We can either reject or fail to reject the null hypothesis and draw our conclusion.
Based on the newspaper article's statement, we can assume that the majority of Americans who do not attend college do so for reasons other than financial constraints. To test this claim, we can conduct a hypothesis test to determine if the data provide strong evidence to support this statement.
Let's set up the null and alternative hypotheses for this test. Our null hypothesis (H0) is that the proportion of Americans who do not attend college due to financial constraints is equal to or greater than 50%. Our alternative hypothesis (Ha) is that the proportion of Americans who do not attend college due to financial constraints is less than 50%.
Next, we need to collect data and calculate the point estimate for the proportion of Americans who do not attend college due to financial constraints. Once we have our point estimate, we can calculate the test statistic and p-value.
If the p-value is less than the significance level (typically 0.05), we can reject the null hypothesis and conclude that there is strong evidence to support the newspaper article's statement. However, if the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the statement.
Based on the results, we can either reject or fail to reject the null hypothesis and draw our conclusion.
To know more about null hypothesis refer here
https://brainly.com/question/28920252#
#SPJ11
suppose sinc(x)=-5/13 where x terminates in quadrant iii. find sin(2x)
The value of sin(2x) is -120/169 when x terminates in quadrant iii.
Since sinc(x) is negative and terminates in quadrant III, we know that sin(x) is negative and cos(x) is positive.
Let's first solve for sin(x) using the given value of sinc(x):
sinc(x) = sin(x)/x = -5/13
sin(x) = -5x/13
Using the Pythagorean identity, we can solve for cos(x):
cos(x) = sqrt(1 - sin^2(x)) = sqrt(1 - 25x^2/169)
Now we can use the double angle formula for sine:
sin(2x) = 2sin(x)cos(x) = 2(-5x/13)(sqrt(1 - 25x^2/169))
To simplify this expression, we can substitute sin(x) = -5x/13:
sin(2x) = -10x(sqrt(1 - 25x^2/169))/13
Note that x terminates in quadrant III, so it is negative. Thus, we can simplify further:
sin(2x) = 10x(sqrt(1 - 25x^2/169))/13
To know more about terminates,
https://brainly.com/question/28914840
#SPJ11
what is the physical reason the bottom of the dip is a horizaontal line rather than a point
The physical reason that the bottom of a dip is a horizontal line rather than a point has to do with the principle of superposition. This principle states that when two or more waves intersect, the resulting wave is the sum of the individual waves.
The physical reason that the bottom of a dip is a horizontal line rather than a point has to do with the principle of superposition. This principle states that when two or more waves intersect, the resulting wave is the sum of the individual waves. When two waves with equal amplitude and frequency but opposite phase intersect, they cancel each other out completely, resulting in a horizontal line. This is what happens at the bottom of a dip, where the crests of two waves meet and cancel each other out, leaving only the troughs. If the waves were not perfectly aligned, the bottom of the dip would still be a horizontal line, but the line would be slightly curved instead of perfectly straight. In summary, the principle of superposition is the physical reason why the bottom of a dip is a horizontal line rather than a point.
To know more about horizontal line visit:
https://brainly.com/question/10863938
#SPJ11
Larry spent 25% less buying his English reading book than Curly Moe spent 10% less than Curly Moe spent more than Larry by what percent? Moe spent more than Larry
Let's break down the information step by step to find the percent by which Moe spent more than Larry.
Larry spent 25% less buying his English reading book than Curly.
Moe spent 10% less than Curly.
Let's assume Curly spent $100 on the book.
Larry spent 25% less than Curly:
Larry's spending = Curly's spending - 25% of Curly's spending
Larry's spending = $100 - 0.25 * $100
Larry's spending = $100 - $25
Larry's spending = $75
Moe spent 10% less than Curly:
Moe's spending = Curly's spending - 10% of Curly's spending
Moe's spending = $100 - 0.10 * $100
Moe's spending = $100 - $10
Moe's spending = $90
Now, let's calculate the percent by which Moe spent more than Larry:
Percent difference = (Moe's spending - Larry's spending) / Larry's spending * 100
Percent difference = ($90 - $75) / $75 * 100
Percent difference = $15 / $75 * 100
Percent difference = 0.2 * 100
Percent difference = 20%
Therefore, Moe spent 20% more than Larry on the English reading book.
