Answer:
0.48
Step-by-step explanation:
The problem at hand
[tex]500 = (2)(10^{5x})[/tex]
First divide out 2 on both side of the = sign
[tex]500 = (2)(10^{5x})[/tex]
[tex]\frac{500}{2} = \frac{(2)(10^{5x})}{2}[/tex]
[tex]250 = 10^{5x}[/tex]
Now take the base 10 log on each side of the = sign
[tex]\log_{10} (250) = \log_{10} (10^{5x})[/tex]
Now move the exponent to the left like so
[tex]\log_{10} (250) = 5x \log_{10} (10)[/tex]
Rule you need to know. [tex]\log_a (a) = 1[/tex]
[tex]\log_{10} (250) = 5x (\log_{10} (10))[/tex]
[tex]\log_{10} (250) = 5x(1)[/tex]
[tex]\log_{10} (250) = 5x[/tex]
Now divide 5 from both sides of the equation
[tex]\frac{\log_{10} (250)}{5} = \frac{5x}{5}[/tex]
[tex]\frac{\log_{10} (250)}{5} = x[/tex]
[tex]x = \frac{\log_{10} (250)}{5}[/tex]
[tex]x = 0.4795880017[/tex]
Round to nearest hundredths
[tex]x = 0.48[/tex]
Side Note:
You could approach this problem in a different manner.
For instance, we could have done the following
[tex]x = \frac{\log_{10} (250)}{5(\log_{10} (10))}[/tex]
Also, you did not have to use log with a base 10. You could have used the natural log, which is [tex]\ln_e (x)[/tex]
[tex]x = \frac{\ln_{e} (250)}{5(\ln_{e} (10))}[/tex]
Solving the equation gives 0.48 when rounded to the nearest hundredth.
To solve the equation [tex]500 = (2)(105x)[/tex] , we will first isolate the exponential term. The steps are as follows:
Divide both sides of the equation by 2 to get 250 = 105x.
Take the common logarithm (log) of both sides of the equation to get [tex]log(250) = log(105x).[/tex]
Using logarithmic properties, we have log(250) = 5x log(10)
Now we simplify further since log(10) is 1, so log(250) = 5x.
Divide both sides by 5 to solve for x, which gives [tex]x = log(250) / 5.[/tex]
Using a calculator with a LOG button, we find log(250) approximately equals 2.39794 and, therefore, x is approximately 0.47959 when rounded to five decimal places.
However, we are asked to round x to the nearest hundredth, so the final answer is x = 0.48.
I am a rectangle. two of my sides are each 7 inches long. My area is 28 square inches. What is the length of each of my other two sides?
Answer:
4
Step-by-step explanation:
The formula for a rectangle is base times height so if one side is 7 inches then you need to figure out what times seven equals 28, which would be four.
If one pair of sides is 7 inches and the area is length times width then the answer would be whatever you multiple by 7 to get 28, so it would be 4 inches for each of the other two sides.
1. How do you determine whether a function is an inverse of another function?
Add the functions.
Multiply the functions.
Find the composite of the functions.
Apply the vertical line test.
2. Which of the following is the inverse function of f(x) = 3x?
f(x) = x + 3
f(x) = x/3
f(x) = x - 3
f(x) = x3
3. Which of the following statements is true?
A function will always pass the vertical line test.
All the answers are correct.
If the function has an inverse function, then the inverse function will pass the vertical line test.
If a function has an inverse function, then the original function will pass the horizontal line test.
4. What is the inverse function of f(x) = 3(x - 2)3?
5. Which of the following is the inverse function of f(x) = 2x - 3?
f(x) = (2x - 3 + 3)/2
f(x) = x+ 3/2
f(x) = x/2 + 3
f(x) = (x+3)/2
1. If f(x) and g(x) are inverse functions, then f(g(x)) = g(f(x)) = x. Finding the composite of the two functions will tell you if they are inverses.
2. To find the inverse of a function, swap x and y, then solve for y.
... x = 3y
... x/3 = y . . . . . matches f(x) = x/3
3. A function will pass the vertical line test. If its inverse is also a function, that, too, will pass the vertical line test. Since the inverse of a function is that function reflected across y=x, any inverse function that passes the vertical line test corresponds to an original function that passes the horizontal line test. (A vertical line reflected across y=x is a horizontal line.)
4. See 2.
... x = 3(y -2)³
... (x/3) = (y -2)³ . . . . divide by 3
... ∛(x/3) = y -2 . . . . .take the cube root
... 2+∛(x/3) = y . . . . .add 2
... f(x) = 2+∛(x/3) . . . . is the inverse
5. See 2.
... x = 2y -3
... x+3 = 2y . . . . . add 3
... (x+3)/2 = y . . . .divide by 2
... f(x) = (x+3)/2 . . . . is the inverse
A composite function is the combination of multiple functions.
The correct answers are:
Find the composite of the functions. The inverse of f(x) = 3x is [tex]f'(x) = \frac x3[/tex].All answers are trueThe inverse of [tex]f(x) = 3(x - 2)^3[/tex] is: [tex]f^{-1}(x) =2 + \sqrt[3]{\frac x3}[/tex]The inverse of [tex]f(x) =2x - 3[/tex] is [tex]f^{-1}(x) = \frac{x + 3}{2}[/tex]1. Test for inverse function
To test if two functions are inverse of one another, we simply find their composites.
Assume the functions are g(x) and h(x).
We simply test for [tex]g(h^{-1}(x))[/tex] and [tex]h(g^{-1}(x))[/tex]
If they are equal, then both functions are inverse functions
2. Inverse of f(x) = 3x
Rewrite as:
[tex]y = 3x[/tex]
Swap y and x
[tex]x = 3y[/tex]
Make y the subject
[tex]y = \frac x3[/tex]
Hence, the inverse function is: [tex]f'(x) = \frac x3[/tex]
3. True statements
A function has unique ordered pairs; so, it will pass the vertical line test.
Because it has unique ordered pairs, the inverse function will pass the vertical line tests, and the horizontal line tests.
Hence;
(b) All answers are correct
4. Inverse of [tex]f(x) = 3(x - 2)^3[/tex]
Rewrite as:
[tex]y = 3(x - 2)^3[/tex]
Swap x and y
[tex]x = 3(y - 2)^3[/tex]
Solve for y: Divide both sides by 3
[tex](y -2)^3 = \frac x3[/tex]
Take cube roots of both sides
[tex]y -2 = \sqrt[3]{\frac x3}[/tex]
Add 2 to both sides
[tex]y =2 + \sqrt[3]{\frac x3}[/tex]
Hence, the inverse function is: [tex]f^{-1}(x) =2 + \sqrt[3]{\frac x3}[/tex]
5. The inverse of [tex]f(x) =2x - 3[/tex]
Rewrite as:
[tex]y =2x - 3[/tex]
Swap x and y
[tex]x =2y - 3[/tex]
Solve for y: Add 3 to both sides
[tex]2y = x + 3[/tex]
Divide both sides by 2
[tex]y = \frac{x + 3}{2}[/tex]
Hence, the inverse function is: [tex]f^{-1}(x) = \frac{x + 3}{2}[/tex]
Read more about inverse functions at:
https://brainly.com/question/10300045
1. What is 45% of 36 feet?
*Please Show Work*
What is 45% of 36 feet?
ANSWER AND EXPLANATIONTo find the percent of a number, you have to change the percent into a decimal or a fraction and multiply by the number.
DECIMAL
To change a percent into a decimal, remove the percent sign and move the decimal point 2 places to the left.
[tex]45 \% \rightarrow 0.45[/tex]
Now that you have your decimal, multiply by 36:
[tex]0.45 \times 36 = 16.2[/tex]
ANSWER = 16.2 feet
FRACTION
To change a percent into a fraction, make the percent number as the numerator(top number) and 100 as the denominator(bottom number) since fractions are out of 100.
[tex]45 \% \rightarrow \frac{45}{100}[/tex]
Now that you have your fraction, multiply by 36:
[tex]\frac{45}{100} \times 36 = \frac{1620}{100} \rightarrow 16.2[/tex]
ANSWER = 16.2 feet
If you have any questions, feel free to ask in the comments! :)
Answer:
Step-by-step explanation:
36feet=100%
18feet=50%
48.2=45%
2x − y = 3
4x = 6 + 2y
a. infinitely many solutions
b. x = 2, y = 1
c. y = 2x - 3
d. x = 4, y = 5
Answer:
a. Infinitely many solutions
Step-by-step explanation:
The given equations are 2x - y = 3
4x = 6 + 2y
We can use substitution method to solve these system of equations.
2x - y = 3
y = 2x - 3
Now plug in y = 2x - 3 in the second equation, we get
4x = 6 + 2(2x - 3)
4x = 6 + 4x - 6
4x = 4x
Here we get infinitely many solution.
Both the equations are the same.
Thank you.
I need help with this please
Each of these sequences goes into the classification box above it.
Step-by-step explanation:If the difference of terms is a constant, it is arithmetic.
... (3 -(-1)) = 4 = (7 -3), so the first sequence is arithmetic
If the ratio of terms is a constant, it is geometric.
... 12/36 = 1/3 = 4/12, so the second sequence is geometric
The third sequence has neither constant differences nor constant ratios, so is neither arithmetic nor geometric.
a certain tv can be purchased from the manufacturer for $160. A certain online retailer gas a standard markup for 30%, and a certain superstore has a standard markup of 40%
what is the price of the tv when purchased online?
Answer:
208
Step-by-step explanation:
basically you can plug this into a calculator, just by pressing 160 + 30(then the percent sign), followed by the equal sign. or you can do it on paper by dividing 160 by 100, which gives you 1.6. then you multiply that by 30, with leaves you with 48. and because 48 is 30% of 160, you do 48 + 160 equals 208.
Find the unknown side lengths in similar triangles PQR and ABC
A=
B=
Answer:
A=6
B=8
Step-by-step explanation:
The hypotenuse QR is twice the length of BC, so PQ will be twice the length of AB, 2·3 = 6; and PR will be twice the length of AC, 2·4 = 8.
In similar triangles PQR and ABC:
Side PQ (a) is 40/3 units.
Side PR (b) is 50/3 units.
To find the unknown side lengths in similar triangles PQR and ABC, we can use the properties of similar triangles. Two triangles are similar if their corresponding angles are congruent, and their corresponding sides are in proportion.
In this case, we have triangles PQR and ABC:
PQR:
RQ = 10
QP = a
RP = b
ABC:
AB = 3
AC = 4
BC = 5
Since the triangles PQR and ABC are similar, the ratios of corresponding sides must be equal. Specifically, the ratio of the sides in triangle PQR to the sides in triangle ABC should be the same. We can set up proportions to solve for a and b:
RQ / AB = QP / AC = RP / BC
10 / 3 = a / 4 = b / 5
Now, we can solve for a and b separately.
From the first part of the proportion:
10 / 3 = a / 4
Cross-multiply:
10 * 4 = 3 * a
40 = 3a
Now, divide by 3 to solve for a:
a = 40 / 3
From the second part of the proportion:
10 / 3 = b / 5
Cross-multiply:
10 * 5 = 3 * b
50 = 3b
Now, divide by 3 to solve for b:
b = 50 / 3
So, the unknown side lengths are:
a = 40/3
b = 50/3
Therefore, in similar triangles PQR and ABC:
Side PQ (a) is 40/3 units.
Side PR (b) is 50/3 units.
for such more question on triangles
https://brainly.com/question/1058720
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Notes: Each calculator is $5 dollars and the shipping cost $15. Write a linear relationship between that shows the cost and the number of calculators purchased.
Answer:
y = 5x+15
Step-by-step explanation:
The cost per calculator is 5
The shipping cost is 15
Let y = total cost
Let x = number of calculators
y = 5x+15
Help Please
What is the solution of the system?
Use the elimination method.
-4x - 2y = -12
2x + 4y = -12
Enter your answers in the boxes
(x, y) = (6, -6)
Step-by-step explanation:Divide the first equation by 2 to get equal and opposite coefficients for x.
... -2x -y = -6
Add this to the second equation to eliminate x.
... (2x +4y) +(-2x -y) = (-12) +(-6)
... 3y = -18 . . . . . . . . simplify
... y = -6 . . . . . . . . . . divide by 3
Substitute this vaue into any of the equations to find x. We choose to use the reduced first equation above.
... -2x -(-6) = -6
... -2x = -12 . . . . subtract 6
... x = 6 . . . . . . . divide by -2
The solution to the system is (x, y) = (6, -6).
help please !!!
What is the recursive rule for an=−3n+1 ?
an=
a1=
To find a1, put 1 in the given equation and evaluate.
... a1 = -3·1 +1
... a1 = -2
Each time n increases by 1, an is 3 less than the previous value. So, you can write the recursion relation as ...
... a[n] = a[n-1] - 3
A jetski rental company charges a $50 deposit, plus $25 per hour to rent a jetski. This can be represented by the formula T = 25h + 50, where T is the total cost, and h is the number of hours rented. If the deposited is changed to $40 and the hourly rate is changed to $35, how much more money will the company make on a hour of rental?
Answer:
None, the answer will be the same
Step-by-step explanation:
find each side length,round to the nearest tenth if necessary 11.
We can use a modified form of the Pythagorean Theorem to find the length of x, also known as side b.
Pythagorean Theorem:
a^2 + b^2 = c^2
We can fill in the values of a^2 and c^2, and then solve for b.
14^2 + b^2 = 25^2
196 + b^2 = 625
Subtract 196 from both sides.
b^2 = 429
√ both sides.
b = 20.7
The value of x, or b, is equal to 20.7.In △ABC, AB=8, BC=10, and AC=12. Let M, N, and K be the midpoints of the sides of △ABC. Find length of each side of △MNK.
Answer:
The side lengths are 4, 5, and 6.
Step-by-step explanation:
Each midsegment is half the length of the parallel side, so the side lengths of ΔMNK are 4, 5, and 6.
It isn't clear which point is the midpoint of what segment. If it is true that ...
M is the midpoint of ABN is the midpoint of BCK is the midpoint of ACthen ...
MN = AC/2 = 6NK = AB/2 = 4KM = BC/2 = 5Answer:
4, 5, 6
Step-by-step explanation:
Lisa purchased a concert ticket on a web site. The original price of the ticket was $75. She used a coupon code to received a 20% discount. The web site applied a 10% service fee to the discount price. Lisa's ticket was less than the original price by what percent?
12%
Step-by-step explanation:Her discounted price was 100% - 20% = 80% of the original price. The service fee made it be 100% + 10% = 110% of that, so her final price was ...
... 110% × 80% = 88%
of the original ticket price.
This represents a discount of 100% - 88% = 12% from the original.
classify what type of angle this is
Question
classify what type of angle this is
Answer:
IsoscelesStep-by-step explanation:
2 equal side and 2 equal angles, it is an isosceles.
Which ordered pairs lie on the graph of the exponential function f(x)=−3^(x−1) +2 Select each correct answer.
(−1, 2)
(1, 1)
(0, 0)
(4,−25)
(1, 1), (4, -25)
Step-by-step explanation:You can evaluate the function to see.
f(-1) = -3^(-1-1)+2 = -3^(-2)+2 = -1/9 +2 ≠ 2
f(1) = -3^(1-1) +2 = -1 +2 = 1
f(0) = -3^(0-1) +2 = -1/3 +2 ≠ 0
f(4) = -3^(4 -1) +2 = -27 +2 = -25
_____
Or, you can graph the points and the curve.
Answer:
(1, 1), (4, -25)
Step-by-step explanation:
Change the fraction to a decimal. a. 6⁄100 b. 43⁄100 c. 3⁄10 d. 4 23⁄1,000
6/100 = 0.06
43/100 = 0.43
3/10 = 0.3
23/1,000 = 0.023
Hope this helps!
Final answer:
To convert fractions to decimals, divide the numerator by the denominator and combine with any whole number for mixed numbers, resulting in 0.06, 0.43, 0.3, and 4.023 respectively for the given fractions.
Explanation:
The question asks to change fractions to decimals. Here are the step-by-step conversions:
a. 6⁄100: This fraction means 6 divided by 100, which is 0.06.
b. 43⁄100: Similarly, 43 divided by 100 is 0.43.
c. 3⁄10: Dividing 3 by 10 gives you 0.3.
d. 4 23⁄1,000: For the mixed number, you have the whole number 4 and the fraction 23⁄1,000. The fraction part is 23 divided by 1,000, which is 0.023. So, you combine the whole number and the decimal to get 4.023
Converting fractions to decimals involves dividing the numerator by the denominator and adding any whole number part if it's a mixed number.
50 POINTS FOR CORRECT ANSWER @PlatoNation
REPORTED IF INCORRECT
Answer:
About 2614 years.
Step-by-step explanation:
We are given k, and the information that N/N0 = 0.77, so the C-14 function becomes:
[tex]N=N_0\cdot e^{-kt} \\0.77N_0 = N_0\cdot e^{-kt}\\0.77 = e^{-0.0001 t}[/tex]
and we can solve for t:
[tex]0.77 = e^{-0.0001 t}\\\ln0.77 = \ln e^{-0.0001 t}\\\ln 0.77 = -0.0001 t\implies\\t = -\frac{\ln0.77}{0.0001}=2613.65\approx 2614\,\,\,\mbox{years}[/tex]
The estimated age of the bird skeleton is 2614 years.
the scale on a map is 1 cm for every 400 km .If the Maine and Japan are 22 cm apart on the map, what is the distance between Maine and Japan?
Answer:
8,800
Step-by-step explanation:
400 km
1 cm
=
d
22 cm
Select the correct answer. What is the mode of this data set? {41, 43, 45, 3, 11, 23, 24, 27, 29, 45, 12, 19, 22, 49, 25}
The mode is the number in the set that appears the most.
In the given data set, the number 45 is listed twice while all the other numbers are only listed once.
The mode is 45.
Answer:
45
Step-by-step explanation:
The value which appears most often or has the highest frequency in a data set is said to be the mode.
Here we are given the following data set:
{41, 43, 45, 3, 11, 23, 24, 27, 29, 45, 12, 19, 22, 49, 25}
For this data set, we can see that the number / element 45 has occurred the most often which is twice. So the mode of this data set will be 45.
Choose all of the unit vectors
To choose unit vectors, one must understand that they have a magnitude of one and are directed along the axes in space. For any point P or S, the unit vectors are (i_p, j_p, k_p) or (i_s, j_s, k_s) respectively, each with a magnitude of one.
Explanation:To determine which vectors are unit vectors, you must know that a unit vector has a magnitude (length) of one and indicates direction in space. The given information states that for a point P in space, the unit vectors are (î_p, â_p, k_p). Each of these vectors has a magnitude of one and points in the direction of increasing x, y, and z coordinates, respectively. Similarly, for point S, you have (i_s, j_s, k_s), also with a magnitude of one.
The special types of unit vectors such as î (i-hat), â (j-hat), and k (k-hat) are always of magnitude one and are parallel to the x, y, and z axes, respectively. The vector dê, represents a vector of length d pointing in the positive x-direction, implying dê is also a unit vector if d equals one.
Therefore, in the context provided, all options (a), (b), (c), and (d) are correct if their vectors have a magnitude of one and adhere to the rules to be considered unit vectors.
keep on getting 10x+12
[tex]\dfrac{13x+10}{2x^2-5x-25}[/tex]
Step-by-step explanation:Multiply the first fraction by (x-5)/(x-5) and the second by (2x+5)/(2x+5). Now, you have both fractions with the common denominator (2x+5)(x-5).
[tex]\dfrac{3}{2x+5}+\dfrac{5}{x-5}=\dfrac{3(x-5)}{(2x+5)(x-5)}+\dfrac{5(2x+5)}{(2x+5)(x-5)}\\\\=\dfrac{3(x-5)+5(2x+5)}{(2x+5)(x-5)}=\dfrac{3x-15+10x+25}{2x^2-5x-25}\\\\=\dfrac{13x+10}{2x^2-5x-25}[/tex]
Which expressions are equivalent to 70 × 5.3
Answer:
35 x 10.6, 140 x 2.65 and 371 x 1
Step-by-step explanation:
my sides are all the same length. my area is 9 square meters. what is the length of one of my sides?
Answer:
3
Step-by-step explanation:
if the length and width is 3, 3 times 3 is 9
Reuben attached a wire between two poles on a hill as shown which is the closest to x the distance between the two poles
Answer:
75 ft
Step-by-step explanation:
Here we are given a right angled triangle with a known angle of 20°, length of the hypotenuse to be 80 and we are to find the length of the base x.
For that, we can use the formula for cosine for which we need an angle and the lengths of base and hypotenuse.
[tex]cos \alpha =\frac{base}{hypotenuse}[/tex]
So putting in the given values to get:
[tex]cos 20=\frac{x}{80} \\\\x= cos 20*80\\\\x=75.17[/tex]
Therefore, the value of x is the closest to 75 ft.
The heights of two cylinders are in the ratio 3:1 if the volumes of two are same find the ratio of their respective radii
Answer:
[tex]\sqrt{3}[/tex] :1
Step-by-step explanation:
Ratio of height of two cylinders are 3:1
Let C2 has the height x
then height of C1 is 3x
Let r1 is the radius of C1
and r2 is the radius of C2
As given that volume of both are equal
Also we know that formula for the volume of the cylinder is
V= π r²h
for C1
V= π (r1)²h
for C2
V=π (r2)²h
As volume of both are same so equating them
π (r1)²h1 = π (r2)²h2
as h1 =3x and h2=x
putting values
π (r1)²(3x) = π (r2)²(x)
cancelling out π and x from both side of the equation
3(r1)²= (r2)²
Taking square root of both sides give
[tex]\sqrt{3(r1)^{2} }=\sqrt{(r2)^{2} }[/tex]
r1 ( [tex]\sqrt{3}[/tex]) = r2
or
r1 : r2 = [tex]\sqrt{3}[/tex] :1
The hikers plan to visit a scenic lookout. They will rest after they hike 2 miles. Then they will hike the remaining 1 3/4 miles to the lookout. The trail the hikers will use to return from the lookout is 1/2 mile shorter than the trail they will use to go to the lookout. Each hiker will bring 1/4 gallon of water for each mile to and from the lookout. Determine the total distance, in miles, each hiker will hike? and Determine the total number of gallons of water each hiker will bring ?
Answer:
7 miles1 3/4 gallonsStep-by-step explanation:
The distance to the lookout is the sum of distances before and after the rest stop:
... "to" distance = 2 mi + 1 3/4 mi = 3 3/4 mi
The distance from the lookout is 1/2 mile shorter, so is ...
... "from" distance = 3 3/4 mi - 2/4 mi = 3 1/4 mi
Then the total hike is ...
... total distance = "to" distance + "from" distance
... = 3 3/4 mi + 3 1/4 mi = 6 4/4 mi
... total distance = 7 mi
The water each hiker will bring is ...
... (7 mi) × (1/4 gal/mi) = 7/4 gal = 1 3/4 gal
Each hiker will hike a total of 7 miles, and they will need to bring 1.75 gallons of water for the entire trip.
First, we need to determine the total distance each hiker will travel:
Initial hike to rest: 2 milesRemaining hike to the lookout: 1 3/4 miles or 1.75 milesTotal distance to the lookout: 2 + 1.75 = 3.75 milesThe return trail is described as 1/2 mile shorter than the trail to the lookout. Therefore:
Return trail distance: 3.75 - 0.5 = 3.25 milesSumming up the distances:
Total hiking distance: 3.75 + 3.25 = 7 milesCalculating Total Water Needed:
Each hiker brings 1/4 gallon of water per mile:
Total miles hiked: 7 milesWater needed per mile: 1/4 gallonTotal water needed: 7 * 1/4 = 1.75 gallonsThus, each hiker will hike a total of 7 miles and will need to bring 1.75 gallons of water for the entire trip.
the average temperature in Alaska in January is -9°F in February it is -16°F which month has the coldest temperature
Answer:
February
Step-by-step explanation:
February is colder by 7°F
-9 - 7 = -16
~
Answer:February
Step-by-step explanation:
If you see the number line below -16 is more far than -9
-------------------------------------------------------------------------------------------------
' ' '
-16 -9 0
0=9(k-2/3)+33 solve for k
Answer:
k = -3
Step-by-step explanation:
Simplify, divide by 9, add the opposite of the constant.
0 = 9k -9·2/3 +33
0 = 9k +27
0 = k +3
-3 = k
Which of the following functions is graphed below ?
See the attachment
Step-by-step explanation:The solid dot on the right-hand portion of the curve means the function is defined for x ≥ 2. Choices A and C have that condition.
The function is linear for x ≥ 2, so matches selection C, not A.