Solve 3|x - 61 = 12.
Construct the 90% confidence interval for the proportion of students at the college who have completed their required English 101 course. Enter your answers as decimals (not percents) accurate to three decimal places. The Confidence Interval is
Answer:
The confidence interval has an lower limit of [tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = \pi - 1.645\sqrt{\frac{\pi(1-\pi)}{n}}[/tex] and an upper limit of [tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = \pi + 1.645\sqrt{\frac{\pi(1-\pi)}{n}}[/tex], in which [tex]\pi[/tex] is the sample proportion and [tex]n[/tex] is the size of the sample.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = \pi - 1.645\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = \pi + 1.645\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The confidence interval has an lower limit of [tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = \pi - 1.645\sqrt{\frac{\pi(1-\pi)}{n}}[/tex] and an upper limit of [tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = \pi + 1.645\sqrt{\frac{\pi(1-\pi)}{n}}[/tex], in which [tex]\pi[/tex] is the sample proportion and [tex]n[/tex] is the size of the sample.
true or false m angle 5 is greater than m angle 8
Answer:
True
Step-by-step explanation:
You can see that Angle 5 is slightly greater than 90°, so it is obtuse
Angle 8 is less than 90°, and is acute
Since obtuse angles are larger than acute angles, Angle 5 is greater than Angle 8.
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help me this question
x2 + 5x + 9.
Find the equation of the axis of symmetry for the parabola y =
Answer:
x = -5/2
Step-by-step explanation:
From the quadratic equation
the axis of symmetry for quadratics of the form
y = ax² + bx + c is
x = -b/2a
x² + 5x + 9
x = -5/2
Please help answer these math riddles
Answer:
Challenge B is 1.827
Step-by-step explanation:
I need more letters to submit this.
What is the probability that Omar will get to drive the car after the first roll?
Answer:
1/6
Step-by-step explanation:
For Omar to drive, he has to get a six when a die is rolled ;
The probability that Omar will get to drive his car is :
Required outcome = (6) = 1
Total possible outcomes = (1,2,3,4,5,6)
P(rolling a 6) = required outcome / Total possible outcomes
P(rolling a 6) = 1/6
Probability of Omar driving his car is 1/6
a map shows that the top of a hill is 200m above sea level and the bottom of a lagoon is 15m below sea level. express these distancesat a distances from sea level and what is difference between the two heights
Answer:
200 m
-15 m
215 m
Step-by-step explanation:
Given :
Top of hill = 200 m above sea level ; height of hill top is positive 200m = 200 m
Bottom of lagoon = 15m *below sea level ; bottom of lagoon = - 15m
We have related the height of the two points with respect to sea level ; points above sea level are represented as positive ; points below are represented as negative.
Difference between the two heights :
Hill top - bottom of lagoon :
200 m - (-15) m
200 m + 15 m
215 m
Difference between the heights is 215 m
Construct a data set that has the given statistics.
n = 7
x = 12
S = 0
Answer:
The desired data-set is: {12,12,12,12,12,12,12}
Step-by-step explanation:
n = 7
Data set of 7 elements.
x = 12
Mean of 12
S = 0
Standard deviation of 0.
Desired data-set:
Since the desired standard deviation is 0, all the elements in the data-set will be the same. Since the mean is 12, all elements is 12. 7 elements.
The desired data-set is: {12,12,12,12,12,12,12}
A teacher offers 8 extra credit assignments.what is the domain of this graph
A 200-liter tank initially full of water develops a leak at the bottom. Given that 20% of the water leaks out in the first 5 minutes, find the amount of water left in the tank 10 minutes after the leak develops if the water drains off at a rate that is proportional to the amount of water present.
Answer:
127.53 liters left after 10 minutes
Step-by-step explanation:
Let
[tex]A \to Amount[/tex]
[tex]t \to time[/tex]
Given
[tex]A(0) = 200[/tex] --- initial
[tex]A(5) = 200 * (1 - 20\%) = 160[/tex] --- the amount left, after 5 minutes
Required
[tex]A(10)[/tex] --- amount left after 5 minutes
To do this, we make use of:
[tex]A(t) = A(0) * e^{kt}[/tex]
[tex]A(5) = 160[/tex] implies that:
[tex]160 = 200 * e^{k*5}[/tex]
Divide both sides by 200
[tex]0.80 = e^{k*5}[/tex]
Take natural logarithm of both sides
[tex]\ln(0.80) = \ln(e^{k*5})[/tex]
[tex]\ln(0.80) = \ln(e^{5k})[/tex]
[tex]\ln(0.80) = 5k\ln(e)[/tex]
So, we have:
[tex]-0.223 = 5k[/tex]
Divide by 5
[tex]k = -0.045[/tex]
So, the function is:
[tex]A(t) = A(0) * e^{kt}[/tex]
[tex]A(t) = 200 * e^{-0.045t}[/tex]
The amount after 10 minutes is:
[tex]A(10) = 200 * e^{-0.045*10}[/tex]
[tex]A(10) = 200 * e^{-0.45}[/tex]
[tex]A(10) = 127.53[/tex]
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On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these
flowers rapidly increases as the trees blossom.
