the answers are c and d
Scott is reading two books at the same time to prepare for a report he is writing. So far, he has read 407 of the total number of 557 pages, which is Three-fifths of the shorter book and StartFraction 5 Over 6 EndFraction of the longer book. Which system of equations can be used to determine the total number of pages in the shorter book, x, and the total number of pages in the longer book, y?
Answer:
The system of equations are
x+y=557
[tex]\frac35x+\frac56 y=407[/tex]
The total pages in shorter book is 245
The total pages in longer book is 312
Step-by-step explanation:
Given that,
Scott has read 407 of the total number of 557 pages, which [tex]\frac35[/tex] of the shorter book and [tex]\frac56[/tex] of longer book.
Total number of pages of shorter book be x and longer book be y.
Then,
[tex]\frac35[/tex] page of the shorter book [tex]=\frac35 x[/tex]
[tex]\frac56[/tex] pages of the longer book = [tex]\frac56y[/tex]
So, he has read [tex]=\frac35x+\frac 56y[/tex]
Total number of pages of both book is = x+y
According to the problem,
x+y=557.........(1)
[tex]\frac35x+\frac56 y=407[/tex].......(2)
We can write equation (2) as
[tex]\frac35x+\frac56 y=407[/tex]
[tex]\Rightarrow \frac{18x+25y}{30}=407[/tex]
[tex]\Rightarrow {18x+25y}=407\times 30[/tex]
[tex]\Rightarrow {18x+25y}=12,210[/tex]......(3)
Now 18 times of equation (1) subtract from equation (3)
18x+25y=12210
18x+18y=10026
- - -
_______________
25y-18y=12,210-10,026
⇒7y=2,184
[tex]\Rightarrow y=\frac{2184}{7}[/tex]
⇒y= 312
Plug y=312 in equation (1)
x+312=557
⇒x=557-312
⇒x=245
The total pages in shorter book is 245
The total pages in longer book is 312
The system of equation that can be used to determine the total number of pages in the shorter book x, and the total number of pages in the longer book, y is
3 / 5 x + 5 / 6 y = 407
x + y = 557
How to model a system of equation?Scott has read 407 of the total number of 557 pages, which is 3 / 5 of the shorter book and 5 / 6 of longer book.
x = number of pages in the shorter book
y = number of pages in the longer book
Therefore, the system of equation that can be used to determine the total number of pages in the shorter book x, and the total number of pages in the longer book, y is as follows;
3 / 5 x + 5 / 6 y = 407
x + y = 557
learn more on system of equation here: https://brainly.com/question/27631842
#SPJ5
You are throwing darts at a dart board. You have a chance of striking the bull's-eye each time you throw. If you throw 3 times, what is the probability that you will strike the bull's-eye all 3 times?
Answer:
Correct answers is
[tex] \frac{1}{216} [/tex]
Step-by-step explanation:
Given: The chances of striking the bull's-eye each time of throw =\frac{1}{6}
Since, if we throe dart on dart board , each event will be independent of the other.
Then, If we throw 3 times, what is the probability that we will strike the bull's-eye all 3 times is given by :-
[tex]p(strike \: bulls \: eye \: ) = \frac{1}{6} x \frac{1}{6} x \frac{1}{6} = \frac{1}{216} [/tex]
Hence, the probability that we will strike the bull's-eye all 3 times is 1/216
Answer:
1/216
Step-by-step explanation:
Find the probability of this event. Enter the answer as a fraction in simplest form, as a decimal to the nearest hundredth, and as a percent to the nearest whole number. You choose a movie CD at random from a case containing 4 comedy CDs, 5 science fiction CDs, and 7 adventure CDs. The CD is not a comedy.
Answer:
0.75 is the probability of selecting a CD that is not comedy.
Step-by-step explanation:
We are given the following in the question:
Number of comedy CD = 4
Number of science CD = 5
Number of adventure CD = 7
Total number of CD,n = 16
We have to find the probability for selecting a random CD that is not comedy.
Formula:
[tex]\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}[/tex]
P( Non-Comedy CD) =
[tex]=\dfrac{\text{n(Non-Comedy)}}{n}\\\\=\dfrac{5+7}{16} = \dfrac{12}{16}=\dfrac{3}{4}= 0.75 = 75\%[/tex]
Thus, 0.75 is the probability of selecting a CD that is not comedy.
A new shopping mall records 120 total shoppers on their first day of business. Each day after that, the number of shoppers is 10% more than the number of shoppers the day before. What is the total number of shoppers that visited the mall in the first 7 days?
Answer:
193 shoppers
Step-by-step explanation:
2nd 120 +12
3rd 132+13.2
4rd 145.2+ 14.52
5th 159.72+15.972
6th 175.692 +17.5692
7th 193.2612
Jose scores 544 points in his math test. He needs at least 650 to get an A, write and solve the minimum number of points Jose needs to score on the remaining test,n, in order to get an A
Answer:
The correct answer is x [tex]\geq[/tex] 106, where x is the marks score by Jose in his remaining test, n.
Step-by-step explanation:
Jose scored 544 points in his math test.
Jose needs minimum of 650 points to get an A.
Let Jose scores x in the remaining test, n.
Jose needs to score an A. So, to reach 650 points, Jose need to score a minimum of 650 - 544 = 106 points.
Thus the value of x must be greater than of equal to 106, in his remaining test, n, to ensure that Jose gets an A.
⇒ x [tex]\geq[/tex] 106.
A manufacturer of a new medication on the market for Alzheimer's disease makes a claim that the medication is effective in 65% of people who have the disease. One hundred eighty individuals with Alzheimer's disease are given the medication, and 115 of them note the medication was effective. Does this finding provide statistical evidence at the 0.05 level that the effectiveness is less than the 65% claim the company made? Make sure to include parameter, conditions, calculations, and a conclusion in your answer.
Answer:
[tex]z=\frac{0.639 -0.65}{\sqrt{\frac{0.65(1-0.65)}{180}}}=-0.309[/tex]
[tex]p_v =P(z<-0.309)=0.379[/tex]
So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults with the medication was effective is not significantly less than 0.65
Step-by-step explanation:
Data given and notation
n=180 represent the random sample taken
X=115 represent the adults with the medication was effective
[tex]\hat p=\frac{115}{180}=0.639[/tex] estimated proportion of adults with the medication was effective
[tex]p_o=0.65[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that true proportion is less than 0.65.:
Null hypothesis:[tex]p \geq 0.65[/tex]
Alternative hypothesis:[tex]p < 0.65[/tex]
When we conduct a proportion test we need to use the z statisitc, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.639 -0.65}{\sqrt{\frac{0.65(1-0.65)}{180}}}=-0.309[/tex]
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.
Since is a left tailed test the p value would be:
[tex]p_v =P(z<-0.309)=0.379[/tex]
So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults with the medication was effective is not significantly less than 0.65
Answer:
H0: p = 0.65
Ha: p < 0.65
Sample proportion = 115 / 180 = 0.6389
Test statistics
z = - p / sqrt( p( 1 -p ) / n)
= 0.6389 - 0.65 / sqrt ( 0.65 * 0.35 / 180)
= -0.31
Critical value at 0.05 level = -1.645
Since test statistics falls in non-rejection region, do not reject H0.
We conclude at 0.05 level that we fail to support the claim.
Step-by-step explanation:
1: Mr. Alter bought a block of fudge that weighed 75 pounds. He cut the fudge into 6 equal pieces. What was the weight of each piece of fudge? A 930 pounds B 830 pounds C 307 pounds D 730 pounds
Answer: The weight of each piece of fudge is 12.5 pounds
Step-by-step explanation: To find how much each piece of fudge weighs simply divide 75 by 6 to get the equal weight for 6 pieces.
75/6 = 12.5 pounds per piece.
2 + 2 x 2
plz help me it hard
Answer:
There is no way. Its 6.
Step-by-step explanation:
2 x 2 is 4
4 +2 is 6
25 POINTS FOR FIRST ANSWER
ANSWER ASAP PLZ
1 is union so all all the numbers inside the circles:
{8,9,14,15,16,17}
2 is intersection so the numbers where the circles cross each other
{14,17}
3. A’ is any number not included with A
There are 10 total numbers.
7 are not associated with A
Probability would be 7/10 = 0.70
When the area in square units of an expanding circle is increasing twice as fast as its radius in linear units
Answer:
r=1/π
Step-by-step explanation:
Area of the circle is defined as:
Area = πr²
Derivating both sides
[tex]\frac{dA}{dr}[/tex]=2πr
[tex]\frac{dA}{dt}[/tex] = [tex]\frac{dA}{dr}[/tex] x [tex]\frac{dr}{dt}[/tex] = 2πr[tex]\frac{dr}{dt}[/tex]
If area of an expanding circle is increasing twice as fast as its radius in linear units. then we have : [tex]\frac{dA}{dt}[/tex] =2[tex]\frac{dr}{dt}[/tex]
Therefore,
2πr [tex]\frac{dr}{dt}[/tex] = 2 [tex]\frac{dr}{dt}[/tex]
r=1/π
Answer:
r = 1/π
Step-by-step explanation:
Here we have
Area of a circle given as
Area = πr²
Where:
r = Radius of the circle
When the area of the circle is expanding twice as fast s the radius we have
[tex]\frac{dA}{dt} =2 \times \frac{dr}{dt}[/tex]
However,
[tex]\frac{dA}{dt} = \frac{dA}{dr} \times \frac{dr}{dt}[/tex] and
[tex]\frac{dA}{dr} = \frac{d\pi r^2}{dr} = 2\pi r[/tex]
Therefore, we have
[tex]\frac{dA}{dt} =2 \times \frac{dr}{dt} = 2\pi r \times \frac{dr}{dt}[/tex]
Cancelling like terms
[tex]1= \pi r[/tex]
Therefore, [tex]r = \frac{1}{\pi }[/tex].
Sarah used her calculator to work out the value of a number y .
The answer on her calculator display began.
7.8
Complete the error interval for y.
[......] ≤ y < [......]
The error interval for y is 7.8 ≤ y < 7.9.
Explanation:The error interval is determined by the decimal digits that will determine the value of y. Since the calculator display shows 7.8, y will be between 7.8 and the next smallest number, which will be 7.9. Therefore, the error interval for y is:
7.8 ≤ y < 7.9
Learn more about Error Interval here:https://brainly.com/question/31950158
#SPJ12
The error interval for y is [7.8, 7.9).
Explanation:To find the error interval for y, we need to consider the decimal place immediately after the given value on Sarah's calculator display. Since the given value is 7.8, we look at the digit after the decimal point, which is 0. If this digit is 5 or greater, we round up the previous digit. In this case, 0 is not greater than 5, so we do not round up. Therefore, the error interval for y is [7.8, 7.9).
Learn more about error interval here:https://brainly.com/question/31950158
#SPJ3
What is the length of the shortest side of a triangle that has vertices at (4, 6), (-2, 0), and (-6, 3)?
A.
B.
C.
D.
Answer:
5
Step-by-step explanation:
Figuring the short side, it becomes a nice 3, 4, 5 triangle
so the short side is 5 units.
Hope this helped
:)
Final answer:
The length of the shortest side of the triangle is the length of side BC, which is calculated to be 5 units using the distance formula.
Explanation:
To find the length of the shortest side of the triangle with the given vertices, we will calculate the length of each side using the distance formula √((x2-x1)² + (y2-y1)²) and then determine the shortest one.
Side AB: [tex]\sqrt{((-2-4)^2 + (0-6)^2)}[/tex] = √(36+36) = √72 ≈ 8.5Side AC: [tex]\sqrt{((-6-4)^2 + (3-6)^2)[/tex]= √(100+9) = √109 ≈ 10.4Side BC: [tex]\sqrt{((-6+2)^2 + (3-0)^2)}[/tex] = √(16+9) = √25 = 5Therefore, the length of the shortest side is the length of side BC, which is 5 units.
A math camp wants to hire counselors and aides to fill its staffing needs at minimum cost. The average monthly salary of a counselor is $2400 and the average monthly salary of an aide is $1100. The camp can accomodate up to 45 staff members and needs at least 30 to run properly. They must have at least 10 aides, and * may have up to 3 aides for every 2 counselors. How many counselors and how many aides should the camp hire to minimize cost
Answer: They must hire 12 Counselors and 18 Aides
Step-by-step explanation: The most important factor here is the fact that they need to minimize hiring costs. The math camp can afford to hire up to 45 members of staff and can as well run properly with 30 members of staff.
The camp must have at least 10 aides (simply put, any number above 10 will do). Also they may have up to 3 aides for every 2 counselors, that is the ratio of counselor to aide has been given as;
2 : 3
If the math camp decides to hire the minimum required in order to minimize cost, they would be hiring 30, and that would be divided according to the following ratio;
(Counselor):
30 x 2/5 = 12
(Aide):
30 x 3/5 = 18
Hence they would be hiring 12 counselors at a cost of
2400 x 12 = 28800
And 18 Aides at a cost of
1100 x 18 = 19800
Therefore the total (minimum) cost of hiring staff is $48,600
The problem is a mathematical optimization problem, solved using systems of inequalities. The camp's optimal hiring strategy can be obtained by satisfying a set of constraints and minimizing a cost function.
Explanation:This problem can be solved using systems of inequalities in mathematics. Let's let C represent the number of counselors and A represent the number of aides. Here are the constraints you need to consider:
The camp can accommodate up to 45 staff members: C + A ≤ 45 The camp needs at least 30 staff members to run properly: C + A ≥ 30 They must have at least 10 aides: A ≥ 10 The camp may have up to 3 aides for every 2 counselors: A ≤ (3/2)C
Also, keep in mind that the camp wants to minimize costs, and the average monthly salary is $2400 for counselors and $1100 for aides, so you need to minimize the total cost function: 2400C + 1100A. By solving this system of inequalities and minimizing the cost function, the camp will have an optimal hiring strategy.
Learn more about Mathematical Optimization here:https://brainly.com/question/32199704
#SPJ3
Suppose a coffee cup has a diameter of 8cm and a height of 9cm. What is the volume of the cup ? (to the nearest whole number)
A) 81 cm^3
B) 226 cm^3
C) 452 cm^3
D) 1018 cm^3
Answer:
452 cm^3
Step-by-step explanation:
The volume of a cilinder is [tex]\pi (radius^{2})(height)[/tex]
The diameter of the cup is 8cm, the formula of the radius is [tex]\frac{diameter}{2}[/tex]
So the radius would be [tex]\frac{8}{2}[/tex] = 4cm
We change variables in the formula of the volume [tex]\pi(4^{2})(9)[/tex] = 144[tex]\pi[/tex] = 452cm^3
Answer:
i needed the same thing woa
Mason is having new tires put on his wheel chair. The tires are regularly 56, but this weekend, they are on sale for 25% off. Mason wants to know the sale price for the tires
Answer:
the tires are 42 dolars
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
25% × 56 =
(25 ÷ 100) × 56 =
(25 × 56) ÷ 100 =
1,400 ÷ 100 =
14
A plane has an airspeed of 134 km divided by h. It is flying on a bearing of 78 degrees while there is a 21 km divided by h wind out of the northeast (bearing 225 degrees). What are the ground speed and the bearing of the plane?
The ground speed of the plane is approximately 116.88 km/h, and its bearing is about 83.44°, given an airspeed of 134 km/h on a 78° bearing and a 21 km/h wind from 225°.
The plane's ground speed is approximately 116.88 km/h, and its bearing is roughly 83.44°. This calculation incorporates the plane's airspeed of 134 km/h at a bearing of 78° and a wind speed of 21 km/h from a bearing of 225°.
First, we decompose the velocities into horizontal and vertical components. For the plane's airspeed, the horizontal component is about 27.81 km/h, and the vertical component is around 131.04 km/h. Similarly, for the wind, the horizontal and vertical components are approximately -14.85 km/h each. By adding the horizontal components of the airspeed and wind, we get 12.96 km/h. Likewise, adding the vertical components yields 116.19 km/h.
Using these components, we calculate the resultant velocity vector's magnitude, approximately 116.88 km/h, using the Pythagorean theorem. The direction, or bearing, is computed to be approximately 83.44° using the inverse tangent function.
Therefore, the plane moves at a speed of about 116.88 km/h, slightly northeast of east, due to the combined effect of its airspeed and the wind.
2 + y = 11
Solve the equation.
Answer:
the answer is 9
Step-by-step explanation:
Employees at a large computer company earn sick leave in one-minute increments depending on how many hours per month they work. They can then use the sick leave time any time throughout the year. Any unused time goes into a sick bank account that they or other employees can use in the case of emergencies. The human resources department has determined that the amount of unused sick time for individual employees is uniformly distributed between 0 and 480 minutes. The company has decided to give a cash payment to any employee that returns over a specified amount of sick leave minutes. Assuming that the company wishes no more than 5 percent of all employees to get a cash payment, what should the required number of minutes be?
Answer:
The required amount of minutes is 5796.05 minutes
Step-by-step explanation:
Here, since we have that the sick leave is given as 1 minute per hour worked per month and
The amount of unused sick leave is uniformly distributed between 0 and 480
Therefore, there are 481 employees, counting from 0 to 480 with 0 included
Where the company wishes no more than 5% of all employees get cash payment then we have
Total number of minutes = 1 to 481 = 115921 minutes
Therefore, we have 5% of 115921 = 5796.05 minutes
The balance amount of minutes = 115921 minutes - 5796.05 minutes
= 110124.95 minutes.
Leigh drive 1470 km from smith falls ON to thunder bay ON she stopped 370 km from smith falls About what percent of her trip has she completed when she stopped
Answer:
75%
Step-by-step explanation:
Here, we are asked to calculate the percentage of a trip that has been completed by Leigh.
Firstly, we identify the total length of the trip, this is 1470km. She stopped 370km from her destination. The length of the distance traveled is 1470km - 370km = 1100km
Now we proceed to calculate what percentage of the journey is this.
We calculate this by placing it over the total length multiplied by 100%
That would be
1100/1470 * 100 = 74.82 approximately 75%
Susan owns a home that is worth $128,318.74, a 2005 truck worth $10,615.00, and has investments that total $4,459.16. Susan owes $93,987.74 on her mortgage, $2,874.46 in student loans, and $1,214.92 on her credit card. What is Susan's Net Worth?
Answer:
Net worth is defined as:
Assets - Liabilities.
Assets are what you own.
Liabilities are what you have to pay.
So, home + truck + investments are assets.
Likewise, mortgage + student loans + credit cards are liabilities.
Doing the math, Susan's net worth is
Assets - Liabilities
$143,392.90 - $98,077.12 =
$45,315.78
Susan's net worth is $45,315.78
Good luck!
Susan's net worth is calculated by subtracting her total liabilities (mortgage, student loans, and credit card debt) from her total assets (home, truck, and investments). Therefore, Susan's net worth is $45,315.78.
Explanation:The question is about calculating Susan's net worth. Net worth is calculated by subtracting the total liabilities from total assets. In Susan's case, her assets include her house, truck, and investments, which total to $143,392.90 ($128,318.74 for the house, $10,615.00 for the truck, and $4,459.16 for her investments). Her liabilities include her mortgage, student loans, and credit card debt, which sums up to $98,077.12 ($93,987.74 for the mortgage, $2,874.46 for the student loans, and $1,214.92 for the credit card debt). To calculate Susan's net worth, subtract total liabilities from total assets. Therefore, Susan's net worth is $45,315.78 ($143,392.90 - $98,077.12).
