The 68.26% confidence interval for the mean of the population, using the z-distribution, is given as follows:
(15.88 ounces, 16.12 ounces).
What is a z-distribution confidence interval?The bounds of a z-distribution confidence interval are presented as follows:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which the parameters are given by:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value of the z-distribution.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population. -> as the z-distribution is used when the population standard deviation is known.The confidence level is of 68.26%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.6826}{2} = 0.8413[/tex], so the critical value is z = 1.
The values of the remaining parameters are given as follows:
[tex]\overline{x} = 16, \sigma = 1.4, n = 144[/tex]
Hence the lower bound of the interval is obtained as follows:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 16 - \frac{1.4}{\sqrt{144}} = 15.88[/tex]
The upper bound of the interval is obtained as follows:
[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 16 + \frac{1.4}{\sqrt{144}} = 16.12[/tex]
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Use the annuity formula to determine the accumulated amount in the annuity if $80 is invested for 40 years at 6.0% compounded semiannually .
The accumulated amount in the annuity if $80 is invested for 40 years at 6% is $25,709.04.
What is the accumulated amount?An annuity is when a series of payment is made over a specified period of time. An annuity can either be an ordinary annuity or a beginning annuity. An ordinary annuity is when the series of payment is made at the end of the period. A beginning annuity is when the annuity payment is made at the beginning of the period.
In this question, the annuity would last for 40 years and payments would be made twice a year.
The formula that can be used to determine the accumulated amount is:
Accumulated amount = annuity factor x payment
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = annual interest rate / number of compounding = 6% / 2 = 3%n = number of payment period = number of years x number of compounding = 2 x 40 =80 yearsAccumulated amount = $80 x [{(1.03^80) - 1} / 0.03]
Accumulated amount = $80 x 321.36302
Accumulated amount = $25,709.04
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The length of the fifth rectangular slate is 16 inches. If its length and width are each decreased by 2 inches, the area will be 56 square inches less than the original area. What is the width of the original rectangular slate?
The width of the original rectangular slate is 14 inches.
What is the width?A rectangle is an object that has four sides. The opposite sides are of equal length. A rectangle has two diagonals that are of equal length that bisect each other at right angles.
The area of a rectangle = length x width
Area of the new rectangular slate = (16 - 2) x (w - 2) = (16 x w) - 56
Area of the new rectangular slate = 14 x (w - 2) = 16w - 56
Area of the new rectangular slate = 14w - 28 = 16w - 56
In order to determine the value of w, take the following steps:
Combine similar terms together: 56 - 28 = 16w - 14w
Add similar terms together: 28 = 2w
Divide both sides of the equation by 2 : w = 28 / 2
w = 14
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For every dozen bagels you buy, the cost increases $15. Which equation represents the cost, y, and the number of bagels, x?
a. y=1.25 + x
b. y=15x
c. x=15y
d. y=1.25x
The equation that represents the cost, y, and the number of bagels, x is D. y=1.25x
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It should be noted that 1 dozen = 12
The equation the represents the information will be:
y = (15/12) × x
y = 1.25 × x
y = 1.25x
where x = number of bagels
The equation is y = 1.2x.
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Please help! How do u get this?
The component form of the vector that translates C to D is <7, -3>
How to determine the component form of the vector?A translation is a movement in a straight line.
In order to determine the component form of the vector that translates C to D, we have to subtract the coordinate values of point C from the coordinate values of the image C:
(x, y) = D - C
The movement from C to D on the x-axis is 7 units to the right (positive 7) while movement on the y-axis is 3 units down (negative -3). Thus:
(x, y) = (7, -3)
In vector form, <x, y> = <7, -3>
Therefore, the vector that translates C to D is <7, -3>
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Find another point on a line that includes the points (-5, 4) and (4, 1).
The other points (7.3, 2.2) are on a line that includes points (-5, 4) and (4, 1).
What is the equation of a line?
The equation of a line is written as axe + by + c = 0, which is its conventional form. In this equation, the variables x and y are the constant term, while the coefficients a and b are the coefficients. It is a first-order equation with the variables x and y.
Slope using the formula:
[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
We have two points, (-5, 4) and (4, 1).
m = (1 - 4) ÷ (4 - (-5))
m = −1/3
m = -0.3
Line Equations with Slope : y - y1 = m(x - x1)
Using the coordinates of one of the points on the line, insert the values in the x1 and y1 spots to get an equation of a line in point-slope form.
Let's use a point from the original example above (4, 1). and the slope we calculated as -0.3. Put those values in the point-slope format to get an equation of that line in the point-slope form:
y - 1 = -0.3(x - 4)
y = -0.3x + 2.2
Using the equation y = -0.3x + 2.2, set x=0 to find the y-intercept.
y = -0.3(0) + 2.2
y = 2.2
The y-intercept is 2.2
Using the equation y = -0.3x + 2.2, set y=0 to find the x-intercept.
0 = 3x - 6
0 = -0.3x + 2.2
0.3x = 2.2
x = 7.3
The x-intercept is 7.3.
Hence, the other points (7.3, 2.2) are on a line that includes the points (-5, 4) and (4, 1).
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Which pairs of fractions include a fraction equivalent to 1/2 and a fraction equivalent to 3/4 help me PLEASE
Answer:
4/8 and 8/16
Step-by-step explanation:
Multiply 1/2 and 3/4 to find a common fraction between them (4/8) then multiply that fraction by any number greater than 1 to find another fraction equivalent
Use the number line below, where RS
I need help with this please
Answer:
y = 6RS = 39ST = 38Step-by-step explanation:
You have segment RT of length 77 with point S on it dividing it into segments RS=6y+3 and ST=5y+8. You want to know the value of y and the lengths of segments RS and ST.
Segment sum theoremThe segment sum theorem tells you the whole is the sum of the parts:
RS +ST = RT
(6y +3) +(5y +8) = 77 . . . . . use given values
Solution11y +11 = 77 . . . . . . . . . . . . collect terms
y +1 = 7 . . . . . . . . . . . . . . . divide by 11
y = 6 . . . . . . . . . . . . . . . . . subtract 1
The lengths of the parts are ...
RS = 6y +3 = 6(6) +3 = 39
ST = 5y +8 = 5(6) +8 = 38
what is the point slope for the top and slope intercept for the bottom? TIA
Answer:
It looke like the point given is (1,2) and the slope is 3
Point slope form: y - 2 = 3(x -1)
Slope Intercept form: y = [tex]\frac{-1}{3}[/tex]x + 1
Step-by-step explanation:
Point slope As they name implies, you need a point and a slope. The picture is a little hard to read, but it looks like the point plotted is (1,2) The slope is the change in y over the change in x. It looks like from that point to get back on the line only using horizontal and vertical moves, we would move up three and 1 to the right to get back on the line at point (2,5).
The point slope form of a line is:
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex]) Plug in 2 for [tex]y_{1}[/tex] and 1 for [tex]x_{1}[/tex] amd 3 for m
y = 2 = 3( (x-1)
Slope intercept form: As the names implies we need a slope and a yi-intercept.
The slope is [tex]\frac{-1}{3}[/tex]. Select a point on the line. If you can only move veritacl and horizontal. You would move down 1 unit and three units to the right. The y intercept is where the line crosses the y axis. In this case 1
y = [tex]\frac{-1}{3} x + 1[/tex]
The following angles are supplementary to each other.
m∠A = (4x + 30)° and m∠B = (2x − 30)°
Determine x.
15
20
30
60
According to the sum of the given supplementary angles, we find out that the value of x is 30.
It is given that ∠A and ∠B are supplementary where,
∠A = (4x + 30)° and,
∠B = (2x - 30)°
We have to find out the value of x.
We know that two supplementary angles add up to 180°.
Since ∠A and ∠B are supplementary angles, therefore
∠A + ∠B = 180°
=> (4x + 30) + (2x - 30) = 180°
=> 6x = 180°
=> x = 30
Thus, for the given supplementary angles, the value of x is 30.
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**According to the sum of the given supplementary angles, we find out that the value of x is 30.
It is given that ∠A and ∠B are supplementary where,
∠A = (4x + 30)° and,
∠B = (2x - 30)°
We have to find out the value of x.
We know that two supplementary angles add up to 180°.
Since ∠A and ∠B are supplementary angles, therefore
∠A + ∠B = 180°
=> (4x + 30) + (2x - 30) = 180°
=> 6x = 180°
=> x = 30 **
Need soon pls! Super easy
Answer:
choose 2nd option
Step-by-step explanation:
2. Which choice best describes this function? *
exponential growth
O exponential decay
O quadratic growth
O quadratic decay
Which variables would the scatter plot at the right be most likely to represent?
p1
Question 2 options:
The number of people at a concert and the total concession sales
The number of guests at a hotel and the total water consumption
The number of siblings a person has and the person's GPA
The total number of miles driven and the total gallons of gas used
The scatter plot shows the number of days since several people filled their cars with gas and the gallons of gas in their tank. Which is the most reasonable estimate of the gallons of gas in a tank if it has been 3 days since filling up?
Question 1 options:
10 gallons
13 gallons
23 gallons
17 gallons
1) The scatter plot at the right most likely represents the number of siblings a person has and the person’s GPA.
2) The most reasonable estimate of the gallons of gas in a tank if it has been 3 days since filling up is; 17 gallons
How to Interpret a Scatter Plot Diagram?1) Scatter plots are defined as the graphs that present the particular relationship between two variables in a data-set.
A scatter plot is also defined as a chart type that is usually used to observe and visually display the relationship between variables.
From the given scatter plot, we can say that the scatter plot at the right would most likely be used to represent the number of siblings a person has and the person’s GPA.
2) From the given scatter plot, we can see that the x-axis shows the number of days left since filling up while the y-axis represents the gallons of gas.
Now, we want to find out the most reasonable estimate of the gallons of gas in a tank if it has been 3 days since filling up. We will trace 3 on the x-axis and the corresponding value on the y-axis would be approximately 17 gallons.
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can someone pls help me i don’t get this
A weightlifter lifts
72
k
g
. Which of the following weights is the same as
72
k
g
?
(
1
k
g
=
1
,
000
g
)
720 g
720,000 g
72,000 g
30,000 g
Answer:
I think 72,000 because since the weightlifter is lifting 72 and it is kg. It is turned into grams. multiplied by 1000 so 72000
Mae has $215 in her account and withdraws $120 one time. Each month her balance is below $100, she pays a $7 fee. Write an equation to express her balance for the next x months, if she makes no deposits or withdrawals .
Answer: 930$ and the expression is 1000$ - 70$ = 930$
Step-by-step explanation:
if she has under 100 dollars in her bank account every month for 10 months therefore multiplying it by 10 giving you 1000 but we cant forget about the 7$ monthly fee. 7 times 10 = 70 1000- 70 = 930$
Answer:
Step-by-step explanation:
It takes 1 3/4 of a pint of paint
to paint one wall of a room
and 1 4/5 of a pint of paint for
the second wall. How
many pints of paint are
used on the two walls?
3 11/20
Step-by-step explanation:
1 3/4+1 4/5=
7/4+9/5=
7/4x5/5=35/20
9/5x4/4=36/20
35/20+36/20=71/20=3 11/20
(2a^2 +a + 3) divided by (a - 1)
The value of the equation (2a^2 +a + 3) divided by (a - 1) is 2a + 3.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, the equation is illustrated as:
(2a² +a - 3) divided by (a - 1). This will be
(2a² +a - 3) / (a - 1)
It should be noted that (2a² +a + 3) will be:
(2a² +a + 3)
= 2a² - 2a + 3a - 3
= 2a(a - 1) + 3(a - 1)
= (2a + 3)(a - 1)
This will be:
= (2a + 3)(a - 1) / (a - 1)
= 2a + 3
The value is 2a + 3.
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Complete question
(2a^2 +a - 3) divided by (a - 1)
. What is the present value of an annuity that pays $100 per month for 10 years if money worth 6%
compounded monthly?
The present value of an annuity is $736.01
We know that the formula for Present Value of Annuity:
PV = P * [1 - (1 + r)^(-n)]/r
where, PV = present value of an ordinary annuity
P = value of each payment
r = interest rate per period
n = number of periods
From given data:
P = $100, n = 10 and r = 0.06
So, the present value would be,
PV = 100 * [1 - (1 + 0.06)^(-10)]/0.06
PV = 100 * 7.3601
PV = $736.01
Therefore, the present value of an annuity is $736.01
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Sari put $1230 in a savings account at a simple interest rate of 4.5% per year. Avi put $1105 in a savings account at a simple interest rate of 5.5% per year. Who will have earned more interest after 4 years? How much more?
Answer:
Avi
$21.61
Step-by-step explanation:
I = Prt
Sari: I = Prt = $1230 × 0.045 × 4 = $221.40
Avi: I = Prt = $1105 × 0.055 × 4 = $243.01
$243.01 - $221.40 = $21.61
Answer:
Avi
$21.61
PLS HELP! 50 points
Brett and Julian sign up to run in the Memorial Day race in their town. There are two different events at this race, a 5k and a 10k. Brett signed up for the 5k and Julian signed up for the 10k. Think of when both Brett and Juan would have finished 3/5 of their races. How many kilometers has each person run at this point?
The number of kilometers that Brett and Julian would have run at the 3 / 5 point are:
Brett - 3kmJulian - 6 km How to find the number of kilometers?Brett is running the 5k race at the Memorial Day race which means that when he runs 3 / 5 of the race, he would have ran a total of :
= Distance on Brett's race x Proportion ran
= 5 x 3 / 5
= 15 / 3
= 3 km
Julian on the other hand, is in the 10 k race which means that when they get to 3 / 5 of the race, they would have ran:
= 10 x 3 / 5
= 30 / 5
= 6 km
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Consider a collection of envelopes consisting of two red envelopes three blue envelopes one green envelope and one yellow envelope if two envelopes are selected at random with replacement determine the probability that at least one envelope is red envelope
The probability that at least one envelope is red envelope is 2/7.
