Step-by-step explanation:
n mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. ... For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with common difference of 2.
A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of ounces and a standard deviation of ounce. You randomly select cans and carefully measure the contents. The sample mean of the cans is ounces. Does the machine need to be reset? Explain your reasoning. ▼ Yes No , it is ▼ very unlikely likely that you would have randomly sampled cans with a mean equal to ounces, because it ▼ lies does not lie within the range of a usual event, namely within ▼ 1 standard deviation 2 standard deviations 3 standard deviations of the mean of the sample means.
Complete question is;
A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 128 ounces and a standard deviation of 0.20 ounce. You randomly select 35 cans and carefully measure the contents. The sample mean of the cans is 127.9 ounces. Does the machine need to be? reset? Explain your reasoning.
(yes/no)?, it is (very unlikely/ likely) that you would have randomly sampled 35 cans with a mean equal to 127.9 ?ounces, because it (lies/ does not lie) within the range of a usual? event, namely within (1 standard deviation, 2 standard deviations 3 standard deviations) of the mean of the sample means.
Answer:
Yes, we should reset the machine because it is unusual to have a mean equal to 127.9 from a random sample of 35 as the mean of 127.9 doesn't fall within range of a usual event with 2 standard deviations of the mean of the sample means.
Step-by-step explanation:
We are given;
Mean: μ = 128
Standard deviation; σ = 0.2
n = 35
Now, formula for standard error of mean is given as;
se = σ/√n
se = 0.2/√35
se = 0.0338
Normally, the range of values should be within 2 standard deviations of mean. In this case, normal range of values will be;
μ ± 2se = 128 ± 0.0338
This gives; 127.9662, 128.0338
So, Yes, we should reset the machine because it is unusual to have a mean equal to 127.9 from a random sample of 35 as the mean of 127.9 doesn't fall within range of a usual event with 2 standard deviations of the mean of the sample means.
NEED HELP ASAP
Which point represents the center of the circle shown below?
Answer:
Point O represents the center of the circle
Step-by-step explanation:
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Each cylinder is 12 cm high with a diameter of 8 cm.
Calculate the volume of each cylinder.
Use 3 as a value for π
Give your answer using the correct units.
Answer:
Volume = 576cm^3Step-by-step explanation:
[tex]h = 12 cm\\d = 8cm\\r =d/2 = 8/2 =4\\V = ?\\V =\pi r^2h\\\\V= 3 \times 4^2\times12\\V = 576 cm^3[/tex]
What is the exact distance from (−1, 4) to (6, −2)? square root of 80. units square root of 82. units square root of 85. units square root of 89. units
Answer:
[tex]\sqrt{85}[/tex].
Step-by-step explanation:
[tex]x[/tex]-coordinates:
First point: [tex]-1[/tex].Second point: [tex]6[/tex].Difference: [tex]|-1 - 6| = |-7| = 7[/tex].[tex]y[/tex]-coordinates:
First point: [tex]4[/tex].Second point: [tex]-2[/tex].Difference: [tex]|4 - (-2)| = |6| = 6[/tex].Refer to the diagram attached. Consider these two points as the two end points of the hypotenuse of a right triangle. The lengths of the two legs are equal to:
the difference between the two [tex]x[/tex]-coordinates, [tex]7[/tex], and the difference between the two [tex]y[/tex]-coordinates, [tex]6[/tex].Apply Pythagorean Theorem to find the length of the hypotenuse (which is equal to the distance between the two points in question.)
[tex]\begin{aligned}\text{Hypotenuse} &= \sqrt{(\text{First Leg})^2 + (\text{Second Leg})^2} \\ &= \sqrt{7^2 + 6^2} \\ &= \sqrt{85}\end{aligned}[/tex].
Answer:
C
Step-by-step explanation:
Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (x, y, z)→(7, 0, 2) e−xysin π z 4
Answer:
The limit of the function is 0Step-by-step explanation:
Given the limit of the function [tex]\lim_{(x,y,z) \to (7,0,2)} e^{-xy}sin\dfrac{\pi z}{4} }[/tex]
First step is to substitute the given values of x, y and z into the function given as shown;
[tex]\lim_{(x,y,z) \to (7,0,2)} e^{-xy}sin\dfrac{\pi z}{4} }\\\\= e^{-(7)(0)}sin\dfrac{\pi (2)}{4} }\\\\\\= e^{-0}sin\dfrac{\pi}{2} }\\\\\\= 1*sin\frac{\pi}{2} \\\\= 1*sin90^0\\\\= 1* 0\\\\= 0[/tex]
The limit therefore exist since the limit of the function at the given point gave us a finite value which is zero.
Given v(x) = g(x) (3/2*x^4 + 4x – 1), find v'(2).
Answer:
Step-by-step explanation:
Given that v(x) = g(x)×(3/2*x^4+4x-1)
Let's find V'(2)
V(x) is a product of two functions
● V'(x) = g'(x)×(3/2*x^4+4x-1)+ g(x) ×(3/2*x^4+4x-1)
We are interested in V'(2) so we will replace x by 2 in the expression above.
g'(2) can be deduced from the graph.
● g'(2) is equal to the slope of the tangent line in 2.
● let m be that slope .
● g'(2) = m =>g'(2) = rise /run
● g'(2) = 2/1 =2
We've run 1 square to the right and rised 2 squares up to reach g(2)
g(2) is -1 as shown in the graph.
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's derivate the second function.
Let h(x) be that function
● h(x) = 3/2*x^4 +4x-1
● h'(x) = 3/2*4*x^3 + 4
● h'(x) = 6x^3 +4
Let's calculate h'(2)
● h'(2) = 6 × 2^3 + 4
● h'(2) = 52
Let's calculate h(2)
●h(2) = 3/2*2^4 + 4×2 -1
●h(2)= 31
■■■■■■■■■■■■■■■■■■■■■■■■■■
Replace now everything with its value to find V'(2)
● V'(2) = g'(2)×h(2) + g(2)× h'(2)
● V'(2)= 2×31 + (-1)×52
●V'(2) = 61 -52
●V'(2)= 9
how many solutions are there to this non-linear systems/graph a. one solution,b.two solutions,c.no solutions
Solve for 2 in the diagram below.
120°
32°
T=
Step-by-step explanation:
Hello, there!!!
It's so simple here,
Here,
we have is 1 angle is 120°and other is 3x°.
now,
3x°=120° {because when two st.line intersects eachother then the opposite angle formed are equal}
so, 3x°=120
or, x=120°/3
=40°
Therefore, the value of x is 40°.
Hope it helps....
How is multiplying 3 - 2i by ia represented on the complex plane?
Drag a term or measure into each box to correctly complete the statements
The complex number 3 - 2i lies in quadrant IV
of the complex plane. When any complex number is multiplied by the
imaginary unit, the complex number undergoes a
90°
rotation in a counterclockwise direction This means that
the complex product of 3 - 2i and 22 lies in
quadrant I
of the complex plane.
The equation is represented 3 units to the left of the complex plane and 2 units up.
What is complex equation?A complex equation is an equation that involves complex numbers when solving it. A complex number is a number that has both a real part and an imaginary part.
Well to see how this is represented, we first need to multiply it out so we can see how it looks when it is simplified!
[tex]=(3-2i)(i^2)\\\\\\i^2=-1\\\\\\=(3-2i)(-1)\\\\\\=(-3+2i)[/tex]
We know that on a complex plane, our imaginary numbers are represented on the vertical axis.
So the original expression, (3-2i) would have been 3 units to the right on a complex graph and 2 units downward!
The equation I input above should be pretty straightforward, but one thing I didn't mention was that i^2 should = -1 when dealing with complex numbers!
Therefore, the equation 3-2i * i^2 is equal to -3 + 2i, this is graphed 3 units to the left and to units upward!
To know more about complex numbers follow
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what does 7g equal in like a verbal form
Answer:
see below
Step-by-step explanation:
7g can be "split" as 7 * g. The "*" means multiplication so a verbal form of this expression could be "7 times a number g" or "The product of 7 and a number g".
Jill works at a cell phone store. Jill earns $175 every week plus $45 for every phone p that she sells. if Jill makes $445 at the end of the week how many phones did she sell?
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▹ Answer
6 phones
▹ Step-by-Step Explanation
$445 - $175 = $270
$270 ÷ $45 = 6
6 phones
Hope this helps!
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━━━━━━━☆☆━━━━━━━
Adrianna has a court to play basketball with her friends.
The it is 600 square feet. It is 30 feet long. How many feet across is
court?
Answer:
Hey there!
The area of a rectangle is the length times width.
Thus, we can write the equation, 600=30w.
Solving for the width, we get that the width is equal to 20 ft.
Let me know if this helps :)
Answer:
20 feet across.
Step-by-step explanation:
You will have to do a simple equation solve.
x is how many feet across the court is.
* could be our multiplying sign
600 = 30*x
Now divide 30 on both sides. 30 will cross out (since 30/30 is 1 and anything times 1 is the same number as it was before) on the right side and 600/30 is 20 so we change the 600 to 20.
That leaves 20 = x.
So it is 20 feet across.
Solve for W.
W/9 = g
Answer:
W = 9 * g
Step-by-step explanation:
W/9 = g
W = 9 * g
The expression W/9 = g can be written as W = 9g after cross multiplication.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
W/9 = g
To solve for W
Make subject as W:
W = 9g
By cross multiplication.
Thus, the expression W/9 = g can be written as W = 9g after cross multiplication.
Learn more about the expression here:
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You have worked these hours this week: 5 4/5, 6 1/3, 8 2/5, 4 2/3. How many hours did you work
1472 minutes
OR
24 hours and 32 minutes
OR
1 day and 32 minutes
OR
1 day, half an hour, and 2 minutes
Using the addition operator, the total number of hours worked this week would be 26.65 hours
Given the work hours thus :
Converting to improper fraction :
29/4 + 19/3 + 42/5 + 14/3Taking the L. C. M ; = 60
(435 + 380 + 504 + 280) / 60
= 1599 / 60
= 26.65 hours.
Hence, total hours worked would be 26.65 hours.
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Which quadratic equation would be used to solve for the unknown dimensions?
0 = 2w2
512 = w2
512 = 2w2
512 = 2l + 2w
Answer:
C
Step-by-step explanation:
Answer:
C: 512 = 2w2
Step-by-step explanation:
on edge
explain why the APR does not compare loans for different lengths of time
Answer:
APR does not tell you how long your rate is locked for. A 15-year loan may have a lower interest rate, but could have a higher APR, since the loan fees are amortized over a shorter period of time. It is not wise to compare a 30-year loan with a 15-year loan using their respective APRs.
Step-by-step explanation:
3 divided by 6 it hard
Answer:
3/6 = 1/2 = 0.5
Step-by-step explanation:
3 / 6 = 1/2 = 0.5
Find the vector and parametric equations for the line through the point P(0, 0, 5) and orthogonal to the plane −1x+3y−3z=1. Vector Form: r
Answer:
Note that orthogonal to the plane means perpendicular to the plane.
Step-by-step explanation:
-1x+3y-3z=1 can also be written as -1x+3y-3z=0
The direction vector of the plane -1x+3y-3z-1=0 is (-1,3,-3).
Let us find a point on this line for which the vector from this point to (0,0,5) is perpendicular to the given line. The point is x-0,y-0 and z-0 respectively
Therefore, the vector equation is given as:
-1(x-0) + 3(y-0) + -3(z-5) = 0
-x + 3y + (-3z+15) = 0
-x + 3y -3z + 15 = 0
Multiply through by - to get a positive x coordinate to give
x - 3y + 3z - 15 = 0
The rate of change in sales S is inversely proportional to time t (t > 1), measured in weeks. Find S as a function of t when the sales after 2 and 4 weeks are 162 units and 287 units, respectively.
Answer:
S = 250/tStep-by-step explanation:
If the rate of change of sales is inversely proportional to the time t, this is expressed mathematically as ΔS ∝ 1/Δt
ΔS = k/Δt where k is the constant of proportionality
If ΔS = S₂-S₁ and Δt = t₂-t₁
S₂-S₁ = k/ t₂-t₁
If the sales after 2 and 4 weeks are 162 units and 287 units respectively, then when S₁ = 162, t₁ = 2 and when S₂ = 287, t₂ = 4.
On substituting this values into the given functions, we will have;
287 - 162 = k/4-2
125 = k/2
cross multiplying
k = 125* 2
k = 250
Substituting k = 250 into the function ΔS = k/Δt
ΔS = 250/Δt
S = 250/t
Hence the value of S as function of t when the sales after 2 and 4 weeks are 162 units and 287 units, respectively is expressed as S = 250/t
How would the margin of error change if the sample size increased from 200 to 400 students? Assume that the proportion of students who say yes does not change significantly.
Answer:
(MOE) the Margin of Error will decrease by the square root of 2
Step-by-step explanation:
The Margin of Error (MOE) is an inverse function of sample size n ( more precisely of the square root of sample size ). That relation means changes in sample size ( keeping constant other variables of the distribution) will imply opposite changes in the Margin of Error. If we double the sample size increasing it from 200 up to 400, the Margin of Error will decrease by the square root of 2
find the total area of the prism
Answer:
63.5
Step-by-step explanation:
When comparing more than two treatment means, why should you use an analysis of variance instead of using several t tests?
Answer:
Because it increases the risk of Type 1 error
Step-by-step explanation:
ANOVA is the analysis of the variance .
When comparing more than two treatment means we use ANOVA because a t test increases the risk of type 1 error .
For example if we wish to compare 4 population means there will be 4C2 = 6 separate pairs and to test the null hypothesis that all four population means are equal would require six two sample t test. Similarly to test 10 population mean would require 45 separate two sample t test.
This has two disadvantages .
First the procedure is too lengthy and tediuos.
Second the overall level of significance greatly increases as the number of t- tests increases.
The analysis of the variance compares two different estimates of variance using the F distributionto determine whether the population means are equal.
Which of the following correctly shows the quotient of 80 divided by 5 ?
Answer:16
Step-by-step explanation:
Just divide 80 by 5 or skip count by fives.
Simplify cube root of 7 over fifth root of 7. 7 to the power of one fifth 7 to the power of eight fifteenths 7 to the power of five thirds 7 to the power of two fifteenths
Answer:
[tex]\huge\boxed{7^{\frac{2}{15}}}[/tex]
Step-by-step explanation:
[tex]\dfrac{\sqrt[3]7}{\sqrt[5]7}\qquad\text{use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\=\dfrac{7^\frac{1}{3}}{7^\frac{1}{5}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=7^{\frac{1}{3}-\frac{1}{5}}\qquad\text{find the common denominator (15)}\\\\=7^{\frac{(1)(5)}{(3)(5)}-\frac{(1)(3)}{(5)(3)}}=7^{\frac{5-3}{15}}=7^{\frac{2}{15}}[/tex]
Answer:
D. 7 to the power of two fifteenths
Step-by-step explanation:
algebra and trigonometry difference
Answer:
Algebra deals with knowing the value of unknown variables and functional relationships, while trigonometry touches on triangles, sides and angles and the relationship between them.
Algebra is more on polynomial equations, x and y while trigonometry more on sine, cosine, tangent, and degrees.
Trigonometry is much more complicated than algebra but algebra has its uses in our daily lives, be it calculating distance from point to another or determining the volume of milk in a milk container.
Step-by-step explanation:
Answer:
Although both Algebra II and Trigonometry involve solving mathematical problems, Algebra II focuses on solving equations and inequalities while Trigonometry is the study of triangles and how sides are connected to angles.
hope this answer helps u
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Two math classes took the same quiz. The scores of 10 randomly selected students from each class are listed below. • Sample of Class A: 75, 80, 60, 90, 85, 80, 70, 90, 70, 65 • Sample of Class B: 95, 90, 85, 90, 100, 75, 90, 85, 90, 85 Based on the medians of the scores for each class, what inference would you make about the quiz scores of all the students in Class A compared to all the students in Class B? Explain your reasoning to justify your answer.
Answer:
Step-by-step explanation:
First you have to find the medians which is when you put the numbers in number order and find the one in the middle.
Class A: 60,65,70,70,75,80,80,85,90,90
=77.5
Class B: 75,85,85,85,90,90,90,90,95,100
=90
That the class B is more advanced, and they probably studied.
If there are 80 students in a class and 20 are seniors, what proportion of students are not seniors?
Answer:
3/4
Step-by-step explanation:
First find the number that are not seniors
80 -20 = 60
60 are not seniors
The ratio of not seniors to total
60/80
Divide top and bottom by 20
3/4
Answer:
60 students
Step-by-step explanation:
80 -20 = 60
The height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. When graphed, the function gives a line with a slope of −0.4. See the figure below. Suppose that the height of the candle after 11 hours is 16.6 centimeters. What was the height of the candle after 6 hours?
Answer:
height of the candle after 6 hours= 18.6 centimeters
Step-by-step explanation:
the function gives a line with a slope of −0.4.
the height of the candle after 11 hours is 16.6 centimeters.
after 6 hours, the height will be
But slope= y2-y1/x2-x1
Y2 is the unknown
Y1 = 16.6
X1= 11 hours
X2= 6 hours
y2-y1/x2-x1= -0.4
(Y2-16.6)/(6-11)= -0.4
(Y2-16.6)/(-5)= -0.4
(Y2-16.6)= -5( -0.4)
(Y2-16.6)= 2
Y2 = 2+16.6
Y2 = 18.6 centimeters
height of the candle after 6 hours= 18.6 centimeters
-40=-8(x+2) solve the equation
Answer:
x = 3
Step-by-step explanation:
-40 = -8 (x + 2)
-8 (x + 2) = -40 --- divide both sides by - 8
-8 (x + 2) -40
-------------- = ----------
-8 -8
x + 2 = 5 --- subtract 2 from both sides
x + 2 - 2 = 5 - 2 then simplify
x = 3
Answer:
x=3
Step-by-step explanation:
First, write out the equation as you have been given it:
[tex]-40=-8(x+2)[/tex]
Then distribute the -8 to the terms inside the parenthesis:
[tex]-40=-8x-16[/tex]
Next, add 16 to both sides:
[tex]-40+16=-8x-16+16\\-24=-8x[/tex]
Finally, divide both sides by -8:
[tex]\frac{-24}{-8}=\frac{-8x}{-8}\\3=x[/tex]
Therefore, x=3.
For a free lunch giveaway, a restaurant draws 1 card from a bowl of business cards. Val puts in 5 cards. The bowl has 50 cards. What is the probability that Val will win?
Answer:The probability Val will win is 1/5 or 10/50 or 2/10
Step-by-step explanation:
