Answer:
1. 144 2. 16 3. 1 4. 3x-6
Step-by-step explanation:
So think of this as a function in a function. So you work from the inside to the outside. So for problem 1, we start with f(4)) [you read it "f of 4"] so what is the solution when x = 4, since f(x) means the function of x so f(4) means 'the function of 4' inside f(x).
Since f(x) = 3x then f(4) = 3(4) [notice how you substitute the 4 everywhere you see a letter x]
so f(4) = 12, now you work the next part h(f(4)) since f(4)=12 then h(12)
So take the h(x) function which is h(x) = \(x^{2}\) then h(12) = \(12^{2}\) so h(12) = 144
which of the elements in set P are irrational
Answer:
-\(\sqrt{1}\), \(\sqrt{2}\), \(\frac{π}{2}\)
Step-by-step explanation:
square roots and pie are irrational.
$21 for 7books. How much for 14 books?
Answer:
69
Step-by-step explanation:
cause im funny
Answer:
$42
Step-by-step explanation:
If it is $21 for 7 books, then we just double it for 14 books.
21*2 = 42.
I hope this helps you. :)
Angle Bisector Theorem (vs. Median)
Segment B D bisects LABC. Solve for x.
Round to the nearest tenth, if necessary.
In the given triangle ABC, the line BD bisects the angle LAB and divides the side AC into two segments, AC1 and AC2.
What is angle?Angle is a geometric shape formed by two lines that intersect each other. It is measured in degrees and is represented by the symbol θ (theta). Angles are used in mathematics to measure the size of an object or shape. They are also used to describe the direction of a line or the relationship between two lines. Angles can be acute, right, obtuse, or straight.
The Angle Bisector Theorem states that in a triangle, the line that bisects an angle will also divide the opposite side into two segments, each of which is proportional to the other sides of the triangle. Therefore, in the given triangle ABC, the line BD bisects the angle LAB and divides the side AC into two segments, AC1 and AC2.
The ratio of the lengths of AC1 and AC2 is the same as the ratio of the lengths of AB and BC. Equivalently, this can be expressed as:
AB/BC = AC1/AC2
Given that AB= 8 and BC=6, the ratio becomes 8/6 = AC1/AC2. Solving for AC1, we get AC1 = 8x/6.
In addition, we are given that BD = 5. Therefore, AC1 + AC2 = 5. Substituting for AC1 and solving for x, we get:
8x/6 + AC2 = 5
8x/6 = 5 - AC2
8x = 6(5 - AC2)
x = (30 - 6AC2)/8
Since we know that AC2 = 5 - AC1, we can substitute it in the above equation to get:
x = (30 - 6(5 - 8x/6))/8
x = (30 - 40 + 48x/6)/8
x = (90 + 48x/6)/8
x = 15 + 8x/6
6x = 15×6 - 8×15
6x = 90 - 120
x = -30/6
x = -5
Hence, x = -5.
To know more about angle click-
https://brainly.com/question/28451077
#SPJ1
What is the slope of a line parallel to the line whose equation is 9x-3y=-54
Answer:
21
Step-by-step explanation:
subtract 9 on both sides to make your x axis by itself
y=mx+b
since -3y and -63 will cancel out each other and make a positive when you divide
-3y /63
y=21
also your when the x is alone it is always 1
rise
-------
run
Help pls thank you!!!!!!!!!!!! First to answer it RIght will receive Brainliest!!!!!!!!!!!!!!!!!!!
Answer:
C
Step-by-step explanation:
hope this helps!
have a great day :)
problem 1 (100 points) fig. 1 depicts a sample power system. suppose the three units are always running, with the following characteristics: unit 1: pmin
The total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.
In the given power system depicted in Figure 1, there are three units that are always running. Each unit has specific characteristics regarding their minimum power output (Pmin), maximum power output (Pmax), and incremental cost (Ci). Let's discuss the characteristics of each unit and calculate the total cost of power generation for a given load demand.
Unit 1:
Pmin = 200 MW
Pmax = 500 MW
Ci = $50/MWh
Unit 2:
Pmin = 150 MW
Pmax = 400 MW
Ci = $40/MWh
Unit 3:
Pmin = 100 MW
Pmax = 300 MW
Ci = $30/MWh
To calculate the total cost of power generation for a given load demand, we need to determine the optimal power output for each unit. We start by considering the units with the lowest incremental cost first.
Suppose the load demand is D MW. We allocate the load demand to the units as follows:
Step 1: Check if Unit 1 can meet the load demand within its power range. If yes, allocate the load demand to Unit 1 and calculate the cost:
Cost1 = Ci * P1, where P1 is the power output of Unit 1.
Step 2: If there is still remaining load demand, allocate it to Unit 2:
Cost2 = Ci * P2, where P2 is the power output of Unit 2.
Step 3: If there is still remaining load demand, allocate it to Unit 3:
Cost3 = Ci * P3, where P3 is the power output of Unit 3.
Finally, the total cost of power generation, Cost_total, is the sum of Cost1, Cost2, and Cost3:
Cost_total = Cost1 + Cost2 + Cost3
To find the optimal power output for each unit, we consider the load demand and compare it to the minimum and maximum power output limits for each unit. The power allocation is based on meeting the load demand while minimizing the overall cost of power generation.
In summary, given the characteristics of the three units in the power system (Pmin, Pmax, and Ci), the total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.
Learn more about demand here
https://brainly.com/question/14274996
#SPJ11
3 number sentences with the answer of 2021.
Number sentence may have exponents, parenthesis, etc.
The points 4,0 and 7,6 lie on a particular line, what is its equation in slope - intercept form?
\((\stackrel{x_1}{4}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{6}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{4}}}\implies \cfrac{6}{3}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{2}(x-\stackrel{x_1}{4})\implies y = 2x-8\)
Dregg guessed the answers to three multiple-choice questions on a test. If each questions had 5 different choices, how many different answer combinations were there?
There were 10 different combinations to the multiple choice questions.
What is Combination?Combination is defined as “An arrangement of objects where the order in which the objects are selected does not matter.” The combination means “Selection of things”, where the order of things has no importance.
It is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.
\(C_{n,r} = \frac{n!}{(n-r)! r!}\)
where n = 5
r = 3
\(C_{5,3} = \frac{5!}{(5-3)!3!} \\= \frac{5!}{2!3!}\)
= \(\frac{5(4)(3!)}{2!3!}\)
= 20/2
= 10 ways
Learn more about combinations here: https://brainly.com/question/11732255
#SPJ1
How many of the following statements are true?
19)
a
d Any set of ordered pairs is a function.
d The domain of a relation is the set containing the first
member of its ordered pairs.
d The independent variable in a relation is the variable
used for the range.
d A function is a relation in which each domain value is
paired with exactly one range value.
A) 1
B) 2
C) 3
D) 4
Answer:
A) 1
Step-by-step explanation:
yeah-ya,.................. right?
30. You can work at most 25 hours next week. You need to earn at least $85 to cover your gas and food
expenses. Your babysitting job pays $7.50 per hour and your math tutoring job pays $6 per hour.
a) Define your variables.
b) Write two inequalities that represent the constraints of the scenario.
Between what two integers does log 2 1000 lie
Solution:
Given;
\(\log_21000\)From law of logarithm;
\(\log_ba=\frac{\log_{10}a}{\log_{10}b}\)Thus;
\(\begin{gathered} \log_21000=\frac{\log_{10}1000}{\log_{10}2} \\ \operatorname{\log}_21000=\frac{\operatorname{\log}_{10}10^3}{\operatorname{\log}_{10}2} \\ \end{gathered}\)Another law of logarithm;
\(\log_ba^c=c\log_ba\)Thus;
\(\begin{gathered} \log_21000=\frac{3\log_{10}10}{\log_{10}2} \\ \log_aa=1 \\ \log_21000=\frac{3\left(1\right)}{\log_{10}2} \\ From\text{ a table of common logarithm;} \\ \log_{10}2=0.3010 \\ \log_21000=\frac{3}{0.301} \\ \log_21000=\frac{3000}{301} \\ \log_21000=9\text{ remainder 291} \\ \end{gathered}\)FINAL ANSWER
\(\log_21000\text{ lies between }9\text{ and }10\)
Amari gathered a random sample of oranges in her town. She calculated data on different variables. For one of the variables that she collected, she constructed a bar graph.
Which of the following variables did she use?
Type of orange
Diameter of the oranges
Number of navel oranges
Price per pound of oranges
Based οn the given οptiοns, it is mοst likely that Amari used the variable "Type οf οrange" tο cοnstruct the bar graphs.
What is a bar graph?A bar graph is a chart that displays categοrical data using rectangular bars with heights οr lengths prοpοrtiοnal tο the values they represent. The bars can be οriented hοrizοntally οr vertically, and each bar represents a categοry οr grοup οf categοries.
In a bar graph, the x-axis typically represents the categοries being cοmpared, while the y-axis represents the frequency, cοunt, οr percentage οf the οbservatiοns that belοng tο each categοry. The height οr length οf each bar is determined by the value οr frequency οf the categοry it represents.
The variable that Amari used tο cοnstruct a bar graph is nοt specified. Hοwever, since a bar graph is a type οf chart that displays categοrical data with rectangular bars, it is likely that she used a variable that represents a categοrical variable, such as the type οf οrange (e.g. Valencia, Navel, Blοοd, etc.).
Therefοre, based οn the given οptiοns, it is mοst likely that Amari used the variable "Type οf οrange" tο cοnstruct the bar graph.
To know more about bar graphs visit:
brainly.com/question/13298277
#SPJ1
How do you write the standard form of the equation of the circle with center (2, 3) and radius 4?
Answer:(x-2)^2+(y-3)^2=16
Step-by-step explanation:
standard from of equation of circle: (x-h)^2+(y-k)^2=r^2
r=4,
(h,k)=(2,3)
(x-2)^2+(y-3)^2=16
The standard form of the equation of the circle with center (2, 3) and radius 4 is (x - 2)^2 + (y - 3)^2 = 16.
To write the standard form of the equation of a circle, we use the formula (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle and r represents the radius.
In this case, the center of the circle is (2, 3) and the radius is 4. So, we substitute these values into the formula:
(x - 2)^2 + (y - 3)^2 = 4^2
Simplifying further, we get:
(x - 2)^2 + (y - 3)^2 = 16
Therefore, the standard form of the equation of the circle with center (2, 3) and radius 4 is (x - 2)^2 + (y - 3)^2 = 16.
Learn more:About standard form here:
https://brainly.com/question/29000730
#SPJ11
SOMEONE HELP I CANT FAIL
Answer:
40
Step-by-step explanation:
He can do 8 problems in 5 minutes. 25 minutes is 5 times more than 5. 8 times 5 is 40
Answer:
40 problems
Step-by-step explanation:
8 divided by 5 equals 1.6 meaning in one minute there are 1.6 problems answered, and so 1.6*25= 40. Meaning that there are after 25 minutes 40 problems will be solved.
Please help! I’ll give brainliest
Answer:
The answer is 40
Step-by-step explanation:
So if you add 172+94+36 you will get 302 so then you subtract 342 - 302 and you get 40
The directed line segment CA is divided by the point B in a ratio of 1:4. Finish graphing the segment BA where point A is the endpoint of segment CA.
The coordinate of point A is,
⇒ (10, - 3)
We have to given that,
The directed line segment CA is divided by the point B in a ratio of 1:4.
Here, Coordinates are,
C = (- 5, 7)
B = (- 2, 5)
Let us assume that,
Coordinate of A = (x, y)
Hence, We can formulate;
⇒ - 2 = 1 × x + 4 × - 5 / (1 + 4)
⇒ - 2 = (x - 20) / 5
⇒ - 10 = x - 20
⇒ x = 10
⇒ 5 = 1 × y + 4 × 7 /(1 + 4)
⇒ 5 = (y + 28) / 5
⇒ 25 = y + 28
⇒ y = - 3
Thus, The coordinate of point A is,
⇒ (10, - 3)
Learn more aboput the line segment visit:
https://brainly.com/question/280216
#SPJ1
Suppose that p(x) is the density function for heights of American men, in inches, and suppose that p(69) = 0.18. Think carefully about what the meaning of this mathematical statement is. Approximately what percent of American men are between 68.9 and 69.1 inches tall? Approximately percent. Suppose that the average height of American men is 69 inches. Would you expect p(75) > p(69) or p(75) < p(69)? P(75) > p(69) p(75) < p(69) Suppose P(h) is the cumulative distribution function of p. If P(69) = 0.5, estimate each of: P(68.9) approximately P(68.8) approximately
Assume that p(x) represents the density function for American men's heights in inches and that p(69) = 0.18. Consider the implications of this mathematical statement carefully. How many men in America are between 68.9 and 69.1 inches tall on average? Percentage, roughly.
If p(x) is the density function for the heights of American men, then p(69) = 0.18 means that the probability density at x = 69 inches is 0.18.
We can integrate the density function over the range [68.9, 69.1] to determine the approximate percentage of American men who are between 68.9 and 69.1 inches tall:
P(68.9 ≤ x ≤ 69.1) = ∫₀.₁₃ p(x) dx ≈ 0.036
So, approximately 3.6% of American men are between 68.9 and 69.1 inches tall.
We would anticipate p(75) p(69) if American men are on average 69 inches tall because the distribution is most likely symmetric around the mean and taper off as we move away from the mean in either direction.
P(69) = 0.5 indicates that 50% of American men have heights that are less than or equal to 69 inches if P(h) is the cumulative distribution function of p. We can use the density function and integrate over the corresponding intervals to estimate P(68.9) and P(68.8):
P(x ≤ 68.9) ≈ ∫₀.₁₃ p(x) dx ≈ 0.5 - 0.036/2 ≈ 0.482
P(x ≤ 68.8) ≈ ∫₀.₂₃ p(x) dx ≈ 0.5 - 0.036 - 0.013 ≈ 0.451
So, approximately 48.2% of American men have heights less than or equal to 68.9 inches, and approximately 45.1% have heights less than or equal to 68.8 inches.
Learn more about the probability density function:
https://brainly.com/question/14214648
#SPJ11
Melissa bought some books for each and received a discount of off of her total purchase. She spent after the discount. How many books did she buy?
(a) Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers , , and . Let represent the number of books.
(b) Solve the equation in part (a) to find the number of books.
The equation that represents the number of books will be 6x - 8 = 58. And the number of books will be 11.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Melissa bought some books. She spent a total of $58 after a discount of $8 off of her total purchase. Each book cost $6.
Let 'x' be the number of books. Then the equation is given as,
6x - 8 = 58
Simplify the equation, then we have
6x - 8 = 58
6x = 66
x = 11
The equation that represents the number of books will be 6x - 8 = 58. And the number of books will be 11.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ1
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. I estimate that the probability of my getting married in the next 3 years is 0.7. math
The statement "I estimate that the probability of my getting married in the next 3 years is 0.7" does make sense.
As individuals, we can make personal estimates or predictions about events that are relevant to our lives, such as the probability of getting married in a certain timeframe. These estimates are based on our own subjective beliefs, experiences, and expectations. While they may not be based on precise mathematical calculations or rigorous statistical analysis, they can still reflect our personal opinions or perceptions.
In this case, the person is providing an estimate that they believe there is a 0.7 (or 70%) probability of getting married within the next 3 years. This estimate is a subjective assessment of their own chances based on various factors such as their current relationship status, personal goals, or cultural norms.
It is important to note that personal estimates like this are not necessarily based on concrete evidence or universally applicable probabilities. They can vary greatly from person to person and are subjective in nature. However, they can still hold personal meaning and influence one's decision-making or expectations regarding future events.
Learn more about probability here:
https://brainly.com/question/31828911
#SPJ11
The surface of an air hockey table has a perimeter of 32 feet its area is 60 ft.what are the dimensions of the air hockey table
need to fill in the blanks for part 1
The Parent function f(x) = (x) is Horizontal shift: Right 2 units and Vertical shift: Down 6 units.
What is parent function?A family of functions simplest version of an equation is a parent function. A family of functions is a group of functions that exhibit the same traits as or undergo the same transformations as their parent function. There are various degree values that can be used to represent a parent function, including degrees 1, 2 and 3.
The parent function is the simplest form of the type of function given
f(x) = (x)
The transformation being described is from f(x) = (x) to g(x) = 3(x-2) -6
f(x) = (x)--> g(x) = 3(x-2) -6
The horizontal shift depends on the value of h. the horizontal shift is described as:
g(x) = f(x+h) - The graph is shifted to the left h units.
g(x) = f(x-h) - The graph is shifted to the right h units.
Horizontal shift: Right 2 units
The vertical shift depends on the value of k. The vertical shift is described as:
g(x) = f(x)+k – The graph is shifted up k units.
g(x) = f(x)-k – The graph is shifted down k units.
Vertical Shift: Down 6 units
The graph is reflected about the x-axis when
g(x) = -f(x)
Reflection about the x-axis is none
The graph is reflected about the y-axis when
g(x) = f(-x)
Reflection about the y-axis is none
Compare and list the transformations.
Parents function: f(x) = (x)
Horizontal shifts: Right 2 units
Vertical shifts: Down 6 units
To learn more about parent function visit:
brainly.com/question/17939507
#SPJ1
What is equivalent to 0.325 in as a fraction
Answer:
0.325 as a fraction is expressed as 13/40
Step-by-step explanation:
What is a fraction ?
A fraction is a portion of any quantity out of a whole. It consists of a numerator and a denominator.
To convert a decimal number into a fraction, we write the given number as the numerator and place 1 in the denominator right below the decimal point followed by the number of zeros required accordingly. Then, this fraction can be simplified.
In this case, 0.325 has three numbers after the decimal, so, we place 1000 in the denominator and remove the decimal point.
⇒ 325/1000
After reducing this fraction we get,
⇒ (325 ÷ 25) / (1000 ÷ 25) = 13/40
So, 0.325 as a fraction is 13/40.
(Hi fyi this answer took a lot of time & effort to make sure it was accurate, precise and to the point to be produced, so if you could opt this answer as the brainliest it would mean the world to me,)
Stay positive and Take care,
A fellow mate,
Cheers !
Which graph shows the line of best fit for the data ?
The bottom left graph is the line of best fit for the graph in this problem.
What are residuals?For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:
Residual = Observed - Predicted.
Hence the graph of the line of best fit should have the smallest possible residual values, meaning that the points on the scatter plot are the closest possible to the line.
For this problem, we have that the bottom left graph has the smaller residuals, hence it shows the line of best fit for the data.
More can be learned about residuals at brainly.com/question/1447173
#SPJ1
In the diagram below, DE is parallel to XY. What is the value of y?
8
100
ya
O A. 120
B. 100
o
C. 80
o
D. 60
PREVIOUS
Answer:
100 is answer for math picture
Answer: 80
Step-by-step explanation:
180-100 = 80, y=80
How do solve for M if I don’t know the answer to the problem 1/2m+40
Answer:
m=80
Step-by-step explanation:
1/2 times 80 =40
what the slope to this
(19,-2)(-11-10)
Answer:
4/15
Step-by-step explanation:
If Samantha paid $4,450 in total for the used car, taxes, and fees, create an equation to model Samantha’s total expenses, and use the equation to determine the cost of the car, d. Explain how you determined your answer.
The cost of the car will be less than or equal to $4,450.
What is a equation?
An equation is a mathematical statement that indicates the equality of two expressions. It contains one or more variables and usually includes mathematical operations such as addition, subtraction, multiplication, division, or exponentiation.
Let the cost of the car be "d" (in dollars). Then, the total expenses, including taxes and fees, can be expressed as:
Total expenses = Cost of the car + Taxes + Fees
We can represent the cost of the car as "d", and the taxes and fees as a fixed amount "t". Therefore, the equation to model Samantha's total expenses can be written as:
Total expenses = d + t
From the problem, we know that Samantha paid a total of $4,450 for the car, taxes, and fees. Therefore, we can write:
d + t = 4450
To find the cost of the car, we need to isolate the variable "d" on one side of the equation. We can do this by subtracting "t" from both sides of the equation:
d + t - t = 4450 - t
Simplifying the equation, we get:
d = 4450 - t
To determine the cost of the car, we need to know the value of "t", which represents the total taxes and fees. Unfortunately, the problem does not provide this information, so we cannot determine the exact cost of the car. However, we do know that the cost of the car will be less than or equal to $4,450, since the total expenses cannot be negative.
To learn more about equation, visit the link:
https://brainly.com/question/22688504
#SPJ1
use the function qnorm() in posit to find the value z such that the area to the left of z under the standard normal curve is 0.025. round your answer to 4 digits after the decimal point
z-value is -1.9599
How to find the value of z?To find the value z such that the area to the left of z under the standard normal curve is 0.025, you can use the qnorm() function in R as follows:
Open R or RStudio.Type the following command: `qnorm(0.025)`Press Enter.The output will be the z-value you are looking for. To round your answer to 4 digits after the decimal point, you can use the round() function in R:
Type the following command: `round(qnorm(0.025), 4)`Press Enter.The output will be the rounded z-value, which should be approximately -1.9599.
Learn more about z-score
brainly.com/question/15016913
#SPJ11
WILL MARK BRAINLEIEST
Answer:
y-intercept is -1
Step-by-step explanation:
this is the answer because the line crosses at -1 in the y line