Answer:
x≤3
Step-by-step explanation:
9-3x≥2(x-3)
9-3x≥2x-6
-3x-2x≥-6-9
-5x≥-15
-5x/-5≥-15/-5
x≤3
A researcher predicts that listening to music while solving math problems will make a particular brain area more active. To test this, a research participant has her brain scanned while listening to music and solving math problems, and the brain area of interest has a percentage signal change of 58. From many previous studies with this same math problems procedure (but not listening to music), it is known that the signal change in this brain area is normally distributed with a mean of 35 and a standard deviation of 10. (a) Using the .01 level, what should the researcher conclude
Answer:
As the P-value (0.0107) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that listening to music while solving math problems will make a particular brain area more active.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that listening to music while solving math problems will make a particular brain area more active.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=35\\\\H_a:\mu> 35[/tex]
The significance level is 0.01.
The sample has a size n=1.
The sample mean is M=58.
The standard deviation of the population is known and has a value of σ=10.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{10}{\sqrt{1}}=10[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{58-35}{10}=\dfrac{23}{10}=2.3[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>2.3)=0.0107[/tex]
As the P-value (0.0107) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that listening to music while solving math problems will make a particular brain area more active.
Plot the point (5, 5). Using a line tool, create AB with a length of 4 units from point A. Turn on the trace feature at point B, and move point B
around point A. keeping the length of AB fixed.
Answer:
Step-by-step explanation:
Plotting a point A and tracing a point B at 4 units from A results in a circle.
▪The locus of a point at equal distance from a fixed point is a circle.
▪Point A is (5,5) and length of AB is 4 units
This implies that the radius of circle is 4 units.
▪The point B can be swirled around A keeping the distance AB constant.
▪The resulting figure is a circle.
▪This circle is plotted and attached below.
I hope this helped. I am sorry if you get it wrong
Answer:
This is the right answer for Edementum and Plato users
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The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 255.4 and a standard deviation of 63.9. (All units are 1000 cells/muL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 63.7 and 447.1? b. What is the approximate percentage of women with platelet counts between 191.5 and 319.3?
Answer:
a) From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data
b) [tex] P(191.5<X<319.5)[/tex]
We can find the number of deviations from the mean for the limits using the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
And replacing we got:
[tex] z=\frac{191.5-255.4}{63.9}= -1[/tex]
[tex] z=\frac{319.3-255.4}{63.9}= 1[/tex]
So we have values within 1 deviation from the mean and using the empirical rule we know that we have 68% of the values for this case
Step-by-step explanation:
For this case we have the following properties for the random variable of interest "blood platelet counts"
[tex]\mu = 255.4[/tex] represent the mean
[tex]\sigma = 63.9[/tex] represent the population deviation
Part a
From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data
Part b
We want this probability:
[tex] P(191.5<X<319.5)[/tex]
We can find the number of deviations from the mean for the limits using the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
And replacing we got:
[tex] z=\frac{191.5-255.4}{63.9}= -1[/tex]
[tex] z=\frac{319.3-255.4}{63.9}= 1[/tex]
So we have values within 1 deviation from the mean and using the empirical rule we know that we have 68% of the values for this case
A driver travels a distance of 119 miles between 09:50 and 11:35. Work out the average speed of the driver
Answer:
68 miles per hour.
Step-by-step explanation:
The time taken for the driver to drive 119 miles is 105 minutes.
The average speed is equal to distance divided by the time taken.
105 minutes is equal to 1.75 hours.
[tex]S=119/1.75[/tex]
[tex]S =68[/tex]
The driver's average speed is 68 miles per hour.
Answer:
Speed = 68 mph
Step-by-step explanation:
Given:
Distance = 119 miles
Time = 1 hour 45 minutes = 1.75 hours
Required:
Speed = ?
Formula:
Average Speed = Total Distance Covered / Total Time Taken
Solution:
Speed = 119/1.75
Speed = 68 mph
Can someone please help me I’m stuck
Answer:
The answer is the first option. ΔRED ~ ΔTAN
Step-by-step explanation:
This is because the letters should be in the same order. Notice how T and R are in the same spots so are E and A, as well as D and N.
Suppose that the function g is defined, for all real numbers, as follows.
Answer:
g(-5) = 2
g(0) = -2
g(1) = 2
Step-by-step explanation:
g(-5) satisfies x <-2, since -5 is less than -2.
g(0) satisfies -2≤x≤1 since 0 is greater than 2 but less than 1. When we plug in 0 into (x+1)^2 -2, we get -2.
g(1) satisfies -2≤x≤1 since it says that x is less than OR EQUAL TO 1. We then plug in 1 into (x+1)^2 -2 and get 2.
Seven new employees, two of whom are married to each other, are to be assigned seven desks that are lined up in a row. If the assignment of employees to desks is made randomly, what is the probability that the married couple will have adjacent desks
Answer:
2/7
Step-by-step explanation:
Seven employees can be arranged in 7! ways. n(S) = 7!
Two adjacent desks for married couple can be selected in 6 ways viz.,(1, 2), (2, 3), (3,4), (4, 5), (5,6),(6,7).
This couple can be arranged in the two desks in 2! ways. Other five persons can be arranged in 5! ways.
So, number of ways in which married couple occupy adjacent desks
= 6×2! x 5! =2×6!
so, the probability that the married couple will have adjacent desks
[tex]\frac{n(A)}{n(s)} =\frac{2\times6!}{7!} \\=\frac{2}{7}[/tex]
Please answer this correctly
Answer:
There are 10 teams.
Step-by-step explanation:
Given that the question wants at least 48 swimmers so any numbers above 47 are counted.
In this diagram, there are 10 teams consisting 48 swimmers and above, 48, 52, 53, 63, 76, 79, 82, 84, 85 and 86.
Answer:
10 teams have 48 or more swimmers.
Step-by-step explanation:
If we look at stem 4 there is one team with 48 members.
So counting from there we have:
1 + 2 + 1 + 2 + 4
= 10 teams.
if f(x) =2x-1 and g(x)=x^2-3x-2, fins (f+g)(x)
Answer:
[tex](f+g)(x)=x^2-x-3[/tex]
Step-by-step explanation:
If [tex]f(x)=2x-1[/tex], and [tex]g(x)=x^2-3x-2[/tex], then the addition [tex](f+g)(x)[/tex] equals:
[tex](f+g)(x)=2x-1+x^2-3x-2=x^2-3x+2x-2-1=x^2-x-3[/tex]
consider the exponential function f(x)= 1/5(15x) what is the value of the growth factor of the function?
Answer:
15
Step-by-step explanation:
The general form of an exponential equation is ...
f(x) = (initial value)(growth factor)^x
That is, the "growth factor" is the base of the exponent. In your equation ...
f(x) = (1/5)(15^x)
the growth factor is 15.
Answer:
D
Step-by-step explanation:
because you put the one and the five and BOOM the inter carol makes the wheel go round and round.
What is the value of m in the equation one-half m minus three-fourths n equals 16, when n equals 8? a.20 b.32 c.44 d.48
Answer:
C. 44
Step-by-step explanation:
[tex] \frac{1}{2} m - \frac{3}{4} n = 16 \\ \\ \frac{1}{2} m - \frac{3}{4} \times 8 = 16..( plug \: n = 8) \\ \\ \frac{1}{2} m - 3 \times 2 = 16 \\ \\ \frac{1}{2} m - 6 = 16 \\ \\ \frac{1}{2} m = 16 + 6 \\ \\ \frac{1}{2} m = 22 \\ \\ m = 22 \times 2 \\ \\ m = 44[/tex]
The value of m in the given equation is equal to 3.
Given the following data:
n = 8To find the value of m in the given equation:
How to solve a word problem.In this exercise, you're required to determine the value of m in the given equation. Thus, we would translate the word problem into an algebraic equation.
[tex]\frac{1}{2m} -\frac{3}{4n} =16[/tex]
Substituting the value of n in the equation, we have;
[tex]\frac{1}{2m} -\frac{3}{4(8)} =16\\\\\frac{1}{2m} -\frac{3}{32} =16\\\\16m-32=16\\\\16m=16+32\\\\16m=48\\\\m=\frac{48}{16}[/tex]
m = 3.
Read more on word problems here: brainly.com/question/13170908
Compute the standard error for sample proportions from a population with proportion p= 0.55 for sample sizes of n=30, n=100 and n=1000 . Round your answers to three decimal places.
Given Information:
Population proportion = p = 0.55
Sample size 1 = n₁ = 30
Sample size 2 = n₂ = 100
Sample size 3 = n₃ = 1000
Required Information:
Standard error = σ = ?
Answer:
[tex]$ \sigma_1 = 0.091 $[/tex]
[tex]$ \sigma_2 = 0.050 $[/tex]
[tex]$ \sigma_3 = 0.016 $[/tex]
Step-by-step explanation:
The standard error for sample proportions from a population is given by
[tex]$ \sigma = \sqrt{\frac{p(1-p)}{n} } $[/tex]
Where p is the population proportion and n is the sample size.
For sample size n₁ = 30
[tex]$ \sigma_1 = \sqrt{\frac{p(1-p)}{n_1} } $[/tex]
[tex]$ \sigma_1 = \sqrt{\frac{0.55(1-0.55)}{30} } $[/tex]
[tex]$ \sigma_1 = 0.091 $[/tex]
For sample size n₂ = 100
[tex]$ \sigma_2 = \sqrt{\frac{p(1-p)}{n_2} } $[/tex]
[tex]$ \sigma_2 = \sqrt{\frac{0.55(1-0.55)}{100} } $[/tex]
[tex]$ \sigma_2 = 0.050 $[/tex]
For sample size n₃ = 1000
[tex]$ \sigma_3 = \sqrt{\frac{p(1-p)}{n_3} } $[/tex]
[tex]$ \sigma_3 = \sqrt{\frac{0.55(1-0.55)}{1000} } $[/tex]
[tex]$ \sigma_3 = 0.016 $[/tex]
As you can notice, the standard error decreases as the sample size increases.
Therefore, the greater the sample size lesser will be the standard error.
The product of Holly's savings and 3 is 39.
Use the variable h to represent Holly's savings.
Answer:
3h = 39Step-by-step explanation:
The question is incomplete. Here is the complete question.
Translate this sentence into an equation. The product of Holly's height and 3 is 39. Use the variable h to represent Holly's height.
Let holly's savings be h. If the product of Holly's savings and 3 is 39, this can be represented mathematically as h*3 = 39
To get holly's savings "h', we will divide both sides of the equation by 3
h*3 = 39
h*3/ 3= 39/3
h = 13*3/ 3
h = 13 * 3/3
h = 13*1
h = 13
Holly's savings is 13 and the required equation is 3h =39
Deepak wrote out the steps to his solution of the equation StartFraction 5 Over 2 minus 3 x minus 5 plus 4 x equals negative StartFraction 7 Over 4 EndFraction – 3x – 5 + 4x = –. A table titled Deepak's Solution with 3 columns and 5 rows. The first row is, blank, Steps, Resulting equation. The second row has the entries, 1, Use the distributive property to simplify. StartFraction 5 Over 2 minus 5 plus 4 x minus 3 x equals negative StartFraction 7 Over 4 EndFraction. The third row has the entries, 2, Simplify by combining like terms, negative StartFraction 5 Over 2 plus x equals negative StartFraction 7 Over 4 EndFraction. The fourth row has the entries, 3, Use the addition property of equality, negative StartFraction 5 Over 2 EndFraction plus StartFraction 5 Over 2 EndFraction plus x equals negative StartFraction 7 Over 4 EndFraction plus StartFraction 10 Over 4 EndFraction. The fifty row has the entries, 4, Simplify by combining like terms, x equals StartFraction 3 Over 4 EndFraction. Which step has an incorrect instruction? Step 1 Step 2 Step 3 Step 4
Answer:
Step 1
Step-by-step explanation:
Deepak given problem is: [tex]\dfrac52-3x-5+4x=-\dfrac74[/tex]
[tex]\left|\begin{array}{c|cc}$Steps&$Resulting Equation\\$1, Use the distributive property to simplify.&\dfrac52-5+4x-3x=-\dfrac74\\$2, Simplify by combining like terms&-\dfrac52+x=-\dfrac74\end{array}\right|[/tex]
[tex]\left|\begin{array}{c|cc}$3, Use the addition property of equality&-\dfrac52+\dfrac52+x=-\dfrac74+\dfrac{10}{4}\\$4, Simplify by combining like terms&x=\dfrac34\end{array}\right|[/tex]
In Step 1, he simply rearranged like terms. He did not use the distributive property. Therefore, the instruction in Step 1 was incorrect.
Answer:
step 1
Step-by-step explanation:
Im need help on this question
If the rectangular menu is 3 feet long by 2 feet wide, what is the area of the menu?
Answer:
Step-by-step explanation:
Area of rectangular menu
Length × breadth
3×2=6sq feet
Answer:
6 ft^2
Step-by-step explanation:
area of rectangle = length * width
area = 3 ft * 2 ft
area = 6 ft^2
what are the possible values of x in 8x^2+4=-1 a. 2+-iroot/3 b. -1+-i/6 c.-1+-i/4 d.1+-i/4 e. 1+-i root 2/4
Answer:
x = ± i sqrt(5/8)
Step-by-step explanation:
8x^2+4=-1
Subtract 4 from each side
8x^2+4-4=-1-4
8x^2 = -5
Divide by 8
8/8x^2=-5/8
x^2 = -5/8
Take the square root of each side
sqrt(x^2) = ±sqrt(-5/8)
x = ±sqrt(-5/8)
x = ±sqrt(5/8) sqrt(-1)
x = ± i sqrt(5/8)
Bradley and Kelly are flying out kites at a park one afternoon. And model of Bradley and Kelly skates are shown Below on the coordinate plane as the kites BRAD and KELY, respectively:
Answer: b) they ARE similar because BRAD:KELY is 1:2
Step-by-step explanation:
In order for the shapes to be similar they must have congruent angles and proportional sides.
With the options a through d given, we can assume that their sides are proportional. Since BRAD is smaller than KELY, BRAD would have the smaller number in the ratio.
Answer:
They are similar because Brad and Kelly are 1:2
Step-by-step explanation:
At many golf clubs, a teaching professional provides a free 10-minute lesson to new customers. A golf magazine reports that golf facilities that provide these free lessons gain, on average, $2 comma 1002,100 in green fees, lessons, or equipment expenditures. A teaching professional believes that the average gain is notis not $2 comma 1002,100. Complete parts a through c below. a. In order to support the claim made by the teaching professional, what null and alternative hypotheses should you test? Upper H 0H0: muμ equals= $2 comma 1002,100 Upper H Subscript aHa: muμ not equals≠ $2 comma 1002,100 b. Suppose you select alphaαequals=0.100.10. Interpret this value in the words of the problem. The probablility that the null hypothesis is rejected when the average gain is less than $2 comma 1002,100 is
Answer:
Given:
Mean, u = 2100
A golf magazine reports the mean gain to be $2100, while the teaching professional believes the average gain is not $2100.
Here the null and alternative hypotheses would be:
Null hypothesis:
H0: u = 2100
Alternative hypothesis:
Ha: u ≠ 2100
b) Here, given the level of significance,[tex] \alpha [/tex] as 0.10. This means that:
The probability that the null hypothesis H0 is rejected when average gain is $2100 is 0.10
Graph the function f(x) = 21(0.5)x.
Answer:
is m= 10.5 espero que te ayude
Based on a poll, 40% of adults believe in reincarnation. Assume that 6 adults are randomly selected, and find the indicated probability. Complete parts (a) through (c) below.
a. What is the probability that exactly 5 of the selected adults believe in reincarnation? Round to 3 decimal places.
b. What is the probability that all of the selected adults believe in reincarnation?
c. What is the probability that at least 5 of the selected adults believe in reincarnation?
Answer:
a. 3.686 %
b. 0.41 %
c. 4.096%
Step-by-step explanation:
We make use of the binomial probability equation, which is as follows:
P = [n! / (n - r)! r!] p ^ r * q ^ (n - r)
where,
n total number samples = 6
r is the selected number, depends on each point (a, b, c)
p is the of believing in reincarnation = 0.40
q = 1 - p = 0.60
to. What is the probability that exactly 5 of the selected adults believe in reincarnation?
So we use r = 5
P = [6! / ((6 - 5)! * 5!)] * [0.40 ^ 5 * 0.60 ^ (6 - 5)]
P = 6 * 0.006144
P = 0.0368 = 3.686%
b. What is the probability that all of the selected adults believe in reincarnation?
So we use r = 6
P = [6! / ((6 - 6)! * 6!)] * [0.40 ^ 6 * 0.60 ^ (6 - 6)]
P = 1 * 0.004096
P = 0.004096 = 0.41%
c. What is the probability that at least 5 of the selected adults believe in reincarnation?
So we use r = 5 to 6
P (r = 5) = [6! / ((6 - 5)! * 5!)] * [0.40 ^ 5 * 0.60 ^ (6 - 5)]
P (r = 5) = 6 * 0.006144
P (r = 5) = 0.0368 = 3.686%
P (r = 6) = [6! / ((6 - 6)! * 6!)] * [0.40 ^ 6 * 0.60 ^ (6 - 6)]
P (r = 6) = 1 * 0.004096
P (r = 6) = 0.004096 = 0.41%
The total is the sum of all:
P (total) = 3.686% + 0.41%
P (total) = 4.096%
Mario has $150 to spend on food for a party. He ordered pizzas that cost $8 each and bottles of soda that cost $2 each which inequality represents how much he can
spend without running out of money?
Answer:
8p + 2s <= 150
Step-by-step explanation:
Let p = number of a pizza.
Let s = price of a bottle of soda.
The inequality is
8p + 2s <= 150
Calculate the interest produced by a principal of $ 4,500 at 5% annual simple interest in 8 months.
Answer:
4,500 x 5 = 22,500
4,500 divided by 5 = 900
4,500 plus 5 = 4,505
4,500 minus 5 = 4,495
Step-by-step explanation:
it is either one of those that u have to choose from good luck
George earned e extra credit points. Kate earned 35 fewer extra credit points than George. Choose the expression that
shbws how many extra credit points Kate earned.
O A. 35
B.35e
C.35 + e
D. e - 35
Ronat Selection
Answer:
D. e - 35
Step-by-step explanation:
We have that:
George earned e extra points.
Kate earned k extra points.
Kate earned 35 fewer extra credit points than George.
This means that k is e subtracted by 35, that is:
k = e - 35
So the correct answer is:
D. e - 35
The probability that a person in the United States has type B+ blood is 12%. Three unrelated people in the United States are selected at random. Complete parts (a) through (d). (a) Find the probability that all three have type B+ blood. The probability that all three have type B+ blood is nothing. (Round to six decimal places as needed.)
Answer:
The probability that all three have type B+ blood is 0.001728
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they have type B+ blood, or they do not. The probability of a person having type B+ blood is independent of any other person. 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.
The probability that a person in the United States has type B+ blood is 12%.
This means that [tex]p = 0.12[/tex]
Three unrelated people in the United States are selected at random.
This means that [tex]n = 3[/tex]
Find the probability that all three have type B+ blood.
This is P(X = 3).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.12)^{3}.(0.88)^{0} = 0.001728[/tex]
The probability that all three have type B+ blood is 0.001728
Suppose f(x)=x^2. Find the graph of f(x-2)
The answer is
Answer:
f(x-2) = (x-2)²
or
f(x-2) = x² -4x + 4
Step-by-step explanation:
Simply plug in (x - 2) into f(x) to find your graph.
Edit (With Picture):
You are moving the graph right 2.
Answer:
Step-by-step explanation:
f(x) = x²
f(x - 2) = (x - 2)²
f(x - 2) = x² - 4x + 4
The grafic is below.
I hope I've helped you.
How did the temperature change if: at first it increased by 25 % and then decreased by 40% ?
Please help!!
Answer:
At first it increases by 25%, then you have 1.25x the original temp. A drop of 40% gives you .6 x 1.25, or 75% of the original temperature
Step-by-step explanation:
found that on the web for yuh. I really hope it helped.
Answer:
decreased by 25%
Step-by-step explanation:
You deal a pile of cards, face down, from a standard 52-card deck. What is the least number of cards the pile must have before you can be assured that it contains at least five cards of the same suit
Answer:
we need at least 17 - card deck
Step-by-step explanation:
From the information given :
We can attempt to solve the question by using pigeonhole principle;
"The pigeonhole principle posits that if more than n pigeons are placed into n pigeonholes some pigeonhole must contain more than one pigeon"
Thus; the minimum number of pigeon; let say at least n pigeons sit on at least one same hole among m hole can be represented by the formula:
m( n - 1 ) + 1
where ;
pigeons are synonymous to card
pigeonholes are synonymous to suits
So; m = 4 ; n = 5
∴ 4 (5 -1 ) + 1 ⇒ 4 (4) + 1
= 16 + 1
= 17
Hence; we need at least 17 - card deck
Sandy borrowed 6709R.O from a bank to buy a piece of land. If the bank charges 12 1/3 % compounded each two months, what amount will she have to pay after 2 years and half? Also find the interest
paid by her.
Answer:
Step-by-step explanation:
Using the compound interest formula
[tex]A = P(1+\frac{r}{n} )^{nt}[/tex]
A = final amount after t years
P = amount borrowed = Principal = 6709R
r = rate (in %) = 12 1/3%
n = number of times the interest is applied = 2 months
t = time the period elapsed = 2 1/2 years
[tex]A = 6709(1+\frac{\frac{37}{300} }{\frac{2}{12} } )^{\frac{2}{12} *\frac{5}{2} } \\A = 6709(1+0.1233/0.1667)^{2\0.41667} \\A = 6709(1+0.7397)^{2\0.41667} \\A = 6709(1.7397)^{2\0.41667} \\A = 6709(3.81195)\\A = 25,574.373[/tex]
She will have to pay 25,574.373R after 2 and a half years
interest paid by her = Amount - Principal
Interest paid by her = 25,574.373 - 6709
Interest paid by her = 18,865.373R
In a study of the effectiveness of airbags in cars, 11,541 occupants were observed in car crashes with airbags available, and 41 of them were fatalities. Among 9,853 occupants in crashes with airbags not available, 52 were fatalities. (a) Construct a 95% confidence interval for the difference of the two population fatality rates. (please keep 4 decimal places throughout for accuracy) (b) Based on the confidence interval
Answer:
Please the read the answer below
Step-by-step explanation:
In order to find the 95% confidence interval for the difference of the two populations, you use the following formula (which is available when the population size is greater than 30):
CI = [tex](p_1-p_2)\pm Z_{\alpha/2}(\sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2}})[/tex] (1)
where:
p1: proportion of one population = 52/9853 = 0.0052
p2: proportion of the other population = 41/11541 = 0.0035
α: tail area = 1 - 0.95 = 0.05
Z_α/2: Z factor of normal distribution = Z_0.025 = 1.96
n1: sample of the first population = 52
n2: sample of the second population = 41
You replace the values of all parameters in the equation (1) :
[tex]CI =(0.0052-0.0035)\pm (1.96)(\sqrt{\frac{0.0052(1-0.0052)}{52}+\frac{0.0035(1-0.0035)}{41}})\\\\CI=0.0017\pm0.026[/tex]
By the result obtained in the solution, you can conclude that the sample is not enough, because the margin error is greater that the difference of proportion of each sample population.