Eborah finds that the theoretical probability of flipping "heads" on a fair coin was 50%. After she flipped the fair coin 100 times, she calculated that she flipped "heads" 45 times. What is the percent difference in theoretical and experimental probability?
Answer:
5%
Step-by-step explanation:
Given that:
Theoretical probability = 50%
The experimental probability = number of desired outcome / number of trials
Hence, experimental probability = 45 / 100 = 0.45
0.45 = 0.45 * 100% = 45%
Percentage difference in theoretical and experimental probability :
Theoretical - experimental
50% - 45% = 5%
If KJ=4 and KM= 2, find ML
Answer:
6
Step-by-step explanation:
(whole secant) * (external part) = (tangent)^2
(KL) * (KM) = KJ^2
(KM+ ML) * KM = KJ^2
(2+ ML) * 2 = 4^2
(2+ ML) * 2 =16
Divide each side by 2
(2+ ML) = 8
Subtract 2 from each side
ML = 6
Find the equation of the line shown.
please I need it soon as possible
Answer:
Y=2x+0.5
Step-by-step explanation:
The gradient is 2/1=2x
The y-intercept looks to be around 0.5
Answer:
y = [tex]\frac{1}{2}[/tex] x + [tex]\frac{1}{2}[/tex]
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 )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (1, 1) ← 2 points on the line
m = [tex]\frac{1-0}{1-(-1)}[/tex] = [tex]\frac{1}{1+1}[/tex] = [tex]\frac{1}{2}[/tex] , then
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (1, 1 ) , then
1 = [tex]\frac{1}{2}[/tex] + c ⇒ c = 1 - [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{2}[/tex]
y = [tex]\frac{1}{2}[/tex] x + [tex]\frac{1}{2}[/tex] ← equation of line
(PLEASE HELP 30 POINTS)
Select all the correct answers.
Liam owns some rectangular plots of land. All of the plots are the same length, x, and the width of each plot is 5 yards less than the length. The
total number of plots Liam owns is 20 more than the length of a plot. If the total area of all the plots Liam owns is 2,688 square yards, which
statements about the length of each plot are true?
The equation x3 - 15x2 - 100x - 2,688 0 can be used to find the length of each plot.
The equation x3 + 25x2 + 100% -2,688 = 0 can be used to find the length of each plot.
o o o o o
The equation x3 + 15x2 - 100x - 2,688 = 0 can be used to find the length of each plot.
The length of each plot is 12 yards.
The length of each plot is 8 yards.
Answer:
We have to:
"All of the plots are the same length, x"
L = x
"and the width of each plot is 5 yards less than the length"
W = x-5
"The total number of plots Liam owns is 20 more than the length of a plot"
20 + x
"the total area of all the plots Liam owns is 2,688 square yards"
A = (20 + x) * (x) * (x-5)
A = (20x - 100 + x ^ 2 -5x) * (x)
A = (x ^ 2 + 15x - 100) * (x)
2688 = (x ^ 3 + 15x ^ 2 - 100x)
x ^ 3 + 15x ^ 2 - 100x = 2688
x ^ 3 + 15x ^ 2 - 100x - 2688 = 0
Answer:
*** The equation x3 + 15x2 - 100x - 2.688 = 0 can be used to find the length of each plot.
Answer:x^3+15x^2-100x-2,688=0
Step-by-step explanation:
Five athletes are in a 100k race. How many different ways can they finish based on their order?
Answer:
120 different ways
Step-by-step explanation:
The first person can be 5 different ways
Now there are 4 people left
The second person can be 4 different ways
And so on
5*4*3*2*1
120 different ways
Find the area of the shaded region. Leave your answer in terms of pi.
Answer:
[tex]\displaystyle A_\text{shaded}=18-\frac{9}{2}\pi \text{ units}^2[/tex]
Step-by-step explanation:
First, find the area of the rectangle:
[tex]A_\text{rect}=9(3)=18\text{ units}^2[/tex]
In order to find the area of the shaded region, we can subtract the areas of the two sectors from the total area of the rectangle.
Find the area of the sectors. We can use the sector formula:
[tex]\displaystyle A=\pi r^2\cdot \frac{\theta}{360^\circ}[/tex]
The left sector has a radius of three units and an angle of 90°. Hence, its area is:
[tex]\displaystyle A_\text{L}=\pi (3)^2\cdot \frac{90}{360}=9\pi\cdot \frac{1}{4}=\frac{9}{4}\pi[/tex]
The right sector is identical to the left sector. So, the total area of the two sectors is:
[tex]\displaystyle A_{\text{T}}=\frac{9}{4}\pi +\frac{9}{4}\pi =\frac{9}{2}\pi[/tex]
Hence, the area of the shaded region is:
[tex]\displaystyle A_\text{shaded}=18-\frac{9}{2}\pi \text{ units}^2[/tex]
PLEASE HELP 25 POINTS
Evaluate 4(3 - 1)^2
O A. 16
O B. 128
O C. 64
O D. 32
The graph is a line that passes trough the coordinates (2, 11) and (8, 14). Which is an equation in terms of x and y for this function?
A. y = 1/2 x + 10
B. y = 2/3 x + 9
C. y = 3/2 x + 8
D. y = 2x + 7
Answer:A
Step-by-step explanation:
m=(14-11)/(8-2)
m=3/6
m=1/2
y = 1/2x+b substitute one of the points
11=1/2(2)+b
11=1 + b
b=10
y = 1/2x+10
simpifly fully, does anyone know the answer.
Answer:
Step-by-step explanation:
Note : In multiplication if the bases are same u can add their exponent while in division if the bases are same u can subtract their exponent.
Hope this helps u !!
Can someone help me ASAP please and thank you
Answer:
65 + 30x.
Step-by-step explanation:
The $65 is a one-time fee for when you first purchase the instrument. The $30 is every month you rent it, and x = the months you rent it.
Therefore, to find the whole cost over time, you would do
65 (first month) + 30x (how much you'll spend over the time you rent the instrument).
Based on past experience, the main printer in a university computer centre is operating properly 90% of the time. Suppose inspections are made at 10 randomly selected times. A) What is the probability that the main printer is operating properly for exactly 9 inspections. B) What is the probability that the main printer is operating properly for at least 3 inspections? C) What is the expected number of inspections in which the main printer is operating properly?
Answer:
a) 38.74% probability that the main printer is operating properly for exactly 9 inspections.
b) Approximately 100% probability that the main printer is operating properly for at least 3 inspections.
c) The expected number of inspections in which the main printer is operating properly is 9.
Step-by-step explanation:
For each inspection, there are only two possible outcomes. Either it is operating correctly, or it is not. The probability of the printer operating correctly for an inspection is independent of any other inspection, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Based on past experience, the main printer in a university computer centre is operating properly 90% of the time.
This means that [tex]p = 0.9[/tex]
Suppose inspections are made at 10 randomly selected times.
This means that [tex]n = 10[/tex]
A) What is the probability that the main printer is operating properly for exactly 9 inspections.
This is [tex]P(X = 9)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 9) = C_{10,9}.(0.9)^{9}.(0.1)^{1} = 0.3874[/tex]
38.74% probability that the main printer is operating properly for exactly 9 inspections.
B) What is the probability that the main printer is operating properly for at least 3 inspections?
This is:
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.9)^{0}.(0.1)^{10} \approx 0[/tex]
[tex]P(X = 1) = C_{10,1}.(0.9)^{1}.(0.1)^{9} \approx 0[/tex]
[tex]P(X = 2) = C_{10,2}.(0.9)^{2}.(0.1)^{8} \approx 0[/tex]
Thus:
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0 + 0 + 0 = 0[/tex]
Then:
[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0 = 1[/tex]
Approximately 100% probability that the main printer is operating properly for at least 3 inspections.
C) What is the expected number of inspections in which the main printer is operating properly?
The expected value for the binomial distribution is given by:
[tex]E(X) = np[/tex]
In this question:
[tex]E(X) = 10(0.9) = 9[/tex]
What is the measure of x?
Answer:
x=4
Step-by-step explanation:
(whole secant) x (external part) = (tangent)^2
(x+5) *x = 6^2
x^2 +5x = 36
Subtract 36 from each side
x^2 +5x - 36 = 0
Factor
( x-4) (x+9) = 0
Using the zero product property
x-4 = 0 x+9 =0
x = 4 x=-9
Cannot be negative since that is negative length
x=4
Plz help me solve this problem
The answer is 19 they worked it out right above the question.
Answer:
19
Step-by-step explanation:
3(x+6) = 5(x-4)
Distribute
3x+18 = 5x-20
Subtract 3x from each side
18 = 2x-20
Add 20 to each side
38 = 2x
Divide by 2
19 = x
The solution is 19
If my weekly pocket money goes up by 50% each year . How much will I be getting a week after 3 years if I start on £1 a week ?
Answer: £3.38
Step-by-step explanation:
In the first year, the pocket money goes up by:
= 1 + (1 * 50%)
= £1.50
In the second year:
= 1.50 + (1.50 * 50%)
= £2.25
In the third year:
= 2.25 * ( 2.25 * 50%)
= £3.38
Need to make a rectangular pen for pigs that will enclose a total area of 169 square feet. What is the least amount of fencing that will be needed?
Answer:
The least amount of fencing needed for the rectangular pen is 72.19 feet.
Step-by-step explanation:
The area and perimeter equations of the pen are, respectively:
[tex]p = 2\cdot (x + y)[/tex] (1)
[tex]A = x\cdot y[/tex] (2)
Where:
[tex]p[/tex] - Perimeter, in feet.
[tex]A[/tex] - Area, in square feet.
[tex]x[/tex] - Width, in feet.
[tex]y[/tex] - Length, in feet.
Let suppose that total area is known and perimeter must be minimum, then we have a system of two equations with two variables, which is solvable:
From (2):
[tex]y = \frac{A}{x}[/tex]
(2) in (1):
[tex]p = 2\cdot \left(x + \frac{A}{x}\right)[/tex]
And the first and second derivatives of the expression are, respectively:
[tex]p' = 2\cdot \left(1 -\frac{A}{x^{2}} \right)[/tex] (3)
[tex]p'' = \frac{4\cdot A}{x^{3}}[/tex] (4)
Then, we perform the First and Second Derivative Test to the function:
First Derivative Test
[tex]2\cdot \left(x - \frac{A}{x^{2}} \right) = 0[/tex]
[tex]2\cdot \left(\frac{x^{3}-A}{x^{2}} \right) = 0[/tex]
[tex]x^{3} - A = 0[/tex]
Given that dimensions of the rectangular pen must positive nonzero variables:
[tex]x^{3} = A[/tex]
[tex]x = \sqrt[3]{A}[/tex]
Second Derivative Test
[tex]p'' = 4[/tex]
In a nutshell, the critical value for the width of the pen leads to a minimum perimeter.
If we know that [tex]A = 169\,ft^{2}[/tex], then the value of the perimeter of the rectangular pen is:
[tex]x = \sqrt[3]{169\,ft^{2}}[/tex]
[tex]x \approx 5.529\,ft[/tex]
By (2):
[tex]y = \frac{A}{x}[/tex]
[tex]y = \frac{169\,ft^{2}}{5.529\,ft}[/tex]
[tex]y = 30.566\,ft[/tex]
Lastly, by (1):
[tex]p = 2\cdot (5.529\,ft + 30.566\,ft)[/tex]
[tex]p = 72.19\,ft[/tex]
The least amount of fencing needed for the rectangular pen is 72.19 feet.
If (x) = 3x - 1 and g(x) = x + 2, find (f - g)(x).
Answer:
2x-3
Step-by-step explanation:
f (x) = 3x - 1
g(x) = x + 2
(f - g)(x) = 3x-1 - ( x+2)
Distribute the minus sign
= 3x-1 -x-2
Combine like terms
= 3x-x-1-2
= 2x-3
(f - g )( x ) = 2 x - 3
step-by-step explanation:f ( x ) = 3x - 1
g ( x ) = x + 2
(f - g )(x ) = ( 3x - 1 ) - ( x + 2. )remove unnecessary parantheses
3 x - 1 - x - 2collect like terms
3x - x - 1 -22 x -3what is the measure of the supplement of a 65.4 angle
Answer:
65 degree angle but when straight 180 degree angle
Step-by-step explanation:
sry if wrong :)
If I had 2 500 apples and sold 200 how much apples would I have left
Answer:
2300 apples
Step-by-step explanation:
2500 - 200 = 2300
Answer:
2300
Step-by-step explanation:
2500 - 200 = 2300
Note: "have left" means the answer after subtraction.
A researcher selects a sample of participants to test for differences in employment rates among part-time and full-time teachers. Because there are many more women in teaching jobs than men, the researcher selected more women than men for her study to ensure that it represented the actual distribution of men and women teachers in the job sector. Which type of quota sampling was used in this example
Answer: proportionate
Step-by-step explanation:
Proportional quota sampling is when the total number of people that are to be surveyed are decided in advance. This form of sampling is usually used in opinion polls and surveys.
Since due to the fact that there are many more women in teaching jobs than men, the researcher selected more women than men for her study to ensure that it represented the actual distribution of men and women teachers in the job, then this was decided in advance and indicates the proportionate quota sampling.
Determine the dot product between the two vectors. u=< 5,3 > and v =< 12,4 >
Answer:
v . u = < v1 , v2 > . <u1 , u2> = v1 u1 + v2 u2
Step-by-step explanation:
find the y-intercept of the line that has a slope of -3 and passes through (9,0)
9514 1404 393
Answer:
27
Step-by-step explanation:
For point (x, y) and slope m, the y-intercept can be found from the equation ...
b = y -mx
b = 0 -(-3)(9) = 27
The y-intercept is +27. The corresponding ordered pair is (0, 27).
A hiker is standing 40 feet away from a tree that is 50 feet tall.
What is the angle of elevation from the hikers foot to the top of the tree??
HELP ME PLEASE ITS URGENT
Answer:
87.9°
Step-by-step explanation:
arctan(50/40)=87.9°
Is the Function exponential?
Answer:
y = 4x+ 5 is the equation that describes the data...
that is a linear equation ... the slope is 4 thus "the y value increases 4 for every 1 unit increase in x"
Step-by-step explanation:
find the solutions to the equation below check all the apply 5x^2+7x-5=0
Answer:
e and f
Step-by-step explanation:
there is a great app to use called algebrator it helps me everyday for things like this <3
HELP ASAP!! ILL MARK BRAINLIEST!! Anna must solve this equation.
(x^2)/4=x
Which three steps could Anna use to correctly solve the equation? Select from the drop-down menus to order the steps used to solve the equation.
Answer:
question 1:
step #1:divide both sides by x
step #2:multiply both sides by 4
step #3: plug it into equation
Step-by-step explanation:
question 1:
step #1: divide both sides by x
you get x/4 = 1
step #2:multiply both sides by 4
you get x = 4
step #3: plug it into equation
4 squared/4 = 4
Help its due rn!!!!!!!!!! Please
Answer:
D po
Step-by-step explanation:
yan po!sana nakatulong po
What is the original price of an item cost if the tax is 9.25% and the discount is 25% and the new price after discount and tax is $62.28?
Answer: $ 91.50.
Step-by-step explanation:
Let x be the original price.
Since discount is applied before tax.
New price = (Original price - Discount)-Tax rate (Original price - Discount)
, where Discount = Discount rate x Original price.
Substituting values, we get
[tex]62.28=(x-0.25x)-0.0925(x-0.25x)[/tex]
[tex]62.28=(0.75x)-0.0925(0.75x)[/tex]
[tex]62.28=0.75x-0.069375x[/tex]
[tex]62.28=0.680625x[/tex]
[tex]x=\frac{62.28}{0.680625}[/tex]
[tex]x=91.50[/tex]
Hence, the original price was $ 91.50.
The Titanus beetle can measure 16710 centimeters in length, and the Giant Weta beetle can measure 8510 centimeters in length. How much longer is the Titanus than the Giant Weta?
Answer:
The answer you're looking for is 8,200cm
Step-by-step explanation:
Ramiro tiene que reemplazar un vidrio roto de su casa, que tiene forma rectangular y mide 3,23m y 2,55m. Cuántos metros cuadrados de vidrio tiene que comprar
Answer:
8,24 metros cuadrados de vidrio
Step-by-step explanation:
Área de un rectángulo = Largo × Ancho
De la pregunta anterior
Longitud = 3,23 m
Ancho = 2,55 m
Área del rectángulo = 3,23 m × 2,55 m
= 8.2365 m²
Aproximadamente = 8,24 m²
Por tanto, Ramiro tiene que comprar 8,24 metros cuadrados de vidrio
Solve the simultaneous equations
2x+4y=1
3x-5y=7
Answer:
Step-by-step explanation:
Step 1: Add -4y to both sides.
2x+4y+−4y=1+−4y
2x=−4y+1
Step 2: Divide both sides by 2.
2x
2
=
−4y+1
2
x=−2y+
1
2
Step 1: Add 5y to both sides.
3x−5y+5y=7+5y
3x=5y+7
Step 2: Divide both sides by 3.
3x
3
=
5y+7
3
x=
5
3
y+
7
3
