To determine the interval in which about 95% of the data lies, we can use the concept of standard deviation and the properties of the normal distribution.
Given that the average monthly mileage is 1,100 miles and the standard deviation is 100 miles, we can apply the empirical rule (also known as the 68-95-99.7 rule) for normally distributed data. According to this rule:
- Approximately 68% of the data lies within one standard deviation of the mean.
- Approximately 95% of the data lies within two standard deviations of the mean.
- Approximately 99.7% of the data lies within three standard deviations of the mean.
Since the standard deviation is 100 miles, we can conclude that about 95% of the data lies within two standard deviations of the mean.
Therefore, the interval within which about 95% of the data lies is:
1,100 miles ± (2 * 100 miles) = 1,100 miles ± 200 miles
So, the interval is from 900 miles (1,100 miles - 200 miles) to 1,300 miles (1,100 miles + 200 miles).
d = 5t + 20
your answer is there so i'll be on my way, Have a nice day!!
Solve for x. Assume that lines which appear tangent are tangent.
The value of x for the angle m∠TUV subtended by the arc TV at the circumference is equal to 3
What is angle subtended by an arcThe angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.
arc TV = 2(m∠TUV)
54x - 2 = 2(80)
54x - 2 = 160
54x = 160 + 2 {collect like terms}
54x = 162
x = 162/54 {divide through by 3}
x = 3
Therefore, the value of x for the angle m∠TUV subtended by the arc TV at the circumference is equal to 3.
Read more about angle here:https://brainly.com/question/24423151
#SPJ1
Dan will spin this wheel once. What are all the possible outcomes of the experiment? Separate each answer with a comma followed by a space (1 point)
There are 10 possible results when Dan spins the wheel of destiny with the numbers 2, 4, 6, 8, 10, 12, 14, 16, and 20.
Every possible result is represented by a different number, and Dan has an equal probability of choosing any of them.
The wheel serves as a tool for randomization, adding a degree of ambiguity and unpredictability to the experiment. There are 20 possible outcomes total, with increments of 2 between the lowest and highest numbers.
Thus, these results stand in for various values that Dan might get from spinning the wheel. We may analyse the likelihood and probable range of results for this particular experiment by taking into account all the conceivable possibilities.
For more details regarding probability, visit:
https://brainly.com/question/31828911
#SPJ1
In ⊙Q, what is m∠1?
A. 66
B. 57
C. 33
D. 47
Note that in Circle Q, m∠1 = 66° (Option A)
How did we arrive at this?Note that inthe circle above, the angle which creates the arc 114° lies ont he same line with ∠1. Since sum of angles on a Straight line sum up to 180°.
∠1 = 180 -114 = 66°
A circle is defined as a form made up of points in a two-dimensional plane that are equidistant from a particular location. A circle is defined as a closed curve with no corners or vertices. Circles define several circular forms in our everyday lives.
Circular shapes include:
Tangent Circles: Two or more circles that intersect at a single point.Concentric Circles are defined as two or more circles with the same center but differing radii.Congruent Circles: Two or more circles that share the same radius but have distinct centers.Learn more about Circles at:
https://brainly.com/question/29142813
#SPJ1
HELP PLEASE! Fred enrolled in college to pursue a degree in physics. He is told there is a 70% chance that he will get less than 60 on his first test. He is also told if he gets less than 60 on this test, the probability he passes the course is 55%. Otherwise, there is a 70% chance he passes the course. What is the probability he gets more than 60 on the first test, but fails the course? A. 0.12 B. 0.09 C. 0.21 D. 0.30
Step-by-step explanation:
Fred has two possible outcomes on his first test: he either scores less than 60 or he scores 60 or higher.
If he scores less than 60, there is a 55% chance he will pass the course, and a 45% chance he will fail. We know there is a 70% chance he will score less than 60, so the probability that he scores less than 60 and fails the course is 0.7 * 0.45 = 0.315.
If he scores 60 or higher, there is a 70% chance he will pass the course, and a 30% chance he will fail. We don't know the exact probability that he scores 60 or higher, but we know that it is 1 - 0.7 = 0.3 (since there is a 70% chance he scores less than 60). So the probability that he scores 60 or higher and fails the course is 0.3 * 0.3 = 0.09.
Adding these two probabilities together gives us the total probability that Fred gets more than 60 on the first test but fails the course: 0.315 + 0.09 = 0.405. However, we are looking for the probability that he gets more than 60 but fails, so we need to subtract the probability that he scores less than 60 and fails: 0.405 - 0.315 = 0.09. Therefore, the answer is B. 0.09.
i think so...
