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Related Questions
-7*3^0.25x=-10 what is the solution of the equation
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Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
x = 1.08547955
A jogger is running home. His distance from home, as a function of time, is modeled by y=-7x +8.
Which statement best describes the function?
A. The function is nonlinear.
B. Not enough information is given.
C. The function is linear at some points and nonlinear at other points.
D. The function is linear.
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Answer: the function is a liner
Step-by-step explanation: trust
Consider the feasible region in the xy-plane defined by the following linear inequalities.
x≥0
y ≥0
x ≤ 10
x +y≥ 5
x + 2y ≤ 18
Part 2 Exercises:
1. Find the coordinates of the vertices of the feasible region. Clearly show how each vertex is determined and which lines form the vertex.
2. What is the maximum and the minimum value of the function Q = 60x+78y on the feasible region?
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Answer:
1. (0,5), (0,9), (10,4), (10,0), (5,0)
2. [tex]Q_{max}=912[/tex]
[tex]Q_{min}=300[/tex]
Step-by-step explanation:
1.
In order to determine the coordinates of the vertices of the feasible region, we must first graph each of the inequalities. The feasible region is the region where all the inequalities cross each other. In this case it's the region shaded on the attached picture.
The first point is the intercept between the equations x=0 and x+y=5 so in order to find this first coordinate we need to substitute x=0 and solve for y.
0+y=5
y=5
(0,5)
The next point is the intercept between the equations x=0 and x+2y=18, so again, we substitute x for zero and solve for y:
0+2y=18
[tex]y=\frac{18}{2}[/tex]
y=9
(0,9)
The next coordinate is the intercept between the lines x=10 and x+2y=18, so we substitute x for 10 and solve for y:
10+2y=18
2y=18-10
2y=8
[tex]y=\frac{8}{2}[/tex]
y=4, so the oint is
(10,4)
The next point is the intercept between the lines x=10 and y=0, so the point is:
(10,0)
The final point is the intercept between the equations: y=0 and x+y=5. We substitute y for zero and solve for x:
x+0=5
x=5
so the point is:
(5,0).
2. In order to determine the maximum and minimum value of the function Q=60x+78y on the feasible region, we must evaluate it for each of the points found on part 1.
(0,5)
Q=60(0)+78(5)
Q=390
(0,9)
Q=60(0)+78(9)
Q=702
(10,4)
Q=60(10)+78(4)
Q=912
(10,0)
Q=60(10)+78(0)
Q=600
(5,0)
Q=60(5)+78(0)
Q=300
So now we compare the answers and pick the minimum and maximum results.
We get that:
[tex]Q_{max}=912[/tex]
when x=10 and y=4
and
[tex]Q_{min}=300[/tex]
When x=5 and y=0
The feasible region is the possible set of a constraint
The vertices are: [tex]\mathbf{(x,y) \to (0,5), (0,9), (5,0)}[/tex]The maximum and the minimum values are 702 and 300, respectively.(a) The coordinates of the vertices at the feasible region
The constraints are given as:
[tex]\mathbf{x \ge 0}[/tex]
[tex]\mathbf{y \ge 0}[/tex]
[tex]\mathbf{x \le 0}[/tex]
[tex]\mathbf{x + y\ge 5}[/tex]
[tex]\mathbf{x + 2y\ge 18}[/tex]
See attachment for the graph of the constraints
From the graph, the vertices are:
[tex]\mathbf{(x,y) \to (0,5), (0,9), (5,0)}[/tex]
(b) The minimum and the maximum values of objective function Q
The objective function is:
[tex]\mathbf{Q=60x +78y}[/tex]
Substitute [tex]\mathbf{(x,y) \to (0,5), (0,9), (5,0)}[/tex] in Q
[tex]\mathbf{Q=60(0) +78(5) = 390}[/tex]
[tex]\mathbf{Q=60(0) +78(9) = 702}[/tex]
[tex]\mathbf{Q=60(5) +78(0) = 300}[/tex]
Hence, the maximum and the minimum values are 702 and 300, respectively.
Read more about feasible regions at:
https://brainly.com/question/7243840
josie walks 3/4 miles in 1/5 hour. what is josie’s speed in miles per hour
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Answer:
Speed = 3.75 miles per hour.
Step-by-step explanation:
Speed can be defined as distance covered per unit time. Speed is a scalar quantity and as such it has magnitude but no direction.
Mathematically, speed is given by the equation;
[tex]Speed = \frac{distance}{time}[/tex]
[tex]S = \frac{d}{t}[/tex]
Given the following data;
Distance, d = 3/4 miles
Time, t = 1/5 hour
Substituting into the equation, we have;
[tex]Speed, S= \frac{3/4}{1/5}[/tex]
[tex]Speed, S = \frac{3}{4}*5[/tex]
[tex]Speed, S = \frac{15}{4}[/tex]
Speed, S = 3.75mph.
Therefore, Josie's speed is 3.75 miles per hour.
At a bake sale, students sold 145 chocolate chip cookies, 95 oatmeal cookies, and 87 sugar cookies. What percent of the cookies sold were oatmeal? Round to the nearest tenth
Answers
Answer:
29.05% of cookies sold were oatmeal cookies.
Step-by-step explanation:
Students sold chocolate chip cookies = 145
Students sold oatmeal cookies = 95
Students sold sugar cookies = 87
Total cookies sold = 145+ 95 + 87
Total cookies sold= 327
The formula used to find percentage is : [tex]Percentage = \frac{part}{whole}*100[/tex]
Now, finding percent of the cookies sold that were oatmeal
Percentage of oatmeal cookies sold = [tex]\frac{95}{327}*100[/tex]
Percentage of oatmeal cookies sold = 29.05 %
So, 29.05% of cookies sold were oatmeal cookies.
A computer manufacturer built a new facility for assembling computers. There were construction and new equipment costs. The company paid for these costs and made combined profits of $40 million after 4 years, while profits increased $30 million per year. Select the correct graph of this function. (2 points)
A)There is a graph of a line that has a y intercept that is approximately $80 million and passes through the point of approximately x equals 2 years and y equals $140 million.
B)There is a graph of a line that has a y intercept that is approximately negative $80 million and an x intercept that is approximately 2.7 years.
C)There is a graph of a line that has a y intercept that is approximately negative $45 million and an x intercept that is approximately 2 years.
D)There is a graph of a line that has a y intercept that is approximately negative $45 million and an x intercept that is approximately 0.6 years.
Answers
Answer:
I am not really good at this but...if I had to choose the ones that make sense
A and B
Step-by-step explanation:
Your are incresing the amount is going up, so if you go backwards you woild have to the negatuves.
Then again I woild not trust my math for the second answer cause I am no good at math.
Suppose that $2000 is placed in a savings account at an annual rate of 4.6%, compounded quarterly. Assuming that no withdrawals are made, how long will it take for the account to grow to $3000? Do not round any intermediate computations, and round your answer to the nearest hundredth.
If necessary, refer to the list of financial formulas.
Answers
Answer:
It will take 35.46 quarters for the account to grow to $3000.
Step-by-step explanation:
Since the annual rate is compounded quarterly, this can be calculated using the formula for calculating the future value as follows:
FV = PV * (1 + r)^n ............................ (1)
Where;
FV = future value or the amount the deposit expected to grow to = $3,000
PV = Present value or the amount place in the savings = $2,000
r = Quarterly rate = Annual rate / 4 = 4.6% / 4 = 0.046 / 4 = 0.0115
n = number of quarters it will take for the loan to grow to $3000 = ?
Substituting the values into equation (1) and solve for n, we have:
$3,000 = $2,000 * (1 + 0.0115)^n
$3,000 / $2,000 = (1.0115)^n
1.50 = (1.0115)^n
Loglinearise both sides, we have:
log(1.50) = n log(1.0115)
0.176091259055681 = n * 0.00496588710682352
n = 0.176091259055681 / 0.00496588710682352
n = 35.4601816891322
Rounding to the nearest hundredth, which also implies to rounding to 2 decimal places, we have:
n = 35.46
Since the the annual rate is compounded quarterly, it will therefore take 35.46 quarters for the account to grow to $3000.
Suppose that $2000 is placed in a savings account at an annual rate of 4.6%, compounded quarterly. Assuming that no withdrawals are made, it will take him 8.86 years for the account to grow to $3000
From the information given:
The principal amount placed in the savings account (P) = 2000The annual interest rate = 4.6%number of times interest is compounded n = 4By using the compound interest formula:
[tex]\mathbf{A = P( 1+\dfrac{r}{n})^{nt}}[/tex]
replacing the values from above, we have:
[tex]\mathbf{3000= 2000( 1+\dfrac{0.046}{4})^{4t}}[/tex]
[tex]\mathbf{\dfrac{3000}{2000}= ( 1+\dfrac{0.046}{4})^{4t}}[/tex]
[tex]\mathbf{\dfrac{3000}{2000}= ( 1+0.0115)^{4t}}[/tex]
[tex]\mathbf{\dfrac{3000}{2000}= ( 1.0115)^{4t}}[/tex]
[tex]\mathbf{log(\dfrac{3000}{2000})= 4t \times log ( 1.0115)}[/tex]
[tex]\mathbf{0.17609= 4t \times0.004966}[/tex]
[tex]\mathbf{t = \dfrac{0.17609}{4 \times 0.004966 }}[/tex]
t = 8.86 years to the nearest hundredth.
Learn more about compound interest here:
https://brainly.com/question/14295570?referrer=searchResults
S= √3+2√3+3√3+...10√3
write S as a√3
Answers
Answer:
S = 55√3Step-by-step explanation:
S=
√3+2√3+3√3+...10√3 =√3( 1 + 2 + 3+...+ 10) =√3(1/2)(10)(10 + 1) =√3(55) =55√3S = 55√3
Answer:
s=✓3(1+2+3+...10)
s=✓3[10/2×(10+1)]
here, applying sum of 1st n natural number is n/2×(n+1)
so, s=✓3×5×11
hence, s=55✓3.
Consider the limaçon with equation r = 3 + 4cos(θ). How does the quotient of a and b relate to the existence of an inner loop?
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A polar graph that is a limacon has a formula similar to [tex]r=a+bcos\theta[/tex]
Option B is correct.
A limacon has a formula similar to [tex]r=a+bcos\theta[/tex]
Case 1 . If a < b or [tex]\frac{b}{a}>1[/tex]
Then the curve is limacon with an inner loop.
Case 2. If a>b or [tex]\frac{b}{a}<1[/tex]
Then the limacon does not have an inner loop.
Here, given that, [tex]r=3+4cos\theta[/tex]
It is observed that, a < b or [tex]\frac{b}{a}>1[/tex]
Therefore, the curve is limacon with an inner loop.
Hence, option B is correct.
Learn more:
https://brainly.com/question/10381605
Evaluate the expression 16!/12!4!
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Answer: Sorry i don't really understand the question
Step-by-step explanation:
16!/12!4!
16x15x14x13/ 4x3x2x1 = 43680/24 = 1820
See the photo for the entire worked problem.
6 is the ______ root of 36
Answers
6(6) = 36
Answer:
6 is the square root of 36
Andre looks at a box of paper clips. He says: "I think the number of paper clips in the box is less than 1,000."
Lin also looks at the box. She says: "I think the number of paper clips in the box is more than 500."
Choose an inequality to show Andre's statement, using LaTeX: p
p
p
for the number of paper clips.
Group of answer choices
p > 1000
1000 > p
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Answer:
Andre says: "I think the number of paper clips in the box is less than 1000.
The equality that shows Andre's statement, or information:
p p p (for the number of clips)
So,
p>1000
1000>p
Hope that helps...
If I work four days from 6-4:30 and earn $600. How much of taxes is being taken off my check
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Answer:
80$
Step-by-step explanation:
Does anyone know the solution to this question
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Answer:
Graph A
Step-by-step explanation:
3x+y=5
y=-3x+5
4x-y=2
-y=-4x+2
4=2x-2
What is the answer to
5 + 3 x 3x -2 X=2
Answers
Answer:
x = 1/6
Step-by-step explanation:
You finance a $500 car repair completely on credit, you will just pay the minimum payment each month for the next three months. The APR is 18.99% and the minimum payment each month is 4% of the balance. Determine the finance charge, carry-over balance, and minimum payment required for each of the next two months, and the starting balance for month 2 in the table below.
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Answer:
Determination of the Finance Charge, Carry-over balance, Minimum Payment for each of the next two months:
Finance Charge:
First month = $7.91
Second month = $7.72
Carry-over balance:
First month = $487.59
Second month = $475.50
Minimum Payment:
First month = $20.32
Second month = $19.81
Starting balance (Carry-over balance + Finance charge):
First month = $507.91
Second month = $495.31
Step-by-step explanation:
a) Data and Calculations:
Credit Finance = $500
APR = 18.99%
Minimum monthly payment = 4% of the balance
Monthly rate of interest = 0.1899/12 = 0.015825
Finance Charge:
First month = $7.91 ($500 * 0.015825)
Second month = $7.72 ($487.59 * 0.015825)
Carry-over balance:
First month = $487.59($507.91 - $20.32)
Second month = $475.50 ($495.31 - $19.81)
Minimum Payment:
First month = $20.32 ($507.91 * 4%)
Second month = $19.81 ($495.31 * 4%)
Starting balance (Carry-over balance + Finance charge):
First month = $507.91 ($500 + $7.91)
Second month = $495.31 ($487.59 + $7.72)
Not quite sure about the answer but it seems simple. Please answer!
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Answer:
Its A
Step-by-step explanation:
simplify (3x+2) (y-2) - (7y+3) (y-3)
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Answer:
3 x y − 7 y 2 − 6 x + 20 y + 5
Step-by-step explanation:
WILL MARK AS BRAINLIEST!!!!!
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explanation: -1-4=-5 0-4=-4 1-4=-3 2-4=-2
What is the decimal expansion for 14 over 33?
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Hi! I believe your answer is 0.42, (simplified form of 0.42424242424) which is 14/33 (or [tex]\frac{14}{33}[/tex] ) as a decimal. I hope this helps you! Good luck and have a great day. ❤️✨
Solve the inequality 8y - 3(y - 2)< 2y + 4(2y + 4) write solution in interval notation
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Answer: y>-2
Step-by-step explanation:
8y-3(y-2) < 2y+4(2y+4)
8y-3y+6 < 2y+8y+16
6-16<2y+8y-8y+3y
-10<5y
y>-2
Answer:
(−∞,−2)
Step-by-step explanation:
Start by simplifying each side as much as possible by distributing and combining like terms to get
8y−3(y−2)8y−3y+65y+6>2y+4(2y+4)>2y+8y+16>10y+16
Subtract 10y from both sides to collect the variables on the left, then subtract 6 from both sides to collect all the constants on the right.
5y+65y+6−10y−5y+6−5y+6−6−5y>10y+16>10y+16−10y>16>16−6>10
Divide each side by −5 to solve for y. Since −5<0, the inequality changes direction.
−5y−5y−5y>10<10−5<−2
In interval notation, we write this as (−∞,−2).
Write the fractional equivalent (in reduced form) to each number
10
0.125 =
0.16
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0.125 —> 1/8
0.16 —> 4/25
Mr. Johnson listed each class’s average on a quiz in fraction form. Based on the chart, Which shows the classes ordered from the highest average to the lowest average?
A. C,D,A,B
B. C,A,D,B
C. B,D,A,C
D. B.A,D,C
Answers
Answer:
C
Step-by-step explanation:
I'm not sure if my picture made since because I'm not the best at drawing but that's how I'd explain it
If 1 inch represents 10 miles on a map then how many inches will represent 120 miles ?
Answers
Answer:
12 inches
Step-by-step explanation:
We can write this as a proportion:
inches/miles = inches/miles
1/10 = x/120
Solving for x, we get 12 inches.
A XYZ is translated left 4 units to form the image A X'Y'Z'.
What are the coordinates of the vertices of A X'Y'Z' ?
Enter your answer by filling in the boxes.
Plz Help
Answers
Answer:
y(1,6) x(-4,6) z(1,1)
Step-by-step explanation:
Answer:
X(-8,6)Y(-3,6)Z(-3,1)
Step-by-step explanation:
just moving the coordinate over to the left 4 times
The price of a technology stock was $9.66 yesterday. Today, the price fell to $9.55. Find the percentage decrease.
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-4x+6y=-7
-13x-2y=-4
Elimination or substitution
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Answer:
substitution
Step-by-step explanation:
Juan got grades of 68 and 73 on his first two math tests. What grade must he get on the third test if all were weighted equally and he wants to raise his grade to a 75 average?
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Answer: 84
Step-by-step explanation: Multiply 75 by 3. That is 225, and is the value the three numbers must add up to. 73+68=141. 225-141 is 84.
Katie played 5 consecutive games of soccer without being taken off the field. Then, after a single game on the sidelines, she played another 7 consecutive games. What is the percent of increase in the number of consecutive games she played?
Answers
Liam had a container of oatmeal that contained 5 and one-half cups of oatmeal. Liam ate StartFraction 4 over 9 EndFraction cup of oatmeal every morning before school for a week. Which is the best estimate of the number of cups of oatmeal that Liam had left in the container at the end of the five-day week?
2 and one-half
3
3 and one-half
5
Answers
Answer:
3
Step-by-step explanation: