Answer:
B. y = -2/3x + 12
Step-by-step explanation:
Formula to find the slope when given two points on a line:
y2 - y1
x2 - x1
Substitute the two given points (6, 8) (9, 6):
6 - 8
9 - 6
Slope = -2/3x
We found the slope! And the answer choices already gave us one y-intercept, which is 12. The last thing we do is we form an equation with the information we solved and that was given to us.
y = slope (x) + y-intercept
y = -2/3x + 12
The answer choice that matches this equation is B.
In conclusion, the equation that best estimates the line of best fit shown above is answer choice B.
An equation of a line with given coordinates is y= -2/3 x+12. Therefore, option B is the correct answer.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
From the given graph, the coordinate points are (6, 8) and (9, 6).
We know that, the formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).
Here, slope = (6-8)/(9-6)
= -2/3
Substitute m=-2/3 and (x, y)=(6, 8) in y=mx+c, we get
8=-2/3 (6)+c
8=-4+c
c=12
So, equation of a line is y= -2/3 x+12
Therefore, option B is the correct answer.
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The blue dot is at what value on the number line?
Answer:
-19
Step-by-step explanation:
By looking at the 2 numbers provided, -10 and -4, you can work out that there is a gap of 6 numbers as(-4) - (-10) = 6
There are 2 intervals between -10 and -4, so each interval is
6/2 = 3
a gap of 3
This means the number to the left of -4 is -7, then -10 which works.
From there, you count how many intervals there is between -10 and the ?
There are 3 intervals, so you have to decrease -10 by -3x3 or -9
Therefore the ? is -19
Another way is to just count it directly
The number directly left of -10 is going to be -13, then -16 and finally -19
Given the sequence 4, 8, 16, 32, 64, ..., find the explicit formula.
128Answer:
128
Step-by-step explanation:
vì 4+4=8
8+8=16
16+16=32
32+32=64
64+64=128
Pamela drove her car 99 kilometers and used 9 liters of fuel. She wants to know how many kilometers (k)left parenthesis, k, right parenthesis she can drive with 12 liters of fuel. She assumes the relationship between kilometers and fuel is proportional.
How many kilometers can Pamela drive with 12 liters of fuel?
Answer:
132 kilo meters
Step-by-step explanation:
Pro por tions:
9 lite rs ⇒ 99 km
12 lite rs ⇒ P km
P = 99*12/9
P = 132 km
Answer:
132
Step-by-step explanation:
give person above brainliest :))
If you use a 5/8 inch drill bit instead of a 3/16 that the project called for ,your hole will be too . by inches
Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.) f(x) = x + 3 x2 − 2x − 15
Answer:
-3 (removable), +5
Step-by-step explanation:
Maybe you have ...
[tex]f(x)=\dfrac{x+3}{x^2-2x-15}=\dfrac{x+3}{(x+3)(x-5)}=\dfrac{1}{x-5}\quad x\ne-3[/tex]
This will have discontinuities (points where the function is undefined) at ...
x = -3x = 5The discontinuity as x = -3 is removable by defining f(-3) = -1/8.
what is the probability that the 2 cards you will draw will be blackjacks?
Answer:
Need more explation of the question
Step-by-step explanation:
What is the solution to the system of equations?
y = 2/3x+3
x=-2
Answer:
solution (-2, 5/3 ).
Step-by-step explanation:
Given : y = + 3 and x = –2.
To find : What is the solution to the system of equations.
Solution : We have given that y = + 3 ------equation (1)
and x = –2. ------equation (2)
On plugging the x = -2 in equation (1)
y = + 3
y = + 3 .
On simplification we get ,
y = .
Therefore, solution (-2, 5/3 ).
In high school, a teacher gave two sections of a class the same arithmetic test. The results were as follows:
Section I: Mean 45, Standard
Deviation 6.5
Section II: Mean 45,
Standard deviation 3.1
What conclusions is correct?
Answer:
Section I test scores are more dispersed that that of section II.
Step-by-step explanation:
Consider the data collected from the arithmetic test given to two sections of a school.
Section I: Mean = 45, Standard Deviation = 6.5
Section II: Mean = 45, Standard deviation = 3.1
The mean of both the sections are same, i.e. 45.
So there is no comparison that can be made from the center of the distribution.
The standard deviation for section I is 6.5 and the standard deviation for section II is 3.1.
The standard deviation is a measure of dispersion, i.e. it tells us how dispersed the data is from the mean or how much variability is present in the data.
The standard deviation for section I is higher than that of section II.
So, this implies that section I test scores are more dispersed that that of section II.
there are 3 blouse and 2 pieces cloths for sale in the market. how many possible sets are there?
Answer:
Each item could be included in a set or not included. That gives 2^5 = 32 ways to choose sets, including 1 set with no items, 5 sets of 1 item, 10 sets of 2 items, 10 sets of 3 items, 5 sets of 4 items, and 1 set of 5 items.
Find the sum of all solutions to this equation : ((2x-4)/x+1)) * ((2x+8)/2) * ((2x-70)/(x+2)) =0
Answer:
x=0 or x=2 or x=−4 or x= (7)(2)
Step-by-step explanation:
can someone help me pls
express 24.123eight to base ten
To convert [tex]24.123[/tex] in base 8, also notated with [tex]24.123_8[/tex] into base 10 simply multiply each digit with 8 to the power of its position relative to the decimal point.
So,
[tex]24.123_8=2\cdot8^1+4\cdot8^0+1\cdot8^{-1}+2\cdot8^{-2}+3\cdot8^{-3}=20.162109375_{10}[/tex]
Hope this helps :)
(08.01 MC)
The volume of a pyramid that fits exactly inside a cube is 9 cubic feet. What is the volume of the cube? (5 points)
Select one:
a. 3 cubic feet
b. 6 cubic feet
c. 18 cubic feet
d. 27 cubic feet
Answer:
d. 27 cubic feet
Step-by-step explanation:
volume of cube = s^3 = B * s
volume of pyramid = (1/3) * B * h
The volume of a pyramid is 1/3 of the area of the base multiplied by the height. The volume of a cube is the area of the base multiplied by the height. Since the volume of a pyramid has the fraction 1/3 and the volume of the cube does not, then the volume of a cube is 3 times greater than the volume of a pyramid that fits inside and has the same base area.
volume of pyramid = 9 cu ft
volume of cube = 3 * 9 cu ft = 27 cu ft
Answer: d. 27 cubic feet
Answer:
27 ft^3 (Answer d)
Step-by-step explanation:
Here the volume of the pyramid is (1/3) the volume of the cube:
Letting s represent the length of one side of the base,
(1/3)(s)^2(s) = 9 ft^3, equivalent to s^3 = 27.
Solving for s, we get s = 3 ft.
Thus, the volume of the cube is V = s^3 = (3 ft)^3 = 27 ft^3 (Answer d)
Rotation 90° counterclockwise around the origin of the point (-8,1)
A rope that is 6 meters long will be cut into 24 pieces that are all of the same lengths. What will the length of each piece, in centimeters? (Note: 100 centimeters = 1 meter)
Answer: 25 cm
Step-by-step explanation: 6 meters = 600 cm
600 / 24 = 25
If (x+2) is a Factor x^3 + 2x^2 + 2x + k then find the value of K.
Answer:
4
Step-by-step explanation:
if x+2 is a factor of the above expression then,
x=-2
so putting the value of x in above expression we get,
(-2)^3+2×(-2)^2+2×(-2)+k=0
or,-8+8-4+k=0
k=4
Answer:
Step-by-step explanation:
If (x + 2) is a factor of a polynomial then ( - 2 ) is the zero of that polynomial ⇒ ( - 2 )³ + 2( - 2 )² + 2( - 2 ) + k = 0 ⇒ k = - 4
What is the difference between squaring and cubing a value?
Answer:
squaring a number is multiplying it by itself twice and cubing a number is multiplying the number three times itself
Step-by-step explanation:
for example 2²=2×2
=4
and 2³=2×2×2
=8
The numerator of a fraction is 8 less than the denominator of a fraction. The value of the fraction is 3/5, find the value of the fraction.
Hello!
Answer:
[tex]\huge\boxed{\frac{12}{20}}[/tex]
To find the numerator and denominator, we can set up a proportion where:
x = denominator
x -8 = numerator
[tex]\frac{3}{5} = \frac{x-8}{x}[/tex]
Cross multiply:
[tex]3(x) = 5(x - 8)[/tex]
[tex]3x = 5x - 40[/tex]
Simplify:
[tex]3x - 5x = -40\\\\-2x = -40\\\\x = 20[/tex]
Substitute in this value of x to find the numerator and denominator:
[tex]\frac{(20) - 8}{(20)} = \frac{12}{20}[/tex]
Hope this helped you! :)
[tex] \LARGE{ \boxed{ \rm{ \orange{ Solution:}}}}[/tex]
Let the numerator be x
It is given that,
Denominator - 8 = NumeratorThen,
⇛ Denominator- 8 = x
⇛ Denominator = x + 8
According to condition -2)
⇛ Fraction = 3/5
⇛ x/x + 8 = 3/5
Cross multiplying,
⇛ 3(x + 8) = 5x
⇛ 3x + 24 = 5x
⇛ 24 = 5x - 3x
⇛ 24 = 24
Flipping it out,
⇛ 2x = 24
⇛ x = 24/2 = 12
Then,
⇛ x + 8 = 12 + 8 = 20
Numerator = 12Denominator = 20[tex] \large{ \therefore{ \boxed{ \rm{ \pink{Then, \: the \: fraction = \dfrac{12}{20} }}}}}[/tex]
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Find the mass and center of mass of the solid E with the given density rho. E is the cube 0 ≤ x ≤ a, 0 ≤ y ≤ a, 0 ≤ z ≤ a; rho(x, y, z) = 9x2 + 9y2 + 9z2.
Answer:
mass = 9a^5
center of mass = [tex]\frac{7a}{12}, \frac{7a}{12}, \frac{7a}{12}[/tex]
Step-by-step explanation:
Finding the mass of the solid E
given density function : p ( x,y,z ) = [tex]9x^2 + 9y^2 + 9z^2[/tex]
Mass = [tex]\int\limits^a_0 \int\limits^a_0 \int\limits^a_0 {9(x^2+y^2+z^2)} \, dx dydz[/tex] [tex]= \int\limits^a_0 \int\limits^a_0 {9(\frac{a^3}{3}+ay^2+az^2 )} \, dydz[/tex]
[tex]= \int\limits^a_0 {9(\frac{a^4}{3}+\frac{a^4}{3} +a^2z^2 )} \, dz[/tex] [tex]= \int\limits^a_0 {9(\frac{2a^4}{3}+a^2z^2 )} \, dz[/tex] [tex]= 9 ( \frac{2a^5}{3} + \frac{a^5}{3} )[/tex]
( taking limits as a and 0 )
hence Mass = 9 [tex](a^5)[/tex]
finding the center of mass
attached below is solution
12345 are divisible by 15 with exlpin
Answer:
hfwhww45 5h wahdaw 5656 adshjdawh bh4 54
Step-by-step explanation:
5767
12345
Sum of digits = 1+2+3+4+5
= 15
Which means divisible by 3
Ends with 0 or 5 = Yes ends with 5
Therefore the number is divisible by 15
12345÷15 = 823
Divisiblity rule of 15 = Any number is divisible by 15 if the sum of the digits is divisible by 3 and the number ends with a 0 or 5.
Must click thanks and mark brainliest
the function y= -16t^2 + 248, models the hight y in feet of a stone t seconds after it dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground?
Answer:
[tex]t \: = 3.92 \: sec[/tex]
Step-by-step explanation:
When (t =0)
Height of cliff = 248 feet = 75.5m
Using Newton's equations of motion:
[tex]s = ut + \frac{1}{2} a {t}^{2} [/tex]
75.5 = 0 * t + 4.9 * t^2
Solving further :
[tex]t \: = 3.92 \: sec[/tex]
if k = p+2q/3 , find the value of p when k=7 and q=3
Answer:
p = 5
Step-by-step explanation:
hopefully it is clear and understandable :)
How many faces does the polyhedron have? 3 5 6 9
Answer:
there are many types of polyhedron.
Basically about which one you want to know?
Step-by-step explanation:
Pentahydron. A polyhedron with 5 faces.
Hexahyderon. A polyhedron with 6 faces.
HeptahyderonA polyhedron with 7 faces.
Octahyderon. A polyhedron with 8 faces.
Similarly there are three more...
Please tell me if it was helpful to you.
If not, then ask me again..
I cant seem to get the second one right...
Rx=1 means to reflect the given point on the line of x= 1
The mapping for the reflection on line x is x = k
(-2,7) = (-2(1) - -2,7) = (4,7)
The missing value is 7
15% of 80 is 60% of what number? There were no answer choices please help!
Answer:
80
Step-by-step explanation:
15 percent of 80 is 12
and 12 is 60 percent of 80!
hope this helps :)
Renting a car costs $30 per day, or $600 per month. Renting daily is cheaper for a few days, but after how many days are the two options equal (after which renting monthly is cheaper)?
Answer:
20 days
Step-by-step explanation:
Renting a car costs $30 per day.
y = 30x
Renting a car costs $600 per month
y = 600
Set the two equations equal to each other.
30x = 600
(30x)/30 = (600)/30
x = 20
After 20 days, the two options have an equal cost.
Rewrite to make true: There are five terms in the series (attached)
Answer:
There are six terms in the series
Step-by-step explanation:
We can see that n starts from 0, and ends at 5. There are therefore 6 terms in this series - as 0 is included. Therefore there will be 6 terms in this series, not 5.
There are six terms in the given series.
An economics professor conducts an experiment to determine if viewing his online video reviews improve the performance of his students on exams. He uses only economics students enrolled in his classes. The treatment group will watch the videos prior to the first exam, and the control group will not watch the videos. Then the scores of the first exam will be compared.
Which of the following variables’ effects could be mitigated by the random assignments? Check all that apply.
Intelligence
Study habits
Professor
Course textbook
Work schedule
Answer:
1,2,5
A,B,E
Intelligence
Study habits
Work schedule
ED2021
Intelligence and study habits could be mitigated by random assignments.
Options A and B are the correct answer.
What is a random assignment?Random assignment refers to the process of randomly assigning participants to either the treatment or control group in an experiment.
We have,
Random assignment is done to minimize the effect of extraneous variables, such as intelligence and study habits, that could potentially affect the results of the experiment.
By randomly assigning participants to either the treatment or control group, the differences between the two groups are assumed to be due to chance alone.
Variables such as the professor, course textbook, and work schedule are not affected by random assignments.
These variables are considered to be controlled variables that are held constant across both the treatment and control groups.
Thus,
Intelligence and study habits could be mitigated by random assignments.
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A random sample of 35 undergraduate students who completed two years of college were asked to take a basic mathematics test. The mean and standard deviation of their scores were 75.1 and 12.8, respectively. In a random sample of 50 students who only completed high school, the mean and standard deviation of the test scores were 72.1 and 14.6, respectively In order to test the equal variance assumption for two populations, Can we assume population variances are equal at the 10% significance level? (sigma subscript 1 superscript 2 space equals space sigma subscript 2 superscript 2 )
Answer:
The 90 % confidence limits are (-2.09, 8.09).
Since the calculated values do not lie in the critical region we accept our null hypothesis.
Step-by-step explanation:
The null and alternative hypothesis are given by
H0: σ₁²= σ₂² against Ha: σ₁² ≠ σ₂²
Confidence interval for the population mean difference is given by
(x`1- x`2) ± t √S²(1/n1 + 1/n2)
Where S ²= (n1-1)S₁² + S²₂(n2-1)/n1+n2-2
Critical value of t with n1+n2-2= 50+ 35-2= 83 will be -1.633
Now calculating
S ²=34* (12.8)²+ (14.6)²*49/83= 192.96
Now putting the values in the t- test
(75.1 -72.1) ± 1.633 √ 192.96(1/35 +1/50)
=3 ± 5.09
=-2.09, 8.09 is the 90 % confidence interval for the difference
The 90 % confidence limits are (-2.09, 8.09).
Since the calculated values do not lie in the critical region we accept our null hypothesis.
Which is a graph of g(c) = (0.5)x+3^ -4
Answer:
I've attached a graph with this, that's your answer