A statistical indicator of the strength of the association between the relative movements of two variables is the correlation coefficient.
To gauge how strongly two variables are related to one another, correlation coefficients are used.
A statistical indicator of the strength of the association between the relative movements of two variables is the correlation coefficient. The values are in the -1.0 to 1.0 range. There was a measurement error in the correlation if the estimated value was larger than 1.0 or lower than -1.0. Perfect negative correlation is shown by a correlation of -1.0, and perfect positive correlation is shown by a correlation of 1.0. A correlation of 0.0 indicates that there is no linear link between the two variables' movements. Finance and investing can benefit from the usage of correlation statistics.
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$1,000 is deposited into a savings account. interest is compounded annually. after 1 year, the value of the account is $1,020. after 2 years, the value of the account is $1,040.40. this scenario can be represented by an exponential function of the form f(x)=1000(b)^x , where f(x) is the amount in the savings account, and x is time in years. what is the value of b ?
The value of b is [tex]1 \cdot02[/tex].
What is compound interest?
Compound interest is when you earn interest on both the money you have saved and the interest you earn.
Formula for compound interest is
[tex]A= P(1+\frac{r}{100})^n[/tex] ...................(1)
where, A = total amount( principal + interest )
r = rate of interest in compound interest
n = number of years
Given,
For [tex]n=1[/tex]
Principal amount [tex]p=\$ 1000[/tex]
Total amount [tex]A=\$ 1020[/tex]
For [tex]n=2[/tex]
Principal amount [tex]p=\$ 1000[/tex]
Total amount [tex]A=\$ 1040[/tex]
This scenario can be represented by an exponential function of the form of [tex]f(x)=1000(b)^x[/tex]
Comparing the above function with equation (1), we get
[tex]A=f(x)\\P=1000\\b=(1+\frac{r}{100})[/tex]
For 1st year
[tex]f(x)=1000(b)^1\\\Rightarrow 1020=1000(b)\\\Rightarrow b=\frac{1020}{1000}\\\Rightarrow b= \frac{102}{100}\\\Rightarrow b= 1\cdot02[/tex]
now, check the amount for 2nd year
[tex]f(x)=1000 \times (1 \cdot01}^2\\\Rightarrow f(x)=1000 \times \frac{102}{100}\times \frac{102}{100}\\\Rightarrow f(x)=1040[/tex]
Hence, the value of b is [tex]1 \cdot02[/tex] .
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Write the numbers in order from least to greatest. -3, 1 ¹/4, -1 3/4, ¹/10
7. Try It #7 Look at the graph in Figure 22 and identify the following for the function j(t):
e. Is j(t) an increasing or decreasing function (or neither)?
Answer:
The function of j(t) is decreasing.
Step-by-step explanation:
In the question two functions are given as h(t)=3t-4 and j(t)=5-t.
It is required to find whether j(t) is an increasing/decreasing or neither function.
To solve this question, first find the slope of the function. If, the slope is positive the function is increasing and if the slope is negative the function is decreasing.
Step 1 of 1
Find the slope of the function j(t) by comparing these to the standard form.
y=mx+b
Then, m=-1
Since the slope is negative.
Therefore, the function is decreasing.
A state patrol officer saw a car start from rest at a highway on ramp. She radioed ahead to a highway patrol officer 30 miles along the highway. When the car reached the location of the second officer 28 minutes later, it was clocked going 60 mph. The driver of the car was given a ticket for exceeding the 60 mph speed limit. Why can the office conclude the driver exceeded the speed limit
The office concluded that the driver exceeded the speed limit by 64.3mi/h.
Given that the second cop, who arrived 28 minutes later, was recorded traveling at 60 mph while the patrol officer was traveling 30 miles along the roadway.
According to the mean value theorem, There exists a value of x = c such that f'(c) = [f(b)-f(a)][b-a] if f(x) is continuous on the closed interval [a,b] and differentiable on the open interval (a,b).
This implies the following in "lay man's" terms:
the instantaneous speed (the speed at any given time) must be equal to his average speed
Since the driver is driving along the highway, we can assume his position to be continuous and differentiable
his average speed is defined as:
average speed=[x(b)-x(a)]÷[b-a] where x represents his position
average speed=[30 - 0]÷[(28÷60) - 0]
average speed=30÷0.466
average speed=64.3mi/hr
Since the time is given in minutes, we convert it in hours by dividing it by 60.
Therefore, by the MVT the police officers can determine that at some point in time (even though he was only driving 60mph at the second patrol officer's location) since his average speed was approximately 64.3 mi/hr there was a point in time during the 28 minutes that his speed exceeded 60 mph.
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Find the surface area of the square pyramid.
Answer:
[tex]39 yd^2[/tex]
Step-by-step explanation:
So, let's start by calculating the surface area of the base, which in this case is a square. The area of a square can be calculating by taking any of the lengths and squaring it, since all the sides should be equal if it's a square. Since one of the sides of the square is 3 yd, you have the equation: [tex](3 yd)^2 = 9yd^2[/tex]. Now to calculate the area of the four triangles. The area of a triangle can be calculating by using the formula: [tex]\frac{1}{2}bh[/tex], and in this case the base is 3 yd, and the height is 5 yd (lengths can be determined by looking at the given values in the diagram). But there's 4 of the triangles so we multiply it all by 4, and this gives you the equation: [tex]4(\frac{1}{2}(5 yd)(3 yd)) = 4(\frac{15 yd^2}{2}) = 4(7.5 yd^2)=30yd^2[/tex]. So now all that's left is to add this to the area of the square which gives you the equation: [tex]30yd^2+9yd^2=39yd^2[/tex] which is the surface area
A pattern of rectangles is formed by decreasing the length and increasing the width, each by the same amount. The relationship between x, the amount of increase, and A, the area of the rectangle represented by the increase, is quadratic.
Which graph could represent the area of each rectangle in terms of the change in the length and width?
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A straight line decreases from 0 to 9 units.
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A line decreases from 0 to 3 units, increases from 3 to 6 seconds, and decreases from 6 to 9 seconds.
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A line increases from 0 to 3 seconds then decreases from 3 to 9 seconds.
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A curved line decreases from 0 to 9 units.
The graph that can represent the area of each rectangle in terms of the change in the length and width is C. A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A line increases from 0 to 3 seconds then decreases from 3 to 9 seconds.
How to illustrate the information?It should be noted that a graph gives a diagrammatic representation of an information.
Here, the rectangles are formed by decreasing the length and increasing the width, each by the same amount.
Thai can be illustrated by the third graph in the option as the line increases from 0 to 3 seconds then decreases from 3 to 9 seconds.
In conclusion, the correct option is C.
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Answer:
(っ◔◡◔)っ ♥ the answer is C ♥
Step-by-step explanation:
got it right on edge
Which is the principal value of \arcsin\left(0.98\right)arcsin(0.98)\arcsin, left parenthesis, 0, point, 98, right parenthesis?
The principal value of arc sin(0.98)=78.5°.
What is principal value?The value of the inverse function at a place that falls within the range of the unit of the principal value is the primary value of the trigonometric function at that point.
Trigonometric function solutions with a value between 0 and 2π are known as principal values of trigonometric functions. The primary values of trigonometric functions are values smaller than 2π, which is the interval at which the trigonometric function's value repeats.
The principal value of the inverse trigonometric function is always the positive value whenever any positive value and the negative value are presented in a way that these two values are equal.
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10. The figure is reflected across line m and then reflected across line n. What type of transformation is the result?
reflection
translation
rotation
Find m∠PQR.
A. 90
B. 77
C. 81
D. 72
Answer:
D) 72°
Step-by-step explanation:
Tangent:
[tex]\sf \boxed{\angle PQR =\dfrac{Difference \ between \ major \ arc \ and \ minor \ arc }{2}}[/tex]
∠PQR = 2x + 252 - (2x + 108)
2x +72 = (2x + 252 - 2x - 108) ÷ 2
2x + 72 = (2x - 2x + 252 - 108) ÷ 2
2x + 72 = 144 ÷ 2
2x + 72 = 72
2x + 72-72 = 72 - 72
2x = 0
[tex]\sf \boxed{\bf x = 0}[/tex]
m∠PQR = 2x + 72
= 2*0 + 72
= 72°
A cylinder has a radius of 5x-1. Write a simplified expression for its volume where V= pi r^2 h
The volume of the cylinder whose radius is 5x-1 unit is 25x²πh + πh - 10xπh.
What is the volume of a right circular cylinder?
Suppose that the radius of the considered right circular cylinder is 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
The right circular cylinder is the cylinder in which the line joining centre of the top circle of the cylinder to the centre of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.
Given that the radius of the cylinder is (5x-1), while the height of the cylinder is h. Therefore, the volume of the cylinder is,
The volume of the cylinder = π × (5x-1)² × h
= (25x² + 1 - 10x)πh
= 25x²πh + πh - 10xπh
Hence, the volume of the cylinder is 25x²πh + πh - 10xπh.
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prove it. this question is from trigonometry
Answer:
See below for step-by-step proof.
Step-by-step explanation:
[tex]\textsf{Given expression}:[/tex]
[tex]\cos^6 \theta+\sin^6 \theta[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies (\cos^2 \theta)^3+(\sin^2 \theta)^3[/tex]
[tex]\textsf{Use the identity}\quad a^3+b^3=(a+b)^3-3ab(a+b):[/tex]
[tex]\implies (\cos^2 \theta+\sin^2 \theta)^3-3 \cos^2 \theta\sin^2 \theta (\cos^2 \theta+\sin^2 \theta)[/tex]
[tex]\textsf{Use the identity}\quad \sin^2 \theta + \cos^2 \theta=1:[/tex]
[tex]\implies (1)^3-3 \cos^2 \theta\sin^2 \theta (1)[/tex]
[tex]\implies 1-3 \cos^2 \theta\sin^2 \theta[/tex]
[tex]\implies 1-3 (\cos \theta\sin \theta)^2[/tex]
[tex]\textsf{Use the identity}\quad \sin 2 \theta=2 \sin \theta \cos \theta \implies \dfrac{1}{2}\sin 2 \theta= \sin \theta \cos \theta:[/tex]
[tex]\implies 1-3 \left( \dfrac{1}{2}\sin 2 \theta\right)^2[/tex]
[tex]\implies 1-\dfrac{3}{4} \sin^2 2 \theta[/tex]
[tex]\textsf{Use the identity}\quad \sin^2 2\theta + \cos^2 2\theta=1 \implies \sin^2 2\theta=1-\cos^2 2\theta[/tex]
[tex]\implies 1-\dfrac{3}{4} \left(1-\cos^2 2 \theta\right)[/tex]
[tex]\implies 1-\dfrac{3}{4} +\dfrac{3}{4}\cos^2 2 \theta[/tex]
[tex]\implies \dfrac{1}{4} +\dfrac{3}{4}\cos^2 2 \theta[/tex]
[tex]\textsf{Factor out }\dfrac{1}{4}:[/tex]
[tex]\implies \dfrac{1}{4}\left(1+3\cos^2 2 \theta\right)[/tex]
[tex]\textsf{Use the identity}\quad \cos (4 \theta)=2 \cos^2 2\theta - 1 \implies \cos^2 2 \theta=\dfrac{1}{2}\cos 4 \theta+\dfrac{1}{2}:[/tex]
[tex]\implies \dfrac{1}{4}\left(1+3\left(\dfrac{1}{2}\cos 4 \theta+\dfrac{1}{2}\right)\right)[/tex]
[tex]\implies \dfrac{1}{4}\left(1+\dfrac{3}{2}\cos 4 \theta+\dfrac{3}{2}\right)[/tex]
[tex]\implies \dfrac{1}{4}\left(\dfrac{5}{2}+\dfrac{3}{2}\cos 4 \theta\right)[/tex]
[tex]\implies \dfrac{1}{4} \cdot \dfrac{1}{2}\left(5+3\cos 4 \theta\right)[/tex]
[tex]\implies \dfrac{1}{8}\left(5+3\cos 4 \theta\right)[/tex]
If f(x) = -3x - 5 and g(x) = 4x - 2, find (f+ g)(x)
Answer:
(f+g)(x)=f(x)+g(x)
=(-3x-5)+(4x-2)
= -3x-5+4x-2. collect like term
= -3x+4x-5-2
= x-7. the final answer
4. The temperature at 6:00 a.m. was 45°F and the temperature at 10:30 a.m. was 12.8°C. What was the change in temperature between 6:00 a.m. and 10:30 a.m.? I will give brainllest
Answer:
10.04°F
Step-by-step explanation:
(12.8°C × 9/5) + 32 = 55.04 - 45 = 10.04
having issues with solving this
By applying the concept of finite sum and the properties of the series, we conclude that the finite sum [tex]p = \sum \limit_{x=1}^{3} 2^{x}+ 2[/tex] is equal to the value of 34.
How to find the result of finite sum
Let be a sum of the form [tex]p = \sum\limits_{i= 1}^{n} a_{i}[/tex], where n represents an integer. This kind of sum represents a finite sum, whose expanded form is presented below:
p = a₁ + (a₁ + a₂) + (a₁ + a₂ + a₃) + ... + (a₁ + a₂ + a₃ + ... + aₙ₋₁ + aₙ) (1)
If we know that [tex]p = \sum \limit_{x=1}^{3} 2^{x}+ 2[/tex], then the result of the finite sum is:
p = (2 + 2¹) + (2 · 2 + 2¹ + 2²) + (3 · 2 + 2¹ + 2² + 2³)
p = 4 + (4 + 6) + (6 + 14)
p = 4 + 10 + 20
p = 34
By applying the concept of finite sum and the properties of the series, we conclude that the finite sum [tex]p = \sum \limit_{x=1}^{3} 2^{x}+ 2[/tex] is equal to the value of 34.
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There are 27000lb of wheat to be transported, the transport company wants to know how many metric tonnes of wheat they would be transporting.
Answer:
Around 12.25
Step-by-step explanation:
There are around 2205 (2204.62) lbs per metric tonnes.
So 27000/2204.62 or 27000/2205 gives you between 12.24-12.25
I am studying geometry this summer but can’t solve this question what would be the correct answer
Which of these tables represents a linear function?
Answer:
a
Step-by-step explanation:
a is the anwer because b/c it has a constant rate of change unlike the others
Giving 30 points and brainlist for the answer.
Ella needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 3 hours and charged her $61 for parts. The total was $226. Write and solve an equation which can be used to determine x, the cost of the labor per hour
Find the inverse function.
f(x) =
f-¹(x) =
=
=
2x+5
4
4x + [?]
[
Answer: [tex]f^{-1} (x)=\frac{4x-5}{2}[/tex]
Step-by-step explanation:
Let [tex]f(y)=x\\[/tex].
[tex]\implies x=\frac{2y+5}{4}\\\\4x=2y+5\\\\4x-5=2y\\\\y=\frac{4x-5}{2}\\\\\therefore f^{-1} (x)=\frac{4x-5}{2}[/tex]
Given that BZ BA, if WV = 24, find ZY.
A. 48
B. 24
C. 12
D. 6
The computation shows that the value of the length of ZY will be B. 24.
How to illustrate the information?Let the assumed figures be:
BZ = 48
BA = 12
WV = 24
ZY = Unknown
Let's assume that the opposite sides in the quadrilateral are the same, the value of ZY will be:
ZY = (48 × 12)/24
ZY = 24
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Answer:
C.12
Step-by-step explanation:
Trust
Find the equivalent expression of the following: x3 (x2 + 5x + 7)
1. x5 + 5x3 + 7x2
2. x6 + 5x4 + 7x3
3. x5 + 4x4 + x4 + 8x3 – x3
4. x5 + 3x4 + x4 + 6x3 + x3
The product of the given function is x^5 + 5x^4 + 7x^3
Product of polynomial functionsThe leading degree of a polynomial function is always greater than or equal to 2.
Given the products below;
x^3 (x^2 + 5x + 7)
Expand
(x^3)(x^2) + 5x(x^3) + 7x^3
Simplify
x^5 + 5x^4 + 7x^3
Hence the product of the given function is x^5 + 5x^4 + 7x^3
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The equivalent expression of x³(x² + 5x + 7) is x⁵ + 5x⁴ + 7x³
How to find equivalent expression?The equivalent expression of the expression can be found as follows;
x³(x² + 5x + 7)
let's open the bracket by multiplying.
Therefore,
x³(x² + 5x + 7) = x⁵ + 5x⁴ + 7x³
Hence,
The equivalent expression of x³(x² + 5x + 7) is x⁵ + 5x⁴ + 7x³
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Elliott is standing at the top of a store escalator that leads to the ground floor below. The angle of depression from the top of the escalator to the floor is 42.51°, and the escalator is 16 feet long. How far is the top of the escalator from the ground floor? Round your answer to the nearest foot.
41 feet
17 feet
12 feet
11 feet
Answer: 11
Step-by-step explanation:
[tex]\sin 42.51^{\circ}=\frac{x}{16}\\\\x=16 \sin 42.51^{\circ} \approx 11[/tex]
At a football match, one-third of spectators support the Reds and the rest support the Blues. At half-time 345 Blues supporters leave because their team is losing and the remaining Blues supporters now make up one-third of the total. How many Reds supporters are there?
The number of Red supporters are 345
How to determine the value
From the given information, we have that
Red supporters = 1/3 x
Let the total number of supporter be x
1/3 x + blues = x
1/3x + 1/3x + 345 = x
2/3x + 345 = x
Collect like terms
[tex]x - \frac{2x}{3} = 345[/tex]
[tex]\frac{1}{3} x = 345[/tex]
Cross multiply
[tex]x = 3[/tex] × [tex]345[/tex]
[tex]x = 1035[/tex]
We have red supporters = 1/3x
⇒ [tex]\frac{1}{3}[/tex] × [tex]1035[/tex]
⇒ [tex]345[/tex]
Thus, the number of Red supporters are 345
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During the sale, Carly pays $54 for a wheelbarrow. What was the original price?
The original price of the wheelbarrow is £75
How to determine the original price?Let the original price be x.
From the question, the amount paid is:
Amount paid = 54
The reduced price is calculated as:
Reduced = Original price * (1 - discount)
This gives
x * (1- 20%) = 54
Evaluate the difference
x * 0.8 = 54
Divide by 0.8
x = 67.5
Hence, the original price is $67.5
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Complete question
The price of a wheelbarrow is reduced by 20%. During the sale, Carly pays $54 for a wheelbarrow. What was the original price?
What is EB and DY? DY, EY, and FY are bisectors, and the answers can be "can not be determined"
Based on Pythagoras' theorem, EB is equal to 38.7 and DY is 17.7.
What is the length of the sides EB and DY?The length of the sides EB and DY are obtained using Pythagoras theorem.
Since EY is a perpendicular bisector;
EB = √(64.2² - 51.2²)
EB = 38.7
Since, DY is a perpendicular bisector;
DY = √64.2² - 61.7²)
DY = 17.7
Therefore, EB is equal to 38.7 and DY is 17.7.
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Is Figure B a scale copy of Figure A?
Answer:
No.
Step-by-step explanation:
The ratio of the lengths of the vertical sides from A to B is 2/4 which equals 1/2.
The ratio of the lengths of the horizontal sides of A to B is 4/11.
Since 4/11 is not equal to 1/2, figure B is not a scale copy of figure A.
a woman is 40 years old. her daughter is one quarter her age. what years and months is her daughter
Answer:
10 years old or 120 months old
Please Help I would really appreciate it
By evaluating in x = 25 we get:
∠1 = 120°∠2 = 60°How to get the angles?Here we know that the measure of angle 1 is given by:
∠1 = 5x - 5
And the given value of x is 25, then if we just evaluate the above expression, then we get:
∠1 = 5*25 - 5 = 120
And for angle 2 we will have:
∠2 = 2*25 - 10 = 60
Notice that the sum of these two angles is equal to 180°, which is what we should get when adding two supplementary angles.
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Is it possible to design a pair of nonstandard dice, with positive integers on the faces (not necessarily all distinct), so that the probability of rolling any given total on those two dice is the same as the probability of rolling that total on two standard dice
you can reduce it to factors of degree 2 or less).
The two dice do not need to be identical. If it is possible, do it. If it is not possible, prove that it is not possible.
Some hints I got were to try to construct a pair of nonstandard dice such that the generating function for their sum matches the corresponding g.f. for a pair of standard dice and to note that the g.f. for a pair of standard dice can be factored quite a bit (you can reduce it to factors of degree 2 or less).
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