Answer:1260
Step-by-step explanation:
Kissing has 7 letters, and there are 2 paris of the same letter.
[tex]\frac{7!}{2!2!}[/tex] = [tex]\frac{7*6*5*4*3*2*1}{4}[/tex]= 1260
A company makes wax candles shaped like rectangular prisms. Each candle is 7cm long, 2cm wide, and 10cm tall. If they used 5740cm^3 of wax, how many candles did they make?
Answer: 41 candles
Step-by-step explanation:
Multiply the dimensions of the candle first.
V = l*w*h
7 * 2 = 14
14 * 10 = 140
Now, divide the total amount of wax used by the amount of wax used for one candle.
5,740 / 140 = 41
I rlly rlly rlly need help! Complete the following proof. Given: Points R, S, T, Q on circle O Prove: m\overarc RS + m\overarc ST + m\overarc TQ + m\overarc RQ
Answer:
[tex]m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ}) + m(major\ arc RQ) = 360\ degree[/tex]
Step-by-step explanation:
As we can see in the figure that
The R, S, T ,and Q are the points on the circle O.
Also
The measurement of the circular arc is equivalent to the measurement of the angle at the center of the arc
So by this
[tex]m(\widehat{RS})=m(\angle ROS)[/tex]
[tex]m(\widehat{ST})=m(\angle SOT)[/tex]
[tex]m(\widehat{TQ})=m(\angle TOQ)[/tex]
m(major arc RQ) = m(∠QOR)
So,
[tex]m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ}) + m(major\ arc RQ) = m(\angle ROS)+m(\angle SOT)+m(\angle TOQ)+m(\angle QOR)[/tex]
And as we know that
All angles sum = 360°
Therefore
[tex]m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ}) + m(major\ arc RQ) = 360\ degree[/tex]
26 points - Help, if you can: An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 3,500 feet and Plane B is at an altitude of 2,601 feet. Plane A is gaining altitude at 40.25 feet per second and Plane B is gaining altitude at 55.75 feet per second. 1. How many seconds will pass before the planes are at the same altitude? 2. What will their altitude when they're at the same altitude?
Answer:
1. 58 seconds
2. 5834.5 feet
Step-by-step explanation:
The equation [tex]A(t) = 40.25t + 3500[/tex] can be used to represent the height of plane A at time t seconds. Similarly, the equation [tex]B(t) = 55.75t + 2601[/tex] represents the height of plane B after t seconds. To solve for when the planes are at the same height, we can set these two equations equal to get [tex]40.25t + 3500 = 55.75t + 2601 \Rightarrow 15.5t = 899 \Rightarrow t = 58.[/tex] So, [tex]\boxed{\boxed {58}}[/tex] seconds will pass before the planes are at the same altitude. Plugging in t=58 into either of the equations, we see their altitudes will be [tex]\boxed{\text{5834.5 feet}}[/tex] .
A portfolio has average return of 13.2 percent and standard deviation of returns of 18.9 percent. Assuming that the portfolioi's returns are normally distributed, what is the probability that the portfolio's return in any given year is between -43.5 percent and 32.1 percent?
A. 0.950
B. 0.835
C. 0.815
D. 0.970
Answer:
B. 0.835
Step-by-step explanation:
We can use the z-scores and the standard normal distribution to calculate this probability.
We have a normal distribution for the portfolio return, with mean 13.2 and standard deviation 18.9.
We have to calculate the probability that the portfolio's return in any given year is between -43.5 and 32.1.
Then, the z-scores for X=-43.5 and 32.1 are:
[tex]z_1=\dfrac{X_1-\mu}{\sigma}=\dfrac{(-43.5)-13.2}{18.9}=\dfrac{-56.7}{18.9}=-3\\\\\\z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{32.1-13.2}{18.9}=\dfrac{18.9}{18.9}=1\\\\\\[/tex]
Then, the probability that the portfolio's return in any given year is between -43.5 and 32.1 is:
[tex]P(-43.5<X<32.1)=P(z<1)-P(z<-3)\\\\P(-43.5<X<32.1)=0.841-0.001=0.840[/tex]
y =3x + 5 is the equation of a straight line graph. What is its gradient?
Answer:
3.
Step-by-step explanation:
y= mx + c whereas m is the gradient and c is the y-intercept.
This table represents a quadratic function with a vertex at (1, 2). What is the
average rate of change for the interval from x = 5 to x = 6?
Answer:
D: 9
Step-by-Step Explanation:
The average rate is synonymous with the slope. Since we want to find the average rate of change from x = 5 to x = 6, we will use the two points (5, 18) and (6, ?). We will need to find ? first.
Since the table represents a quadratic function and we are given the vertex, we can use the vertex form of a quadratic:
[tex]\displaystyle f(x)=a(x-h)^2+k[/tex]
Where (h, k) is the vertex.
The vertex is (1, 2). Hence:
[tex]f(x)=a(x-1)^2+2[/tex]
To determine a, pick a sample point from the table and solve for a. We can use (2, 3). Hence:
[tex](3)=a((2)-1)^2+2[/tex]
Solve for a:
[tex]1=a(1)^2\Rightarrow a=1[/tex]
Hence, our function is:
[tex]f(x)=(x-1)^2+2[/tex]
Evaluate the function when x = 6:
[tex]\displaystyle f(6)=(6-1)^2+2=27[/tex]
So, our two points are (5, 18) and (6, 27).
Again, to find the average rate of change between x= 5 and x = 6, find the slope between their two points. Hence:
[tex]\displaystyle m=\frac{27-18}{6-5}=9[/tex]
Our answer is D.
Find the midpoint of AB when A=(1,-2) B=(1,-1)
Answer:
Midpoint Of AB = ( 1+1/2 , -2-1/2)
= (2/2 , -3/2)
= ( 1 , -1.5)
Hope this helps
Please mark Branliest.
Answer:
-2,0
Step-by-step explanation:
what is the probability out of a 52 deck of cards that a jack or a heart are pulled
Answer:
about 32.7% or 17/52
Step-by-step explanation:
Cars enter a car wash at a mean rate of 4 cars per half an hour. What is the probability that, in any hour, exactly 5 cars will enter the car wash? Round your answer to four decimal places.
Answer:
The probability that, in any hour, exactly 5 cars will enter the car wash is P(x=5)=0.0920.
Step-by-step explanation:
This can be modeled as a Poisson random variable.
The mean rate is the parameter of the Poisson distribution:
[tex]\lambda=4\;\text{cars/half an hour}=8\;\text{cars/hour}[/tex]
The probability that exactly k cars will enter the car wash can be calculated as:
[tex]P(x=k)=8^{k} \cdot e^{-8}/k![/tex]
Then, the probability that exactly 5 cars will enter the car wash is:
[tex]P(5)=8^{5} \cdot e^{-8}/5!=32768*0.0003/120=0.0920\\\\[/tex]
The probability that, in an hour, exactly 5 cars will enter the car wash will be 0.0920.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1.
Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
The mean rate is found as;
[tex]\rm \lambda =4 \ cars / half \ an \ hour = 8 car / hour[/tex]
The probability that exactly k cars will enter the car wash
[tex]P(x=K) = \frac{8^k e^{-8}}{k\!}\\\\P(x=5) = \frac{8^5 e^{-8}}{5\!}\\\\ P(x=5)=0.0920[/tex]
Hence the probability that, in an hour, exactly 5 cars will enter the car wash will be 0.0920.
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Rearrange e = 2f to make fthe subject.
=
Answer:
f = e/2
Step-by-step explanation:
e = 2f
Switch sides.
2f = e
Divide both sides by 2.
f = e/2
Answer:
f=e/2
Step-by-step explanation:
To make f the subject, we want to isolate f.
e=2f.
We see that e is equal to two times f, or two f's.
Divide by 2 to isolate f.
e/2=f
However, normally we want f on the left side, so we have:
f=e/2
A driver travels a distance of 119 miles between 09:50 and 11:35. Work out the average speed of the driver
Answer:
68 miles per hour.
Step-by-step explanation:
The time taken for the driver to drive 119 miles is 105 minutes.
The average speed is equal to distance divided by the time taken.
105 minutes is equal to 1.75 hours.
[tex]S=119/1.75[/tex]
[tex]S =68[/tex]
The driver's average speed is 68 miles per hour.
Answer:
Speed = 68 mph
Step-by-step explanation:
Given:
Distance = 119 miles
Time = 1 hour 45 minutes = 1.75 hours
Required:
Speed = ?
Formula:
Average Speed = Total Distance Covered / Total Time Taken
Solution:
Speed = 119/1.75
Speed = 68 mph
Please help. Question in picture
Answer:
x - intercept answers are (1,0),(-3,0),(3,0)
y - intercept answer is (0,9)
Step-by-step explanation:
A television network, Network A, is scheduling its fall lineup of shows. For the Tuesday night 8 p.m. slot, Network A has selected its top show. If its rival network, Network B, schedules its top show during the same time slot, Network A estimates that it will get 1.1 million viewers. However, if Network B schedules a different show during that time slot, Network A estimates that it will get 1.9 million viewers. Network A believes that the probability that Network B will air their top show is 0.7 and the probability that Network B will air another show is 0.3. Determine the expected number of viewers for Network A's top show.
Answer:
1,280,000 (1.28 million.)
Step-by-step explanation:
If Network B schedules its top show (with a probability of 0.7), Network A will get 1.1 million viewers.
If Network B schedules a different show during that time slot, (with a probability of 0.3), Network A will get 1.9 million viewers.
Therefore, the probability distribution table of number of viewers of Network A is:
[tex]\left|\begin{array}{c|c|c}$Number of Viewers, x&1.1$ million&$1.7 million\\P(x)&0.7&0.3\end{array}\right|[/tex]
Therefore, the expected number of viewers for Network A's top show
= (1100000 X 0.7) + (1700000 X 0.3)
=1,280,000
The expected number of viewers for Network A's top show is 1.28 million.
What position did Theodore Roosevelt hold before he became president?
Answer:
He served as Assistant Secretary of the Navy under President William McKinley
hope i helped
-lvr
On August 1, 2021, a company accepts an $8,000, 9-month note receivable. For 2021, the company reports interest revenue of $200. What is the interest rate on the note?
Answer:
6%
Step-by-step explanation:
We have to calculate the interest rate in the note, we must follow the following steps, calculate the amount of time remaining from the year 2021, as follows:
interest is for 5 months i.e. from Aug 01 to Dec 31 for year 2021 , so it means it would be 5/12 months.
We have to calculate the interest as follows:
I = P * R * T
We replace:
200 = 8000 * R * 5/12
we solve for R
200 * 12/5 = 8000 * R
R * 8000 = 480
R = 480/8000
R = 0.06
Which means that the interest rate on the note is 6%
By rewriting the formula for the Multiplication Rule, you can write a formula for finding conditional probabilities. The conditional probability of event B occurring, given that event A has occurred, is P (B A) = P (A and B) P (A).
Use the information below to find the probability that a flight arrives on time given that it departed on time.
1. The probability that an airplane flight departs on time is 0.91.
2. The probability that a flight arrives on time is 0.86.
3. The probability that a flight departs and arrives on time is 0.81.
Answer:
89.01% probability that a flight arrives on time given that it departed on time.
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Departing on time
Event B: Arriving on time.
The probability that a flight departs and arrives on time is 0.81.
This means that [tex]P(A \cap B) = 0.81[/tex]
The probability that an airplane flight departs on time is 0.91.
This means that [tex]P(A) = 0.91[/tex]
Find the probability that a flight arrives on time given that it departed on time.
[tex]P(B|A) = \frac{0.81}{0.91} = 0.8901[/tex]
89.01% probability that a flight arrives on time given that it departed on time.
The mean age of 5 people in a room is 40 years. A person enters the room. The mean age is now 36. What is the age of the person who entered the room?
Answer:
[tex]\boxed{\sf \ \ \ age = 16 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
as the mean age of 5 people is 40
it means that the sum of the 5 ages is 40*5=200
now a person enters the room, let's note x his age
the new mean is
[tex]\dfrac{200+x}{6}=36[/tex]
[tex]<=>200+x=6*36=216\\<=> x = 216-200=16\\[/tex]
So the age of the new person is 16
hope this helps
The city of Oakdale wishes to see if there is a linear relationship between the temperature and the amount of electricity used (in kilowatts). Using the estimated regression equation found by using Temperature as the predictor variable, find a point estimate Kilowatt usage when the Temperature is 90 degrees outside?
The question is incomplete. The complete question is as follows.
The city of Oakdale wishes to see if there is a linear relantionship between the temperature and the amount of electricity used (in kilowatts). Using the estimated regression equation found by using Temperature as the predictor variable, find a pont estimate Kilowatt usage when the Temperature is 90 degrees outside?
Temperature(x) Kilowatts(y)
73 680
78 760
85 910
98 1510
93 1170
83 888
92 923
81 837
76 600
105 1800
Answer: The point estimate is 1132.5 Kilowatts
Step-by-step explanation: Regression analysis is used to find an equation that fits the data. Once this equation is found, it's used to make predictions. One of the regressions is linear regression.
To find the linear regression model:
1) Create a table with the following: ∑y; ∑x; ∑xy; ∑x²; ∑y²;
2) Use these equations to find coefficients a and b:
a = (∑y)(∑x²) - (∑x)(∑yx) / n(∑x²) - (∑x)²
b = n(∑xy) - (∑x)(∑y) / n(∑x²) - (∑x)²
3) Substitute the coefficients into the equation of form: y = a + bx
For the table above, the linear regression equation is:
y = - 2004 + 34.85x
When Temperature is 90, i.e. x = 90:
y = - 2004 + 34.85*90
y = 1132.5
The estimate Kilowatt is 1132.5.
Drinks are prepared and arranged on a table for a party. The probability that a drink is grape juice is 0.3. The probability that a drink has a straw is 0.3. The probability that a drink is grape juice and has a straw is 0.1. Use the addition rule to determine the probability that a drink is grape juice or has a straw. Enter your answer as a decimal, rounded to the nearest tenth, like this: 0.4
Answer:
0.5
Step-by-step explanation:
P(grape or straw) = P(grape) + P(straw) − P(grape and straw)
P(grape or straw) = 0.3 + 0.3 − 0.1
P(grape or straw) = 0.5
Fill in the blanks.
In a normal distribution, ____________ percent of the data are above the mean, and___________ percent of the data are below the mean. Similarly, _____________ percent of all data points are within 1 standard deviation of the mean, ___________percent of all data points are within 2 standard deviations of the mean, and___________ percent are within 3 standard deviations of the mean.
Answer:
In a normal distribution, 50 percent of the data are above the mean, and 50 percent of the data are below the mean. Similarly, 68 percent of of all data points are within 1 standard deviation of the mean, 95 percent of all data points are within 2 standard deviations of the mean, and 99.7 percent are within 3 standard deviations of the mean.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
Also:
The normal distribution is symmetric, which means that 50% of the data is above the mean and 50% is below.
Then:
In a normal distribution, 50 percent of the data are above the mean, and 50 percent of the data are below the mean. Similarly, 68 percent of of all data points are within 1 standard deviation of the mean, 95 percent of all data points are within 2 standard deviations of the mean, and 99.7 percent are within 3 standard deviations of the mean.
In a normal distribution, 50 percent of the data are above the mean, and 50 percent of the data are below the mean. Similarly, 68 percent of all data points are within 1 standard deviation of the mean, 95 percent of all data points are within 2 standard deviations of the mean, and 99.9 percent are within 3 standard deviations of the mean.
The normal distribution is a probability distribution that is important in many areas. It is, in fact, a family of distributions of the same form, each with different location and scale parameters: the mean and standard deviation respectively. The standard normal distribution is the normal distribution with mean equal to zero, and standard deviation equal to one. The shape of its probability density function is similar to that of a bell.
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i struggle pls help me ;-;
Answer:
8
Step-by-step explanation:
you have to work out 8 times 10 witch is 80 and then you do 54 take waya 80 divided by 2
Two-fifths of one less than a number is less than three-fifths of one more than that number. What numbers are in the solution set of this problem
A.x<-5
B.x>-5
C.x>-1
D.x<-1
Answer:
B. x > -5
Step-by-step explanation:
It seems you have a number x such that ...
[tex]\dfrac{2}{5}(x-1)<\dfrac{3}{5}(x+1)\\\\2x-2<3x+3\qquad\text{multiply by 5, eliminate parentheses}\\\\-5<x\qquad\text{subtract $2x+3$}[/tex]
This matches choice B: x > -5.
The total number of shares in Marks brothers is increased by 12.8% how many shares will there be after the increase
Answer:
Total number of shares is to increase by 12.8%
Step-by-step explanation:
After increase the number of shares will be 87984. hope this helps you :)
Each year, a daylily farm sells a portion of their daylilies and allows a portion to grow and divide. The recursive formula
an = 1.5(2n-1)-100
represents the number of daylilies, a, on the farm after n years. After the fifth year, the farmers estimate
they have 2,225 daylilies. How many daylilies were on the farm after the first year?
Answer:
600
Step-by-step explanation:
We can solve the recursive formula for the previous term in terms of the present one:
a[n-1] = (a[n] +100)/1.5
Working backward, we find ...
a[4] = (a[5] +100)/1.5 = (2225 +100)/1.5 = 1550
a[3] = (1550 +100)/1.5 = 1100
a[2] = (1100 +100)/1.5 = 800
a[1] = (800 +100)/1.5 = 600
There were 600 daylilies on the farm after the first year.
Answer:
C. 600
Step-by-step explanation:
The base of a cube has an area of
of 180 cm'. Calculate:
i) the side of the cube.
ii) the total surface area of the cube
Answer:
Step-by-step explanation:
i) the side of the cube is V180=V36*5=6V5
ii) the total surface is 6*180=1080 cm^2
HELP 36x^2+84xy+49y^2=
a- (6x+7y)(6x-7y)
b- (12x + 7y) (3x+7y)
c- (6x + 7y)^2
d- (6x-7y)^2
Answer:
C. (6x + 7y)²
Step-by-step explanation:
When you factor out this equation, you will get a square binomial. Since all coefficients are positive, your choice between C and D is C, as it creates all positive coefficients when expanded.
There is a bag filled with 5 blue and 4 red marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting exactly 1 blue?
Answer:
40/81.
Step-by-step explanation:
Prob(Picking a blue on one pick) = 5/(5+4) = 5/9.
Prob(Picking a red on one pick) = 4/(5+4) = 4/9.
Required probability is either the first pick is blue OR the second pick is blue. (The other probability on one pick is of course a red marble.)
Probability of at least 1 blue = P(red)*P(blue) + P(blue)*P(red)
= 4/9 * 5/9 + 5/9*4/9
= 20/81 + 20/81
= 40/81.
Another way of solving this is by using a tree diagram.
Based on the above, the probability of getting exactly 1 blue marble is 40/81.
What is the probability of getting exactly 1 blue?Scenario 1: Blue on the first draw, red on the second draw:
The probability of drawing a blue marble on the first draw is 5/9, as there are 5 blue marbles out of a total of 9 marbles in the bag. After replacing the marble, the probability of drawing a red marble on the second draw is also 4/9, as there are still 4 red marbles and 9 marbles in total.Scenario 2: Red on the first draw, blue on the second draw:
The probability of drawing a red marble on the first draw is 4/9. After replacing the marble, the probability of drawing a blue marble on the second draw is 5/9.
To find the total probability, one has to add the probabilities of the two scenarios:
Probability of exactly 1 blue marble = (Probability of Scenario 1) + (Probability of Scenario 2)
= (5/9) * (4/9) + (4/9) * (5/9)
= 20/81 + 20/81
= 40/81
Therefore, the probability of getting exactly 1 blue marble is 40/81.
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A 0.05 significance level is being used to test a correlation between two variables. If the linear correlation coefficient r is found to be 0.591 and the critical values are r = ±0.878, what can you conclude?
Answer:
Null hypothesis: [tex]\rho =0[/tex]
Alternative hypothesis: [tex]\rho \neq 0[/tex]
The statistic to check the hypothesis is given by:
[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]
And is distributed with n-2 degreed of freedom. df=n-2
For this case since the calculated values is on the interval (-0.878, 0.878) we can FAIL to reject the null hypothesis and on this case the correlation would be not significant at 5% of significance
Step-by-step explanation:
In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:
Null hypothesis: [tex]\rho =0[/tex]
Alternative hypothesis: [tex]\rho \neq 0[/tex]
The statistic to check the hypothesis is given by:
[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]
And is distributed with n-2 degreed of freedom. df=n-2
For this case since the calculated values is on the interval (-0.878, 0.878) we can FAIL to reject the null hypothesis and on this case the correlation would be not significant at 5% of significance
Sara is a librarian and works at least 10 hours per week. If Sara would like to work extra shifts, they are added to her
schedule in two-hour increments. Which equation models the number of hours that Sara will work at the library this
week? Assume x is the number of two-hour increments and y is the total number of hours worked.
Answer:
y = 10 + 2x
or
y = 2x + 10
Step-by-step explanation:
She works a fixed 10 hours each week, so we start with
y = 10
Now she adds 2-hour increments. She can have 0, 1, 2, or another number of increments. x represents the number of increments. Since each increment is 2 hours, 2x represents the number of hours added by the increments. Now we add 2x to the fixed number of hours.
y = 10 + 2x
or
y = 2x + 10
Answer:
y = 2x + 10
Step-by-step explanation:
The effect of caffeine on taste is tested by randomly giving one sample of participants regular soda and another sample is given decaffeinated soda.
A) Dependent samples
B) Independent samples
Answer:
The correct answer is A. Both samples are dependent samples.
Step-by-step explanation:
Both samples are dependent samples, since to verify the effects of one, it is necessary to compare it with the effects and characteristics of the other.
Thus, in the case, it is intended to check the effects of caffeine on taste by using a regular soda sample first, and then comparing it with a decaffeinated soda sample. Therefore, the effects of one sample will be checked and compared with the other sample, so that there is a dependency relationship between the two, since neither could prove the hypothesis on its own.
