Using the Empirical Rule, it is found that 68% of the cars driven by the students at Chillville have gas mileages between 24.0 and 32.0 miles per gallon.
What is the Empirical Rule?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In this problem, considering the mean of 28 mpg and the standard deviation of 4 mpg, we have that 24.0 and 32.0 mpg is within 1 standard deviation of the mean, hence the percentage is of 68%.
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help me please if that's okay , thank you sm
Answer:
9. is true
10. is false
hope this helps
Step-by-step explanation:
Step-by-step explanation:
9 is true and 10 is true as well
Solve the differential equation (2x+y)dx+(x−2y)dy = 0
Answer:
y(x) = 1/2 (x - sqrt(5 x^2 + c_1)) or y(x) = 1/2 (x + sqrt(5 x^2 + c_1))
Step-by-step explanation:
Solve 2 x + y(x) + (dy(x))/(dx) (x - 2 y(x)) = 0:
Let P(x, y) = 2 x + y and Q(x, y) = x - 2 y.
This is an exact equation, because (dP(x, y))/(dy) = 1 = (dQ(x, y))/(dx).
Define f(x, y) such that (df(x, y))/(dx) = P(x, y) and (df(x, y))/(dy) = Q(x, y).
Then, the solution will be given by f(x, y) = c_1, where c_1 is an arbitrary constant.
Integrate (df(x, y))/(dx) with respect to x in order to find f(x, y):
f(x, y) = integral(2 x + y) dx = x^2 + x y + g(y) where g(y) is an arbitrary function of y.
Differentiate f(x, y) with respect to y in order to find g(y):
(df(x, y))/(dy) = d/(dy) (x^2 + y x + g(y)) = x + (dg(y))/(dy)
Substitute into (df(x, y))/(dy) = Q(x, y):
x + (dg(y))/(dy) = x - 2 y
Solve for (dg(y))/(dy):
(dg(y))/(dy) = -2 y
Integrate (dg(y))/(dy) with respect to y:
g(y) = integral-2 y dy = -y^2
Substitute g(y) into f(x, y):
f(x, y) = x^2 - y^2 + y x
The solution is f(x, y) = c_1:
x^2 - y^2 + y x = c_1
Solve for y:
y(x) = 1/2 (x - sqrt(5 x^2 - 4 c_1)) or y(x) = 1/2 (x + sqrt(5 x^2 - 4 c_1))
Simplify the arbitrary constants:
Answer: y(x) = 1/2 (x - sqrt(5 x^2 + c_1)) or y(x) = 1/2 (x + sqrt(5 x^2 + c_1))
9x-8y= 1
18x - 16y= 2
Answer:
all real numbers.
Step-by-step explanation:
9x - 8y = 1
18x - 16y = 2
if you look at the first equation, you can figure out what y equals.
9x - 8y = 1
add 8y to both sides
9x = 1 + 8y
subtract 1 from both sides
9x - 1 = 8y
divide both sides by 8
[tex]\frac{9x - 1}{8}[/tex] = y
now, substitute y in the second equation.
18x - 16y = 2
18x - 16([tex]\frac{9x - 1}{8}[/tex]) = 2
18x - 2(9x - 1) = 2
18x - 18x +2 = 2
2 = 2
the answer is all real numbers, because regardless of what x equals, 2 will always equal 2.
On a coordinate plane, a straight line and a parallelogram are shown. The straight line has a negative slope and has a formula of y = negative x. The parallelogram has points G (negative 2, negative 3), F (1, negative 3), E (negative 1, negative 5), and H (2, negative 5).
What are the coordinates of the image of vertex F after a reflection across the line
y = –x?
A. (–1, –3)
B. (3, –1)
C. (1, 3)
D. (–3, 1)
Answer:
B. (3, –1)
Step-by-step explanation:
Reflection in the line y=-x is described by the transformation ...
(x, y) ⇒ (-y, -x)
Then the point of interest becomes ...
F(1, -3) ⇒ F'(3, -1) . . . . matches choice B
Answer:
The correct answer is B
Step-by-step explanation:
This is correct because it is correct
find the area of a triangle if do math problem 5 stars and brainly points
Answer:
24
Step-by-step explanation:
area of a triangle = 1/2 ( base length * height )
given base length : 6
given height : 8
area of triangle = 1/2(8*6)
==> multiply 8 and 6
area of triangle = 1/2(48)
==> multiply 1/2 and 48
area of triangle = 24 square units
Lukas is able to package and ship 416 cards in an 8-hour workday. How many cards can Lukas package a ship 32 hours?
Answer:
1664 cards
Step-by-step explanation:
416 divided by 8 is 52 and 52 times 32 is 1664.
What is the slope between the points (–2, 1) and (2, 6)?
5/4
-4/5
4/5
-5/4
To find the slope, we must know the equation
--> [tex]slope = \frac{y2-y1}{x2-x1}\\[/tex]
Now using the information given, (-2,1) and (2,6), let's plug that into the equation
--> [tex]slope = \frac{6-1}{2--2} = \frac{5}{4}[/tex]
In this case, the slope is 5/4
Hope that helped!
Answer:
[tex]\rn\hookrightarrow 5/4[/tex]
Step-by-step explanation:
[tex]Solution,\\\\Let,\\(x_1,y_1)=(-2,1)\\\\(x_2,y_2)=(2,6)\\\\Now,\\\\\rn\hookrightarrow Slope=\frac{y_2-y_1}{x_2-x_1}\\\\\rn\hookrightarrow Slope=\frac{6-1}{2-(-2)} \\\\\rn\hookrightarrow Slope=\frac{5}{4}[/tex]
John had $20. He earned $5, spent $10, earned $5 again, and then spent $3. After this series of earnings and expenses, how much money did he owe or have left?
Answer:
$17
Step-by-step explanation:
So first
The total money John have is $20
then he earned $5 which means $20+$5 = $25
After that he spent $10 = $25- $10 = $15
Again earned $5 = $15+$5=$20
At last spent $3 = $20-$3=$17
Hence the total money he owe or have left is $17
A population of beetles are growing according to a linear growth model. The initial population (week 0) is
P
0
=
5
, and the population after 7 weeks is
P
7
=
47
.
After how many weeks will the beetle population reach 113?
9514 1404 393
Answer:
18 weeks
Step-by-step explanation:
We are given the (time, population) pairs (0, 5) and (7, 47). With these values, we can use the two-point form of the equation of a line to write the equation of the linear model.
p = (p2 -p1)/(t2 -t1)(t -t1) +p1
p = (47 -5)/(7 -0)(t -0) +5
p = 6t +5 . . . . . the linear model matching the given points.
For p = 113, the time (number of weeks) is ...
113 = 6t +5
108 = 6t . . . . . . subtract 5
18 = t . . . . . . . . . divide by 6
After 18 weeks, the beetle population will reach 113.
20 - (+7) + - (6) = whats the answer
20 - (+7) + - (6)
Answer: 7
Answer:
Answer is 7
20-(+7)+(-6)= ?
(20-7)-6
13-6
7
please help on number 5 and 6 i’ll give 15 points
Celeste drinks at least 8 cups of water each day. She drinks her water from a bottle that holds 2 cups of water. So far, she drank 1.5 cups of water. Solve the inequality that shows the number of bottles of water Celeste should drink so that she drinks at least 8 cups of water.
Step-by-step explanation:
8 cups total a day
1 bottle holds 2 cups (Celeste drinks 4 bottles a day = 8 cups)
If she drank 1.5 bottles already, she needs to drink 2.5 bottles
Let x be the number of bottles she needs to drink to have at least 8 cups
The inequality is x >= 2.5 bottles
Cube the following numbers.
a. 1
b. 2
c. 4
d. 8
Answer:
I need to know the equation, but if you have to cube them then you will find your answer right away if you google how to cube numbers.
Step-by-step explanation:
Sorry for the bad answer.
Divide.
1.95 -0.5
please answer asap:(
Answer:
Step-by-step explanation:
3.9
If y(x) = 4x, what is x when y(x) = 4?
Replace y(x) with 4:
4 = 4x
Divide both sides by 4:
x = 1
(6 points) which answer describe the shape below? Check all that apply
What is the value of h in the figure below? In this diagram, ABAD - ACBD.
h
16
C
25
A.
16
9
B. 400
C. 12
D.
9
E. 225
0 0
F. 16
Answer:
h =12
Step-by-step explanation:
[tex]In\: \triangle ABC, \: \angle ABC = 90\degree \: \&\:\\ BD\perp AC[/tex]
Therefore, by geometric mean property:
[tex]BD = \sqrt {AD\times CD} \\
h = \sqrt {(AC-CD) \times CD} \\
h = \sqrt {(25-16) \times 16} \\
h = \sqrt {9 \times 16} \\
h = \sqrt {144} \\
\huge \red {\boxed {h = 12}} \\
[/tex]
Answer:
Step-by-step explanation:
12
A construction crew is placing a square in a wall for a new window.
The window is 3 1/8 feet wide.
The wall has a length of 11 3/8 feet.
The crew wants to position the window at the center of the wall.
How far from each edge of the wall should the window be positioned?
Answer:
4 1/3 feet
Step-by-step explanation:
11 3/8 - 3 1/8 = 8 2/3
8 2/3 / 2 = 4 1/3
Frank owed Alan $30. One week he paid him $14. Another week he paid him $8.50 What percentage of the $30 does Frank still owe to Alan?
CORRECT AND SERIOUS ANSWERS ONLY ORELSE REPORT
Answer:
fraction: 98/100 = 49/50decimal: 0.98percent: 98%Step-by-step explanation:
The fraction will represent the number of shaded squares over the total number of squares. You have correctly identified it as 98/100. That fraction can be reduced, if you like, to 49/50.
The pronunciation of your fraction is "ninety-eight hundredths." The decimal number with that same pronunciation is 0.98.
The symbol % and the symbol /100 have identical meaning. This makes them essentially interchangeable.
98/100 = 98%
Your numbers are ...
98/100 (or 49/50), 0.98, and 98%.
_____
Additional comment
We have shown you that % is a shorthand way to write /100. There is another similar symbol: ‰ is shorthand for /1000.
1/100 is one percent. 1/1000 is one mil.
.helooooooooo......... help
Answer:
B
Step-by-step explanation:
Determine the type of transformation.
Two shapes that look like the letter L. The first shape is the letter L with black continuous lines and the L points to the East. The second shape is also the letter L and it is red with dotted lines, and it is attached to the top of the first L but this L is pointing upwards. Two shapes that look like the letter L. The first shape is the letter L with black continuous lines and the L points to the East. The second shape is also the letter L and it is red with dotted lines, and it is attached to the top of the first L but this L is pointing upwards.
reflection
rotation
translation
none of these
(HELP) What is the length of xy in xyz?
Answer:
xy=6
Step-by-step explanation:
sin θ= opposite side÷ hypotenuse
sin 30°= xy÷12
sin 30°=1/2
Therefore,
1/2=xy÷12
1/2×12=xy
xy=6
A vertical wall AB which is 5m high was built on level ground. The distance of a point C on the ground from the base of the wall is 12m. Calculate the distance from the top of the wall to the point C..
What type of transformation of △ABC results in △A′B′C′ ? reflection rotation translation I don't know. Two triangles on the coordinate plane. Triangle A B C is formed by the points A at 1 comma 2, B at 3 comma negative 1, and C at 5 comma 1. Triangle A prime B prime C prime is formed by the points at A prime 2 comma negative 1, B prime at negative 1 comma negative 3, and C prime at 1 comma negative 5.
Using translation concepts, it is found that a 90º clockwise rotation of the triangle around the origin took place.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, considering the points on triangles ABC and A'B'C', the change is modeled by:
(x,y) -> (y, -x).
Which is a 90º clockwise rotation of the triangle around the origin.
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WILL MARK AS BRAINLIEST
The points (-7,r) and (-3, 4) lie on a line with slope - 3/4.
Find the missing coordinate r
for A (xa ; ya) and B (xb ; yb)
the slope is (yb - ya) / (xb - xa)
here :
slope = - 3/4 = (4 - r) / (-3 - (-7))
(4 - r) / 4 = - 3/4
so 4 - r = - 3
then r = 7
check
points (-7 ; 7) and (-3 ; 4)
slope = (4 - 7) / (-3 - (-7) = -3/4
Find the area of the figure.
3inches
5inches
7 inches
7 inches
4 inches
Answer:
26 inches
Step-by-step explanation:
You need to add 3+5+7+7+4= 26 because you need to find the area of the figure which the inches are area to add and get how many inches in the figure. Sorry if you don't get it but the answer is 26 inches.
Simplify the following expression
Answer:
25
Step-by-step explanation:
sarah and Noah work at Read
That's the question????
On her way home from work, Sandra fills up her car. She likes the idea of using gasoline with ethanol, but thinks her car can only handle 30% ethanol. At the gas station, she can use regular gas with 10% ethanol or E70 fuel with 70% ethanol.
How many gallons of each type of fuel should Sandra use if she wants to fill up her car with 9 gallons of fuel containing 30% ethanol?
Answer:
6 gallons of 10% ethanol gas and 3 gallons of the E70 fuel.
Step-by-step explanation:
Let the volume of 10% ethanol gas be x gallons and the volume of 70% be y gallons.
The resulting mixture ( 9 gallons) must have a strength of 30% ethanol.
SO WE HAVE THE SYSTEM:
x + y = 9
0.10x + 0.70y = 0.30 * 9
0.10x + 0.70y = 2.7
Multiplying the first equation by -0.10:
-0.10x - 0.10y = -0.9
Adding the last 2 equations:
0 + 0.60y = 1.8
y = 1.8 / 0.6 = 3 gallons.
So x = 9 - 3 = 6 gallons.
6 gallons of 10% ethanol gas and 3 gallons of the E70 fuel.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Let the volume of 10% ethanol gas be x gallons and the volume of 70% be y gallons.
The resulting mixture ( 9 gallons) must have a strength of 30% ethanol.
x + y = 9
0.10x + 0.70y = 0.30 * 9
0.10x + 0.70y = 2.7
Multiplying the first equation by -0.10:
-0.10x - 0.10y = -0.9
Adding the last 2 equations:
0 + 0.60y = 1.8
y = 1.8 / 0.6 = 3 gallons.
So x = 9 - 3 = 6 gallons.
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