Water used in three minutes in the shower is 12.6 gallons.
What is unit rate?An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.
Given Data
Elyse uses 42 gallons of water for a 10-minute shower,
Let
the time in minutes at position x
y=the quantity of water in gallons
The fact that
[tex]\frac{y}{x}[/tex] = [tex]\frac{42}{10}[/tex] = 4.2x
The unit price equals
The slope of the linear equation is equal to the unit rate.
then
y=4.2x
Problem
How much water will Elyse use in her shower for three minutes?
x = 3 minutes
substituting in the previous equation
y = 4.2x
y = 4.2(3)
y = 12.6
Water used in three minutes in the shower is 12.6 gallons.
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Will give branliest to the first person to answer. Pls answer ASAP. 40 points!! I'd appreciate your help so much!
Question: Which is the graph of the equation y - 1 = 2/3 (x - 3)?
Answer:
Option 2
Step-by-step explanation:
Using point-slope form, the line passes through (3, 1).
Option 2 is the only choice that satisfes this.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: Graph \:\: 2[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The equation is given in its point slope form :
[tex]\qquad \tt \rightarrow \:y - 1 = \dfrac{2}{3} (x - 3)[/tex]
And the general equation in point slope form is :
[tex]\qquad \tt \rightarrow \:y - y_1 = m(x - x_1)[/tex]
by comparing these two, we can get
[tex]{ y_1 = 1 } [/tex][tex]{ x_1 = 3 } [/tex]And [tex]{ (x_1 , y_1) } [/tex] satisfies the equation, so the line (graph) of this equation should have point (3 , 1) lying on it.
And the only graph satisfying this condition is graph 2, therefore The graph 2 is the required graph.
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Define centroid. If (X₁,Y₁), (X2,Y2) and (x3.3) are the vertices of a triangle, find the co- ordinates of the centroid of that triangle. (Note: Show derivation)
The coordinates of a centroid of a triangle with vertices [tex](x_1,y_1),(x_2,y_2),(x_3,y_3)[/tex] are [tex](\frac{x_1+x_2+x_3}{3}, \frac{{y_1+y_2+y_3} }{3})[/tex].
Centroid of a triangle
For a triangle, the centroid is obtained by the intersection of its medians. The line segments of medians join vertex to the midpoint of the opposite side. All three medians meet at a single point (concurrent). The point of concurrency is known as the centroid of a triangle.
Let KLM be a triangle with the vertex coordinates [tex](x_1,y_1),(x_2,y_2),(x_3,y_3)[/tex] as K,L and M respectively.
Let the midpoints of the side LM, KL and KM are D, E, and F, respectively. The centroid of a triangle is represented as “G.”
As D is the midpoint of the side LM, we can write,
D = ((x2+x3)/2, (y2+y3)/2)
Now, we know that, G intersects AD in the ratio 2:1 , we get
Hence, using section formula we can write,
The x-coordinates of G will be:-
x = (2(x2+x3)/2 + 1.x1 )/ (2+1) = (x2+x3+x1)/3 = (x1+x2+x3)/3
The y-coordinates of G will be :-
y =(2(y2+y3)/2 + 1.y1 )/ (2+1) = (y2+y3+y1)/3 = (y1+y2+y3)/3
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Africa is 8.2 times 10 to the 3rd power Brazil is 4.4x10 to the third power , what’s the difference
Find the slope of the line that passes through the following points: (4,-2) and (-4,-4)
The value of of slope of is 1/4.
How to calculate the value of the slope?It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope of lines in a coordinate plane can aid in anticipating whether the lines are parallel, perpendicular, or none at all without actually using a compass.
Any two distinct places along the line can be used to determine the slope of any line. When two different places on a line are considered, the slope of a line formula compares the "vertical change" to the "horizontal change" in each case. The difference between the line's y and x coordinate changes is known as the slope of the line. Net changes in the y and x coordinates are as follows: y = y and x = x.
m = [tex]y_{2} - y_{1} /x_{2} x_{1}[/tex]
m = 1/4
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HELP PLEASE!!!
Which equation matches the graph of the greatest integer function given below?
Answer:
the answer you are looking for is D
An angle measures 21.8° less than the measure of its complementary angle. What is the measure of each angle?
The measure of each angle is 34.1° and 55.9°
What are complementary angles?complementary angles are angles that gives 90° when added to together.
if the first angle is x and the other complementary angle is y,
then x+y=90
x= y-21.8
representing y-21.8 for x in equation x+y=90
y+ y-21.8= 90°
2y= 111.8
y= 55.9°
and x= 34.1°
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From Devon's total he decided to pay back his brother $17.50 and his best friend the $49 for
concert tickets. How much does Devon now have?
Answer:
Subtract 66.5 from Devon's total to find how much he has left
Given f ( x ) = 1 x + 12 , find the average rate of change of f ( x ) on the interval [ 9 , 9 + h ] . your answer will be an expression involving h
Given,
f(x) = 1x + 12
expression to be in form of h
To find on the interval: [9, 9 + h]
∵ Average rate of change of f(x) on interval (a,b) is
A = f(b) - f(a) / b - a
⇒ f(9) = 1 x 9 + 12 = 21
⇒ f(9 + h) = 9 +h + 12 = 21 + h
⇒ f(b) - f(a) = 21 + h - 21 = h
⇒ (b-a) = 9 + h - 9 = h
∴ Average rate of change = h / h
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Find the inverse Laplace of [tex]\displaystyle{L^{-1}\left \{ \dfrac{1}{s^3} + \dfrac{1}{s}\right \}}[/tex]
Compute the Laplace transform of [tex]f(t)=t^n[/tex], where [tex]n[/tex] is a non-negative integer.
[tex]\displaystyle L\left\{t^n\right\} = I_n = \int_0^\infty t^n e^{-st} \, dt[/tex]
Integrate by parts with
[tex]u=t^n \implies du = nt^{n-1} \, dt[/tex]
[tex]dv = e^{-st} \, dt \implies v = -\dfrac1s e^{-st}[/tex]
[tex]\displaystyle I_n = \frac ns \int_0^\infty t^{n-1} e^{-st} \, dt = \frac ns I_{n-1}[/tex]
By substitution,
[tex]\displaystyle I_n = \frac ns I_{n-1} = \frac{n(n-1)}{s^2} I_{n-2} = \cdots = \frac{n(n-1)\cdots(n-(k-1))}{s^k} I_{n-k}[/tex]
so that for [tex]k=n[/tex], we end up with
[tex]\displaystyle I_n = \frac{n(n-1)\cdots1}{s^n} I_0 = \frac{n!}{s^n} \int_0^\infty e^{-st} \, dt = \frac{n!}{s^{n+1}}[/tex]
We then have the inverse transform relation
[tex]\displaystyle L^{-1}\left\{ \frac1{s^n} \right\} = \frac{t^{n-1}}{(n-1)!}[/tex]
and so
[tex]L^{-1}\left\{ \dfrac1{s^3} + \dfrac1s \right\} = \dfrac{t^2}{2!} + \dfrac{0!}{t^0} = \boxed{\dfrac{t^2}2 + 1}[/tex]
Please Help
Deanna completed 60% of the levels in a recently released video game. If there are 75 levels in
the video game, how many levels did Deanna complete
Answer:
45 levels
Step-by-step explanation:
60% of 75 is 45 i think
C. For whole number n, n³ will be odd if n is odd and even if n is even.
Answer:
yes
Step-by-step explanation:
Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 4 ≤x≤ 8.
Hence the average rate of change, in simplest form is -10 .
What is average rate of change?
The average rate at which one item is changing in relation to another is known as the average rate of change. A method that computes the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.Examples of average rates of change include: 80 km/h is the average speed of a bus. In a lake, fish population growth occurs at a pace of 100 per week.Using the coordinate points from the table ( 4,53) ( 8, 13 )
Substitute the coordinate into the expression
Average rate of change = y₂ - y₁/x₂ - x₁
= 13 - 53/8 - 4
= - 4 0/4 ⇒ -10
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( Please help + Will mark brainliest )
Answer the question in photo.
Answer: 5/3
Step-by-step explanation:
The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.
We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.
Sonya wants to sew ribbon along each side of a square pillow. The expression 4 ⋅ 144−−−√ gives the exact amount of ribbon she will need for a pillow with an area of 144 square inches. How much ribbon, in inches, must Sonya buy to have the exact amount?
She buy 48 inches of ribbon to have the exact amount that she needs.
Given,
Area of the ribbon = 144 sq. inches
and, We know the formula for side of square is =[tex]\sqrt{Area of a square }[/tex]
Plug the value of area of square in above formula
Side of a Square = [tex]\sqrt{144}[/tex] = 12 inches
Now, we get the side of a square i.e., 12 inches
According to the question:
Sonya wants to sew ribbon along each side of a square pillow.
So, we need to find the perimeter of the square pillow.
and, Perimeter of a square is = 4 x side
=> Perimeter = 4 x 12 = 48 inches.
Therefore, She buy 48 inches of ribbon to have the exact amount that she needs.
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is x+y^2 linear?
sos this math hw is killing me rn
Answer:
Not linear
Step-by-step explanation:
Can be written into the form of [tex]y=mx+b\\[/tex].
56 out of 79 as a percentage
Which expression has a value of 24?
PLS HELP ASAP
A –6 • 2 – (–7)–6 • 2 – (–7)
B 9 • 4 ÷ 2 + (–3)9 • 4 ÷ 2 + (–3)
C –9 + 3 – 6 • (–5)–9 + 3 – 6 • (–5)
D 9 ÷ 3 • 10 – (–1) + 3
Answer:
a) the answer it 10 so no
b) the answer is −39 so nah
c) the answer is 48, nope
d) the answer is 34, did you mean to write 34 instead of 24?
Step-by-step explanation:
geometry, is this answer correct?
Answer: yes, the value of x is 4 and angle HEB is 36 degrees
Step-by-step explanation:
1a. Find the value of angle CEB
Given that line segment AB and line segment EC are perpendicular you know they are right angles and therefore are equal to 90 degrees
2a.set up an equation
After noticing that angle CEB is 90 degrees you know that angle HEB+CEH=90 degrees: 13x+9x+2
3a. Solve the equation
13x+9x+2=90
22x+2=90 | combine like terms
22x=88 | subtract 2 from both sides
x=4 | divide by 22 on both sides
1b. Set up equation
Knowing x=4 and that angle HEB is 9x the equation is 9(4)
2b. Solve the equation
9(4)
36
Here is the set of numbers: 4, 5, 11, 12, 5, 38, 44
Based on your results of Mean and Median, is the Mean or Median larger in value?
Please answer with complete sentence(s), which explains why and how you made your choice.
Based on the results of Mean and Median, we can say that Mean is larger than median in value .
Mean of n observations can be calculated using the formula
Mean = (sum of all observations)/(number of observations) .
After arranging the data in ascending or descending order , the middle value can be called as Median .
In the question ,
the set of numbers is given as 4, 5, 11, 12, 5, 38, 44
rewriting them in ascending order ,we get 4, 5, 5, 11, 12 ,38 ,44 .
the sum of all the number = 4+5+5+11+12+38+44
= 119
number of observations = 7
hence the mean = 119/7 = 17
So, mean = 17
from the set of numbers 4, 5, 5, 11, 12 ,38 ,44 we can see that
the middle value of the set of numbers is 11 .
So , median = 11 .
On comparing the mean = 17 and the median = 11 ,
we can say that the mean is greater than median.
Therefore , based on the results of Mean and Median, we can say that
Mean is larger than median in value .
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Which of the following is a whole number?
-76
0
-34
11
-57
Answer:
11
Step-by-step explanation:
A whole number is an integer greater than 0.
-76 , -34 , -57 are all negative so they are not whole numbers.
0 is too small so it also is not a whole number.
By ruling out those numbers you are left with 11 which is positive and greater than 0. Therefore, the correct answer is 11.
Answer:
0 and 11
Step-by-step explanation:
Whole numbers are set yo to be real numbers that include zero and all positive numbers while it excludes fractions, negative integers and decimals.
Therefore, from our question, 0 and 11 are whole numbers while -76, -34 and -57 are excluded because they are negative integers.
Prove the Lines are Parallel detailed two column proof for the following Given: 1 and 3 are supplementary Prove: a || b
The line a and b from the given line diagram is parallel since <2 and <3 are corresponding angles.
Column proof of angles
An angle is the point where two lines meet or intersect. From the given line diagram, we are told that <1 and <2 are supplementary.
Since the sum of supplementary angles is 180 degrees, hence;
<1 + <3 = 180 degrees
Also <1 + <2 = 180 degrees (sum of angles on a straight line)
<1 = 180 - <3
<1 = 180 - <2
Equate
180 - <3 = 180 - <2
-<3 = -<2
<2 = <3 (corresponding angle)
Since <2 is equivalent to <3, hence the line a is parallel to b
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write an equation of a parabola in the vertex form if a = -3 and the vertex is (-3,5)
help pls and thanks
Answer:
43°
Step-by-step explanation:
Alternate interior angle are congruent.
Find a point-slope form for the line that satisfies the stated conditions
Slope 4, passing through (- 2,1)
The equation of the line in point-slope form is ……
Answer:
y=4x+9
Step-by-step explanation:
y-Y1= m× x-X1
Y-1 = 4×X+2
y-1 = 4x+8
y=4x+9
f(x) = 2x + 10
Find f(20)
The function F(20) is 50
What is function ?The most common symbols for a function are the letters f, g, and h. A function's value at an element of its domain x is denoted by the notation f(x), and the numerical value obtained from the function evaluation at a specific input value is denoted by substituting that value for x. For instance, the value of f at x = 4 is denoted by the notation f(x) (4). When a function isn't given a name and is instead represented by the expression E, the value of the function at, say, x = 4 may be shown by the notation E|x=4.
Given that :f(x) = 2x + 10
f(x) = 2x + 10
F(20)= 2(20) + 10
F(20)= 40 + 10
F(20)= 50
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Please help me... 5 points
Answer:
Step-by-step explanation:
8(2+3)
Simplify the following 4 + (-125)
Answer:
4 + (-125)
= 4 - 125
= -121
Which is the surface area of the cube?
Answer:
54 cm
Step-by-step explanation:
A cube has six sides. The area of each face is found by squaring the length of a side. To get the total surface area of the cube, you'll multiply the area of one face by the number of faces.
a = edge
Area = 6a to the power of 2
the lifespans of lizards in a particular zoo are normally distributed. the average lizard lives 3.13.13, point, 1 years; the standard deviation is 0.60.60, point, 6 years. use the empirical rule (68-95-99.7\%)(68−95−99.7%)left parenthesis, 68, minus, 95, minus, 99, point, 7, percent, right parenthesis to estimate the probability of a lizard living between 2.52.52, point, 5 and 4.34.34, point, 3 years.
The probability of a lizard living for more than 2.5 years is 16%.
What is defined as the normally distributed?The proper term for just a probability bell curve is the normal distribution.The mean of a normal distribution is zero, and the standard deviation is one. It has a skew of 0 and a kurtosis of 3.Although all symmetrical distributions are normal, not all normal distributions are symmetrical.The average lifespan of a lizard is 3.1 years, with a standard deviation of 0.6 years.
Average lizard u = 3.1,
standard deviation σ = 0.6
To calculate the likelihood of a lizard living for more than 2.5 years;
p(X<2.5)
μ + aσ = 2.5
3.1 + a(0.6) = 2.5
a(0.6) = −0.6
a = −1
To calculate the probability, apply the empirical rule.
The total area = 100% (since total probability always is 1)
Area from μ to ∞ = p(X > μ) = 50%
Area between (μ−σ) and (μ+σ) = 68%
Area between (μ−σ) and μ is p((μ−σ) < X < μ) =34%
Thus,
p(X< (μ−σ)) = 1 − (p((μ−σ) < X < μ) + p(X > μ))
= 1 − (0.34 + 0.5)
p(X< (μ−σ)) = 0.16
Therefore, the probability that a lizard will live longer than 2.5 years 16%.
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a women earns 16% more than her husband. Together they make 72,360 per year. what is the husbands annual salary
well, her husband makes "x" in salary, hmmm hers is 16% more than that, so
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{16\% of x}}{\left( \cfrac{16}{100} \right)x}\implies 0.16x[/tex]
so she really makes x + 0.16x = 1.16x, and we know their total is 72,360, so
[tex]\stackrel{husband}{x} + \stackrel{hers}{1.16x} = 72360\implies 2.16x=72360\implies x=\cfrac{72360}{2.16}\implies \boxed{x = 33500}[/tex]