The 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]
Suppose that we have:
Sample size n > 30Sample mean = [tex]\overline{x}[/tex]Sample standard deviation = sPopulation standard deviation = [tex]\sigma[/tex]Level of significance = [tex]\alpha[/tex]Then the confidence interval is obtained as
Case 1: Population standard deviation is known[tex]\overline{x} \pm Z_{\alpha /2}\dfrac{\sigma}{\sqrt{n}}[/tex]
Case 2: Population standard deviation is unknown.[tex]\overline{x} \pm Z_{\alpha /2}\dfrac{s}{\sqrt{n}}[/tex]
For this case, we're given that:
Sample size n = 90 > 30Sample mean = [tex]\overline{x}[/tex] = 138Sample standard deviation = s = 34Level of significance = [tex]\alpha[/tex] = 100% - confidence = 100% - 90% = 10% = 0.1 (converted percent to decimal).At this level of significance, the critical value of Z is: [tex]Z_{0.1/2}[/tex] = ±1.645
Thus, we get:
[tex]CI = \overline{x} \pm Z_{\alpha /2}\dfrac{s}{\sqrt{n}}\\CI = 138 \pm 1.645\times \dfrac{34}{\sqrt{90}}\\\\CI \approx 138 \pm 5.896\\CI \approx [138 - 5.896, 138 + 5.896]\\CI \approx [132.104, 143.896] \approx [130.10, 143.90][/tex]
Thus, the 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]
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Work out m and c for the line: 2 x + 3 y + 4 = 0
Answer:
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Answer:
m = - , c = -
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
2x + 3y + 4 = 0 ( subtract 2x + 4 from both sides )
3y = - 2x - 4 ( divide all terms by 3 )
y = - x - ← in slope- intercept form
with slope m = - and y- intercept c = -
pls help!! and thank you
find the area of the circles
Answer:
10) 25π OR 78.5398...yd 11) 1/4π OR 0.785398...ft 12) 100π OR 314.159265....in
Step-by-step explanation:
area of a circle = πr^2 (π x radius squared)
the radius is just half the diameter
so for eg:
number 10)
diameter = 10 yd so radius = 5 yd
5 squared = 25
π x 25 yd = 25π OR 78.5398...yd
i hope this helped :)
y= -2x - 3
y= 7x + 6 solve by elimination
Answer:
x = y = - 1
Step-by-step explanation:
y = - 2x - 3
y = 7x + 6 -----> equation 1.
So,
7x + 6 = - 2x - 3
7x + 2x = - 3 - 6
9x = - 9
Divide 9 on both sides,
9x / 9 = - 9 / 9
x = - 1
Substitute x = - 1 in equation 1,
y = 7x + 6
= 7 ( - 1 ) + 6
= - 7 + 6
= 6 - 7
y = - 1
Therefore,
x = y = - 1
Step-by-step explanation:
please mark me as brainlest
Find the size of angle x.
Answer:
x = 56°
Explanation:
x + 124° = 180°x = 180° - 124°x = 56°Note: A straight line has total 180°
Answer:
x = 56°
Step-by-step explanation:
x + 124° = 180° ( being linear pair )
X = 180° - 124°
X = 56°
If x and y intercepts of the line are 3/2 and 5/4 respectively then the equation of the line is
Answer:
10x + 12y -15 =0
Step-by-step explanation
What is the value of k?
Answer:
10°
Step-by-step explanation:
According remote interior angles, 4k + 5 + 6k + 10 = 115.
10k + 15 = 115
10k = 100
k = 10
Hope this helps :)
Have a nice day!
Answer:
k = 10°
Step-by-step explanation:
According to the exterior angle theorem, the exterior angle will be equal to the two opposite inside angles added together. It will look like the following, and we solve for k from there.
115° = (4k + 5)° + (6k + 10)°
115° = 4k° + 5° + 6k° + 10°
115° = 6k° + 4k° + 10° + 5°
115° = 10k° + 15°
100° = 10k°
10° = k
k = 10°
What is the relationship between the difference in
the means and the MADs?
Answer:
Its the second one in the photo
Step-by-step explanation:
it's the second because when I clicked it I got it right.
Twenty wooden spheres, each with a radius of 2 inches, are packed snugly into a square box that is 18 inches on each side. The remaining space is filled with packing beads. What is the volume occupied by the spheres?
Vsphere=[tex]\frac{4}{3}\pi r^3[/tex]
Answer:
670.21 inches^3
Step-by-step explanation:
To find the volume of the spheres, all you need to know is the formula for the volume of a sphere, which you've included in your problem. From the problem, you also know that r = 2. From here, you calculate the volume of 1 of the spheres, which turns out to be:
V = 33.51032
Since there are 20 spheres in this box, you multiple the volume of a single sphere by 20 to get the total volume occupied by the spheres.
V = 20 * 33.51032
V = 670.2064
If you round to 2 decimal places, this becomes 670.21.
what are the slope and y - intercept of the equation 6x+3y=-12
Answer:
Slope= -2
y-intercept= -4
Step-by-step explanation:
To find the slope and y-intercept of a given equation, first rearrange the equation such that it is in the slope-intercept form. In the slope-intercept form, the coefficient of y is 1 and the rest are moved to the left hand side of the equation.
[tex]\textcolor{steelblue}{\text{Slope-intercept form}}[/tex]
y= mx +c, where m is the slope and c is the y-interceptGiven equation: 6x +3y= -12
Let's leave the y term on the left of the equation and bring the rest to the right.
3y= -6x -12
To ensure that the coefficient of y is 1, divide both sides by 3.
y= -2x -4
The equation is now in the slope-intercept form.
The slope is the coefficient of x (the number that comes before x), thus the slope is -2. The y-intercept is -4.
The measure of an angle is 63.9. What is the measure of its supplementary angle?
Answer:
116.1
Step-by-step explanation:
supplementary-180
complimentary-90
180-63.9= 116.1
Bryan decided to ride his bike along a new route home from school to avoid some construction. Before leaving school, he estimated how long the route would take. When Bryan arrived home, he saw the ride had taken him 16 minutes. His estimate had been 25% more than that. How long had Bryan estimated it would take to ride home from school?
Work Shown:
Estimate = 1.25*(actual time)
Estimate = 1.25*(16)
Estimate = 20
Bryan estimated it would take 20 minutes.
Note: The multiplier 1.25 represents an increase of 25%
What is 3(b+8) in Distributive Property
Answer:
3b + 24
Step-by-step explanation:
3*b=3b
3*8=24
therefore the answer is 3b+24
Hope this helps:)...if not then sorry for wasting your time and may God bless you:)
14. How much interest will you earn if depositing $25,000 to grow continuously at 9%
interest rate for 12 years?
Answer:
Step-by-step explanation:
i think this is the answer
The question is in the attachment.
Answer:
0.0816
Step-by-step explanation:
Given:
Total number of students = 5000Number of students taking an online class = 1200Number of students prefer watching baseball to football = 1700Let O = Students taking an online class
Let B = Students prefer watching baseball to football
Therefore,
P(O) = 1200/5000 = 0.24
P(B) = 1700/5000 = 0.34
If events O and B are independent,
⇒ P(O ∩ B) = P(O) · P(B)
= 0.24 × 0.34
= 0.0816
What is the distance between the points (10,6) and (1,4)? If necessary, round
your answer to two decimal places.
A. 9.22 units
B. 7.81 units
C. 61 units
D. 85 units
Distance:-
[tex]\\ \rm\Rrightarrow \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt{(10-1)^2+(6-4)^2}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt{9^2+2^2}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt{81+4}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt{85}[/tex]
[tex]\\ \rm\Rrightarrow 9.22units[/tex]
What fraction is equivalent to four tenths and has a denominator of 100?
Answer:
[tex]\frac{40}{100}[/tex]
Step-by-step explanation:
You can multiply on the upper and bottom part by the same number without changing the fraction so [tex]\frac{4}{10}=\frac{4\cdot 10}{10\cdot 10}=\frac{40}{100}[/tex]
Please help me!!
If there is an equation let's say
15y = 6/x
Can you multiply 15y by 6
to get 15/6y=x
Or do you need to multiply by x and divide by 15
Answer:
Yes Girlie, you need to multiply by x and divide by 15!!!!!!!!!
Step-by-step explanation:
Mai thinks Tyler’s answer is incorrect. She says, “If expressions are equivalent then they are equal for any value of the variable. Why don’t you try to substitute the same value for in all the equations and see where they are not equal?” 1. Find the step where Tyler made an error. 2. Explain what he did wrong. 3. Correct Tyler’s work.
Mai's statement implies that Tyler's steps do not form an equivalent expression
Tyler's error is in step 3.
How to determine Tyler's error?Tyler's steps of solving the expression is given as:
9 - 4 ( 5x - 6 )9 + (-4) ( 5x + -6 )9 + -20x + -63 - 20xTyler's error is in step 3.
This is so because:
9 + (-4) ( 5x + -6 ) in step 2 is not equivalent to 9 + -20x + -6 in step 3
In actual sense, Tyler's error is in multiplying the (-4) and (-6)
The correct solution is as follows:
9 - 4 ( 5x - 6 )9 + (-4) ( 5x + -6 )9 + -20x +2433 - 20xRead more about equivalent expressions at:
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Find the area of a right triangle with side lengths 12 cm, 35 cm, and 37cm
Answer:
210 cm²
Step-by-step explanation:
The area of the triangle can be found using the triangle area formula:
A = 1/2bh
A = 1/2(12 cm)(35 cm) = 210 cm²
_____
Additional comment
The legs (short sides) of the right triangle are effectively the base and height of the triangle.
The area of the right angle triangle is 210 square centimeters if the side lengths are 12 cm, 35 cm, and 37cm
What is a right-angle triangle?It is defined as a triangle in which one angle is 90 degrees and the other two angles are acute angles. In a right-angled triangle, the name of the sides are hypotenuse, perpendicular, and base.
We have a right angle triangle with side lengths of 12cm, 35cm, and 36cm
Here the base length b = 12 cm
The height of the right angle triangle h = 35 cm
We know the formula for the area of the right angle triangle is given by:
[tex]\rm A = \frac{1}{2} bh[/tex]
[tex]\rm A = \frac{1}{2} \times 12\times 35[/tex]
A = 210 square centimeters
Thus, the area of the right angle triangle is 210 square centimeters if the side lengths are 12 cm, 35 cm, and 37cm
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Fill in the missing numbers in the sequence: 0.1, 0.25, 0.4, __, 0.7 ?
The area of the triangle below is 3/40
square meters. What is the length of the base? Express your answer as a fraction in simplest form.
Answer:
b = 3/4
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh
3/ 40 = 1/2 b ( 1/5)
Multiply
3/40 = 1/10 b
Multiply each side by 10
10 *3/40 = 10* 1/10 b
3/4 = b
what is the area of a triangle with a base with a length of 3 1/2 inches and a height of 3 inches
Answer: 5.25 square inches
Step-by-step explanation:
A=(1/2)bh=(1/2)(3.5)(3)=5.25
8. Charlotte is given the equation 3x - 4y = 12. She needs to create a graph of the equation, but
isn't sure how since she is only familiar with
graphing from slope-intercept form. Devise a plan
to help Charlotte graph the equation in the space
below, and then draw your graphed line.
Answer/Step-by-step explanation:
Note:
Graphing From An Equation:
Equation are frequently written in slope-intercept form { y = mx+b}.
Which "m" represents the slope and "b" represents the y-intercept.
Solutions and Equation:
Solutions to linear equations contain any points located on the graphed line.
Ordered Pair = Solution to an equation if it's values are substituted in the equation which makes it true
Solve:
{x = 0 } 3(0) - 4y = 12
-4y = 12 (0, -3 )
-4y/-4 = 12/-4
y = -3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
{y = 0} 3x-4(0) =12
3x = 12 (4,0)
3x/3 = 12/3
x = 4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~Lenvy~
Please help with both questions
Refer to the attachment for your answer, just remember the fact that as x is an integer in 2nd question and x > 3.66... so x's smallest value will just be 4, and in 1st question you can use the number line for a better understanding
In this lab, you observed how pollutants affected the ________
of water. You also modeled and observed how pollution affected freshwater sources, including surface water and the water in the _________
Answer: PH, ground
Step-by-step explanation: edge2022
In this lab, you observed how pollutants affected the" PH "of water. You also modeled and observed how pollution affected freshwater sources, including surface water and the water in the" ground "
What is water pollution?
Water pollution can be defined as the abnormal accumulation of strange elements in the water with harmful consequences to natural ecosystems.
Water pollution involves all the possible ways in which any water body can be contaminated with harmful elements.
The source of water pollution is human activities, producing the biggest damage to natural ecosystems.
Contaminating elements might be either gasses, solid material, or liquid material Such as Chemical elements, microbiota, heavy metals, and sediments affect all forms of life.
You can learn more about water pollution at
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i need help
will give 30 points
Answer:
Step-by-step explanation:
What is the correct answer for this?
Answer:
55.5 cubic yards
Step-by-step explanation:
Here,
Length ( l ) = 5 yd
Base ( b ) = 3.7 yd
Height ( h ) = 3 yd
To find : Volume
This shape is a cuboild.
Formula : -
Volume of cuboild = lbh
Volume of cuboild
= 3 x 5 x 3.7
= 55.5 cubic yards
[tex] \huge\fbox\orange{ANSWER} [/tex]
[tex] \mathsf \purple{v = l \times w \times h}[/tex]
[tex] \mathsf \pink{v = 5 \times 3.7 \times 3}[/tex]
[tex] \mathsf \purple{v = 55.5 {yd}^{3} }[/tex]
55.5 cubic yards
Find the solution of the system of equations.
x+2y=9
-6x+4y=-46
Answer:
x=-3.5 and y=6.25
Step-by-step explanation:
x+2y=9
x=9-2y
-6(9-2y)+4y=46
-54+12y+4y=46
16y-54=46
16y = 100
y = 100/16 = 50/8 = 25/4 = 6.25
x+2(6.25)=9
x+12.5=9
x= -3.5
What is the slope for a line that is perpendicular to the line x = -6?
Answer:
There is not a slope perpendicular to the lie x = -6
Step-by-step explanation:
In this equation, you are given a line, x = -6.
This is in fact a line with an undefined slope. The slope for a perpendicular intersection is the opposite reciprocal of the slope.
Eg. If you have the line y = 2x
The reciprocal is y = 1/2x, the opposite means negative
So the slope that would intersect this line perpendicularly is y = -1/2x.
There is an undefined slope in this, therefore, you cannot find the slope for a line perpendicular to x = -6.
If it were an option, I would choose "no slope"
The dot plot below shows the results of a recent patient survey at Brookwood Medical Center. Use
the data to answer the following questions. If necessary, round your answer to the nearest tenth.
Find the mean and median scores.
Answer:
the median is 3.5
Step-by-step explanation:
there are 27 dots 27/2=13.5 therefore the answer is the 13th dot and a half 3.5 :) (i dont know for sure but i think the mean is 3)
The mean is 3 and the median is 3 for this list of numbers.
From the dot pot,
Arrange the number in order:
1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5
Now,
Mean = Average of all the values.
Median = Midvalue of the number.
Now,
There are 30 numbers in the list, so the mean is:
Mean = 90/30 = 3
To find the median, we need to find the middle number.
Since there are an even number of numbers in the list, we take the average of the two middle numbers:
The middle two numbers are both 3, so the median is:
Median = (3 + 3)/2 = 3
Therefore,
The mean is 3 and the median is 3 for this list of numbers.
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