Answers
Answer:
a) 4 calories per minute
b) 0.25
Step-by-step explanation:
a) If you look at the line it intercepts the x and y axis at the origin (0,0). therefore if you take any point on the line you will see that the calories per minute are constant:
Look at point (40,10)
Calories per minute = x/y = 40/10 = 4
Look at point (80,20)
Calories per minute = x/y = 80/20 = 4
b) you can use any two points on the line. Lets use point 1 as (20,5) and point 2 as (60,15).
The slope of a straight line is defined as:
slope = (y2-y1)/(x2-x1) = (15-5)/(60-20) = 0.25
Related Questions
Find the product. 8y 3(-3y 2)
Answers
For this case we must find the product of the following expression:
[tex]8y ^ 3 (-3y ^ 2) =[/tex]
We have to by law of signs of multiplication:
[tex]+ * - = -[/tex]
Also, by definition of multiplication of powers of the same base, we put the same base and add the exponents, then the expression is rewritten as:
[tex]-24y ^ {3 + 2} =\\-24y ^ 5[/tex]
Answer:
[tex]-24y ^ 5[/tex]
Answer:
The Answer is -24y^5
Step-by-step explanation:
We know this because multiplying 8 by -3 = -24
Then we have to combine the exponents and we get 5.
Hope I helped. I used a website called mathwa3 to help, the 3 stands for a y.
Have a great day!!!
[tex]cos\frac{x}{2} =[/tex]±[tex]\sqrt{\frac{1+cosx}{2} }[/tex], if A=[tex]\frac{x}{2}[/tex] then cosA=
Answers
Answer:
[tex]\cos{A}=\pm\sqrt{\dfrac{1+\cos{x}}{2}}[/tex]
Step-by-step explanation:
[tex]\cos{A}=\cos{\frac{x}{2}}=\pm\sqrt{\dfrac{1+\cos{x}}{2}}[/tex]
Apparently, you're supposed to recognize that the formula tells you the value of cos(x/2).
Emails arrive at the server of a company at the rate of an average of 10 per hour. It is assumed that a Poisson process is a good model for the arrivals of the emails. What is the probability (to 2 decimal places) that the time between two consecutive emails is more than two minutes?
Answers
Answer:
0.37
Step-by-step explanation:
we have given that emails arrives at the server at the rate of 10 per hour means [tex]\frac{10}{60}=0.166[/tex] per minute
we have to find the probability that the time difference between the two email is more than 2 minute
so probability [tex]P\left ( X> 2 \right )=e^{-2\lambda }=e^{-2\times 0.166}=0.7166[/tex]
The probability that the time between two consecutive emails arriving at the server is more than two minutes is 0.72 (or 72%).
Given:
- Average rate of email arrivals [tex](\( \lambda \))[/tex] = 10 per hour
1. Understanding the Poisson Process:
- In a Poisson process, the time between events (in this case, email arrivals) follows an exponential distribution.
- If [tex]\( \lambda \)[/tex] is the average rate of events per unit time (here, per hour), the time between events (interarrival time) T follows an exponential distribution with parameter [tex]\( \lambda \)[/tex].
2. Parameter Conversion:
- Since [tex]\( \lambda = 10 \)[/tex] emails per hour, we convert this to the rate per minute:
[tex]\[ \lambda_{\text{minute}} = \frac{10}{60} = \frac{1}{6} \text{ emails per minute} \][/tex]
3. Probability Calculation:
- We are interested in the probability that the time between two consecutive emails is more than two minutes.
- Let X denote the time between two consecutive emails. X follows an exponential distribution with rate [tex]\( \lambda_{\text{minute}} = \frac{1}{6} \)[/tex].
[tex]\[ P(X > 2) = e^{-\lambda_{\text{minute}} \cdot 2} \][/tex]
Substitute [tex]\( \lambda_{\text{minute}} = \frac{1}{6} \)[/tex]:
[tex]\[ P(X > 2) = e^{-\frac{1}{6} \cdot 2} \] \[ P(X > 2) = e^{-\frac{1}{3}} \][/tex]
4. Calculating the Probability:
- Use a calculator to find [tex]\( e^{-\frac{1}{3}} \)[/tex].
