Answer: 40000
Step-by-step explanation:
The formula to find the sample size is given by :-
[tex]n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2[/tex], where p is the prior estimate of the population proportion.
Here we can see that the sample size is inversely proportion withe square of margin of error.
i.e. [tex]n\ \alpha\ \dfrac{1}{E^2}[/tex]
By the equation inverse variation, we have
[tex]n_1E_1^2=n_2E_2^2[/tex]
Given : [tex]E_1=0.05[/tex] [tex]n_1=1000[/tex]
[tex]E_2=0.025[/tex]
Then, we have
[tex](1000)(0.05)^2=n_2(0.025)^2\\\\\Rightarrow\ 2.5=0.000625n_2\\\\\Rightarrow\ n_2=\dfrac{2.5}{0.000625}=4000[/tex]
Hence, the sample size will now have to be 4000.
The new sample size will have to be approximately 4000.
The formula to calculate the sample size (n) needed to estimate a population proportion with a given maximum allowable error (E) and confidence level (usually 95% or 1.96 standard deviations for a two-tailed test) is given by:
[tex]\[ n = \left(\frac{z \times \sigma}{E}\right)^2 \][/tex]
Given that the original maximum allowable error was 0.05 and the sample size calculated was 1000, we can set up the equation:
[tex]\[ 1000 = \left(\frac{1.96 \times 0.5}{0.05}\right)^2 \][/tex]
Now, we want to find the new sample size when the maximum allowable error is reduced to 0.025. The new sample size can be calculated by:
[tex]\[ n_{new} = \left(\frac{z \times \sigma}{E_{new}}\right)^2 \][/tex]
Since \( z \) and[tex]\( \sigma \)[/tex] remain constant, and only \( E \) changes, the relationship between the original sample size and the new sample size is inversely proportional to the square of the ratio of the original error to the new error:
[tex]\[ n_{new} = n_{old} \times \left(\frac{E_{old}}{E_{new}}\right)^2 \] \[ n_{new} = 1000 \times \left(\frac{0.05}{0.025}\right)^2 \] \[ n_{new} = 1000 \times \left(\frac{0.05}{0.025}\right)^2 \] \[ n_{new} = 1000 \times \left(2\right)^2 \] \[ n_{new} = 1000 \times 4 \] \[ n_{new} = 4000 \][/tex]
Therefore, the new sample size will have to be approximately 4000 to reduce the maximum allowable error to 0.025."
All the fourth-graders in a certain elementary school took a standardized test. A total of 81% of the students were found to be proficient in reading, 74% were found to be proficient in mathematics, and 64% were found to be proficient in both reading and mathematics. A student is chosen at random.(a) What is the probability that student is proficient in mathematics but not in reading?(b) What is the probability that student is proficient in reading but not in mathematics?
Answer:
The probability that a student is proficient in mathematics, but not in reading is, 0.10.
The probability that a student is proficient in reading, but not in mathematics is, 0.17
Step-by-step explanation:
Let's define the events:
L: The student is proficient in reading
M: The student is proficient in math
The probabilities are given by:
[tex]P (L) = 0.81\\P (M) = 0.74\\P (L\bigcap M) = 0.64[/tex]
[tex]P (M\bigcap L^c) = P (M) - P (M\bigcap L) = 0.74 - 0.64 = 0.1\\P (M^c\bigcap L) = P (L) - P (M\bigcap L) = 0.81 - 0.64 = 0.17[/tex]
The probability that a student is proficient in mathematics, but not in reading is, 0.10.
The probability that a student is proficient in reading, but not in mathematics is, 0.17
By vector methods, find the cosine of the angle between the lines (x - 1)/(3) = (y - 0.5)/(2) = z and x = y = z
Answer:
The angle between the lines [tex]\frac{x-1}{3}= \frac{y-0.5}{2}=\frac{z-0}{1}[/tex] and [tex]\frac{x-0}{1}= \frac{y-0}{1}=\frac{z-0}{1}[/tex] is [tex]\sqrt{\frac{6}{7}}[/tex]
Step-by-step explanation:
The equation of a line with direction vector [tex]\vec{d}=(l,m.n)[/tex] that passes through the point [tex](x_{1},y_{1},z_{1})[/tex] is given by the formula
[tex]\frac{x-x_{1}}{l}= \frac{y-x_{1}}{m}=\frac{z-z_{1}}{n},[/tex] where l,m, and n are non-zero real numbers.
This is called the symmetric equations of the line.
