The following are quality control data for a manufacturing process at Kensport Chemical Company. The data show the temperature in degrees centigrade at five points in time during a manufacturing cycle. Sample x R 1 95.72 1.0 2 95.24 0.9 3 95.18 0.9 4 95.44 0.4 5 95.46 0.5 6 95.32 1.1 7 95.40 0.9 8 95.44 0.3 9 95.08 0.2 10 95.50 0.6 11 95.80 0.6 12 95.22 0.2 13 95.56 1.3 14 95.22 0.6 15 95.04 0.8 16 95.72 1.1 17 94.82 0.6 18 95.46 0.5 19 95.60 0.4 20 95.74 0.6 The company is interested in using control charts to monitor the temperature of its manufacturing process. Compute the upper and lower control limits for the R chart. (Round your answers to three decimal places.) UCL
Answers
Answer: The upper control limit is 1.40581
The lower control limit is 0.000
Explanation: Check attachment
The upper control limit (UCL) for the R chart is 1.986 and the lower control limit (LCL) is 0.
To compute the upper and lower control limits for the R chart, we need to calculate the average range (R-bar) and the control limits.
First, let's calculate the range (R) for each sample by subtracting the smallest value from the largest value:
Sample 1: 1.0
Sample 2: 0.9
Sample 3: 0.9
Sample 4: 0.4
Sample 5: 0.5
Sample 6: 1.1
Sample 7: 0.9
Sample 8: 0.3
Sample 9: 0.2
Sample 10: 0.6
Sample 11: 0.6
Sample 12: 0.2
Sample 13: 1.3
Sample 14: 0.6
Sample 15: 0.8
Sample 16: 1.1
Sample 17: 0.6
Sample 18: 0.5
Sample 19: 0.4
Sample 20: 0.6
Next, calculate the average range (R-bar) by summing up all the ranges and dividing by the number of samples:
R-bar = (1.0 + 0.9 + 0.9 + 0.4 + 0.5 + 1.1 + 0.9 + 0.3 + 0.2 + 0.6 + 0.6 + 0.2 + 1.3 + 0.6 + 0.8 + 1.1 + 0.6 + 0.5 + 0.4 + 0.6) / 20
R-bar = 0.735
To calculate the upper control limit (UCL) for the R chart, multiply the R-bar by a constant factor. For small sample sizes like this (n=5), the constant factor is typically 2.704:
UCL = R-bar * 2.704
UCL = 0.735 * 2.704
UCL = 1.986
Finally, to calculate the lower control limit (LCL) for the R chart, multiply the R-bar by another constant factor. For small sample sizes like this, the constant factor is typically 0:
LCL = R-bar * 0
LCL = 0
Therefore, the upper control limit (UCL) for the R chart is 1.986 and the lower control limit (LCL) is 0.
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Related Questions
Los Angeles workers have an average commute of 26 minutes. Suppose the LA commute time is normally distributed with a standard deviation of 13 minutes. Let X represent the commute time for a randomly selected LA worker. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(
26
Correct,
13
Correct)
b. Find the probability that a randomly selected LA worker has a commute that is longer than 34 minutes.
c. Find the 70th percentile for the commute time of LA workers.
Answers
Answer:
(a) [tex]X\sim N(\mu=26,\ \sigma^{2}=13^{2})[/tex].
(b) The probability that a randomly selected LA worker has a commute that is longer than 34 minutes is 0.2676.
(c) The 70th percentile for the commute time of LA workers is 33 minutes.
Step-by-step explanation:
The random variable X is defined as the commute time for LA workers.
The mean commute time is, μ = 26 minutes and the standard deviation of the commute times is, σ = 13 minutes.
(a)
It is provided that the LA commute time fr workers is normally distributed.
Then the distribution of the random variable X can be defined as follows:
[tex]X\sim N(\mu=26,\ \sigma^{2}=13^{2})[/tex].
(b)
Compute the value of P (X > 34) as follows:
[tex]P(X>34)=P(\frac{X-\mu}{\sigma}>\frac{34-26}{13})[/tex]
[tex]=P(Z>0.62)\\=1-P(Z<0.62)\\=1-0.73237\\=0.26763\\\approx 0.2676[/tex]
*Use a z-table.
Thus, the probability that a randomly selected LA worker has a commute that is longer than 34 minutes is 0.2676.
(c)
The pth percentile is a data value such that at least p% of the data set is less than or equal to this data value and at least (100 - p)% of the data set are more than or equal to this data value.
The 70th percentile for the commute time of LA workers can be written as follows:
P (X < x) = 0.70
⇒ P (Z < z) = 0.70
The value of z for this probability is:
z = 0.53
*Use a z-table.
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\0.53=\frac{x-26}{13}\\\\x=26+(0.53\times 13)\\\\x=32.89\\\\x\approx 33[/tex]
Thus, the 70th percentile for the commute time of LA workers is 33 minutes.
temperatures at several times of the day are shown in the coordinate plane below. the x-axis represents the number of hours before or after noon. for example -1 would represent 11 a.m. the y-axis represents the temperature in degrees celsius at 5pm the temperature is half way between the temperature at 2pm and the temperature at 8pm. what coordinates represent the temperature at 5pm
Answers
11.What is mzB to the nearest tenth?
A
14.1
B
22.9
A 87.40
B 52.0°
С
D
31.6°
38.0°
Answers
Answer:
31.6°
Step-by-step explanation:
<B = arctan (14.1/22.9) = 31.6°
Let’s look at another one of Homer’s rocket launches. It was launched from ground level with an initial velocity of 208 feet per second. Its distance in feet from the ground after t seconds is given by S(t) = -16t2 + 208t. What is the maximum altitude (height) the rocket will attain during its flight? (Think about where the maximum value of a parabola occurs.)
Answers
Answer:
Smax = 676 ft
the maximum altitude (height) the rocket will attain during its flight is 676 ft
Step-by-step explanation:
Given;
The height function S(t) of the rocket as;
S(t) = -16t2 + 208t
The maximum altitude Smax, will occur at dS/dt = 0
differentiating S(t);
dS/dt = -32t + 208 = 0
-32t +208 = 0
32t = 208
t = 208/32
t = 6.5 seconds.
The maximum altitude Smax is;
Substituting t = 6.5 s
Smax = -16(6.5)^2 + 208(6.5)
Smax = 676 ft
the maximum altitude (height) the rocket will attain during its flight is 676 ft
The student senate at a local university is about to hold elections. A representative from the women’s sports program and a representative from the men’s sports program must both be elected. Two candidates, an incumbent and a challenger, are vying for each position and early polling results are presented next. A hypothesis test must be performed to determine whether the percentages of supporting votes are different between the two incumbent candidates. In a sample of 100 voters, 67 said that they would vote for the women’s incumbent candidate. In a separate sample of 100 voters, 55 said they would vote for the men’s incumbent candidate. Let p1 and p2 be the proportions of supporting votes for the incumbent candidates representing women’s and men’s sports programs, respectively. Which of the following are the competing hypotheses to determine whether the percentages of supporting votes are different between the two incumbent candidates?a. H0: p1 ≤ p2, Ha: p1 > p2.b. H0: p1 ≥ p2, Ha: p1 < p2.c. H0: p1 = p2, Ha: p1 ≠ p2.d. H0: p = p0, Ha: p ≠ p0.
Answers
The competing hypotheses to determine whether the percentages of supporting votes are different between the two incumbent candidates are: a. H0: p1 ≤ p2, Ha: p1 > p2.
Null Hypothesis (H0): This represents the statement we want to test and assume to be true in the absence of evidence to the contrary. The null hypothesis (H0) states that there is no difference between the proportions of supporting votes for the incumbent candidates representing women's and men's sports programs.
Alternative Hypothesis (Ha): This represents the statement we want to disprove or find evidence for against the null hypothesis. The alternative hypothesis (Ha) states that the proportion of supporting votes is greater for the women's incumbent candidate than for the men's incumbent candidate.
Which of the following is not a condition required for a valid ANOVA F-test for a completely randomized experiment? 1. The sample chosen from each of the populations is sufficiently large. 2. The variances of all the sampled populations are equal. 3. The sampled populations all have distributions that are approximately normal. 4. The samples are chosen from each population in an independent manner.
Answers
Answer:
1. The sample chosen from each of the populations is sufficiently large.
Step-by-step explanation:
ANOVA is known as analysis of variance and it is a statistical process which is used to test the degree to which two or more groups vary or differ in an experiment.
The variances of all the sampled populations are usually equal. The sampled populations all have distributions that are approximately normal and the samples are chosen from each population in an independent manner.
The one that is not a condition required for a valid ANOVA F-test for a completely randomized experiment is A. The sample chosen from each of the populations is sufficiently large.
It should be noted that ANOVA is known as analysis of variance. It is a statistical process that is used to test the degree to which two or more groups vary in an experiment.When doing the ANOVA, it should be noted that it isn't necessary for all the sample chosen from each of the populations to be sufficiently large.Learn more about ANOVA on:
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You run a small trucking company that transports goods from Bristol, TN to Winslow, AZ. This trip should take 32 hours and 16 minutes (1936 minutes) if done in accordance with safety regulations. However, you believe that your employees have not been following these rules, because they are completing the trip too quickly. You decide to test your hypothesis. You record the time it takes for your employees to make the trip and record the following results
X =1736 minutes s = 635; n = 46
A) State your null and alternative hypotheses
B) Carry out the test with α=005, and state your conclusion
C) Carry out the test with α=0.01, and state your conclusion
D) Does your conclusion change with the change in a?
Answers
Answer:
a) Null hypothesis: [tex]\mu \geq 1936[/tex]
Alternative hypothesis: [tex]\mu <1936[/tex]
b) [tex] t = \frac{1736-1936}{\frac{635}{\sqrt{46}}}= -2.136[/tex]
The degrees of freedom are:
[tex] df = n-1= 46-1=45[/tex]
The p value for this case since is a left tailed test is given by:
[tex] p_v = P(t_{45} <-2.136) = 0.0191[/tex]
And since the p value is lower than the significance level 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly lower than 1736
c) [tex] p_v = P(t_{45} <-2.136) = 0.0191[/tex]
And since the p value is higher than the significance level 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is NOT significantly lower than 1736
d) For this case the answer is yes since when we change the significance level from 0.05 to 0.01 we see that the final decision changes.
Step-by-step explanation:
Part a
We are trying to proof the following system of hypothesis:
Null hypothesis: [tex]\mu \geq 1936[/tex]
Alternative hypothesis: [tex]\mu <1936[/tex]
Part b
We have the following data given:
[tex]\bar X =1736[/tex] minute s = 635; n = 46
And the statistic for this case is given by:
[tex] t = \frac{\bar X- \mu}{\frac{s}{\sqrt{n}}}[/tex]
And replacing we got:
[tex] t = \frac{1736-1936}{\frac{635}{\sqrt{46}}}= -2.136[/tex]
The degrees of freedom are:
[tex] df = n-1= 46-1=45[/tex]
The p value for this case since is a left tailed test is given by:
[tex] p_v = P(t_{45} <-2.136) = 0.0191[/tex]
And since the p value is lower than the significance level 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly lower than 1736
Part c
We have the same statistic t = -2.136
[tex] p_v = P(t_{45} <-2.136) = 0.0191[/tex]
And since the p value is higher than the significance level 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is NOT significantly lower than 1736
Part d
For this case the answer is yes since when we change the significance level from 0.05 to 0.01 we see that the final decision changes.
Null and alternative hypotheses are created for a t-test regarding trip times. The t-test is conducted at two different significance levels (α = 0.05 and α = 0.01). The conclusion may change with adjustments to α.
Explanation:The hypotheses for this statistical test would be:
Null Hypothesis (H0): The drivers are adhering to the safety regulations, meaning the average trip time is equal to 1936 minutes (µ = 1936). Alternative Hypothesis (HA): The drivers are not adhering to safety regulations, meaning the average trip time is not equal to 1936 minutes (µ ≠ 1936).
To test these hypotheses, we can perform a two-sided t-test. We are given:
Mean trip time (X) = 1736 minutes Standard deviation (s) = 635 minutes Number of observations (n) = 46 trips
For α = 0.05, if the t-statistic's associated p-value is lesser than α, we reject the null hypothesis. Likewise, for α = 0.01, the same process is undertaken.
The conclusion reached will depend on the calculated p-value. If the p-value is less than the chosen α, we will reject the null hypothesis and conclude that the drivers are not following safety regulations. If the p-value is greater than α, we fail to reject the null hypothesis and cannot conclude that drivers are not following safety regulations.
The test conclusion may change with changes in α, as α establishes the threshold for rejecting the null hypothesis.
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The length of a rectangle is 4 more than twice the width. The perimeter is 56 cm. Find the width and the area of the rectangle.
Answers
Answer:
W=12 area=192 12×16
Area192
Step-by-step explanation:
2(4+w)+2w=56
8+4w=56
-8
4w= 48
/4
W=12
To solve the problem, a system of equations is used based on the given conditions. Through algebraic process, we discover the width (W) to be 8 cm and the length (L) to be 20 cm. Consequently, the rectangle's area is calculated to be 160 cm².
Explanation:The given problem falls under algebra and can be solved through a system of equations. According to the problem, the length of a rectangle is 4 more than twice the width. So we can denote the length of the rectangle as L and the width as W, forming Equation 1: L = 2W + 4.
The perimeter of a rectangle is known to be 2L + 2W. Given that perimeter is equal to 56 cm, we can plug in L from Equation 1 to Equation 2: 2(2W + 4) + 2W = 56. Simplifying this, we get 6W + 8 = 56. By solving for W, we find W as 8 cm. Substituting W = 8 cm into Equation 1, L comes out as 20 cm.
Next, the area of a rectangle is calculated using the formula L * W, which yields the area as 160 cm².
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In ΔBCD, the measure of ∠D=90°, the measure of ∠C=42°, and CD = 7.5 feet. Find the length of DB to the nearest tenth of a foot.
Answers
We have been given that in ΔBCD, the measure of ∠D=90°, the measure of ∠C=42°, and CD = 7.5 feet. We are asked to find the length of DB to nearest tenth of foot.
First of all, we will draw a right triangle using our given information.
We can see from the attachment that DB is opposite side to angle C and CD is adjacent side to angle.
We know that tangent relates opposite side of right triangle to adjacent side of right triangle.
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(\angle C)=\frac{DB}{CD}[/tex]
[tex]\text{tan}(42^{\circ})=\frac{DB}{7.5}[/tex]
[tex]7.5\cdot\text{tan}(42^{\circ})=\frac{DB}{7.5}\cdot 7.5[/tex]
[tex]7.5\cdot\text{tan}(42^{\circ})=DB[/tex]
[tex]7.5\cdot0.900404044298=DB[/tex]
[tex]DB=7.5\cdot0.900404044298[/tex]
[tex]DB=6.753030332235\approx 6.8[/tex]
Therefore, the length of DB is approximately 6.8 feet.
Write an equation to represent the following statement.
j divided by 9 is 5.
______
Solve for j.
j=______
Answers
Answer:
j / 9 = 5
j = 45
Step-by-step explanation:
j / 9 = 5
Multiply each side by 9
j/9 * 9 = 5*9
j = 45
a fibonacci sequence begins 1 1 2 3 5 8 what is the 7th number in the sequence. what is the 9th number in the sequence
Answers
1
1 + 0 = 1
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
8 + 13 = 21
13 + 21 = 34
21 + 34 = 55
1, 1, 2, 3, 5, 8, 13, 21, 34, 55
Hope this helps! :)
The 7th number in the Fibonacci sequence is 13 and the 9th number is 21.
Explanation:The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. The sequence starts with 1, 1, and then each subsequent number is the sum of the two numbers before it.
To find the 7th number in the sequence, we can continue the pattern: 1, 1, 2, 3, 5, 8. So, the 7th number is 13.
To find the 9th number in the sequence, we continue the pattern: 1, 1, 2, 3, 5, 8, 13, 21. So, the 9th number is 21.
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A triangular prism has ( ) faces its the 2nd question in the edenuity assignment pls help u will get brainliest
Answers
Answer:
5 faces
Step-by-step explanation:
Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. use the 68-95-99.7 rule to find the percentage of buyers who paid: between $147,700 and $152,300 If the standard deviation is $2300.
Answers
Answer:
We want to find the percentage of values between 147700 and 152300
[tex] P(147700 <X<152300)[/tex]
And one way to solve this is use a formula called z score in order to find the number of deviations from the mean for the limits given:
[tex] z= \frac{x-\mu}{\sigma}[/tex]
And replacing we got:
[tex] z=\frac{147700-150000}{2300}=-1[/tex]
[tex] z=\frac{152300-150000}{2300}=1[/tex]
So then we are within 1 deviation from the mean so then we can conclude that the percentage of values between $147,700 and $152,300 is 68%
Step-by-step explanation:
We define the random variable representing the prices of a certain model as X and the distirbution for this random variable is given by:
[tex] X \sim N(\mu = 150000, \sigma =2300[/tex]
The empirical rule states that within one deviation from the mean we have 68% of the data, within 2 deviations from the mean we have 95% and within 3 deviations 99.7 % of the data.
We want to find the percentage of values between 147700 and 152300
[tex] P(147700 <X<152300)[/tex]
And one way to solve this is use a formula called z score in order to find the number of deviations from the mean for the limits given:
[tex] z= \frac{x-\mu}{\sigma}[/tex]
And replacing we got:
[tex] z=\frac{147700-150000}{2300}=-1[/tex]
[tex] z=\frac{152300-150000}{2300}=1[/tex]
So then we are within 1 deviation from the mean so then we can conclude that the percentage of values between $147,700 and $152,300 is 68%
Final answer:
Using the 68-95-99.7 rule in statistics, about 68% of buyers paid between $147,700 and $152,300 for a new home, given the mean price is $150,000 and the standard deviation is $2,300.
Explanation:
The student is asking a question that involves the application of the 68-95-99.7 rule (also known as the empirical rule) in statistics, which describes how data is distributed in a normal distribution. Specifically, the student wants to know the percentage of buyers who paid between $147,700 and $152,300 for a new home, given that the mean price is $150,000 and the standard deviation is $2,300.
According to the 68-95-99.7 rule, approximately 68% of data within a normal distribution falls within one standard deviation of the mean in both directions, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
In this scenario, the range from $147,700 to $152,300 is $2,300 away from the mean (which is one standard deviation), so approximately 68% of the home prices would fall within this range.
Which is a reasonable first step that can be used to solve the equation 2(x + 6) = 3(x - 4) + 5?
a.
Combine like terms, 3 and 5, on the right side of the equation
b.
Distribute 2 to x on the left side of the equation and 3 to x on the right of the equation.
c.
Distribute 2 to (X+6) and 3 to (x-4)
d.
Apply the subtraction property of equality to move the 6 from the left side of the equation to the right side.
Answers
Suppose the monthly charges for cell phone plans are normally distributed with mean mu equals $ 70 and standard deviation sigmaequals$16. (a) Draw a normal curve with the parameters labeled. (b) Shade the region that represents the proportion of plans that charge less than $54. (c) Suppose the area under the normal curve to the left of Xequals$54 is 0.1587. Provide an interpretation of this result.
Answers
Answer:
a) The picture with the normal distribution is attached.
b) The picture with the normal distribution with the region X<54 shaded is attached.
c) The area under the normal curve to the left of X=$54 is 0.1587.
This means that there is a probability P=0.1587 that a randomly picked monthly charge for a cell phone plan is under $54.
It can also be interpreted that approximately 15.87% of the cell phone plans have a monthly charge that is less than $54.
Step-by-step explanation:
A store owner puts in an order for product X and product Y for a total of 4,000 units. It costs $0.10 per item to ship of product X and $0.04 per item to ship product Y. If the total shipping cost is $352, which system of equations can be used to determine how much of product X and product Y the store owner bought?
Answers
Answer:
x + y = 4,000
0.1x + 0.04y = 352
Step-by-step explanation:
Product A represents x and product B represents y. The first equation is the total number of items the store owner buys. The second equation is cost per item for both products. The above system of equations can be used to determine how much product A and product B the store owner bought.
Answer:
C. [tex]\left \{ {{x+y=4,000} \atop {0.1x+0.04y=352}} \right.[/tex]
Step-by-step explanation:
Edge 2020
In the 2020 presidential election, there are N = 1; 000; 000 eligible voters in Yolo county. Each votes with probability p = 49% for Donald Trump and with probability q = 51% for Joe Biden. Votes of different voters are independent. Assume that all voters do vote. What is the probability that Joe Biden wins Yolo county? Wining the Yolo county means getting more than half of the votes.
Answers
Answer:
100% probability that Joe Biden wins Yolo county
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.
For a proportion q in a sample of size n, the mean is [tex]\mu = q[/tex] and the standard deviation is [tex]\sigma = \frac{q(1-q)}{\sqrt{n}}[/tex]
In this problem, we have that:
[tex]q = 0.51, n = 1000000[/tex]
So
[tex]\sigma = \sqrt{\frac{0.51*0.49}{\sqrt{1000000}} = 0.0005[/tex]
What is the probability that Joe Biden wins Yolo county?
This is the probability that he gets more than 50% = 0.5 of the votes, so it is 1 subtracted by the pvalue of Z when X = 0.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.5 - 0.51}{0.0005}[/tex]
[tex]Z = -20[/tex]
[tex]Z = -20[/tex] has a pvalue of 0
1 - 0 = 1
100% probability that Joe Biden wins Yolo county
Answer:
100% probability that Joe Biden wins Yolo county
Step-by-step explanation:
During the chess championship, each player played with each other two games. Players who win in a game were awarded 1 point, while those who draws were given a half-point. Losing a game was worth zero points. The three best players scored together 24 points, which is twice less than the sum of points of all other players scored. How many players were participating in the championship?
Answers
Answer:
9
Step-by-step explanation:
If 24 points is half the number of points all other players scored, then the points scored by all other players total 24·2 = 48.
All points together total ...
24 + 48 = 72
A point is awarded for each game, so there were a total of 72 games.
N players will play a total of (N/2)(N-1) games if they play each opponent once. Here, each opponent is played twice, so the total number of games played by N players is ...
N(N-1) = 72
9·8 = 72 ⇒ N = 9
The number of players in the championship was 9.
how many lines of symmetry does a circle have
Answers
Answer:
acircle has infintely many axes of symmetry
Step-by-step explanation:
Answer:
infinite
Step-by-step explanation:
there are no corners what so ever and a circle is symetric, so no matter how many lines you put it will be correct
Simplify this expression
3.1 - 3.8n - 2n +6
Answers
Answer: 9.1 - 5.8n
Step-by-step explanation:
All you need to do here is combine like terms.
Lets identify the two sets of like terms:
-3.8n and -2n
AND
3.1 and 6
So, you will add or subtract them as needed.
I will start by combining 3.8n and -2n
= 3.1 -3.8 -2n + 6
= 3.1 + 6 -5.8n
Now combine the 3.1 and 6.
= 9.1 - 5.8n
This is your answer!
what is the base of log (x+7)
Answers
Explanation:
It depends upon the 'base" of your log. Let us say that is 10 ; we can write:
log _10( x + 7 ) = 1
using the definition of log we can write:
x + 7 =10 ^1
and:
x = 10 − 7 =3
if you have a different base use the one you got instead of 10 .
Answer:
10
Step-by-step explanation:
Generally we use the base 10 to any logarithmic function , which is known as common Base
so the base of log (x+7) is 10
A farmer sells 9.2 kilograms of apples and pears at the farmer's market.
3
5
of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market?
Answers
Answer: 1 .9 kilograms
Step-by-step explanation:
9.5/5=1.9
since the apples account for 4 parts, we multiply 4 times the value of 1 of the 5 parts
4x1.9=7.6
Now we subtract from the original weight of everything.
9.5-7.6=1.9
Final answer:
To calculate the weight of pears sold, subtract the weight of apples (three-fifths of the total) from the total weight of 9.2 kg, resulting in 3.68 kg of pears sold at the market.
Explanation:
The farmer sells 9.2 kilograms of apples and pears in total. To find out the weight of the pears sold, we need to first calculate the weight of the apples, which is three-fifths (3/5) of the total weight, and subtract that from the total weight.
First, calculate the weight of apples:
Multiply the total weight (9.2 kg) by 3/5 to find the weight of the apples.9.2 kg times 3/5 = 5.52 kg (weight of apples).Then, to find the weight of the pears sold, subtract the weight of the apples from the total weight:
Subtract the weight of apples (5.52 kg) from the total weight (9.2 kg).9.2 kg - 5.52 kg = 3.68 kg (weight of pears).Therefore, the farmer sold 3.68 kilograms of pears at the farmer's market.
Find the diameter of a circle with a
circumference of 27 centimeters. Use 3.14
for T. Round to the nearest tenth.
Answers
To find the diameter of a circle when given the circumference, use the formula d = C/π. Substituting the given circumference of 27 centimeters and using 3.14 for π, the diameter of the circle is approximately 8.6 centimeters.
Explanation:This problem pertains to the mathematical concept of geometry, specifically dealing with the properties of a circle. Given the circumference of the circle, we can use the formula for the circumference of a circle, which is C = πd where C is the circumference, π is a constant (approximately 3.14), and d is the diameter of the circle. We're told the circumference is 27 centimeters, and we're using 3.14 for π.
To find the diameter, we'll need to rearrange the formula to solve for d, which gives us d = C/π. Substituting the given numbers, we find d = 27 / 3.14. Performing this calculation gives a diameter of approximately 8.6 centimeters when rounded to the nearest tenth.
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To find the diameter of a circle with a circumference of 27 cm, divide the circumference by π (3.14). This results in a diameter of approximately 8.6 cm.
Finding the Diameter of a Circle
To find the diameter of a circle given its circumference,
we use the formula for the circumference: C = πd
where C is the circumference and d is the diameter.
Given that the circumference C is 27 centimeters and π is approximately 3.14,
we can solve for the diameter as follows:
First, set up the equation: 27 = 3.14d
Next, solve for d by dividing both sides by 3.14: d = 27 / 3.14
Perform the division to get: d ≈ 8.6
Therefore, the diameter of the circle is approximately 8.6 centimeters.
One side of the triangle is 5 meters longer than the second side. The third side is four times. If the perimeter of the triangle is 65 meters, how long is the second side
Answers
Answer - 10 meters
10 meters
Explanation:
Using the ratios given, we have the three sides in terms of one side.
(x, x+5, 4x)
The perimeter is the sum of all of them:
65 = x+x+5+4x ; 65 = 6x+5
6x = 60 ; x = 10
x+5 = 15
4x = 40
A company conducted a survey to see whether it's new toothpaste was more popular with children or adults. Of the adults surveyed about 11% use the toothpaste. Compare this with the percentage of children who use the toothpaste. Select a true statement.
Answers
Answer:
c 24%use it thats what I got
The B is A greater percentage of children (28%) use the toothpaste is correct.
For each data value in the table, move the decimal point over 2 spots.
We focus on the children's row only since each answer choice has of children mentioned, and also the instructions make this mention as well.
There are 7 children who use the toothpaste out of 25 children overall.
So 6/25 = 0.24 = 24% of the children use the toothpaste.
What is the formula for probability?
The probability is the ratio of the number of outcomes divided by the total number of outcomes.
This is a greater percentage than the adults (11%) who use toothpaste.
The 11% comes from 8 adults out of 75 adults
Total who use the toothpaste,
So 8/75 = 0.1067 = 10.67%
which rounds to 11%.
Therefore the probability for toothpaste is 24% and 11% for adults.
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In the triangle, what is sin 45 degrees? Give your answer in simplest radical form.
Answers
The value of sin 45 is 1/ √2
What is angle?An angle is a combination of two rays (half-lines) with a common endpoint.
As per the diagram,
AC= 1 unit, BC= 1 unit
Applying Pythagoras theorem,
AB² = AC² + BC²
AB² = 1²+ 1²
AB² = 2
AB= √2
Now, sine is the ratio between the opposed side and the hypothenuse.
So, sin 45 = 1/ √2 = √2/√2
In radical form = 0.7071
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Final answer:
The sin of 45 degrees is √2/2. This value is found using the properties of an isosceles right triangle and applying the Pythagorean theorem.
Explanation:
In the case of a 45-degree angle in a right triangle, the sine function can be calculated using the properties of an isosceles right triangle. The sin of 45 degrees is equal to the ratio of the opposite side to the hypotenuse. In an isosceles right triangle where the two legs are equal, this ratio is the same for both legs.
By the Pythagorean theorem, we know that in an isosceles right triangle, if each leg is of length 1, the hypotenuse will be √2. Therefore, sin 45 degrees equals the length of the leg (1) divided by the length of the hypotenuse (√2), which simplifies to √2/2 or 1/√2. Expressing this in simplest radical form, we obtain √2/2.
This value is derived from understanding that the sum of the squares of the lengths of the legs equals the square of the hypotenuse, which gives us the equation 1² + 1² = c², where c is the hypotenuse. Simplifying gives us a hypotenuse of √2, and the sine of 45 degrees equals 1/√2, or √2/2 after rationalizing the denominator.
VitaComp manufactures non-pharmaceutical pills and pellets from dry ingredients, using a collection of machinery it maintains in a large job shop. Machine AA-23 molds circular pellets to an average diameter of 65 mm, with normally distributed natural variation expressed by a 1 mm standard deviation when the machine is in control. VitaComp has just agreed to mold a batch of plant food pellets of the 65mm design. To monitor the plant food job, it will sample 100 pellets randomly each hour, and chart their average diameter on a mean chart prepared for this purpose, using a z-value of 1.67. What is the Upper Control Limit of the mean chart described here?
Answers
Answer:
Check the explanation
Step-by-step explanation:
UCL = MEAN + (Z * STDEV / SQRT(N))
MEAN = 65
Z = 1.67
STDEV = 1
N = 100
UCL = 65 + (1.67 * 1 / SQRT(100)) = 65.167
he complex formsof the sine and cosine functions are:ieexixix2sinand2cosixixeex, where eis the Euler e, and 1i.Differentiate the complex form of cosxto showthatxxdxdsin)(cos.[Hints:The Quotient Rule may be used, but it is not necessaryif you factor out a constant first.√−1=iis a constant. In fact, you can use it to multiply a fraction by iiif that helps...]
Answers
Answer:
[tex]\cos'(z) = -\sin(z)[/tex]
Step-by-step explanation:
According to the information given by the problem
[tex]\sin(z) = {\displaystyle \frac{e^{iz} - e^{-iz} }{2i} }[/tex]
[tex]\cos(z) = {\displaystyle \frac{e^{iz} + e^{-iz} }{2} }[/tex]
Now, if you compute the derivative of [tex]\cos[/tex] you get that
[tex]\cos'(z) = {\displaystyle \frac{ ie^{iz}-i e^{iz} }{2} } = {\displaystyle \frac{ i ( e^{iz}- e^{iz} )}{2} }\\\\= {\displaystyle \frac{ i ( e^{iz}- e^{iz} )}{2} } *\frac{i}{i} }\\\\= {\displaystyle - \frac{ e^{iz}- e^{iz} }{2i} } = -\sin(z)[/tex]
Which of the following statements is false for an F distribution? a. Degrees of freedom for the numerator can be smaller than the degrees of freedom for the denominator. b. The exact shape of the distribution is determined by two numbers of degrees of freedom. c. Degrees of freedom for the numerator can be larger or equal to the degrees of freedom for the denominator. d. Degrees of freedom for the denominator cannot be smaller than the degrees of freedom for the numerator. e. Variables that are F distributed range from 0 to .
Answers
Answer:
A. True
B. True
C. True
D. False
Step-by-step explanation:
Option D is the only clear option that is false.
The S distribution is a statistical tool used to check the homogeneity of two independent estimates when studying population variance.
When using an F distribution, The ratio of the degree of freedom of the numerator to the denominator can be >1, = 1 or < 1.
This implies that degrees of freedom for the denominator can be smaller than the degrees of freedom for the numerator.
This makes option D false and hence the correct answer
Final answer:
The F distribution in ANOVA tests has specific characteristics based on degrees of freedom, with critical values for hypothesis testing.
Explanation:
False statement: d. Degrees of freedom for the denominator cannot be smaller than the degrees of freedom for the numerator.
The F distribution is used in ANOVA tests, with the shape determined by the degrees of freedom for the numerator and denominator. Critical values for the F distribution correspond to different probabilities for hypothesis testing.
Build a fence around his rectangular garden. The length is 30 feet. The width is 6 yards. How many feet of fencing is needed
Answers
The final answer is 96 sq feet.