Learn more about percent here: brainly.com/question/31323953
#SPJ11
Rory currently has $1200 saved in his bank account. In 8 years, Rory will be 32 years old and have $1580.17 saved in his bank account.
A: Write an exponential equation in the form y=ab^x that represents Rory's bank account x years from now if the interest rate remains the same. Round values to 3 decimal places, if necessary.
B: How much can Rory expect to have in his bank account when he is 50 years old?
C: How much can Rory expect to have in his bank account if he lived to be 100 years old?
Answer:
[tex]\textsf{A)} \quad y=1200\cdot 1.035^x[/tex]
B) $2,935.15
C) $16,392.60
Step-by-step explanation:
The general form of an exponential function is:
[tex]\boxed{y=ab^x}[/tex]
where:
a is the initial value.b is the base (growth/decay factor) in decimal form.Given:
y is the account balance (in dollars).x is the number of years from now.If Rory currently has $1,200 saved in his bank account, then the initial value is a = 1200.
If in 8 years time, the account balance will be $1,580.17, then y = 1580.17 when x = 8.
Substitute x = 8, y = 1580.17 and a = 1200 into the exponential function and solve for b:
[tex]\begin{aligned}y&=ab^x\\\\\implies 1580.17&=1200 \cdot b^8\\\\\dfrac{1580.17}{1200}&=b^8\\\\\sqrt[8]{\dfrac{1580.17}{1200}}&=b\\\\b&=1.03499993...\\\\b&=1.035\; \sf (3\;d.p.)\end{aligned}[/tex]
Therefore, the exponential equation that represents Rory's bank account x years from now if the interest rate remains the same is:
[tex]\boxed{y=1200\cdot 1.035^x}[/tex]
[tex]\hrulefill[/tex]
Part BIf 8 years from now Rory will be 32 years old, then he is currently 24 years old, since 32 - 8 = 24.
To calculate how much Rory can expect to have in his bank account when he is 50 years old, substitute x = 26 into the equation created in Part A, since 50 - 24 = 26.
[tex]\begin{aligned}y&=1200 \cdot 1.035^{26}\\y&=2935.1502...\end{aligned}[/tex]
Therefore, Rory can expect to have $2,935.15 in his bank account when he is 50 years old.
[tex]\hrulefill[/tex]
Part CTo calculate how much Rory can expect to have in his bank account when he is 100 years old, substitute x = 76 into the equation created in Part A, since 100 - 24 = 76.
[tex]\begin{aligned}y&=1200 \cdot 1.035^{76}\\y&=16392.5995...\end{aligned}[/tex]
Therefore, Rory can expect to have $16,392.60 in his bank account when he is 100 years old.
determine the number of arrangements of the letters in georgiatech such that all the e's are consecutive.
The number of arrangements of the letters in "georgiatech" with all the e's consecutive is 60,480.
To determine the number of arrangements of the letters in "georgiatech" such that all the e's are consecutive, we can treat the three e's as a single unit. So, we have 9 distinct letters: g, o, r, g, i, a, t, c, h, and the "eee" unit.
The total number of arrangements of these 9 letters is 9!. However, within the "eee" unit, the three e's can be arranged among themselves in 3! ways. Therefore, we need to divide the total number of arrangements by 3!.
Hence, the number of arrangements of the letters in "georgiatech" such that all the e's are consecutive is:
9! / 3! = 362,880 / 6
= 60,480
To know more about arrangements,
https://brainly.com/question/31962614
#SPJ11
use the quadratic formula to solve x^2-10x+21=0
By using the quadratic formula, the roots of the quadratic equation are x = -7 and x = -3.
What is a quadratic equation?In Mathematics and Geometry, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph with a maximum exponent of two (2).
