The table below shows the radius y, in inches, created by growing algae in x days:
Time (x)
(days) 5 10 15 20
Radius (y)
(inches) 1 3 9 22
Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and radius of the algae. [Choose the value of the correlation coefficient from 1, 0.94, 0.5, 0.02.] (4 points)
Part B: What is the value of the slope of the graph of radius versus time between 5 and 10 days, and what does the slope represent? (3 points)
Part C: Does the data in the table represent correlation or causation? Explain your answer. (3 points)
Answers
Part B. To determine the slope, the equation would be Δy/Δx. For x=5 and x=10, the slope would be
Slope = (3-1)/(10-5) = 2/5 or 0.4. This is the instantaneous rate of change at the interval of 5 to 10 days.
Part C. The difference between causation and correlation is identifiable if you know the direct relationship between the variables. In this case, the increase in radius is not caused by time. The problem does not state so. But we know from the trend shown on a graph, that there is a correlation between these variables. Therefore, the answer is correlation.
Related Questions
Simplify this using the imaginary i
Answers
Create a factorable polynomial with a GCF of 2y. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.
I already made my polynomial, 4y^1 + 6y^3
I just don't understand how to get two equivalent forms(please explain if you can)
Answers
2y(2 + 3y^2) <== here is one form
another form would be to multiply ur equation by a multiple of ur GCF 2, such as 4
4(4y^1 + 6y^3) = 16y^1 + 24y^3 <== another form
Three cards are drawn with replacement from a standard deck. what is the probability that the first card will be a diamond, the second card will be a black card, and the third card will be an ace? express your answer as a fraction or a decimal number rounded to four decimal places.
Answers
there are 13 diamonds per deck
26 black cards
4 aces
so a 13/52 chance for a diamond
a 26/52, reduced to 1/2 chance for a black card
and a 4/52 chance for an ace
13/52 x 1/2 x 4/52 = 52/5408 = 1/104 probability
The lengths of the sides of a triangle are in the extended ratio 1 : 2 : 5. the perimeter of the triangle is 32 ft. the length of the longest side is:
Answers
x + 2x + 5x = 32
8x = 32
x = 32/8
x = 4
longest side = 5x = 5*4 = 20 ft
The length of longest side of the triangle is 20 ft .
What is perimeter of the triangle?The perimeter of a triangle is defined as the total length of its boundary.
The basic formula used to calculate the perimeter of a triangle is:
Perimeter = sum of the three sides
According to the question
The lengths of the sides of a triangle are in the extended ratio 1 : 2 : 5 .
Let common constant factor within ratio = x
Therefore,
Sides of triangle = x , 2x , 5x
and the perimeter of the triangle = 32 ft
i.e
according to the formula of perimeter of a triangle:
Perimeter = sum of the three sides
Now,
Substituting the value in formula
[tex]32 = x + 2x + 5x[/tex]
[tex]32 = 8x[/tex]
[tex]x = 4[/tex]
The sides of triangle is : 4 ft , 2*4 , 5*4
: 4 ft , 8 ft , 20 ft
Hence, the length of longest side of the triangle is 20 ft
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How to solve this? Please help!
Answers
The temperature dropped 2° F every hour for 6 hours. What was the total number of degrees the temperature changed in the 6 hours
Answers
-2 x 6, -2 stands for the drop, 6 stands for the hours.
-2 x 6 = -12, meaning the temperature dropped -12 degrees.
Describe the transformation of the graph of f into the graph of g as either a horizontal or vertical stretch. f(x)=sqrt(x) and g(x)=sqrt(0.5x)
Answers
[tex]\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]
[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{{{ B}}}[/tex]
with that template in mind, let's see [tex]\bf f(x)=\sqrt{x}\qquad \begin{array}{llll} g(x)=&\sqrt{0.5x}\\ &\quad \uparrow \\ &\quad B \end{array}[/tex]
so B went form 1 on f(x), down to 0.5 or 1/2 on g(x)
B = 1/2, thus the graph is stretched by twice as much.
