Answer:
We conclude that the true average percentage of Silicon Dioxide is smaller than 5.5.
Step-by-step explanation:
We are given that the desired percentage of Silicon Dioxide (SiO2) in a certain type of aluminous cement is 5.5.
16 independently obtained samples are analyzed and a sample mean of 5.25 was obtained. Suppose that the percentage of SiO2 in a sample is normally distributed with a sigma of 0.3.
Let [tex]\mu[/tex] = true average percentage of Silicon Dioxide.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\geq[/tex] 5.5 {means that the true average is greater than or equal to 5.5}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 5.5 {means that the true average is smaller than 5.5}
The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean percentage of Silicon Dioxide = 5.25
σ = population standard deviation = 0.3
n = sample size = 16
So, the test statistics = [tex]\frac{5.25-5.5}{\frac{0.3}{\sqrt{16} } }[/tex]
= -3.33
The value of z test statistics is -3.33.
Now, the P-value of the test statistics is given by;
P-value = P(Z < -3.33) = 1 - P(Z [tex]\leq[/tex] 3.33)
= 1 - 0.9996 = 0.0004
Since, the P-value of the test statistics is less than the level of significance as 0.0004 < 0.01, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the true average percentage of Silicon Dioxide is smaller than 5.5.
Answer:
The true average percentage of Silicon Dioxide (SiO2) is less than 5.5.
Step-by-step explanation:
In this case we need to test whether the true average percentage of Silicon Dioxide (SiO2) in a certain type of aluminous cement is smaller than 5.5.
The hypothesis can be defined as follows:
H₀: The true average percentage of Silicon Dioxide (SiO2) is 5.5, i.e. μ = 5.5.
Hₐ: The true average percentage of Silicon Dioxide (SiO2) is less than 5.5, i.e. μ < 5.5.
The information provided is:
[tex]\bar x=5.25\\\sigma=0.30\\n=16\\\alpha =0.01[/tex]
As the population standard deviation is provided, we will use a z-test for single mean.
Compute the test statistic value as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}=\frac{5.25-5.5}{0.30/\sqrt{16}}=-3.33[/tex]
The test statistic value is -3.33.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected.
Compute the p-value for the two-tailed test as follows:
[tex]p-value=P(Z<-3.33)=0.00043[/tex]
*Use a z-table for the probability.
The p-value of the test is 0.00043.
p-value = 0.00043 < α = 0.05
The null hypothesis will be rejected at 5% level of significance.
Thus, it can be concluded that the true average percentage of Silicon Dioxide (SiO2) is less than 5.5.
What is the length of line segment KJ?
2 \sqrt{3} units
3 \sqrt{2} units
3 \sqrt{3} units
3 \sqrt{5} units
Please consider the attached file.
We can see that triangle JKM is a right triangle, with right angle at M. Segment KM is 6 units and segment MJ is 3 units. We can also see that KJ is hypotenuse of right triangle.
We will use Pythagoras theorem to solve for KJ as:
[tex]KJ^2=KM^2+MJ^2[/tex]
[tex]KJ^2=6^2+3^2[/tex]
[tex]KJ^2=36+9[/tex]
[tex]KJ^2=45[/tex]
Now we will take positive square root on both sides:
[tex]\sqrt{KJ^2}=\sqrt{45}[/tex]
[tex]KJ=\sqrt{9\cdot 5}[/tex]
[tex]KJ=3\sqrt{5}[/tex]
Therefore, the length of line segment KJ is [tex]3\sqrt{5}[/tex] and option D is the correct choice.
Answer:
3√5Step-by-step explanation:
what is the length of line segment kJ
Data were collected on the age (in years) and price (in thousands of dollars) of a random sample of 25 used Cars. The computer output from a regression analysis is provided.
Model Summary
R-sq R-sq(adj)
89.9% 87.4%
Coefficients
Term Coef SE Coef T-Value P-Value
Constant 15.29 0.58 26.18 0.000
Age -1.71 0.13 -13.55 0.000
What is the value of the intercept? Enter the value exactly how it is displayed in the output.
Answer:
vaulue is 4
Step-by-step explanation:
What’s the correct answer for this?
