Answer:
[tex]\theta = \frac{4\pi}{3}[/tex]
Step-by-step explanation:
Given
Let A represent the Length of Arc CD and C, represents the circumference
[tex]A = \frac{2}{3} C[/tex]
Required
Find the central angle (in radians)
The length of arc CD in radians is as follows;
[tex]A = r\theta[/tex]
Where r is the radius and [tex]\theta[/tex] is the measure of central angle
The circumference of a circle is calculated as thus;
[tex]C = 2\pi r[/tex]
From the question, it was stated that the arc length is 2-3rd of the circumference;
This means that
[tex]A = \frac{2}{3} C[/tex]
Substitute [tex]2\pi r[/tex] for C and [tex]r\theta[/tex] for A
[tex]A = \frac{2}{3} C[/tex] becomes
[tex]r\theta = \frac{2}{3} * 2\pi r[/tex]
[tex]r\theta = \frac{4\pi r}{3}[/tex]
Divide both sides by r
[tex]\frac{r\theta}{r} = \frac{4\pi r}{3}/r[/tex]
[tex]\frac{r\theta}{r} = \frac{4\pi r}{3} * \frac{1}{r}[/tex]
[tex]\theta = \frac{4\pi r}{3} * \frac{1}{r}[/tex]
[tex]\theta = \frac{4\pi}{3}[/tex]
Hence, the measure of the central angle; [tex]\theta = \frac{4\pi}{3}[/tex]
Answer:
The answer is C on Edge 2020
Step-by-step explanation:
I did the assignment
Suppose that 45% of students in a college have a smart phone. If you select three students at random, what is the probability that all three have a smart phone? Give your answer as a decimal (to at least 3 places) or fraction
Answer:
[tex] P(X=3)[/tex]
And we can use the probability mass function and we got:
[tex]P(X=3)=(3C3)(0.45)^3 (1-0.45)^{3-3}=0.091[/tex]
Then the probability that all three have a smart phone is 0.091
Step-by-step explanation:
Let X the random variable of interest "number of students with smartphone", on this case we now that:
[tex]X \sim Binom(n=3, p=0452)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find this probability:
[tex] P(X=3)[/tex]
And we can use the probability mass function and we got:
[tex]P(X=3)=(3C3)(0.45)^3 (1-0.45)^{3-3}=0.091[/tex]
Then the probability that all three have a smart phone is 0.091
Which of the following statements are equivalent to the statement "Every integer has an additive inverse" NOTE: (The additive inverse of a number x is the number that, when added to x, yields zero. Example: the additive inverse of 5 is -5, since 5+-5 = 0) Integers are{ ... -3, -2,-1,0, 1, 2, 3, ...} All integers have additive inverses. A. There exists a number x such that x is the additive inverse of all integers.B. All integers have additive inverses.C. If x is an integer, then x has an additive inverse.D. Given an integer x, there exists a y such that y is the additive inverse of x.E. If x has an additive inverse, then x is an integer.
Answer:
B, C and D
Step-by-step explanation:
Given:
Statement: "Every integer has an additive inverse"
To find: statement that is equivalent to the given statement
Solution:
For any integer x, if [tex]x+y=0[/tex] then y is the additive inverse of x.
Here, 0 is the additive identity.
Statements ''All integers have additive inverses '', '' If x is an integer, then x has an additive inverse'' and ''Given an integer x, there exists a y such that y is the additive inverse of x'' are equivalent to the given statement "Every integer has an additive inverse".
Does anybody know why these are wrong?
Answer:
They aren't wrong. The program is.
Step-by-step explanation:
The numbers you entered are the answers that matches the correct answers. It is a program error.
There are 11 students in our Science class left to give their presentations. Today we will have time for 6 presentations. How many different ways can the teacher choose the presenters?
Answer:
He has 2,772 ways
Step-by-step explanation:
Hello,
the teacher has to choose 6 students and there are 11 students in total.
When he chooses the first student he has 11 choices
if he has to choose 1 students he has 11 ways to do it
then for the second one he has 11-1=10 choices
if he has to choose 2 students he has (11*10)/2 ways to do it (we do not count the duplicate - for instance if he chooses Steve and then Nils or Nils and then Steve this is only one group (Steve, Nils) we do not care of the order)
Then for the third student he has 10-1=9 choices
if he has to choose 3 students he has (11*10*9)/(2*3) ways to do it (we do not take into account the order of ppl in the group)
and so on and so forth
...
if he has to choose 6 students he has (11*10*9*8*7*6)/(2*3*4*5)
so he has 2,772 ways
Answer:
C. 462 is correct. I did the test.
Step-by-step explanation:
I need help ASAP thank you
Answer:
Volume: 1080
Surface area: 654
Step-by-step explanation:
Part A:
How to solve surface Area: 2×(9×15 + 9×8 + 15×8)
How to solve volume: 9x15x8
Part B:
Surface Area
Part C:
Volume
Hope this helps
Dialiting a triangle changes the angles and side length of the triangle true or false
Answer:
False
Step-by-step explanation:
Dilation changes the side lengths, but not the angles. The given statement is FALSE.
Zachary used the calculations shown to find how much he would spend on 16 ounces of pistachios. 6 ounces of pistachios cost $7.50 StartFraction 7 dollars and 50 cents Over 6 ounces EndFraction = StartFraction dollar-sign question mark Over 1-ounce EndFraction Unit price = $0.80 per ounce What was his first error?
A. The price per ounce should have been $45.00 per ounce.
B. The price per ounce should have been $1.25 per ounce.
C. The final cost should have been $20.00.
D. The final cost should have been $16.80.
Answer:
The price per ounce should have been 1.25 per ounce
Step-by-step explanation:
The price per ounce should have been 1.25 per ounce
(found it online)
XD - don't delete/report!
Brainleist!Answer:
1.25
Step-by-step explanation:
The driver of a car traveling at 42 ft/sec suddenly applies the brakes. The position of the car is s equals 42 t minus 3 t squared comma t seconds after the driver applies the brakes. How far does the car go before coming to a stop?
Answer:
after 7 seconds the driver applied the brakes to stop the car.
Step-by-step explanation:
Given:
The position of the car s(t)=[tex]42t-3t^2[/tex]
∴Speed of the car =[tex]\frac{ds}{dt}=\frac{d(42t-3t^2)}{dt}=42-6t[/tex]
When car stopped the speed of car=0
[tex]\Rightarrow42-6t=0\\\Rightarrow6t=42\\\Rightarrow\ t=7[/tex]
Therefore, after 7 seconds the driver applied the brakes to stop the car.
Which shows the most reasonable way to estimate 3 4/7 (-2 1/12) using compatible fractions
Answer:
B). 3 1/2(-2) = -7
Step-by-step explanation:
Let's evaluate the expression so as to be able to get the right estimate.
3 4/7 (-2 1/12)
=3 4/7 (-25/12)
= 25/7 * -25/12
= 25/7 * -25/12
= -625/84
= -7 37/84
Approximately it's equal to ,-7
Answer:
b
Step-by-step explanation:
got it right on edge
Three hunters X, Y and Z aim at a bird on top of a tree. Their individual probabilities of killing the bird are 3/5, 2/3 and 5/6 respectively.
Find the probability that
i. Only X and Y kill the bird
ii. Only two of them kill the bird
iii. Only Z kill the bird
iv. Only one of them kill the bird
v. None of them kill the bird
vi. All of them kill the bird
Answer:
i. Only X and Y kill the bird = 2/5
ii. Only two of them kill the bird= 0.11
iii. Only Z kill the bird= 5/6
iv. Only one of them kill the bird= 1/3
v. None of them kill the bird= 0
vi. All of them kill the bird= 1
Step-by-step explanation:
Probability of x= 3/5
Probability of y = 2/3
Probability of z = 5/6
i. Only X and Y kill the bird
= 3/5 * 2/3
= 2/5
ii. Only two of them kill the bird
=Either x and y or x and z or y and z
= 2/5 or 1/2 or 5/9
= 0.111
iii. Only Z kill the bird
= 5/6
iv. Only one of them kill the bird
= 3/5 or 2/3 or 5/6
= 1/3
v. None of them kill the bird
0
vi. All of them kill the bird
1
Estimate the area of the circle equal three decimal 14 round to the nearest hundredth if necessary9
Answer:
49π m² or 153.94 m²
Step-by-step explanation:
Area of a circle: A = πr²
We are given r as 7, so simply plug it in
A = π(7)^2
A = 49π m²
An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 181 lb. The new population of pilots has normally distributed weights with a mean of 140 lb and a standard deviation of 27.3 lb.
Required:
a. If a pilot is randomly selected, find the probability that his weight is between 150 lb and 201 lb. The probability is approximately__________.
b. If 39 different pilots are randomly selected, find the probability that their mean weight is between 150 lb and 201 lb. The probability is approximately__________.
c. When redesigning the ejection seat which probability is more relevant
Answer:
(a) The probability that his weight is between 150 lb and 201 lb is 0.3428.
(b) The probability that the sample mean weight is between 150 lb and 201 lb is 0.011.
(c) When redesigning the ejection seat, the probability of a single pilot is more relevant as discussed in part (a).
Step-by-step explanation:
We are given that the seat was designed for pilots weighing between 130 lb and 181 lb.
The new population of pilots has normally distributed weights with a mean of 140 lb and a standard deviation of 27.3 lb.
Let [tex]\bar X[/tex] = sample mean price for a movie in the United States
SO, X ~ Normal([tex]\mu=140,\sigma^{2} =27.3^{2}[/tex])
(a) The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{ X-\mu}{\sigma}} }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean weights = 140 lb
[tex]\sigma[/tex] = standard deviation = 27.3 lb
Now, the probability that his weight is between 150 lb and 201 lb is given by = P(150 lb < X < 201 lb) = P(X < 201 lb) - P(X [tex]\leq[/tex] 150 lb)
P(X < 201 lb) = P( [tex]\frac{ X-\mu}{\sigma}} }[/tex] < [tex]\frac{ 201-140}{27.3}} }[/tex] ) = P(Z < 2.23) = 0.9871
P(X [tex]\leq[/tex] 150 lb) = P( [tex]\frac{ X-\mu}{\sigma}} }[/tex] [tex]\leq[/tex] [tex]\frac{ 150-140}{27.3}} }[/tex] ) = P(Z [tex]\leq[/tex] 0.37) = 0.6443
The above probability is calculated by looking at the value of x = 2.23 and x = 0.37 in the z table which has an area of 0.9871 and 0.6443.
Therefore, P(150 lb < X < 201 lb) = 0.9871 - 0.6443 = 0.3428.
(b) Let [tex]\bar X[/tex] = sample mean weight
The z-score probability distribution for the sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean weight = 140 lb
[tex]\sigma[/tex] = standard deviation = 27.3 lb
n = sample of pilots = 39
Now, the probability that the sample mean weight is between 150 lb and 201 lb is given by = P(150 lb < [tex]\bar X[/tex] < 201 lb) = P([tex]\bar X[/tex] < 201 lb) - P([tex]\bar X[/tex] [tex]\leq[/tex] 150 lb)
P([tex]\bar X[/tex] < 201 lb) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{201-140}{\frac{2.73}\sqrt{39} } }[/tex] ) = P(Z < 13.95) = 0.9999
P([tex]\bar X[/tex] [tex]\leq[/tex] 150 lb) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{150-140}{\frac{2.73}\sqrt{39} } }[/tex] ) = P(Z [tex]\leq[/tex] 2.29) = 0.9889
Therefore, P(150 lb < [tex]\bar X[/tex] < 201 lb) = 0.9999 - 0.9889 = 0.011.
(c) When redesigning the ejection seat, the probability of a single pilot is more relevant as discussed in part (a) because it is important to look after the safety of each and every pilot not of a particular sample.
write (n^3)^2 without exponets
Step-by-step explanation:
[tex]( {n}^{3} )^{2} = {n}^{6} = n \times n \times n \times n \times n \times n [/tex]
Answer:
n x n x n x n x n x n
Step-by-step explanation:
(n^3)^2 = n^6 = n x n x n x n x n x n
100 pts A quality assurance check is 90% accurate for non-defective devices and 96% accurate for defective devices. Of the devices checked, 18% are defective. What is the probability of an incorrect conclusion? Round your answer to the nearest tenth of a percent.'
90% of 18% = .9*.18 = 0.162 = 16.2%
So 18 - 16.2 = 1.8 = 18% of them labeled as not defective
are actually defective.
Please mark me brainliest!
Answer:
1.8%
Step-by-step explanation:
90% × 18% = 16.2%
18% - 16.2% = 1.8%
1.8% is the probability of an incorrect conclusion.
Which of the following is NOT a solution to 2x+3y=12? A. (5,-3) B. (9,-2) C. (0,4) D. (6,0)
Answer:
B
Step-by-step explanation
A red car is driving along the road in the direction of the police car and is 130 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 75 feet per second. How fast is the red car actually traveling along the road
Complete question:
A police car is located 50 feet to the side of a straight road. A red car is driving along the road in the direction of the police car and is 130 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 75 feet per second. How fast is the red car actually traveling along the road.
Answer:
The red car is traveling along the road at 80.356 ft/s
Step-by-step explanation:
Given
Police car is 50 feet side off the road
Red car is 130 feet up the road
Distance between them is decreasing at the rate of 75 feet per sec
Let x be how far the police is off the road.
Let y be how far the red car is up the road.
Let h be the distance between the police and the red car.
This forms a right triangle so we can use the Pythagorean theorem, to solve for h
h² = x² + y²
h² = 50² + 130²
h² = 19400
h = √19400
h = 139.284 ft
Again;
Let dx/dt be how fast the police is traveling toward the road.
Let dy/dt be how fast the red car is traveling along the road.
Let dh/dt be how fast the distance between the police and the car is decreasing.
Recall that, h² = x² + y² (now differentiate with respect to time, t)
2h(dh/dt) = 2x(dx/dt) + 2y(dy/dt)
divide through by 2
h(dh/dt) = x(dx/dt) + y(dy/dt)
since the police car is not, dx/dt = 0
and dy/dt is the how fast is the red car actually traveling along the road
139.284(75) = 50(0) + 130(dy/dt)
10446.3 = 0 + 130(dy/dt)
dy/dt = 10446.3 / 130
dy/dt = 80.356 ft/s
Therefore, the red car is traveling along the road at 80.356 ft/s
Water has a density of 1.00g/cm^3 per cubic centimeter. What is the mass of half a liter of water?
Answer:
The mass of half a liter of water is 500g, that is, 0.5kg.
Step-by-step explanation:
Density is mass divided by the volume, that is:
[tex]d = \frac{m}{v}[/tex]
Here, we have to be careful. Since the density is in grams per cm³, m has to be in grams and v in cm³.
We have that:
[tex]d = 1[/tex]
What is the mass of half a liter of water?
One liter is 1000 cm³.
So half a liter is 1000/2 = 500 cm³, which means that [tex]v = 500[/tex]
Then
[tex]d = \frac{m}{v}[/tex]
[tex]1 = \frac{m}{500}[/tex]
[tex]m = 500[/tex]
The mass of half a liter of water is 500g, that is, 0.5kg.
What is the measure of the third angle in the similar triangles below?
25
65
85
115
Answer:
65
Step-by-step explanation:
We know that,
The Sum of all angles of the triangle is 180°.
As given in the question,
Triangle PQR is similar to Triangle WXY
Therefore ,
Let the third angle be 'x'.
35° + 80° + x = 180°
115 + x = 180°
x = 180° - 115°
x = 65°.
Hence, 65° is the appropriate answer to the question.
I hope my answer helped!!
An employee earns a 25% commission rate on his sales. One day he earned $175. What was his amount of sales?
Answer:
sales = $700
Step-by-step explanation:
he earned commission of 175
this is 25% of sales
if 25% = 175
what about 100%
sales = (100*175)/25
sales = $700
Answer:700
Step-by-step explanation:
4. Factor the expression.
4b2 + 28b + 49
QA (2b + 7)2
OB (2b - 72
C (-2b + 7)2
OD 2(b - 7)2
Answer:
A. [tex](2b+7)^2[/tex]
Step-by-step explanation:
[tex]4b^2 +28b + 49\\=(2b)^2 + 2\times 2b\times 7 + (7)^2\\=(2b+7)^2[/tex]
Help meeeee and thank u so much god bless u haha
Answer:
[See Below]
Step-by-step explanation:
For Point Slope Form:Point slope form is: [tex]y-y_1=m(x-x_1)[/tex]
'm' is the slope
(x1, y1) is a coordinate point.
Slope:Slope is rise over run. [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
We are given the points (-1,5) and (3,-3).
[tex]\frac{-3-5}{3-(-1)}=\frac{-8}{4}= -2[/tex]
The slope of the line is -2.
I will use (-1,5) as the point:
[tex]y-y_1=m(x-x_1)\rightarrow\boxed{y-5=-2(x+1)}[/tex]
For Slope Intercept:Slope intercept is: [tex]y=mx+b[/tex]
'm' - Slope
'b' - y-intercept
We can use the point slope equation to convert it into slope intercept form:
[tex]y-5=-2(x+1)\\\\y-5=-2x-2\\\\y-5+5=-2x-2+5\\\\\boxed{y=-2x+3}[/tex]
For Standard Form:Standard form is [tex]Ax+By=C[/tex]
Using out slope intercept form equation:
[tex]y=-2x+3\\\\y+2x=-2x+2x+3\\\\1y+2x=3\\\\\boxed{2x+1y=3}[/tex]
Can some on help me on this question?
Answer:
x=10 and x-7 is the answer
Step-by-step explanation:
a)2x-7=13
2x=13+7
2x=20
x=20/2
x=10
b)3x+4=25
3x=25-4
3x=21
x=21/3
x=7
i hope it will help you
Answer:
a) [tex]x=10[/tex]
b) [tex]x=7[/tex]
Step-by-step explanation:
a)
2x-7=13
Add 7 to both sides
2x=20
Divide both sides by 2
x=10
b)
3x+4=25
Subtract 4 from both sides
3x=21
Divide both sides by 3
x=7
Jose contributes to an employer-sponsored 401(k) plan. For the first 6% of
Jose's salary, his employer matches 100% of his 401(k) contributions, and
from 6% to 12%, Jose's employer matches 50% of his 401(k) contributions,
Jose's salary is $50,000, and last year he contributed $6000 to his 401(k)
plan. What was the total amount that was contributed to his 401(k) last year?
