Answer:
Step-by-step explanation:
Form a set of values we get
n = 17
And with the help of a calculator
μ₀ = 438,47
σ = 14,79
Normal Distribution is : N ( 438,47 ; 14,79 )
c)
CI = 95 % means α = 5 % α/2 = 2,5 % α/2 = 0,025
and as n < 30 we should use t-student distribution with n -1 degree of freedom df = 16. t score for 0,025 and 16 s from t-table 2,120
By definition:
CI = [ μ₀ ± t α/2 ; n-1 * σ/√n ]
CI = [ μ₀ ± 2,120* 14,79/√17 ]
CI = [ μ₀ ± 7,60 ]
CI = [ 438,47 ± 7,60 ]
CI = [ 430,87 ; 446,07 ]
95% confidence interval for true average degree of polymerization is [430.87 ; 446.07] and this interval suggest that 441 is a plausible value for true average degree of polymerization and also this interval does not suggest that 451 is a plausible value.
Given :
Sample = [ 418, 421, 421, 422, 425, 428, 431, 435, 437, 438, 445, 447, 448, 453, 458, 462, 465 ]95% confidence interval.The total number of values given is, n = 17
Mean, [tex]\mu_0=438.47[/tex]
Standard Deviation, [tex]\sigma = 14.79[/tex]
The normal distribution is given by: N (438.47 ; 14.79)
If Cl is 95% then [tex]\alpha[/tex] is 5% and [tex]\alpha /2[/tex] is 2.5%
[tex]\alpha /2 = 0.025[/tex]
Now, use t-statistics distribution with (n-1) degree of freedom df = 16
So, the t score for 0.025 and 16 s from t-table 2.120.
[tex]\rm Cl = [\mu_0 \pm t_{\alpha /2};(n-1)\times \dfrac{\sigma}{\sqrt{n} }][/tex]
[tex]\rm Cl = [\mu_0 \pm 2.120\times \dfrac{14.79}{\sqrt{17} }][/tex]
[tex]\rm Cl = [\mu_0 \pm 7.60][/tex]
Cl = [430.87 ; 446.07]
Yes, the interval suggests that 441 is a plausible value for true average degree of polymerization.
No, the interval does not suggest that 451 is a plausible value.
For more information, refer to the link given below;
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There is a circle with a center of 0,0 on a coordinate plane. There is one point on the circle's circumference in which the x:y ratio is 3:1. What is a possible coordinate?
Answer:
(3, 1)
Step-by-step explanation:
A circle with radius √10 and centre at (0, 0) will have a point (3, 1) on its circumference.
A researcher examines typing speed before a typing class begins, halfway through the class, and after the class is over. 4. Identify the number of levels: 5. Identify the type of design: 6. Identify the dependent variable:
Answer:
Number of levels = 2
Type of design = Repeated measure
Dependent variable = Typing Speed
Step-by-step explanation:
The number of levels in an experiment simply refers to the number of experimental conditions in which participants are subjected to. In the scenario above, the number of levels is 2. Which are ; Halfway through the class and After the class is over.
The type of designed employed is REPEATED MEASURE, this is because the participants all took part in each experimental condition.
The dependent variable is TYPING SPEED, which is the variable which is measured with respect to the independent variable. Hence the observed value depends on period that is (halfway through the class or after the class is over).
If
A. x = 62; mZROS = 31°
B. x = 60; mZROS = 28°
C. x= 31; mZROS = 62°
D. X = 28; mZROS = 60°
Answer:
x = 31
ROS = 62
Step-by-step explanation:
QOR + ROS = 90 degrees as indicated by the box
28+ 2x = 90
Subtract 28 from each side
2x = 90 -28
2x = 62
Divide by 2
2x/2 = 62/2
x = 31
ROS = 2x = 2*31 = 62
Answer:
C. x= 31; mZROS = 62°
Step-by-step explanation:
90=28+2x
2x= 90-28
2x= 62
x= 62/2
x=31°
2(x)= 2× 31 = 62
I hope I helped you^_^
The place value of 7 in 87534 is____________
I’m confused of how to do this
Answer:
y≤0
Step-by-step explanation:
The line is 0 for all x so y must be the one being manipulated
Because the line is solid and shaded on the negative side, y must be less than or equal to 0
✨Plz help me with my Homework!✨
This is “Finding unit rate”
Plz!
Please answer this and show the work/explain.
2/7m - 1/7 = 3/14
What is the equation of a horizontal line passing through the point (-7,5)?
Oy = 5
Oy = -7
Ox=5
Ox= - 7
Answer:
1st option, y = 5
Step-by-step explanation:
when the line is horizontal, it's parallel to the x axis
Answer:
y = 5
Step-by-step explanation:
The equation of a horizontal line parallel to the x- axis is
y = c
where c is the value of the y- coordinates the line passes through
The line passes through (- 7, 5 ) with y- coordinate 5 , then
y = 5 ← is the equation of the line
Write the expression in exponential form.
log . N = x
Answer:
N = x2
Step-by-step explanation:
Follpwing the format
Please help me answer this?
9514 1404 393
Answer:
h'(3) = 26
Step-by-step explanation:
h(x) = 3f(x) +5g(x) +3 . . . . . . . given
h'(x) = 3f'(x) +5g'(x) . . . . . . . . take the derivative
h'(3) = 3f'(3) +5g'(3) . . . . . . . use x=3
h'(3) = 3(2) +5(4) = 26
A scientist needs 120mL of a 20% acid solution for an experiment. The lab has available a 10% solution and a 25% solution. How many milliliters of the 10% solution and how many milliliters of the 25% solution should the scientist mix to make the 20% solution?
Answer:
40 mL of 10% acid
80 mL of 25% acid
Step-by-step explanation:
x = volume of 10% acid solution
y = volume of 25% acid solution
Total volume is:
x + y = 120
Total amount of acid is:
0.10 x + 0.25 y = 0.20 (120)
Solve by substitution.
0.10 x + 0.25 (120 − x) = 0.20 (120)
0.10 x + 30 − 0.25 x = 24
0.15 x = 6
x = 40
y = 80
I need help with this please
Answer:
its the 1st one
Step-by-step explanation:
they need to know what the Total
Answer:
English; 12
French; 9
Both; 7
Step-by-step explanation:
28 - 19 = 9, therefore there are only 9 students who can only speak French
28 - 16 = 12, therefore there are only 12 students who can only speak English
12 + 9 = 21, then subtract 21 from the 28 total students
28 - 21 = 7, therefore there are only 7 students who can speak both
A math class has a total of 31 students. The number of females is seven less than the number of meals. How many miles and how many females are in the class?
Answer:
Male-19&Female-13
Step-by-step explanation:
See the image for solution
Hope it helps
Have a great day
find the mean deviation about mean for rhe following data 3,9, 5, 3, 12, 10, 18, 4, 7, 19, 21
Class 11th
Answer:
10.1(approx)
Step-by-step explanation:
3+9+5+3+12+10+18+4+7+19+21/11
=111/11=10.09/10.1(approx )
SEE IMAGE FOR SOLUTION.
HOPE IT HELPS.
HAVE A GREAT DAY
gaurrik had 15 marbles lakhima had 22 marbles and kairuv had 30 marbles how many marbles did they have altogether?
Answer:
67 marbles
Step-by-step explanation:
15+30=45
45+22=67
Step-by-step explanation:
you cannot add some simple numbers ? you don't know how to use a calculator ?
to solve this yourself is way shorter than putting this in here.
15 + 22 + 30 = 67
The distance that Sarah travels varies directly to how long she drives. She travels 440 miles in 8 hours. Write the equation that relates the distance, d, to the time, t. How many miles can Sarah travel in 6 hours?
Answer:
330
Step-by-step explanation:
If d = distance, t = time, and s = speed, then the relationship between the 3 is s * t = d.
Solve for speed by dividing the distance over the time, s = d/t. Then, plug in the speed which in this case is 55 mph and then multiply by the time of 6 hours.
(b) Suppose you want to study the length of time devoted to commercial breaks for two different types of television programs. Identify the types of programs you want to study (e.g., sitcoms, sports events, movies, news, children's programs, etc.). How large should the sample be for a specified margin of error
Answer:
The correct option is b.
