Solution :
[tex]$H_0: p = 0.5$[/tex]
[tex]$H_a: p > 0.5$[/tex]
Alpha, α = 0.01
The sample proportion is :
[tex]$p'=\frac{x}{n}$[/tex]
[tex]$=\frac{513}{806}$[/tex]
= 0.636
Test statistics, [tex]$z=\frac{p'-p}{\sqrt{\frac{pq}{n}}}$[/tex]
[tex]$z=\frac{0.636-0.5}{\sqrt{\frac{0.5\times 0.5}{806}}}$[/tex]
[tex]$z=\frac{0.136}{0.0176}$[/tex]
z = 7.727
The p value = 0.00001
Here we observe that p value is less than α, and so we reject the hypothesis [tex]H_0[/tex].
Therefore, there is sufficient evidence,
Which ordered pair is a solution to the system of inequalities? y ≥ –x + 2 y > x – 5
A) (–5,–2)
B) (–1,1)
C) (0,0)
D) (3,2)
Answer:
it should be letter c
Step-by-step explanation:
I hope this help
Answer:
D) (3,2)Step-by-step explanation:
One way of solution is to plot the lines and points and confirm the answer visually.
See attached.
Another way is to substitute the coordinates and verify if they satisfy both of the inequalities.
Each of the methods gives us the correct answer choice of D.
People were asked if they owned an artificial Christmas tree. Of 78 people who lived in an apartment, 38 own an artificial Christmas tree. Also it was learned that of 84 people who own their home, 46 own an artificial Christmas tree. Is there a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees
Answer:
The p-value of the test is 0.4414, higher than the standard significance level of 0.05, which means that there is not a a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees.
Step-by-step explanation:
Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Apartment:
38 out of 78, so:
[tex]p_A = \frac{38}{78} = 0.4872[/tex]
[tex]s_A = \sqrt{\frac{0.4872*0.5128}{78}} = 0.0566[/tex]
Home:
46 out of 84, so:
[tex]p_H = \frac{46}{84} = 0.5476[/tex]
[tex]s_H = \sqrt{\frac{0.5476*0.4524}{84}} = 0.0543[/tex]
Test if the there a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees:
At the null hypothesis, we test if there is no difference, that is, the subtraction of the proportions is equal to 0, so:
[tex]H_0: p_A - p_H = 0[/tex]
At the alternative hypothesis, we test if there is a difference, that is, the subtraction of the proportions is different of 0, so:
[tex]H_1: p_A - p_H \neq 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the samples:
[tex]X = p_A - p_H = 0.4872 - 0.5476 = -0.0604[/tex]
[tex]s = \sqrt{s_A^2 + s_H^2} = \sqrt{0.0566^2 + 0.0543^2} = 0.0784[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{-0.0604 - 0}{0.0784}[/tex]
[tex]z = -0.77[/tex]
P-value of the test and decision:
The p-value of the test is the probability of the difference being of at least 0.0604, to either side, plus or minus, which is P(|z| > 0.77), given by 2 multiplied by the p-value of z = -0.77.
Looking at the z-table, z = -0.77 has a p-value of 0.2207.
2*0.2207 = 0.4414
The p-value of the test is 0.4414, higher than the standard significance level of 0.05, which means that there is not a a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees.
Instructions: Given the following constraints, find the maximum and minimum values for
z
.
Constraints: 2−≤124+2≥0+2≤6 2x−y≤12 4x+2y≥0 x+2y≤6
Optimization Equation: =2+5
z
=
2
x
+
5
y
Maximum Value of
z
:
Minimum Value of
z
:
Answer:
z(max) = 16
z(min) = -24
Step-by-step explanation:
2x - y = 12 multiply by 2
4x - 2y = 24 (1)
4x + 2y = 0 add equations
8x = 24
x = 3
4(3) + 2y = 0
y = -6
so (3, -6) is a common point on these two lines
z = 2(3) + 5(-6) = -24
4x - 2y = 24 (1)
x + 2y = 6 add equations
5x = 30
x = 6
6 + 2y = 6
y = 0
so (6, 0) is a common point on these two lines
z = 2(6) + 5(0) = 12
4x + 2y = 0 multiply by -1
-4x - 2y = 0
x + 2y = 6 add equations
-3x = 6
x = -2
-2 + 2y = 6
y = 4
so (-2, 4) is a common point on these two lines
z = 2(-2) + 5(4) = 16
Help please. I need the answer
what is 9 divided by 7
Answer: 1.28571428571. This number is infinite.
Step-by-step explanation:
Answer:
1.29 rounded
Step-by-step explanation:
a Merchant of New York bought some goods from Nepal worth Rs 55680 if 1 dollar = rs 72.50 and £1= Rs 128 if by sending money through London he saves 19.80 Dollars find the rate of exchange between new York and London?
Answer:
$1.85 = £1
Step-by-step explanation:
55680/72.50 = 786
55680/128 = 435
435x = (786 + 19.80)
x = 805.8/435
x = 1.85
Answer:
£1 = $1.72
Step-by-step explanation:
55680/72.50=768
55680/128=435
768.00 - 19.80 = 748.20
x = 748.20 / 435
x = $1.72
Solve the inequality is it a,b,c,d?
Answer:
B
Step-by-step explanation:
-2/3x<31/3
x>-31/2
x>-15 1/2
Answer:
x > - 15 1/2
Step-by-step explanation:
-2/3 x -10 < 1/3
Multiply each side by 3
3(-2/3 x -10 < 1/3)
-2x -30 < 1
Add 30 to each side
-2x-30+30 <1+30
-2x < 31
Divide by -2 remembering to flip the inequality
-2x/-2 > 31/-2
x > -31/2
x > - 15 1/2
I will give brainliest. I need help ASAP.
Answer:
\I got not answer cause im da BUDDHA
But gimme brainliest squekky plssss
Find the time it takes for $6,400 to double when invested at an annual interest rate of 19%, compounded
continuously.
years
Find the time it takes for $640,000 to double when invested at an annual interest rate of 19%, compounded
continuously.
years
Give your answers accurate to 4 decimal places.
Question Holn Video M Message instructor
9514 1404 393
Answer:
3.6481 years
Step-by-step explanation:
The doubling time is not a function of the amount invested. It can be found by considering the account balance multiplier:
2 = e^(rt) = e^(0.19t)
Taking logs, we can solve for t:
ln(2) = 0.19t
t = ln(2)/0.19 ≈ 3.6481431
Rounded to 4 decimal places, the doubling time is 3.6481 years, for either balance.
16. Find the equation of the line that has slope m = 1/2 and passes through (4, 10).
Give your answer in slope-intercept form
Answer:
Step-by-step explanation:
Recall that the equation of a line is y = mx + b.
Excellent. Let's plug in the values we are given into the general equation for a line. We get 10 = 1/2 * 4 + b.
Simplify to 10 = 2 + b, and we get b = 8.
Our final equation, then, is y = 1/2 x + 8.
Hope this helps!
A spring has natural length 20 cm. Compare the work W1 done in stretching the spring from 20 cm to 30 cm with the work W2 done in stretching it from 30 to 40 cm. (Use k for the spring constant) How are W2 and W1 related?
Answer:
W₂ is three times W₁ (W₂ = 3W₁)
Step-by-step explanation:
Applying,
W = ke²/2............. Equation 1
Where W = workdone in stretching the spring, k = spring constant, e = extension.
For W₁,
W₁ = ke₁²/2
Given: e₁ = 30-20 = 10 cm = 0.1 m
Substitute these value into equation 1
W₁ = k(0.1²)/2
W₁ = 0.005k Joules
For W₂,
W₂ = (ke/2)-W₁
Given: e = (40-20) = 20 cm = 0.1 m
Substitute these value into equation 1
W₂ = (k×0.2²/2)-0.005
W₂ = 0.015k Joules.
W₂/W₁ = 0.015k/0.005k
W₂/W₁ = 3
Therefore,
W₂ = 3W₁
In the Spring of 2021 the statistics course did a survey of the average number of parking tickets students received by gender. Which has been shared below. Based on the data below which statement would be the best null hypothesis?
Gender # of hours
male 6
female 8
female 8
male 3
female 7
female 5
male 3
male 2
female 9
female 7
female 2
female 3
male 9
female 0
female 2
male 4
male 9
female 12
female 15
female 3
female 6
male 7
female 3
female 8
male 3
male 6
female 7
female 8
Answer:
There is no difference between the two groups.
Step-by-step explanation:
The test hypothesis (null and alternative) are usually employed in evaluating if there is a statistical significance in a claim about the mean, standard deviation or variance of a sample and it's population parameter.
When comparing two independent variables, The null hypothesis usually establish that there is no difference between the mean value of samples, while the alternative hypothesis is the opposite.
The data given shows values for two independent groups ; Male and Female.
The null hypothesis will be:
H0 : There is no difference between the two groups.
H0 : μ1 - μ2 = 0
The function below models the correlation between the number of hours a plant is kept in sunlight (x) and the height (y), in mm, to which it grows: y = 2 + 4x What does the y-intercept of this function represent? (1 point) The original height of the plant was 4 mm. The original height of the plant was 2 mm. The height of the plant increases by 2 mm for every hour of sunlight it receives. The height of the plant increases by 4 mm for every hour of sunlight it receives.
Answer:
The original height of the plant was 2 mm
Step-by-step explanation:
Given
[tex]y = 2 + 4x[/tex]
Required
Interpret the y-intercept
The y-intercept is when [tex]x = 0[/tex]
So, we have:
[tex]y = 2 + 4 *0[/tex]
[tex]y = 2 + 0[/tex]
[tex]y = 2[/tex]
This implies that the original or initial height was 2 mm
The cost of producing x units of a particular commodity is 2 C(x) = x' +6x +45 shillings, and the production level t hours into a particular production run is x(1)=0.312 +0.04 units. At what rate is cost changing with respect to time after 5 hours?
Complete question is;
The cost of producing x units of a particular commodity is C(x) = ⅔x² + 6x + 45 shillings and the production level t hours into a particular production run is x(t) = 0.3t² + 0.04t. At what rate is cost changing with respect to time after 5 hours?
Answer:
dC/dt = 49.45
Step-by-step explanation:
Since C(x) = ⅔x² + 6x + 45
And x(t) = 0.3t² + 0.04t
This means that;
C(x) = C(x(t))
The rate at what cost is changing with respect to time is given as;
dC/dt
Thus, from chain rule;
dC/dt = (dC/dx) × (dx/dt)
dC/dx = (4/3)x + 6
dx/dt = 0.6t + 0.04
Now, when t = 5, then;
x(5) = 0.3(5)² + 0.04(5)
x = 7.7
Thus;
dC/dx = (4/3)x + 6 = (4/3)(7.7) + 6 = 16.267
At 5 hours,
dx/dt = 0.6(5) + 0.04 = 3.04
Thus;
dC/dt = 16.267 × 3.04
dC/dt = 49.45
Solve the system of equations.
4x + 3y + 5z = 6
6x + 8y + 6z = 4
4x + 2y + z = 8
(x = 1, y = -1,2 = 1)
b. (x = 3, y = -3,2 = 3)
a.
C. (x = 0, y = 0, 2 = 2)
d. (x - 2, y --2, z = 0)
rewrite -4<x<-1 using absolute value sign
[tex] - | 4 | < x < - |1| [/tex]
dunno if that's the desired form tough, but it states the same definition
The given inequality rewritten using absolute value sign as |-4|<x<|-1|.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is -4<x<-1.
An absolute value inequality is an expression with absolute functions as well as inequality signs.
Here, using absolute value sign we get
|-4|<x<|-1|
Therefore, the given inequality rewritten using absolute value sign as |-4|<x<|-1|.
To learn more about the inequalities visit:
https://brainly.com/question/20383699.
#SPJ2
Slope 0; through (-5, -1)
with steps please.
Step-by-step explanation:
0 slope means it has in x.
so the equation is y=-1, because that is the coord for the points'y axsis
If we decrease a dimension on a figure, how is the figure’s area affected?
The area decreases.
The area increases.
The area becomes 0.
The area remains the same.
Answer:
A) area decreases
Step-by-step explanation:
Example: we have a 2 by 3 rectangle with area of 2*3 = 6. If we cut the first dimension in half, then we have a 1 by 3 rectangle that has area 1*3 = 3. The area has decreased. To keep the area the same, we would have to increase the other dimension some specific amount.
HOPE THIS HELPS
HAVE A GOOD DAY :)
ITS RASPUTIN002
Maybe you have considered buying a term life insurance policy. The expected value of any term life insurance product yields a positive expected value for the insurance company and a negative expected value for you, meaning the insurance company will make profits by selling their insurance products. Would you still buy the term life insurance? Why or why not? Are there other examples other than insurance that uses this same concept?
Answer:
Yes one should consider to buy the policy as important to have insured plan that help at the time of need.
Step-by-step explanation:
Term of life insurance is a form of life insurance which guarantees the payment of the stated death benefit. If the person des during the plan the term expires. The policy has no value other than guarantee benefits. The term life insurance will make products by selling products and thus it's necessary to have insurance. Health, age, and life expectancy are some of the points that need to consider for buying plans.a store sells pencils pens and markers that sells two times as many markers as pencils and three times as many pens as pencils is the store sells a total of 1950 pencils and pens and markers in a week how many of each were sold
Answer:
Pencils = 325 ; Pens = 975 ; Markers = 650
Step-by-step explanation:
Let :
Number of Pencils = x
Number of pens = y
Number of markers = z
2 times as many markers as pencils
z = 2x
3 times as many pens as pencils
y = 3x
x + y + z = 1950
Write z and y in terms of x in the equation :
x + 3x + 2x = 1950
6x = 1950
Divide both sides by 6
6x / 6 = 1950 / 6
x = 325
Number of pencils = 325
Pens = 3 * 325 = 975
Markers = 2 * 325 = 650
Pencils = 325 ; Pens = 975 ; Markers = 650
If it takes 247.2 yards of yarn to knit 2.5 baby bibs, how many yards of yarn would it take to knit 4 baby bibs? SHOW ALL WORK! ONLY ANSWER IF YOU KNOW THE ANSWER!
Answer:
395.52
Step-by-step explanation:
247.2/2.5=98.88(1 bib)
98.88x4=395.52(4 bibs)
Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for metal sheets of a particular type, its mean value and standard deviation are 75 GPa and 1.7 GPa, respectively. Suppose the distribution is normal. (Round your answers to four decimal places.)
Required:
a. Calculate P(79 <= P <= 81) when n = 25.
b. How likely is it that the sample mean diameter exceeds 81 when n = 36?
Answer:
a) P(79 <= P <= 81) = 0.9968
b) P( X > 81 ) = 0.0002
Step-by-step explanation:
mean value = 75 GPa
standard deviation = 1.7 GPa
a) Determine P(79 <= P <= 81)
given that : n = 25
attached below is the detailed solution
P(79 <= P <= 81) = 0.9968
b) Determine how likely the sample mean diameter will exceed 81
given that n = 36
mean diameter = 81
P( X > 81 ) = 0.0002
prove that.
lim Vx (Vx+ 1 - Vx) = 1/2 X>00
Answer:
The idea is to transform the expression by multiplying [tex](\sqrt{x + 1} - \sqrt{x})[/tex] with its conjugate, [tex](\sqrt{x + 1} + \sqrt{x})[/tex].
Step-by-step explanation:
For any real number [tex]a[/tex] and [tex]b[/tex], [tex](a + b)\, (a - b) = a^{2} - b^{2}[/tex].
The factor [tex](\sqrt{x + 1} - \sqrt{x})[/tex] is irrational. However, when multiplied with its square root conjugate [tex](\sqrt{x + 1} + \sqrt{x})[/tex], the product would become rational:
[tex]\begin{aligned} & (\sqrt{x + 1} - \sqrt{x}) \, (\sqrt{x + 1} + \sqrt{x}) \\ &= (\sqrt{x + 1})^{2} -(\sqrt{x})^{2} \\ &= (x + 1) - (x) = 1\end{aligned}[/tex].
The idea is to multiply [tex]\sqrt{x}\, (\sqrt{x + 1} - \sqrt{x})[/tex] by [tex]\displaystyle \frac{\sqrt{x + 1} + \sqrt{x}}{\sqrt{x + 1} + \sqrt{x}}[/tex] so as to make it easier to take the limit.
Since [tex]\displaystyle \frac{\sqrt{x + 1} + \sqrt{x}}{\sqrt{x + 1} + \sqrt{x}} = 1[/tex], multiplying the expression by this fraction would not change the value of the original expression.
[tex]\begin{aligned} & \lim\limits_{x \to \infty} \sqrt{x} \, (\sqrt{x + 1} - \sqrt{x}) \\ &= \lim\limits_{x \to \infty} \left[\sqrt{x} \, (\sqrt{x + 1} - \sqrt{x})\cdot \frac{\sqrt{x + 1} + \sqrt{x}}{\sqrt{x + 1} + \sqrt{x}}\right] \\ &= \lim\limits_{x \to \infty} \frac{\sqrt{x}\, ((x + 1) - x)}{\sqrt{x + 1} + \sqrt{x}} \\ &= \lim\limits_{x \to \infty} \frac{\sqrt{x}}{\sqrt{x + 1}+ \sqrt{x}}\end{aligned}[/tex].
The order of [tex]x[/tex] in both the numerator and the denominator are now both [tex](1/2)[/tex]. Hence, dividing both the numerator and the denominator by [tex]x^{(1/2)}[/tex] (same as [tex]\sqrt{x}[/tex]) would ensure that all but the constant terms would approach [tex]0[/tex] under this limit:
[tex]\begin{aligned} & \lim\limits_{x \to \infty} \sqrt{x} \, (\sqrt{x + 1} - \sqrt{x}) \\ &= \cdots\\ &= \lim\limits_{x \to \infty} \frac{\sqrt{x}}{\sqrt{x + 1}+ \sqrt{x}} \\ &= \lim\limits_{x \to \infty} \frac{\sqrt{x} / \sqrt{x}}{(\sqrt{x + 1} / \sqrt{x}) + (\sqrt{x} / \sqrt{x})} \\ &= \lim\limits_{x \to \infty}\frac{1}{\sqrt{(x / x) + (1 / x)} + 1} \\ &= \lim\limits_{x \to \infty} \frac{1}{\sqrt{1 + (1/x)} + 1}\end{aligned}[/tex].
By continuity:
[tex]\begin{aligned} & \lim\limits_{x \to \infty} \sqrt{x} \, (\sqrt{x + 1} - \sqrt{x}) \\ &= \cdots\\ &= \lim\limits_{x \to \infty} \frac{\sqrt{x}}{\sqrt{x + 1}+ \sqrt{x}} \\ &= \cdots \\ &= \lim\limits_{x \to \infty} \frac{1}{\sqrt{1 + (1/x)} + 1} \\ &= \frac{1}{\sqrt{1 + \lim\limits_{x \to \infty}(1/x)} + 1} \\ &= \frac{1}{1 + 1} \\ &= \frac{1}{2}\end{aligned}[/tex].
Answer:
Hello,
Step-by-step explanation:
[tex]\displaystyle \lim_{x \to \infty} \sqrt{x}*(\sqrt{x+1}-\sqrt{x} ) \\\\\\= \lim_{x \to \infty}\dfrac{ \sqrt{x}*(\sqrt{x+1}-\sqrt{x} )*(\sqrt{x+1}+\sqrt{x} )}{\sqrt{x+1} +\sqrt{x} } \\\\= \lim_{x \to \infty} \dfrac{\sqrt{x} *1}{\sqrt{x+1} +\sqrt{x} } \\\\\\= \lim_{x \to \infty} \dfrac{1} {\sqrt {\dfrac {x+1} {x} }+\sqrt{\dfrac{x}{x} } } \\\\\\=\dfrac{1} {\sqrt {1}+\sqrt{1} } \\\\\\=\dfrac{1} {2} \\[/tex]
The triangles are similar, find y
Answer:
y = 3.6
x = 3.5
Step-by-step explanation:
The triangles are similar.
[tex]\frac{3}{2.4} = \frac{x}{2.8} = \frac{4.5}{y}[/tex]
Find y:
[tex]\frac{4.5}{y} = \frac{5}{4}[/tex]
[tex]4.5 * 4 = 5y => 18 = 5y => y = 3.6[/tex]
Find x:
[tex]\frac{x}{2.8} = \frac{5}{4}[/tex]
[tex]2.8 * 5 = 4x => 14 = 4x => x = 3.5[/tex]
Find the mean for the amounts: $17.482: $14.987: $13.587$14.500, $18.580. $14.993
Answer:
The mean of these numbers is 15.68816 with a repeating 6.
Step-by-step explanation:
Find the measure of the incanted angle to the nearest degree
Answer:
15.4 degrees
Step-by-step explanation:
b= 53
h = 55
cos -¹( 53/53)= 15.4
by solving a pair of linear equation X + Y is equal to 20 and x-y=10 the value of 'x' and 'y' are
Answer:
x=15, y=5
Step-by-step explanation:
x+y=20
x-y=10
Adding both equations;
(x+x) + (y-y) = 20+10
2x = 30
x = 30/2 = 15
Substitute x=15 into x+y=20
y= 20-x = 20-15= 5
at which value will the graph of y=csc x have a zero
Answer:
y = csc(x) does not have any zero.
Step-by-step explanation:
If we have:
y = f(x)
a zero of that function would be a value x' such that:
y = f(x') = 0
Here we basically want to solve:
y = csc(x) = 0
First, remember that:
csc(x) = 1/sin(x)
now, the values of sin(x) range from -1 to 1.
So we want to solve:
1/sin(x) = 0
notice that a fraction:
a/b = 0
only if a = 0.
Then is easy to see that for our equation:
1/sin(x) = 0
The numerator is different than zero, then the equation never will be equal to zero.
Then:
y = csc(x) = 1/sin(x)
Does not have a zero.
Các mô hình h i quy sau đây có ph i mô hình tuy n tính hay không? N u là môồảếếhình h i quy phi tuy n, hãy đ i v mô hình h i quy tuy n tính?ồếổềồếa) iiiuXY++=21lnββb) iiiuXY++=lnln21ββc) iiiuXY++=1ln21ββd) eiiuXiY++=21ββe) eiiu
5. a) Find the difference between the place values of two 5's in 95237508.
Answer:
4999500
Step-by-step explanation:
first 5 = 5000000
second 5 = 500
difference = 5000000-500
