Answer:
ŷ = -0.08522X + 157.7779
The slope = - 0.1
Intercept = 157.8
Step-by-step explanation:
Given the data :
Duration __ Height
240 140
237 154
122 140
267 140
113 160
258 140
232 150
105 150
186 160
248 155
243 125
241 136
214 140
114 155
272 130
227 125
237 125
238 139
203 125
270 140
218 140
226 135
250 141
245 140
120 139
267 110
103 140
270 135
241 140
239 135
General regression equation :
y = mx + c
Where
y = predicted variable
x = predictor / explanatory variable
m = slope or gradient
c = Intercept
The regression equation obtained ;
ŷ = -0.08522X + 157.7779
To one decimal place :
ŷ = -0.1X + 157.8
The slope = - 0.1
Intercept = 157.8
the range of what function include-4
A large tank is partially filled with 100 gallons of fluid in which 20 pounds of salt is dissolved. Brine containing 1 2 pound of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is then pumped out at a slower rate of 4 gal/min. Find the number of pounds of salt in the tank after 35 minutes.
Answer:
Step-by-step explanation:
From the given information:
[tex]R_{in} = ( \dfrac{1}{2} \ lb/gal) (6)\ gal /min \\ \\R_{in} = 3 \ lb/min[/tex]
Given that the solution is pumped at a slower rate of 4gal/min
Then:
[tex]R_{out} = \dfrac{4A}{100+(6-4)t}[/tex]
[tex]R_{out}= \dfrac{2A}{50+t}[/tex]
The differential equation can be expressed as:
[tex]\dfrac{dA}{dt}+ \dfrac{2}{50+t}A = 3 \ \ \ ... (1)[/tex]
Integrating the linear differential equation; we have::
[tex]\int_c \dfrac{2}{50 +t}dt = e^{2In |50+t|[/tex]
[tex]\int_c \dfrac{2}{50 +t}dt = (50+t)^2[/tex]
multiplying above integrating factor fields; we have:
[tex](50 +t)^2 \dfrac{dA}{dt} + 2 (50 + t)A = 3 (50 +t)^2[/tex]
[tex]\dfrac{d}{dt}\bigg [ (50 +t)^2 A \bigg ] = 3 (50 +t)^2[/tex]
[tex](50 + t)^2 A = (50 + t)^3+c[/tex]
A = (50 + t) + c(50 + t)²
Using the given conditions:
A(0) = 20
⇒ 20 = 50 + c (50)⁻²
-30 = c(50) ⁻²
c = -30 × 2500
c = -75000
A = (50+t) - 75000(50 + t)⁻²
The no. of pounds of salt in the tank after 35 minutes is:
A(35) = (50 + 35) - 75000(50 + 35)⁻²
A(35) = 85 - [tex]\dfrac{75000}{7225}[/tex]
A(35) =69.6193 pounds
A(35) [tex]\simeq[/tex] 70 pounds
Thus; the number of pounds of salt in the tank after 35 minutes is 70 pounds.
Find the distance of a line given the following points. R(3, 1), W(-1, -2)
Answer:
[tex]\sqrt{13}[/tex]
Step-by-step explanation:
we can solve this using the distance formula: [tex]\sqrt{(x_{2}-x_1)^{2} + (y_{2}-y_1)^{2}}[/tex]
[tex]x_1, y_1[/tex] is (3, 1)
[tex]x_2, y_2[/tex] is (-1, -2)
[tex]\sqrt{(1-3)^2 + (-2-1)^2}[/tex]
which simplifies to: [tex]\sqrt{(-2)^2 + (-3)^2}[/tex]
then: [tex]\sqrt{2^2 + 3^2}[/tex] or: [tex]\sqrt{4+9}[/tex]
your final answer is: [tex]\sqrt{13}[/tex] or about 3.61
i Wnte 2x2x3x3x5 using exponents.
the number in unit form is all mixed up convert it tostandard form
Answer:
Step-by-step explanation:
What number?
One number is four times the other number. The larger number is also 87 more than the smaller number.
Find the larger number.
