Use the chain rule:
[tex]y=\ln(\sin(3x))[/tex]
[tex]y'=(\ln(\sin(3x)))'[/tex]
[tex]y'=\dfrac{(\sin(3x))'}{\sin(3x)}[/tex]
[tex]y'=\dfrac{\cos(3x)(3x)'}{\sin(3x)}[/tex]
[tex]y'=\dfrac{3\cos(3x)}{\sin(3x)}[/tex]
[tex]y'=3\cot(3x)[/tex]
Autism and Maternal Antidepressant Use A recent study41 compared 298 children with Autism Spectrum Disorder to 1507 randomly selected con- trol children without the disorder. Of the children with autism, 20 of the mothers had used antidepres- sant drugs during the year before pregnancy or the first trimester of pregnancy. Of the control children, 50 of the mothers had used the drugs.
(a) Is there a significant association between prena- tal exposure to antidepressant medicine and the risk of autism? Test whether the results are sig- nificant at the 5% level.
(b) Can we conclude that prenatal exposure to antidepressant medicine increases the risk of autism in the child? Why or why not?
Answer:
(a) We conclude that there is a significant association between prenatal exposure to antidepressant medicine and the risk of autism at 5% significance level.
(b) Yes, we can conclude that prenatal exposure to antidepressant medicine increases the risk of autism in the child.
Step-by-step explanation:
We are given that Autism and Maternal Antidepressant Use A recent study 41 compared 298 children with Autism Spectrum Disorder to 1507 randomly selected control children without the disorder.
Of the children with autism, 20 of the mothers had used antidepressant drugs. Of the control children, 50 of the mothers had used the drugs.
Let [tex]p_1[/tex] = proportion of mothers who had used drugs having Autism Spectrum Disorder in their children.
[tex]p_2[/tex] = proportion of mothers who had used drugs not having Autism Spectrum Disorder in their children.
(a) Null Hypothesis, [tex]H_0[/tex] : [tex]p_1=p_2[/tex] {means that there is no significant association between prenatal exposure to antidepressant medicine and the risk of autism}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1\neq p_2[/tex] {means that there is a significant association between prenatal exposure to antidepressant medicine and the risk of autism}
The test statistics that would be used here Two-sample z test for proportions;
T.S. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of mothers who had used drugs having Autism Spectrum Disorder in their children = [tex]\frac{20}{298}[/tex] = 0.067
[tex]\hat p_2[/tex] = sample proportion of mothers who had used drugs not having Autism Spectrum Disorder in their children = [tex]\frac{50}{1507}[/tex] = 0.033
[tex]n_1[/tex] = sample of children with Autism Spectrum Disorder = 298
[tex]n_2[/tex] = sample of children without Autism Spectrum Disorder = 1507
So, the test statistics = [tex]\frac{(0.067-0.033)-(0)}{\sqrt{\frac{0.067(1-0.067)}{298}+\frac{0.033(1-0.033)}{1507} } }[/tex]
= 2.281
The value of z test statistics is 2.281.
Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.
Since our test statistic doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that there is a significant association between prenatal exposure to antidepressant medicine and the risk of autism.
(b) Yes, we can conclude that prenatal exposure to antidepressant medicine increases the risk of autism in the child because if we reconsider our hypothesis for one-tailed test in which the null hypothesis states that the prenatal exposure to antidepressant medicine does not increases the risk of autism in the child.
For this hypothesis also, our test statistics will be more than the critical value of z and due to which we reject our null hypothesis and conclude that prenatal exposure to antidepressant medicine increases the risk of autism.
A variety of stores offer loyalty programs. Participating shoppers swipe a bar-coded tag at the register when checking out and receive discounts on certain purchases. A typical Saturday morning shopper who does not participate in this program spends $120 on her or his order. In a sample of 80 shoppers participating in the loyalty program, each shopper spent $130 on average during a recent Saturday, with standard deviation $40. Is this statistical proof that the shoppers participating in the loyalty program spent more on average than typical shoppers?
Answer:
[tex]t=\frac{130-120}{\frac{40}{\sqrt{80}}}=2.236[/tex]
Now we can find the degrees of freedom:
[tex]df=n-1=80-1=79[/tex]
Now we can calculate the p value with the alternative hypothesis using the following probability:
[tex]p_v =P(t_{(79)}>2.236)=0.0141[/tex]
Using a significance level of 0.01 or 1% we have enough evidence to FAIL to reject the null hypothesis and we can conclude that shoppers participating in the loyalty program NOT spent more on average than typical shopper at this significance level assumed
Step-by-step explanation:
Information given
[tex]\bar X=130[/tex] represent the sample mean
[tex]s=40[/tex] represent the sample standard deviation
[tex]n=80[/tex] sample size
[tex]\mu_o =120[/tex] represent the value to verify
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to verify if shoppers participating in the loyalty program spent more on average than typical shoppers (120) , the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 120[/tex]
Alternative hypothesis:[tex]\mu > 120[/tex]
The statistic for this case is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{130-120}{\frac{40}{\sqrt{80}}}=2.236[/tex]
Now we can find the degrees of freedom:
[tex]df=n-1=80-1=79[/tex]
Now we can calculate the p value with the alternative hypothesis using the following probability:
[tex]p_v =P(t_{(79)}>2.236)=0.0141[/tex]
Using a significance level of 0.01 or 1% we have enough evidence to FAIL to reject the null hypothesis and we can conclude that shoppers participating in the loyalty program NOT spent more on average than typical shopper at this significance level assumed
A test of sobriety involves measuring the subject's motor skills. Twenty randomly selected sober subjects take the test and produce a mean score of A with a standard deviation of B. At the 0.01 level of significance, test the claim that the true mean score for all sober subjects is equal to 35.0. Use the critical value method of testing hypotheses.
Answer:
Step-by-step explanation:
Hello!
The variable of interest is:
X: motor skills of a sober subject.
n= 20
X[bar]= 37.1
S= 3.7
The claim is that the average score for all sober subjects is equal to 35.0, symbolically: μ= 35.0
The hypotheses are:
H₀: μ = 35.0
H₁: μ ≠ 35.0
α: 0.01
The statistic to use, assuming all conditions are met, is a one sample t- test
[tex]t= \frac{X[bar]-Mu}{\frac{S}{\sqrt{n} } } ~t_{n-1}[/tex]
[tex]t_{H_0}= \frac{37.1-35.0}{\frac{3.7}{\sqrt{20} } } = 2.34[/tex]
This test is two-tailed, meaning, the rejection region is divided in two and you'll reject the null hypothesis to low values of t or to high values of t:
[tex]t_{n-1;\alpha /2}= t_{19; 0.005}=-2.861[/tex]
[tex]t_{n-1;1-\alpha /2}= t_{19; 0.995}= 2.861[/tex]
The decision rule using this approach is:
If [tex]t_{H_0}[/tex] ≤ -2.861 or if [tex]t_{H_0}[/tex] ≥ 2.861, you reject the null hypothesis.
If -2.861 < [tex]t_{H_0}[/tex] < 2.861, you do not reject the null hypothesis.
The value is within the non rejection region, the decision is to not reject the null hypothesis.
I hope this helps!
24.3 cm
8.5 cm
9.7 cm
Answer:
area: 144.5 cm^2
Step-by-step explanation:
Maybe you want the area of this figure.
The area of a trapezoid is given by the formula ...
A = (1/2)(b1 +b2)h
Using the given dimensions, the area is ...
A = (1/2)(9.7 cm +24.3 cm)(8.5 cm)
A = (1/2)(34 cm)(8.5 cm) = 144.5 cm^2
In ΔCDE, the measure of ∠E=90°, DC = 5, CE = 4, and ED = 3. What ratio represents the sine of ∠C?
