The cost of purchase of celery for the soup is $0.37
1 pound = 16 ounce
Each cup of celery weigh 4½ ounce = 9/2 ounce
16 ounce = 1 pound
9/2 ounce = (9/2)1/16 = 0.281
The yield percent for celery is 72%.
72% of x = 0.281
(72/100) x = 0.281
x = 0.281/(72/100)
x = 0.39 pound
each bunch weigh 1. 75 pound
Amount of bunch needed = 0.39/1.75 = 0.22
the celery for the soup cot if you purchae celery for $1. 66 a bunch
The cost of purchase = 0.22 x 1.66 = 0.37
Therefore, the cost of purchase of celery for the soup is $0.37
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water flows into an empty reservoir at a rate of gal/hour . what is the quantity of water in the reservoir after 9 hours?
The quantity of water in the reservoir after 9 hours be, 2835 gallons.
Given, water flows into an empty reservoir at a rate of 2800 + 15t gal/hour.
we have to find the quantity of water in the reservoir after 9 hours.
at the rate of 2800 + 15t
put t = 9
So, the quantity of water in the reservoir after 9 hours be,
2800 + 15(9)
2800 + 135
= 2835
So, the quantity of water in the reservoir after 9 hours be, 2835 gallons.
Hence, the quantity of water in the reservoir after 9 hours be, 2835 gallons.
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please help me out with this
the probability pete will catch fish when he goes fishing is 0.9. pete is going fishing 4 days next week. the expected number of days pete will catch fish is . a. 0.4 b. 0.9 c. 3.6 d. 4
The expected number of days pete will catch fish is 0.36. So the option 3 is correct.
In the given question, the probability pete will catch fish when he goes fishing is 0.9.
Pete is going fishing 4 days next week.
We have to find the expected number of days pete will catch fish.
From the question,
Pete is going fishing 4 days next week. So n=4
The probability pete will catch fish when he goes fishing is 0.9. So P(F)=0.9
The formula for variance is:
Variance = n*p*(1-p)
Variance = 4*0.9*(1-0.9)
Variance = 4*0.9*0.1
Variance = 0.36
So the expected number of days pete will catch fish is 0.36. So the option 3 is correct.
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Problem 1 (A Few Random Steps) Consider four molecules, all starting at the origin, which undergo a 1d random walk, each with a 50% chance of going left or right along the x-axis at each time step. A. After 1 time step, what is the probability that 2 particles have gone left and 2 have gone right? Give your answer as a decimal number between 0 and 1 to 3 decimal places. B. After 2 time steps, what is the probability that all of the particles are at the origin? Give your answer as a decimal number between 0 and 1 to 3 decimal places. C. After 2 time steps, what is the probability that none of the particles are at the origin? Give your answer as a decimal number between 0 and 1 to 3 decimal places. D. After two time steps, what is the probability that one or more particles are not at the origin? Give your answer as a decimal number between 0 and 1 to 3 decimal places.
The probability that 2 particles have gone left and 2 have gone right is 0.375, considering four molecules, all starting at the origin, which undergo a 1d random walk, each with a 50% chance of going left or right along the x-axis at each time step.
Define probability.Probability measures how likely something is to happen. It is calculated mathematically as a fraction, ratio, or percentage. The formula of the favourable outcome over the total outcomes is used to describe probability. The likelihood of flipping a coin heads is one example. Given that there is only one head and two total sides, 50% of the time, a head will land up-side-down.
Given,
4 particles given,
P(left) = 0.5 = P(right)
Possible combinations in total,
2 × 2 × 2 ×2
16
Combinations that are accepted,
RRLL, LLRR, LRLR, RLRL, RLLR, LRRL
Probability of 2 left and 2 right:
= 6/16
= 3/8
= 0.375
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THE CUBE THAT VOLUME 8CM CUBIC THEN THE SUM OF ALL EDGE LENTHS =
Answer:
6
Step-by-step explanation:
8 cube root is 2
there are 3 different lengths
3x2=6
Hello guys please help me on Composite and Inverse Functions
The inverse function of f(x) is [tex]\frac{x + 2}{3}[/tex] and [tex]f^{-1}(13)[/tex] = 5
What is an inverse function?
An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by [tex]f^{-1}[/tex] One should not confuse (-1) with exponent or reciprocal here.
if f(x) = 3x - 2
setting y = 3x - 2 and making x the subject of the formulae,
we have
3x - 2 = y
3x = y + 2
x = [tex]\frac{y + 2}{3}[/tex]
replacing y with x and x with [tex]f^{-1}[/tex](x)
[tex]f^{-1}[/tex](x) = [tex]\frac{x + 2}{3}[/tex]
the value of [tex]f^{-1}[/tex](13) , we substitute x = 13,
[tex]f^{-1}[/tex](13) = 13 + 2 / 3
[tex]f^{-1}[/tex](13) = 15/3
[tex]f^{-1}[/tex](13) = 5
In conclusion, the inverse function is [tex]f^{-1}[/tex](x) = [tex]\frac{x + 2}{3}[/tex] and [tex]f^{-1}[/tex](13) = 5
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What is the lateral area of the prism? 73.5 feet 73.5 square feet 84 feet 84 square feet
Answer:The lateral surface area of the triangular prism will be 84 square feet.correct option is D.
What is the surface area of the triangular prism?Let the sides of the triangle be a, b, c, and a height of H. Then the surface area of the prism is given as SA = H(a + b + c)A triangular prism has bases with three congruent sides, each measuring 4 feet. The height of each triangle is approximately 3.5 feet.The distance between the triangular bases is 7 feet.Then the lateral surface area will beSA = 7 (4 + 4 + 4)SA = 7 x 12SA = 84 square feet. the correct option is D
Step-by-step explanation:
According to a poll, 85% of California adults (428 out of 506 surveyed) feel that education is one of the top issues facing California. We wish to construct a 90% confidence Interval for the true proportion of California adults who feel that education is one of the top issues facing California. Find a 90% confidence interval for the population proportion, (Round your answers to three decimal places) *) Additional Materials Book Submit Answer The mean age of De Anza College students in a previous term was 26.6 years old. An instructor thinks the mean age for online students is older than 26.6. She randomly surveys 99 online students and finds that the sample meanis 29.7 with a standard deviation of 2.1. Conduct a hypothesis test at the level Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though) Parta) Part () Parte) Purt (d Part() O Partin Part ol Parthi Part 9 Construct a 95% confidence interval for the true mean. Sketch the graph of the situation Label the point estimate and the lower and upper bounds of the confidence interval (Round your answers to two decimal places) 95% CI: 29.7 X Enter a number A survey in the N.Y. Times Almanac finds the mean commute time (one way) is 25.4 minutes for the 15 largest US cities. The chamber of commerce in a cty feels that the commute time is less and wants to publicize this fact. The mean for 25 randomly selected commuters is 22.4 minutes with a standard deviation of 5 minutes. At the 0.10 level, is the city's commute significantly less than the mean commute time for the 15 largest US cities? Note: If you are using a Student's e-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Parta) Part) State the p-value. (Round your answer to four decimal places) Enter a number Part (0)
The population proportion's 90% confidence interval is 0.824 < p < 0.876 when 85% of California people (428 out of 506 polled) believe that education is one of the state's most problems.
Given that,
85% of California people (428 out of 506 polled) believe that education is one of the state's most problems. For the true percentage of California adults who believe that education is one of the state's top problems, we want to build a 90% confidence interval.
We have to find the population proportion's 90% confidence interval.
We know that,
Let
n = 506, p = 0.85
90% Confidence interval :
At α = 0.1, two critical value, z base c = normal variable(0.1/2) = 1.645
Lower Bound = p - z base c×√(p ×(1- p)/n) = 0.85 - 1.645×√(0.85×0.15/506) = 0.824
Upper Bound = p + z base c×√(p ×(1- p)/n) = 0.85 + 1.645×√(0.85×0.15/506) = 0.876
0.824 < p < 0.876
Therefore, The population proportion's 90% confidence interval is 0.824 < p < 0.876 when 85% of California people (428 out of 506 polled) believe that education is one of the state's most problems.
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Jill’ fih weigh 8 time a much a her parakeet. Together they weigh 63 ounce. How much doe the fih weigh
Answer:
”fih” weighs 56 ounces
Step-by-step explanation:
8p=f
f+p=63
f- fih
p- parakeet
p+8p=63
9p=63
/9. /9
p=7
Parakeet weighs 7 ounces now to find the weight of the fih
8(7)=f
56=f
Fih weighs 56 ounces
Hopes this helps please mark brainliest
Two gamblers play a version of roulette with a wheel as shown in the file P05_63.xlsx. Each gambler places four bets, but their strategies are different, as explained below. For each gambler, use the rules of probability to find the distribution of their net winnings after four bets. Then find the mean and standard deviation of their net winnings. The file gets you started.
a. Player 1 always bets on red. On each bet, he either wins or loses what he bets. His first bet is for $10. From then on, he bets $10 following a win, and he doubles his bet after a loss. (This is called a martingale strategy and is used frequently at casinos.) For example, if he spins red, red, not red, and not red, his bets are for $10, $10, $10, and $20, and he has a net loss of $10. Or if he spins not red, not red, not red, and red, then his bets are for $10, $20, $40, and $80, and he has a net gain of $10.
b. Player 2 always bets on black and green. On each bet, he places $10 on black and $2 on green. If red occurs, he loses all $12. If black occurs, he wins a net $8 ($10 gain on black, $2 loss on green). If green occurs, he wins a net $50 ($10 loss on black, $60 gain on green).
The mean is 65.0646 and standard deviation is 39.082 when we can see the complete form of the table in the picture.
Given that,
As seen in the spreadsheet file P05 63.xlsx, two gamblers engage in a game of wheel-based roulette. Each gambler lays four bets, but each uses a different strategy, as will be seen later. Use the probabilities to determine the distribution of each gambler's net earnings after four bets. Then calculate their net wins' mean and standard deviation. You can get going with the file.
We have to find the mean and standard deviation.
We know that,
In the picture we can see the complete table.
Here, we calculated probability as,
For example take a first row
P(red=4, black=0, green=0) = (18/37)⁴ + 0 + 0 = 0.056
So the mean is 65.0646 and standard deviation is 39.082.
Therefore, The mean is 65.0646 and standard deviation is 39.082 when we can see the complete form of the table in the picture.
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If a first order is half completed in 2mins, what is the rate constant
The rate constant of the scenario is 4 minutes
How to determine the rate constant?From the question, we have the following parameters that can be used in our computation:
Half completed in 2 minutes
This means that the full completion is 4 minutes
These parameters can be represented as
(x, y) = (1, 4)
The rate constant of the statement can then be represented as the slope and the slope is then calculated as
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (0, 0) and (1, 4)
Substitute the known values in the above equation
So, we have the following equation
rate constant = (4 - 0)/(1 - 0)
Evaluate the quotient
rate constant = 4
Hence, the rate constant is 4 minutes
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how many zeros are at the end of (20!)2 when it is written in decimal form? fill in the blanks below to show how to use the result of part (b) to answer this question.
Therefore there are four zeros on the end of the number.
There are 8 zeroes at the end of [tex]20!^{2}[/tex]
Here, we are given an expression- [tex]20!^{2}[/tex]
To find the number of zeroes in any expression, we need to find the number of multiples of 10 in the expression.
10 is made up of 2 prime numbers, that are- 2 and 5
Thus, the number of multiples of 5 and 2 will give us the number of zeroes.
In 20!, the multiples of 5 will be- 5, 10, 15 and 20
⇒ there are total 4 multiples of 5 in 20!
Now, looking at the multiples of 2, we can see that there will definitely be more than 4 multiples, some of them are- 2, 4, 6, 8, 10 and so on
But since there are only 4 multiples of 5, there will be only 4 multiples of 10 and hence only 4 zeroes in the expansion of 20!
If we square 20!, the number of zeroes will also double and become 8
Thus, there are 8 zeroes at the end of [tex]20!^{2}[/tex]
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The graph of function f(x) is the one in option D.
