Given that In a 2014 Pew Research survey of a representative sample of 3748 scientists connected to the American Association for the Advancement of Science (AAAS), 98% of them (3673 out of 3748) say they believe in evolution.
To calculate a 95% confidence interval for the proportion of all scientists who say they believe in evolution. We need to find out the Margin of Error, Standard Error, and Sample Proportion Margin of Error Formula to calculate Margin of Error is given below;
\[\text{Margin of Error}=\text{Critical Value}\times\text{Standard Error}\]
Where,\[\text{Critical Value}=1.96\]
This value can be obtained using the Standard Normal Distribution table. Standard Error Formula to calculate Standard Error is given below;\[\text{Standard Error}=\sqrt{\frac{\text{Sample Proportion}\times(1-\text{Sample Proportion})}{\text{Sample Size}}}\]Sample Proportion\[=0.98\]Sample Size\[=3748\]
Putting these values in the Standard Error formula,\[\text{Standard Error}=\sqrt{\frac{0.98\times0.02}{3748}}\] \[\text{Standard Error}=0.007\]
Putting the calculated value of Standard Error and the Critical Value in the formula to calculate Margin of Error,\[\text{Margin of Error}=1.96\times0.007\] \[\text{Margin of Error}=0.014\]Now, we have Margin of Error and Sample Proportion\[=0.98\]
Formula to calculate the confidence interval is given below;\[\text{Confidence Interval}=\text{Sample Proportion}+\text{Margin of Error}\] and \[\text{Sample Proportion}-\text{Margin of Error}\]
Substituting the values, the 95% confidence interval is given below;\[0.98\pm0.014\]So, the 95% confidence interval for the proportion of all scientists who say they believe in evolution is\[0.966\le p\le0.994\]Hence,
the answer is, 0.966 ≤ p ≤ 0.994.
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A circle with a shaded sector has a circumference of 12 pi millimeters. What is the area of the shaded sector? Express the answer in terms of Pi.
Answer:
The answer is C. 8 mm
Step-by-step explanation:
For me, i was able to divide the 80 by 12 and get 6.667 thus i was able to round up and conclude the answer in the answer choices
Answer:
c
Step-by-step explanation:
What are the solutions to the quadratic equation 4(x + + 2)2 = 36
O x= -11 and x = 7
Ox= -7 and x = 11
O x= -5 and x = 1
Ox= -1 and x = 5
Answer:
x= -1 and 5
hope that helps
The solutions to the quadratic equation [tex]4(x+2)^2=36[/tex] are x = -5 and x = 1.
Given the following data:
[tex]4(x+2)^2=36[/tex]How to solve a quadratic equation.In this exercise, you're required to determine the value of x by solving for the factors (roots) of the given quadratic equation.
In Mathematics, the standard form of a quadratic equation is given by;
[tex]ax^2 + bx + c =0[/tex]
Where:
a = 4.b = 16.c = -20.Dividing both sides by 4, we have:
[tex]4(x+2)^2=36\\\\(x+2)^2=9[/tex]
Taking the square root of both sides, we have:
[tex]x+2=\pm3\\\\x=\pm 3-2[/tex]
x = -5 or 1.
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f (x) = -3x + 1
g(x) = x2 + 2x – 5
Find g (f (x))
Answer: f
= x = − 3 x + 1 = x = 1 4 g = x 2 + 2 x − 5f( x ) = f ( x )
Step-by-step explanation:
A scientist used 60 grams of sodium nitrate during an experiment. One ounce is approximately equal to 28.3 grams. Which measurement is closest to the number of ounces of sodium nitrate the scientist used?
Answer:
2
Step-by-step explanation:
60 divided by 28.3 which gives u 2.120141342756184
so round it which gives u 2
Find the midpoint of the segment with the following endpoints.