The angle between two lines [tex]\frac{x-x_{1}}{l_{1} }= \frac{y-y_{1}}{m_{1} }=\frac{z-z_{1}}{n_{1}}[/tex] and [tex]\frac{x-x_{2}}{l_{2} }= \frac{y-y_{2}}{m_{2} }=\frac{z-z_{2}}{n_{2}}[/tex] equal the angle subtended by direction vectors, [tex]d_{1}[/tex] and [tex]d_{2}[/tex] of the lines
[tex]cos (\theta)=\frac{\vec{d_{1}}\cdot\vec{d_{2}}}{|\vec{d_{1}}|\cdot|\vec{d_{2}}|}=\frac{l_{1} \cdot\l_{2}+m_{1} \cdot\ m_{2}+n_{1} \cdot\ n_{2}}{\sqrt{l_{1}^{2}+m_{1}^{2}+n_{1}^{2}} \cdot \sqrt{l_{2}^{2}+m_{2}^{2}+n_{2}^{2}}}[/tex]
Given that
[tex]\frac{x-1}{3}= \frac{y-0.5}{2}=\frac{z-0}{1}[/tex] and [tex]\frac{x-0}{1}= \frac{y-0}{1}=\frac{z-0}{1}[/tex]
[tex]l_{1}=3, m_{1}=2,n_{1}=1\\ l_{2}=1, m_{2}=1,n_{2}=1[/tex]
We can use the formula above to find the cosine of the angle between the lines
[tex]cos(\theta)=\frac{3 \cdot 1+2 \cdot 1 +1 \cdot 1}{\sqrt{3^{2}+2^{2}+1^{2}} \cdot \sqrt{1^{2}+1^{2}+1^{2}}} = \sqrt{\frac{6}{7}}[/tex]
In the equation g = 312 ÷ α , the variable g can be described best as the 1. number of degrees that a skateboarder turns when making α rotations. 2. total number of groups, g, with α students each that can be made if there are 312 students to be grouped. 3. weight of a bag containing α grapefruits if each piece of fruit weighs 312 grams. 4. total number of goats that can graze on 312 acres if each acre can feed α goats. 5. number of grams of fuel, g, needed to raise the temperature of a solution, α, to a temperature of 312◦F.
Answer:
5) True. G is the Number of grams of fuel, g, needed to raise the temperature of a solution, α, to a temperature of 312◦F.
Step-by-step explanation:
Hi!
Let's examine better this equation: [tex]g=\frac{312}{a}[/tex]
What we have here 312 is a dependent variable, and it is inversely proportional to a. The more a increases the more g decreases.
1) Number of degrees that a skateboarder turns when making "α" rotations
[tex]g=\frac{312}{a}[/tex]
1 rotation ----------- 312°
2 rotation ----------- 156°
Here we have a problem. The skateboarder must necessarily and randomly turn 312°, and its fractions. But in a circle, the rotation cannot follow this pattern.
False
2) The total number of groups, g, with "α" students each that can be made if there are 312 students to be grouped.
[tex]g=\frac{312}{a}[/tex]
1 group --------------- 312 students
2 groups ------------ 156 students
5 groups -------------62.4 students
Even though 312 is divisible for 1,2,3,4 it is not for 5,7,9, and the group is a countable, natural category.
False
3) Weight of a bag containing "α" grapefruits if each piece of fruit weighs 312 grams
[tex]g=\frac{312}{a}[/tex]
g=1 bag with 1 grapefruit-------------- 312 g
g=1 bag with 2 grapefruits ---------- 156 g
That doesn't make sense, since for this description. The best should be g=312a and not g=312/a.
False
4) The total number of goats that can graze on 312 acres if each acre can feed "α" goats.
Since there's a relation
1 acre can feed ----------------- 1 goat
312 acres can feed ----------------g
g= 312/1 = 312 acres can feed 1 goat (1 acre for 1 goat)
g=312/2= since 312 acres can feed 156 goats (1 acre for 2 goats)
g =312/3 = 312 acres can feed 104 (1 acre for 3 goats)
Clearly, this function g=312/a does not describe this since the ratio is not the same, as long as we bring more goats to graze on those 312 acres.
False
5) Number of grams of fuel, g, needed to raise the temperature of a solution, α, to a temperature of 312◦F
g= number of grams of a fuel
a= initial temperature of a solution
g=312/a
Let's pick a=100 F initial temperature
g=312/100
g=3.12 grams
Let's now pick 200F as our initial temperature.
g=312/200 g=1.56 grams of solution
The more heat needed to raise, the more fuel necessary. Then True
If the interest rate is 3% and a total of $4,370.91 will be paid to you at the end of 3 years, what is the present value of the sum
Answer:
The present value (or initial investment) is $4000.00
Step-by-step explanation:
I'm going to assume that the correct formula here is
[tex]A(t)=P(1+r)^t[/tex]
and we are looking to solve for P, the principle investment. We know that A(t) is 4370.91; r is .03 and t is 3:
[tex]4370.91=P(1+.03)^3[/tex] and
[tex]4370.91=P(1.03)^3[/tex] and
4370.91 = 1.092727P so
P = 4000.00
precalc question: a warhead fired from an enemy ship in the persian gulf is a dud and only travels 100 meters before it hits the water. If it had an initial velocity of 489 meters per second, find the time from the initial launch of the warhead to impact
a)0.2 s
b)30.8 s
c)100 s
d) 0.31 s
Answer:
0.2s is the time from the initial launch of the warhead to impact.
Step-by-step explanation:
This is a rule of three problem
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication.
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.
In this problem, our measures have a direct relationship.
The problem states that in a second, the warhead travels 489 meters. How long it takes to travel 100 meters? So
1s - 489m
xs - 100m
489x = 100
[tex]x = \frac{100}{489}[/tex]
x = 0.2s.
0.2s is the time from the initial launch of the warhead to impact.
Convert 120 kW to W? MW?
Answer: 120000 W and 0.12 MW
Step-by-step explanation:
The expression 120 kW uses a metric prefix "k" (kilo) which is the same as multiply by 1000. So you can replace k by 1000 to convert the expression to the unit W.
120 kW= 120(1000) W= 120000 W.
To convert 120kW to MW, where the prefix M (mega) is equivalent to 1000000, you can use a conversion factor like (1 MW / 1000 kW) and multiply the expression by it.
Notice that (1 MW / 1000 kW) = 1, so the expression remains unaltered.
Then,
120 kW (1 MW / 1000 kW) = 0.12 MW
Show that Z2[i] = {a + bi | a,b € Z2} is not a field
Step-by-step explanation:
On a field every element different from 0 should have a multiplicative inverse. Let's check that in Z2[i] not ALL nonzero elements have multiplicative inverses.
Z2 is made of two elements: 0 and 1, and so Z2[i] is made of four elements: 0+0i,0+1i, 1+0i, 1+1i (which we can simplify from now on as 0, i, 1, 1+i respectively). Now, let's check that the element 1+i doesn't have a multiplicative inverse (we can do this by showing that no matter what we multiply it by, we're not getting 1, which is the multiplicative identity)
[tex](1+i)\cdot 0 = 0[/tex] (which is NOT 1)
[tex](1+i)\cdot i = i+i^2=i-1=1+i[/tex] (which is NOT 1) (remember -1 and 1 are the same in Z2)
[tex](1+i)\cdot 1 = 1+i[/tex] (which is NOT 1)
[tex](1+i)\cdot (1+i) = 1+i+i+i^2=1+2i-1=0+0i=0[/tex] (which is NOT 1) (remember 2 is the same as 0 in Z2)
Therefore the element 1+i doesn't have a multiplicative inverse, and so Z2[i] cannot be a field.
Company A charges $331.35 per week for a compact car with unlimited miles. Company B charges $175 per week plus $0.53 per mile, for the same car. How many miles must be driven in a week so that company A is a better deal than company B?
Answer:
Company A is a better deal than Company B for the number of miles greater than 295 miles
Step-by-step explanation:
Let
y ----> the charge per week in dollars
x ----> the number of miles
we have
Company A
[tex]y=331.35[/tex] -----> equation A
Company B
[tex]y=0.53x+175[/tex] -----> equation B
Solve the system by substitution
Equate equation A and equation B and solve for x
[tex]331.35=0.53x+175[/tex]
[tex]0.53x=331.35-175\\0.53x=156.35\\x=295\ mi[/tex]
For x=295 miles the charge in Company A and Company B is the same
therefore
Company A is a better deal than Company B for the number of miles greater than 295 miles
Find an equation of a line passing through the point (8,9) and parallel to the line joining the points (2,7) and (1,5).
Answer:
2x - y - 7 = 0
Step-by-step explanation:
Since the slope of parallel line are same.
So, we can easily use formula,
y - y₁ = m ( x ₋ x₁)
where, (x₁, y₁) = (8, 9)
and m is a slope of line passing through (x₁, y₁).
and since the slope of parallel lines are same, so here we use slope of parallel line for calculation.
and, Slope = m = [tex]\dfrac{y_{b}-y_{a}}{x_{b}-x_{a}}[/tex]
here, (xₐ, yₐ) = (2, 7)
and, [tex](y_{a},y_{b}) = (1, 5 )[/tex]
⇒ m = [tex]\dfrac{5-7}{1-2}[/tex]
⇒ m = 2
Putting all values above formula. We get,
y - 9 = 2 ( x ₋ 8)
⇒ y - 9 = 2x - 16
⇒ 2x - y - 7 = 0
which is required equation.
Answer:
y=2x-8
Step-by-step explanation:
In order to solve this you first have to calculate the slope of the parallel line, since that would be equal to the slope of our line:
[tex]Slope=\frac{y2-y1}{x2-x1}[/tex]
Now we insert the values into the formula:
[tex]Slope=\frac{y2-y1}{x2-x1}\\Slope=\frac{5-7}{1-2}\\Slope= \frac{-2}{-1}\\ Slope:2[/tex]
And remember that the formula for general line is:
[tex]Y-y1= M(x-x1)\\y-9=2(x-8=\\y=2x-16+9\\y=2x-7[/tex]
So the equation for the line passing through point 8,9 and parallel to the line joining 2,7 and 1,5 would be y=2x-7
Larry Calanan has earnings of S518 in a week. He is single and claims 2 withholding allowances. His deductions include FICA, Medicare, federal withholding, state disability insurance, state withholding, union dues of $15, and charitable contributions of $21. Find his net pay.
Answer:
$482
Step-by-step explanation:
Data provided:
Total earning per week = $518
Medicare, federal withholding, state disability insurance, state withholding, union dues = $15
charitable contributions = $21
Now,
The total deductions = $15 + $21 = $36
also,
Net pay = Total income - Total deductions
thus,
Net pay = $518 - $36
or
Net Pat = $482
what is the area,in square centimeters,of a circle that has a circumference of 16 centimeters?
Answer: [tex]20.38\ cm^2[/tex]
Step-by-step explanation:
We know that the circumference of a circle is given by :-
[tex]C=2\pi r[/tex], where r is the radius of the circle .
Given : Circumference of circle = 16 cm
Then, [tex]16=2\pi r[/tex]
i.e [tex]r=\dfrac{16}{2\pi}=\dfrac{8}{\pi}[/tex] (1)
We know that the area of circle is given by :-
[tex]A=\pi r^2[/tex]
i.e. [tex]A=\pi (\dfrac{8}{\pi})^2[/tex] [From (1)]
i.e. [tex]A=\pi (\dfrac{64}{\pi^2})[/tex]
i.e. [tex]A=\dfrac{64}{\pi}[/tex]
Put [tex]\pi=3.14[/tex]
[tex]A=\dfrac{64}{3.14}=20.3821656051approx20.38\ cm^2[/tex]
Hence, area of circle = [tex]20.38\ cm^2[/tex]
Find the arc length of the given curve on the specified interval.
(6 cos(t), 6 sin(t), t), for 0 ≤ t ≤ 2π
Answer:
Step-by-step explanation:
Given that
[tex]r(t) = (6cost, 6sint, t), 0\leq t\leq 2\pi\\r'(t) = (-6sint, 6cost, 1),\\||r'(t)||=\sqrt{(-6sint)^2 +(6cost)^2+1} =\sqrt{37}[/tex]
Hence arc length = [tex]\int\limits^a_b {||r'(t)||} \, dt[/tex]
Here a = 0 b = 2pi and r'(t) = sqrt 37
Hence integrate to get
[tex]\int\limits^{2\pi} _0 {\sqrt{37} } \, dt\\ =\sqrt{37} (t)\\=2\pi\sqrt{37}[/tex]
Write a differential equation whose only solution is the trivial solution y = 0. Explain your reasoning
Answer:
[tex]2e^{y'}y=0[/tex]
Step-by-step explanation:
The solution for this differential equation [tex]2e^{y'}y=0[/tex] have to be the trivial solution y=0. Because the function [tex]e^{x}[/tex] always have values different of zero, then the only option is the trivial solution y=0.
