In order to find the correlation coefficient r, we can use the formula:
[tex]r=\frac{7\sum ^{}_{}(xy)-\sum ^{}_{}x\sum ^{}_{}y}{\sqrt[]{\lbrack7\sum ^{}_{}x^2-(\sum ^{}_{}x)^2\rbrack\cdot\lbrack7\sum ^{}_{}y^2-(\sum ^{}_{}y)^2\rbrack}}[/tex]where the sum must be taken upon all 7 values of x and y.
So, let's find each term and then use them in the formula:
[tex]\begin{gathered} 7\sum ^{}_{}(xy)=7(0\cdot63+0.5\cdot72+1\cdot75+3\cdot81+3.5\cdot84+4\cdot90+5\cdot93) \\ =7\cdot1473=10311 \end{gathered}[/tex][tex]\begin{gathered} \sum ^{}_{}x\sum ^{}_{}y=(0+0.5+1+3+3.5+4+5)\cdot(63+72+75+81+84+90+93) \\ =17\cdot558=9486 \end{gathered}[/tex][tex]\begin{gathered} 7\sum ^{}_{}x^2-(\sum ^{}_{}x)^2 \\ 7\cdot(0^{2^{}}+0.5^2+1^2+3^2+3.5^2+4^2+5^2)-(0+0.5+1+3+3.5+4+5)^2 \\ 7\cdot63.5-17^2 \\ 444.5-289 \\ 155.5 \end{gathered}[/tex][tex]\begin{gathered} 7\sum ^{}_{}y^2-(\sum ^{}_{}y)^2 \\ 7\cdot(63^2+72^2+75^2+81^2+84^2+90^2+93^2)-(63+72+75+81+84+90+93)^2 \\ 7\cdot45144-558^2 \\ 316008-311364 \\ 4644 \end{gathered}[/tex]Now, we need to use them in the formula to find r:
[tex]r=\frac{10311-9486}{\sqrt[]{155.5\cdot4644}}=\frac{825}{\sqrt[]{722142}}\cong0.9708[/tex]Finally, round the answer to the 3 decimal places, we find
r = 0.971
very confused on this , if possible please explain step by step
The resultant of the subtraction of the equation 8x³ + 2x² - 5x -6 from the equation 9x³ + 3x² - 6x + 4 is x³ + x² - x + 10.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects.
The group's total number of items decreases or becomes lower when we subtract from it.
As per the given equations,
9x³ + 3x² - 6x + 4 and 8x³ + 2x² - 5x -6
The subtraction of both equations will be,
⇒ [9x³ + 3x² - 6x + 4] - [8x³ + 2x² - 5x -6 ]
⇒ 9x³ + 3x² - 6x + 4 - 8x³ - 2x² + 5x + 6
⇒ 9x³ - 8x³ + 3x² - 2x² - 6x + 5x + 4 + 6
⇒ x³ + x² - x + 10.
Hence "The resultant of the subtraction of the equation 8x³ + 2x² - 5x -6 from the equation 9x³ + 3x² - 6x + 4 is x³ + x² - x + 10".
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if you walk 2 1/4 miles in 3/4 hours how far can you walk in 2 1/2 hours
FIrst calculate the speed, as follow:
speed = distance/time
distance = 2 1/4 mi = 2.25 mi
time = 3/4 h = 0.75 h
speed = 2.25 mi/0.75 h = 3 mi/h
next, for the distance traveled in 2 1/2 hours, use:
distance = speed x time
time = 21/2 h = 2.5 h
distance = (3 mi/h) x (2.5 h)
distance = 7.5 mi =7 1/2 mi
Hence, you can walk 7 1/2 miles in 2 1/2 hours
Find sin S, sin R, cos S, cos R.sin S =sin R =cos S =cos R =
From the basic knowledge of Trignometry,
We are meant to find sin S , sin R , cos S and cos R:
sin S = opposite / Hypoteuse = 18 / 26
sin R = opposite / Hypotenuse = 16 / 26
cos S = Adjacent / Hypotenuse = 16 / 26
cos R = Adjacent / Hypotenuse = 18 / 26
Use the sequence below to complete each task. -2, 8, -32,... a. Identify the common ratio (r). b. Write an equation to represent the sequence. C. Find the 10th term (a,0)
hello
we're required to write an equation to represent the sequence
-2, 8, -32
first of all, let's identify the first term
first term = -2
common ratio = ?
c
a business has total revenues of $55,000 and total expenses of $63,000. what is the net income or net loss? a. $11800b.-$11800c. $8000d.-$8000
Recall that:
[tex]NetIncome=Revenues-Expenses.[/tex]Since the business has a total revenue of $55,000 and total expenses of $63,000, therefore the net income is:
[tex]\begin{gathered} NetIncome=\text{ \$}55,000-\text{ \$}63,000 \\ =-\text{ \$}8000. \end{gathered}[/tex]Answer: Option D.
yasir received a 50% increase in his allowance this year. He now receives £33 a week. What was his weekly allowance last year?
Answer:
£22
Step-by-step explanation:
x+1/2x=33
1.5x=33
33/1.5=22
The weekly allowance for Yasir last year is £22.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Yasir received a 50% increase in his allowance this year. He now receives £33 a week.
The weekly allowance for last year will be calculated as,
1.5 x (X) = £33
X = £33 / 1.5
X = £330 / 15
X = £22
Therefore, Yasir's weekly allowance for last year is £22.
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2, 4, 5, 6, 6, 7
What is the mean of the list of numbers above?
Answer: 5
Step-by-step explanation: add up the numbers to get 30 then divide by 6 (the amount of numbers) to get 5
Answer: 5
Step-by-step explanation:
the mean is the average. add the numbers together then divide by how many addends you have.
2 + 4 + 5 + 6 + 6 + 7 = 30
30/6 = 5
:)
6.Landscaping Calculate the area (in square feet) of a flower garden shaped like a circularsector with radius 60 ft and central angle 40 degrees.
The area of the circular sector is given as:
[tex]\begin{gathered} \text{Area}=\frac{\theta}{360}\times\pi r^2 \\ \end{gathered}[/tex]Given that, radius= 60ft and angle =40 degrees
[tex]\begin{gathered} \text{Area}=\frac{40}{360}\times3.14\times60\times60 \\ \text{Area}=\frac{452160}{360} \\ \text{Area}=1256\text{square f}eet \end{gathered}[/tex]A car rental agency charges a fixed fee plus a daily rate. The function f (x) = 30x + 10 expresses the total cost of renting a car for x days. Suppose the agency doubles the fixed fee and increases the daily rate by $5. Which function represents these changes? A. f(x) = 60 (x + 5) + 10 B.f(x) = 60x + 15 C. f(x) = 30 (x + 5) + 20 D. f (x) = 35x + 20
In the given equation:
f(x) = 30x+ 10, where x is the number of days
We can see that at the beggining, when x = 0, then f (0) = 30 · 0+ 10 = 10
Then, renting a car costs at least $10, so $10 is the fixed fee
Each day that passes $30 is being multiplicated, then it cost $300 per day.
Then, the equation is expressed by
f(x)= daily rate · x + fixed fee
If the agency doubles the fixed fee, it would be that 2 · $10 = $20
If the agency increases the daily rate by $5, in addition, then $30 + $5 = $35 woul be the cost each day.
Then, with these new costs we reaplce our equation
f(x)= daily rate · x + fixed fee
f(x)= 35 · x + 20
Answer: D. f (x) = 35x + 20Expand and simplify(3x+4)(2x + 3)
Answer:
6x²+17x+12
Step-by-step explanation:
open the bracket
3x(2x+3) 4(2x+3)
6x²+9x+8x+12
6x²+17x+12
hope it helps
please mark brainliest
Answer:
6x^2 + 17x + 12
Step-by-step explanation:
first (distribute):
(3x+4)(2x+3)
3x(2x+3) + 4(2x + 3)
then (distribute) again:
3x(2x+3) = 6x^2 + 9x
4(2x + 3) = 8x + 12
then (combine terms):
6x^2 + 9x + 8x + 12
6x^2 + 17x + 12
11 – 8 (5 – 2) help
Answer
11 - 8 (5 -2) = -13
Explanation
11 - 8 (5 -2)
To solve this, we will first solve the one in the bracket
11 - 8 (5 -2)
= 11 - 8 (3)
= 11 - 24
= -13
Hope this Helps!!!
What is the equation of the
line that goes through
(-1, 3) and is perpendicular
to y = 4x - 7?
Answer:
Step-by-step explanation:Perpendicular lines have a slope that is the negative reciprocal of the given line.
For example, if a given line has the slope 3/2, the the perpendicular line would have the slope -2/3.
For the given line: y = 4x - 7, the perpendicular line would have a slope of -1/4
There isn't enough info in the question to determine the y-intercept. Literally, any y-intercept could work and the line would still be perpendicular. Is the line supposed to pass through a certain point?
Your answer would be something like: y = -1/4 x + b
b is the y-intercept...if your question paper is multiple choice, choose the answer with the slope of -1/4. If it's supposed to pass through a certain point (x,y) replace x and y with the values in that point and solve for b to get the y-intercept.
a commuter travels 67 km in 32 min .what is it's speed in kilometer per hour?
125.625 kilometers per hour
Explanations:Note:
60 minutes = 1 hour
32 minutes = 32/60 hours
The speed is the distance traveled in 1 hour
Distance = 67 km
Time = 32/60 hours
Speed = Distance / time
[tex]\begin{gathered} Speed\text{ = 67 }\div\text{ }\frac{32}{60} \\ \text{Speed = 67 }\times\text{ }\frac{60}{32} \\ \text{Speed = }\frac{4020}{32} \\ \text{Speed = }125.625\text{ km per hour} \end{gathered}[/tex]hi, i need aloy of help
Answer:
XY ≈ 14.32
Step-by-step explanation:
XY² = XZ² + ZY²
XY² = 6² +13²
XY² = 36 + 169
XY² = 205
XY = [tex]\sqrt{205\\[/tex]
XY ≈ 14.32
Evaluate the expression.3 – 5 (11 + 4) = 52
In order to evaluate this expression, let's calculate the operations in the left side and compare the final value with the value in the right side:
[tex]\begin{gathered} 3-5(11+4)=52 \\ 3-5\cdot15=52 \\ 3-75=52 \\ -72=52 \end{gathered}[/tex]Since the values don't match, so the expression is FALSE.
Who is Caleb? What is his job? Hpw p;d ois;O?
Answer:
oiutwecldvi ufa
Step-by-step explanation:
9m^2 - 49factor each expression. Be sure to check for the greatest common factor first.
We need to factor the following polynomial:
[tex]9m^2-49[/tex]We can see that:
[tex]9m^2=3^2m^2=(3m)^2[/tex]And
[tex]49=7^2[/tex]Then, we can use the following factor rule:
[tex]x^2-y^2=(x-y)(x+y)[/tex]We have that:
[tex]x=3m,y=7[/tex]Then, we can factor the polynomial as follows:
[tex]9m^2-49=(3m)^2-(7)^2=(3m-7)(3m+7)[/tex]In summary, we have:
[tex]9m^2-49=(3m-7)(3m+7)[/tex]Can someone tell me how to solve it with a picture on how you did it. Teacher told me to show my work. It hard pls Helppp
The solution to the given inequality in interval notation is: -6 ≤ v ≤ 3
How to solve the given inequality?In this exercise, you're required to determine all the values of v that simultaneously satisfy given inequality. First of all, we would have to eliminate the fraction on the left-hand side of the inequality by adding using an appropriate lowest common denominator of 3 as follows:
(2 × |4v + 6|)/3 - 2/1 ≤ 10
[(2 × |4v + 6|) - (3)2]/3 ≤ 10
[(2 × |4v + 6|) - 6]/3 ≤ 10
Cross-multiplying, we have:
(2 × |4v + 6|) - 6 ≤ 10 × 3
(2 × |4v + 6|) - 6 ≤ 30
Adding 6 to both sides, we have:
(2 × |4v + 6|) - 6 + 6 ≤ 30 + 6
(2 × |4v + 6|) ≤ 36
Dividing both sides by 2, we have:
(2 × |4v + 6|)/2 ≤ 36/2
|4v + 6| ≤ 18
Evaluating the absolute value function, we have:
4v + 6 ≤ ±18
For the positive interval, we have:
4v ≤ 18 - 6
4v ≤ 12
v ≤ 12/4
v ≤ 3.
For the negative interval, we have:
4v ≥ -18 - 6
4v ≥ -24
v ≥ -24/4
v ≥ -6
Lastly, we would express the solution as an interval notation as follows:
-6 ≤ v ≤ 3
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Pythagorean Theorem• Create a real-world problem involving three lengths that form a right triangle• Give the measurement of the “legs”, then solve for the missing hypotenuse
Solution
Problem
A ladder is leaning on a wall that is 6 feet tall. The distance from the bottom of the ladder to the wall is 8 feet wide.
Solution
Therefore, using the Pythagorean Theorem, 6^2 + 8^2 = 36 + 64 = 100. The square root of 100 is 10. The triangle's hypotenuse or the ladder's length is 5 feet.
type the correct answer in the Box spell all words correctly which type of coordinates does Andrews. Take Andrew studying mathematics and studying about the (blank (coordinate system in this system the coordinates of the of a point are dependent on the distance of the point from the origin and the angle of the start of the points substance at the origin
Where the coordinates of a points pedepend on the distance to the origin of the coordinate system and also depend on the angle, the coordinate system is a POLAR coordinate system.
Tracy's Termite Control has a net worth of $750,000. The assets total $980,235. Find the amount of the liabilities.$1,730,235$730,235$229,765$230,235None of these choices are correct.
Tracy's Termite Control has a net worth of $750,000.
The assets total $980,235.
Recall that the assets are the sum of liabilities and equity.
[tex]Assets=Liabilities+Equity[/tex]For the given case,
Assets = $980,235
Equity = $750,000
Let us substitute these values into the above formula and solve for liabilities
[tex]\begin{gathered} Assets=Liabilities+Equity \\ 980,235=Liabilities+750,000 \\ Liabilities=980,235-750,000 \\ Liabilities=\$230,235 \end{gathered}[/tex]Therefore, the amount of the liabilities is $230,235
The 4th option is the correct answer.
A monk crossbred plants, which can have purple or white flowers, and obtained 518 plants with white flowers and 229 plants with purple flowers. Find the
empirical probability that a plant had each type of flower.
The probability a plant had white flowers is. (Round to the nearest hundredth as needed.)
Probability that a plant had each type of flower. 0.36 and 0.64
What is Probability?
Probability is a branch of mathematics that quantifies the Probability of an event occurring or the Probability of a statement being true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the improbability of the event and 1 indicating certainty.
Number of white flower plants = 660
Number of purple flower plants = 368
To discover the empirical Probability that a plant had each sort of flower.
Formula
empirical Probability is found by rehashing an test and watching the outcomes.
P(event) = (the number of time the occasion happens) ÷ (add up to number of trial)
Here, Total number of plants = (660+368) = 1028
Now, Probability of white flower plant = = 0.64
And,
Probability of purple flower plant = = 0.36
Hence, The empirical Probability of white flower is 0.64 and the empirical Probability of purple flower is 0.36
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Based on statistics from a worldwide health organization, in 2005 there were22.6 million people worldwide living with a certain disease, and 1.9 million deaths from the disease. By 2015,the number of people living with the disease had grown to 38.9 million deaths were reported. Find the percent change for each statistic, and write any conclusion you can draw.
Percent change of people living with the disease = 72.1%
Percent change of number of death = 5.2%
Explanation:The Number of people living with the disease increased from 22.6 million in 2005 to 38.9 million in 2015
To get the percentage, we will apply the formula:
[tex]percent\text{ change = }\frac{New\text{ value - Old value}}{Old\text{ value}}\times\text{ 100\%}[/tex][tex]\begin{gathered} new\text{ value = 38.9 million, old value = 22.6 million} \\ percent\text{ change = }\frac{38.9\text{ - 22.6}}{22.6}\text{ }\times100 \\ percent\text{ change = 0.721 }\times\text{ 100\% = 72.1\%} \end{gathered}[/tex]The number of death increased from 1.9 million to 2 million from 2005 to 2015:
[tex]\begin{gathered} new\text{ value = 2 million, old value = 1.9 million} \\ The\text{ percent change = }\frac{2-1.9}{1.9}\times100\text{ \%} \\ The\text{ percent change = 0.052 }\times\text{ 100\% = 5.2\%} \end{gathered}[/tex]Conclusion:
The number of people living with the disease increased drastically within 10 years.
But the percent change in the number of death isn't as high as the number of people living with the disease. It means the disease is highly infectious but has a low death rate
which of the relations has a domain of (-5, 0, 5)
Choice A
Is the answer
m^2+5mn+5n^2factor each polynomial completely. If a polynomial is prime, state this.
m²+5mn+5n²
To factor the above, we need two factors of 5n², such the sum gives 5n and the product gives 5n²
No such factors exists, hence the polynomial is prime.
Polynomial equation
Using the Factor Theorem, the polynomial function with the desired characteristics is given by:
f(x) = -x(x² + 9)(x - 1)(x - 2).
Factor TheoremThe Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex] is given by the rule presented as follows.
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative), determining the end behavior of the function.
For this function, we have:
Two complex roots, hence a factor of (x² + 9).A root at x = 0, hence f(x) = ax(x² + 9).The two other roots are free, hence I am going to attribute x = 1 and x = 2, hence the equation is:
f(x) = ax(x² + 9)(x - 1)(x - 2).
The end behavior is that the function increases to the left and decays to the right, meaning that the leading coefficient is negative, hence a possible function is given by:
f(x) = -x(x² + 9)(x - 1)(x - 2).
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Roots of Quadratics 50 PTS!!!
The values of k for the different quadratic equation solutions are as follows
a the equation 2x² - x + 3k = 0 has two distinct real roots
k < 1/24b. the equation 5x² - 2x + (2k − 1) = 0 has equal roots
k = 3/5ci the equation -x² + 3x + (k + 1) = 0 has real roots
k > -3.25d the equation 3kx² - 3x + 2 = 0 has no real solutions
k < ± 1.633How to solve quadratic equations to get different answersQuadratic equations of the form ax² + bx + c = 0 is solved using the formula
[tex]-b+\frac{\sqrt{b^{2}-4ac } }{2a}[/tex] OR [tex]-b-\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]
The equation b² - 4ac is called the discriminant and it is used as follows
To solve the equation and get two real roots: 2x² - x + 3k = 0
b² - 4ac > 0substituting the values gives
(-1)² - 4 * 2 * 3k > 0
1 - 24k > 0
1 > 24k
divide through by coefficient of k
k < 1/24
To solve the equation and get equal roots: 5x² - 2x + (2k − 1) = 0
b² - 4ac = 0substituting the values gives
(-2)² - 4 * 5 * (2k - 1) = 0
4 - 40k + 20 = 0
-40k = -24
divide through by coefficient of k
k = 3/5
To solve the equation and get real roots -x² + 3x + (k + 1) = 0
b² - 4ac > 0substituting the values gives
(3)² - 4 * -1 * (k+1) > 0
9 + 4k + 4> 0
4k > -13
divide through by coefficient of k
k > -3.25
To solve the equation and get no real solutions 3kx² - 3x + 2 = 0
b² - 4ac < 0substituting the values gives
(-3)² - 4 * 3k * 2 < 0
9 - 24k² > 0
9 > 24k²
divide through by coefficient of k²
k² < 24/9
k < ± 1.633
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Answer:
ax² + bx + c = 0 is solved using the formula
Step-by-step explanation:
If a car moves along a perfectly straight road at a velocity of 24 m/s, how far will the car go in 35 minutes?
Answer:
distance = rate x time
Step-by-step explanation:
distance = ?
rate = 24 m/s
time = (35 x 60) = 2100 s
thus,
distance = 24 x 2100 = 50400 m
Catalina is moving to a new house. Her old house is 3.5 miles away from her new house. How many feet are between Catalina’s old and new house?
18480 feet are between her old and new house
Given{x=7y-9 2x-14y= -18I think the solution is b? Am I correct?
there are infintely many solutions. The solution set is {(x, y)| x = 7y - 9} or {(x, y)| 2x - 14y = -18 (option B)
Explanation:Given:
x = 7y - 9 . . .(1)
2x - 14y = -18 . . . (2)
To find:
the solution of the system of equations
To determine the value of x and y, we will apply the substitution method:
we will substitute for x in equation (2):
2(7y - 9) - 14y = -18
2(7y) + 2(-9) - 14y = -18
14y - 18 - 14y = -18
14y - 14y - 18 = -18
0 - 18 = -18
-18 = -18
The left-hand side of the equation is equal to the right side of the equation.
when this happens, it is called infinitely many solutions.
Hence, there are infintely many solutions. The solution set is {(x, y)| x = 7y - 9} or {(x, y)| 2x - 14y = -18 (option B)