(9,6) and (5,2)
Answer:
[tex]M(7 ; 4)[/tex]
Step-by-step explanation:
midpoint -M
[tex]M(\frac{x_{1}+x_{2}}{2} ; \frac{y_{1}+y_{2}}{2} )[/tex]
[tex]M(\frac{9+5}{2} ; \frac{6+2}{2} )[/tex]
[tex]M(7 ; 4)[/tex]
Answer:
(7, 4 )
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
Here (x₁, y₁ ) = (9, 6) and (x₂, y₂ ) = (5, 2) , then
midpoint = ( [tex]\frac{9+5}{2}[/tex] , [tex]\frac{6+2}{2}[/tex] ) = ([tex]\frac{14}{2}[/tex] , [tex]\frac{8}{2}[/tex] ) = (7, 4 )
what is the solution
a: (6,5)
b: (5,6)
c: (1,2)
d: (2,1)
Answer:
(5,6)
Step-by-step explanation:
I'm guessing you mean the coordinates for the point where the lines intersect
Answer:
I believe it is b: (5,6)
Explanation:
The point (5,6) is the only point on the graph that both lines go through.
A tree casts a shadow that is 231 cm long. Janet is 170 cm tall and she casts a shadow that is 102 cm long. How tall is the tree?
Answer:
139 cm
Step-by-step explanation:
The null hypothesis is that the laptop produced by HP can run on an average 120 minutes without recharge and the standard deviation is 25 minutes. In a sample of 50 laptops, the sample mean is 130 minutes. Test this hypothesis with the alternative hypothesis that average time is not equal to 120 minutes. What is the p- value?
The p-value for testing the hypothesis that the average runtime of HP laptops is not equal to 120 minutes, based on a sample mean of 130 minutes from a sample of 50 laptops, is approximately 0.0006 (rounded to four decimal places).
To calculate the p-value, we use the t-test. Given the null hypothesis that the average runtime is 120 minutes, the alternative hypothesis is that it is not equal to 120 minutes. We compare the sample mean to the hypothesized population mean using the t-distribution.
Using the formula for the t-statistic:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
t = (130 - 120) / (25 / sqrt(50))
t = 10 / (25 / 7.0711)
t = 2.8284
The degrees of freedom for the t-distribution are (sample size - 1) = (50 - 1) = 49.
Using the t-distribution table or statistical software, we find that the two-tailed p-value for a t-value of 2.8284 with 49 degrees of freedom is approximately 0.0006.
Therefore, the p-value for this hypothesis test is approximately 0.0006.
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Let f be the function given by f(x) = 2 cos x +1. What is the approximation for f(1.5) found by using 1 the tangent line to the graph off at x = ? 2 (A) -2 (B) 1 (C) 1-2 (D) 4-2
To approximate the value of f(1.5) using the tangent line to the graph of f at x = 1, we first find the derivative of f(x) to determine the slope of the tangent line at x = 1. The derivative is f'(x) = -2 sin x. Evaluating f'(x) at x = 1, we find the slope to be approximately -1.6829.
Next, we use the point-slope form of a line to find the equation of the tangent line. We have the point (1, f(1)) ≈ (1, 1.5839) and the slope -1.6829. Plugging these values into the point-slope form, we obtain the equation of the tangent line as y ≈ -1.6829x + 3.2668.
Finally, we substitute x = 1.5 into the equation of the tangent line to approximate f(1.5). After calculation, we find that f(1.5) is approximately 0.0009.
Therefore, the approximation for f(1.5) using the tangent line to the graph at x = 1 is approximately 0.0009.
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ect
Use the number line interactive to evaluate the
following expressions.
8 + 3 =
+
16
(-8) + (-5) =
<
(-8) + 2 =
Answer:
1. 11
2. -13
3. -6
Step-by-step explanation:
Hope this helps. Have a great day! (I got this correct on edge :})
Beth filled 48 jars with paint. If each jar holds 1 pint of paint, how many gallons of paint did Beth use?
The gallons of paint that Beth used is 6 gallons.
How many gallons did Beth use?The first step is to convert pint to gallon:
1 pint = 0.125 gallon
The second step is to multiply 0.125 by 48 : 0.125 x 48 = 6 gallons
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Plz help I’ll give brainliest
Answer:
2) 4/5
3) 3
Step-by-step explanation:
2) 4/8-3=4/5
3)5x-4=3x+2
2x=6
x=3
Answer:
2) 4/5
3)x=3
Step-by-step explanation:
1) 4/8-3= 4/5
2) 5x-4=3x+2
bring 3x to left side and bring -4 to right side (remember signs will be reversed that is 3x becomes -3x and -4 will be 4
5x-3x=4+2
2x=6
x=6/2
x=3
put 3 in place of x
5*3-4=3*3+2
15-4=9+2
11=11
3. A piece of wire 16 feet long is strung from
the top of the side of a house to the
ground. The distance from the base of the
house to where the wire meets the ground
is 9 feet, as shown in the picturt.
st
19 lei
(The figure is not drawn to scale.)
How tall, in feet, is the house?
B. 20
C. 175
D. 337
Answer:
its c because its not a b or d and its alround 13 feet
Step-by-step explanation:
You earn $10 per hour working as a manager at a grocery store. You are required to work at the grocery store at least 8 hours per week. You also teach music lessons for $15 per hour. You need to earn at least $120 per week, but you do not want to work more than 20 hours per week. a. Write a system of linear inequalities that represents the situation. Use x for hours worked at the grocery store and y for hours teaching music lessons. i need the inequility for total work. please fast
Answer:
without numbers= 10x + 15y = 120
Step-by-step explanation:
grocery store= 10x (x=8 in this case)
music lessons= 15y
Answer fast plsssssss
Answer:
i cat see it
Step-by-step explanation:
Question is in picture
If n e z, use modulo to show that -13n2 +5n+23 is odd.
The given expression -13n^{2}+5n+23[/tex] is odd using modulo.
We are given to show that -13n2 + 5n + 23 is odd by using modulo.
Let's try to understand what modulo means:Modulo is a mathematical operation that finds the remainder when one number is divided by another. It is represented by the percentage symbol (%).
Now we can use the concept of modulo to show that -13n2 + 5n + 23 is odd.Note:An integer is odd if it is not even. In other words, odd numbers can't be divided evenly by 2. They leave a remainder of 1 when divided by 2.To show that -13n2 + 5n + 23 is odd, we need to take the given expression modulo 2.$$-13n^2 + 5n + 23 \; \mathrm{mod} \; 2$$We know that every odd integer can be written in the form of 2n + 1 where n is an integer. Now we just have to show that the expression -13n2 + 5n + 23 can be written in the form 2n + 1.$$-13n^2 + 5n + 23 \equiv 1 \; \mathrm{mod} \; 2$$Let's assume k is an integer such that $$-13n^2 + 5n + 23 = 2k + 1$$Rearranging the above expression, we get$$-13n^2 + 5n + 22 = 2k$$Now, we can use the concept of odd and even numbers. We know that an even number can be represented in the form 2n, where n is an integer. Now we just have to show that the expression -13n2 + 5n + 22 can be represented in the form 2n.$$-13n^2 + 5n + 22 = -13n^2 + 13n - 8n + 22$$$$= 13(n-1)(n-2) - 8$$We know that the product of two odd numbers is odd, and the subtraction of an even number from an odd number is odd. Here, (n-1) and (n-2) are consecutive integers, which means one of them is even and the other is odd. Therefore, the product (n-1)(n-2) is even. Hence, the above expression is odd.Since -13n2 + 5n + 23 is equivalent to 1 modulo 2, which means it can be represented in the form of 2n+1. Therefore, -13n2 + 5n + 23 is odd.
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4. Evaluate the expression for the given value of each variable.
5a2 -7 -b3
when a = -2 and b = -3
please help!
NO LINKS!!!
Answer:
-18
Step-by-step explanation:
5a2-7-b3
[tex]5*a*2-7-b*3[/tex]
[tex]5\cdot \left(-2\right)\cdot \left(2\right)-7-\left(-3\right)\cdot 3[/tex]
Therefore, -18 is your answer.
Hope this helped! :)
The product of 3x^3-5x² + 3 and 2x² + 5x – 4 in Z7[x] / < x² +1 > is_________a. 2x + 3 b.2x+2 c. 2x d. 2x + 1
The product of 3x³-5x² + 3 and 2x² + 5x – 4 in Z7[x] / < x² +1 > is 2x + 1.
The product of the polynomials 3x³-5x² + 3 and 2x² + 5x – 4 in Z7[x] / < x² +1 > can be determined using polynomial long division.
To perform the division, we divide 3x³-5x² + 3 by x² + 1. The result of this division gives us the quotient and the remainder. In this case, the quotient is 2x and the remainder is 2x + 1.
The quotient represents the coefficient of x in the resulting product, while the remainder represents the constant term. Therefore, the resulting product is d. 2x + 1.
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PLEASE HELP ME!!! I REALLY NEED TO KNOW THIS...
So my math teacher hates me and i did this for a answer:
5x³ + x² + 16 , this is a different question, and i got the points.
But for a answer that was right and she mared wrong i did this:
2x²+4
(I know it is right because my sister and me have the same math. and she got a 10/10 on this)
My sister's answer : 2x^2 + 4.
Are they the same or not?!
Answer:
The exact same
Step-by-step explanation:
^ just means put it up like 3^2=3²
A researcher was interested in how students' college major affected their opinions on environmental safety. To investigate this a researcher gave a environmental safety questionnaire to 20 random business majors and 20 random neuroscience majors. Their responses to the questionnaire were not normally distributed. What is the most appropriate statistical test for these data from the list below? Wilcoxon Signed Rank test Student's t-test O Wilcoxon Ranked Sum test Paired t-test
The most appropriate statistical test for these data from the list below would be: the Wilcoxon Ranked Sum test.
Why is the Wilcoxon Ranked Sum test best?The Wilcoxon Ranked Sum test is the best for the analysis because it does not assume a normal distribution. The Wilcoxon ranked sum test compares two independent populations to determine if there is a statistical significance between them.
In the example given there is no normal distribution, so the Wilcoxon Ranked Sum test will analyze the responses differently to confirm if there is a relationship.
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Which equation is not equivalent to 2x+10=-8
Answer:
2x+10=-8
x=9
3x=9
x=3
2x=8
x=4
4x=20
x=5
Step-by-step explanation:
Kallen was invited to a birthday party for his best friend. He wanted to buy a gift that was $43.87 and wrapping paper that was $2.94. If he earns $8.25 for each lawn he mows and his mom agrees to match all his earnings how many lawns will he need to complete to buy the gift and wrapping
Answer: 6
Step-by-step explanation:
The total amount needed by Kallen for the gift and the wrapping paper will be:
= $43.87 + $2.94
= $46.81
Since he earns $8.25 for each lawn he mows, the number of lawns they he will need to complete to buy the gift and wrapping will be:
= $46.81 / $8.25
= 5.67
= 6 lawns approximately
He'll need to mow 6 lawns
Help pleaseeeeeeeeeee
Answer:
5 is c 6 is b
Step-by-step explanation:
Answer:
5) C 6) B
Step-by-step explanation:
Yw
if an equation indicates addition in its presentation, in order to solve for the unknown you must: a. add b. subtract c. multiply d. divide
If an equation indicates addition in its presentation, in order to solve for the unknown, you must perform the inverse operation, which is subtraction.
Equations typically involve an equality between two expressions, with one or more unknown variables.
To isolate the unknown variable and determine its value, you need to perform operations on both sides of the equation to simplify and solve for the variable.
When an equation shows addition, you can undo that operation by subtracting the same value from both sides of the equation. This ensures that the equation remains balanced and maintains equality.
For example, consider the equation:
x + 5 = 10
To solve for x, you need to eliminate the 5 added to x. To do so, you subtract 5 from both sides of the equation:
x + 5 - 5 = 10 - 5
x = 5
By subtracting 5 from both sides, you isolate the variable x and find that its value is 5.
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Write an equation for two angles A and B that are supplementary.
A. a + b = 180
B. a + b = 100
C. 2ab = 180
D. a + b = 90
Answer:
A. a + b = 180 is the correct option.
i dont have a question for this. look at the photo
Answer:
first is no second is yes third is no fourth is yes
Step-by-step explanation:
I'm not sure btw
A local fast food chain had revenue represented by the polynomial 6x ^ 2 + 5x - 8 for one fiscal year and expenses for that same fiscal year represented by the polynomial 4x ^ 2 - 3x + 7 7. What was the company's profit for the fiscal year?
Answer:
2x^2+8x - 16
Step-by-step explanation:
Profit = Revenue - Cost
P(x) = R(x) - C(x)
Given
R(x) = 6x ^ 2 + 5x - 8
C(x) = 4x ^ 2 - 3x + 7
P(x) = 6x ^ 2 + 5x - 8-(4x ^ 2 - 3x + 7)
P(x) = 6x ^ 2 + 5x - 8 - 4x ^ 2 + 3x - 8
Collect the like terms;
P(x) = 6x^2-4x^2+5x+3x-8-8
P(x) = 2x^2+8x - 16
Hence the company's profit for the fiscal year is 2x^2+8x - 16
Calculate the volume of a cube with side lengths of 2.8 yards.
Answer:
21.952 [tex]yards^{3}[/tex]
Step-by-step explanation:
The volume of a cube is side length cubed.
So [tex]2.8^{3}[/tex] = 21.952
or each of the following functions, find the constant c such that f(x)is a pdf; find the cdf, f(x)= p(x ≤ x); graph the pdf and cdf; and find μ and σ2: (a) f(x)= 4xc for 0 ≤ x ≤ 1
c = 1/2 ,the mean is μ = 1/2, the CDF of f(x) is 2x^2 and the variance is σ² = 1/6.
The given pdf is f(x) = 4xc for 0 ≤ x ≤ 1.
To find the constant c such that f(x) is a pdf: We know that, For f(x) to be a pdf, it must satisfy the following two conditions:
The integral of f(x) over its support should be equal to 1. f(x) must be greater than or equal to 0 for all values of x. So,
Let us find the value of c first integral of f(x) from 0 to 1 should be equal to 1, therefore∫f(x)dx = ∫(4xc)dx for 0 ≤ x ≤ 1∫f(x)dx = 4∫xc dx for 0 ≤ x ≤ 1∫f(x)dx = 4[c(x^2/2)]_0^1∫f(x)dx = 2c
Therefore,∫f(x)dx = 1 implies 2c = 1 or c = 1/2.
Now we know the value of c. Let us find the CDF of f(x): CDF of f(x) = P(x ≤ X) = ∫f(t)dt from -∞ to x= ∫f(t)dt from 0 to x= ∫(4xt)dt from 0 to x= 2x^2 from 0 to x= 2x^2Therefore, the CDF of f(x) is 2x^2.
Graph of the PDF of f(x)For graphing the PDF of f(x), we need to know the values of x for which f(x) is defined as well as its shape and maximum value.f(x) = 4xc for 0 ≤ x ≤ 1The given function is a straight line with a slope of 4c and intersects the x-axis at 0 and the y-axis at 0.
We know that c = 1/2, thus (x) = 2x for 0 ≤ x ≤ 1The graph of f(x) will look as follows: Graph of the CDF of f(x)The graph of the CDF of f(x) will look as follows:
We can find the mean and variance of the PDF of f(x) using the following formulae: Mean, μ = ∫xf(x)dx from -∞ to ∞.Variance, σ² = ∫(x - μ)²f(x)dx from -∞ to ∞.
Substituting f(x) and its limits in the above formulae, we get: Mean, μ = ∫xf(x)dx from 0 to 1= ∫(2x^2)x dx from 0 to 12(1^4 - 0^4)/4= 1/2.
Variance, σ² = ∫(x - μ)²f(x)dx from 0 to 1= ∫(x - 1/2)²(2x)dx from 0 to 1= 1/6.
Therefore, the mean is μ = 1/2, and the variance is σ² = 1/6.
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