(a)
i. The mean of all 855 salaries of 2012 professional baseball players to 3 decimal places is 3.319 million dollars.
ii. The standard deviation of all 855 salaries of 2012 professional baseball players to 3 decimal places is 4.104 million dollars.
iii. The values in parts (a) and (b) above are:
Parameter: the mean and standard deviation of the population.
Numerical summaries of the population.
iv. The distribution of salaries for professional baseball players in 2012 is right-skewed with a single peak and several outliers at the high end.
(b)
i. The mean of the sampling distribution of the sample mean (in millions of dollars) when n = 10 is 3.319 million dollars.
ii. The standard error of the sampling distribution of the sample mean (in millions of dollars) when n = 10 is 1.298 million dollars.
iii. The shape of the sampling distribution of the sample mean when n = 10 is approximately normal.
(c) The value of the sample mean (in millions of dollars) from the first random sample of size n = 10 is 2.167 million dollars.
(d) The value of the sample mean (in millions of dollars) from the second random sample of size n = 10 is 2.384 million dollars.
(e) The value of the sample mean (in millions of dollars) from the third random sample of size n = 10 is 3.913 million dollars.
(f)
i. The mean of the three sample means is 2.821 million dollars.
ii. The standard deviation (i.e., standard error) of the three sample means is 0.911 million dollars.
(g)
i. We would expect to see a value of 3.319 million dollars for the mean of the sample means (in millions of dollars) of size n = 10.
ii. We would expect to see a value of 1.298 million dollars for the standard error of the sample means (in millions of dollars) of size n = 10.
The mean and standard error are obtained from the applet and are reported to 3 decimal places. The shape of the sampling distribution of the sample mean when n=10 is approximately normal due to the Central Limit Theorem.
The applet provides the histogram of the 10 observations selected for the sample, as well as the mean and standard deviation of the observations in the sample. The student is required to click "Generate 1 Sample" three times and report the sample means from each of the three random samples of size n=10.
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some help me evaluate (15 points)
Answer:
2/3^-3 = 27/8 = 3 3/8 = 3.375
Step-by-step explanation:
A is the correct answer
Below is the basic floor plan of a college basketball court. (3 points for each part)
a. The area of the circle in the middle of the court where the opening jump ball
takes place is 113.04 square feet. If ߨ is 3.14, what is the radius of the jump ball
circle?
b. The circle at each end of the court that surrounds the free throw line is the same
size as the jump ball circle. (In other words, they have the same radius.) What is
the area of the rectangle (called the lane) whose length is 19 feet and whose
width is the free throw line?
a. The radius of the jump ball circle is 6 feet. b. The area of the rectangle (lane) is 228 square feet.
Describe Area?Area is a measure of the size of a two-dimensional shape or surface, typically expressed in square units, such as square meters (m²), square feet (ft²), or square centimeters (cm²). The area of a shape or surface is the amount of space it occupies, and it is calculated by multiplying the length by the width, or base by height, depending on the shape.
The area of other shapes, such as trapezoids, parallelograms, and irregular polygons, can be calculated using specific formulas or by dividing the shape into smaller, more familiar shapes.
Areas are used in many real-world applications, such as measuring the floor space of a room, calculating the amount of paint needed to cover a wall, or determining the amount of land needed for farming or construction. Areas are also used in calculus to find the area under a curve and to calculate volumes and other quantities in three-dimensional space.
a. The area of the circle is given as 113.04 square feet. Using the formula for the area of a circle, A=πr², we can solve for the radius, r:
113.04 = 3.14r²
r² = 113.04/3.14
r² = 36
r = √36
r = 6 feet
Therefore, the radius of the jump ball circle is 6 feet.
b. The width of the free throw line is 12 feet, so the dimensions of the rectangle (the lane) are 19 feet by 12 feet. The area of a rectangle is given by the formula A = lw, where l is the length and w is the width. Thus, the area of the lane is
A = 19 x 12
A = 228 square feet
Therefore, the area of the rectangle (lane) is 228 square feet.
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the coefficient of friction as the function of temperature is being done experimentally and given by the following equation :
μ(T)=0.0068e^(-)T-37.03)^2/(-19.77)^2 + 0.1338
According to Logger Pro after proccessing the data, the RMSE or root mean square error value is 0.000711079.
What could we interpret from the value of RMSE?
Can predict the friction coefficient as a function of temperature with high accuracy.
We can interpret the following from the value of RMSE:The value of RMSE is a metric used to measure the accuracy of the predicted and observed data. A lower value of RMSE indicates that the experimental data is in agreement with the theoretical model used, while a higher value of RMSE indicates that the experimental data does not agree with the theoretical model used.The RMSE value of 0.000711079 in the experiment implies that the experimental results are in good agreement with the model, and the model used can predict the friction coefficient as a function of temperature with high accuracy.
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1/2 inches equals 2 feet hi how many inches is 87 feet
Answer: 43.5 inches
Step-by-step explanation:
Divide the 87 by the 2 to get the number of half inches it equates to
Eva placed 6 leaves on her work table alongside two 6-inch rulers. How many leaves on the table have a length of 2 inches?
PLESE HLEP PLESE
the answer depends on how Eva has arranged the leaves on the rulers. If she has not counted any leaves with a length of 2 inches, then the answer is 0. If she has counted some leaves with a length of 2 inches, then the answer is 3 or less, depending on how many she has counted.
by the question.
If we assume that all the leaves are different and none of them are cut or torn, then we can count the number of leaves with a length of 2 inches.
Since the rulers are 6 inches long, we can use them to measure the length of the leaves. If a leaf is 2 inches long, then it is one-third the length of a ruler. Therefore, we can place three 2-inch leaves end-to-end on the ruler.
Since Eva has two rulers, she can measure the length of six leaves in total. If we assume that all the leaves are different, then there are two possibilities:
All six leaves are longer than 2 inches. In this case, we cannot count any leaves with a length of 2 inches.
At least one leaf is 2 inches long. In this case, we can count the number of 2-inch leaves by counting how many times we can place three 2-inch leaves end-to-end on the rulers.
For example, if Eva places three 2-inch leaves on one ruler and none on the other, then she has counted 3 leaves with a length of 2 inches. If she places two 2-inch leaves on one ruler and one on the other, then she has also counted 3 leaves with a length of 2 inches.
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Music Systems, Inc. allows a 10% discount if a purchase is paid for within 30 days. An additional 5% discount is given if the purchase is paid for within 15 days. Brent Goodson buys a sound system that originally cost $360. If he pays the entire amount at the time of purchase, how much does he pay for his system after the successive discounts?
Answer:
Brent paid $306 for the system.
Step-by-step explanation:
To figure out what he paid for his system, you will use multiplication to figure out how much the discount took off.
First, you would multiply the original cost to the discount they gave him, which is 15%.
360 * .15 = 54
The discount would take $54 off his purchase.
Next, you would use subtraction to find out what he paid in total.
360 - 54 = 306
Brent paid $306 in total after the discounts.
Dunn has a rectangular TV with an area of 78 square inches. The TV is 7 inches longer than it is wide. Which equation can be used to determine length and the width of the TV? (write in terms of x only)
Dunn's TV is 13 inches lοng and 6 inches wide.
What is the quadratic equatiοns?A quadratic equatiοn is a type οf pοlynοmial equatiοn in which the highest degree οf the variable (usually x) is 2. It has the general fοrm:
ax² + bx + c = 0
Let x be the width οf the TV. Since the TV is 7 inches lοnger than it is wide, its length wοuld be x + 7.
The area οf a rectangle is equal tο its length multiplied by its width. Therefοre, we can set up the equatiοn:
area = length x width
Substituting the values we have:
78 = (x + 7) x x
Simplifying:
78 = x² + 7x
Re-arranging and setting the equatiοn tο zerο:
x² + 7x - 78 = 0
This is a quadratic equatiοn that can be sοlved using the quadratic fοrmula:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 7, and c = -78.
Plugging these values intο the fοrmula, we get:
x = (-7 ± √(7² - 4(1)(-78))) / 2(1)
Simplifying:
x = (-7 ± √(49 + 312)) / 2
x = (-7 ± √(361)) / 2
x = (-7 ± 19) / 2
We take the pοsitive rοοt because x represents a length, which must be a pοsitive value. Therefοre:
x = (12) / 2 = 6
This means that the width οf the TV is 6 inches, and its length is 6 + 7 = 13 inches.
Hence, Dunn's TV is 13 inches lοng and 6 inches wide.
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area of a shaded compound shape
Answer:394.5
Step-by-step explanation:
diameter of circle is 26 so,
radius=r=d/2=13
Area of trapezium=(a+b)/2*h=(19+26)/2*5=45*5/2=225/2=112.5
Area of circle=
[tex]\pi R^{2}=169\pi \\if \ we \ assume \ \pi =3,\\169\pi =169*3=507[/tex]
Area of shaded shape=507-112.5=394.5
PLEASE HELP!!!
A cylindrical piece of iron pipe is shown below. The wall of the pipe is 1.25 inch thick: what is the approximate inside volume of the pipe?
Diameter=6 in
Height = 16in
Answer: 11.24
Step-by-step explanation:
add them all together and then divide by 2
What is 36-8z factoring out the greatest common factor
36-8z = 4(9-2z) this is the factored form of 36-8z.
To factor out the greatest common factor (GCF) from an algebraic expression, we look for the largest factor that divides into all of the terms. In this case, the terms 36 and 8z have a common factor of 4, which is the GCF.
To factor out the GCF, we divide each term by 4, which gives us:
36/4 = 9
8z/4 = 2z
Therefore, we can rewrite 36-8z as:
36-8z = 4(9-2z)
This is the factored form of 36-8z after factoring out the greatest common factor. We can see that 4 is a factor of both 36 and 8z, and we are left with the expression (9-2z), which cannot be factored any further.
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Ming rental car for her bike to carry tools and Wood to school for a science project her toolbox weighs 20 pounds in the car can make carry messing with 5050 pounds each woodboard weighs 3 pounds W represent the number of words she can carry
Ming can carry a maximum of 1676 wood boards in the car. Ming rental car for her bike to carry tools and Wood to school for a science project her toolbox weighs 20 pounds in the car can make carry messing with 5050 pounds each wood board weighs 3 pounds.
Ming rents a cart for her bike to carry tools and wood to school for her science project. Her toolbox weighs 20 pounds and the cart can carry a maximum of 50 pounds. Each wood board weighs 3 pounds. Let w represent the number of wood boards she can carry.
Let x be the number of wood boards Ming can carry.
Then, the weight of the wood boards is 3x pounds.
Adding the weight of the toolbox, the total weight is 20 + 3x pounds.
The car can carry a maximum of 5050 pounds, so we can set up an inequality:
20 + 3x ≤ 5050
Subtracting 20 from both sides:
3x ≤ 5030
Dividing both sides by 3:
x ≤ 1676.67
Since x represents the number of wood boards, it must be a whole number. Therefore, Ming can carry a maximum of 1676 wood boards in the car.
Ming rents a cart for her bike to carry tools and wood to school for her science project. Her toolbox weighs 20 pounds and the cart can carry a maximum of 50 pounds. Each wood board weighs 3 pounds. Let w represent the number of wood boards she can carry.
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I NEED HELP ASAP PLEASE !!
Answer:
Step-by-step explanation:
divide 150 by sides of rectangle = 4 .
= 37.5 then multiply x3 = 112.5
Calculate 5 605 × 25 without using a calculator
Answer:140125
Step-by-step explanation:
Answer: 5605 x 25 is 140,125
Step-by-step explanation:
Multiply the ones digit in the bottom number by each digit in the top number
6 × 4 = 24
Put the 4 in Ones place
Carry the 2 to Tens place
6 × 3 = 18
Add the 2 that you carried = 20
Put the 0 in the Tens place
Carry the 2 to the Hundreds place
Add the 2 that you carried = 14
This is the last number to multiply so write the whole number answer. No need to carry the 1.
Move one place to the left. Multiply the tens digit in the bottom number by each digit in the top number.
5 × 4 = 20
Add a row to your multiplication answer
When you write your answer, shift one column to the left
Put the 0 in Ones place
Carry the 2 to Tens place
5 × 3 = 15
Add the 2 that you carried = 17
Put the 7 in the Tens place
Carry the 1 to the Hundreds place
5 × 2 = 10
Add the 1 that you carried = 11
This is the last number to multiply so write the whole number answer. No need to carry the 1.
Add the numbers in the columns using long addition
4 + 0 = 4
0 + 0 = 0
4 + 7 = 11
write the 1 and carry 1
1 + 1 + 1 = 3
Once you add the columns you can see the long multiplication result: 234 × 56 = 13104.
The greatest five digit number which is exactly divisible by eight
Answer:
99992
Step-by-step explanation:
I dont know how to do this
pls answer if u know with simple working
Answer: 10 sticks
Step-by-step explanation:
First one is one stick second is 4 sticks and 3rd is 7 sticks
add 3 extra sticks and you get 10
A bag contains 3 red marbles and 4 blue marbles. A Marble is taken at random and replaced. Another marble is taken from the bag. Work out the probability that the two marbles are the same color
give your answer as a fraction
The probability that the two marbles are the same colour is 3/7. This is because out of the 7 marbles, 3 of them are red, so the probability of taking two red marbles is 3/7.
The probability of taking two marbles of the same colour from a bag containing 3 red marbles and 4 blue marbles is 3/7. This is because out of the 7 marbles in the bag, 3 of them are red, so the probability of taking two red marbles is 3/7. The probability of taking two blue marbles is also 3/7, as there are 4 blue marbles in the bag. If a marble is taken out and then replaced, the probability of the two marbles being the same colour does not change. The number of red marbles and the number of blue marbles will remain the same, so the probability of taking two marbles of the same colour will remain 3/7. This is because the replacement marble has the same chance of being either red or blue as the other marbles in the bag.
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Find the equation of the line.
Use exact numbers.
�
=
y=y, equals
�
+
x+x, plus
A coordinate plane. The x- and y-axes each scale by one. A graph of a line goes through the points zero, negative two and four, one.
y = 2x + 4 is the equation of the line that connects the coordinates (0, 4) and (1, 6).
The points that the line passes through are (0, 4) and (1, 6). The equation of a line can be found by using the point-slope form:
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is one of the line's points.
Then, we may determine the line's slope:
[tex]m = \frac{(y2 - y1)}{(x2 - x1)}[/tex]
where (x1, y1) = (0, 4) and (x2, y2) = (1, 6)
[tex]m = (6 - 4) / (1 - 0) = 2[/tex]
Now we can use the point-slope form with one of the points, say (0, 4):
y - 4 = 2(x - 0)
Simplifying, we get:
y - 4 = 2x
Adding x to both sides, we get:
y = 2x + 4
So the equation of the line that passes through the points (0, 4) and (1, 6) is y = 2x + 4.
The complete question is"=
Find the equation of the line. Use exact numbers. y=y=y, equals x+x+x, plus
A coordinate plane. The x- and y-axes each scale by one. A graph of a line goes through the points zero, four and one, six.
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how do you solve this
(a) The value of angle VUW is 31⁰.
(b) The value of angle WUX is 59⁰.
What is the value of angle WUX?
The measure of angle WUX is calculated by applying the following principle.
So angle ∠VUW is calculated as follows;
m ∠VUW = ¹/₂ arc UVW (angle formed by chords at circumference is twice the angle of opposite tangent)
m ∠VUW = ¹/₂ x ( 242 - 180)
m ∠VUW = 31⁰
The value of angle WUX is calculated as follows;
m ∠WUX = 90 - 31⁰ ( sum of angles subtended by the diameter of a circle)
m ∠WUX = 59⁰
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a little stuck on this, please help!!
A clothing store has an inventory of at least $4400 in men's jackets. A leather jacket costs $100 and nylon
costs $88 write the system of the qualities
Step-by-step explanation:
Let x be the number of leather jackets and y be the number of nylon jackets.
The total cost of leather jackets is $100x and the total cost of nylon jackets is $88y.
The problem states that the inventory of men's jackets is at least $4400, so we have:
100x + 88y ≥ 4400
This is the system of inequalities:
100x + 88y ≥ 4400
x ≥ 0 (since we cannot have a negative number of jackets)
y ≥ 0 (since we cannot have a negative number of jackets)
Whats The Area Of Sector and length of arc
Area of sector = 56.977 square inches and Arc length = 15.380 inches (rounded to three decimal places).in order to get these answer we need to use simple sector area formula
what is Area of sector ?
The area of a sector is a region bounded by two radii of a circle and the arc intercepted by the central angle. The formula for the area of a sector is:
Area of sector = (angle / 360) x πr²
In the given question,
To find the area of a circle sector, we need to use the formula:
Area of sector = (angle / 360) x πr²
where r is the radius of the circle, and angle is the central angle of the sector in degrees.
In this case, the radius is 22 inches, and the central angle is 44 degrees. So, we can plug these values into the formula:
Area of sector = (44/360) x π(22)²
Area of sector = (11/90) x π(484)
Area of sector = 56.977 square inches (rounded to three decimal places)
To find the arc length of the sector, we need to use the formula:
Arc length = (angle / 360) x 2πr
where r is the radius of the circle, and angle is the central angle of the sector in degrees.
In this case, the radius is 22 inches, and the central angle is 44 degrees. So, we can plug these values into the formula:
Arc length = (44/360) x 2π(22)
Arc length = (11/90) x 44π
Arc length = 15.380 inches (rounded to three decimal places).
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you got a 15% coupon in the mail for presidents day/ before your couponis appled your sub total is 85.28. what is your final bill after your coupon is applied and you pay 6.5% tax
Answer:
The amount of the discount is calculated by multiplying the subtotal by 15%:
discount = 0.15 x 85.28 = 12.79
The new subtotal after the discount is applied is:
new subtotal = 85.28 - 12.79 = 72.49
The tax on the new subtotal is calculated by multiplying the new subtotal by 6.5%:
tax = 0.065 x 72.49 = 4.71
The final bill, including the tax, is the sum of the new subtotal and the tax:
final bill = 72.49 + 4.71 = 77.20
Therefore, the final bill after the coupon is applied and the tax is paid is $77.20.
1.) A shoe salesman sold $4,125 in shoes. He earns a 4% commission. If his base salary is $2000, how much did he earn in total. Be sure to show the formula you use to solve.
The salesman earned a total sum of $2,165.
How much did the shoe salesman earn in total?Given that, a shoe salesman sold $4,125 in shoes and earns a 4% commission, his base salary is $2000.
The amount of commission earned by the shoe salesman is equal to the product of the total sales and the commission rate, which is 4% or 0.04 as a decimal:
Commission = Total sales x Commission rate
Commission = $4,125 × 0.04
Commission = $165
To find the total earnings of the salesman, we add his commission to his base salary:
Total earnings = Base salary + Commission
Total earnings = $2,000 + $165
Total earnings = $2,165
Therefore, the salesman earned $2,165.
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Simplify -4/5(30x-40)+(42x+4) Write your answer in factored form.
Answer:
Step-by-step explanation:
[tex]-\frac{4}{5} (30x-40)+(42x+4)=-\frac{4}{5} (10)(3x-4)+2(21x+2)[/tex]
[tex]=-8(3x-4)+2(21x+2)[/tex]
[tex]=-24x+32+42x+4[/tex]
[tex]=-18x+36[/tex]
[tex]=-18(x-2)[/tex]
the j and k in the jk-ff (and jk-latch) are very much like the s and r in the sr-ff (and sr-latch), respectively. the j acts like the s and the k acts like the r. the only difference for these devices in 3701 is which of the following?
The only difference between the JK-FF (and JK-latch) and the SR-FF (and SR-latch) is that the JK-FF (and JK-latch) has an additional JK control line. This additional control line allows the device to toggle its state when the control line is pulsed.
The JK-FF and JK-latch function similarly to the SR-FF and SR-latch. The J acts like the S and the K acts like the R.
When the J and K lines are both low, the device acts like the S and R lines are both low for the SR-FF.
However, when the J and K lines are both high, the device will toggle its state, which does not happen with the SR-FF.
The additional JK control line can be used to create different circuits, like a toggle circuit or a pulsed output circuit.
The toggle circuit will change the output from one state to another each time the control line is pulsed, while the pulsed output circuit will produce an output pulse of fixed length.
The JK-FF and JK-latch can also be used to create a counter circuit which counts up or down depending on the J and K lines.
The only difference between the JK-FF (and JK-latch) and the SR-FF (and SR-latch) of the following is that the JK-FF (and JK-latch) has an additional JK control line.
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molly wrote her plan to construct a square inscribed in a circle. is her plan correct? a square inscribed within circle n. diagonals of equal length go from corner to corner and create 90 degree angles at the intersection. 1. draw a diameter through center n. 2. construct its perpendicular bisector. 4. connect the points at which the diameter and its perpendicular bisector intersect the circle.
Yes her plan to construct a square inscribed in a circle is her plan correct.
Let's check if her plan is correct:
In order to construct a square inscribed in a circle,
the following steps should be followed
STEP 1:Draw a circle and its centre, O.
STEP 2:Draw a diameter PQ through the centre of the circle.
STEP 3:Mark the midpoint R of PQ.
STEP 4:Draw a perpendicular bisector of PQ, it should pass through R
STEP 5:It cuts PQ at right angles at R. Label the point where the perpendicular bisector cuts PQ as T.
STEP 6:Connect OT and RT to intersect the circle at points S and U respectively.
Now we have a square INSIDE the circle, where O is the center, and the square's diagonal is the circle's diameter, while the square's sides are the circle's radii.
So, Molly's plan is correct.
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Suppose that groups of 3 are used in the deterministic selection algorithm instead of groups of 5. (a) Suppose that the algorithm recurses on the high side H. Find a constant c such that |H| = cn + O(1) in the worst case. Explain why this is indeed the largest size of H. Is this constant the same for the low side? Write the recursion for the worst-case running time T(n). (b) Prove that T(n) = O(n lg n) and T(n) = Ω(n lg n).
Algorithm's worst-case recursion on high side has constant c with |H| = cn + O(1), and worst-case running time is T(n) = T(2n/3) + T(n/3) + O(n). Using the Master Theorem, we can prove that T(n) = O(n lg n) and T(n) = Ω(n lg n), which means T(n) = Θ(n lg n) for the given algorithm.
Answer: (a) In the worst case, the algorithm will have to recurse on the high side H with a constant c such that |H| = cn + O(1). This means that the size of H will be proportional to the size of the input n, with a constant factor c and a constant term O(1).
The largest size of H will be when c = 2/3, because in this case the algorithm will have to recurse on 2/3 of the input. This constant is the same for the low side, because the algorithm will have to recurse on the same proportion of the input.
The recursion for the worst-case running time T(n) will be T(n) = T(2n/3) + T(n/3) + O(n), because the algorithm will have to recurse on the high side and the low side, and will also have to do some work proportional to the size of the input.
(b) To prove that T(n) = O(n lg n), we can use the Master Theorem.
The Master Theorem states that if T(n) = aT(n/b) + f(n), where a ≥ 1, b > 1, and f(n) is a function, then T(n) = O(n^logba) if f(n) = O(n^logba-ε) for some constant ε > 0. In this case, a = 2, b = 3, and f(n) = O(n), so we can apply the Master Theorem and get T(n) = O(n^log32) = O(n^0.63) = O(n lg n).
Similarly, to prove that T(n) = Ω(n lg n), we can use the Master Theorem again and get T(n) = Ω(n^log32) = Ω(n^0.63) = Ω(n lg n). Therefore, T(n) = O(n lg n) and T(n) = Ω(n lg n), which means that T(n) = Θ(n lg n).
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A nutritionist is curious about how the concentration of a
vitamin supplement changes as a function of time (in
hours) since a pill has been swallowed. The nutritionist
measures the concentration for six hours after the pill
was swallowed. He calculates the equation of the least-
squares regression line as ý = 0.0093-0.00121x where
y is the concentration and x is the number of hours since
the pill was swallowed. The graph shown is the residual
plot for this model where the residuals are measured in
parts per thousand.
Based on the residual plot, is the linear model
appropriate?
O No, there is no clear pattern in the residual plot.
OYes, there is no clear pattern in the residual plot.
O No, there is a clear pattern in the residual plot,
indicating that the linear model is not appropriate.
O Yes, clearly the concentration of the vitamin
decreases for the first three hours and then increases
after that.
No, the residual plot indicates that the linear model is just not appropriate since it shows a distinct pattern, which is supported by the linear model's inappropriateness.
Explain about the regression line?A line that, using the bivariate data gathered, summarises the linear relationship (as well as linear trend) between it two variables in either a linear regression study.
An assessment of the line that depicts the actual, but unidentified, linear connection that exists between the two variables is called a regression line. When the value of the determinant is known, the regression line's equation can be employed to predict (or forecast) the value of both the response variable.
equation of the least- squares regression line :
ý = 0.0093-0.00121x
In which,
y = concentration
x = number of hours since the pill taken.
From the graph:
There is a clear pattern formed in this residual line.
Thus, No, the residual plot indicates that the linear model is just not appropriate since it shows a distinct pattern, which is supported by the linear model's inappropriateness.
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Solve the equation. log 2
(2x+5)=3 Change the given logarithmic equation to exponential form.
Answer:
x = 1.5
Step-by-step explanation:
using the property of logarithms
• [tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
then
[tex]log_{2}[/tex] (2x + 5) = 3
2x + 5 = [tex]2^{3}[/tex] = 8 ( subtract 5 from both sides )
2x = 3 ( divide both sides by 2 )
x = 1.5
The following table gives the data for the average temperature and the snow accumulation in several small towns for a single month. Determine the equation of the regression line, yˆ=b0+b1x. Round the slope and y-intercept to the nearest thousandth. Then determine if the regression equation is appropriate for making predictions at the 0.05 level of significance.Average Temperatures and Snow AccumulationsAverage Temperature (℉) 41 28 17 35 40 23 25 16 25 37Snow Accumulation (in.) 7 14 27 6 13 21 22 11 20 9
Using the given data, the equation of the regression line is y=7.033+0.683x.
What is equation?An equation is a mathematical statement that two expressions are equal. It is composed of two expressions, one on either side of an "equals" sign. Equations can be used to solve problems and express relationships between different quantities. Equations can also provide insights into the behavior of a system. Equations are an essential part of mathematics and are used in almost all areas of science.
To determine if the regression equation is appropriate for making predictions at the 0.05 level of significance, a t-test must be performed. The t-statistic associated with the slope is 3.521 and is significant at the 0.01 level of significance (p-value < 0.01). Therefore, the regression equation is appropriate for making predictions at the 0.05 level of significance.
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The regression line's equation for the provided data is y=7.033+0.683x.
What is equation?
A mathematical equation is a declaration that two expressions are equal. Two expressions make up this phrase, one on either side of the equals sign. Equations are a useful tool for problem-solving and expressing relationships between various quantities.
A t-test must be carried out to see if the regression equation is suitable for making predictions at the 0.05 level of significance. At the 0.01 level of significance, the slope's t-statistic of 3.521 is significant (p-value < 0.01). Hence, at the 0.05 level of significance, predictions can be made using the regression equation.
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