Answer:
Step-by-step explanation:
To determine the time it takes for the same hose to fill the larger aquarium, we need to compare the volumes of the two aquariums and consider the rate at which the hose fills the smaller one.
The volume of a rectangular prism (such as an aquarium) is given by the formula: Volume = length × width × height.
Let's calculate the volume of the two aquariums:
For the first aquarium:
Volume = 9 inches × 13 inches × (height not given)
For the second (larger) aquarium:
Volume = 24 inches × 30 inches × 34 inches
Since the height of the first aquarium is not provided, we cannot directly compare the volumes. However, we can determine a proportion between the two based on the known measurements.
If the time it takes to fill the first aquarium is 2 minutes, we can establish a ratio:
(9 inches × 13 inches × height of the first aquarium) / (24 inches × 30 inches × 34 inches) = 2 minutes / x minutes
To find the value of x, the time it takes to fill the larger aquarium, we rearrange the equation:
x = (24 inches × 30 inches × 34 inches) / (9 inches × 13 inches × height of the first aquarium) * 2 minutes
Without knowing the height of the first aquarium, we cannot determine the exact time it takes to fill the larger aquarium.
One of the most rapidly growing populations in the
world is that of South Sudan. According to the CIA
World Factbook, this population is growing at the rate
of 4.1% per year. Use logarithms to find the doubling
time for the population of South Sudan at this rate of
exponential growth. Compare your answer with the
doubling time approximation
This value is quite close to the doubling time approximation of 18 years that is often used for populations growing at a rate of 4% per year.
The given rate of growth = 4.1%
We know that,
The doubling time is the amount of time required for a population to double in size or value.
It is used to calculate population growth, inflation, resource extraction, commodities consumption, compound interest, the volume of malignant tumors, and a variety of other things that tend to develop over time. When the relative growth rate is constant (rather than the absolute growth rate), the amount grows exponentially and has a constant doubling time or period, which may be determined simply from the growth rate.
Formula for calculating the doubling time using logarithms is:
doubling time = ln(2) / (annual growth rate)
Since 41% = 0.041
doubling time = ln(2) / (0.041)
doubling time = 16.85 years
So the doubling time for South Sudan's population at this growth rate is approximately 16.85 years ≈ 18 years
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You have narrowed your job offers down to the
following two cities:
$17,000-San Antonio, TX - $5,400 in Benefits - Cost
of Living Index = 85.3
$23,500-Phoenix, AZ - $1,200 in Benefits - Cost of
Living Index = 96.2
1) In your own words, which city is more expensive to
live in?
2) Please convert both job offers into a salary in an
average USA city (Round your answers to the nearest
cent/two decimal places)!
3) Which job offer is better and why?
Edit View Insert Format Tools Table
12pt v
Paragraph
V
The salary plus benefits and the cost of living index for the two cities indicates;
1) Phoenix
2) San Antonio; $25,262.37, Phoenix; $21,901.35
3) San Antonio, because of the higher adjusted salary
What is the cost of living index?The cost of living index is a measure of how expensive it is to reside in a city, compared with the national average costs.
1) The cost of living index for the cities indicates that Phoenix, with a cost of living index of 96.2 is more expensive to live in than San Antonio, Texas with a cost of living index of 85.3
2) The job offers can be evaluated by converting the salary from one city to another as follows;
(Salary in City A) × (Cost of living index for City B)/(Cost of living index for City A)
Therefore, we get;
San Antonio: ($17,000 + $5,400)×96.2/85.3 ≈ $25,262.37
Phoenix: ($23,500 + $1,200)*85.3/96.2 ≈ $21,901.35
3) The job offer that is better, based on the conversion of the job offers into adjusted salary for the two Cities of $25,262.37 vs $21,901.35, indicates that the San Antonio job offer is better
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You take out a home mortgage for $271,000 for 40 years. How much more total interest, in dollars, do you pay for a loan with an annual percentage rate of 7% than for a loan with an annual percentage rate of 5%? Round your answer to the nearest cent.
The additional interest on the loan by the rates is $2150241.13
Calculating how much more total interest you payFrom the question, we have the following parameters that can be used in our computation:
Principal, P = $271,000
Time = 40 years
Rates = 7% and 5%
The interest is calculated as
I = P(1 + r)ˣ - P
So, we have
Interest 1 = 271000 * (1 + 7%)⁴⁰ - 271000 = 3787078.07443Interest 2 = 271000 * (1 + 5%)⁴⁰ - 271000 = 1636836.94099Calculate the difference in the interests
Difference = 3787078.07443 - 1636836.94099
So, we have
Difference = 2150241.13344
Approximate
Difference = 2150241.13
Hence, the additional interest is $2150241.13
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Claudia dumped her 200-penny coin collection on the floor and counted the number of pennies that landed heads up. Claudia repeated this process 5 times and had an average of 84 pennies landing heads up on each try. Which of the following statements is true?
A. The theoretical probability of a penny landing heads up is 21/50 .
B. Each penny has a greater probability of landing heads up than tails up.
C. If Claudia had repeated this process fewer times, the average number of pennies landing heads up would be closer to 100.
D. If Claudia had repeated this process more times, the average number of pennies landing heads up would be closer to 100.
Given a20=−40
and a37=−91
, find the common difference, the first five terms, and the formula for the arithmetic sequence.
The common difference is -3, and the terms are 17, 14, 11, 8, 5 and the formula is a(n) = 17 - 3(n - 1)
Finding the common difference, and the termsFrom the question, we have the following parameters that can be used in our computation:
a20 = -40
a37 = -91
An arithmetic sequence is represented as
a(n) = a + (n - 1) * d
Where
d = common difference
Using the given terms, we have
a + 19d = -40
a + 36d = -91
So, we have
17d = -51
Divide
d = -3
This also means that
a + 19(-3) = -40
So, we have
a = 17
Calculating the first five terms, we have
17, 14, 11, 8, 5
This also means that the nth term is a(n) = 17 - 3(n - 1)
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a. Your food total for dinner is $32.50.
leave a 20% tip on the food total. Find
Sales tax is an additional $1.95. You
total and the total amount you pay for
the percent of sales tax on the food
dinner.
The percent of sales tax on the food total is 6%.
To solve this problem
We must first determine the 20% of the total amount of food that is the tip:
Tip = 0.2 * $32.50 = $6.50
The total cost of the meal before tax is:
Total cost before tax = food total + tip = $32.50 + $6.50 = $39.00
The cost of the lunch, including the sales tax of $1.95, is
Sales tax and the total cost before taxes = $39.00 + $1.95 = $40.95.
The final price of the lunch, including tax and tip, is thus $40.95. You can compute the percentage of sales tax on the entire amount of food as follows:
Percent of sales tax on food = (sales tax / food total) * 100%
= ($1.95 / $32.50) * 100%
= 6%
So, the percent of sales tax on the food total is 6%.
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A bag of marbles has 12 green marbles, 5 red marbles, 8 blue marbles and 7 yellow marbles. What is the probability of randomly selecting a blue marble?
Probability = # of desired options / # of total options
Our desired option is blue and there are 9 blue marbles in the bag.
There are 32 total marbles (options) in the bag.
P(blue) = 9 / 32 = 0.28125 = 28.125%
Hope this helps!
Select the graph of the solution. Click until the correct graph appears. |x| + 1 < 3
The graph of the modulus function is plotted
Given data ,
Let the modulus function be represented as A
Now , the value of A is
| x | + 1 < 3
On simplifying the inequality , we get
Subtracting 1 on both sides , we get
| x | < 2
When x is positive or zero: In this case, the absolute value of x is equal to x itself. Therefore, we have x < 2
When x is negative: In this case, the absolute value of x is equal to -x. Therefore, we have -x < 2
Hence , the graph of function is plotted
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A price study tracked the cost of a bag of groceries over a five-year period. The data can be modeled by a function of the form C=a(b)x
C
=
a
(
b
)
x
, where x
x
represents the number of years since the study began.
Grocery Price Study
Years Since
Study Began Cost
($)
0 30.00
1 32.10
2 34.35
3 36.75
4 39.32
Which value is the best prediction of the cost of the groceries nine years after the beginning of the study?
To find the best prediction of the cost of the groceries nine years after the beginning of the study, we need to use the given data to find the values of a and b in the function C=a(b)x. So, the best prediction of the cost of the groceries nine years after the beginning of the study is $53.34.
To do this, we can use the first data point where x = 0:
30 = a(b)^0
This simplifies to:
30 = a
So, we know that a = 30.
Next, we can use any other data point to solve for b. Let's use the second data point where x = 1:
32.10 = 30(b)^1
This simplifies to:
32.10 = 30b
b = 1.07
Now we can use the function C = 30(1.07)^x to find the best prediction of the cost of the groceries nine years after the beginning of the study:
C = 30(1.07)^9
C ≈ $53.34
Therefore, the best prediction of the cost of the groceries nine years after the beginning of the study is $53.34.
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What is the surface area of the cylinder with height 8 mi and radius 4 mi? Round your answer to the nearest thousandth.
Answer:
301.593 mm²
Step-by-step explanation:
surface area of cylinder = 2π r² + 2π r h
where r = radius and h = height
so we have surface area = 2π (4)² + 2π (4) (8)
= 32π + 64π
= 96π mm² (in exact form)
= 301.593 mm² (to one-thousandth of mm)
a circle has a center at (3,5). If point A(5,2) lies on the circle, which of the following is the slope of the tangent line to circle C at point A?
1. 3/2
2. 2/3
3. -3/2
4. -2/3
Answer:
2. 2/3-------------------
We know the tangent is perpendicular to radius.
Find the slope of the radius using its endpoints:
slope(radius) = (2 - 5)/(5 - 3) = - 3/2Perpendicular lines have negative reciprocal slopes, therefore the slope of the tangent is:
slope(tangent) = - 1 / ( - 3/2) = 2/3The matching choice is 2.
Below are two inequalities and the graphs of their lines without the shading. By imagining where the shading should be, identify which point would satisfy BOTH inequalities.
The coordinates in the solution to the systems of inequalities is (-2, 1)
Solving the systems of inequalitiesFrom the question, we have the following parameters that can be used in our computation:
y > -x - 4
y > 2x - 6
By imagining where the shading should be, we have
y > -x - 4: Shaded up righty > 2x - 6: Shaded up leftFrom the imagined graph, we have solution to the system to be the shaded region
The coordinates in the solution to the systems of inequalities is (-2, 1)
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d to fil
table.
(a) Does the parabola open upward or downward?
O upward
O downward
(b) Find the coordinates of the vertex.
(D
vertex:
(c) Find the intercept(s).
For both the x- and y-intercept(s), make sure
to do the following.
. If there is more than one, separate them
with commas.
If there are none, select "None".
x-intercept(s):
y-intercept(s):
(d) Find the equation of the axis of symmetry.
equation of axis of symmetry:
The graph is interpreted below
(a) the parabola open downward
(b) the coordinates of the vertex is (1, 9)
(c) the intercept(s)
x-intercept(s): (-2, 0) and (4, 0)
y-intercept(s): (0, 8)
(d) the equation of axis of symmetry: x = 2
How to find the intercepts of the parabolaTo find the intercepts of a parabola, you need to determine the points where the parabola intersects the x-axis (x-intercepts) and the y-axis (y-intercept).
Examining the graph shows that the points are
x-intercept(s) (Roots): (-2, 0) and (4, 0)
y-intercept(s): (0, 8)
Also, investing the graph shows that the graph opens upward and the vertex which is the maximum point is (1, 9)
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find the solution to the system of eqautions shown below.
y=(x-3)^2-47
y=17
Suppose,
[tex]y=(x-3)^2-47 ----------------(1)\\y=17 -------------------------(2)[/tex]
Put [tex]y=17[/tex] in place of x in the first equation:
[tex]17=(x-3)^2-47[/tex]
To both sides, add [tex]47[/tex]:
[tex]64=(x-3)^2[/tex]
Add the square roots of both sides together:
[tex]8=x-3[/tex] or [tex]-8=x-3[/tex]
To each sides, add [tex]3[/tex]:
[tex]x=11 or -5[/tex]
As a result, the following are the equations' solutions:[tex]x=-5, y=17 or x=11, y=17[/tex].
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Solve for X (look at photo for answer choices)
The numerical value of x in the inscribed angle and intercepted arc is 4.
What is the numerical value of x?An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.
The relationhip between an an inscribed angle and intercepted arc is expressed as:
Inscribed angle = 1/2 × intercepted arc.
From the image:
Inscribed angle XZY = 14x + 4
Intercepted arc XY = 30x
Value of x = ?
Plug these values into the above formula and solve for x.
Inscribed angle = 1/2 × intercepted arc.
14x + 4 = 1/2 × 30x
14x + 4 = 15x
15x = 14x + 4
15x - 14x = 4
x = 4
Therefore, x has a value of 4.
Option D) 4 is the correct answer.
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please help me solve
Answer:
D
Step-by-step explanation:
First, to find the length of the side FH we will use the Pythagorean theorem which states [tex]a^2+b^2=c^2[/tex]. We can say that FH = a, FG = b, and HG = c. Since we know the values of b and c, we will rearrange the formula to solve for a [tex]a = \sqrt{c^2-b^2}[/tex]. That will be [tex]\sqrt{18^2-12^2)[/tex] which gives us 13.4 for the missing side.
Now to solve for the angles we will use simple trigonometry. Since we know that [tex]sin(\theta) = \frac{opposite} {hypotenuse}[/tex], we can do inverse trigonometry for the missing angles [tex]sin^{-1}(\frac{opposite}{adjacent}) = \theta[/tex]. For angle H, we can do [tex]sin^{-1}(\frac{12}{18})[/tex] which gives us 41.8 degrees. For angle G we can do [tex]sin^{-1}(\frac{13.4}{18})[/tex] and we get 48.1 degrees. We could also use inverse cos and trig to solve it.
Looking at the answer choices, only answer choice D is correct.
Please help with this 4-5
Triangle D has been dilated to create triangle D'. Use the image to answer the question.
6
D
04
Determine the scale factor used.
3
10
13
24
The scale factor from triangle D to triangle D' is 4
Calculating the scale factor from Dto D'?From the question, we have the following parameters that can be used in our computation:
The triangles
From the triangles, we have the following parameters
Side length of D = 8Corresponding side length of D' = 32Using the above as a guide, we have the following:
Scale factor of the dilation = Corresponding side length of D' / Side length of D
So, we have
Scale factor of the dilation = 32/8
Evaluate
Scale factor of the dilation = 4
Hence, the scale factor of the dilation is 4
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Help please which one
Answer:
6in
Step-by-step explanation:
angle C = 55 <-- 180-70-55=55
meaning the triangle is an isosceles so two sides would be the same.
if a household uses 196kwh of electricity consumption, excluding vat
The cost of electricity consumption (excluding VAT) for a household using 196 kWh in a month is given by [tex]\( \text{Cost} = 196 \, \text{kWh} \times r \), where \( r \)[/tex]represents the rate per kilowatt-hour charged by the electricity provider.
To determine the cost of electricity consumption excluding VAT, we need to know the rate charged per kilowatt-hour (kWh) by the electricity provider. Let's denote this rate as [tex]\(r\)[/tex] (in currency per kWh).
The total cost of electricity consumption (excluding VAT) can be calculated by multiplying the electricity usage in kWh by the rate:
[tex]\[ \text{Cost} = \text{Usage} \times \text{Rate} \][/tex]
Given that the household uses 196 kWh in a month, the cost can be expressed as:
[tex]\[ \text{Cost} = 196 \, \text{kWh} \times r \][/tex]
Please note that we still need the specific rate per kWh from the electricity provider to calculate the actual cost.
The cost of electricity consumption (excluding VAT) for a household using 196 kWh in a month is given by [tex]\( \text{Cost} = 196 \, \text{kWh} \times r \), where \( r \)[/tex]represents the rate per kilowatt-hour charged by the electricity provider.
Note: The given question is incomplete. The complete question is:
If a household uses 196kWh of electricity in a month how much would they pay for their electricity consumption excluding VAT?
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Polygon PSRT is drawn with vertices at P(1, 5), S(1, 0), R(−2, −3), T(−4, 2). Determine the image vertices of P′ if the preimage is rotated 90° counterclockwise.
P′(1, 5)
P′(−1, −5)
P′(5, −1)
P′(−5, 1)
The image vertices of P′ are P′(-5, 1), S′(0, 1), R′(3, -2), and T′(-2, -4).
To determine the image vertices of P′ after rotating the preimage 90° counterclockwise, we can apply the following transformation rules for a 90° counterclockwise rotation about the origin:
(x, y) → (-y, x)
Using these rules, we can find the image vertices of the polygon:
P (1, 5) → P′ (-5, 1)
S (1, 0) → S′ (0, 1)
R (-2, -3) → R′ (3, -2)
T (-4, 2) → T′ (-2, -4)
Therefore, the image vertices of P′ are P′(-5, 1), S′(0, 1), R′(3, -2), and T′(-2, -4).
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What number can make 24
Numbers:
5577
The arithmetic operations used to make the number 24 is (7 - 5) × (7 - 5) = 24
To make the number 24 using the digits 5, 5, 7, and 7, you can use the following arithmetic operations:
(7 - 5) × (7 - 5) = 24
In this case, we subtract 5 from 7 to get 2, and then multiply the result by itself to get 24.
7-5=2.
Subtract the second 5 from the remaining 7: 7-5=2.
Multiply 2 and 2: 2x2=24.
Number 24 was created using 5, 5, 7, and 7.
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Please help hurry soon
Answer:
0.3947368421 = approx 39%
Step-by-step explanation:
Add up all the number of times rolled on the right column.
=6+3+5+6+9+9
= 38 total rolls
Add up the number of times a 4 or a 5 were rolled:
= 6+ 9 = 15
Divide 15/38
=15/38=0.3947368421 = approx 39%.
The volume of a tree stump can be modeled by considering it as a right
cylinder. Mila measures its radius as 22 in and its volume as 49265 cubic
inches. Find the height of the stump in inches. Round your answer to the
nearest tenth if necessary.
The height of the tree stump is approximately 32.5 inches. Where its radius as 22 in and its volume as 49265 cubic inches.
The volume of a right cylinder is calculated as follows:
V = πr²h
where V denotes volume, r denotes radius, and h denotes height.
We are provided the radius and volume of the tree stump in this scenario. We may plug these values into the algorithm to find the height:
49265 = π(22²)h
Simplifying the right-hand side, we get:
49265 = 484πh
Dividing both sides by 484π, we get:
h = 49265 / (484π)
h = 49265 / (484 * 3.14)
h = 49265/ 1519.76
h = 32.416
h ≈ 32.5
Therefore, the height of the tree stump is approximately 32.5 inches.
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.which set of measurements could be the lengths of the sides of a right triangle
1,2,3
5,10,12
8,15,16
9,40,41
A triangle with side lengths of 9, 40, and 41 is a valid right triangle.
The set of measurements 9, 40, and 41 could be the lengths of the sides of a right triangle. This is because these measurements satisfy the Pythagorean theorem,
which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, 9² + 40² = 41²,
which confirms that this set of measurements is valid for a right triangle. Additionally, 9 and 40 are both smaller than 41, which is consistent with the fact that the hypotenuse of a right triangle is always the longest side.
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please help
Common internal tangent
point of tangency
Center
chord
secant
diameter
common external tangent
radius
semi-cirele
Major arc
Minor arc
From the given circles HJ is common external tangent.
From the given circles A and B,
1) EF is diameter.
2) EGf is semicircle.
3) G is point of tangency
4) HJ is common external tangent
5) CDK is semicircle
6) BF is radius
7) A is center.
8) KF is common external tangent
9) CD is segment
10) GK is chord
11) CK is minor arc
Therefore, from the given circles HJ is common external tangent.
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Show all of your work. Partial credit is only available if all your work is shown.
Match the numbers in Column I with their square roots in Column II. (1 point each)
Column I
____ 1. √844
____ 2. √900
____ 3. √650
____ 4. √784
____ 5. √699
____ 6. √805
____ 7. √729
Show all of your work. Partial credit is only available if all your work is shown.
Match the numbers in Column I with their square roots in Column II. (1 point each)
Column I
____ 1. √844
____ 2. √900
____ 3. √650
____ 4. √784
____ 5. √699
____ 6. √805
____ 7. √729
Answer:
[tex]\sqrt{844}=2\sqrt{211}=29.05[/tex]
[tex]\sqrt{900} =30[/tex]
[tex]\sqrt{650}=5\sqrt{26}=25.49[/tex]
[tex]\sqrt{784}=28[/tex]
[tex]\sqrt{699} =\sqrt{699}=26.43[/tex]
[tex]\sqrt{805}=\sqrt{805}=28.37[/tex]
[tex]\sqrt{729}=27[/tex]
Step-by-step explanation:
1.
[tex]\sqrt{844}[/tex]
[tex]\sqrt{2} *\sqrt{422}[/tex]
[tex]1\sqrt{422}[/tex]
[tex]1\sqrt{2} *\sqrt{211}[/tex]
[tex]1+1\sqrt{211}[/tex]
[tex]2\sqrt{211}[/tex]
[tex]29.05[/tex]
2.
[tex]\sqrt{900}[/tex]
[tex]\sqrt{9} *\sqrt{100}[/tex]
[tex]3\sqrt{100}[/tex]
[tex]3 \sqrt{25} *\sqrt{4}[/tex]
[tex]3*5*2[/tex]
[tex]30[/tex]
3.
[tex]\sqrt{650}[/tex]
[tex]\sqrt{25}*\sqrt{26}[/tex]
[tex]5\sqrt{26}[/tex]
[tex]25.49[/tex]
4.
[tex]\sqrt{784}[/tex]
[tex]\sqrt{4} *\sqrt{196}[/tex]
[tex]2\sqrt{196}[/tex]
[tex]2\sqrt{49}*\sqrt{4}[/tex]
[tex]2*7*2[/tex]
[tex]28[/tex]
5.
[tex]\sqrt{699}[/tex]
[tex]26.43[/tex]
(can't be simplified)
6.
[tex]\sqrt{805}[/tex]
[tex]28.37[/tex]
(Can't be simplified)
7.
[tex]\sqrt{729}[/tex]
[tex]\sqrt{9}*\sqrt{81}[/tex]
[tex]3*9[/tex]
[tex]27[/tex]
Please help quickly! (will mark brainliest!)
Answer:
1.
The cost of the carpet is given in dollars per square foot.
First I calculated the number of square feet which is the area of the carpet.
Then I multiplied the area of the carpet in square feet by the unit cost of the carpet.
2.
$576
Step-by-step explanation:
A = LW
A = 12 ft × 12 ft
A = 144 ft²
Unit cost of carpet: $4/ft²
cost of carpet = unit cost × area of carpet
cost of carpet = $4/ft² × 144 ft² = $576
1.
The cost of the carpet is given in dollars per square foot.
First I calculated the number of square feet which is the area of the carpet.
Then I multiplied the area of the carpet in square feet by the unit cost of the carpet.
2.
$576
a cooling machine requires at room temperature to be lowered from 50°Celsius at the rate of 5° Celsius every hour. What will be the room temperature after 8 hours after process begins?
The room temperature after 8 hours after the process begins would be 10°C.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represent the slope or rate of change.x and y are the points.c represent the y-intercept or initial value.Based on the information provided above, a linear equation that models the cooling machine is given by;
y = mx + c
y = -5x + 50
By substituting the given parameter (x = 8 hours), we have the following:
y = -5(8) + 50
y = -40 + 10
y = 10°C
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Find an equivalent ratio in simplest terms: 15 : 20
Answer: 3:4
Step-by-step explanation: just divide it by 5
4x5=20
3*5=15
if the ratio was 6:15 then you would dive it by 2 because 2 is equivalent to 6 and 7.
Hope this helps :)