A student is given that point P(a, b) lies on the terminal ray of angle Theta, which is between StartFraction 3 pi Over 2 EndFraction radians and 2Pi radians. The student uses the steps below to find cos Theta. Which of the following explains whether the student is correct? The student made an error in step 3 because a is positive in Quadrant IV; therefore, cosine theta = StartFraction a Over StartRoot a squared + b squared EndRoot EndFraction = StartFraction a StartRoot a squared + b squared EndRoot Over a squared + b squared EndFraction. The student made an error in step 3 because cosine theta = StartFraction negative b Over StartRoot a squared + b squared EndRoot EndFraction = Negative StartFraction b StartRoot a squared + b squared EndRoot Over a squared + b squared EndFraction. The student made an error in step 2 because r is negative in Quadrant IV; therefore, r = Negative StartRoot a squared + b squared EndRoot. The student made an error in step 2 because using the Pythagorean theorem gives r = plus-or-minus StartRoot (a squared) minus (b squared) EndRoot = StartRoot a squared minus b squared EndRoot.
Answers
Answer:
A.
The student made an error in step 3 because a is positive in Quadrant IV; therefore,
[tex]cos\theta = \frac{a\sqrt{a^2 + b^2}}{a^2 + b^2}[/tex]
Step-by-step explanation:
Given
[tex]P\ (a,b)[/tex]
[tex]r = \± \sqrt{(a)^2 + (b)^2}[/tex]
[tex]cos\theta = \frac{-a}{\sqrt{a^2 + b^2}} = -\frac{\sqrt{a^2 + b^2}}{a^2 + b^2}[/tex]
Required
Where and which error did the student make
Given that the angle is in the 4th quadrant;
The value of r is positive, a is positive but b is negative;
Hence;
[tex]r = \sqrt{(a)^2 + (b)^2}[/tex]
Since a belongs to the x axis and b belongs to the y axis;
[tex]cos\theta[/tex] is calculated as thus
[tex]cos\theta = \frac{a}{r}[/tex]
Substitute [tex]r = \sqrt{(a)^2 + (b)^2}[/tex]
[tex]cos\theta = \frac{a}{\sqrt{(a)^2 + (b)^2}}[/tex]
[tex]cos\theta = \frac{a}{\sqrt{a^2 + b^2}}[/tex]
Rationalize the denominator
[tex]cos\theta = \frac{a}{\sqrt{a^2 + b^2}} * \frac{\sqrt{a^2 + b^2}}{\sqrt{a^2 + b^2}}[/tex]
[tex]cos\theta = \frac{a\sqrt{a^2 + b^2}}{a^2 + b^2}[/tex]
So, from the list of given options;
The student's mistake is that a is positive in quadrant iv and his error is in step 3
Answer:
a on e2020 :)
Step-by-step explanation:
Related Questions
A supermarket charges 3.24 for a carton of milk. They mark up the milk by 35% in order to make a profit. What is the original cost of the milk
Answers
Answer:
$ 2,4
Step-by-step explanation:
135% .............$ 3,24
100% .............$ x
x = 3,24×100/135
= 324/135
= $ 2,4
You are reading the draft of a scientific paper that your co-worker has written. In the paper, he draws a sample from a population and computes the following two confidence intervals for : A 95% confidence interval of (90.21,100.37) A 99% confidence interval of (93.61.98.53) How do you know your co-worker made a mistake? He computed more than one confidence interval using the same sample data. Your co-worker did not round to 3 decimal places in his confidence interval upper and lower bounds The 99% confidence interval should be wider than the 95% confidence interval He is not a statistic, so it doesn't make any sense to compute confidence intervals for it. There is nothing wrong with his statements.
Answers
Answer:
The correct option is (C).
Step-by-step explanation:
The general form of a confidence interval is:
[tex]CI=SS\pm CV\cdot SE[/tex]
Here,
SS = Sample statistic
CV = critical value
SE = standard error
The width of the confidence interval is:
[tex]\text{Width}=2\cdot CV\cdot SE[/tex]
The width of the confidence interval is dependent upon the critical value and hence dependent upon the confidence level.
As the confidence level increases the critical value increases hence in turn increasing the width of the interval.
And as the confidence level decreases the critical value decreases hence in turn decreasing the width of the interval.
In this case the 95% confidence interval is, (90.21,100.37).
And the 99% confidence interval is, (93.61.98.53).
It is clear by looking at the two intervals that the 95% confidence interval is wider than the 99%. Thus, this clearly indicates that the co-worker made a mistake.
The correct option is (C).
Researchers fed mice a specific amount of Dieldrin, a poisonous pesticide, and studied their nervous systems to find out why Dieldrin causes seizures. The absolute refractory period, time required for nerves to recover after a stimulus, was measured and varies Normally. The measurements, in milliseconds, for six mice were 2.2, 2.4, 2.5, 2.5, 2.6, and 2.7. (10 points) Part A: Find the mean refractory period and the standard error of the mean. (2 points) Part B: Calculate a 98% confidence interval for the mean absolute refractory period for all mice when subjected to the same treatment. (4 points) Part C: Suppose the mean absolute refractory period for unpoisoned mice is known to be 2.3 milliseconds. Dieldrin poisoning should slow nerve recovery and therefore increase this period. Do the data give good evidence to support this theory? What can you conclude from a hypothesis test? Justify your response with statistical reasoning. (4 points)
Answers
Answer:
Step-by-step explanation:
Part A
Mean = (2.2 + 2.4 + 2.5 + 2.5 + 2.6 + 2.7)/6 = 2.48
Standard deviation = √(summation(x - mean)²/n
n = 6
Summation(x - mean)² = (2.2 - 2.48)^2 + (2.4 - 2.48)^2 + (2.5 - 2.48)^2 + (2.5 - 2.48)^2 + (2.6 - 2.48)^2 + (2.7 - 2.48)^2 = 0.1484
Standard deviation = √(0.1484/6
s = 0.16
Standard error = s/√n = 0.16/√6 = 0.065
Part B
Confidence interval is written as sample mean ± margin of error
Margin of error = z × s/√n
Since sample size is small and population standard deviation is unknown, z for 98% confidence level would be the t score from the student t distribution table. Degree of freedom = n - 1 = 6 - 1 = 5
Therefore, z = 3.365
Margin of error = 3.365 × 0.16/√6 = 0.22
Confidence interval is 2.48 ± 0.22
Part C
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ = 2.3
For the alternative hypothesis,
H1: µ > 2.3
This is a right tailed test
Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 6
Degrees of freedom, df = n - 1 = 6 - 1 = 5
t = (x - µ)/(s/√n)
Where
x = sample mean = 2.48
µ = population mean = 2.3
s = samples standard deviation = 0.16
t = (2.48 - 2.3)/(0.16/√6) = 2.76
We would determine the p value using the t test calculator. It becomes
p = 0.02
Assuming significance level, alpha = 0.05.
Since alpha, 0.05 > than the p value, 0.02, then we would reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed significant evidence that the mean absolute refractory period for all mice when subjected to the same treatment increased.
A tourist can bicycle 28 miles in the same time as he can walk 8 miles. If he can ride 10 mph faster than he can walk, how much time (in hr) should he allow to walk a 25-mile trail? (Hint: How fast can he walk?) ________ hr. (enter a fraction)
Answers
Answer:
The answer is [tex]\frac{25}{4}[/tex]
Step-by-step explanation:
Velocity formula:
[tex]v = \frac{d}{t}[/tex]
In which v is the velocity, d is the distance, and t is the time.
A tourist can bicycle 28 miles in the same time as he can walk 8 miles. He can ride 10 mph faster than he can walk:
This means that:
[tex]v = \frac{8}{t}[/tex]
And
[tex]v + 10 = \frac{28}{t}[/tex]
[tex](v + 10)t = 28[/tex]
From the first equation:
[tex]vt = 8[/tex]
So
[tex]vt + 10 = 28[/tex]
[tex]8 + 10t = 28[/tex]
[tex]10t = 20[/tex]
[tex]t = \frac{20}{10}[/tex]
[tex]t = 2[/tex]
He walks 8 miles in two hours, so:
[tex]v = \frac{8}{2} = 4[/tex]
4 miles per hour.
How much time (in hr) should he allow to walk a 25-mile trail?
This is t when [tex]d = 25[/tex]. So
[tex]v = \frac{d}{t}[/tex]
[tex]4 = \frac{25}{t}[/tex]
[tex]4t = 25[/tex]
[tex]t = \frac{25}{4}[/tex]
The answer is [tex]\frac{25}{4}[/tex]
Please only answer if you are 100% sure about the answer.
Answers
Answer:
Choice C.
Step-by-step explanation:
Your choice is correct
2 stands for a starting point which is 2 feet from the home
As the ant moves, over time, the distance increases according to the function
Suppose that the scores of a standardized test are normally distributed with an unknown mean and standard deviation. A random sample of 21 scores is taken and gives a sample mean of 95 points and a sample standard deviation of 8 points.
df t0.10 t0.05 t0.025 t0.01 t0.005
17 1.333 1.740 2.110 2.567 2.898
18 1.330 1.734 2.101 2.552 2.878
19 1.328 1.729 2.093 2.539 2.861
20 1.325 1.725 2.086 2.528 2.845
21 1.323 1.721 2.080 2.518 2.831
Find the margin of error for a 95% confidence interval estimate for the population mean using the Student's t-distribution
Use the portion of the table above. Round the final answer to two decimal places.
Provide your answer below:
ME = _______.
Answers
Answer:
ME = 3.64
Step-by-step explanation:
Given:
Sample size, n = 21
Sample mean, X' = 95
Standard deviation [tex] \sigma [/tex] = 8.
Confidence interval = 95%
Significance level [tex] \alpha[/tex] = 0.05
Required:
Find margin of error
To find the margin of error, use the formula below:
[tex] M.E = \frac{\sigma}{\sqrt{n}} * t_\alpha_/_2; _d_f [/tex]
Where,
[tex] t_\alpha_/_2 = 0.05/2 = 0.025[/tex]
degree of freedom, df = n - 1 = 21 - 1 = 20
Therefore,
[tex] M.E = \frac{8}{\sqrt{21}} * t_0_._0_2_5; _2_0 [/tex]
Using the table at 95% Confidence interval, we have:
[tex] = \frac{8}{\sqrt{21}} * 2.086 [/tex]
[tex] = 3.6416 [/tex]
Rounding to 2 decimal places,
ME = 3.64
a) There are 390 people in Terminal 2 of an airport. The table below shows how many people
are travelling to each destination.
Destination Number of travellers
Naples 130
Barcelona 98
Paris 78
Liverpool 84
For a sample of 30 participants, describe how a sample could be obtained using a stratified
sampling process
Answers
Answer:
To obtain a stratified sample of 30 participants, we divide the people according to their destination, ending up with four groups(Naples, Liverpool, Barcelona, Paris). Finally, we choose some members each of those groups. Adding the members choosing from all groups, we have 30 members.
Step-by-step explanation:
Samples may be classified as:
Convenient: Sample drawn from a conveniently available pool.
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
In this question:
A stratified sample divided all the people into groups, and then surveyes some elements(some people) of each group.
Population: 390 people in the terminal.
Groups: 4 groups. Those traveling to Naples, those traveling to Barcelona, those traveling to Paris and those traveling to Liverpool.
Stratified sample of 30:
To obtain a stratified sample of 30 participants, we divide the people according to their destination, ending up with four groups(Naples, Liverpool, Barcelona, Paris). Finally, we choose some members each of those groups. Adding the members choosing from all groups, we have 30 members.
Please answer this correctly
Answers
Answer:
75%
Step-by-step explanation:
The numbers that are not 5 are 6, 7, and 8.
3 numbers are not 5 out of 4 total numbers on the spinner.
3/4 = 0.75
= 75%
Answer:
75%
Step-by-step explanation:
Total no.s = 4
Divided in parts = 25%
P(not 5) = 75%
The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years.
Required:
a. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites.
b. State the null and alternative hypotheses.
c. Which distribution (normal or Student's t) would you use for this hypothesis test?
d. Calculate the test statistic and p-value.
e. Does it appear that the means are the same? Why or why not?
Answers
Answer:
b. The null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]
c. Student's t distribution, as it is a two-sample test for the difference between means.
d. Test statistic t = 5.42.
P-value = 0
e. They appear to be significantly different, as the sample data gives strong evidence that the difference is greater than 0.
Step-by-step explanation:
This is a hypothesis test for the difference between populations means.
The claim is that the mean life spans in the county is significantly different for whites and nonwhites.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]
The significance level is 0.05.
The sample 1 (white), of size n1=124 has a mean of 45.3 and a standard deviation of 12.7.
The sample 2 (non-white), of size n2=82 has a mean of 34.1 and a standard deviation of 15.6.
The difference between sample means is Md=11.2.
[tex]M_d=M_1-M_2=45.3-34.1=11.2[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{12.7^2}{124}+\dfrac{15.6^2}{82}}\\\\\\s_{M_d}=\sqrt{1.301+2.968}=\sqrt{4.269}=2.066[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{11.2-0}{2.066}=\dfrac{11.2}{2.066}=5.42[/tex]
The degrees of freedom for this test are:
df=n_1+n_2-2=124+82-2=204
This test is a two-tailed test, with 204 degrees of freedom and t=5.42, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t>5.42)=0.0000002[/tex]
As the P-value (0.0000002) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the mean life spans in the county is significantly different for whites and nonwhites.
Decide whether the Experiment is a Binomial Experiment. If it is not, explain why:
You observe the gender of the next 850 babies born at a local hospital. The random variable represents the number of boys.
You draw a marble 350 times from a bag with three colors of marbles. The random variable represents the color of marble that is drawn.
Testing a cough suppressant using 820 people to determine if it is effective. The random variable represents the number of people who find the cough suppressant to be effective.
Answers
Answer:
Experiment 1 and 3 are clear binomial experiments.
Experiment 2 needs tweaking to be a binomial experiment.
Check Explanation.
Step-by-step explanation:
A binomial experiment is one in which
1) The probability of success doesn't change with every run or number of trials.
2) It usually consists of a fixed number of runs/trials with only two possible outcomes, a success or a failure.
3) The outcome of each trial/run of a binomial experiment is independent of one another.
Checking each of the experiments one at a time
- You observe the gender of the next 850 babies born at a local hospital. The random variable represents the number of boys.
For this experiment,
1) The probability of success doesn't change with every run or number of trials as it is a 50% chance that each child examined is a boy.
2) It consists of a fixed number of runs (850) with only two possible outcomes, success (if it's a boy) and failure (if it's a girl).
3) The probability of each trial being a boy is independent from all the other trials.
Hence, this experiment is a binomial experiment.
- You draw a marble 350 times from a bag with three colors of marbles. The random variable represents the color of marble that is drawn.
For this experiment,
1) If the marbles aren't being replaced after each draw, the probability of success, that is, picking a particular marble colour changes from trial to trial.
2) Although, it consist of a fixed number of runs/trials, there are more than two possible outcomes with 3 types of colours. Unless the experiment focuses on one colour and treats the other two colours as 'others', this condition too isn't satisfied.
3) Without replacement, the probability of success (picking a particular marble colour) in one trial isn't independent of the other trials.
This is not a binomial experiment as it doesn't satisfy all the required conditions to be one.
- Testing a cough suppressant using 820 people to determine if it is effective. The random variable represents the number of people who find the cough suppressant to be effective.
1) The probability of success doesn't change with every run or number of trials as it is the same chance that each person finds the cough suppressant to be effective.
2) It consists of a fixed number of runs (820) with only two possible outcomes, success (cough suppressant is effective) and failure (cough suppressant isn't effective).
3) The probability of each trial being a person that finds the cough suppressant to be effective, is independent from all the other trials.
Hence, this experiment is a binomial experiment.
Hope this Helps!!!
find X such that: 7x + 24x = 25x
Answers
Answer:
[tex]\boxed{ x = 0}[/tex]
Step-by-step explanation:
7x + 24x = 25 x
31 x = 25 x
Subtracting 25x to both sides
31x - 25x = 0
6x = 0
Dividing both sides by 6
=> x = 0
Answer:
x = 0
Step-by-step explanation:
7x + 24x = 25x
Combine like terms.
31x = 25x
Subtract 25x on both sides.
6x = 0
Divide both sides by 6.
x = 0
Find two positive numbers whose product is 16 and whose sum is a minimum. (If both values are the same number, enter it into both blanks.) (smaller number) (larger number)
Answers
Answer:
4 and 4
Step-by-step explanation:
We have 2 numbers that will be X and Y
X * Y = 16 => Y = 16 / X
We must minimize the sum, therefore:
S = X + Y
S = X + 16 / X
we derive and equal 0 and we are left with:
dS / dA = 1 - 16 / (X ^ 2) = 0
1 = 16 / X ^ 2
X ^ 2 = 16
X = 4
in the case of Y:
Y = 16/4 = 4
Therefore the numbers are 4 and 4.
The two positive numbers are 4 and 4
Let the two numbers be x and y
If the product of both numbers is 16, hence;
xy = 16 ........................... 1
If the sum will be at the minimum, hence x + y = minimum
From equation1, x = 16/ y
Substitute into the second equation to have;
16/y + y = A(y)
A(y) = 16/y + y
For the expression to be at a minimum, hence dA/dy = 0
dA/dy = -16/y² + 1
0 = -16/y² + 1
0 - 1 = -16/y²
-y² = -16
y = √16
y = 4
Recall that xy = 16
4x= 16
x = 4
Hence the two positive numbers are 4 and 4
LEarn more here: https://brainly.com/question/13598452
PLEASE HELP ASAP! 80 points!! What is the surface area of the solid that can be formed by this net? The net of a rectangular prism. It has a length of 5 inches, height of 1 inch, and width of 4 inches.
Answers
Answer:
58 inches²
Step-by-step explanation:
The formula for the surface area of a net rectangular prism is:
[tex]2(lw+hl+hw)[/tex]
l is length
w is width
h is height
[tex]2((5)(4)+(1)(5)+(1)(4))[/tex]
[tex]2(20+5+4)[/tex]
[tex]2(29)=58[/tex]
Answer:
[tex]\boxed{Surface \ Area = 58 \ in.^2}[/tex]
Step-by-step explanation:
Surface Area of Rectangular Prism = [tex]2(wl+lh+wh)[/tex]
Where l = 5 in. , h = 1 in. and w = 4 in.
SA = 2[(4)(5)+(5)(1)+(4)(1)]
SA = 2(20+5+4)
SA = 2(29)
SA = 58 in.²
Please answer this correctly
Answers
Answer:
80%
Step-by-step explanation:
The probability of getting a four is 1/5
The probability of getting a odd is3/5
So u add them and it gives u 4/5 which in decimal is .8 which in percent is 80%
Hope this helps
- (3/4) times (- 3/8) times ___= -3/4
Answers
Answer:
x = -8/3
Step-by-step explanation:
Step 1: Write equation
-3/4(-3/8)(x) = -3/4
Step 2: Multiply
9/32(x) = -3/4
Step 3: Divide
x = -3/4/(9/32)
x = -3/4(32/9)
x = -8/3
Answer:
-8/3
Step-by-step explanation:
-(3/4) x (-3/8)= 9/32
9/32 times (-8/3) = -3/4
Answer: -8/3
A triangular tent door has an area of 15 square feet. The height is five feet. What is the base?
Answers
Answer:
Base = 6 feet
Step-by-step explanation:
Area of Triangle = [tex]\frac{1}{2} Base*Height[/tex]
For finding Base:
Base = [tex]\frac{2(Area)}{Height}[/tex]
Where Area = 15, Height = 5
Base = [tex]\frac{2(15)}{5}[/tex]
Base = 2*3
Base = 6 feet
Answer:
The base is 6 feet long.,
Step-by-step explanation:
Area of a triangle = 1/2 * base * height so we have
1/2 b h = 15
1/2 b * 5 = 15
2.5 b = 14
b = 15/2.5
b = 6 feet.
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of eight large boxes and four small boxes has a total weight of two hundred and one kilograms. A delivery of three large boxes and two small boxes has a total weight of eighty two kilograms. How much does each type of box weigh?
Answers
Answer:
Weight of Large Box = 18.5 kg
Weight of Large Box = 13.25 kg
Step-by-step explanation:
Given:
There are two types of boxes i.e. Large and Small
Let the weight of Large boxes = L kg
Let the weight of Small boxes = S kg
As per given statement:
A delivery of eight large boxes and four small boxes has a total weight of two hundred and one kilograms.Writing equation for above:
[tex]8L + 4S = 201[/tex] ....... (1)
A delivery of three large boxes and two small boxes has a total weight of eighty two kilograms.Writing equation for above:
[tex]3L + 2S = 82 ....... (2)[/tex]
Now, by solving the equations (1) and (2), we can get the values of L and S.
Multiplying equation (2) with 2 and subtracting from equation (1):
[tex]8L + 4S = 201[/tex]
-
[tex]2 \times (3L + 2S) = 82 \times 2[/tex]
[tex]8L + 4S = 201[/tex]
-
[tex]6L + 4S = 164[/tex]
--------------------
[tex]2L = 37[/tex]
L = 18.5 Kg
Putting value of L in equation (1):
[tex]8 \times 18.5 + 4S = 201\\\Rightarrow 148 + 4S = 201\\\Rightarrow 4S = 201 - 148\\\Rightarrow 4S = 53\\\Rightarrow S = 13.25\ kg[/tex]
So, the answer is:
Weight of Large Box = 18.5 kg
Weight of Large Box = 13.25 kg
The manufacturer of widgets spends $5 to make each widget and sells them for $8. The manufacturer also has fixed costs each month of $1200. Find the number of widgets, x, that the manufacturer needs to sell in order to break-even.
Answers
Answer:
400
Step-by-step explanation:
The manufacturer spends $5 to make each widget and sells them for $8. This means that each widget gives him a profit of $3.
8 - 5 = 3
You need to figure out how many widgets it will take for the manufacturer to make up for the costs each month ($1200).
3x = 1200
(3x)/3 = 1200/3
x = 400
The manufacturer needs to sell 400 widgets.
Answer:
Step-by-step explanation:
He sells them 8 dollars and uses 5 dollars worth of material.
His profit is 8 - 5 = 3 dollars.
He has to sell enough to overcome the 1200 dollars.
1200 / 3 = 400
He breaks even after selling 400 widgets.
4, Homework 1, Jenny's mom says she has an hour before bedtime.Jenny spends 3/5 of The hour texting a friend and 3/8 of The remaining Time brushing her Teeth and on her pajamas. She spends the rest of the Time reading her book. How long did Jenny read?
Answers
Answer: 15 minutes is spent on reading
Step-by-step explanation:
1 hour = 60 minutes
Jeny spends 3/5th texting
= 3/5 x 60 = 36 minutes
Remaining = 60 - 36 = 24 minutes
3/8 on brushing and pyjamas
= 3/8 x 24 = 9 minutes
Remaining time is 60-36-9 = 15
Answer:
15 minutes
Step-by-step explanation:
3/5 texting
1 hour * 3/5 =
60 minutes * 3/5 =36 minutes
60 -36 = 24 minutes left
3/8 of that time brushing teeth
24 * 3/8 = 9 minutes
24 - 9 = 15
That leaves 15 minutes for reading
Suppose that you spin the double wheel pictured to the right. Assuming that the wheels are independent and each outcome is equally likely, determine the probability that you get red on both wheels.
A spinner consists of two concentric unequal circular wheels with the smaller one placed on the larger. The smaller wheel is divided into 8 equal sectors. The number of sectors for each color is as follows, where the label is listed first and the number of sectors is listed second: red, 3; blue, 2; yellow, 1; grey, 2. The larger wheel is divided into 12 equal sectors. The number of sectors for each color is as follows, where the label is listed first and the number of sectors is listed second: red, 4; blue, 2; yellow, 2; grey, 2; green, 2.
B=blue
G=green
Y=yellow
R=red
g=grey
The probability is:_________
Answers
Answer:
0.125
Step-by-step explanation:
Smaller Wheel
Total Number of Equal Sectors = 8
The number of Red sectors =3
The probability of obtaining red on the smaller wheel [tex]=\dfrac38[/tex]
Larger Wheel
Total Number of Equal Sectors = 12
The number of Red sectors =4
The probability of obtaining red on the larger wheel [tex]=\dfrac{4}{12}[/tex]
Assuming that the wheels are independent and each outcome is equally likely, the probability that we get red on both wheels
[tex]=\dfrac38 \times \dfrac{4}{12}\\\\=\dfrac18\\\\=0.125[/tex]
The probability is: 0.125
Given that triangle DAE ~ triangle BAC, what is the length of side AE?
Answers
Answer:
12
Step-by-step explanation:
For polygons that are similar to each other, the ratio of their corresponding sides are usually equal to each other, as they are proportional.
Therefore, given that ∆DAE is similar to ∆BAC, AD = 6, AB = 6+4 = 10, AE = x, AC = x + 8, therefore:
AD/AB = AE/AC
6/10 = x/(x+8)
Cross multiply
6*(x+8) = x*10
6x + 48 = 10x
Subtract 6x from both sides
48 = 10x - 6x
48 = 4x
Divide both sides by 4
48/4 = x
x = 12
Length of side AE = 12
four divided by the sum of x and three
Answers
Answer:
4/ (x+3)
Step-by-step explanation:
The sum of x and 3
(x+3)
4 is divided by the above
4/ (x+3)
A group of up to 40 people are going to a trip to Washington DC. Some will travel in a van that holds 12 people, and the rest will buy train tickets. Write an inequality that can be used to find the number of train tickets that the group will need.
Answers
You are told up to 40 people are going and that the van holds 12.
40-12 = 28
So up to 28 people will need to buy train tickets.
Let n be the number of people buying train tickets and x is the total number of people going
N <= (x-12)
What is 75miles/hr in feet/second?(1mile = 5280feet)
Answers
Answer:
110 feet/sec
Step-by-step explanation:
75 miles x 5280 feet
= 396000
396000/60 min
=6600
6600/60 secs
=110 feet/second
Convert the following Fahrenheit degrees to Celsius. a. 104° F b. 41° F c. 131° F d. 95° F
Answers
Answer:
a) 104 F=30 C
b) 41 F=5 C
c) 131 F=55
d) 95 F= 35 C
Step-by-step explanation:
Use the place value chart to write 9.807.
Answers
Answer:
9 ones, 8 tenths, 0 hundredths, 7 thousandths
Step-by-step explanation:
Answer:
9 thousands
8 hundreds
0 tens
7 ones
Step-by-step explanation:
Hope it helped!
Determine whether the pair of equations represent parallel lines, perpendicular lines, or neither.
12x + 4y = 16
24x + 8y = 36
Answers
Answer:
Parallel
Step-by-step explanation:
Parallel lines have the same slope but different y-intercepts. If you multiply the top equation by 2, you get:
2(12x + 4y = 16)
24x + 8y = 32
This shows that both lines have the same slope, but then you find the y-intercepts, they are different:
1st equation y-int = 4
2nd equation y-int = 9/2 or 4.5
Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $43,000 and $61,600. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired.
Required:
a. What is the planning value for the population standard deviation (to the nearest whole number)?
b. How large a sample should be taken if the desired margin of error is as shown below (to the nearest whole number)?
1. $500?
2. $200?
3. $100?
Answers
Answer:
a. 4650
b.
1. 332
2. 2076
3. 8306
Step-by-step explanation:
a. The planning value for population standard deviation is,
s = (maximum - minimum) / 4
s = (61600 - 43000) / 4
s = 4650
that is, it would be 4650, the planning value for population standard deviation
b. we have to:
n = (z * s / E) ^ 2
z for confidence level 95% is 1.96, E = 500; 200; 100
replacing:
1.
n = (1.96 * 4650/500) ^ 2
n = 332.2 = 332
2.
n = (1.96 * 4650/200) ^ 2
n = 2076.6 = 2076
3.
n = (1.96 * 4650/100) ^ 2
n = 8306.4 = 8306
Find the inequality represented by the graph.
Answers
Answer:
[tex]x \geqslant \frac{y + 4}{3} [/tex]Explanation;
Associated line with this equation is:
y=mx+c
when,
X=0
y=-4
so, c=-4
X=1
y=-1
[tex] - 1 = m- 4 \\ - m = - 4 + 1 \\ - m = - 3 \\ m =3 \\ [/tex]
[tex]y = 3x - 4 \\ or \: y + 4 = 3x \\ or \: \frac{y + 4}{3} = x[/tex]
Inequality representated by graph:
[tex]x \geqslant \frac{y + 4}{3} [/tex]
Hope this helps...
Good luck on your assignment...
There are two boxes containing only black and orange pens.
Box A has 4 black pens and 16 orange pens.
Box B has 2 black pens and 3 orange pens.
A pen is randomly chosen from each box. List these events from least likely to most likely.
Event 1: choosing a black pen from Box A.
Event 2: choosing a black or orange pen from Box A.
Event 3: choosing a white pen from Box B.
Event 4: choosing a black pen from Box B.
Answers
Answer:
Event 3 -> Event 1 -> Event 4 -> Event 2
Step-by-step explanation:
The probability of choosing a certain pen is the number of that pen in the box over the total number of pens in the box.
So we have that:
Event 1: We have 4 black pen and 20 total pens, so P = 4 / 20 = 1 / 5
Event 2: All pens are black or orange so the probability is 1.
Event 3: We don't have white pens, so the probability is 0.
Event 4: We have 2 black pen and 5 total pens, so P = 2 / 5
Listing from least likely to most likely, we have:
Event 3 -> Event 1 -> Event 4 -> Event 2