The highest and lowest scores on a test taken by 80 students are within 19 points of the average of the exam. The average for this exam was a 72. Set up an equation to solve for the highest and lowest scores. Show your original equation and the process used to find the highest and lowest exam score.
1. So start off by asking yourself, how will I get this answer? Absolute values!
2. So what the question is asking is for you to build and equation that shows us how to solve for the highest and lowest grades that are 19 points above and below the average of 72.
3. So your unknown is x, and for us to be able to plug in our highest and lowest scores it will always have to = 19 (that’s the rule we got from the question)
So now this is where your absolute value comes in.
4. Set it up
| x - 72 | = 19
5. Solve it
72-19=53 Minimum
72+19=91 Maximum
6. | 53 - 72 | = 19
| 91 - 72 | = 19
Find T, N, and kappa for the plane curve Bold r left parenthesis t right parenthesis equalsleft parenthesis 7 Bold cos t plus 7 t Bold font size decreased by 1 sin t right parenthesis Bold i plus left parenthesis 7 Bold sin t minus 7 t Bold font size decreased by 1 cos t right parenthesis Bold j, t greater than 0 .
Find T, N, and for the plane curve r(t) = (7 cost + 7t sin t)i + (7 sin t - 7t cos t)j, t> 0.
Answer:
Step-by-step explanation:
r(t) = (7 cost + 7t sin t)i + (7 sin t - 7t cos t)j
[tex]\frac{d \bar r t}{dt} =(7\frac{d}{dt}\cos t + 7\frac{d}{dt} (t \sin t)i+(7\frac{d}{dt} \sin t-7\frac{d}{dt} t \cos t)j[/tex]
[tex]=(7(-\sin t)+7(1* \sin t+t \cos t))i+(7 \cost -7(1*\cos t - t \sin t))j\\\\=7((-\sin t+\sin t+t \cos t)i+(\cos t-\cos t+t \sin t)j)\\\\=7((t\cos t)i+(t\sin t)j)[/tex]
[tex]\bar r'(t)=\frac{d \bar r t}{dt} =(7t\cos t)i+(7t\sin t)j---(1)\\\\11\bar r(t)=\sqrt{(7t\cos t)^2+(7t\sin t)^2}\\\\=\sqrt{49t^2(\cos^2t+\sin^2 t)} \\\\=7t[/tex]
[tex]\bar T (t)=\frac{\bar r'(t)}{11\bar r(t)11} =\frac{(7t\cos t)i+(7t\sin t)j}{7t} \\\\\barT(t)=(\cos t)i+(\sin t)j[/tex]
[tex]\bar T'(t)=\frac{d}{dt} (\cos t)i+\frac{d}{dt} (\sin t) j\\\\\bar T'(t)=(-\sin t)i+(\cos t)j---(2)\\\\11\bar T'(t)=\sqrt{(-\sin t)^2+(\cos t)^2} \\\\=\sqrt{\sin^2t+\cos^2t} \\\\=1[/tex]
[tex]\bar N(t)=\bar T'(t)=\frac{(-\sin t)i+(\cos t)j}{(1)} \\\\ \large \boxed {\bar N(t)=(-\sin t)i+(\cos t)j}[/tex]
[tex]K(t)=\frac{|\b\r T'(t)|}{\bar r (t)|} \\\\=\frac{|-\sin t i+\cos t j|}{|7t\cos t +7t \sin t j|}[/tex]
Using eq (1) and (2)
[tex]K(t)=\frac{\sqrt{(-\sin t)^2+(\cos t)^2} }{\sqrt{(7t\cos t)^2+(7t\sin t)^2} }\\\\=\frac{\sqrt{\sin^2 t+\cos^2t} }{\sqrt{49t^2(\cos^2 t+\sin^2t)} }\\\\=\frac{\sqrt{1} }{\sqrt{49t^2\times 1} } \\\\ \large \boxed {K(t)=\frac{1}{7t} }[/tex]
Someone let me know this answer
Graph a line with a slope of -5 that contains the
point (-3,-4).
y
6
.
.
2
-6
-4
2
4
-6
Answer:
Step-by-step explanation: idk
Luke collected 1,034 baseball cards, 1,289 football cards, and 1,566 hockey cards. Use mental math to find the number of cards in Luke’s collection. Solve this problem any way you choose.
Answer:
3889
Step-by-step explanation:
you add all the numbers to get the answer
Answer:3889
Step-by-step explanation:So what u want to do is add them
1034
1289
1566
3889
You have received an order of 100 robotic resistance spot welders which contains 5 defective welders. You randomly select 15 welders from the order without replacement to inspect to check whether they are defective.
(a) Determine the PMF of the number of defective welders in your sample? Remember to list all possible values of the random variable.
(b) Determine the probability that there are at least 4 defective welders in the sample? Hint: No need to calculate the final numerical results. Appropriately plugging in numbers in the mathematical expression is sufficient
Answer:
a)
[tex]P(X = 0) = h(0,100,15,5) = \frac{C_{5,0}*C_{95,15}}{C_{100,15}} = 0.4357[/tex]
[tex]P(X = 1) = h(1,100,15,5) = \frac{C_{5,1}*C_{95,14}}{C_{100,15}} = 0.4034[/tex]
[tex]P(X = 2) = h(2,100,15,5) = \frac{C_{5,2}*C_{95,13}}{C_{100,15}} = 0.1377[/tex]
[tex]P(X = 3) = h(3,100,15,5) = \frac{C_{5,3}*C_{95,12}}{C_{100,15}} = 0.0216[/tex]
[tex]P(X = 4) = h(4,100,15,5) = \frac{C_{5,4}*C_{95,11}}{C_{100,15}} = 0.0015[/tex]
[tex]P(X = 5) = h(5,100,15,5) = \frac{C_{5,5}*C_{95,10}}{C_{100,15}} = 0.00004[/tex]
b) 0.154% probability that there are at least 4 defective welders in the sample
Step-by-step explanation:
The welders are chosen without replacement, so the hypergeometric distribution is used.
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
100 welders, so [tex]N = 100[/tex]
Sample of 15, so [tex]n = 15[/tex]
In total, 5 defective, so [tex]k = 5[/tex]
(a) Determine the PMF of the number of defective welders in your sample?
There are 5 defective, so this is P(X = 0) to P(X = 5). Then
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,100,15,5) = \frac{C_{5,0}*C_{95,15}}{C_{100,15}} = 0.4357[/tex]
[tex]P(X = 1) = h(1,100,15,5) = \frac{C_{5,1}*C_{95,14}}{C_{100,15}} = 0.4034[/tex]
[tex]P(X = 2) = h(2,100,15,5) = \frac{C_{5,2}*C_{95,13}}{C_{100,15}} = 0.1377[/tex]
[tex]P(X = 3) = h(3,100,15,5) = \frac{C_{5,3}*C_{95,12}}{C_{100,15}} = 0.0216[/tex]
[tex]P(X = 4) = h(4,100,15,5) = \frac{C_{5,4}*C_{95,11}}{C_{100,15}} = 0.0015[/tex]
[tex]P(X = 5) = h(5,100,15,5) = \frac{C_{5,5}*C_{95,10}}{C_{100,15}} = 0.00004[/tex]
(b) Determine the probability that there are at least 4 defective welders in the sample?
[tex]P(X \geq 4) = P(X = 4) + P(X = 5) = 0.0015 + 0.00004 = 0.00154[/tex]
0.154% probability that there are at least 4 defective welders in the sample
Between what two consecutive integers does the square root of 24 lie
4 and 5!
4 squared is 16, which is less than 24, and 5 squared is 25, which is more than 24!
[tex]\sqrt{24}[/tex] lies between two consecutive numbers 4 and 5
Given :
Given square root of 24
Lets write all the perfect square numbers
[tex]\sqrt{4}=2\\\sqrt{9}=3\\\sqrt{16} =4\\\sqrt{25} =5\\\sqrt{36} =6\\\sqrt{49}=7[/tex]
From the above perfect square root numbers, we can see that square root (24) lies between [tex]\sqrt{16} \; and\; \sqrt{25}[/tex]
So we can say that [tex]\sqrt{24}[/tex] lies between 4 and 5
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Suppose a large shipment of stereos contained 18% defectives. If a sample of size 306 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 6%
Answer:
99.36% probability that the sample proportion will differ from the population proportion by less than 6%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a sample proportion p in a sample of size n, we have that the sampling distribution of the sample proportions has [tex]\mu = p, s = \sqrt{\frac{p(1-p)}{n}}[/tex].
In this question:
[tex]n = 306, p = 0.18, \mu = 0.18, s = \sqrt{\frac{0.18*0.82}{306}} = 0.0220[/tex].
What is the probability that the sample proportion will differ from the population proportion by less than 6%
This is the pvalue of Z when X = 0.18 + 0.06 = 0.24 subtracted by the pvalue of Z when X = 0.18 - 0.06 = 0.12. So
X = 0.24
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.24 - 0.18}{0.022}[/tex]
[tex]Z = 2.73[/tex]
[tex]Z = 2.73[/tex] has a pvalue of 0.9968
X = 0.12
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.12 - 0.18}{0.022}[/tex]
[tex]Z = -2.73[/tex]
[tex]Z = -2.73[/tex] has a pvalue of 0.0032
0.9968 - 0.0032 = 0.9936
99.36% probability that the sample proportion will differ from the population proportion by less than 6%
After four years in college, Josie owes $9500 in student loans. The interest rate on the federal loans is 11% and the rate on the private bank loans is 7%. The total interest she owed for one year was $901.00. What is the amount of each loan?
Step-by-step explanation:
federal= $4180
(9500*0.11*4)
private=$2660
(9500*0.07*4)
plz answer the question below
Answer:123456
Step-by-step explanation:
A circle's radius that has an initial radius of 0 cm is increasing at a constant rate of 5 cm per second.
a. Write a formula to expresses the radius of the circle, r (in cm), in terms of the number of seconds, t since the circle started growing.r=
b. Write a formula to express the area of the circle, A (in square cm), in terms of the circle's radius, r (in cm). A =
c. Write a formula to expresses the circle's area, A (in square cm), in terms of the number of seconds, t, since the circle started growing. A =
d. Write your answer to part (c) in expanded form - so that your answer does not contain parentheses. A =
Answer:
a) [tex]r(t)=5t[/tex]
b) [tex]A=\pi\cdot r^2[/tex]
c) [tex]A=\pi\cdot (5t)^2[/tex]
d) [tex]A=25\pi t^2[/tex]
Step-by-step explanation:
We know that the circle is increasing its radio from an initial state of r=0 cm, at a rate of 5 cm/s.
This can be expressed as:
[tex]r(0)=0\\\\dr/dt=5\\\\r(t)=r(0)+dr/dt\cdot t=0+5t\\\\r(t)=5t[/tex]
a) Radius of the circle, r (in cm), in terms of the number of seconds, t since the circle started growing:
[tex]r(t)=5t[/tex]
b) Area of the circle, A (in square cm), in terms of the circle's radius, r (in cm):
[tex]A=\pi\cdot r^2[/tex]
c) Circle's area, A (in square cm), in terms of the number of seconds, t, since the circle started growing:
[tex]A=\pi\cdot r^2\\\\A=\pi\cdot (5t)^2[/tex]
d) Expanded form for the area A:
[tex]A=\pi\cdot (5t)^2=25\pi\cdot t^2[/tex]
What value of x will make the equation true?
( 15 )( V5) = x
Answer:
[tex]x=15\sqrt{5}[/tex]
Step-by-step explanation:
[tex]15 \times \sqrt{5} = x[/tex]
[tex]33.54102 \approx x[/tex]
7x + 3 = 5 and y - 1= 6
Answer:
first answer is x= -5 second answer is y=7.
Step-by-step explanation:
7-5=2. 2+3=5.
7-1=6.
How can I trust your guys
Answer:
Step-by-step explanation:
you just do, everyone in here needs help so i dont think theres people in here just messing arround, you can trust.
Answer:
because we are amazing as always.
Step-by-step explanation:
Please dont do this or i will report u.
bye
The result of rounding the whole number 2,746,052 to the nearest hundred thousands place is:
Answer:
2700000
Step-by-step explanation:
Because it is not at 750000 it gets rounded down
√15(√6+6) A. √21+6√15 B. 3√10+6√15 C. √90+6 D. √90+6√15
Answer:
Before A. 32.7247330577, A. 27.8204757722, B. 32.7247330577, C. 15.4868329805, and D. 32.7247330577
Step-by-step explanation:
Used a calculator. Not that Hard.
What is the solution of StartRoot x minus 4 EndRoot + 5 = 2? x = –17 x = 13 x = 53 no solution
The solution to the given function is determined as 13.
Solution of the function
The solution of the function is calculated as follows;
[tex]\sqrt{x - 4} \ +\ 5 = 2[/tex]
collect similar terms together
[tex]\sqrt{x - 4} \ = 2-5\\\\\sqrt{x - 4} \ = -3[/tex]
square both sides of the equation
[tex](\sqrt{x - 4} )^2 = (-3)^2\\\\x - 4 = 9\\\\x = 9 + 4\\\\x = 13[/tex]
Thus, the solution to the given function is determined as 13.