Answer:
As E is right angle , CD is hypotenuse , and ED is perpendicular and CE is the base .
Thus sinC = Perpendicular/ Hypotenuse
sinC = ED/CD
sinC = 3/5
The sine of an angle in a right triangle is the ratio of the side opposite to
the angle to the hypotenuse side.
[tex]\underline{sin\angle C \ is \ \dfrac{3}{5}}[/tex]Reasons:
The given parameters of ΔCDE are;
∠E = 90°, DC = 5, CE = 4, ED = 3
Required: The ratio that represents the sine of ∠C
Solution:
Given that ∠E = 90° therefore;
ΔCDE is a right triangle
DC = The hypotenuse side = 5
ED = 3 = The side opposite ∠C
[tex]sin\angle C = \mathbf{\dfrac{Opposite \ leg \ length}{Hypotenuse \ length}}[/tex]
Therefore;
[tex]\underline{sin\angle C \ is \ \dfrac{3}{5}}[/tex]
Learn more about trigonometric ratios here:
https://brainly.com/question/4232719
HELP ASAP!!
What is the area of the composite figure below?
A) 84 square inches
B) 90 square inches
C) 98 square inches
D) 104 square inches
Answer:
84 square inches
Step-by-step explanation:
First, separate this shape into two shapes you can easily find the area of. You can do this by turning it into a rectangle and a rhombus.
Say the rectangle has measurements of 5 by 6 inches. The area of that rectangle will be 30 square inches. Save this value to add on later.
The rhombus now has a height of 4 (because the side length 10 minus the side length 6 equals 4), and two bases by the values of 12 and 15. The area of a rhombus can be found with the equation:
a = 1/2(b1 + b2) x h
Simply plug in those values to find the area of the rhombus, 54. Now add the area of the rhombus and the area of the rectangle to get 84 square inches as your final area.
if a triangle has a base of 5 cm and a height of 6 cm what’s it’s area?
Answer:
the area is 30 you have to muiltly the two together
Step-by-step explanation:
Which step in conducting research should be done before writing a research question?
Ab
Interview an expert about your topic.
Use evidence to support your position.
Decide on a subject that you are interested in
O Make a plan to learn more about your topic.
Answer:
It is C
Step-by-step explanation:
You have to make a subject to research before your make a question, because you dont know what your looking for then.
I know i might be late but can i have brainliest if its correct so i can level up?
Thank you!
Answer:
cthe therd one
Step-by-step explanation:
you need a subject to research before you make a question,
so you can also begon with your work like assimgments.
Area of the base, B = 42 square meters
and height = 3 meters
Answer:
14
Step-by-step explanation:
all i did was divided 42 by 3 and got 14
Which equation represents a line that passes through (5,1) and has a slope of 1/2
Answer:
Step-by-step explanation:
Since you did not post answer choices, there's not too much I can tell you. One thing for sure is that the equation must have 1/2x. This represents the slope at which the equation is increasing. To find which equation passes through (5,1), all you have to do is plug in 5 into the x in your equation. After you solve, if the y you get is equal to the y value of 1, you know that is the line that alsses through (5,1). I hope this helps.
Answer b
Step-by-step explanation:
It’s fast
which graphs represents a proportional relationship between x and y?
On a multiple-choice test, each question has 4 possible answers. A student does not know
answers to three questions, so the student guesses.
What is the probability that the student gets all three questions right?
Answer:
1.56% probability that the student gets all three questions right
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the student guesses the answer correctly, or he does not. The probability of the student guessing the answer of a question correctly is independent of other questions. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Each question has 4 possible answers, one of which is correct.
So [tex]p = \frac{1}[4} = 0.25[/tex]
Three questions.
This means that [tex]n = 3[/tex]
What is the probability that the student gets all three questions right?
This is [tex]P(X = 3)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.25)^{3}.(0.75)^{0} = 0.0156[/tex]
1.56% probability that the student gets all three questions right
A pyramid has a volume of 1,994 inches cubed and a rectangular base with the dimensions 18 inches by 9 inches. What is the height of the pyramid?
Answer:D)36
Step-by-step explanation:
Took the test
What are the solutions of this quadratic equation? 4x^2 + 3 = 4x + 2
Answer:
The answer is ±0.5 or ±1/2
Step-by-step explanation:
When you solve by using the quadratic formula, you get double roots that will solve the equation. Hope this helps!!
The solution of the quadratic equation is 1/2 and 1/2.
We have to find, the solution of the quadratic equation is [tex]4x^2 + 3 = 4x + 2[/tex].
To determine the solution of the quadratic equation following all the steps given below.
Equation; [tex]4x^2 + 3 = 4x + 2[/tex]
Step1; The equation is written in the standard form of the quadratic equation.[tex]4x^2 + 3 = 4x + 2\\\\4x^2 + 3 - 4x - 2=0\\\\4x^2 -4x +1 =0[/tex]
Step2; Factorize the equation for finding the solution of the equation,[tex]\rm 4x^2-4x +1 = 0\\\\4x^2-2x -2x + 1= 0\\\\2x(2x-1) - 1 (2x-1)=0\\\\(2x-1) ( 2x-1) = 0[/tex]
Step3; The solution for the equation is,[tex]\rm 2x- 1= 0 , \ 2x = 1 , \ x = \dfrac{1}{2}\\\\And \ 2x- 1= 0 , \ 2x = 1 , \ x = \dfrac{1}{2}\\\\[/tex]
Hence, The required solution of the equation is 1/2 and 1/2.
For more details refer to the link given below.
https://brainly.com/question/19776811
A local aquarium is filled halfway with water. How many cubic inches of water are in the aquarium?
Answer:
The aquarium contains [tex]\frac{x}{2}[/tex] cubic inches of water
Step-by-step explanation:
Given: A local aquarium is filled halfway with water.
To find: Volume of water in the aquarium
Solution:
Volume refers to the three-dimensional space enclosed by a boundary. S.I. unit of volume is [tex]m^3[/tex]
Let x cubic inches denotes volume of an aquarium.
As a local aquarium is filled halfway with water,
the aquarium contains [tex]\frac{x}{2}[/tex] cubic inches of water.
Answer:
Step-by-step explanation:
Showing results for The aquarium contains cubic inches of waterStep-by-step explanation:Given: A local aquarium is filled halfway with water.To find: Volume of water in the aquarium Solution:Volume refers to the three-dimensional space enclosed by a boundary. S.I. unit of volume is Let x cubic inches denotes volume of an aquarium.As a local aquarium is filled halfway with water,the aquarium contains cubic inches of water.
90 units needed 8units per case
Answer: 90/8=11.25
Step-by-step explanation:
solve
[tex]y {4 - 2y {3 = 0}^{?} }^{?} [/tex]
please
Step-by-step explanation:
y4 - 2y3 = 0
y3(y - 2) = 0
y3 = 0
y = 0
Y - 2 = 0
Y = 2
Help please! ASAP!!
The first choose is incorrect or correct
The second choose is 84 28 42 56
The third choose is 126 84 63 42
Answer:
Correct
Step-by-step explanation:
Amount of granular of 10 batch of raisin nut = 28 cups
To find raisin nut 30 batches = 28 x 3 = 84
Amount of granula of 10 batch of honey almond energy = 42
To find honey almond 15 batches = 42 + 21 = 63
help me plsssssssssssss
Answer:
The radius is 5 cm
Step-by-step explanation:
The formula for the area of a circle is : [tex]\p*radius^2[/tex]
To work out the length of the radius you would first need to divide the area of 78.5 cm by pi (pi=3.14), this gives you [tex]25cm^2\\[/tex]. This is because by dividing the area by pi we are isolating the value of the radius squared.
The final step is to work out the radius. You can do this by finding the square root of the radius squared which is 25, this gives you 5 cm. This means that the radius is 5 cm. This is because the square root is a number that when squared equals that number.
1) Divide 78.5 by pi.
[tex]78.5/\pi=25cm^2[/tex]
2) Find the square root of 25 cm squared.
[tex]\sqrt{25} =5 cm[/tex]
In this question pi is 3.14
A major home improvement store conducted its biggest brand recognition campaign in the company's history. A series of new television advertisements featuring well-known entertainers and sports figures was launched. A key metric for the success of television advertisements is the proportion of viewers who "like the ads a lot." A study of 1,189 adults who viewed the ads reported that 230 indicated that they "like the ads a lot." The percentage of a typical television advertisement receiving the "like the ads a lot" score is believed to be 22%. Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad (i.e. if there is evidence that the population proportion of "like the ads a lot" for the company's ads is less than 0.22) at a 0.01 level of significance. 1) State H subscript 0 and H subscript 1. (2 points) 2) What critical value should the company officials use to determine the rejection region? (2 points) 3) What is the value of the test statistic? (4 points) 4) What is the conclusion of the hypothesis test? Is there evidence that the population proportion of "like the ads a lot" for the company's ads is less than 0.22?
Answer:
Step-by-step explanation:
Identify: Hypothesized π = 0.22 n =1189 X = 230
Estimate the sample proportion, p, of defective items. p= X/n = 230/1189 = 0.1934
List the formula for the standard error of a proportion. [tex]\sqrt{PQ/n}[/tex]
Estimate the standard error of a proportion. [tex]\sqrt{PQ/n} = \sqrt{0.22\times 0.78/1189} = 0.0120[/tex]
State the null and alternative hypotheses below.
H0: P = 0.22
H1: P<0.22
Illustrate the acceptance and rejection regions of the diagram to the right.
check the attached image below for the diagram
Identify the critical Z , -1.645
Fornulate the decision rule and list below.
If Z calculated is less than Z critical we reject null hypothesis
Calculate your test statistic.
[tex]Z= \frac{p-P}{\sqrt{PQ/n}} = \frac{0.1934-0.22}{0.0120}= -2.217[/tex]
Do you accept or reject the null hypothesis at 0.05 level of significance? Reject
State your conclusion. Should the quality control manage accept the shipment or return it?
WE have sufficient evidence that the population proportion of "like the ads a lot" for the company's ads is less than 0.22 at a 0.05 level of significance.
If a 0.01 level of significance had been used in the test, would you have accepted or rejected the null hypothesis?
at 0.01 level of significance the critical value of Z is -2.33
Since Z calculated is greater than Z critical value we accept the null hypothesis
According to the picture, whats the answer?
Answer:
126 in^2
Step-by-step explanation:
The surface area can be found from the surface area formula:
SA = 2(LW +LH +WH)
I like to rearrange it slightly to ...
SA = 2(LW +H(L +W))
For the given dimensions, the area is ...
SA = 2(6·3 + 5(6 +3)) = 2(18 +45) = 126 . . . . square inches
there are 7 rows of 9 people . how many people in all ?
There are 7 rows of 9 people then there will be 63 people in all.
MultiplicationMultiplication refers to the product of two numbers or more than two numbers. It states the result when a number is taken times.
How to find the number of people?There are 7 rows of 9 people.
This means in each row, there are 9 people.
Then the number of people in 7 rows will be 7 multiplied by 9 i.e.,
[tex]7\times9=63[/tex]
So, the number of people will be 63.
Learn more about multiplication here- https://brainly.com/question/10590363
#SPJ2
standard form of y=-3 (x-2)²
Answer:
y = [tex]-3x^2+12x-12[/tex]
Step-by-step explanation:
(x-2)^2 = (x-2)(x-2) => [tex]x^2-4x+4[/tex]
now, multiple every term by negative 3 and you get...
-3x^2+12x-12
6x + 12 = −6x − 35
- How is this solved?
Step-by-step explanation:
here,
6x+12= -6x-356x+6x = -35-12
12x= -47
x= -47
[tex] \frac{ - 47}{12} [/tex]
Write as a fraction in lowest terms:
0.126126126..=a/b
A=
b =
DONE
Answer:
a= 14
b= 111
Step-by-step explanation:
just took it
What is the product of 3rad3cis(pi/8) and 3rad5cis(2pi/3)
Answer:
[tex]9\sqrt{15}*cis(\dfrac{19\pi}{24})[/tex]
Step-by-step explanation:
To multiplying complex numbers in polar form, follow these steps:
Multiply the polar magnitudes of the complex numbers.Add the angles of the complex numbers.Given the two complex number in polar form
[tex]3\sqrt{3}\:cis(\dfrac{\pi}{8})\:\:and\:\:3\sqrt{5}\:cis(\dfrac{2\pi}{3})\\\\3\sqrt{3}\:cis(\dfrac{\pi}{8})*3\sqrt{5}\:cis(\dfrac{2\pi}{3})=(3\sqrt{3}*3\sqrt{5})*cis(\dfrac{\pi}{8}+\dfrac{2\pi}{3})[/tex]
[tex]=9\sqrt{15}*cis(\dfrac{3\pi+8*2\pi}{24})\\\\=9\sqrt{15}*cis(\dfrac{19\pi}{24})[/tex]
Answer: 34.86cis (2.49)
Step-by-step explanation: I took the quiz.
X Nate brought $37.75 to the art supply store he bought a brush a SketchBook and a paint set the brush was 1/4 as much as a SketchBook and the Sketchbook cost 2/3 the cost of the paint set Nate had $2 left over after buying these items.
Answer:
cost of paint set =$19.5
cost of Sketchbook = $13
cost of brush = $3..25
Step-by-step explanation:
Total money with Nate = $37.75
Let the cost of paint set be $x
As the Sketchbook cost 2/3 the cost of the paint set
Thus cost of Sketchbook = $(2/3)x
Cost of brush is 1/4 of Sketchbook
Thus cost of brush = (1/4)*(2/3)x =$ 1/6x
Total cost of all the three item in terms of x is
x + (2/3)x + ( 1/6)x
=>(6x+4x+x)/6 = 11x/6
Given that after money spent on buying all the three thing Nate has left $2
subtracting money spent on buying three things from total money is equal to $2
Mathematically it can be written as
$37.75 - 11x/6 = $2
=> $37.75 - $2 11x/6
=>$35.75 = 11x/6
=> $35.75*6 = 11 x
=> $214.5 = 11x
=> $214.5/11 = x
=> x = 19.5
Thus,
cost of paint set = x = $19.5
cost of Sketchbook = $(2/3)x =$(2/3)*19.5 = $13
cost of brush = $ 1/6x = $ (1/6)*19.5 = $3.25
What’s the correct answer for this?
Answer:
Answer is the first one :)
Step-by-step explanation:
√(-7-5)² + (-7-9)²
answer is 20
hope this helps
Answer:
A.
Step-by-step explanation:
In the attached file
hey can you guys help me with this? thx a lot! <3
Choose the answer based on the most efficient method as presented in the lesson.
If the first step in the solution of the equation -x + 6 = 5 - 3x is "subtract 5," then what should the next step be?
add x
add 3x
subtract 6
Answer:
add x
Step-by-step explanation:
get the constants on one side, and the variables on the other for easiest solving.
A square has side length of 9 which is the following a correct way to find the area of the square
Answer:
b means one of the sides of a square it doesn't matter because all sides are the same
Formula for a square is
b^2 or b*b