If a₁ = 3 and an+1 = (an)² + 1 then find the value of a3.
Answer:
Step-by-step explanation:
Given:
a₁ = 3
an+1 = (an)² + 1To find:
a₃Solution:
We can use the recursive formula given to find the value of a₃.a₂ = a₁ + 1² = 3 + 1 = 4
a₃ = a₂² + 1 = 4² + 1 = 17Therefore, the value of a₃ is 17.Answer: a₃ = 17
"Consider the following circle with radius 1. The lines A and B are radii, and have a length of 1. Find the area of the shaded region."
I got an area of 1.06 (Rounded), I'm just wondering if that is correct. Any help would be appreciated!
Answer:
[tex]\textsf{Area}=\dfrac{5\pi -3}{12} \approx 1.06\; \sf square\;units \;(3\;s.f.)\end{aligned}[/tex]
Step-by-step explanation:
To find the area of the shaded region, subtract the area of the isosceles triangle from the area of the sector.
An isosceles triangle is made up of two congruent right triangles.
To find the height of the right triangles (and thus the height of the isosceles triangle), use the cosine trigonometric ratio.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
Given values:
The angle is half the apex angle: θ = 5π/12.The side adjacent the angle is the height of the triangle: x.The hypotenuse is the radius: H = 1.Substitute these values into the cosine ratio to calculate the height of the right triangles (and thus the height of the isosceles triangle):
[tex]\cos \left(\dfrac{5\pi}{12}\right)=\dfrac{x}{1}[/tex]
[tex]x=\cos \left(\dfrac{5\pi}{12}\right)[/tex]
[tex]x=\dfrac{\sqrt{6}-\sqrt{2}}{4}[/tex]
The base of one of the right triangles can be found by using the sine trigonometric ratio.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
Given values:
The angle is half the apex angle: θ = 5π/12.The side opposite the angle is the base of the right triangle: y.The hypotenuse is the radius: H = 1.Substitute these values into the sine ratio to determine the base of the right triangle:
[tex]\sin \left(\dfrac{5\pi}{12}\right)=\dfrac{y}{1}[/tex]
[tex]y=\sin \left(\dfrac{5\pi}{12}\right)[/tex]
[tex]y=\dfrac{\sqrt{6}+\sqrt{2}}{4}[/tex]
The base of the isosceles triangle is twice the base of the right triangle, so the base of the isosceles triangle = 2y.
Therefore the area of the isosceles triangle is:
[tex]\begin{aligned}\textsf{Area of isosceles triangle}&=\dfrac{1}{2} \cdot \sf base \cdot height\\\\&=\dfrac{1}{2}\cdot 2y \cdot x\\\\&=\dfrac{1}{2} \cdot 2\left(\dfrac{\sqrt{6}+\sqrt{2}}{4}\right) \cdot \left(\dfrac{\sqrt{6}-\sqrt{2}}{4}\right)\\\\&=\left(\dfrac{\sqrt{6}+\sqrt{2}}{4}\right) \cdot \left(\dfrac{\sqrt{6}-\sqrt{2}}{4}\right)\\\\&=\dfrac{4}{16}\\\\&=\dfrac{1}{4}\sf \;square\;units\end{aligned}[/tex]
To find the area of the sector of the circle, use the area of a sector formula (where the angle is measured in radians).
[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\dfrac12 r^2 \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}[/tex]
Given values:
r = 1θ = 5π/6Substitute the values into the formula:
[tex]\begin{aligned}\textsf{Area of the sector}&=\dfrac{1}{2} \cdot (1)^2 \cdot \dfrac{5\pi}{6}\\\\&=\dfrac{1}{2} \cdot 1 \cdot \dfrac{5\pi}{6}\\\\&=\dfrac{1}{2} \cdot \dfrac{5\pi}{6}\\\\&=\dfrac{5\pi}{12}\;\; \sf square\;units\end{aligned}[/tex]
Finally, to find the area of the shaded region, subtract the area of the isosceles triangle from the area of the sector:
[tex]\begin{aligned}\textsf{Area of the shaded region}&=\sf Area_{sector}-Area_{isosceles\;triangle}\\\\&=\dfrac{5\pi}{12}-\dfrac{1}{4}\\\\&=\dfrac{5\pi}{12}-\dfrac{3}{12}\\\\&=\dfrac{5\pi -3}{12}\\\\&=1.05899693...\\\\&=1.06\; \sf square\;units \;(3\;s.f.)\end{aligned}[/tex]
Therefore, the area of the shaded region is (5π - 3)/12 or approximately 1.06 square units (3 significant figures).
Help need asap please write a statement and proof
The theorems that demonstrate that AC ⊥ BD are Angle Bisector Theorems and Perpendicular Bisector Postulate.
Proof that AC ⊥ BDRecall that according to the angle bisector theorem, an angle bisector of a triangle divides the opposing side into two segments that are proportionate to the triangle's other two sides. An angle bisector is a ray that splits a given angle into two equal-sized angles.
In this case
∠1 ≅ ∠2 - Given
hence they is bisected by AX
Also ∠5 ≅ ∠6. This means that they are bisected by CX
Since AX and CX form AC, and
AC = CA (Reflexive Property)
Also
BD = DB (Reflexive Property)
Then it means that AC ⊥ BC (QED)
Recall that the perpendicular bisector principle deals with congruent triangle segments, allowing for congruent diagonals from the vertices to the circumcenter.
Learn more about Angle Bisector:
https://brainly.com/question/12896755
#SPJ1
What is 2 wholes and 2/4 - 1 and 3/4 equal
Answer:
Step-by-step explanation:
I don't quite understand the problem but:
2 2/4 -1 =1 1/2, and 3/4 can't be simplified more.
make x subject
u= cos 0.5x
By making x the subject of the formula in this equation u = cos(0.5x) gives x = 2cos⁻¹(u).
How to make x the subject of the formula?In Mathematics and Geometry, an equation can be defined as a mathematical expression which shows that two (2) or more thing are equal. This ultimately implies that, an equation is composed of two (2) expressions that are connected by an equal sign.
In this exercise, you are required to make "x" the subject of the formula in the given mathematical equation by using the following steps.
By taking the arc cosine of both sides of the equation, we have the following:
u = cos(0.5x)
cos⁻¹(u) = 0.5x
By multiplying both sides of the mathematical equation by 2, we have the following:
2 × cos⁻¹(u) = 0.5x × 2
x = 2cos⁻¹(u)
Read more on expression here: brainly.com/question/25767785
#SPJ1
De 1. A mechanic performs oil changes on automobiles. The table shows the linear relationship between the number of oil changes completed after different amounts of time.
Number of
Hours
Number of Oil
Changes
4.5
9
16.5
24
1.5
3
5.5
8
What is the rate of change of the number of oil changes with respect to the number of hours?
The rate of change of the number of oil changes with respect to the number of hours will be 3.
The table is given below.
Number of hours Number of oil changes
1.5 4.5
3 9
5.5 16.5
8 24
It is the average amount by which the function varied per unit throughout that time period. It is calculated using the line gradient linking the interval's ends on the graph depicting the function.
Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]
The rate of change is calculated as,
Average rate = (24 - 9) / (8 - 3)
Average rate = 15 / 5
Average rate = 3
More about the average rate change link is given below.
https://brainly.com/question/28744270
#SPJ1
You roll two fair dice. Find the theoretical probability that the sum of
the outcomes is 2 or 5
[tex]|\Omega|=6^2=36\\A=\{(1,1),(1,4),(4,1),(2,3),(3,2)\}\\|A|=5\\\\P(A)=\dfrac{5}{36}\approx13.9\%[/tex]
9) The line plot below shows the heights in inches for a basketball team. How much taller is the tallest player than the shortest player on the basketball team?
14 inches taller by the tallest player than the shortest player on the basketball team. The correct option is A .
To determine how much taller the tallest player is than the shortest player on the basketball team, we need to examine the given line plot and calculate the difference between their heights.
To find the height difference, we need to identify the tallest and shortest players on the team. The line plot should display the heights of each player, allowing us to determine these values.
Once we have these heights, we can subtract the height of the shortest player from the height of the tallest player to calculate the difference.
Based on the options provided, we can consider each possibility:
A. If the height difference is 14 inches, then the tallest player is 14 inches taller than the shortest player. B. If the height difference is 10 inches, then the tallest player is 10 inches taller than the shortest player.
C. If the height difference is 13 inches, then the tallest player is 13 inches taller than the shortest player. D. If the height difference is 12.5 inches, then the tallest player is 12.5 inches taller than the shortest player.
Learn more about possibility here:
https://brainly.com/question/30584221
#SPJ1
The point (-4,1) falls in which quadrant?
O Quadrant I
O Quadrant IV
O Quadrant II
Quadrant III
Answer:
The correct answer is option C. (-4,2) lies in the Quadrant II .
The senior class at Legion Academy wants to buy jerseys to wear to the basketball games. The cost of
the jerseys can be modeled by the equation C=0 .1x² + 2.4x + 25, where C is the amount, it costs to buy x
jerseys. How many jerseys can they purchase for $430?
The number of jerseys they can purchase for $430 is 53 jerseys.
What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Based on the information provided about the cost of the jerseys, we have the following quadratic function;
C = 0.1x² + 2.4x + 25
430 = 0.1x² + 2.4x + 25
0.1x² + 2.4x + 25 - 430 = 0
0.1x² + 2.4x - 405 = 0
By solving the quadratic function using the quadratic formula, we have:
[tex]x = \frac{-(-2.4)\; \pm \;\sqrt{(2.4)^2 - 4(0.1)(-405)}}{2(0.1)}\\\\[/tex]
x = 52.76 ≈ 53 jerseys.
Read more on quadratic equation here: brainly.com/question/4053652
#SPJ1
Caitlyn needs to mail a USB drive to a friend. She uses 45-cent stamps and 7-cent stamps to pay $1.91 in postage. How many of each stamp did Caitlyn use?
What two names can be used to describe this triangle?
Use the drop-down menus to classify the triangle based on its side lengths and
angle measures
The Triangle is Equilateral and Equiangular.
We will use theses property of Equilateral Triangle as
All three sides of an equilateral triangle have the same length.Each interior angle of an equilateral triangle measures 60 degreesWe have a Triangle.
The Triangle all three angles measured 60 degree each.
and, We know the equilateral Triangle all angles measures 60 degree.
Now, from the figure all the three sides of triangle are equal.
and, we know Equilateral triangle have the three sides equal
Thus, the Triangle is Equilateral and Equiangular.
Learn more about Equilateral Triangle here:
https://brainly.com/question/17824549
#SPJ1
Enter the number that belongs in the green box
Answer:
? ≈ 9.09
Step-by-step explanation:
using the Sine rule in the triangle
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]
where a, b , c are the sides opposite angles A , B , C
we require the third angle in the triangle
third angle = 180° - (51 + 109)° = 180° - 160° = 20°
then with
a = 4 , ∠ A = 20°
b = ? , ∠ B = 51°
[tex]\frac{4}{sin20}[/tex] = [tex]\frac{?}{sin51}[/tex] ( cross- multiply )
? × sin20° = 4 × sin51° ( divide both sides by sin20° )
? = [tex]\frac{4sin51}{sin20}[/tex] ≈ 9.09 ( to the nearest hundredth )
Please help! What is the surface area of the cylinder with height 4 m and radius 8 m? Round your answer to the nearest thousandth.
Make sure to round please.
The surface area of the cylinder is 948m²
What is surface area of cylinder?The area occupied by a three-dimensional object by its outer surface is called the surface area. The surface of a cylinder is expressed as ;
SA = 2πr(r+h)
Where r is the radius of the base and h is the height of the cylinder.
r =8m
h = 4m
SA = 2 × 3.14 × 8 (8+4)
SA = 78.96 × 12
SA = 947.52 m²
to the nearest whole number
SA = 948 m²
therefore the surface area of the cylinder is 948 m²
learn more about surface area of cylinder from
https://brainly.com/question/27440983
#SPJ1
Determine f(4) for A piecewise function
f(x) = x^3 ..........x<-3
2x^2-9 ....-3 ≤ x≤ 4
5x+4 ........ x>4
PLEASE SHOW ALL WORK!!!!!!!!!!!!!!
23
24
41
64
thank you!
the answer is 23 i need the work though
The value of f(4) for the piecewise function f(x) is found to be 23, hence, option A is correct answer.
The given function is a piecewise function which means it is defined by different formulas for different intervals of x. We need to evaluate f(4) using the formula that applies for the interval that contains 4. Since 4 is in the interval -3 ≤ x ≤ 4, we use the formula f(x) = 2x² - 9 for f(4). To find f(4), we substitute 4 for x in the formula,
f(4) = 2(4)² - 9
Evaluating 2(4)²,
f(4) = 2(16) - 9
Simplifying 2(16) - 9:,
f(4) = 23
Therefore, f(4) = 23. So, the correct answer is Option A.
To know more about piecewise function, visit,
https://brainly.com/question/27262465
#SPJ1
Complete question - Determine f(4) for A piecewise function
f(x) = x³ ____ x<-3
f(x) = 2x²-9 ____ -3 ≤ x≤ 4
f(x) = 5x+ ____ when x>4
A. 23
B. 24
C. 41
D. 64
URGENT PLEASE HELP!!!!
