Answers
Given:
Two populations
Sample Size (n₁) = 202
Success (x₁) = 122
Sample size (n₂) = 340
Success (x₂) = 220
Find: test statistic and p-value of this sample
Solution:
Based on the given data, we have two proportions here and its sample size is large. The test statistic that is appropriate for this would be Test of Two Proportions and the formula is:
[tex]z=\frac{p_1-p_2+cont\text{ }}{\sqrt[]{\frac{p(1-p)}{n_1}+\frac{p(1-p)_{}}{n_2}}}[/tex]in which,
[tex]p=\frac{x_1+x_2}{n_1+n_2}[/tex]Let's solve the value of p first. Let's plug in the given data that we have above.
[tex]p=\frac{122+220}{202+340}=\frac{342}{542}=\frac{171}{271}[/tex]Now that we have the value of p, let's calculate p₁ and p₂. Formula is:
[tex]\begin{gathered} p_1=\frac{x_1}{n_1}=\frac{122}{202}=\frac{61}{101} \\ p_2=\frac{x_2}{n_2}=\frac{220}{340}=\frac{11}{17} \end{gathered}[/tex]Lastly, let's calculate the value of cont or continuity correction. Formula is:
[tex]cont=\frac{F}{2}(\frac{1}{n_1}+\frac{1}{n_2})\text{ }[/tex]For our claim p₁ < p₂, our F = 1.
[tex]cont=\frac{1}{2}(\frac{1}{202}+\frac{1}{340})=0.0039458[/tex]Let's plug these values to the test of two proportions formula:
[tex]\begin{gathered} z=\frac{p_1-p_2+cont\text{ }}{\sqrt[]{\frac{p(1-p)}{n_1}+\frac{p(1-p)_{}}{n_2}}} \\ z=\frac{\frac{61}{101}-\frac{11}{17}+0.0039458}{\sqrt[]{\frac{\frac{171}{271}(1-\frac{171}{271})}{202}+\frac{\frac{171}{271}(1-\frac{171}{271})_{}}{340}}} \end{gathered}[/tex][tex]z=\frac{-0.03915259}{\sqrt[]{\frac{0.2328399668}{202}+\frac{0.2328399668}{340}}}=\frac{-0.03915259}{0.04286603008}\approx-0.913[/tex]Hence, the test statistic is -0.913.
The equivalent p-value for this is 0.1805.
The p-value is greater than α = 0.05.
Since p-value is greater than α, we fail to reject the null hypothesis.
Related Questions
Find the area of this figure.Triangle: Rectangle: Half circle: Total area:
Answers
To determine the area of the figure given we need to divide the composite figure into figures in which we know how to find the area. We divide the figure into a triangle, a rectangle and a circle.
The area of a triangle is given by:
[tex]A=\frac{1}{2}bh[/tex]where b is the base and h is the height. For the triangle shown the base is 6 and its height is 6, therefore:
[tex]A=\frac{1}{2}(6)(6)=\frac{36}{2}=18[/tex]The area of the rectangle is given by:
[tex]A=lw[/tex]where l is the length and w is the width. For this triangle the length is 9 and the width is 6 then we have:
[tex]A=(9)(6)=54[/tex]The area of a circle is given by:
[tex]A=\pi r^2[/tex]where r is the radius of the circle. The circle shown has a diameter of 6; we know that the radius is half the diameter, then the radius is 3. Plugging the radius, we have:
[tex]A=(3.14)(3)^2=28.26[/tex]Now we add the areas of each figure, therefore we have:
[tex]18+54+28.26=100.26[/tex]A rectangular garden covers 690 square meters. The length of the garden is 1 meter more than three times its width. Find the dimensions of the gardenThe length isand the width is01(Type whole numbers.)
Answers
Ok, so
We got the situation here below:
We know that the area of the garden is 690 m².
So, we got that the height (1+3x) multiplied by the width (x), should be equal to 690.
[tex]\begin{gathered} (1+3x)(x)=690 \\ x+3x^2=690 \end{gathered}[/tex]We have to solve:
[tex]3x^2+x-690=0[/tex]If we solve this quadratic equation, we obtain two solutions.
One of both solutions is negative, so we will not use it.
The second one is positive and equals to 15. So, x=15.
Now that we know that x=15, we replace:
x, (Width) is equal to 15 meters.
1+3x (Length), is equal to 46 meters.
Therefore, these are the dimensions of the garden.
Width: 15 meters
Lenght: 46 meters.
Please help me help help me please help help me out
Answers
1) We can find the inverse function, by following some steps. So let's start with swapping the variables this way:
[tex]\begin{gathered} f(x)=\sqrt[3]{x-1}+4 \\ y=\sqrt[3]{x-1}+4 \end{gathered}[/tex]2) Now let's isolate that x variable getting rid of that cubic root:
[tex]\begin{gathered} x=\sqrt[3]{y-1}+4 \\ x-4=\sqrt[3]{y-1} \\ (x-4)^3=(\sqrt[3]{y-1})^3 \\ (x-4)^3=y-1 \\ y=(x-4)^3+1 \end{gathered}[/tex]Note that when we isolate the y on the left we had to adjust the sign dividing it by -1, to get y, not -y.
100 POINTS!! I NEED THIS KNOWW!!!!The number line shows the distance in meters of two birds, A and B, from a worm located at point X:A horizontal number line extends from negative 3 to positive 3. The point labeled as A is at negative 2.5, the point 0 is labeled as X, and the point labeled B is at 2.5.Write an expression using subtraction to find the distance between the two birds.Show your work and solve for the distance using additive inverses.
Answers
The expression used to represent the distance between the two birds on the number line is 2.5 - (-2.5) and the distance is 5 units.
Let us represent the bird A is sitting at one point on the number line.
Bird B is sitting at another point.
Both of them are at a an equal distance from a worm which is at the position O which is the origin.
Now it is given that A and B are at the positions of the number line marked 2.5 and -2.5
Now the distance between A and B can be calculated by finding the distance between A and O and adding the additive inverse to it to get the distance between O and B using subtraction.
AO = 2.5 - 0 = 2.5 units
The additive inverse of this is -2.5 units.
Therefore the distance AB :
= AO - BO
= 2.5 -(-2.5)
=2.5 +2.5
=5 units.
Hence they are at a distance of 5 units from each other.
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According to the complex conjugates theorem, if -3+i is a root of a function what else is a root?
Answers
To have an understanding of the question, we need to understand what the complex conjugates theorem is.
In a simpler form, what the complex conjugate theorem is saying is that perhaps, we have a Polynomial N with a complex root x + yi, then the complex conjugate of x + yi which in this case is x -yi is also a root of the polynomial N
Applying this to the question at hand;
x = -3 and y = 1
We find the conjugate of the above by negating y( turning it to a negative number)
So its conjugate will be -3 -i
Summarily; According to the complex conjugates theorem, if -3+i is a root of a function , -3 - i is also a root of the function
how would I simplify 3x^3-12x÷3x^3+6x^2-24x?
Answers
To simplify:
[tex]3x^3-12x\div3x^3+6x^2-24x[/tex]On division we get,
[tex]\begin{gathered} \frac{3x^3-12x}{3x^3+6x^2-24x}=\frac{3x(x^2-4)}{3x(x^2+2x-8)} \\ =\frac{(x^2-4)}{(x^2+2x-8)} \\ =\frac{(x+2)(x-2)}{(x-2)(x+4)_{}} \\ =\frac{x+2}{x+4} \end{gathered}[/tex]Hence, the simplest form is,
[tex]\frac{x+2}{x+4}[/tex]Consider the function g. 9(-) = 6() For the x-values given in the table below, determine the corresponding values of g(x) and plot each point on the graph.. -1 0 1 2 g(x) Drawing Tools Click on a tool to begin drawing * Delete Undo Reset Select Point 14 13 12 11 10 9 00 reserved.
Answers
we have the function
[tex]g(x)=6(\frac{3}{2})^x[/tex]Find out the value of function g(x) for each value of x
so
For x=-1
substitute the value of x in the function g(x)
[tex]\begin{gathered} g(-1)=6(\frac{3}{2})^{-1} \\ g(-1)=6(\frac{2}{3}) \\ g(-1)=4 \end{gathered}[/tex]For x=0
[tex]\begin{gathered} g(0)=6(\frac{3}{2})^0 \\ g(0)=6 \end{gathered}[/tex]For x=1
[tex]\begin{gathered} g(1)=6(\frac{3}{2})^1 \\ g(1)=9 \end{gathered}[/tex]For x=2
[tex]\begin{gathered} g(2)=6(\frac{3}{2})^2 \\ g(2)=13.5 \end{gathered}[/tex]using a graphing tool
plot the different points
so
we have
(-1,4)
(0,6)
(1,9)
(2,13.5)
see the attached figure to better understand the problem
please wait a minute
How many different ID cards can be made if there are four digits can be used more than once? What if digits can be repeated?
Answers
ANSWERS
1) 5,040
2) 10,000
EXPLANATION
1) If we have 10 numbers (from 0 to 9), the ID cards have 4 of them and the digits do not repeat, we have 10 numbers to choose from for the first digit, 9 numbers for the second digit, 8 numbers for the third digit, and 7 numbers for the fourth digit. So,
[tex]10\cdot9\cdot8\cdot7=5,040[/tex]Hence, there are 5,040 different ID cards that can be made if no digit can be used more than once.
2) In this case, the numbers can be repeated, so for each of the four digits we have 10 options to choose from,
[tex]10\cdot10\cdot10\cdot10=10^4=10,000[/tex]Hence, there are 10,000 different ID cards that can be made if digits can be repeated.
Need answer to pictured problem! The answer should be in reference to trig identities
Answers
Step 1. The expression that we have is:
[tex]cos^2(5x)[/tex]and we need to find the equivalent expression.
Step 2. The trigonometric identity we will use to solve this problem is:
[tex]cos^2A=1-sin^2A[/tex]In this case:
[tex]A=5x[/tex]Step 3. Applying the trigonometric identity to our expression, substituting 5x in the place of A:
[tex]cos^2(5x)=\boxed{1-sin^2(5x)}[/tex]This is shown in option d).
Answer:
[tex]\boxed{d)\text{ }1-s\imaginaryI n^2(5x)}[/tex]Select the point that satisfies y≤ x²-3x+2.
Answers
The point A (4, 4) satisfies the equation y≤ x²-3x+2.
To check for the equation, substitute each point into the inequality and check validity of solution
A (4, 4)
4 ≤ 16 - 12 + 2 ⇒ 4 ≤ 6 → True hence valid solution
B (3, 3 )
3 ≤ 9 - 9 + 2 ⇒ 3 ≤ 2 → False hence not valid
C (1, 1 )
1 ≤ 1 - 3 + 2 ⇒ 1 ≤ 0 → False hence not valid
D (2, 2 )
2 ≤ 4 - 6 + 2 ⇒ 2 ≤ 0 → False hence not valid
Therefore, the point A (4, 4) satisfies the equation y≤ x²-3x+2.
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Disclaimer: The question given by you is incomplete, the complete question is
Select the point that satisfies y ≤ x² - 3x + 2.
A. (4, 4)
B. (3, 3)
C. (1, 1)
D. (2, 2)
Answer:
The point A (4, 4) satisfies the equation y≤ x²-3x+2.
Step-by-step explanation:
Directons: Write each equation in slope-intercept form. Identify the slope and y-intercept.
Answers
Given:
The equation is x - y = -8.
Explanation:
The slope intercept form of linear equation is,
[tex]y=mx+c[/tex]Here, m is slope and c is y-intercept.
Simplify the given equation to obtain in slope-intercept form.
[tex]\begin{gathered} x-y=-8 \\ y=x+8 \\ y=1\cdot x+8 \end{gathered}[/tex]So slope of line is m = 1 and y-intercept is 8.
Answer:
Equation in slope ntercept form: y = x + 8
Slope: 1
Y-intercept: 8 OR (0,8)
base: 4 in. area: 22 in
Answers
Area of a triangle
The area of a triangle of base length b and height h is:
[tex]A=\frac{b\cdot h}{2}[/tex]We are given the area as A=22 square inches and the base length b=4 inches. We are required to find the height.
Solving for h:
[tex]h=\frac{2\cdot A}{b}[/tex]Substituting:
[tex]h=\frac{2\cdot22in^2}{4in}=\frac{44in^2}{4in}=11in[/tex]The height is 11 inches
The organizer of a conference is selecting workshops to include. She will select from 5 workshops about genetics and 8 workshops about ethics. In how many ways can she select 6 workshops if fewer than 3 must be about genetics?
Answers
We have the following:
- 5 possible about genetics and need fewer than 3 (so it can be 0, 1 or 2).
- 8 about ethics
- want to select 6 in total.
We can calculate all the possible ways by doing it in three situations:
1 - From the 6, 0 will be genetics and 6 will be ethics
2 - From the 6, 1 will be genetics and 5 will be ethics
3 - From the 6, 2 will be genetics and 4 will be ethics
All of these will have to add up to find the total number of ways.
1 - 0 genetics, 6 ethics:
Since no genetics will be chosen, we can choose any 6 from the 8 possible about ethics, that is, we have a situation of "8 choose 6"
The equation for a situation "n choose k" and the number of ways in it is:
[tex]n=\frac{n!}{k!(n-k)!}[/tex]So, if we have "8 choose 6":
[tex]n_1=\frac{8!}{6!(8-6)!}=\frac{8\cdot7\cdot6!}{6!2!}=\frac{8\cdot7}{2}=4\cdot7=28[/tex]So, in this first we have 28 ways.
2 - 1 genetics, 5 ethics:
Here, we will have one equation for each and the total number of ways will be the multiplication of both.
For genetics, we have to pick 1 from 5, so "5 choose 1":
[tex]\frac{5!}{1!(5-1)!}=\frac{5\cdot4!}{4!}=5_{}[/tex]For ethics, we have to pick 5 from 8, so "8 choose 5":
[tex]\frac{8!}{5!(8-5)!}=\frac{8\cdot7\cdot6\cdot5!}{5!3!}=\frac{8\cdot7\cdot6}{3\cdot2}=8\cdot7=56[/tex]So, the total number of ways is the multiplicatinos of them:
[tex]n_2=5\cdot56=280[/tex]3 - 2 genetics, 4 ethics:
Similar to the last one.
For genetics, we have to pick 2 from 5, so "5 choose 2":
[tex]\frac{5!}{2!(5-2)!}=\frac{5\cdot4\cdot3!}{2\cdot3!}=\frac{5_{}\cdot4}{2}=5\cdot2=10[/tex]For ethics, we have to pick 4 from 8, so "8 choose 4":
[tex]\frac{8!}{4!(8-4)!}=\frac{8\cdot7\cdot6\cdot5\cdot4!}{4!4!}=\frac{8\cdot7\cdot6\cdot5}{4\cdot3\cdot2}=2\cdot7\cdot5=70[/tex]So, the total number of ways is the multiplicatinos of them:
[tex]n_3=10\cdot70=700[/tex]Now, the total number of ways is the sum of all these possibilities, so:
[tex]\begin{gathered} n=n_1+n_2+n_3 \\ n=28+280+700 \\ n=1008 \end{gathered}[/tex]So, the total number of ways is 1008.
Estimate a 15% tip on a dinner bill of $89.14 by first rounding the bill amount to the nearest ten dollars. 1
Answers
Let:
C = Cost of the dinner
T = Tip
r = Percentage of the tip
[tex]\begin{gathered} C=89 \\ r=0.15 \\ T=C\cdot r \\ T=89\cdot0.15 \\ T=13.35 \end{gathered}[/tex]Answer:
$13.35
Can you please help me
Answers
The area for a trapezoid can be found through the fromula
[tex]A=\frac{1}{2}(B+b)\cdot h[/tex]in which B represents the major base, b the minor base and h the height of the trapezoid.
According to this the area of the trapezoid is going to be:
[tex]\begin{gathered} A=\frac{1}{2}(37+22)\cdot23 \\ A=\frac{1}{2}(59)23 \\ A=\frac{1357}{2}cm^2 \\ A=678.5cm^2 \end{gathered}[/tex]Solve this equation.
2/3x−1/5x=x−1
A. 1 13/15
B. 1 7/8
C. 1 7/15
D. 7/8
Answers
Answer:
your answer would be c 1 7/15 tell me if I'm wrong
Step-by-step explanation:
Answer:
B 1 7/8
Step-by-step explanation:
2/3x−1/5x=x−1
1. multiply both sides by 15
10x-3x=15x-15
2. collect like terms
7x = 15x -15
3. move the variable to the left
7x-15x=-15
4. collect like terms
-8x = -15
5. divide both sides by -8
x=15/8
or
1 7/8
Admission to the fair costs $6.00. Each ride costs you$0.50. You have $22.00 to spend at the fair on rides and admission. Express the number of tickets you can buy as an inequality.
Answers
Let:
x = Number of rides
Total money spent = $6.00 + $0.50x
Since you have $22.00 to spend at the fair on rides and admission:
[tex]\begin{gathered} 6+0.5x\leq22 \\ \text{solving for x:} \\ 0.5x\leq22-6 \\ 0.5x\leq16 \\ x\leq\frac{16}{0.5} \\ x=32 \end{gathered}[/tex]Translate the following into algebraic equation and solve: Twice the sum of a number and five is equal to 40.
Answers
Let:
x = Unknown number
Twice the sum of a number and five:
[tex]2(x+5)[/tex]Is equal to 40:
[tex]2(x+5)=40[/tex]Solve for x:
Expand the left hand side using distributive property:
[tex]2x+10=40[/tex]Subtract 10 from both sides:
[tex]2x=30[/tex]Divide both sides by 2:
[tex]x=15[/tex]Find area under standard normal curve between -1.69 and 0.84
Answers
Required:
We need to find the area under the standard normal curve between -1.69 and 0.84
Explanation:
We need to find P(-1.69
P-value form z-table is
[tex]P(x<-1.69)=0.045514[/tex][tex]P(x<0.84)=0.79955[/tex]We know that
[tex]P(-1.69Substitute know values.[tex]P(-1.69Final answer:0.7540 is the area under the standard normal curve between -1.69 and 0.84.
The boxplot below shows salaries for Construction workers and Teachers.ConstructionTeacher2025465030 35 40Salan (thousands of S)If a person is making the median salary for a construction worker, they are making more than what percentage ofTeachers?They are making more than% of Teachers.Check Answer
Answers
Const Workers , Teachers
Median salary of const Worker =45
Median salary of teacher = 40
Then, they are making more than 100% of teachers
Answer is
100%
For the rotation -1046°, find the coterminal angle from 0° < O < 360°, the quadrant and the reference angle.
Answers
Solution
Step 1
In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.
Step 2
The reference angle is the smallest possible angle made by the terminal side of the given angle with the x-axis. It is always an acute angle (except when it is exactly 90 degrees). A reference angle is always positive irrespective of which side of the axis it is falling.
Coterminal angle
[tex]\begin{gathered} Coterminal\text{ angle = -1046 + 3}\times360 \\ Coterminal\text{ angle = -1046 + 1080} \\ Coterminal\text{ angle = 34} \end{gathered}[/tex]Quadrant = 1st quadrant
Reference angle
0° to 90°: reference angle = angle
Reference angle = 34
Final answer
Would to ask question about composite shape perimeter. Having trouble sending drawing
Answers
First let's split the shape in two, like this:
As you can see, now we have a triangle on the right, the length of the base of this triangle is the length of the bottom side of the original figure minus the lenght of the top side of the original figure, we can find it like this:
b = 100 ft - 70 ft = 30 ft
The height of the triangle "h" equals the height of the rectangle, which is 50 ft, then we can find the length of the missing side a (the hypotenuse of the triangle) by means of the Pythagorean theorem, like this:
[tex]\begin{gathered} a^2=h^2+b^2 \\ a=\sqrt[]{h^2+b^2} \end{gathered}[/tex]Where "a" is the length of the hypotenuse, "h" is the height and "b" is the base. By replacing 30 for b and 50 for h, we get:
[tex]a=\sqrt[]{50^2+30^2}=\sqrt[]{2500+900}=10\sqrt[]{34}=58.3[/tex]Then the length of the missing side of the composite shape is around 58.3 ft:
Now that we know the lengths of the sides of this figure we can calculate its perimeter by summing them up, like this:
Perimeter = 70 + 50 + 100 + 58.3 = 278.3
The perimeter of this plot of land equals 278.3 ft
Find an equation for the line that’s passes through the following points shown in the picture. ( Please fins answer in timely answer very brief explaination :) )
Answers
The general equation of line passing through the points (x_1,y_1) and (x_2,y_2) is,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Determine the equation of line passing thgrough the point (-6,-1) and (2,5).
[tex]\begin{gathered} y-(-1)=\frac{5-(-1)}{2-(-6)}(x-(-6)) \\ y+1=\frac{6}{8}(x+6) \\ y+1=\frac{3}{4}x+\frac{9}{2} \\ y=\frac{3}{4}x+\frac{9}{2}-1 \\ =\frac{3}{4}x+\frac{7}{2} \end{gathered}[/tex]So equation of line is y = 3/4x + 7/2.
what's the solution to this system
Answers
Remember that
when solving a system by graphing, the solution is the intersection point both graphs
so
In this problem
the intersection point is (-2,2)
therefore
the solution is (-2,2)Determine if the expression -w is a polynomial or not. If it is a polynomial, state thetype and degree of the polynomial.The given expression representsJa polynomial. The polynomial is aand has a degree of
Answers
SOLUTION
We want to show if the expression -w is a polynomial or not
-w can also be written as
[tex]-1(w^1)[/tex]Since it has one term, and the power or exponent is not negative number or fraction, it is a polynomial.
Since it has one term, it is a monomial
So it is a polynomial called a monomial.
Since it has an exponent or power of 1
It is a polynomial of degree 1
According to the graph of H(w) below, what happens when w gets very large?H)5.6.20.00)A. H(w) gets very large.B. H(w) approaches a vertical asymptote.C. H(w) equals zero.D. H(w) gets very smallSUBMIT
Answers
Considering the graph H(w),
As w gets larger, H(w) continues to approach a horizontal asymptote.
Hence, H(w) gets very small.
Therefore, the correct option is option D
Find the circumference of the circle. Give the exact circumference and then an approximation. Use i 3.14. diamater of 17cm
Answers
To find the circumference of the circle, we will follow the steps below
Formula for the circumference of a circle is
C = 2 π r
where C = circumference of the circle
π is a constant
r is the radius of the circle
From the question, diameter is 17 cm
radius is half the diameter
That is:
radius = 17/2 = 8.5 cm
π = 3.14
Substituting the parameter in the formula given will yield
C = 2 x 3.14 x 8.5 cm
C =53.38 cm
The exact circumference is 53.38 cm
The circumference is approximately 53 cm to the nearest whole number
Find the value of r so that the line through (-4, r) and (-8, 3) has a slope of -5.
Answers
The value of r is -17.
Given,
Points (-4,r) and (-8,3)
slope=-5
Let
A(x1,y1)=(-4,r)
B(x2,y2)=(-8,3)
To find 'r' use formula,
[tex]slope=\frac{y2-y1}{x2-x1}\\ \\-5=\frac{3-r}{-8-(-4)}\\\\-5=\frac{3-r}{-8+4}\\\\-5=\frac{3-r}{-4}\\\\20=3-r\\\\20-3=-r\\\\17=-r\\\\-17=r[/tex]
Thus, the value of r is -17.
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Simplify Remove all perfectsquares from inside the square root. v52
Answers
The square root we need to simplify is:
[tex]\sqrt[]{52}[/tex]We need to find an expression equivalent to 54 which includes a perfect square number (4, 16, 25, etc,...)
In this case, we note that:
[tex]52=4\times13[/tex]We substitute this in the square root:
[tex]\sqrt[]{4\times13}[/tex]And we calculate the square root of 4 which is 2, and that goes outside the square root:
[tex]2\sqrt[]{13}[/tex]we left the number 13 inside the square root because the square root of 13 is not exact.
Answer:
[tex]2\sqrt[]{13}[/tex]Solve the proportions 28/35=8/r
Answers
ANSWER
r = 10
EXPLANATION
To solve for r first we have to put r in the numerator. To do that, we have to multiply both sides of the proportion by r:
[tex]\begin{gathered} \frac{28}{35}\cdot r=\frac{8}{r}\cdot r \\ \frac{28}{35}r=8 \end{gathered}[/tex]Now, we have to multiply both sides by 35:
[tex]\begin{gathered} \frac{28}{35}r\cdot35=8\cdot35 \\ 28r=280 \end{gathered}[/tex]And finally divide both sides by 28:
[tex]\begin{gathered} \frac{28r}{28}=\frac{280}{28} \\ r=10 \end{gathered}[/tex]