If the coefficient of determination is a positive value, then the correlation coefficient can be negative or positive, which means the value of the correlation coefficient is between -1 and +1. If the variable x increases, the variable y also increases, and if the variable x decreases, then the variable y also decreases.
What is the Coefficient of Determination?The coefficient of determination is a statistical measurement which examines how differences in one variable can be explained by the difference in a second variable, when predicting the outcome of a given event. The coefficient of determination is a number between 0 and 1 that measures how well a statistical model predicts an outcome. This provides a measure of how well observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model.
Learn more about coefficient of determination at: https://brainly.com/question/28335905
#SPJ4
Find the dimensions of a rectangle with perimeter 72 m whose area is as large as possible. Step 1 Let / and w represent the length and the width of the rectangle, measured in m. Let A represent the area of the rectangle, measured in m2. Writing an equation for A in terms of land w gives us the following. m2 A= in terms of/ and w Let P represent the perimeter of the rectangle, measured in m. Writing an equation for gives us the following. P= m
By using the concept of maxima, it can be calculated that
Length of the rectangle of perimeter 72 m with maximum area is 18 m
Breadth of the rectangle of perimeter 72 m with maximum area is 18 m
What is maxima of a function?
Maxima of a function gives the maximum value of the function in a given interval or in the whole domain.
Let the length of the rectangle be l m and width of the rectangle be w m
Perimeter (P) = 2(l + w)
By the problem,
2(l + w) = 72
l + w = [tex]\frac{72}{2}[/tex]
l + w = 36
w = 36 - l
Area (A) = l [tex]\times[/tex] w
A = l [tex]\times[/tex] (36 - l) = [tex]36l - l^2[/tex]
Differentiation with A with respect to l
[tex]\frac{dA}{dl} = 36 - 2l[/tex]
For maximum area,
[tex]\frac{dA}{dl} = 0[/tex]
36 - 2l = 0
2l = 36
l = [tex]\frac{36}{2}[/tex]
l = 18 m
[tex]\frac{d^2A}{dl^2} = -2 < 0[/tex]
Hence area is maximum
w = 36 - 18 = 18 m
Length of the rectangle of perimeter 72 m with maximum area is 18 m
Breadth of the rectangle of perimeter 72 m with maximum area is 18 m
To learn more about maxima of a function, refer to the link-
https://brainly.com/question/82347
#SPJ4
find the 10th nth term of 2n²
Answer:
Step-by-step explanation:
1. in semiconductor manufacturing, wet chemical etching is often used to remove silicon from the backs of wafers prior to metalization. the etch rate is an important characteristic in this process and known to follow a normal distribution. two different etching solutions have been compared, using two random samples of 10 wafers for each solution. the observed etch rates are as follows (in mils per minute): solution 1 9.9 9.4 9.3 9.6 10.2 10.6 10.3 10.0 10.3 10.1 solution 2 10.2 10.6 10.7 10.4 10.5 10.0 10.2 10.7 10.4 10.3. (a) Do the data support the claim that the mean etch rate is the same for both solutions? In reaching your conclusions, use a fixed-level test with \alpha = 0.05α=0.05 and assume that both population variances are equal. (b) Calculate a P-value for the test in part (a). (c) Find a 95% CI on the difference in mean etch rates. (d) Construct normal probability plots for the two samples. Do these plots provide support for the assumptions of normality and equal variances? Write a practical interpretation for these plots.
P-value for the test is 0.011.
(a) We have two samples
y₁₁ = μ₁ + e₁₁
...
y₁,₁₀ = μ₁ + e₁,₁₀
y₂,₁ = μ₂ + e₂₁
...
y₂,₁₀ = μ₂ + e₂,₁₀
with unknown means μ₁ and μ₂. The total number of observation n = 20,
number of parameters p = 2.
First, we estimate the means of both samples:
û₁ = [tex]\frac{1}{10}[/tex] ∑ y₁i = 9.97, û₂ = [tex]\frac{1}{10}[/tex] ∑ y₂i = 10.4
The residual sum of squares
SSres = ∑(y₁i - û₁)^2 + ∑(y₂i - û₂)^2 = 2.081.
