Answer:
Step-by-step explanation:
Hello!
Out of 846 patients taking a prescription drug daily, 18 complained of flulike symptoms.
It is known that the population proportion of patients that take the drug of the competition and complain of flulike is 1.8%
Be the variable of interest:
X: number of patients that complained of flulike symptoms after taking the prescription drug, out of 846.
sample proportion p'= 18/846= 0.02
You have to test if the population proportion of patients that experienced flulike symptoms as a side effect is greater than 1.8% (p>0.018)
Assuming that the patients for the clinical trial were randomly selected.
The expected value for this sample is np=846*0.02= 1658 (the expected value of successes is greater than 10) and the sample is less than 10% of the population, you can apply the test for the proportion:
The hypotheses are:
H₀: p ≤ 0.018
H₁: p > 0.018
α: 0.01
[tex]Z= \frac{p'-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]≈N(0;1)
[tex]Z_{H_0}= \frac{0.02-0.018}{\sqrt{\frac{0.018*0.982}{846} } }= 0.437[/tex]
The p-value for this test is 0.331056
The decision rule is
If p-value ≤ α, reject the null hypothesis
If p-value > α, do not reject the null hypothesis
The p-value is greater than α, the decision is to reject the null hypothesis.
So at 1% significance level there is no significant evidence to reject the null hypothesis, you can conclude that the population proportion of patients that took the prescription drug daily and experienced flulike symptoms as a side effect is less or equal to 1.8%
I hope this helps!
CAN ANYONE HELP ME PLEASE? Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $106. Two adults and three children must pay $75. Find the price of the adult's ticket and the price of a child's ticket.
Answer:
The adult ticket costs $18 and the children ticket costs $13.
Step-by-step explanation:
Let the price of the adult ticket be a.
Let the price of the children ticket be c.
Three adults and four children must pay $106. This implies that:
3a + 4c = 106 _______(1)
Two adults and three children must pay $75. This implies that:
2a + 3c = 75 ________(2)
We have two simultaneous equations:
3a + 4c = 106 _____(1)
2a + 3c = 75 ______(2)
Multiply (1) by 2 and (2) by 3 and subtract (1) from (2):
6a + 9c = 225
- (6a + 8c = 212)
c = $13
Put this value of c in (2):
2a + 3*13 = 75
2a + 39 = 75
=> 2a = 75 - 39
2a = 36
a = 36/2 = $18
Therefore, the adult ticket costs $18 and the children ticket costs $13.
Which of the following triangles can be proven similar through AA?
A)
B)
C)
D)
Answer:
The options that have two angles, which are A and D prove both triangles to be similar.
Step-by-step explanation:
The postulate AA is exactly what it sounds like, and you can find the two angles, which will prove the similarity of two triangles sharing those two angles.
The reason being is if two angles are the same between the two triangles, the third can't be different.
If one termite can destroy 1.2mg of wood per day, how many kilograms of wood can 10 termites destroy in 1 week? *Can someone please explain how to do this*
Answer:
10 termites will destroy 0.000084kg of wood per week
Step-by-step explanation:
Convert milligram to kilogram
1.2mg=(1.2 / 1,000,000)kg
1.2mg=0.0000012kg
1 termite destroys=0.0000012kg per day
10 termites will destroy (per day) =0.0000012×10 termites per day
10 termites in one day will destroy=0.000012kg
There are 7 days in a week
Therefore,
10 termites will destroy=destruction per day × 7 days
=0.000012×7
=0.000084kg per week
of the 1248 students enrolled 24% did not like the new mascot design. what is the mean of this binomial distribution
A. 299.5
B. 948.5
C. 17.3
D. 300.3
Answer: A. 299.5
Step-by-step explanation:
1248 · 24%
1248 · 0.24=299.50
Four friends are on a basketball team. During a game, each friend kept track of how many shots they attempted and how many of those attempts they made. Henry made 0.45 of his shots. Allison made Arthur made of her shots. of his shots. Trevor missed 58% of his shots. Which friend had the best record for the number of shots made?
Answer:
Henry had the best record for the number of shots made
Step-by-step explanation:
From the given information.
Four friends are on a basketball team.
Henry
Allison
Arthur
Trevor
We are being told that Henry made 0.45 of his shots out of all his attempts
Allison made Arthur made of her shots of his shots.
i,e Arthur did the work for Allison , so out of Arthur's shot , we have to figured out Allison shots,
Trevor missed 58% of his shots.
i.e Trevor failed 0.58 of his shot, If he failed 0.58 shot
Then the attempts Trevor made is :
= 1 - 0.58
= 0.42
SO , Trevor made 0.42 shots out of all his attempt
N:B We are not given any information about Arthur's shots , so we can't determine Allison shot as well.
Therefore; we will focus on only Henry and Trevor shots
So ;
Henry made 0.45 of his shots
Trevor made 0.42 out of his shots
We can thereby conclude that :
Henry had the best record for the number of shots made
State the degrees of freedom error in each of the following tests. (a) A consultant measures job satisfaction in a sample of 14 supervisors, 14 managers, and 14 executives at a local firm. (b) A researcher tests how nervous public speakers get in front of a small, medium, or large audience. Ten participants are randomly assigned to each group. (c) A high school counselor has 8 students in each of five classes rate how much they like their teacher.
Answer:
.
Step-by-step explanation:
g There are 60 mountain climbers in a club. 10 of these have climbed Mt. Everest. 15 have climbed Mt. Rainier. 8 have climbed both. How many have not climbed either mountain?
Answer:
43 mountain climbers have not climbed either mountain.
Step-by-step explanation:
Total number of mountain climbers, i.e. n(U) = 60
Number of mountain climbers who have climbed Mt. Everest, n(E) = 10
Number of mountain climbers who have climbed Mt. Rainier, n(R) = 15
Number of mountain climbers who have climbed both, n(E [tex]\cap[/tex] R) = 15
Using the formula to find number of climbers who have climbed either of the mountains:
[tex]n(A \cup B) = n(A)+n(B)-n(A\cup B )[/tex]
[tex]\therefore n(E \cup R) = n(E)+n(R)-n(E\cup R )\\\Rightarrow n(E \cup R) = 10+15-8 = 17[/tex]
To find, who have not climbed either mountain:
[tex]n(E\cup B)'=n(U) - n(E\cap B)\\\Rightarrow n(E\cup B)'=60 - 17 = \bold{43}[/tex]
So, the answer is:
43 mountain climbers have not climbed either mountain.
PLEASE PLEASE PLEASE HELP PLEAS :( THE SECOND ONE JEJEJEJDD PLEASEEEEEE
Answer:
P
Step-by-step explanation:
Count the line endings in each letter as you write it down.
Answer:
I agree with tonb .Ace,he's/she's right
Actividad 1.1<br />Investigue sobre el tema de diferenciabilidad en un punto para encontrar los valores de "a" y "b" tales que<br />la función<br />definida a continuación sea diferenciable en t = 2, luego construya su gráfica.<br />at +b, sit < 2<br />f(t) = {2t2 – 1, si 2 st<br />1
Answer:
a = 8
b = -8
Step-by-step explanation:
You have the following function:
[tex]f(x)\\\\=at+b;\ \ t<2\\\\2t^2-1;\ \ 2\leq t[/tex]
A function is differentiable at a point c, if the derivative of the function in such a point exists. That is, f'(c) exists.
In this case, you need that the function is differentiable for t=2, then, you have:
[tex]f'(t)=a;\ \ \ \ t<2 \\\\f'(t)=4t;\ \ \ 2\leq t[/tex]
If the derivative exists for t=2, it is necessary that the previous derivatives are equal:
[tex]f'(2)=a=4(2)\\\\a=8[/tex]
Furthermore it is necessary that for t=2, both parts of the function are equal:
[tex]8(2)+b=2(2)^2-1\\\\16+b=8-1\\\\b=-8[/tex]
Then, a = 8, b = -8
ALGEBRA HELP PLEASE THANKS Evaluate the expression using exponential rules. Write the result in standard notation. [tex]\frac{4 x 10^{-4} }{20 x 10^{2} }[/tex]
Answer:
[tex]2 \times 10 {}^{ - 7} [/tex]
Step-by-step explanation:
[tex] \frac{4 \times 10 {}^{ - 4} }{20 \times 10 {}^{2} } = \frac{0.0004}{2000} = 2 \times 10 {}^{ - 7} [/tex]
Hope this helps ;) ❤❤❤
WHY IS THERE ANY HELP? PLEASE Solve the system of equations by using the substitution method. [tex]\left \{ {{x+y=6} \atop {x=2y}} \right.[/tex] Is there a solution, no solution, or infinite number? If there's a solution, what's the ordered pair?
Answer:
There is a solution. The ordered pair is (4, 2).
Step-by-step explanation:
Solve the system of equations by using the substitution method.
[tex]x+y=6\\x=2y[/tex]
Substitute x as 2y in the first equation and solve for y.
[tex]2y+y=6\\ 3y=6\\(3y)/3=6/3\\y=2[/tex]
Substitute y as 2 in the second equation and solve for x.
[tex]x=2(2)\\x=4[/tex]
What is the square root of -16?
Answer:-8
Step-by-step explanation:
Need Help with these (Giving brainiest if you can solve these)
Answer: try using sine for this equasion
Step-by-step explanation:
Brainliest for the correct awnser!!! The function is not an example of a rational function. True or false?
Answer:
true
Step-by-step explanation:
Question
Given that cot(0)= -1/2
and O is in Quadrant II, what is sin(0)? Write your answer in exact form. Do not round.
Provide your answer below:
Answer:
sin(O) = 2/sqrt(5) or 2sqrt(1/5)
Step-by-step explanation:
using 1+cot^2(x) = csc^2(x)
we have, taking reciprocal on both sides,
sin(x) = 1/sqrt(1+cot^2(x)
= 1/sqrt(1+(-1/2)^2)
= 1/sqrt(5/4)
= 2/sqrt(5) or 2sqrt(1/5)
Since angle x is in the second quadrant, sin(x) is positive.
A man walking on a railroad bridge is 2/5 of the way along the bridge when he notices a train at a distance approaching at the constant rate of 45 mph . The man can run at a constant rate in either direction to get off the bridge just in time before the train hits him. How fast can the man run?
Answer:
The Man needs to run at 9 mph
Step-by-step explanation:
Let M stand for the man's speed in mph. When the man
runs toward point A, the relative speed of the train with respect
to the man is the train's speed plus the man's speed (45 + M).
When he runs toward point B, the relative speed of the train is the
train's speed minus the man's speed (45 - M).
When he runs toward the train the distance he covers is 2 units.
When he runs in the direction of the train the distance he covers
is 3 units. We can now write that the ratio of the relative speed
of the train when he is running toward point A to the relative speed
of the train when he is running toward point B, is equal to the
inverse ratio of the two distance units or
(45 + M) 3
----------- = ---
(45 - M) 2
90+2 M=135-3 M
⇒5 M = 45
⇒ M = 9 mph
The Man needs to run at 9 mph
Answer: 9 mph
Step-by-step explanation:
Given that a man walking on a railroad bridge is 2/5 of the way along the bridge when he notices a train at a distance approaching at the constant rate of 45 mph .
If the man tend to run in the forward direction, he will cover another 2/5 before the train reaches his initial position. The distance covered by the man will be 2/5 + 2/5 = 4/5
The remaining distance = 1 - 4/5 = 1/5
If the man can run at a constant rate in either direction to get off the bridge just in time before the train hits him, the time it will take the man will be
Speed = distance/time
Time = 1/5d ÷ speed
The time it will take the train to cover the entire distance d will be
Time = d ÷ 45
Equate the two time
1/5d ÷ speed = d ÷ 45
Speed = d/5 × 45/d
Speed = 9 mph
Find the area under the standard normal probability distribution between the following pairs of z-scores. a. z=0 and z=3.00 e. z=−3.00 and z=0 b. z=0 and z=1.00 f. z=−1.00 and z=0 c. z=0 and z=2.00 g. z=−1.58 and z=0 d. z=0 and z=0.79 h. z=−0.79 and z=0
Answer:
a. P(0 < z < 3.00) = 0.4987
b. P(0 < z < 1.00) = 0.3414
c. P(0 < z < 2.00) = 0.4773
d. P(0 < z < 0.79) = 0.2852
e. P(-3.00 < z < 0) = 0.4987
f. P(-1.00 < z < 0) = 0.3414
g. P(-1.58 < z < 0) = 0.4429
h. P(-0.79 < z < 0) = 0.2852
Step-by-step explanation:
Find the area under the standard normal probability distribution between the following pairs of z-scores.
a. z=0 and z=3.00
From the standard normal distribution tables,
P(Z< 0) = 0.5 and P (Z< 3.00) = 0.9987
Thus;
P(0 < z < 3.00) = 0.9987 - 0.5
P(0 < z < 3.00) = 0.4987
b. b. z=0 and z=1.00
From the standard normal distribution tables,
P(Z< 0) = 0.5 and P (Z< 1.00) = 0.8414
Thus;
P(0 < z < 1.00) = 0.8414 - 0.5
P(0 < z < 1.00) = 0.3414
c. z=0 and z=2.00
From the standard normal distribution tables,
P(Z< 0) = 0.5 and P (Z< 2.00) = 0.9773
Thus;
P(0 < z < 2.00) = 0.9773 - 0.5
P(0 < z < 2.00) = 0.4773
d. z=0 and z=0.79
From the standard normal distribution tables,
P(Z< 0) = 0.5 and P (Z< 0.79) = 0.7852
Thus;
P(0 < z < 0.79) = 0.7852- 0.5
P(0 < z < 0.79) = 0.2852
e. z=−3.00 and z=0
From the standard normal distribution tables,
P(Z< -3.00) = 0.0014 and P(Z< 0) = 0.5
Thus;
P(-3.00 < z < 0 ) = 0.5 - 0.0013
P(-3.00 < z < 0) = 0.4987
f. z=−1.00 and z=0
From the standard normal distribution tables,
P(Z< -1.00) = 0.1587 and P(Z< 0) = 0.5
Thus;
P(-1.00 < z < 0 ) = 0.5 - 0.1586
P(-1.00 < z < 0) = 0.3414
g. z=−1.58 and z=0
From the standard normal distribution tables,
P(Z< -1.58) = 0.0571 and P(Z< 0) = 0.5
Thus;
P(-1.58 < z < 0 ) = 0.5 - 0.0571
P(-1.58 < z < 0) = 0.4429
h. z=−0.79 and z=0
From the standard normal distribution tables,
P(Z< -0.79) = 0.2148 and P(Z< 0) = 0.5
Thus;
P(-0.79 < z < 0 ) = 0.5 - 0.2148
P(-0.79 < z < 0) = 0.2852
4km in the ratio 9:4:7
Answer:
500km
Step-by-step explanation:
add all the proportions and then divide by 3. with conversion.
here are the 2 questions in the 2 pics separated lol
Answer:
60 and 87
Step-by-step explanation:
Question 1: The chance of losing would be 100% - 40% = 60%.
Question 2: Again, we just have to do 100% - 13% = 87%.
Answer:
Below
Step-by-step explanation:
First question:
Jade has a 40% chance of winnig wich could be expressed as 2/5
The chance of losing is the remainning pourcentage from 100%
●100-40 =60%
60% is the chance of losing wich could be expressed as 3/5
The sum of 3/5 and 2/5 is 1 so it's true.
■■■■■■■■■■■■■■■■■■■■■■■■■
Same method for the 2nd question:
The person has a 13 % chance of winning.
The chance of losing is 87%
● 100-13 =87
The average student loan debt for college graduates is $25,800. Suppose that that distribution is normal and that the standard deviation is $14,150. Let X = the student loan debt of a randomly selected college graduate. Round all probabilities to 4 decimal places and all dollar answers to the nearest dollar The middle 20% of college graduates' loan debt lies between what two numbers?
which of the following is equivalent to the expression below? log2-log14 A. LOG(1/7) B. LOG(-12) C. LOG 12 D. LOG 7
Answer:
The answer is option A.
Step-by-step explanation:
Using the properties of logarithms
that's
[tex] log(x) - log(y) = log( \frac{x}{y} ) [/tex]
log 2 - log 14 is
[tex] log(2) - log(14) = log( \frac{2}{14} ) [/tex]
Simplify
We have the final answer as
[tex] log( \frac{1}{7} ) [/tex]
Hope this helps you
Answer:
log ( 1/7)
Step-by-step explanation:
log2-log14
We know that log ( a/b) = log a - log b
log (2 /14)
log ( 1/7)
Section 8
Find the mean of these numbers:
24 18
37
82 17
26
Answer:
[tex]\boxed{Mean = 34.33}[/tex]
Step-by-step explanation:
Mean = Sum of Observations / No. Of Observations
Mean = (24+18+37+82+17+26)/6
Mean = 206 / 6
Mean = 34.33
Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods.
[infinity] n = 1 n2/5n n = 1
lim n→[infinity] an + 1/an =
a. converges
b. diverges
Answer:
A. The series CONVERGESStep-by-step explanation:
If [tex]\sum a_n[/tex] is a series, for the series to converge/diverge according to ratio test, the following conditions must be met.
[tex]\lim_{n \to \infty} |\frac{a_n_+_1}{a_n}| = \rho[/tex]
If [tex]\rho[/tex] < 1, the series converges absolutely
If [tex]\rho > 1[/tex], the series diverges
If [tex]\rho = 1[/tex], the test fails.
Given the series [tex]\sum\left\ {\infty} \atop {1} \right \frac{n^2}{5^n}[/tex]
To test for convergence or divergence using ratio test, we will use the condition above.
[tex]a_n = \frac{n^2}{5^n} \\a_n_+_1 = \frac{(n+1)^2}{5^{n+1}}[/tex]
[tex]\frac{a_n_+_1}{a_n} = \frac{{\frac{(n+1)^2}{5^{n+1}}}}{\frac{n^2}{5^n} }\\\\ \frac{a_n_+_1}{a_n} = {{\frac{(n+1)^2}{5^{n+1}} * \frac{5^n}{n^2}\[/tex]
[tex]\frac{a_n_+_1}{a_n} = {{\frac{(n^2+2n+1)}{5^n*5^1}} * \frac{5^n}{n^2}\\[/tex]
aₙ₊₁/aₙ =
[tex]\lim_{n \to \infty} |\frac{ n^2+2n+1}{5n^2}| \\\\Dividing\ through\ by \ n^2\\\\\lim_{n \to \infty} |\frac{ n^2/n^2+2n/n^2+1/n^2}{5n^2/n^2}|\\\\\lim_{n \to \infty} |\frac{1+2/n+1/n^2}{5}|\\\\[/tex]
note that any constant dividing infinity is equal to zero
[tex]|\frac{1+2/\infty+1/\infty^2}{5}|\\\\[/tex]
[tex]\frac{1+0+0}{5}\\ = 1/5[/tex]
[tex]\rho = 1/5[/tex]
Since The limit of the sequence given is less than 1, hence the series converges.
The measure of position called the midquartile of a data set is found using the formula StartFraction Upper Q 1 plus Upper Q 3 Over 2 EndFraction . Find the midquartile of the given data set. 23 37 49 34 35 41 40 26 32 22 38 42
Answer:
35.25
Step-by-step explanation:
Give the data set:
23 37 49 34 35 41 40 26 32 22 38 42
We are expected to calculate the midquartile of the given data set.
22 23 26 32 34 35 37 38 40 41 42 49
First step is to find the lower quartile which comprises of
22 23 26 32 34 35
Here the Q1 is (26+32)/2 = 58/2= 29
Second step to find the upper quartile which comprises of
37 38 40 41 42 49
Here the Q3 is (40+41) /2 = 81/2 = 41.5
Then to find the midquartile which is (Q1+Q3) /2 where Q1 is 29 and Q3 is 41.5
= (29+41.5)/2
= (70.5) /2 = 35.25
An estimator is said to be consistent if: the difference between the estimator and the population parameter grows smaller as the sample size grows larger. it is an unbiased estimator. the variance of the estimator is zero. the difference between the estimator and the population parameter stays the same as the sample size grows larger.
Answer:
the difference between the estimator and the population parameter grows smaller as the sample size grows larger.
Step-by-step explanation:
In Statistics, an estimator is a statistical value or quantity, which is used to estimate a parameter.
Generally, parameters are the determinants of the probability distribution. Thus, to determine a normal distribution we would use the parameters, mean and variance of the population.
An estimator is said to be consistent if the difference between the estimator and the population parameter grows smaller as the sample size grows larger. This simply means that, for an estimator to be consistent it must have both a small bias and small variance.
Also, note that the bias of an estimator (b) that estimates a parameter (p) is given by; [tex]E(b) - p[\tex]
Hence, an unbiased estimator is an estimator that has an expected value that is equal to the parameter i.e the value of its bias is equal to zero (0).
A sample variance is an unbiased estimator of the population variance while the sample mean is an unbiased estimator of the population mean.
Generally, a consistent estimator in statistics is one which gives values that are close enough to the exact value in a population.
Find the solution(s) of the system of equations: x2 + y2 = 8 y = x – 4 options: (–2,–6) (2,–2) and (–2,–6) (2,–2) No solutions
Answer: x=2 y=-2
(2,-2) one solution
Step-by-step explanation:
Solve by substitution
[tex]\begin{bmatrix}x^2+y^2=8\\ y=x-4\end{bmatrix}[/tex]
[tex]\mathrm{Subsititute\:}y=x-4[/tex]
[tex]\begin{bmatrix}x^2+\left(x-4\right)^2=8\end{bmatrix}[/tex]
[tex]2x^2-8x+16=8[/tex]
[tex]\mathrm{Isolate}\:x\:\mathrm{for}\:2x^2-8x+16=8:\quad x=2[/tex]
[tex]\mathrm{For\:}y=x-4[/tex]
[tex]\mathrm{Subsititute\:}x=2[/tex]
[tex]y=2-4[/tex] [tex]2-4=-2[/tex]
[tex]y=-2[/tex]
[tex]The\:solutions\:to\:the\:system\:of\:equations\:are[/tex]
[tex]x=2,\:y=-2[/tex]
How do you write in decimals eight and three tenths
Answer:
8.3
Step-by-step explanation:
RVLC2019] IC/Off
In AMNO, m = 20, n = 14, and mZM = 51°. How many distinct triangles can be formed given these measurements?
O There are no triangles possible.
VX
O There is only one distinct triangle possible, with m N= 33º.
O There is only one distinct triangle possible, with mZN 147º.
O There are two distinct triangles possible, with m2N 33° or mZN-147º.
Done
) Intro
DO
There is only one distinct triangle possible, with m N= 33º. Therefore, option B is the correct answer.
What is sine rule?Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.
The formula for sine rule is sinA/a=sinB/b=sinC/c
Given that, in ΔMNO, m = 20, n = 14, and m∠M = 51°.
Now, sin51°/20=sinN/14
0.7771/20=sinN/14
0.038855=sinN/14
sinN=14×0.038855
sinN=0.54397
N=33°
Therefore, option B is the correct answer.
Learn more about the sine rule here:
https://brainly.com/question/22288720.
#SPJ7
Show that between any two terminating decimals ,there is another terminating decimal
Answer:
1.5+1.7/2=1.6
Step-by-step explanation:
11. Caroline wraps packages at a store. She wraps
9 packages each hour. Which statement is true
about the number of packages she wraps?
A. In 2 hours, Caroline wraps an odd number of
packages.
B. In 3 hours, Caroline wraps an even number of
packages.
C. In 5 hours, Caroline wraps an odd number of
packages.
D. In 7 hours, Caroline wraps an even number of
packages.
Answer:
C. in five hours Caroline wraps an odd number of packages
Step-by-step explanation:
for A until hours you would multiply 2 by 9 and 2 by 9 is 18 and that's an even number so it's not A.
A eliminated.
for B in 3 hours 3 by 9 is 27 and that's an odd number so B is automatically eliminated.
for C in 5 hours all you would do is multiply the 9 by 5 and 9 by 5 is 45 and 45 is indeed an odd number so C is your answer.
for D 7 by 9 is 63 and 63 is an odd number so we already know that C is the answer but still we got to check and D is wrong because 63 is not an even number.