Answer:
the equation is y = (-2/15 in/min)x + 43 in
Step-by-step explanation:
We'll represent elapsed time with the letter t. Then 12 p.m. corresponds to t = 0 sec. Between 12 p.m. and 12:15 p.m., the change in time was 15 min and the change in water depth was (45 - 41) in., or 4 in.
Thus, the water depth changes by 4 in (a decrease) over 30 min.
Part A: The water depth rate of change is -4 in/30 min, or -2 in/15 min, or
(-2/15 in)/min (the depth is decreasing).
Part B: We need to derive a linear function that describes the water depth at any given time x (or t). Two points on the graph of this line are
(15 min, 45 in) and (35 min, 41 in): the 'run' is 30 min and the 'rise' is -4 in.
As in Part A, the slope of this line is (-2/15 in)/min.
The desired equation is then y = mx + b, or 45 in = (-2 in/15 min)(15 min) + b, or 45 in = 2 in + b, or 43 in = b. Then, in its most general form,
the equation is y = (-2/15 in/min)x + 43 in
A student in ms. campbells class are participating in a recycling project. after 3 days the class collected 24 cans. they collected the same number of cans each day. how many cans did the class collect in 6 days
Answer:
144
Step-by-step explanation:
multiply 24 times 6
Answer: Ms. Campbell's class collected 48 cans in 6 days. The ratio is 8 cans per day.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Days of collection of the recycling project = 3
Number of cans collected in the first 3 days = 24
Students collect the same number of cans each day
2. How many cans did Ms. Campbell's class collect in 6 days?
Let's use the Direct Rule of Three, for answering this question:
Cans Days
24 3
x 6
3x = 144
x = 144/3
x = 48
Ms. Campbell's class collected 48 cans in 6 days.
Simplify this expression.
4m
10(m + n)
Answer:
4m+10mn
Step-by-step explanation:
because we can't simplify any further, we can just multiply 10 by m AND n when you do this, its like multipling 2 variblies, like bxh = bh.
A chef buys a 1-gallon jug of milk for a cookie recipe. He first uses 1/4 of the milk. Then he uses 2/3 of the remaining milk. How much milk is left in the jug?
Answer:
1/12 of a jug is what is left
can anyone please help me with this ?
Answer:Do you have a word bank???
Can someone answer this for me?
Answer:
the answer is B
Step-by-step explanation:
Henry wants to double his cake recipe that uses 2 cup 10tbsp of flour. How much flower will he need?
Answer:
5 cups and 4 tbsp
Step-by-step explanation:
4 cups and 20 tbsp of flour
There are 16 tablespoons in 1 cup
5 cups and 4 tbsp
The last square of the chessboard is square 64.
How many pennies are on square 64?
Answer: C. 2^63
second part: greater than
Step-by-step explanation:
The number of pennies on square 64 is 2^63
What is a square?A square is a quadrilateral, that have its four sides to be equal, and all its angles to be right-angles
From the question, the number of pennies on a square is:
[tex]T_n = 2^{n-1[/tex]
So, we have:
[tex]T_{64} = 2^{64 - 1}[/tex]
Evaluate the difference
[tex]T_{64} = 2^{63[/tex]
Hence, the number of pennies on square 64 is 2^63
Read more about patterns at:
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Twice one number added to another
number is 18. If the second number is equal
to 12 less than 4 times the first number, find
the two numbers.
First complete the equations below, where x stands for
the first number and y stands for the second number.
2x + y = 18; y = [?]x-[]
Answer:
The Answer is: The first number is 5 and the second one is 8.
please give me brainliest!! :)
Step-by-step explanation:
Let f = first number and s = second number
Twice the first number added to the second number is 18:
2f + s = 18
The second number is equal to 4 times the first number minus 12:
s = 4f - 12
Substitute:
2f + (4f - 12) = 18
6f - 12 = 18
6f = 18 + 12
6f = 30
f = 5, is the first number.
Solve for the 2nd number:
s = 4(5) - 12 = 20 - 12 = 8, is the second number.
Proof:
2f + s = 18
2(5) + 8 = 18
18 = 18
Hope this helps! Have an Awesome Day! :-)
Answer:
y = 8
x = 5
Step-by-step explanation:
This is a system of equations problem
Set up your two conditions:
2x + y = 18
y = 4x - 12
rearrange them to match
y = -2x + 18
y = 4x - 12
combine them by subtracting one equation from the other in such a way that it eliminates one variable. In this case I choose to subtract each value from the second equation from the first one
0 = -6x + 30
solve
6x = 30
x = 5
plug in the x value to solve for y
2(5) + y = 18
10 + y = 18
y = 8
which equation best fits the graft data
Answer:
I think it's C
Step-by-step explanation:
Answer:
The answer is C
Step-by-step explanation:
A graph can only be curved when it has an exponential. B and C are slopes so it cannot be that.
Six friends go to a movie theater. In how many different ways can they sit together in a row of six empty seats?
Answer:
720
I think..i hope it helps
The number of ways that 6 friends can sit together in a row of six empty seats is 720.
What is Permutation?Permutation is defined as the calculation of a set such that it defines the number of ways that something can be arranged.
Given that,
Six friends go to a movie theater.
They have to be arranged in 6 different positions.
6 friends can be arranged in 6 different positions as 8P₈ ways.
Number of ways = 8P₈
= 8! / (8 - 8)!
= 8! / 0!
= 8!
= 720
Hence the number of ways that 6 friends can be arranged is 720 ways.
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Out of 2,000 students in a high school, 800 of them were randomly selected and asked if they want the school’s mascot to change. Out of those surveyed, 250 want it to change.
With a desired confidence level of 99% and a corresponding z*-score of 2.58, what is the margin of error for this sample survey?
Answer:800
0.31
0.69
4.2
Step-by-step explanation:
Answer:
800
0.31
0.69 (nice)
4.2
Step-by-step explanation:
edgu 2020
A town has a population of 20000 and grows at 4% every year. To the nearest
year, how long will it be until the population will reach 39400?
Answer:
The population will reach 39,400 after 17 years.
Step-by-step explanation:
Given that, The population grows at a rate 4%. The population of the town is 20,000 at a certain time.
Exponential function:
[tex]y(t)=y_0(1+r)^t[/tex]
y(t) = The population after t years
[tex]y_0[/tex] = Initial population.
r = Rate of grow
t = Time.
y(t)= 39400, [tex]y_0[/tex] = 20,000, r= 4%=0.04, t=?
[tex]39400=20000(1+0.04)^t[/tex]
[tex]\Rightarrow \frac{39400}{20000}=(1.04)^t[/tex]
[tex]\Rightarrow \frac{197}{100}=(1.04)^t[/tex]
Taking ln both sides
[tex]\Rightarrow ln|\frac{197}{100}|=ln|(1.04)^t|[/tex]
[tex]\Rightarrow ln|\frac{197}{100}|=t\ ln|(1.04)|[/tex]
[tex]\Rightarrow t= \frac{ln|\frac{197}{100}|}{ln|(1.04)|}[/tex]
[tex]\Rightarrow t\approx 17[/tex]
The population will reach 39,400 after 17 years.
Final answer:
To find the time it takes for a town's population to grow from 20,000 to 39,400 at a 4% annual growth rate, the exponential growth formula is used. After rearranging the equation and taking natural logarithms, it's found that it will take approximately 18 years for the population to reach 39,400.
Explanation:
Population Growth Calculation
To calculate how long it will take for a town's population of 20,000 to grow to 39,400 with an annual growth rate of 4%, we can use the formula for exponential growth:
P(t) = P_0 × (1 + r)^t
where:
P(t) is the future population
P_0 is the initial population
r is the growth rate (expressed as a decimal)
t is the time period in years
Starting with 20,000 people and wanting to get to 39,400:
39400 = 20000 × (1 + 0.04)^t
To solve for t, we need to:
Rewrite the equation as: (1 + 0.04)^t = 39400 / 20000
Take the natural logarithm of both sides: ln((1 + 0.04)^t) = ln(39400 / 20000)
Simplify: t × ln(1 + 0.04) = ln(1.97)
Divide by ln(1 + 0.04) to isolate t: t = ln(1.97) / ln(1.04)
Use a calculator to find the numerical value for t.
When calculated, t is approximately 18 years. Therefore, it will take roughly 18 years for the town's population to grow from 20,000 to 39,400.
Work out the equation of the line which passes through the point (1,-2)and is parallel to the point y=x+4
Answer:
y = x - 3
Step-by-step explanation:
Basically, if the lines are parallel, they have the same slope, right? So that part is already complete
And to get the rest of the equation, plug in the points -2 and 1 into the equation for the x values. Then set the equation to solve for b
After you do that you should get b = -3
The slope is 1 and the y-int is -3
Thank me later ;)
a building measure 8.4m wide by 9.3 the rest is in picture
Answer:
26.309932 MN if gravity was normal gravity force and on basis salt water was 1030 kg/m3
Step-by-step explanation:
The rule below is something I just found.
To calculate the force of gravity of an object, use the formula: force of gravity = mg, where m is the mass of the object and g is the acceleration of the object due to gravity. Since g is always 9.8 m/s^2, just multiply the object's mass by 9.8 and you'll get its force of gravity
5/3 to the power of 3
Suppose y varies directly with x. Write an equation if y=75when x=25
Answer:
y = 3x
Step-by-step explanation:
The standard format of a directly proportional equation goes by the format of y = k × x. The question asks us to write an equation if y = 75 when x = 25 and y varies directly with x.
So we substitute the values y = 75 and x = 25 in the equation y = k × x
K = constant, we have to work this out
75 = k × 25
75 ÷ 25 = k
k = 75 ÷ 25
k = 3
k = 3 So then we put this back into the original y = k × x to find our final equation which is y = 3x
Wilson is 6 years older than Mary. Wilson's age is 10 years less than five times Mary's age. The equations below model the relationship between Wilson's age (w) and Mary's age (m):
w = m + 6
w = 5m - 10
Which is a possible correct method to find Wilson's and Mary's ages?
Solve W + 6 = 5w - 10 to find the value of w.
Write the points where the graphs of the equations intersect the x axis.
Solve m + 6 = 5m - 10 to find the value of m.
Write the points where the graphs of the equations intersect the y axis.
Final answer:
The correct method to find Wilson's and Mary's ages with the given equations is to solve the equation m + 6 = 5m - 10 by substitution, which will give you the value of Mary's age (m). After finding m, you can then solve for Wilson's age (w).
Explanation:
Among the provided methods to find Wilson's and Mary's ages based on the given equations w = m + 6 and w = 5m - 10, the correct approach is to solve m + 6 = 5m - 10 to find the value of m, Mary's age. This is due to the fact that by substituting the expression for w from the first equation into the second, we isolate m and solve for it directly. Here is how you'd solve it step by step:
First, substitute w from the first equation into the second equation, resulting in m + 6 = 5m - 10.
Next, rearrange the terms to get all the m terms on one side: 5m - m = 10 + 6.
Then, simplify to find that 4m = 16.
Last, divide both sides by 4 to get m = 4.
Once you have m, substitute it back into either of the original equations to find w. In this case, w = 4 + 6 = 10.
Graphical solutions involving the x or y axis do not apply directly to solving the system of equations and are therefore not correct methods for this particular problem.
Janell has a 10 inch by 12 inch photograph. She wants to scan the photograph
Complete Question:
Janeel has a 10 inch by 12 inch photograph. She wants to scan the photograph, then reduce the results by the same amount in each dimension to post on her Web site. Janeel wants the area of the image to be one eight of the original photograph. Write an equation to represent the area of the reduced image. Find the dimensions of the reduced image.
Correct Answer:
A) [tex](10-x)(12-x)=15[/tex]
B) Dimensions are : Length = 10-x = 3 inch , Breadth = 12-x = 5 inch
Step-by-step explanation:
a. Write an equation to represent the area of the reduced image.