O A. $10,500
B. $17,200
C. $14,500
D. $16,000
Answer:
(A)$10,500
Step-by-step explanation:
Joe contributed $6000 out of a salary of $50,000.
6% of $50,000=$3000
Since his employer matches 100% of his contributions for the first 6%:
The employer adds $3000.
For the other $3000, Jose's employer matches 50%.
Therefore, the employer adds:
50% X 3000=$1500
Total Contribution by Jose's Employer = $3000+1500=$4500
Therefore, the total amount that was contributed to Jose's account last year
=Joe's Contribution + Employer's Contribution
=6000+4500
=$10,500
The correct option is A.
The correct answer is $10,500.
Which of the following are equations for the line shown below? Check all that apply.
A. Y= x-2
B. Y-1=(x-3)
C. Y=x-2
D. Y+4=(x+2)
Answer: D. [tex]y+4=(x+2)[/tex]
Step-by-step explanation: Once you subtract [tex]4[/tex] from both sides, in order to solve for y (as the equation needs to be in the slope-intercept form, otherwise known as [tex]y=mx+b[/tex]), you end up with [tex]y=x-2[/tex], which is the right answer. It is the correct answer because the y-intecept shown in the equation matches what is on the graph, in addition to the fact that the slope is just [tex]x[/tex].
What is the answer?
Answer:
C. 2.75P
Step-by-step explanation:
The original value was P.
It increased by 275%. That means it increased by 275% of P.
275% of P = 2.75P
The increase in value is 2.75P.
Now we add the increase to the original value of P to find today's value.
2.75P + P = 3.75P
Answer: C. 2.75P
If you roll two fair six sided dice, what is the probability that the sum is 9 is higher
Answer:
Answer = 27.78%
Step-by-step explanation:
There are 10 outcomes with sum 9 or higher.
There the required probability is 10/36 = 5/18 = nearly 27.78% chances of getting a sum of 9 or higher on rolling two 6-sided dice.
idk if this is correct
The Venn diagram below is used for showing odd numbers and prime numbers.
Place the numbers 1, 2, 3, 4 and 5 in the Venn diagram.
Answer:
See attached
Step-by-step explanation:
Given the numbers 1,2,3,4 and 5
Odd Numbers =1, 3 and 5Prime Numbers = 2, 3 and 5Let O be the event that the number is Odd
Let E be the event that the number is Prime
Then the intersection of Odd and Prime Numbers: [tex]O \cap P =\{3,5\}[/tex]
Since 4 is neither odd nor prime, we place it outside of the two circles.
See the attached diagram for the required Venn diagram.
AABC is a right triangle. If AC = 4 and BC = 10, find AB. Leave your answer in simplest radical form.
Answer:
[tex] 2 \sqrt{21} is \: the \: ans[/tex]
Step-by-step explanation:
given;abc is a right angled triangle.
by takingr eference reference angle c
p=ab=? ,h=bc=10 ,b=ac=4.
by the Pythagoras relation we get;
[tex]p = \sqrt{h {}^{2} - b {}^{2} } [/tex]
so ,p=
[tex] \sqrt{10 {}^{2} - 4 {?}^{2} } [/tex]
==
=
[tex] = 2 \sqrt{21} [/tex]
is ans
The National Association of Realtors estimates that 23% of all homes purchased in 2004 were consideredinvestment properties. If a sample of 800 homes sold in 2004 is obtained what is the probability that between175 and 200 homes are going to be used as investment property
Answer:
0.9099
Step-by-step explanation:
1) =
=
200
800
= .25
2) Identify = . = .23
3) Find the z-value.
=
−
(1−)
=
.25−.23
.23(1−.23)
800
= 1.34
4) The probability is 0.9099.
As an estimation we are told £3 is €4.
Convert €48 to pounds.
Answer: £36
Step-by-step explanation:
4 Euros = £3
48 Euros (4x12) = £36 (3x12)
Answer:
£ 36.00
Step-by-step explanation:
£ 3 = € 4
Divide both sides by 4.
£ 3/4 = € 1
1 euro is 3/4 pound.
48 × 3/4 = 36
£ 36 = € 48
48 pounds is 36 euros.