The unbiased variance estimate is
[tex]s^{2}[/tex] = [tex]\frac{1}{n - p}[/tex]SSres
= [tex]\frac{2.081}{18}[/tex]
[tex]s^{2}[/tex]= 0.116
In testing the null hypothesis H₀ : μ₁ = μ₂, the test statistic of the t-test is defined as
T = |û₁ - û₂|/([tex]\sqrt{s^{2}(\frac{1}{10}+\frac{1}{10} ) }[/tex])
T= 2.83.
Since t18(0.05/2) = 2.1
the hypothesis H₀ is rejected, at the significance level 5%. In other words, under the standard assumptions, the data do not support the claim that the mean each rate is the same for both solutions, at the level of significance 5%.
(b)
p = P(|T18| > T)
= 2P(T18 > T)
p = 0.011.
To know more about P-value here
https://brainly.com/question/22385506
#SPJ4
3x (2a - b)-y(2a - b) factorise
Answer: The correct answer is (3x−y)(2a−b)
Step-by-step explanation:
Factor 3x(2a−b)−y(2a−b)
6ax−2ay−3bx+by
=(3x−y)(2a−b)
A bicycle that originally costs $373 is on sale for $285. An electric scooter that originally costs $450 is on sale for $351. Which item is the better deal? Explain how you know.
Answer:
The bicycle that originally cost $375 is the best to be sale at 285. a discount of $88 unlike the discount of an electric scooter.
Four equivalent forms of a quadratic function are given. which form displays the y-intercept of the function?
The quadratic function f(x) = 3x^2 + 6x – 144 displays the y-intercept of the function.
In the given question, four equivalent forms of a quadratic function are given.
We have to choose which form displays the y-intercept of the function.
The given quadratic functions are:
f(x) = 3(x^2 + 2x - 48)
f(x) = 3(x + 1)^2 - 147
f(x) = 3x^2 + 6x – 144
f(x) = 3(X + 8)(x-6)
As we know that in y intercept form x=0.
A quadratic equation's Y intercept is the location where the graph's Y-axis is broken. This implies that the x axis's coordinates must be zero.
Put x = 0 in the equation to determine the Y intercept in a quadratic equation. You will also receive the Y interception.
Since we have to find the y intercept in the given form so the function
f(x) = 3x^2 + 6x – 144 given in a standard form and y intercept is clearly seen in this function.
So, the function f(x) = 3x^2 + 6x – 144 displays the y-intercept of the function.
To learn more about quadratic function link is here
brainly.com/question/1863222
#SPJ4
The right question is
Four equivalent forms of a quadratic function are given. Which form displays the y-intercept of the function?
f(x) = 3(x2 + 2x - 48)
f(x) = 3(x + 1)2 - 147
f(x) = 3x2 + 6x – 144
f(x) = 3(X + 8)(x-6)
two cities are 145 miles apart. a truck travels this distance in 2.5 hours. a car is 1.5 times as fast as the truck. how long does it take for the car and the truck to meet if they leave at the same time, and travel toward each other
By using the travel distance formula, we found out that it takes 1 hour for the car and the truck to meet if they leave at the same time and travel toward each other.
It is given to us that -
Two cities are 145 miles apart
Truck travels this distance in 2.5 hours
Car is 1.5 times as fast as the truck
We have to find out the time taken for the car and the truck to meet if they leave at the same time, and travel toward each other.
We know that -
[tex]Speed = \frac{Distance}{Time}[/tex] ----- (1)
Let us say that the speed of the truck is given by [tex]S_{t}[/tex] and the speed of the car is given by [tex]S_{c}[/tex].
Now, from equation (1), we can say that the speed of the truck,
[tex]S_{t}=\frac{145}{2.5} \\= > S_{t}= 58 miles per hour[/tex] ----- (2)
It is given to us that the car is 1.5 times as fast as the truck
=> [tex]S_{c}= 1.5 * 58\\= > S_{c}= 87 miles per hour[/tex] ----- (3)
It is mentioned that the car and the truck leave at the same time to meet each other.
Let us say that the truck meets the car at a distance 'd'.
