14912 years ago, the tree that was used to kill the support pole died which is one-sixth of the carbon-14 of a modern, living tree.
What are the properties of logarithms?There are four basic properties of logarithms:
logₐ(xy) = logₐx + logₐy.
logₐ(x/y) = logₐx - logₐy.
logₐ(xⁿ) = n logₐx.
logₐx = logₓa / logₓb.
One-sixth of a modern, living tree's carbon-14 is present in an ancient structure.
Assume that the half-life of carbon-14 is 5770 years
As per the given condition, the expression would be
[tex]A(t) = A_o}\dfrac{1}{2} ^{(\frac{t}{5770} )}\\A(t) = (0.167)A_o}[/tex]
[tex](0.167)A_o} = A_o}\dfrac{1}{2} ^{(\frac{t}{5770} )}[/tex]
[tex](0.167) = \dfrac{1}{2} ^{(\frac{t}{5770} )}[/tex]
Take the logarithms of both sides to get:
[tex]log(0.167) =log \dfrac{1}{2} ^{(\frac{t}{5770} )}[/tex]
Using logₐ(xⁿ) = n logₐx.
⇒ log 0.167= (t/5770) log (0.5)
⇒ log 0.167/ log (0.5)= (t/5770)
⇒ 3 = (t/5770)
⇒ t = 3 × 5770
⇒ t = 14912
Hence, 14912 years ago, the tree that was used to kill the support pole died.
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Find the surface area or volume of each rectangular prism. Show your work on a
separate sheet of paper.
Answer:
Formulas for a rectangular prism:
Volume of Rectangular Prism: V = lwh.
Surface Area of Rectangular Prism: S = 2(lw + lh + wh)
Space Diagonal of Rectangular Prism: (similar to the distance between 2 points) d = √(l2 + w2 + h2)
2.5 of what is 3?
Need help ASAP
You are lubricating several motors in the shop. One motor must be lubricated with of 3/16 an ounce of grease, and one larger motor must be lubricated with 3/8 of an ounce of grease. How many ounces of grease will you require? Your answer should be a fraction of an ounce, reduced to its lowest terms.
Given: p: x is a perfect square. q: x is even
What is a value of x that makes p and q true?
16
30
81
99
Answer:
16
Step-by-step explanation:
16: 16=4^2 and is even. 16/2=8
30: 30 is even, 30/2=15. However, the square root of 30 is between 5 and 6([tex]\sqrt{25}[/tex]and [tex]\sqrt{36}[/tex]).
81: 81=9^2, but 81 is not even. 81/2=40.5.
99: 99 is not even and doesn't have a square root. The square root of 100 is 10, so the square root of 99 is around 9.9, slightly less than 10.
Write down two prime numbers that have a sum of 20
3 and 17
7 and 13
Step-by-step explanation:
........
help me with this precal
Answer: Ok
Step-by-step explanation:
9-0-0
denny is in the car repair business. Denny recently calculated his total cost conditions. He found that the total cost of repairing s cars is TC(s)=2s^2+10
If the market price is $20, how many cars will Denny be willing to repair?
When the market price is $20, the number of cars that Denny will be willing to repair is 5 cars.
How to calculate the value?It should be noted that the total revenue will be:
= price × quantity
= 20 × s
= 20s
where s = number of cars
The marginal revenue will be 20.
The total cost is given as:
= 2s² + 10
The marginal cost will be 4s
We will equate the marginal. This will be:
4s = 20
Divide
s = 20/4
s = 5
Therefore, the number is 5.
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To make barstools, Federico rents a shop for $1510 a month and calculates the materials for each stool are $45. Find the total cost for him to make 98 stools in a month.
Answer:
4410
Step-by-step explanation:
45 x 98 = 4410
can someone help me with this
Wilson hires a financial analyst to analyse costs and profits for his cereal production business. The analyst determines that Wilson’s eventual profit function is given as: , where x is the number of bags of cereal produced. At what point or number of bags of cereal will Wilson’s profit start decreasing
The company's profit will start to decline if it only produces one bag.
Given f(x) = 2x⁴ ₋ 4x³ ₊ 7
Differentiate it with respect to x.
therefore, f'x) = 8x³ ₋ 12x²
= 4x²(2x ₋ 3)
For decreasing, f'(x) ≤ 0
⇒ 4x²(2x ₋ 3) ≤ 0
⇒ 2x ₋ 3 ≤ 0
⇒ x ≤ 3/2
Since the number of bags are represented by x.
Hence, x ∈ N
Therefore, x = 1 is only possibility.
Therefore, if the company only produces one bag, its profit begins to decline.
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Your question was incomplete. Please find the missing the content here.
Wilson hires a financial analyst to analyse costs and profits for his cereal production business. The analyst determines that Wilson's eventual profit function is given as: pi = 2x⁴ ₋ 4x³ ₊ 7 where x is the number of bags of cereal produced. At what point or number of bags of cereal will Wilson's profit start decreasing?
PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!!!
Using the normal distribution, it is found that 55.7% of response times are between 4 and 6 minutes.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For this problem, the mean and the standard deviation are given, respectively, by:
[tex]\mu = 4.5, \sigma = 1.2[/tex]
The proportion between 4 and 6 minutes is the p-value of Z when X = 6 subtracted by the p-value of Z when X = 4, hence:
X = 6:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (6 - 4.5)/1.2
Z = 1.25
Z = 1.25 has a p-value of 0.8944.
X = 4:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (4 - 4.5)/1.2
Z = -0.42
Z = -0.42 has a p-value of 0.3372.
0.8944 - 0.3372 = 0.5572 = 55.72%.
Hence:
55.7% of response times are between 4 and 6 minutes.
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4x+3y=7 x+2y=-2
put both in slope-intercept form
Answer:
Second equation Answer: [tex]y=-\frac{1}{2}x-1[/tex]
First equation Answer: [tex]y=-\frac{4}{3}x~+\frac{7}{3}[/tex]
Step-by-step explanation:
Concept:
The general equation of a line in slope-intercept form is given below as
[tex]y=mx+c[/tex]
where
[tex]m=slope[/tex]
[tex]c=intercept[/tex]
First equationThe first equation is given below as
[tex]4x+3y=7[/tex]
We will make y the subject of the formula to change the equation in slope-intercept form
[tex]4x+3y=7[/tex]
subtract 4x from both sides
[tex]4x-4x+3y=7=-4x[/tex]
[tex]3y=-4+7[/tex]
divide both sides by 3
[tex]\frac{3}{y} =\frac{-4x}{3} +\frac{7}{3}[/tex]
[tex]y=-\frac{4}{3}x~+\frac{7}{3}[/tex]
Hence,
The equation of 4x+3y=7 in slope intercept form is given below as
[tex]y=-\frac{4}{3}x~+\frac{7}{3}[/tex]Second EquationThe second equation is given below as
[tex]x+2y=-2[/tex]Subtract x from both sides[tex]x-x+2y=-2-x[/tex][tex]2y=-x-2[/tex]divide through by 2[tex]\frac{2y}{2} =-\frac{x}{2} =-\frac{2}{2}[/tex][tex]y=-\frac{1}{2}x-1[/tex]Hence,
The equation of x+2y=-2 in slope-intercept form is
[tex]y=-\frac{1}{2}x-1[/tex]Hope this Helps! <3Answered by:AshTheNeko
.
A polling organization conducts a study to estimate the percentage of households that have high-speed Internet access. It mails a questionnaire to 1495 randomly
Internet access. Of the 1495 households selected, 22.
a) The best description of the bias in the survey is A. Nonresponse bias.
b) To remedy this bias, B. The polling organization should try contacting households that do not respond by phone or face-to-face.
What is nonresponse bias?Nonresponse bias is the type of bias when survey participants are not interested in the survey or send an empty or unsatisfactory response.
Nonresponse bias means that the sample is filled with those who are not willing or able to respond, making the number of non-respondents surpass the number of respondents.
Thus, a response of 22/1,495 is too significant to be ignored, meaning that the nonresponse bias is much more critical.
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Question Completion:responded.
a) Which of these best describes the bias in the survey?
A. Nonresponse bias
B. Sampling bias
C. Undercoverage bias
D. Response bias
b) How can the bias be remedied?
A. The polling organization should mail the questionnaire to a greater number of households.
B. The polling organization should try contacting households that do not respond by phone or face-to-face.
C. The polling organization should mail the questionnaire to each person in the household.
Mark Ogara rented a truck from Avis Rent-A-Car for the weekend (2 days). The base rental price was $30.45 per day plus 15 3/4 cents per mile. Mark drove 415.85 miles.
How much does Mark owe?
ound your answer to the nearest cent.
The amount that he owes will be $6610.54.
How to compute the value?From the information, the base rental price was $30.45 per day plus 15 3/4 cents per mile. Mark drove 415.85 miles.
Therefore the amount that will be paid will be:
= ($30.45 × 2) + (15.75 × 415.85 miles)
= $60.90 + $6549.64
= $6610.54
The cost is $6610.54.
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Jaspare is planning a road trip. He has found 14 places that he wants to visit, but only has time to stop at 5 places. He is visiting the places in a specific order. How many different ways can he plan his trip?
The number of different ways to plan his trip is 240240
In how many different ways can he plan his trip?The given parameters are
Places, n = 14
Stops, r = 5
From the question, we understand that the places are in specific order
This represents permutation
So, the number of different ways to plan his trip is
Ways = [tex]^nP_r[/tex]
This gives
Ways = [tex]^{14}P_5[/tex]
Apply the permutation formula
Ways = 14!/9!
Evaluate
Ways = 240240
Hence, the number of different ways to plan his trip is 240240
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PLSSS HELP ANSWER, THE QUESTION IS IN THE SCREENSHOT
[tex]y(\pi/3)=1 \implies 1=C-2\cos(\pi/3) \\ \\ 1=C-1 \\ \\ C=0 \\ \\ \therefore y=\boxed{-2\cos x}[/tex]
PLS CHECK IF THIS ANSWER IS CORRECT
WILL MARK BRAINLIEST
Answer:
I'm pretty sure the answer is 6.
Step-by-step explanation:
Labeling the rooms A, B, and C makes it easier.
Room A - All BUT 4
Room B - All BUT 4
Room C - All BUT 4
Since you can see each room is all but four, you can split the 4 into 2 into 2 OTHER rooms than the one stated. For example, Room A is all but 4, so 2 go to Room B and the other 2 go to Room C because each room is all BUT 4.
Basically, 2+2+2 = 6
Which of the following systems of equations has the same
solution as
-2x+2y=-2;3x-y=9
a.
A. 4x = 16;3x-y=9
B. [-2x+2y=-2;16x-2y = 9
C. -3x-7y=3;3x-y=9
D. [-2x+2y=-2;x+y=11
Answer:
Step-by-step explanation:
16/4
How do you find the range and domain of this graph?
Answer: Domain {-4,-2,2}
Range{4,6}
Step-by-step explanation:
Find the measure of KNM
Ximena launches a toy rocket from a platform. The height of the rocket in feet
is given by h(t) = -16t² + 40t +96 where t represents the time in
seconds after launch. What is the appropriate domain for this situation?
The apprοpriate dοmain fοr this situatiοn is t ≥ 0.
What is Functiοn?In mathematics, a functiοn is a relatiοn between a set οf inputs and a set οf pοssible οutputs with the prοperty that each input is related tο exactly οne οutput. It can be thοught οf as a rule οr a machine that takes inputs and prοduces οutputs accοrding tο a specific set οf instructiοns οr οperatiοns.
The dοmain οf a functiοn represents the set οf all pοssible input values fοr which the functiοn is defined. In this case, the functiοn h(t) represents the height οf the rοcket as a functiοn οf time t after launch.
Since time cannοt be negative in this cοntext (we can't have negative secοnds), the apprοpriate dοmain fοr this situatiοn is t ≥ 0, which means the functiοn is defined fοr all nοn-negative values οf t after the rοcket is launched.
Therefοre, the apprοpriate dοmain fοr this situatiοn is t ≥ 0.
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Use properties of operations to add (−3) and (−17)
14
20
-20
-14
Answer:
Step-by-step explanation:
-20
Triangle XYZ has translated 4 units up and 3 units left to yield ΔX'Y'Z'. What is the distance between any two corresponding points on ΔXYZ and ΔX'Y'Z′?
The distance between any two point is 5 unit.
What is distance?
The measurement of distance between two objects or points can be quantitative or occasionally qualitative. Distance in physics or common language can refer to a physical length or an assumption based on other factors.
As per the question
Triangle xyz is translated = 4units
And triangle xyz left to yield=3 unit
The distance between the corresponding is hypotenuse of the triangle is-
Buy applying Pythagorus theorem we can get C^2=a^2+b^2
As we know a,b=legs
c=hypotenus
C^2=a^2+b^2C^2
=3^2+4^2
=9+16
=25C =√25 =5 unit
Therefore, the distance between any two point is 5 unit.
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←
Assume log x=0.27 and log by = 0.81. evaluate the following expression logb x/y
By evaluating following logarithm equation and we we get the value of required expression is -0.54.
What is logarithm?
The logarithm is the opposite of exponentiation as a function. This indicates that the base b of another fixed number, the logarithm of a given number x, is the exponent that must be raised in order to obtain the given number x.
As per the question
we have to assume x
log x=0.27
log by=0.81
We have to calculate log bx/y by following expression
We know loge (a/b)= log_e a-log_e b
We know (x)= logb y
=0.27-0.81
= -0.54
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Three line segments form the letter Z. Rotate the letter Z counterclockwise around the midpoint of segment BC by 180 degrees. Describe the result.
Answer:
i don't known the question you are asking
Which matrix represents the system of equations shown below?
4x+2y=4
12x - y = 26
-2
OA. [12326]
12 -1 26
-4
OB. 12 -1 -26
4 2 14
OC. [2²1]
12 -1 26
4x 2y 4
OD. [12x ²Y |26]
-y
So matrix which show equation 4x+2y=4 is [tex]\left[\begin{array}{ccc}4&2&4\\12&-1&26\end{array}\right][/tex] .
Given that we have an equation that is 4x+2y=4
So equation is a statement that the values of two mathematical expressions are equal (indicated by the sign =).
So in order to write this equation in matrix form we have to write it into augmented matrix
So augmented matrix is a matrix whose elements are the coefficients of a set of simultaneous linear equations with the constant terms of the equations entered in an added column.
Therefore the matrix will be:
[tex]\left[\begin{array}{ccc}4&2&4\\12&-1&26\end{array}\right][/tex] .
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Solve for x.
12x + 7 < -11
OR 5x8 > 40
Answer:
-3/2
Step-by-step explanation:
x < -3/2
a car rental company charges a daily rate of $26 plus $0.10 per mile for a certain car. Suppose that you rent that car for a day and your bill (before taxes) is $71. How many miles did you drive?
Answer: 450 miles
Step-by-step explanation: we can put the info we got from the question into an equation. since the car was only rented for a day, the daily rate that was paid was $26. and $0.10 for every mile the car was driven. So we can put into the equation 71 = 26 +0.10m, where m represents miles. Now subtract 26 from both sides and we get 45 = 0.10m. Divide both sides by 0.10 and we get m= 450
PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!!!
The proportion of users that park bike on the trail is 0.1728
How to determine the proportion of users that park bike on the trail?The table represents the given parameters
From the table, we have the following parameters
Suburban total = 243
Users that park bike on the trail = 42
The proportion of users that park bike on the trail is then calculated as
P = Users that park bike on the trail/Suburban total
This gives
P = 42/243
Evaluate
P = 0.1728
Hence, the proportion of users that park bike on the trail is 0.1728
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At a local pizzeria, a pizza with one topping is 9.99. You can add additional toppings for 1.25 each. The pizzeria's menu lists 10 different toppings. Write a function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings. Find the domain and range.
The function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings is C(x) = 9.99 + 1.25x
The domain is x >= 0 and the range is c(x) >= 9.99
Write a function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings.The given parameters are:
One topping = 9.99
Additional topping = 1.25 each
We have x to represent the number of toppings
This means that
C(x) = One topping + Additional topping * x
So, we have
C(x) = 9.99 + 1.25x
How to find the domain and range?We have
C(x) = 9.99 + 1.25x
The smallest number of topping is 0
So, the domain is x >= 0
Substitute 0 for x in C(x) = 9.99 + 1.25x
C(0) = 9.99 + 1.25(0)
This gives
C(0) = 9.99
So, the range is c(x) >= 9.99
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Answer:
C(x) = 8.74 + 1.25x
Domain: 1 ≤ x ≤ 10
Range: [9.99, 21.24]
Step-by-step explanation:
a) We need to find the function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings.
We know that a pizza with one topping is $9.99 and that you can add additional toppings for 1.25 each.
So the equation is C(x) = 9.99 + 1.25x right?
Not really... Since $9.99 is the price of a pizza and 1 topping, we need to subtract 1 from x otherwise we would be paying for a pizza with 2 toppings when we had ordered a pizza with 1!
So the new equation is:
C(x) = 9.99 +1.25(x - 1)
or, C(x) = 9.99 + 1.25x - 1.25
or, C(x) = 1.25x + 8.74
b) We need to find the Domain of C(x).
We know that the pizzeria's menu lists 10 different toppings and that a pizza has at least one topping.
So we can choose up to 10 different toppings. And we need at least 1 topping.
∴ Domain is 1 ≤ x ≤ 10.
b) We need to find the Range of C(x).
We know that the domain of C(x) is 1 ≤ x ≤ 10, and that a pizza with 1 topping is $9.99.
Since we already know the minimum (9.99) all we have to do is find the maximum. We can do that by plugging in 10 into C(x) since it is the maximum of our domain.
C(10) = 1.25(10) + 8.74
or, C(10) = 12.50 + 8.74
or, C(10) = 21.24
∴ Range of C(x) = [9.99, 21.24]
Answer:
C(x) = 8.74 + 1.25x
Domain: 1 ≤ x ≤ 10
Range: [9.99, 21.24]