How to graph the function?To graph the function f(x), we just need to graph all the points on the table on a coordinate axis and then connect the points with a line.
Here we have the points:
(-2, 16/9)
(-1, 4/3)
(0, 1)
(1, 3/4)
(2, 9/16)
The graph of the five points can be seen in the image below.
Comparing it with the given options, we can see that the correct option is D.
(you can see that is not A because the first point is incorrect).
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how many grams of pure zinc oxide powder must be added to 450 g of a 1.5% ointment to make a 11% zinc oxide ointment? round to one decimal place.
The amount of zinc oxide need to be added to 450 g of 1.5% ointment to make a 11% zinc oxide ointment is 48 gram.
A fraction represent the number of parts in total or whole. Fraction is sometimes denoted in percentage, e.g. 20% means a fraction of 20/100.
In the given problem, let w is the amount of zinc oxide need to be added.
Original weight of Zinc oxide = 1.5% x 450 g
After adding w gram of zinc oxide, weight of zinc oxide = 1.5% x 450 + w
Original weight of ointment = 450 g
After adding w gram of zinc oxide, weight of ointment = 450 + w
Hence, the new fraction of zinc oxide:
(1.5% x 450 + w) / (450 + w) = 11%
1.5% x 450 + w = 11% x 450 + 11% w
9.5% x 450 = 89% w
w = 48
Hence, the amount of zinc oxide need to be added is 48 gram.
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What is the measure of the angle of an isosceles?.
The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.
What is the measure of the angle of an isosceles?
Properties of an Isosceles Triangle
The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.
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A car that travel at 20 mile in 1/2 hour at contant peed i traveling at the ame peed a a car that travel 30 mile in 3/4 at a contant peed. Explain why
It is true that the speed of both cars is the same.
What is an example of continuous speed?
When something is going at a fixed, steady pace or at an average speed, it is said to be moving at constant speed or uniform rate. As an illustration, a car travels 3 hours. In the first hour, it travels 30 miles, in the second hour, 45 miles, and in the third hour, 75 miles.
Detailed explanation:
Car A is moving at a pace of 40 miles per hour since it covers 20 miles in less than 30 minutes.
In order to determine whether or not Car B is moving at the same speed as Car A, let's build up a proportion for the 30 miles it travels in 3/4 of an hour.
30 miles in one hour equals x miles in one hour. multiply by cross
Divide both sides by (3/4) to get 30.
40 = x
As a result, the speeds of Car A and Car B are equal.
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At a carnival, Preton and hi brother collected 53 piece of candy all together. Each of them ate 5 piece of candy that evening. The next day, Preton had 19 piece left. How many piece did Preton' brother have left?
The total number of pieces that Preston's brother has left is 24.
What is the subtraction operation?
In mathematics, the operation of eliminating items from a collection is represented by the subtraction operation. The negative symbol (-) is used to denote subtraction.
Given, Preston and his brother collected 53 pieces of candy.
Each of them ate 5 pieces of candy.
And, Preston had 19 pieces left.
The number of candies Preston's brother have left = 53 - (5*2 + 19) = 24
Hence, the total number of pieces that Preston's brother has left is 24.
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What is an example of a obtuse triangle?.
Answer:
A triangle where the angles in the inside are 100 degrees, 40 degrees, and 40 degrees.
Step-by-step explanation:
The angles inside a triangle always add up to 180 degrees
And an obtuse triangle is a triangle whose biggest angle is bigger than 90 degrees
100 is biggest angle out of the three angles we're using to make the triangle and 100 is bigger than 90.
Adding the three angles we're using also makes 180 (100 + 40 + 40)
Two building are 18. 5 meter apart. The angle of elevation from the top of one building to the top of the other i 18 degree. If the taller building i 15 meter tall, how tall i the horter building?
Using the angle of elevation we calculate the height of the smaller building to be approximately 8.99 meters.
Let the height of the smaller building be x.
Distance between the two buildings = 18.5 meters.
Angle of elevation = 18°
From the properties of trigonometric ratios we know that:
tan 18° = (15 - x) / 18.5 as tan is the ratio of perpendicular and base of a triangle.
solving we get :
15 - x = 6.011 m
or, x = 8.99 m
The shorter building is approximately 8.99 meters tall.
The angle of elevation is described as "the angle formed between the horizontal line and the line of sight when an observer looks upwards" in mathematics. It is always higher and at a greater angle than the observer.
An angle of depression is produced when someone looks down, which is the opposite of an angle of elevation.
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At a real estate agency, an agent sold a house for $307,000. The commission rate is 5.5% for the real estate agency and the commission rate for the agent is 25% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
The commission which real estate agency gets is $16885.
The commission which the agent get is $76750
How to calculate the commission?The selling price for a house = $ 307,000
The commission rate for real estate agency = 5.5 %
The commission rate for the agent = 25 %
So, the commission which real estate agency gets:
= 5.5 % of $307,000
= 0.055 × $ 307,000
= $16885
The commission which agent get:
= 25% of $ 382,000
= 0.25 × $ 307,000
= $76750
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in this scenario, what is the test statistic? a sociologist would like to test the claim that the average age of a u.s. adult getting married is different than 27 years old. sample size
There is not sufficient evidence to claim that the average age of a US adult getting married is different than 27 years old.
μ₀ = 27
h = 30
X = 26
σ = 7
Hypothesis test at α = 0.025
Null & Alternative hypothesis
H₀: μ = 27
Ha: μ = 27
Test statistics = Z
Z= x-μ/(σ/√h)
= 26-27/(7/√30)
Z = -0.78
p-value
p-value from Z-table at |Z|= 0-78,
two-tailed is p-value = 0.4354
decision-
here p-value = 0-4354 > α=0·025 Since we fail to reject H₀ at 2.5%
Hence, there is not sufficient evidence to claim that the average age of a US adult getting married is different than 27 years old.
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Is the average of a sum the sum of the averages?.
The average of a sum and the sum of the averages are not same.
The average of a sum is mean of sum of data. Total sum divided by total number of sum.
Whereas , The sum of the average is sum of mean of data. Total sum of averages of data.
These two terms are not same.
For example : Assume x₁ , x₂ , x₃ , . . . , xₙ be a data
S₁ , S₂ , . . . , Sₙ be sum of data
A₁ , A₂ , . . . , Aₙ be average of data
where n is total number of sum of data
The Average of sum will be = S₁ + S₂ + . . . + Sₙ / n
The sum of average will be = A₁ + A₂ + . . . + Aₙ
Hence, The average of sum and Sum of average are different.
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Reflect the given triangle over the line y=-x. 3 6 3 -3 3 3 [?] [ -3 [ ] [ 3
The points of the vertices of the triangle after reflection on the line y = -x is given by A'(3,-3) , B'(-3,-6) and B'(-3,-6) .
We know that when a point is reflected around a line on the coordinate axes then the coordinates reflect following some rules.
Now when the point (a,b) is reflected around the line y = -x then ,the coordinates of the image becomes (-b,-a)
Therefore :
A(3,-3)→A'(3,-3 , does not change as the point lies on the line y=-x)
B(6,3)→B'(-3,-6)
C(3,3)→B'(-3,-6)
In a transition known as reflection over a line k, each point of the original figure (pre-image) must have an image that is the same distance from the line of reflection as the first comment but is on the other side of the line. Remember that a flip is a reflection. The size of the figure does not alter when it is reflected.
A figure created by a line reflection that is consistent with the original figure is called an isometry (a transformation that preserves length). Because naming the figure in a reflection implies changing the order of the letters, a reflection is more accurately referred to as a non-direct or opposing isometry .
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Answer: 3 -3 -3
-3 -6 -3
Step-by-step explanation:
frog took three jumps. The first jump was 2/3 m long, the second was 5/6 m long and
the third was 1/3 m long. How far did the frog jump in all?
The frog jumped the total length of 11/6m.
How to add two fractions?If the fractions have the same denominators then their numerators are added keeping the denominators as the same.
For fractions with different denominators the LCM of the denominators are taken then that is divided by the numerators of each fraction and the number obtained is multiplied to each of them to get the equivalent fraction.
Given that,
The length of first jump of the frog is 2/3m.
The length of second jump of the frog is 5/6m.
And, length of third jump of the frog is 1/3m.
Thus, the sum of all the jumps is given as,
2/3 + 5/6 + 1/3
The LCM of denominators is 6. So, the sum becomes,
(2 × 2 + 5 × 1 + 1 × 2)/6
= 11/6.
Hence, total length of the frog's jump is 11/6m.
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the value added and subtracted from a point estimate in order to develop an confidence interval of the population parameter is known as the
The margin error is the amount that is added to and subtracted from a point estimate in order to create a confidence range for the population parameter.
The margin error, or error rate, in statistics refers to how inaccurate survey results utilizing random samples are. A larger statistical margin of error indicates a decreased likelihood of relying on a survey's or poll's results, indicating a decreased level of trust in the results' capacity to fairly represent a community. It is an essential tool for market research since it demonstrates the level of trust that should be placed by the researchers in survey results.
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researchers collected data regarding the blood pressure of 20 individuals. for each individual, they recorded the blood pressure (mm hg), age (years), weight (kg), body surface area (m2), duration of hypertension (years), pulse (beats/min) and a stress index. the data is listed below. the researchers are interested in whether a relationship exists between blood pressure and any (or all) of the factors recorded. the problem examines different levels of regression fits starting with multiple items and moving to fewer items. you may use minitab.
Yes, there is a relationship exists between blood pressure and all of the factors recorded.
On what factor blood pressure depends upon?Blood pressure is the force of blood acting against the artery walls. The proper circulation of blood from the heart to the body's organs and tissues depends on normal pressure. Blood is pushed into the remainder of the body with each heartbeat. Pressure is higher close to the heart and lower farther away.
The amount of blood the heart pumps and the size of the arteries through which it travels are two factors that affect blood pressure. The pressure is typically higher the more blood being pumped and the narrower the artery. Systole, when the heart contracts, and diastole, when the heart relaxes, are both used to assess blood pressure.
Start by entering the data into the data table in Minitab. Select Multiple Regression, and then click OK in the Regression Analysis window. Choose Weight and Age as the Dependent and Pulse and Stress as the Independent variables in the Multiple Regression box. Next, select the OK button located in the Output box. The multiple regression fit is represented by the three values: umbcr: The weight and age regression coefficient has an umbcr value of 85.4. This indicates that the blood pressure rises by 0.84 mm Hg for every unit increase in weight and by 1.14 mm Hg for every unit increase in age.
Agc: The regression coefficient for age and weight has an agc value of 1.75. Accordingly, the heart rate rises by 0.075 beats per minute for every unit increase in weight and by 0.135 beats per minute for every unit increase in age. Weight BSA: The weight and body surface area's regression coefficient, or weight BSA, is 2.10. In other words, the body surface area grows by 0.21 square metres for every unit increase in weight and by 0.41 square metres for every unit increase in age.
Hypertension persistence: The regression coefficient for hypertension persistence is 87.01 years, and this number represents the persistence of hypertension. This means that the blood pressure rises by 3.06 mm Hg for every additional year of hypertension. Pulse: The pulse value, or the regression coefficient for pulse, is 905 beats per minute. This indicates that the blood pressure rises by 2.49 mm Hg for every additional beat per minute in the heartbeat. Stress index: The regression coefficient for the stress index is 943, and this is the stress index value. This means that the blood pressure rises by 2.35 mm Hg for every 1 unit increase in the stress index.
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Find the common ratio r for the following geometric sequence.
{1, −5, 25, −125, 625, . . .}
r = _
Answer:
-5
Step-by-step explanation:
its because each term is being mutliplied by -5
hopes this helps please mark brainliest
Answer:
The common ratio is r = - 5------------------
Given Geometric sequence 1, −5, 25, −125, 625, . .The common ratio is the ratio of any term by the previous oner = -5/1 = - 5r = 25 / - 5 = - 5r = -125/25 = - 5r = 625 / - 125 = - 56.10.22 we are given n 1 numbers from the set {1, 2, . . . , 2n}. prove that there are two numbers among them such that one divides the other.
The two numbers among them are such that one divides the other.
The Collection of well-defined objects or elements is known as a set. The objects in a set are called elements. The Set contains a finite number of elements. The Set is denoted by any capital letter like A, B etc. Elements of the set can be numbers, alphabets etc.
The elements of the set are listed inside the curly brackets { ..... }. There are various types of sets. Cardinal number or cardinality denotes the number of elements in the set. Cardinality is denoted by n( X ) where X is a set. The number of subsets of the set is given by 2^n.
As per the question,
numbers = n + 1set = { 1, 2 . . . . . . . . . 2n }Let us divide the set into two sets,
A = { 1, 3 . . . . . n } and B = { 2, 4 . . . . . . 2n }
A and B contain the same number of elements i.e. two sets have equal sizes. Element of B is one of the elements of A multiplied by 2 or elements of B multiplied by 2. So, if we remove the powers of 2 i.e we divide each element by [tex]2^{k}[/tex]. Then there exist another 2 sets [tex]A ^{'}[/tex] and [tex]B^{'}[/tex] such that [tex]A ^{'}[/tex] U [tex]B^{'}[/tex] = [tex]A ^{'}[/tex] .
By using the pigeonhole principle, [tex]A ^{'}[/tex] consists of n elements and we add +1 to it additionally.
Therefore, When we are given n + 1 numbers from set { 1, 2 . . . . 2n }, there are two numbers among them such that one divides the other.
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There is a line through the origin that divides the region bounded by the parabola and the x-axis into two regions with equal area. What is the slope of that line?.
The slope of that line is 1.031.
Given data,
There is a line through the origin that divides the region bounded by the parabola y = 5x - 3x² and the x-axis into two regions with equal area,
y = 5x - 3x²
5x - 3x² = 0
x(5 - 3x) = 0
x = 0 , x = 5/3
→ Area under y = 5x - 3x² is A = [0 to 5/3] 5x - 3x² dx
A = [0 to 5/3] 5x²/2 - 3x³/3
A = [0 to 5/3] 5x²/2 - x³
A = 5(5/3)2/2 - (5/3)3 = 125/54
∴ The lines passing through the origin are in the form of y = mx,
mx = 5x - 3x²
3x² + mx - 5x = 0
3x² + x(m -5) = 0
x(3x + (m -5)) = 0
x = 0 , x = (5 -m)/3
→ Area under y = 5x - 3x² and y = mx is (125/54)/2 = 125/108
∴ (5 -m)3/18 - (5 -m)3/27 = 125/108
(5 -m)3/54 = 125/108
(5 -m)3 = 125/2
(5 -m) = 3.9685
m = 5 - 3.9685
m = 1.0315
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Silicone implant augmentation rhinoplasty is used to correct congenital nosedeformities. The success of the procedure depends on various biomechanicalproperties of the human nasal periosteum and fascia. The article "Biomechnics inAugmentation Rhinoplasty" reported that for a sample of 10 (newly deceased)adults, the mean failure strain (%) was 26.0, and the standard deviation was 3.5.(p. 277 #35)a. Assuming a normal distribution for failure strain, estimate true average strain ina way that converys information about precision and reliability.b. Predict the strain for a single adult in a way that conveys information aboutprecision and reliability. How does the prediction compare to the estimatecalculated in part (a)?
In Asian nations, augmentation rhinoplasty is one of the most often performed cosmetic operations, with silicone implants being the most frequently utilized component.
Despite potential benefits, the use of alloplastic materials in rhinoplasty is frequently avoided in Western nations due to worries about the possibility of infection and implant extrusion. The silicone augmentation rhinoplasty has become a widespread operation in Asia due to the region's cumulative experience with long-term positive results.
Surgical technique, implant design, and surgeon expertise all have a substantial impact on the likelihood of complications with silicone implants. If precautions are taken, silicone implants can be used safely for nasal dorsal augmentation.
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