Answer:
Step-by-step explanation:
From the summary of the given data;
After the second dose, 137 of 452 subjects in the experimental group (group 1) experienced drowsiness as a side effect.
Let consider [tex]p_1[/tex] to be the probability of those that experience the drowsiness in group 1
[tex]p_1[/tex] = [tex]\dfrac{137}{452}[/tex]
[tex]p_1[/tex] = 0.3031
After the second dose, 31 of 99 subjects in the control group (group 2) experienced drowsiness as a side effect.
Let consider [tex]p_2[/tex] to be the probability of those that experience the drowsiness in group 1
[tex]p_2[/tex] = [tex]\dfrac{31}{99}[/tex]
[tex]p_2[/tex] = 0.3131
The objective is to be able to determine if the evidence suggest that a lower proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2 at the α=0.05 level of significance.
In order to do that; we have to state the null and alternative hypothesis; carry out our test statistics and make conclusion based on it.
So; the null and the alternative hypothesis can be computed as:
[tex]H_o :p_1 =p_2[/tex]
[tex]H_a= p_1<p_2[/tex]
The test statistics is computed as follows:
[tex]Z = \dfrac{p_1-p_2}{\sqrt{p_1 *\dfrac{1-p_1}{n_1} +p_2 *\dfrac{1-p_2}{n_2}} }[/tex]
[tex]Z = \dfrac{0.3031-0.3131}{\sqrt{0.3031 *\dfrac{1-0.3031}{452} +0.3131 *\dfrac{1-0.3131}{99}} }[/tex]
[tex]Z = \dfrac{-0.01}{\sqrt{0.3031 *\dfrac{0.6969}{452} +0.3131 *\dfrac{0.6869}{99}} }[/tex]
[tex]Z = \dfrac{-0.01}{\sqrt{0.3031 *0.0015418 +0.3131 *0.0069384} }[/tex]
[tex]Z = \dfrac{-0.01}{\sqrt{4.6731958*10^{-4}+0.00217241304} }[/tex]
[tex]Z = \dfrac{-0.01}{0.051378 }[/tex]
Z = - 0.1946
At the level of significance ∝ = 0.05
From the standard normal table;
the critical value for Z(0.05) = -1.645
Decision Rule: Reject the null hypothesis if Z-value is lesser than the critical value.
Conclusion: We do not reject the null hypothesis because the Z value is greater than the critical value. Therefore, we cannot conclude that a lower proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2
[tex]3\sqrt{2} - 5 \sqrt{18}[/tex] Help is appreciated!! Thank you so much! :D ❤❤
please help me ☣️☢️☢️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️▫️
Answer:
acute isosceles triangle
vertex angle, y = 44.0 degrees. (smallest angle)
Step-by-step explanation:
If the sides are in the ratio 4:4:3,
two of the sides have equal lengths, so it is an isosceles triangle.
Also, the sum of square of the two shorter sides is greater than the square of the longest side, so it is an acute triangle.
To find the smallest angle, we draw the perpendicular bisector of the base (side length 3) and form two right triangles.
The base angle x is given by the ratio
cos(x) = 1.5/4 = 3/8
Consequently the base angle is arccos(3/8) = 68.0 degrees.
The vertex angle equals twice the complement of 68.0
vertex angle, y = 2 (90-68.0) = 44.0 degrees. (smallest angle)
Mai invests $20,000 at age 20. She hopes the investment will be worth $500,000 when she turns 40. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal? Round to the nearest tenth of a percent.
Answer:16.1%
Step-by-step explanation:
Answer:
The investment needs the rate of growth to be approximately 16.1%.
Step-by-step explanation:
We wish to estimate what percent of adult residents in a certain county are parents. Out of 500 adult residents sampled, 175 had kids. Based on this, construct a 99% confidence interval for the proportion p of adult residents who are parents in this county. Express your answer in tri-inequality form. Give your answers as decimals, to three places.
Answer:
The 99% confidence interval is [tex]0.3003 < I < 0.3997[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 500[/tex]
The the number that are parents x = 175
The proportion of parents is mathematically represented as
[tex]\r p = \frac{x}{n}[/tex]
substituting values
[tex]\r p = \frac{175}{500}[/tex]
[tex]\r p = 0.35[/tex]
The level of confidence is given as 99% which implies that the level of significance is
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha =[/tex]1%
[tex]\alpha = 0.01[/tex]
The critical value for this level of significance is obtained from the table of critical value as
[tex]t_{x, \alpha } = t_{175, 0.05} = 2.33[/tex]
Generally the margin of error is mathematically evaluated as
[tex]M =\frac{ t_{175, 0.01 } * \sqrt{\r p (1-\r p)} }{\sqrt{n} }[/tex]
substituting values
[tex]M =\frac{ 2.33 * \sqrt{\r 0.35 (1-0.35)} }{\sqrt{500} }[/tex]
[tex]M = 0.0497[/tex]
Generally the 99% confidence interval is mathematically represented as
[tex]I = \r p \pm M[/tex]
[tex]\r p -M < I < \r p + M[/tex]
substituting values
[tex]0.35 -0.0497 < I < 0.35 + 0.0497[/tex]
[tex]0.3003 < I < 0.3997[/tex]
What is the equation of the following line? Be sure to scroll down first to see all answer options.
A.
y = 18x
B.
y = 9x
C.
y = -9x
D.
y = - x
E.
y = -18x
F.
y = x
Answer:
y=9x
Step-by-step explanation:
rise over run the rise is the y=9 and run is x=1.
9/1=9x
What is the quotient in polynomial form?
Answer:
Step-by-step explanation:
We are given the polynomial [tex]x^3+2^2-2x+3[/tex] and we are dividing by (x+3). So by performing one step of synthetic division we get
1 2 -2 3|-3
-3 3 -3
1 -1 1 0
So the quotient in polynomial form is [tex]x^2-x+1[/tex]
These two polygons are similar.
Find the value of z.
z = [?]
Answer:
Definitely 3 hmmm..
Step-by-step explanation:
6/2=3 so 9/z=3
tfo 9/3=3
The missing variables have values of 12, 5, 9, and 3, respectively, for x, y, w and z.
Given that there are two similar polygons with dimension:
Larger polygon = 9, 6, w, 15, x.
Smaller polygon = z, 2, 3, y, 4.
We need to find the missing value of the side length.
According to the definition of the similar polygons, the corresponding sides shows proportionality.
9/z = 6/2 = w/3 = 15/y = x/4
Solving for each variable =
i) Solve for z:
9/z = 6/2
Cross-multiplying:
6z = 9 × 2
6z = 18
Dividing both sides by 6:
z = 18/6
z = 3
ii) Solve for w:
6/2 = w/3
Cross-multiplying:
2w = 6 × 3
2w = 18
Dividing both sides by 2:
w = 18/2
w = 9
iii) Solve for y:
6/2 = 15/y
Cross-multiplying:
6y = 30
Dividing both sides by 6:
y = 5
iv) Solve for x:
6/2 = x/4
Cross-multiplying:
2x = 24
Dividing both sides by 2:
x = 12
Hence the values of the missing variables are x = 12, y = 5, w = 9 and z = 3.
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In the equation, the value of a is:
Answer:
Please check if the answer is a = 4 or not
When a fish is selected at random from a tank, the probability that it has a green tail is 0.54, the probability that it has red fins is 0.18, and the probability that it has both a green tail and red fins is 0.02. What is the probability that the selected fish will not have a red fin or a green tail? A) 28% B) 70% C) 2% D) 30%
Answer:
the answer is C
Step-by-step explanation:
hope this helps
The probability that the selected fish will not have a red fin or a green tail is 0.30.
To find the probability.
What is probability?probability is the ratio of the number of favorable outcomes and the total number of possible outcomes.
Given that:
G=fish has green tail
R=fish has red fin
G^R = fish has both a red fin and a green tail
P(G)=.54
P(R) = .18
P(G^R) = .02
P(GvR) = P(G) + P(R) - P(G^R) = .54 + .18 - .02 =
P(GvR) =.72 - .02 = .7
P(neither G nor R) = 1-.7 = .3 = 30%
So, the probability that the selected fish will not have a red fin or a green tail is 0.30.
Learn more about probability here:
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Imagine you have a data set with 9,987 names. The data set is sorted alphabetically. You want to find out if the name "David Joyner" is in the data set. Using a linear search, what is the minimum number of names we might have to check?
Answer:
1
Step-by-step explanation:
David Joyner might be the first name, so you may only have to check 1 name.
Solve the equation for X. 2(2x-4)=3(x+4) A -4 B 4 C 20 D 6
Answer:
X=20
Step-by-step explanation:
The answer is C
Given: (in picture as I cannot type it like that.) Name the postulate or theorem you can use to prove: (also in the picture) A. HL Theorem B. AAS Theorem C. SAS Postulate D. ASA Postulate
Answer:
You need to use the AAS (angle angle side) congruency theorem
Step-by-step explanation:
youre welcome!!!
Answer:
The Angle-Angle-Side Postulate (AAS)
Step-by-step explanation:
It is given that angle 1 and 2 are equivalent so that is angle #1
It is given that angle 3 and 4 are also equivalent so that is angle #2
And finally, it is given that side TS and side TR are equivalent giving you that last side you need to prove the type of Postulate it is
If this helped, please consider giving me brainliest, it will help me a lot
Have a good day! :)
In a sequence, the 40th term is 70, the 41st term is 72 and the 42nd term is 74.
a) State the term-to-term rule
b) Work out the first term
c) Work out the 80th term
Answer:
term to term rule is +2
The first term is -8
80th term is 150
Step-by-step explanation:
70 to 72 is adding 2
72 to 74 is adding 2
term to term rule is +2
The equation for a sequence like this is
xn = a + d(n−1)
where n is the term number a is the first term and d is the term to term rule
Using the 40th term is 70
70 = a + 2( 40-1)
70 = a + 2( 39)
70 = a + 78
Subtract 78 from each side
-8 = a
The first term is -8
80th term
xn = a + d(n−1)
x80 = -8 +2 (80-1)
= -8+2(79)
= -8+158
= 150
Digital music distribution provides an opportunity for everyone to get their music heard. In order to get on a service like iTunes, one needs to pay for distribution through a service like Tunecore or CD Baby. These services make sure that your music is heard in the different platforms. Suppose the distributor charges the artist a $50.00 cost for distribution, and the streaming services pays $4.00 per one thousand streams. Model the profit for the total number of streams by answering the questions below: Use the cost for distribution to build your y-intercept. What is the y-intercept? Hint: the y-intercept is a point on the y axis, so your answer should be an ordered pair. Hint: you have to keep in mind that any time you pay for something, you are SPENDING money, if your y-intercept is incorrect, all your numbers will be off Use the payment per thousand streams to build your slope. What is the slope? Use the slope-intercept format (y = mx + b) to give the equation of the line. What is the equation of this line? Graph the line by adjusting the sliders below. Show your line by attaching an image below. After how many streams will you pay for the distributor charges? (hint: this is where the line crosses the x-axis, round to the nearest thousand) How many streams would it take to profit $300,000? Challenge Question: In 2019, Old Town Road became one of the most streamed songs of all time passing the previous record holders, Despacito and One Sweet Day. The second week the song was #1, it set an all time streaming record. It was streamed 143 million times (143,000,000) in the US, nearly 30 million higher than the previous record holder Drake, In My Feelings. Calculate the profit earned using these numbers. (Hint: use the slope intercept format to build this equation).
Answer:
the answer is 1.00
Step-by-step explanation:
pls mark me as the brainliest and tell me thanks
Solve the given simultaneous equations : 2x + 3y = 17 ; 3x - 2y = 6
Answer:
x= 4, y=3
Step-by-step explanation:
2x + 3y = 17
3x - 2y = 6
----------
If we double the first and triple the second equation, and add up, we can get rid of y:
4x+6y= 34+9x - 6y= 18-----------------13x= 52x= 4Then it is easy to find the value of y:
2*4+3y= 173y= 9y= 3Answer is: x= 4, y=3
The ratio of men to women working for a company is 7 to 5 . If there are 90 women working for the company, what is the total number of employees?
Answer:
The Total of employees
=216 employees
Step-by-step explanation:
Ratio of men to women is 7 to 5
Meaning
Men/women= 7/5
If their are 90 women
Let men= x
X/women= 7/5
X= women *7/5
X= 90*7/5
X= 18*7
X= 126
There are a total of 126 men
The Total of employees=men + women
The Total of employees=126+90
The Total of employees
=216 employees
Line segment TS is tangent to circle O at point N.
Circle O is shown. Line segment Q N goes from one side of the circle to the other side. Tangent T S intersects the circle at point N. Point P is on the circle between points Q and N. Point R is on the circle between points Q and N. Angle Q N T is 74 degrees.
If the measure of Angle Q N T is 74°, what is the measure of Arc Q P N?
37°
74°
148°
212°\
Answer:
148°
Step-by-step explanation:
The measure of the intercepted arc QN is twice the measure of inscribed angle QNT.
arc QN = 2(74°) = 148°
_____
Comment on the question and answer
Your description "on the circle between points Q and N" is ambiguous. You used the same description for both points P and R. The interpretation we used is shown in the attachment. If point P is on the long arc NQ, then the measure of arc QPN will be the difference between 148° and 360°, hence 212°. You need to choose the answer that matches the diagram you have.
__
We call angle QNT an "inscribed angle" because it is a degenerate case of an inscribed angle. The usual case has the vertex of the angle separate from the ends of the arc it intercepts. In the case of a tangent meeting a chord, the vertex is coincident with one of the ends of the intercepted arc. The relation between angle measure and arc measure remains the same: 1 : 2.
Answer:
148
Step-by-step explanation:
Edge 2020
1. Manuel quiere fabricar banderitas chilenas para venderlas en los partidos de la selección nacional. Si se demora 1 hora en hacer 45 banderitas y trabaja 5 horas diarias. ¿Cuántos días se demorará en fabricar 1800 banderitas?
Answer:
[tex]\large \boxed{\text{Eight days}}[/tex]
Step-by-step explanation:
1. Calculate the hours
[tex]\text{Hours} = \text{1800 flags} \times \dfrac{\text{1 h}}{\text{45 flags}} = \textbf{40 h}[/tex]
2. Calculate the days
[tex]\text{Days} = \text{40 h} \times \dfrac{\text{1 da}}{\text{5 h}} = \text{8 da}\\\\\text{It will take $\large \boxed{\textbf{eight days}}$ to make 4500 flags.}[/tex]
6th grade math , help me please :)
Answer:
a= 7/20
b=35
Step-by-step explanation:
A was simple because 7 people with blue eyes for every 20 people written in fraction form. For b they say what if it was 100 total people so 20 x 5 = 100 so 7 x 5= 35 so your answer to b is 35
A circular garden has a diameter of 12 feet. About how much trim is needed to surround the garden by placing trim on the garden's circumference?
Trim = circumference
= 2[tex]\pi r[/tex]
= 2 x 3.14 x 6
= 37.68 feet
An important proportion that the ancient Greeks used was the
the ancient Greek used the golden ratio
Answer:
An important proportion that the Ancient Greeks used was the Golden Mean, the a0
Step-by-step explanation:
Also known as Golden Ratio, Divine Proportion, or Golden Section
3 + 5x, for x = 10
A. 350
B. 120
C. 53
D. 75
Answer:C
Step-by-step explanation:
Pemdas
3+5(10)
5*10=50
3+50=53
A fair die is rolled. What is the probability of rolling a 3 or a 4?
Answer:
2/6 which when simplified, is equal to 1/3
Answer:
1/3
Step-by-step explanation:
What is the missing side lenght in the triangle below?
Answer:
45
Step-by-step explanation:
Let's call the missing side x
This is a right triangle and in right triangles the square length of hypotenuse is equal to sum of square length of base and side lengths
53^2 = 28^2 + x^2
x = 45
What is the equation of the line whose y-intercept is 3 and slope is 1? A.y = x + 3 B.y = 3x + 1 C.y = x - 3
Answer:
The answer is option A
Step-by-step explanation:
Equation of a line is y = mx + b
where
m is the slope
b is the y intercept
From the question
b / y intercept = 3
m / slope = 1
Substitute these values into the below equation
y = mx + b
We have the answer as
y = x + 3
Hope this helps you
Answer: A. Y= x+3
Step-by-step explanation: since the value of the slope is 1 it would go next to the x but x is also equal to 1x. And you add 3 since the y intercept is 3 and the format of the equation is y equals slope plus the y intercept hope this helps
the initial population of a town is 16,237 and it grows with a doubling time of 24 years. what will the popluation be in 2 years.
Answer: 17,203 people
Step-by-step explanation:
The formula for solving this is;
[tex]P(t) = P_{0} (2)^{t/dt}[/tex]
Where;
P(t) is the population at time t
[tex]P_{0}[/tex] is the initial population
t is the year of interest
dt is the amount of time it takes to double.
[tex]P(t) = P_{0} (2)^{t/dt}[/tex]
[tex]P(2) = 16,237 (2)^{2/24}[/tex]
= 17,202.50
= 17,203 people
Choose the correct equation for the parabola based on the given information. Given: Focus:(4,-3) Vertex: (-2,-3) a. 24(y+3) = (x+2)^2 b. 24(x+2)=(y+3)^2 c. 6(x-4)= (y+3)^2 d. 6(y+3)=(x-4)^2
Answer: b. 24(x + 2) = (y + 3)²
Step-by-step explanation:
Vertex: (-2, -3)
Focus: (4, -3)
↓
same y-value so equation will be y²
Equation: a(x - h) = (y - k)²
a = 4p where p is the distance from Vertex to Focush is the x-coordinate of the Vertexk is the y-coordinate of the VertexGiven: h = -2, k = -3, a = 4[4 - (-2)] --> a = 24
Input those values into the equation: 24(x + 2) = (y + 3)²
A researcher studying public opinion of proposed Social Security changes and asks a random sample of adult Americans whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many adult Americans does the researcher need to sample in the following cases
(a) if 37% of all adult Americans support the changes?
(b) 25% of all adults Americans support the changes?
Complete question is;
A researcher studying public opinion of proposed Social Security changes and asks a random sample of 30 adult Americans whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many adult Americans does the researcher need to sample in the following cases
(a) if 37% of all adult Americans support the changes?
(b) 25% of all adults Americans support the changes?
Answer:
A) 13 adults
B) 23 adults
Step-by-step explanation:
A) We are given;
p = 37% = 0.37
Since we are told that this is an approximately normal distribution, we will use the formula;
np(1 - p) ≥ 10
Thus;
0.37n(1 - 0.37) ≥ 10
n ≥ 10/(0.63 × 0.37)
n ≥ 42.9
We need a whole number, thus n = 43
From the question, we have already 30 adults , so the required number of adults are; 43 - 30 = 13 adults
B) We are given;
p = 25% = 0.25
Since we are told that this is an approximately normal distribution, we will use the formula;
np(1 - p) ≥ 10
Thus;
0.25n(1 - 0.25) ≥ 10
n ≥ 10/(0.75 × 0.25)
n ≥ 53.33
n ≈ 53
From the question, we have already 30 adults , so the required number of adults are; 53 - 30 = 23 adults
What is the range of y=log2(x-6)
Answer:
6<y<∞
Step-by-step explanation:
Logarithmic curves can never go left to 0 and go on forever to the right.
x=6 would make the function 0, so 6 is the lower limit and infinity would be the upper limit.
WILL MAKE BRAINLIST----- Describe both rotational symmetry and reflection symmetry. Find four examples of symmetry in your classroom.
Answer:
When an obect has rotational symmetry, that means the object will look the same after a certain amount of rotating. When an object has reflection symmetry, it means the object mirrors itself at the midpoint.
Step-by-step explanation: