Answer:
(A) What is the z- score of the sample mean?
The z- score of the sample mean is 0.0959
(B) Is this sample significantly different from the population?
No; at 0.05 alpha level (95% confidence) and (n-1 =79) degrees of freedom, the sample mean is NOT significantly different from the population mean.
Step -by- step explanation:
(A) To find the z- score of the sample mean,
X = 75 which is the raw score
¶ = 74 which is the population mean
S. D. = 10.43 which is the population standard deviation of/from the mean
Z = [X-¶] ÷ S. D.
Z = [75-74] ÷ 10.43 = 0.0959
Hence, the sample raw score of 75 is only 0.0959 standard deviations from the population mean. [This is close to the population mean value].
(B) To test for whether this sample is significantly different from the population, use the One Sample T- test. This parametric test compares the sample mean to the given population mean.
The estimated standard error of the mean is s/√n
S. E. = 16/√80 = 16/8.94 = 1.789
The Absolute (Calculated) t value is now: [75-74] ÷ 1.789 = 1 ÷ 1.789 = 0.559
Setting up the hypotheses,
Null hypothesis: Sample is not significantly different from population
Alternative hypothesis: Sample is significantly different from population
Having gotten T- cal, T- tab is found thus:
The Critical (Table) t value is found using
- a specific alpha or confidence level
- (n - 1) degrees of freedom; where n is the total number of observations or items in the population
- the standard t- distribution table
Alpha level = 0.05
1 - (0.05 ÷ 2) = 0.975
Checking the column of 0.975 on the t table and tracing it down to the row with 79 degrees of freedom;
The critical t value is 1.990
Since T- cal < T- tab (0.559 < 1.990), refute the alternative hypothesis and accept the null hypothesis.
Hence, with 95% confidence, it is derived that the sample is not significantly different from the population.
Find the measures of the angles in the figure.
Answer:
[tex]120^o,\,120^o,\,60^o,\,\,\,and\,\,\,60^o[/tex]
which agrees with the first answer in the list of possible options.
Step-by-step explanation:
We can use the fact that the addition of all four internal angles of a quadrilateral must render [tex]360^o[/tex]. Then we can create the following equation and solve for the unknown "h":
[tex]2h+2h+h+h = 360^o\\6h=360^o\\h=60^o[/tex]
Therefore the angles of this quadrilateral are:
[tex]120^o,\,120^o,\,60^o,\,\,\,and\,\,\,60^o[/tex]
Answer:60,60,120,120
Step-by-step explanation:All qualdrilaterals equal to 360, so if you add all of the different numbers you should get 360
An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers that activate correctly. The researchers estimate the probability of a sprinkler to activate correctly to be 0.7. Suppose that you are an inspector hired to write a safety report for a large ballroom with 10 sprinklers. Assume the sprinklers activate correctly or not independently. (a) What is the probability that all of the sprinklers will operate correctly in a fire
Answer:
probability that all of the sprinklers will operate correctly in a fire: 0.0282
Step-by-step explanation:
In order to solve this question we will use Binomial probability distribution because:
In the question it is given that the sprinklers activate correctly or not independently. The number of outcomes are two i.e. sprinklers activate correctly or not.A binomial distribution is a probability of a success or failures outcomes in an repeated multiple or n times.
Number of outcomes of this distributions are two.
The formula is:
b(x; n, P) = [tex]C_{n,x}*p^{x} * (1 - p)^{n-x}[/tex]
b = binomial probability also represented as P(X=x)
x =no of successes
P = probability of a success on a single trial
n = no of trials
[tex]C_{n,x}[/tex] is calculated as:
[tex]C_{n,x}[/tex] = n! / x!(n – x)!
= 10! / 10!(10-10)!
= 1
According to given question:
probability of success i.e. p = 0.7 i.e. probability of a sprinkler to activate correctly.
number of trials i.e. n = 10 as number of sprinklers are 10
To find: probability that all of the sprinklers will operate correctly in a fire
X = 10 because we have to find the probability that "all" of the sprinklers will operate correctly and there are 10 sprinklers so all 10 of them
So putting these into the formula:
P(X=x) = [tex]C_{n,x}*p^{x} * (1 - p)^{n-x}[/tex]
= C₁₀,₁₀ * 0.7¹⁰ * (1-0.7)¹⁰⁻¹⁰
= 1 * 0.0282 * (0.3) ⁰
= 1 * 0.0282 * 1
P(X=x) = 0.0282
What is the angle between the given vector and the positive direction of the x-axis? (Round your answer to the nearest degree.) i + 3 j
Answer:
72°
Step-by-step explanation:
Given two vectors a and b, The vector i+3j will form a right angled triangle with the x-axis (i.e the horizontal axis).
The opposite side of the triangle on the Cartesian plane will be 3units along the y axis while the adjacent will be 1 unit along the x axis.
The angle between thus two vectors is expressed as tan (theta) = opp/adj
tantheta = 3/1
theta = tan^-1(3)
Theta = 71.57° ≈ 72° to nearest degree
A rectangle's length and width are in a ratio of 10:1. The perimeter is 66 feet. What are the length and width?
hii
Step-by-step explanation:
length-10x
width-x
perimeter-2(l+b)
66=2(10x+x)
66-2=10x+x
64=11x
x=11/64
lenght-11
width-64
Suppose that MNO is isosceles with base NM. Suppose also that =m∠N+4x7° and =m∠M+2x29°. Find the degree measure of each angle in the triangle.
Answer:
m∠N = 51°
m∠M = 31°
m∠O = 98°
Step-by-step explanation:
It is given that ΔMNO is an isosceles triangle with base NM.
m∠N = (4x + 7)° and m∠M = (2x + 29)°
By the property of an isosceles triangle,
Two legs of an isosceles triangle are equal in measure.
ON ≅ OM
And angles opposite to these equal sides measure the same.
m∠N = m∠M
(4x + 7) = (2x + 29)
4x - 2x = 29 - 7
2x = 22
x = 11
m∠N = (4x + 7)° = 51°
m∠M = (2x + 9)° = 31°
m∠O = 180° - (m∠N + m∠M)
= 180° - (51° + 31°)
= 180° - 82°
= 98°
Find the difference of functions at x= - 3, (g - f)(-3), given f(x) and g(x): g(x) = x^2−15, and f(x) =2x
Answer:
0
Step-by-step explanation:
Solution:-
We are given two functions as follows:
[tex]f ( x ) = x^2 - 15\\\\g ( x ) = 2x[/tex]
We need to determine the composite function defined as ( g - f ) ( x ). To determine this function we need to make sure that both function exist for all real positive value of x.
The function f ( x ) is a quadratic function which has real values for all values of x. Similarly, function g ( x ) is a linear line that starts from the origin. Hence, both functions are defined over the domain ( -∞, ∞ )
We will perform arithmetic operation of subtracting function f ( x ) from g ( x ) as follows:
[tex][ g - f ] ( x ) = g ( x ) - f ( x )\\\\\\( g - f ) ( x ) = x^2 - 15 - 2x\\\\[/tex]
Now evaluate the above determined function at x = -3 as follows:
[tex]( g - f ) ( -3 ) = ( -3 )^2 - 2 ( -3 ) - 15\\\\( g - f ) ( -3 ) = 9 + 6 - 15\\\\( g - f ) ( -3 ) = 0[/tex]
What is the equation of the following line? Be sure to scroll down first to see all answer options.
A.
y = 18x
B.
y = 9x
C.
y = -9x
D.
y = - x
E.
y = -18x
F.
y = x
Answer:
y=9x
Step-by-step explanation:
rise over run the rise is the y=9 and run is x=1.
9/1=9x
a study of the annual population of toads in a county park shows the population, S(t), can be represented by the function S(t) = 152(1.045)^t, where the t represents the number of years since the study started. based on the function, what is the growth rate?
Answer: 0.045 is the growth rate.
Step-by-step explanation:
A generic exponential growth function can be written as:
f(t) = A*(1 + r)^t
where A is the initial amount.
t is the unit of time.
r is the rate of growth.
For example if we have an increase of 10% per year, with an initial population of 100 we have that:
A = 100, r = 10%/100% = 0.10, t = number of years.
the equation will be:
f(t) = 100*(1 + 0.10)^t
Now, in this case the equation is:
S(t) = 152*(1.045)^t
We can write this as:
S(t) = 152*(1 + 0.045)^t
Then 152 is the initial amount and 0.045 is the growth rate.
Which description is true about the transformation shown? It is a dilation because the transformation is isometric. It is a dilation because the transformation is not isometric. It is a stretch because the transformation is isometric. It is a stretch because the transformation is not isometric.
The true statement about the given transformation is; B: It is a dilation because the transformation is not isometric.
What is the Transformation?An isometric transformation is a shape-preserving transformation in the plane or in space. They include reflection, rotation and translation.
Now, from the given attachment showing the two figures, we can see that there is a dilation which means that it can't be isometric as the definition of Isometric transformation does not include Dilation.
Read more about Transformation at; https://brainly.com/question/4289712
#SPJ5
Answer:
b
Step-by-step explanation:
just took the test
Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = zeyi + x cos(y)j + xz sin(y)k, S is the hemisphere x2 + y2 + z2 = 16, y ≥ 0, oriented in the direction of the positive y-axis.
Stokes' theorem equates the surface integral of the curl of F to the line integral of F along the boundary of the hemisphere. The boundary itself is a circle C (the intersection of the hemisphere with the plane y = 0) with equation
[tex]x^2+z^2=16[/tex]
Parameterize this circle by
[tex]\mathbf r(t)=4\cos t\,\mathbf i+4\sin t\,\mathbf k[/tex]
with [tex]0\le t\le2\pi[/tex].
The surface is oriented such that its normal vector points in the positive y direction, which corresponds to the curve having counterclockwise orientation. The parameterization we're using here already takes this into account.
Now compute the line integral of F along C :
[tex]\displaystyle\iint_S\mathrm{curl}\mathbf F(x,y,z)\cdot\mathrm d\mathbf S=\int_C\mathbf F(x,y,z)\cdot\mathrm d\mathbf r[/tex]
[tex]=\displaystyle\int_0^{2\pi}\mathbf F(4\cos t,0,4\sin t)\cdot\frac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^{2\pi}(4\sin t\,\mathbf i+4\cos t\,\mathbf j)\cdot(-4\sin t\,\mathbf i+4\cos t\,\mathbf k)\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^{2\pi}-16\sin^2t\,\mathrm dt[/tex]
[tex]=-8\displaystyle\int_0^{2\pi}(1-\cos(2t))\,\mathrm dt=\boxed{-16\pi}[/tex]
Line integral of F along C is,
[tex]\rm \int \int_S curl F(x,y,z) dS = -16\pi[/tex]
Step-by-step explanation:
Given :
Hemisphere - [tex]x^2 +y^2+z^2=16[/tex]
Calculation :
Accordind to Stoke's theorem the surface integral of the curl of F to the line integral of F along the boundary of the hemisphere. The boundary itself is a circle C (the intersection of the hemisphere with the plane y = 0) with equation
[tex]x^2+z^2=16[/tex]
then parameterize the circle,
[tex]\rm r(t) = 4 cos(t) \;\hat{i} + 4 sin(t)\;(\hat{k})[/tex]
with , [tex]0\leq t\leq 2\pi[/tex]
Line integral of F along C is,
[tex]\rm \int \int_S curl F(x,y,z) dS = \int_{C}^{} F(x,y,z) \;dr[/tex]
[tex]= \int_{0}^{2\pi} F(4cos(t),0,4sin(t)) \;\dfrac{dr}{dt}.dt[/tex]
[tex]= \int_{0}^{2\pi}(4sin(t)i+4cos(t) j).(-4sin(t)i+4cos(t)k) \;dt[/tex]
[tex]= \int_{0}^{2\pi} -16sin^2tdt[/tex]
[tex]=-8 \int_{0}^{2\pi} (1-cos(2t))dt[/tex]
[tex]= -16\pi[/tex]
For more information, refer the link given below
https://brainly.com/question/8130922?referrer=searchResults
PLEASE HELP QUICK! Determine x value of: sqrt x + 8 - sqrt x - 4 = 2
Answer:
x=8
Step-by-step explanation:
[tex]\sqrt{x+8}-\sqrt{x-4}=2\\\sqrt{x+8}=2+\sqrt{x-4}\\\left(\sqrt{x+8}\right)^2=\left(2+\sqrt{x-4}\right)^2\\x+8=x+4\sqrt{x-4}\\8=4\sqrt{x-4}\\8^2=\left(4\sqrt{x-4}\right)^2\\64=16x-64\\x=8[/tex]
I hope u can understand help asap
i think u can see sho T=5n+20
Answer:
T(n) = 5n + 20
Step-by-step explanation:
1 candy has a mass of 5 g.
n candies have a mass of 5n grams.
The box has a mass of 20 grams.
total mass = mass of candies + mass of box
T(n) = 5n + 20
n T(n)
0 20
25 145
50 270
75 395
100 520
A rectangular parking lot has an area of 7/10 km 2.The width is 1/3 km 2 .What is the length of the parking lot written as a improper fraction ,in kilometers
Answer:
[tex]\dfrac{21}{10}\text{ km}[/tex].
Step-by-step explanation:
It is given that,
Area of rectangular plot [tex]=\dfrac{7}{10}\text{ km}^2[/tex]
Width of rectangular plot [tex]=\dfrac{1}{3}\text{ km}[/tex]
We need to find the length of the parking lot.
We know that,
[tex]\text{Area of rectangle}=length\times width[/tex]
[tex]\dfrac{7}{10}=length\times \dfrac{1}{3}[/tex]
[tex]\dfrac{7\times 3}{10}=length[/tex]
[tex]length=\dfrac{21}{10}[/tex]
Therefore, length of the parking lot is [tex]\dfrac{21}{10}\text{ km}[/tex].
Identify the correct HYPOTHESES used in a hypothesis test of the following claim and sample data:
Claim: "The average battery life (between charges) of this model of tablet is at least 12 hours."
A random sample of 80 of these tablets is selected, and it is found that their average battery life is 11.58 hours with a standard deviation of 1.93 hours. Test the claim at the 0.05 significance level.
a. H0: p = 12 vs. H1: p < 12
b. H0: ? = 12 vs. H1: ? < 12
c. H0: p = 12 vs. H1: p > 12
d. H0: ? = 12 vs. H1: ? > 12
Answer:
The null hypothesis is ;
H0 ≥ 12
While the alternative hypothesis H1 is ;
H1 < 12
Step-by-step explanation:
Here, we want to correctly identify the null hypothesis H0 and the alternative hypothesis H1
The null hypothesis is as follows ;
H0 ≥ 12
While the alternative hypothesis H1 is ;
H1 < 12
Determine the t critical value for a lower or an upper confidence bound in each of the following situations. (Round your answers to three decimal places.)
a. Confidence level = 95%, df = 10
b. Confidence level = 95%, df = 15
c. Confidence level = 99%, df = 15
d. Confidence level = 99%, n = 5
e. Confidence level = 98%, df = 23
f. Confidence level = 99%, n = 32
Answer:
A. 1.812
B. 1.753
C. 2.602
D. 3.747
E. 2.069
F. 2.453
Step-by-step explanation:
A. 95% confidence level, the level of significance = 5% or 0.05
Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 10 degrees of freedom = 1.182
B. 95% confidence interval = 0.05 level of significance
Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 15 degrees of freedom = 1.753
C. 99% confidence interval = 0.01 level of significance
Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 15 degrees of freedom = 2.602
D. 99% confidence interval = 0.01 level of significance; DF (n - 1) = 5- 1 = 4
Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 4 degrees of freedom = 3.747
E. 98% confidence interval = 0.02 level of significance
Using t-table, the critical value for a lower or an upper confidence bound at 0.02 significance level with 23 degrees of freedom = 2.069
F. 99% confidence interval = 0.01 level of significance; df (n - 1) = 32 - 1 = 31
Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 31 degrees of freedom = 2.453
In a soccer league, the ratio of boys to girls is 4 to 6. There are a total of 50 players in the soccer league. Determine how many girls play in the soccer league.
Answer:
30
Step-by-step explanation:
We can call the number of boys 4x and girls 6x so we can write:
4x + 6x = 50
10x = 50
x = 5, therefore the number of girls is 6x = 6 * 5 = 30.
Answer:
30
Step-by-step explanation:
In the ratio 4:6, we can think of this like 4 boys and 6 girls out of 10 team members.
We can find how many girls play by multiplying 6 by 5, since 50 divided by 10 is 5.
6(5) = 30, so 30 girls play in the soccer league.
whats the steps when solving 40-:8+3^(2)+(15-7)*2
Answer:
Step-by-step explanation:
Assuming the colon between 40 and 8 is a mistype...
PEMDAS(Parenthesis, Exponents, Multiplication + Division, Addition + Subtraction)
[tex]40-8+3^2+(15-7)*2\\\\Parenthesis\\\\40-8+3^2+8*2\\\\Exponents\\\\40-8+9+8*2\\\\Multiplication\\\\40-8+9+16\\\\Subtraction\\\\32+9+16\\\\Addition\\\\41+16\\\\Addition\\\\57[/tex]
Hope it helps <3
━━━━━━━☆☆━━━━━━━
▹ Answer
57
▹ Step-by-Step Explanation
You need to follow PEMDAS:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
40 - 8 + 3² + (15 - 7)* 2
40 - 8 + 9 + (15 - 7) * 2
40 - 8 + 9 + 8 * 2
40 - 8 + 9 + 16
= 57
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
One kind of candy (jelly) sells for $5 a pound and another (chocolate) for $10 a pound. How many pounds of each should be used to make a mixture of 10 pounds of candy (both kinds) that sells for a total $80 (i.e. $8/pound)?
Answer:
chocolate: 6 poundsjelly: 4 poundsStep-by-step explanation:
Let x represent the number of pounds of chocolate in the mix. Then the total price of 10 pounds of mix is ...
10x +5(10 -x) = 80
5x +50 = 80
5x = 30
x = 6 . . . . . . . . pounds of chocolate
10 -x = 4 . . . . . pounds of jelly candy
6 pounds of chocolate and 4 pounds of jelly should be used to make the mixture.
anyone know how to do this. im hella lost right now
Answer:
a=6
b=5.5
Step-by-step explanation:
not very sure but..
since 8X2=16,
a=3X2
b=11/2
A sector with a central angle measure of 200 degrees has a radius of 9 cm. What is the area of the sector?
Answer:
[tex]\boxed{Area\ of\ sector = 141.4\ cm^2}[/tex]
Step-by-step explanation:
Radius = r = 9 cm
Angle = θ = 200° = 3.5 radians
Now,
[tex]Area \ of \ sector = \frac{1}{2} r^2 \theta[/tex]
Area = 1/2 (9)²(3.5)
Area = 1/2 (81)(3.5)
Area = 282.7 / 2
Area of sector = 141.4 cm²
Answer:
45 pi cm^2 or 141.3 cm^2
Step-by-step explanation:
First find the area of the circle
A = pi r^2
A = pi (9)^2
A = 81 pi
A circle has 360 degrees
The shaded part has 200
The fraction that is shaded is
200/360 =5/9
Multiply by the total area
5/9 * 81 pi
45 pi
Using 3.14 for pi
141.3
45 pi cm^2 or 141.3 cm^2
Which expressions are equivalent to: 3(−2a - 4)+3a? A: -6a - 12 +3a B: 3a+12 C: none of the above smh
Answer:
AStep-by-step explanation:
3(−2a - 4)+3a
=-6a - 12 +3a
A: -6a - 12 +3a
[tex]hope \: this \: helps[/tex]
Answer:
the answer is A
Step-by-step explanation:
you have to distribute the number 3 throughout the parentheses so (3*-2a-3*4)+3a = -6a-12+3a
Hypothesis Testing
Problem 1. Adults saving for retirement
In a recent survey conducted by Pew Research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement. Does
the sample evidence suggest that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement? Use a 0.05 level of significance
1. State the null and alternative hypothesis.
2. What type of hypothesis test is to be used?
3. What distribution should be used and why?
4. Is this a right, left, or two-tailed test?
5. Compute the test statistic.
6. Compute the p-value.
7. Do you reject or not reject the null hypothesis? Explain why.
8. What do you conclude?
Problem 2: Google Stock
Google became a publicly traded company in August 2004. Initially, the stock traded over 10 million shares each day! Since the initial offering, the volume of stock traded daily has
decreased substantially. In 2010, the mean daily volume in Google stock was 5.44 million shares, according to Yahoo!Enance. A random sample of 35 trading days in 2014 resulted in a
sample mean of 3.28 million shares with a standard deviation of 1.68 million shares. Does the evidence suggest that the volume of Google stock has changed since 2007? Use a 0.05 level of
significance
1. State the null and alternative hypothesis.
2. What type of hypothesis test is to be used?
3. What distribution should be used and why?
4. Is this a right, left, or two-tailed test?
5. Compute the test statistic.
6. Compute the p-value.
7. Do you reject or not reject the null hypothesis? Explain why
8. What do you conclude?
Answer:
Problem 1: We conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.
Problem 2: We conclude that the volume of Google stock has changed.
Step-by-step explanation:
Problem 1:
We are given that in a recent survey conducted by Pew Research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement.
Let p = proportion of adult Americans without a high school diploma who are worried about having enough saved for retirement
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 50% {means that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement}
Alternate Hypothesis, [tex]H_A[/tex] : p > 50% {means that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement}
This is a right-tailed test.
The test statistics that would be used here is One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of adult Americans who were worried about having enough saved for retirement = [tex]\frac{156}{295}[/tex] = 0.53
n = sample of adult Americans = 295
So, the test statistics = [tex]\frac{0.53-0.50}{\sqrt{\frac{0.50(1-0.50)}{295} } }[/tex]
= 1.03
The value of z-test statistics is 1.03.
Also, the P-value of the test statistics is given by;
P-value = P(Z > 1.03) = 1 - P(Z [tex]\leq[/tex] 1.03)
= 1 - 0.8485 = 0.1515
Now, at a 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.
Since the value of our test statistics is less than the critical value of z as 1.03 < 1.645, so we insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.
Problem 2:
We are given that a random sample of 35 trading days in 2014 resulted in a sample mean of 3.28 million shares with a standard deviation of 1.68 million shares.
Let [tex]\mu[/tex] = mean daily volume in Google stock
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 5.44 million shares {means that the volume of Google stock has not changed}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 5.44 million shares {means that the volume of Google stock has changed}
This is a two-tailed test.
The test statistics that would be used here is One-sample t-test statistics because we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean volume in Google stock = 3.28 million shares
s = sample standard deviation = 1.68 million shares
n = sample of trading days = 35
So, the test statistics = [tex]\frac{3.28-5.44}{\frac{1.68}{\sqrt{35} } }[/tex] ~ [tex]t_3_4[/tex]
= -7.606
The value of t-test statistics is -7.606.
Also, the P-value of the test statistics is given by;
P-value = P([tex]t_3_4[/tex] < -7.606) = Less than 0.05%
Now, at a 0.05 level of significance, the t table gives a critical value of -2.032 and 2.032 at 34 degrees of freedom for the two-tailed test.
Since the value of our test statistics doesn't lie within the range of critical values of t, so we sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the volume of Google stock has changed.
Sam invest $4000 in an account that compounds interest continuously and earns 5.5% how long will it take for his money to reach $80,000 round to the nearest 10th of a year
Answer:
54.5 years.
Step-by-step explanation:
From the above question, we are asked to find the time
The formula for Time(t) =
t = log(A/P) / n[log(1 + r/n)]
A = Amount accumulated after a particular interest and period of time = $80,000
P = Principal (Money invested) = $4,000
r = rate = 5.5% = 0.055
n = compounding frequency = compounding continuously
n = number of days in a year × number of hours in a day
= 365 days × 24 hours = 8760
t = log(A/P) / n[log(1 + r/n)]
t = log(80,000/4,000) /8760[log(1 + 0.055/8760)]
t = log(80000 ÷ 4000) ÷ (8760 × [log(1 + 0.0000062785)]
t = 54.468367222 years
Approximately to the nearest tenth of a year, therefore, the length of time it will it take for his money to reach $80,000 is 54.5 years
Answer:
54.5
Step-by-step explanation:
The exact heights of different elephants Choose the correct answer below. A. The data are continuous because the data can only take on specific values. B. The data are discrete because the data can take on any value in an interval. C. The data are discrete because the data can only take on specific values. D. The data are continuous because the data can take on any value in an interval.
Answer:
Option d: The data are continuous because the data can take on any value in an interval.
Step-by-step explanation:
The data are continuous if they can take on any value within a range. In this case study, there are different elephants including small/young ones and big ones/old ones.
Thus, their heights will vary and can take on any value within a particular range.
Find the probability of each event. A six-sided die is rolled seven times. What is the probability that the die will show an even number at most five times?
Answer:
[tex]\dfrac{15}{16}[/tex]
Step-by-step explanation:
When a six sided die is rolled, the possible outcomes can be:
{1, 2, 3, 4, 5, 6}
Even numbers are {2, 4, 6}
Odd Numbers are {1, 3, 5}
Probability of even numbers:
[tex]\dfrac{\text{Favorable cases}}{\text{Total cases }} = \dfrac{3}{6} = \dfrac{1}{2}[/tex]
This is binomial distribution.
where probability of even numbers, [tex]p =\frac{1}{2}[/tex]
Probability of not getting even numbers (Getting odd numbers) [tex]q =\frac{1}{2}[/tex]
Probability of getting r successes out of n trials:
[tex]P(r) = _nC_r\times p^r q^{n-r}[/tex]
Probability of getting even numbers at most 5 times out of 7 is given as:
P(0) + P(1) +P(2) + P(3) +P(4) + P(5)
[tex]\Rightarrow _7C_0\times \frac{1}{2}^0 \frac{1}{2}^{7}+_7C_1\times \frac{1}{2}^1 \frac{1}{2}^{6}+_7C_2\times \frac{1}{2}^2 \frac{1}{2}^{5}+_7C_3\times \frac{1}{2}^3 \frac{1}{2}^{4}+_7C_4\times \frac{1}{2}^4 \frac{1}{2}^{3}+_7C_5\times \frac{1}{2}^5 \frac{1}{2}^{2}[/tex]
[tex]\Rightarrow (\dfrac{1}{2})^7 (_7C_0+_7C_1+_7C_2+_7C_3+_7C_4+_7C_5)\\[/tex]
[tex]\Rightarrow (\dfrac{1}{2})^7 (1+7+\dfrac{7 \times 6}{2}+\dfrac{7 \times 6 \times 5}{3\times 2}+\dfrac{7 \times 6 \times 5}{3\times 2}+\dfrac{7 \times 6}{2})\\\Rightarrow \dfrac{120}{128} \\\Rightarrow \dfrac{15}{16}[/tex]
Please help me. The function g(x) is a transformation of f(x). If g(x) has a y-intercept at 3, which of the following functions could represent g(x)?
The graph shows f(x) to have a y intercept at -1, which is where the diagonal line crosses the y axis. We want the y intercept to move to 3. So we must add 4 to the old y intercept to get the new y intercept.
We do this with every single point on f(x) to get g(x) = f(x)+4. This shifts the graph up 4 units.
The graph of a linear equation g(x)=-1/3x +2 can be obtained from the graph f(x)=1/3x by using infinite sets of elementary translation (i.e reflection and shifting). List out five of those sets
Answer:
{Rx, T(-6, 4)}{Rx, T(-3, 3)}{Rx, T(0, 2)}{Rx, T(3, 1)}{Rx, T(9, -1)}Step-by-step explanation:
We assume you are not interested in five infinite sets of translations. Rather, we assume you want to pick 5 translations from the infinite set of possibilities.
The attached graph shows f(x), g(x), and 5 lines (dashed or dotted) that represent possible reflections and shifts of the function f(x).
The function f1 represents a reflection of f(x) about the x-axis, followed by a left-shift of 6 units. To make it match g(x), we need to shift it upward 4 units. Then the set if translations is ...
g(x) = f(x) ... {reflected over the x-axis, shifted left 6, shifted up 4}
Along the same lines, other possibilities are ...
g(x) = f(x) ... {reflected over the x-axis, shifted left 3, shifted up 3}
g(x) = f(x) ... {reflected over the x-axis, shifted left 0, shifted up 2}
g(x) = f(x) ... {reflected over the x-axis, shifted right 3, shifted up 1}
g(x) = f(x) ... {reflected over the x-axis, shifted right 9, shifted down 1}
___
Additional comment
All of the transformations listed above use reflection in the x-axis. Reflection could use the y-axis, as well. Reflection of the basic function f(x) in the y-axis will have the identical effect as reflection in the x-axis. The listed translations would apply unchanged.
Please help me with this!
Answer:
5:1
Step-by-step explanation:
20/4= 5
1*5 = 5
5:1 ratio
Hope this helps!
what’s the opposite of negative two
Answer: The answer is two
Step-by-step explanation: If you look for opposites of a number its either negative or positive. So when the answer is negative, the opposite is positive and if the answer is positive, the opposite is negative.
Answer:
[tex]\boxed{2}[/tex]
Step-by-step explanation:
The opposite of a number is the number that is the same distance from 0 on the number line.
-2 opposite is 2.
2.CommerceThe weight distribution of parcels sent in a certain manner is normal with meanvalue 12 pounds and standard deviation 3.5 pounds. The parcel service wishes to establish aweight valuecbeyond which there will be a surcharge. What value ofcis such that 99% ofall parcels are under the surcharge weight
Answer:
the value of c is 20.155 such that 99% of all parcels are under the surcharge weight.
Step-by-step explanation:
Given that :
The mean value [tex]\mu[/tex] = 12
The standard deviation [tex]\sigma[/tex] = 3.5
Let Consider Q to be the weight of the parcel that is normally distributed .
Then;
Q [tex]\sim[/tex] Norm(12,3.5)
The objective is to determine thewight value of c under which there is a surcharge
Also, let's not that 99% of all the parcels are below the surcharge
However ;
From the Percentiles table of Standard Normal Distribution;
At 99th percentile; the value for Z = 2.33
The formula for the Z-score is:
[tex]Z = \dfrac{X- \mu}{\sigma}[/tex]
[tex]2.33 = \dfrac{X - 12}{3.5}[/tex]
2.33 × 3.5 = X - 12
8.155 = X - 12
- X = - 12 - 8.155
- X = -20.155
X = 20.155
the weight value of c under which there is a surcharge = X + 1 (0) since all the pounds are below the surcharge
c = 20.155 + 1(0)
c = 20.155
Thus ; the value of c is 20.155 such that 99% of all parcels are under the surcharge weight.