The value of the correlation is -0.0721 and it is a weak negative correlation
How to determine the correlation coefficient?
The points are given as:
(12, 28), (15, 50), (18, 14), (21, 28), (24, 36)
Enter the above points in a graphing calculator.
From the graphing calculator, we have the following summary:
X Values
Sum X = 90Mean = 18∑(X - Mx)^2 = SSx = 90Y Values
Sum Y = 156Mean = 31.2∑(Y - My)^2 = SSy = 692.8X and Y Combined
N = 5∑(X - Mx)(Y - My) = -18R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
This gives
r = -18 / √((90)(692.8)) = -0.0721
So, the correlation coefficient is -0.0721
The above is a negative correlation because it is less than 0 and it is a weak correlation because it is closer to 0 than -1
Hence, the correlation is a weak negative correlation
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Graph f(x) = 3/4x - 2
The equation of the function is the graph of line.
What is the equation of line?The equation of line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
The function is given below.
f(x) = (3/4)x – 2
The function is an equation of line.
The graph of the function is given below.
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Determine the amount of interest the principal in each account had earned. (From Example 2)
3. On March 3, Raul Avila deposited $10,000 in a savings account that pays 5.5% interest compounded daily until June 21.
4. On March 26, Samuel Griffin deposited $20,000 in a savings account that pays 5.5% interest compounded daily until July 24.
The amount of interest that the principal in each account had earned is as follows:
Raul Avila = $167.12
Samuel Griffin = $364.91
How is compound interest computed?The compound interest can be calculated using the compound interest formula:
A = P(1 + \frac{r}{n})^{nt}
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
It can also be computed using an online finance calculator as follows:
Data and Calculations:Raul Avila:N (# of periods) = 110 days
I/Y (Interest per year) = 5.5%
PV (Present Value) = $10,000
PMT (Periodic Payment) = $0
Results:
FV = $10,167.12
Total Interest = $167.12
Samuel Griffin:N (# of periods) = 120 days
I/Y (Interest per year) = 5.5%
PV (Present Value) = $20,000
PMT (Periodic Payment) = $0
Results:
FV = $20,364.91
Total Interest = $364.91
Thus, using the online finance calculator, the compound interests for each principal have been computed as $167.12 and $364.91, respectively.
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5,679 is invested, part at 12% and the rest at 7%. If the interest earned from the amount invested at 12% exceeds the interest earned from the amount invested at 7% by $407.50, how much is invested at each rate? (Round to two decimal places if necessary.)
The amount of money invested at 12% was $4327 while $1442 was invested at 7%.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount invested at 12% and y represent the amount invested at 7%, hence:
x + y = 5679 (1)
Also:
0.12x = 0.07y + 407.5 (2)
From both equations:
x = 4327, y = 1442
The amount of money invested at 12% was $4327 while $1442 was invested at 7%.
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Geometry
On one side of a 216 square foot rectangular room is 12 feet. How long is the other side?
Answer:
18 ft.
Step-by-step explanation:
Area: 216 sq. ft.
1 side: 12 ft.
Area=l x w
216=12 x ?
216/12 = x
x = 18
PLEASE I BEG HELP ASAP PLEASE
Claus used this picture to explain why the area of a circle is equal to 2
π
r
2
. What is NOT true about the parallelogram he formed?
Answer:
The perimeter of the parallelogram is 2πr
Step-by-step explanation:
The area of the circle should be the same as the area of the parallelogram. Therefore, the area of the circle cannot equal the area of the parallelogram.
Hope this helps. (:
50 POINTS
ANSWER ONLY IF YOU KNOW OR ELSE YOUR GETTING REPORTED
If you are given a circle with center C, how do you locate the vertices of a square inscribed in circle C.
The vertices of an inscribed square of a circle are located on the circumference and on perpendicular diameters
How can the vertices of the square be located?The vertices of a square inscribed in a circle can be located as follows;
Draw a diameter of the circle (a line passing through the center and reaches opposite sides of the circle Draw a second diameter, perpendicular to the above first drawn diameter of the circleJoin the points of intersection of the two lines to complete the drawing of an inscribed square of the circleThe points where the two diameters meet are the vertices of the squareLearn more about geometric construction here: https://brainly.com/question/4062148
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On October 23, 2011, one U.S. dollar was worth 13.65 Mexican pesos.
(a) On that date, how many pesos was 81.35 dollars worth?
Round your answer to the nearest hundredth of a peso.
0 pesos
(b) On that date, how many dollars was 91.03 pesos worth?
Round your answer to the nearest hundredth of a dollars. I need help with both of these math problems.
Taking into account the rule of three, 1110,4275 Mexican pesos was 81.35 dollars worth and 6.67 dollars was 91.03 Mexican pesos worth.
Rule of threeThe rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.
That is, what is intended with it is to find the fourth term of a proportion knowing the other three.
If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.
To solve a direct rule of three, the following expression must be followed, being a, b and c known data and x the variable to be calculated:
a ⇒ b
c ⇒ x
So: [tex]x=\frac{cxb}{a}[/tex]
Amount of Mexican pesos in this casesOn October 23, 2011, one U.S. dollar was worth 13.65 Mexican pesos. So, you can apply the following rules of three:
If 1 dollar is equal to 13.65 Mexican pesos, 81.35 dollars is equal to how many Mexican pesos?1 dollar ⇒ 13.65 Mexican pesos
81.35 dollars ⇒ x
So: [tex]x=\frac{81.35 dollarsx13.65 Mexican pesos}{1 dollar}[/tex]
Solving:
x= 1110,4275 Mexican pesos
f 13.65 Mexican pesos is equal to 1 dollar, 91.03 Mexican pesos is equal to how many dollars?13.65 Mexican pesos ⇒ 1 dollar
91.03 Mexican pesos ⇒ x
So: [tex]x=\frac{91.03 Mexican pesosx 1 dollar}{13.65 Mexican pesos}[/tex]
Solving:
x= 6.67 dollars
In summary, 1110,4275 Mexican pesos was 81.35 dollars worth and 6.67 dollars was 91.03 Mexican pesos worth.
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50 POINTS!!! Find the geometric probabilty of landing in the shaded area of the picture. The small circle has a diamter of 6 meters and the larger circle has a diameter of 54 meters. Show and explain all work.
Using the areas of the circles, the probability of landing in the shaded area of the picture is of 1/81.
What is the area of a circle?The area of a circle of diameter d is given as follows:
[tex]A = 0.25\pi d^2[/tex].
For the smaller circle, the diameter is d = 6, hence the area is:
[tex]A_s = 0.25\pi \times 6^2 = 9\pi[/tex]
For the larger circle, the diameter is d = 54, hence the area is:
[tex]A_l = 0.25\pi \times 54^2 = 729\pi[/tex]
Hence the probability(desired area divided by total area) is:
[tex]p = \frac{9\pi}{729\pi} = \frac{1}{81}[/tex].
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The following formula gives the total surface area S of a cylinder with radius r and height h.
S=2πr(r+h)
Find the total surface area of a cylinder with radius 4 and height 8. Enter an exact answer in terms of π. Do not include S= in your answer.
The total surface area of a cylinder with radius 4 and height 8 is 96π.
Surface area of a cylinderIt follows from the task content that the total surface area of the cylinder is to be determined. The total surface area of the cylinder is given by the formular;
S=2πr(r+h)
where,S = surface arear = radius = 4h = height = 8S=2πr(r+h)
= 2 × π × 4(4 + 8)
= 2 × π × 4(12)
= 2π × 48
= 96π
Hence, the total surface area of the cylinder in terms of π is; 96π.
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What is the slope of the line that passes through (0,5) and (10,0)?
Answer:
-1/2
Step-by-step explanation:
[tex] m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
[tex]m = \dfrac{0 - 5}{10 - 0} = \dfrac{-5}{10} = -\dfrac{1}{2}[/tex]
Answer: slope = -1/2
What is this expression in simplified form?
Answer:
A
Step-by-step explanation:
-6-5
A. 2
C. 3
3
2
A
1
4-3-2-10
-1
-21B
-3
C
E
D
F
1 2 3
In the similarity
transformation of AABC
to ADFE, AABC was dilated by
a scale factor of [? ], reflected
across the [ ], and moved
through the translaton [ ].
B. 1/2
D. 1/3
Answer: A
Step-by-step explanation:
Following the first two steps of the sequence of transformations,
[tex]A(-4,-2) \longrightarrow (-2,-1) \longrightarrow (-2,1)[/tex]
We need to map this onto D(1,1), which involves a translation 3 units right.
In the similarity transformation of ΔABC to ΔDFE, ΔABC was dilated by a scale factor of [1/2 ], reflected across the [x-axis ], and moved through the translation [(X+3, Y+0)].
So, correct option is: A.
Here, we have,
from the given fugre we get,
A =( -4, -2)
Following the first two steps of the sequence of transformations,
Dilated by a factor of 1/2 => A' = ( -2, -1)
reflected across the X-axis => A''=( -2, 1)
and moved through the translation becomes D = ( 1,1)
We need to map this onto D(1,1), which involves a translation 3 units right.
so, translation=> ( -2 + 3, 1+0) => (X+3, Y+0)
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What are the values of x and y?
Answer:
its D hope this helps
Step-by-step explanation:
pls mark brainliest
trigonometry question
worth 100 points!
desperately need help
Answer:
Height is 40√2 m or 56.57 m
Explanation:
Use Pythagoras theorem: a² + b² = c²
where 'a' and 'b' are the legs and 'c' is the hypotenuse
Here given:
a = 20 meterb = heightc = 60 meterSubstitute values:
(20)² + (h)² = 60²
400 + h² = 3600
h² = 3600 - 400
h² = 3200
h = √3200
h = 40√2
h = 56.6 meter
What numbers can u add to make 8243
Answer:
puede ser su raiz que seria 90.79
Step-by-step explanation:
what is the answer (3^3/3^4)^5
Answer:
Exact Form:
1/243
Decimal Form:
0.00411522…
Solve for x in the triangle. Round your answer to the nearest tenth.
[tex]x = 12.9[/tex]
Step-by-step explanation:Note:
The following is sin formula:
[tex] \sin( \theta) = \frac{opposite}{hypotenuse} [/tex]
1) Using the sin formula
[tex]sin(59) = \frac{x}{15} [/tex]
2) Multiply both sides by 15
[tex]15 \sin(59) = \frac{x}{15} \times 15[/tex]
3) Divide both sides by sin(59)
[tex] \frac{15 \sin(59) }{ \sin(59) } = \frac{x}{ \sin(59) } [/tex]
4) Find the value of x
[tex]x = 15 \sin(59) [/tex]
[tex]x = 12.9[/tex]
What is the slope of the line graphed below?
OA. -
OB.
312
O c. //
C.
O D. 23/0
10
(-3,-1)
(0, 1)
Answer:
Your answer is -2/-3
The formula to calculate slope is y2-y1/x2-x1
I think it will help you
an airplane flies 3300 miles with the wind in 3 hours 18 minutes. it takes 4 hours and 24 mins to make the return flight against the same wind. find the speed of the airplane and the speed of the wind.
Answer:
The speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.
Step-by-step explanation:
Let’s assume the speed of the plane =x miles/hr
And let the speed of wind =y miles/hr
So, the speed of the aeroplane in the direction of wind =(x+y) miles/hr
Speed of the aeroplane in the opposite direction of wind =(x–y) miles/hr
We know that, distance=speed×time
Then according to the given conditions, we have
3300=(x+y)×(3+(18/60))
here convert 18mins to hour by dividing by 60 and add to 3hrs.
