Answer:
B.) 0.708
Step-by-step explanation:
Given the following data :
Cost of advertising (in thousands of $) (x) :
9
2
3
4
2
5
9
10
Number of product sold (in thousands of $) (y) :
85
52
55
68
67
86
83
73
Using the pearson Coefficient of correlation calculator, the correlation Coefficient obtained for the data above is : 0.7077 = 0.708 (3 decimal places).
This depicts a strong positive correlation between the cost of advertising and the number of product sold as the correlation Coefficient is both positive and close to 1. This means payibg a high cost for advert will almost usually result in a corresponding increase in the number of products sold.
Goran is sitting in a movie theater, 5 meters from the screen. The angle of elevation from his line of sight to the top of the screen is 18, and the angle of depression from his line of sight to the bottom of the screen is 48. Find the height of the entire screen.
Answer:
Approximately
Height of screen= 7.1 meters
Step-by-step explanation:
Angle of elevation= 18°
Angle of depression= 58°
Distance of Goran from screen= 5 m
Height of screen from the attachment below
X+y
First let's determine angle a and b
a= 180-90-18
a= 72°
b= 180-90-48
b= 43°
Using sine formula
5/sin a= x/sin 18
5/sin 72= x/sin18
(5*sin 18)/sin 72= x
1.6246 = x
X= 1.6246 m
Y/sin 48= 5/sin b
Y= (5*sin 48)/sin 43
Y= (5*1.08965779)
Y= 5.4483 m
Height of screen= x+y
Height of screen= 1.6246+5.4483
Height of screen= 7.0729
Approximately
Height of screen= 7.1 meters
Chiang is filling a 50ft container with water at a rate of 0.5 ft/ min. interpret the key features for this situation
Answer:
The key features are
50ft³ = the volume
0.5ft³/min = rate
Time= 100 minutes
Step-by-step explanation:
Chiang is filling a 50ft container with water at a rate of 0.5 ft/ min.
50ft³ = the volume
0.5ft³/min = rate
There is a key future missing which is the time it will take to fill the 50 ft³ container
Time = volume/rate
Time= 50 ft³/0.5ft³/min
Time= 50/0.5 min
Time = 100 min
The key features are
50ft³ = the volume
0.5ft³/min = rate
Time= 100 minutes
Which expression is equivalent to : (-4x-3y-5)2
A triangle has a base of 16 inches and a height of 18 inches. What is its area?
Answer:
The answer is
144 square inchesStep-by-step explanation:
Area of a triangle is given by
[tex]A = \frac{1}{2} bh[/tex]where
b is the base
h is the height
From the question
b = 16 inches
h = 18 inches
Substitute the values into the above formula and solve for the area
That's
[tex]A = \frac{1}{2} \times 16 \times 18 \\ = 8 \times 18 \: \: \: \: \: \: [/tex]We have the final answer as
144 square inchesHope this helps you
Suppose that on each play of a game, a gambler either wins 1 with probability p or loses 1 with probability 1–p (or q). The gambler keeps betting until she or he is either up a total of n or down a total of m. What is the probability the gambler will quit an overall winner? You must consider both cases when p = 0.5 and when p ≠ 0.5
Answer:
Step-by-step explanation:
From the given information,
Considering both cases when p = 0.5 and when p ≠ 0.5
the probability that the gambler will quit an overall winner is:
[tex]P = \dfrac{1 - (\dfrac{1-p}{p} )^K}{1- (\dfrac{1-p}{p})^N } \ \ \ is \ p \neq 0.5 \ and\ K/N = \dfrac{1}{2}[/tex]
where ;
N.k = n and k = m
Hence, the probability changes to:
[tex]P = \dfrac{1 -(\dfrac{1-p}{p})^m}{1 -(\dfrac{1-p}{p})^{m+n}}[/tex] is p ≠ 0.5 and k/N = [tex]\dfrac{m}{m+n}[/tex] is P = 0.5
Gasoline at a particular gas station costs $2.78 per gallon. If Cory buys $18 of gas, how many gallons did he buy?
Answer:
Cory bought 6.474 gallons of gasolline.
Step-by-step explanation:
The total cost of gasoline ([tex]C[/tex]), measured in dollars, is given by the following expression:
[tex]C = n\cdot c[/tex]
Where:
[tex]n[/tex] - Amount of gasoline, measured in gallons.
[tex]c[/tex] - Unit cost, measured in dollars per gallon.
Given that [tex]C = \$\,18[/tex] and [tex]c = \$\,2.78\,\frac{1}{gal}[/tex], the amount of gasoline is cleared and calculated:
[tex]n = \frac{C}{c}[/tex]
[tex]n = \frac{\$\,18}{\$\,2.78\,\frac{1}{gal} }[/tex]
[tex]n = 6.474\,gal[/tex]
Cory bought 6.474 gallons of gasolline.
what is. - 3 7/8 × - 4 3/5 help please
Answer: 1/ 40 x (-155x-184)
Answer:
[tex]:\quad \frac{713}{40}=17\frac{33}{40}[/tex]
Step-by-step explanation:
[tex]-3\frac{7}{8}\times \:-4\frac{3}{5}\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 3\frac{7}{8}=\frac{31}{8}\\-\frac{31}{8}\times \:-4\frac{3}{5}\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 4\frac{3}{5}=\frac{23}{5}\\-\frac{31}{8}\times \:-\frac{23}{5}\\\mathrm{Apply\:rule}\:-\left(-a\right)=a\\=\frac{31}{8}\times \frac{23}{5}\\\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}\\[/tex]
[tex]=\frac{31\times \:23}{8\times \:5}\\\\=\frac{713}{40}\\\\\mathrm{Convert\:improper\:fractions\:to\:mixed\:numbers}:\\\quad \frac{713}{40}=17\frac{33}{40}[/tex]
Please help me it’s in my math class
Answer:
1-70: Purple- 9/10= 0.18= 2 marbles
Orange- 16/50= 0.32= 3 marbles
Yellow- 6/50= 0.12= 1 marble
Green- 19/50= 0.38= 4 marbles
1-71: Part A. 3/6= 1/2
Part B. 4/6= 2/3
How many solutions exist for 2 |x - 1| = 8?
A. 0
B. 1
C. 2
D. 3
Answer:
I believe the correct answer is C.
Step-by-step explanation:
So to get 0 solutions the absolute value would have to equal a negative number. To get 1 solution the absolute value would have to equal 0. To get 2 solutions the absolute value would have to equal a positive number.
2 |x - 1| = 8
divide by 2
|x - 1| = 4
The absolute value equals a positive so it has 2 solutions.
On the njmber line below, the numbers x and y are the same distance from 0. What is x + y? Explain how you found your answer
Answer:
Step-by-step explanation:
either x+y=0
∵ if they are on number line and at same distance. then x=-y
or x+y=0
You take thirty measurements in order to find the length of a rod, you calculate the average and obtain the value L0. Supposed that now a different person takes twenty measurements as well of the same rod, then calculates the average and obtains the same L0 as you. Does it mean that both of you obtain a result with the same precision and accuracy
Answer:
Yes, it means that both of you obtain a result with the same precision and accuracy.
Step-by-step explanation:
It is provided that two different people took measurements in order to find the length of a rod.
The first person took 30 measurements.
The second person took 20 measurements.
Both the people got the same average length, i.e. L₀.
In statistics, a larger sample leads to an error free result.
So, for the first person the larger sample helped reducing the chance of any sort of error that may be present.
For the second person, the average is same as the first even when their sample size is less than the first.
This may happen because the sample was selected with a certain precision and accuracy.
Thus, both of them obtain a result with the same precision and accuracy.
The length of a rectangle is one more than four times its width. If the perimeter of the rectangle is 62 meters, find the dimensions of the rectangle.
Answer:
Length = 25 meters
Width = 6 meters
Step-by-step explanation:
62 = 2(a+b)
a = 4b + 1
a = length
b = width
then:
62 = 2((4b+1)+b)
62/2 = 4b+b+1
31 = 5b + 1
31 - 1 = 5b
30 = 5b
b = 30/5
b = 6m
a = 4b + 1
a = 4*6 + 1
a = 24 + 1
a = 25m
Check:
62 = 2(6+25)
62 = 2*31
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=570(0.98)^x
Answer:
decay2% decreaseStep-by-step explanation:
The growth factor is the base of the exponent: 0.98. Its relation to the rate of change is ...
growth factor = 1 + rate of change
0.98 = 1 + (-0.02)
So, the rate of change is -0.02 = -2%. Since the rate of change is a 2% decrease, it represents decay.
x(2x + 3) + (x - 3)(x - 4)
Answer:
3x²-4x+12
Step-by-step explanation:
Answer:
[tex]=3x^2-4x+12[/tex]
Step-by-step explanation:
So we have the expression:
[tex]x(2x+3)+(x-3)(x-4)[/tex]
To simplify, distribute the left side and the right:
[tex]=x(2x)+x(3)+(x-3)(x)+(x-3)(-4)[/tex]
Distribute:
[tex]=(2x^2+3x)+(x^2-3x)+(-4x+12)[/tex]
Combine like terms:
[tex]=(2x^2+x^2)+(3x-3x-4x)+(12)[/tex]
Simplify:
[tex]=3x^2-4x+12[/tex]
f(x) = (10/x)^3 what is the value of f(2)?
Rachel, Hong, and Manuel have a total of 95 in their wallets. Hong has 3 times what Manuel has. Rachel has $10 more than Manuel. How much does each have?
Answer:
Rachel has 27
Hong has 51
Manuel has 17
Step-by-step explanation:
Let R represent Rachel, H represent Hong, and M represent Manuel.
They combined have a total of 95. Thus:
[tex]R+H+M=95[/tex]
Hong has 3 times what Manuel has. Therefore:
[tex]H=3M[/tex]
Rachel has 10 more than Manuel. Therefore:
[tex]R=10+M[/tex]
Substitute:
[tex]R+H+M=95\\(10+M)+(3M)+M=95[/tex]
Combine like terms:
[tex]5M+10=95[/tex]
Subtract 10 from both sides:
[tex]5M=85[/tex]
Divide by 5:
[tex]M=17[/tex]
Therefore, Manuel has 17.
Now, find Rachel and Hong's money.
[tex]H=3M\\H=3(17)=51[/tex]
So, Hong has 51.
And for Rachel:
[tex]R=10+M\\R=10+17=27[/tex]
Rachel has 27.
trough: (2,2) parallel to y=x+4
Answer:
y = x
Step-by-step explanation:
The slopes of parallel lines are the same, so we know the equation will be ...
y = x + constant
We can find the constant by using the given point's values for x and y:
2 = 2 + constant
Obviously, the constant is zero.
The equation of the parallel line through (2, 2) is y = x.
ILL GIVE YOU BRAINLIST ! Marlene is given 7 feet of fabric to design a dress. She uses 6 1/9 feet of fabric. How much fabric is left?
Answer:
This question is a lot easier than it seems. What you have to do here is subtract 6 1/9 from 7.
This will give you 0.8 of the fabric left, or 8/9.
A Women making $29 an hour gets a 15% raise. How much money will she make after 4 hours of working with the increased hourly pay?
Answer:
$133.4
Step-by-step explanation:
1. Find the increased pay:
29 * 1.15 = 33.35
2. Find how much she makes in 4 hrs
33.35 * 4 = 133.4
If f(x) = х2 – 2х + 3, thеn find
f(-3).
Answer:
[tex]\huge\boxed{\sf f(-3) = 18}[/tex]
Step-by-step explanation:
[tex]\sf f(x) = x^2 - 2x + 3[/tex]
Put x = -3
[tex]\sf f(-3) = (-3)^2 -2(-3) + 3\\f(-3) = 9 + 6 + 3\\f(-3) = 18[/tex]
For what positive values of k does the function y=sin(kt) satisfy the differential equation y''+144y=0 ?
Answer:
The positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12
Step-by-step explanation:
To determine the positive values of k that the function y = sin(kt) satisfy the differential equation y''+144y=0.
First, we will determine y''.
From y = sin(kt)
y' = [tex]\frac{d}{dt}(y)[/tex]
y' = [tex]\frac{d}{dt}(sin(kt))\\[/tex]
y' = kcos(kt)
Now for y''
y'' = [tex]\frac{d}{dt}(y')[/tex]
y'' = [tex]\frac{d}{dt}(kcos(kt))[/tex]
y'' = [tex]-k^{2}sin(kt)[/tex]
Hence, the equation y'' + 144y = becomes
[tex]-k^{2}sin(kt)[/tex] + [tex]144(sin(kt))[/tex] [tex]= 0[/tex]
[tex](144 - k^{2})(sin(kt)) = 0[/tex]
[tex](144 - k^{2})= 0[/tex]
∴ [tex]k^{2} = 144\\[/tex]
[tex]k =[/tex] ±[tex]\sqrt{144}\\[/tex]
[tex]k =[/tex] ± [tex]12[/tex]
∴ [tex]k = +12[/tex] or [tex]-12[/tex]
Hence, the positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12
The positive value of k that satisfies the differential equation is k = 12.
To find the value of k that satisfies the equation, we differentiate the function y = sin(kt) twice to obtain y" and we insert it into the differential equation y" + 144y = 0.
So, y' = dy/dt
= dsin(kt)/dt
= kcos(kt)
y" = dy'/dt
y" = dkcos(kt)/dt
y" = -k²sin(kt)
So, substituting y and y" into the differential equation, we have
y" + 144y = 0
-k²sin(kt) + 144sin(kt) = 0
-k²sin(kt) = -144sin(kt)
k² = 144
k = ±√144
k = ±12
Since we require a positive value, k = 12
So, the positive value of k that satisfies the differential equation is k = 12.
Learn more about differential equations here:
https://brainly.com/question/18760518
32 POINTS! WILL MAKE BRAINLIEST. ANSWER ASAP
A card is selected at random from a standard 52-card deck. (a) What is the probability that it is an ace
Answer:
4/52 = 1/13
Step-by-step explanation:
explain how you can rename 5,400 as hundreds.
Answer:
The correct answer would be 54 hundreds
Step-by-step explanation:
If we are considering how many hundreds something has, we can simply take away two 0's and use that number. We take the two 0's off and then we have the right number of hundreds
Answer:
Hey there!
Five-thousand four-hundred can be expressed as fifty-four hundred.
Let me know if this helps :)
43,761 rounded to the nearest thousands
Answer:
44,000
Step-by-step explanation:
The number 43,761 rounded to its nearest thousands is 4400.
What is place value?The place value of a number is given as:
Example:
1234.567
1 = thousand place value
2 = hundred place value
3 = tens place value
4 = ones place value
5 = tenths place value
6 = hundredths place value
7 = thousandths place value
We have,
43,761
3 is in the thousand place.
So,
We will round 3761 to its nearest thousand value.
There are two options:
3000 or 4000
If It is greater than 3499 it will round to 4000.
If it is less than 3500 it will round to 3000.
Now,
3761 > 3499.
So,
The number is rounded to 4000.
Thus,
43,761 is rounded to 4400.
Learn more about place value here:
https://brainly.com/question/27734142
#SPJ2
If you get this you are a critical thinker.
I enter the garden.
There are 34 people.
You kill 30.
How many people are in the garden.
Step-by-step explanation:
I'm not sure, but I think just 0
Because no one will even stand there and watch you kill 30 people
The police will come for you and the 1 dead person will be sent away lol
a cylinder container can hold 2.45l of water. it radius is 4.00cm. what is the the volume of it in cm3
Answer:
Step-by-step explanation:
Ion know
Given m parallel to I, and m2 7 = 94, find the measure of angle 5
O 10
045
O 97
O 120
Answer:
97
Step-by-step explanation:
Translate to an algebraic expression. m plus the product of 6 and n
Assume that the two polygons are similiar, with the same orientation.
Write a proportion to determine the lengths of the sides labeled by variables.
(DO NOT SOLVE. You will solve the proportion in the next question.)
Answer:
4/6=t/(t+1)
Step-by-step explanation:
4/6=t/(t+1)