Answer:
B
Step-by-step explanation:
The function that models the situation is an exponential decay function of the form:
t(m) = a(1 - r)^m
where:
t(m) is the number of trees after m months
a is the initial number of trees (5,500 in this case)
r is the monthly rate of decrease (3.2% or 0.032 as a decimal)
Substituting the values given in the options, we get:
A) t(m) = 5,500(0.032)^m
B) t(m) = 5,500(1-0.032)^m = 5,500(0.968)^m
C) t(m) = 5,500(1.032)^m
D) t(m) = 5,500(1-0.968)^m = 5,500(0.032)^m
Option B is the correct answer as it correctly models the situation with exponential decay with a starting value of 5,500 trees and a monthly rate of decrease of 3.2%.
Answer: The formula for exponential decay is given by:
t(m) = a(1-r)^m
where
a = initial value
r = decay rate
Here, the initial value is 5,500 and the monthly decay rate is 3.2% or 0.032. So the function that can be used to find the number of trees in the forest at the end of m months is:
t(m) = 5,500(1 - 0.032)^m
t(m) = 5,500(0.968)^m
Therefore, the answer is (D) t(m) = 5,500(0.968)^m.
Your welcome (;
Which of the following comparisons are true? Select all that apply. A. 3 . 2 > 0 . 32 B. 4 . 7 < 4 . 70 C. 2 . 6 > 2 . 59
Therefοre, οnly the cοmparisοns (A and C) are true.
What is Cοmparisοn?In mathematics, a cοmparisοn is a statement that describes the relatiοnship between twο quantities οr expressiοns. Cοmparisοns can be used tο determine if twο values are equal, if οne value is greater than οr less than anοther value, οr if twο values are prοpοrtiοnal tο each οther.
A. 3.2 > 0.32
This cοmparisοn is true. 3.2 is greater than 0.32 because 3.2 has a whοle number value οf 3, which is greater than the whοle number value οf 0 in 0.32.
B. 4.7 < 4.70
This cοmparisοn is false. 4.7 is nοt less than 4.70 because the extra zerο in 4.70 dοes nοt change its value, and .7 is nοt less than .70.
C. 2.6 > 2.59
This cοmparisοn is true. 2.6 is greater than 2.59 because the extra 9 in 2.59 dοes nοt change its value, and 6 is greater than 5.
Therefοre, οnly the cοmparisοns (A and C) are true.
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Need help this is due in an hour. Please help. :)
By answering the presented question, we may conclude that Thus function f(x) = y = (5, 7, 1, 4, 9, 5, 3, 2) and x = (3, 8, 9, 13, 10, 6, 5, 4).
what is function?Mathematicians examine numbers and their variations, equations and associated structures, forms and their locations, and prospective positions for these things. The term "function" refers to the relationship between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs in which each input leads to a single, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible functions are on functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions.
A. Assume f(x) = (4x - 7). To obtain the inverse of f(x), we must swap x and y in the function and solve for y.
As a result, g(x) = (x + 7)/4 is the inverse of f(x).
B. We must demonstrate that f(g(x)) = x for any x in g's domain.
f(g(x)) = f((x + 7)/4) = 4((x + 7)/4) - 7 = x + 7 - 7 = x + 7 - 7 = x.
As a result, f(g(x)) = x, confirming that g(x) is really the inverse of f. (x).
C. Assuming the function:
| x | 5 8 9 13 10 6 5 4 |\s|—-|—-|—-|—-|—-|—-|—-|—-|\s| f(x) | 3 7 1 4 9 5 3 2 |
Thus f(x) = y = (5, 7, 1, 4, 9, 5, 3, 2) and x = (3, 8, 9, 13, 10, 6, 5, 4).
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Write 9/11 in the form √a where a is an integer to be found.
Answer:
To write 9/11 in the form √a, we need to simplify the fraction so that it has a square root in the numerator or the denominator. We can do this by multiplying the numerator and denominator by √11:
9/11 × (√11/√11) = (9√11)/(11√11) = (√(9 × 11))/(√(11 × 11)) = √99
Therefore, 9/11 can be written in the form √99, where a = 99.
The midpoint of AB is M(-6,-4). If
the coordinates of A are (-4, -3), what
are the coordinates of B?
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -4}{2}~~~ ,~~~ \cfrac{ y -3}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M} }{(-6~~,~~-4)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -4 }{2}=-6\implies x-4=-12\implies \boxed{x=-8} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -3 }{2}=-4\implies y-3=-8\implies \boxed{y=-5}[/tex]
PLEASE HELP ASAP!!! I REALLY NEED IT, THANK YOU
I'm pretty sure that this is correct I'm sorry I tried my best
PLEASE HELP! I NEED IT FOR A PRACTICE TEST!!
The wοrk dοne in pushing the car up the incline is 39,672 fοοt-pοunds.
What is Dοt Prοduct?The dοt prοduct is a mathematical οperatiοn that takes twο vectοrs and prοduces a scalar. It is the prοduct οf the magnitudes οf the twο vectοrs and the cοsine οf the angle between them.
Tο calculate the wοrk dοne, we need tο find the fοrce applied tο the car and the distance it was mοved.
First, let's calculate the fοrce required tο push the car up the incline. We can use the weight οf the car and the angle οf the incline tο find the fοrce required.
The weight οf the car is given as 1850 pοunds. The fοrce required tο push the car up the incline is equal tο the cοmpοnent οf the weight that acts parallel tο the incline. This is given by:
fοrce = weight * sin(angle)
where the angle is 7 degrees.
Plugging in the values, we get:
fοrce = 1850 * sin(7) = 220.4 pοunds
Nοw, we need tο find the distance that the car was pushed up the incline. This is given as 180 feet.
Using the dοt prοduct, the wοrk dοne can be calculated as:
wοrk = fοrce * distance * cοs(angle)
where the angle is the angle between the fοrce and the displacement vectοrs. In this case, the fοrce and displacement are in the same directiοn, sο the angle is 0 degrees and cοs(0) = 1.
Plugging in the values, we get:
wοrk = 220.4 * 180 * cοs(0) = 39,672 fοοt-pοunds
Therefοre, the wοrk dοne in pushing the car up the incline is 39,672 fοοt-pοunds.
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Let A denote the event of placing a $1 straight bet on a certain lottery and winning. Suppose that, for this particular lottery, there are 2,352 different ways that you can select the four digits (with repetition allowed)
in this lottery, and only one of those four-digit numbers will be the winner. What is the value of P(A)? What is the value of P(A)?
What is the value of P(A)?
P(A)= (Round to five decimal places as needed.)
What is the value of P(A)?
P(A)=(Round to five decimal places as needed.)
Answer:
The probability of winning the lottery, denoted by P(A), can be calculated as follows:
P(A) = number of winning outcomes / total number of possible outcomes
Since there is only one winning four-digit number and there are 2,352 possible four-digit numbers, we have:
P(A) = 1/2352
Using a calculator, we get:
P(A) ≈ 0.00042
Therefore, the value of P(A) is approximately 0.00042 or 4.2 × 10^(-4) (rounded to five decimal places).
Step-by-step explanation:
At a Halloween sale, every item in the store is advertised as one-fourth off the original price. If an item is marked with a sale price of $150, what was its original price? Show or explain how you got your answer.
Answer:
$200.00
Step-by-step explanation:
We are asking what is 75% of what number is 150. If we take off 1/4 or 25% we are leaving on 3/4 or 75%
.75 x = 150 Divide both sides by .75
[tex]\frac{.75x}{.75}[/tex] = [tex]\frac{150}{.75}[/tex]
x = 200
Check:
200 x .25 = 50 To find the discount.
200 - 50 = 150 Subtract the discount from the original price to find the sale's price.
Helping in the name of Jesus.
Help with math problems
The graph of inequalities are attached accordingly.
What are graph of inequalities and what value do they provide in real life?Graphs of inequalities are visual representations of solutions to inequality equations.
These graphs consist of shaded regions on a coordinate plane that indicate all the points that satisfy a given inequality. In real life, graphs of inequalities are used in many areas, including business, finance, and science.
For example, a company may use a graph of inequalities to determine the feasible production and pricing strategies that will maximize profits. Similarly, a biologist may use a graph of inequalities to analyze the optimal conditions for the growth of a particular species. The graphs of inequalities provide a quick and easy way to understand and visualize complex mathematical relationships.
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In the given polygon EFGHIJ if JG = 12 cm JD = 10 cm, JC 8 cm, JA = 5 = cm JB = 3 cm then find the area E of the polygon. EA, IB, FC and DH are perpendiculars drawn on the diagonal JG.
We may use the trapezoid area formula to get the areas of trapezoids EJFG, FGHJ, and HJIE. The entire area of polygon EFGHIJ may then be calculated by adding these regions together.
To begin, we must determine the lengths of segments JF, JH, JE, and JI. We can get these lengths using the Pythagorean theorem: JF = (JG2 - FG2) = (122/102) = 44 = 211 cm JH = (JG2 - GH2) = (122) - 82 = √80 = 4√5 cm JE =(JF2 - EF2) =(21112 - 52) =(44 - 25) = 19 cm JI = (JH2 - IH2) = (452 - 32) = (80 - 9) = 71 cm We can now calculate the trapezoidal areas: Trapezoid area EJFG = (JE + JF) * FG / 2 = (211 + 19) * 5 / 2 = 511 + 519 cm2 Trapezoid area FGHJ = (FG + GH + JF) + JH) * HJ / 2 = (10 + 8 + 211 + 45) * 12 / 2 = 120 + 1211 + 245. HJIE = (JI + JE + IH + HE) trapezoid area * JH / 2 = (√71 + √19 + 3 + 3) * 4√5 / 2 = 10√5 + 2√71 cm^2 Lastly, we may sum these areas to calculate the total area of polygon EFGHIJ: E = trapezoid area EJFG + trapezoid area FGHJ + trapezoid area HJIE E = (5√11 + 5√19) + (120 + 12√11 + 24√5) + (10√5 + 2√71) E = 5√11 + 5√19 + 120 + 12√11 + 24√5 + 10√5 + 2√71 E = 120 + 15√11 + 34√5 + 15√19 + 2√71 E ≈ 372.9 cm^2 As a result, the area of polygon EFGHIJ is 372.9 square centimeters.
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Same items have same prices.
Different items have different prices.
1. How much is a helmet?
2. How much is a bell?
3.How much is a lock?
4. Explain how you figured out the prices.
Answer:
Helmet = 29, Bell = 10, Lock = 24
HELP ASAP WILL GIVE 100 POINTS AND BRAINLYEST IF YOU DON"T ANSWER WITH THE INTENT TO ANSWER CORRECTLY I WILL REPORT YOU
√49 is a perfect square and therefore rational.
√50 is also a perfect square and therefore rational.
∛127 is a non perfect cube and therefore irrational.
∛125 is rational because it is equal to a whole number.
What is a perfect square?It can be expressed as the product of two equal integers. Perfect squares are also known as 'whole squares' or 'complete squares'.
√49 is a perfect square and therefore rational.
This is because the square root of 49 can be expressed as a common fraction 7/7. The square root of 49 = 7, which is a whole number.
√50 is also a perfect square and therefore rational.
The square root of 50 can be expressed as a common fraction 5/5. The square root of 50= 5, which is a whole number.
∛127 is a non perfect cube and therefore irrational.
This is because the cube root of 127 cannot be expressed as a common fraction. The cube root of 127 = approximately 4.9, which is not a whole number.
∛125 is rational because it is equal to a whole number.
The cube root of 125 can be expressed as a common fraction 5/5. The cube root of 125 = 5, which is a whole number.
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Use the double angle identities to find the following value.
If cosθ = √10/8 and 3π/2 < θ < 2π, find sin2θ
Answer:
We can use the double angle identity for sine to find sin2θ:
sin2θ = 2sinθcosθ
Since cosθ = √10/8 and 3π/2 < θ < 2π, we know that θ is in the fourth quadrant, where sine is negative. We can use the Pythagorean identity to find the value of sinθ:
sin²θ + cos²θ = 1
sin²θ = 1 - cos²θ
sinθ = -√(1 - cos²θ)
Substituting the value of cosθ, we get:
sinθ = -√(1 - (√10/8)²) = -√(1 - 5/16) = -√(11/16) = -√11/4
Now we can plug in the values of sinθ and cosθ into the double angle identity for sine:
sin2θ = 2sinθcosθ = 2(-√11/4)(√10/8) = -√110/16 = -√(11/4)(10/16) = -√(55/8)
Therefore, sin2θ = -√55/8 when cosθ = √10/8 and 3π/2 < θ < 2π.
Question 6
8.2
#6
Quadrilateral LMQW is shown.
mL-14x-10
mM-231-4
mN-6x422
IF LMNW is a parallelogram, what is the value of y
Type your answer as a whole number,
Answer:
Value of y is 6
Step-by-step explanation:
Two features of a parallelogram:
1. Opposite angles are equal:
which means:
m∠L = m∠N
∴[tex]14x - 10 = 6x + 22[/tex]
Bring like terms together and make x the subject of the equation:
[tex]14x - 6x = 22 + 10[/tex]
[tex]8x = 32[/tex]
[tex]x = \frac{32}{8}[/tex]
∴x = 4
Substitute this value of x to determine the measurement of ∠N:
m∠L = [tex]14(4) - 10[/tex]
= 46°
∴m∠N = 46°
2. Adjacent angles are supplementary:
which means:
m∠M + m∠N = 180°
[tex](23y - 4) + 46 = 180[/tex]
Expand the parenthesis, bring like terms together and make y the subject of the equation:
[tex]23y - 4 + 46 = 180[/tex]
[tex]23y = 180 - 46 + 4[/tex]
[tex]23y = 138[/tex]
[tex]y = \frac{138}{23}[/tex]
∴y = 6
for which equation is x=5 a solution
a. 2+x=3
b. 3x=15
c. x/2=10
d. x-7=12
Pleace write how do you get the answer full explanation Pleace
Answer: b
Step-by-step explanation:
Okay, so what you need to do is plug in the 5 for x in all equations. once you do that, then you’ll see if the statement makes sense.
A would be= 2 + 5 = 3 and that would be 7=3 which it doesn’t
B would be 3(5)=15 and that would be 15=15
C would be 5/2=10 and thats not true because that would be 2.5=10
And lastly D would be 5-7=12 and that's nit true because that would be -2=12 and that's not true
want points? ANSWER NOW.
The expression 3x − 10 represents the time it takes a commuter to travel in the morning to work. The expression 12x + 8 represents the time it takes a commuter to travel in the evening from work. What is the total travel time?
15x − 2
9x − 2
15x + 2
9x + 2
Answer: 15x-2 (answer A)
Step-by-step explanation:
To find the total travel time, we need to add the time it takes to travel in the morning and the time it takes to travel in the evening:
Total travel time = (3x - 10) + (12x + 8)
Simplifying the expression by combining like terms, we get:
Total travel time = 15x - 2
Therefore, the total travel time is 15x - 2. So, the answer is (a) 15x - 2.
Answer:
Step-by-step explanation:
The expression 3x − 10 represents the time it takes a commuter to travel in the morning to work. The expression 12x + 8 represents the time it takes a commuter to travel in the evening from work. What is the total travel time?
15x − 2
9x − 2
15x + 2
9x + 2
the answer is (a) 15x-2 hope that helps :)
Need help with This Math
Answer:
C. The areas of the shaded regions are equal
Step-by-step explanation:
The area of a circle of radius r = πr²
The area of the shaded region in the left figure
= Area of outer circle - Area of inner circle
= π(AC)² - π(AB)²
Since RT = AC and RS = AB, substituting for AC and AB gives us
π(AC)² - π(AB)² = π(RT)² - π(RS)²
The expression on the right is the area of the shaded region in the left circle
So the shaded regions of both figures have the same area
Answer
C. The areas of the shaded regions are equal
It is suggested that the sequence 21, 1kkak=+...produces only prime numbers.
The answers to each question are:
(a) a1 = 3, a2 = 5, a4 = 17 are prime numbers.
(b) 9 is not a prime number,
What are the prime numbers?
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, it can only be divided evenly by 1 and itself. Examples of prime numbers include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and so on.
(a) [tex]a_{k} = 2 ^ k + 1[/tex]
[tex]a_{1} = 2^1 + 1 = 3[/tex]
[tex]a_{2} = 2 ^ 2 + 1 = 5[/tex]
[tex]a_{4} = 2 ^ 4 + 1 = 17[/tex]
a1, a2, a4 are prime numbers.
(b) We know when k = 3 an [tex]a_{3} = 2 ^ 3 + 1 = 9[/tex].
9 is not a prime number, it can be divide by 3 * 3 so the Sequence does not always produce a prime number.
Hence, the answers to each question are:
(a) a1 = 3, a2 = 5, a4 = 17 are prime numbers.
(b) 9 is not a prime number,
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Complete question:
It is suggested that the sequence [tex]a_{k} = 2 ^ k + 1[/tex], k...I produces only prime numbers.
(a) Show that a, a, and a, produce prime numbers.
(b) Prove by counter-example that the sequence does not always produce a prime number.
Which equation represents the inverse of y=(x+5)^2, for x>0?
Answer:
b
Step-by-step explanation:
A farmer notices that there is a linear relationship between the number of bean stalks, n, she plants and the yield, Y. When she plants 3 stalks, each plant yields 115 ounces of beans. When she plants 8 stalks, each plant yields 190 ounces of beans.
Answer:
Step-by-step explanation:
We can use the information given to find the equation of the line that represents the relationship between the number of bean stalks and the yield. The equation of a line is typically given by the slope-intercept form, y = mx + b, where y is the dependent variable (in this case, the yield), x is the independent variable (the number of bean stalks), m is the slope, and b is the y-intercept.
To find the slope of the line, we can use the formula:
m = (Y2 - Y1) / (n2 - n1)
where (n1, Y1) and (n2, Y2) are two points on the line. We can use the two data points given in the problem to find the slope:
m = (190 - 115) / (8 - 3) = 15
To find the y-intercept, we can use the point-slope form of a line, which is:
y - Y1 = m(x - n1)
where (n1, Y1) is one of the points on the line. We can use the point (3, 115):
y - 115 = 15(x - 3)
Simplifying:
y = 15x - 20
Therefore, the equation that represents the relationship between the number of bean stalks and the yield is:
Y = 15n - 20
This equation tells us that for each additional bean stalk planted, the yield increases by 15 ounces, and the y-intercept of -20 indicates that even if no bean stalks were planted, there would still be a yield of -20 ounces (which doesn't make physical sense in this case, but is a mathematical artifact of the linear regression).
The sum of 6 and b is at most - 17.
You can invest in taxable bonds that are paying a yield of 9.1 percent or a municipal bond paying a yield of 7.35 percent. Assume your marginal tax rate is 21 percent. a. Calculate the after-tax rate of return on the taxable bond? (Round your percentage answers to 2 decimal places. (e.g., 32.16)) b. Which security bond should you buy?
The after-tax rate of return on a taxable bond is calculated by multiplying the pre-tax yield by one minus the tax rate. In this case, it would be 9.1% x (1 - 0.21) = 7.19%. The municipal bond is tax-free, so its after-tax rate of return is equal to its pre-tax yield of 7.35%. Therefore, you should buy the municipal bond as it has a higher after-tax rate of return than the taxable bond.
classifying paralelagrams
a. Length of GK = [tex]\sqrt{34}[/tex] and Length of adjacent to GK = [tex]\sqrt{34}[/tex]
b. Slope of GK = [tex]\frac{5}{3}[/tex] and Slope of adjacent to RS = [tex]-\frac{3}{5}[/tex]
c. The parallelogram GHJK is Square.
Define the term parallelogram?A quadrilateral with two sets of parallel sides is referred to as a parallelogram. As a result, a parallelogram's opposite sides are parallel and congruent in length, and its opposite angles are similarly congruent.
Given in figure GHJK, the vertices are G(-3, 6), H(2, 3), J(-1, -2), K(-6, 1)
a. Length of line = [tex]\sqrt{({x_{2}-x_{1})^{2} } + ({y_{2}-y_{1})^{2}}[/tex]
for points G(-3, 6) and K(-6, 1)
Length of GK = [tex]\sqrt{(-6+3)^{2} + (1-6)^{2} }[/tex] = [tex]\sqrt{34}[/tex]
Length of GK = [tex]\sqrt{34}[/tex]
Length of adjacent side (GH, KJ) to GK = [tex]\sqrt{(2+3)^{2} + (3-6)^{2} }[/tex] = [tex]\sqrt{34}[/tex]
Length of adjacent to GK = [tex]\sqrt{34}[/tex]
b. [tex]Slope = \frac{(y_{2} -y_{1})}{(x_{2} -x_{1})}[/tex]
Slope of GK = [tex]\frac{(1 - 6)}{(-6 + 3)}[/tex] = [tex]\frac{5}{3}[/tex]
Slope of GK = [tex]\frac{5}{3}[/tex]
Slope of adjacent side to GK = [tex]\frac{3-6}{2+3}[/tex] = [tex]-\frac{3}{5}[/tex]
Slope of adjacent to RS = [tex]-\frac{3}{5}[/tex]
c. All sides are equals to [tex]\sqrt{34}[/tex]
So, length of diagonal GJ = [tex]\sqrt{({-3+1))^{2} } + ({6+2})^{2}} = \sqrt{68}[/tex]
and length of diagonal HK = [tex]\sqrt{({2+6))^{2} } + ({3-1})^{2}} = \sqrt{68}[/tex]
All sides and diagonals are equal then parallelogram GHJK is Square.
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Write the expression as the sine, cosine, or tangent of an angle.
The simplified expression is: cos(13π/35)
What is trignometry?Trigonometry is a branch of mathematics that studies the relationships between angles and the sides of triangles. It deals with functions such as sine, cosine, and tangent and their inverses, and is used extensively in fields such as engineering, physics, and astronomy.
We can simplify the given expression using the identity:
cos(A - B) = cos(A) cos(B) + sin(A) sin(B)
We can rewrite the given expression as:
cos(4π/7) cos(π/5) - sin(4π/7) sin(π/5)
= cos(4π/7 - π/5) [using the identity]
To simplify further, we can find a common denominator for 4/7 and 1/5:
4/7 = 20/35 and 1/5 = 7/35
Then, we can write:
4π/7 - π/5 = (20π/35) - (7π/35) = 13π/35
This expression cannot be further simplified using trigonometric identities, and is written only in terms of the cosine function.
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77 94 251 142 90 198 246 180
The range of this sample data
Answer:
251 - 77 = 174
Therefore, the range of this sample data is 174.
Step-by-step explanation:
instead of measuring the length of a stick as 3.06 my student measured in length as 2.955 m find the air percent.
well, the error is 3.06 - 2.955 = 0.105.
now, if we take 3.06(origin amount) to be the 100%, what's 0.105 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 3.06 & 100\\ 0.105& x \end{array} \implies \cfrac{3.06}{0.105}~~=~~\cfrac{100}{x} \\\\\\ 3.06=10.5\implies x=\cfrac{10.5}{3.06}\implies x\approx 3.43[/tex]
Find the Pearson correlation coefficient r for the given points. Round any intermediate calculations to no less than six decimal places, and round your final answer to three decimal places.
(1,6)
, (2,10)
, (3,4)
, (4,4)
, (5,8)
, (6,2)
, (7,2)
There is a moderate negative linear relationship between x and y for the given points.
When determining if there is a linear relatiοnship between twο quantitative variables, Pearsοn's cοrrelatiοn is used. Just that—a linear relatiοnship between thοse variables—is the research hypοthesis.
[tex]\mathrm{r = (n \Sigma xy - \Sigma x\Sigma y) / \sqrt{(n\Sigma x^2- (\Sigma x)^{2)(n\Sigma y)}^2 - (\Sigma y)^2)}}[/tex]
where n is the number οf pοints, Σxy is the sum οf the prοducts οf x and y cοοrdinates, Σx is the sum οf x cοοrdinates, Σy is the sum οf y cοοrdinates, Σx² is the sum οf squares οf x cοοrdinates, and Σy² is the sum οf squares οf y cοοrdinates.
First, we need tο find these values frοm the given pοints. We can use a table tο οrganize οur calculatiοns:
x y xy x² y²
1 6 6 1 36
2 10 20 4 100
3 4 12 9 16
4 4 16 16 16
6 2 12 36 4
7
The table continues:
|x ||y ||xy ||x² ||y² | |- |- |- |- |- | 1 6 6 1 36
|| || || || || || || || || ||
The table continues:
|x ||y ||xy ||x² ||y² | |- |- |- |- |- | 1 6 6 1 36
|| || || || ||
The table continues:
|x ||y ||xy ||x² ||y² | |- |- |- |- |- | 1 ||6 ||6 ||1 ||36 | 2 ||10 ||20 ||4 ||100 | 3 ||4 ||12 ||9 ||16 | 4 ||4 ||16 ||16 ||16 | 5||8||40||25||64| 6||2||12||36||4| 7||2||14||49||4|
Now we can add up each column to get:
Σx = 28 Σy = 36 Σxy = 120 Σx² = 140 Σy² = 240
Next, we can plug these values into the formula and simplify. Remember to round any intermediate calculations to no less than six decimal places.
r = (7(120) - (28)(36)) / √[(7(140) - [tex](28) ^{* * * * * * * * * *} (240) - (36)^ {* * *}[/tex]
r = (840 - 1008) / √[(980 - 784) (1680 - 1296)]
r = (-168) / √[196(384)]
r = (-168) / (√75264)
r = (-168) / (274.343596)
r ≈ (-0.612487)
Finally, we round our answer to three decimal places.
r ≈ -0.612
This means that there is a moderate negative linear relationship between x and y for the given points.
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Solve for x in the triangle. Round your answer to the nearest tenth.
The value of x in the given triangle is obtained as 4.21. The solution has been obtained by using trigonometry.
What is trigonometry?
A branch of mathematics known as trigonometry is concerned with the study of right-angle triangles, including their sides, angles, and relationships.
We are given perpendicular as 7 and base as x.
We know that tan θ is the ratio of perpendicular to base.
Here, θ = 59°
So,
⇒ Tan 59° = [tex]\frac{7}{x}[/tex]
⇒ 1.66 = [tex]\frac{7}{x}[/tex]
⇒ 1.66x = 7
⇒ x = [tex]\frac{7}{1.66}[/tex]
⇒ x = 4.21
Hence, the value of x in the given triangle is obtained as 4.21.
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Write an equation to represent the cost to make one item of clothing based on how many hours it takes to make it
Answer: Let's assume that the cost to make one item of clothing is directly proportional to the number of hours it takes to make it. We can use the equation:
Cost = k * Hours
where "Cost" is the cost to make one item of clothing, "Hours" is the number of hours it takes to make one item of clothing, and "k" is the proportionality constant that relates the cost to the number of hours.
In other words, if it takes x hours to make one item of clothing, then the cost to make one item is:
Cost = k * x
The value of k will depend on factors such as the cost of materials, the wages of the workers, and other expenses involved in the production process. The value of k can be determined based on the actual cost and number of hours for a particular item of clothing.
Step-by-step explanation:
use rational exponents to rewrite and simplify the expression
The solution of the given problem of expressions comes out to be ⁶√x⁷*∛x² = [tex]x^{(11/6)[/tex].
What dοes an expressiοn actually mean?Calculatiοns that cοmbine jοining, remοving, and randοm subdivisiοn must be dοne with ever-changing factοrs. They cοuld accοmplish the fοllοwing if they united: An prοgramme, sοme data, and a mathematical prοblem. Fοrmulas, cοmpοnents, and arithmetic οperatiοns like adds, subtractiοns, mistakes, and grοupings can all be fοund in a declaratiοn οf truth.
Here,
Using rational exponents, it is possible to formulate the expression 6x7*x2 more concisely:
=> ⁶√x⁷*∛x² = [tex]x^{(7/6)} \times x^{(2/3)[/tex]
Now, we can include the exponents to further simplify:
=> [tex]x^{(7/6)} * x^{2/3)} = x^{(7/6 + 2/3)[/tex]
We can add 3 and 6 to discover a common denominator of 18 for the numbers 6 and 3. Then, we could type:
=> [tex]x^{(7/6 + 2/3)} = x^{(21/18 + 12/18)}[/tex]
We can now multiply the exponents:
=> [tex]x^{(21/18 + 12/18)} = x^{(33/18)[/tex]
Further reducing the exponent, we can write:
=> [tex]x^{(33/18) }= x^{(11/6)[/tex]
Therefore, in simplified version, ⁶√x⁷*∛x² = [tex]x^{(11/6)[/tex].
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