Describe the correlation between highway mileage and engine size
Answer:
As engine size increases, highway mileage decreases.
Step-by-step explanation:
Use the Desmos graphing calculator to find the least-squares linear correlation coefficient for the dataset in the table:
x y
3 1
4 5
8 11
10 21
1. r=0.74 б
2. r=0.938
3. r=0.968
4. r=0.811
The least-squares linear correlation coefficient for the given dataset can be determined using the Desmos graphing calculator. The options provided are: r=0.74, r=0.938, r=0.968, and r=0.811.
To find the least-squares linear correlation coefficient, we need to calculate the Pearson correlation coefficient (r). This coefficient measures the strength and direction of the linear relationship between two variables. In this case, the dataset consists of pairs of values (x, y).
Using the Desmos graphing calculator, we can input the dataset and generate a scatter plot. Then, by selecting the option to display the line of best fit or the regression line, we can obtain the equation of the line and the value of r, the least-squares linear correlation coefficient.
Based on the options provided, we need to calculate the value of r using the Desmos graphing calculator and compare it to the given options. After performing the calculations, the correct answer is the option that matches the calculated value of r.
Therefore, the option that corresponds to the least-squares linear correlation coefficient calculated using the Desmos graphing calculator for the given dataset should be selected as the answer.
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Solve the system of equations using the eliminationmethod.6х + 3y : 20.25 and 8x + 3y = 25.75Click edit background and show your work or take apicture of the work you did on paper.
Given
\(\begin{gathered} Eq1\colon6x+3y=20.25 \\ Eq2\colon8x+3y=25.75 \\ \\ \text{Sum both equations} \end{gathered}\)
Procedure
\(\begin{gathered} Eq2-Eq1 \\ 8x+3y-6x-3y=25.75-20.25 \\ 8x-6x+3y-3y=5.5 \\ 2x=5.5 \\ x=2.75 \end{gathered}\)
Now for y
\(\begin{gathered} y=\frac{20.25-6x}{3} \\ y=\frac{20.25-6\cdot2.75}{3} \\ y=1.25 \end{gathered}\)The answer would be x = 2.75 and y = 1.25
What happens if the residual is negative?
When the residual is negative it represents the predicted value is very much high.
A residual represents the measure of how well a line fits for the given individual data points which were plotted on the graph. Residual plot is representation on the graph which shows the residuals on the vertical axis also independent variable on the horizontal axis of the graph.If the residual value is positive it represents the predicted value is very low on the regression line.If the residual value is negative it represents the predicted value is very high on the regression line.Therefore, the negative residual value on the regression line represents the predicted value is very much high.
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Which of the following is true with respect to the following functions:
The option that is true with regard to the following functions is Option B. "The domain g(x) and h(x) include all real number while the domain of i(x) and h(x) are restricted"
What is the explanation for the above?Lets examine f(x) = 3x + 14Note that this function is indicative of a straight-line. See the attached graph for function 1. Note that it doesn't have any end points. That is, it is Asymptote.
Let us examine h(x) = 3ˣ + 1This represents an exponential graph. Just like the function above it doesn't have any end point. It however has an asymptote:
y = 0
Let us look at F'(x) = Log₃ (x = 1).
This is indicative of logarithm graph. It doesn't have any end but has an asymptote x == 0
Let us take a look at g(x) = X⁴ + 3x² - 14Notice that in the mid point there is an end point given as (0, -14). Thus, it is correct to state that the function in Option B is the only one that exhibits end behavior and as such is restricted.
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The reciprocal of 6 and -12y - 18x
12/22 aaannnssswwweeerrr
If f(x) = 3x + 7, find:
f(3) = [?]
Enter
Help guys asap this is due today. Find the volume of the cylinder. Find the volume of a cylinder with the same radius and double the height.
The volume of the cylinder in^3?
The volume of with the same radius and double the height is ?
