Answer:
y = x₂ - 1.5 × x₁.
Step-by-step explanation:
Regression model is a technique of analysis in which a variable known as dependent variables and another variables known as the independent variables are analyzed to determine their relationship.
So, from the question given above we have that; "Suppose that participants who adhere to a particular weight loss program lose an average of 1.5 lbs per week".
Also, we are given that time = x1 (in weeks) and weight = x2 (in pounds). Therefore the regression equation is given as below;
y = x₂ - 1.5 × x₁.
Use the perimeter formula P = 2 l + 2 w to find the perimeter, P , of a rectangular lot if the width, w , is 70 feet and the length, l , is 105 feet.
Answer:
P = 350 feet
Step-by-step explanation:
P = 2L + 2W
W = 70 feet
L = 105 feet
plug in values:
P = 2(105) + 2(70)
P = 210 + 140
P = 350 feet
Hector made a batch of pancakes for his guests. He used 6 cups of milk, 3 eggs, and 9 cups of pancake mix. What is the constant of proportionality for the ratio of pancake mix to milk? Two-thirds StartFraction 6 over 9 EndFraction Three-halves StartFraction 9 over 6 EndFraction
Step-by-step explanation:
The ratio simplified is 3:2 which is for every three cups of pancake mix there is 2 cups of milk. In this situation for each batch Vector wants to make of pancake he has to have 9 cups of pancake mix for every 6 cups of milk or the original 9:6 ratio.
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The constant of proportionality for the ratio of pancake mix to milk is 3/2. Hence, 3rd option is the right choice.
What do we mean by the constant of proportionality?When two or more ratios are in proportion, their simplest form is always the constant. This simplest form is the constant of proportionality.
How do we solve the given question?We are informed that Hector made a batch of pancakes for his guests. He used 6 cups of milk, 3 eggs, and 9 cups of pancake mix.
We are asked to find the constant of proportionality for the ratio of pancake mix to milk.
As pancake mix and milk are the ingredients used, they will always be in proportion. So to calculate their constant of proportionality, we take the ratio of pancake mix to milk and reduce it to its simplest form.
The ratio of pancake mix to milk = 9/6
Reducing this to its simplest form, we get the constant of proportionality = 3/2
∴ The constant of proportionality for the ratio of pancake mix to milk is 3/2. Hence, 3rd option is the right choice.
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Find a formula for the sum of n terms. Use the formula to find the limit as n → [infinity]. lim n → [infinity] n 2 + i n 8 n i = 1
Complete Question
Find a formula for the sum of n terms. [tex]\sum\limits_{i=1}^n ( 8 + \frac{i}{n} )(\frac{2}{n} )[/tex]
Use the formula to find the limit as [tex]n \to \infty[/tex]
Answer:
[tex]K_n = \frac{n + 73 }{n}[/tex]
[tex]\lim_{n \to \infty} K_n = 1[/tex]
Step-by-step explanation:
So let assume that
[tex]K_n = \sum\limits_{i=1}^n ( 8 + \frac{i}{n} )(\frac{2}{n} )[/tex]
=> [tex]K_n = \sum\limits_{i=1}^n ( \frac{16}{n} + \frac{2i}{n^2} )[/tex]
=> [tex]K_n = \frac{2}{n} \sum\limits_{i=1}^n (8) + \frac{2}{n^2} \sum\limits_{i=1}^n(i)[/tex]
Generally
[tex]\sum\limits_{i=1}^n (k) = \frac{1}{2} n (n + 1)[/tex]
So
[tex]\sum\limits_{i=1}^n (8) = \frac{1}{2} * 8* (8 + 1)[/tex]
[tex]\sum\limits_{i=1}^n (8) = 36[/tex]
[tex]K_n = \frac{2}{n} \sum\limits_{i=1}^n (8) + \frac{2}{n^2} \sum\limits_{i=1}^n(i)[/tex]
and
[tex]\sum\limits_{i=1}^n (i) = \frac{1}{2} n (n + 1)[/tex]
Therefore
[tex]K_n = \frac{72}{n} + \frac{2}{n^2} * \frac{1}{2} n (n + 1 )[/tex]
[tex]K_n = \frac{72}{n} + \frac{1}{n} (n + 1 )[/tex]
[tex]K_n = \frac{72}{n} + 1 + \frac{1}{n}[/tex]
[tex]K_n = \frac{72 + 1 + n }{n}[/tex]
[tex]K_n = \frac{n + 73 }{n}[/tex]
Now [tex]\lim_{n \to \infty} K_n = \lim_{n \to \infty} [\frac{n + 73 }{n} ][/tex]
=> [tex]\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [\frac{n}{n} + \frac{73 }{n} ][/tex]
=> [tex]\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [1 + \frac{73 }{n} ][/tex]
=> [tex]\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [1 ] + \lim_{n \to \infty} [\frac{73 }{n} ][/tex]
=> [tex]\lim_{n \to \infty} [\frac{n + 73 }{n} ] = 1 + 0[/tex]
Therefore
[tex]\lim_{n \to \infty} K_n = 1[/tex]
Please help! Attachment below
Answer:
that means the system has no solutions
Julio wants to purchase a truck. The purchase price of the truck is $ 38 , 000.00 The dealership will allow him to pay cash or finance the truck for a down payment of $ 5 , 000.00 and 60 monthly payments of $ 750.00. Julio chooses to finance the truck.
Answer:
88,000
Step-by-step explanation:
If the down payment is $5,000and the monthly payment is $750. Then the amount of the truck through finance is $50,000.
What is finance?The big-scale money management, particularly by governments or huge corporations.
Julio wants to purchase a truck.
The purchase price of the truck is $ 38,000.00.
The dealership will allow him to pay cash or finance the truck for a down payment of $ 5,000.00 and 60 monthly payments of $ 750.00.
Julio chooses to finance the truck.
If he makes the payment through finance. Then the amount of the money he has to pay will be
Amount = 5000 + 60 × 750
Amount = 5000 + 45000
Amount = $50,000
If he makes the payment through finance. Then the amount of money he has to pay is 50,000 dollars.
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In 2011, a U.S. Census report determined that 68% of college students are working students. A researcher thinks this percentage has changed and surveys 144 college students. The researcher reports that 93 of the 144 are working students. Is there evidence to support the researcher's claim at the 1% significance level
Answer:
We will fail to reject the null hypothesis and conclude that there is sufficient evidence not to support the researchers claim.
Step-by-step explanation:
We are given;
Population proportion; p = 68% = 0.68
Sample proportion; p^ = 93/144 = 0.6548
n = 144
The hypotheses are:
Null hypothesis;H0: p = 0.68
Alternative hypothesis;Ha: p ≠ 0.68
np = 144 × 0.6548 > 5 and nq = n(1 - p) = 144(1 - 0.68) > 5.
Since np and nq are more than 5, we can use the z-test .
z-formula in this case is;
z = (p^ - p)/√(p(1 - p))
Plugging in the relevant values, we have;
z = (0.6548 - 0.68)/√(0.68(1 - 0.6548))
z = -0.0252/0.4845
z = -0.052
From the z-table attached, we have a p-value of approximately 0.4801
P-value is higher than the significance level of 0.01.
Thus,we will fail to reject the null hypothesis and conclude that there is no sufficient evidence to support the researchers claim.
Which is the recursive formula for the explicitly defined sequence?
an = 8n-3
Answer : [tex]a_{n+1}=a_n+8[/tex]
Step-by-step explanation:
The given explicit formula : [tex]a_n=8n-3[/tex] , where n is a natural number.
At n=1 , [tex]a_1=8-3=5[/tex]
At n=2, [tex]a_2=8(2)-3=16-3=13[/tex]
At n=3 , [tex]a_3=8(3)-3=24-3=21[/tex]
We can see the common difference is 8.
So we can write [tex]a_{n+1}=a_n+8[/tex]
Hence, the recursive formula for the explicitly defined sequence is [tex]a_{n+1}=a_n+8[/tex]
A car is traveling at a rate of 84 miles per hour. What is the car’s rate in miles per minute? How many miles will the car travel in 2 minutes? Do not round answer.
Answer:
2.4
Step-by-step explanation:
60 min in a hour
84/60= 1.4
1.4 x 2 = 2.4
Name the sets of number to which each number belongs.
25/11
ON, R(natural, real numbers
O Q(rational numbers)
Q, R (rational, real numbers)
O W, R (whole, real numbers)
The correct answer is C. Q, R (rational, real numbers)
Explanation:
The number [tex]\frac{25}{11}[/tex] is a fraction, which means it represents proportions of a whole. This number can be classified as rational, which is represented by the letter Q because this category of numbers includes those numbers that can be represented as a fraction and the number provided is naturally a fraction. Moreover, this number is also a real number, which is a broad category of numbers represented by the letter R that includes rational numbers such as fractions. This means this number is rational and because of this, it is also real.
On the other hand, this number is not natural because this includes regular numbers such as 3, 43, or 3947 but not fractions, and it is not a whole number because a fraction does not represent a whole number but just a proportion.
how to write 32 as well
exponential form
Answer:
2^5
Step-by-step explanation:
2^5 = 2 x 2 x 2 x 2 x 2 = 32
Step-by-step explanation:
2x2x2x2 now that is the exact way to solve it mark me as a brilliantis
Can the following be assumed from a diagram? The measures of angles
Estimate by rounding the divisor to the nearest tens place and the dividend to the nearest
compatible number. Then find the quotient.
Enter the remainder, if any, as a fraction in simplest form.
59 ) 5,613
The estimate is?
The quotient is?
Answer:
Estimate: 90
Quotient: 95
Remainder: 8/59
Step-by-step explanation:
Consider the strategic games described below. In each case, state how you would classify the game according to the six dimensions outlined in the text.
(i) Are moves sequential or simultaneous?
(ii) Is the game zero sum or not?
(iii) Is the game repeated?
(iv) Is there imperfect information, and if so, is there incomplete (asymmetric) information?
(v) Are the rules fixed or not?
(vi) Are cooperative agreements possible or not? If you do not have enough information to classify a game in a particular dimension, explain why not.
a.) Garry and Ross are sales representatives for the same company, Their manager informs them that of the two of them, whoever sells more this year wins a Cadillac.
b.) On the game show The Price is Right, four contestants are asked to guess the price of a television set. Play starts with the leftmost player, and each player's guess must be different from the guess of the previous players. The person who comes closest to the real price, without going over it, wins the television set.
c.) Six thousand players each pasy $10,000 to enter the World Series of Poker. Each starts the tournament with $10,000 in chips, and they play No-Limit Texas Hold'Em ( a type of poker) until someone wins all the chips. The top 600 players each receive prize money according to the order of finish, with the winner receiving more than 8,000,000.
d.) Passengers on Dessert Airlines are not assigned seats: passengers choose seats once they board. The airline assign the order of boarding according to the time the passenger checks in, either on the Web site up to 24 hours before takeoff or in person at the airport.
Answer:
game show The Price is Right, four contestants are asked to guess the price of a television set. Play starts with the leftmost player, and each player's guess must be different from the guess of the previous players. The person who comes closest to the real price, without going over it, wins the television set.
c.) Six thousand players each pasy $10,000 to enter
Which of the following fall(s) at a z-score of 0.0 in a normal distribution? Mean Median Mode Mean, media and mode
Answer: Median Mode Mean
Step-by-step explanation:
A normal distribution a symmetric distribution where most of the values lies around the central peak where Mean, median mode all lies together and the value of z=0 (as z-value given the distance of data values from mean with respect to the standard deviation).
i.e. Z-score of 0 has 50% of the area to the left and 50% area to the right.
Hence, at a z-score of 0.0 in a normal distribution Mean, Median and Mode all fall together.
Find the numbers b such that the average value of f(x) = 7 + 10x − 9x2 on the interval [0, b] is equal to 8.
Answer:
The numbers [tex]b[/tex] such that the average value of [tex]f(x) = 7 +10\cdot x - 9\cdot x^{2}[/tex] on the interval [0, b] is equal to 8 are [tex]b_{1} \approx 1.434[/tex] and [tex]b_{2} \approx 0.232[/tex].
Step-by-step explanation:
The mean value of function within a given interval is given by the following integral:
[tex]\bar f = \frac{1}{b-a}\cdot \int\limits^b_a {f(x)} \, dx[/tex]
If [tex]f(x) = 7 +10\cdot x - 9\cdot x^{2}[/tex], [tex]a = 0[/tex], [tex]b = b[/tex] and [tex]\bar f = 8[/tex], then:
[tex]\frac{1}{b}\cdot \int\limits^b_0 {7+10\cdot x -9\cdot x^{2}} \, dx = 8[/tex]
[tex]\frac{7}{b}\int\limits^b_0 \, dx + \frac{10}{b} \int\limits^b_0 {x}\, dx - \frac{9}{b} \int\limits^b_0 {x^{2}}\, dx = 8[/tex]
[tex]\left(\frac{7}{b} \right)\cdot b + \left(\frac{10}{b} \right)\cdot \left(\frac{b^{2}}{2} \right)-\left(\frac{9}{b} \right)\cdot \left(\frac{b^{3}}{3} \right) = 8[/tex]
[tex]7 + 5\cdot b - 3\cdot b^{2} = 8[/tex]
[tex]3\cdot b^{2}-5\cdot b +1 = 0[/tex]
The roots of this polynomial are determined by the Quadratic Formula:
[tex]b_{1} \approx 1.434[/tex] and [tex]b_{2} \approx 0.232[/tex].
The numbers [tex]b[/tex] such that the average value of [tex]f(x) = 7 +10\cdot x - 9\cdot x^{2}[/tex] on the interval [0, b] is equal to 8 are [tex]b_{1} \approx 1.434[/tex] and [tex]b_{2} \approx 0.232[/tex].
A dishwasher is priced at $635.50. There is an 8% sales tax rate. What is
the sales tax for the dishwasher in dollars and cents?
i need this answer right away!!!
Trans wants to buy a bicycle that costs $192. He plans to save $6 each week . How many weeks will it take him to save enough money ?
Answer:
32 weeks
Step-by-step explanation:
Total amount = 192
Each week he saves = 6
Number of weeks = x
=> 6x = 192
=> 6x/6 = 192/6
=> x = 32
It will take 32 weeks for him to buy the bicycle.
chemist is using 332 milieters of solution of acid and water if 14.4% of the solution is acid how many milliliters of acid is there
Answer:
332*14.4% = 332*.144 = 47.808
6x=2x+44 solve for x
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 11}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{6x = 2x + 44}[/tex]
Move 2x to left hand side and change it's sign
⇒[tex] \sf{6x - 2x = 44}[/tex]
Collect like terms
⇒[tex] \sf{4x = 44}[/tex]
Divide both sides of the equation by 4
⇒[tex] \sf{ \frac{4x}{4} = \frac{44}{4} }[/tex]
Calculate
⇒[tex] \sf{x = 11}[/tex]
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Three bells ring at an interval of 10,20,and 30 minutes respectively. If they all ring together at 10:30 p.m.,at what time will they again ring together?
Answer:
11:30 PM
Step-by-step explanation:
This question is essentially asking for the lowest common multiple of 10, 20, and 30. If we write out all the multiples of each, we get:
10: 10, 20, 30, 40, 50, 60, 70, ...
20: 20, 40, 60, 80, ...
30: 30, 60, 90, ...
As you can see, the lowest common multiple is 60, and 60 minutes after 10:30 PM is 11:30 PM.
4) Martin compares the prices of paper towels. A 3-roll package is priced at $2.89. A single
rollis priced at $89. Based on price alone, which is the better buy?
Answer:
assuming prices are correctly shown: 3-roll packageassuming a typo: single rolls.Step-by-step explanation:
If single rolls are indeed priced at $89 each, the 3-roll package is a much better buy.
We suspect that the single rolls are priced at $0.89 each, which means you can buy 3 of them for less than $2.70. At this price, single rolls are a better buy.
Triangle ABC has vertices A (1,3), B (-2,-1), and C (3,-2). Triangle ABC has been translated
right 4 and down 2. This translation can be written in coordinate notation as
Answer:
A(5,1) B(-6,2) C(7-4)
Step-by-step explanation:
half of 5/6. thanks
Answer: 41.665
Step-by-step explanation:
5/6 as a percent is 83.33.
83.33 divided by 2 equals 41.665.
So, the answer is 41.665.
Hope this helps!
Answer: 0.4166667
Explanation: Make 5/6 to 0.8333. Divide the decimal by 2.
Hope it helps!
lovelymoonlight
In the last 10 years, the population of Indonesia has grown at a rate of 1.12% per year to 258,316,051. If this rate continues, what will be the population in 10 more years? Round your answer to the nearest whole number.
Answer:
288750006
Step-by-step explanation:
Growth rate:
1.12% or 1.0112 timesCurrent population:
258,316,051Predicted population after 10 years:
258,316,051*(1.0112)^10 = 288,750,006.168≈ 288,750,006 roundedAnswer:288,929,825
Step-by-step explanation:
This is the right answer.
