The machine will use 90 gallons of water to wash 24.5 pounds of laundry.
What is Direct Variation?If two quantities change by the same amount, they are said to follow a direct variation. As a result, when one quantity changes, the other follows suit, increasing when the first increases and decreasing when the first decreases. To put it another way, two quantities are said to be directly proportional to one another if the ratio of the first to the second is a constant term. The coefficient or constant of proportionality is the name given to this constant quantity. Assuming that x and y are two quantities that are directly varying, they are stated as follows:y ∝ x
Consequently, y = kx, where k is the proportionality constant.
Given:
The amount of water used by a washing machine varies directly with the weight of the load being washed.
Let's assume,
The amount of water used by a washing machine is y.
The weight of the load being washed is x.
According to the question,
y = 28 gallons
x = 7 pounds
Putting the values we get,
y = kx
28 = k × 7
k = 4
Now, we have to find y when x = 24.5
y = 4 × 24.5 = 98
Hence the machine will use 90 gallons of water to wash 24.5 pounds of laundry.
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Answer the following prompt using the continuous growth formula A=Pe^rt
You have received a report of a mysterious illness that seems to turn the infected humans into mindless zombies has broken out in a major American city. Since the hungry zombies prey upon innocent people, the outbreak grows continuously at a rate of 12% per day. The outbreak begins with 8 people.
1. Write the formula that matches this scenario.
2. How many zombies will there be after 5 days?
3. How many days will it take for the zombie population to reach 3,700,00 (about the population of Los Angeles, CA)?
The solution to the questions are
The formula of the scenario is A = 8 * e^0.12tThe number of zombies after 5 days is 15The number of days is 39How to determine the formula?The general formula is given as
A = Pe^rt
In this case, we have
P = Initial number of people
r = rate
t = time
From the question, we have
P = 8
r = 12% = 0.12
So, we have
A = 8 * e^0.12t
The number of zombies after 5 daysThis means that t = 5
So, we have
A = 8 * e^(0.12 * 5)
Evaluate
A = 15
The number of days to reach 3,700,00This means that A = 3,700,00
So, we have
8 * e^0.12t = 3,700,00
Divide by 8
e^0.12t = 46250
Take the logarithm of both sides
0.12t = log(46250)
This gives
0.12t = 4.7
Divide
t = 39
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Please answer this for me¡ <3
Answer:
3⁶
------
4¹⁵
Step-by-step explanation:
( 4⁻³ )³
( ------------- )
( 3⁻² × 4² )
Switch numbers with negative exponents
( 3² )³
( ------------- )
( 4³ × 4² )
( 9 )³
( ------------- )
( 64 × 16 )
( 9 )³
( ------------- )
( 1024 )
Multiply 9 and 1024 by the 3rd power
729
-------------
1,073,741,824
Simplified would be:
3⁶
------
4¹⁵
I hope this helps!
your mom is planning to put up fence in front of your house. If the perimeter of the lot is is X + 8x 16. What is the measure of the front side?
Answer:
[tex]x + 8 \times 16 \\ 8 - 16 = 8[/tex]
14. There are 3 teaspoons in a tablespoon. Show how to convert 15 teaspoons to tablespoons using a
ratio table and using a conversion factor.
There are 3 teaspoons in a tablespoon, 15 teaspoons to tablespoons using a ratio table and using a conversion factor will be total as 5 tablespoons.
What is a ratio table?The consistent relationship between two values is shown in a ratio table. A rate is a unique ratio that is used to compare two quantities with different units of measurement. There are various ways to examine a ratio table.
What is displayed in a ratio table?Equivalent ratios between two quantities are displayed in ratio tables. In order to find an equal ratio, you can make a ratio table by multiplying (or dividing) the quantities in the ratio by the same number.
You can use a ratio table to determine equal ratios and solve difficulties.
What is an example of a conversion factor?A conversion factor is a kind of number that is used to multiply or divide one set of units into another.
If any kind of a conversion is required, it must be done using the proper and correct conversion factor to get an identical value. For instance, 12 inches equals a total of one foot when converting between inches and feet.
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write an expression using exponents that represents the volume of a cube with egde length 4/7 yard. what is the volume of the cube?
Answer:
[tex]\sf \dfrac{64}{343} \ cubic \ yard[/tex]
Step-by-step explanation:
Volume of cube:[tex]\sf \boxed{\bf Volume \ of \ cube =a^3}[/tex]
Here, a is the edge of the cube.
[tex]\sf a =\dfrac{4}{7} \ yard[/tex]
[tex]\sf Volume \ of \ cube = \dfrac{4}{7}*\dfrac{4}{7}*\dfrac{4}{7}[/tex]
[tex]\sf =\dfrac{64}{343} \ cubic \ yard[/tex]
Simplify 4.5p(2 − 0.2p).
9p − 0.9p2
9p − 0.2p2
9 − 0.2p2
9 − 0.9p2
Answer:
9p-0.9p^2
Step-by-step explanation:

What is the value of -3 + |-17|?
a ball dropped vertically, falls d t seconds.
d is directly proportional to the sqaure of t.
the ball drop 80 meters in the 4 seconds
how far does the ball drop in the next 8 seconds
If the ball drops 80 meters in the 4 seconds, the time it takes the ball to drop in the next 8 seconds is; 720 meters
How to utilize constant of proportionality?
We are told that a ball dropped vertically falls a distance of d in t seconds and that d is directly proportional to the square of t. Thus;
D ∝ t²
Thus;
D = kt²
where d is the constant of proportionality.
We are given that D = 80 m when t = 4 seconds and as such we have;
80 = k*4²
k = 80/16
k = 5
Therefore, the equation of motion is;
D = 5t²
When t = 8 + 4 = 12 seconds, we have;
D = 5 * 12²
D = 5 * 144
D = 720 m
Therefore, the distance the ball drops in the next 8 seconds
= 720 - 80
= 640 m.
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lest to greatest3.008 3.825 3.09 3.18
Answer: 3.825, 3.180, 3.090, 3.008
Step-by-step explanation:
Answer: 3.008, 3.09, 3.18, 3.825
Step-by-step explanation: Least to greatest just means smallest to largest.
In a particular college class, 60% of the students are female. Of the female students, 75% have long hair. One student is picked randomly in the class. What is the probability that it is a female with long.
The probability of selecting a female student with long hair is 45%
Let there be a total of 100 students in the class
Since 60% of the students are female, therefore out of 100 students 60 will be female students
Now, out of these 60 students, 75% have long hair, As a result, = 75% of 60 = 45 female students will have long hair
Probability of selecting female student with long hair = Number of female students with long hair/ Total number of students in the class
= 45/100
So, there is a 0.45 or 45% chance that a female student with long hair is selected
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Find an equation in standard form of the parabola that passes through (0, 0), (-2, -6), and (3, -3)
Answer:
[tex]y = - \frac{ {4x}^{2} }{5} + \frac{7x}{5} [/tex]
There is a line that includes the point (-6,-2) and has a slope of 0 what is its equation in slope-intercept form?
IF THE SLOPE IS 0 IT MEANS THAT THERE IS NO CHANGE IN THE Y COORDINATE OF THE LINE.FOR ANY VALUE OF X GIVEN
THEREFORE THE EQUATION WILL BE
[tex]y = (0)( - 6) - 2 \\ y = - 2[/tex]
THE EQUATION IS
[tex]y = - 2[/tex]
HOPE THIS HELPS
Answer:
The slope-intercept form would be: y = 0x - 2
David traveled 4/5 of his trip by bicycle and the rest of the distance by foot. If the whole trip was 160km, how many kilometres dad he travel by foot?
Answer:
Step-by-step explanation:
I will explain it in a screenshot. That all the way is divided into 5 parts. And 4 of them were by bicycle, and 1 part is by walk. So we divide all the way to 5 and multiply to leftover 1 piece.
Approximating 39 by following the steps below
Answer:
sqrt(39) is between 6 and 7
Step-by-step explanation:
Start by looking at perfect squares
1^2 =1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2= 49
39 is between 36 and 49
so sqrt(39) is between 6 and 7
Solve the equation for w.
w divided by 1.4 minus 3.7 equals 6.5
2
3.92
14.28
7.3
the answer is 14.28
Step-by-step explanation:
w/1.4_3.7=6.5
w/1.4=6.5+3.7
w/1.4=10.2
w=10.2*1.4
w=14.28
Answer: 14.28!
Step-by-step explanation:
I got a perfect 100% on my exam! This answer was right can i get brainliest?
If F, G, and H are the midpoints of the sides of AJKL, FG = 37, KL = 48, and GH = 30, find each of the following measures. FH= JL= KJ= FJ=
For the given, F, G and H are the midpoints of the sides of ΔJKL, FG = 37, KL = 48, and GH = 30, then measure of FH = 24, measure of JL = 74, measure of KJ = 60 and measure of FJ = 30.
As given in the question,
F, G, and H are the midpoints of the sides of ΔJKL.
F is the midpoint of KJ, G is the midpoint KL, H is the midpoint of JL
Measure of the required sides are as follow:
FH = (KL / 2) (by midpoint theorem)
= (48/2)
= 24
JL = 2 x FG (by midpoint theorem)
= 2 x 37
= 74
KJ = 2 x GH (by midpoint theorem)
= 2 x 30
= 60
FJ = GH = 30 (by midpoint theorem)
Therefore, for the given, F, G and H are the midpoints of the sides of ΔJKL, FG = 37, KL = 48, and GH = 30, then measure of FH = 24, measure of JL = 74, measure of KJ = 60 and measure of FJ = 30.
The complete question is:
If F, G, and H are the midpoints of the sides KJ, KL, and JL respectively of ΔJKL, FG = 37, KL = 48, and GH = 30, find each of the following measures. FH= JL= KJ= FJ=
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Determine the value of z
A. 20 degrees
B. 36 degrees
C. 88 degrees
D. 124 degrees
WE STILL HAVE TO FIND THE TWO UNKNOWNS FIRST. TO BE ABLE TO GET Z
x°+144°=180°(angles on a straight line)
x°=180°-144°
x=36°
y°+56°=180°(angles on a straight line)
y°=180°-56°
y=124°
z°+y°+x°=180°(sum of angles in a triangle)
z°+124°+36°=180°
z°=180°-124°-36°
z=20°
What is the scientific notation of 500,000,000,000
Answer:
The scientific notation for 500000000000 is 5 × 1011
Step-by-step explanation:
The 11 is going to be a superscripts(meaning its going to be placed at the top right corner of the 10)
A man earned wages of 41,500 received 1900 and interest from a savings account and contributed 2900 to a tax deferred retirement plan he was entitled to a personal exemption of $4050 and had deductions totally $6660 find his gross income adjusted gross income and taxable income
Answer:
Gross Income = $ 43400
Adjusted Gross Income=$40500
Taxable Income = $33840
Step-by-step explanation:
given that-
Income paid to man
Wages = $41,500
Savings Interest = $1900
Tax Def Contribution=$2900
Deductions= $6660
personal exemption =$4050
Gross Income = Income paid to man = 41500 + 1900 = $ 43400
Adjusted Gross Income = Income - Tax Def Contribution = $43400-$2900=$40500
Taxable Income = AGI - Deductions = 40500 - 6660 = $33840
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Can someone pls help me? This is urgent! If u do thank you so much!
The slope of g(x) is [tex]\frac{-2}{5}[/tex] times the slope of f(x)
The x-intercept of f(x) is 8 more than the y-intercept of g(x)
As x approaches -∞, f(x) approaches ∞ and g(x) approaches -∞
Given,
f(x) = 10-5x
g(x) = -6+2x
The slope of f(x) = -5
The slope of g(x) = 2
Hence the slope of g(x) is [tex]\frac{-2}{5}[/tex] times slope of f(x)
For x-intercept assign zero value to f(x). Thus,
10-5x = 0
=> x = 2
So intercept of f(x) = 2
y-intercept of g(x) = -6
Hence x-intercept of f(x) is 8 more than y-intercept of g(x)
As x approaches -∞, f(x) = 10-(5 times (-∞)) = ∞
As x approaches -∞, g(x) = -6 + 2x = -6 + 2(-∞) = -∞
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What is
the circumference of
a circle with a radius of 9.7 inches?
Use 3.14 for
pi.
Enter your answer as a decimal in the box.
The circumference of circle with radius 9.7inch is 60.916 inch.
What is circumference of circle ?The perimeter of a circle is known as its circumference. It is the length of the circle's whole perimeter. The diameter of a circle and the constant are multiplied to get the circumference of the circle. This measurement of a circle's circumference is necessary for someone to cross a circular park or for a circle-shaped table to have a border. The units of the circumference are the same as the units of length and it is a linear value.
A circle is a closed round object whose border points are all equally spaced apart from the center, which is a fixed point.
Given that :the circle with a radius of 9.7 inches
Circumference of a circle is [tex]2\pi r[/tex]
2 ×3.14×9.7 = 60.916
The circumference of circle with radius 9.7inch is 60.916 inch.
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Find the average rate of change:
The table has an average rate of change of 3
How to determine the average rate of change?The table represents the given parameter
From the table, we have the following interval is given as
[3, 7]
This can be rewritten as
x = 3 to x = 7
From the attached table, we have
f(3) = 7
f(7) = 19
The average rate of change of the function is then calculated as
Rate = [f(b) - f(a)]/[b - a]
This gives
Rate = [19 - 7]/[7 - 3]
Evaluate
Rate = 3
Hence, the average rate of change is 3
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At a garage sale, Liyah priced
her scooter for $15.50. She
ended up selling it for $10.75.
Find the percent of decrease
in the price of the scooter.
Round to the nearest tenth if
necessary
Answer:30.6452% decrease
Step-by-step explanation:
-Subtract starting value(original price) minus final value
-Divide that amount by the absolute value of the starting value
-Multiply by 100 to get percent decrease
-If the percentage is negative, it means there was an increase and not an decrease.
rearrange the distance Formula d=rd to solve for time
Answer:
[tex]t=d/r[/tex]
Step-by-step explanation:
Assuming you meant [tex]d=rt[/tex], dividing both sides by [tex]r[/tex] yields [tex]t=d/r[/tex].
Solve.
7. Maria walks at a speed of 2 1/2 miles per hour. How long will it take her to walk a
10-mile trail?
Answer:
4 hours :)
Step-by-step explanation:
Lets multiply to solve :)
1 hr: 2 1/2
2 hrs: 5
3 hrs: 7 1/2
4 hrs: 10 hrs
it will take 4 hours to walk 10 miles :)
Have an amazing day!!
Please rate and mark brainliest!
Help pleaseeee. A private club was reduced by members in weeks. Its size changed by the same number of members each week. What was the change in the club's size each week?
Answer: it was changed by 9 members per week.
Step-by-step explanation:
how many liters of a 25\%%, percent saline solution must be added to 333 liters of a 10\, percent saline solution to obtain a 15\, percent saline solution?
please help me to solve this hard question.I need your help right now
Answer:
θ = 110.61°
Step-by-step explanation:
It's not that hard :)
Let a = θ/3
Then sin a = 3/5 = 0.6
a = sin⁻¹(a) = 36.87°
=> θ/3 = 36.87°
θ = 3 x 36.87
θ = 110.61°
Please helppppp
Which inequality is NOT part of the system of inequalities that defines a polygonal convex set that includes all points in the interior of a square whose vertices are: A(4, 4), B(4, -4), C(-4, -4) and D(-4, 4)?
The inequality that is not part of the system of inequalities that defines a polygonal convex set that includes all points in the interior of a square whose vertices are: A(4, 4), B(4, -4), C(-4, -4) and D(-4, 4) is y ≤ -4. This is option C
How to find the inequalities that does not define the points in the interior of a square.given data
A(4, 4)
B(4, -4)
C(-4, -4)
D(-4, 4)
Looking at the given points the coordinates we can see that:
x coordinates has points:
4 4-4-4This is basically 4 and -4 which is represented as -4 ≤ x ≤ 4
y coordinates has points:
4 -4-44This is basically 4 and -4 which is represented as -4 ≤ y ≤ 4
The inequality that is different from the one listed above is in option C making it the correct option.
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Use an integer or a fraction to describe a slope of this line please!
Answer:
Step-by-step explanation: