Answer:
B. 9
Step-by-step explanation:
We are given that y varies inversely with x. Recall that inverse variation has the form:
[tex]\displaystyle y=\frac{k}{x}[/tex]
Where k is the constant of variation.
We are given that y = 18 when x = 12. Hence:
[tex]\displaystyle (18)=\frac{k}{(12)}[/tex]
Solve for k. Multiply both sides by 12:
[tex]k=12(18)=216[/tex]
Thus, our equation is:
[tex]\displaystyle y=\frac{216}{x}[/tex]
We want to find x when y = 24. Substitute:
[tex]\displaystyle \frac{24}{1}=\frac{216}{x}[/tex]
Cross-multiply:
[tex]24x=216[/tex]
Divide both sides by 24. Hence:
[tex]x=9[/tex]
Our answer is B.
Answer:
B
Step-by-step explanation:
Given that y varies inversely with x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
To find k use the condition y = 18 when x = 12 , then
18 = [tex]\frac{k}{12}[/tex] ( multiply both sides by 12 )
216 = k
y = [tex]\frac{216}{x}[/tex] ← equation of variation
When y = 24 , then
24 = [tex]\frac{216}{x}[/tex] ( multiply both sides by x )
24x = 216 ( divide both sides by 24 )
x = 9
The table shows the relationship between the number of faculty members and the number of students at a local school. What is the missing value?
Faculty
Students
1
17
2
34
3
51
4
?
17
68
85
102
Answer:
68
Step-by-step explanation:
I did it on my test
The missing value in the table is 68. The correct answer would be option (B).
What is the linear relationship?A linear relationship is a connection that takes the shape of a straight line on a graph between two distinct variables - x and y. When displaying a linear connection using an equation, the value of y is derived from the value of x, indicating their relationship.
The table shows the relationship between the number of faculty members and the number of students at a local school.
Faculty Students
1 17
2 34
3 51
4 ?
The relationship between the number of faculty members and the number of students at the local school is that for every faculty member, there are 17 students.
Therefore, if there are 4 faculty members, we can find the number of students by multiplying 4 by 17, which gives us 68.
Thus, the missing value in the table is B. 68.
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20 marbles, 4 red, 6 blue,2 green, 8 yellow, one marble taken out , replaced, one taken out. Probability that he will pull red marble first, then green marble
Step-by-step explanation:
red=4/19
green2/1
i didnt get the qn prperly..was a marbke taken out second time？ and not replaced？
is this a direct variation
y=2x + 3
pls give an explanation if you don’t have one still pls give an answer
Answer:
No.
Step-by-step explanation:
y/x has to be the same number no matter what except at point (0 0) which it must also include for it to be a direct variation.
*y=2x+3 is not a direct variation because you can not write it as y/x=k where k is some constant number. If we were y=2x, then yes since y/x=2.
*You could also take two points and see if they are proportional. That is, you can see if y2/x2 gives the same value as y1/x1 where (x1,y1) and (x2,y2) are points on the line y=2x+3. This must work for every pair of points on the linear relation except at x=0 (where you would or should have y=0 if it is directly proportional).
Let's try it out. If x=1, then y=2(1)+3=5.
5/1=5
If x=2, then y=2(2)+3=7
7/2=3.5
As you can see 5 doesn't equal 3.5.
*For it to be a direct variation, it also must contain the point (0,0) and be a diagonal line when graphed. It can also be written in form y=kx where k is a constant number. This fails two of the the things I mentioned. It doesn't contain point (0,0) because y=2(0)+3=3 not 0. It cannot be written in form y=kx because of the plus 3.
If it were y=2x, then the answer would be yes.
A basketball team is to play two games in a tournament. The probability of winning the first game is .10.1 the first game is won, the probability of winning the second game is 15. If the first game is lost, the probability of winning the second game is 25. What is the probability the first game was won if the second game is lost? Express the answer with FOUR decimal points.
Answer:
[tex]P(\frac{A}{B'})[/tex]=0.111
Step-by-step explanation:
Given:
The probability of winning the first game is 10.1
The first game is won
The probability of winning the second game is 15
If the first is lost, the probability of winning the second game is 25
Solution:
[tex]P(B)=P(A)P(\frac{B}{A})+P(A')P(\frac{B}{A'})\\ =0.1(0.15)+(0.3)*0.25)\\P(B)=0.24 ------(1)\\P(\frac{A}{B})=\frac{P(\frac{B}{A})P(A) }{P(B)}\\ =\frac{0.15(0.1)}{0.24}\\ =0.0625 ------(2)\\P(B')=1-P(B)=0.76 ------(3)\\P(A)=P(B)P(\frac{A}{B})+P(B')P(\frac{A}{B'})\\0.1=0.24(0.0625)+0.76(p(\frac{A}{B'} ))\\P(\frac{A}{B'})=0.111[/tex]
Answer:
[tex]P(W_1/W_2')=0.1110[/tex]
Step-by-step explanation:
Probability of winning the first game be considering the given factors be, [tex]W_1=0.1[/tex]
Probability of winning the second game be considering the given factors be, [tex]W_2[/tex]= probability of winning the second game when the first game is won + probability of winning the second game when the first game is lost:
[tex]P(W_2)=P(W_1).P(W_2/W_1)+P(W_1').P(W_2/W_1')[/tex]
[tex]P(W_2)=0.1\times 0.15+0.9\times 0.25[/tex]
[tex]P(W_2)=0.24[/tex]
Hence the probability of losing the second game:
[tex]P(W_2')=1-P(W_2)[/tex]
[tex]P(W_2')=0.76[/tex]
Probability of winning the first game when the second game is won:
[tex]P(W_1/W_2)=\frac{P(W_2/W_1).P(W_1)}{P(W_2)}[/tex]
[tex]P(W_1/W_2)=\frac{0.15\times 0.1}{0.24}[/tex]
[tex]P(W_1/W_2)=0.0625[/tex]
Probability of winning the first game be considering the given factors, [tex]W_1[/tex]= probability of winning the first game when the second game is won + probability of winning the first game when the second game is lost:
[tex]P(W_1)=P(W_2).P(W_1/W_2)+P(W_2').P(W_1/W_2')[/tex]
[tex]0.1=0.24\times0.0625+0.76\times P(W_1/W_2')[/tex]
[tex]P(W_1/W_2')=0.1110[/tex]
2/5 e +4 = 9
Help please
Answer:
e=12.5 or e=25/2
Step-by-step explanation:
which statements are true for the functions g(x)=x^2 and h(x)=-x^2? Check all that apply
Answer:
if x=0 then they have same value
1 and 2 options are out
for x=-1
g(-1)=1
h(-1)=-1
3 is true
4th
FALSE
for all values except 0, g(x)>h(x)
correct ones are
g(x) > h(x) for x = -1.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
Step-by-step explanation:
Which description of the graph of the linear inequality y > 3x – 8 is correct?
Options :
A.The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded below the line
B.The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded above the line.
C. The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded below the line.
D.The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above the line
Answer:
D.The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above the line
Step-by-step explanation:
The equation y > 3x – 8
Interpreting as a linear relation :
y > ax + b
Where, a = slope ; b = intercept
a = 3 ; that is a slope value of 3
b = -8 ; that is an intercept value of - 8
Since the inequality is >, a dashed line is used (dashed like is used for > and <) ; since we a have a greater than sign, the graph will be shaded above the dashed line.
Answer: The answer is D on edu 2021
Step-by-step explanation:
D.The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above the line
Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a = 0. What do you notice? How do you explain what happened?
Answer:
Lf(x) = Lg(x) = Lh(x) = 1 - 2x
value of the functions and their derivative are the same at x = 0
Step-by-step explanation:
Given :
f(x) = (x − 1)^2,
g(x) = e^−2x ,
h(x) = 1 + ln(1 − 2x).
a) Determine Linearization of f, g and h at a = 0
L(x) = f (a) + f'(a) (x-a) ( linearization of f at a )
for f(x) = (x − 1)^2
f'(x ) = 2( x - 1 )
at x = 0
f' = -2
hence the Linearization at a = 0
Lf (x) = f(0) + f'(0) ( x - 0 )
Lf (x) = 1 -2 ( x - 0 ) = 1 - 2x
For g(x) = e^−2x
g'(x) = -2e^-2x
at x = 0
g(0) = 1
g'(0) = -2e^0 = -2
hence linearization at a = 0
Lg(x) = g ( 0 ) + g' (0) (x - 0 )
Lg(x) = 1 - 2x
For h(x) = 1 + ln(1 − 2x).
h'(x) = -2 / ( 1 - 2x )
at x = 0
h(0) = 1
h'(0) = -2
hence linearization at a = 0
Lh(x) = h(0) + h'(0) (x-0)
= 1 - 2x
Observation and reason
The Linearization is the same in every function i.e. Lf(x) = Lg(x) = Lh(x) this is because the value of the functions and their derivative are the same at x = 0
You deposit $2000 in an account earning 4% interest compounded monthly. How much will you have in the account in 10 years? $ Enter an integer or decimal number (more..]
Answer:
$2,981.67
Step-by-step explanation:
(-3,-7) is it a solution
Answer:
It could be a solution
Step-by-step explanation:
This depends on what equation you are solving. It could be a solution for a quadratic or even a transformation problem.
Find the missing length (picture below)
Answer:
Step-by-step explanation:
because these are similar triangles, that is, one is a bigger of smaller version of the other, then we know, that the bigger triangle is just 2 times bigger than the smaller, or 2x of any side of the small one
sooo 2(20) =40
so we know that side n of the bigger triangle is 40
A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 47.0 and 57.0 minutes. Find the probability that a given class period runs between 51.25 and 51.5 minutes.
Answer:
0.025 = 2.5% probability that a given class period runs between 51.25 and 51.5 minutes.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
Uniformly distributed between 47.0 and 57.0 minutes.
This means that [tex]a = 47, b = 57[/tex]
Find the probability that a given class period runs between 51.25 and 51.5 minutes.
[tex]P(c \leq X \leq d) = \frac{51.5 - 51.25}{57 - 47} = 0.025[/tex]
0.025 = 2.5% probability that a given class period runs between 51.25 and 51.5 minutes.
prove the identity sin3x=3sinx-4sin³x
Hi
we know that sin(A+B)=Sin(A)Cos(B)-Cos(A) Sin (B)
cos(2x)=1-2sin²(x)
sin(2x)=2sin(x)cos(x)
Exp:- Sin(3x)=Sin(x+2x)
Sin(x)cos(2x)+cos(x)sin(2x)
sin(x){1-2sin²(x)}+2cos²(x)sin(x)
sin(x)-2sin³(x)+2sin(x){1-sin²(x)}
sin(x)-2sin³(x)+2sin(x)-2sin³(x)
3sin(x)-4sin³(x)
Hope it helps....
Find the value of x (please)
9514 1404 393
Answer:
(a) 21
Step-by-step explanation:
The product of the lengths to the near and far circle intercepts are the same for the two lines. For the tangent, the near and far intercepts are the same point, so we have ...
(36)(36) = (27)(27+x)
48 = 27+x . . . . . . . . . . divide by 27
x = 21 . . . . . . . . subtract 27
Find m angle QSRIf m angle TSQ=15x , m angle TSR=173^ , and m angle QSR=10x-2
[tex]{\color{red}{\huge{\underbrace{\overbrace{\mathfrak{\:\:\:\:\:\:\:꧁"Answer"꧂\:\:\: }}}}}}[/tex]
[tex]\small\color{blak}{{\underline{\bold{ Find \:a X } } } }[/tex]
[tex]\small\color{black}{{\underline{\bold{173°=15z+10x-2 } } } } \\ = 173 = 25x - 2 \\ = - 25x = - 2 - 173 \\ = - 25x - 175 \\ = \small\color{blue}{{{\boxed{\tt\red{} \:\:\:\:\:\:\:\:\:\: x=7\:\:\:\: }}}}[/tex]
[tex]\small\color{blak}{{\underline{\bold{ Find\:a\:m<QSR } } } }[/tex]
[tex]\small\color{blak}{{\underline{\bold{ 10(7)-2 } } } }\\=70-2\\=\small\color{red}{{{\boxed{\tt\red{} \:\:\:\:\:\:\:\:\:\: m<QSR=68°\:\:\:\: }}}}[/tex]
[tex]\Large\color{red}{{\underline{\mathfrak {{꧁"Carry\:on\: learning"꧂ }}}}}[/tex]
The measure of angle QSR is 68 degrees.
What is substitution?Substitution means putting numbers in place of letters to calculate the value of an expression.
According to the given question.
m ∠TSQ = 15x
m ∠TSR = 173 degrees
m ∠QSR = 10x -2
Since,
m ∠TSR = m ∠TSQ + ∠QSR
Substitute the value of m ∠TSR, m ∠TSQ and m ∠QSR in the above expression.
⇒ [tex]173 = 15x + 10x - 2[/tex]
⇒ [tex]173 = 25x - 2[/tex]
⇒ [tex]175 = 25x[/tex]
⇒ [tex]x = \frac{175}{25}[/tex]
⇒ [tex]x = 7[/tex]
Again, for finding the value of angle QSR substitute the value of x in 10x - 2.
Therefore,
m ∠QSR = 10(7) - 2
⇒ m ∠QSR = 70 - 2
⇒ m ∠QSR = 68 degrees
Hence, the measure of angle QSR is 68 degrees.
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how many numbers divisible by 5 are possible, show your calculation. (Its a other language so dont look at the text)
(Will mark brainliest!!!) 20 PTS !!
Sixty percent of all children in a school do not have cavities. The probability, rounded to four decimal places, that in a random sample of 9 children selected from this school, at least 6 do not have cavities is:
Answer:
probability[Number of 6 random sample do not have cavities] = 0.8
Step-by-step explanation
Given:
Number of student do not have cavities = 60%
Number of random sample = 9 children
Find:
Probability[Number of 6 random sample do not have cavities]
Computation:
n = 9
p = 60% = 0.6
P(At least 6)
Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than 6)
Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than or equal to 6)
Probability[Number of 6 random sample do not have cavities] = 0.8
Cai wants to buy cherries and apples to make a fruit tart. Cherries cost $3.75 per
pound and apples cost $2.25 per pound. How much does he spend if he buys 2
pounds of cherries and 1.5 pounds of apples? How much does he spend if he buys x
pounds of cherries and y pounds of apples?
Dale hikes up a mountain trail at 2 mph. Because Dale hikes at 4 mph downhill, the trip down the mountain takes 30 minutes less time than the trip up, even though the downward trail is 3 miles longer. How many mile did Dale hike in all?
Answer:
13 miles
Step-by-step explanation:
He hikes 4 mph downhill and it takes 30 minutes or 0.5 hours lesser than the trip uphill at 2 mph.
Thus, if the distance upward is x and we are told the distance downhill is 3 miles longer.
Then, since time = distance/speed, we have;
((x + 3)/4) + 0.5 = x/2
Multiply through by 4 to get;
x + 3 + (0.5 × 4) = 2x
x + 5 = 2x
2x - x = 5
x = 5 miles
Now, it means distance uphill = 5 miles and distance downhill = 5 + 3 = 8 miles
Thus, total distance covered = 8 + 5 = 13 miles
Reflections were shown across the x- and y-axes but reflections can occur across any line. The figure above shows quadrilateral EFGH reflected about the line y=x. Which best describes what happens to the ordered pair for this reflection?
1. (x,y) → (y,x)
2. (x,y) → (-x,-y)
3. (x,y) → (-y,-x)
4. There is no relationship between the points.
Answer:
1. (x,y) → (y,x)
Step-by-step explanation:
Coordinate of point E:
Before the transformation, the coordinate of point E was given by (3,-6).
After the transformation, we have E'(-6,3), which eliminates options 2 and 3.
For the other points, we will also get, (x,y) -> (y,x), which is the rule given when the original figure is reflected over the line y = x, and thus, the correct answer is given by option 1.
Maya has already run 1 mile on her own, and she expects to run 1 mile during each track practice. How many miles would Maya have run after 48 track practices?
Answer:
Step-by-step explanation:
48+1=49
Find the volume of the figure. Express answers in terms of , then round to the nearest
whole number
Please help :)
Answer:
26244π in³
Step-by-step explanation:
Applying,
Voluem of a sphere
V = 4/3(πr³).......... Equation 1
Where r = radius of the sphere, π = pie
From the diagram,
Given: r = 54/2 = 27 in
Substitute these value in equation 1
V = 4/3(27³)(π)
V = 26244π in³
Hence the volume of the figure expressed in terms of π is 26244π in³
The following data was obtained from 32 people aged 25-29 who were asked how many hours of TV they watched per week.
4,2,8,9,4,5,10,11,7,8,3,4,10,3,8,5,1,7,0,4,3,2,2,1,1,0,2,3,5,2,1,1.
Group the data in intervals and record the frequency of each interval as well as the cumulative frequency and relative frequency. Make a table showing this information.
Graph the data using frequency histogram.
Graph the data using a cumulative frequency chart.
Instructions: Solve the following linear
equation.
- 2x + 38 = 2(3 + 3x)
2-
Answer:
Step-by-step explanation:
-2x +38 = 2(3 + 3x)
-2x + 38 = 2*3 + 2*3x
-2x + 38 = 6 + 6x
Add 2x to both sides
38 = 6 + 6x + 2x
Combine like terms
38 = 6 + 8x
Subtract 8 from both sides
38 - 6 = 8x
8x = 32
Divide both sides by 8
x = 32/8
x = 4
Answer:
x = 4
Step-by-step explanation:
-2x + 38 = 2(3 + 3x)Use distributive property to multiply 2 by 3 and 3x
-2x + 38 = 2 ×3 + 2 × 3x -2x + 38 = 6 + 6xsubtract 6x from both side
-2x + 38 - 6x = 6 + 6x - 6xcombine -2x and -6x to get -8x
-8x + 38 = 6subtract 38 from both side
-8x + 38 - 38 = 6 - 38subtract 38 from 6 to get -32
-8x = -32divide both side by -8
[tex] \small \sf \frac{-8x}{ -8} = \frac{-32}{-8} \\ \\ \small \sf x = \frac{- 32}{-8}[/tex]
divide -32 by -8 to get 4
x = 4Is x-3 a factor of x- 9x² - 14x + 24?
9514 1404 393
Answer:
no
Step-by-step explanation:
We assume you are concerned with the cubic
x³ -9x² -14x +24
Its factors are all irrational, as shown in the attached graph. x-3 is not a factor.
__
x-3 is a factor if the expression evaluates to zero when x=3. Here, it does not.
((x -9)x -14)x +24 for x=3 is ...
((3 -9)(3) -14)(3) +24 = (-18 -14)(3) +24 = -96 +24 = -72
The remainder from division by x-3 is not zero, so x-3 is not a factor.
Help and explain too (using elimination to solve systems of equations ) !!!!!
Answer:
x=3 y=5
Step-by-step explanation:
it's simultaneous equations so you first try matching the x or the y on both equations
on the first equation the ys are matching so:
4x+y=17
2x+y=11
2x=6
x=3
now that you have x you substitute it back into the equation to get y
6+y=11
-6 -6
y=5
Answer:
(3,5)
(3,2)
(7,0)
(8,1)
Step-by-step explanation:
1.)
Subtract the two equations
(4x+y)-(2x+y)=17-11
2x=6
x=3
plug this into the first equation
4(3)+y=17
y=5
2.) we need one set of the same variable's coefficents to match (so that when we add/subtract the two equations a variable cancels out). To do this multiply the first equation by 1.5
1.5(3x+2y)=13*1.5
4.5x+3y=19.5
Subtract the second equation
(4.5x+3y)-(2x+3y)=19.5-12
2.5x=7.5
x=3
plug this into the first equation
3(3)+2y=13
2y=4
y=2
3.)
Mulitply the first equation by 3
3(x-2y)=7*3
3x-6y=21
subtract this and the second equation
(3x-6y)-(3x+y)=21-21
-7y=0
y=0
plug this into the first equation
x-2(0)=7
x=7
3.)
add the two equations
(x+5y)+(x-5y)=13+3
2x=16
x=8
plug this into the first equation
8+5y=13
5y=5
y=1
math help plz
how to divide polynomials, how to understand and step by step with an example provided please
Answer:
hiiiiiii....!!! how r u
HELPPPP ME ASAP
If f(x) = x2, g(x) = 5x, and h(x) = x +4, find each value.
Find g[h(-2)]
9514 1404 393
Answer:
10
Step-by-step explanation:
Put the values where the arguments are and do the arithmetic.
g(h(-2)) = g(-2+4) = g(2) = 5(2)
g(h(-2)) = 10
I litterally don't understand how to do this-
Answer:
Consider points (-1, 0) and (0, 1) :
[tex]{ \tt{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ { \tt{slope = \frac{1 - 0}{0 - ( - 1)} }} \\ { \boxed{ \bf{slope = 1}}}[/tex]
Answer:
slope 1
Step-by-step explanation:
above ANS is correct mark it as branliest ANS
When the suns rays are at an angle of 39° the distance from the top of Dakotas head to the tip of the shadow is 77 inches, about how tall is Dakota?
Answer:
48.45in
Step-by-step explanation:
To get the height of Dakota, we will use the SOH CAH TOA
Given the following
angle of elevation = 39degrees
distance from the top of Dakotas head to the tip of the shadow = 77in (Hyp)
Required
Height of Dakota (Opp)
Sin 39 = opposite/hyp
Sin39 = H/77
H = 77sin39
H = 77(0.6293)
H = 48.45in
Hence the Dakota is 48.45in