Answer:
0.2693
Step-by-step explanation:
Thus is a binomial probability problem :
p = 0.36
1 - p = 0.64
n = 9
x = 3
Using the binomial probability relation :
P(x =x) = nCx * p^x * (1 - p)^(n - x)
P(x = 3) = 9C3 * 0.36^3 * 0.64^6
P(x = 3) = 84 * 0.36^3 * 0.64^6
P(x = 3) = 0.2693
write an equation of a line passing thru the point (-4,-11) and perpendicular to the line 4x+5y= -45
Answer:
y = 5/4x - 6
Step-by-step explanation:
First, put 4x + 5y= -45 in y = mx + b form
4x + 5y= -45
5y = -4x - 45
y = -4/5x - 9
So, the slope is -4/5. Perpendicular lines have a opposite reciprocal slope, so the line's slope will be 5/4
To find the equation of the perpendicular line, plug in the slope and given point into y = mx + b, and solve for b
y = mx + b
-11 = 5/4(-4) + b
-11 = -5 + b
-6 = b
Plug in b and the slope into y = mx + b
y = 5/4x - 6
So, the equation is y = 5/4x - 6
please help me solve this
9514 1404 393
Answer:
sin(θ) ≈ -0.92
cos(θ) ≈ 0.38
tan(θ) = -2.40
Step-by-step explanation:
Let r represent the distance of the point from the origin. The Pythagorean theorem tells us ...
r² = (5)² + (-12)²
r² = 169
r = √169 = 13
The trig relations for a point on the terminal ray are ...
(x, y) = (r·cos(θ), r·sin(θ))
Then ...
sin(θ) = y/r = -12/13 ≈ -0.92
cos(θ) = x/r = 5/13 ≈ 0.38
tan(θ) = y/x = -12/5 = -2.40
NED HELP ASAP PLEASE
On a unit circle, the terminal point of 0 is (1/2,square root 3/2). What is 0 if 0°< 0<360°?
A. 45°
B. 15°
C. 30°
D. 60°
No links please
The value of θ if 0°< 0<360° on a unit circle where the terminal point of 0 is (1/2,square root 3/2), is 60°.
What is a terminal point?The terminal point of a circle or circular path is the measure of the angle in degrees or radians over the circle, at the endpoint on the coordinate plane.
On a unit circle, the terminal point of θ is,
[tex]\left(\dfrac{1}{2},\dfrac{\sqrt{3}}{2}\right)[/tex]
The image of the unit circle is attached below. The value of theta at terminal point (1/2,square root 3/2) is 60 degrees.
Thus, the value of θ if 0°< 0<360° on a unit circle where the terminal point of 0 is (1/2,square root 3/2), is 60°.
Learn more about the terminal point here;
https://brainly.com/question/4256586
#SPJ2
Answer:
Step-by-step explanation:
Its D, 60 degrees
I just took it
There are 25 students in Ms. Hunter's class. Seventeen of the students in her class rode the bus home today. The rest walked home. Which model best represents the percentage of students that rode the bus home and the percentage of students that walked home?
A 32% walked home 68% rode the bus
B 68% walked home 32% rode the bus
C 8% walked home 17% rode the bus
D 17% walked home 25% rode the bus
Answer:
68% rode the bus; 32% walked home
Step-by-step explanation:
0 3. The pentagon ABCDE is graphed on a coordinate plane with vertices A(0, 0), B(3,5),
pentagon's area?
25 sq. units
15 sq. units
40 sq. units
Answer:
Option A
Step-by-step explanation:
The complete question is
The pentagon ABCDE is graphed on a coordinate plane with vertices A(0, 0), B(3, 5), C(3, 8), D(8, 5), and E(8, 0). What is the pentagon's perimeter?
Solution -
We will find the length of all the sides of pentagon and then add them
Length of AB = Sqrt ((3-0)^2+(5-0)^2) = Square root of 9+25 = 5.83
Length of BC = Sqrt ((3-3)^2+(8-5)^2) = Square root of 9 = 3
Length of CD = Sqrt ((8-3)^2+(5-8)^2) = Square root of 5^2+-3^2
= 5.83
Length of DE = Sqrt ((8-8)^2+(0-5)^2) = Square root of 25 = 5
Length of EA = Sqrt ((8-0)^2+(0-0)^2) = Square root of 64= 8
Perimeter=8+5+5.83+5.83+3= 27.66 units =27.66 units
Option A
Answer:
40 sq. units
Step-by-step explanation:
Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 36 hours. hours and a standard deviation of 5.5 hours. As a part of its quality assurance program, Power +, Inc. tests samples of 9 batteries.
a. What can you say about the shape of the distribution of the sample mean?
b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)
c. What proportion of the samples will have a mean useful life of more than 38 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)
d. What proportion of the sample will have a mean useful life greater than 34.5 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)
e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Answer:
a) By the Central Limit Theorem, it is approximately normal.
b) The standard error of the distribution of the sample mean is 1.8333.
c) 0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.
d) 0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours
e) 0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 36 hours and a standard deviation of 5.5 hours.
This means that [tex]\mu = 36, \sigma = 5.5[/tex]
a. What can you say about the shape of the distribution of the sample mean?
By the Central Limit Theorem, it is approximately normal.
b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)
Sample of 9 means that [tex]n = 9[/tex]. So
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{5.5}{\sqrt{9}} = 1.8333[/tex]
The standard error of the distribution of the sample mean is 1.8333.
c. What proportion of the samples will have a mean useful life of more than 38 hours?
This is 1 subtracted by the pvalue of Z when X = 38. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{38 - 36}{1.8333}[/tex]
[tex]Z = 1.09[/tex]
[tex]Z = 1.09[/tex] has a pvalue of 0.8621
1 - 0.8621 = 0.1379
0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.
d. What proportion of the sample will have a mean useful life greater than 34.5 hours?
This is 1 subtracted by the pvalue of Z when X = 34.5. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{34.5 - 36}{1.8333}[/tex]
[tex]Z = -0.82[/tex]
[tex]Z = -0.82[/tex] has a pvalue of 0.2061.
1 - 0.2061 = 0.7939
0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours.
e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours?
pvalue of Z when X = 38 subtracted by the pvalue of Z when X = 34.5. So
0.8621 - 0.2061 = 0.656
0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours
The radius of the cylindrical construction pipe is 2.5ft, if the pipe is 25ft long, what is the volume? Use the value 3.14 for pi, and round your answer to the nearest whole number. Be sure to include the correct unit in your answer
Answer:
Step-by-step explanation:
r = 2.5 ft
h = 25 ft
Volume of cylindrical pipe = πr²h
= 3.14 * 2.5* 2.5 * 25
= 490.625 {as tenth place value is ≥ 5, add 1 to the whole number}
= 491 cubic feet
Will give brainliest for correct answer
Answer:
4 = function
5 = function
6 = not a function
Step-by-step explanation:
The first two pass the vertical line test
while the last ne doesn't
The distance around a triangle is 34 centimeters. If two sides are equal and the length of the third side is 6 centimeters, what is the length of each of the other two sides?
Subtract 6 from the total then divide by 2.
34-6 = 28
28/2 = 14
The length of the other two sides are 14 cm each
What’s the median of 70,77,80,81,82,87,88
Answer:
Hello There!!
Step-by-step explanation:
You order them but in this case they are already ordered and the middle number is 81 so that is the median(also knows as the middle).
hope this helps,have a great day!!
~Pinky~
Answer:
The median is 81.
Step-by-step explanation:
You can find the median in the middle if it all of them add up to odd.(like your’s say 70, 77, 80,... so that You will count them all. In total you have seven numbers and it’s odd).
if it is an even numbers, you mulitply the middle two numbers and divide them by two. That is the median for even numbers.
Plz help me ASAP no bots plz
Answer:
...
Step-by-step explanation:
the vertex is (-1 , 0)
false
true
the domain is R (all real numbers) ( -♾, +♾ )
the range is negative infinity -♾
A florist uses 7 red roses for every 4 white roses in her bouquets. Select the ratio of white roses to red roses. Please select 3 answers. 4 : 7
4 to 7
7 to 4
4/7
7/4
7 : 4
Answer:
Step-by-step explanation:
7 red roses
4 white roses
the answer would be 4 to 7, 4/7, and 4:7
I hope this helps!
Simplify the expression
4p−5(p+6)
Please help, thank you :)
Answer:
-p - 30
Step-by-step explanation:
Hope this helps
Answer:
-p-30
Step-by-step explanation:
4p-5(p+6) Distribute -4 to p and 6
4p-5p-30 simplify by adding the p variables
-p-30
In the first week of July, a record 1,100 people went to the local swimming pool. In the second week, 100 fewer people went to the pool than in the first week. In the third week, 130 more people went to the pool than in the second week. In the fourth week, 350 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
[tex]if \: a = 3 + 2 \sqrt{2} .find \: a \times \frac{1}{a} [/tex]
Answer:
1
Step-by-step explanation:
Given that,
[tex]a=3+2\sqrt{2}[/tex]
We need to find the value of [tex]a\times \dfrac{1}{a}[/tex].
So,
[tex]=3+2\sqrt{2} \times \dfrac{1}{3+2\sqrt{2}}\\\\=\dfrac{3+2\sqrt{2}}{3+2\sqrt{2}}[/tex]
As numerator and dinominator is same. It means,
[tex]=\dfrac{3+2\sqrt{2}}{3+2\sqrt{2}}\\\\=1[/tex]
So, the value of the given expression is equal to 1.
Wells Fargo has realized that they lose home mortgage business to other banks that can process the loan applications with less variability in the time it takes to process each application. The bank recently studied this problem, and found that the processing time T is normally distributed with a mean of 13 days. They didnt measure the standard deviation, but they know that 50% of all applications were processed in between 10.5 and 15.5 days. After learning all this, they then fired half of their mortgage loan officers and replaced them with new recruits. They then sampled 25 applications, and found a sample mean of 13 days (same as the old) and a sample standard deviation of 2.5 days.
(a) Test whether their actions have significantly changed their processing time T.
(b) Based on the sample of 25 applications, give a 90% confidence interval for the parameter that
has changed.
Answer: B
Step-by-step explanation:
A C (prima) = 14cm AC= 5cm
Cual es la razón de la homotecia?
9. Sheldon rides his bike on a
Saturday to complete his
errands throughout the day,
He starts and ends his journey
at his home.
D
E
Each line segment of the graph
is referred to by the letters A
through G.
Distance (miles from home)
А оло
NA
B
F
G
Math Bits
1 2 3 4 5 6 7 8 9 10
Time (hours)
Х
How many times did Sheldon stop during his journey
What is 5/4 minus 1/3?
Answer:
11/12
Step-by-step explanation:
5/4 ---- 15/12
1/3------ 4/12
11/12
Answer:
11/12
Step-by-step explanation:
Hello! The answer to this question is 11/12. In this case, we want to make the denominator the same. To make the denominator the same we need to find the lowest common multiple. In this case the lowest common multiple is 12, (because 12 is the smallest number that 3 and 4 are both factors for.) 4x3=12 so now the denominator in 5/4 is 12 but whatever we do the bottom we do to the top. So since we multiplied the bottom (denominator) by 3 we have to multiply the top (numerator) by 3 as well. 5x3=15. Therefore, we now changed 5/4 to 15/12. Now, we have to do the same to the 1/3. 3x4= 12. 1x4=4. Now we have the two numbers, 15/12 and 4/12. 15/12-4/12=11/12! Therefore, your answer is 11/12. Hope this explanation helps! Happy learning!
3. A taxi cab company charges $3.00 for 1 minute and $5.50 for 6 minutes.
a) Calculate the slope. What does it mean according to the question?
b) Calculate the y-intercept. What does it mean according to the question?
c) How much would it cost for a 30-minute cab ride?
d) How far could you travel for $50?
Answer:
a) 1/2
b)2.5
c)17.5
Step-by-step explanation:
The question gives you two points on the line. From this, you can calculate the slope. Since slope is m=[tex]y_2-y_1/x_2-x_1[/tex], the work for question a is as follows:
m= 5.5-3/6-1
m=1/2 or 0.5
Now, you can use the information given to calculate the y-intercept. Use any of the two points to fill in x and y, and use the slope you just calculated to fill in for m. Fill in the equation and use algebra to isolate the variable and solve for b.
y=mx+b
3=0.5(1)+b
3-0.5=b+0.5-0.5
2.5=b
Finally, plug in all the numbers to find the answer for question c.
y=0.5x+2.5
y=0.5(30)+2.5
y=17.5
True or False: When conducting a survey of a group of people, you must interview every person in that population.
simplify
[tex] {a}^{3} - {b}^{3} [/tex]
Answer:
[tex] {a}^{3} - {b}^{3} [/tex]
[tex] = (a - b)( {a}^{2} + ab + {b}^{2} )[/tex]
Hence, simplified.
The coordinates of the vertices of ABC are A(-5, 2) B(-2, 4), and C(-4, 7). What are the coordinates of the image of A after the translation (x, y) = (x+6, y-5)?
Translation will reduce x coordinate by 2: (0,4), (5,6) and (3,2)
Rotation 90 CCW will change (x,y) to (-y,x): (-4,0),(-6,5),(-2,3)
Find the length of are ab
Answer:
20.97?
Step-by-step explanation:
Use the Sine rule!
the number of bacteria present in a culture after t minutes is given as b=10e
Answer:
Step-by-step explanation:
I have no clue I just need 5 pionts
What is 0.36 written as a rational number?
Answer:
If you mean what is the square root of 36, then the answer is 6.
6 × 6 = 36.
Remeber sqaure root means what two numbers multplied together equal another number. It is irrational when the number doesn't repeat or terminate.
Hope this helps!!
Describe the cross section
let f(x)=ln(x^2) and g(x)=√e^3x. find fog(x) and its domian
Answer:
[tex](f\ o\ g)(x) = 3x[/tex]
[tex]-\infty < x < \infty[/tex]
Step-by-step explanation:
Given
[tex]f(x) = ln(x^2)[/tex]
[tex]g(x)=\sqrt{e^{3x}}[/tex]
Solving (a): (f o g)(x)
This is calculated as:
[tex](f\ o\ g)(x) = f(g(x))[/tex]
We have:
[tex]f(x) = ln(x^2)[/tex]
[tex]f(g(x)) = \ln((g(x))^2)[/tex]
Substitute: [tex]g(x)=\sqrt{e^{3x}}[/tex]
[tex]f(g(x)) = \ln(\sqrt{e^{3x}})^2[/tex]
Evaluate the square
[tex]f(g(x)) = \ln(e^{3x})[/tex]
Using laws of natural logarithm:
[tex]\ln(e^{ax}) = ax[/tex]
So:
[tex]f(g(x)) = \ln(e^{3x})[/tex]
[tex]f(g(x)) = 3x[/tex]
Hence:
[tex](f\ o\ g)(x) = 3x[/tex]
Solving (b): The domain
We have:
[tex]f(g(x)) = 3x[/tex]
The above function has does not have any undefined points and domain constraints.
Hence, the domain is: [tex]-\infty < x < \infty[/tex]
PLEASE HELP!!
Rita and her two children live in subsidized housing and pay monthly rent of $230. The cost of heating
is included in the rent. The electric bill averages $56 a month while the water and sewage bill averages
$35 for every 3 months of use. Telephone costs average $19.50 a month. Rita carries no renters
insurance on her personal property. What is Rita's total annual cost of renting?
Answer:
$3806
Step-by-step explanation:
230.0
56.0
+ 19.50
305.50
305.5x12=3666
35x4=140
3666+140=3806
Which equation shows y = (x − 4)2− 3 written in standard form?
Answer:
2 x − y = 11
Step-by-step explanation: