Grayson surveyed some students at his school about their favorite colors. Of the students surveyed, 2 said orange was their favorite color, while 36 of the students had other favorite colors. What is the experimental probability that the next student Grayson talks to will pick orange?
Using it's concept, it is found that there is a 0.0526 = 5.26% experimental probability that the next student Grayson talks to will pick orange.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In an experimental probability, these number of outcomes are taken from previous trials.
In this problem, 2 out of 38 students picked orange as their favorite color, hence the probability that the next student picks orange is given by:
p = 2/38 = 1/19 = 0.0526.
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The idea of a rigid motion is a significant concept in geometry. Explain what a rigid motion is and why it is important. Using the diagram below identify the specific rigid motions used for the following shapes.
Answer:
a rigid motion does not affect the overall shape of an object but moves an object from a starting location to an ending location the resultant figure in cogruent to the original figure.a rigged motionis when an object is moved from one location to another and the size and shape have not changed.hope it helps :)
HELP ASAP!!
Person A leaves a $16 tip for a meal that costs $123. Person B leaves a tip of $12 for a meal that costs $89. Who is the better tipper? Explain.
# 5 pls !!
find dy/dx by implicit differentiation
Step-by-step explanation:
[tex]5. {x}^{3} - xy + {y}^{2} = 4[/tex]
[tex] \frac{dy}{dx} ( {x}^{3} - xy + {y}^{2} ) = \frac{dy}{dx} (4)[/tex]
[tex]3 {x}^{2} - x(1) \frac{dy}{dx} + 1(y) + 2y \frac{dy}{dx} [/tex]
Combine the dy/dx.
[tex] \frac{dy}{dx} ( - x + 2y) + y + 3 {x}^{2} [/tex]
[tex] \frac{dy}{dx} ( - x + 2y) = - 3 {x}^{2} - y[/tex]
[tex] \frac{dy}{dx} = \frac{ - 3 {x}^{2} - y}{ - x + 2y} [/tex]
[tex] \frac{3 {x}^{2} + y }{x - 2y} [/tex]
Answer:
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{y-3x^2}{2y-x}[/tex]
Step-by-step explanation:
using the product rule to differentiate - xy then
3x² - (x[tex]\frac{dy}{dx}[/tex] + y(1) ) + 2y[tex]\frac{dy}{dx}[/tex] = 0
3x² - x[tex]\frac{dy}{dx}[/tex] - y + 2y[tex]\frac{dy}{dx}[/tex] = 0
3x² + [tex]\frac{dy}{dx}[/tex] (2y - x) - y = 0 (subtract 3x² - y from both sides )
[tex]\frac{dy}{dx}[/tex] (2y - x) = y - 3x² ← divide both sides by (2y - x)
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{y-3x^2}{2y-x}[/tex]
Find the surface area of each of the following figures using the given values.
Answer:
Step-by-step explanation:
1. the surface area of a square is 6 * s^2
a. 6 * 5^2 = 150 sq ft
b. 6 * 6^2 = 216 sq in
c. 6 * 12^2 = 864 sq mm
2. the surface area of a rectangle is 2(l*w + w*h + l*h)
a. 2(2*5 + 5*7 + 2*7) = 118 sq ft
b. 2(16*11 + 11*10 + 16*10) = 892 sq in
3. the surface area of a sphere is 4pi * r^2
a. 4pi * 12^2 = 576pi or 1809.6 units sq
b. 4pi * 16^2 = 1024pi or 3216.99 units sq
c. d = 2r, r = 5, 4pi * 5^2 = 100pi or 314.2 units sq
4. the surface area of a cylinder is (2pi * r^2) + (2pi*r * h)
a. (2pi * 6^2) + (2pi * 6 * 12) = 216pi or 678.6 units sq
b. (2pi * 2^2) + (2pi * 2 * 10) = 48pi or 150.8 units sq
c. (2pi * 3^2) + (2pi * 3 * 5) = 48pi or 150.8 units sq
5. r = d/2 = 0.5, using formula from question 4:
(2pi * 0.5^2) + (2pi * 0.5 * 4) = 4.5pi or 14.14 ft sq
Lester bought 6.16 pounds of bologna at the deli. Renee bought 1.33 pounds
of bologna. How much more bologna did Lester buy than Renee? Do not
include units in your answer.
Answer:
5.32
Step-by-step explanation:
MARK A BRAIN LESS
CARRY ON LEARNING
B BRAIN LY FAST
Which one has a greater quantity:
The volume of a prism with a base area of 24.3 cm2 and height 14 cm or
The volume of a pyramid with a base area 24.3 cm2 and height 14 cm
Answer:
The volume of a prism with a base area of 24.3 cm2 and height 14 cm
What kind of transformation converts the graph of f(x) = -8x2 - 8 into the graph of g(x) =
-x² – 1?
vertical stretch
vertical shrink
horizontal stretch
horizontal shrink
Submit
Answer:
horizontal stretch
Step-by-step explanation:
For f(x) to turn into g(x), you must divide the function by 8. When we divide a function, this is known as a horizontal stretch because as you can see, the function gets wider. See the help image below with different examples.
Just a future tip: when you're in doubt, graph it out!
Horizontal stretch is the transformation which converts the graph of f(x) = -8x²- 8 into the graph of g(x) = -x² – 1. Option C is correct.
The general form of the quadratic function is f(x) = a(x - h)² + k, where (h, k) represents the vertex of the parabola.
In this case, for f(x) = -8x² - 8, the vertex is at (0, -8).
For g(x) = -x² - 1, the vertex is at (0, -1).
Comparing the two functions, you can see that the coefficient in front of x² changes from -8 to -1.
This change in the coefficient results in a horizontal stretch or compression of the parabola.
In this case, the graph has been horizontally stretched to transform from f(x) to g(x).
Hence, Option c is correct. Horizontal stretch is the transformation which converts the graph of f(x) = -8x²- 8 into the graph of g(x) = -x² – 1.
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Solve for 1/4 of x is 6
Answer: x=24
Step-by-step explanation:
1/4x=6x=6/0.25x=24Other way to do it is 6x4=24James bought a car for $17.528 which included a 4.5% tax
a) How tax did he pav? b) He received a 15% discount off the
original price of the car. What was the original price?
Answer:
(1) the tax is 788.76
(2) 19312.23
Step-by-step explanation:
Hope this helps
Find the perimeter of the figure.
Step-by-step explanation:
perimeter=(8cm×5)+24cm
=40cm+24cm
=64cm
A company makes three sizes of juice bottles: small, medium, and large.
• The ratio of small bottles to medium bottles made is 2:3.
• The ratio of medium bottles to large bottles made is 3:5,
The company makes s small bottles every minute.
Enter an expression in terms of s to represent the number of large bottles the company makes every minute.
An expression in terms of s that represents the number of large bottles is : L = [tex](\frac{15s}{2} /3})[/tex]
Ratio of different sizes of bottlesThe company makes s small bottles every minute
let ; M represent the number of medium bottles made every minute
L represent the number of large bottles made every minute
small bottles to medium = 2 : 3
small bottles to medium = s : M
M is the unknown, so to find how many medium bottles that has been made, we must cross multiply
2M = 3s
M = [tex]\frac{3s}{2}[/tex] medium bottles made every minute
medium bottles to large bottles = 3 : 5
medium bottles to large bottles = M : L
where M = [tex]\frac{3s}{2}[/tex]
The equation becomes:
3 : 5
[tex]\frac{3s}{2}[/tex] : L
L is the unknown, so to find how many Large bottles that has been made, we must cross multiply
3L =( [tex]\frac{3s}{2}[/tex] ) * 5
L = [tex](\frac{15s}{2} /3})[/tex]
L = ( [tex]\frac{5}{2}[/tex] s)
L = 2.5 s
therefore the large bottles the company makes every minute is 2.5s large bottles
we can conclude that the expression for the number of large bottles the company makes every minute with respect to s is : L = 2.5 s
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Please Help!!!!
A ball was thrown upward into the air. The height in feet of the ball, above the ground, t seconds after being thrown can be determined by the expression -16t² + 40t + 3. What is the meaning of the 3 in the expression?
A.) the ball took three seconds to reach its maximum height
B.) the ball took three seconds to reach the ground
C.) the ball was thrown from a height of three feet
D.) the ball reached a maximum height of three feet
Answer:
The ball was thrown from a height of [tex]3\; {\rm ft}[/tex].
Step-by-step explanation:
The expression for the height of this ball, [tex]h(t) = -16\, t^{2} + 40\, t + 3[/tex], represents a parabola (with respect to time [tex]t[/tex].)
In this expression, "[tex]3[/tex]" represents the [tex]y[/tex]-intercept of the parabola- the output of the parabola when the input is [tex]t = 0[/tex]. The reason is that when [tex]t = 0\![/tex], terms of this parabola that include [tex]t[/tex] ([tex](-16\, t^{2})[/tex] and [tex]40\, t[/tex]) would evaluate to [tex]0[/tex]:
[tex]\begin{aligned}h(0) &= -16\times 0^{2} + 40\times 0 + 3 = 3\end{aligned}[/tex].
In the case of this ball, the term "[tex]3[/tex]" means that height of this ball is [tex]3\; {\rm ft}[/tex] when [tex]t = 0[/tex] (right when the ball was thrown.) Thus, the ball was thrown from a height of [tex]3\; {\rm ft}[/tex].
What is the height of the building? (show your work) GIVING BRAINLIEST!
Answer:
so
Step-by-step explanation:
what I did was count the lines start from 5m and go on from there hope this helps :)
can someon3 help me with this it like 4 or 5 minutes
Answer:
C. 360-85=12h
Step-by-step explanation:
360=85+12h
360-85=12h
PLEASE HELP ASAP
Subtract 5y2 – 64 – 11 from 6y2 + 2y + 5.
Your answer should be a polynomial in standard
form.
Answer:
[tex]y^2 + 2y + 80[/tex]
Step-by-step explanation:
[tex]6y^2 + 2y + 5 - (5y^2 - 64 - 11)[/tex]
[tex]6y^2 + 2y + 5 - 5y^2 + 64 + 11[/tex] [pay attention to the signs :)
[tex]y^2 + 2y + 80[/tex]
Lucy is 15 years old and has $1000, she invests in a CD paying 8% interest. How many times will her money double by the time she is 60?
Answer:
5
Step-by-step explanation:
(1 + i ) ^45 i = interest in decimal 45 = years
(1.08)^45 = ~~ 32
when she is 65 it will be worth 32 000
so it doubles 5 times (1000 2000 4000 8000 16000 32000)
On a standardized exam, the scores are normally distributed with a mean of 450 and a standard deviation of 25. Find the z-score of a person who scored 470 on the exam.
A Z-score helps us to understand how far is the data from the mean. The z-score of a person who scored 470 on the exam is 0.8.
What is Z-score?A Z-score helps us to understand how far is the data from the mean. It is a measure of how many times the data is above or below the mean. It is given by the formula,
[tex]Z = \dfrac{X- \mu}{\sigma}[/tex]
Where Z is the Z-score,
X is the data point,
μ is the mean and σ is the standard variable.
Given the mean is 450, while the standard deviation is 25, therefore, the value of the z-score can be written as,
[tex]Z = \dfrac{X- \mu}{\sigma}\\\\Z(X=470) = \dfrac{470- 450}{25} = 0.8[/tex]
Hence, the z-score of a person who scored 470 on the exam is 0.8.
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A bag with 8 marbles has 4 yellow marbles, 3 blue marbles, and 1 red marbles. What is the probabillity that it chosen at random and is yellow?
Answer:
1/2 = 0.5 = 50%
Step-by-step explanation:
Given:
Yellow marbles = 4Blue marbles = 3Red marbles = 1Total marbles = 8[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
[tex]\implies \sf P(yellow) = \dfrac{4}{8}=\dfrac12[/tex]
This can also be written as 0.5 or 50%
Probability of yellow:-
P(Y):-
4/81/20.5What are the dimensions of the large rectangle and the small rectangle?
Answer:
there is no picture to give an answer
Answer:
I need the picture to answer the question...
Step-by-step explanation:
Help help math math maths
Answer: X = 7
Step-by-step explanation:
1) 20 / 5 = 4
2) X - 2 = 5
3) 7 - 2 = 5
4) 4 x 5= 20
6) 20 / 5 = 4
7) X = 7
Me sucking at math needs help again
10 Points
Answer:
1 is alternate exterior
2 is none of these
3 and 5 are corresponding
4 is alternate interior
Step-by-step explanation:
find the measures of the missing angles
Answer:
I cannot see the attachment
Step-by-step explanation:
Calculate the interest rate for an account that was
compounded semi-annually, had an initial deposit of
$9,000 and was worth $13,373.53 after 10 years.
Answer:
Intrest rate is 3645%
20(36.45%) = $4374
Step-by-step explanation:
Semi-annualy = 6 months
Start: $9,000
After 10-years (120 months): $13,373.53
Since it's gaining money every 6 months, it gains money over 20 months.
(120/6 = 20)
After removing the starting cost, it gains $4,373.53 over 20 months.
(13,373.53 - 9,000 = 4,373.53)
$4,373.53 spread out over 20 months equals around $218.68 every 6 months.
(4,373.53 ÷ 20 = 218.6765)
(218.6765 ≈ 218.68)
$218.68 over 6 months equals about $36.45 every month
(218.68 ÷ 6 = 36.44666)
(36.4666 ≈ 36.45)
The intrest rate is 3645%
(3645% ÷ 100% = 36.45)
SOLVE THE EQUATION and explain YOUR ANSWER
Using the given quadratic function, it is found that:
a) The vertex is (-2.5, -15.5).
b) The y-intercept is of -3.
c) The solutions are x = -0.28, x = 5.28.
What is the quadratic function?It is modeled by:
f(x) = 2x² - 10x - 3.
Which means that the coefficients are a = 2, b = -10, c = -3.
What is the vertex of the function?It is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex]
[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]
Hence:
[tex]x_v = -\frac{-10}{4} = -2.5[/tex]
[tex]y_v = -\frac{(-10)^2 - 4(2)(-3)}{8} = -15.5[/tex]
The vertex is (-2.5, -15.5).
What is the y-intercept of the equation?It is the value of coefficient c, hence it is of -3.
What are the solutions?[tex]\Delta = b^2 - 4ac = (-10)^2 - 4(2)(-3) = 124[/tex]
[tex]x_1 = \frac{10 + \sqrt{124}}{4} = 5.28[/tex]
[tex]x_2 = \frac{10 - \sqrt{124}}{4} = -0.28[/tex]
The solutions are x = -0.28, x = 5.28.
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Help I have a d in this class
2. Elana's Family. Elana's Family.
if i have 2489 friends and 72% of those friends want burgers, and 25% of the 72% want chips too, how many want chios
Answer:
448.02
Step-by-step explanation:
72% of 2489 is 1,792.08
25% of 1,792.08 is 448.02
Write an equation for the translation of "left 7 units
Y=|x|
i need the answer to this lol
(3×1/2) + (6×3/4) + (3×1) + 1 1/4 +1 1/2=
Help help help math math
[tex] \frac{2 |x - 3| }{5} = 6 \\ [/tex]
[tex]5 \times \frac{2 |x - 3| }{5} = 5 \times 6 \\ [/tex]
[tex]2 |x - 3| = 30[/tex]
[tex] \frac{2 |x - 3| }{2} = \frac{30}{2} \\ [/tex]
[tex] |x - 3| = 15[/tex]
[tex]x - 3 = 15[/tex]
[tex]x - 3 + 3 = 15 + 3[/tex]
[tex]x = 18[/tex]
OR[tex]x - 3 = - 15[/tex]
[tex]x - 3 + 3 = - 15 + 3[/tex]
[tex]x = - 12[/tex]