The image of D (1, 2) is D' ( 2, 7).
The image of E (-3 -5) is E' ( -10, 0).
The image of F (4, -1) is F' ( 11, 4).
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given points are;
D (1, 2), E(-3, -5) and F(4, -1)
Now, The rule is to find the image of points is;
(x, y) → (3x - 1, y + 5)
Hence,
The image of D (1, 2) = (3 * 1 - 1, 2 + 5)
= (3-1, 7)
= (2, 7)
The image of E (-3 -5) = (3*-3 - 1, -5 + 5)
= (-9-1, 0)
= (-10, 0)
The image of F (4, -1) = (3*4 - 1, -1 + 5)
= (12-1, 4)
= ( 11, 4 )
Therefore, The image of D (1, 2) is D' ( 2, 7).
The image of E (-3 -5) is E' ( -10, 0).
The image of F (4, -1) is F' ( 11, 4).
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How do you simplify (2/3) with a sqrt of 2
Ashley received a $22 discount on a radio she bought for $96.00. What is the percent of discount she saved?
Answer:
18.64% discount
Step-by-step explanation:
If she had a $22 discount and bought the radio for $96, then the original cost was $118.
discount = (22 * 100) / 118
Solve: -7+5 > 2. Write your solution in interval notation.
(If there is no solution, enter your answer as Ø.)
Answer:
-7+5 >2
-7+5=2
collect like terms
-7 =2-5
-7 = -3
therefore: -7>-3Hope this helpsGood luck ✅0.39 x 10^9
Put in scientific notation and explain how it works.
Answer:
3.9 x [tex]10^{8}[/tex]
Step-by-step explanation:
0.39 is not in scientific notation. For a number to be in scientific notation the first factor has to be 1 or greater, but less then 10. 0.39 is less than one.
First we must write 0.39 in scientific notation. We need to move the decimal so that the number is greater than 1, but less than ten. If we move the decimal one place to the right, we get 3.9. The standard number is smaller than 3.9. How much smaller? [tex]10^{-1}[/tex] smaller.
0.39 in scientific notation would be 3.9 x [tex]10^{-1}[/tex]. We cannot forget the [tex]10^{9}[/tex], so our number looks like this now:
3.9 x [tex]10^{-1}[/tex] x [tex]10^{9}[/tex] The product of powers principle tells us that if we have powers with the same bases, we can add the exponents.
3.9 x [tex]10^{-1+9}[/tex]
or 3.9 x [tex]10^{8}[/tex]
A produce packing company prepares crates of apples to ship to supermarkets. Suppose
that the weight of a randomly selected crate is known to be Normally distributed, with
a mean of 14 kg and a standard deviation of 1.4 kg.
(a) Find the weight of a particular crate such that the probability of randomly selecting a heavier crate is 0.05.
(b) Find the probability that a randomly selected crate will weigh more than 16kg.
(c) If 20 crates are randomly and independently selected, what is the probability that
at least 2 of them will weigh more than 16kg?
a. The weight of a particular crate such that the probability of randomly selecting a heavier crate is 0.05 is 16.30kg.
b. The probability that a randomly selected crate will weigh more than 16kg is 0.0764.
c. The probability that.at least 2 of them will weigh more than 16kg is 0.4584.
How to calculate the probability?a. From the information, there is a mean of 14 kg and a standard deviation of 1.4 kg. The weight will be:
Let the weight = x
X = (Z × mean × standard deviation)
= (1.645 × 1.4 ×14)
= 16.30kg
b. The probability that a randomly selected crate will weigh more than 16kg will be:
P(z > 16)
= P(Z > 16-14/1.40)
= P(Z > 1.43)
Looking under the normal distribution table, the value is 0.0764.
c. The probability that at least 2 of them will weigh more than 16kg when 20 crates are randomly and independently selected will be through binomial distribution where n = 20 and p = 0.0764.
This will give a value of:
= 1 - 0.5416
= 0.4584
Therefore, the probability that.at least 2 of them will weigh more than 16kg is 0.4584.
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A test consists of 100 multiple choice questions, each with five possible
answers, only one of which is correct. A student randomly guesses at all
100 questions.
Use the Mean And Standard deviation to determine how many questions correct we could usually expect from a student who randomly guesses at all 100 questions.
Mean = 20; standard deviation = 4;
Let x be the success of receiving the right response.
The total number of trials in this case is 100.
The likelihood of receiving the right response is p = 1/5.
In light of the average number of correct answer;
μₓ = np
μₓ = 100 * (1/5);
μₓ = 20;
The standard deviation is now; σ = √(n)(p)(1 - p)
σ = √(100)(1/5)(4/5)
σ = 4
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Given a regular pentagon with radius 5, and each side of length 6, find the area of the pentagon. A) 120 square units B) 60 square units C) 45 square units D) 30 square units
The area of the regular pentagon is 60 square units
How to determine the area of the pentagon?The given parameters are
Radius, r = 5 units
Side length, l = 6 units
The area of the pentagon is calculated as
A = 1/4√[25 + 10√5] * l^2
Substitute 6 for l in the above equation
So, we have
A = 1/4√[25 + 10√5] * 6^2
Evaluate the product
A = 60 (approximated)
Hence, the area of the regular pentagon is 60 square units
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what do r and y mean??
What is 639 ÷ 0.3 I neeed I help pls this is due Tomorrow help pls
Answer:
Step-by-step explanation:
639÷0.3=
2130
the answer is
639÷0.3=
2130
How far could you travel walking backwards in 15 minutes based on you speed for the 5 meter trial?
The correct answer answers will vary
Students should apply their findings to the calculation to determine a distance.
S=D÷T. The speed would be equal to the time and the speed from the 5-meter trial of walking backwards.
ought should be 15 minutes. To calculate the distance, students must multiply the speed by the time.
The distance that an item travels in relation to the amount of time it takes to do so may be used to define speed. In other terms, it is a measurement of an object's motion's speed without direction Velocities are what we get when speed and direction are combined.
The speed formula, which was developed by scientists, is used to determine different types of speed. The speed equation is:
Speed=Distance/Time
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The Washington Football Team won 6 of their 13 games. What percentage of their games did they win?
Answer:
46.2%
Step-by-step explanation:
6 divided by 13 multiplied by 100. rounded up
What is the standard form of 10 to 5 power
Answer:
100,000
Step-by-step explanation:
Multiply 10 by 10 by 10 by 10 by 10 to get 100000
How many times larger is 7.785 x 10^10 than 1.5 x 10^8?
05.19
19.3
193
519
Answer:
(d) 519
Step-by-step explanation:
You want the ratio of (7.785×10^10) to (1.5×10^8) expressed in standard form.
DivisionSince you want the result in standard form, it can work well to make the numerator and denominator powers of ten be the same.
[tex]\dfrac{7.785\times10^{10}}{1.5\times10^8}=\dfrac{7785\times10^7}{15\times10^7}=\dfrac{7785}{15}=\boxed{519}[/tex]
15. Isabel made the following graph to show
the daily share price for Company XYZ.
What was the change in the price from
Monday to Friday?
The change in the price from Monday to Friday is $0.75
How to determine what was the change in the price from Monday to Friday?The graph that completes the question is added as an attachment
From the attachment, we have:
Monday = $0.75
Friday = $1.50
There are 5 days between Monday and Friday
So, we have the change in the price from Monday to Friday to be
Change = Friday - Monday
This gives
Change = $1.50 - $0.75
Evaluate
Change = $0.75
Hence, the change in the price from Monday to Friday is $0.75
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PLS HELP!!! NEED ASAP WILL MARK BRAINLIEST. WORTH 100 POINTS
Solve the inequality. Graph the solution, if possible.
1. |y-2|+11>0
2. 3|2a+8|-11≤-5
3. 1/3|2x+3|-1≤8
please show how you got your answer or if it’s no solution, thank u !
Answer:
1-13 and 2-13 and 4-13 because if you add them that is the answer
HW 3 Linear Function Models: Problem 9
Previous Problem Problem List Next Problem
(3 points)
A new highway has just opened and tolls will be collected from vehicles using the highway. The toll will be 119 cents for cars which travel 20 miles of the
highway. The toll will be 184 cents for cars which travel 33 miles of the highway. Let T(d) be a function which gives the total toll (in cents) which will be
charged to a car which travels d miles along the highway. Assume T(d) is a linear function. Find T'(d).
T(d) =
What will be the toll to travel 96 miles?
cents
Answer:
T(d) = 5d +19T(96) = 499 . . . centsStep-by-step explanation:
Given two points on the linear toll function T(d) are (20, 119) and (33, 184), you want the equation for the function T(d), and the value of T(96).
SlopeIt is usually convenient to write the equation of a line in slope-intercept form when you want to find the value at a particular point. To use that form, we need to know the slope of the line. It is given by the formula ...
m = (y2 -y1)/(x2 -x1)
Using the given points, we have ...
m = (184 -119)/(33 -20) = 65/13 = 5
Point-slope equationThe point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
Using the first point and the slope we found, the equation is ...
y -119 = 5(x -20)
Slope-intercept equationSolving the above equation for y, we get ...
y = 5x -100 +119 . . . . . . . simplify, add 119
y = 5x +19 . . . . . . . . . . combine terms
Using variables d and T instead of x and y, the function is ...
T(d) = 5d +19
Toll for 96 milesThe value T(96) is ...
T(96) = 5(96) +19 = 480 +19 = 499
The toll for 96 miles is 499 cents.
Aniela took 10 pages
of notes over the span of 4
classes. If Aniela worked at a
constant rate, how many notes
did she take in one class?
Answer: Aniela took 2.5 pages of notes per class
Step-by-step explanation: If you take the total amount of pages of notes taken and divide it by the number of classes you get the rate of pages of notes per class. So 10 pages/4 classes = 2.5 pages/class
Find the difference between 8.72 and 0.872
Answer:
Step-by-step explanation:
Find the difference between 8.72 and 0.872. This just means to subtract 0.872 from 8.72. [tex]8.72-0.872=7.848[/tex]
The longer side of a golden rectangle has length of 13. In order to find the length of the shorter side, divide 13 by what
in order to find the shorter side of a golden rectangle we need to divide 13
by 1.6180.
A golden rectangle is a rectangle in geometry whose side lengths are in the golden ratio, or display style 1:tfrac 1+sqrt 5 2 which is display style 1:varphi 1:varphi (the Greek letter phi), where display style var phi var phi is roughly 1.618.
All rectangles made by including or excluding a square from one end are also golden rectangle, which is a unique example of self-similarity.
Length of longer side a = 13
let the length of shorter side is b.
them by the property of golden rectangle,
a : b = 1: (1+sqrt 5)/2
by substitution method
13 : b = 1 : (1+sqrt 5)/2
b = 8.034
so to get the length of shorter side we need to divide by 1.6180
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If the measure of angle 2=a+15 and the measure of angle 3=a+35, find a if HL is perpendicular to HJ
The value of a if HL is perpendicular to HJ is 20
How to determine the value
From the information given, we have that;
HL = angle 2 = a + 15HJ = angle 3 = HJIt is important to note that perpendicular lines always intersect each other and the angle between perpendicular lines is equivalent to 90 degrees.
Then, we have that;
Angle 2 + angle 3 = 90 degrees
Substitute the values
a + 15 + a + 35 = 90
collect like terms
2a + 50 = 90
2a = 90 - 50
subtract like terms
2a = 40
Make 'a' the subject
Divide both sides by 2
2a/2 = 40/2
a = 20
Thus, the value of a if HL is perpendicular to HJ is 20
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Help!
Let y=0. Evaluate the expression.
4(6y+1)
4
0
244
5
Answer:
Given y = 0,
[tex]\sf 4(6y+1)\\4(6* 0+1)\\(6 * 0 + 1)\\(6 * 0)\\= 0\\= 0 + 1\\= 1\\= 1 * 4\\= 4[/tex]
Thus, the answer is 4.
Write the equation of the line that is parallel to y 2/3 = x + 1 and passes through the point (–6, –1).
The linear equation with the given information is
2y+2 = 3x+18
Given :
The slope of Parallel Lines:
Slopes of parallel lines are equal. The parallel lines are equally inclined with the positive x-axis and hence the slope of parallel lines is equal. If the slopes of two parallel lines are represented as m1, m2 then we have
In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.
The net change in the y-coordinate is represented by Δy and the net change in the x-coordinate is represented by Δx.
Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,
m = change in y/change in x = Δy/Δx
Where “m” is the slope of a line.
The slope of the line can also be represented by
tan θ = Δy/Δx
So, tan θ to be the slope of a line.
Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The slope is usually represented by the letter ‘m’
m1 = m2.
y 2/3 = x + 1 ...1
2y = 3x+3
y = 3/2x +3/2
m1= 3/2
x,y = -6,-1
y = mx +b
(y-y1 ) =m (x-x1) +b
m1=m2
m2= 3/2
(y +1) = 3/2 (x+6)
2(y+1 )= 3x+18
the equation of the line that is parallel to y 2/3 = x + 1 and passes through the point (–6, –1) = 2y+2 = 3x+18
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40 POINTS! Use the following figure to answer BOTH parts the question.
(a) Describe in words a sequence of transformations that maps ∆ABC to ∆A''B''C''.
(b) Write an ordered-pair rule for each transformation in the sequence.
Answer:
BC to ∆A''
Step-by-step explanation:
Differentiate with respect to y
[tex]5y = {y} ln( {x}^{2} ) [/tex]
Answer:
[tex]{ \tt{5y = y ln( {x}^{2} ) }} \\ { \tt{impossible}}[/tex]
The equation C= 8h+25 represents the cost in dollars, C, to rent a canoe, where h is the number of hours the canoe is rented.
What is the cost to rent a canoe for 4 hours?
The cost to rent a canoe for 4 hours is $57.
How to calculate the cost?It should be noted that the equation given is illustrated as equation C= 8h+25 represents the cost in dollars, C, to rent a canoe.
C = 8h + 25.
where h = number of hours
C = 8h + 25
When h = 4..
C = 8h + 25
C = 8(4) + 25
C = 32 + 25
C = 57
Therefore, the cost to rent a canoe for 4 hours is $57.
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how do you find the perimeter on a coordinate plane
Answer: You draw the shape on the coordinate plan and then you can count the number of unit squares
Step-by-step explanation:
4.)
Find the area of the polygon with the given vertices:
E(3, 1), F(3,-2), G(-2,-2)
Perimeter EFG =____
Beth is making a beanbag seat in the shape of a cube. Each side of the seat is 2 feet long. Beth needs to find the volume of the seat so that she can buy the correct amount of bean. Beans are sold in bags that hold 2 cubic feet of beans. How many bags should Beth buy?
With the help of the volume of cube it is concluded that Beth should buy 4 bags of beans.
What Is Volume of Cube?The volume of a cube is the total three-dimensional space that it occupy. A cube's volume is expressed as cubic units. The SI unit of volume is the cubic meter [tex](m^3)[/tex], which is the volume occupied by a cube with each side measuring 1 m.
The first thing to do in this case is to find the volume of the cube, which will be given by:
V = [tex]L ^ 3[/tex]
where, L = sides of the cube.
Substituting we have:
V = [tex](2) ^ 3[/tex]
V = [tex](8) ^ 3[/tex]
Since, beans are sold in bags that hold two cubic feet of beans.
Now, to find the number of bags, we calculate
n = 8/(2)
n = 4
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In a survey of 400 households regarding ownership of HDTVs and DVD players, the following data were obtained. 315 households own one or more HDTVs. 150 households own one or more HDTVs and one or more DVD players. 16 households do not own an HDTV or a DVD player. How many households only own one or more DVD players?
Number of households only own one or more DVD players = 219
Total number of households considered for the survey = 400
Let n(A) represent the number of households only own one or more HDTVs.
Then n(A) = 315
Let n(B) denotes the number of households only own one or more DVD players. We need to find n(B).
Number of households own one or more HDTVs and one or more DVD players, n(A∩B) = 150
Number of households do not own an HDTV or a DVD player = 16
So the number of households which own an HDTV or a DVD player, n(A∪B) = 400 - 16 = 384
Then we have the formula relating n(A∪B), n(A), n(B) and n(A∩B).
n(A∪B) = n(A) + n(B) - n(A∩B)
⇒ n(B) = n(A∪B) - n(A) + n(A∩B)
= 384 - 315 + 150
= 219
The number of households only own one or more DVD players = 219
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Which of the following describe 0?