The relationship between the elapsed time t, in days, since the beginning of spring, and the number of locusts,
L(t), is modeled by the following function:
5.9
L(t) = 750.
(1)
Complete the following sentence about the rate of change in the locust population.
2
The population of locusts gains of its size every
3
days.
Answer:
5.9
Answer directly from Khan
PLEASE HELP ASAP !!! WILL MARK BRAINLIEST TO WHOEVER ANSWERS CORRECTLY
Answer:
See below.
Step-by-step explanation:
Alternate Interior Angles - 1
Alternate Exterior Angles - 2
Corresponding Angles - 4
Same-side Exterior Angles - 5
Same-side Interior Angles - 3
Answer:38292
A
Step-by-step explanation:w
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Consider the sequence:
1000,-500,250,-125
What is the 7th number in the sequence? Write your answer as a fraction
Answer:
The 7th number in the sequence is [tex]\frac{125}{8}[/tex]
Step-by-step explanation:
Geometric sequence:
In a geometric sequence, the quotient between consecutive terms is always the same, called common ratio.
The nth term of a geometric sequence is given by:
[tex]A_n = A(0)r^{n-1}[/tex]
In which A(0) is the first term and r is the common ratio.
1000,-500,250,-125
This means that [tex]A(0) = 1000, r = -\frac{500}{1000} = -\frac{1}{2}[/tex]
So
[tex]A_n = A(0)r^{n-1}[/tex]
[tex]A_n = 1000(-\frac{1}{2})^{n-1}[/tex]
What is the 7th number in the sequence?
This is [tex]A_7[/tex]. So
[tex]A_7 = 1000(-\frac{1}{2})^{7-1} = \frac{1000}{64} = \frac{125}{8}[/tex]
The 7th number in the sequence is [tex]\frac{125}{8}[/tex]
If one point on a graph is (5,5) and the slope of the line is -4, write the equation of the line in slope-
intercept form.
Answer:
y = -4x + 25
Step-by-step explanation:
[tex](x_1, y_1) = (5, 5) \ ; \ slope ,\ m = -4[/tex]
Equation of line :
[tex](y - y_1) = m(x - x_1)[/tex]
[tex](y - 5) = -4(x-5)\\y - 5 = -4x + 20\\y = -4x +20 + 5\\y = -4x + 25[/tex]
Answer:
0=4x+y-5
Step-by-step explanation:
slope(m)=-4
y-intercept(c)=5
now, the equation joining the straight line satisfy the equation,
y=mx+c
or, y= -4x+5
or, 4x+y-5=0
or, 0=4x+y-5
it is the required equation.
there are 6 glass bottles and eight plastic bottles on a rack. I f one is chosen at random, what is the probability of picking a glass bottle? Which simulation can be used to represent this situation
Answer:
6:8
Step-by-step explanation:
6 is the ratio of glass bottles and 8 is the plastic or you can put 3:4 because you divide the number b 2
Wll mark Brainlest helllppoooooo
Answer:
Step-by-step explanation:
f(x) = (2x^2 + 1)
( f(3 + h) - f(3) ) / h
f(3 + h) = 2(3 + h)^2 + 1)
f(3 + h) = 2(9 + 6h + h^2) + 1
f(3 + h) = 18 + 12h + 2h^2 + 1
f(3 + h) = 19 + 12h +2h^2
f(3) = 2*(3^2) + 1
f(3) = 2(9) + 1
f(3) = 19
f(3 + h) - f(3) = 2h + 2h^2 The 19s cancel out
f(3 + h) - f(3) = 2h(1 + h^2)
( f(3 + h) + f(3) ) / h = 2h ( 1 + h^2) / h = 2 ( 1 + h^2)
Answer:
Step-by-step explanation:
Which expression is equivalent to
3/14x + (- 1) + (- 4) – 2/7x?
Choose the correct answer below.
A. -5 1/14x - 5
B. 5 1/14x + 5
C. -1/14x - 5
D. 5/14x - 5
Answer:
A and b
Step-by-step explanation: Because ....
someone asap
A small factory has 3 machines for producing protractors. The high speed machines produces 61% the protractors but 6% of its output is defective. The medium speed machine produces 24% of the protractors, of which 4%o are defective. The low speed machine, which has a defective rate of 2% produces the remainder.
{a) Draw a tree diagram.
(b) What is the probability of a protractor not being defective given it came from a low speed machine?
(c). Knowing that a protractor is defective, what ls the probability it came from the high speed machine?
Teresa received a $90 gift card for a coffee store. she used it in buying some coffee that cost her $8.21 per pound. After buying the coffee, she had $65.37 left on her card. how many pounds of coffee did she buy?
Answer:
3 Pounds of Coffee
Step-by-step explanation:
To find out how much she spent on the pounds of coffee, you would have to takeaway $65.37 away from the total of $90 which will give you $24.63, which is how much she has spent on the coffee. To find out how many pounds of coffee she bought, you would have to divide $24.63 by $8.21 giving you 3, which is how many pounds of coffee Teresa bought.
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HELP!! Create a system of equations with the solution (-4, 1)
9514 1404 393
Answer:
x -y = -5
3x +y = -11
Step-by-step explanation:
We assume you want two linear equations. Since you know a point on each line, the only thing you need to choose is the slope of the two lines through that point. We can make the slopes be +1 and -3, for example. Then the point-slope equations are ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -1 = +1(x +4)
y -1 = -3(x +4)
We can use these equations "as is", or put them in whatever form you like. I personally prefer "standard form:" ax+by=c.
First equation:
y -1 = x +4 . . . . . . eliminate parentheses
-5 = x -y . . . . . . . keep positive x term, put x and y together, separate from the constant
x - y = -5 . . . . . . standard form
Second equation:
y -1 = -3x -12 . . . . eliminate parentheses
3x +y = -11 . . . . . . add 3x+1 to both sides
__
A system of equations with solution (-4, 1) is ...
x - y = -53x + y = -11Find the volume of the prism.
Answer:
Its A.
Step-by-step explanation:
remember its rectangle 1 + rectange 2.Once i did that i have seen the total volume must be greater then answer B
so it must be a
Help me please if you can't don't touch it
Answer:
The correct answer is A
Step-by-step explanation:
AD=7, BD=3, DE=6. Find BC
Answer:
the answer to this is 10 i think sorry if it is wrong
Step-by-step explanation:
The triangles are similar and the measure of BC = 60/7 units
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be ΔABC
Let the second triangle be ΔADE
Now , ΔABC and ΔADE are similar triangles
where corresponding sides of similar triangles are in the same ratio
So , AD / AB = DE / BC
On simplifying , we get
7 / 10 = 6 / BC
Multiply by BC on both sides , we get
BC ( 7/10 ) = 6
Multiply by 10 on both sides , we get
7BC = 60
Divide by 7 on both sides , we get
BC = 60/7
Hence , the measure of BC = 60/7 units
To learn more about similar triangles click :
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which number represents 4%
Answer:
4
Step-by-step explanation:
What is the value of k?
9514 1404 393
Answer:
k = 10
Step-by-step explanation:
The exterior angle is equal to the sum of the remote interior angles.
115° = (4k +5)° +(6k +10)°
115 = 10k +15 . . . . . . . . . . . divide by °, simplify
100 = 10k . . . . . . . . . . . . subtract 15
10 = k . . . . . . . . . . . . . . divide by 10
Jill went on 8 hikes. The hikes were 6 miles, 4 miles, 2 miles, 3 miles, 7 miles, 5 miles, and 1 mile. What was the range of the lengths of Jill's hikes? :)
Answer:
range is 6
Step-by-step explanation:
The smallest number in this data set is 1 mile, the largest is 7 miles
the range is the difference between the biggest and smallest number so 7-1 = 6. The range is 6
Find the perimeter of the figure.
graph the line with intercept 6 and slope
[tex] - \frac{3}{2} [/tex]
Given:
The y-intercept of a line = 6
The slope of the line = [tex]-\dfrac{3}{2}[/tex]
To find:
The graph of the given line.
Solution:
The slope intercept form of a line is:
[tex]y=mx+b[/tex]
Where, m is the slope and b is the y-intercept.
Putting [tex]m=-\dfrac{3}{2}[/tex] and [tex]b=6[/tex] in the above equation, we get
[tex]y=-\dfrac{3}{2}x+6[/tex]
At [tex]x=0[/tex],
[tex]y=-\dfrac{3}{2}(0)+6[/tex]
[tex]y=0+6[/tex]
[tex]y=6[/tex]
At [tex]x=2[/tex],
[tex]y=-\dfrac{3}{2}(2)+6[/tex]
[tex]y=-3+6[/tex]
[tex]y=3[/tex]
Plot these two points (0,6) and (2,3) on a coordinate plane and connect them by a straight line to get the graph of the required line.
The required graph is shown below.
Last year, nine employees of an electronics company retired. Their ages at retirement are listed below in years. Find the mean retirement age.56 65 62 53 68 58 65 52 56
Answer:
59.44
Step-by-step explanation:
Nine employees If an electronic company retired last year
The retirement ages are listed below
56, 65, 62, 53, 68, 58, 65, 52, 56
The mean retirement age can be calculated as follows
= 56+65+62+53+68+58+65+52+56/9
= 535/9
= 59.44
Hence the mean retirement age is 59.44