Answer:
116Step-by-step explanation:
Let numbers be x and y
Then we have equations:
x = 4yx = y + 87Comparing
4y = y + 874y - y = 873y = 87y = 87/3y = 29Then, the larger number is
x = 4*29 = 116juanito has a rope 1.75 meters long. He needs to cut it into shorter ropes each 0.1 meter long
Answer:
17.5
Step-by-step explanation:
[tex]1.75 \div 0.1 = 17.5[/tex]
please help this is so confusing!!!
Answer:
$16.50 on 3 bags of dog food
Step-by-step explanation:
First you would do 27.50/5 to find out how much one bag costs.
The symbol / mean to divide. So 27.50 divided by 5 is 5.50. We need to know the ammount of 3 bags. Hence, we evaluate 3 times 5.50 which equals to our answer, $16.50 on 3 bags of dog food. I hope this will help you succeed!
what is the constant of porportionality between 9 and 4.5
Answer:
1/2
Step-by-step explanation:
88) 4 times a number decreased by 8 equals 40
A) x=80 B) x = 40 C) x=8
D) x = 12
Select the correct answers in the table.
Rachel enjoys exercising outdoors. Today she walked 5 2/3 miles in 2 2/3hours. What is Rachel’s unit walking rate in miles per hour and in hours per mile?
A.) 2 1/8
B.) 2 4/9
C.) 8/17
D.) 3 1/8
Note: there hours and miles, but you have to give two answers, one for miles one for hours THANKS XD lolol <3
Answer:
b
Step-by-step explanation:
Which of the following is a postulate or theorem used to prove two triangles are congruent? ASA SSS AAA SAS
9514 1404 393
Answer:
ASA, SSS, SAS
Step-by-step explanation:
AAA is a postulate used to prove similarity. Congruence cannot be proved without including at least one side.
ASA, SSS, SAS postulates can be used to prove congruence
Use the tape diagram to write an equivalent ratio in simplest form. Write your ratio using a colon and no spaces.
Answer:
4:3
Step-by-step explanation:
There are 8 yellow spots and 6 blue spots
8:6
We can divide each side by 2 since they are both even
8/2: 6/2
4:3
Answer:
4:3
Step-by-step explanation:
need help somebody pleaseee
Answer:
The second one I believe
A car travels 1295 feet in 5 seconds. How far can the car travel in 50 seconds?
Answer:
12950
Step-by-step explanation:
Someone please help ASAP!!!!
Answer:
3/5 = 6/10, which is 0.6 in decimal form
Refer to the accompanying data set and construct a % confidence interval estimate of the mean pulse rate of adult females; then do the same for adult males. Compare the results. Click the icon to view the pulse rates for adult females and adult males. Construct a % confidence interval of the mean pulse rate for adult females. nothing bpm nothing bpm (Round to one decimal place as needed.) Construct a % confidence interval of the mean pulse rate for adult males. nothing bpm nothing bpm (Round to one decimal place as needed.) Compare the results.
A. The confidence intervals overlap, so it appears that there is no significant difference in mean pulse rates between adult females and adult males.
B. The confidence intervals overlap, so it appears that adult males have a significantly higher mean pulse rate than adult females.
C. The confidence intervals do not overlap, so it appears that adult females have a significantly higher mean pulse rate than adult males.
D. The confidence intervals do not overlap, so it appears that there is no significant difference in mean pulse rates between adult females and adult males.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The 95% confidence interval of mean pulse rate for adult female is [tex]71.98 < \mu < 79.88 [/tex]
The 95% confidence interval of mean pulse rate for adult male is [tex]62.89 < \mu < 70.57 [/tex]
The correct option is C
Step-by-step explanation:
Generally the sample mean for Male pulse rate is mathematically represented as
[tex]\= x_1 = \frac{\sum x_i }{n}[/tex]
= > [tex]\= x_1 = \frac{81 + 74 + \cdots + 59 }{40 }[/tex]
= > [tex]\= x_1 = 66.73[/tex]
Generally the standard deviation for male pulse rate is mathematically represented as
[tex]\sigma_1 = \sqrt{\frac{\sum (x - \= x)^2 }{n-1 } }[/tex]
=> [tex]\sigma_1 = \sqrt{\frac{\sum (81 - 66.73 )^2 + (74 - 66.73 )^2+ \cdot + (59 - 66.73 )^2 }{40-1 } }[/tex]
=> [tex]\sigma_1 = 12.24[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma_1 }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{12.4 }{\sqrt{40} }[/tex]
=> [tex]E =3.84 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x_1 -E < \mu < \=x_1 +E[/tex]
=> [tex]66.73 -3.84 < \mu < 66.73 +3.84 [/tex]
=> [tex]62.89 < \mu < 70.57 [/tex]
Generally the sample mean for Female pulse rate is mathematically represented as
[tex]\= x_2 = \frac{\sum x_i }{n}[/tex]
= > [tex]\= x_2 = \frac{81 + 94 + \cdots + 73 }{40 }[/tex]
= > [tex]\= x_2 = 75.93[/tex]
Generally the standard deviation for Female pulse rate is mathematically represented as
[tex]\sigma_2 = \sqrt{\frac{\sum (x - \= x)^2 }{n-1 } }[/tex]
=> [tex]\sigma_2 = \sqrt{\frac{\sum (81 - 66.73 )^2 + (94 - 66.73 )^2+ \cdot + (73 - 66.73 )^2 }{40 } }[/tex]
=> [tex]\sigma_2 = 12.73[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma_2 }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{12.73 }{\sqrt{40} }[/tex]
=> [tex]E =3.95 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x_2 -E < \mu < \=x_2 +E[/tex]
=> [tex]75.93 -3.95 < \mu < 75.93 + 3.95 [/tex]
=> [tex]71.98 < \mu < 79.88 [/tex]
How to solve (10 points)
Answer:
side 1: 10 = 15
side 2: 6 = 11
im not 100% sure this is correct
Step-by-step explanation:
13-8 = 5
so we add 5 on each side
10 + 5 = 15
6 + 5 = 11
The product of two consecutive even integers is 2208. What is their sum?
Answer:
±94
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Standard Form: ax² + bx + c = 0Solving Quadratic EquationsConsecutive IntegersStep-by-step explanation:
Step 1: Define
x (1st consecutive term)
x + 2 (2nd consecutive term)
Step 2: Set up equation
x(x + 2) = 2208
Step 3: Solve for x
Distribute x: x² + 2x = 2208Rewrite in Standard Form: x² + 2x - 2208 = 0Factor quadratic: (x - 46)(x + 48) = 0Find roots: x = -48, 46Step 4: Identify Consecutive Integers
Possibility 1: x = -48
1st Consecutive Even Term: -48
2nd Consecutive Even Term: -48 + 2 = -46
Possibility 2: x = 46
1st Consecutive Even Term: 46
2nd Consecutive Even Term: 46 + 2 = 48
Step 5: Find sums
Possibility 1: x = -48
-48 + -46 = -94
Possibility 2: x = 46
46 + 48 = 94
What is 3/5 plus 4/8
Answer: 11/10 is your answer
Step-by-step explanation: Hoped this helped
Answer:
1.1
Step-by-step explanation:
3/5 + 4/8 = 1.1
Vocabulary How can you tell when an equation in one variable has infinitely many solutions or no solution? When you solve for the variable, you will end up with a true statement, like 2 = 2, for an equation with no solution. You also will end up with a true statement for an equation with infinitely many solutions. When you solve for the variable, you will end up with a false statement, like 0 = 2, for an equation with no solution. You will also end up with a false statement for an equation with infinitely many solutions. When you solve for the variable, you will end up with a false statement, like 0 = 2, for an equation with no solution. You will end up with a true statement, like 2 = 2 for an equation with infinitely many solutions. When you solve for the variable, you will end up with a true statement, like 2 = 2, for an equation with no solution. You will end up with a false statement, like 0 = 2 for an equation with infinitely many solutions.
Answer: Choice C) When you solve for the variable, you will end up with a false statement, like 0 = 2, for an equation with no solution. You will end up with a true statement, like 2 = 2 for an equation with infinitely many solutions.
For example, let's say we had the equation x = x+2. Subtracting x from both sides leads to 0 = 2 which is a false statement. No matter what we replace x with, the equation x = x+2 is always false. That's why we don't have any solutions here.
For an equation like x + 2 = x + 2, subtracting x from both sides leads to 2 = 2 which is always true. A true equation is one where the same number is on both sides. No matter what we replace x with, the equation will be true. Therefore, there are infinitely many solutions.
To tell when an equation in one variable has infinitely many solutions or no solution;
When you solve for the variable, you will end up with a false statement, like 0 = 2, for an equation with no solution. You will end up with a true statement, like 2 = 2 for an equation with infinitely many solutions.The condition for an equation with no solution warrants that the equation upon evaluation yields a false statement as in the case of 1 = 2. In this case, such an equation has no solution.
The condition for an equation with infinitely many solutions warrants that the equation upon evaluation yields a true statement as in the case of y + 5 = y + 5. In this case, such an equation has infinitely many solution.
Read more;
https://brainly.com/question/11966980
your class is having a car wash for a fundraiser. it costs $27.95 for supplies. your class charges $5 per car. write an expression for the profit of the car. find the profit if the class washes 34 cars.
Answer:
5x-27.95=profit
5(34)-27.95
170-27.95
$142.05
Which phrases can be represented by the expression 60w?
The answer is 60 plz correct me
Find the whole, given the part and the percent. 50% of what number is 60
Answer:
50% of 120 is 60
Step-by-step explanation:
So 60 is half of 120, and 60 times 2 is 50 :)
(Brainliest?)
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Let x as that number ,
So :
[tex] \frac{50}{100} x = 60 \\ [/tex]
[tex] \frac{1}{2} x = 60 \\ [/tex]
Multiply sides by 2
[tex]2 \times \frac{1}{2} x = 2 \times 60 \\ [/tex]
[tex]x = 120[/tex]
Thus that number is 120 .
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
PLEASE HELP!!!!
IT IS NOT A
A. Yes; 20 hours/painter
B. Yes; 8 hours/painter
C. No; Does not pass through the origin
D. None of the above
Answer:
C
Step-by-step explanation:
Answer:
Pretty sure it's
D. None of the above
evaluate the expression when x=4/5 and y=-2/9: 3y-x
Answer:
-2/15
Step-by-step explanation:
PLEASE HELP ASAP 80 POINTS!!!!
Theresa volunteers at a food sheif. when she started, there were 213 oranges. After filling X bags of three oranges each, there were fewer than 51 oranges left. How many bags of oranges did Theresa fill?
Write an expression in terms of X for the number of oranges that Theresa bagged.
Part B: Write an expression in terms of X for the number of oranges that are left (have yet to be bagged).
Part C: Write an inequality using the expression from Part B to represent this scenario.
Part D: Solve the inequality for the variable X. Use opposite operations on both sides of the inequality until you get X on one side of the inequality by itself.
Part E: Did you have to flip the inequality sign? Explain why or why not.
Part F: What does the result from Part D tell you about Theresa's situation? Does the answer make sense? Explain.
Part G: Think about graphing the inequality you found in Part D on a number line. What would it look like?
Choose the correct number:
1. open circle on 54 and arrow pointing right
2. open circle on 54 and arrow pointing left
3. closed circle on 54 in arrow pointing right
4. closed circle on 54 and arrow pointing left
Answer:
A- The expression 3x represents the number of oranges that she bagged
B- 213 − 3x (or -3x + 213)
C- 213 − 3x < 51 (or -3x + 213 < 51)
D- x >54
E-Yes, I had to flip the inequality sign because I divided both sides of the inequality by a negative number (-3).
F- x > 54 means Theresa filled more than 54 bags of oranges. It makes sense because if Theresa made more than 54 bags of 3 oranges each, there would be fewer than 51 oranges left over.
G- Number 1 is correct.
Step-by-step explanation:
I did it./ Hope it helped : )
Answer:
everyone mark Praezhan brainleist thank you Praezhan so much
Step-by-step explanation:
Which expression represents 4 less than twice a number, n?
Answer:
x = 2n - 4
Step-by-step explanation:
hope this helped have a great day
helppppp please I will give brainliest
Answer:
-3/4
Step-by-step explanation:
Answer:
B. 4/3
Step-by-step explanation:
The slope is rise over run or the change in y over the change in x. To find the slope count how many units y increases by then divide that by how many units x increases. In this graph y goes up by 4 and x increases by 3, so 4/3. Another way to find slope is the slope formula which is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], then plug in any two points and solve them.
Please help with my homework
It's 65. Because you add the other angles and get 90+25 and get 115. 180 -115 = 65.
Answer:
c=65°
Step-by-step explanation:
180-90=90
90-25=65
hopefully this helps :)