Answer:
C. y=1/2 x + 5
Step-by-step explanation:
In the attached file
Riley is saving up to buy a new television. She needs a total of $1,397.68. Riley has saved $200.08 already and earns $79.84 per week at her job. How many weeks does Riley need to work to save enough money to buy the new television?
Answer:
14
Step-by-step explanation:
i uses a calculator and kept adding up
What is the quotient of the division below?
3387-
45
46
48
49
Answer:
3199
Step-by-step explanation:
3387 – 45 – 46 – 48 – 49 = 3199
Answer:
It is 48
Step-by-step explanation:
trust me I did the test.
PLS HELP!! AND HURRY!! Find an expression for the nth term ( tn ) in each of the following sequences:
1, 4, 7, ...
If the pattern continues, so that each term is separated by a distance of 3, then the sequence is given by the recursive rule
[tex]\begin{cases}a_1=1\\a_n=a_{n-1}+3&\text{for }n>1\end{cases}[/tex]
From this definition, we can write [tex]a_n[/tex] in terms of [tex]a_1[/tex]:
[tex]a_2=a_1+3[/tex]
[tex]a_3=a_2+3=(a_1+3)+3=a_1+2\cdot3[/tex]
[tex]a_4=a_3+3=(a_1+2\cdot3)+3=a_1+3\cdot3[/tex]
[tex]a_5=a_4+3=(a_1+3\cdot3)+3=a_1+4\cdot3[/tex]
and so on, up to
[tex]a_n=a_1+(n-1)\cdot3[/tex]
(notice how the subscript on a and coefficient on 3 add up to n)
or
[tex]a_n=1+3(n-1)=3n-2[/tex]
Answer:
n=1/2 of n x 8 divided by 4 -2
Step-by-step explanation:
Mr.McNeil bought two magazines for 7.45 and one book for 14.95. If the sales tax is 6% , what is the total cost of Mr.McNeil’s purchase?
Answer:
total cost = $22.4 + $1.12 = $23.52
Step-by-step explanation:
Mr McNeil bought 2 magazines for $7.45 and 1 book for $14.95 . The sales tax is 6% . The total cost of Mr McNeil can be calculated as follows.
He bought 2 magazines for $7.45 .This means the sum of the prize of the 2 magazine he bought is $7.45 and the prize for the single book he bought is $14.95. The total cost of the items he bought excluding the sales tax is the sum of the whole items he bought.
total cost excluding sales tax = $7.45 + 14.95 = $22.4
The sales tax is 5% which can be calculated as follows
5/100 × 22.4 = 112/100 = $1.12
The total cost of Mr McNeil purchase including his sales tax is
total cost = $22.4 + $1.12 = $23.52
Based on data from the 1980 Census the average age of a Na'alehu County, Hawaii resident is 39 years with a standard deviation of 22. 6. The data is normally distributed. If 100 residents are surveyed, Determine the Inter Quartile range (IQR) for the average age of the residents of this County. Please explain how you derived your answer:
Answer:
yes
Step-by-step explanation:
I need help please and thank you
Answer:
2.2×10⁹
Step-by-step explanation:
The distributive property is useful here. Recognize that 10⁹ is a common factor:
(5.4×10⁹) - (3.2×10⁹) = (5.4 -3.2)×10⁹ = 2.2×10⁹
Answer: 2.2×10⁹
Step-by-step explanation:
The Tennessean, an online newspaper located in Nashville, Tennessee, conducts a daily poll to obtain reader opinions on a variety of current issues. In a recent poll, 762 readers responded to the following question:
"If a constitutional amendment to ban a state income tax is placed on the ballot in Tennessee, would you want it to pass?" Possible responses were Yes, No, or Not Sure. Determine:
a. What was the sample size for this poll?
b. Are the data categorical or quantitative?
c. Would it make more sense to use averages or percentages as a summary of the data for this question?
d. Of the respondents, 67% said Yes, they would want it to pass. How many individuals provided this response?
Answer:
(a) The sample size for this poll is, n = 762.
(b) The data is categorical.
(c) It would make more sense to use percentages as a summary of the data for this question.
(d) Approximately 511 individuals provided the response "Yes".
Step-by-step explanation:
(a)
It is provided that in a recent poll, 762 readers responded to the following question:
"If a constitutional amendment to ban a state income tax is placed on the ballot in Tennessee, would you want it to pass?"
The possible responses were Yes, No, or Not Sure.
So, the sample size for this poll is, n = 762.
(b)
The outcomes of the poll are:
1: Yes
2: No
3: Not Sure
The data is categorical.
Categorical data can take labels such as, Gender (M/F), indicators (0/1) and so on.
(c)
Averages can be computed only for quantitative variable.
So, it would make more sense to use percentages as a summary of the data for this question.
That is, the percentage of people saying Yes, No and Not sure.
(d)
The percentage of people saying Yes is, 67%.
Compute the number of people saying Yes as follows:
[tex]n(\text{Yes})=P(\text{Yes})\times n[/tex]
[tex]=0.67\times 762\\=510.54\\\approx 511[/tex]
Thus, approximately 511 individuals provided the response "Yes".
90 is 50% of what number? 180 120 45
So the right answer is 180
Look at the attached picture
Hope it will help you
Good luck on your assignment
Answer:
50%=0.5
Y x 0.5 = 90
We undo the equation and divide instead of multiply
90 / 0.5 = 180
Double check by changing Y with 180
180 x 0.5 = 90
180 is the answer
Hope this helps
Step-by-step explanation:
Fill in the boxes. 300 000 cm =____ m=____km
Answer:3000m and 3km
Step-by-step explanation:
To convert from cm to m,divide by 100 and from m to km,divide by 1000
magine that you are conducting a one-variable chi-square test to investigate the hypothesis that there are equal numbers of cat lovers and dog lovers in the office at work. Having conducted a survey, you found 150 preferred dogs and 120 preferred cats. What would the expected frequencies be in each cell? 135 150 and 120 270 More information is needed to calculate the expected frequencies.
Answer:
a. 135 is correct
Step-by-step explanation:
We have the following information:
dogs lover: 150
cats lover: 120
as the null hypothesis:
H, there are equal number of dogs lover and cats lover, so the expected frequency in each cell will be equal and that is:
f = (150 + 120) / 2
f = 270/2 = 135
so option a. 135 is correct
what is the correlation coefficient of the linear fit of the data shown below, to the nearest hundreth
Answer:
theres no picture.
Step-by-step explanation:
Answer:
C) -0.89 i think
Step-by-step explanation:
Solve 5(x − 8) = 50.
Answer:
x = 18
Step-by-step explanation:
5(x - 8) = 50
Divide both sides by 5.
x - 8 = 10
Add 8 to both sides.
x = 18
Answer:
x=18
Step-by-step explanation:
5(x − 8) = 50.
5x-40=50
+40 +40
5x/5=90/5
x=18
Juan selects 2 colored pencils randomly. There are 4 green, 3 yellow, 4 red, 3 blue and 2 orange. What is the probability Juan chooses a red, replaces it, and then chooses an orange?
A: 1 over 32
B: 1 over 30
C: 8 over 225
D: 3 over 8
I need Help..please??
Answer:
56
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
Two cars leave towns 1000 kilometers apart at the same time and travel toward each other. One car's rate is 20 kilometers per hour less than the other's. If they meet in 5 hours, what is the rate of the slower car?
Answer:
90 km/hr
Step-by-step explanation:
If x is the speed of the slower car, and x+20 is the speed of the faster car, then:
5x + 5(x+20) = 1000
x + x + 20 = 200
2x + 20 = 200
x + 10 = 100
x = 90
Which system of equations has one solution?
Answer:
A is correct, when two lines have 1 intersection (1 solution).
Step-by-step explanation:
B Two lines are parallel => No intersection (no solution).
C Two lines are coincident => Many intersection (many solutions).
Hope this helps!
:)
Step-by-step explanation:
As these two lines are not parallel so going to intersect at one point so having one solution
A car travels 10km southeast and then 15 km in a direction 60 degrees north of east. What is the magnitude of the car's resultant vector?