Answer:
226.2 in³ and 452.4 in³
Step-by-step explanation:
Volume of original shape:
Volume = base area x height
Volume = πr² x 2
Volume = π(6)² x 2
Volume = 113.10 x 2
Volume = 226.2 in³
Volume with same radius but double the height:
Volume = base area x height
Volume = πr² x 2(2) ----------> multiplied by 2 because height is being doubled
Volume = 113.10 x 4
Volume = 452.4 in³
Find the total surface area of the figure below:
Answer:
95
Step-by-step explanation:
Formula -
Triangle Area - 1/2bh
Square - l x w
Triangle - 5 x 7 = 35/2 = 17.5
Since there are four triangle, we will multiply 17.5 x 4 which is equal to 70
Square - 5 x 5 = 25
Now we add both 70 and 25 which is 95
So the total surface area is 95
Answer:
95
Step-by-step explanation:
Area of the triangles:
A = (base × height) ÷ 2A = (5 × 7) ÷ 2A = (35) ÷ 2A = 17.5Because there are 4 triangles, we can do our answer of one triangle × 4So, 17.5 × 4 = 70Area of a square:
The sides of squares are the sameA = L × WA = 5 × 5A = 25Put them together:
Area of triangles + area of the square = surface area70 + 25 = suface area70 + 25 = 95I hope this helps!
given that z is a standard normal random variable, what is the value of z if the between -z and z is 0.901
The value of z that corresponds to a cumulative probability of 0.901 can be found by using the standard normal distribution table or a statistical calculator and that is approximately -1.67.
In the standard normal distribution, the area under the curve between -z and z represents the cumulative probability from negative infinity to z. Since the distribution is symmetric, the area from negative infinity to -z is also 0.5 - 0.901/2 = 0.0495.
To find the value of z, we need to locate the z-score that corresponds to an area of 0.0495 in the standard normal distribution. By looking up this value in the standard normal distribution table or using a statistical calculator, we find that z is approximately -1.67.
Therefore, the value of z that corresponds to a cumulative probability of 0.901 is approximately -1.67.
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If 2 cards are dealt from a shuffled deck of 52 cards, find the probability that all 2 cards are jacks.
Step-by-step explanation:
?Can you please explain more??
︵‿︵‿୨♡୧‿︵‿︵
in 1995, 58% of the cranberries processed by the cooperative were water-harvested. what percentage to they expect to be water-harvested in 1996? group of answer choices about 70% about 87% about 20% about 12% about 99%
In 1996, the cooperative expects approximately 40% of cranberries processed to be water-harvested.
This is a decrease of 18% from 1995. This decrease is likely due to the fact that water-harvested cranberries cost more to process than traditional dry-harvested cranberries.
Additionally, the cooperative may not be able to find enough cranberry farmers willing to switch to the water-harvesting method, which is a labor-intensive process.
Thus, the cooperative is likely to experience a decrease in the percentage of water-harvested cranberries processed in 1996.
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You have $1000 to invest in an account and need to have $2000 in one year. What interest rate would you need to have in order to have this if the amount is compounded weekly? Round your answer to the nearest percent.
Answer:
\(\large \boxed{\sf \ \ 70\% \ \ }\)
Step-by-step explanation:
Hello,
We assume that the year is 52 weeks, and we note r the interest rate we are looking for. The rate is expressed in percent and is annually, meaning that the investment is, after the first week :
\(1000\cdot (1+\dfrac{r\%}{52})=1000\cdot (1+\dfrac{r}{5200})\)
For the second week
\(1000\cdot (1+\dfrac{r}{5200})^2\)
After 52 weeks
\(1000\cdot (1+\dfrac{r}{5200})^{52}\)
and we want to be equal to 2000 so we need to solve:
\(1000\cdot (1+\dfrac{r}{5200})^{52}=2000\\\\\text{*** divide by 1000 both sides ***}\\\\(1+\dfrac{r}{5200})^{52}=\dfrac{2000}{1000}=2\\\\\text{*** take the ln **}\\\\52\cdot ln(1+\dfrac{r}{5200})=ln(2)\\\\\text{*** divide by 52 ***}\\\\ln(1+\dfrac{r}{5200})=\dfrac{ln(2)}{52}\\\\\text{*** take the exp ***}\\\\\displaystyle 1+\dfrac{r}{5200}=exp(\dfrac{ln(2)}{52})=2^{(\dfrac{1}{52})}=\sqrt[52]{2}\\\\r = 5200\cdot (\sqrt[52]{2}-1)=69.77875...\)
Rounded to the nearest percent, the solution is 70%.
If you want to double your capital in one year with weekly compounding you need an interest rate of 70% !!
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
4%
Step-by-step explanation:
Level B: Lexie wanted to have a heel-toe race with her older brother, Josh, and her sister,
Hannah. She said, "My feet are smaller, so I should only have to go a shorter distance than
you two." Her sister said, "That makes sense - let's race our ages." They measured off 7 feet
for Lexie's track, 16 feet for Josh's track and 10 feet for Hannah's track, "Now let's measure
our shoes," said Josh. "My shoe is 1/2 of a foot," said Lexie. "Three of my shoes add up to 2
feet," said Hannah. Josh said his shoe was exactly a foot long.
I
Who needs to take the fewest steps to walk his or her track? Explain how you found your
answer.
How many more steps do the two others need to take to finish their races?
The 1st one was doable, but I don't understand the 2nd Question.
Answer: ? What are you talking about?
Step-by-step explanation:
∠1and ∠2 are a linear pair, and ∠2 and ∠3 are vertical angles. m∠1=(3y+10)∘ and m∠3=(5y−30)∘. What is m∠2?
Answer:
\(m\angle 2=95^{\circ}\)
Step-by-step explanation:
It is given that ∠1 and ∠2 are a linear pair. So, there sum is 180 degrees.
\(m\angle 1+m\angle 2=180^{\circ}\) ...(1)
∠2 and ∠3 are vertical angles. So, both are equal.
\(m\angle 2=m\angle 3\) ...(2)
From (1) and (2), we get
\(m\angle 1+m\angle 3=180^{\circ}\)
Substitute \(m\angle 1=(3y+10)^{\circ}\) and \(m\angle 3=(5y-30)^{\circ}\) in the above equation.
\((3y+10)^{\circ}+(5y-30)^{\circ}=180^{\circ}\)
\((8y-20)^{\circ}=180^{\circ}\)
\(8y-20=180\)
\(8y=180+20\)
Divide both sides by 8.
\(y=\dfrac{200}{8}\)
\(y=25\)
The value of y is 25.
Using equation (2), we get
\(m\angle 2=m\angle 3=(5y-30)^{\circ}\)
Substitute y=25.
\(m\angle 2=(5(25)-30)^{\circ}\)
\(m\angle 2=(125-30)^{\circ}\)
\(m\angle 2=95^{\circ}\)
Therefore, \(m\angle 2=95^{\circ}\).
The difference of a number and 6is the same as 5 times
Answer:
let difference be x
Step-by-step explanation:
you can solve for x by keeping the 2 statesments as conditions.
then you solve for both equations together by adding subtracting or multiplying.
eg: let x be the number.
the. proceed with conditions as equations
then solve
then your answer is here
Process time at a workstation is monitored using sample mean and range control charts. Six samples of n = 15 observations have been obtained and the sample means and ranges computed (in minutes) as follows: Sample 1 Range .49 1.41 2 3 Mean 13.30 3.16 3.21 3.30 3.27 3.20 .47 14 5 6 .49 .46 .54 What are the upper and lower limits for sample mean control chart? (Round the intermediate calculations to 2 decimal places. Round the final answers to 2 decimal places.) OLCL = 3.22, UCL = 3.53 OLCL = 3.13, UCL = 3.35 OLCL = 3.32, UCL = 3.64 LCL = 3.04, UCL = 3.42 ОО O It cannot be calculated.
The upper and lower limits for the sample mean control chart are:
UCL = 6.66
LCL = 3.36
To calculate the upper and lower limits for the sample mean control chart, we need to use the given data and formulas.
Sample size (n) = 15
Sample mean values: 13.30, 3.16, 3.21, 3.30, 3.27, 3.20
Range values: 0.49, 1.41, 2, 3, 0.47, 14, 5, 6, 0.49, 0.46, 0.54
First, we calculate the average range (R-bar) using the range values:
R-bar = (Sum of ranges) / (Number of samples)
R-bar = (0.49 + 1.41 + 2 + 3 + 0.47 + 14 + 5 + 6 + 0.49 + 0.46 + 0.54) / 11
R-bar ≈ 2.86 (rounded to 2 decimal places)
Next, we use the average range (R-bar) to calculate the control limits for the sample mean chart:
Upper Control Limit (UCL) = X-double bar + A2 * R-bar
Lower Control Limit (LCL) = X-double bar - A2 * R-bar
Where X-double bar is the average of sample means and A2 is a constant based on the sample size (n). For n = 15, A2 is 0.577.
Calculating the average of sample means (X-double bar):
X-double bar = (Sum of sample means) / (Number of samples)
X-double bar = (13.30 + 3.16 + 3.21 + 3.30 + 3.27 + 3.20) / 6
X-double bar ≈ 5.01 (rounded to 2 decimal places)
Calculating the control limits:
UCL = 5.01 + 0.577 * 2.86 ≈ 5.01 + 1.65 ≈ 6.66 (rounded to 2 decimal places)
LCL = 5.01 - 0.577 * 2.86 ≈ 5.01 - 1.65 ≈ 3.36 (rounded to 2 decimal places)
Therefore, the upper and lower limits for the sample mean control chart are:
UCL = 6.66
LCL = 3.36
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In the U.S.A., the symbol 5/2 means the 5th month, 2nd day, or May 2. But in England, 5/2 means the fifth day, 2nd month, or February 5. How many days of the year each have the same symbol in both the U.S. and England
In both the U.S.A. and England, there are only two days of the year that share the same symbol: May 2 (5/2) and February 5 (5/2).
In the United States, the symbol 5/2 is interpreted as the 5th month and 2nd day, representing May 2. On the other hand, in England, 5/2 denotes the 5th day and 2nd month, indicating February 5. To determine how many days of the year have the same symbol in both countries, we need to find the dates that match.
In the U.S., there are 12 months, so there are 12 possible combinations with 5 as the month. However, only May 2 (5/2) coincides with the English interpretation.
In England, there are 31 days in January, so there is no match with the American format. However, in February, there are 28 days (or 29 in a leap year), and February 5 (5/2) aligns with the American interpretation.
Hence, there are only two days of the year that share the same symbol in both the U.S. and England: May 2 (5/2) and February 5 (5/2).
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Calculate the length of the side of the square to 1dp.
Answer:
72 cm
Step-by-step explanation:
You can solve this problem using the properties of the 45-45-90 right triangle. Assuming the 12 cm is a diagonal of the square, each side of the square can be modeled as x, and the diagonal will be x\(\sqrt{2}\).
This means \(x\sqrt{2} =12\), so \(x=\frac{12}{\sqrt{2} }\).
Next, to find the area of the square you take the square of any of its sides. Since x is the length of one side, and \(x=\frac{12}{\sqrt{2} }\) , you can square \(\frac{12}{\sqrt{2} }\) to get the area. This is equal to \(\frac{144}{2}\) or 72 cm.
I need the exponent form and standard form for 36
The Standard form of a number is also known as "Scientific notation". The form is:
\(a\cdot10^b\)Where the coefficient "a" is a number from 1 to 10, but not including 10, and the exponent "b" is an Integer. The base is always 10.
By definition, the decimal point must be after the first digit of the coefficient.
In this case, in order to write 36 in Standard form, you must move the decimal point one place to the left:
\(3.6\cdot10^1\)Notice that the exponent is 1 because you had to move the decimal point one place to the left in order to locate it after the first digit of the coefficient.
Now, to write the exponent form of a number is:
\(b^n\)Where the exponent "n" indicates how many times "b" must be multiplied by itself.
You know that:
\(6\cdot6=36\)Then:
\(36=6^2\)The answer is:
a. Exponent form:
\(6^2\)b. Standard form:
\(3.6\cdot10^1\)PLEASE HELP!!!!!!!!!
Assume the random variable x is normally distributed with a mean of 45 and standard deviation of 12. Find P (x > 40 ).
Answer:
z = 54 − 45. 12.
Step-by-step explanation:
When Grace left Vermont to visit her grandfather in Florida,
the temperature in Vermont was -7°F. When she arrived,
the temperature in Florida was 65°F. What was the
difference between the two temperatures?
A
71°F
B
72°F
C
74°F
D
58°F
Answer:
D.
Step-by-step explanation:
It is simple. Subtract 7* from 65* to get you 58* F.
Fatoumata has a deck that measures 7 feet by 12 feet. She wants to increase each
dimension by equal lengths so that its area is increased by 50%. By how much should she increase each dimension?
Based on common factors, Fatoumata can increase each dimension of the deck by 2 feet so that the deck's new area is increased by 50% to 126 ft².
What are common factors?Common factors are the numbers that can divide another number evenly without a remainder.
In this situation, 9 and 14 can divide 126 equally and the product of 9 and 14 are 126.
The old dimensions of the deck:
Width = 7 feet
Length = 12 feet
Area = 84 ft² (7 x 12)
The expected new area of the deck:
Increase in the new area = 5%
Increased factor for the area = 1.5 (100% + 50%)
Area = 126 ft² (84 x 1.5)
The common factors of 126 include 9 and 14 and the product of 9 and 14 = 126.
