When faced with an unknown variable in a maths problem, it is advised to find the subject formula and then use it to solve the equation to find the answer.
What is an Unknown Variable?This refers to the type of variable in a given equation that has to be solved for because its properties or value is not known.
Hence, we can see that when faced with an unknown variable in a given math problem, it is better to find the subject formula, then input the value of this into an equation, to find the value of the variable.
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A farmer raises only cows and Sheep. He wants to raise no more than 16 animals, including no more than 12 sheep. He spends birr 5 to raise a cow and Br 2 to raise a sheep. He has Br 50 available for this purpose. Cows sell birr 100 and sheep birr 50. Required: How many of each animal should he raise to maximize profit? What is the maximum profit?
The maximum profit will be 956 birrs for both cows and sheep.
What is profit?The amount of money earned by any seller on the cost price is called the profit.
Given that:-
A farmer raises only cows and Sheep. He wants to raise no more than 16 animals, including no more than 12 sheep. He spends birr 5 to raise a cow and Br 2 to raise a sheep. He has Br 50 available for this purpose. Cows sell birr 100 and sheep birr 50.From the given data we can see that the total number of animals cows and sheep is 16.
C + S = 16
To raise a cow need 2 Br
To raise Sheep need 5 Br
The number of sheep is 12 and cows 4.
So the amount required to raise sheep and cows is:-
Sheeps = 12 x 2 = 24 Br
Cows = 4 x 5 = 20 Br
Total = 44 Br
The selling price of cows and sheep are 100 and 50 Br.
Cows = 100 x 4 = 400Br
Sheeps = 50 x 12 = 600 Br
Total = 1000 Br
So the profit will be calculated as follows:-
P = 1000 - 44 = 956 Br
Therefore the maximum profit will be 956 birrs for both cows and sheep.
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Model 3xfx Write the inverse of the rational function used to represent the situation in model 3, .
A biologist has tracked the population of Antarctic penguins in a marine reserve since 2012. He represents the population with the rational function f(x)=15x+50/x+5, where is the number of years that have passed since 2012 and () is the number of penguins.
A kitchen measures 20 feet long and 10 feet wide. A scale drawing is made using a scale factor of 124.
What is the length of the kitchen in the scale drawing?
5/12
5/6
5/4
Drag and drop a number to correctly complete the statement.
The length of the kitchen in the scale drawing is Response area ft.
The length of the kitchen in the drawing using the scale factor is: B. 5/6.
How to Find Length Using Scale Factor?We are given a scale factor of 1:24.
Let the length of the kitchen in the drawing = x
Actual length of kitchen = 20 ft.
Using the scale factor, we have:
1/24(20) = 20/24
= 5/6
The length of the kitchen in the drawing is: B. 5/6.
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Alex's recipe calls for 1/3 cup of chocolate chips for every 2 cups of flour. If he increases the
amount of flour to 3 cups, how many cups of chocolate chips will he need?
Answer:
1/2 cup of chocolate chips
Step-by-step explanation:
Given ratio:
chocolate chips : flour = 1/3 cups : 2 cupsLet x be the unknown amount of chocolate chips:
[tex]\implies \sf \dfrac{1}{3}:2=x:3[/tex]
[tex]\implies \sf \dfrac{\frac{1}{3}}{2}=\dfrac{x}{3}[/tex]
Cross multiply:
[tex]\implies \sf 3 \cdot \dfrac{1}{3}=2 \cdot x[/tex]
[tex]\implies \sf 1=2x[/tex]
[tex]\implies \sf x=\dfrac{1}{2}[/tex]
Therefore, 1/2 a cup of chocolate chips will be needed for 3 cups of flour.
Let that be x
1/3/2=x/31/6=x/3x=3/6x=1/2 cupWhich function is the inverse of f(x)=1/2x+5?
Consider the set S of bit strings defined recursively by:
The correct option regarding the recursively defined strings is given by:
c) Both i) and ii).
Which of the strings belong to alphabet S?First we start with string 101, we have that:
101 -> 1w -> 10w -> 101
Which belongs to alphabet S.
For string 001, we have that:
001 -> 0w -> 00w -> 001.
Which belongs to alphabet S.
Hence statement c is correct.
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The Carter family just left the local pet store with Rex, their new family dog. The pet store owner told the Carter family that for the next 6 months, Rex would grow at an average rate of 9 pounds per month. Currently, Rex is 2 months old and weighs 6 pounds. Age, in months 2 3 4 5 6 7 8 Weight, in pounds 6 Part A: Complete the given table that represents Rex’s current weight, in pounds, as a function of his age, in months Part B: Graph the data in the table from Part A. Be sure to label the graph and all data points. Part C: Create a linear model that represents the Rex’s current weight, in pounds, as a function of his age, in months. Part D: If Rex continues to grow at the rate of 9 pounds per month beyond the expected six months, how much will Rex weight by the time he is one year old? Upload your table, graph, and solution below.
The graph is attached and all the sub parts have been answered.
What is a function ?A function is away of relating a dependent variable to an independent variable .
It is given that
Current weight of Rex at 2 months =6 pounds
Let x represents the age in months of Rex
then a linear model that represents the Rex’s current weight, in pounds, as a function of his age, in months. is
Let y be the current weight of Rex
then
y = 6 + 9(x -2)
The table that represents Rex’s current weight, in pounds, as a function of his age, in months
2 6
3 15
4 24
5 33
6 42
7 51
8 59
The graph is plotted for the given data and attached .
If Rex continues to grow at the rate of 9 pounds per month beyond the expected six months, how much will Rex weight by the time he is one year old
6 + 9*(12-2)
96 pounds.
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sketch the graph of y =sine3x
The graph of [tex]\mathbf{y=\sin{3x}}[/tex] is given by,
Here given the function is [tex]y=\sin{3x}[/tex]
when [tex]x=0\Rightarrow y=\sin{3\times 0}=\sin0=0[/tex], then it passes through the origin (0,0).
When [tex]x=\frac{\pi}{6}\Rightarrow y=\sin{3\times\frac{\pi}{6}}=\sin\frac{\pi}{2}=1[/tex]
Since we know that, [tex]-1\leq\sin{x}\leq1,\forall x[/tex], then the function has maximum height at [tex]x=\frac{\pi}{6}[/tex].
Again when [tex]x=\frac{\pi}{3}\Rightarrow y=\sin{(3\times\frac{\pi}{3})}=\sin\pi=0[/tex], again the function is 0.
So clearly the function is the Oscillating function with a maximum value of the function as 1 and a minimum value of the function as -1.
Range of the oscilaltion of the function = 1-(-1) = 1+1 = 2
Using graphing calculator we get the graph of function [tex]y=\sin3x[/tex],
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Which graph represents y=12+2x
Which of the following is the solution to 7√22 + 3√7
The value of this irrational Expression is 40.77 .
What is an Expression ?An expression is a mathematical statement consisting of variables , constants and mathematical operators.
The expression given is
7√22 +3√7
√22 = 4.69
√7 = 2.65
32.83 + 7.94
40.77
The value of this irrational Expression is 40.77 .
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or
What is (fg)(x)?
f(x)=
–
3x+1
g(x)=x2
Write your answer as a polynomial or a rational function in simplest form.
The value of (fg)(x)= 3x³+ x²
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given:
f(x) = -3x+1
g(x) = [tex]x^{2}[/tex]
Now, (fg)(x)
=f(x) * g(x)
= (-3x+1) * ([tex]x^{2}[/tex])
=-3x³+ x²
Hence, (fg)(x)= 3x³+ x²
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Let's say that the turkey sat on the counter for an additional hour (beyond the 390 minutes) and its temperature cooled to 80 degrees. Write that value in function notation
The value of the temperature in function notation is gotten as; f(x) = 91 - 11x
How to write a function Notation?Let us first find the relationship between temperature and how long the turkey sits out.
The temperature after the normal 390 minutes is equal to approximately 6.5 hours.
Let us create a ratio and solve for x, which represents the temperature change during that extra hour after the "normal time sitting out".
Thus;
(7.5/6.5) = (80/80+ x)
Solving for x gives x = -10.7.
This means that for every extra hour it sits out, the turkey cools approximately 11°. When we add that to 80°, we have 91° which is the expected temperature after 390 minutes (6.5 hours) of sitting out.
Thus, the motion as a function of time is;
f(x) = 91 - 11x
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Need number 5 answered please!!!
Answer:
-3 is a zero of the function False
-1 is a zero of the function True
1 is a zero of the function False
2 is a zero of the function True
4 is a zero of the function False
Answer these 10 questions for 30 points. serious answers only or report and low rating
Answer:
11. always
12. always
13. always
14. never
15. never
16. always
17. always
18. sometimes
19. sometimes
20. never
Step-by-step explanation:
11. A line can be defined by at least two points
12. A plane can be defined by at least three points
13. If two planes intersect, then they form a line at the intersection.
14. If two lines intersect, then they form a point at the intersection (not a segment).
15. A line does not have any endpoints (infinite in both ways).
16. If two planes are not parallel they will always intersect.
17. If two lines are not parallel they will always intersect.
18. Two points are sometimes collinear. It depends on where they are.
19. Two points are sometimes coplanar. It depends on where they are.
20. Ray MN and NM are not the same ray because the end points are different.
On December 1, Jasmin Ernst organized Ernst Consulting. On December 3, the owner contributed $85,360 in assets in exchange for its common stock to launch the business. On December 31, the company’s records show the following items and amounts. Cash $ 7,010 Cash dividends $ 3,390 Accounts receivable 18,350 Consulting revenue 18,350 Office supplies 4,480 Rent expense 4,820 Office equipment 19,360 Salaries expense 8,370 Land 46,040 Telephone expense 910 Accounts payable 9,740 Miscellaneous expenses 720 Common stock 85,360
The income statement illustrates that the net income will be $3530.
How to calculate the income statement?The income statement will be:
Revenue
Consulting revenue 18350
Expenses
Miscellaneous expenses 720
Rent expense 4820
Salaries expense 8370
Telephone expenses 910
Total expenses 14820
Net income = 18350 - 14820 = 3530
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A company is considering producing some new products. Based on past records, management believes that there is a 70% chance that each of these will be successful, and a 30% chance of products were predicted to be successful based on market research 90% of the time. However, failure. Market research may be used to revise these probabilities. In the past, the successful for products that failed, the market research predicted these would be successes 20% of the time.
The probability that the results indicate an unsuccessful market for the product and the product is actually unsuccessful is P=0.77.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Events:
S: success
F: failure
MS: market research forecast a success
MF: market research forecast a failure
The information we have is:
P(S)=0.70
P(F)=0.30
P(S|MS)=0.90
P(F|MS)=0.20
If P(F|MS)=0.20, we can derive that P(F|MF)=0.80. That is, the failed products were predicted to be a failure based on market research 80 per cent of the time.
We also can conclude that P(S|MF)=0.10.
We can calculate the probability of having a forecast of a failure, given that the product is actually unsuccessful as:
[tex]P(MF|F) = \dfrac{P(F|MF)\times P(F)}{P(F|MF)\times P(F)+P(S|MF)\times P(S)}[/tex]
[tex]P(MF|F) =\frac{(0.8\times 0.3)}{0.8\times 0.3)+(0.1\times 0.7}[/tex]
[tex]P(MF|F) =\dfrac{0.24}{0.31}=0.77[/tex]
The probability that the results indicate an unsuccessful market for the product and the product is actually unsuccessful is P=0.77.
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Which of the following is the graph of y=-(x-2)^3 -5
The graph is shown in the attached image.
Suppose line g is the line with the equation y = x. Given A (7,-3) , B (6,3), and C (-2,-7), what are the coordinates of the vertices of a’b’c’ for the reflection
Answer: A'(-3, 7), B'(3, 6), C'(-7, -2)
Step-by-step explanation:
Reflecting over y = x maps (x,y) onto (y,x).
What is the interval in which both f (x) and g(x) are positive?
A. (–1, ∞)
B. (2, ∞)
C. (3, ∞)
D. (–∞, 2) ∪ (2, ∞)
The age of trees in a forest is known to be approximately normal with an average age of 40 years and a standard
deviation of 10 years. What is the standardized score for a tree that is 34 years old?
A. 1.90
B.-0.60
C. -1.90
D. 0.60
Answer:
B -o.60
Step-by-step explanation:
34 - 40 = -6. -6 divide by 10 = -3/5 or - 0.6. So answer is B
How can triangles be proven similar by the SAS similarity theorem?
Answer: Option (2)
Step-by-step explanation:
We need the angle to be included between the two mentioned sides.
This eliminates the first and fourth options.Also, the sides need to be corresponding for the ratio, and both sides of the triangle need to be in either the numerators or the denominators.
This eliminates the third option.Find the solution to the system
of equations.
y = x + 2 =
X
24-3-2-1
-4
3
1
-1
-2
-3
-4
123
234
y = -x
([?], [])
Entor
Answer:
(-2, 1)
Step-by-step explanation:
You can read the solution from graph. The solution is where the two lines intersect. That happens in point (-2, 1).
---
Alternative:
If you want to be sure, you can alway double check by solving the system of equations.
First equation: [tex]y = \frac{1}{2}x + 2[/tex]
Second equation: [tex]y = -\frac{1}{2}x[/tex]
Substituting y in first equation with y from second.
[tex]y = \frac{1}{2}x + 2[/tex]
[tex]-\frac{1}{2}x = \frac{1}{2}x + 2[/tex]
Adding [tex]\frac{1}{2}x[/tex] on both sides.
[tex]-\frac{1}{2}x + \frac{1}{2}x = \frac{1}{2}x + 2 + \frac{1}{2}x[/tex]
[tex]0 = 1x + 2[/tex]
[tex]0 = x + 2[/tex]
[tex]-2 = x[/tex]
Substituting x with -2.
[tex]y = -\frac{1}{2}x[/tex]
[tex]y = -\frac{1}{2}(-2)[/tex]
[tex]y = 1[/tex]
As you see you get the same result as from reading the graph, (-2, 1).
Math: Evaluating a piece wise function...help!
The values of the functions are g(-0.5) = -1, g(0.3) = 0 and g(0.5) = 1
How to evaluate the piece wise function?The function is given as:
[tex]g(x) = \left[\begin{array}{cc}-2&-2.5 < x \le -1.5\\-1&-1.5 < x \le -0.5\\0&-0.5 < x < 0.5&1&0.5 \le x < 1.5\end{array}\right[/tex]
To calculate g(-0.5), we make use of the domain -1.5 < x ≤ -0.5
At this domain;
g(x) = -1
So, the value of g(-0.5) is
g(-0.5) = -1
To calculate g(0.3), we make use of the domain -0.5 < x 0.5
At this domain;
g(x) = 0
So, the value of g(0.3) is
g(0.3) = 0
To calculate g(0.5), we make use of the domain 0.5 ≤ x 1.5
At this domain;
g(x) = 1
So, the value of g(0.5) is
g(0.5) = 1
Hence, the values of the functions are g(-0.5) = -1, g(0.3) = 0 and g(0.5) = 1
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Is it true that: If f"(c) > 0, then the slope of
the tangent line to the graph of the function at
x = c is positive.
Answer:
yes
Step-by-step explanation:
the FIRST derivative of a function tells us the slope of a tangent line to the curve at any point. if is positive, then the curve must be increasing. If is negative, then the curve must be decreasing.
the SECOND derivative gives us the slope of the slope function (in other words how fast the slope of the original function changes, and if it is accelerating up - positive - or if it is avengers down - negative).
so, the first derivative would be fully sufficient to get the answer of if the slope of the function at that point is positive or negative.
but because it is only a "if" condition and not a "if and only if" condition, the statement is still true.
there are enough cases, where the slope is positive, but the second derivative is not > 0 (usually = 0).
but if even the second derivative is positive, then, yes, the slope of the original function must be positive too.
A bakery sold 27 mocha cupcakes in a day, which was 9% of the total number of
cupcakes sold that day. How many total cupcakes did the bakery sell that day?
Answer:
300 cupcakes
Step-by-step explanation:
[tex]27 = .09c[/tex]
[tex]c = \frac{27}{.09} = \frac{2700}{9} = 300[/tex]
In total, the bakery sold 300 cupcakes on a certain day.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, A bakery sold 27 mocha cupcakes in a day, which was 9% of the total number of cupcakes sold that day.
let, 'x' be the total number of cupcakes sold that day.
Therefore, 9% of 'x' is 27 which is,
(9/100)×x = 27.
0.09x = 27.
x = 27/0.09.
x = 300.
So, The number of cupcakes sold that day is 300.
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Given the equation below, which of the following shows the quadratic formula
correctly applied?
2x² -9x+4 =0
Answer:
Step-by-step explanation:
[tex]x=\frac{-(-9)\pm\sqrt{(-9)^2-4(2)(4)} }{2 \times 2} \\x=\frac{9\pm\sqrt{81-32} }{4} \\x=\frac{9\pm\sqrt{49} }{4} \\x=\frac{9 \pm 7}{4} \\either~x=\frac{9+7}{4} =\frac{16}{4} =4\\or\\x=\frac{9-7}{4} =\frac{2}{4} =\frac{1}{2}[/tex]
a dog is moving at a constant speed of 8 m/s. what is the dog’s acceleration
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: Acceleration_{dog} = 0[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
A dog is moving at a constant speed of 8 m/s, that concludes that there's no change in its speed with respect to time.
And Acceleration is define as rate of change in velocity, but since velocity/speed is constant. change in velocity = 0
Henceforth, Acceleration of dog is 0 as well.
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer: Acceleration = 0 ✅
Step-by-step explanation:
Hii, let me help you out! (:
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part 1Acceleration means "change in speed (which is also known as velocity, V, in physics) per a specific amount of time.
Part 1 is Successfully completed!
↪
Part 2Our Dog ProblemNow let's focus on finding the acceleration of the dog.
Like I said above, [tex]\sf Acceleration=change\;in\;speed\;per\;a\;specific\;amount\;of\;time[/tex]
Well, we are provided with the information that the dog's speed is constant. This means that it doesn't change. So the dog keeps on moving at a speed of 8 m/s. This means that its speed doesn't change, so the change in speed is 0. And this means that its acceleration is 0.
Voila! There's our answer, cheers! (:
___________________Hope I helped! Best wishes.
Reach far. Aim high. Dream big.
[tex]\underbrace[/tex]
a woman at a point a on the shore of a circular lake with radius 1.2 mi wants to arrive at the point B diametrically opposite A on the other side of the lake in the shortest possible time (see the figure). she can walk at the rate of 5 mi/h from C to B and row a boat at 3.5 mi/h from A to C . setting T (x) function to the time by interlaced AC, x is interlacted AC. how to move for shortest.
The angle θ to the diameter that she should row is; θ = 56.44°
How to find the angle of an arc?It should be noted that;
a = 90° - θ. Thus;
b = 2θ
For any circle, the angle subtended (in radians) is equal to the arc length (d_w ) divided by the radius (1.2). Thus; d_w = 4θ .
The time required to walk this distance is given by;
t_w = 4θ/5 = 0.8θ
The distance rowed is given by: cos θ = d_r/2.4
d_r = 2.4cos θ while the time needed for it is;
t_r = 2.4cos θ/3.5
t_r = 0.6857θ
Thus, total time is;
T(θ) = t_r + t_w
T(θ) = 0.6857θ + 0.8θ
T(θ) = 1.4857θ
Now we need the critical numbers:
T'(θ) = 1 - 1.2 sin θ
At T'(θ) = 0, we have;
1 - 1.2 sin θ = 0
1/1.2 = sin θ
θ = sin⁻¹(1/1.2)
θ = 56.44°
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(3x+7)(x+7)=0
What are the two possible values?
For the given equation, either 3x + 7 = 0 or x + 7 = 0
Now,
3x + 7 = 03x = -7 x = -7/3or
x + 7 = 0x = -7So, possible values of x is : -7 and -7/3
[tex](3x + 7)(x + 7) = 0 \\ \\ \\3x + 7 = 0 \\ \\ 3x = - 7 \\ \\ x = \frac{ - 7}{3} . \\ \\ \\ x + 7 = 0 \\ \\ x = - 7.[/tex]
Name all the fractions that are between 12/13 and 19/20
whose NUMERATORS are one less than the DENOMINATORS.
The fractions that are between 12/13 and 19/20 are 13/14, 14/15, 15/16, 16/17, 17/18, and 18/19 total number of fractions is 6
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
Fractions that are between 12/13 and 19/20 such that:
The numerator(N) is one less than the denominator(D).
N = D - 1
N = (12, 19)
D = (13, 20)
D = 14, N = 13
D = 15, N = 14
D = 16, N = 15
D = 17, N = 16
D = 18, N = 17
D = 19, N = 18
The fractions that are between 12/13 and 19/20:
N/D = {13/14, 14/15, 15/16, 16/17, 17/18, 18/19}
Thus, the fractions that are between 12/13 and 19/20 are 13/14, 14/15, 15/16, 16/17, 17/18, and 18/19 total number of fractions is 6
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