A.) f(x-2)+f(2x)
To find this expression, we can substitute the definition of f(x) into the expression and simplify:
f(x-2)+f(2x) = [10(x-2)-4] + [10(2x)-4]
= 10x - 20 - 4 + 20x - 4
= 30x - 28
Therefore, f(x-2)+f(2x) = 30x - 28.
Compute f(2a) - f(a) for any value of a ?Given f(x) = 10x - 4, we need to find f(2a) - f(a).
f(2a) = 10(2a) - 4 = 20a - 4
f(a) = 10a - 4
Therefore,
f(2a) - f(a) = (20a - 4) - (10a - 4)
= 10a
Answer: f(2a) - f(a) = 10a. This means that the difference between the function evaluated at 2a and a is simply 10 times a.
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Find all real numbers z for which the equation (z-5)x^2-zx+5=0 has exactly one real solution.
By making the discriminant equal to zero, we can see that the quadratic equation has one real solution only for z = 10.
For which values of z the quadratic equation has only one real solution?For a general quadratic equation:
a*x^2 + b*x + c = 0
We define the discriminant as:
D = b^2 - 4ac
The quadratic equation will have only one real solution only if the discriminant is equal to zero.
Here the quadratic is:
(z - 5)*x^2 - z*x + 5 = 0
Then the discriminant is:
(-z)^2 - 4*5*(z - 5)
And that must be equal to zero, then we need to solve:
z^2 - 20*(z - 5) = 0
z^2 - 20z + 100 = 0
Using the quadratic formula we will get:
[tex]z = \frac{20 \pm \sqrt{(-20)^2 - 4*1*100} }{2} \\\\z = \frac{20 \pm 0}{2} \\\\z = 10[/tex]
So the quadratic equation has one real solution only for z = 10.
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Consider the two triangles. How can the triangles be proven similar by the SSS similarity theorem?
To prove that ΔUVW and ΔXYZ are similar by the SSS Similarity Theorem: a. show that the ratios UV/XY, WU/ZX, and WV/ZY are equivalent.
What is the SSS Similarity Theorem?
The SSS Similarity Theorem states that two triangles are similar if the ratio of all three pairs of corresponding sides of two triangles are equivalent.
Given ΔUVW and ΔXYZ, where:
UV corresponds with XY, thus UV/XY = 50/40 = 1.25
WU corresponds with ZX, thus WU/ZX = 40/32 = 1.25
WV corresponds with ZY, thus WV/ZY = 60/48 = 1.25
Since all the ratio of all three corresponding sides of both triangles are equivalent, therefore both triangles can be proven to be similar by the SSS Similarity Theorem.
Therefore, to prove that ΔUVW and ΔXYZ are similar by the SSS Similarity Theorem: a. show that the ratios UV/XY, WU/ZX, and WV/ZY are equivalent.
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A lighthouse is situated 10m back from a 35m high cliff. If the beacon is 8m above the base of the lighthouse, how far from the cliff does the shadow extend?
Answer: the shadow will extend 43.75m
Step-by-step explanation:
David's phone has about 10,000 songs. The distribution of play time for these songs is heavily skewed to the right with a mean of 225 seconds and a standard deviation of 60 seconds. Suppose we choose an SRS of 10 songs from this population and calculate the mean play time i of these songs.
a) Calculate the mean and standard deviation of the sampling distribution.
b) Interpret the standard deviation from part (a)
On solving the provided question, we can say that The following are the mean and standard deviation of the sample distribution of x: Average: 225 sec. 19 second standard deviation.
What is standard deviation?Standard deviation is a statistic that expresses the variability οr variance of a grοup of numbers. While a high standard deviation suggests that the values are mοre dispersed, a low standard deviation suggests that the values tend tο be closer to the established mean.
A measure of hοw dispersed the data are frοm the mean is the standard deviation (οr ). When the standard deviation is lοw, the data tend to be grouped around the mean, and when it is large, the data are mοre dispersed. The average variability of the data set is measured as standard deviation. It reveals the average deviation of each scοre from the mean.
The median matches the median οf the population.
The pοpulation standard deviation is divided by the square root of the sample size tο produce the standard deviation.
The following are the criteria fοr this issue:
average population of 225 seconds.
60 second population standard deviatiοn.
10 second sample size.
Consequently, the following is the standard deviation fοr the sample distributiοn of x:
19 seconds are equal to 60/√(10).
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Joseph selects a card from a standard deck of 52 cards and then replaces it afterwards. He decides to record the total number of red cards that he selects and calculates the proportion of red cards that he has selected so far after each pick. He then constructs a graph to visualize his results. Which of the following statements is FALSE?O The theoretical probability for selecting a red card in each pick is 0.5. O For a given number of selections, we can use Joseph's graph to find the number of diamonds that he has picked so far. O This is an example of the law of large numbers. O The relative frequency of selecting a red card changes with the increase in number of selections.
He then constructs a graph to visualize his results, For a given number of selections, we can use Joseph's graph to find the number of diamonds that he has picked so far is FALSE.
Probability refers to potential. A arbitrary event's circumstance is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to read the liability of colorful events. The degree to which commodity is likely to be is principally what probability means.
You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
We are only interested in finding red card so we can't differentiate between diamond or hearts at any time. Hence,
The false statement is:
For a given number of selections, we can use Josephs graph to find the number of diamonds that he has picked so far.
Option B is correct.
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A
B
C
D
Pick a letter
Answer: D
Step-by-step explanation:
1 in.=1488 milesx5=7440 miles.
Area= pi x r^2
=pi x (7440)^2 or option D.
Hope this helps :)
-0.2x+3 / 2 = -0.6 ??
Answer:
Step-by-step explanation:
-0.2x+3 / 2 = -0.6 =>
-0.2x = -(3/2) - 0.6 => (facotorize out -1)
x = ((3/2)-0.6)/0.2 =>
x = 4.5
An investment of $65,000 is increasing at a rate of 3.2% per year. Which function represents how to find the value of the investment after t years?
Answer:
I honestly don't know I just need points
what happend if you do rise over run
PLEASE GIVE BRAINLIEST
thank you and have a good day :)
Answer:
You figure out the slope
Step-by-step explanation:
Rise/Run is a formula that calculates the slope. This determines the direction of the line and how steep it is.
Answer:
its a math term yw my boy
Step-by-step explanation:
Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD?
Oy=2x-2
Oy = 2x + 2
Oy=x+2
Oy=x-2
The required equation of the line representing line CD is y = x + 2. Option C is correct.
The equation of the line passing through two points is given by the equation,
y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁) - - - -- -(1)
Here,
Line CD passes through points (0, 2) and (4, 6)
Let (0, 2) and (4, 6) equal to (x₁, y₁) and (x₂, y₂) respectively.
Substitute this point in equation 1 to get the equation of the line representing CD,
So,
y - 2 = (6 - 2)/(4-0) (x - 0)
y = x + 2
Thus, the required equation of the line representing line CD is y = x + 2. Option C is correct.
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just confusing can someone help due today
Step-by-step explanation:
It's a long answer. You have to find the area of the large triangle, the small triangle than subtract the two
A = 1/2(b)(h)
For the big triangle
A = 1/2(16)(4) = 1/2(64) = 32
For the small triangle
A = 1/2(8)(2)
We use 8 and 2 because that's half of 16 and 4, since at the bottom it says A and B are midpoints
A = 1/2(8)(2) = 1/2(16) = 8
Now we subtract
32-8 = 24 units
Find HP
Round to the nearest whole meter
Check the picture below.
Make sure your calculator is in Degree mode.
For his birthday, Tyler's parents gave him $7,000.00 which they put into a savings account that earns 15% interest compounded quarterly. When Tyler started college, he withdrew the entire balance of $26,725.00 and used it to pay for tuition. How long was the money in the account?
The number of years the interest was compounded quarterly is given by the equation b = 9.098 years
What is Compound Interest?Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
Let the amount after b years be A = $ 26,725.00
The number of years be = b
The number of times the interest is applies n = 4 ( quarterly )
Let the principal amount be P = $ 7,000
A = P ( 1 + r/n )ⁿᵇ
Substituting the values in the equation , we get
t = ln ( A/P ) / n [ ln ( 1 + r/n ) ]
t = b = n ( 26,725.00 / 7,000.00 ) / ( 4 × [ ln ( 1 + 0.15/4 ) ] )
On simplifying the equation , we get
b = ln ( 26,725.00 / 7,000.00 ) / ( 4 × [ ln ( 1 + 0.0375 ) ] )
b = ln ( 3.81785714 ) / 4 [ ln ( 1.0375 ) ]
On further simplification , we get
b = 9.098 years
Hence , the number of years the interest was applied is 9 years 1 months
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Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value.
n=3
4 and 2i are zeros
f(1)=-30
The function for the given zeros is f(x)=2x³-8x²+8x-32.
What are the zeros of the polynomial function?The zeros of polynomial refer to the values of the variables present in the polynomial equation for which the polynomial equals 0.
Given that, n=3.
x=4 and x=2i
We then know that the third root must be x=-2i
Now, f(x)=a(x-4)(x-2i)(x+2i)
= a(x-4)(x²-(-2i)²)
= a(x-4)(x²-(-4))
= a(x-4)(x²+4)
= ax²(x-4)+4(x-4)
f(x)= a(x³-4x²+4x-16)
f(1)=a(1³-4×1²+4×1-16)
-30=a(1-4+4-16)
a=2
Now, f(x)=2(x³-4x²+4x-16)
f(x)=2x³-8x²+8x-32
Therefore, the function is f(x)=2x³-8x²+8x-32.
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A true-false quiz contains six questions. In how many ways can a student answer the questions if the student answers two of the questions with "false" and the other four with "true"?
Answer: In each question you have two options, T and F. Then in 6 questions you have 2 options for the first, two for the second, two for the third... At the end you get 2·2·2·2·2·2 = 26 options and 26 = 64.
Step-by-step explanation:
A square a triangle and a parallelogram are used to form the figure shown. What is the area of the figure in square feet?
A) 213.04
B) 210.64
C) 231.04
D) 207
The area of the attached figure is 32 square mm
What is the area of the figure?The similar question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
A square a triangle and a parallelogram
The shapes can be combined to
a triangle and a parallelogram
So, we have
Area = Sum of individual areas
Using the dimensions of the shapes as a guide, we have the following:
Area = 0.5 * 2 * 8 + 4 * 6
This gives
Area = 32
Hence, the area is 32 square mm
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Convert 2π radians into degrees.
Answer:
360
Step-by-step explanation:
Every 1/2pi is 90 degrees.
Going down the list...
1/2pi is 90
pi is 180
3/2pi is 270
2pi is 360
what does the term 52s represents?
52s represents the cost for the snowboard times s days.
What is an expression ?
An expression consists of one or more numbers or variables along with one more operation.
Given :
expression : 52s + 10
Since it represents , total cost to rent a snow board for s days plus the fee for the helmet
Therefore , 52 is the cost of the snowboard rental per day.
s represents the day(s) that the equipment is rented out.
Hence , 52s represents the cost for the snowboard times s days.
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Given question is incomplete , the complete question is given below:
At the ski shack customers can rent skis snowboards boots and poles by the day. josh rents a snowboard and a helmet. The expression 52s + 10 represents the toatak cost to rent a snow board for s days plus the fee for the helmet what dose the term 52s represent
A newspaper advertisement contains the following information. Busy Body Fitness Center Inventory Reduction Blowout! Sale prices is 20% off original price! Sale Price Upright bike $720. In dollars, what was the original price of the upright bike? Write your answer on the line below.
The original price of the upright bike is $3,600.
What is the original price of the upright bike?
Percentage is the fraction of an amount that is usually expressed as a number out of hundred. The sign that is used to represent percentages is %. Percentage is a measure of frequency.
Original price of the upright bike = sales price / percent discount
= $720 / (20/100)
$720 / 0.2
= $3,600
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The box plot shows the times for sprinters on a track team.
A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 44, 48, 50.5, 53, and 56 are all marked by the box plot. The graph is titled Sprinters' Run Times, and the line is labeled Time in Seconds.
Which of the following is the five-number summary for this data?
Min = 42, Q1 = 44, Median = 50, Q3 = 54, Max = 56
Min = 41, Q1 = 43, Median = 49.5, Q3 = 56, Max = 58
Min = 44, Q1 = 48, Median = 50.5, Q3 = 53, Max = 56
Min = 44, Q1 = 45, Median = 49, Q3 = 56, Max = 58
The summary of the given data is Min = 44, Q1 = 48, Median = 50.5, Q3 = 53, Max = 56 . So option C is correct.
What is the median?The middle number of data in a collection is known as the median. Three alternative metrics are employed in mathematics to determine the average value for a given group of integers. They are the median, mode, and mean. The measures of central tendency are this trio of measurements.
Median = [(n/2)th term + {(n/2)+1}th term]/2 (for even)
Median = {(n+1)/2}th term (for odd)
Based on the given information,
we can see that the box plot shows the values of 44, 48, 50.5, 53, and 56.
These values represent the minimum, lower quartile (Q1), median, upper quartile (Q3), and maximum, respectively.
Therefore, the five-number summary for this data is:
Min = 44,
Q1 = 48,
Median = 50.5,
Q3 = 53,
Max = 56
So the answer is: Min = 44, Q1 = 48, Median = 50.5, Q3 = 53, Max = 56
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What are the features of the function f(x) = -2 log_3 (x + 8) graphed below?
The domain of the function is set of all real numbers except 8. Range of the function is set of all real numbers. The given function does not have asymptotes.
What is a function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
Domain: The domain of the function is the set of all real numbers greater than -8, since the argument of the logarithm, x + 8, must be positive.
Range: The range of the function is all real numbers.
Asymptotes: The function does not have any vertical asymptotes.
Transformation: The function is a reflection of the standard logarithmic function over the x-axis, with a vertical scaling factor of -2. This means that the function will start from the origin and increase without bound.
Behavior near x = -8: As x approaches -8 from the right, the value of the function approaches negative infinity. As x approaches -8 from the left, the value of the function approaches positive infinity.
The domain of the function is set of all real numbers except 8. Range of the function is set of all real numbers. The given function does not have asymptotes.
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Which is a counterexample of the following conditional? "If a number is divisible by seven, then it is odd." 28 21 7 1
PLS JUST DROP THE ANSWER
The counterexample of the given conditional statement is "14 is even number and is divisible by 7."
What is a counterexample?Counterexamples are used in math to contradict a statement. Counterexamples are used to prove the limitations of possible theorems.
The given statement is "If a number is divisible by seven, then it is odd."
Number, 14, 28, 42, 56 are even numbers and they are divisible by seven.
Therefore, the counterexample of the given conditional statement is "14 is even number and is divisible by 7."
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Answer: the answer is 28
Step-by-step explanation: 28 is divisible by 7 and it is a even number
The world population is 2000 was approximately 6.08 billion (6,080,000,000). The annual rate of increase is 1.26%.
a. What is the world population in 2010?
b. What is the population in 2023?
Answer:
6.89 billion for year 2010
7.15 billion for year 2023
Step-by-step explanation:
f(x) = [tex]a(1 + r) ^{x}[/tex]
f(x) = [tex]6.08(1+ .0126)^{10}[/tex]
f(x) = 6.89 Rounded to 2 places
f(x) = [tex]6.08(1+ .0126)^{13}[/tex]
f(x) = 7.15 Rounded to 2 places
please help i am so confused its eulerian circuit
According to the information in the graph, the cheapest route to travel through all cities would be: Atlanta - Dallas - San Francisco - Los Angeles - New York - Detroit - Atlanta.
How to calculate the cheapest option to travel to all cities?To calculate the cheapest option to travel to all cities, we must identify our starting point in the city of Atlanta and analyze which is the cheapest option to travel. In this case, it would be the Detroit or Dallas option (at this point we can choose either one).
Once we choose Dallas, we must apply a location strategy so that the next move leaves us in a suitable position to go to the cities of the east coast. Therefore, the best option would be San Francisco and then Los Angeles.
After this, the best (cheaper) option would be to take transportation to New York, Detroit, and finally to Atlanta. Finally, we must add the values of the displacements to know what the total value is:
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The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 5.8% per hour. How many hours does it take for the size of the sample to double?
It will take 5.189 hours to get doubled the size of Sample.
What is Exponential Function?A relation of the form y = [tex]a^x[/tex], with the independent variable x ranging over the entire real number line as the exponent of a positive number a.
Given:
Growth rate = 5.8%
The continuous exponential growth model for populations is given by:
P(t)= [tex]P_0 e^{rt[/tex]
So, r= 5.8%
r = 0.058
Now, the time taken to double the sample then P(t) = 2P(0).
So, P(t)= [tex]P_0 e^{0.058t[/tex]
2P(0) = [tex]P_0 e^{0.058t[/tex]
[tex]e^{0.058t[/tex] = 2
Taking log on both side
log [tex]e^{0.058t[/tex] = log 2
0.058 t = 0.301
t= 0.301/ 0.058
t = 5.189
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Put a decimal point in the number 26583 so that the 5 has a value of
100
50
The number as decimal is 26583.0
How to rewrite the number as decimalFrom the question, we have the following parameters that can be used in our computation:
Number = 26583
Also, we have the required value of 5 to be
Required = 100
Using the above as a guide, we have the following:
The number 5 must have a value of 100 in the new number i.e. 500
So, we have
Number = 26583
Rewrite as
Number = 26500 + 83
This means that we add 5 at the end
So, we have
Number = 26583.0
Hence, the new number is 26583.0
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Determine three distinct points on the line 2 x+2 y=32. Enter your points as ordered pairs (x, y)(x,y) separated by commas.
Graph the line 2 x+2 y=32x by plotting two of the points you found on the line.
What is the slope of the line 2 x+2 y=32
What does the slope say about the relationship between the lengths and widths of rectangles with perimeter 32?
The distinct points are (1, 15), (2, 14) and (3, 13)
The slope implies that as the length increases by 1, the width decreases by 1
How to determine the distinct pointsFrom the question, we have the following parameters that can be used in our computation:
2x + 2y = 32
Divide by 2
So, we have the following representation
x + y = 16
Make y the subject
y = 16 - x
Set x = 1, 2 and 3
So, we have
y = 16 - 1 = 15
y = 16 - 2 = 14
y = 16 - 3 = 13
So, the points are (1, 15), (2, 14) and (3, 13)
The slope is calculated as
y = mx + c
Where m = slope
When compared, we have
slope = -1
This means that as x increases, y decreases
The graph is attached
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Analyze the function f(x) = - tan 4x. Include:
- Domain and range
- Period
- Two Vertical Asymptotes
For the function f(x) = -tan 4x,
Domain = π[(2n+1)/8] < x < π[(2n+3)/8] Range = set of all real numbers The period = π /4Two vertical asymptotes = π/8 and -π/8Given the function
f(x) = -tan 4x
The domain of the function is the set of all possible inputs of the function
The range is set of all possible outputs of the function
Here the function is
f(x) = -tan 4x
Domain of the function will be
π[(2n+1)/8] < x < π[(2n+3)/8]
The range of the given function is set of all real numbers
The period = π /4
Two vertical asymptotes are π/8 and -π/8
Therefore, the domain, range period and the two vertical asymptotes of the function has been found
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A plane leaves the ground with an elevation angle of 6 degrees. The plane travels 10 miles horizontally. How high the plane is at that time?
Responses
A. 1.05
B 5.10
C 9.95
D 10.06
E 95.14
F 95.67
Answer:
Below
Step-by-step explanation:
If you draw this diagram you will see a right triangle with legs = height
and 10 miles
for the 6 degree angle ( in the right triangle)
tan ( 6) = opposite leg / adjacent leg
tan (6) = height / 10
or 10 * tan 6 = height ( in miles)
1.05 miles high
Which is stronger? 3 scoops of coffee for 4 cups of water, or 4 scoops of coffee for 6 cups of water? Show Your Work.
The stronger one is 4 scoops of coffee for 6 cups of water.
How strong coffee is made?Strong coffee is prepared by employing a greater coffee grounds-to-water ratio. Typically, 2 teaspoons of coffee grinds are used for every 6 ounces of water in a strong cup of coffee. To make a truly strong cup of coffee, use 3 teaspoons of ground coffee for every 6 ounces of water. If you use a French press, you need also increase the steeping time.
In the given question, it is stronger to use 4 scoops of coffee for 6 glasses of water. This is due to the fact that there are more coffee grounds in relation to the amount of water, resulting in a higher concentration of coffee in the combination.
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