Out of 413
applicants for a job, 127
have over 10
years of experience and 51
have over 10
years of experience and have a graduate degree.
Step 1 of 2 : What is the probability that a randomly chosen applicant has a graduate degree, given that they have over 10
years of experience? Enter a fraction or round your answer to 4
decimal places, if necessary.
Given that a randomly selected applicant has more than 10 years of experience, the likelihood that they have a graduate degree is roughly 0.4016.
To find the probability that a randomly chosen applicant has a graduate degree given that they have over 10 years of experience, we need to use conditional probability. We can use the formula:
P(grad degree | over 10 years of experience) = P(grad degree and over 10 years of experience) / P(over 10 years of experience)
From the given information, we know that:
P(grad degree and over 10 years of experience) = 51 (number of applicants with over 10 years of experience and a graduate degree)
P(over 10 years of experience) = 127 (number of applicants with over 10 years of experience)
So, plugging in these values:
P(grad degree | over 10 years of experience) = 51 / 127
Using a calculator, we get:
P(grad degree | over 10 years of experience) ≈ 0.4016
Therefore, the probability that a randomly chosen applicant has a graduate degree, given that they have over 10 years of experience, is approximately 0.4016.
Learn more about probability here:
https://brainly.com/question/30034780
#SPJ1
2 ( a + 4b) +5 + 7b +6
Answer:
2a+15b+11
Step-by-step explanation:
2*a + 2*4b + 5 + 7b + 6
2a + 8b + 5 + 7b + 6
2a + 8b + 7b + 5 + 6
2a + 15b + 11
PLEASE HELP I WILL MARK YOU BRAINLIEST
Answer:
18.85 meters
Step-by-step explanation:
V=πr2h=π·12·6≈18.84956
Mr. Sharp is considering a $100,000 investment in a company that has invented a revolutionary new jet ski. Mr. Sharp's advisors tell him that the company has a 30% probability of success. If it succeeds, Mr. Sharp's investment will be worth $2,000,000. If it fails, the investment will be worthless. What is the expected value of the investment? Should Mr. Sharp invest the $100,000?
The expected value of the investment is $600,000.
The expected value of the investment is calculated by multiplying the possible outcomes by their respective probabilities and summing them up. In this case, the possible outcomes are a success or a failure, with probabilities of 0.3 and 0.7 respectively.
If the company succeeds, the investment will be worth $2,000,000. If it fails, the investment will be worth $0. Therefore, the expected value is:
(0.3 x $2,000,000) + (0.7 x $0) = $600,000
This means that the expected value of the investment is $600,000.
Since the expected value of the investment is positive, Mr. Sharp should invest the $100,000. However, it's important to note that expected value is just an estimate and does not guarantee a positive return on investment. There is always a risk associated with any investment, and Mr. Sharp should carefully consider his risk tolerance and financial goals before making any investment decisions.
for such more question on expected value
https://brainly.com/question/15858152
#SPJ11
4x(3+6) devided by 2
After considering the given data we conclude that the value generated after performing divison of the given expression is 18x, under the condition that we follow the principles of divison.
Let us proceed by evaluating the given expression by applying division
4x(3+6) divided by 2
= 4x9/2
= 36x/2
= 18x
Division is considered one of the four basic mathematical operations, then the other three are addition, subtraction, and multiplication.
In short , division is referring to the breaking down of a given bigger number or expression into simpler yet smaller forms to meet the criteria of performing a function.
To learn more about divison
https://brainly.com/question/30126004
#SPJ1
Find the direction angle of w = 8j
Round your answer to the nearest tenth of a degree
Rounding to the nearest tenth of a degree, the direction angle of w = 8j is 90.0 degrees.
To find the direction angle of a vector, we can use the formula:
θ = arctan(y/x)
In this case, the vector w is given as w = 0 + 8j, which means its x-component is 0 and its y-component is 8.
Plugging the values into the formula, we get:
θ = arctan(8/0)
However, the division by zero is undefined, indicating that the x-component of the vector is zero, and thus the vector lies along the y-axis.
When a vector lies along the y-axis, its direction angle is either 90 degrees or -90 degrees.
In this case, since the vector is pointing upwards (in the positive y-direction), the direction angle is 90 degrees.
For similar question on direction angle.
https://brainly.com/question/29196928
#SPJ11
Help pls on test (i need answer quick)
Answer: Thats a Trapezoid
Step-by-step explanation:
A trapezoid is a quadrilateral with one pair of opposite sides parallel. It can have right angles (a right trapezoid), and it can have congruent sides (isosceles), but those are not required.
PLEASE HELP ME
Look at table and solve.
Identify the number of positive and negative residuals, the residual with the greatest absolute value, and the residual with the least absolute value. Is the model a good fit?
There are __?_ positive residuals and __?_ negative residuals.
The residual with the greatest absolute value is__ , and the residual with the least absolute value is__ .
Question 3
The absolute values of the residuals are relatively (small or large) , and in general, the data points (are or are not)evenly dispersed about the line of fit.
So, the equation y=−x+9.6 (Is or is not) a good fit.
There are 2 positive residuals and 4 negative residuals.
The residual with the greatest absolute value is -4.8, and the residual with the least absolute value is 0.5.
The absolute values of the residuals are relatively large, indicating that the model does not fit the data well. In general, the data points are not evenly dispersed about the line of fit.
Using the equation y=−x+9.6, we can calculate the predicted values for y as follows:
When x = 1: y = -(1) + 9.6 = 8.6
When x = 2: y = -(2) + 9.6 = 7.6
When x = 3: y = -(3) + 9.6 = 6.6
When x = 4: y = -(4) + 9.6 = 5.6
When x = 5: y = -(5) + 9.6 = 4.6
When x = 6: y = -(6) + 9.6 = 3.6
We can then calculate the residuals by subtracting the predicted values from the actual values of y:
When x = 1: residual = 5.8 - 8.6 = -2.8
When x = 2: residual = 8.7 - 7.6 = 1.1
When x = 3: residual = 2.9 - 6.6 = -3.7
When x = 4: residual = 0.8 - 5.6 = -4.8
When x = 5: residual = 5.1 - 4.6 = 0.5
When x = 6: residual = 1.7 - 3.6 = -1.9
There are 2 positive residuals and 4 negative residuals.
The residual with the greatest absolute value is -4.8, and the residual with the least absolute value is 0.5.
The absolute values of the residuals are relatively large, indicating that the model does not fit the data well. In general, the data points are not evenly dispersed about the line of fit.
Therefore, we can say that the equation y=−x+9.6 is not a good fit for this data.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
In certain deep parts of oceans, the pressure of sea water,P, in pounds per square foot, at a depth of d feet below the surface, is given by the following equation P=14+ 4d/9
If a scientific team uses special equipment to measure the pressure under water and find it to be 306 pounds per square foot, at what depth is the team making their measurements?
It is important to note that this equation assumes a constant density of seawater, which is not always the case in the deep ocean. In addition, the pressure at a given depth can vary depending on factors such as temperature and salinity. This equation should be used with caution and in conjunction with other measurements and data analysis techniques.
The given equation for pressure in pounds per square foot at a depth of d feet is P = 14 + 4d/9. We are given that the pressure measured by the scientific team is 306 pounds per square foot. To find the depth at which this pressure is measured, we need to solve the equation for d.
Substituting P = 306 in the equation, we get:
306 = 14 + 4d/9
Multiplying both sides by 9, we get:
2754 = 126 + 4d
Subtracting 126 from both sides, we get:
2628 = 4d
Dividing both sides by 4, we get:
d = 657 feet
The scientific team is measuring the pressure at a depth of 657 feet below the surface of the ocean.
For such more questions on Measurements:
https://brainly.com/question/27122947
#SPJ11
Jack puts 80 socks in a basket he sort 50 socks into one pile how many socks does he need to sort
gabriela recorded the ages of her shirts which of these best describes the shape of the distribution
Based on the image attached, The the shape of the distribution is option c) data skewed right.
What is data skewed right?The term Right skewed is one where the mean is more prominent than the middle. The mean overestimates the foremost common values in a emphatically skewed dispersion. Cleared out skewed: The mean is less than the median. The mean is one that has little of the common values in a rightly skewed dissemination.
So, therefore, if most of the information are on the cleared out side of the histogram but many larger values are on the proper, the information are said to be skewed to the right.
Read more about data skewed right here:
https://brainly.com/question/16410052
#SPJ1
See text below
Gabriela recorded the ages of her shirts.
·
0 1 2 3 4 5 6 7 8 9 10
Age (years)
Which of these best describes the shape of the distribution?
Choose 1 answer:
Roughly symmetric
Skewed left
Skewed right
Good Question (141)