This implies that the distance travelled by the car to meet the truck at a given point = (145-d) --- (4)
From equation (1), we can say that
[tex]Time = \frac{Distance}{Speed}[/tex]
Also, we know that -
Time taken by truck to travel d miles = Time taken by car to travel (145-d) miles
[tex]\frac{d}{58}=\frac{145-d}{87} \\= > 87d = 8410-58d\\= > 145d=8410\\= > d = 58[/tex]
Thus, the truck will travel 58 miles to meet car after they leave at the same time.
So, the time taken for the car and truck to meet =
[tex]\frac{58 miles}{58 miles per hour} = 1 hour[/tex]
Therefore, according to the distance formula, it takes 1 hour for the car and the truck to meet if they leave at the same time and travel toward each other.
To learn more about travel distance visit https://brainly.com/question/25237191
#SPJ4
find the angle abc in the given figure
Answer:
∠ ABC = 50°
Step-by-step explanation:
∠ ABC and 130° are a linear pair and sum to 180° , that is
∠ ABC + 130° = 180° ( subtract 130° from both sides )
∠ ABC = 50°
calculate the mean of a given group of data points. you should not hard-code the dimensionality of the data points.
To calculate the mean of grouped data, the first step is to determine the midpoint of each interval, or class. These midpoints must then be multiplied by the frequencies of the corresponding classes. The sum of the products divided by the total number of values will be the value of the mean.
Mean = Sum / Number of terms
mean_of_points(data):
"""Calculate the mean of a given group of data points. You should not hard-code the dimensionality of the data points.
Arguments:
data: a list of lists representing a group of data points
Returns: a list of floats as the mean of the given data points """
To know more about data here
https://brainly.com/question/10173601
#SPJ4
drag each statement to the appropriate bin depending on whether it applies to the descending limb of the loop of henle, the ascending limb of the loop of henle, or the collecting duct
The proximal tubule reabsorbs all of the filtered glucose and amino acids, as well as salt, chloride, potassium, and bicarbonate. So the option b is correct.
In the given question, we have to check most of the glucose that is filtered through the glomerulus undergoes reabsorption in the:
a. distal tubule
b. proximal tubule
c. descending limp of the loop of Henle
d. ascending limb of the loop of Henle
The proximal tubule reabsorbs all of the filtered glucose and amino acids, as well as salt, chloride, potassium, and bicarbonate. Additionally, sodium ion and glucose were co-transported in the proximal tubule by the co-transporter SGLT (sodium dependent glucose transporter). The ability to transport glucose distinguishes two SGLT (SGLT1 and SGLT2). Since SGLT2 is abundant in the S1 and S2 segments of the proximal tubule and SGLT1 has a high affinity for glucose, it filters 90% of the glucose. Option (b) is correct, therefore.
Option (a) is False, since the distal tubule is crucial to maintaining a healthy acid-base balance. The amount of extracellular fluid is regulated.
The descending limb of the Henle loop, which is involved in reabsorption of salt, urea, and water, makes option (c) incorrect.
Option (d) is likewise untrue because the ascending limb of the loop of Henle allows for the reabsorption of sodium, calcium, bicarbonate, chloride, and magnesium but not glucose.
To learn more about proximal tubule link is here
brainly.com/question/14314040
#SPJ4
The write answer is;
Most of the glucose that is filtered through the glomerulus undergoes reabsorption in the:
a. distal tubule
b. proximal tubule
c. descending limp of the loop of Henle
d. ascending limb of the loop of Henle
is the following sentence a statement? why or why not? the sentence in this box is a lie. statement. the sentence is neither true nor false, and so it is a statement. statement. the sentence is true. therefore, it is a statement. statement. the sentence is false. therefore, it is a statement. not a statement. the sentence is false, and so it is not a statement. not a statement. the sentence is neither true nor false, and so it is not a statement.
The last option is correct that is not a statement. Since the statement is neither true nor untrue, it cannot be considered a statement.
Given that,
We have to find the following sentence a statement or not.
We know that,
The statement is the sentence in this box is a lie.
The sentence in the box may be true or a lie we don't know exactly
So it is not a statement
A statement must give a confirmed information
Hence last option is correct
Therefore, The last option is correct that is not a statement. Since the statement is neither true nor untrue, it cannot be considered a statement.
