Answers
Answer:
Inequalities:
x + y ≤ 3515x + 10y ≥ 400[tex]\begin{array}{|l|c|c|}\cline{1-3} \vphantom{\dfrac12} & \sf Viable & \sf Nonviable\\\cline{1-3} \vphantom{\dfrac12} (10,25)& \checkmark & \\\cline{1-3} \vphantom{\dfrac12} (10,20)&&\checkmark \\\cline{1-3} \vphantom{\dfrac12} (20,12)&\checkmark& \\\cline{1-3} \vphantom{\dfrac12} (35,0)&\checkmark& \\\cline{1-3} \vphantom{\dfrac12} (20,20)&&\checkmark \\\cline{1-3}\end{array}[/tex]
Step-by-step explanation:
Part ADefinition of variables:
Let x = the number of hours cutting grass.Let y = the number of hours tutoring.Given information:
Cutting grass = $15 per hourTutoring reading = $10 per hourSave at least $400Work no more than 35 hoursThe inequality that represents Barrett working no more than 35 hours is:
x + y ≤ 35The inequality that represents Barrett earning at least $400 is:
15x + 10y ≥ 400Part BTo determine if each point is a viable or nonviable solution, substitute each point into the two inequalities. If both inequalities are true, the solution is viable.
[tex]\begin{aligned}(10,25) \implies 10+25 &\leq 35\\35& \leq 35 \leftarrow \sf true\\\\ \implies 15(10)+10(25)&\geq400\\400&\geq 400 \leftarrow \sf true\end{aligned}[/tex]
Therefore, point (10, 25) is a viable solution.
[tex]\begin{aligned}(10,20) \implies 10+20 &\leq 35\\30& \leq 35 \leftarrow \sf true\\\\ \implies 15(10)+10(20)&\geq400\\350&\geq 400 \leftarrow \sf false\end{aligned}[/tex]
Therefore, point (10, 20) is not a viable solution.
[tex]\begin{aligned}(20,12) \implies 20+12 &\leq 35\\32& \leq 35 \leftarrow \sf true\\\\ \implies 15(20)+10(12)&\geq400\\420&\geq 400 \leftarrow \sf true\end{aligned}[/tex]
Therefore, point (20, 12) is a viable solution.
[tex]\begin{aligned}(35,0) \implies 35+0 &\leq 35\\32& \leq 35 \leftarrow \sf true\\\\ \implies 15(35)+10(0)&\geq400\\525&\geq 400 \leftarrow \sf true\end{aligned}[/tex]
Therefore, point (35,0) is a viable solution.
[tex]\begin{aligned}(20,20) \implies 20+20 &\leq 35\\40& \leq 35 \leftarrow \sf false\\\\ \implies 15(20)+10(20)&\geq400\\500&\geq 400 \leftarrow \sf true\end{aligned}[/tex]
Therefore, point (20, 20) is not a viable solution.
[tex]\begin{array}{|l|c|c|}\cline{1-3} \vphantom{\dfrac12} & \sf Viable & \sf Nonviable\\\cline{1-3} \vphantom{\dfrac12} (10,25)& \checkmark & \\\cline{1-3} \vphantom{\dfrac12} (10,20)&&\checkmark \\\cline{1-3} \vphantom{\dfrac12} (20,12)&\checkmark& \\\cline{1-3} \vphantom{\dfrac12} (35,0)&\checkmark& \\\cline{1-3} \vphantom{\dfrac12} (20,20)&&\checkmark \\\cline{1-3}\end{array}[/tex]
Related Questions
Mean, Median and Mode of the following set of numbers.
13, 11, 17, 14, 20, 6, 15, 15, 12, 6, 13, 24, 22, 19
Answers
Median = 14.5 ((14+15)/2)
Mode = 6, 13, 15
Hope this helps :)
Answer:
Mean: [tex]14 \frac{11}{207}[/tex]
Median: 14.5
Mode: 6, 13, and 15
Step-by-step explanation:
We will start by arranging these numbers from smallest to greatest to get the median and mode:
6, 6, 11, 12, 13, 13, 14, 15, 15, 17, 19, 20, 22, 24
To get the mode, we will look. There are two 6, 13, and 15. So those three are our modes. Then, since there are 14 numbers, we will split the list in half and find the average of the two most inward numbers. We get:
6, 6, 11, 12, 13, 13, 14 15, 15, 17, 19, 20, 22, 24
Our two most inward numbers are 14 and 15, so we add the two together and then divide by 2, giving us:
14 + 15 = 29/2 = 14.5
So our median is 14.5.
Finally, we will add up all the numbers together, then divide by 14 to get our mean. We get:
6 + 6 + 11 + 12 + 13 + 13 + 14 + 15 + 15 + 17 + 19 + 20 + 22 + 24 = 207
Then we divide by 14:
[tex]\frac{207}{14} = 14 \frac{11}{207}[/tex]
So, our median is [tex]14 \frac{11}{207}[/tex].
Hope this helped!
PLEASE HELPP!!!!!!!!!
Answers
The number of tickets that Sam can buy, given the amount he has to spend and the price of admission, is 36 tickets.
The rate of change is $ 0.75 per attraction.
The table on the number of tickets and total cost is:
Number of tickets 1 5 10 15
Total cost $ 10. 75 $ 13.75 $17.50 $ 21. 25
How to find the cost of tickets ?The number of tickets that Sam can buy when he has $ 37 is:
= (Amount to spend - Cost of admission ) / Cost per ticket
= ( 37 - 10 ) / 0.75
= 36 tickets
The rate of change is therefore the $ 0.75 charged per ticket per event.
The number of tickets for $ 10. 75 is:
= ( Total cost - Cost of admission ) / cost per ticket
= ( 10. 75 - 10 ) / 0.75
= 1 ticket
The cost of 5 tickets :
= ( Number of tickets x cost per ticket) + cost of admission
= (5 x 0. 75 ) + 10
= $ 13. 75
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Given the graph of the function F(x) below, what happens to
F(x) when x goes from 0 to 1?
Answers
For the graph of the function F(x), when x goes from 0 to 1, F(x) is a negative number with large absolute value. Option D is correct.
What is absolute value?A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value.
When the value of x goes from 0 to 1 the function shifts and the value is decreased gradually, thus giving F(x) as negative number with a large absolute value.
Hence, option D is the correct answer.
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4.1.5 Quiz: Solving Linear Equations
Question 1 of 5
How many solutions does 5 + = +6+ have?
A. Infinitely many solutions
B. No solutions
OC. One solution
D. Two solutions
Answers
The given system of equations has infinitely many solutions. Option A is correct.
Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
Given equation,
- 6x - 2y = 10 - - - -1
y = - 3x - 5 - - - -2
From equation 1
-6x - 2y = 10
Reform the equation,
-2y = 6x + 10
Divide the above equation by -2,
y = -3x - 5
Since the above equation is equivalent to equation 2, therefore the system of equations has infinitely many solutions.
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A population of pea aphids doubles every week. The population begins with 300 individual pea aphids. In how many weeks will the population reach 9,600 individuals?
Answers
Answer:
To find out how many weeks it will take for the pea aphid population to reach 9,600 individuals, we need to determine how many times the population needs to double to reach that number.
We can use logarithms to find this out. Using the rule log(A) / log(B) = log(A) to base B, we can calculate the number of times the population needs to double.
log(9600) / log(2) = log(9600) to base 2 = 9.98
So the population needs to double 9.98 times.
Since the population doubles every week, it will take 9.98 weeks for the population to reach 9,600 individuals.
Vote Branliest!
Answer: 5 weeks
Step-by-step explanation: Based on the information given, let's conduct an equation. It'd look something like this:
300 * [tex]2^{x}[/tex] = 9600
Now, we need to "reduce" the greatest common factors on both sides of the equation. This is so we can find the value of "x" It should look like this:
[tex]2^{x}[/tex] = 32
Now, we need to covert both sides to have the same base, which should look like this:
[tex]2^{x} = 2^{5}[/tex]
Based on the information given, we now know that x = 5, making it have a constant rate of 5 weeks to reach 9,600 individuals. I hope this helped!
Find an ordered pair (x, y) that is a solution to the equation.
-x+2y=7
(x, y) = (_, _)
Answers
To answer this, you get to pick any x-value and then solve for y OR you can pick any y-value and solve for x.
For this one, let's pick x = 3. We'll then substitute 3 in for x in the equation:
- (3) + 2y = 7
and then solve for x:
-3 + 2y = 7
Add 3 to both sides:
2y = 10
Divide by 2 on both sides:
y = 5
This shows that (3,5) is a solution for the equation.
Again, you could pick any x-value and solve for y OR pick any y-value and solve for x. There are an infinite number of solutions.
The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has 180 calories, and 108 calories are from fat. What percent of the total calories is from fat?
Answers
Answer:
60% of the total calories is from fat
Step-by-step explanation:
We already have our first value 180 and the second value 108. Let's assume the unknown value is Y which answer we will find out.
As we have all the required values we need, Now we can put them in a simple mathematical formula as below:
STEP 1Y =
108
180
By multiplying both numerator and denominator by 100 we will get:
STEP 2Y =
108
180
×
100
100
=
60
100
STEP 3Y = 60
Winston leaned a 32-foot ladder against the side of a building. The
base of the ladder is 3 feet from the base of the building. The top of
the ladder is 15 feet from the top of the building. How tall is the
building? Provide an answer accurate to the nearest tenth of a foot.
Answers
Answer:
the building is approximately 28.3 feet tall, accurate to the nearest tenth of a foot.
Step-by-step explanation:
The height of the building can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the building is the hypotenuse, and the base of the ladder and the top of the ladder form the other two sides.
The height of the building can be found using the following formula:
h = √(32^2 - 15^2)
h = √(1024 - 225)
h = √(799)
h ≈ 28.3 ft
A coefficient is a number that is blank by a blank or an expression
Answers
A coefficient is a number that is multiplied by a function or an expression.
What is a coefficient?A coefficient is a multiplier to a function or an expression.
For example, in a polynomial function, the coefficients are the terms that multiply the powers of x.
Taking the standard quadratic function as follows:
y = ax² + bx + c.
The coefficients are a, b and c.
Considering this concept, the blanks are completed on the answer at the beginning.
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Could you please verify this answer ?
Answers
Answer:
The equation that this graph corresponds to is y -3/4x + 8
Step-by-step explanation:
The answer choice you chose is correct.
Help me find the answer for this question
Answers
The graphs of the functions f(x) and g(x) are attached with the answer.
What is a function?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.The set X is called the domain of the function and the set Y is called the codomain of the function.Functions whose domain are the non - negative integers, known as sequences, are often defined by recurrence relations.Given a function as [tex]${\displaystyle f\colon X\to Y}[/tex] its graph is, formally, the set -[tex]${\displaystyle G=\{(x,f(x))\mid x\in X\}.}[/tex]
Given are the functions f(x) and g(x).
The given functions are -
f(x) = [tex]$100(\frac{3}{5})^{x}[/tex]
g(x) = [tex]$100(\frac{2}{5})^{x}[/tex]
Refer to the graphs of the function f(x) and g(x).
Therefore, the graphs of the functions f(x) and g(x) are attached with the answer.
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b) Three interior angles of an n-sided polygon are 136', 138' and 146'. The remaining angles are 165' each. Find the value of n.
Answers
By solving a linear equation we will see that the polygon has 19 sides.
How to find the number of sides of the polygon?Remember that for a polygon of n sides, the sum of the interior angles is equal to:
(n - 2)*180°
Here we also know that 3 angles are:
136°, 138°, and 146°
And the rest of the angles (n - 3) angles are of 165° each.
Then the sum of the interior angles gives:
136° + 138° + 146° + (n - 3)*165°
And that must be equal to the expression above, so we can write the linear equation:
136° + 138° + 146° + (n - 3)*165° = (n - 2)*180°
420° + n*165° - 495° = n*180° - 360°
n*165° - 75° = n*180° - 360°
360° - 75° = n*180 - n*165
285° = n*15°
285°/15° = n
19 = n
That is the solution.
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Using Squeeze/Sandwich Theorem,
Calculate the limit of : lim [(x,y) -> (0,0)] (3 . x^2 . y / (x^2 + y^2))
Answers
Using Squeeze theorem, the limit of the function is 0
What is the LimitThe Squeeze Theorem states that if f(x,y) <= g(x,y) <= h(x,y) for all x,y in a region around (x0,y0) and lim (x,y)->(x0,y0) g(x,y) = L, then lim (x,y)->(x0,y0) f(x,y) = lim (x,y)->(x0,y0) h(x,y) = L.
We can use the Squeeze Theorem to find the limit of the given function by finding two other functions that bound it and have known limits as (x,y) approaches (0,0).
We can see that
(x^2+y^2)/(x^2+y^2) <= 3x^2y/(x^2+y^2) <= (3xy)/(x^2+y^2)
As x,y approaches 0, the first inequality approaches 1 and the second one approaches 0, so the limit of the given function is also 0.
Therefore, lim [(x,y) -> (0,0)] (3 . x^2 . y / (x^2 + y^2)) = 0.
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Solve for x 2/5=6/21-x
Answers
The value of x is 6
How to calculate the value of x ?2/5 = 6/21-x
Cross multiply both sides
2(21-x)= 30
42-2x= 30
collect the like terms
-2x= 30-42
-2x= -12
Divide both sides by the coefficient of x which is 2
2x/2 = 12/2
x= 6
Hence the value of x is 6
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how to solve this long division
Answers
Answer:
Step-by-step explanation:
Answer:
0.5 is the answer
Step-by-step explanation:
2 clearly cannot be divided by 4
So what we have to do is put a 0 over the 2 and a decimal in the place after the 2 and bring down a 0 making it 20÷4=5
Don't forget the decimal point that was necessary to create the 20
That makes the answer 0.5
What is the probability of getting the sum ‘10’, when you role 2 dices?
Answers
Answer:
total probability (1,1),(1,2),(1,3)(1,4) (1,5)(1,6)
(2,1) (2,2) (2,3) (2,4) (2,5)(2,6)
(3,1)(3,2)3,3 3,4) (3,5) (3,6)
(4,1) (4,2)(4,3)(4,4)(4,5)(4,6)
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)
3/36=1/12
Step-by-step explanation:
What is the answer of this triangle congruence question.
Answers
The value of x in the triangles are 9.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given:
The triangles are congruent.
That means, their corresponding angles are also congruent.
In ΔJKL,
the sum of all the angles of the triangle is 180°.
So,
x²-2x + x + 29 + 3x + 52 = 180
x² + 2x - 99 = 0
Solving the quadratic equation,
x² +11x - 9x - 99 = 0.
x (x + 11) -9 (x + 11) = 0
x = 9 and x = -11
Here, we take x = 9.
Therefore, the value of x is 9.
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Select the correct answer.
Which type of investment offers both capital gains and interest income?
Α. property
B. CDs
C. stocks
D. bonds
Answers
Answer:
D
Step-by-step explanation:
Assuming a Perfectly Competitive firm has the following cost function: TC = 1000 + 600Q – 10Q2 + 0.05Q3 . Minimum AVC is
Answers
Therefore , to calculate the average AVC, use the formula: TC at 0 output is 5, which equals fixed cost (FC) of 5.
How are AVC, AFC, and TC calculated?The fixed cost per unit of output is known as the AFC, and the variable cost per unit of output is known as the AVC. We previously stated that Bob's Bakery can produce 100 loaves with FC = 40, VC = 500, and TC = 540. ATC = TC/Q = 540/100 = 5.4 as a result. Additionally, AVC = 500/100 = 5 and AFC = 40/100 = 0.4.
Here,
Total cost is equal to total fixed cost plus total variable cost, or TC.
In order to obtain the VC at each output, we must first subtract 5 from the TCs for all subsequent output levels.
AVC is now equal to VC divided by Q.
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A landscape supply business charges $35
Answers
Driving down a mountain, Bob Dean finds that he descends 3200 feet in elevation by the time he is
3.9 miles (horizontally) away from the high point on the mountain road. Find the slope of his descent. (1 mile = 5280 feet).
Answers
Answer:
-0.155
Step-by-step explanation:
You want the slope of Bob's descent when he descends 3200 feet in a horizontal distance of 3.9 miles.
SlopeTo find the slope of Bob Dean's descent, we can use the formula:
slope = (change in elevation) / (change in horizontal distance)
ApplicationIn this case, the change in elevation is 3200 feet and the change in horizontal distance is 3.9 miles.
slope = -3200 feet / (3.9 miles)
To convert the horizontal distance to feet, we multiply by 5280 (the number of feet in a mile)
slope = -3200 feet / (3.9 * 5280 feet)
slope = -3200 / 20,592
slope ≈ -0.1554
The slope of Bob Dean's descent is about -0.155.
__
Additional comment
As a percent grade, this is a 15.5% grade, very steep. He will need to check his brakes before he starts down.
What can you say back to someone who asked: " How you been today?"
Answers
Answer:I think being honest with them just tell them how you really feel not because just they ask and you just say I am fine how are you just tell how you really feel about that day. Be honest ...
Step-by-step explanation:
How I've been today? Quite magnificent. Thank thou for your generosity.
The brain volumes (cm³) of 20 brains have a mean of 1085.2 cm³ and a standard deviation of 125.6 cm³. Use the
given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or
significantly high. For such data, would a brain volume of 1386.4 cm³ be significantly high?
Answers
If the brain volumes (cm³) of 20 brains have a mean of 1085.2 cm³ and a standard deviation of 125.6 cm³. For such data: it is significantly low for a brain because 1386.4 cm³ is less than the upper limit.
How to find the lower and upper limits?Mean = 1085.2 cm³
Standard deviation = 125.6 cm³
Hence,
Lower limit = Mean - 2 x Standard deviation
Lower limit =1085.2 - 2 x 125.6
Lower limit =1161.2 - 251.2
Lower limit =910
Upper Limit = Mean + 2 x Standard deviation
Upper Limit = 1161.2 + 2 x 125.6
Upper Limit =1161.2 +251.2
Upper Limit =1412.4
The limit of values is from 910 to 1412.4.
A value below 910 will be is considered low and a value above 1412.4 will be considered high
Therefore 1386.4 cm³ is less than the upper limit. Thus it is significantly low for a brain.
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The chart below describes the speed of four painters. Which painter is the fastest?
Answers
This because if you divide the sq ft by the number of hours its the highest. Painter A is 200, paintee B is 225, painter c is 120, and painter d is 250.
need help asap help help help help help help!!!!!!!!!!!
Answers
Answer:
Step-by-step explanation:
Triangle HIJ is similar to triangle KLM find the measure of side KL around your answer to the nearest tenth if necessary
Answers
The measure of side KL from triangle KLM is 22 units.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
Given that, triangle HIJ is similar to triangle KLM.
From the similar triangles,
JH/MK =HI/KL
31/13.9 =49/KL
31KL=49×13.9
31KL=681.1
KL=681.1/31
KL=21.97
KL≈22
Therefore, the measure of side KL is 22 units.
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In an elastic collision, momentum and kinetic energy are conserved.T or F?
Answers
Answer: True. In an elastic collision, both momentum and kinetic energy are conserved. This means that the total momentum and total kinetic energy of the system before the collision is equal to the total momentum and total kinetic energy of the system after the collision.
Step-by-step explanation:
16 People fit comfortably in a 8 feet by 9 feet area. Use this value to estimate the size of a crowd that is
5 feet deep on both sides of the street along a 2-mile section of a parade route.
Answers
Answer:
Step-by-step explanation:
It is impossible to accurately estimate the size of the crowd without knowing how many people are standing in each foot of space. However, if we assume that 16 people fit in a 9 ft x 8 ft area, then we can estimate the size of the crowd in a 2-mile section of the parade route that is 5 feet deep on both sides of the street.
Assuming a 5-foot deep crowd on both sides of the parade route, we can estimate that there would be 40 feet of crowd on one side of the parade route and 40 feet of crowd on the other side of the parade route. This means that there would be a total of 80 feet of crowd across the 2-mile parade route.
Using the assumption that 16 people fit in a 9 ft x 8 ft area, we can estimate that there would be 1280 people across the 2-mile parade route (80 feet x 16 people). This is a rough estimate, as it does not account for the gaps between people, which would likely reduce the total number of people in the parade route.
20/04 cash deposit balance 29 385 48 how was it calculated
Answers
Find the area of the circle shown. Use 3.14 as an approximation for π. Round your answer to the nearest tenth.
Answers
19.63
Step-by-step explanation: area of circle=pi*r^2
3.14*2.5^2
3.14*6.25
=19.625 rounded to nearest tenth is 19.63