For the statement below, write the claim as a mathematical statement. State the null and alternative hypotheses and identify which represents the claim. An amusement park claims that the mean daily attendence at the park is people. Write the claim as a mathematical statement. A. B. C. D. E. F. Choose the correct null and alternative hypotheses below. A. : : B. : : C. : : D. : : E. : : F. : : Identify which is the claim. A. The null hypothesis : is the claim B. The alternative hypothesis : is the claim C. The alternative hypothesis : is the claim D. The alternative hypothesis : is the claim. E. The null hypothesis : is the claim
The question is not complete, so i have attached it.
Answer:
A) Option B: μ ≤ 19,000
B) Option C:
H0: μ ≤ 19,000
Ha: μ > 19,000
C) Option D: The null hypothesis H0: μ ≤ 19,000 is the claim
Step-by-step explanation:
A) From the question, we are told that an amusement park claims that the mean daily attendence at the park is at most 19,000 people.
Now, since it's at most 19000 people, it means that they are either 19000 or less. So the claim is;
μ ≤ 19,000 which is option B
B) Now, the claim is usually the null hypothesis. Thus, the null hypothesis is;
H0: μ ≤ 19,000
While the alternative hypothesis which states the opposite of the claim is;
Ha: μ > 19,000
So, option C is the correct answer
C) The claim is μ ≤ 19,000
Now, this also happens to be the null hypothesis.
Thus, the null hypothesis H0: μ ≤ 19,000 is the claim.
So option D is correct.
which equation is equivalent to the given equation? x^2+16x=22
a. (x+8)^2=86
b. (x+8)^2=38
c. (x+16)^2= 278
d. (x+4)^2= 22
Answer:answer is a (x+8)^2=86
Step-by-step explanation:
x+8=±√
86
2 Break down the problem into these 2 equations.
x+8=\sqrt{86}x+8=√
86
x+8=-\sqrt{86}x+8=−√
86
3 Solve the 1st equation: x+8=\sqrt{86}x+8=√
86
.
x=\sqrt{86}-8x=√
86
−8
4 Solve the 2nd equation: x+8=-\sqrt{86}x+8=−√
86
.
x=-\sqrt{86}-8x=−√
86
−8
5 Collect all solutions.
x=\sqrt{86}-8,-\sqrt{86}-8x=√
86
−8,−√
86
−8
x
2
+16x−22=0
2 Use the Quadratic Formula.
x=\frac{-16+2\sqrt{86}}{2},\frac{-16-2\sqrt{86}}{2}x=
2
−16+2√
86
,
2
−16−2√
86
3 Simplify solutions.
x=-8+\sqrt{86},-8-\sqrt{86}x=−8+√
86
,−8−√
86
The equivalent equation x² + 16x = 22 will be (x + 8)² = 86. Then the correct option is A.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
The equation is given below.
x² + 16x = 22
Add both side 64.
x² + 16x + 64 = 22 + 64
(x + 8)² = 86
Then the correct option is A.
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The product of 5 and the cube of x, increase by the difference of 6 and x3
Answer:
[tex]4x^{3} +6[/tex]
Step-by-step explanation:
The product of 5 and the cube of x[tex]5*x^3\\\\=5x^3[/tex]
the difference of 6 and x^3[tex]6-x^3[/tex]
I understand as increase as sum so
[tex](5x^3)+(6-x^3)\\\\5x^3+6-x^3\\\\(5-1)x^3+6\\\\4x^3+6[/tex]
What is 1/3 times 1/3 times 1/3
Answer:
1/27
Step-by-step explanation:
since the numerator is only one, just go ahead and write one on the numerator spot. Then you multiply the bottom 3^3 is 27, therefore you get 1/27th
Answer:
1/3 cubed is 1/27
Step-by-step explanation:
1/3*1/3*1/3 is equal to 1/27
plz say answer for this grade 7
The full circle = 360 degrees
so x = all the full circle minus the other 3 angles
Now we sum the three angles we know [100, 46, 64]:
100 + 46 +64 = 210 degrees
Now we calculate x
x = 360 - 210 = 150 degrees
Every week, you spend $15.35 on coffee. There are 52 weeks in a year. How much money do you spend on coffee in a year?
Answer:
$798.20
Step-by-step explanation:
15.35 × 52 = 798.20