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Answer:
No solution
Step-by-step explanation:
Edge.
Find the volume of the cone.
Either enter an exact answer in terms of T or use 3.14 for and round your final answer to the nearest
hundredth.
What type of probability is used in this scenario a bag has 10 red marbles 7 blue marbles and 12 yellow marbles the probability of drawing a yellow at random is 12/29
Apply the distributive property to create an equivalent expression.
1/2 (2a−6b+8) = ?
Answer:
a-3b+4
Step-by-step explanation:
1/2 (2a−6b+8) =
=1/2*2a-1/2*6b+1/2*8
=a-3b+4
Answer:
a - 3b + 4
Explanation:
According to the instructions, we must apply the distributive property to create an equivalent expression.
* reminder
distributive property formula: a (b + c) = ab + ac
Let's start by applying the distributive property to the expression.
[tex]\displaystyle\frac{1}{2} (2a - 6b + 8)\\\\\displaystyle\frac{1}{2} (2a) + \displaystyle\frac{1}{2} (-6b) + \displaystyle\frac{1}{2} (8)[/tex]
Simplify by multiplying.
[tex]\displaystyle\frac{1}{2}(2a)+\displaystyle\frac{1}{2}(-6b)+\displaystyle\frac{1}{2}(8)\\\\a+\displaystyle\frac{1}{2}(-6b)+\displaystyle\frac{1}{2}(8)\\\\a-3b+\displaystyle\frac{1}{2}(8)\\\\a-3b + 4[/tex]
Therefore, an equivalent expression to the given expression is a - 3b + 4.
Use trigonometric substitution to evaluate the integral 13 + 12x − x2 dx . First, write the expression under the radical in an appropriate form so that a trigonometric substitution can be performed. 13 + 12x − x2
I don't see a square root sign anywhere, so I'll assume the integral is
[tex]\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx[/tex]
First complete the square:
[tex]13+12x-x^2=49-(6-x)^2=7^2-(6-x)^2[/tex]
Now in the integral, substitute
[tex]6-x=7\sin t\implies\mathrm dx=-7\cos t\,\mathrm dt[/tex]
so that
[tex]t=\sin^{-1}\left(\dfrac{6-x}7\right)[/tex]
Under this change of variables, we have
[tex]7^2-(6-x)^2=7^2-7^2\sin^2t=7^2(1-\sin^2t)=7^2\cos^2t[/tex]
so that
[tex]\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx=-7\int\sqrt{7^2\cos^2t}\,\cos t\,\mathrm dt=-49\int|\cos t|\cos t\,\mathrm dt[/tex]
Under the right conditions, namely that cos(t) > 0, we can further reduce the integrand to
[tex]|\cos t|\cos t=\cos^2t=\dfrac{1+\cos(2t)}2[/tex]
[tex]\displaystyle-49\int|\cos t|\cos t\,\mathrm dt=-\frac{49}2\int(1+\cos(2t))\,\mathrm dt=-\frac{49}2\left(t+\frac12\sin(2t)\right)+C[/tex]
Expand the sine term as
[tex]\dfrac12\sin(2t)}=\sin t\cos t[/tex]
Then
[tex]t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \sin t=\dfrac{6-x}7[/tex]
[tex]t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \cos t=\sqrt{7^2-(6-x)^2}=\sqrt{13+12x-x^2}[/tex]
So the integral is
[tex]\displaystyle-\frac{49}2\left(\sin^{-1}\left(\dfrac{6-x}7\right)+\dfrac{6-x}7\sqrt{13+12x-x^2}\right)+C[/tex]
Ellie goes out to dinner with her family. The total bill is $57. They decide to leave a 20% tip. How much money should they leave as their tip?
Answer:
78doalrse
Step-by-step explanation:
solos w
Answer:
$11.40
Step-by-step explanation:
This question asks us to find how much money the family should leave as their tip.
To find the tip, multiply the cost of the total bill by the tip rate.
cost of bill * tip rate
The total bill was $57, and they are leaving a 20% tip
$57 * 20%
Convert 20% to a decimal by dividing by 100 or moving the decimal place 2 spaces to the left.
20/100=0.20
20.0--> 2.0 --> 0.20
20%=0.20
$57 * 0.20
Multiply 57 and 0.20
11.4= $11.40
The family should leave a tip of $11.40
Solve for x in the following 4/2.6=5/x
The value of X is 3.25
Look at the attached picture
Hope it will help you
Good luck on your assignment
Classify the triangle shown below. Check all that apply.
100°
40°
40°
A. Obtuse
B. Right
C. Isosceles
D. Equilateral
O E. Acute
F. Scalene
Answer:
obtuse
isosceles
Step-by-step explanation:
It has one angle bigger than 90 so it is obtuse
It has two angles that measure the same so it has two sides that measure the same so it is isosceles
The given triangle is an Obtuse triangle.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
We have to given that;
All the angles are,
100°
40°
40°
Here, It has one angle bigger than 90 so it is obtuse.
And, It has two angles that measure the same so it has two sides that measure the same so it is isosceles.
Thus, The given triangle is an Obtuse triangle.
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Choose the function whose graph is given by:
The function whose graph is given is y = sin (x - 2).
Option B is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The graph of y = sin(x - 2) is a sinusoidal function that is shifted 2 units to the right from the standard sine function y = sin(x).
The sine function oscillates between -1 and 1 as x increases, and the value of x at which the function reaches its minimum or maximum value is a multiple of π.
When we subtract 2 from x in the equation y = sin(x - 2), the entire graph is shifted to the right by 2 units, which means that the minimum and maximum points occur at x-values that are 2 units greater than they would be for the standard sine function.
The graph of y = sin(x - a) is a sinusoidal function that is shifted a units to the right from the standard sine function.
So, in this case, the graph of y = sin(x-2) looks like the standard sine function shifted 2 units to the right.
The amplitude and period of the function remain the same as the standard sine function, but the phase shift changes.
Thus,
The function whose graph is given is y = sin (x - 2).
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The length of a rectangular patio is 7 feet and the width is 6 feet. The patio is surrounded by a sidewalk that is x feet wide. Find the expression that represents the area of the patio, including the sidewalk
Answer: A = (7ft + x)*(6ft + x)
Step-by-step explanation:
The area of a rectangle is equal to A = L*W
where W is width and L is lenght.
Here we have that the width is 6 feet + x feet and the lenght is 7 feet + x feet
(because we also are counting the area of the sidewalk)
Then the total area is:
A = (7ft + x)*(6ft + x)
POSSIBLE POINTS: 1
In the US, the average citizen receives an annual dose of 360 mrem of radiation. If eating a banana creates a 0.01 mrem dose, how many bananas
are equivalent to the annual dose of an average citizen?
720 bananas
36.000 bananas
25,000 bananas
180,000 bananas
Answer:
36,000
Step-by-step explanation:
So all we have to do is divide 360 by 0.01. that equals 36,000
Persia make a flower arrangement using the eight longest flowers which is the combined height of flowers Persia uses
Answer:
Persia should measure the length of each flower that she used in creating this flower arrangement and add up all the values to get the total height (i.e., the combined height) of the eight flowers used. Make sure to keep the units consistent all throughout the calculation to avoid any errors. For example, if centimetres are used to measure height of one flower, use centimetres all throughout and not switch to using inches at any point.
Hope that answers the question, have a great day!
Answer:
61 1/2
Step-by-step explanation:
math is ez
Answers? can someone help me please
2.Sketch the region whose area is given by the integral and evaluate the integral.
3.Evaluate the given integral by changing to polar coordinates.....
2. The integration region,
[tex]\left\{(r,\theta)\mid\dfrac\pi6\le\theta\le\dfrac\pi2\land2\le r\le3\right\}[/tex]
corresponds to what you might call an "annular sector" (i.e. the analog of circular sector for the annulus or ring). In other words, it's the region between the two circles of radii [tex]r=2[/tex] and [tex]r=3[/tex], taken between the rays [tex]\theta=\frac\pi6[/tex] and [tex]\theta=\frac\pi2[/tex]. (The previous question of yours that I just posted an answer to has a similar region with slightly different parameters.)
You can separate the variables to compute the integral:
[tex]\displaystyle\int_{\pi/6}^{\pi/2}\int_2^3r^2\sin^2\theta\,\mathrm dr\,\mathrm d\theta=\left(\int_{\pi/6}^{\pi/2}\sin^2\theta\,\mathrm d\theta\right)\left(\int_2^3r^2\,\mathrm dr\right)[/tex]
which should be doable for you. You would find it has a value of 19/72*(3√3 + 4π).
3. Without knowing the definition of the region D, the best we can do is convert what we can to polar coordinates. Namely,
[tex]r^2=x^2+y^2[/tex]
so that
[tex]\displaystyle\iint_De^{x^2+y^2}\,\mathrm dA=\iint_Dre^{r^2}\,\mathrm dr\,\mathrm d\theta[/tex]
