The distance driven in city is 386.4 miles and same in highway is 213.6 miles.
Let the distance driven in city be x and driven in highway be y.
Now given that the mileage in city is 46 miles per gallon and in highway same is 51 miles per gallon.
The car is driven 621 miles in 13 gallon.
So suitable system of linear equations in two variables to solve this is,
x+y = 621 ……(1)
x/46+y/51 = 13 …….(2)
From (2) we get,
51x+46y = 30498
5x+46(x+y) = 30498
5x+46*621 = 30498
5x = 30498-28566
5x = 1932
x = 386.4
So from (1) we get,
y = 621-x = 621-386.4 = 213.6
Hence the car drove 386.4 miles in city and 213.6 miles in highway.
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What is the equation of the line that passes through the points (-2, 1) and (6, 3)?
Answer:
y = [tex]\frac{1}{4}[/tex] x + [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 1 ) and (x₂, y₂ ) = (6, 3 )
m = [tex]\frac{3-1}{6-(-2)}[/tex] = [tex]\frac{2}{6+2}[/tex] = [tex]\frac{2}{8}[/tex] = [tex]\frac{1}{4}[/tex] , then
y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (6, 3 ) , then
3 = [tex]\frac{3}{2}[/tex] + c ⇒ c = 3 - [tex]\frac{3}{2}[/tex] = [tex]\frac{3}{2}[/tex]
y = [tex]\frac{1}{4}[/tex] x + [tex]\frac{3}{2}[/tex] ← equation of line
. Which is the better investment?
a. $1,200 at 9% simple interest for 2 years
b. $1,200 at 8% compound interest for 2 years
Answer:
200 at 9% simple interest for 2 years
Answer:
a
Step-by-step explanation:
Hope it helps and have a nice day!!!! :)
X
y
1
9
2
7
3₂
3
6
4
7
1 -2
a. Graph the points above as a scatter plot.
b. Calculate the correlation coefficient.
8
-5
10
-8
10
X is top y is bottom
The correlation coefficient of points is a negative correlation.
The given coordinates are (1, 9), (2, 7), (3, 6), (4, 1), (7, -2),(8, -5) and (10, -8).
What is scatter plot?Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.
• A scatter plot with increasing values of both variables can be said to have a positive correlation.
• A scatter plot with an increasing value of one variable and a decreasing value for another variable can be said to have a negative correlation.
The given coordinate points are plotted on graph.
From the graph (scatter plot) we can see that, the points have a negative correlation.
Therefore, the correlation coefficient of points is a negative correlation.
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A student has these scores on their assignments. The teacher is considering dropping a lowest score. What effect does eliminating the lowest value, 0, from the data set have on the mean and median? 0, 40, 60, 70, 75, 80, 85, 95, 95, 100
The effect of eliminating the lowest value, 0, from the data set have on the mean and median of the data set is;
There is a difference of 7.5 between the mean without 0 and mean with 0There is a difference of 2.5 between the median without 0 and median with 0What is mean and median?The mean of a given data is the sum of all observations divided by the number of observations
The median of a given set of data refers to the middlemost observation, obtained after arranging the data in ascending or descending order.
Given data:
0, 40, 60, 70, 75, 80, 85, 95, 95, 100
a) Mean without '0' = (40+ 60+ 70+ 75+ 80+ 85+ 95+ 95+ 100) / 9
= 700/9
= 77.777
Median without '0' = 40, 60, 70, 75, 80, 85, 95, 95, 100
= 80
Mean with ' 0' = 0+ 40+ 60+ 70+ 75+ 80+ 85+ 95+ 95+ 100 / 10 = 70
Median with '0' = 0, 40, 60, 70, 75, 80, 85, 95, 95, 100
= (75 + 80) / 2
= 77.5
So therefore,
Difference in mean = Median without '0' - Mean with ' 0'
= 77.77 - 70
= 7.7
Difference in median = Median without '0' - Median with '0'
= 80 - 77.5
= 2.5
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A restaurant has a 33,500 gallon aquarium and a 500 gallon aquarium. About how many times is the capacity of the smaller aquarium?
Answer:
67 times
Step-by-step explanation:
33,500 divided by 500 is equivalent to 67
Write the first four terms of two different arithmetic sequences with a common difference of −3. The first sequence starts with −12 and the second sequence starts with 12.