Given:
A collection of envelopes consisting of two red envelopes three blue envelopes one green envelope and one yellow envelope if two envelopes are selected at random with replacement.
Total = 2 + 3 + 1 + 1
= 5 + 2
= 7
Number of possible outcomes = 7
Number of favorable outcomes = 2
Probability that at least one envelope is red envelope is = 2/7
= 0.2857
Therefore the probability that at least one envelope is red envelope is 2/7.
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A manufacturer knows that their items have a normally distributed length, with a mean of 13.6 inches, and standard deviation of 2.4 inches. If one item is chosen at random, what is the probability that it is less than 13.1 inches long?
If one item is chosen at random, the probability that it is less than 13.1 inches long is equal to 0.4176.
How to determine the probability?First of all, we would determine the z-score of this data set. Mathematically, the z-score of a given sample score in a normal distribution can be calculated by using this formula:
Z-score = (x - μ)/σ
Where:
x represents the sample score.σ represents the standard deviation.μ represents the mean score.Substituting the given parameters into the formula, we have;
Z-score, z = (13.1 - 13.6)/(2.4)
Z-score, z = -0.5/2.4
Z-score, z = -0.208
If one item is chosen randomly, the probability that it would be less than 13.1 inches long is given by this mathematical expression:
P(x < 13.1) = P(z < -0.208)
P(z < -0.2083) = 0.4176.
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From the chart, estimate (roughly) the number of transistors per IC in 2012. Using your estimate and Moore's Law, what would you predict the number of transistors per IC to be in 2040?
The estimates for the number of transistors per IC, using an exponential function, are given as follows:
2012: 4,194,304,000.2040: 6.87 x 10¹³.What is the format of an exponential function?The format of an exponential function is presented as follows:
[tex]y = ab^\frac{x}{n}[/tex]
In which the parameters of the function are listed as follows:
a is the initial value of the function.b is the rate of change of the function.n is the period relative to the rate of change.Moore's Law states that the number of transistors per IC doubles every two years, hence the values of parameters b and n both have values of two, hence:
b = 2, n = 2.
The number of transistors per IC in the reference year of 1972 was of 4000, hence the initial value is of:
a = 4000.
Then the exponential function is:
[tex]y = 4000(2)^{\frac{x}{2}}[/tex]
2012 is 2012 - 1972 = 40 years after 1972, hence the estimate is given as follows:
[tex]y = 4000(2)^{\frac{40}{2}} = 4,194,304,000[/tex]
2040 is 68 years after 1972, hence hence the estimate is given as follows:
[tex]y = 4000(2)^{\frac{68}{2}} = 6.87 \times 10^{13}[/tex]
Missing InformationThe chart is given by the image at the end of the answer.
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In ΔNOP, \overline{NP} NP is extended through point P to point Q, m∠OPQ = (6x-15)∘, m∠PNO=(2x+18)∘ , and m∠NOP=(2x−13)∘. What is the value of x?
At Keller's Bike Rentals, it costs $16 to rent a bike for 4 hours. How many hours of bike use does a customer get per dollar?
The customer will rent 4 bikes per dollar
How to calculate the number bikes per dollar?Keller's bike deal with renting of bikes
At the Keller's bike rentals it costs $16 to rent a bike for 4 hours
Therefore the number of bikes per dollar can be calculated as follows
16= 4
x= 1
Cross multiply
4x= 16
x= 16/4
x= 4
Hence it costs a customer 1 dollar to get 4 bikes
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¿Como se escribe siete millones setecientos cuarenta mil novecientos treinta y dos?
The 23 members of the westview journalism club are trying to raise at least 2,100 to buy new publishing desgin software. The members have already raised 1180. How much should each student still raise, on average, to meet the goal?
PLEASEE ASAAPP
Based on the number of members in the Westview Journalism Club, the amount that each student should raise on average to meet the goal is $40.
How to find the average amount?The amount that the students would have to raise is the amount that is remaining from the amount already raised. This can be found as:
= Amount that club needs to raise - Amount already raised
= 2, 100 - 1, 180
= $920
The average amount that each student has to raised to meet the target would then be based on the number of students in the club which is 23 members.
The average amount is therefore:
= Amount that still needs to be raised / Number of students in the Westview Journalism Club
= 920 / 23
= $40
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Help please. Need it soon as possible
Answer:
Step-by-step explanation:
1=205
2=63
3=45
4=5
graph this problem and post the answer
A graph of the given set of functions has been plotted and shown in the image attached below.
What is a function?In Mathematics, a function simply refers to a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable to an output variable.
What is a graph?In Mathematics, a graph is a type of chart that is typically used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).
By critically observing the graph of this set of functions (see attachment), we can reasonably infer and logically deduce that they both represent parallel lines, with function f(x) being transformed to produce function h(x).
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