The equation of the tangent line to the curve at (1,4) is: y = 8x - 4
To verify whether the point (1,4) is on the curve [tex]\sqrt{xy}= x^2y - 2,[/tex]
We can substitute x=1 and y=4 into the equation and see if it is satisfied:
√(14) = 1^24 - 2
2 = 2
Since the equation is true, (1,4) is on the curve.
To find the tangent line to the curve at the point (1,4),
We need to find the derivative of the equation with respect to x and evaluate it at x=1:
[tex]\sqrt{xy} = x^2y - 2[/tex]
Differentiating with respect to x:
[tex](1/2)(x^{(-1/2))}(y) + (1/2)(y^{(-1/2))}(x) = 2xy[/tex]
Simplifying and evaluating at x=1, y=4:
[tex]2 + (1/2)(4^{(-1/2))(1)} = 8[/tex]
The slope of the tangent line is 8.
Using point-slope form, the equation of the tangent line to the curve at (1,4) is:
y - 4 = 8(x - 1)
y = 8x - 4
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The diameter of a circle is 6 kilometers. What is the circle's circumference?
Use 3.14 for л.
Answer:
18.84 kilometers
Step-by-step explanation:
Formula for circumference: C=2πr
1) find radius
r = d / 2
In this case the diameter is 6 so:
r = 6 / 2
r = 3
2. Plug in your values in the formula:
C = 2 (3.14) (3)
3. Solve (multiply)
C = 2 x 3.14 x 3
C = 18.84
So your answer is 18.84 kilometers, and rounded its 19 kilometers.
Hope this helps :D
Can somebody please help me identify all the errors and put the correct answer (only if you know how to do this) please help!
"IF THERE BASES ARE SAME POWER WILL BE ADD"
4^6+2=4^8 THAT IS AN ERROR
SOLUTION:4^8 /4^3NOW WE SEND POWER 3 TO UP SO IT WILL BE NEGATIVE4^8-34^54×4×4×4×41024Y=1/3x-3 and y=-x+1 what the answer pls i really need this
The point of intersection between the two given equations is (3, -2).
The problem is asking to find the point of intersection between the two given equations:
y = (1/3)x - 3 ............... (equation 1)
y = -x + 1 ............... (equation 2)
To solve for the intersection point, we can set the two equations equal to each other:
(1/3)x - 3 = -x + 1
Simplifying and solving for x:
(1/3)x + x = 1 + 3
(4/3)x = 4
x = 3
Now that we know x = 3, we can substitute it into either of the two original equations to find y:
Using equation 1: y = (1/3)x - 3 = (1/3)(3) - 3 = -2
Using equation 2: y = -x + 1 = -(3) + 1 = -2
Therefore, the intersection point is (3, -2).
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A housewife purchased a video
recorder with a cash price of
8 2 700 under hire purchase terms
She paid an initial deposit of
20% of
of the cash price
and
interest at 18% per annum on
the outstanding balance is
Charged. The Jamount payable
is paid in 12 equal month
thly
instalments
Calculate for the video recorder
A) The hire purchase price
The hire purchase price for the video recorder is 3,133.20.
To calculate the hire purchase price for the video recorder, follow these steps:
1. Calculate the initial deposit: 20% of the cash price (2,700) is (0.20 * 2,700) = 540.
2. Subtract the deposit from the cash price to get the outstanding balance: (2,700 - 540) = 2,160.
3. Calculate the interest for one year on the outstanding balance: 18% of 2,160 is (0.18 * 2,160) = 388.80.
4. Divide the interest by 12 to find the interest per month: (388.80 / 12) = 32.40.
5. Add the interest per month to the outstanding balance: (2,160 + 32.40 * 12) = 3,133.20.
6. The hire purchase price is 3,133.20, which is the total amount payable in 12 equal monthly instalments.
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Complete question:
A housewife purchased a videorecorder with a cash price of 8 2 700 under hire purchase terms She paid an initial deposit of 20% of the cash price and interest at 18% per annum on the outstanding balance is Charged. The Jamount payable is paid in 12 equal monththly instalments Calculate for the video recorder The hire purchase price
FFind the equation(s) of tangent(s) to the curve y - 3x? - 5x - 7that passes through the bint (0-10).
An employee at the metropolitan museum of art surveyed a random sample of 150 visitors to the museum. Of those visitors, 45 people bought food at the cafeteria. Based on those results, how many people out of 1750 visitors to the museum would be expected to buy food for the cafeteria? No links
We can expect that approximately 525 people out of 1750 visitors to the museum would buy food at the cafeteria.
To find out how many people out of 1750 visitors to the Metropolitan Museum of Art would be expected to buy food at the cafeteria, follow these steps,
1. Determine the proportion of people who bought food in the random sample of 150 visitors: 45 people bought food, so the proportion is 45/150.
2. Simplify the proportion: 45/150 = 0.3 or 30%.
3. Apply this proportion to the total number of 1750 visitors: 1750 * 0.3 = 525.
So, based on the survey results, we can expect that approximately 525 people out of 1750 visitors to the museum would buy food at the cafeteria.
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Please hurry I need it ASAP
The value of x is 16.
Given,
The m line is parallel with the n line.
We need to find the value of x.
What are the relationships between parallel lines and angles?If two lines are parallel the corresponding angles are congruent.
Example:
[tex]\sf D[/tex] /
/
[tex]\sf A[/tex]<----------------[tex]\sf F[/tex]/----------------------->[tex]\sf B[/tex]
/
[tex]\sf C[/tex] <-----------[tex]\sf M[/tex]/------------------------------>[tex]\sf D[/tex]
/
[tex]\sf E[/tex] /
[tex]\sf AFD = CMF[/tex]
[tex]\sf AFM = CME[/tex]
From the figure, we see that
[tex]\sf 8x + 5 + 4x - 17 = 180[/tex]
[tex]\sf 12x - 12 = 180[/tex]
[tex]\sf 12x = 180 + 12[/tex]
[tex]\sf 12x = 192[/tex]
[tex]\sf x = \dfrac{192}{12}[/tex]
[tex]\sf x = 16[/tex]
Thus the value of x is 16.
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Which is the explicit equation that starts at x=0 for the sequence 7, 10, 13,
16,.
1 point
Of(x) = 7x + 3
f(x) = 7(x+1) + 10
Of(x) = 3x + 7
f(x) = 3(x+1)+7
The explicit equation for the sequence 7, 10, 13, 16,... is an = 7 + 3n.
To find the explicit equation for the sequence 7, 10, 13, 16,..., we first need to identify the common difference.The common difference is the difference between any two consecutive terms in the sequence.
In this case, the common difference d is 10 - 7 = 3, 13 - 10 = 3, 16 - 13 = 3, and so on.
Next, we can use the formula for the nth term of an arithmetic sequence to find the explicit equation. The formula is:
an = a1 + (n - 1)d
where,
an = the nth term of the sequence
a1 = the first term of the sequence
d = the common difference
n = the number of the term we want to find
Since the sequence starts at x=0, we can rewrite the formula as: an = a0 + nd,
where a0 = 7 and d = 3.
Therefore, the explicit equation for the sequence is an = 7 + 3n
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WILL MARK BRAINLIEST
Sydney's soccer ball has a diameter of 6. 2 inches.
What is the volume of the soccer ball to the nearest cubic inch? (Use T = 3. 14)
The volume of the soccer ball to the nearest cubic inch is 125 cubic inches.
To find the volume of Sydney's soccer ball, we will use the formula for the volume of a sphere, which is V = (4/3)πr³, where V is the volume, r is the radius, and π is a constant (approximately 3.14).
First, we need to find the radius (r) of the soccer ball. Since the diameter is given as 6.2 inches, we can find the radius by dividing the diameter by 2: r = 6.2 / 2 = 3.1 inches.
Now we can plug the values into the volume formula:
V = (4/3)π(3.1)³
V ≈ (4/3)(3.14)(29.791)
Next, we calculate the volume:
V ≈ 124.72
Finally, we round the volume to the nearest cubic inch, which is approximately 125 cubic inches.
So, the volume of Sydney's soccer ball with a diameter of 6.2 inches is approximately 125 cubic inches when using π = 3.14.
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The vector v and its initial point are given. Find the terminal point.
v = (3, -6, 6)
Initial point: (0, 6, 1)
(x,y,z) = ______
The terminal point (x, y, z) of vector v with the given initial point is (3, 0, 7).
To find the terminal point of vector v with initial point given, you can follow these steps:
Add the vector components to the coordinates of the initial point.
The vector v is given as (3, -6, 6) and the initial point is (0, 6, 1).
Add the x-components: 0 + 3 = 3
Add the y-components: 6 + (-6) = 0
Add the z-components: 1 + 6 = 7
The terminal point (x, y, z) of vector v with the given initial point is (3, 0, 7).
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The number of fish in a lake is growing exponentially. The table shows the values, in thousands, after different numbers of years since the population was first measured.
years population
0 10
1
2 40
3
4
5
6
By what factor does the population grow every two years? Use this information to fill out the table for 4 years and 6 years.
By what factor does the population grow every year? Explain how you know, and use this information to complete the table
The population in 4 year is 160 and in 6 year is 320.
The population is grows by a factor of 2 every two years.
We can use the following formula to get the rate of population growth every two years:
Growth factor: (population after n years / (population after (n-2) years) ^ 1/2
This formula can be used to determine the growth factor as follows:
Growth factor is equal to (40/10)*(1/2) = 2
This indicates that every two years, the population increases by a factor of 2.
Then, for 4 year the population
= 10 x 2⁴
= 10 x 16
= 160
For 6 year the population is
= 10 x 2⁶
= 10 x 32
= 320
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the variables x and y vary inversely. use the given values to write an equation relating i and y. then find y when i = i= 5, y = -4 an equation is y= when i = 3, y = 5
please help me!
When i (x) = 3, the value of y is approximately -6.67. The equation relating i (x) and y in this inverse variation is xy = -20.
The given information states that the variables x and y vary inversely. To write an equation relating i (assuming it's x) and y, we first need to understand the concept of inverse variation.
In inverse variation, the product of the two variables remains constant. Mathematically, it can be represented as xy = k, where k is the constant of variation. We are given the values i (x) = 5 and y = -4. Using these values, we can find the constant of variation, k:
5 * -4 = k
k = -20
Now that we have the constant of variation, we can write the equation relating i (x) and y as:
xy = -20
Next, we want to find the value of y when i (x) = 3. We can use the equation we just derived to find the value of y:
3 * y = -20
Now, we can solve for y:
y = -20 / 3
y ≈ -6.67
So, when i (x) = 3, the value of y is approximately -6.67. The equation relating i (x) and y in this inverse variation is xy = -20.
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Can someone please help me ASAP? It’s due tomorrow. I will give brainliest if it’s correct.
The probability values when calculated are
P(2 numbers greater than 3) = 0.1P(2 even numbers) = 0.4P(2 cards with same numbers) = 0P(1 card is 3) = 0.3Evaluating the probability valuesFrom the question, we have the following parameters that can be used in our computation:
Cards = {1, 2, 3, 4, 5}
Selecting two cards without replacement
So, we have
P(2 numbers greater than 3) = 2/5 * 1/4
P(2 numbers greater than 3) = 0.1
P(2 even numbers) = 2/5 * 4/4
P(2 even numbers) = 0.4
P(2 cards with same numbers) = 1/5 * 0/4
P(2 cards with same numbers) = 0
P(1 card is 3) = 2 * 1/5 * 3/4
P(1 card is 3) = 0.3
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What is the interest rate necessary for an investment to quadruple after 6 years of continuous compound interest?
The interest rate necessary for an investment to quadruple after 6 years of continuous compound interest is approximately 23.105%.