Learn more about Net Worth here:https://brainly.com/question/36453917
#SPJ12
3/4 of the students at Timber Elementary play sports. Of those students, 1/5 of them play soccer. What fraction of the students at Timber Elementary play soccer?
Answer:
3/20 of the students play soccer
Step-by-step explanation:
1. Divide the amount of students that play sports, 3/4 by the amount of those that play soccer, 1/5
2. 3/4 divided by 1/5= 3/20
Answer:
3/20
Step-by-step explanation:
The circumference of a circle is 16 pi ft.
What's the radius
Answer:
2.54648 ft
Step-by-step explanation:
r = 8/π (ft.) Therefore, the radius of the circle when its circumference is 16 feet is r ≈ 2.54648 ft. C = 2 (3.14159) (2.54648) ft :)
Suppose the supply function for a certain item is given by S(q)= (q+6)2 and the demand funtion is given by D(q)= (1000)/(q+6).
A. Find the point at which supply and demand are in equilibrium?
B. Find the consumer's surplus?
C. find the producer's surplus?
Answer: The equilibrium point is where; Quantity supplied = 100 and Quantity demanded = 100
Step-by-step explanation: The equilibrium point on a demand and supply graph is the point at which demand equals supply. Better put, it is the point where the demand curve intersects the supply curve.
The supply function is given as
S(q) = (q + 6)^2
The demand function is given as
D(q) = 1000/(q + 6)
The equilibrium point therefore would be derived as
(q + 6)^2 = 1000/(q + 6)
Cross multiply and you have
(q + 6)^2 x (q + 6) = 1000
(q + 6 )^3 = 1000
Add the cube root sign to both sides of the equation
q + 6 = 10
Subtract 6 from both sides of the equation
q = 4
Therefore when q = 4, supply would be
S(q) = (4 + 6)^2
S(q) = 10^2
S(q) = 100
Also when q = 4, demand would be
D(q) = 1000/(4 + 6)
D(q) = 1000/10
D(q) = 100
Hence at the point of equilibrium the quantity demanded and quantity supplied would be 100 units.
A. The point at which supply and demand are in equilibrium is [tex]q=4[/tex].
B. The consumer's surplus is 178.16 .
C. The producer's surplus is 66.6 .
Given,
The supply function for a certain item is,
[tex]S(q)= (q+6)^2[/tex]
The demand function is,
[tex]D(q)= \dfrac{1000}{ (q+6)}[/tex]
Now we know that the supply and demand are in equilibrium where the supply and demand functions are equal.
So for equilibrium,
[tex]S(q)= D(q)[/tex]
[tex](q+6)^2=\dfrac{1000}{q+6}[/tex]
[tex](q+6)^3=1000[/tex]
[tex]q+6=\sqrt[3]{1000}[/tex]
[tex]q+6=10[/tex]
[tex]q=4[/tex]
Hence the point is [tex]q=4[/tex], at this point supply and demand are in equilibrium.
At equilibrium the supply is [tex](4+6)^2=100[/tex] and demand is also 100.
so, [tex](q^*,p^*)[/tex] is [tex](4,100)[/tex]
Now, the consumer's surplus will be,
[tex]\int\limits^{q^*}_0 {D(q)} \, dq-p^*q^*=\int\limits^4_0 {\dfrac{1000}{q+6} } \, dq -4\times 100[/tex]
[tex]\int\limits^{q^*}_0 {D(q)} \, dq-p^*q^*=1000[log10-log6]-400[/tex]
[tex]\int\limits^{q^*}_0 {D(q)} \, dq-p^*q^*=1000[1-0.778]-400[/tex]
[tex]\int\limits^{q^*}_0 {D(q)} \, dq-p^*q^*=1000\times 0.22184-400[/tex]
[tex]\int\limits^{q^*}_0 {D(q)} \, dq-p^*q^*=221.84-400[/tex]
[tex]\int\limits^{q^*}_0 {D(q)} \, dq-p^*q^*=178.16[/tex]
Now, the producer's surplus will be,
[tex]p^*q^*-\int\limits^{q^*}_0 {s(q)} \, dq=400-\int\limits^{4}_0(q+6)^2dq[/tex]
[tex]p^*q^*-\int\limits^{q^*}_0 {s(q)} \, dq=400-\frac{1}{3} [1000-0][/tex]
[tex]p^*q^*-\int\limits^{q^*}_0 {s(q)} \, dq=\dfrac{200}{3}[/tex]
[tex]p^*q^*-\int\limits^{q^*}_0 {s(q)} \, dq=66.66[/tex]
For more details on Demand and Supply function follow the link:
https://brainly.com/question/2254422
Martin has collected 18 U.S. stamps and 12 international stamps. He wants to display them in identical groups of U.S. and international stamps, with no stamps left over. What is the greatest number of groups Martin can display them in?
A ball is hit into the air with an initial velocity of 100 ft/s. Its height, h(t), after t seconds is given by the function h(t) = -16t² + 100t + 5. What is the ball's maximum height?
at maximum. dt/dh=0
if you differentiate you will get
-32t=-100
t=3.125
kira has a rope that is 5 meters long. she cuts a piece that is 1.51 meters long. how long is the remaining piece of rope
Answer:
3.49
Step-by-step explanation:
5-1.51=3.49
Answer:
3.49 meters long
Step-by-step explanation:
5-1.51 = 3.49
- If you need this further explained please let me know. I would be glad to help.
3 3/4 divided by 5/7
Answer:
5 1/4
Step-by-step explanation:
Dividing by a fraction is the same as multiplying by its inverse.
(3 3/4)/(5/7) = (15/4)/(5/7) = (15/4)·(7/5) = 21/4 = 5 1/4
_____
Many graphing calculators (and some scientific calculators) will do this mixed-number arithmetic for you.
You are given the exponential function g(x) = 3 x . Which option below gives the formula for a new function h created by stretching g by a factor of 3 along the y-axis?
h(x) = 3x+1
h(x) = 3x-1
h(x) = x · 3x+1
h(x) = x · 3x-1
Answer:
A. [tex]h(x) = 3^{x+1}[/tex]
Step-by-step explanation:
Stretching means that original function is multiplied by a constant, which is equal to 3 in this case:
[tex]h(x) = 3 \cdot g (x)[/tex]
[tex]h(x) = 3\cdot 3^{x}[/tex]
[tex]h(x) = 3^{x+1}[/tex]
The answer is A.
Answer:
A
Step-by-step explanation:
Find the arc length of the partial circle.
Answer:
[tex]11[/tex]
Step-by-step explanation:
[tex] \frac{90}{360} \times 2 \times \pi \times 7 \\ \frac{1}{4} \times 2 \times \frac{22}{7} \times 7 \\ = 11[/tex]
Answer:
11
Step-by-step explanation:
[tex] = \frac{1}{2} \pi \: r \\ = \frac{1}{2} \times \frac{22}{7} \times 7 \\ = \frac{1}{2} \times 22 \\ = 11[/tex]
The painting by itself is a rectangle with length 20 cm and width 16 cm. The painting and frame together form a larger rectangle with length 25 cm and width 20 cm Find the area of the frame.
Answer:
The area of frame is 180 square meters.
Step-by-step explanation:
We are given the following in the question:
Dimension of rectangular painting:
Length, l = 20 cm
Width, w = 16 cm
Dimension of frame:
Length, L = 25 cm
Width, W = 20 cm
We have to find the area of frame.
Area of rectangle =
[tex]A = l\times w[/tex]
Area of frame =
[tex]A-a\\=(L\times W)-(l\times w)\\=(25\times 20)-(20\times 16)\\=180\text{ square meters}[/tex]
Thus, the area of frame is 180 square meters.