Comparing the number of same-size bottles drank to the amount of ounces of water consumed. So, option c is correct.
What is meant by constant rate of change?When the ratio of the output to the input stays constant at every given point along the function, the rate of change is said to be constant. A linear function's change will occur at a steady rate.
Comparing the number of same-size bottles drank to the amount of ounces of water consumed.
We say there is a constant rate of change when a quantity varies uniformly in relation to the change of another quantity.
Therefore, there is a constant rate of change if one quantity is directly proportionate to the other.
The number of identical-sized bottles drank is directly proportionate to the number of ounces of water consumed. As a result, the rate of change in water ounces in relation to the quantity of identical-sized bottles is constant. The quantity of the remaining alternatives are not directly proportionate to one another.
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How do I take an antiderivative of the following equation?
[tex]dy/dx+ky-77k=0[/tex]
The required anti derivative of given function is -(ky^2)/2 + 77ky.
What is integration(anti-derivative)?Anti-differentiation or integration is the converse interaction to separation. For instance, if f (x) = 2x, we realize that this is the subordinate of f(x) = x^2.
According to question:We have,
dy/dx +ky - 77k = 0
dy/dx = -ky + 77k
Integrate with respect to x
∫dy/dx = ∫(-ky + 77k)
∫dy/dx = -∫ky +∫77k
y = -(ky^2)/2 + 77ky
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The required antiderivative is [tex]y=e^{-(kx+c)} +77[/tex]
What is antiderivative?
In calculus, a differentiable function F whose derivative is identical to the original function f is known as an antiderivative, inverse derivative, primitive function, primitive integral, or indefinite integral of a function f. F' = f can be used to represent this.
[tex]\frac{dy}{dx} = 77k - ky\\\\dx=\frac{dy}{77k-ky} \\\\dx = \frac{dy}{77-y} \times \frac{1}{k} \\\\kdx = \frac{dy}{77-y} \\\\-\frac{dy}{y-77} =kdx\\\\log(y-77)=-(kx+c)\\\\y=e^{-(kx+c)} +77[/tex]
Hence, The required antiderivative is [tex]y=e^{-(kx+c)} +77[/tex]
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Liam works at a zoo. He was looking at some data showing the masses of their
5
55 African elephants. The mean mass of the elephants was
3
,
800
kg
3,800kg3, comma, 800, start text, k, g, end text, and the median mass was
3
,
600
kg
3,600kg3, comma, 600, start text, k, g, end text. The smallest elephant, named Lola, weighed
2
,
700
kg
2,700kg2, comma, 700, start text, k, g, end text.
Lola then got very sick and lost weight until her mass reached
1
,
800
kg
1,800kg1, comma, 800, start text, k, g, end text.
How will Lola's mass decreasing affect the mean and median?
Median won't change, however Mean will fall by 180.
What do mean and median?By summing all the numbers in a data collection and dividing by the total number of values in the set, one may get the mean (average) of the data set. When a data collection is sorted from least to largest, the median represents the midpoint value.
African elephants total 555 in number.
Elephants had a 3800 kg average mass.
Elephants had a 3600 kg median mass.
Lola, the elephant that was the smallest, weighed 2700 kg.
Later, Lola became really ill and lost a lot of weight, reaching a mass of 1800 kg.
What effect will Lola's weight loss have on the mean and median as well as Currently, the median is 3600 and the lowest is 2700.
now 2700 becomes 1800
so Median remains the same as 3600
No change in Median
The mean mass of the elephants was 3800 kg
=> total weight = 5 x 3800 = 19000 kg
2700 kg becomes 1800 kg
Hence new total mass = 19000 - 2700 + 1800 = 181000 kg
New Mean = 18100/5 = 3620 kg
Mean reduced by 3800 - 3620 = 180 kg
No change in Median weight
Mean reduced by 180 kg
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From the graph, estimate what numbers should go into the empty cells in the first two columns. Do not complete the columns on the right of the dividing line.
The first two columns of the table, considering logarithms, are completed as follows:
2 - 10^0.3.5 - 10^0.7.9 - 10^(0.95).4 - 10^(0.6).2.51 - 10^(0.4).How to complete the table?The table is completed in this problem applying the logarithms.
This is because on the first column we had that:
10^(0.3) = 2, which means that log10(2) = 0.3.
(log10(x) represents the logarithm of base 10 of x).
For the second row, the decimal approximation is found applying the power of 10^0.7, hence:
10^0.7 = 5.
For the third and fourth rows, to obtain the power of 10 expression, we need to calculate the logarithms of these numbers, as follows:
log10(9) = 0.95.log10(4) = 0.6.Hence the power of 10 expressions are given as follows:
9 = 10^(0.95).4 = 10^(0.6).For the fifth row, we just need to calculate the exponential expression, hence:
10^(0.4) = 2.51.
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help meeeeeeeeeee pleaseee
(a) 794g of the initial sample will be left in the sample after 25 years. (b) Time taken to decay to half of its original amount is 3.39 years.
Isotopes(200g) are atoms that have the same number of protons in their nucleus, but a different number of neutrons. This means that they have the same atomic number, but a different atomic mass. Because of this, isotopes have different physical and chemical properties. Isotopes can be stable, meaning that they do not undergo radioactive decay, or they can be unstable, meaning that they will undergo radioactive decay over time.
(a) Substituting 25 for t in the expression, we get:
[tex]A(25) = 200e^{0.0541 \times 25}[/tex]
[tex]= 200e^{1.3525}[/tex]
Thus, after 25 years, there will be
[tex]200e^{1.3525} = 2003.97[/tex]
794 g of the initial sample left in the sample.
(b) We want to find t such that
[tex]A(t) = 200e^{0.0541}[/tex]
= 100.
Solving for t, we get:
[tex]= 200e^{0.0541} \times t=100[/tex]
Dividing both sides by 200 and applying the natural logarithm to both sides, we get:
0.0541 × t = ln(0.5)
Therefore,
[tex]t = \frac{ln(0.5)}{0.0541}[/tex]
= 3.39 years.
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ABCD is a rhombus and side AE Is congruent to EC prove triangle AEB is congruent to CEB
ABCD is a rhombus and side AE Is congruent to EC. Then triangle AEB is congruent to CEB.
What is a rhombus?A rhombus is one type of parallelogram and has 4 sides and 4 vertices.
Every side is equal in length and opposite angles are equal.
Given that the side AE is congruent to EC of rhombus.
That means, AE ≅ EC.
And the diagonals of rhombus bisects each other.
Both the triangle AEB and triangle CEB share the same side which is BE.
That means BE ≅ BE, by the reflexive property.
And the sides AB and BC are the sides of rhombus.
So, AE ≅ BC.
Therefore, if ABCD is a rhombus and side AE Is congruent to EC. Then triangle AEB is congruent to CEB.
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Gina puts $ 4500 into an account earning 7.5% interest compounded continuously. How long will it take for the amount in the account to grow to $ 5150?
Time in years =
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5150\\ P=\textit{original amount deposited}\dotfill & \$4500\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ t=years \end{cases}[/tex]
[tex]5150=4500e^{0.075\cdot t} \implies \cfrac{5150}{4500}=e^{0.075t}\implies \cfrac{103}{90}=e^{0.075t} \\\\\\ \log_e\left( \cfrac{103}{90} \right)=\log_e(e^{0.075t})\implies \log_e\left( \cfrac{103}{90} \right)=0.075t \\\\\\ \ln\left( \cfrac{103}{90} \right)=0.075t\implies \cfrac{\ln\left( \frac{103}{90} \right)}{0.075}=t\implies\stackrel{\textit{about 1 year and 291 days}}{ 1.8\approx t}[/tex]
If ABTS = AGHD, BS = 25, IS = 14, BT = 31, GD = 4x - 11, m2S = 56, mLB = 21°, and mLH = (7y + 5)°, find the values of x and y.
Answer:
x = 8
y = 2
Step-by-step explanation:
Evaluate the following:
Logc1 = ?
The given logarithmic expression can be evaluated as Logc1 = 0.
What is Logarithm?Logarithm function is defined as the inverse of the exponential function.
If a^(b) = c, then b = log(c) at the base of a.
Logarithm of any number is always positive.
For negative numbers, the logarithm are complex numbers.
The given expression is Logc1.
It implies that it is the logarithm of 1 with c as a base.
Sine, the logarithm of 1 to any base is equal to zero, the given expression can be evaluated as follows,
Logc1 = 0
Hence, the value of the given expression is 0.
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Cailen needs at least $150 to buy an X-box. She earns $15 for each lawn she mows and has $30 in savings. Write an inequality to determine how many lawns Cailen must mow to buy an x-box. How many lawns must she mow to buy the x-box?
total = 15x + 30
EDIT: She has to mow 8 lawns. I didn't read the question
there you go its that simple
olivia wants to have a 90 average in algebra, where tests count for 55%, quizzes count for 30% and homework counts for 15%.If she has a 92 test average and 100% HW average, what must her quiz average be? Let x = the average of the
Olivia wants to have a 90 average in algebra, where tests count for 55%, quizzes count for 30% and homework counts for 15%. The quiz average is 82%.
What do you mean by Average?It is forming the outcome of multiplying the total of multiple quantities by their sum and then dividing this result by the number of quantities
Given,
She has test count = 55%,
quizzes count = 30%,
homework counts = 15%
If she had
test count = 92%
Homework counts = 100%
quizzes count = ?
Let x be the test count
x = (90 - (0.55(92) + 0.15(100)))/0.30x
= 82
Olivia must have an 82 average on quizzes in order to have a 90 average in algebra.
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A table of 1,022 guests are attending a reception. If each table can seat exactly 12 people,what is the least number of tables needed to seat all guests?
Answer:
86
Step-by-step explanation:
If you did 1,022 divided by 12, you would get something crazy like 85.16666666666. So round up.
Three times the quantity of a number c increased by 7 is equal to the same number, c, decreased by 15
After solving the given equation, we know that the value of c is -11.
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.
As in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others.
Let's learn more about math equations in this tutorial.
The three primary forms of linear equations are point-slope, standard, and slope-intercept.
Sc, we have the equation:
3c + 7 = c - 15
Now, calculate this equation for c as follows:
3c + 7 = c - 15
3c - c = -15 - 7
2c = -22
c = -22/2
c = -11
Therefore, after solving the given equation, we know that the value of c is -11.
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Three times the quantity of a number c increased by 7 is equal to the same number, c, decreased by 15. What is c in this situation?
x^-3=1/343 what does x equals please show all work.
Answer:
Step-by-step explanation:
X^-3=1/343
X^-3=1/7^3
X^-3=7^-3
Since the powers are equal, the bases should also be equal.
Therefore, X=7
3. Diana uses 30 grams of coffee beans to
make 48 fluid ounces of coffee. When
company comes she makes 96 fluid ounces of coffee. How many grams of coffee
beans does Diana use when company comes?
A. 160
B. 60
C. 98.2
D. 14.4
Answer:
Step-by-step explanation:
The grams of coffee beans Diana uses when the company comes is:
62.5 grams
A container is a hemisphere of radius 30cm.
Sand fills the container at a rate of 4000 cm³ per minute.
Does it take less than a quarter of an hour to fill the container?
You must show your working.
Since the time is 0.24 hour. Yes, it takes less than a quarter of an hour to fill the container
How to determine if it takes less than a quarter of an hour to fill the container?Given: A container is a hemisphere of radius 30cm
Sand fills the container at a rate of 4000 cm³ per minute
A hemisphere is half a sphere. Thus:
The volume of a hemisphere = 1/2 × 4/3 πr³ = 2/3 πr³
The volume of a hemisphere = 2/3 × π × 30 = 56548.67 cm³
Rate = Volume / Time
Time = Volume/Rate
Time = 56548.67 /4000 = 14.14 minutes
In hours: Time = 14.14/60 = 0.24 hour
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Find a rectangular equation for the plane curve defined by the parametric equations.
X = t + 4, y = t^2 ; - ∞ < t < ∞
Answer:
[tex]y=x^2-8x+16[/tex]
Step-by-step explanation:
[tex]x=t+4 \implies t=x-4 \\ \\ y=(x-4)^2=x^2-8x+16[/tex]
If you sold 30% of a business for 500 dollars how much is the bussnis worth
it would be 1600 i hope this helps
26034 i hope this help man pls pls
What is an equation of the line that passes through the points (-4, 8)(−4,8) and (6, 3)(6,3)
Answer:
y=-1/2x+6
Step-by-step explanation:
slope: -5/10 = -1/2
y=mx+b
y=-1/2x+b
substitute points to find b: 8=-1/2(-4)+b
8=2+b
6=b
Select the correct answer. Solve for x. x2 + 4x - 21 = 0 A. -3, -7 B. -3, 7 C. 3, -7 D. 3, 7
Answer:
Answer: the correct option is(C) 3, -7.
Step-by-step explanation:
Describe the graph of the proportional relationship represented by the equation y = 7.5x.
The graph is a line that goes through points (0, 0) and (7.5, 7.5).
The graph is a line that goes through points (0, 0) and (15, 2).
The graph is a line that goes through points (0, 0) and (7.5, 1).
The graph is a line that goes through points (0, 0) and (1, 7.5).
The graph of the proportional relationship represented by the equation y = 7.5x is The graph is a line that goes through points (0, 0) and (1, 7.5)
What is a graph of linear function?A linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
c = y intercept
considering the given equation y = 7.5x.
c = 0
hence the graph passed through (0, 0)
substituting x = 1 gives y = 7.5 hence (1, 7.5) is another point
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Which of the following statements is correct based on the number line below?
-8
-6
A
B
C
D
-4 -2
P
200
808
Q
0 2 4
6
√68 is to the right of Point Q because it is less than 8.
√68 is between points P and Q because it is less than 0 and greater than 8.
√68 is between points P and Q because it is greater than 0 and less than 8.
68 is to the right of Point Q because it is greater than 8.
Find the equation of a line parallel to y=−7+4x that passes through the point (-2,-1)
To find the equation of a line that is parallel to y=−7+4x and passes through the point (-2,-1), we can use the point-slope form of the equation of a line. The point-slope form of the equation of a line is:
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line, and m is the slope of the line.
Since the given line y=−7+4x is in slope-intercept form, we can find the slope by taking the coefficient of x, which is 4. This means that the slope of the line is 4.
We can then use the point-slope form to find the equation of the line that is parallel to y=−7+4x and passes through the point (-2,-1). Plugging in the values for the slope and the point, we get:
y - (-1) = 4(x - (-2))
Simplifying this expression gives us:
y + 1 = 4(x + 2)
Which simplifies to:
y = 4x + 5
So the equation of the line that is parallel to y=−7+4x and passes through the point (-2,-1) is y = 4x + 5.
find the circumference of the circle use 3.14 r=6
The circumference of the circle with the dimensions radius = 6 and π = 3.14 is 37.68
What is the circumference of a circle?The circumference of a circle refers to the line that bounds a circle or other two-dimensional figure.
Circumference of a circle = 2πr
Where,
π = 3.14Radius, r = 6Circumference of a circle = 2πr
= 2 × 3.14 × 6
= 37.68
Therefore, the circumference of the circle is given by 37.68
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Use the formula A=P\left(1+r/n)^nt to solve the compound interest problem.
Find how long it takes a 1700$ investment to earn 500$ interest if it is invested at 2% interest compounded quarterly.
500$ interest will be earned in approximately years. (Round to the nearest tenth.)
It will take 12.91 years to earn $ 500 in interest
What is Compound interest:
Compound interest refers to the interest added to a loan or deposit. It is the concept that we employ every day on a regular basis. Amounts are based on both the principal amount and Rate of interest when calculating compound interest.
The formula used for
Amount, A = P(1+r/n)^ntP = Principal amount
r = Rate of interest
n = Number of compounds in a year
t = Time period in years
And the formula for
Compound Interest, C.I = A - P
Here we have
Principal amount = 1700,
Rate of interest = 2% = 2/100 = 0.02 on decimals
Given that compound interest gained = $ 500
Number of compounds = 4 times
Let a be the time period
By the given formula,
Amount, A = 1700(1+0.02/4)^4t
= 1700(1+0.005)^4t
= 1700 (1.005)^4t
Compound interest = 1700 (1.005)^4t - 1700
From the given data,
Compound interest = $ 500
=> 1700 (1.005)^4t - 1700 = 500
=> 1700 (1.005)^4t = 2200
=> (1.005)^4t = 1.294
Take logs on both sides
=> log (1.005)^4t = log 1.294
=> 4t log (1.005) = log (1.294)
=> 4t = log(1.294)/log(1.005)
=> 4t = 0.111934276/ 0.00216606176
[ Use calculator for log(1.294) and log(1.005) ]
=> 4t = 51.6764012
=> t = 12.9191003
=> t = 12.91
Therefore,
It will take 12.91 years to earn $ 500 in interest
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Divide. Give the quotient and remainder.
133 2
Answer:
Quotient: 66
Remainder: 1
Step-by-step explanation:
133/2 = 66.5
66.5 =
66 + 0.5 =
66 + 1/2 = 66 1/2
1/2 * 2 = 1 ==> Remainder: 1
Whole number : 66
Quotient: 66
Remainder: 1
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High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 18 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized?
The top 18 percent of scores fall within two standard deviations of the mean.
What is publicly recognized?Publicly recognized refers to something that is well-known or acknowledged by the public or by a large segment of the population. This could include a famous person, a popular business, or an important event or achievement. Public recognition is often seen as an indicator of success, as it shows that the person or thing being recognized has achieved something noteworthy or has had a positive influence on the public. Examples of publicly recognized things include awards, honors, and other achievements.
Assuming a normal distribution, a student needs to score at least two standard deviations above the mean to be publicly recognized. This is because the top 18 percent of scores fall within two standard deviations of the mean. This can be expressed mathematically as:
P(x > μ + 2σ) = 0.18
where μ is the mean and σ is the standard deviation.
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Find the intercept of the line 4x−3y=17
Answer:
see attachment
Step-by-step explanation:
From question 28 -29
Help please
By using the concept of vector, it can be calculated that
28) First option is correct
29) Fourth option is correct
What is vector?
Anything that has both magnitude and direction and follow the vector addition law is called vector.
28) The vectors are
[tex]\vec{v} = -2i-5j,[/tex]
[tex]\vec{w} = -3i+j[/tex]
[tex]\vec{v}. \vec{w} = (-2i-5j).( -3i+j) = 6 - 5 = 1\\|\vec{w}|^2 = (-3)^2+(1)^2 = 9 + 1 = 10\\\vec{v_1} = \frac{1}{10}( -3i+j) = \frac{-3}{10}i+\frac{1}{10}j[/tex]
[tex]\vec{v_2} = (-2i-5j) - (-\frac{3}{10}i - \frac{1}{10}j)\\\vec{v_2}= (-2+\frac{3}{10})i+(-5 - \frac{1}{10}j)\\\vec{v_2}=-\frac{17}{10}i - \frac{51}{10}j\\[/tex]
First option is correct
29) P = (1, 2) and Q = (-6, -1)
Position vector = (-6-1)i + (-1-2)j = -7i - 3j
Fourth option is correct
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Determine algebraically whether the given function is even, odd, or neither.
f(x) = -5x² + |2x|
well, as you already know, to check if a function is EVEN, we simply check what's f( -x ), if f( -x ) = f( x ), then voila!!. and if f( -x ) = -f( x ), then oddly enough, is an ODD function.
well, let's plug in " -x " to see what we get anyway
[tex]f(x)=-5x^2 + |2x|\implies \boxed{f(x)=-5x^2 + 2x} \\\\[-0.35em] ~\dotfill\\\\ f(-x)=-5(-x)^2 + |2(-x)|\implies f(-x)=-5(-x)(-x) + |-2x| \\\\\\ f(-x)=-5(+x^2) +2x\implies \boxed{f(-x)=-5x^2 + 2x}~\hfill \stackrel{\textit{\LARGE Even}}{f(-x)=f(x)}[/tex]
John Morse corporation buys a van for $16,000. The estimated life of the van is four years. The residual value of the van is $4,000. After two years, the van is sold for $8,000. What was the difference between the book value and the amount received from selling the van if John used the straight-line method of depreciation?
A.$4,000
B. $12,000
C. $8,000
D. $2,000
The difference between book value and the amount received is $2000
What was the difference between the book value and the amount received ?
van cost = $16000
Estimated life= 4 years
Residual value= $4000
using straight line method of depreciation
Depreciation per year= 16000-4000/4= 3000
Therefore book value after two years = $16000- 2*3000= $10000
Selling price of book after 2 years= $8000
hence the difference between book value and the amount received
10000-8000= $2000
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