Meirke turns on the water full blast to fill the bath tub with water, then turns off the water when he hears his phone ring. He goes and answers the quick phone call and returns to the bathroom and turns on the water again. He once again gets distracted and goes off to text with his friends for a while, remembering to turn off the water to prevent a water disaster. He then comes back to the bath tub and the water is now all cold. He decides to pull the plug which slowly drains all the water out of the tub. Pick the graph that best describes this situation of water level in the tub.
Answers
Meirke turns on the water full blast to fill the bathtub with water.
Expect an increasing slope here.
Then turns off the water when he hears his phone ring.
Expect a zero slope (flat curve) here since he turned off the tap.
He goes and answers the quick phone call and returns to the bathroom and turns on the water again.
Again, expect an increasing slope here.
He once again gets distracted and goes off to text with his friends for a while, remembering to turn off the water to prevent a water disaster.
Again, expect a zero slope (flat curve) here since he turned off the tap.
He then comes back to the bathtub and the water is now all cold. He decides to pull the plug which slowly drains all the water out of the tub.
Expect a decreasing slope (less steep) here.
The 1st and 3rd graph is straight away incorrect since they match up the above situation.
The 2nd and 4th graphs match with the above situation.
The 4th graph shows a steeper slope meaning that water drains very fast so it is also incorrect.
Only the 2nd graph is correct since it exactly follows the situation.
1. increasing slope
2. zero slope (flat curve)
3. increasing slope
4. zero slope (flat curve)
5. decreasing slope (less steep, slowly drains)
Therefore, the 2nd graph best describes this situation of water level in the tub.
Related Questions
Three-fourths of the yard is covered with grass and one-fourth is used as a garden. The sprinkler could only water 1/5 of the yard, so the rest died. Use the model to find out how much of the grass died.
Answers
3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.
Let's start by breaking down the information given:
- Three-fourths of the yard is covered with grass.
- One-fourth of the yard is used as a garden.
- The sprinkler could only water 1/5 of the yard.
To find out how much of the grass died, we need to determine the portion of the grass that was not watered by the sprinkler.
Let's assume the total area of the yard is represented by the value 1. Therefore, we can calculate the area of the grass as 3/4 of the total yard, which is (3/4) * 1 = 3/4.
The sprinkler can only water 1/5 of the yard, so the portion of the grass that was watered is (1/5) * (3/4) = 3/20.
To find the portion of the grass that died, we subtract the watered portion from the total grass area:
Portion of grass that died = (3/4) - (3/20) = 15/20 - 3/20 = 12/20.
Simplifying, we get:
Portion of grass that died = 3/5.
Therefore, 3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.
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Two-fifths of Aika’s stamp collection are European stamps.
One-half of her European stamps are from France.
What fraction of Aika’s stamps are from France?
1. 4/5
2. 1/5
3. 1/10
4. 3/10
Answers
Answer:
2. ⅕
Step-by-step explanation:
⅖ = European (½) = 2/10 = ⅕
Watch help video
In AUVW, the measure of
represents the cosine of
Answers
Answer:
80/89
Step-by-step explanation:
Select the values that make the inequality -q> -7 true. Then write an equivalent inequality, in terms of q. (Numbers written in order from least to greatest going across.)
Answers
The inequality relation -q > -7 can be represented in the form of q as q < 7
The numbers in set A = { -8 , -7.1 , -7 , -6.9 , -6 , -2 , 0 , 2 , 6 , 6.9 }
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be A
The value of A is - q > - 7
Now , multiplying by (-1) on both sides of the equation , we get
( -1 ) ( -q ) > ( -1 ) ( - 7 )
The inequality relation will change the sign from > to < and ,
q < 7
So , the value of the inequality relation A is q < 7
Now , all the values in the number line which satisfy the inequality equation q < 7 are given in set A
The numbers in set A = { -8 , -7.1 , -7 , -6.9 , -6 , -2 , 0 , 2 , 6 , 6.9 }
Hence , The inequality relation -q > -7 can be represented in the form of q as q < 7 and numbers in set A = { -8 , -7.1 , -7 , -6.9 , -6 , -2 , 0 , 2 , 6 , 6.9 }
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4.1 Exponential Functions
189
Work these problems. (See Example 5.)
37. Finance If money loses value, then as time passes, it takes
more dollars to buy the same item. Use the results of Exercise
36(a) to answer the following questions.
(a) Suppose a house costs $105,000 today. Estimate the cost of
the same house in 10 years. (Hint: Solve the equation
.74t =
$105,000.)
(b) Estimate the cost of a $50 textbook in 8 years.
Answers
we can estimate the cost of a $50 textbook in 8 years to be approximately $32.78.
What is logarithms?
Logarithms are mathematical functions that are used to solve equations involving exponents. Specifically, a logarithm is the inverse operation of exponentiation. Just as exponentiation involves raising a base to a power, logarithms involve finding the power to which a base must be raised to produce a given value.
The logarithm of a number y with respect to a base b is written as logb y, and it is defined as the exponent to which the base b must be raised to produce the number y. In other words, if \(b^x = y\), then logb y = x.
According to the question:
In Exercise 36(a), we found that the value of a dollar decreases by 26% over 5 years. We can use this information to answer the following questions:
(a) To estimate the cost of the same house in 10 years, we need to solve the equation:
0.74t = 105,000
where t is the time in years. Solving for t, we get:
\(t = log(105,000) / log(0.74) = 17.9\)
So it will take approximately 17.9 years for the value of the dollar to decrease by 26% enough to make the $105,000 house cost the same as it does today. Therefore, we can estimate the cost of the same house in 10 years to be:
\($105,000 * (1 / 0.74)^(10/17.9) = $211,775.22\)
(b) To estimate the cost of a $50 textbook in 8 years, we need to find the value of k in the exponential function:
\(V(t) = V(0) * e^kt\)
where V(0) is the initial value (in this case, $50), t is the time in years, and V(t) is the value after t years. We know that the value of a dollar decreases by 26% over 5 years, so we can use this information to find k:
\(0.74 = e^(k*5)\)
Taking the natural logarithm of both sides, we get:
ln(0.74) = 5k
Solving for k, we get:
k ≈ -0.064
So the exponential function for the value of a dollar over time is:
\(V(t) = $50 * e^{-0.064t}\)
To estimate the cost of the textbook in 8 years, we can plug in t = 8 into this function and solve:
\(V(8) = $50 * e^{-0.064*8} = $32.78\)
Therefore, we can estimate the cost of a $50 textbook in 8 years to be approximately $32.78.
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A pair of equations is shown below:
y = 7x − 9
y = 3x − 1
Part A: In your own words, explain how you can solve the pair of equations graphically. Write the slope and y-intercept for each equation that you will plot on the graph to solve the equations. (6 points)
Part B: What is the solution to the pair of equations? (4 points)
Answers
If you graph y=7x-9 and y=3x-1 the two lines will intersect at one point. That is how you graphically "solve" the system of equations.
Both of these lines are of the form y=mx+b where m is the slope and b is the y-intercept.
So for y=7x-9, the slope is 7 and the y-intercept is -9
For y=3x-1, the slope is 3 and the y-intercept is -1
....
The solution for this system occurs when both coordinates are equal to each other so we can say:
7x-9=3x-1 subtract 3x from both sides
4x-9=-1 add 9 to both sides
4x=8 divide both sides by 4
x=2, making y=3x-1 become:
y=3(2)-1=6-1=5, so the solution to the system of equations is:
(2,5)
Answer:
Part A: If you graph the pair of equations shown above both lines will intersect at one point and that is how you would solve the system of equations graphically. The y intercept and slope for each equation would be for y = 7x − 9 it would have a slope of 7 and y intercept of -9 and y = 3x − 1 would have a slope of 3 and y intercept of -1.
Part B:The solution to the pair of equations is (2,5)
Which expression is equival 81 1/3?
Answers
Answer: 3^3 Square root 3
Step-by-step explanation:
CAN ANYONE HELP ANSWER THIS
Answers
9514 1404 393
Answer:
58
Step-by-step explanation:
The marked points on the graph show that the number of hot cocoas sold decreases by 6 when the temperature goes up by 6 degrees. That is, the line has a slope of -1. The y-intercept is 100, so the equation of the line can be written as ...
y = mx +b . . . . . line with slope m and y-intercept b
y = -x +100
Then for x = 42, the expected value of y is ...
y = -42 +100 = 58
Mei Mei can expect to sell 58 hot cocoas on a day when the high is 42°F.
A store is having a sale on jelly beans and almonds. For 3 pounds of jelly beans and 5 pounds of almonds, the total cost is $27. For 9 pounds of jelly beans and
7 pounds of almonds, the total cost is $51. Find the cost for each pound of jelly beans and each pound of almonds.
Cost for each pound of jelly beans:
Cost for each pound of almonds:
Answers
Answer:
Cost for each pound of jelly beans: $2.75
Cost for each pound of almonds: $3.75
Step-by-step explanation:
Let J be the cost of one pound of jelly beans.
Let A be the cost of one pound of almonds.
Using the given information, we can create a system of equations.
Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:
\(\implies 3J + 5A = 27\)
Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:
\(\implies 9J + 7A = 51\)
Therefore, the system of equations is:
\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)
To solve the system of equations, multiply the first equation by 3 to create a third equation:
\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)
\(9J+15A=81\)
Subtract the second equation from the third equation to eliminate the J term.
\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)
Solve the equation for A by dividing both sides by 8:
\(\dfrac{8A}{8}=\dfrac{30}{8}\)
\(A=3.75\)
Therefore, the cost of one pound of almonds is $3.75.
Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.
Using the first equation:
\(3J+5(3.75)=27\)
\(3J+18.75=27\)
\(3J+18.75-18/75=27-18.75\)
\(3J=8.25\)
\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)
\(J=2.75\)
Therefore, the cost of one pound of jelly beans is $2.75.
Find the area of the triangle.
b ft
h yd
Question content area bottom
Part 1
The area of the triangle is
enter your response here or
enter your response here .
Answers
The area of the triangle is 52.32 square units
Finding the area of the trianglefrom the question, we have the following parameters that can be used in our computation:
The triangle (see attachment)
The base of the triangle is calculated as
base = 12 * tan(36)
The area of the triangle is then calculated as
Area = 1/2 * base * height
Where
height = 12
So, we have
Area = 1/2 * base * height
Substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * 12 * tan(36) * 12
Evaluate
Area = 52.32
Hence, the area of the triangle is 52.32 square units
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Please help me in this math problem
Answers
Answer:
Step-by-step explanation: well, you will more than likely get it at least 60%-80% of the time! If this doesn't help i can try to explain in a lot more detail unless someone does for me!
Ifx-10 is a factor of x2 - 8x - 20, what is the other
factor?
x +
Answers
Answer:
\( f(x) = x^2 -8x -20\)
We know that one factor is (x-10). We know that we need to find two values that added we got -8 and multiplied we got -20. So then we can set the following options:
\( a(10) = -20\)
\( a-10= -8\)
And solving for a we got:
\( a = -8+10=-2\)
And we got:
\( a = -2\)
So then the other factor would \( x +2\)
Step-by-step explanation:
For this case we have the following expression:
\( f(x) = x^2 -8x -20\)
We know that one factor is (x-10). We know that we need to find two values that added we got -8 and multiplied we got -20. So then we can set the following options:
\( a(10) = -20\)
\( a-10= -8\)
And solving for a we got:
\( a = -8+10=-2\)
And we got:
\( a = -2\)
So then the other factor would \( x +2\)
Answer:
Step-by-step explanation:
Solve the equation below for x by graphing
3x =8_2x
Answers
The solution to the equation 3x = 8 - 2x is x = 1.6.
To solve the equation 3x = 8 - 2x by graphing, we can plot the two sides of the equation as functions of x and find the point(s) where they intersect. Here's a step-by-step explanation:
Express the equation in the form of y = f(x). Rearrange the equation:
3x + 2x = 8
5x = 8
x = 8/5 or 1.6
Graph the functions y = 3x and y = 8 - 2x on the same coordinate plane. The line represented by y = 3x is upward sloping, and the line represented by y = 8 - 2x is downward sloping.
Plot the points (1.6, 3(1.6)) and (1.6, 8 - 2(1.6)) on the graph.
The point of intersection represents the solution to the equation. In this case, the lines intersect at (1.6, 4.8).
Therefore, the solution to the equation 3x = 8 - 2x is x = 1.6.
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Which choice is equivalent to the quotient shown here when x > 0?
98x³+√72x²
O A. TV₂
OB. √26x
7x
O C. 7
6
OD. √98x3 - 72x²
Answers
Answer:
A.\( \frac{7}{6} \sqrt{x} \)
Step-by-step explanation:
Solution Given:
\( \sqrt{98{x}^{3} } \div \sqrt{72 {x}^{2} } \)
Bye using indices formula
\( \sqrt{x} \div \sqrt{y} = \sqrt{ \frac{x}{y} } \)
we get
\( \sqrt{ \frac{98{x}^{3} }{72 {x}^{2} } } \)
\( \sqrt{ \frac{49 {x}^{3} }{ 36 {x}^{2} } }\)
\( \sqrt{ \frac{{7}^{2} {x}^{3 - 2} }{{6}^{2} } } \)
\( \frac{7}{6} \sqrt{x} \)
A recipe calls for 1/2 cup of ingredient A for every 1 1/5
Cups of ingredient B. You use 4 cups of ingredient A.
How many cups of ingredient B do u need?
Answers
Answer:
You need 9 3/5 (9.6) cups of ingredient B
Step-by-step explanation:
Ingredient A. Ingredient B
1/2 cups. 1 1/5 cups = 6/5
4 cups. X
(Cross multiplication)
(4)*(6/5)/(1/2)
(24/5) * 2/1 = 48/5
NEED HELP QUICK!!! Ron is trying to find the LCM of 4 and 6. His work is shown at the right. What is Ron's mistake? Explain how to find the correct LCM of 4 and 6.
Answers
The LCM of 4 and 6 is 12.
What is Least Common Multiple?Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.
For example, common multiples of 4 and 6 are 12, 24 and 36, but the lowest of those is 12; therefore, the lowest common multiple of 4 and 6 is 12.
Given:
4: 2 x 2
6: 2 x 3
Now, as there is one 2 common in both then it will be written for one time.
and the rest uncommon numbers are written as same as well.
So, LCM( 4, 6)= 2 x 2 x 3 = 12
Hence, the LCM of 4 and 6 is 12.
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Increase 2,400 by 5%
Answers
Increasing 2400 by 5% gives us 2520
we can increase the value by using the formula:
\(initial value+ percentage increase *initial value\) = increased percentage
in the aforementioned question we have
initial value = 2400
percentage increase = 5%
thus we can find out the increased percentage by:
2400 + 2400 X (5/100)
=2400 + 120
=2520
the value by which 2400 is increased is 120
to arrive at the increased value which is 2520
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Sierra, an Event Planner for Hilton, has group medical insurance with an annual premium of $8,245. Her employer pays 74%. If she is paid semi monthly, a) what is her portion of the annual premium? b) her medical insurance deduction per pay period?
Answers
9514 1404 393
Answer:
$2,143.70$89.32Step-by-step explanation:
If 74% is paid by Hilton, then Sierra pays 26% of $8245 per year. Her annual share is ...
0.26 × $8245 = $2143.70 . . . Sierra's share
__
Then the deduction in each of her 24 pay periods is ...
$2143.70/24 = $89.32 . . . per pay period
Which expression is equivalent to
2(a + 4b) + 5 + 7b + 6
A) 2a + 15b + 11
B) 6a + 12b + 6
C) 6a + 7b + 11
D) 2a + 11b + 11
Answers
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 0 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 10. There are two dots above 1 and 4. There are three dots above 2 and 5. There are 4 dots above 3.
Which of the following is the best measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 3.
The IQR is the best measure of variability, and it equals 9.
The range is the best measure of variability, and it equals 3.
The range is the best measure of variability, and it equals 9.
Answers
The range is the best measure of variability for this data, and its value is 4.
Which of the following is the best measure of variability for the data, and what is its value?The line plot displays the number of roses purchased per day at a grocery store, with the data values ranging from 0 to 4 (since there are no dots above 4).
The best measure of variability for this data is the range, which is the difference between the maximum and minimum values in the data set. In this case, the minimum value is 0 and the maximum value is 4, so the range is:
Range = Maximum value - Minimum value = 4 - 0 = 4
Therefore, the range is the best measure of variability for this data, and its value is 4.
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Alice and Bob each have a certain amount of money. If Alice receives n dollars from Bob, then she will have 7 times as much money as Bob. If, on the other hand, she gives n dollars to Bob, then she will have 2 times as much money as Bob. If neither gives the other any money, what is the ratio of the amount of money Alice has to the amount Bob has?
Answers
The ratio of the amount of money Alice has to the amount Bob has is approximately 3.36 : 1.
How to find the ratio of money ?According to the problem, two equations can be set up:
If Alice receives n dollars from Bob, then she will have 7 times as much money as Bob. This gives us the equation:
A + n = 7(B - n)
If Alice gives n dollars to Bob, then she will have 2 times as much money as Bob. This gives us the second equation:
A - n = 2(B + n)
We can rearrange these equations to make them easier to solve:
8n = 7B - A
3n = A - 2B
Setting these equal to each other, since they are both equal to 24n, gives:
21B - 3A = 8A - 16B
37B = 11A
A / B = 37 / 11
= 3. 36
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Find the length of x. (show your work)
Answers
What is the correlation between the x and y variables? y increases as x decrease y is constant y decreases as x increases y increases as x increases
Answers
when the value of x increases, the value of y remains the same
implies that the graph is a horizontal line and the value of y remains unchanged.
this is valid from the graph point of view.
but it really depends on the value of x.
y = x implies an equal increase or decrease of both variables.
Given the equation x - 6= 0, what is thevalue of x?
Answers
Solve for x:
Add 6 to both sides:
\(\begin{gathered} x-6+6=+6 \\ x=6 \end{gathered}\)Sarah needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 4.25 hours and charged her $54 for parts. The total was $585.25. Write and solve an equation which can be used to determine
x
x, the cost of the labor per hour.
Answers
Answer:
See below
Step-by-step explanation:
$ (585.25 -54) / 4.25 hr = x = $ 125 / hr
What’s the value of 2/3 * 1/8
Answers
Answer:
The simplified value is 1/12.
Step-by-step explanation:
Since we need to multiply these fractions, we can just multiply the numerators and denominators together in order to find the answer.
2/3 x 1/8 =
2/24 =
1/12
Therefore, the simplified value is 1/12.
Hope this helps! :D
Help me plssssss I suck at this
Answers
Answer: 7
Step-by-step explanation:
Answer:
35 more bottles than bags of popcorn
Step-by-step explanation:
Simply multiply both 14 and 21 by 5 and then subtract the larger number by the smaller one and you get your answer
Find the value of the expression (4x – 12) + (xy – 5) when x=6 and y = 2
Answers
Answer:
19
Step-by-step explanation:
Let us solve the parenthesis first according to PEDMAS (Parenthesis, Exponent, which ever comes first from left to right Multiplication and Division, which every comes first from left to right Addition and Subtraction.)
x=6, y=2
4x-12
Substitute using the given values
4*6 - 12 = 24 - 12 = 12
xy - 5
Substitute using the given values
6*2 - 5 = 12 - 5 = 7
Add up the two answers because we need to find the value of (4x - 12) + (xy - 5)
12 + 7 = 19
The answer is 19
Hope this helps :)
Have a nice day!
what is the following quotient? 1/1+sqrt3
Answers
Answer:
4 answer
Step-by-step explanation:
The quotient 1 / (1 + √3) is (- 1 +√3) / 2.
Option D is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
1 / (1 +√3)
Rationalize the denominator.
1 / (1 +√3) x (1 -√3) / (1 -√3)
{ a² - b² = (a + b) (a - b) ]
(1 -√3) / (1 - 3)
(1 -√3) / -2
-(1 -√3) / 2
(- 1 +√3) / 2
Thus,
The final expression is (- 1 +√3) / 2
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I GIVEEEE BRAINLILST
Answers
Answer:
its a scale factor of 4
Step-by-step explanation: