The equation of the hyperbola with given x and y axes will be x² + y² = 4 that is option D is correct.
The hyperbola x² + y² = 4 is a standard form of the equation for a hyperbola centered at the origin, which means that the hyperbola passes through the point (0,0). However, the given information states that the hyperbola passes through the point (2,2). This can be achieved by shifting the hyperbola to the right and up by 2 units, resulting in the equation (x-2)² + (y-2)² = 4.
The asymptotes of a hyperbola are the lines that the hyperbola approaches but never touches as it extends to infinity. The asymptotes of a hyperbola centered at the origin are the x-axis and y-axis. Since this hyperbola has been shifted to the right and up by 2 units, the asymptotes are the x-axis and y-axis shifted by 2 units in the same direction. Therefore, the x- and y-axes are the asymptotes of this hyperbola.
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How do I write an equation for an arithmetic sequence?
The equation for an arithmetic sequence will be;
⇒ T(n) = a + (n - 1) d
Where, 'a' is first term of an arithmetic sequence, 'd' is common difference and 'n' is number of terms.
What is Arithmetic sequence?An arithmetic sequence is the sequence of numbers where each consecutive numbers have same difference.
Given that;
The sequence is an arithmetic sequence.
Now,
Since, The sequence is an arithmetic sequence.
Let 'a' is first term of an arithmetic sequence, 'd' is common difference and 'n' is number of terms.
Then, The nth term of an arithmetic sequence is,
⇒ T(n) = a + (n - 1) d
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Rewrite
17/5
as a mixed number.
Simplifying assumptions identified for the use of cost behavior pattern data include:a) linearity and relevant range.b) fixed range and variability.c) fixed activity and linearity.d) relevant range and liquidity.
linearity and relevant range include the use of cost behavior pattern data.
what is linearity?the existence of a chain of thoughts or actions wherein one directly follows another: True autobiographies rarely have a linear structure. We don't have a linear existence. Constantly thrown off balance is the narrative's traditional linearity.
what is relevant range?The accounting phrase "relevant range" refers to the production or activity parameters that a company must adhere to in order to keep its fixed costs constant. Fixed costs in accounting are constant and unaffected by particular production rates.
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1. A study explored the effect of ethanol on sleep time. Fifteen rats were randomized to one of three treatments. Treatment 1 was water (control). Treatment 2 waas 1g of ethanol per kg of body weight, and Treatment 3 was 2g/kg. The amount of REM sleep (in minutes) in a 24hr period was recorded: Treatment 1: 63, 54, 69, 50, 72 Treatment 2: 45, 60, 40, 56 Treatment 3: 31, 40, 45, 25, 23, 28
(a) Graph the data. Why did you choose the graph that you did and what does it tell you?
(b) Create an ANOVA table for the data using the formulas provided in class. Show your work. You may use R to check your answers.
(c) Evaluate the ANOVA assumptions graphically. Was ANOVA appropriate here?
(d) Based on the ANOVA table, make a conclusion in the context of the problem.
(e) Create 95% CIs for all pairwise comparisons of means using the Tukey method. Do this without R show your work. (You may use R to check your work). Summarize your results using letter codes. What do you conclude?
We have to find a problem at the 5% significance level.
Sample size = 10.
We're losing one till test if the Significant value is at five and 10. The critical value of W. C. is 44. When we look at the test, we're supposed to do one tailed. Which tail is it?
We are asked if one is more effective than the other.
Everything is mostly positive here, and we find what our values are. Mhm. 10 patients who used love level high school obtained additional sleep hours by using the following data set High bromide.
That's the control group minus the other one.
The control group is made up of people. I'm not sure if it's a left or right tail, so we'll just calculate the two ends.
The other tail is going to be divided by two and the right tail is going to be 44. 55 minutes 44 is going to be 11. It's very handy. Okay. If it's less than 11 it won't reject and if it's greater than 44 it will reject. Is it sound good? We had 10 students who were at the positive values and they were 1.9 plus 0.8 plus 1.1 plus 0.1. We get 23.4 for our nut. Okay. Critical value leads us straight to the middle. We failed to reject the null hypothesis and this was just a right tail test. If we tried it again at the 1% significance level, it would change our values to be 50. We did 10 tons 11 divided by two. Fifty is going to be five. Again, 23.4 lands us right in there.
We failed to reject the hypothesis again.
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A healthcare provider tested patients experiencing gluten intolerance to determine if they had celiac disease. The relative frequency table summarizes the data.
Tested positive Tested negative Row Totals
Has celiac disease 51% 22% 73%
Does not have celiac disease 14% 13% 27%
Column Totals 65% 35% 100%
What percentage of all patients had a false positive result?
13%
14%
22%
51%
Answer: Option B: 14%
Step-by-step explanation: The only option that seems suitable is option B. You can't have celiac disease and test negative.
Answer:
I think it is 51% or 22%
I am not sure which one, but I think it should be 51% or 22%.
a textbook store sold a combined total of 366 psychology and history textbooks in a week. The number of history textbooks sold was 40 less than the number of psychology textbooks sold. how many textbooks of each type were sold?
Answer:
Step-by-step explanation:
We have two types of textbooks. Let's use "x" to represent the number of math textbooks and "y" to represent the number of history textbooks.
Altogether, the bookseller sold 240 math and history textbooks. So:
x + y = 240
Now, the number of history textbooks sold was 72 less than the number of math books sold. So:
y = x - 72
Now we can substitute for y in the equation and solve:
x + y = 240
x + (x - 72) = 240
2x - 72 = 240
2x = 312
x = 156
The bookseller sold 156 math textbooks.
Since y = x - 72, he must have sold 84 history textbooks.
Let's check our answers:
x + y = 240
156 + 84 = 240
That is true, so we did get the correct answers
6 Question 5 (5 points) Two masses, m and M. are placed along x-axis at a and b, respectively. Find the center of mass for the system (x, y). 9 (a+b)/2,0 12 0. (a+b)/2 15 O (am+bM)/2,0 (am+bM)/(m+M), O 18 O, (am+bM)/(m+M)
The center of mass for the system (x, y) is [tex]\left(\frac{a m+b M}{m+M}, 0\right)[/tex].
What is center of mass?
The unique location where the weighted relative position of the scattered mass adds to zero is known as the center of mass in physics. Here is where a force may be applied to produce a linear acceleration without also producing an angular acceleration.
The center of mass is a position defined relative to an object or system of objects. It is the average position of all the parts of the system, weighted according to their masses.
Centre of mass is
[tex]x=\frac{m a+M b}{m+M}[/tex]
and y=0
[tex](x, y)=\left(\frac{a m+b M}{m+M}, 0\right)[/tex]
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Perform the following mathematical operation and report the answer to the appropriate number of significant figures.
We know the least precise place value is in the 10's place.
67.4 +43 +30 + 42.10 = [?]
it's not 182.5 / 137.9 / 182
Answer:
200
Step-by-step explanation:
The sum is 182.5, which is 200 to 1 significant figure.
which of the following scheduling times is needed to obtain the material if it is extrenally produced
Therefore , the answer to this problem is that planned delivery time is the amount of time required to get material.
What is scheduling time?Time scheduling is a group of methods for creating and presenting schedules that indicate when work will be done. All of these methods' outcomes are typically displayed as activities or bars on a timeline known as a Gantt chart.
Here,
Obtaining the substance requires the following scheduling if it is externally manufactured.
So ,
When a material is purchased outside, the planned delivery time is the amount of time required to get the material.
Therefore , the answer to this problem is that planned delivery time is the amount of time required to get material.
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The complete question is "which of the following scheduling times is needed to obtain the material if it is externally produced or not ?
a.In-house production time.
b.Goods issue processing time.
c. Planned delivery time.
d. Goods receipt processing time."
Question 1. An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Over Age of 18: n1 = 500 Number of accidents = 180 Under Age of 18: n2 = 600 Number of accidents = 150 We are interested in determining if the accident proportions differ between the two age groups. Let pu represent the proportion under and po the proportion over the age of 18. The null hypothesis is Pu-Po = 0 Pu-P. £0 Pu-P.10 Pu - P. 30 Question 2. Refer to Question 1. What is the value of the pooled proportion? Round your answer to three decimal places.
Question 3. Refer to Questions 1 and 2. Determine the value of the standard error of the difference in the proportions. Round your answer to four decimal places.
The pooled proportion is 0.200 and the standard error of the difference in the proportions is 0.0201.
1. The null hypothesis is Pu-Po = 0, which means that the proportion of people under 18 who had accidents is the same as the proportion of people over 18 who had accidents.
2. To calculate the pooled proportion, we first add the total number of people in each group (500 + 600 = 1100). Then we add the total number of accidents in each group (180 + 150 = 330). Finally, we divide the total number of accidents by the total number of people to get the pooled proportion (330/1100 = 0.200).
3. The standard error of the difference in the proportions can be calculated using the formula SE = SQRT(P1*(1-P1)/n1 + P2*(1-P2)/n2), where P1 is the proportion of people under 18 who had accidents, P2 is the proportion of people over 18 who had accidents, and n1 and n2 are the number of people in each group. In this case, P1 = 150/600 = 0.250, P2 = 180/500 = 0.360, n1 = 600, and n2 = 500. Plugging these values into the formula gives us SE = SQRT(0.250*(1-0.250)/600 + 0.360*(1-0.360)/500) = 0.0201.
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______ is thermal energy that is transferred from something at a higher temperature to something at a lower temperature.
a.Heat b.State c.Plasma d.Charge
Answer: Heat
Step-by-step explanation:
Heat is thermal energy that flows from something at a higher temperature to something at a lower temperature.
Answer:
it is heat
A
Step-by-step explanation:
among all option it is only heat that is a thermal energy
HEAT is thermal energy that is transferred from something at a higher temperature to something at a lower temperature
ADDITIONAL INFORMATIONS
state means the particular condition that someone or something is in at a specific time.
plasma means the colourless fluid part of blood, lymph, or milk, in which corpuscles or fat globules are suspended.
charge means is the physical property of matter that causes it to experience a force when placed in an electromagnetic field.
PLS RATE ASBRAINLIEST
Three percent of a man's body is essential fat; for a woman the percentage is closer to 12.5%. As the name implies, essential fat is necessary for a normal healthy body. Fat is stored in small amounts throughout the body. Too much fat, however, can be dangerous to your health. For men between 18 and 39 years old, a healthy percent of body fat ranges from 8% to 19%; for women of the same age, it's 21% to 32%. Measuring body fat can be tedious and expensive. The "standard reference" measurement is by dual-eneregy X-ray absorptiometry (DEXA), which involves two low-dose X-ray generators and takes from 10 to 20 minutes. Because of the time and expense involved with the DEXA method, health professionals would like to be able to make a useable prediction of body fat from easily measurable variables such as weight or waist size.This Excel file shows the waist size (inches), weight (pounds) and percent body fat for 20 individuals. Question 1. What is the slope of the least squares regression line of %body fat on waist size? Correct: Your answer is correct. (use 4 decimal places). Question 2. Find sb1, the estimate of the standard deviation ?b1 of the least squares slope b1 (use 4 decimal places). Correct: Your answer is correct. sb1, estimate of ?b1 Question 3. Determine the 90% confidence interval for the slope of the least squares regression line of %body fat on waist size. Correct: Your answer is correct. lower bound Correct: Your answer is correct. upper bound Question 4. Determine a 90% confidence interval for the mean %body fat found in people with 40-inch waists (use 2 decimal places). lower bound upper bound Question 5. Determine a 90% prediction interval for the %body fat of an individual with a 40-inch waist (use 2 decimal places). lower bound upper bound
Waist (in.) Weight (lb) Body Fat (%)
32 175 6
36 181 21
38 200 15
33 159 6
39 196 22
40 192 31
41 205 32
35 173 21
38 187 25
38 188 30
33 188 10
40 240 20
36 175 22
32 168 9
44 246 38
33 160 10
41 215 27
34 159 12
34 146 10
44 219 28
4) Lower bound = 24.06
Use Dergy Willing
upper bound = 28.55
5)Lower bound = 18.12
upper bound = 34.4
Healthy body=A healthy body is maintained by good nutrition, regular exercise, avoiding harmful habits, making informed and responsible decisions about health, and seeking medical assistance when necessary. Health is a state of complete physical, mental and social well-being and not merely the absence of disease or infirmity .A state of complete physical, mental and social wellbeing and not merely the absence of disease or infirmity'.
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Which inequality matches the graph?
is this right?
Answer:
Your Answer is A.
Step-by-step explanation:
First look at the inequality graph.
We can note that its a variable is greater than 2. (p >2)
Then looking at our options.
Option A can be.
Option B can't be it since its greater than or equal to.
Option C can be.
Option D can't be since dividing or multiplying by a negative switches the signs greater than to less than or vice versa.
Leaving only option A or C.
Solve A and C.
Option A5p + 4 > 14
5p > 10
p > 2
Option C.5p - 4 > 14
5p > 18
p > 18/5
Consider the figure shown.
What is the value of q?
A 25°
B 72°
C 108°
D 180°
The value of ∠q is 72 degree. So the option B is correct.
In the given question we have to find the value of q.
The given options are:
A 25 degree
B 72 degree
C 108 degree
D 180 degree
As we know that the angle of straight line is 180 degree.
From the given diagram we can see that the two angel of one line that is cut by another line, is given.
So the third angle of one line that is cut by another line is
25 + 83 + x = 180
x + 108 = 180
Subtract 108 on both side, we get;
x = 72
Using the corresponding angle theorem
∠q = 72 degree
Hence, the value of ∠q is 72 degree. So the option B is correct.
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A tablet that regularly sells for $330 was
on sale for 15% off. If Jeremiah paid
$302.94 total including tax, what is the N
sales tax rate?
Answer:
The sales tax rate is 7.96%.
Step-by-step explanation:
To determine the sales tax rate, we need to first calculate the amount of the discount on the tablet by multiplying the regular price by the discount percentage:
Discount = Regular price * Discount percentage
Discount = $330 * 15%
Discount = $49.50
Next, we can calculate the total price of the tablet before taxes by subtracting the discount from the regular price:
Total price before taxes = Regular price - Discount
Total price before taxes = $330 - $49.50
Total price before taxes = $280.50
Finally, we can calculate the sales tax rate by dividing the total amount of taxes paid by the total price of the tablet before taxes and multiplying by 100% to express the result as a percentage:
Sales tax rate = (Total amount of taxes paid / Total price before taxes) * 100%
Sales tax rate = ($302.94 - $280.50) / $280.50 * 100%
Sales tax rate = $22.44 / $280.50 * 100%
Sales tax rate = 7.96%
Therefore, the sales tax rate is 7.96%.
3. suppose that a particular nfl team claims that the mean weight of their defensive players is 315 pounds. a rivaling team thinks that the mean weight of the defensive players on that team is different from 315 pounds they claim. suppose they sample 15 of the defensive players and find the players to have a mean weight of 300 pounds with sample standard deviation 8 pounds. set up an appropriate hypothesis test and make conclusions at significance level 0.08. assume weights are normally distributed.
The appropriate hypothesis test results that it reject the null hypothesis and accept the alternative hypothesis. The z score of -7.26 is in the rejection area
How to calculate hypothesis test?
The general form to calculate the hypothesis is by using the sample data and assuming the null hypothesis is true, calculate the value of the test statistic.
Here the hypothesis test for the population mean μ, we use the t-statistic t = x − (μ*s) / n
where the t-distribution with n - 1 degrees of freedom.
Here we have given that suppose that a particular NFL team claims that the mean weight of their defensive players is 315 pounds.
And we need to find appropriate hypothesis test and make conclusions at significance level 0.08 and here we have to assume weights are normally distributed.
While we looking into the given question, we have identified that weights are normally distributed.
Then the value of the given data are written as
data = 315 ,
n= 15 ,
Mean = 300,
standard deviation = 8,
Significance level= 0.08
Then the hypothesis is written as,
The critical value (cutoff point) is 1.761.
Where in left-tail hypothesis testing, any z score less than the critical value will be rejected. Since -7.26 is less than 1.761, we reject the null hypothesis. We accept the alternative hypothesis
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For the following pair of lines, Identify the system by type.
consistent
inconsistent
equivalent
Both lines are not connecting each other. So there is no solution. So the pair of lines, identify the system of inconsistent.
In the given question, we have to check the following pair of lines, Identify the system by type.
(a) consistent
(b) inconsistent
(c) equivalent
As we know that;
A system is consistent if it has at least one solution. A consistent system is dependent if there are an endless number of possible solutions. Both equations show the same line on a graph when you plot the equations.
A inconsistent system has no solution. There is no solution because the graphs of the lines do not connect, making the graphs parallel.
Even if the vertices of two graphs differ or are rearranged, we will pronounce them equivalent if they have the same edge structure.
As we can see that in the graph that both lines are not connecting each other. So there is no solution. So the pair of lines, identify the system of inconsistent.
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Refer to Exhibit 1-3. According to the data provided in this table, what is the approximate slope of the line between points A and B, if these data were graphed with X on the horizontal axis and Y on the vertical axis?
-0.29
The slope of the line between points A and B based on data provided in the table is -0.29. (Option A)
The slope of the line refers to is the change in y coordinate with respect to the change in x coordinate. The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.
From the table point A is (5, 18) and B is (12, 16).
The formula of the slope = Δy/ Δx = (y2 – y1)/(x2 – x1)
Hence the slope of line between points A and B is
Slope = (16 – 18)/(12 – 5) = -2/7 = -0.29
Note: The question is incomplete as it is missing options which are A) -0.29 B) -3.5 C) 0.29 D) 3.50 E) -1.00
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Chung read 5/8 of a book one day and 1/5 of the book less than this the next day. What fraction of the book did Chung read on the second day? Did he finish the book in two days?
The fraction of the book chung read on the second day is 17/40 and No, he didn't finish the book in two days
What are fractions?fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. In proper fractions the denominator is greater than the numerator but in improper, the denominator is lesser than the numerator.
Chung read 5/8 of a book
let's represents the volume pages of the book by x
therefore chung read 5/8 × x = 5x/8
on the second day, he read 1/5 less of the previous day = 5x/8-1/5x = 17x/40 i.e he read 17/40 of the book on the second day
the volume of pages left = x - (17×/40+5×/8)
x-22x/40
the fraction of remaining page left = (40-22)x/40
= 28x/40
divide through by 4
7/10 of x
therefore 7/10 of the book is still left to be read. This means chung didn't finish reading the book on the second day.
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A local theatre sells out for their show. They sell all 500 tickets for a total purse of $7,860.00. The tickets were priced at $15 for students, $12 for children, and $18 for adults. If the band sold three times as many adult tickets as children's tickets, how many of each type were sold?
The number of each type of tickets sold are;
180 adults tickets
260 students tickets
60 children tickets
How to solve simultaneous equation word problems?
Let us solve to get the solution using 3 variables.
Let c be the number of children's tickets
Let s be the number of student tickets
Let a be the number of adult tickets
We are told that the total number of tickets was 500
Thus;
a + s + c = 500 ------(1)
The number of adult tickets was 3 times the number of children's tickets. Thus;
a = 3c ------(2)
The total cost of the tickets was $8070. Thus;
18a + 15s + 12c = 7860 ----(3)
We conclude that solving these three equations simultaneously gives us;
a = 180 adults
s = 260 students
c = 60 children
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At Rachel’s 11th birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the mean difference between their jumping and relaxed times would be zero. Test their hypothesis.At Rachel’s 11th birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping.
Relaxed time (seconds)
Jumping time (seconds)
26
21
47
40
30
28
22
21
23
25
45
43
37
35
29
32
The test statistic is 1.507 and the corresponding p value is 0.175539
Fail to reject H₀ because the p value is greater than the significance level 0.05.
There is enough evidence to warrant rejection of the claim that the mean difference between their jumping and relaxed times would be zero.
To find the mean and standard deviation for the paired differences, prepare the table:
Calculate the value of d bar:
d bar = ∑d/n
= 5+7+...+(-3)/8
= 14/8
= 1.75
Calculate the standard deviation of the (d)
Sd = √(d₁-dbar)²/n-1
= √(5-1.75)²+(7.1-75)²+..+(-3-1.75)²/8-1
= √10.785714
= 3.284
The mean and standard deviation of the eight girls were timed to see how long they could be zero.
Null hypothesis H₀: meand = 0
Alternative hypothesis H₁ : mean d ≠ 0
Level of significance α = 0.05
Decision rule : Reject H₀ when p value < 0.05 level of significance.
The null hypothesis is the 8 girls mean difference between their jumping and relaxed time is equal to the zero and alternative hypothesis is the 8 girls mean difference between their jumping and relaxed time is not equal to the zero.
from the available info, d bar = 1.75 Sd = 3.284
Calculate the test statistic value.
t = 1.75 - 0/3.284/√8
= 1.507
calculate the degree of freedom.
df = n-1
= 8-1
= 7
Calculate the p value of the test
P value = (=TDIST(1.507,7,2)) (use MS Excel function)
= 0.175539
Hence the test statistic is 1.507 and the corresponding p value is 0.175539
Fail to reject H₀ because the p value is greater than the significance level 0.05.
There is enough evidence to warrant rejection of the claim that the mean difference between their jumping and relaxed times would be zero.
There is no evidence to warrant rejection of the claim that the mean difference between their jumping and relaxed times would be zero.
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Diane has quarters, dimes, and
pennies in her pocket. The value of her
money is $1.55. There are 4 more
dimes than quarters and the number of
pennies equals the sum of the number
of quarters and dimes.
How many pennies does Diane have?
Answer: The solution here is found by establishing a system of linear equations.
A system of equations with x unknowns can be evaluated for an exact solution if the system has x equations.
Within the question, we are asked to discover the values of two different unknowns - dimes and nickels.
Therefore, we'll need two equations to obtain an exact solution, both of these will come directly from the problem itself.
Let d represent the number of dimes Diane has and let n represent the number of nickels.
Equation 1
We know from the given information that the total number of coins (both dimes and nickels) is equal to 19.
Subsequently, we can generate the equation d + n = 19.
Equation 2
We know that the individual value of a dime is $0.10 or 0.1 dollars, therefore the total value of the dimes is equal to the individual value of a dime multiplied by the total number of dimes.
The resultant expression for the total value of the dimes is (0.1)*d
We know that the individual value of a nickel is $0.05 or 0.05 dollars, therefore the total value of the nickels is equal to the individual value of a nickel multiplied by the total number of nickels.
The resultant expression for the total value of the nickels is (0.05)*n
We know that Diane only has dimes and nickels, and the total value of all her coins must be equal to the total value of the dimes plus the total value of the nickels. This value is given within the problem to be $1.55 or 1.55 dollars.
Subsequently, our second equation within the system is (0.1)*d + (0.05)*n = 1.55.
Now, we can solve the system of equations using whichever means is most convenient. For this example, I will solve the system by substitution
First, solve for one of the variables —> Equation 1 —> d + n = 19 —> d = 19 - n
Second, substitute the value of d into Equation 2 —> (0.1)*(19 - n) + (0.05)*n = 1.55
Recall that 0.1 = 1/10 and 0.05 = 1/20
Equation 2 —> (1/10)*19 - (1/10)*n + (1/20)*n = (31/20) —> (19/10) - (n/10) + (n/20) = (31/20)
Find the least common denominator of all fractions in the equation (20 in this case), convert the fractions to have like denominators, and solve.
(19/10)*(2/2) - (n/10)*(2/2) + (n/20) = (31/20) —> (38/20) - (2n/20) + (n/20) = (31/20) —> (38/20) - (n/20) = (31/20) —> (n/20) =(38/20) - (31/20) =(7/20) —>n = 7
Substitute solution into Equation 1 to solve for d
d + 7 = 19 —> d = 12
q+4+q + 10q+40 + 25q = 155
37q + 44 = 155
37q = 111
q = 3 (# of quarters)
d = q+4 = 7 (# of dimes)
p = d+q = 7+3 = 10 (# of pennies)
Step-by-step explanation:
what is the slope linear relationship (1,3) and (-2,-1)
The slope linear relationship (1,3) and (-2,-1) is 4/3.
What is line?
A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.
Find the line y=m x+b passing through (1,3),(-2,-1).
Compute the slope [tex]$(1,3),(-2,-1): \quad m=\frac{4}{3}$[/tex]
Compute the y intercept: [tex]$\quad b=\frac{5}{3}$[/tex]
Construct the line equation [tex]$\mathbf{y}=\mathbf{m} x+b$[/tex] where [tex]$m=\frac{4}{3}$[/tex]and [tex]$b=\frac{5}{3}$[/tex]
[tex]y=\frac{4}{3} x+\frac{5}{3}$$[/tex].
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A fair die is rolled six times. Calculate the probability of obtaining exactly two 3s. (Round your answer to four decimal places.)
Show work in steps so I can understand how to set up the problem and solve it better. Been stuck on this for awhile! Thanks
The Total Probability of getting exactly two 3s in two throws is 1/36
What is Probability?
A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Solution:
Probability of Obtaining 3 in the first throw = 1/6
Since, the number of possible outcome is 11 and total outcomes are 6
Similarly the probability of getting 3 in the second throw is 1/6
Therefore, total probability = 1/6 * 1/6 = 1/36
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Next, you select the basic statistics that can help your team better understand the ratings system in your data. Assume the first part of your code is: trimmed_flavors_df %>% You want to use the summarize() and mean() functions to find the mean rating for your data. Add the code chunk that lets you find the mean value for the variable Rating.
Based on the rating system and the summarize() and mean() functions, the code chunk to add is summarize(mean(Rating)) and the mean rating is 3.185933.
To determine the mean value for the variable Rating, you must add the code chunk summarize(mean(Rating)). Trimmed flavors df%>% summarize(mean(Rating)) is the right code. In this section of the code:
You can display summary statistics using the summarize() method. To generate specific statistics, you can combine the summarize() method with others like mean(), sd(), and max().
In this instance, you compute the mean value for the variable Rating using the mean() function.
The average score is 3.185933.
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Write a function in the form
y = mx + b.
Answer:
y=3/4x-2
Step-by-step explanation:
A pack of gray wolves was reintroduced to a forest. The table gives the size of this population of wolves over time. Which model, in which t represents the time in years, best fits the data in the table?
The exponential equation that represents the population of wolves over time is -
y = 12(1.12)ˣ
What is logarithmic function?The exponential function is a mathematical function denoted by eˣ. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers.Inverse : Complex logarithmAt zero : 1Fields of application : Pure and applied mathematicsFixed point : −Wₙ(−1) forMotivation of invention : Analytic proofsIn mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number [x] to the base [b] is the exponent to which [b] must be raised, to produce [x]. We can write -[tex]y = log_{e}x[/tex]
Given is a table as shown in the question.
Assume the exponential equation to be -
y = A(B)ˣ
At [x] = 0, [y] = 12 -
12 = A(B)⁰
A = 12
and
At [x] = 2, [y] = 15 -
15 = A(B)²
(B)² = 15/12
(B)² = 1.25
(B) = √(1.25)
(B) = 1.118
(B) = 1.12
The equation will be -
y = 12(1.12)ˣ
Therefore, the exponential equation that represents the model is -
y = 12(1.12)ˣ
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Answer:
It's answer B
Step-by-step explanation:
How much do you have after investing $1000 at 9% compounded continuously for 2 years and nine months
Answer:
$1,127.49
Step-by-step explanation:
Compound interest formulas
Hence, if a two-year savings account containing $1,000 pays a 9% interest rate compounded daily, it will grow to $1,127.49 at the end of two years
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the effectiveness of a blood-pressure drug is being investigated. an experimenter finds that, on average, the reduction in systolic blood pressure is 55.9 for a sample of size 29 and standard deviation 7.4. estimate how much the drug will lower a typical patient's systolic blood pressure (using a 80% confidence level). assume the data is from a normally distributed population.
We can use the confidence interval formula to estimate how much the drug will lower a typical patient's systolic blood pressure with 80% confidence.
The confidence interval formula is:
Sample mean ± (t-score × standard error)
Where the t-score is calculated from the t-distribution using the number of degrees of freedom (n-1) and the confidence level (80%).
Using the given information, we can calculate the t-score as follows:
t-score = 1.711 (for 80% confidence level and 28 degrees of freedom)
Therefore, the confidence interval is:
55.9 ± (1.711 × (7.4/√29))
= 55.9 ± 4.125
So, with 80% confidence, we can say that the drug will lower a typical patient's systolic blood pressure by between 51.8 and 60.0.
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Can someone explain question 2 the perfect square trinmial please please please
The values of m and n required to form perfect square trinomials are given as follows:
a) m = -10, n = 25.
b) m = 6, n = 9.
c) m = 12, n = 180.
d) m = -7/2, n = 49/16.
What are perfect square trinomials?Perfect square trinomials are expressions that have either of these two formats:
(x + y)² = x² + 2xy + y².(x - y)² = x² - 2xy + y².The term that multiplies x is always the multiplication of 2 by both of the two terms that are added.
Hence in item 1, the expression is completed as follows:
x² - 10x = (x - 5)² - 25 = x² - 10x + 25 - 25
Meaning that m = -10, n = 25.
In item 2, the expression is completed as follows:
x² + 6x = (x + 3)² - 9 = x² + 6x + 9 - 9.
Hence m = 6, n = 9.
In item 3, the expression is completed as follows:
5x² + 60x = 5(x² + 12x) = 5(x + 6)² - 180 = 5(x² + 12x + 36) - 180 = 5(x² + 12x + 180 - 180).
Hence m = 12, n = 180.
In item 4, the expression is completed as follows:
2x² - 7x = 2(x² - 7/2x) = 2(x² - 7/4x)² - 49/32 = (2x² - 7/2x + 49/16 - 49/16).
Hence m = -7/2, n = 49/16.
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