Answer:
Actual SAT Score = 815.284
Equivalent ACT Score = 15.811
The equivalent ACT Score = 29.95
Step-by-step explanation:
From the given information:
Scores on the SAT test are normally distributed with :
Mean = 982
Standard deviation = 198
If a student gets an SAT score that is the 20-percentile
Then ;
P(Z ≤ z ) = 0.20
From the standard z-score for percentile distribution.
z = -0.842
Therefore, the actual SAT Score can be computed as follows:
Actual SAT score = Mean + (z score × Standard deviation)
Actual SAT score = 982 + (- 0.842 × 198)
Actual SAT score = 982 + ( - 166.716)
Actual SAT score = 982 - 166.716
Actual SAT Score = 815.284
Scores on the ACT test are normally distributed with a mean of 19.6 and a standard deviation of 4.5.
Mean = 19.6
Standard deviation = 4.5
Equivalent ACT Score = 19.6 + (- 0.842 × 4.5)
Equivalent ACT Score = 19.6 + ( - 3.789)
Equivalent ACT Score = 15.811
If a student gets an SAT score of 1437, find the equivalent ACT score.
So , if the SAT Score = 1437
Then , using the z formula , we can determine the equivalent ACT Score
[tex]z = \dfrac{X - \mu}{\sigma}[/tex]
[tex]z = \dfrac{1437 - 982}{198}[/tex]
[tex]z = \dfrac{455}{198}[/tex]
z =2.30
The equivalent ACT Score = 19.6 + (2.30 × 4.5)
The equivalent ACT Score = 19.6 + 10.35
The equivalent ACT Score = 29.95
When six basketball players are about to have a free-throw competition, they often draw names out of a hat to randomly select the order in which they shoot. What is the probability that they shoot free throws in alphabetical order? Assume each player has a different name. P(shoot free throws in alphabetical order)=
Answer as a fraction = 1/720
Answer in decimal form (approximate) = 0.001388
Answer in percent form (approximate) = 0.1388%
========================================================
Explanation:
Let A = 1 to indicate the number of ways to get the names to line up in alphabetical order.
There are B = 6*5*4*3*2*1 = 720 different ways to arrange the six people. Notice how I started at 6 and counted my way down to 1, multiplying all along the way. This can be shortened to factorial notation to say 6! = 720. Or you could use the nPr permutation formula to get the same result (use n = 6 and r = 6).
Once you have the values of A and B, we form the fraction A/B = 1/720 which is the probability of getting the names in alphabetical order.
If you need the answer in decimal form, then use your calculator to find
1/720 = 0.001388
which converts over to 0.1388%
The number 16 has four fourth roots. In other words, there are four complex numbers that can be entered in the square in the equation below: __^4 = 16 Find them.
Answer:
Step-by-step explanation:
Hello, we know that the z complex solutions of
[tex]z^4=1[/tex]
are
1, i, -1, -i
so, the solutions of [tex]z^4=16=2^4[/tex] are
2, 2i, -2, -2i
Thank you
This table represents a quadratic function.
What is the value of “a” in the function’s equation?
A. -1/2
B. 1/2
C. 2
D. 1
Answer:
I think 1/2 is the ans
Step-by-step explanation:
quadratic function equation
would help
30 points and brainliest for the right answer :) I would like to know how to do this, so an explanation would be nice :P Thanks for the help!
Answer:
Below
Step-by-step explanation:
● (a)
Let's determine the difference between the outputs of any two inputs that are one unit apart.
Let m be that difference.
2 and 3 are one unit apart since when you substract 2 from 3 you get 1.
● 3-2 = 1
Let's calculate m.
The output of 2 and 3 are respectively 45 and 53.
● m = 53 - 45
● m= 8
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's determine the difference between the outputs of any two inputs that are 2 units apart.
Let m' be that difference
3 and 1 are 2 units apart since when you substract 1 from 3 you get 2.
● 3-1 = 2
The outputs of 1 and 3 are respectively 37 and 53.
● m'= 53-37
● m' = 16
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's determine the difference between the outputs of two inputs that are 3 units apart.
Let m" be that difference
0 and 3 are 3 units apart since when you substract 0 from 3 you get 3.
● 3-0 = 3
Let's calculate m":
The outputs of 0 and 3 are respectively 29 and 53
● m" = 53-29
● m" = 24
■■■■■■■■■■■■■■■■■■■■■■■■■■
● m = 8
● m'= 16
● m" = 24
Notice that all these values are multiples of 8.
● 8 = 8×1
● 16 = 8×2
● 24 = 8×3
Notice that each time the difference m is multiplied by the units that are between the inputs.
This is explained by the fact that the function is a linear one.
When the input interval grows the difference between the outputs grows two.
Answer:
Step-by-step explanation:
find the equation of the linear function in the form of y=mx+b
m=y2-y1/x2-x1 =-3+11/-4+5=8
y=8x+29 ( when x=0, y=b=29)
out put : -3 and -11 -3-(-11)=8 which is 1 unit
out put : 21 and 5 21-5=16 which is 2 unit (2*8)
output :53 and 29 53-29=24 which is 3 units (3*8)
ratio of change = f(b)-(f(a)/b-a
at point -3 and -11 : f(-3)-f(-11)/-4+5=-3+11/1=8
at point 21 and 5 : 21-5/-1+3=16/2=8
the graph always increasing and always equal 8
Find x. A. 332–√ B. 113–√ C. 33 D. 443–√
Answer:
C. 33.
Step-by-step explanation:
The sides of a 45-45-90 triangle are in the ratio 1:1:√2 so the side opposite to 45 degrees = 11√6 / √2.
Consider the larger triangle containing the 60 degree angle:
tan 60 = x / (11√6 / √2).
x = tan 60 * 11√6 / √2
x = 33.
The value of the variable x will be 33 units. Then the correct option is C.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
The diagram is shown below.
Let h be the height of the triangle.
The value of h is given by the sine of angle 45°. Then the value of the height h will be
sin 45° = h / 11√6
h = 11√6 × 1/√2
h = 11√3 units
The value of h is given by the tangent of angle 60°. Then the value of the height h will be
tan 60° = x / h
x = 11√3 × √3
x = 11 × 3
x = 33 units
Thus, the value of the variable x will be 33 units.
Then the correct option is C.
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
#SPJ5
Find the total surface area.
Answer:
160cm²
Step-by-step explanation:
To find the surface area of this prism, you just need to add up the areas of each side. To simplify the calculations a bit, we can take multiples of the sides which are the same. For example, here we have two equal trapezoids on each end, so we can multiply the area by two when adding.
The work is in the attachment.
solve for x 7x - 3/4 = 6x - 5/8
Answer: x=0.125 or 1/8
Step-by-step explanation:
[tex]7x-\frac{3}{4}=6x-\frac{5}{8}[/tex]
add 3/4 on both sides
[tex]7x-\frac{3}{4}+\frac{3}{4}=6x-\frac{5}{8}+\frac{3}{4}[/tex]
[tex]7x=6x+\frac{1}{8}[/tex]
subtract 6x on both sides
[tex]x=\frac{1}{8}[/tex]
Answer:
x = 1/8
Step-by-step explanation:
7x - 3/4 = 6x - 5/8
7x - 3/4 + 3/4 = 6x - 5/8 + 3/4
7x = 6x + 1/8
7x - 6x = 6x + 1/8 - 6x
x = (6x - 6x) + 1/8
x = 1/8
you have decided to hire a disc jockey for your party. the second dj you interviewed has 3 times as many songs as the first dj. the third dj had half as many songs as the second dj. write an expression to represent the number of songs the third has if the first dj had r songs. explain how you arrived at your answer
Answer:
The third DJ had (3r)/2 songs. Multiply r by 3 because the second DJ had 3 times as many as the first. Then divide that number by 2 because the third DJ has half as many.
Step-by-step explanation:
Answer:
The third DJ had (3r)/2 songs. Multiply r by 3 because the second DJ had 3 times as many as the first. Then divide that number by 2 because the third DJ has half as many.
Step-by-step explanation:
just did
how to find y in this equation 11=12-14y
What axis does the independent quantity go on?
Azila is a salesgirl for a cosmetic product. Her salary is RM375 per week with 5% commission of her weekly sales. What is the least value of a product that Aliza must sell if she targets a minimum salary of RM550 for a particular week?
Answer:
RM3,500
Step-by-step explanation:
Salary=RM375 per week
5% commission per week
If she target a minimum of RM 550.
Let x=minimum Sales
RM550=RM375 + 5% of x
RM550=RM375 + 0.05x
RM550 - RM375=0.05x
RM175=0.05x
Divide both sides by 0.05
RM175/0.05=0.05x/0.05
RM3,500=x
For Azila to earn a minimum of RM550 in a week, her salary will be RM375 plus 5% commission on the sales of RM3,500 value of product.
Check:
5% of RM3,500
=0.05*3,500
=RM175
Plus
Salary of RM375
RM175 + RM375=RM550
What is the perimeter of the figure shown?
Answer:
[tex]\boxed{16 units}[/tex]
Step-by-step explanation:
Hey there!
Well since all the sides are congruent and there are 8 sides we can make the following expression,
P = 2*8
P = 16
Hope this helps :)
Answer:
16
Step-by-step explanation:
The sides of this figure are equal to each other .
the permiter is the sum of the sides
The figure has 8 sides.
● P = 8 × 2
● P = 16
the fastest land dwelling creature is the cheetah. fact or
opinion
Answer:
True.
Step-by-step explanation:
Cheetahs can reach speeds of 109.4–120.7 km/h (68.0–75.0 mph), and some have been recorded at over 80mph. The cheetah can accelerate from 0 to 96.6 km/h (60.0 mph) in under three seconds, though endurance is limited.
The second fastest land animal is the Pronghorn antelope at 98kph (60mph).
Answer:
It is a Fact because it can run 70mph or 112kph
Express 0.00013745 to 3 significant figures.
Answer:
0.000137
To 1 significant figure: 0.0001
To 2 significant figures: 0.00014
To 3 significant figures: 0.000137
To 4 significant figures: 0.0001375
To 5 significant figures: 0.00013745
3) Find f(3) for the function below.
f(x) = 2x² – 3x
Answer:
9
Step-by-step explanation:
f(x) = 2x² – 3x
Let x=3
f(3) = 2 * 3^2 - 3*3
= 2 *9 - 9
= 18-9
= 9
Answer:
f(3) = 9Step-by-step explanation:
[tex]f(x) = 2x^2 -3x\\ f(3) = ?\\\\ f(3) = 2(3)^2 -3(3)\\ f(3) = 2(9) - 9\\ f(3) = 18- 9\\ f(3) = 9[/tex]
The volume of a sphere whose diameter is 18 centimeters is
π cubic centimeters. If its diameter were reduced by half, its volume would be
of its original volume.
Answer:
volume before reducing is 8 times the volume after reducing
Step-by-step explanation:
volume before reducing=
V=4/3πr³=
V=4/3π(9)³=972π cm³
diameter reduced to half=18/2=9 cm
radius=d/2=9/2=4.5 cm
volume of sphere when diameter reduced by 1/2=
V=4/3πr³
v=4/3 (π)(4.5)³=121.5π
volume before reducing is 8 times the volume after reducing
Answer:
The volume of a sphere whose diameter is 18 centimeters is 972 π cubic centimeters. If its diameter were reduced by half, its volume would be 1/8 of its original volume.
Step-by-step explanation:
Correct for plato :)
Let f(x) = 7x − 13. Find f−1(x)
Step-by-step explanation:
let f(x)=y
y=7x-13
y+13=7x
y+13/7=x
f-1(x)=x+13/7
explanation pls? step by step i get confused on these questions! thank you!
Answer:
5xyz
Step-by-step explanation:
10x^2 y^2z and 15xyz^2
Rewriting
2*5*x*x*y*y*z and 3*5 *x*y*z*z
What is common to both terms
5 x y z
The greatest common factor is 5xyz
Answer:
the GCF is 5(xyz)
Step-by-step explanation:
For the numbers, you want to find the largest number that both of the coefficients can be divided by. I'm not sure if your answer choices include variables, but if they do, its only xyz, nothing can be squared because both equations have different variables squared.
Find the value of tetha in 2 cos 3 tetha = 1
Answer:
Step-by-step explanation: 2cos3 theta=1. Cos 3theta=1/2. Since cos 60°= 1/2. Therefore cos 3theta=cos 60°. Theta=20°.
can we chat girl in comment
It takes 1.5 seconds for a grandfather clock's pendulum to swing from left (initial position) to right, covering a horizontal distance of 10 inches. Which function models the horizontal displacement as a function of time in seconds? y = 5 cosine (StartFraction 2 pi Over 3 EndFraction x) y = 5 cosine (StartFraction 4 pi Over 3 EndFraction x) y = 10 cosine (StartFraction 2 pi Over 3 EndFraction x) y = 10 cosine (StartFraction 4 pi Over 3 EndFraction x)
Answer:
Step-by-step explanation:
Given functions are
y = 5 cos ( 2π / 3 ) t
y = 5 cos ( 4π / 3 ) t
y= 10 cos ( 2π / 3 ) t
y = 10 cos ( 4π / 3 ) t
The pendulum half oscillation from left extreme to right extreme takes 1.5 s
So its time period of oscillation T = 1.5 x 2 = 3 s .
standard equation of oscillation is
y = A cos ω t where A is amplitude and ω is angular frequency .
Amplitude of oscillation A = 10 / 2 = 5 inch .
Among the given equation of motion only first two has amplitude equal to 5 . So both the last two are ruled out .
The angular frequency of first motion as per given equation
ω = 2π / 3
If time period is T
2π / T = 2π / 3
T = 3 s
So it matches with the time period of oscillation of pendulum .
Hence the first equation truly represents the oscillation of pendulum.
The function models the horizontal displacement as a function of time in seconds is [tex]\rm y = 10 sin(\dfrac{2\pi}{3})t[/tex] and this can be determined by using the given data.
Given :
It takes 1.5 seconds for a grandfather clock's pendulum to swing from left (initial position) to right, covering a horizontal distance of 10 inches.
For the oscillation the standard equation is given below:
[tex]\rm y = A\;cos \;\omega t[/tex]
where A is the amplitude, [tex]\omega[/tex] is the angular velocity, and t is the time.
Now, determine the time period that is:
T = 1.5 [tex]\times[/tex] 2
T = 3sec
Now, the angular frequency is given by:
[tex]\omega = \dfrac{2\pi}{3}[/tex]
So, the function models the horizontal displacement as a function of time in seconds is given below:
[tex]\rm y = 10 sin(\dfrac{2\pi}{3})t[/tex]
Therefore, the correct option is C).
For more information, refer to the link given below:
https://brainly.com/question/40973
If each of the 4 shelves holds 14 movies, how many movies does Betty have on her shelving unit? Show your work.
Answer:
62
Step-by-step explanation:
4x + 6
4(14) + 6 (substituting x = 14)
56 + 6
62
-3 = k/12 help please
Answer:
-36 = k
Step-by-step explanation:
-3 = k/12
Multiply each side by 12
-3*12 = k/12 *12
-36 = k
Answer: k= -36
Step-by-step explanation:
[tex]-3=\frac{k}{12}[/tex]
multiply both sides by 12
[tex]\frac{12k}{12}=12\left(-3\right)[/tex]
12*(-3)=-36
[tex]\frac{12k}{12}=12\left(-3\right)[/tex]
k=-36
Maureen plants tulips in a rectangular flower bed that is 2 cubed feet wide and 2 Superscript 4 feet long.
Answer:
The area would be 128ft^2
2^4 i= 2x2x2x2
2^3 = 2x2x2
multiply them and you get 128ft6^2
Answer:
128ft^2
Step-by-step explanation:
took the quiz just now :D
draw a graph of 2x - 3y = 6
Answer:
Slope:[tex]\frac{2}{3}[/tex]
y-intercept:-2
Step-by-step explanation:
The 3 question please with explained
Answer:
Step-by-step explanation:
Rectangle:
length = l = 12 cm
Width = w = 0.8 cm
Use Pythagorean theorem to find the diagonal
Diagonal² = l² + w²
= 12² + 0.8²
= 144 + 0.64
= 144.64
Diagonal = √144.64 = 12.03 cm
Diagonal of square = diagonal of rectangle
= 12.03 cm
To find the side of square again use Pythagorean theorem,
side² + side² = 12.03²
2 sides² = 144.64
side² = 144.64/2
side² = 72.32
side = √72.32
Side = 8.50 cm
Suppose you roll a fair six-sided die 25 times. What is the probability that you roll 5 or more 6’s on that die?
A. 0.3883
B. 0.5937
C. 0.5
D. 0.4063
Answer:
D. P(5+ 6's) = 0.4063
Step-by-step explanation:
Binomial distribution.
For the distribution to be applicable, the experiment must
1. Have a know and constant number of trials
2. Probability of success of each trial remains constant (and known if available)
3. Each trial is a Bernoulli trial, i.e. with only two outcomes, success or failure.
4. Independence between trials.
Let
n = number of trials = 25
p = probability of success of each trial = 1 / 6
x = number of successes (0 ≤ x ≤ n) = 5
C(n,x) = number of combinations of picking x identical objects out of n
Applying binomial distribution
P(x,n) = probability of x successes in an experiment of n trials.
= C(n,x) * p^x * (1-p)^(n-x)
For n = 25 trials with probability of success (roll a 6) = 1/6
and x = 5,6,7,8,...25
It is easier to calculate the complement by
P(5+ 6's) = 1 - P(<5 6's)
= 1 - ( P(0,25) + P(1,25) + P(2,25) + P(3,25) + P(4,25) )
1- (
P(0,25) = C(25,0) * (1/6)^0 * (5/6)^25 = 0.0104825960103961
P(1,25) = C(25,1) * (1/6)^1 * (5/6)^24 = 0.05241298005198051
P(2,25) = C(25,2) * (1/6)^2 * (5/6)^23 = 0.1257911521247532
P(3,25) = C(25,3) * (1/6)^3 * (5/6)^22 = 0.1928797665912883
P(4,25) = C(25,4) * (1/6)^4 * (5/6)^21 = 0.2121677432504171
)
= 1 - 0.59373
= 0.40626
= 0.4063 (to 4th decimal place)
The cost to rent a car at one agency is $24.50 per day plus an additional $15.99 fee for insurance. At a different agency, the cost to rent a car is $27.50 per day, but the insurance is only an additional $3.99 fee. Which equation could be used to find the number of days, d, at which the rental fee is the same for both agencies?
Answer:
d=4
Step-by-step explanation:
Agency 1:
Total cost of renting a car=24.50d + 15.99
Agency 2:
Total cost of renting a car=27.50d + 3.99
Where, d=No. of days of renting the car
Which equation could be used to find the number of days, d, at which the rental fee is the same for both agencies?
The equation is by equating agency 1 and agency 2 equation
24.50d + 15.99 = 27.50d + 3.99
Collect like terms
24.50d - 27.50d = 3.99 - 15.99
-3d = -12
Divide both sides by -3
d= -12 / -3
=4
d=4
Check
Agency 1:
24.50d + 15.99
= 24.50(4) + 15.99
= 98 + 15.99
= 113.99
Agency 2:
27.50d + 3.99
= 27.50(4) + 3.99
= 110 + 3.99
= 133.99
Answer:
24.5d + 15.99 = 27.5d + 3.99
Step-by-step explanation:
The other person who answered this question was correct, they just explained it all the way through and since you guys skim through everything instead of reading, I'll put the answer. :)
Simplify.
2x (3-1) + 3
O 7
O 8
10
O 11
Answer:
(2,−6)+(9,9)
(12,−5)⋅(5,6)
(4,4)⋅(4,4)
Step-by-step explanation:
Try one of these answers
Answer:
Let's simplify step-by-step.
2x(3−1)+3
=4x+3
Step-by-step explanation:
2x[3-1]=6x-2x=4x
4x+3
In circle L, arc MNOP is 120° and the radius is 5 units. Which statement best describes the length of arc MNOP? one half the area of circle L one third the area of circle L one half the circumference of circle L one third the circumference of circle L
Question
In circle L, arc MNOP is 120° and the radius is 5 units. Which statement best describes the length of arc MNOP?
• one half the area of circle L
• one third the area of circle L
• one half the circumference of circle L • one third the circumference of circle L
Answer:
• one third the circumference of circle L
Step-by-step explanation:
In the question, we are told that:
In circle L, arc MNOP is 120° and the radius is 5 units.
We are asked to find the statement amongst the options that describes the arc length MNOP of Circle L
Step 1
Find the Area of circle
Area of a circle = πr²
r = 5 units
Area of a circle = π × 5²
Area of a circle = π × 25
Area of a circle = 78.53981634 square units
Step 2
Find the arc length of a circle
Arc length = 2πr × θ /360
r = 5 units
θ = 120°
Arc length = 2 × π × r × 120/360
Arc length = 2 × π × r × (1/3)
Arc length = 2 × π × 5 × (1/3)
Arc length = 10.47198 units
Step 3
Circumference of a circle = 2πr
= 2 × π × 5
= 31.415926536 units
Since the Circumference of a circle = 2πr
Arc length of the circle for the above calculation, = 2πr × 1/3
Therefore, the statement that best describes the arc length MNOP of Circle L is:
" the arc length MNOP is one third the circumference of circle L"
Answer:
the arc length MNOP is one third the circumference of circle L
Step-by-step explanation:
i fishie yupo
For the function F defined by F(x)=x2−2x+4, find F(5). For the function F defined by F ( x ) = x 2 − 2 x + 4 , find F ( 5 ) . A. 32 32 B. 39 39 C. 19 19 D. 4
Answer:
C. 19
Step-by-step explanation:
Given the function defined by F(x)=x²−2x+4, in order to get f(5), we will have to simply substitute x = 5 into the formula given as shown;
F(5) = 5²-2(5)+4
F(5) = 25 - 10 + 4
F(5) = 15 + 4
F(5) = 19
Hence, for the function F defined by F(x)=x²−2x+4, F(5) = 19