Step-by-step explanation:
The complete question is:
Suppose you want to study the length of time devoted to commercial breaks for two different types of television programs. Identify the types of programs you want to study (e.g., sitcoms, sports events, movies, news, children's programs, etc.). How large should the sample be for a specified margin of error.
(a) It depends only on the specified margin of error.
(b) It depends on not only the specified margin of error, but also on the confidence level.
(c) It depends only on the confidence level.
Solution:
The (1 - α) % confidence interval for population mean is:
[tex]CI=\bar x\pm z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}[/tex]
The margin of error for this interval is:
[tex]MOE=z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}[/tex]
Then the sample size formula is:
[tex]n=[\frac{z_{\alpha/2}\times \sigma}{MOE}]^{2}[/tex]
The sample size is dependent upon the confidence level (1 - α) %, the standard deviation and the desired margin of error.
Thus, the correct option is b.
The size of the sample 'n' depends on not only the specified margin of error, but also on the confidence level.
Given :
Suppose you want to study the length of time devoted to commercial breaks for two different types of television programs.
The following steps can be used in order to determine the size of the sample be for a specified margin of error:
Step 1 - The formula of the confidence interval is given below:
[tex]\rm CI =\bar{x}+z_{\alpha /2}\times \dfrac{\sigma }{\sqrt{n} }[/tex]
Step 2 - Now, for this interval, the formula of margin of error is given below:
[tex]\rm MOE = z_{\alpha /2}\times \dfrac{\sigma}{\sqrt{n} }[/tex]
Step 3 - Solve the above expression for sample size 'n'.
[tex]\rm n = \left(\dfrac{z_{\alpha /2}\times \sigma}{MOE}\right)^2[/tex]
From the above steps, it can be concluded that the correct option is B) It depends on not only the specified margin of error, but also on the confidence level.
For more information, refer to the link given below:
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Assume that thermometer readings are normally distributed with a mean of 0C and a standard deviation of 1.00C. A thermometer is randomly selected and tested. For the case below, draw a sketch, and find the probability of the reading. (The given values are in Celsius degrees.) Between and
Answer: 0.0546 and 0.9829
Step-by-step explanation:
solution:
= P( 1.50< Z <2.25 )
= P(Z <2.25 ) - P(Z <1.50 )
Using z table,
= 0.9878-0.9332
=0.0546
b.
= P( -2.12< Z <3.73 )
= P(Z <3.73) - P(Z <-2.12 )
Using z table,
= 0.9999-0.0170
=0.9829
Driver's Delight is considering building a new track. They have a circular space
with a diameter of 150 feet. Compute the circumference of the circular space.
Use 3.14 for it. Round your answer to the nearest hundredth, if necessary.
Answer:
The answer is 471 feetStep-by-step explanation:
Since the the track is circular
Circumference of a circle = πd
where
d is the diameter
π = 3.14
From the question
diameter = 150 feet
Circumference = 150π
= 150(3.14)
We have the final answer as
Circumference = 471 feetHope this helps you
Answer:
471.23 ft
Step-by-step explanation:
The circumference of this space is C = πd = (150 ft)π, or approximately
471.23 ft
A doctor orders Quinidine for an adult patient weighing 110 lb at a dosage of 25 mg/kg/day q6h. How many
milligrams should the patient receive each day?
Answer:
Total amount receive each day = 1250 mg per day
Number of dosage = 1250 / 4 = 312.5 mg per meal
Step-by-step explanation:
Given:
Weight of patient = 110 lb
Dosage = 25 mg/kg/day
Find:
Total amount receive each day
Computation:
Weight of patient = 110 lb
1 lb = 0.453592
Weight of patient = 110 (0.453592)
Weight of patient = 49.89
Weight of patient = 50 kg (Approx)
Total amount receive each day = 50 kg × 25 mg/kg/day
Total amount receive each day = 1250 mg per day
Number of dosage = 1250 / 4 = 312.5 mg per meal
PLZ HELP 55 POINTS Two quantities, x and y, are related proportionally such that 3x=2y . Which equation shows the same proportional relationship? A x/y=3/2 B x/2=y/3 C x/3=y/2 D x/2=3/y
Answer:
B
Step-by-step explanation:
3x = 2y
One way to solve this is to simply plug in values. If we say the following:
x = 2
y = 3
Then, we can start testing.
A: [tex]x/y = 3/2[/tex]
by plugging 2 and 3 in, we see that A doesn't work.
B: x/2 = y/3
This works! First we should look at the other equations.
C: x/3 = y/2
Nope.
D: x/2 = 3/y
This also works, but only with certain numbers. If we were to make x = 4, and y = 6, this wouldn't work.
You could also find out all of this using algebra. so, our anwser is B.
Find the radius of the circle with equation x^2 + y^2 - 10x - 16y + 53 = 0.
Answer:
radius = 10.5 unitsStep-by-step explanation:
Equation of a circle is given by
x² + y² + 2gx + 2fy + c = 0
To find the radius of the circle we use the formula
[tex]r = \sqrt{ {g}^{2} + {f}^{2} - c } [/tex]
where g and f is the center of the circle
From the question
x² + y² - 10x - 16y + 53 = 0
Comparing with the general equation above we have
2g = - 10 2f = - 16
g = - 5 f = - 8
c = 53
Substitute the values into the above formula
That's
[tex]r = \sqrt{ ({ - 10})^{2} + ( { - 8})^{2} - 53 } [/tex]
[tex]r = \sqrt{100 + 64 - 53} [/tex]
[tex]r = \sqrt{111} [/tex]
We have the final answer as
radius = 10.5 unitsHope this helps you
A person standing close to the edge on top of a 96-foot building throws a ball vertically upward. The quadratic function h = − 16 t 2 + 116 t + 96 models the ball's height above the ground, h , in feet, t seconds after it was thrown. a) What is the maximum height of the ball? b) How many seconds does it take until the ball hits the ground?
Answer: a) 306.25 feet b) 8 s
Step-by-step explanation:
Actually we have to find the function' s h(t) maximum meaning.
To do that we have to find the corresponding t - let call it t max
As known t max= (t1+t2)/2 where t1 and t2 are the roots of quadratic equation' s
Lets find the roots t1 and t2
-16*t^2+116*t+96=0 divide by 4 each side of the equation
-4*t^2 +29*t+24=0
D=29^2+24*4*4=1225 =35^2
t1=(-29-35)/(-8)=8
t2=(-29+35)/(-8)=-6/8=-3/4=-0.75
t max= (8+(-0.75))= 7,25/2=3.625 s
h max= -16*t max ^2+116*t +96= -16*3.625^2+116*3.625+96=306.25 feet
b) t2=8s is the time when the ball hits the ground.
Answer:
a) 306.25 ft
b) 8 seconds
Step-by-step explanation:
a) The time at the maximum height is found from the equation for the axis of symmetry:
ax^2 +bx +c has axis of symmetry at x=-b/(2a)
For the given equation, the t-value at the vertex is ...
t = -116/(2(-16)) = 3.625 . . . seconds
At that time, the height is ...
h = (-16(3.625) +116)(3.625) +96 = (58)(3.625) +96 = 306.25
The maximum height is 306.25 feet.
__
b) The ball will hit the ground when h=0. From the vertex values in the first part, we know we can rewrite the equation in vertex form as ...
h(t) = -16(t -3.625)^2 +306.25
This will be 0 when ...
0 = -16(t -3.625)^2 +306.25
(t -3.625)^2 = 306.25/16
t = 3.625 +√19.140625 = 3.625 +4.375 = 8
The ball will hit the ground after 8 seconds.
Because the sum of angle measures in each triangle is 180°, the
sum of interior angle measures in a quadrilateral is
2 x 180°=
Answer:
It's 360
Step-by-step explanation:
2 x 180 = 360
A rectangle is divided into 25 equal parts. How many of these parts must be shaded in order to cover three fifths of the rectangle?
Answer:
15 parts must be shaded
Step-by-step explanation:
3/5 × 25 = 15
15/25 = 3/5
Have a great day.
15 parts must be shaded in order to cover three fifths of the rectangle.
What is a rectangle?
"A rectangle has two pairs of equal opposite parallel sides, four right angles and two diagonals. The diagonals of a rectangle are congruent.
They also bisect each other. Each diagonal divides the rectangle into two congruent right triangles."
Given
A rectangle is divided into 25 equal parts.
Number of parts must be shaded in order to cover three fifths of the rectangle
= [tex]\frac{3}{5}[/tex] × [tex]25[/tex]
= 15
Checking whether the 15 parts must be shaded in order to cover three fifths of the rectangle
= [tex]\frac{15}{25}[/tex]
= [tex]\frac{3}{5}[/tex]
Hence, 15 parts must be shaded in order to cover three fifths of the rectangle.
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PLEASE HURRY! i walked north 8 miles, the west 4 miles, and finally south 5 miles, at the end how far was i from where i started
Answer:
5 miles away
Step-by-step explanation:
If you walked north 8 miles, then west 4 miles, then south 5 miles, you have, in total, travelled 4 miles west and [tex]8-5=3[/tex] miles north.
This creates a triangle, in which we can find the the length of the hypotenuse to find how far away you are now.
We can use the Pythagorean theorem since this is a right triangle.
[tex]a^2+b^2=c^2\\3^2+4^2=c^2\\9+16=c^2\\25=c^2\\c=5[/tex]
Hope this helped!
Answer:
5 miles away
Step-by-step explanation:
Staff at a fast food restaurant make up the cleaning solution in their spray bottles from a concentrate. In each 300mL bottle they pour 50mL of concentrate and fill the bottle the rest of the way with water. What is the ratio of concentrate to water used?
Answer:
1 : 5
Step-by-step explanation:
So 50mL is for thye concentrate then the rest is water which means the water is 300mL - 50mL = 250mL of water.
Ratio of concrentrate to water = 50mL: 250mL
To write a ratio you first write down the one stated first then the other one.
50mL : 250mL CAN BE SIMPLIFIED. This is done by dividing both parts by the highest common factor which is 50.
It then becomes 1 : 5.
HOPE THIS HELPED
It cost Evan $17.70 to send 177 text messages. How many text messages did he send if he spent $19.10
Answer:
191
Step-by-step explanation:
17.70---- 177
19.10-----191
First just take 177/17.70= 10
all you have to do is multiply by 10
so
19.10= 191
The number of text messages he can send with $19.10 is 191 messages
solve using ratio
let
x = number of text messages he can send with $19.10
cost of messages : number of messages
$17.70 : 177 = $19.10 : x
17.70 / 177 = 19.10 / x
cross product
17.70 × x = 177 × 19.10
17.70x = 3380.7
divide both sides by 17.70
x = 3380.7 / 17.70
x = 191 messages.
Therefore, number of text messages he can send with $19.10 is 191 messages
Read more:
https://brainly.com/question/24425126
A study of 25 graduates of four-year public colleges revealed the mean amount owed by a student in student loans was $55,051. The standard deviation of the sample was $7,568.
Required:
a. Construct a 90% confidence interval for the population mean.
b. Confidence interval for the population men between _______ up to_______________
Answer:
a
The 90% confidence interval is [tex]52561.13 < \mu < 57540.8[/tex]
b
Confidence interval for the population men between $52561.13 up to $57540.8
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 25[/tex]
The sample mean is [tex]\= x = \$ 55,051[/tex]
The standard deviation is [tex]\sigma = \$ 7,568[/tex]
Given that the confidence level is 90% then the level of confidence is mathematically represented as
[tex]\alpha = 100 -90[/tex]
[tex]\alpha = 10\%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table the values is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{ \alpha }{2} } * \frac{ \sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.645 * \frac{ 7568}{ \sqrt{ 25} }[/tex]
[tex]E = 2489.9[/tex]
The 90% confidence interval is mathematically evaluated as
[tex]\= x -E < \mu < \= x +E[/tex]
substituting values
[tex]55051 - 2489.8 < \mu < 55051 + 2489.8[/tex]
[tex]52561.13 < \mu < 57540.8[/tex]
The x-intercept of the line y = 4x - 16 is the point (_,0)
Answer:
the point is (4,0)
Step-by-step explanation:
The x-intercept is the point on the x-axis where y=0.
Set y=0
0=4x-16
16=4x
x=4, y=0
So the notation for the point is (4,0).
Good luck!
Answer:
(4, 0)
Step-by-step explanation:
4x - 16 = 0
4x = 16
x = 4