Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 6 hours of burning, a candlehas a height of 19.4 centimeters. After 20 hours of burning, its height is 11 centimeters. What is the height of the candle after 8 hours?
Answers
Given that the height of a candle (in centimeter) is a linear function of time (in hour) it has been burning.
Let at time t, the height of the candle be h
Since h is a linear function of t, let us assume
\(h=at+b\)After 6 hours of burning, the candle has a height of 19.4 centimeters.
After 20 hours of burning, its height is 11 centimeters.
So, the line representing h passes through the points (6,19.4) and (20,11)
Using two-point formula
\(\begin{gathered} \frac{h-11}{19.4-11}=\frac{t-20}{6-20} \\ \frac{h-11}{8.4}=\frac{t-20}{-14} \\ h=-\frac{3}{5}t+23 \end{gathered}\)So, the height of the candle is
\(h=-\frac{3}{5}t+23\)Now, putting t=8, it gives
\(\begin{gathered} h=23-\frac{3}{5}\times8 \\ =23-\frac{24}{5} \\ =\frac{115-24}{5} \\ =\frac{91}{5} \end{gathered}\)So, after 8 hours, the height of the candle is 18.2 centimeters.
Related Questions
The managers at Smith's BBQ have been asked to cut back Total Wages by 2.5% in the next two
weeks to account for slow sales. Using the Current Week as the benchmark, what would be the
estimate for the reduced Total Wages for the next two weeks combined?
Answers
The required estimate for the reduced Total Wages for the next two weeks combined would be approximately 1.95 times the amount of money being paid to all employees over the course of a week in the Current Week.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
To estimate the reduced Total Wages for the next two weeks combined, we can use the following formula:
Reduced Total Wages = Current Total Wages x (1 - Wage Reduction Percentage)
Reduced Total Wages = C × (1 - 0.025) × 2
Simplifying this expression, we get:
Reduced Total Wages = C × 0.975 × 2
Reduced Total Wages = 1.95C
Therefore, the estimate for the reduced Total Wages for the next two weeks combined would be approximately 1.95 times the amount of money being paid to all employees over the course of a week in the Current Week.
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if you double a number and then add 36, you get 4 over 11 (4/11) of the original number,
what is the original number?
Answers
Answer:
The original number is -22
Step-by-step explanation:
We'll label our mystery number x.
2x + 36 = 4x/11
Multiply both sides by 11
4x = 22x + 396
Isolate x to one side (for this I subtract 4x from both sides, but you can also subtract 22x if you'd like)
0 = 18x + 396
Isolate x pt 2
18x = -396
Divide both sides by 18 to find your answer!
x = -22
Plug in to confirm
-44 + 36 = -88/11S
8 = 8
Please solve this
∫ (log(1 + x ^ 2))/((x + 1) ^ 2) dx
Answers
The final result of the integral is:
∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,
where Li(x) is the logarithmic integral function and C is the constant of integration.
We have,
To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.
Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:
∫ (log(1 + (u-1)²) / u²) du.
Expanding the numerator, we have:
∫ (log(1 + u² - 2u + 1) / u²) du
= ∫ (log(u² - 2u + 2) / u²) du.
Now, let's split the logarithm using the properties of logarithms:
∫ (log(u² - 2u + 2) - log(u²)) / u² du
= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.
We can simplify the second integral:
∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.
Using the power rule for integration, we can integrate both terms:
∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.
Now, let's focus on the second integral:
∫ (log(u) / u³) du.
This integral does not have a simple closed-form solution in terms of elementary functions.
It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).
Therefore,
The final result of the integral is:
∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,
where Li(x) is the logarithmic integral function and C is the constant of integration.
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Which is greater 3/4 or 11/12
Answers
Answer:
11/12
Step-by-step explanation:
3/4=.75
11/12=.91666......
Answer:
11/12
Step-by-step explanation:
3/4 = 9/12
What is
1 2/3-2 1/3
?
Answers
Answer:
I believe it's -2/3
\(1\frac{2}{3} - 2\frac{1}{3} = -\frac{2}{3}\)
Answer:
Convert the mixed numbers to improper fractions, then find the LCD and combine.
Exact Form: −2/3
Decimal: -0.6
Brainliest Please!!!?!!!
eighty-two percent of all women who submit to pregnancy tests are pregnant. a new pregnancy test gives a false positive result with probability 0.02 and a correct positive result with probability 0.95. define the events: p: {a woman is pregnant} and : {the pregnancy test is positive}. a)
Answers
The probability that a woman is actually pregnant given that the test is positive is 0.974 (or 97.4%).
a) To find the probability that a woman is actually pregnant given that the test is positive, we can use Bayes' theorem:
P(p|+) = P(+|p) P(p) / P (+)
where P(p) is the prior probability of a woman being pregnant (which is 0.82), P (+) is the probability of a positive test result, and P(+|p) is the conditional probability of a positive test result given that the woman is pregnant.
We are given that the test has a false positive rate of 0.02, which means that P(+|~p) = 0.02 (where ~p denotes "not pregnant"). We are also given that the test has a correct positive rate of 0.95, which means that P (+|p) = 0.95. Therefore, we can calculate:
P (+) = P(+|p) P(p) + P(+|~p) P(~p)
= 0.95 * 0.82 + 0.02 * (1 - 0.82)
= 0.802
Substituting into Bayes' theorem, we get:
P(p|+) = 0.95 * 0.82 / 0.802
= 0.974
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Which function has the following characteristics? • A vertical asymptote at x = 3 • A horizontal asymptote at y = 2 Domain: {** +3] 2x - 8 X - 3 y=x2-9 2 9 x² - 4 4 OB. V C. 2x2 - 18 x² - 4 4 2x2 - 8 O D. ** - 9
Answers
SOLUTION
To get this, note that the vertical asymptote can be gotten by setting the denominator to be equal to 0.
If we do this, we will notice that the vertical asymptote of option A and option D is x = 3
That is
for option A
\(\begin{gathered} y=\frac{2x-8}{x-3} \\ x-3=0 \\ x=3 \end{gathered}\)For option D
\(\begin{gathered} y=\frac{2x^2-8}{x^2-9} \\ x^2-9=0 \\ x^2=9 \\ x=3 \end{gathered}\)So, the answer is either option A or D.
But to get the correct answer, let us look at the graphs for both functions
Graph of A
\(y=\frac{2x-8}{x-3}\)From the graph, you can see that the domain is defined at x = 3. Notice that the green line cut across x = 3.
Now let's check Graph of option D
\(y=\frac{2x^2-8}{x^2-9}\)From the graph, you can see that the domain is defined at x = -3 and x = 3. Notice that the purple and green line cut across x = -3 and x = 3. So, the domain here is
\(x=\pm3\)Hence
need answer for 6 and 7 question ASAP will give brainlist to who answered
Answers
Answer:
6. x = 2
7. 35721
Step-by-step explanation:
Question 6Given equation:
\(8^{-4} \times 8^7=8^{2x-1}\)
\(\textsf{Apply the exponent rule} \quad a^b \cdot a^c=a^{b+c}:\)
\(\implies 8^{-4+7}=8^{2x-1}\)
\(\implies 8^{3}=8^{2x-1}\)
\(\textsf{Apply the exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):\)
\(\implies 3=2x-1\)
Add 1 to both sides:
\(\implies 3+1=2x-1+1\)
\(\implies 4=2x\)
Divide both sides by 2:
\(\implies \dfrac{4}{2}=\dfrac{2x}{2}\)
\(\implies 2=x\)
Therefore, x = 2.
Question 7Given identity:
\(\sf (a-b)^2=a^2-2ab+b^2\)
To find the square of 189, rewrite 189 as (200 - 11).
Therefore, a = 200 and b = 11.
Substitute these values into the given identity and solve:
\(\begin{aligned}\sf (a-b)^2 & =\sf a^2-2ab+b^2\\\implies \sf 189^2 = (200-11)^2 & =\sf 200^2-2(200)(11)+11^2\\& = \sf 40000 - 400(11)+121\\& = \sf 40000-4400+121\\& = \sf 35600+ 121\\& = \sf 35721 \end{aligned}\)
Simplify this expression (7p+3)+(5p-4)
Answers
Answer:
12p -1
Step-by-step explanation:
(7p+3)+(5p-4)
Combine like terms
7p+5p +3-4
12p -1
What is the distance between the points (-2,1) and (5,-4)
Answers
Considering the definition of distance between two points, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.
Distance between two pointsThe distance between two points is equal to the length of the segment that joins them. Therefore, to determine the distance between two different points, you must calculate the squares of the differences between their coordinates and then find the root of the sum of said squares.
In other words, the distance between two points in space is the magnitude of the vector formed by said points.
So, given the coordinates of two distinct points (x1, y1) and (x2, y2), the distance between two points is the square root of the sum of the squares of the difference of the coordinates of the points:
distance= \(\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)
Distance between the points (-2,1) and (5,-4)In this case, you know:
(x1, y1): (-2,1)(x2, y2): (5,-4)Replacing in the definition of distance:
distance= \(\sqrt{(5-(-2))^{2} +(-4-1)^{2} }\)
distance= \(\sqrt{(5+2)^{2} +(-5)^{2} }\)
distance= \(\sqrt{7^{2} +(-5)^{2} }\)
distance= \(\sqrt{49+25 }\)
distance= √74= 8.6023
Finally, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.
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How many two-digit counting numbers are greater than 80 or a multiple of 5?
There are numbers that meet the given conditions.
(Type a whole number.)
Answers
Answer:
10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90y95
Which point satisfies both of the following inequalities? -3x + 5y< 15. 5x+y>-5
Answers
Explanation.
eWe are told to find the points that satisfy the systems of inequalities
The systems of equations are
\(undefined\)What is the image point of (1,8) after a translation right 1 unit and up 5 units?
(And lease if you don't know the answer or send me one of those bitly links don't answer.)
Answers
Answer:
(2,13)
Step-by-step explanation:
This assignment is due today plsss help !!!
Answers
Graph f(x) =2/3x-3
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
f(x)=2/3.3=1/6=0,2
f(x)=0,2
Determine the measure of x in the diagram below:
x = °
Answers
The measure of angle x on the straight line is 130 degrees.
What is the measure of angle x?The sum of interior angles in a triangle equals 180 degrees.
To determine the value of x, we first determine its suplemetary angle x .
Hence:
40 + 90 + ( suplemetary angle of x ) = 180
Solve for the suplementary angle:
130 + ( suplemetary angle of x ) = 180
Suplementary angle of x = 180 - 130
Suplemetary angle of x = 50 degree
Now, we can find the measure of angle x.
Note that, sum of angles on a straight line equals 180 degree.
Hence:
x + ( suplemetary angle of x ) = 180
x + 50 = 180
Solve for x
x = 180 - 50
x = 130 degrees.
Therefore, the value of x is 130 degrees.
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Write
13/8
as a mixed number,
Answers
Answer:
1 5/8
Step-by-step explanation:
Answer:
1 and 5/8
Step-by-step explanation:
hdhdbfhfhfvvfvfvfhd
Solve the system of linear equations using substitution. Use a pencil and paper. Which expression would be easier to substitute into the other equation, in order to solve this problem? Explain your reasoning.
x=4y-9
x+4y=3
Answers
Answer:
(- 3, 1.5)
--------------------------
Given system:
x = 4y - 9x + 4y = 3The first expression is ready to be substituted as no further operation is required to simplify it.
4y - 9 + 4y = 38y - 9 = 38y = 12y = 12/8y = 1.5Find x:
x = 4*1.5 - 9x = 6 - 9x = - 3Solve T=M(3+FG) for G.
G=?
Answers
My answer was wrong, delete this answer or disregard
(7^3)^3
Simplify.
Rewrite the expression in the form 7^n
Answers
Step-by-step explanation:
✧ \( \underline{ \underline{ \large{ \tt{R\: E \: M \: E \: M \: B \: E \: R}}} }: \)
If \(( {x}^{a} )^{b} \) is an algebraic term then \( {(x}^{a} )^{b} = {x}^{a \times b} \) i.e When an algebraic term in the index form is raised to another index , the base is raised to the product of two indices.
⟶ \( \large{ \tt{( {7}^{3} ) ^{3} = {7}^{3 \times 3} = {7}^{9}}} \)
☥ \( \boxed{ \boxed{ \large \tt{Our \: Final \: Answer : \underline{ \tt{ {7}^{9}}}}}} \)
Hope I helped ! ♡
⋆ Have a wonderful day / night ! ♪
Let me know if you have any questions regarding my answer! ツ
\( \underline{ \underline{ \mathfrak{Carry \: On \: Learning}}}\) !! ✎
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A game is played with a circular spinner that contains 8 different colors. The design
of the spinner is the order in which the colors are arranged. How many ways can
this spinner be designed?
Answers
Answer:
64 ways
Step-by-step explanation:
there are 8 different colors, with 8 different possibilities on the color arrangement.
x^2+y^2≤ 4y, x^2+y^2≤4x
Answers
Answer:
0 what is the question man what
3 points
A rectangular prism and a cylinder have the same height. The length of each side of the prism base is equal to the diameter of the cylinder. Which shape has a greater
volume? Use the drop-down menus to explain your answer.
Volume of a Rectangular Prism: V = lwh
Volume of a Cylinder: V = ²h
✓has the greater volume because the choose your answer... V
The choose your answer...
extra space between the two figures.
fits within the
choose your answer....
with
Answers
The rectangular prism has a greater volume than the Cylinder.
Since the rectangular prism has a greater volume than the cylinder because the rectangular prism fully occupies the space within its boundaries, while the cylinder has empty space above and below it.
The cylinder is rounded shape leaves gaps between its curved surface and the boundaries of the rectangular prism.
Therefore, the rectangular prism could hold more volume than the cylinder as it utilizes the entire space within its shape efficiently.
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This year a train ticket costs £24.97
Last year a train ticket for the same journey cost £22.70
Write this year’s cost as a percentage of last year’s cost.
Answers
Answer:
10%
Step-by-step explanation:
24.97 - 22.70=2.27
Increased price÷initial price×100%
2.27÷22.70×100%=10%
According to the theater room which statement about parallelogram ABCD is true?
Answers
We will have the following:
AO is congruent with OC and DO is congruent with OB. [Option 4]
You invest $15,000 into two different accounts. One of the accounts has 4% interest and the other has 3.2% interest. After one year, you have accumulated a total of $545.60 in interest. How much was initially invested in the account with 4% interest?
Answers
Answer:
(4%) ... $8200
Step-by-step explanation:
x + y = 15000
.04x + .032y = 545.60
y = 15000 - x
.04x + .032(15000 - x) = 545.60
.008x = 65.6
x=8200
The cost a company pays a lender for a loan is called interest.
The account received an initial investment of 8200 with 4% interest.
What is meant by interest?The cost of borrowing money is called interest, and it is typically expressed as a percentage, such as an annual percentage rate (APR). Lenders may charge interest to borrowers for using their funds, or borrowers may charge interest to lenders for using their funds.
The cost a company pays a lender (creditor) for a loan is called interest. Although many different arrangements are possible, interest payments are typically based on the remaining balance of a loan and paid on a monthly basis. At a predetermined interest rate, interest is typically calculated as a percentage of the loan balance.
From the given information, we get
x + y = 15000 ........(1)
0.04x + 0.032y = 545.60 ..........(2)
From (1),
y = 15000 - x
substitute the value of y in the above equation, we get
⇒ 0.04x + 0.032(15000 - x) = 545.60
simplifying the above equation, we get
⇒ 0.008x = 65.6
x = 8200
Therefore, 8200 was initially invested in the account with 4% interest.
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For the following data set, find Q1, Q2, Q3 and the interquartile range.
15, 12, 23, 15, 7, 8, 21, 10, 12, 14, 16, 24, 19
Answers
Answer: q1=11 q2=15 q3=20
Step-by-step explanation:
If 3^14 + 3^14 + 3^14 = 3^x, what is the value of x?
Answers
The value of x = 15.
The equation given is \(3^{14}\) + \(3^{14}\) + \(3^{14}\) = \(3^{x}\).
We can simplify this equation by adding the three terms on the left-hand side, which gives us 3(\(3^{14}\)) =\(3^{15}\).
Therefore, x = 15.
To understand why this is the case, we need to remember the laws of exponents.
The law of exponents states that when we multiply two numbers with the same base, we can add their exponents.
So, for example, \(3^{2}\) * \(3^{3}\) = \(3^{2+3}\) = \(3^{5}\).
Using this law, we can see that \(3^{14}\) +\(3^{14}\) + \(3^{14}\) is the same as 3 * \(3^{14}\).
And since 3 is also a factor of \(3^{15}\), we can combine the terms to get \(3^{15}\).
Therefore, x = 15.
We arrived at this conclusion by using the law of exponents to combine the terms on the left-hand side of the equation.
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why is the fractions 1/3 and 2/6 are equivalent
Answers
Answer:
They both equal 0.333333333
Step-by-step explanation:
When you look them up, it will show you a decimal and they are both the same.
Pls help will mark brainliest
Answers
Answer:
2462.4 square inches
Step-by-step explanation:
we know the shorted side of the wall is 36 inches so we divide 2.5 to 36 to see how much bigger the actual wall is to the scale
36/2.5= 14.4
The actual wall is 14.4 times bigger than the scale
14.4 x 4.75= 68.4
68.4 x 36= 2462.4 inches