[tex]\[ e^{-\frac{1}{3}} \approx 0.7165 \][/tex]
Therefore, the probability that the time between two consecutive emails is more than two minutes is approximately 0.72 (rounded to two decimal places).
This result aligns with the characteristics of a Poisson process with an average arrival rate of 10 emails per hour.
Drag the tiles to the boxes to form correct pairs.
Multiply the sets of numbers and match them with their products.
Answers
Answer:
[tex](-\frac{3}{4})(\frac{7}{8})[/tex] ↔ [tex]-\frac{21}{32}[/tex]
[tex](\frac{2}{3})(-4)(9)[/tex] ↔ [tex]-24[/tex]
[tex](\frac{5}{16})(-2)(-4)(-\frac{4}{5})[/tex] ↔ [tex]-2[/tex]
[tex](2\frac{3}{5})(\frac{7}{9})[/tex] ↔ [tex]\frac{91}{45}[/tex]
Step-by-step explanation:
The first expression is
[tex](-\frac{3}{4})(\frac{7}{8})[/tex]
On simplification we get
[tex]-\frac{3\times 7}{4\times 8}[/tex]
[tex]-\frac{21}{32}[/tex]
Therefore the product of [tex](-\frac{3}{4})(\frac{7}{8})[/tex] is [tex]-\frac{21}{32}[/tex].
The second expression is
[tex](\frac{2}{3})(-4)(9)[/tex]
On simplification we get
[tex](\frac{2}{3})(-36)[/tex]
[tex]-\frac{72}{3}[/tex]
[tex]-24[/tex]
Therefore, the product of [tex](\frac{2}{3})(-4)(9)[/tex] is [tex]-24[/tex].
Similarly,
[tex](\frac{5}{16})(-2)(-4)(-\frac{4}{5})\Rightarrow (\frac{5}{16})(8)(-\frac{4}{5})=(\frac{5}{2})(-\frac{4}{5})=-2[/tex]
[tex](2\frac{3}{5})(\frac{7}{9})=(\frac{13}{5})(\frac{7}{9})=\frac{91}{45}[/tex]
The sets of numbers are:
(-7)(-1.2) <-> 8.4
(-2 1/2)(-2) <-> 5
(2.5)(-2)<->-5
(7) (-1.2) <-> -8.4
The given expressions involve multiplication and follow the product rule of signs. According to this rule, the product of two numbers with the same sign is positive, while the product of two numbers with different signs is negative.
(-7)(-1.2) = 8.4: Both numbers have the same sign (negative * negative), so the product is positive. The result is 8.4.
(-2 1/2)(-2) = (-5/2)(-2) = 5: Again, both numbers are negative, so the product is positive. The calculation involves multiplying mixed numbers, where -2 1/2 is equivalent to -5/2. The result is 5.
(2.5)(-2) = -5: The numbers have different signs (positive * negative), so the product is negative. The result is -5.
(7)(-1.2) = -8.4: Once more, the numbers have different signs (positive * negative), leading to a negative product. The result is -8.4.
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What is the third term in the binomial expansion of (3x+y^3)^4
Answers
Answer:
The last choice is the one you want.
Step-by-step explanation:
Use the 5th row of Pascal's Triangle. Since you have a 4th degree polynomial, there will be 5 terms in it. The 5 coefficients, in order, are:
1, 4, 6, 4, 1
We will use these coefficients only up to and including the third one, since that is the one you want. Binomial expansion using Pascal's Triangle looks like this:
[tex]1(3x)^4(y^3)^0+4(3x)^3(y^3)^1+6(3x)^2(y^3)^2+...[/tex]
That third term is the one we are interested in. That simplification gives us:
[tex]6(9x^2)(y^6)[/tex]
Multiply 6 and 9 to get 54, and a final term of:
[tex]54x^2y^6[/tex]
The third term of the given binomial expansion is [tex]54(x^{2})(y^{5})\\[/tex]
What is binomial expansion?The binomial expansion is based on a theorem that specifies the expansion of any power [tex](a+b)^{m}[/tex] of a binomial (a + b) as a certain sum of products [tex]a^{i} b^{i}[/tex], such as (a + b)² = a² + 2ab + b².
How to find the third term in the binomial expansion of (3x+y^3)^4 ?We know that the binomial expansion of [tex](a+b)^{m}[/tex] can be written as [tex]mC_{0}(a^{m-0}) +mC_{1}(a^{m-1})b+ mC_{2}(a^{m-2})b^{2}+..................+mC_{m}b^{m}[/tex]So the (r+1)th term will be [tex]mC_{r}(a^{m-r})b^{r}[/tex]The given term is [tex](3x + y^{3}) ^{4}[/tex]
The third term in the expansion will be
[tex]4C_{2}(9x^{2})(y^{3})^{2}\\ = 54(x^{2})(y^{5})\\[/tex]
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Can someone let me know if I simplified these equations correctly or at least show me how to do it?
Answers
Answer:
Your work is correct as far as it goes. Now eliminate the terms that are zero.
Step-by-step explanation:
Multiplying anything by zero gives zero. Adding zero is like adding nothing. Zero is called the "additive identity element" because ...
a + 0 = a
Adding zero doesn't change anything. You can (and should) drop the zero if your goal is to simplify the expression.
[tex]a. \quad x_{f}=v_{0}\\\\b. \quad x_{f}=v_{0}t\\\\c. \quad v_{f}^2=v_{0}^2[/tex]
Can you use the Law of Cosines in the triangle below? Why or why not?
Answers
Answer:
Yes
Step-by-step explanation:
The law of cosines relates the three sides of a triangle with the cosine of the angle opposite one of them. It is useful for finding an angle of the triangle when only the side lengths are given, as here.
What ia the measure of x?
Answers
Answer:
58
Step-by-step explanation:
Rule: the exterior angle = the sum of the two angles that do not share a side with the exterior angle. Put in much simpler terms <DAB = <B + <C
Solution
<C + <B = <DAB
<C + 56 = 114 Subtract 56 from both sides
<C +56-56 = 114-56 Combine
<C = 58
x = 58
Choose the correct absolute value inequality and graph for the solution -1.2≤x≤2
options:
|5x-2|>=8
|5x-2|<=8
Answers
Answer:
[tex]\large\boxed{|5x-2|\leq8}[/tex]
Step-by-step explanation:
[tex]-1.2\leq x\leq2\qquad\text{multiply all sides by 5}\\\\-6\leq5x\leq10\qquad\text{subtract 2 from both sides}\\\\-8\leq5x-2\leq8\iff|5x-2|\leq8[/tex]
The cost in dollars to manufacture x pairs of shoes is given by 12,000 + 19x. This month, the manufacturer produced 1000 more pairs of shoes than last month. The average cost per pair dropped by $0.43.
a) Write an expression for the average cost per pair of shoes. Use this expression to write an equation to represent there situation.
b) Solve your equation
c) Are there any mathematical restrictions on the domain? Explain.
d) Determine reasonable domain in the context of the problem. Use your answers to parts I and II to answer the question.
Answers
Answer:
(a) The expression for the average cost per pair of shoes is [tex]A(x)=\frac{12000}{x}+19[/tex] and equation for the situation is [tex]\frac{12000}{x}+19-(\frac{12000}{x+1000}+19)=0.43[/tex].
(b) x=[tex]x\approx 4806[/tex]
(c) The average function is not defined for x=0, so the domain of the function is all real numbers except 0.
(d) The reasonable domain is all natural numbers.
Step-by-step explanation:
The cost in dollars to manufacture x pairs of shoes is given by
[tex]C(x)=12000+19x[/tex]
where, x is the pairs of shoes.
(a)
The expression for the average cost per pair of shoes.
[tex]A(x)=\frac{C(x)}{x}[/tex]
[tex]A(x)=\frac{12000+19x}{x}[/tex]
[tex]A(x)=\frac{12000}{x}+19[/tex]
This month, the manufacturer produced 1000 more pairs of shoes than last month. The average cost per pair dropped by $0.43.
[tex]A(x)-A(x+1000)=0.43[/tex]
[tex]\frac{12000}{x}+19-(\frac{12000}{x+1000}+19)=0.43[/tex]
Therefore the expression for the average cost per pair of shoes is [tex]A(x)=\frac{12000}{x}+19[/tex] and equation for the situation is [tex]\frac{12000}{x}+19-(\frac{12000}{x+1000}+19)=0.43[/tex].
(b)
On solving the above equation we get
[tex]\frac{12000}{x}-\frac{12000}{x+1000}=0.43[/tex]
[tex]\frac{12000000}{x^2 + 1000 x} = 0.43[/tex]
[tex]12000000=0.43(x^2 + 1000 x)[/tex]
[tex]12000000=0.43x^2 + 430x[/tex]
[tex]0=0.43x^2 + 430x-12000000[/tex]
Using graphing calculator we get
[tex]x\approx -5806.31,4806.31[/tex]
The pair of shoe can not be native and decimal value.
[tex]x\approx 4806[/tex]
Therefore the solution is [tex]x\approx 4806[/tex].
(c)
The average cost function is
[tex]A(x)=\frac{12000}{x}+19[/tex]
The function is not defined if the denominator is 0.
The above function is not defined for x=0, so the domain of the function is all real numbers except 0.
(d)
In the average function x represents the number of pair of shoe.
It means the value of x must be a positive integer.
Since the average function is not defined for x=0, So the reasonable domain of average function is
Domain={x : x∈Z⁺, x≠0}
Domain=N
Therefore the reasonable domain is all natural numbers.
HELPPPP!!!!!!!!!!!!!!!! (10 points) We want to know the probability that a student selected randomly from her class would have an “A” (90 or above) in her class. Find the probability. Explain HOW to find the probability
Answers
Answer:
23 out of 91
around 1/3 of the class
Step-by-step explanation:
the total number of students so around the third part of the class
Y – 4 = 20 A. The difference between a number and 4 is 20. B. The product of a number and 4 is 20. C. A number combined with 4 is 20. D. The quotient of a number and 4 is 20.
Answers
Answer:
A
Step-by-step explanation:
Subtraction means "difference". The only choice there that has the word "difference" in it is choice A.
Apple trees cost $ 30 each, and cherry trees cost $ 40 each. Rohan has $ 600 to spend on fruit trees.
a) Let x represent the number of apple trees purchased, and let y represent the number of cherry trees purchased.
b) Write an equation that illustrates the different ways Rohan can purchase apple trees and cherry trees and spend exactly $ 600 .
Equation:
Answers
Answer:
A) Apples: $30x
Cherry: $40y
B) ($30x)+($40y)=600
What is the slope of the line x = 3?
Answers
Answer:
1/3 = .33
THE UNIT RATE IS 1 TO 3
Answer:
infinite slope
Step-by-step explanation:
Note that x=3 is simply a vertical straight line that passes through the point (3,y) for all real values of y
Also recall that the slope of a vertical straight line is undefined (or infinite slope)
hence the slope of x=3 is infinite.
Evaluate the expression
5⋅x3x2\dfrac{5\cdot x^3}{x^2}
x
2
5⋅x
3
start fraction, 5, dot, x, start superscript, 3, end superscript, divided by, x, start superscript, 2, end superscript, end fraction
for
x=2x=2
x=2
x, equals, 2
Answers
The simplified expression for [tex]\((5 \cdot x^3) / (x^2)\) is \(5 \cdot x\).[/tex]
When x = 2, the result is [tex]\(5 \times 2 = 10.[/tex]
The answer is 10.
To evaluate the expression[tex]\((5 \cdot x^3) / (x^2)\) for \(x = 2\),[/tex] we first need to simplify the given expression.
Given:
[tex]\[ \dfrac{5 \cdot x^3}{x^2} \][/tex]
Simplifying, we divide the powers of x :
[tex]\[ x^3 / x^2 = x^{3-2} = x^1 = x. \][/tex]
So the expression simplifies to:
[tex]\[ 5 \cdot x. \][/tex]
Now substitute x = 2 :
[tex]\[ 5 \cdot 2 = 10[/tex]
Thus, the value of [tex]\((5 \cdot x^3) / (x^2)\) when \(x = 2\)[/tex] is: 10.
Question : Evaluate the expression [tex]\[ \dfrac{5 \cdot x^3}{x^2} \][/tex]for x = 2. start fraction, 5, dot, x, cubed, divided by, x, squared, end fraction for x=2x=2x, equals, 2.
If f(x) = 2x + 2 and g(x) = x3, what is (gºf)(2)?
Answers
Answer:
216
Step-by-step explanation:
(g∘f)(x) = g(f(x))
f(2) = 2·2 +2 = 6
g(f(2)) = g(6) = 6³ = 216
Answer:
216
Step-by-step explanation:
Correct Plato
Name an intersection of plane GFL and plane that contains points A and C
Answers
The intersection of plane GFL and a plane that contains points A and C can be any plane that passes through those two points.
In mathematics, an intersection of two planes is the set of points that are common to both planes.
In this case, we want to find the intersection of plane GFL and a plane that contains points A and C.
Since both points A and C lie on the same plane, any plane that contains both points A and C would intersect plane GFL at those points.
Therefore, any plane that passes through points A and C would be an intersection of plane GFL and a plane that contains points A and C.
Examples of planes that contain points A and C are:
A plane that contains the line segment AC
A plane that is perpendicular to line AC at point A
A plane that is perpendicular to line AC at point C
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A new board game comes with a deck of 20 cards: 5 red, 3 blue, 2 orange, and 10 green.
After the deck is shuffled, the player is to choose the top card and note its color, replace
the card, shuffle the deck again, and then choose the top card again and note its color.
What is the probability that both cards selected are blue?
Answers
A student's course grade is based on one midterm that counts as 5% of his final grade, one class project that counts as 15% of his final grade, a set of homework assignments that counts as 35% of his final grade, and a final exam that counts as 45% of his final grade. His midterm score is 75, his project score is 93, his homework score is 78, and his final exam score is 70. What is his overall final score? What letter grade did he earn (A, B, C, D, or F)? Assume that a mean of 90 or above is an A, a mean of at least 80 but less than 90 is a B, and so on.
Answers
Answer:
76.5CStep-by-step explanation:
Apply the weights to the scores and add them up:
5% × midterm + 15% × project + 35% × homework + 45% × final
= 0.05(75) +0.15(93) +0.35(78) +0.45(70)
= 76.5
The student has a solid letter grade of C.
The student's overall final score is 76.5 which is between 70 and 79, the students earned a C.
To calculate the student's overall final score, we can use the following formula:
Final grade = (midterm score * midterm weight) + (project score * project weight) + (homework score * homework weight) + (final exam score * final exam weight)
where midterm weight is the percentage of the final grade that the midterm counts for, project weight is the percentage of the final grade that the project counts for, homework weight is the percentage of the final grade that the homework assignments count for, and final exam weight is the percentage of the final grade that the final exam counts for.
In this case, the midterm weight is 5%, the project weight is 15%, the homework weight is 35%, and the final exam weight is 45%. The student's midterm score is 75, his project score is 93, his homework score is 78, and his final exam score is 70.
Therefore, the student's overall final score is calculated as follows:
Final grade = (75 * 0.05) + (93 * 0.15) + (78 * 0.35) + (70 * 0.45)
Final grade = 3.75 + 13.95 + 27.3 + 31.5
Final grade = 76.5
Therefore, the student's overall final score is 76.5.
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Determine whether the two triangles are similar. HELP ASAP! I AM RUNNING OUT OF POINTS!!
Answers
Answer:
ΔKLJ ~ ΔRPQ by AA~
Step-by-step explanation:
Angle angle similarity needs two corresponding angles in two triangles to be same. The two given triangles are similar by: ΔKLJ ~ ΔRPQ by AA~
How to find measure of missing third angle in a triangle?It is a theorem in mathematics that sum of internal angles of a triangle equate to [tex]180^\circ[/tex]
Suppose that two angles are given as [tex]a^\circ[/tex] and [tex]b^\circ[/tex] and let there is one angle missing. Let its measure be [tex]x^\circ[/tex]
Then, by the aforesaid theorem, we get:
[tex]a^\circ + b^\circ + x^\circ = 180^\circ\\\\ \text{Subtracting a + b degrees from both sides} \\\\x^\circ = 180^\circ - (a^\circ + b^\circ)[/tex]
What is Angle-Angle similarity for two triangles?Two triangles are similar if two corresponding angles of them are of same measure. It is because when two pairs of angles are similar, then as the third angle is fixed if two angles are fixed, thus, third angle pair also gets proved to be of same measure. This makes all three angles same and thus, those two triangles are scaled copies of each other. Thus, they're called similar.
For given case, we've got
[tex]m\angle K = m\angle R\\m\angle J = m\angle Q\\[/tex]
Thus, for the rest of the angle pair, we have:
[tex]m\angle L = 180 - (m\angle J + m\angle K) = 180 - (m\angle Q + m\angle R) = m\angle P\\\\m\angle L = m\angle P[/tex]
Thus, given two triangles are similar by angle-angle similarity.
Thus,
The two given triangles are similar by: ΔKLJ ~ ΔRPQ by AA~
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In the coin value formula, V(t)= P(1+r)^t, which parts form the base of the exponential function? Which parts from the constant, or initial value? Which parts form the exponent?
Answers
Answer:
Step-by-step explanation:
The base of the exponential function is 1 + r.
The initial value is P.
The exponent is t.
The base of the exponential function is 1 + r
exponent is t, and
initial value is P
What is exponential function?The mathematical expression for an exponential function is f (x) = a ˣ, where “x” denotes a variable and “a” denotes a constant. This constant is referred to as the base of the function and should be greater than zero. The most common use exponential function is with base e
Given A coin formula V(t) = P(1+r)^t
to find the initial value put t = 0
V(0) = P(1+r)⁰
V(0) = P
P is the initial value
and exponent is the term which is in the power of any exponential function
here t is exponent and (1+r) is base function
Hence according to coin formula The base of the exponential function is 1 + r; exponent is t; and initial value is P.
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The value of a collector’s item is expected to increase exponentially each year. The item is purchased for $500. After 2 years, the item is worth $551.25. Which equation represents y, the value of the item after x years?y = 500(0.05)xy = 500(1.05)xy = 500(0.1025)xy = 500(1.1025)x
Answers
Answer:
y = 500(1.05)^x.
Step-by-step explanation:
551.25 = 500x^2 where x is the multiplier for each year.
x^2 = 551.25/500
x = 1.05
So the value after x years is 500(1.05)^x.
Answer: [tex]y=500(1.05)^x[/tex]
Step-by-step explanation:
The exponential growth equation is given by :-
[tex]y=A(1+r)^x[/tex] (1)
, where A is the initial value of , r is the rate of growth ( in decimal) and t is the time period ( in years).
Given : The value of a collector’s item is expected to increase exponentially each year.
The item is purchased for $500. After 2 years, the item is worth $551.25.
Put A= 500 ; t= 2 and y= 551.25 in (1), we get
[tex]551.25=500(1+r)^2\\\\\Rightarrow\ (1+r)^2=\dfrac{551.25}{500}\\\\\Rightarrow (1+r)^2=1.1025[/tex]
Taking square root on both sides , we get
[tex]1+r=\sqrt{1.1025}=1.05\\\\\Rightarrow\ r=1.05-1=0.5[/tex]
Now, put A= 500 and r= 0.5 in (1), we get the equation represents y, the value of the item after x years as :
[tex]y=500(1+0.5)^x\\\\\Rightarrow\ y=500(1.05)^x[/tex]
A pair of angles which share a common side and vertex is called
Answers
Answer: Adjacent Angles
A pair of angles which share a common side and vertex is called adjacent angles.
What is an angle measure?When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Given:
A pair of angles which share a common side and vertex.
If two angles share a side and a vertex, they are said to be adjacent in geometry.
In other words, adjacent angles do not overlap and are placed precisely next to one another.
Therefore, the right definition is adjacent angles.
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Which of the following is the correct notation for -48-89
Answers
Answer:
Step-by-step explanation:
Because 48 and 89 have the same sign, that is, the negative sign, their sum takes on that sign:
-48
-89
---------
-137
Does the point “is on the circle shown? Explain.
Answers
Answer:
Option 2: Yes, the distance from (-2,0) to (1,√7) is 4 units
Step-by-step explanation:
The point is:
(1,√7)
If the point lies on the circle, then the distance of point and the center of circle should be equal to the radius of the circle.
The radius can be viewed from the diagram that it is 4 units.
The center is: (-2,0)
Now, distance:
[tex]d = \sqrt{(x_2-x_1)^{2}+ (y_2-y_1)^{2}}\\ d = \sqrt{(-2-1)^{2}+ (0-\sqrt{7} )^{2}}\\ d = \sqrt{(-3)^{2}+ (-\sqrt{7} )^{2}}\\=\sqrt{9+7}\\ =\sqrt{16}\\ =4[/tex]
Hence, option 2 is correct ..
What is this (pic provided) written as a single log?
Answers
Answer:
Step-by-step explanation:
when logs are added, they can be multiplied to produce a simplified log.
log_5(4*7) + log_5(2)
log_5(4*7*2)
log_5(56)
Sue graphed the formula for converting temperatures from Fahrenheit to Celsius. If the temperature is 50 degrees Fahrenheit, what is the temperature in Celsius? 5 degrees Celsius 10 degrees Celsius 15 degrees Celsius 20 degrees Celsius
Answers
For this case, we have by definition that:
[tex]C = (F-32) * \frac {5} {9}[/tex]
If they tell us that the base temperature is 50 degrees Fahrenheit, then we substitute:
[tex]C = (50-32) * \frac {5} {9}\\C = 18 * \frac {5} {9}\\C = 2 * 5\\C = 10[/tex]
Finally, the temperature equals 10 degrees Celsius.
Answer:
10 degrees Celsius
The temperature in Celsius when it is 50 degrees Fahrenheit is 10 degrees Celsius, calculated using the conversion formula Celsius = (Fahrenheit - 32) × 5/9.
Explanation:To convert a temperature from Fahrenheit to Celsius, we use the formula: Celsius = (Fahrenheit - 32) × 5/9. If the temperature is 50 degrees Fahrenheit, we subtract 32 from 50, giving us 18. Then we multiply 18 by 5/9, resulting in 10. Therefore, the temperature in Celsius is 10 degrees Celsius.
Step-by-step conversion:Start with the Fahrenheit temperature: 50°F.Subtract 32 from the Fahrenheit temperature: 50 - 32 = 18.Multiply by 5/9 to convert to Celsius: 18 × 5/9 = 10°C.Thus, when the temperature is 50°F, it is equivalent to 10°C.
Safari Adventure Theme Park is a selfguided theme park in which people drive through a park filled with African wildlife. They are given a map and a written guide to the wildlife of the park. They charge $20.00 per car plus $2.00 per person in the car. The number of people per car can be represented by the random variable X which has a mean value μX = 3.2, and a variance σ2x = 1.4. What is the mean of the total amount of money per car that is collected entering the park?
Answers
Answer:
$26.40
Step-by-step explanation:
For a linear function, the mean of the function is the function of the mean:
20 + 2.00·μX = 20 + 2.00·3.2 = 20 + 6.40 = 26.40 . . . . dollars
The mean total amount collected per car entering the Safari Adventure Theme Park is $26.40.
The mean of the total amount of money collected per car entering the park can be calculated by finding the expected value of the total amount, considering the price per car and per person. In this case, the mean total amount collected per car = price per car + (mean number of people per car) * price per person. Substituting the given values: 20 + 3.2 * 2 = $26.40.
the vertex of this parabola is at (5,5). when the x-value is 6, the y-value is -1. what is the coefficient of the squared in the parabola's equations
Answers
Answer: OPTION D.
Step-by-step explanation:
The vertex form of a quadratic function is:
[tex]y= a(x - h)^2 + k[/tex]
Where (h, k) is the vertex of the parabola and "a" is the coefficient of the squared in the parabola's equation.
We know that the vertex of this parabola is at (5,5) and we also know that when the x-value is 6, the y-value is -1.
Then we can substitute values into [tex]f (x) = a(x - h)^2 + k[/tex] and solve for "a". This is:
[tex]-1= a(6- 5)^2 + 5\\\\-1=a+5\\\\-1-5=a\\\\a=-6[/tex]
Answer:
D
Step-by-step explanation:
If f(x) = 2x - 3 and g(x) = Radical over x-8,
what is (fºg)(24)?
Answers
Answer:
5
Step-by-step explanation:
Plug in 24 for x in your g(x) equation.
[tex]g(24)=\sqrt{24-8} \\g(24)=\sqrt{16} \\g(24)=4[/tex]
Next, plug in your g(x) value, 4, to your f(x) equation for x.
[tex]f(4)=2(4)-3\\f(4)=8-3\\f(4)=5[/tex]