For which equations below is x = -3 a possible solution? Select three options.
x = 3
x = -3
|-x1 = 3
|-x) = -3
-la = -3
Answer:
x=-3
|-x| = 3
|x| = 3
Step-by-step explanation:
we know that
If a number is a solution of a equation, then the number must satisfy the equation
Verify each case
case 1) we have
x=3
substitute the value of x=-3
-3=3 -----> is not true
therefore
x=-3 is not a solution of the given equation
case 2) we have
x=-3
substitute the value of x=-3
-3=-3 -----> is true
therefore
x=-3 is a solution of the given equation
case 3) we have
|-x| = 3
substitute the value of x=-3
|-(-3)| = 3
|3| = 3
3=3-----> is true
therefore
x=-3 is a solution of the given equation
case 4) we have
|x| = 3
substitute the value of x=-3
|(-3)| = 3
3=3-----> is true
therefore
x=-3 is a solution of the given equation
case 5) we have
-|x| = 3
substitute the value of x=-3
-|(-3)| = 3
-3=3-----> is not true
therefore
x=-3 is not a solution of the given equation
Is it possible for a simple, connected graph that has n vertices all of different degrees? Explain why or why not.
Answer:
It isn't possible.
Step-by-step explanation:
Let G be a graph with n vertices. There are n possible degrees: 0,1,...,n-1.
Observe that a graph can not contain a vertice with degree n-1 and a vertice with degree 0 because if one of the vertices has degree n-1 means that this vertice is adjacent to all others vertices, then the other vertices has at least degree 1.
Then there are n vertices and n-1 possible degrees. By the pigeon principle there are two vertices that have the same degree.
Let P(x) denote the statement "2x+5 > 10." Which of the following is true?
P(0)
P(3)
P(2)
P(1)
Answer: P(3) is True
Step-by-step explanation:
The given statement is an inequality denoted as P(x). To find out which of the options is true you have to evaluate each given value of X in the inequality and perform the arithmetic operations, then you have to see if the expression makes sense.
For P(0): Replace X=0 in 2x+5>10
2(0)+5>10
0+5>10
5>10 is false because 5 is not greater than 10
For P(3): Replace X=3 in 2x+5>10
2(3)+5>10
6+5>10
11>10 is true because 11 is greater than 10
For P(2): Replace X=2 in 2x+5>10
2(2)+5>10
4+5>10
9>10 is false
For P(1): Replace X=1 in 2x+5>10
2(1)+5>10
2+5>10
7>10 is false
Vanessa walks from her house to a bus stop that is 400 yards away. If Vanessa is 22 yards from her house, how far is she from the bus stop? yards Preview 400 − 22 = 400-22= 378. If Vanessa is 163.4 yards from her house, how far is she from the bus stop? yards Preview 400 − 163.4 = 400-163.4= 236.6. Let the variable x x represent Vanessa's varying distance from her house (in yards). As Vanessa walks from her house to the bus stop, the value of x x varies from to . How many values does the variable x x assume as Vanessa walks from her house to the bus stop? Preview
Answer:
[tex]0\le x\le 400[/tex]
x can take infinitely many values
Step-by-step explanation:
Vanessa walks from her house to a bus stop that is 400 yards away.
If Vanessa is 22 yards from her house, how far is she from the bus stop? Preview: 400 − 22 = 400 - 22 = 378 yards. If Vanessa is 163.4 yards from her house, how far is she from the bus stop? Preview: 400 − 163.4 = 400 - 163.4 = 236.6 yards.Let the variable x represent Vanessa's varying distance from her house (in yards). Then 400 - x yards is how far Vanessa is from the bus stop.
The variable x can take any value from 0 to 400 (0 when Vanessa is at home and 400 when Vanessa is at bus station), so
[tex]0\le x\le 400[/tex]
x can take infinitely many values, because there are infinitely many real numbers between 0 and 400.
Vanessa is 378 yards from the bus stop when she is 22 yards from her house and 236.6 yards away when she is 163.4 yards from her house. The variable x denoting Vanessa's distance from home assumes infinitely many values as she walks to the bus stop.
Explanation:When Vanessa is 22 yards from her house, the distance remaining to reach the bus stop is simply the total distance to the bus stop minus her current position from the house. So, it's 400 yards - 22 yards = 378 yards. Similarly, if Vanessa is 163.4 yards from her house, the remaining distance to the bus stop is 400 yards - 163.4 yards = 236.6 yards.
As Vanessa walks from her house to the bus stop, variable x represents her varying distance from her house. The value of x starts at 0 when she is at her house and increases up to 400 yards as she reaches the bus stop. The variable x can assume infinitely many values, as it can represent any real number between 0 and 400, indicating her position at any given moment along her path.
-1.8-3.9=
A. -2.1
B.5.7
C.2.1
D.-5.7
In order to get the answer to this question you will have to use KCC (Keep, Change, Change) and then solve.
[tex]-1.8 - 3.9=[/tex]
Using KCC:
[tex]-1.8-3.9=-1.8+-3.9[/tex]
[tex]-1.8 + -3.9 = -5.7[/tex]
[tex]= -5.7[/tex]
Therefore your answer is option D "-5.7."
Hope this helps.
Answer:
D "-5.7."
Step-by-step explanation:
Experience raising New Jersey Red chickens revealed the mean weight of the chickens at
five months is 4.35 pounds. The weights follow the normal distribution. In an effort to increase
their weight, a special additive is added to the chicken feed. The subsequent
weights of a sample of five-month-old chickens were (in pounds):
4.41 4.37 4.33 4.35 4.30 4.39 4.36 4.38 4.40 4.39
At the .01 level, has the special additive increased the mean weight of the chickens? Estimate
the p-value.
Answer:
p-value = 0.1277
Step-by-step explanation:
p-value is the probability value tell us how likely it is to get a result like this if the Null Hypothesis is true.
Firstly we find the mean and standard deviation of the given data set.
⇒ Mean = [tex]\frac{4.41 +4.37+ 4.33+ 4.35 +4.30 +4.39 +4.36+ 4.38+ 4.40+ 4.39}{10}[/tex]
⇒ Mean = 4.368
[tex]Standard deviation(\sigma) = \sqrt{\frac{1}{n}\sum_{i=1}^{n}{(x_{i}-\bar{x})^{2}} }[/tex]
where, [tex]\bar{x}[/tex] is mean of the distribution.
⇒ Standard Deviation = 0.034
Applying t- test:
Let out hypothesis is:
H₀: μ = 4.35
H₁: μ ≠ 4.35
Now,
Here, μ = Population Mean = 4.35
[tex]\bar{x}[/tex]= Sample Mean = 4.368
σ = Standard Deviation = 0.034
n = 10
[tex]t=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
Putting all values we get, t = 1.6777 with (10 -1) = 9 degree of freedom.
Then the p-value at 99% level of significance.
⇒ p-value = 0.1277
To test whether the special additive has increased the mean weight of the chickens, we can use a t-test. We will calculate the t-value and the p-value and compare the p-value with the significance level of 0.01.
Explanation:To test whether the special additive has increased the mean weight of the chickens, we can use a t-test. We can set up the null hypothesis as follows:
H0: μ = 4.35
And the alternative hypothesis as:
H1: μ > 4.35
We will calculate the t-value and the p-value.
t-value = (mean of the sample - mean of the population) / (standard deviation of the sample / sqrt(sample size))
p-value = P(T > t)
In this case, we have to compare the p-value with the significance level of 0.01.
If the p-value is less than 0.01, we reject the null hypothesis and conclude that the special additive has increased the mean weight of the chickens.
The width of a rectangle is 4 more than half the length.
If the perimeter of the rectangle is 74, what is the width?
Perimeter of rectangle: P = 2l + 2w
width =
length =
Answer:
Width = 15.
Length = 22.
Step-by-step explanation:
If the length is L then the width W = 1/2L + 4.
The perimeter = 2L + 2W, so
2L + 2(1/2L + 4) = 74
2L + L + 8 = 74
3L = 66
L = 22.
So W = 1/2 *22 + 4 = 11 + 4
= 15.
A marketing research company desires to know the mean consumption of milk per week among males over age 32. A sample of 710 males over age 32 was drawn and the mean milk consumption was 4.6 liters. Assume that the population standard deviation is known to be 0.8 liters. Construct the 98% confidence interval for the mean consumption of milk among males over age 32. Round your answers to one decimal place.
Answer:
(4.5, 4.7)
Step-by-step explanation:
Hi!
Lets call X to the consumption of milk per week among males over age 32. X has a normal distribution with mean μ and standard deviation σ.
[tex]X \sim N(\mu, \sigma)[/tex]
When you know the population standard deviation σ of X , and the sample mean is [tex]\hat X[/tex], the variable q has distribution N(0,1):
[tex]q = \frac{\hat X - \mu}{\sigma} \sim N(0,1)[/tex]
Then you have:
[tex]P(-k < q <k ) = P(\hat X -\frac{\sigma}{\sqrt{N} }<\mu<\hat X +\frac{\sigma}{\sqrt{N} })=C[/tex]
This defines a C - level confidence interval. For each C the value of k is well known. In this case C = 0.98, then k = 2.326
Then the confidence interval is:
[tex](4.6 - 2.326*\frac{0.8}{\sqrt{710}}, 4.6 + 2.326*\frac{0.8}{\sqrt{710}})\\ (4.5, 4.7)[/tex]
use a ruler to draw a segment PQ that is 2 inches long then use your compass and straightedge to construct a segment MN with the same length as PQ
Answer:
Look to the attached figure
Step-by-step explanation:
* Lets revise the steps of constructing with the same length of a given
segment
- Use a ruler to draw a segment PQ of length 2 inches long
- Mark a point M that will be one endpoint of the new line segment
- Set the compasses pin on the point P of the line segment PQ
- Open the compass to the point Q
- The compasses width is now equal to the length of the segment PQ
- Without changing the compasses width place the pin of the compass
at point M and draw an arc where the other endpoint will be on it
- Pick a point N on the arc that will be the other endpoint of the new
line segment
- Draw a line from M to N
- The length of MN = The length of PQ
- The attached figure for more understand
9x = 99y
y = 2
x = ?
Answer:
x = 22
Step-by-step explanation:
9x = 99y
y = 2
9x = 99 * 2
99 * 2 = 198
9x = 198
--- ----
9 9
x = 22
Hey!
------------------------------------------------
Solution:
9x = 99y
~Substitute
9x = 99(2)
~Simplify
9x = 198
~Divide 9 to both sides
9x/9 = 198/9
~Simplify
x = 22
------------------------------------------------
Answer:
x = 22
------------------------------------------------
Hope This Helped! Good Luck!
Your waiter at a restaurant suggests you leave a tip of $10 on a $50 bill. What percentage is that?
Answer:
20%
Step-by-step explanation:
To find what percentage is $10 out of $50, we divide 10 by 50:
[tex] \frac{10}{50}=0.2[/tex]
If we want to get the result in percentage form, we simply multiply it by 100%:
[tex]0.2\cdot 100\%=20\%[/tex]
So a tip of $10 on a $50 bill is a tip of 20%.
Input/Output Relationship: Assume that the amount of learning you acquire can be summarized by the following relationship (or equation) and that your motivation to learn and the quality of instruction are both rated on a scale from 1 to 10: Amount of learning acquired = 0.2(number of books read) + 0.25(hours spent studying) + 0.15(quality of instruction) + 0.4(motivation to learn). If your motivation to learn rises from 7 to 9, by how much will the amount of learning acquired rise as a result? Show your work.
Answer:
8%
Step-by-step explanation:
Motivation to learn represents a 40% of the learning acquired and its rated from 1 to 10. An increase from 7 to 9 represents an increase (of motivation to learn of 20%) But since this quality represent 40% of the total, the real increase in learning is 0.2*0.4=0.08 or 8%.
Suppose C is a 3 x 3 matrix such that det (C) = 4. Show that det (C+C) is equal to 32
Step-by-step explanation:
Let's consider C is a matrix given by
[tex]\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right][/tex]
them determinant of matrix C can be written as
[tex]\begin{vmatrix}a & b & c\\ d & e & f\\ g & h & i \end{vmatrix}\ =\ 4.....(1)[/tex]
Now,
[tex]det (C+C)\ =\ \begin{vmatrix}a & b & c\\ d & e & f\\ g & h & i \end{vmatrix}\ +\ \begin{vmatrix}a & b & c\\ d & e & f\\ g & h & i \end{vmatrix}[/tex]
[tex]=\ \begin{vmatrix}2a & 2b & 2c\\ 2d & 2e & 2f\\ 2g & 2h & 2i \end{vmatrix}[/tex]
[tex]=\ 2\times 2\times 2\times \begin{vmatrix}a & b & c\\ d & e & f\\ g & h & i \end{vmatrix}[/tex]
[tex]=\ 8\times 4\ \ \ \ \ \ \ \ from\ eq.(1)[/tex]
= 32
Hence, det (C+C) = 32
A test requires that you answer either part A or part B. Part A consists of 7 true-false questions, and part B consists of 5 multiple-choice questions with one correct answer out of five. How many different completed answer sheets are possible?
Answer: 3253
Step-by-step explanation:
Given : A test requires that you answer either part A or part B.
Part A consists of 7 true-false questions.
i.e. there are 2 choices to answer each question.
Now, the number of ways to answer Part A : [tex]2^7=128[/tex] (1)
Part B consists of 5 multiple-choice questions with one correct answer out of five.
i.e. there are 5 choices to answer each question.
Now, the number of ways to answer Part B : [tex]5^5=3125[/tex] (2)
Now, the number of different ways to completed answer sheets are possible= [tex]128+3125=3253[/tex] [Add (1) and (2) ]
The number of different completed answer sheets possible is 400,000.
Explanation:To find the number of different completed answer sheets, we need to determine the number of ways to choose either part A or part B, and then calculate the number of possible combinations for each part.
For part A, since there are 7 true-false questions, each with 2 choices (true or false), there are 2^7 = 128 possible answer combinations.
For part B, since there are 5 multiple-choice questions, each with 5 choices, there are 5^5 = 3125 possible answer combinations.
To calculate the total number of different completed answer sheets, we multiply the number of choices for part A (128) by the number of choices for part B (3125), giving us a total of 128 * 3125 = 400,000 possible answer sheets.
(a) Find all points where the function f(z) = (x^2+y^2-2y)+i(2x-2xy) is differentiable, and compute the derivative at those points.
Answer:
The given function is differentiable at y = 1.
At y = 1, f'(z) = 0
Step-by-step explanation:
As per the given question,
[tex]f(z)\ = (x^{2}+y^{2}-2y)+i(2x - 2xy)[/tex]
Let z = x + i y
Suppose,
[tex]u(x,y) = x^{2}+y^{2}-2y[/tex]
[tex]v(x,y) = 2x - 2xy[/tex]
On computing the partial derivatives of u and v as:
[tex]u'_{x} =2x[/tex]
[tex]u'_{y}=2y -2[/tex]
And
[tex]v'_{x} =2-2y[/tex]
[tex]v'_{y}=-2x[/tex]
According to the Cauchy-Riemann equations
[tex]u'_{x} =v'_{y} \ \ \ \ \ \ \ and\ \ \ \ \ \ u'_{y} = -v'_{x}[/tex]
Now,
[tex](u'_{x} =2x) \neq (v'_{y}=-2x)[/tex]
[tex](u'_{y}=2y -2) \ = \ (- v'_{x} =-(2-2y) =2y-2)[/tex]
Therefore,
[tex]u'_{y}=- v'_{x}[/tex] holds only.
This means,
2y - 2 = 0
⇒ y = 1
Therefore f(z) has a chance of being differentiable only at y =1.
Now we can compute the derivative
[tex]f'(z)=\frac{1}{2}[(u'_{x}+iv'_{x})-i(u'_{y}+iv'_{y})][/tex]
[tex]f'(z) =\frac{1}{2}[(2x+i(2-2y))-i(2y-2+i(-2x))][/tex]
[tex]f'(z) = i(2-2y)[/tex]
At y = 1
f'(z) = 0
Hence, the required derivative at y = 1 , f'(z) = 0
Find all relative extrema and inflection points for fx)=(2x+7)^4
Answer:
[tex]x=-\frac{7}{2}[/tex] Extrema point.
The function does not have inflection points.
Step-by-step explanation:
To find the extrema points we have:
[tex]f'(x)=0[/tex]
Then:
[tex]f(x)=(2x+7)^4[/tex]
[tex]f'(x)=4(2x+7)^3(2)[/tex]
[tex]f'(x)=8(2x+7)^3[/tex]
Now:
[tex]f'(x)=8(2x+7)^3=0[/tex]
[tex]8(2x+7)^3=0[/tex]
[tex](2x+7)^3=0[/tex]
[tex]2x+7=0[/tex]
[tex]2x=-7[/tex]
[tex]x=-\frac{7}{2}[/tex]
To find the inflection points we need to calculate [tex]f''(x)=0[/tex] but due to that que have just one extrema point, the function does not have inflection points.
8 BASIC LEVEL 1. On weekends, a movie ticket costs $10.50. Form an inequality and solve it to find the maximum number of tickets Kate can buy with $205
Answer:
10.50x ≤ 205
The maximum number of tickets, x, would be 19.
Step-by-step explanation:
Given,
The cost of one ticket = $ 10.50,
The cost of x tickets = 10.50x dollars,
Since, the total cost can not exceed $ 205,
⇒ 10.50x ≤ 205
∵ 10.50 > 0 thus, when we multiply both sides by 1/10.50 the inequality sign will not change,
⇒ x ≤ [tex]\frac{205}{10.50}[/tex] ≈ 19.52
Hence, the maximum number of tickets would be 19.