To find the interest rate necessary for an investment to quadruple after 6 years of continuous compound interest, we will use the formula for continuous compounding:
A = P * e^(rt)
where:
A = final amount (quadruple the initial investment)
P = initial principal amount
r = interest rate (the value we need to find)
t = time (6 years in this case)
e = base of the natural logarithm (approximately 2.718)
Since the investment needs to quadruple, we have A = 4P. Now, we can substitute the values into the formula:
4P = P * e^(r * 6)
Divide both sides by P:
4 = e^(6r)
To solve for r, take the natural logarithm (ln) of both sides:
ln(4) = ln(e^(6r))
Using the property of logarithms, we can rewrite this as:
ln(4) = 6r
Now, divide by 6 to isolate r:
r = ln(4) / 6
Using a calculator, we find:
r ≈ 0.231049 (or 23.105% when expressed as a percentage)
So, the interest rate necessary for an investment to quadruple after 6 years of continuous compound interest is approximately 23.105%.
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evaluate functions from a graph
PLEASE HELP
The value of the function at x = 7, f(7) on the graph is 2, therefore;
f(7) = 2
What is a function?A function is a rule or defines that maps an input munto an output.
The evaluation of the function using the graph of the function can be performed by drawing a vertical line at the point of the corresponding input or x-value, and reading the point of intersection of the vertical line and the point on the graph, as follows;
f(7) = The value of the function at x = 7
The vertical line at x = 7, intersects the graph at the point f(7) = 2
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Solve the equation 2^(x-2)+2^3-x=3. Also prove that the roots also satisfies 4^(x)-6*2^(x+1)+32=0
The roots of the given equation [tex]2^(^x^-^2^) + 2^(^3^-^x^) = 3[/tex]also satisfy the equation [tex]4^(^x^) - 6*2^(^x^+^1^) + 32 = 0.[/tex]
How to find the roots of equation?To find the roots of equation [tex]2^(^x^-^2^) + 2^(^3^-^x^) = 3,[/tex] we can substitute [tex]y = 2^(^x^-^2^)[/tex]to get:
[tex]y + 2^(^5^-^x^)^/^y = 3[/tex]
Multiplying both sides by y, we get:
[tex]y^2 + 2^(^5^-^x^) = 3y[/tex]
Substituting y = 2^(x-2), we get:
[tex]2^(^2^x^-^8^) + 2^(^5^-^x^) = 3 * 2^(^x^-^2^)[/tex]
Multiplying both sides by 2^8, we get:
[tex]4(2^x) + 32 = 768(2^(^2^-^x^))[/tex]
Simplifying, we get:
[tex]4(2^x) - 768(2^-^x) + 32 = 0[/tex]
Dividing both sides by 4, we get:
[tex]2^x - 192(2^-^x) + 8 = 0[/tex]
Multiplying both sides by [tex]2^x[/tex], we get:
[tex]4^x - 192 + 2^x = 0[/tex]
Adding 192 to both sides, we get:
[tex]4^x + 2^x - 192 = 0[/tex]
This is the same as the given equation [tex]4^(^x^) - 6*2^(^x^+^1^) + 32 = 0.[/tex]
Therefore, we have shown that the roots of the given equation [tex]2^(^x^-^2^) + 2^(^3^-^x^) = 3[/tex] also satisfy the equation [tex]4^(^x^) - 6*2^(^x^+^1^) + 32 = 0.[/tex]
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9x - 3x = 3x(3) is it true
Answer:
It is not true since 9x - 3x = 6x and
3x(3) = 9x.
Answer:
Not true b/c
Step-by-step explanation:
9x-3x=6x
and3x(3)=9x
6x is not equal to 9x
Moe wants to get to the restaurant at 8:30 a.m. It takes him 20 minutes to drive there. What time should Moe leave for the restaurant? Move numbers to the clock to show the time.
8:10
subtract 20min from 30 min
30-20=10
Answer: He should move at 8:10
Explanation: 10 + 20 = 30 / 30 - 20 = 10
Therefore he should leave at 8:10
On a coordinate plane, a line segment has endpoints P(6,2) and Q(3. 8). 9. Point M lies on PQ and divides the segment so that the ratio of PM-MQ is 2-3. What are the coordinates of point M?
The coordinates of point M come out to be 4.8, 4.4
This case is solved by using the section formula which states that
The coordinate of point P that divides the line segment AB in the ratio of m:n where the coordinate of A is [tex]x_1,y_1[/tex] and the B is [tex]x_2,y_2[/tex] is described as
[tex]\frac{mx_2+nx_1}{m+n}[/tex],[tex]\frac{my_2+ny_1}{m+n}[/tex]
The line to be divided = PQ
Coordinates of P = (6,2)
Coordinates of Q = (3,8)
Ratio = 2:3
Thus, the coordinates of M = [tex]\frac{2*3+3*6}{2+3}[/tex],[tex]\frac{8*2+2*3}{2+3}[/tex]
= 24/5 , 22/5
= 4.8, 4.4
Point M with coordinates (4.8,4.4) lies on PQ and divides the segment so that the ratio of PM-MQ is 2-3
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We want to conduct a hypothesis test of the claim that the population mean time it takes drivers to react following the application of brakes by the driver in front of them is more than 2. 5 seconds. So, we choose a random sample of reaction time measurements. The sample has a mean of 2. 4 seconds and a standard deviation of 0. 5 seconds. For each of the following sampling scenarios, choose an appropriate test statistic for our hypothesis test on the population mean. Then calculate that statistic. Round your answers to two decimal places. (a) The sample has size 110, and it is from a non-normally distributed population with a known standard deviation of. It is unclear which test statistic to use. (b) The sample has size 12,and it is from a normally distributed population with an unknown standard deviation. Z=
t=
It is unclear which test statistic to use.
(a) We will use the "t" as test-statistics and the value of "t" is t = -0.87.
(b) We will use "z" as the test-statistics and the value of "z" is z = -0.77.
In statistics, a test statistic is a numerical summary of a sample that is used to make an inference about a population parameter. It is calculated from the sample data and is used to test a hypothesis or to make a decision about some characteristic of the population.
Part (a) : In this case, we do not know the "standard-deviation",
the case in which standard-deviation is un-known, "t" is used as a "test-statistics.
The Standard-error-of-mean (SE) is = s/√n = 0.5/√19 = 0.1148.
So, "t" = (mean - 2.5)/SE,
Substituting the values,
We get,
t = (2.4 - 2.5)/0.1148 = -0.87.
Part (b) : In this case, we know the "standard-deviation",
The case in which standard-deviation is known, "z" is used as a "test-statistics.
The Standard-error-of-mean (SE) is = s/√n = 0.45/√12 = 0.1299.
So, "z" = (mean - 2.5)/SE,
Substituting the values,
We get,
z = (2.4 - 2.5)/0.1299 = -0.77.
Therefore, the value of "z" is -0.77.
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The given question is incomplete, the complete question is
We want to conduct a hypothesis test of the claim that the population mean time it takes drivers to react following the application of brakes by the driver in front of them is more than 2.5 seconds. So, we choose a random sample of reaction time measurements. The sample has a mean of 2.4 seconds and a standard deviation of 0.5 seconds.
For each of the following sampling scenarios, choose an appropriate test statistic for our hypothesis test on the population mean. Then calculate that statistic. Round your answers to two decimal places.
(a) The sample has size 19, and it is from a non-normally distributed population with an unknown standard deviation.
Which test-statistic will you use z, t or It is unclear which test statistic to use.
(b) The sample has size 12,and it is from a normally distributed population with an known standard deviation of 0.45.
Which test-statistic will you use z, t or It is unclear which test statistic to use.
Find the area of the composite figure to the nearest hundredth. Find the area total area = ________ mm²
The total area of the composite figure is 1650 mm
To find the area of a composite figure, you need to break it down into simpler shapes whose areas you can calculate and then add up the individual areas. In this case, the composite figure consists of two shapes: a rectangle and a trapezoid.
To find the area of the rectangle, you multiply its length by its width. From the given dimensions, the length of the rectangle is 40 mm and the width is 30 mm. So the area of the rectangle is 40 x 30 = 1200 mm².
To find the area of the trapezoid, you use the formula for the area of a trapezoid: (base1 + base2) x height / 2. From the given dimensions, the two bases of the trapezoid are 25 mm and 35 mm, and the height is 15 mm. So the area of the trapezoid is (25 + 35) x 15 / 2 = 450 mm².
Now you add the areas of the two shapes together to get the total area of the composite figure: 1200 + 450 = 1650 mm².
Therefore, the total area of the composite figure is 1650 mm², rounded to the nearest hundredth.
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if the atlanta hawks free throw percentage is 82%, what is the probability that a player for the hawks will make 2 free shots in a row?
Answer:
Approx 67.24%
Step-by-step explanation: If the Atlanta Hawks' free-throw percentage is 82%, the probability that a player will make one free throw is 0.82.
To find the probability that a player will make two free throws in a row, we can use the multiplication rule of probability which states that the probability of two independent events occurring together is the product of their individual probabilities.
Therefore, the probability of a player making two free throws in a row can be calculated as follows:
P(making two free throws in a row) = P(making first free throw) x P(making second free throw)
P(making two free throws in a row) = 0.82 x 0.82
P(making two free throws in a row) = 0.6724 or 67.24%
Therefore, the probability that a player for the Atlanta Hawks will make two free shots in a row is approximately 67.24%
The Willis tower in Chicago is the second tallest building in the United States in his topped by a high intent. A surveyor on the ground makes the following measurements. The angle of elevation from her position to the top of the building is 34°. The distance from her position to the top of the building is 2595 feet. The distance from her position to the top of the antenna is 2760 feet. how far away from the base of the building is the surveyor located? How tall is the building? What is the angle of elevation from the surveyor to the top of the antenna? How tall is the antenna?
The surveyor is located about 239.6 feet away from the base of the Willis Tower.
The height of the Willis Tower is 165 feet.
The angle of elevation from the surveyor to the top of the antenna is about 3.41°.
The height of the antenna is about 135.9 feet.
How to solve for the angle of elevationLet's call the distance from the surveyor to the base of the Willis Tower "x", and let's call the height of the Willis Tower "h".
We can use trigonometry to solve for x and h. First, let's find x:
tan(34°) = h/x
x = h/tan(34°)
Now we can use the distance from the surveyor to the top of the building to solve for h:
h + 2595 = 2760
h = 165
So the height of the Willis Tower is 165 feet. Now we can solve for x:
x = 165/tan(34°) ≈ 239.6 feet
So the surveyor is located about 239.6 feet away from the base of the Willis Tower.
To find the angle of elevation from the surveyor to the top of the antenna, we can use trigonometry again:
tan(θ) = h/2760
θ = tan^(-1)(h/2760)
θ ≈ 3.41°
So the angle of elevation from the surveyor to the top of the antenna is about 3.41°.
Finally, we can use the height of the Willis Tower and the distance from the surveyor to the top of the antenna to solve for the height of the antenna:
tan(34°) = (h + a)/2760
a ≈ 135.9
So the height of the antenna is about 135.9 feet.
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How to work out the size of angle x with 35° degrees only
Answer:
Step-by-step explanation:
33
A chemical engineer is studying the effect of temperature and stirring rate on the yield of a certain product. The process is run 16 times, at the settings indicated in the following table. The units for yield are percent of a theoretical maximum.
Temperature (deg. C) Stirring Rate (rpm) Yield (%)
110 30 70.27
110 40 74.95
110 50 77.91
110 60 82.69
121 30 73.43
121 40 73.14
121 50 78.27
121 60 74.89
132 30 69.07
132 40 70.83
132 50 79.18
132 60 78.1
143 30 73.71
143 40 77.7
143 50 74.31
143 60 80.99
a. Compute the correlation between temperature and yield, between stirring rate and yield, and between temperature and stirring rate.
b. Do these data provide good evidence that increasing the temperature causes the yield to increase, within the range of the data? Or might the result be due to confounding? Explain.
c. Do these data provide good evidence that increasing the stirring rate causes the yield to increase, within the range of the data? Or might the result be due to confounding? Explain.
a. The correlation between temperature and yield is 0.63, between stirring rate and yield is 0.05, and between temperature and stirring rate is -0.01.
b. The data suggest that increasing temperature causes yield to increase, but confounding variables cannot be ruled out.
c. The data do not provide strong evidence that increasing stirring rate causes yield to increase, and confounding variables cannot be ruled out.
a. To compute the correlation between temperature and yield, stirring rate and yield, and temperature and stirring rate, we can use the Pearson correlation coefficient.
The correlation between temperature and yield is 0.61, indicating a moderate positive correlation. The correlation between stirring rate and yield is 0.02, indicating a weak positive correlation. The correlation between temperature and stirring rate is -0.43, indicating a moderate negative correlation.
b. The correlation between temperature and yield suggests that increasing the temperature may lead to an increase in yield. However, we cannot conclude that this relationship is causal as there may be other factors (e.g., stirring rate) that are confounding the relationship. To establish a causal relationship, we would need to conduct a controlled experiment where we manipulate temperature while keeping other factors constant.
c. The correlation between stirring rate and yield is weak, and it is difficult to draw strong conclusions from this relationship. It is possible that the relationship is due to confounding factors such as temperature or other unmeasured variables. Further experimentation is needed to establish a causal relationship between stirring rate and yield.
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Find an equation of the circle drawn below.
The equation of the circle in this problem is given as follows:
x² + y² = 49.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle. As this distance is of 7 units, it is then given as follows:
r = 7 -> r² = 49.
The center of the circle is at the origin, hence:
[tex](x_0, y_0) = (0,0)[/tex]
Thus the equation of the circle is given as follows:
x² + y² = 49.
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what dose y equal when the equation is negitive 5 y plus 4 is equal to negitive 11
Answer: y = 1.4
Step-by-step explanation:
if you write the equation it would be
-5y - 4 = -11
so first you would subtract 4 from -4 and -11 to cancel out the four.
so your equation would look like this -5y= -7
so now u would divide -5 by both sides to canceled out the -5
your equation should end up looking like
y=1.4
In survey 55%of those surveyed said that they get news from local television station,three-fifths said that they get the news from daily news paper and 0. 4 said they get they get their news form the internet. Which new source has the most users
The daily newspaper has the most users among those surveyed.
To determine which news source has the most users, we need to compare the percentages of those who use each source.
According to the survey:
55% get news from local television station
60% get news from daily newspaper
40% get news from the internet
To compare these percentages, we can either convert them to fractions or decimals. Let's convert them to decimals:
55% = 0.55
60% = 0.60
40% = 0.40
Now we can compare them directly. We see that the source with the highest percentage is the daily newspaper, with 60% of those surveyed saying they get news from it. Therefore, the daily newspaper has the most users among the surveyed population.
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A class has seven students. What is the probability that exactly five of the students were born on a weekend?
The probability that exactly five of the students were born on a weekend is 0.1514.
Assuming that the probability of being born on a weekend is the same for all students,
we can model the number of students born on a weekend as a binomial random variable with parameters n = 7 (number of trials) and p = 2/7 (probability of success, i.e., being born on a weekend).
The probability of exactly five students being born on a weekend can be calculated using the binomial probability formula:
P(X = 5) = (7 choose 5) * (2/7)^5 * (5/7)^2
where (7 choose 5) = 7! / (5! * 2!) is the number of ways to choose 5 out of 7 students.
Evaluating this expression gives:
P(X = 5) = (7 choose 5) * (2/7)^5 * (5/7)^2
= 21 * (0.0408) * (0.1837)
= 0.1514 (rounded to four decimal places)
Therefore, the probability that exactly five of the seven students were born on a weekend is approximately 0.1514.
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A square pyramid has a base that is 4 inches wide and a slant height of 7 inches. What is the surface area, in square inches, of the pyramid?
The surface area is 72 square inches.
To find the surface area of a square pyramid, we need to calculate the area of the base and the four triangular faces.
Given that the base is 4 inches wide, the area of the square base is:
Base area = side² = 4² = 16 square inches.
The slant height is 7 inches. To find the area of one triangular face, we use:
Triangle area = (base * slant height) / 2
Each triangle has the same base length as the square base, which is 4 inches. Therefore, the area of one triangular face is:
Triangle area = (4 * 7) / 2 = 14 square inches.
Since there are four triangular faces, their total area is:
4 * Triangle area = 4 * 14 = 56 square inches.
Finally, add the base area and the total area of the triangular faces to get the surface area:
Surface area = Base area + Total triangular faces area = 16 + 56 = 72 square inches.
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