The transformation of the function f(x) to g(x) is a horizontal stretch.
Step-by-step explanation:The parent function f(x) is given by:
[tex]f(x)=\sqrt{x}[/tex]
and the transformed function g(x) is given by:
[tex]g(x)=\sqrt{0.5x}[/tex]
Now we know that the transformation of the type:
f(x) → f(bx)
is a horizontal stretch if 0<b<1
and is a horizontal shrink if b>1
Here we have:
[tex]b=\dfrac{1}{2}=0.5[/tex]
i.e.
[tex]0<b<1[/tex]
This means that the transformation of the function f(x) to g(x) is a horizontal stretch by a factor of 2.
A construction crew wants to hoist a heavy beam so that it is standing up straight. ey tie a rope to the beam, secure the base, and pull the rope through a pulley to raise one end of the beam from the ground. When the beam makes an angle of 408 with the ground, the top of the beam is 8 ft above the ground. e construction site has some telephone wires crossing it. e workers are concerned that the beam may hit the wires. When the beam makes an angle of 608 with the ground, the wires are 2 ft above the top of the beam. Will the beam clear the wires on its way to standing up straight? Explain.
Answers
Using trigonometry, it can be determined that the beam will clear the wires when it stands up straight. The beam's length remains constant and by finding the height of the beam at different angles, we can confirm that it will not hit the wires.
Explanation:The problem can be solved using trigonometry. Firstly, you need to find out the length of the beam when it makes an 40° angle with the ground. The length of the beam would be 8 ft / sin(40°) around 12.61 ft. Now, when the beam makes a 60° angle with the ground, the top of the beam will be sin(60°) * 12.61 ft = 10.92 ft off the ground. Because the wires are 2 ft above that (at 8 ft + 2 ft = 10 ft), the beam will clear the wires as it stands up straight.
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By applying trigonometry principles, it is determined that the beam will not clear the wires when it is lifted to stand up straight as the top of the beam at 60° angle is lower than the bottom of the wires.
Explanation:To answer whether the beam will clear the wires when it is lifted, we need to apply basic trigonometry principles. First, we determine the height of the beam when it is at a 40° angle with the ground, and we know the top is 8 ft above the ground. We can use the tangent of the angle to relate this height to the length of the beam, which remains constant as the beam is raised.
So we have tan(40°) = 8ft/beam_length. Solving for beam_length, we get beam_length = 8ft/tan(40°) ≈ 9.442ft.
Next, when the beam makes a 60° angle with the ground, it is not fully raised and the wires are 2ft above the beam's top. The length of the beam when it's at this angle is beam_length = 2ft + height_at_60°. We can use the tangent function again to find this height, which gives us tan(60°) = height_at_60°/beam_length.
Solving for height_at_60°, we get height_at_60° = beam_length * tan(60°), substituting beam_length from earlier, height_at_60° = 9.442ft * tan(60°) ≈ 16.34ft.
As the bottom 2 ft of the wires are not cleared by the 16.34 ft high beam, the conclusion is that the beam will not clear the wires when it is being erected up straight.
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An object is thrown upward from the top of an 80ft tower.
The height h of the object after t seconds is represented by the quadratic equation h= -16t^2 + 64t + 80.
After how many seconds will the object hit the ground?
A. 29 seconds
B. 6.4 seconds
C. 5.0 seconds
D. 8.0 seconds
Answers
On the day their child was born, her parents deposited $25,000 in a savings account that earns 11% interest annually. How much is in the account the day the child turns 16 years old (rounded to the nearest cent)? Hint: an = a1(1 + r)n, r ≠ 1, where a1 is the initial amount deposited and r is the common ratio or interest rate.
Answer choices:
$119,614.74 $132,772.36 $128,612.52 $440,000.00
Answers
Total = 25,000 * (1.11)^16
Total = 25,000 * 5.3108943321
Total = 132,772.36
(This is the second answer)
Final answer:
After using the compound interest formula with an initial deposit of $25,000, an annual interest rate of 11%, and a time period of 16 years, the balance rounds to $120,034.10, which does not match any of the provided answer choices.
Explanation:
To find out how much is in the account when the child turns 16 years old, we can use the formula for compound interest: an = a1(1 + r)n, where a1 is the original amount deposited, r is the annual interest rate (expressed as a decimal), and n is the number of years the money is invested. In this case, a1 is $25,000, r is 0.11 (11%), and n is 16.
Using the formula, we calculate the account balance as follows:
Account Balance = 25,000(1 + 0.11)16
Account Balance = 25,000(1.11)16
Account Balance = 25,000(4.801364)
Account Balance = $119,999.10
However, this result is not in the given answer choices, so let's ensure we are rounding to the nearest cent:
Account Balance = $120,034.09 (before rounding)
Account Balance = $120,034.10 (after rounding to the nearest cent)
None of the answer choices matches this amount, so it is possible there has been a mistake in the provided choices or in our calculations. We should double-check the interest rate, time period, and the formula used.
Determine if the function is one-to-one. A decreasing line intercepting the y axis at 0, 5.
Answers
When the reciprocal of three times a number is subtracted from 7, the result is the reciprocal of twice the number. find the number?
Answers
To find the number, we set up the equation 7 - 1/(3x) = 1/(2x) and solve for x.
Explanation:To find the number, we need to set up an equation based on the given information.
Let's assume the number is 'x'.
According to the problem, the reciprocal of three times the number is subtracted from 7 and is equal to the reciprocal of twice the number. We can write this as:
7 - 1/(3x) = 1/(2x)
To solve this equation, we can multiply both sides by the common denominator, which is 6x. This will eliminate the fractions.
6x * 7 - 6x * 1/(3x) = 6x * 1/(2x)
42x - 2 = 3
Subtracting 2 from both sides, we get:
42x = 1
Dividing both sides by 42, we find:
x = 1/42
Therefore, the number is 1/42.
During a period of 11 years 737737 of the people selected for grand jury duty were sampled, and 6868% of them were immigrants. use the sample data to construct a 99% confidence interval estimate of the proportion of grand jury members who were immigrants. given that among the people eligible for jury duty, 69.469.4% of them were immigrants, does it appear that the jury selection process was somehow biased against immigrants?
Answers
Lower margin = p - Z* √[(pq) ÷ n]
Upper margin = p + Z* √[(pq) ÷ n]
Where:
p is the sample proportion
q is 1 - p
Z* is the z-score for the confidence level
n is the number size
--------------------------------------------------------------------------------------------------------------
p = (68% of 737) ÷ 737 = 501.16 ÷ 737 = 0.68
q = 1 - p = 1 - 0.68 = 0.32
Z* = 2.58 (refer to the table attached below)
n = 737
substituting these values into the formula, we have
lower margin = 0.68 - (2.58) √[(0.68×0.32) ÷ 737]
lower margin = 0.68 - (2.58) √(0.0002952510176...)
lower margin = 0.68 - 0.04433180431
lower margin = 0.6357 (rounded to four decimal places)
lower margin = 63.57%
upper margin = 0.68 + 0.04433180431
upper margin = 0.7243 (rounded to four decimal places)
upper margin = 72.43%
The confidence interval is between 63.57% and 72.43%. In other words, we can say that between 63.57% and 72.43% of jury members are immigrant.
The claim of 69.46% is within the confidence interval, hence we can conclude that the selection of grand jury duty is not biased against the immigrant.
A person's part-time job pays $5.50 per hour. Write an expression to represent the amount he earns for working n hours.
The person earns $____ for working n hours.
Answers
What is the factorization of the polynomial graphed below? Assume it has no constant factor.
A. x(x+2)
B. (x-2)(x-2)
C. x(x-2)
D. (x+2)(x+2)
Answers
Answer:
Option: B is correct.
The factorization of the polynomial graphed below is:
f(x)=(x-2)(x-2)
Step-by-step solution:
Clearly from the graph we could see that the graph of the function touches x=2.
that means that x=2 is a root of the function
Also when the graph touches the point of x-axis and does not pass that point than that zero is the repeated zero of the function.
That means that x=2 is a repeated zero of the function f(x).
Hence,
The factorization of the polynomial graphed below is:
f(x)=(x-2)(x-2)
Hence, option B is correct.
( Also in first option:
A) x(x+2)
x=0 must also be an zero but in the graph we could see that x=0 is not a solution.
Hence option A is false.
C)
x(x-2)
again as in option: A x=0 must be a solution.
Hence, option C is false.
D)
(x+2)(x+2)
x=-2 must be a solution but the graph does not touches x=-2.
Hence, option D is incorrect )
GEOMETRY- I just need someone to check my answer!
Answers
What are the real zeros of x^3 + 4x^2 − 9x − 36
Answers
[x3 + 4x2] -9 [ x+4]
take x2 common factor from first praket
x2[x+4] -9 [x+4]
= [x+4] *[x2 -9]
so the zeros of this equation are -4 , 3, -3
Answer:
x = −3, 3, −4
Step-by-step explanation:
The endpoints of segment AC are A( – 7, – 3) and C( 8, 4). Point B is somewhere in between AC. Determine the coordinates of point B if the ratio of the distances between these points is AB : BC = 5 : 2.
Answers
The vertical distance between AC is 7 units
The point B is located such that AB: BC = 5:2, in other words, AB = 5/7 of the line and BC is 2/7 of the line
5/7 of the horizontal distance is (5/7) × 15 = 75/7
2/7 of the vertical distance is (2/7) × 15 = 30/7
The coordinate of B is (75/7, 30/7)
Evaluate 4x - 7 when x = 6
Replace the variables/letters in the expression above with the values assigned to them, so replace all x’s with 6 in this example
implify the expression (following order of operations)
Answers
When [tex]\(x = 6\)[/tex], the expression [tex]\(4x - 7\)[/tex] simplifies to 17 following the order of operations.
To evaluate the expression [tex]\(4x - 7\)[/tex] when [tex]\(x = 6\)[/tex], substitute the value of [tex]\(x\)[/tex] into the expression and simplify using the order of operations.
[tex]\[4x - 7\][/tex]
Replace [tex]\(x\)[/tex] with 6:
[tex]\[4(6) - 7\][/tex]
Following the order of operations (PEMDAS), perform the multiplication first:
[tex]\[24 - 7\][/tex]
Now, perform the subtraction:
[tex]\[17\][/tex]
Thus, when \(x = 6\), the value of [tex]\(4x - 7\)[/tex] is 17.
In this expression, the variable [tex]\(x\)[/tex] is multiplied by 4, and then 7 is subtracted from the result. By substituting the value of [tex]\(x\)[/tex], which is 6 in this case, and simplifying according to the order of operations, we obtain the final result of 17.
If two sides of a triangle are 12 and 17, and the included angle is 60, what is the area of the triangle
Answers
[tex]A= \frac{1}{2}*12*17*sin(60^o) =102* \frac{ \sqrt{3} }{2}=51 \sqrt{3} \approx 88.33 \ units^2[/tex]
Suppose a laboratory has a 30 g sample of polonium-210. The half-life of polonium-210 is about 138 days. How many half-lives of polonium-210 occur in 1104 days? How much polonium is in the sample 1104 days later?
Answers
After 8 half - lives only (1 / 2^8) or (1 / 256) of the original 30 grams will remain.
(1 / 256) = 0.003906250
So, 30 * 0.003906250 = 0.1171875 grams will remain.
Answer:
8 half-lives of polonium-210 occur in 1104 days.
0.1174 g of polonium-210 will remain in the sample after 1104 days.
Step-by-step explanation:
Initial mass of the polonium-210 = 30 g
Half life of the sample, = [tex]t_{\frac{1}{2}}=138 days[/tex]
Formula used :
[tex]N=N_o\times e^{-\lambda t}\\\\\lambda =\frac{0.693}{t_{\frac{1}{2}}}[/tex]
where,
[tex]N_o[/tex] = initial mass of isotope
N = mass of the parent isotope left after the time, (t)
[tex]t_{\frac{1}{2}}[/tex] = half life of the isotope
[tex]\lambda[/tex] = rate constant
[tex]\lambda =\frac{0.693}{138 days}=0.005021 day^{-1}[/tex]
time ,t = 1104 dyas
[tex]N=N_o\times e^{-(\lambda )\times t}[/tex]
Now put all the given values in this formula, we get
[tex]N=30g\times e^{-0.005021 day^{-1}\times 1104 days}[/tex]
[tex]N=0.1174 g[/tex]
Number of half-lives:
[tex]N=\frac{N_o}{2^n}[/tex]
n = Number of half lives elapsed
[tex]0.1174 g=\frac{30 g}{2^n}[/tex]
[tex]n = 7.99\approx 8[/tex]
8 half-lives of polonium-210 occur in 1104 days.
0.1174 g of polonium-210 will remain in the sample after 1104 days.
evaluate 9 + 11g - 4h when g = 2 and h = 7
Answers
9 + 11(2) - 4(7) =
9 + 22 - 28 =
31 - 28 =
3
So, 3 is the answer.
9 + 11(2) - 4(7)
9 + 22 - 28
31 - 28
The final answer is 3.
Can someone simplify 3(2x+1)-8
Answers
3(2x)+3(1)-8
6x+3-8 combine like terms
6x+(3-8)
6x-5
first distribute the 3 through the parenthesis.
6x + 3 - 8
Combine like terms
6x - 5
Three children guessed the number of jelly beans in a jar.the guesses were 98,137 and 164.none of the guesses was correct.one guess was off by 12,another by 27 and the third by 39.how many jelly beans were in the jar.
Answers
If all three guesses for the number of jelly beans 98, 137, and 164 were off by 12, 27, and 39 the correct guess for the number of jelly beans is 125.
The number of jelly beans was 125.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Example:
2x + 3 is an expression
2x - 3 = 4 is an expression
We have,
Three guesses for the number of jelly beans:
98, 137, and 164.
These three guesses were all wrong.
The three guesses were off by:
12, 27, and 39.
The correct guess is 125 because,
98 + 27 = 125
137 - 12 = 125
164 - 39 = 125
Thus,
The number of jelly beans was 125.
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How will the perimeter of the rectangle change if each side is increased by a factor of 10? the long side has 6cm and the short side is 3cm.
a.The perimeter will be 1/10 the original.
b.The perimeter will be 1/100 the original
c.The perimeter will be 10 times the original.
d.The perimeter will be 100 times the original.
Answers
p1=18
p2=2(30+60)
p2=180
p2/p1=180/18=10
c. The perimeter will be 10 times the original.
Answer: Option 'C' is correct.
The perimeter will be 10 times the original .
Step-by-step explanation:
Since we have given that
Length of the rectangle = 6 cm
Breadth of the rectangle = 3 cm
As we know the formula for "Perimeter of rectangle "
[tex]\text{Perimeter of original rectangle }=2(Length+ Breadth)\\\\\text{Preimeter of rectangle }=2(6+3)\\\\\text{Perimeter of rectangle }=18\ cm[/tex]
According to question, each side is increased by a factor of 10
so, Perimeter of new rectangle is given by
[tex]10\times 2\times (6+3)\\\\=180\ cm[/tex]
Hence, Option 'C' is correct.
So, the perimeter will be 10 times the original .
Solve by the linear combination method (with or without multiplication). x + y = 40 0.08x + 0.03y = 1.7
Answers
x + y = 40
.08x+.03y=1.7
We need to multiply the top equation by either a -.08 or a -.03 to eliminate one of the variables. Let's get rid of the y:
-.03(x + y) = -.03(40) which gives us
-.03x - .03y = -1.2
.08x + .03y = 1.7
When we add those together we are left with .05x = .5 and x = 10. If we sub that 10 in for x into the first equation (either would have worked but the first one is way easier to work with!) we get 10 + y = 40 and y = 30. So the solution to the system is (10, 30)
Answer:
-_- Answer is -3
Step-by-step explanation:
Doing the instruction vidio.
A company employs 48 people in various departments. The average annual salary of each employee is $25,000 with a maximum variance of $3,000. What is the range of the total salary that the company pays to its employees annually?
Answers
n = 48, the sample size
m = $25,000, th sample mean
σ = $3000, the maximum variance
The standard deviation is
s = √σ = √(3000) = 54.772
As a rule of thumb, the range is 4 times the standard deviation. Therefore the range is
R = 4*54.772 = 219.09
Half the range is
R/2 = 219.09/2 = 109.45
The required range is
(25000-109.45, 25000+109.45) = (24890.46, 25109.54)
Answer: ($24,890.46, $25,109.54)
Answer:
$1,056,000 ≤ x ≤ $1,344,000
Step-by-step explanation:
took test
Use the three steps to solve the problem. the length of a rectangle is 2 inches less than 3 times the number of inches in its width. if the perimeter of the rectangle is 28 inches, what is the width and length of the rectangle?
Answers
Let the length be l.
l = 3w - 2
Given,
Perimeter = 28
2*( l + w ) = 28
2*( 3w -2 + w ) = 28
4w - 2 = 14 [ Dividing both sides by 2 ]
2w - 1 = 7 [ Dividing both sides by 2 ]
2w = 8
w = 4.
Thus,
l = 3w -2 = 3*4 - 2 = 12 - 2 = 10
Therefore, the length is 10 inches and the width is 4 inches.
A rectangular table top has a perimeter of 24 inches and an area of 35 square inches. find its dimensions.
Answers
let : x the lenght y : the widith
the perimeter is ; 2(x+y) and the area is : xy
so the system : 2(x+y) =24
xy = 35
x+y = 12.....(1)
xy = 35 ...(2)
by (1) : y = 12-x
subsct in (2) : (12-x)x = 35
x²-12x+35 = 0
(x-7)(x-5) = 0
x-7=0 or x-5 = 0
x=7 or x=5
if : x=7 y = 12-7 = 5
if : x=5 y = 12-5 =7
but : x > y
conclusion : one solution (7 , 5).
The dimensions are 7 and 5 inches.
The value of dimensions of rectangle are 5 and 7.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
A rectangular table top has a perimeter of 24 inches and an area of 35 square inches.
Let the dimensions of rectangle are;
Length = L
Width = W
So, We can formulate;
⇒ 2 ( L + W ) = 24
⇒ L + W = 12 ..(i)
And,
⇒ L × W = 35
⇒ L = 35 / W ... (ii)
Substitute the value from (ii) in (i), we get;
⇒ L + W = 12
⇒ 35/W + W = 12
⇒ 35 + W² = 12W
⇒ W² - 12W + 35 = 0
⇒ W² - (7W + 5W) + 35 = 0
⇒ W² - 7W - 5W + 35 = 0
⇒ W (W - 7) - 5 (W - 7) = 0
⇒ (W - 5) (W - 7) = 0
⇒ W = 5
And, W = 7
And, We get;
⇒ L = 35 / W
Put W = 5;
⇒ L = 35 / 5
⇒ L = 7
And,
⇒ L = 35 / W
Put W = 7;
⇒ L = 35 / 7
⇒ L = 5
Thus, The possible values of dimensions are;
⇒ 5 and 7.
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Mentally estimate the total cost of items that have the following prices $1.85 $.98 $3.94 $9.78 and $6.18 round off the answer to the nearest half dollar
A. $22.50
B. $22.59
C. $23.00
D. $22.30
Answers
the first 4 would be rounded up tot he nearest dollar and the last one rounded down to the nearest dollar
doing that I estimate $23.00
Answer is C