Answer:
y = 7.8x + 26
Step-by-step explanation:
Given the following :
Pearson's r = 0.78
Average consumption of ice cream = 5 grams per week (m) with Standard deviation (sd) = 1.5 grams
Average weight = 65 kg with standard deviation of 15kg
Formular for the regression line :
General regression formula :
y = mx + c
y = predicted variable ; m = slope or gradient ; x = predictor variable ; c = intercept
Gradient (m) = change in y / change in x
m = (sd y / sd x) * r
m = (sd weight / sd ice cream) × r
m = (15 / 1.5) × r
m = 10 × 0.78 = 7.8
Intercept:
mean of weight(y) - [Slope×mean of icecream(x)]
65 - [7.8 × 5]
65 - 39 = 26
Hence,
y = 7.8x + 26
How many solutions exist for 2 |x - 1| = 8?
A. 0
B. 1
C. 2
D. 3
Answer:
I believe the correct answer is C.
Step-by-step explanation:
So to get 0 solutions the absolute value would have to equal a negative number. To get 1 solution the absolute value would have to equal 0. To get 2 solutions the absolute value would have to equal a positive number.
2 |x - 1| = 8
divide by 2
|x - 1| = 4
The absolute value equals a positive so it has 2 solutions.
The quality control manager of a light bulb factory needs to estimate the average life of a large shipment of light bulbs. The process standard deviation is known to be 100 hours. A random sample of 64 light bulbs indicated a sample average life of 350 hours. Given the confidence interval calculated above. do you think the manufacturer has the right to state that the light bulbs last on average 400 hours?
a. No.
b. Yes.
c. Maybe.
d. Do not know
Answer:
b) yes
The manufacturer has the right to state that the light bulbs last on average 400 hours
Step-by-step explanation:
Explanation:-
Given sample size 'n' = 64
Given standard deviation of the Population (σ)=100
Mean of the sample (x⁻) = 350 hours
95% of confidence interval is determined by
[tex](x^{-} -Z_{0.95} \frac{S.D}{\sqrt{n} } , x^{-} +Z_{0.95} \frac{S.D}{\sqrt{n} } )[/tex]
([tex](350 -1.96 \frac{100}{\sqrt{64} } , 350+1.96\frac{100}{\sqrt{64} } )[/tex]
(350-24.5 , 350+24.5)
(325.5 , 374.5)
Conclusion:-
Yes
The manufacturer has the right to state that the light bulbs last on average 400 hours
Given m parallel to I, and m2 7 = 94, find the measure of angle 5
O 10
045
O 97
O 120
Answer:
97
Step-by-step explanation:
You take thirty measurements in order to find the length of a rod, you calculate the average and obtain the value L0. Supposed that now a different person takes twenty measurements as well of the same rod, then calculates the average and obtains the same L0 as you. Does it mean that both of you obtain a result with the same precision and accuracy
Answer:
Yes, it means that both of you obtain a result with the same precision and accuracy.
Step-by-step explanation:
It is provided that two different people took measurements in order to find the length of a rod.
The first person took 30 measurements.
The second person took 20 measurements.
Both the people got the same average length, i.e. L₀.
In statistics, a larger sample leads to an error free result.
So, for the first person the larger sample helped reducing the chance of any sort of error that may be present.
For the second person, the average is same as the first even when their sample size is less than the first.
This may happen because the sample was selected with a certain precision and accuracy.
Thus, both of them obtain a result with the same precision and accuracy.
A triangle has a base of 16 inches and a height of 18 inches. What is its area?
Answer:
The answer is
144 square inchesStep-by-step explanation:
Area of a triangle is given by
[tex]A = \frac{1}{2} bh[/tex]where
b is the base
h is the height
From the question
b = 16 inches
h = 18 inches
Substitute the values into the above formula and solve for the area
That's
[tex]A = \frac{1}{2} \times 16 \times 18 \\ = 8 \times 18 \: \: \: \: \: \: [/tex]We have the final answer as
144 square inchesHope this helps you
43,761 rounded to the nearest thousands
Answer:
44,000
Step-by-step explanation:
The number 43,761 rounded to its nearest thousands is 4400.
What is place value?The place value of a number is given as:
Example:
1234.567
1 = thousand place value
2 = hundred place value
3 = tens place value
4 = ones place value
5 = tenths place value
6 = hundredths place value
7 = thousandths place value
We have,
43,761
3 is in the thousand place.
So,
We will round 3761 to its nearest thousand value.
There are two options:
3000 or 4000
If It is greater than 3499 it will round to 4000.
If it is less than 3500 it will round to 3000.
Now,
3761 > 3499.
So,
The number is rounded to 4000.
Thus,
43,761 is rounded to 4400.
Learn more about place value here:
https://brainly.com/question/27734142
#SPJ2
Rachel, Hong, and Manuel have a total of 95 in their wallets. Hong has 3 times what Manuel has. Rachel has $10 more than Manuel. How much does each have?
Answer:
Rachel has 27
Hong has 51
Manuel has 17
Step-by-step explanation:
Let R represent Rachel, H represent Hong, and M represent Manuel.
They combined have a total of 95. Thus:
[tex]R+H+M=95[/tex]
Hong has 3 times what Manuel has. Therefore:
[tex]H=3M[/tex]
Rachel has 10 more than Manuel. Therefore:
[tex]R=10+M[/tex]
Substitute:
[tex]R+H+M=95\\(10+M)+(3M)+M=95[/tex]
Combine like terms:
[tex]5M+10=95[/tex]
Subtract 10 from both sides:
[tex]5M=85[/tex]
Divide by 5:
[tex]M=17[/tex]
Therefore, Manuel has 17.
Now, find Rachel and Hong's money.
[tex]H=3M\\H=3(17)=51[/tex]
So, Hong has 51.
And for Rachel:
[tex]R=10+M\\R=10+17=27[/tex]
Rachel has 27.
a cylinder container can hold 2.45l of water. it radius is 4.00cm. what is the the volume of it in cm3
Answer:
Step-by-step explanation:
Ion know
ILL GIVE YOU BRAINLIST ! Marlene is given 7 feet of fabric to design a dress. She uses 6 1/9 feet of fabric. How much fabric is left?
Answer:
This question is a lot easier than it seems. What you have to do here is subtract 6 1/9 from 7.
This will give you 0.8 of the fabric left, or 8/9.
x(2x + 3) + (x - 3)(x - 4)
Answer:
3x²-4x+12
Step-by-step explanation:
Answer:
[tex]=3x^2-4x+12[/tex]
Step-by-step explanation:
So we have the expression:
[tex]x(2x+3)+(x-3)(x-4)[/tex]
To simplify, distribute the left side and the right:
[tex]=x(2x)+x(3)+(x-3)(x)+(x-3)(-4)[/tex]
Distribute:
[tex]=(2x^2+3x)+(x^2-3x)+(-4x+12)[/tex]
Combine like terms:
[tex]=(2x^2+x^2)+(3x-3x-4x)+(12)[/tex]
Simplify:
[tex]=3x^2-4x+12[/tex]
The length of a rectangle is one more than four times its width. If the perimeter of the rectangle is 62 meters, find the dimensions of the rectangle.
Answer:
Length = 25 meters
Width = 6 meters
Step-by-step explanation:
62 = 2(a+b)
a = 4b + 1
a = length
b = width
then:
62 = 2((4b+1)+b)
62/2 = 4b+b+1
31 = 5b + 1
31 - 1 = 5b
30 = 5b
b = 30/5
b = 6m
a = 4b + 1
a = 4*6 + 1
a = 24 + 1
a = 25m
Check:
62 = 2(6+25)
62 = 2*31
On the njmber line below, the numbers x and y are the same distance from 0. What is x + y? Explain how you found your answer
Answer:
Step-by-step explanation:
either x+y=0
∵ if they are on number line and at same distance. then x=-y
or x+y=0
Assume that the two polygons are similiar, with the same orientation.
Write a proportion to determine the lengths of the sides labeled by variables.
(DO NOT SOLVE. You will solve the proportion in the next question.)
Answer:
4/6=t/(t+1)
Step-by-step explanation:
4/6=t/(t+1)
32 POINTS! WILL MAKE BRAINLIEST. ANSWER ASAP
A set of three scores consists of the values 3, 7, and 2.
Σ2X – 2 =
Σ(X – 1)² =
Answer:
Step-by-step explanation:
Given the set of datas 3, 7 and 2, we are to evaluate the folowing;
Σ2X – 2 and Σ(X – 1)² =where X are the individual datas.
We will substitute each of the data as value of X and ten take the sum as shown;
For Σ2X – 2
Σ2X – 2 = [2(3)-2]+[2(7)-2]+[2(2)-2]
Σ2X – 2 = (6-2)+(14-2)+(4-2)
Σ2X – 2 = 4+12+2
Σ2X – 2 = 18
For Σ(X – 1)² where x values are also 3, 7 and 2 we will have;
Σ(X – 1)² = (3 – 1)²+(7 – 1)²+(2 – 1)²
Σ(X – 1)² = 2²+6²+1²
Σ(X – 1)² = 4+36+1
Σ(X – 1)² = 41
Which expression is equivalent to : (-4x-3y-5)2
If you get this you are a critical thinker.
I enter the garden.
There are 34 people.
You kill 30.
How many people are in the garden.
Step-by-step explanation:
I'm not sure, but I think just 0
Because no one will even stand there and watch you kill 30 people
The police will come for you and the 1 dead person will be sent away lol
For what positive values of k does the function y=sin(kt) satisfy the differential equation y''+144y=0 ?
Answer:
The positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12
Step-by-step explanation:
To determine the positive values of k that the function y = sin(kt) satisfy the differential equation y''+144y=0.
First, we will determine y''.
From y = sin(kt)
y' = [tex]\frac{d}{dt}(y)[/tex]
y' = [tex]\frac{d}{dt}(sin(kt))\\[/tex]
y' = kcos(kt)
Now for y''
y'' = [tex]\frac{d}{dt}(y')[/tex]
y'' = [tex]\frac{d}{dt}(kcos(kt))[/tex]
y'' = [tex]-k^{2}sin(kt)[/tex]
Hence, the equation y'' + 144y = becomes
[tex]-k^{2}sin(kt)[/tex] + [tex]144(sin(kt))[/tex] [tex]= 0[/tex]
[tex](144 - k^{2})(sin(kt)) = 0[/tex]
[tex](144 - k^{2})= 0[/tex]
∴ [tex]k^{2} = 144\\[/tex]
[tex]k =[/tex] ±[tex]\sqrt{144}\\[/tex]
[tex]k =[/tex] ± [tex]12[/tex]
∴ [tex]k = +12[/tex] or [tex]-12[/tex]
Hence, the positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12
The positive value of k that satisfies the differential equation is k = 12.
To find the value of k that satisfies the equation, we differentiate the function y = sin(kt) twice to obtain y" and we insert it into the differential equation y" + 144y = 0.
So, y' = dy/dt
= dsin(kt)/dt
= kcos(kt)
y" = dy'/dt
y" = dkcos(kt)/dt
y" = -k²sin(kt)
So, substituting y and y" into the differential equation, we have
y" + 144y = 0
-k²sin(kt) + 144sin(kt) = 0
-k²sin(kt) = -144sin(kt)
k² = 144
k = ±√144
k = ±12
Since we require a positive value, k = 12
So, the positive value of k that satisfies the differential equation is k = 12.
Learn more about differential equations here:
https://brainly.com/question/18760518
trough: (2,2) parallel to y=x+4
Answer:
y = x
Step-by-step explanation:
The slopes of parallel lines are the same, so we know the equation will be ...
y = x + constant
We can find the constant by using the given point's values for x and y:
2 = 2 + constant
Obviously, the constant is zero.
The equation of the parallel line through (2, 2) is y = x.
Suppose that on each play of a game, a gambler either wins 1 with probability p or loses 1 with probability 1–p (or q). The gambler keeps betting until she or he is either up a total of n or down a total of m. What is the probability the gambler will quit an overall winner? You must consider both cases when p = 0.5 and when p ≠ 0.5
Answer:
Step-by-step explanation:
From the given information,
Considering both cases when p = 0.5 and when p ≠ 0.5
the probability that the gambler will quit an overall winner is:
[tex]P = \dfrac{1 - (\dfrac{1-p}{p} )^K}{1- (\dfrac{1-p}{p})^N } \ \ \ is \ p \neq 0.5 \ and\ K/N = \dfrac{1}{2}[/tex]
where ;
N.k = n and k = m
Hence, the probability changes to:
[tex]P = \dfrac{1 -(\dfrac{1-p}{p})^m}{1 -(\dfrac{1-p}{p})^{m+n}}[/tex] is p ≠ 0.5 and k/N = [tex]\dfrac{m}{m+n}[/tex] is P = 0.5
Which set of data do you believe to be better? Your data or your friend's data?
Answer:
Your friends data
Step-by-step explanation:
The rule of statistics is: the more exact the data, the better.
It looks like you just rounded your data to the nearest tenth. This is good, but not nearly as good as rounding it to the nearest hundredth.
This is because when you have data that is more exact, you get a better estimation for mean, median, etc. This can help make patterns in your data.
This means that your friend had better data than you.
Hope this helped!
Chiang is filling a 50ft container with water at a rate of 0.5 ft/ min. interpret the key features for this situation
Answer:
The key features are
50ft³ = the volume
0.5ft³/min = rate
Time= 100 minutes
Step-by-step explanation:
Chiang is filling a 50ft container with water at a rate of 0.5 ft/ min.
50ft³ = the volume
0.5ft³/min = rate
There is a key future missing which is the time it will take to fill the 50 ft³ container
Time = volume/rate
Time= 50 ft³/0.5ft³/min
Time= 50/0.5 min
Time = 100 min
The key features are
50ft³ = the volume
0.5ft³/min = rate
Time= 100 minutes
Please help me it’s in my math class
Answer:
1-70: Purple- 9/10= 0.18= 2 marbles
Orange- 16/50= 0.32= 3 marbles
Yellow- 6/50= 0.12= 1 marble
Green- 19/50= 0.38= 4 marbles
1-71: Part A. 3/6= 1/2
Part B. 4/6= 2/3
ax + by = c, bx + ay = (1 + c)
Answer:
( x - y ) ( a - b ) = -1
Step-by-step explanation:
ax + by = c and bx + ay = 1 + c
ax + by = c and bx + ay - 1 = c
And now we set c equivalent
ax + by = bx + ay - 1
ax - bx + by - ay = -1
x (a - b) + -y (a - b) = -1
(x - y) ( a - b) = -1
So we can leave it like that, or we can solve for one of the variables.
If we solve for y:
(x - y) ( a - b) = -1
(x - y) = -1 / (a - b)
-y = (-1 / (a - b)) - x
y = (1 / (a-b)) + x
Cheers.
explain how you can rename 5,400 as hundreds.
Answer:
The correct answer would be 54 hundreds
Step-by-step explanation:
If we are considering how many hundreds something has, we can simply take away two 0's and use that number. We take the two 0's off and then we have the right number of hundreds
Answer:
Hey there!
Five-thousand four-hundred can be expressed as fifty-four hundred.
Let me know if this helps :)
Translate to an algebraic expression. m plus the product of 6 and n
if y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8
Answer:
Y varies directly as X.
y=kx.
6=K72.
x=6/72.
x=0.08.
Y=0.08x.
when y=?, x=8.
y=0.08×8=0.64.
A card is selected at random from a standard 52-card deck. (a) What is the probability that it is an ace
Answer:
4/52 = 1/13
Step-by-step explanation:
A Women making $29 an hour gets a 15% raise. How much money will she make after 4 hours of working with the increased hourly pay?
Answer:
$133.4
Step-by-step explanation:
1. Find the increased pay:
29 * 1.15 = 33.35
2. Find how much she makes in 4 hrs
33.35 * 4 = 133.4
Goran is sitting in a movie theater, 5 meters from the screen. The angle of elevation from his line of sight to the top of the screen is 18, and the angle of depression from his line of sight to the bottom of the screen is 48. Find the height of the entire screen.
Answer:
Approximately
Height of screen= 7.1 meters
Step-by-step explanation:
Angle of elevation= 18°
Angle of depression= 58°
Distance of Goran from screen= 5 m
Height of screen from the attachment below
X+y
First let's determine angle a and b
a= 180-90-18
a= 72°
b= 180-90-48
b= 43°
Using sine formula
5/sin a= x/sin 18
5/sin 72= x/sin18
(5*sin 18)/sin 72= x
1.6246 = x
X= 1.6246 m
Y/sin 48= 5/sin b
Y= (5*sin 48)/sin 43
Y= (5*1.08965779)
Y= 5.4483 m
Height of screen= x+y
Height of screen= 1.6246+5.4483
Height of screen= 7.0729
Approximately
Height of screen= 7.1 meters