Complete question: Is the following sentence a statement? Why or why not?
The sentence in this box is at lie.
Statement. The sentence is true. Therefore, it is a statement.
Statement. The sentence is neither true nor false, and so it is a statement.
Statement. The sentence is false. Therefore, it is a statement.
Not a statement. The sentence is false, and so it is not a statement.
Not a statement. The sentence is neither true nor false, and so it is not a statement.
To learn more about statement visit: https://brainly.com/question/26141085
#SPJ4
Write the equation of the parabola in vertex form.
vertex (3,1), point (2,-2)
The equation of parabola in vertex form is [tex]y=-3(x-3)^2+1[/tex].
What is the vertex form of the parabola?
The equation of parabola in vertex form is as follows:
[tex]y=a(x-h)^2+k[/tex]
Here, (h,k) is the coordinate of vetex and a is the constant. From this form of parabola, vertex can be easily determined.
In the above equation, (h,k) is known and a can be determined by sustituting (2,-2) for (x,y).
Substitute (3,1) for (h,k) in the above equation.
[tex]y=a(x-3)^2+1[/tex] .. (1)
Since the point (2,-2) lies on the parabola hence, it must satisfy the above equation. Substitute (2,-2) in the above equation.
[tex]-2=a(2-3)^2+1\\-2=a+1\\a=-3[/tex]
Now, substitute the value of a in equation (1).
[tex]y=-3(x-3)^2+1[/tex]
Hence, the equation of parabola in vertex form is [tex]y=-3(x-3)^2+1[/tex].
Learn more about the vertex form of parabola from the following link:
https://brainly.com/question/17987697
#SPJ1
Jan traveled 260 miles using 8 gallons of gas. What was the cars miles per quart?
31. the measures of 2 angles are in the ratio 5:3. the measure of the larger angle is 30 greater than half the difference of the angles. find the measure of each angle.
The correct answer is the measure of two angles are 37.5° and 22.5°.
It is given that the measure of two angles are in the ratio 5:3 . Let the one angle be 5x and the other angle be 3x.
Difference of the angles = 5x - 3x
According to the question, the measure of the larger angle is 30° greater than half the difference of the angles
Thus we can write it as:
⇒ 5x - 1/2(5x-3x) =30°
⇒ 10x- (5x-3x) = 60°
⇒ 8x = 60°
⇒ x = 7.5°
Thus, the larger angle = 5x = 5×7.5= 37.5° and the smaller angle = 3x = 3× 7.5 = 22.5°
Hence, the measure of two angles are 37.5° and 22.5°.
To find similar questions on 'angle'
visit- https://brainly.com/question/24625299
#SPJ4
in statistical hypothesis testing, the null hypothesis and the alternative hypothesis are stated in terms of:
The correct answer is 'in statistical hypothesis testing, the null hypothesis and the alternative hypothesis are stated in terms of population parameter.
A population parameter is always used to express a statistical hypothesis: The null hypothesis is true if the test statistic's value is within the nonrejection zone.
We look for evidence supporting the null hypothesis when testing a statistical hypothesis. The null hypothesis and the alternative hypothesis are the two variants of the hypothesis that are typically used in research (called the experimental hypothesis when the method of investigation is an experiment).
According to the alternative hypothesis, a population parameter does not equal the given value. Usually, this number is zero, which is the null hypothesis value for an effect of zero.
You can reject the null hypothesis and favour the alternative hypothesis if your sample includes enough evidence to support it.
To know more about 'statistical hypothesis' related questions
visit- https://brainly.com/question/15980505
#SPJ4
At the movies, 60% of the moviegoers bought a soda. 45% of the moviegoers bought popcorn and soda. What is the probability that a person will buy popcorn if they have already decided to buy soda?
The probability that a person will buy pop corn and soda is 9/20
What is Probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.
probability = sample space / total possible outcome
The total possible outcome here is 100
The probability that a person will buy popcorn if they have already decided to buy soda = probability that a person will buy both soda and popcorn
therefore the probability of a person buying both soda and pop corn= 45/100=9/20
learn more about probability from
https://brainly.com/question/24756209
#SPJ1
g a spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min. at what rate is the volume of the snowball decreasing when the radius is 12 cm. (note the answer is a positive number).
Rate at which volume of the snowball decreasing when the radius is 12 cm is 180.864 cm^3/min
Given:
a spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min. at what rate is the volume of the snowball decreasing when the radius is 12 cm.
Let r be the radius of the spherical snowball
Radius is decreasing at rate of 0.1 cm/min.=> dr/dt = -0.1
(negative sign indicates decreasing)
Volume v = 4/3πr^3
dv/dt = 4/3 π 3r^2*dr/dt
= 12π/3*r^2*(-0.1)
= 4π*12^2*(-0.1)
= 4π*144*-1/10
= 4π*(-14.4)
= -57.6π
= 180.864 cm^3/min
Learn more about the volume here:
https://brainly.com/question/1578538
#SPJ4
What is 15 a multiple of?.
The numbers that are n times 15 is known as multiple of 15. The numbers are 15, 30, 45, 60, 75, 90, 105, 120, 135, 150,..............
In the given question we have to find what is 15 a multiple of.
The numbers that are n times 15, where n is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and so forth, are considered multiples of 15. Therefore, multiples are essentially any integer multiplied by n, where n is a list of all natural numbers. Thus, the multiples of 15 have the form of 15n, as in:
15×1, 15×2 ,15×3 ,15×4, 15×5, 15×6, 15×7, 15×8, 15×9, 15×10,....................
15, 30, 45, 60, 75, 90, 105, 120, 135, 150,................................
To learn more about multiple of number link is here
brainly.com/question/11799672
#SPJ4
a 12-lb weight is attached both to a vertically suspended spring that it stretches 6 in. and to a dashpot that provides 3 lb of resistance for every foot per second of velocity. if the weight is pulled down 1 ft below its static equilibrium position and then released from rest at time t
The weight is pulled down 1 ft below its static equilibrium position and then released from rest at time t the phase angle is α=π÷16.
The mass in fps gadgets is m = 0.375 and the spring consistent is [tex]k = 12/5 × (lb)/(lt) = 24lb / ft .[/tex]
The round frequency is given through [tex]ω{0} ^ 2 = k/m = 64 , so ω{0} = 8rad / s[/tex] The damping consistent is[tex]c = 3lb - s / ft so p = i/(2m) = 4[/tex], and the machine is consequently underdamped. Then [tex]ω= (ω{0} ^ 2 - p ^ 2) = sqrt(48) = 4^(3)[/tex]so the overall answer is
[tex]x(t) = Ac ^ (- 4t) cos 4 t + B * c ^ (- 4t) * sin 4 ^3t\\v(t) = A * e ^ (- 4t) * (- 4cos 4 ^3 t - 4^3\\sin 4 * ^3 t) + B * e ^ (- 4t) * (- 4sin 4 * 63 t + 4^3 cos 4 ^3* t)[/tex]
We degree the displacement vertically, thinking about a displacement downwards as being positive, because it corresponds to stretching the string further.
Read more about spring :
https://brainly.com/question/23885190
#SPJ4
the following are six observations collected from treatment 1, four observations collected from treatment 2, and five observations collected from treatment 3. test the hypothesis at the 0.05 significance level that the treatment means are equal. treatment 1 treatment 2 treatment 3 9 13 10 7 20 9 11 14 15 9 13 14 12 15 10 required: a. state the null and the alternate hypotheses.
The Null hypothesis:
H₀: μ₁=μ₂=μ₃
Alternative hypothesis:
H₁: Treatment means are all not same.
Given that,
Test the idea that the treatment means are equivalent at the 0.05 level of significance using the following data: six observations gathered from treatment 1, four observations gathered from treatment 2, and five observations gathered from treatment 3. treatment 1 therapy two therapies Required: 3 9 13 10 7 20 9 11 14 15 9 13 14 12 15 10.
We have to find name the null and the alternative hypotheses.
We know that,
For the given scenario, the null and alternative hypotheses are stated as below:
Null hypothesis:
H₀: μ₁=μ₂=μ₃
Alternative hypothesis:
H₁: Treatment means are all not same.
Therefore, The Null hypothesis:
H₀: μ₁=μ₂=μ₃
Alternative hypothesis:
H₁: Treatment means are all not same.
To learn more about hypothesis visit: https://brainly.com/question/28920252
#SPJ4
excel's can be used to construct a crosstabulation. chart tools sum function pivottable report countif function
Excel's PivotReport Table can be used to construct a crosstabulation.
What is Pivot Report Table?
Data summaries are created using pivot tables. Large data sets can be processed automatically, and the resulting report can include groupings of the data as well as count totals, averages, sums, and other calculations. Pivot report tables offer insight that could be challenging to perceive otherwise.Here is a table with sales data in its original format as an illustration. It includes a list of the goods that salespeople offer. However, it is challenging to evaluate the effectiveness of each salesperson or determine which product brings in the most money. A pivot report table can be used to quickly access data and accurately answer these queries.To know more about pivot report table check the below link:
https://brainly.com/question/29549931
#SPJ4
arianna will roll a standard die 10 times in which she will record the value of each roll. what is a trial of this experiment?
Here rolling of a die is a trial for the experiment.It had 6 possible outcomes.
What is pattern of standard die?The most well-known kind of bite the dust is a six-sided shape with the numbers 1-6 put on the countenances. The worth of the roll is demonstrated by the quantity of "spots" appearing on the top. For the six-sided kick the bucket, inverse countenances are organized to continuously aggregate to seven.
Then,
A preliminary is a strategy that can be limitlessness rehashed and has a clear cut set of conceivable outcomes.Here moving of a kick the bucket is a preliminary for the experiment.It had 6 potential results.
So, option (a) is correct
To know more about standard die visit:
brainly.com/question/20376457
#SPJ4
What is the equation of the line that passes through the point (5,4) and has a slope of 2
Answer:
y=2x-6
Step-by-step explanation:
y-4=2(x-5)
y-4=2x-10
+4
y=2x-6
The Great Grade Six Brain Bogglers I Assignment
88. Pearl's father was 28 when Pearl was 6 years old. Pearl's father is now twice as old as
Pearl. How old is Pearl?
If josue is 5 more than twice Rachel’s age, how old is josue?
(Represent the answer in terms of x)
Answer:
J = 5 + (R x 2)
Step-by-step explanation:
the best way I can answer it is in a equation.
Josue equals whatever 5 + Rachel's doubled age is.
assuming no one is cheating and the coin is fair, if a customer plays twice, what is the chance they make money?
Answer:
Step-by-step explanation:
(1/2)(1/2)=1/4
7
12
+
11
20. Y’all pls help me I got no cle
The solution of the expression will be;
⇒ - 1/30
What is Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Given that;
The expression is,
⇒ - 7/12 + 11/20
Now,
Simplify the expression as;
⇒ - 7/12 + 11/20
LCM of [12, 20] = 60
⇒ - 35/60 + 33/60
⇒ (- 35 + 33) / 60
⇒ - 2/60
⇒ - 1/30
Thus, The solution of the expression will be;
⇒ - 1/30
Learn more about the LCM visit:
https://brainly.com/question/233244
#SPJ1
What are the first 3 factors of 10?.
Step-by-step explanation:
The factors of 10 are 1,2,5,10.
Therefore the first 3 factors of 10 are 1,2,5
suppose that 12 different people call you in a week. what is the probability you will get at least one phone call per day (assume 7 days in the week)? use a mc simulation to estimate this probability with a margin of error of 0.005.
at the start of 2014 tims house was worth £100,000
the value of the house increased by 10% every year
work out the value of his house at the start of 2018
The value of Tim's house at the start of 2018 is £146410
How to determine the value of his house at the start of 2018?From the question, we have the following parameters that can be used in our computation:
Initial value = 100,000
Rate of increase = 10%
The value of the house x years after 2014 can be represented as the following exponential function
Value = Initial value * (1 + rate)ˣ
So, we have
Value = 100000 * (1 + 10%)ˣ
2018 is 4 years after 2014
This means that x = 4
So, we have
Value = 100000 * (1 + 10%)⁴
Evaluate
Value = 146410
Hence, the value is #146410
Read more about exponential functions at
https://brainly.com/question/11464095
#SPJ1