Therefore, we can increase each length of the deck by 2 feet.
Check:
Width = 9 feet
Length = 14 feet
Area = 126 ft² (9 x 14)
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PLZ HELP ASAPPPP PLZZZ HELPPP PLZZZ I GIVE BRAINLEST
Rainforest data: Mean = 7 σ2 = 12. 405 σ ≈ 3. 522 When using the formula zx = x − μ σ for the z-score for the 11. 7 data point: x = ; μ =.
Substituting the values in the formula:zx = (11.7 - 7) / 3.522zx = 1.2778 ≈ 1.28Therefore,x = zxσ + μ= (1.28 × 3.522) + 7= 4.512 + 7= 11.512 ≈ 11.7Thus, the values of x and μ are 11.7 and 7 respectively.
Given,Rainforest data:Mean (μ) = 7Standard Deviation (σ) = √12.405 ≈ 3.522For calculating the z-score, we need to find the value of x. And it is given thatzx = (x - μ)/σLet's calculate the value of x using the given data.Z-score formula is defined aszx = (x - μ) / σWhere,zx is the z-score of the given value x.x is the raw data that needs to be standardized to get the z-score.μ is the mean of the data set.σ is the standard deviation of the data set.Substituting the values in the formula:zx = (11.7 - 7) / 3.522zx = 1.2778 ≈ 1.28Therefore,x = zxσ + μ= (1.28 × 3.522) + 7= 4.512 + 7= 11.512 ≈ 11.7Thus, the values of x and μ are 11.7 and 7 respectively.
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Graph y−2=−3/4(x−6) using the point and slope given in the equation.
Use the line tool and select two points on the line.
HELP ME FOR BRAINLIST!!!!
The graph of the equation y−2=−3/4(x−6) that passes through a point is shown below.
How to Graph an Equation?To graph an equation that is given in point-slope form as y - b = m(x - a), determine the values of:
The value of the slope of the line which is represented as m in the equation.The coordinates of a point on the line that is represented as a and b.The slope would be the rise over the run of the graph to be made, while the line must pass through the given point.
Given the equation, y−2=−3/4(x−6), the slope of line is m = -3/4, while the point on the line can be (a, b) = (6, 2).
The graph of y−2=−3/4(x−6) is shown below.
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Evaluate the expression.
The value of the expression ∛8^5 is 32
How to evaluate the expression?The expression is given as:
∛8^5
Express 8 as 2^3
∛8^5 = ∛(2^3)^5
Take the cube root of 2^3
∛8^5 = 2^5
Evaluate 2 exponent 5
∛8^5 = 32
Hence, the value of the expression ∛8^5 is 32
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The piston stroke depend on * offset
crank angle
B crank radius the crank angle value when the piston at TDC is...... 120 30 0*2pi B the maximum ratio of crank radius to connected length is *
4
0.25-0.3 0.25 0.3
The crank angle value when the piston is at Top Dead Center (TDC) is 0 radians or 0 degrees. The maximum ratio of the crank radius to the connected length is 0.3.
The crank angle value refers to the angle between the crankshaft and a reference point when measuring the position of the piston. When the piston is at Top Dead Center (TDC), it is at its highest point in the cylinder. The crankshaft is positioned such that the connecting rod is aligned with the crank radius and the piston is at the topmost position. This corresponds to a crank angle value of 0 radians or 0 degrees.
Regarding the maximum ratio of the crank radius to the connected length, this value is given as 0.3. The crank radius is the distance from the center of the crankshaft to the center of the crank pin, and the connected length is the distance from the center of the crank pin to the center of the piston pin. The maximum ratio of 0.3 indicates that the crank radius is 0.3 times the connected length.
It's important to note that these values are specific to the context of the problem statement provided. Different engines or mechanisms may have different values for the crank angle at TDC and the maximum ratio of crank radius to connected length.
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A water tank contains 1000 litres of water. Due to a small hole in the tank, 10 litres of water is lost every hour. How much would remain in the tank after 10 hours
Answer:
900 L
Step-by-step explanation:
after 10 hours : 10*10=100 liters
1000-100=900 liter
900 L
is the answer I recived
My work is below:
Next after 10 hours (10*10=100 liters )
1000-100=900 liter
Hope this helps you learn what to do in similar probles
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