Let the reduced dimensions is by x , So the new dimensions are
[tex]length=10-x\\breadth=12-x[/tex]
According to question , Area of new image is :
⇒ [tex]Area = \frac{1}{8}Length(breadth)[/tex]
⇒ [tex]Area = \frac{1}{8}(10)(12)[/tex]
⇒ [tex]Area = 15[/tex]
So the equation will be :
⇒ [tex](10-x)(12-x)=15[/tex]
b. Find the dimensions of the reduced image
Let's solve : [tex](10-x)(12-x)=15[/tex]
⇒ [tex]120-10x-12x+x^2=15[/tex]
⇒ [tex]120-22x+x^2=15[/tex]
⇒ [tex]x^2-22x+105=0[/tex]
By Quadratic formula :
⇒ [tex]x = \frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
⇒ [tex]x = \frac{22 \pm8 }{2}[/tex]
⇒ [tex]x = \frac{22 +8 }{2} , x = \frac{22 -8 }{2}[/tex]
⇒ [tex]x = 15 , x =7[/tex]
x = 15 is rejected ! as 15 > 10 ! Side can't be negative
⇒ [tex]x =7[/tex]
Therefore, Dimensions are : Length = 10-x = 3 inch , Breadth = 12-x = 5 inch
BRAINLIEST!!!!
5. Graph the given relation or equation and find the domain and range. Then determine whether the relation or equation is a function.
(3.9, 5.9), (–1.1, 5.9), (–4.1, 3.9), (–4.1, –2.1)
Given:
Given that the coordinates are (3.9, 5.9), (–1.1, 5.9), (–4.1, 3.9), (–4.1, –2.1)
We need to determine domain and range and also find whether the relation is a function.
Domain:
The domain is the set of all independent x - values.
Thus, we have;
[tex]Domain=\{3.9,-1.1,-4.1\}[/tex]
Thus, the domain is {3.9,-1.1,-4.1}
Range:
The range is the set of all dependent y - values.
Thus, we have;
[tex]Range=\{5.9,3.9,-2.1\}[/tex]
Thus, the range is {5.9,3.9,-2.1}
Function:
We need to determine whether the given relation is a function.
For a relation is said to be a function, if every value of x has only one image in the y - coordinate.
After plotting the graph, it is obvious that the x - value -4.1 has two images 3.9 and 2.1
Hence, the given relation is not a function.
Lance bought 12 quarts of lemonade so that everyone who came to his party could have exactly 1/3 quart. How many people did Lance invite to his party?
Lance invited 36 people to his party.
Step-by-step explanation:
It is given that,
Lance bought 12 quarts of lemonade.Everyone who came to his party could have exactly 1/3 quart.We know that,
The total quarts of lemonade available for the party = 12
Each person in the party consumes = 1/3 quart.
We need to find out how many people did Lance invited to his party.
To find the number of people :
Let us consider 'x' be the number of people invited to the party.
Total lemonade = number of people × lemonade for each person.
⇒ 12 = x × 1/3
⇒ 12×3 = x
⇒ x = 36 people
Therefore, Lance invited 36 people to his party.
Please helpppppp!!!!
Answer:
A. -34.5>x
Step-by-step explanation:
The area is shaded below -34.5, so we know that x has to be less
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x
is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.
x + y = 24
3x + 5y = 100
What does the solution of this system indicate about the questions on the test?
O
The test contains 4 three-point questions and 20 five-point questions.
The test contains 10 three-point questions and 14 five-point questions.
The test contains 14 three-point questions and 10 five-point questions.
The test contains 20 three-point questions and 8 five-point questions.
O
Answer:
The test contains 10 three-point questions and 14 five-point questions.
Step-by-step explanation:
x + y = 24
3x + 5y = 100
Try elimination.
-3x - 3y = - 72
2y = 28
y = 14
Then x = 10
So, we have 10 3-point problems and 14 5-point problems.
Mark and his three friends ate out at Applebee’s. Their bill totaled $104.70. If they left the server a 20% tip, how much would each person pay splitting the bill evenly?
Answer:
$31.41!
Step-by-step explanation:
5 liters at $15.25
x liters at $33.55
Answer:
x=2
Step-by-step explanation:
shdhvejsjheuhchsjcyhejc7738
Answer:
11
Step-by-step explanation:
divide 5 and 15.25
then multiply by 33.55
Factor as the product of two binomials.
X^2 – 10x + 21
The requried expression of the given expression which is a product of two binomials is (x - 3)(x - 7).
What is a polynomial function?A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial, and trinomial, etc. ax+b is a polynomial.
Here,
Given expression,
x² - 10x + 21 = 0
In order to factor the above expression in two binomial expressions, split the 10x in two where the multiplication of two numbers produces 21 and their difference produces -10x,
So,
y = x² -7x -3x + 21
y= x(x - 7) - 3 (x - 7)
y = (x - 3)(x - 7)
Thus, the requried expression of the given expression which is a product of two binomials is (x - 3)(x - 7).
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The Sum of The Angles in a Triangle
Answer:
A=20Step-by-step explanation:
180-110=70
90+70=160
180-160=20
Answer:
20°
Step-by-step explanation:
We know that the exterior angle of a triangle is equal to the sum of interior opposite angles.
<B + <A = <C
90° + <A = 110°
<A = 110° - 90°
<A = 20°
There are 18 offensive players on the hockey team. How many ways can the coach choose a left wing, center, and right wing to start the game?
Answer:
4896 ways
Step-by-step explanation:
We have a total of 18 players, and we want to form groups of three, where the order matters, because there are different roles for each player, so this is a permutation problem.
We solve this problem calculating a permutation of 18 choose 3:
P(18,3) = 18! / (18-3)! = 18! / 15! = 18 * 17 * 16 = 4896
So the coach has 4896 ways to choose the left wing, center and right wing.
Answer: There are 4,896 possible ways
Step-by-step explanation: If there are 18 offensive players on the hockey team, and there is a need to make a selection of three players for three different positions, that means each time you choose one player there is an 18 times 17 (18 x 17) other possibilities for the remaining players. If you choose the next player, there would now be a 17 times 16 (17 x 16) other possibilities for the remaining players, hence we need a formula for the arrangement of 3 players to be chosen from a total of 18.
From the first explanation, if we were to make an arrangement to choose all 18 players the permutation would be given as;
P = 18! (18 factorial)
Which is 18 x 17 x 16 x 15 x 14 x... x 1
However the permutation for selecting just 3 out of the 18 players is given as;
P = 18! ÷ 15!
And this results in;
P = 18 x 17 x 16
P= 4896
Therefore there are 4,896 possible ways
**Note that 18! divided by 15! leaves you with the possible arrangement for 3 persons which is explained as 18 x 17 x 16**
Y is equal to 6 less than the product of x and -1.if the output is -15 what is the input
Choose which one that doesn't belong.
1/20, 20/25, 2/3, 5/4
Explain why you chose the answer above.
Th fraction that does not belong is 5/4.
This is because it is an improper fraction while the others are proper fractions.
A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number belowan example of a fraction = [tex]\frac{2}{9}[/tex]
2 is the numerator while 9 is the denominator A proper fraction is a fraction is which the numerator is smaller in value than the denominator.An example is [tex]\frac{1}{20}[/tex]An improper fraction is a fraction in which the numerator is greater in value than the denominator An example is [tex]\frac{5}{4}[/tex]To learn more about improper fractions, please check : https://brainly.com/question/14549871?referrer=searchResults
Write the slope-intercept form equation of the line that passes through (-2, 3) and (1,-4).
Answer:
y = -7/3 x -5/3
Step-by-step explanation:
We first need to find the slope
m = (y2-y1)/(x2-x1)
=(-4-3)/(1--2)
= (-4-3)/(1+2)
=-7/3
Slope intercept form of a line is
y=mx+b
y = -7/3x +b
Using the point (-2,3)
3 = -7/3(-2)+b
3 = 14/3 +b
Subtract 14/3 from each side
9/3 -14/3 =b
-5/3
y = -7/3 x -5/3
Answer:
[tex]\frac{-7}{3}[/tex]
Step-by-step explanation:
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
plug in the factors given,
[tex]\frac{-4-3}{1--2}[/tex]
then simplify
[tex]\frac{-7}{3}[/tex]