In Mathematics, the standard form of a quadratic equation is represented by the following equation;
ax² + bx + c = 0
Mathematically, the quadratic formula is represented by this mathematical equation:
[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]
For the given quadratic equation x² + 10x + 21 = 0, we have:
[tex]x = \frac{-(10)\; \pm \;\sqrt{(10)^2 - 4(1)(21)}}{2(1)}\\\\x = \frac{-(10)\; \pm \;\sqrt{100 - 84}}{2}\\\\x = \frac{-(10)\; \pm \;\sqrt{(10)^2 - 4(1)(21)}}{2(1)}\\\\x = \frac{-(10)\; \pm \;\sqrt{16}}{2}\\\\x = \frac{-(10)\; \pm \;4}{2}[/tex]
x = (-10 - 4)/2 = -14/2 = -7
x = (-10 + 4)/2 = -6/2 = -3
Read more on quadratic equation here: brainly.com/question/4053652
#SPJ1
Let R be region in the fourth quadrant enclosed by the x-axis and the curve y=x^(2)-2kx, where k is a constant. If the area of the region R is 36 , then the value of k is
Therefore, the value of k is 3 if the area of the region R is 36.
To find the value of k, we need to find the bounds of the integral that will give us the area of region R. Since R is in the fourth quadrant and is enclosed by the x-axis and the curve y=x^(2)-2kx, we need to find the x-intercepts of the curve:
x^(2)-2kx=0
x(x-2k)=0
x=0 or x=2k
Since R is in the fourth quadrant, we only need to consider the x-intercept x=2k. Therefore, the bounds of the integral are from x=0 to x=2k.
The area of region R can be found using the following integral:
A = ∫[0, 2k] (x^2 - 2kx) dx
= [x^3/3 - kx^2] from 0 to 2k
= (8k^3)/3 - 4k^3
= (4k^3)/3
Since we are given that the area of region R is 36, we can set up the following equation:
(4k^3)/3 = 36
Simplifying, we get:
k^3 = 27
Taking the cube root of both sides, we get:
k = 3
To know more about area,
https://brainly.com/question/2292569
#SPJ11
jai read 52 pages in 2 2/3 hours. At what rate, in pages per hour, did he read?
Answer:
19.5 or 19 1/2
Step-by-step explanation:
2 2/3 = 2.6666666666666667
52/ 2 2/3 = 19.5
The figure shows the dimensions for a package to be shipped.
6 in.
4 in.
-12 in.
10 in.
sq. in.
15 in.
What is the minimum amount of wrapping paper, in square inches, needed to cover the package?
The minimum amount of wrapping paper, needed to cover the package surface area is 174 square inches.
Total surface area = Area of 2 similar trapeziums + Area of rectangles of 4 different rectangles
area of a triangle = 1/2 ×Base×Height and area of a rectangle is Length×Breadth.
= 2×1/2(7+3)×3+8×5+8×3+8×3+8×7
= 174 square inches
To learn more about the surface area, here:
brainly.com/question/26403859.
#SPJ1
consider the degree-4 lfsr given by p(x) = x^4 x^2 1. what is the one period of key stream if the sequence has seed (s3, s2, s1, s0) = 1111 in the form of (..., s5, s4, s3, s2, s1, s0)?
The period of the key stream is 16 bits long, and it repeats after these 16 bits.
To find the one period of the key stream generated by the given degree-4 LFSR with feedback polynomial p(x) = x^4 + x^2 + 1 and seed (s3, s2, s1, s0) = 1111, we can simulate the LFSR to generate the sequence of 16 bits that make up one full period of the LFSR.
We start with the seed 1111 and use the LFSR update rule to generate each subsequent bit of the sequence. The update rule for the degree-4 LFSR is to XOR the output bits of the taps at positions 4 and 2 (since p(x) = x^4 + x^2 + 1) with the current input bit, and shift all bits one position to the right.
Here are the steps to generate the key stream:
Start with the seed (s3, s2, s1, s0) = 1111.
Generate the next bit of the sequence by XORing the output bits at positions 4 and 2 with the input bit (which is 1 for the first bit). The output bits at positions 4 and 2 are s3 and s1, respectively, so we have:
s3 XOR s1 XOR 1 = 1 XOR 1 XOR 1 = 1.
This gives us the first bit of the sequence: 1.
Shift all bits one position to the right, so the first bit becomes the second bit, the second bit becomes the third bit, and so on. The sequence now looks like this: 1111 1.
Repeat steps 2 and 3 to generate the next 14 bits of the sequence. Each new bit depends on the current state of the LFSR, which is updated at each step.
Using these steps, we can generate the entire period of the key stream:
1111 1 0011 0 1001
The period of the key stream is 16 bits long, and it repeats after these 16 bits.
Learn more about stream here
https://brainly.com/question/28452815
#SPJ11
In the xy-plane, the graph of the parametric equations x= 5t + 2 and y = 3t, for -3 <= t =< 3, is a line segment with a slope
A) 3/5
B) 5/3
C) 3
D) 5
E) 13
In the xy-plane, the graph of the parametric equations x= 5t + 2 and y = 3t, for -3 <= t =< 3, is a line segment with a slope A) 3/5.
The slope of a line can be determined by finding the derivative of the equation representing the line. In this case, we have the parametric equations x = 5t + 2 and y = 3t.
To find the slope, we can differentiate y with respect to x. Using the chain rule, we have:
dy/dx = (dy/dt)/(dx/dt)
dx/dt = 5 (derivative of 5t + 2 with respect to t)
dy/dt = 3 (derivative of 3t with respect to t)
dy/dx = 3/5
the slope of the line segment represented by the parametric equations is 3/5.
To know more about derivative visit:
brainly.com/question/29144258
#SPJ11
consider the following sample values: 4, 6, 8, 10, 12, 14 what is the sample variance?
The sample variance for the given set of data is 14 square units.
To find the sample variance of a set of data, we first need to find the sample mean. The formula for the sample mean is:
sample mean = (sum of all values in the sample) / (number of values in the sample)
In this case, the sum of the values is:
4 + 6 + 8 + 10 + 12 + 14 = 54
And there are 6 values in the sample. Therefore, the sample mean is:
sample mean = 54 / 6 = 9
Next, we need to find the deviation of each value from the sample mean. To do this, we subtract the sample mean from each value in the sample:
4 - 9 = -5
6 - 9 = -3
8 - 9 = -1
10 - 9 = 1
12 - 9 = 3
14 - 9 = 5
Next, we need to square each of these deviations:
(-5)^2 = 25
(-3)^2 = 9
(-1)^2 = 1
1^2 = 1
3^2 = 9
5^2 = 25
Now we find the sum of these squared deviations:
25 + 9 + 1 + 1 + 9 + 25 = 70
Finally, we divide this sum by the number of values in the sample minus one:
sample variance = 70 / (6 - 1) = 14
Therefore, the sample variance for the given set of data is 14 square units.
Learn more about variance here
https://brainly.com/question/15858152
#SPJ11
find the general solution of the given second-order differential equation. 4y'' + y' = 0
Therefore, the general solution of the given second-order differential equation is y = c1 e^(-x/4) + c2, where c1 and c2 are constants.
To find the general solution of the given second-order differential equation 4y'' + y' = 0, we can use the method of separation of variables.
Let us assume that the solution to the equation is of the form y = e^(rx), where r is a constant.
Differentiating with respect to x, we get y' = re^(rx) and y'' = r^2e^(rx).
Substituting these expressions into the given differential equation, we get:
4y'' + y' = 4(r^2e^(rx)) + (re^(rx)) = 0
Simplifying and factoring out e^(rx), we get:
e^(rx)(4r^2 + r) = 0
This equation holds for all values of x if and only if the coefficient of e^(rx) is zero. Therefore, we get:
4r^2 + r = 0
Solving for r using the quadratic formula, we get:
r = (-b ± sqrt(b^2 - 4ac))/(2a)
where a = 4, b = 1, and c = 0. Substituting these values, we get:
r = (-1 ± sqrt(1^2 - 4(4)(0)))/(2(4)) = (-1 ± sqrt(1))/8
Therefore, the two solutions to the differential equation are:
y1 = e^(-x/4)
y2 = Ce^0 = C
where C is a constant of integration
The general solution to the differential equation is then given by the linear combination of these two solutions:
y = c1 e^(-x/4) + c2
where c1 and c2 are constants of integration that depend on the initial conditions of the problem.
To know more about second-order differential equation,
https://brainly.com/question/15196913
#SPJ11
2.
Carol has a spherical snow
globe with a radius of
2. 25 inches. What is the
approximate volume of the
snow globe in cubic inches?
The approximate volume of the spherical snow globe with a radius of 2.25 inches is calculated to be approximately 47.69 cubic inches.
To determine the volume of the snow globe, we use the formula for the volume of a sphere, V = (4/3)πr^3. In this case, the given radius is 2.25 inches. By substituting this value into the formula and performing the necessary calculations, we find that the volume is approximately 47.69 cubic inches.
This is obtained by evaluating (4/3)π(2.25)^3, which simplifies to approximately 4.18879 * (2.25)^3, and further simplifies to approximately 47.688984 cubic inches. Therefore, the approximate volume of the snow globe is approximately 47.69 cubic inches.
To learn more about volume, click here: brainly.com/question/29255732
#SPJ11
find the sum of the first 70 terms of the arithmetic sequence: 22, 19, 16, 13,…
The sum of the first 70 terms of the arithmetic sequence is 5420.
We can see that the common difference between consecutive terms is -3. Thus, the nth term of the sequence is given by:
a_n = 22 + (n-1)(-3)
We want to find the sum of the first 70 terms of the sequence, which is given by the formula:
S_70 = (n/2)(a_1 + a_70)
where n is the number of terms and a_1 is the first term.
Substituting the given values, we get:
a_1 = 22
a_70 = 22 + (70-1)(-3) = -153
n = 70
Therefore, the sum of the first 70 terms of the sequence is:
S_70 = (70/2)(22 - 153) = -3505
To know more about arithmetic sequence,
https://brainly.com/question/31698434
#SPJ11
What is the expected value of a lottery ticket where there are only 1 chance in 10 millions of winning the grand prize of $50 Million, and 100,000 in 10 millions chances of winning $100?The area under the normal curve between z = -1 and z = -2 is _______than the area under the normal curve between z = 2 and z = 3A.equal toB.less thanC.greater thanD.A, B, or C above depending on the value of the mean
The expected value of the lottery ticket is $6.
To calculate the expected value of a lottery ticket, we multiply the value of each possible outcome by its corresponding probability and sum them up. In this case, we have two possible outcomes:
Winning the grand prize of $50 million with a probability of 1 in 10 million.
Winning $100 with a probability of 100,000 in 10 million.
Let's calculate the expected value:
Expected value = (Probability of winning grand prize * Value of grand prize) + (Probability of winning $100 * Value of $100)
Expected value = (1/10,000,000) * $50,000,000 + (100,000/10,000,000) * $100
Expected value = $5 + $1
Expected value = $6
Therefore, the expected value of the lottery ticket is $6.
Regarding the second part of your question, the area under the normal curve between z = -1 and z = -2 is greater than the area under the normal curve between z = 2 and z = 3.
To know more about expected value refer here:
https://brainly.com/question/32004014
#SPJ11
circle p is described by the equation (x3)(y2)25. which of the following lines are tangent to p?
To determine which of the given lines are tangent to circle p, we need to first find the equation of the circle.
The equation given is (x^3)(y^2)=25, which can be rewritten as y^2=25/(x^3).
Taking the derivative of this equation with respect to x,
we get: 2y(dy/dx) = -(75)/(x^4).
Simplifying this, we get dy/dx = -(75y)/(2x^4).
Now we can substitute the slope of each given line into this equation and find the corresponding value of y. If this value of y satisfies the equation of the circle, then the line is tangent to the circle at that point. We find that only the line y = 5x + 1 satisfies this condition, and therefore it is the only line that is tangent to circle p.
To know more about equation of the circle visit:
https://brainly.com/question/29288238
#SPJ11
can you help me with this
Answer:
she took 6 courses
Step-by-step explanation:
1. 200-50= 150
2. 150÷25 = 6
B. 6 courses
sign-up cost = $50
cost per course = $25
Piper paid = $200
First, subtract the sign-up cost from the amount paid:
$200 - $50 = $150
Now, divide the cost per course to the amount that is left to get the number of courses she took:
$150 ÷ $25 = 6 courses
how many cubic yards of concrete are required for all the 40/80 piers on the project?
To calculate the total cubic yards of concrete required for all the piers on your project, follow these steps:
Step 1: Determine the dimensions of a single pier. You mentioned the piers are 40/80, but we need the exact measurements in feet (width, length, and height) to proceed with the calculation.
Step 2: Calculate the volume of a single pier. Multiply the width, length, and height of a pier to find its volume in cubic feet.
Step 3: Convert the volume of a single pier to cubic yards. Since 1 cubic yard equals 27 cubic feet, divide the volume in cubic feet by 27 to convert it to cubic yards.
Step 4: Calculate the total volume of concrete required for all piers. Multiply the volume of a single pier in cubic yards by the total number of piers on the project.
Once you have the dimensions of a single pier, follow these steps to find the total amount of concrete needed for your project in cubic yards.
To know more about cubic visit:
https://brainly.com/question/30344308
#SPJ11
find the first four nonzero terms in a power series expansion about x0 for a general solution to the given differential equation. w''-18x^2
The first four nonzero terms in a power series expansion about x0 for a general solution to the differential equation w''-18x^2=0 are w(x)=C1 + C2(x-x0)^2 + 27/4 C1(x-x0)^4 + 81/40 C2(x-x0)^6.
To find the power series expansion of w(x), we first assume w(x) can be represented by a power series around x0, i.e., w(x)= ∑(n=0)^∞ a_n(x-x0)^n. Then we differentiate w(x) twice to obtain w''(x) = ∑(n=2)^∞ n(n-1) a_n (x-x0)^(n-2).
Substituting w''(x) into the differential equation and setting it to zero, we have ∑(n=2)^∞ n(n-1) a_n (x-x0)^(n-2) - 18(x-x0)^2 ∑(n=0)^∞ a_n(x-x0)^n = 0.
Collecting like powers of (x-x0), we can write the equation as ∑(n=2)^∞ n(n-1) a_n (x-x0)^(n-2) - 18 ∑(n=2)^∞ a_n (x-x0)^n = 0.
To obtain the first few nonzero terms, we equate coefficients of like powers of (x-x0) and solve the resulting system of equations.
At n=0, we get -18a_0=0, which implies a_0=0.
At n=1, we get -18a_1=0, which implies a_1=0.
At n=2, we get 2(2-1)a_2-18a_0=0, which implies a_2=9a_0/2=0.
At n=3, we get 3(3-1)a_3-18a_1=0, which implies a_3=0.
Thus, the first nonzero term is a_4, and we can solve for it to obtain a_4=27/4 C1.
Similarly, we can solve for a_5, a_6, and so on, to obtain higher order terms in the power series expansion.
Substituting these values back into the power series expansion for w(x), we obtain the first four nonzero terms as w(x)=C1 + C2(x-x0)^2 + 27/4 C1(x-x0)^4 + 81/40 C2(x-x0)^6.
For more questions like Series click the link below:
https://brainly.com/question/28167344
#SPJ11
in testing the null hypothesis h0:p1−p2=0, if h0 is false, the test could lead to:
If the null hypothesis h0:p1−p2=0 is found to be false during testing, it could lead to the rejection of the null hypothesis and acceptance of the alternative hypothesis or Failing to reject the null hypothesis
1. Rejecting the null hypothesis (H0) and accepting the alternative hypothesis (H1): This happens when the sample data provides strong evidence against the null hypothesis, which means there is a significant difference between the two population proportions (p1 and p2).
2. Failing to reject the null hypothesis (H0): This may happen due to a Type II error, where the null hypothesis is false but the test fails to provide enough evidence to reject it. In this case, the difference between the two population proportions may exist, but it is not detected by the test.
So, in summary, if H0 is false in testing the null hypothesis H0: p1 - p2 = 0, the test could lead to either rejecting the null hypothesis and accepting the alternative hypothesis, or failing to reject the null hypothesis due to a Type II error.
Learn more about null hypothesis here, https://brainly.com/question/25263462
#SPJ11
a viral video featured a football quarterback running into the backside of one of his offensive linemen, falling to the ground and dropping the football. in a survey of 444 people, 298 reported having seen the video. create a 95% confidence interval for the proportion of people who have seen the video. use excel to create the confidence interval, rounding to four decimal places.
The 95% confidence interval for the proportion of people who have seen the video is (0.6309, 0.7115), rounded to four decimal places.
The point estimate for the proportion of people who have seen the video is 298/444 = 0.6712.
To create a 95% confidence interval for this proportion, we can use the formula:
point estimate ± z* (standard error)
where z* is the z-score associated with the desired level of confidence (95% in this case), and the standard error is calculated as:
sqrt[(p-hat*(1-p-hat))/n]
where p-hat is the point estimate and n is the sample size.
Using a z-table, the z-score for 95% confidence is 1.96.
Plugging in the values, we get:
point estimate ± z* (standard error)
0.6712 ± 1.96 * sqrt[(0.6712*(1-0.6712))/444]
0.6712 ± 0.0403
Therefore, the 95% confidence interval for the proportion of people who have seen the video is (0.6309, 0.7115), rounded to four decimal places.
Learn more about confidence interval here
https://brainly.com/question/20309162
#SPJ11
∠A and ∠B are complementary angles. if m∠A =(3x+23) and∠B=3x+25) then find the measure of ∠B
Answer:
Step-by-step explanation:
If two angles are complementary, then their sum is 90°.
So we can build an equation using this information.
The angles are 3x + 23 and 3x + 25, respectively.
[tex]\bf{3x+23+3x+25=90}[/tex]
Combine the like terms
[tex]\bf{6x+48=90}[/tex]
Now just solve for x
[tex]\bf{6x=90-48}[/tex]
[tex]\bf{6x=42}[/tex]
[tex]\bf{x=7}[/tex]
Knowing that x = 7, we can plug it into the expressions
3x + 25
3(7) + 25
21 + 25
46
Now the other angle is:
3x + 23
3(1) + 23
21 + 23
44
Hence, the measures of [tex]\angle A[/tex] and [tex]\angle B[/tex] are 44 and 46, respectively.
For a sample size of 115 and a population parameter of 0. 1, what is the standard error of the sampling distribution? round your answer to three decimal places
The standard error of the sampling distribution is approximately 0.028.
What is the standard error of the sampling distribution with a sample size of 115 and a population parameter of 0.1?The standard error measures the variability or dispersion of sample statistics around the population parameter. To calculate the standard error of the sampling distribution, we use the formula SE = sqrt((p * (1 - p)) / n), where SE represents the standard error, p is the population parameter, and n is the sample size. Substituting the given values, with p = 0.1 and n = 115, we can calculate the standard error. Therefore, the standard error of the sampling distribution is approximately 0.028, rounded to three decimal places.
Learn more about Sampling
brainly.com/question/27860316
#SPJ11
use the divergence theorem to evaluate z z s (2x 7y 2023z2) ds where s is the sphere of radius 2 centered at the origin.
Using the divergence theorem, the given surface integral over the sphere of radius 2 centered at the origin is equal to 0.
The divergence theorem states that the flux of a vector field F through a closed surface S is equal to the triple integral of the divergence of F over the region enclosed by S. Mathematically, it can be written as:
∫∫ F ⋅ dS = ∫∫∫ ∇ ⋅ F dV
where F is the vector field, S is the surface, and V is the region enclosed by S.
In this problem, the vector field F is (2x, 7y, 2023z^2). The sphere of radius 2 centered at the origin is a closed surface, denoted by S. Therefore, we can apply the divergence theorem to evaluate the given surface integral over S.
To apply the divergence theorem, we need to compute the divergence of F.
∇ ⋅ F = ∂/∂x (2x) + ∂/∂y (7y) + ∂/∂z (2023z^2) = 2 + 0 + 4046z
The triple integral of the divergence of F over the region enclosed by S is equal to zero since the region is symmetric about the origin and the integrand is an odd function in z.
Thus, we have:
∫∫ F ⋅ dS = ∫∫∫ ∇ ⋅ F dV = 0
Therefore, using the divergence theorem, the given surface integral over the sphere of radius 2 centered at the origin is equal to 0.
Visit here to learn more about vector:
brainly.com/question/30817683
#SPJ11
Solve the right triangle.
The angles of the right angle triangle are as follows:
A = 22.6 degrees
B = 67.4 degrees
How to find the angles of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees.
The sum of angles in a triangle is 180 degrees.
Therefore, the angle A and B can be found using trigonometric ratios as follows:
tan A = opposite / adjacent
tan A = 5 / 12
A = tan⁻¹ 0.41666666666
A = 22.6198324013
A = 22.6 degrees
Therefore,
B = 180 - 90 - 22.6
B = 67.4 degrees
learn more on right triangle here: brainly.com/question/26580326
#SPJ1
The function below gives the cost in dollars to manufacturex items: C(x) = 10,000 + 5x – 10.000 Find the average cost per item over the interval (1,000,1,010]. Continuing with the previous problem find the average cost per item over the interval [999.5, 1000]. Continuing with the previous problem, what is the value of C' (1000) rounded to 1-decimal place?
The average cost per item over the interval (1,000,1,010] is (C(1010) - C(1000)) / (1010 - 1000) = (10,000 + 5(1010) - 10,000 - 5(1000)) / 10 = $5.50.
The average cost per item over the interval [999.5, 1000] is (C(1000) - C(999.5)) / (1000 - 999.5) = (10,000 + 5(1000) - 10,000 - 5(999.5)) / 0.5 = $5.00.
The given function C(x) represents the cost in dollars to manufacture x items. To find the average cost per item over a given interval, we use the formula: (C(b) - C(a)) / (b - a), where a and b are the endpoints of the interval.
For the interval (1,000,1,010], we substitute a = 1000 and b = 1010 into the formula to obtain (C(1010) - C(1000)) / (1010 - 1000). Simplifying the expression using the given function C(x) yields ($10,000 + $5(1010) - $10,000 - $5(1000)) / 10 = $5.50 per item.
For the interval [999.5, 1000], we substitute a = 999.5 and b = 1000 into the formula to obtain (C(1000) - C(999.5)) / (1000 - 999.5). Simplifying the expression using the given function C(x) yields ($10,000 + $5(1000) - $10,000 - $5(999.5)) / 0.5 = $5.00 per item.
To find C'(1000), we differentiate the function C(x) with respect to x, which gives C'(x) = 5. The value of C'(1000) is therefore 5, rounded to 1 decimal place.
For more questions like Cost click the link below:
https://brainly.com/question/30045916
#SPJ11
A bag of 10 apples contains 3 rotten apples and 7 good apples. A shopper selects a sample of 4 apples from the bag. (a) How many dilleront samples are possible? (b) How many samples contain all good applen? (c) How many samples contain at least 1 rotten apple?
There are 210 different samples of 4 apples that can be chosen from the bag.
a. to find the number of different samples of 4 apples that can be chosen from the bag of 10 apples, we use the combination formula:
n choose k = n! / (k!(n-k)!)
where n is the total number of apples (10), and k is the number of apples chosen for the sample (4).
so the number of different samples of 4 apples that can be chosen from the bag of 10 apples is:
10 choose 4 = 10! / (4! * 6!) = 210 b. to find the number of samples that contain all good apples, we need to choose 4 apples from the 7 good apples in the bag. this can be done using the combination formula:
7 choose 4 = 7! / (4! * 3!) = 35
so there are 35 different samples that contain all good apples.
c. to find the number of samples that contain at least 1 rotten apple, we can use the complement rule, which says that the probability of an event happening is 1 minus the probability of the event not happening. in this case, we can find the number of samples that do not contain any rotten apples, and then subtract that from the total number of samples found in part a.
to find the number of samples that do not contain any rotten apples, we need to choose 4 apples from the 7 good apples in the bag. this can be done using the combination formula as in part b:
7 choose 4 = 35
so there are 35 different samples that do not contain any rotten apples.
Learn more about probability here:
https://brainly.com/question/32117953
#SPJ11
Find the amount accumulated after
investing a principle P for t years and an
interest rate compounded quarterly.
P = $1,999 r = 3% t = 18 k = 4
Hint: A = P(1 + E)kt
A = $[?]
every answer i put it says is incorrect please help i don’t know what to do
The amount accumulated after investing $1,999 for 18 years at a 3% interest rate compounded quarterly would be approximately $3423.39
We have to find the amount accumulated after investing a principle P for t years and an interest rate compounded quarterly.
P = $1,999
r = 3% =0.03
t = 18
k = 4
The formula to find the amount is [tex]A =P(1+r/k)^k^t[/tex]
A=1999(1+0.03/4)⁷²
A=1999(1 + 0.0075)⁷²
A=1999(1.0075)⁷²
A = 3423.39
Therefore, the amount accumulated after investing $1,999 for 18 years at a 3% interest rate compounded quarterly would be $3423.39
To learn more on Interest rate click:
https://brainly.com/question/28272078
#SPJ1
does tan^2x = sin^2x/cos^2x
Answer:
Yes they both are equal
