A reflection over a line l moves every point P of the plane to the point P ′ on the perpendicular from P to the line l and on the same distance from l .
If the line is the x -axis, a point P = ( p 1 p 2 ) moves to the point P ′ = ( p 1 , − p 2 ) .
The image of the triangle A B C is the triangle A ′ B ′ C ′ with B ′ = ( 9 , − 5 )
Finding the work done in stretching or compressing a spring.
Hooke's Law for Springs.
According to Hooke's law, the force required to compress or stretch a spring from an equilibrium position is given by F(x)=kx, for some constant k. The value of k (measured in force units per unit length) depends on the physical characteristics of the spring. The constant k is called the spring constant and is always positive.
In this problem we assume that the force applied doesn't distort the metal in the spring.
A 2 m spring requires 11 J to stretch to 2.4 m. Find the force function, F(x), for the spring described.
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached images below to see the step by step explanation to the question above.
Automobile racing, high-performance driving schools, and driver education programs run by automobile clubs continue to grow in popularity. All these activities require the participant to wear a helmet that is certified by the Snell Memorial Foundation, a not-for-profit organization dedicated to research, education, testing, and development of helmet safety standards. Snell "SA" (Sports Application)-rated professional helmets are designed for auto racing and provide extreme impact resistance and high fire protection. One of the key factors in selecting a helmet is weight, since lower weight helmets tend to place less stress on the neck. The following data show the weight and price for 18 SA helmets.
W p
64 252
64 283
64 190
64 197
58 291
47 702
49 907
59 341
66 202
58 305
58 477
52 477
63 379
62 377
54 563
63 255
63 286
a. Develop a scatter diagram with weight as the independent variable.
b. Does there appear to be any relationship between these two variables?
There appears to be a - Select your answer -negativepositiveItem 2 linear relationship between the two variables. The heavier helmets tend to be less expensive.
c. Develop the estimated regression equation that could be used to predict the price given the weight.
The regression equation is (to 1 decimal and enter negative values as negative numbers). If your answer is zero enter "0".
Answer:
Step-by-step explanation:
Hello!
Given the variables
X₁: Weight of a safety helmet for racers
X₂: Price of a safety helmet for racers
Note, there is n= 17 observed values for each variable so for all calculations I'll use this number and disregard the 18 mentioned in the text.
a) Scatterplot in attachment.
b) If you look at the diagram it seems that there is a negative linear regression between the price and the weight of the helmets, meaning, the higher the helmet weights, the less it costs.
c) The estimated regression equation is ^Yi= a + bXi
n= 17; ∑Y= 6466; ∑Y²= 3063392; ∑X= 1008; ∑X²= 60294; ∑XY= 367536
Y[bar]= 380.35; X[bar]= 59.29
[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} } = \frac{367536-\frac{1008*6466}{17} }{60294-\frac{(1008)^2}{17} } = -30.18[/tex]
[tex]a= Y[bar]- bX[bar]= 380.35-(-30.18)*59.29= 2169.77[/tex]
The estimated regression equation for the price of the helmets as a function of their weight is:
^Yi= 2169.77 -30.18Xi
I hope it helps!
Graph-3x2 + 12y2 = 84. What are the domain and range?
Domain (infinity,infinity)
Range (infinity,[tex]\sqrt{7}[/tex])
....................
Answer:
I would love to help you but all I see is dots
Need done ASAP please
Step-by-step explanation:
a. 81 ÷ 9 = 9
b. 40 ÷ 5 = 8
c. 21 ÷ 3 = 7
d. 54 ÷ 6 = 9
e. 42 ÷ 7 = 6
f. 63 ÷ 9 = 7
g. 36 ÷ 4 = 4
h. 45 ÷ 9 = 5
i. 39 ÷ 3 = 12
j. 24 ÷ 6 = 4
Of the 250 students at Moreland middle school, 80% ride the bus to school. Monica wants to know the number of students that ride the bus.
Answer:
200; 80% of 250 is 200
Answer:
Step-by-step explanation:
200
6³=216. Using exponents, write three expressions whose value is 216.
Please help I don't understand.
9514 1404 393
Answer:
216 = 2³·3³ = 8·3³ = 27·2³
Step-by-step explanation:
6³ = 2·2·2·3·3·3
The string of factors can be grouped however you like, and any repeated factors in the group can be expressed using an exponent.
= 2·2²·3³
= 8·3³
= 6·2²·3²
= 6·6²
= 27·2³
What the error? Jonah says a common denominator for 3/4 and 2/5 is 9 what is Jonah error?explain
Answer:
should be 20
Step-by-step explanation:
yes
Answer: She had added the Denominator, instead of finding the LCM.
Explanation: She should've multiplied them by a common number to equal a common Product, and replace the Denominator with the Product. (The correct denominator is 20, because 4 x 5 = 20, and 5 x 4= 20)
Need help with Math question
Answer:
B; {x|x<-8}
Step-by-step explanation:
6. A golfer is standing at the tee,
looking up to the green on a hill. If the
tee is 36 yards lower than the green
and the angle of elevation from the tee
to the hole is 12º, find the distance from
the tee to the hole.
Answer:
173.15 yards is the distance from tee to hole.
Step-by-step explanation:
Please refer to the image attached.
Let A is the position of tee and where the golfer is standing.
C is the position of hole.
CB is the vertical distance between greens and tee.
Angle of elevation, [tex]\angle BAC = 12^\circ[/tex]
To find: side AC.
Using trigonometric functions, we know that value of sine is:
[tex]sin\theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}[/tex]
Here [tex]\theta = \angle BAC = 12^\circ[/tex]
Perpendicular is side CB.
Hypotenuse is side AC.
[tex]sin12^\circ = \dfrac{\text{CB}}{\text{AC}}\\\Rightarrow \text{CB} = \dfrac{36}{sin12^\circ}\\\Rightarrow \text{CB} = 173.15\ yards[/tex]
Hence, 173.15 yards is the distance from tee to hole.
What is the GCF of 45 and 72?
Answer:
The common factors of 45 and 72 are 9, 3, 1
Step-by-step explanation:
Answer:
The GCF of these two numbers is nine.
Step-by-step explanation:
They share three common factors: 1, 3 and 9. The greatest out of all of those is 9. Hope this helps!
apply the distributive property to factor out the gcf of 35+14
Answer:
7(5 +2)
Step-by-step explanation:
From our knowledge of times tables, we know that ...
35 = 5·7
14 = 2·7
so the greatest common factor of 35 and 14 is 7. Factoring that out, we have ...
35 +14 = 7(5 +2)
In a comparison of the body fat percentage of four different ethnic groups, the body fat percentage was measured for 200 African-Americans, 160 Whites, 220 Hispanics, and 310 Others. Because a comparison of average body fat percentage between these groups is desired, an ANOVA test was conducted, which resulted in p-value of 0.11. What conclusion can you make if level of significance is 0.05?
Answer:
There is not enough evidence to support the claim that the fat percentage of at least one of the four ethnic groups is different.
Step-by-step explanation:
The Analysis of Variance (ANOVA) test is used to determine whether there is any significant difference between the mean of various independent groups.
In this case an ANOVA test is being performed to determine whether the fat percentage of four different ethnic groups are different or not.
The hypothesis can be defined as:
H₀: The fat percentage of four different ethnic groups are same, i.e. μ₁ = μ₂ = μ₃ = μ₄.
Hₐ: The fat percentage of at least one of the four ethnic groups is different, i.e. at least one μ[tex]_{i}[/tex] is different.
The significance level of the test is, α = 0.05.
The decision rule is:
If the p-value of the test is less than the significance level, then the null hypothesis will be rejected.And if the p-value of the test is not less than the significance level, then the null hypothesis will not be rejected.The p-value of the ANOVA test is computed as, p-value = 0.11.
p-value = 0.11 > α = 0.05.
The null hypothesis was failed to be rejected.
Hence, it can be concluded that there is not enough evidence to support the claim that the fat percentage of at least one of the four ethnic groups is different.
The perimeter of a rectangular is 20 centimeters the length is 6 centimeters what is the area of the rectangular
Answer:
24 centimeters
Step-by-step explanation:
Since the longer side is 6 then multiply it by 2 which is 12, now subtract it by 20 since that is its perimeter. then u divide 8 by 2 since theres 2 sides. now do 6 times 4 which is 24
1.(1 0) You measure the distance, l, a projectile travels several times using the same apparatus and find the following values (cm): 5.11, 4.89, 5.04, 4.94, 4.93, 5.06 and 5.09. Assuming that the errors are random: a) What is the mean value forl? b) What is the standard deviation for this data set? c) What is the uncertainty associated with your best estimate forl? d) How should one report the result of this measurement along with the uncertainty at the 95 % confidence level? e) If you desire to reduce the statistical uncertainty associated with the reported result using the same apparatus to be only 0.01 cm, how many measurements must be made?
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
What is an equation of the line that passes through the point (- 5, - 6) and is parallel to the line 4x - 5y = 35
Answer:
4x - 5y = 10
Step-by-step explanation:
Any line parallel to 4x - 5y = 35 will have the same equation EXCEPT that the constant will be different.
Starting with 4x - 5y = 35, replace x with the given x-coordinate -5 and the given y-coordinate -6, and finally the given 35 with the constant C:
4(-5) - 5(-6) = C, or
-20 + 30 = C. Thus, C = 10, and the equation of the new line is
4x - 5y = 10
The equation of line is 4x - 5y = 10
What is equation of line?A straight line's general equation is y = mx + c, where m is the gradient. On the y-axis, this number c is referred to as the intercept. Key Point y = mx + c is the equation for a straight line with a gradient of m and an intercept of c on the y-axis.
Given the points (-5,-6)
and parallel to line 4x - 5y = 35...…..(1)
the equation of line is (y - y₁) = m( x - x₁)
for parallel line condition the value of m is equal to both equations
converting eq. 1 in the form of y = mx + c
4x - 5y = 35
we get y = 4/5x -7
here m = 4/5 and c = -7
substitute the value of m in equation of line
where y₁ = -6; x₁ = -5
(y - (-6)) = 4/5(x - (-5))
y +6 = 4/5(x+5)
simplify above eq. we get
4x - 5y = 20
Hence the equation of the line that passes through the point (- 5, - 6) is 4x - 5y = 20
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at 3:30 P.M., the water level in a pool is 14 inches. At 4:00 P.M., the water level is 20 inches. At 5:00 P.M., the water level is 32 inches. What is the constant rate of change?
Answer:
6 inches per 1/2 of an hour
Step-by-step explanation:
in between 4 pm and 5 pm, the water level grows by 12 inches. in between 3:30 pm and 4 pm, the water level grows by 6 inches.
A line has the equation 3x–4y–12=0.
Is the point (2, −1) on the graph?
Answer:
The point (2, -1 ) is not on the graph of the line.
Step-by-step explanation:
3x–4y–12=0
3*2 - 4*(-1) - 12= 0
6 + 4 - 12 =0
10 - 12 = 0
- 2 = 0 , false, so the point (2, -1 ) is not on the graph of the line.
Please help me with my work for math
Answer:
AAA
Stp-by-step explanation:
Tate is paid $17.35 per hour with time and a half overtime. What will his gross pay period in which he worked 35 hours one week and 44 hours next week for a total 79 hours?
Answer:
The new rule has a higher salary level for exemption from overtime, at $684 a week. This means that lower-pay exempt employees may qualify for overtime.
Step-by-step explanation: this is your answer plz rate e the most brainlest
*ill give you BRAINLIST * (have to get it right ) Write the equation of the line with the given slope and y-intercept.
slope = 1
y-intercept = - 3/7
Answer:
Y=x-3/4
Step-by-step explanation:
slope intercept form
(slope=x)(1x=x)
Graph a line with a slope of -3 that contains the points (4,-2)
Answer:
see below for a graph
Step-by-step explanation:
To draw a graph on a grid, locate the point (4, -2) and use the slope to find another point. One such point will be 1 to the left and up 3*, at (3, 1). With two points, you can draw the line through them to complete the graph.
__
For a graphing tool that requires an equation, the point-slope form of the equation can be used:
y -k = m(x -h) . . . . . a line of slope m through point (h, k)
For the given slope and point, the equation of the line is ...
y +2 = -3(x -4)
y = -3x +10
_____
* The slope is "rise" over "run". The slope of -3 means that a run of +1 will result in a rise of -3. The given point is already below the x-axis, so we don't really want to find more points farther down. In order to go up on a line with negative slope, we must choose a point to the left of the given one.
If you flipped a fair coin 18 times about how many times would you expect heads to appear?
Answer:
9 times
Step-by-step explanation:
hope this helps
Answer:
9
Step-by-step explanation:
Mathematically, 9, although reality wise, you could flip the coin and get heads every time, or the opposite.
I think you mean mathematically though, so yes, it would be 9.
which is equivalent to sin^-1 ( sqrt 3/2 )? Give your answer
Give your answer in radians.
Answer: pi/3
Step-by-step explanation:
correct on edge 2020
The equivalent value of trigonometric relation sin⁻¹ ( √3/2 ) = π/3
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the trigonometric relation be represented as A
Now , the value of A is
sin⁻¹ ( √3/2 ) = θ
Now , the value of θ is calculated by
In a triangle , sin θ = opposite / hypotenuse
So , sin θ = √3/2
The value of θ = 60°
So , the measure of 60° in radians is θ = π/3
Hence , the value of θ from the trigonometric relation is π/3
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Describe a free market economy
Answer:
soviet russia
Step-by-step explanation:
just kidding
The free market is an economic system based on supply and demand with little or no government control. ... Based on its political and legal rules, a country's free market economy may range between very large or entirely black market
Countries that have a market economy are Mexico, United States, United Kingdom, Germany, and Canada . These countries have a market economy because the prices of goods and services are set by supply and demand
use the figure to help you explain the statement
The base(b) of a triangle is ----------inches
The height (h) of the triangle is--------inches
The area of a triangle is ------- Square inches
The area of the rectangle is ------ Square centimeters
help fassstttt
Step-by-step explanation:
base is 6 in
height is 4 in
to get the area of a triangle is 1/2base×height
being 1/2(6)(4)=12
to get the area of a rectangle is length×width being 9×8=72
By observing the given figure,
The base(b) of a triangle is 6 inches
The height(h) of a triangle is 4 inches
The area of the triangle is 12 square inches
The area of the rectangle is 72 square centimeter
What is Triangle?A triangle is a polygon with three edges and three vertices
What is Rectangle?A rectangle is a quadrilateral with four right angles
What is Area?Area is the quantity that expresses the extent of a region on the plane or on a curved surface
From the given figure
The base(b) of a triangle is 6 inches
The height(h) of a triangle is 4 inches
The area of a triangle = [tex]\frac{1}{2}bh[/tex]
=[tex]\frac{1}{2}(6)(4)[/tex]
=12 square inches
Length of the rectangle = 8 centimeter
Width of the rectangle = 9 centimeter
Area of the rectangle = l × w = 9×8=72 square centimeter
Hence,
The base(b) of a triangle is 6 inches
The height(h) of a triangle is 4 inches
The area of the triangle is 12 square inches
The area of the rectangle is 72 square centimeter
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You buy $2,500of saving bonds at 1.7%interest.how many years will it take for your investment to equal $3000?
Answer:
It will take 12 years using simple interest
Step-by-step explanation:
2,500 x 1.7% = 42.5
42.5 x 12 + 510
2500 +510 +3010
A large company that produces a "fat-burner" pill claims an average loss of 20 pounds in the first month. A consumer advocacy group believes that this claim is actually just "hype" intended to sell more of the compound. The advocacy group would like to obtain statistical evidence about this issue and takes a random sample of 100 consumers who responded that they had purchased the pill but didn't know what the survey was about. They find that these 100 people lost an average of 18 pounds with a standard deviation of 7.5 pounds. What are the null and alternative hypothesis in this situation
The null and alternative hypothesis for the tests are:
H0: μ = 20
Ha: μ < 20
Given data:
In this situation, the null and alternative hypotheses can be formulated as follows:
Null Hypothesis (H0): The average weight loss of consumers who take the "fat-burner" pill is equal to 20 pounds.
Alternative Hypothesis (Ha): The average weight loss of consumers who take the "fat-burner" pill is less than 20 pounds.
In symbolic notation:
H0: μ = 20
Ha: μ < 20
where μ represents the population mean weight loss of consumers who take the "fat-burner" pill.
The null hypothesis assumes that the claim made by the company is accurate and that the average weight loss is indeed 20 pounds. The alternative hypothesis challenges this claim and suggests that the actual average weight loss may be less than 20 pounds, implying that the "hype" around the pill's effectiveness might be exaggerated.
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The Great Pyramid of Cheops is a square-based pyramid. The base has sides of 230m, and the height is 147m.
Using the same material, what would the height be if you gave the base sides of 240m?
Answer to nearest meter and explained solution please.
Answer:
height = 140.875m
Step-by-step explanation:
Volume of first pyramid= base * height /3 = 230*147/3= 11270
if the base is 240, volume is remain -> height = volume *3 /base
= 11270*3/240 =140.875m
what is 1/10+ 3/100 in fraction from
Answer:
0.13
Step-by-step explanation:
1/10 + 3/100 =
10/100 + 3/100 =
13/100
Hope that this helps you and have a great day:)
