\x=3800[/tex]
5/a - 4/b as a single fraction
Answer:
I'm not completely sure what you mean by a, "single fraction," but I'm pretty sure the answer you are looking for is [tex]\frac{5-4}{a-b}[/tex]
Step-by-step explanation:
from what area of the world is the earliest dated inscription with a symbol for zero?
Answer:
india
Step-by-step explanation:
what is the length of the line?
Answer:
root 61
Step-by-step explanation:
You can use the distance formula or draw a triangle with sides 5 and 6
It is known that 4% of children carry a certain virus, but a leading health researcher suspects that the percentage is actually higher. Which of the following provides the most convincing evidence to support the researcher's suspicion?
A. Out of 5,000 randomly chosen children, 210 children carry the virus.
B. Out of 60 randomly chosen children, 3 children carry the virus.
C. Out of 5,000 randomly chosen children, 250 children carry the virus.
D. Out of 20 randomly chosen children, 1 child carries the virus.
Answer:
(C)Out of 5,000 randomly chosen children, 250 children carry the virus.
Step-by-step explanation:
[tex]\text{Option A}: \dfrac{210}{5000}=0.042=4.2\% \\\text{Option B}: \dfrac{3}{60}=0.05=5\% \\\text{Option C}: \dfrac{250}{5000}=0.05=5\% \\\text{Option D}: \dfrac{1}{20}=0.05=5\%[/tex]
The higher the research sample, the more credible the results. In options A and C, the research sample was 5000. However, since the relative frequency of children carrying the virus is 5% in both, we take the result with a higher number of positives.
Option C is the correct option.
Pleassseee hhheeelllppp
Answer/Step-by-step explanation:
When solving problems like this, remember the following:
1. + × + = +
2. + × - = -
3. - × + = -
4. - × - = +
Let's solve:
a. (-4) + (+10) + (+4) + (-2)
Open the bracket
- 4 + 10 + 4 - 2
= - 4 - 2 + 10 + 4
= - 6 + 14 = 8
b. (+5) + (-8) + (+3) + (-7)
= + 5 - 8 + 3 - 7
= 5 + 3 - 8 - 7
= 8 - 15
= - 7
c. (-19) + (+14) + (+21) + (-23)
= - 19 + 14 + 21 - 23
= - 19 - 23 + 14 + 21
= - 42 + 35
= - 7
d. (+5) - (-10) - (+4)
= + 5 + 10 - 4
= 15 - 4 = 11
e. (-3) - (-3) - (-3)
= - 3 + 3 + 3
= - 3 + 9
= 6
f. (+26) - (-32) - (+15) - (-8)
= 26 + 32 - 15 + 8
= 26 + 32 + 8 - 15
= 66 - 15
= 51
In the multiplication sentence below, which numbers are the factors? Check
all that apply.
10 x 8 = 80
A. 80
B. 8.
I C. 10
Answer:
10 and 8
Step-by-step explanation:
10 and 8 are the factors in this equation because factors are the numbers that are mutiplied together to get the product (The answer to a mutiplication problem) Therefore the factors in this equation are 10 and 8 because those are the numbers that are mutiplied together to get the product.
3z/10 - 4 = -6
someone help?
Answer:
[tex]z=-\frac{20}{3}[/tex]
Step-by-step explanation:
[tex]\frac{3z}{10}-4=-6\\\\\frac{3z}{10}-4+4=-6+4\\\\\frac{3z}{10}=-2\\\\\frac{10\cdot \:3z}{10}=10\left(-2\right)\\\\3z=-20\\\\\frac{3z}{3}=\frac{-20}{3}\\\\z=-\frac{20}{3}[/tex]
Best Regards!
A grocery store manager notices that this month her store sold a total of 597 gallons of ice cream, which represents a decrease of 15% from last month. On the other hand, her store sold 617 pounds of broccoli this month, which represents an increase of 21% from last month. How much ice cream and broccoli did the store sell last month? Round your answers to the nearest integer.
Answer:
(a)The total sales of ice-cream last month is 702 gallons.
(b)The total sales of broccoli last month is 510 pounds.
Step-by-step explanation:
Part A
Total Sales of gallons of ice cream this month = 597
Since it represents a decrease of 15% of last month's sales
Let the total sales of ice-cream last month =x
Then:
(100-15)% of x =597
85% of x=597
0.85x=597
x=597/0.85
x=702 (to the nearest integer)
The total sales of ice-cream last month is 702 gallons.
Part B
Total Sales of broccoli this month = 617 pounds
Since it represents an increase of 21% of last month's sales
Let the total sales of ice-cream last month =y
Then:
(100+21)% of y =617
121% of y=617
1.21y=617
y=617/1.21
y=510 (to the nearest integer)
The total sales of broccoli last month is 510 pounds.
The sum of a number and twice the number is 24 what is the number?
Answer:
x = 8
Step-by-step explanation:
Step 1: Write out the expression
x + 2x = 24
Step 2: Combine like terms
3x = 24
Step 3: Isolate x
x = 8
And we have our final answer!
Answer:
X=8
Step-by-step explanation:
Which of the following is the solution to 9|x-1|=-45
Answer:
No solutions.
Step-by-step explanation:
9|x-1|=-45
Divide 9 into both sides.
|x-1| = -45/9
|x-1| = -5
Absolute value cannot be less than 0.
Answer:
No solution
Step-by-step explanation:
=> 9|x-1| = -45
Dividing both sides by 9
=> |x-1| = -5
Since, this is less than zero, hence the equation has no solutions
Two fair dice are tossed and the number on each die is recorded, e.g. (3,2) indicates the first die had 3 and the second die had a 2. In total, there are 36 (equally likely) outcomes in the sample space. What is the probability the sum of the two dice is 7 or 11? Group of answer choices
Answer:
P(7 or 11) = 0.2222
Step-by-step explanation:
First let's find the cases where we get a sum of 7 and a sum of 11:
The cases where we get a sum of 7 are:
(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)
And the cases where we get a sum of 11 are:
(5,6), (6,5)
So we have a total of 8 cases among the 36 total possible outcomes.
So the probability of the sum of the two dice being 7 or 11 is:
P(7 or 11) = 8 / 36 = 0.2222
A student carried out an experiment to determine the amount of vitamin C in a tablet sample. He performed 5 trials to produce the following results: 490 mg, 502 mg, 505 mg, 495mg, and 492 mg. The manufacturer claims that the tablet contains 500 mg of vitamin C. Do an appropriate statistical analysis to find out whether the results obtained by the student is consistent with bottle claim.
Answer:
There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.
P-value = 0.166.
Step-by-step explanation:
We start by calculating the mean and standard deviation of the sample:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{5}(490+502+505+495+492)\\\\\\M=\dfrac{2484}{5}\\\\\\M=496.8\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}((490-496.8)^2+(502-496.8)^2+(505-496.8)^2+(495-496.8)^2+(492-496.8)^2)}\\\\\\s=\sqrt{\dfrac{166.8}{4}}\\\\\\s=\sqrt{41.7}=6.5\\\\\\[/tex]
Then, we can perform the hypothesis t-test for the mean.
The claim is that the amount of vitamin C in a tablet sample is different from 500 mg.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=500\\\\H_a:\mu< 500[/tex]
The significance level is 0.05.
The sample has a size n=5.
The sample mean is M=496.8.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=6.5.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6.5}{\sqrt{5}}=2.907[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{496.8-500}{2.907}=\dfrac{-3.2}{2.907}=-1.1[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=5-1=4[/tex]
This test is a left-tailed test, with 4 degrees of freedom and t=-1.1, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-1.1)=0.166[/tex]
As the P-value (0.166) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.