Mathematics College

A set of data with a mean of 45 and a standard deviation of 8.3 is normally distributed. Find the value that is +1 standard deviation away from the mean.

Answers

Answer 1

Answer:

  53.3

Step-by-step explanation:

Add one standard deviation to the mean:

  45 +1(8.3) = 53.3

Answer 2

Answer:

53.3

Step-by-step explanation:

+1 standard deviation away from the mean is 45+1(8.3)

Related Questions

Simplify this and show your work :

Answers

-2(x-3) = 5x+1

-2x +6 = 5x+1

subtract 5 x from each side

-7x+6 = 1

subtract 6 from each side

-7x = -5

divide both sides by -7

x = -5/-7 = 5/7

x = 5/7


The three vertices drawn on a complex plane at represented by 0+0i, 4+0i, and 0+3i. What is the length of the hypotenuse

Answers

check the picture below

you can pretty much get the values for "a" and "b" from the grid.

On Saturday, a local hamburger shop sold a combined total of 273 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?

Answers

Final answer:

To determine the number of hamburgers sold on Saturday, we used the given total of 273 burgers and the relationship that cheeseburgers were twice as numerous as hamburgers. By setting up an equation and solving for the number of hamburgers, we found that 91 hamburgers were sold.

Explanation:

The question asks us to determine how many hamburgers were sold on Saturday given that the total number of hamburgers and cheeseburgers sold was 273, and the number of cheeseburgers was two times the number of hamburgers. Let's denote the number of hamburgers as H and the number of cheeseburgers as C. The problem states that C = 2H. The total number of burgers sold was H + C = 273. Substituting C with 2H, we get H + 2H = 273.

Solving for H, we combine like terms to get 3H = 273, and then we divide both sides by 3 to find H = 273 / 3. Therefore, H = 91. So, 91 hamburgers were sold on Saturday.

What are the coordinates of a point on the unit circle if the angle formed by the positive x-axis and the radius is 60?

Answers

Arc length equal to the radius of a circle

in the final event of a track meet, 6 runners run a 100 meter dash. A) How many possible arrangements are there for the medal winners (gold, silver and bronze)? B) state whether it is a combination or permutation

Answers

6 runners, 3 medals, how many ways to give them? well, runner say 2 could get gold or not, bronze or not and silver or not, and so can any other runnner, and the order "does matter", it makes a distinction, thus, is a Permutation

[tex]\bf _nP_r=\cfrac{n!}{(n-r)!}\qquad \qquad _6P_3=\cfrac{6!}{(6-3)!}[/tex]

Answer:

120 possible arrangements.

It is a permutation

Step-by-step explanation:

Imagine that you are going to give the gold medal to any of the 6 runners. There would be 6 possibilities; now, imagine that you are going to give the gold and the silver medals random in the same way: you could give the gold medal to a person and you would have 5 possibilities to give the silver medal (you can't give both medals to the same person). So, note that for each possibility to give the gold medal there would be 5 possibilities to give the silver one.

Analogously, if you give the three medals random and supposing that you have already given the gold one, for each possibility to give the silver medal you would have 4 possibilities to give the bronze one. That is the reason for the calculation to be a multiplication:

N= Total number possibilities:

[tex]N=6*5*4=120[/tex]

This also can be seen as a permutation. A permutation is a reorganization of elements where the order matters. In this case, it is not just relevant who are the winners (who receive the medal), but their order. A combination just helps us to make groups without taking in mind the order, but the permutation does consider that.

The permutation can be learnt by the formula:

[tex]N=\frac{p!}{(p-n)!}[/tex]

where p is the total ef elements and n is the amount of elements of each subgroup that I want to built. In this case, our population 'p'=6, and we want to organize them in groups of 3 (n=3) where it is important for us the order:

[tex]N=\frac{6!}{(6-3)!}=6*5*4=120[/tex]

solve these equations fast.

(6 + 3i)(6 − 3i) =


(4 − 5i)(4 + 5i) =


(−3 + 8i)(−3 − 8i) =

Answers

(6 + 3i)(6 − 3i) = 45
(4 − 5i)(4 + 5i) = 41
(−3 + 8i)(−3 − 8i) = 73

Answer:

The correct answers are 45,41,73

Step-by-step explanation:

6840 round to nearest hundredth

Answers

6800 is 6840 rounded to the nearest hundredth.

How are midsegments of trapezoids and triangles alike? How are they different?

Answers

similarity 1. 

Midsegments of a triangle and a trapezoid are alike, because their endpoints, are the midpoints of the sides they touch. 

similarity 2.
The length of the midsegment of a trapezoid is (large base+small base)/2

whereas, the length of a midsegment of a triangle is base/2. 

difference 1:

Midsegments of triangles and trapezoids are different, because we can draw 3 of them in triangles, but only one in trapezoids. 

(we can only join the midpoints of the nonparallel sides of a trapezoid to form its only midsegment.)



Final answer:

In both trapezoids and triangles, midsegments connect the midpoints of two sides. They are parallel to one side and their lengths are determined by the measurements of certain sides. The main difference lies in the number of midsegments each shape can have: a trapezoid can have only one, while a triangle can have three.

Explanation:

In both trapezoids and triangles, a midsegment is a line segment that connects the midpoints of two sides. The similarity between these midsegments lies in their properties. In both cases, the midsegments are parallel to one of the sides of the figure (the base for the trapezoids and the third side for the triangles) and their length is equivalent to the average of the two bases in a trapezoid and half the length of the base in a triangle.

However, the main difference between midsegments of trapezoids and triangles is the number of such segments each figure can have. A trapezoid has only one midsegment, that connects the midpoints of the non-parallel sides, while a triangle can have up to three midsegments, one for each side of the triangle.

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Which of the following fractions is an equivalent fraction in lowest terms to the fraction ? -276/-540

A. 23/45
B. -23/45
C. 69/135
D. -69/135

Answers

23/45 would be the most simplified form of 276/540
[tex]\bf \cfrac{-276}{-540}\quad \begin{cases} 276=2\cdot 2\cdot 3\cdot 23\\ 540={2\cdot 2\cdot 3}\cdot 3\cdot 3\cdot 5 \end{cases}\implies \cfrac{\underline{-2\cdot 2\cdot 3}\cdot 23}{\underline{-2\cdot 2\cdot 3}\cdot 3\cdot 3\cdot 5} \\\\\\ \cfrac{23}{3\cdot 3\cdot 5}\implies \cfrac{23}{45}[/tex]

The variable Z is directly proportional to X. When X is 5, Z has the value 55.

What is the value of Z when X = 12

Answers

z is directly proportional to x, that means :
z = k.x, with k is the coefficient of proportionality:
Let calculate k:
When x = 5, z = 55. Plug in:
 55 = k.5  → k=55/5 ; k =11
The value of z when  = 12 is : z= kx; z = 11(12) and z = 132

Direct variation is of the form y=kx, in this case:

z=kx, we are given the point (5,55) so we can solve for the constant of variation

55=5k  divide both sides by 5

11=k so our equation is:

z=11x, so when x=12

z=11(12)

z=132

The excluded values of a rational expression are 2 and 5. Which of the following could be this expression?

Answers

A value will be excluded from a rational expression if it causes the denominator to be zero as dividing by zero is undefined.

An example that would work for your specific question is:

[tex] y = \frac{(x - 3)(x-1)}{(x-2)(x-5)} [/tex]

If you plug in either 2 or 5 into this equation the denominator will be zero causing the expression to undefined there, so the values 2 and 5 are excluded from the domain of the expression.

Answer: d on eng

Step-by-step explanation:

Which set of numbers does 8 2/3 belong to

Answers

real and rational numbers

find the coefficient of x^6 in the binomial expression of (2x+3)^9

Answers

Its 2 bc its in front of the variable
By the Binomial Theorem: 
(a + b)^n = sum(k=0 to n) [C(n, k) * a^(n - k) * b^k].

By letting a = 2x, b = 3, and n = 9 
(2x + 3)^9 = sum(k=0 to 9) [C(9, k) * (2x)^(9 - k) * 3^k]. 
As you can see, the power of x is 9 - k. Since we want the x^6 term: 
9 - k = 6 ==> k = 3
Thus, letting k = 3 yields the term containing x^6 to be: 
C(9, 6) * (2x)^(9 - 3) * 3^4 = 435456x^6. 
. 

Balcony and orchestra tickets were sold for a Friday night concert last week. The balcony and orchestra tickets sold for $35 and $45, respectively. If 90 tickets were sold, and the total revenue was $3550 for the night, find the number of balcony and orchestra tickets sold.

Answers

x = balcony and y = orchestra

x + y = 90....x = 90 - y
35x + 45y = 3550

35(90 - y) + 45y = 3550
3150 - 35y + 45y = 3550
-35y + 45y = 3550 - 3150
10y = 400
y = 400/10
y = 40 <== 40 orchestra tickets

x = 90 - y
x = 90 - 40
x = 50 <== 50 balcony tickets



Without using a trigonometric ratio, find the distance from the ship to the buoy, B. Round the distance to the nearest tenth of a mile.

Answers

Without using the trigonometry ratio, we can find the distance between the ship and the buoy by:

the distance between City and Lemont SUBTRACT the vertical distance between City and the point parallel to the Ship

The distance between the City and Lemont can be worked out using the Sin rule 
[tex] \frac{57.8}{sin(36)}= \frac{City-Lemont}{sin(92)} [/tex]
[tex]City-Lemont= \frac{57.9sin(92)}{sin(36)} = 98.27.....[/tex]≈98.3

The vertical distance between the City and the point parallel to the ship can be worked out using the Pythagoras theorem
[tex] \sqrt{57.8^{2}- 44.6^{2} } =36.765... [/tex]≈36.8

The distance between the ship and the Buoy is given:
[tex]98.3-36.8=61.5 [/tex] miles

Felicia invested money at an interest rate of 4%. After six months, she had earned $90.00 interest. How much money did Felicia invest?

Answers

The formula is
I=prt
I interest earned 90
P amount invested?
R interest rate 0.04
T time 6/12
Solve the formula for p
P=I÷rt
P=90÷(0.04×(6÷12))
P=4,500 ....answer

Answer:

the answer is 4500 i got it right

Step-by-step explanation:

A radio telescope has a parabolic surface, as shown below.
If the telescope is 1 m deep and 12 m wide, how far is the focus from the vertex? (5 points)

Answers

check the picture below.

so.. "p" is the distance from the vertex to either, the focus point or the directrix.

thus the focus is "p" units from the vertex.

now, if we set the parabola at the origin, like in the picture, and then use another point on the parabola, let's say we'll use (6,1), then

[tex]\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} (y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\ \boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}})} \\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \begin{cases} h=0\\ k=0 \end{cases}\implies (x-0)^2=4p(y-0)\implies x^2=4py \\\\\\ \begin{cases} x=6\\ y=1 \end{cases}\implies (6)^2=4p(1)\implies \cfrac{6^2}{4}=p\implies \cfrac{36}{4}=p\implies 9=p[/tex]
Final answer:

For a parabolic dish, the focus is at a depth equal to one-fourth of the square of the width of the dish's aperture. Given the width as 12m, the focus of the radio telescope is 36m from the vertex.

Explanation:

For a parabolic dish like a radio telescope, the focus (or focal point) is located at the depth equal to one-fourth of the square of the width (i.e., one-fourth of the square of the diameter) of the dish's aperture.

Given the width (diameter) of the dish is 12 meters, we square it to get 144. Quarter of this value is 36 m. So, the focus is 36 m from the vertex of the parabola represented by the dish's surface.

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Which expression is equivalent to 3(8 + 7)? 24 + 7 24 + 21 11 + 10 11 + 7

Answers

Multiply 3&8 and 3&7, this expands it to 24 + 21.
3(8 + 7) = 3(8) + 3(7)...distributive property
= 24 + 21 

answer is
24 + 21 

Hours worked: 40 Rate: $3.85 Wages: ?

Answers

Answer: $154.00

Step-by-step explanation:

I am assuming you are looking for how much the person made.

Multiply 40 hours times $3.85

$154.00

What are the solutions to the quadratic equation (5y + 6)2 = 24? y = and y = y = and y = y = and y = y = and y =

Answers

For this case we have the following quadratic expression:

[tex] (5y + 6) ^ 2 = 24
[/tex]

From here, we must clear the value of y.

For this, we follow the following steps:

1) We clear the square term:

[tex] (5y + 6) =+/-\sqrt{24} [/tex]

[tex] (5y + 6) =+/-2\sqrt{6} [/tex]

2) Pass the value of 6 by subtracting:

[tex] 5y =-6+/-2\sqrt{6} [/tex]

3) Pass the value of 5 to divide:

[tex] y =\frac{-6+/-2\sqrt{6} }{5} [/tex]

Answer:

The solutions to the quadratic equation are:

[tex] y =\frac{-6+2\sqrt{6} }{5} [/tex]

[tex] y =\frac{-6-2\sqrt{6} }{5} [/tex]

A math teacher gave her class two tests. 27% of the class passed both tests and 51% of the class passed the first test. What percent of those who passed the first test also passed the second test?

Answers

Assume that there are 100 students in the class.

(Working with numbers is easier than working with percentages).

There are 27 students who passed both tests, and 51 who passed only the first test.
The 27 students who passed both tests are included in the 51 who passed the first test.

We are asked "What percent of those who passed the first test also passed the second test?"

so we are asked "what percent of 51 is 27?"

let      51 be 100%
then   27  is [tex] \frac{27*100}{51} [/tex]%=52.941%


Answer: 52.941%

Consider a game in which player 1 moves first. the set of actions available to player 1 is a1={a,b,c}. after observing the choice of player 1, player 2 moves. the set of actions available to player 2 is a2={a,b,c,d}. at how many information sets does player 2 move?

Answers

since player 1 moves first, At the Time player-2 Only has 3 information sets to move at which means from player 1 's A ( player-2 can play a,b,c,d) , player-1's B ( player-2 can play a,b,c,d)and player-1's C ( player-2 can play a,b,c,d).

805 tens in standard form

Answers

805 tens = 805 x 10 = 8,050

To write 8,050 in standard form, we have
[tex]805\ tens=8,050=8.05\times10^3[/tex]

Henry recorded the number of miles he biked each day for a week. His miles were 25, 40, 35, 25, 40, 60, and 75. Enter the data into the statistics calculator. What is the standard deviation of the miles Henry biked to the nearest tenth?

Answers

The standard deviation of the miles Henry biked to the nearest tenth is 17.1. The standard deviation is calculated following the steps below.

Calculation of standard deviation

First calculate the mean of the numbers that where given which is = 25 + 40 + 35 + 25 + 40 + 60+ 75/7

= 300/7

= 42.9

Then for each number, subtract the Mean and square the result.

(25 - 42.9)² = −17.9² = 320.41

(40-42.9)² = -2.9²= 8.42

(35-42.9)² = -7.9² = 62.41

(25-42.9)² = −17.9² = 320.41

(40-42.9)² = -2.9²= 8.42

(60-42.9)² = 17.1²= 292.41

(75-42.9)² = 32.1²= 1030.41

Then work out the mean of those squared differences. That is,

320.41+ 8.42+62.41+320.41+8.42+292.41+1030.41/7

= 2042.89/7

= 291.8

Take the square root of 291.8 which is,

√291.8 = 17.08215443

= 17.1 to the nearest tenth.

Therefore, the standard deviation of the miles Henry biked to the nearest tenth is = 17.1

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Answer:

17.1

Step-by-step explanation:

got it right

Evaluate the integral. (use c for the constant of integration.) sin^2(πx) cos^5(πx) dx

Answers

Using the identity cos^2(A)=1-sin^2(A)
transform 
integral of sin^2(πx)cos^5(πx)dx
=integral of sin^2(πx)[1-sin^2(πx)]^2 cos(πx)dx
=integral of [sin^2(πx)-2sin^4(πx)+sin^6(πx)]cos(πx)dx
using the substitution u=sin(πx), du=πcos(πx)dx
=integral of [u^2-2u^4+u^6] (du/π)
=1/π[u^3/3-(2/5)u^5+u^7/7] + C
back substitute u=sin(πx)
=1/π[sin(πx)^3/3-(2/5)sin(πx)^5+sin(πx)^7/7]
or
=sin(πx)^3/3π-2sin(πx)^5/5π+sin(πx)^7/7π


if x>2, then x^2-x-6/x^2-4=

Answers

consider the expression [tex] \frac{x^{2} -x-6}{ x^{2} -4} [/tex]

To factorize the expression in the denominator we use difference of squares: [tex]x^{2} -4=x^{2} - 2^{2} =(x-2)(x+2)[/tex]

To factorize [tex]x^{2} -x-6[/tex] we use the following method:

[tex]x^{2} -x-6=(x-a)(x-b)[/tex]

where a, b are 2 numbers such that a+b= -1, the coefficient of x,

and a*b= -6, the constant.

such 2 numbers can be easily checked to be -3 and 2

(-3*2=6, -3+2=-1)

So [tex]x^{2} -x-6=(x-a)(x-b)=(x+3)(x-2)[/tex]

[tex] \frac{x^{2} -x-6}{ x^{2} -4}= \frac{(x+3)(x-2)}{(x-2)(x+2)}= \frac{x+3}{x+2} [/tex]


[tex]\frac{x+3}{x+2}= \frac{x+2+1}{x+2}= \frac{x+2}{x+2}+ \frac{1}{x+2}=1+ \frac{1}{x+2}[/tex]

for x>2

[tex]\frac{1}{x+2}\ \textless \ \frac{1}{2+2}= \frac{1}{4} [/tex]

thus

for x>2, 

[tex]1+ \frac{1}{x+2}\ \textless \ 1+ \frac{1}{4}= \frac{5}{4} [/tex]


Answer: 

for x>2

[tex]\frac{x^{2} -x-6}{ x^{2} -4} = \frac{x+3}{x+2} \ \textless \ \frac{5}{4} [/tex], (but the expression is never 0)

a=one half bh solve for b

Answers


A = [1/2] bh

1) Multiply both sides by 2 =>

2A = 2 * [1/2] bh

2A = [2/2]bh

2A = bh

2) Divide both sides by h =>

2A/h = bh / h

=> 2A/h = b

Answer: b = 2A/h

0.063 written as fraction or a mixed number

Answers

63/1000 as a fraction

What is next number after 2 7 8 3 12 9

Answers

2+5=77+1=88-5=33+9=1212-3=9Can someone help me and tell me why i can not figure this out?

Find the half-life of an element which decays by 3.411% each day. Hint: use y = ab^t.

Answers

a/2=a((100-3.411)/100)^t

a/2=a(0.96589)^t

0.5=0.96589^t 

ln(0.5)=t(ln(0.96589))

t=ln(0.5)/ln(0.96589)

t≈19.97 days (to nearest hundredth of a day)

This is about half life of elements with exponential decay.

Half life = 20 years

We are given a decay rate of 3.411% per day.

We are given;

y = ab^(t)

Where;

t is the half life

y = a/2 is the amount of substance remaining after decay

a is amount of substance initially

b = 100% - 3.411% = 96.589% = 0.96589

Thus;

a/2 = a(0.96589)^(t)

a will cancel out to give;

0.5 = 0.96589^(t)

ln (0.5) = t(ln 0.96589)

t = ln(0.5)/ln(0.96589)

t = 19.968 days

This is approximately 20 days.

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