Answer: 15.85km
Step-by-step explanation:
The car starts at the point (0,0)
Let's define east as the positive x-axis and north as the positive y-axis.
first, the car travels 10km southeast, so the angle is -45° from the east.
Then the new position of the car is:
(10km*cos(-45°), 10km*sin(-45°)) = (7.07km, -7.07km)
Now, from this point the car travels 15km with an angle of 60° (counting from the east)
So the new position is:
(7.07km + 15km*cos(60°), -7.07km + 15km*sin(60°)) = (14.57km , 5.91km)
The magnitude of a vector (x, y) is √(x^2 + y^2)
So the magnitude of the vector (14.57km , 5.91km) is:
√((14.57km)^2 + (5.91km)^2) = 15.85km
The magnitude of the car's resultant vector is 15.72.
Given that,
A car travels 10km southeast,
And then 15 km in a direction 60 degrees north of east.
We have to find,
The magnitude of the car's resultant vector.
According to the question,
To resultant direction calculate by using the sum of vectors following all the steps given below.
A car travels 10 km southeast,
And then 15 km in a direction 60 degrees north of east.
The first vector has module is 10 and angle is 315°,
In the south direction, the angle is 270° and east is 360°,
So the angle in southeast,
[tex]\rm = \dfrac{270+360}{2}\\\\= \dfrac{630}{2}\\\\= 315 \ degree[/tex]
The second vector has module 15 and angle = 40°
Decompose both vectors in their horizontal and vertical component:
The horizontal component of the first vector is,
[tex]\rm = 10 \times cos(315) = 10 \times 0.70= 7.07[/tex]
The vertical component of the first vector is,
[tex]= \rm 10 \times sin(315) = -7.07[/tex]
The horizontal component of the second vector is,
[tex]\rm = 15 \times cos(60) = 15 \times 0.5= 7.5[/tex]
The vertical component of the second vector is,
[tex]\rm = 15 \times sin(40) = 15 \times 0.86= 12.99[/tex]
The sum of the horizontal component of the resultant vector is,
[tex]= 7.07+7.5=14.57[/tex]
And the sum of the vertical component of the resultant vector is,
[tex]= -7.07+12.99=5.91[/tex]
The magnitude of the vector (14.57km, 5.91km) is:
Therefore,
The magnitude of the car's resultant vector is,
[tex]\rm Resulatant = \sqrt{(14.57)^2+ (5.91)^2}\\\\ Resulatant = \sqrt{212.28+ 34.92} \\\ \\ Resulatant = \sqrt{247.20}\\\\ Resulatant = 15.72[/tex]
Hence, The required magnitude of the car's resultant vector is 15.72.
For more details refer to the link given below.
https://brainly.com/question/16541081
A Forrest has 800 pine trees but a disease is introduce that kills 1/4 of the pine trees in the forest every year.
Write a function that gives the number of pine trees remaining P(t) in the Forest t years after the disease is introduced
Answer:
If there are 800 trees and 1/4 of them die to this disease.
Step-by-step explanation:
800=400x2=800/2=400 so 100/400 die so 200/800 die so in 4 years time the whole population will die.
Answer:
P(t)=800(3/4)^t
Step-by-step explanation:
3. If a ladder is x feet long, how high up a wall can it safely reach?
Answer:
xsin∅
Step-by-step explanation:
If the ladder is x foot long, and it can safely make a maximum angle ∅ with the floor, then, the maximum height it can reach will be xsin∅
Answer:
Following the 4 to 1 ratio ladder rule
Step-by-step explanation:
set the base 1 foot out from the wall for every 4 feet it reaches up.
find an equation equivalent to r = 10 sin in rectangular coordinates
Answer:
x²+(y-5)²=25
Step-by-step explanation:
To convert polar into rectagular
[tex]->r=\sqrt{x^2+y^2} =>r^2=x^2+y^2\\[/tex]
also, y=rsin θ => sin θ=y/r
r= 10sinθ
r=[tex]\frac{10y}{r}[/tex] => r²=10y
therefore, x²+y²-10y=0
By completing the squares on y²-10y gives
x²+(y-5)²=25
which is the equation of the circle.
This is the Cartesian equation of a circle with center ( 0, 5)
and radius, r=5
Which expression can be used to find the surface area of the following rectangular prism?
Choose 1 answer:
A
10+10+6+6
(Choice B)
B
10+6
(Choice C)
C
15+15+10+10+6
(Choice D)
D
15+15+10+10+6+6
Answer:
The answer is D.
Step-by-step explanation:
Given that the formula of surface area of rectangular prism is S.A = 2(length×width) + 2(length×height) + 2(width×height). Then substitute the values into the formula :
Let length = 5,
Let width = 3,
Let height = 2,
[tex]s.a = 2(5 \times 3) + 2(5 \times 2) + 2(3 \times 2)[/tex]
[tex]s.a = 2(15) + 2(10) + 2(6)[/tex]
[tex]s.a = 15 + 15 + 10 + 10 + 6 + 6[/tex]
Answer:
The answer is D
Step-by-step explanation:
Please help with number four I give brainliest thank you!
Answer:
Step-by-step explanation:
A
Answer:
D.
Step-by-step explanation:
A statistical question can answered by collecting data and having various answers. The other options refer to a specific person/thing and give only one piece of data while the last option refers to many teachers and many pieces of data.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
Give brianliest and 15 points
Answer:
The correct answer is C
Step-by-step explanation:
X+U= [-1, -1] on the top and [0, -23/4] on the bottom
Therefore A-(X+U) gives you [5/3, 7] on the top and [4, 5] on the bottom
Hope this helps! :)
Answer:
Danke Shun!!!!!
Step-by-step explanation:
Oh mein Gott, danke für die kostenlosen Punkte, Kumpel !!
what is the quotinent
Answer:
[tex]\dfrac{3(y-5)}{2}[/tex]
Step-by-step explanation:
[tex]\dfrac{2y^2-6y-20}{4y+12}\div \dfrac{y^2+5y+6}{3y^2+18y+27}=\\\\\dfrac{2(y-5)(y+2)}{4(y+3)}\cdot \dfrac{3(y+3)^2}{(y+3)(y+2)}=\\\\\dfrac{6(y-5)(y+2)(y+3)(y+3)}{4(y+2)(y+3)(y+3)}=\\\\\dfrac{3(y-5)}{2}[/tex]
Hope this helps!
what is the mean absolute deviation of 10, 5, 7, 10, 19, 32, 25?
Answer:
8.4897959183673
Step-by-step explanation:
The initial freshman class at a college is 10% smaller 1
than last year's class. But then during the first week of classes, 20 more
students enroll. If there were 950 students in last year's freshman class,
how many students are enrolled in this year's freshman class after the first
week of classes? *
Answer:
875 students are enrolled in this year's freshman class after the first week of classes.
Step-by-step explanation:
Last year, there were 950 students.
This year, the class is 10% smaller. So it's number of students is 100 - 10 = 90% of last year.
0.9*950 = 855
Initially, this year class had 855 students.
During the first week, 20 enrolled.
855 + 20 = 875.
So
875 students are enrolled in this year's freshman class after the first week of classes.
what symbol makes this comparison true? 200 mL O 2 L <>
Answer:
For the first case converting ml to L we got:
[tex] 200mL *\frac{1L}{1000 mL}= 0.2 L[/tex]
And we see that 0.2 L is lower than 2 L so then:
[tex] 200 mL < 2L[/tex]
And in the other way if we convert L to mL we got:
[tex] 2L *\frac{1000mL}{1L} = 2000 mL[/tex]
And we see that [/tex] 200mL < 2000 mL[/tex]
So then the answer would be <
Step-by-step explanation:
For this case we can solve this problem converting ml to L or converting L to ml.
For the first case converting ml to L we got:
[tex] 200mL *\frac{1L}{1000 mL}= 0.2 L[/tex]
And we see that 0.2 L is lower than 2 L so then:
[tex] 200 mL < 2L[/tex]
And in the other way if we convert L to mL we got:
[tex] 2L *\frac{1000mL}{1L} = 2000 mL[/tex]
And we see that [/tex] 200mL < 2000 mL[/tex]
So then the answer would be <