Answer:
B) This student performed better than 78% of the other test-takers in the verbal part and better than 34% in the quantitative part.
Step-by-step explanation:
In Statistics, Percentile refers to how specific variables can be divided according to the distribution of values in a population of 100 equal groups.
The data value of a given percentile can be determined as 100 times the cumulative relative frequency of that value.
From the given question.
Suppose a test-taker scored at the 78th percentile for their verbal sent to test-takers, the percentiles associated grade and at the 34th percentile for their quantitative grade.
This implies that ;
The student score shows the relation between a particular score of :
78% and the scores of the rest of a group for the verbal test takers &
34% and the scores of the rest of a group for the quantitative test takers.
Therefore; we can conclude that ;
This student performed better than 78% of the other test-takers in the verbal part and better than 34% in the quantitative part.
[tex]Let $u$ and $v$ be the solutions to $3x^2 + 5x + 7 = 0.$ Find\[\frac{u}{v} + \frac{v}{u}.\][/tex]
By the factor theorem,
[tex]3x^2+5x+7=3(x-u)(x-v)\implies\begin{cases}uv=\frac73\\u+v=-\frac53\end{cases}[/tex]
Now,
[tex](u+v)^2=u^2+2uv+v^2=\left(-\dfrac53\right)^2=\dfrac{25}9[/tex]
[tex]\implies u^2+v^2=\dfrac{25}9-\dfrac{14}3=-\dfrac{17}9[/tex]
So we have
[tex]\dfrac uv+\dfrac vu=\dfrac{u^2+v^2}{uv}=\dfrac{-\frac{17}9}{\frac73}=\boxed{-\dfrac{17}{21}}[/tex]
The value of [tex]\frac{u}{v} +\frac{v}{u}[/tex] is [tex]\frac{-17}{21}[/tex].
What is quadratic equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is[tex]ax^{2} +bx+c=0[/tex], where a and b are the coefficients, x is the variable, and c is the constant term.
What is the sum and product of the roots of the quadratic equation?If [tex]ax^{2} +bx+c = 0[/tex] be the quadratic equation then
Sum of the roots = [tex]\frac{-b}{a}[/tex]
And,
Product of the roots = [tex]\frac{c}{a}[/tex]
According to the given question.
We have a quadratic equation [tex]3x^{2} +5x+7=0..(i)[/tex]
On comparing the above quadratic equation with standard equation or general equation [tex]ax^{2} +bx+c = 0[/tex].
We get
[tex]a = 3\\b = 5\\and\\c = 7[/tex]
Also, u and v are the solutions of the quadratic equation.
⇒ u and v are the roots of the given quadratic equation.
Since, we know that the sum of the roots of the quadratic equation is [tex]-\frac{b}{a}[/tex].
And product of the roots of the quadratic equation is [tex]\frac{c}{a}[/tex].
Therefore,
[tex]u +v = \frac{-5}{3}[/tex] ...(ii) (sum of the roots)
[tex]uv=\frac{7}{3}[/tex] ....(iii) (product of the roots)
Now,
[tex]\frac{u}{v} +\frac{v}{u} = \frac{u^{2} +v^{2} }{uv} = \frac{(u+v)^{2}-2uv }{uv}[/tex] ([tex](a+b)^{2} =a^{2} +b^{2} +2ab[/tex])
Therefore,
[tex]\frac{u}{v} +\frac{v}{u} =\frac{(\frac{-5}{3} )^{2}-2(\frac{7}{3} ) }{\frac{7}{3} }[/tex] (from (i) and (ii))
⇒ [tex]\frac{u}{v} +\frac{v}{u} =\frac{\frac{25}{9}-\frac{14}{3} }{\frac{7}{3} }[/tex]
⇒ [tex]\frac{u}{v} +\frac{v}{u} = \frac{\frac{25-42}{9} }{\frac{7}{3} }[/tex]
⇒ [tex]\frac{u}{v} +\frac{v}{u} = \frac{\frac{-17}{9} }{\frac{7}{3} }[/tex]
⇒ [tex]\frac{u}{v} +\frac{v}{u} =\frac{-17}{21}[/tex]
Therefore, the value of [tex]\frac{u}{v} +\frac{v}{u}[/tex] is [tex]\frac{-17}{21}[/tex].
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Which option is equal to 7 1/5
Answer:
D. is the answerStep-by-step explanation:
Question:
7^1/5
The number given has an exponent of a fraction: fraction exponent = 1/5
So, when you have a fraction - you always have a square root - Important!!Since the top is one, the number 7 stays the same. = 7^1 = 7
The bottom is a 5. This means it is to the fifth root.
Answer = D
Hope this helped,
Kavitha
Answer: If 36/7 is one of the options, choose that one.
If the question involves an exponent, you should use the "caret" which is ^ found above the 6 on a keyboard. [Shift + 6]. That helps avoid confusion.
Step-by-step explanation: 7 is equal to 35/5 because 7×5=35
Add 1/5 and you end up with 36/5. A Common rational number.
7^(1/5) = the 5th root of 7. A very small irrational number!
What is an equation of the line that passes through the points (3,−4) and (3,8)
Answer:
x = 3.
Step-by-step explanation:
In this case, the x-value never changes, no matter the value of the y. So, x will always equal 3. Your equation is x = 3.
Hope this helps!
Answer:
x=3
Step-by-step explanation:
the volume v (in cubic inches) of a rectangular cardboard box is modeled by the function v(x)= (18-2x)(3-2x)x, where x is the width (in inches) of the box. Determine the values of x for which the model makes sense. Explain your reasoning. (WILL GIVE BRAINLY FOR BEST ANSWER!!!)
Answer:
0 < x < 3/2
Step-by-step explanation:
The dimensions are positive when ...
18 -2x > 0 ⇒ x < 9
3 -2x > 0 ⇒ x < 3/2
x > 0
So, the values of x where the model makes sense are ...
0 < x < 3/2
A standard deck of of 52 playing cards contains 13 cards in each of four suits : diamonds, hearts , clubs and spades. Two cards are chosen from the deck at random.
Answer:
Probability of (one club and one heart) = 0.1275 (Approx)
Step-by-step explanation:
Given:
Total number of cards = 52
Each suits = 13
FInd:
Probability of (one club and one heart)
Computation:
Probability of one club = 13 / 52
Probability of one heart = 13 / 51
Probability of (one club and one heart) = 2 [(13/52)(13/51)]
Probability of (one club and one heart) = 0.1275 (Approx)
Answer:
D. 0.1275
Step-by-step explanation:
Justo took the Pre-Test on Edg (2020-2021)!!
Please help me with this answer!! I am really stuck...No nonsense answers please.
Answer:
19
Step-by-step explanation:
Inscribed Angle = 1/2 Intercepted Arc
< DBG = 1/2 ( DG)
< DBG = 1/2 ( 360 - BD - BG)
= 1/2 ( 360 - 172 - 150)
= 1/2 (38)
= 19
What is the point- slope of a line with slope -5 that contains the point (2,1) ? ( TOP ANSWER GETS BRAINLEST)
Answer:
C
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = - 5 and (a, b) = (2, - 1), thus
y - (- 1) = - 5(x - 2) , that is
y + 1 = - 5(x - 2) → C
Answer:
y + 1 = - 5(x - 2)Option C is the correct option
Step-by-step explanation:
The general form of point slope form of line is :
[tex]y - y1 =m ( x - x1)[/tex]
Where ( x1 , y1 ) is one point on the line and m is the slope.
In the given problem,
The slope of line ( m ) = - 5
One point on the line = ( x1 , y1 ) = ( 2 , -1 )
The point slope form of the line is:
y - ( - 1 ) = - 5 ( x - 2 )
y + 1 = - 5 ( x - 2 )
Hope this helps..
Best regards!!
A.
The graph that represents x < 4 is
-
--
- 1
-H
-H
The graph that represents 4 sx is
0
2.
4
6.
8
10
12.
14
16
18 20
B.
1
--
--
1
-1
1
0
-5
4 -3
-2
1
2
3
4.
5
C.
--
---
--
--
-6
-4
-2
0
2.
4
6
8
10
12 14
Answer:
BAStep-by-step explanation:
The < symbol does not include the "or equal to" case, so will be graphed with an open circle at the boundary. x < 4 means that values of x less than 4 will be shaded, and there will be an open circle at x=4. Graph B shows this.
__
4 ≤ x means there will be a solid dot at x=4, and values of x greater than 4 will be shaded. Graph A shows this.
Answer: B & A
Step-by-step explanation:
PLEASE help me with this question! This is urgent!
Answer:
second one
Step-by-step explanation:
After eating at a restaurant Alyssa Dan and Nancy decided to divide the bill evenly if each person pay $38 what was the total of the bill
Answer:
$76
Step-by-step explanation:
$38 + $38 = $76
Determine the equation of a line that passes through A(2,5) and is parallel to the line defined by 3x−y+12=0. State the equation in slope y-intercept form
Answer:
y = 3x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
3x - y + 12 = 0 ( subtract 3x + 12 from both sides )
- y = - 3x - 12 ( multiply through by - 1 )
y = 3x + 12 ← in slope- intercept form
with slope m = 3
Parallel lines have equal slopes , thus
y = 3x + c ← is the partial equation
To find c substitute (2, 5) into the partial equation
5 = 6 + c ⇒ c = 5 - 6 = - 1
y = 3x - 1 ← equation of parallel line
3) In a paddling pool there are 30 floating ducks. Each duck is marked with a number on the underside. 15 are marked with the number 1, 9 are marked with the number 2 and 6 are marked with number 3. There are prizes for those who pick a duck with the number 3 on it. What is the probability of Molly picking a duck with the number 3 on it? Give your answer as a fraction in its lowest terms.
Answer: 1/5
Step-by-step explanation:
Given the following :
Total number of ducks in pool = 30
Mark 1 = 15 ducks
Mark 2 = 9 ducks
Mark 3 = 6 ducks
Probability of picking a duck with Mark 3:
Probability = (number of required outcomes / total possible outcomes)
Number of required outcomes = number of ducks with mark 3 = 6 ducks
P(picking a duck with Mark 3) = 6/30
6/30 = 1/5
= 1/5
The advertised size of a computer or television screen is actually the length of the diagonal of
the screen. A computer screen measures 30cm by 22.5cm. Determine the length of its
diagonal.
Answer:
37.5 cm
Step-by-step explanation:
See attached for reference.
let the diagonal be x,
By Pythagorean formula:
x² = (22.5)² + (30)²
x = √[(22.5)² + (30)²]
x = 37.5 cm
Is 5.7c-1.5+3.2c=7.8c-1.5+1.1c a one solution problem?
Answer:
This is NOT a one solution problem.
Step-by-step explanation:
Group all terms with a c in it to the left of the equal sign, and group all numbers to the right of the equal sign.
5.7c-1.5+3.2c=7.8c-1.5+1.1c
5.7c + 3.2c - 7.8c - 1.1c = - 1.5 + 1.5
8.9c - 8.9c = 0
0 = 0
No matter which number you substitute for c, it will always be true. Since you can find infinity of solutions, this is NOT a one solution problem.
What is the sum of the measures of the exterior angles of this triangle
Answer:
360°
Step-by-step explanation:
The sum of all the exterior angles of a triangle is equal to 360 degrees.
Answer:
It would be 360*
Step-by-step explanation:
112+129+119
In 1833 a ship arrived inCalcutta with 120 tons remaining of its cargo of ice. One third of the original cargo was lost because it had melted on the voyage. How many tons of ice was the ship carrying when it set sail? A.40 B.80 C.120 D.150 E.180
Answer: 180
Step-by-step explanation:
Let the tons of ice the ship was carrying when it set sail be y.
We are told that one third of the original cargo was lost because it had melted on the voyage and that it arrived in Calcutta with 120 tons remaining of its cargo of ice.
This means that (1 - 1/3 = 2/3) remained which was the 120 tons remaining. This implies that:
2/3 × y = 120
2y/3 = 120
2y = 120 × 3
2y = 360
y = 360/2
y = 180
The ship was carrying 180 tons of ice when it set sail
Evaluate A/B for a = 1/2 and b = -3/7
Answer:
-7/6
Step-by-step explanation:
If a = 1/2 and b = -3/7, then your given:
1/2 divided by -3/7=
-7/2*3=
-7/6
Sorry if its a bit unclears
Answer:
[tex]\frac{7}{-6}[/tex]
Step-by-step explanation:
To do this you are basically dividing the fractions so when you set up the equation it will look like this [tex]\frac{1}{2}/\frac{-3}{7}[/tex] now that we have this we will take the reciprocal of -3/7 which is 7/-3 and than multiply the 2 fractions we we get 7/-6
On a coordinate plane, a line is drawn from point J to point K. Point J is at (negative 6, negative 2) and point K is at point (8, negative 9). What is the x-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:5? x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1 –4 –2 2 4
Answer:
-2
Step-by-step explanation:
The coordinate of a point that divides a line AB in a ratio a:b from A([tex]x_1,y_1[/tex]) to B([tex]x_2,y_2[/tex]) is given by the formula:
[tex](x,y)=(\frac{bx_1+ax_2}{a+b} ,\frac{by_1+ay_2}{a+b} )=(\frac{a}{a+b}(x_2-x_1)+x_1 ,\frac{a}{a+b}(y_2-y_1)+y_1 )[/tex]
Given that a line JK, with Point J is at ( -6, - 2) and point K is at point (8, - 9) into a ratio of 2:5. The x coordinate is given as:
[tex]x=\frac{2}{2+5} (8-(-6))+(-6)=\frac{2}{7}(14) -6=4-6=-2[/tex]
Line segments can be divided into equal or unequal ratios
The x coordinate of the segment is -2
The coordinates of points J and K are given as:
[tex]J = (-6,-2)[/tex]
[tex]K = (8,-9)[/tex]
The ratio is given as:
[tex]m : n =2 : 5[/tex]
The x-coordinate is then calculated using:
[tex]x = (\frac{m}{m + n }) (x_2 - x_1) + x_1[/tex]
So, we have:
[tex]x = (\frac{2}{2 + 5 }) (8 - -6) -6[/tex]
[tex]x = (\frac{2}{7}) (14) -6[/tex]
Expand
[tex]x = (2) (2) -6[/tex]
Open bracket
[tex]x = 4 -6[/tex]
Subtract 6 from 4
[tex]x = -2[/tex]
Hence, the x coordinate of the segment is -2
Read more about line ratios at:.
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Help me please ty ty ♀️❤️ Appreciate it
Answer:
Pretty Simple!
Now that you know about ratios and all that, this is pretty tame compared to the last problem.
Now, the problem is talking 2D(2 Dimensions)
The ratio is not going to work because it has only one parameter.
Thus, we need to square it!
[tex](\frac{1}{20})^{2} =\frac{1}{400}[/tex]
Thus, we have your correct ratio.
Now, we only need to do the same thing for the triangle problem. Meaning that, we need to compare the ratios, with x as the thing we are looking for.
[tex]\frac{1}{400}=\frac{219}{x} \\x=87,600[/tex]
See? X is practically handed to us.
Hope this helps!
which system of linear inequalities is represented by this graphed solution?
A. y > -1/2x + 2
y ≤ 3x - 1
B. y < -1/2x + 2
y ≥ 3x - 1
C. y > -2x + 2
y ≤ 1/3x - 1
D. y ≤ -1/2x + 2
y < 3x - 1
Answer:
B. y < -1/2x + 2 y ≥ 3x - 1Step-by-step explanation:
The gray shadowed area is below descending function and the line is dashed.
It means coefficient x is m<0 and the sign of inequality is y <
So the inequality wich fit it is y < -1/2x + 2
The blue shadowed area is above ascending function and the line is uninterrupted.
It means coefficient x is m>0 and the sign of inequality is y ≥
So the second inequality of system (y ≥ 3x - 1) also match.
The system of linear inequalities represented by this graphed solutions are y ≤ -1/2x + 2 and y < 3x - 1
The standard equation of a line is expressed as y = mx + b;
m is the slope of the lineb is the y-intercept of the lineFor the blue line, the y-intercept is at y = -1. For the slope passing through (0, -1) and (2, 5):
m = 5+1/2-0
m= 6/2
m = 3
The equation of the line is y = 3x - 1
Since the line is dashed and the left part shaded, the inequality expression will be y < 3x - 1
For the black line, the y-intercept is at y = 2. For the slope passing through (0, 2) and (4, 0):
m = 0-2/4-0
m= -2/4
m = -1/2
The equation of the line is y = -1/2x + 2
Since the line is solid and the lower part shaded, the inequality expression will be y ≤ -1/2x + 2
Hence the system of linear inequalities represented by this graphed solutions are y ≤ -1/2x + 2 and y < 3x - 1
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Campus rentals rent 2 and 3 bedroom apartments for 700$ and 900$ a month respectively. Last month they had six vacant apartments and reported $4600 in lost rent. How many of each type of apartment were vacant?
Answer:
2 - bedroom apartment = 4
3 - bedroom apartment = 2
Step-by-step explanation:
Given the following :
2 - bedroom apartment = $700 / month
3 - bedroom apartment = $900 / month
Last month:
Number of vacant apartment = 6
Amount of Lost rent = $4600
Let a = 2 - bedroom apartment and b = 3 - bedroom apartment
Vacant apartment :
a + b = 6 - - - (1)
Lost rent :
700a + 900b = 4600 - - - (2)
From (1),, a = 6 - b
Substitute a = 6 - b into (2)
700(6 - b) + 900b = 4600
4200 - 700b + 900b = 4600
4200 + 200b = 4600
200b = 4600 - 4200
200b = 400
b = 400/200
b = 2
From (1) ;
a + b = 6
a + 2 = 6
a = 6 - 2
a = 4
a = 2 - bedroom apartment = 4
b = 3 - bedroom apartment = 2
What is the simplest form for the expression (-12.7y-3.1x) Plus 5.9y-(4.2y Plus x)
Answer:
[tex]\boxed{-4.1x-11y}[/tex]
Step-by-step explanation:
[tex](-12.7y-3.1x) + 5.9y-(4.2y + x)[/tex]
Expand brackets.
[tex]-12.7y-3.1x+ 5.9y-4.2y - x[/tex]
Combining like terms.
[tex]- x-3.1x-12.7y+ 5.9y-4.2y[/tex]
[tex]-4.1x-11y[/tex]
Answer:
[tex] \boxed{\red{ - 11y - 4.1x}}[/tex]
Step-by-step explanation:
[tex] (- 12.7y - 3.1x) + 5.9y - (4.2y + x) \\ - 12.7y - 3.1x + 5.9y - 4.2y - x \\ - 12.7y + 5.9y - 4.2y- 3.1x - x \\ = - 11y - 4.1x[/tex]
Choose the equation that is equivalent to the equation shown below. y = 2x + 4a/6b A. x = 2x - 3by B. c = ax-by/z C. b = 6y/2x+4a D. a = 3by-x/2
Answer:
Step-by-step explanation:
y = 2x + 4a/6b y=(12xb+4b )/6b
6yb=12x+4a
a=(-12xb+6yb)/4=
a=3yb/2 -3xb
x=y/2-a/3b
b=2a/(3y-6x)
the solution is for every variable
A tank contains 8000 liters of a solution that is 40% acid. How much water should be added to make a solution that is 30% acid?
Answer:
2,666.67 L of water
Step-by-step explanation:
Solve for W:
1) 3200 = 2400 + 0.3w
2) 800 = 0.3w
Divide both sides by 0.3 to get the variable alone
3) (800)/0.3 = (0.3w)/0.3
4) w = 2,666.67 L
A spinner is separated into 3 equal pieces, as shown below: Mary spins the spinner 6 times. What is the theoretical probability that it stops on the red sector on the last spin?
A.) 1/36
B.) 1/9
C.) 1/3
D.) 2/3
Answer:
C. 1/3
Step-by-step explanation:
Given:
Number of colors listed (Successful Outcome)
Red 1
Yellow 1
Purple 1
Total or Possible outcome= 3
Required:
What is the theoretical probability that it stops on the red sector on the last spin?
Formula:
Probability= Successful outcome ÷ Possible outcome
Solution:
Probability of the spinner stoping on red.
Probability= Successful outcome ÷ Possible outcome
Probability=1÷3
Probability=1/3
Hope it helps ;) ❤❤❤
The theoretical probability that spinner stops on the red sector on the last spin is option (C) [tex]\frac{1}{3}[/tex]
What is Probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Given,
A spinner is separated into 3 equal parts.
Then Mary spins the spinner 6 times.
What is the theoretical probability that it stops on the red sector on the last spin. So only last spin is important, outcomes of first 5 spin is not important and it is independent.
Probability = Number of favorable outcome / Number of Total outcome
Probability (Red sector) = [tex]\frac{1}{3}[/tex]
Hence, the theoretical probability that spinner stops on the red sector on the last spin is option (C) [tex]\frac{1}{3}[/tex]
Learn more about Probability here
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find the area of equilateral triangle whose median is X cm
options:
a.x^2
b.(x^2)/2
c.(x^2)/√3
d.(x^2)/3
.
What is y + 3 = 7(2 – 2) written in standard form?
Answer:
y = -3
Step-by-step explanation:
y + 3 = 7(2 - 2)
y + 3 = 0
Subtract 3 from both sides
y + 3 - 3 = 0 - 3
y = -3
Answer:
7x - y = 17
Step-by-step explanation:
Maybe you want the standard form of the point-slope equation ...
y +3 = 7(x -2)
__
y + 3 = 7x -14 . . . . . eliminate parentheses
17 = 7x -y . . . . . . . . add 14-y
7x - y = 17
Given the formula below, solve for x.
- Vi
ОА.
+ 11
B.
y – 9 + fi
O c.
Ử - VI
m
-fi
D.
mly – yy)
Answer:
Option (C)
Step-by-step explanation:
Given formula of a line passing through [tex](x_1, y_1)[/tex] and slope 'm' is,
[tex]y-y_1=m(x-x_1)[/tex]
Further solving this equation,
[tex]y-y_1=mx-mx_1[/tex] [By distributive property]
[tex]y-y_1+mx_1=(mx-mx_1)+mx_1[/tex] [By adding [tex]mx_1[/tex] on both the sides]
[tex]y-y_1+mx_1=mx[/tex]
[tex]\frac{y-y_1-mx_1}{m}=\frac{mx}{m}[/tex] [Divide the equation by m]
[tex]\frac{y-y_1}{m}-x_1=x[/tex]
Therefore, Option (C) will be the answer.
Please answer this question only if you know correct answer please
Answer:
UV=10.5
Step-by-step explanation:
in triangle XUV it is a right angle at U
sin41=opp/hyp
sin 4` =UV/16
UV=16sin41°
UV=10.5
If QR = 9 and ST = 13 calculate LM.
Answer:
[tex]\boxed{\sf LM = 11}[/tex]
Step-by-step explanation:
According to trapezoid mid-segment theorem:
[tex]LM = \frac{QR+ST}{2}\\ Given \ that\ QR = 9, ST = 13[/tex]
[tex]\sf LM = \frac{9+13}{2}[/tex]
LM = 22/2
LM = 11