Answer:
Step-by-step explanation:
The first arithmetic sequence would be -12, -15, -18, -21. The second sequence would be 12, 9, 6, 3.
amy gets 7 our of 8 math problems correct, mark gets 7 out of 11 problems correct ,and carol gets 7 out of 9 math problems corect. order these fractions from least to Greatest
Answer:
[tex]\frac{7}{11}[/tex], [tex]\frac{7}{9}[/tex], [tex]\frac{7}{8}[/tex]
Hope this helps!
Step-by-step explanation:
One way to find this out is by just plain dividing the numbers, 7 ÷ 11 is 0.636363..., 7 ÷ 9 is 0.7777777..., and 7 ÷ 8 is 0.875. 7/11 is the smallest of all of them, then 7/9, and then 7/8.
400 kilometers in 8 hours at a constant speed
a pair of sunglasses is 30% off . what is the new selling price
Answer:
x=0.3y
Step-by-step explanation:
( x )is new sales price
( y ) is the original price
1) suppose the state space (i.e., a set of possible locations for the robot) consists of all possible positions (x, y) in the plane. how many possible states are there? how many paths are there to the goal? provide assumptions for your answer
There will be infinite number of states and paths when the state space is (x,y) as the state space (i.e., a set of possible locations for the robot) consists of all possible positions (x, y) in the plane.
What is state space?The collection of every possible setup for a system is its state space. It is a common abstraction in the study of artificial intelligence and game theory because it can be used to reason about the behavior of a specific system. A state space is typically introduced into a system description without being given any thought to its precise physical meaning. However, it is well known that choosing an appropriate state space representation makes it simpler for us to comprehend or control a system's property.
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I'll give 45 points and brainiest The coordinates of the vertices of trapezoid EFGH are E(−8, 8), F(−4, 12), G(−4, 0), and H(−8, 4). The coordinates of the vertices of trapezoid E′F′G′H′ are E′(−8, 6), F′(−5, 9), G′(−5, 0), and H′(−8, 3).
Which statement correctly describes the relationship between trapezoid EFGH and trapezoid E′F′G′H′?
Responses
Trapezoid EFGH is congruent to trapezoid E′F′G′H′ because you can map trapezoid EFGH to trapezoid E′F′G′H′ by translating it down 2 units and then reflecting it over the y-axis, which is a sequence of rigid motions.
trapezoid E F G H, is congruent to , trapezoid E prime F prime G prime H prime, because you can map , trapezoid E F G H, to , trapezoid E prime F prime G prime H prime, by translating it down 2 units and then reflecting it over the , y, -axis, which is a sequence of rigid motions.
Trapezoid EFGH is not congruent to trapezoid E′F′G′H′ because there is no sequence of rigid motions that maps trapezoid EFGH to trapezoid E′F′G′H′.
trapezoid E F G H, is not congruent to , trapezoid E prime F prime G prime H prime, because there is no sequence of rigid motions that maps , trapezoid E F G H, to , trapezoid E prime F prime G prime H prime, .
Trapezoid EFGH is congruent to trapezoid E′F′G′H′ because you can map trapezoid EFGH to trapezoid E′F′G′H′ by reflecting it across the x-axis and then translating it up 14 units, which is a sequence of rigid motions.
trapezoid E F G H is congruent to trapezoid E prime F prime G prime H prime because you can map trapezoid E F G H to trapezoid E prime F prime G prime H prime by reflecting it across the x -axis and then translating it up 14 units, which is a sequence of rigid motions.,
Trapezoid EFGH is congruent to trapezoid E′F′G′H′ because you can map trapezoid EFGH to trapezoid E′F′G′H′ by dilating it by a factor of 34 and then translating it 2 units left, which is a sequence of rigid motions.
For the given coordinates of the vertices of trapezoid EFGH and E'F'G'H' the following statement is true and explain the relationship correctly :
"Trapezoid EFGH is not congruent to trapezoid E′F′G′H′ because there is no sequence of rigid motions that maps trapezoid EFGH to trapezoid E′F′G′H′.
trapezoid E F G H, is not congruent to , trapezoid E prime F prime G prime H prime, because there is no sequence of rigid motions that maps , trapezoid E F G H, to , trapezoid E prime F prime G prime H prime,"
As given in the question,
Trapezoid EFGH with coordinates of vertices:
E(−8, 8), F(−4, 12), G(−4, 0), and H(−8, 4).
Trapezoid E'F'G'H' with coordinates of vertices:
E′(−8, 6), F′(−5, 9), G′(−5, 0), and H′(−8, 3).
First option is not correct as there is no translation.
Third, Fourth, and Fifth options are not correct as both the trapezoids are not congruent.
Only option second describe it correctly which is:
Both the trapezoid are not congruent as there is no sequence of rigid motion that maps EFGH to E'F'G'H'.
Therefore, for the given coordinates of the vertices of trapezoid EFGH and E'F'G'H' the following statement is true and explain the relationship correctly :
"Trapezoid EFGH is not congruent to trapezoid E′F′G′H′ because there is no sequence of rigid motions that maps trapezoid EFGH to trapezoid E′F′G′H′.
trapezoid E F G H, is not congruent to , trapezoid E prime F prime G prime H prime, because there is no sequence of rigid motions that maps , trapezoid E F G H, to , trapezoid E prime F prime G prime H prime,"
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The first six numbers of a sequence are shown below. Which function can be used
to find the nth term?
-7, -1, 5, 11, 17, ...
Please Help Asap! Tysm if u do!
Answer:
41
Step-by-step explanation:
the pattern is +6 so the next few would be 23, 29, 35, 41, 47...
the ninth term would be 41
Plot these points of graph f(x)= -(x-5)^2+5 that correspond to x-values 3 and 4. Plot the vertex and reflections of these points in axis
Answer:
On the attached graph
Step-by-step explanation:
See attached graph
A local candy shop sells boxes of chocolate for $3.75 each. If a customer purchases six or more boxes, the cost is only $3.25 per box, plus the customer has an additional $5 fee per order. C(x) represents the total cost and x represents the number of boxes, which can be modeled by the function below.
A piecewise function c of x in two pieces. The function is defined by part 1, which is 3 point 75 times x for x greater than 6, and part 2, which is 3 point 25 times x plus 5 for x is greater than or equal to 6.
Predict the cost of an order with 6 boxes.
$14.50
$22.50
$24.50
$27.50
Answer:
$24.50
Step-by-step explanation:
In order to predict the cost of an order with 6 boxes, x has to be equal to 6.
So we have to use the function 3.25x + 5 for [tex]x\geq 6[/tex].
Then, plug in 6 for x and solve.
3.25(6) + 5 = 19.50 + 5 = 24.50
a homeowner wants to fence in a rectangular space in her yard along one side of her house for her dogs. the total area she can fence in is 650 square feet.
write an expression to find the area of the fenced region.
The required expression for the fenced region is lw = 650.
Given that,
A homeowner wants to fence in a rectangular space in her yard along one side of her house for her dogs. the total area she can fence in is 650 square feet.
What is a rectangle?
The rectangle is 4 sided geometric shape whose opposites are equal in length and all angles are about 90°.
Here,
Let the length of the area be l and the width of the area be w,
The total area she can fence in is 650 square feet.
lw = 650
Thus, the required expression for the fenced region is lw = 650.
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help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
which of the following beverages contains the most alcohol? 12-ounce can of beer 1.5 ounces of 80-proof liquor 5-ounce glass of wine all of these contain the same amount of alcohol
A 12-ounce can of beer contains the same amount of alcohol as a five-ounce glass of wine.
In a five-ounce glass of wine, the percentage of alcohol is 12%, which is the same in the 12-ounce can or bottle of beer, and 1.5 ounces of 86-proof liquor. Although a person under the influence of alcohol will have impaired judgment and therefore must avoid driving, doesn't matter what kind of alcoholic beverage they drink. Digestion of alcohol doesn't take place as soon as you drink it, it is absorbed in your bloodstream which reaches the brain and thus creates impaired judgment.
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Cant get the right answer
The expression equates to R = 926.19
What is a equation?
An equation is a relation equating two mathematical expressions. For example -
2x + 4 = 5x + 7
We have -
R = 21000([0.052/4]/[1+0.052/4]²⁰ - 1]
We have the following equation -
R = 21000([0.052/4]/[1+0.052/4]²⁰ - 1]
R = 21000([0.013/(1.013)²⁰ - 1)
R = 21000([0.013/(1.29475890663 - 1)]
R = 21000(0.0441038411650727)
R = 926.1806644665257
R = 926.19
Therefore, the expression equates to R = 926.19
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A painter work 7 3/4 hours per hour. How.
many hours does this painter work in 5
days a week
Answer: 38.75 hours
Step-by-step explanation: so one thing real quick, you said “A painter worked 7 3/4 hours per hour” that’s not possible so instead I’m guessing you meant 7 3/4 hours per day.
Turn 7 3/4 hours into 7.75 hours then it’s simple, you multiply 7.75x5! You get 38.75 hours!
Answer:
38 3/4
Step-by-step explanation:
7 3/4 times 5 =
7 3/4 = 31/4
31/4 times 5 = 155/4
= 38 3/4
Use synthetic division to divide x^3+8x^2+11x-20 by (x+4). Explain steps
Answer:
X²+4X-5 without a reminder
Determine the coordinates of the preimage given the image below and the composition of a rotation 180 about the origin and a translation 3
units up.
The coordinates of the preimage given in the image below and the composition of a rotation 180 about the origin and a translation 3 units up are: (2, -3), (3, 1), and (-5, 0).
What is a rotation?In Geometry, the rotation of a geometric figure 180° about the origin in a clockwise or counterclockwise direction would produce a point that has the coordinates (-x, -y).
From the graph of the image of triangle A'B'C', we have the following coordinates and they would be reversed to obtain the coordinate of triangle ABC before a translation:
(-x, -y) → (x, y)
Points at A' = (-2, 5) → Points at A = (2, -5)
Points at B' = (-3, 1) → Points at B = (3, -1)
Points at C' = (5, 2) → Points at C = (-5, -2)
Next, we would apply a translation of 3 units up:
Points at A = (2, -5) → (2, -5 + 2) = (2, -3)
Points at B = (3, -1) → (3, -1 + 2) = (3, 1)
Points at C = (-5, -2) → (-5, -2 + 2) = (-5, 0)
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after euclid high school's last basketball game, it was determined that 1/4 of the team's points were scored by alexa and 2/7 were scored by brittany. chelsea scored 15 points. none of the other 7 team members scored more than 2 points. what was the total number of points scored by the other 7 team members?
The total number of points scored by the other 7 team members in Euclid high school's last basketball game is 11.
What is defined as the term two variable equation?If an equation is written in the form ax + by + c=0, where a, b, and c are real integers as well as the coefficients of x and y, i.e., a and b, respectively, really aren't equal to zero, then it is said to be a linear function in two variables.For the given question.
Let 't' be the total points scored.
Alexa = 1/4 t.
Brittany = 2/7 t
Chelsea = 15
Let 'x' be the points scored by remaining 7 team.
Thus, the two variable equation becomes.
1/4 t + 2/7 t + 15 + x = t .....eq 1
Where, x ≤ 14 ( for 7 terams)
Simplifying eq 1.
15 + x = 13/ 28 t
28x + 28 = 13 t
Now, t must be divisible by 28.
Let t = 28 u, u ≥ 0 and divisible by 28.
Thus,
x + 15 = 13u.
Then, u = 2( t = 56) has been the only candidates for which x = 11.
Thus, the total number of points scored by the other 7 team members is 11.
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Peter, Bridget and Caroline share some sweets in the ratio 4:3:1. Peter gets 20 sweets. How many sweets are there altogether?
A television antenna is 10 feet tall. It has three wires that attach to its top and are anchored 8 feet
from its base. How long is each wire?
The length of each wire is 12.8 feet
The television antenna makes an angle 90 with the ground
The height of the antenna is 10 feet
The wires are anchored to the base which is 8 feet
We need to calculate the length of the wires
The height of the wire can be calculated by using pythagoras theorem
h² = b² + p²
h² = 8² + 10²
h² = 64 + 100
h = √164
h = 12.8
Therefore, the length of each wire is 12.8 feet
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Segment RS is reflected over the line y = x and then translated by (x+3, y + 4). The resulting segment
RS" has coordinates R" (-1,4) and S" (-3,-2). What are the coordinates of the segment RS?
The original coordinates are R= (-6,-6) and S = (-4,0)
What is translation?
Translation in mathematics is a property in which we shift each coordinate on a line by a constant value.
We are given that we originally had a segment RS which is reflected over the line y = x and then translated by (x+3, y+4) after this the segment we get the coordinates are R'' (-1,4) and S( -3,-2)
We are asked to find the coordinates of R and S
To find the coordinates we first reverse the process we subtract 3 from both x coordinate and 4 from both y coordinate
Hence we get,
R' = (-1,4)-(3,4)
R' = (-4,0)
And
S' = (-3,-2)-(3,4)
S' = (-6,-6)
Now to find the original coordinates we reverse the coordinates
Hence we get,
R= (-6,-6) and S = (-4,0)
Therefore the coordinates are R= (-6,-6) and S = (-4,0)
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a computer store compiled data about the accessories that 500 purchasers of new tablets bought at the same time they bought the tablet. here are the results: 411 bought cases 82 bought an extended warranty 100 bought a dock 57 bought both a dock and a warranty 65 both a case and a warranty 77 bought a case and a dock 48 bought all three accessories 58 bought none of the accessories find the probability that a randomly selected customer bought: a. exactly one of the accessories. b. exactly two of the accessories. c. at least one of the accessories. d. at least two of the accessories. e. at most one of the accessories. f. at most two of the accessories. g. a case or a warranty, but not both, and did not buy a dock. h. a case but neither of the other two accessories. i. a warranty and a dock but not a case.
The probability that exactly one of the accessories, be 0.678
The probability that exactly two of the accessories, be 0.11
The probability that at least one of the accessories, be 0.884
The probability that at least two accessories, be 0.206
The probability that at most one of the accessories, be 0.794
The probability that at most two of the accessories, be 0.904
The probability that a case or a warranty, but not both be, 0.726
The probability that a case but neither of the other two accessories be, 0.634
The probability that a warranty and a dock but not a case be, 0.018
Given, a computer store compiled data that 500 purchasers of new tablets bought at the same time they bought the tablet.
Let A be the set of purchasers we bought cases,
B be the set of purchasers we bought extended warranty,
C be the set of purchasers we bought dock,
Now, A = 411 , B = 82 , C = 100
also, A∩B = 65 , B∩C = 57 , A∩C = 77 and A∩B∩C = 48 , A'∩B'∩C' = 58
(a) the probability that exactly one of the accessories, be
P(A)-P(A∩B)-P(A∩C)+P(A∩B∩C) + P(B)-P(A∩B)-P(B∩C)+P(A∩B∩C) + P(C)-P(C∩B)-P(A∩C)+P(A∩B∩C) = 411-65-77+48+82-57-65+48+100-57-77+48
= 339/500
= 0.678
(b) the probability that exactly two of the accessories, be
P(A∩B)+P(B∩C)+P(A∩C)-3P(A∩B∩C) = 65+57+77-48-48-48
= 55/500
= 0.11
(c) the probability that at least one of the accessories, be
who bought 1 or 2 or all 3 accessories be,
= 0.678 + 0.11 + 0.096
= 0.884
(d) the probability that at least two accessories, be
who bought 2 or all 3 accessories be,
= 0.11 + 0.096
= 0.206
(e) the probability that at most one of the accessories, be
who bought nothing or one accessories be,
= 0.116 + 0.678
= 0.794
(f) the probability that at most two of the accessories, be
who bought nothing or 1 or 2 accessories be,
= 0.116 + 0.678 + 0.11
= 0.904
(g) the probability that a case or a warranty, but not both
= 0.822 + 0.164 - 0.26
= 0.726
(h) the probability that a case but neither of the other two accessories
= 0.634
(i) the probability that a warranty and a dock but not a case
= 0.018
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15x+12=13x-15
…….?????
Answer:
x_6x=21_15_3x/. x+6x=21+15+3x
Step-by-step explanation:
A cockroach can travel at a speed of 80 centimeters per second. A centipede can travel at 30 meters per
minute. Which can travel faster?
Answer:
The cockroach is faster
Step-by-step explanation:
Make X
the subject of m=n+x/p
Answer:
m+n=x/p
p×(m+n)=(x/p)×p
x=pm+pn
1. [-/1 Points]
DETAILS
Find the x- and y-intercepts.
7x - 6y = 1
x-intercept (x, y) = (
y-intercept (x, y) = (
(x, y) = (
multiply x times y divide by 6 on both sides and you got your answer