⇒x+y= 3300/3.3
⇒x+y=1000 … (i)
And,
3300=(x-y)×(4+(24/60))
here convert 24mins to hour by dividing by 60 and add to 4hrs.
⇒x-y= 3300/4.4
⇒x-y=750 … (ii)
Adding equation (i) and (ii), we get
2x=1750
⇒x= 1750/2
=875
Substituting the value of x in equation (ii), we get
875−y=750
⇒y=875-750
⇒y=125
Therefore, the speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.
Find the midpoint of the line segment with the given endpoints: (-1, -6) and (-6, 5).
Answer:
Step-by-step explanation:
First, we will find the midpoint for the x - coordinate first.
Midpoint (x) = [tex]\frac{-1+(-6)}{2} \\=\frac{-1-6}{2} \\=\frac{-7}{2} \\=-3.5[/tex]
Now we will find the midpoint for the y - coordinate.
Midpoint (y) = [tex]\frac{-6+5}{2} \\=\frac{-1}{2} \\=-0.5[/tex]
Therefore from these 2 values we know that the midpoint of this 2 points is (-3.5,-0.5)
The fifth-grade teachers at Washington High School are decorating bulletin boards to get
ready for the new school year. They have 4 large bulletin boards that each need 9 yards of
border. There is also a small bulletin board that only needs 12 feet of border. If border is sold
in 40-foot rolls, how many rolls will the teachers use?
The teacher will use 3 rolls only to have perfect measurements.
1 yard = 3 feet
4 large bulletin boards are there each needing 9 yards of border.
That means 4 large bulletin boards in total need
9×4 yards of border
= 36 yards of border
= 108 feet of border
Also, there is a small bulletin board that only needs 12 feet border
Hence, in total there is a need for
108 + 12 = 120 feet border.
The border is sold in 40-foot rolls.
Hence, there is a need for 120/40 rolls
i.e. 3 rolls
Hence, the teacher will use 3 rolls only.
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Answer:
The answer is 3
Step-by-step explanation:
a = 2√3 ft.;c = 4 ft.
A = 8√3 sq. ft.
True
False
False . The equation a= 2√3 ft.;c = 4 ft is: A= 2√3 ft².
Area of the triangleGiven:
a = 2√3 ft,
c = 4 ft,
Lengths of the sides of a right triangle = a and b
Hypotenuse= c
Hence:
Using Pythagorean theoremc²=a²+b²
4²=(2√3)²+b²
16=12+b²
4=b²
b=2
Area of triangle
A=1/2×a×b
A=1/2×2√3×2
A=4√3÷2
A=2√3 sq.ft
The Area of the triangle is 2√3 ft².
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what fraction is 40cm of 2cm
2/40 = 1/20.
We are able to simplify by dividing 2 and 40 by the greatest common factor (GCF), which was 2. We know this because 2 and 40 can be divided by 2.
2cm is 1/20th of 40cm.
Estimate the solution to the system of equations.
You can use the interactive graph below to find the solution.
\begin{cases} -3x+3y=9 \\\\ 2x-7y=-14 \end{cases}
⎩
⎪
⎪
⎨
⎪
⎪
⎧
−3x+3y=9
2x−7y=−14
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
x= -1\dfrac25, y=2\dfrac35x=−1
5
2
,y=2
5
3
x, equals, minus, 1, start fraction, 2, divided by, 5, end fraction, comma, y, equals, 2, start fraction, 3, divided by, 5, end fraction
(Choice B)
B
x= -1\dfrac25, y=1\dfrac35x=−1
5
2
,y=1
5
3
x, equals, minus, 1, start fraction, 2, divided by, 5, end fraction, comma, y, equals, 1, start fraction, 3, divided by, 5, end fraction
(Choice C)
C
x= -2\dfrac25, y=2\dfrac35x=−2
5
2
,y=2
5
3
x, equals, minus, 2, start fraction, 2, divided by, 5, end fraction, comma, y, equals, 2, start fraction, 3, divided by, 5, end fraction
(Choice D)
D
x= -2\dfrac25, y=1\dfrac35x=−2
5
2
,y=1
5
3
x, equals, minus, 2, start fraction, 2, divided by, 5, end fraction, comma, y, equals, 1, start fraction, 3, divided by, 5, end fraction
The solution to the system of equations is x = -1.4 and y = 1.6
How to estimate the solution?The system of equations is given as:
-3x + 3y = 9
2x - 7y = -14
Divide the first equation by 3
-x + y = 3
Make y the subject
y = 3 + x
Substitute y = 3 + x in 2x - 7y = -14
2x - 7(3 + x) = -14
Expand
2x - 21 - 7x = -14
Evaluate the like terms
-5x = 7
Divide by -5
x = -1.4
Substitute x = -1.4 in y = 3 + x
y = 3 - 1.4
Evaluate
y = 1.6
Hence, the solution to the system of equations is x = -1.4 and y = 1.6
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Answer:
Question:
Estimate the solution to the system of equations.
You can use the interactive graph below to find the solution.
⎪y=−2x−5
⎨y=2x−2
ANSWER:
CORRECT (SELECTED)
x= -3/4
y= -3 1/2
On an average day, 34customers buy a bag of grapes at Jerry's Market. There are an average of 47grapes in each bag. Round to the nearest ten and then multiply to estimate the number of grapes Jerry's customers buy every day.
The total number of grapes bought in a day is 1600 .
What is an Equation ?An equation is a mathematical statement which relates two algebraic expression with an equal sign.
It is given that
34 customers buy a bag of grapes at Jery's Market.
There are an average of 47 grapes in each bag.
Let the no. of grapes = x
Then
x = 34 * 47
x = 1598
rounded to the nearest ten
The total number of grapes bought in a day is 1600 .
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In the following figure AEDC is a square, BA= BC and AE = AC. The area of AEDC is 25 cm² and angle B=90°, Calculate the length of AB.
A triangular prism is a prism which has both of its base sides as a rectangle. The length of side AB is 5/(√2) cm.
What is a triangular prism?Suppose you've got a triangle. Now, stretch it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.
Usually, when we talk about a triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.
The area of AEDC is 25 cm². Therefore,
AEDC = AC²
25 cm² = AC²
AC = 5 cm
In ΔABC,
AB² + BC² = AC²
Since AB=BC,
2(AB²) = AC²
AB² = 25/2
AB = 5/√2 cm
Hence, the length of side AB is 5/(√2) cm.
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The slope indicates initial conditions.
O True
O False
The answer is: True
[tex] \\ \\ \\ [/tex]
I need help with this please!!!
Answer: 3/11
The question is just asking you to select three people out of the group of eleven. And because we don't know there ages, the probability they are the oldest three in the group would be 3/11 or 3 out of 11.
The question is down below
Answer:
108 cmStep-by-step explanation:
The ratio is 1 : 3, so we multiply the numbers by 3
4 * 3 = 12
3 * 3 = 9
So, the length is 12 and the width is 9.
12 * 9 = 108
So the area is 108
Hope this helps!
2. David determines that 3 sqrt 2 cis(7pi/4) = -3+3i. When he considers the graphical representation of these numbers, he knows he made an error. Clearly explain in complete sentences what David observed, and where David made his mistake. State the correct rectangular equivalence of 3 sqrt 2 cis(7pi/4).
The correct rectangular equivalence of 3sqrt(2)·cis(7pi/4 ) is:
3sqrt(2)·cos( 7pi/4 ) + i·sqrt(2)·sin( 7pi/4 ) = 3 - 3i.
Where did David go wrong?David mistakenly interchanged the Sin function and the Cos function when he was calculating the problem.
Hence the correct rectangular equivalence is:
3sqrt(2)·cos( 7pi/4 ) + i·sqrt(2)·sin( 7pi/4 ) = 3 - 3i.
What is rectangular equivalence?An equation is rectangular in form when it is comprised of Variables like X and Y and can be represented on a Cartesian Plane.
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