Assignment
Active
Identifying and Describing Population Change
Organism
Number
per
square
meter
(1991)
Number
per
square
meter
(1994)
Number
per
square
meter
(1997)
Unionid mussels are native to the Hudson River in New
York State. In the early 1990s, zebra mussels were
introduced into the Hudson River. The table shows the
number of unionid mussels and zebra mussels over the
course of six years.
How did the population of unionid mussels change
after zebra mussels were introduced? Why did this
change occur?
Unionid
mussels
8
3
2
I
Zebra
mussels
4
1,329
3,181
Answers
The population of unionid mussels start decreasing approximately at the rate of 75% after zebra mussels were introduced .
The change occurs as zebra mussels consuming almost all the resources available into the Hudson River.
Change in the population of the unionid mussels and zebra mussels over the course of six years are as follow,
population of unionid mussels in 1991 in number per square meter
= 8
Then in the year 1994 it become 3 number per square meter
And finally in the year 1994 it become 2 number per square meter
Change in population of unionid mussels from 1991 to 1997
= [( 2 - 8 )/ 8] × 100
= -75%
Negative sign indicate that decrease in the population.
Now ,
Change in population of zebra mussels is given by,
In 1991 in number per square meter = 4
In 1994 in number per square meter = 1,329
In 1997 in number per square meter = 3,181
Change in population of zebra mussels from 1991 to 1997
= [( 3181 - 4 )/ 4] × 100
= 79425%
There is increase in the population of zebra mussels in thousands.
Reason of change is zebra mussels introduced into the Hudson River
and they eating almost all the resources available in the area.
Zebra mussels consumes large amount of phytoplankton and other small organisms available in the water .
Due to lack of resource availability unionid mussels population decreasing year by year.
learn more about population here
brainly.com/question/15601264
#SPJ4
The above question is incomplete, the complete question is:
Unionid mussels are native to the Hudson River in New
York State. In the early 1990s, zebra mussels were
introduced into the Hudson River. The table shows the
number of unionid mussels and zebra mussels over the
course of six years.
How did the population of unionid mussels change
after zebra mussels were introduced? Why did this
change occur?
attached data.
Related Questions
right triangles & trigonometry can someone help me!!!!!!! please
Answers
Answer:
angles on a straight line add up to 180°
Step-by-step explanation:
90+51=141
180-141
=31
<MLJ=31°
72+90=162
180-162=18
<KJL=18°
Let u=In(x) and v=ln(y), for x>0 and y>0.. Write In (x³ Wy) in terms of u and v. Find the domain, the x-intercept and asymptotes. Then sketch the graph for f(x)=In(x-3).
Answers
To find ln(x³y) in terms of u and v, we can use the properties of logarithms. ln(x³y) can be rewritten as ln(x³) + ln(y), and using the property ln(a^b) = bˣ ln(a), we have 3ln(x) + ln(y) = 3u + v.
How can ln(x³y) be written in terms of u and v, where u = ln(x) and v = ln(y)?To find ln(x³y) in terms of u and v, we can use the properties of logarithms. ln(x³y) can be rewritten as ln(x³) + ln(y), and using the property ln(a^b) = bˣ ln(a), we have 3ln(x) + ln(y) = 3u + v.
The domain of the function f(x) = ln(x-3) is x > 3, since the natural logarithm is undefined for non-positive values. The x-intercept occurs when f(x) = 0, so ln(x-3) = 0, which implies x - 3 = 1. Solving for x gives x = 4 as the x-intercept.
There are no vertical asymptotes for the function f(x) = ln(x-3) since the natural logarithm is defined for all positive values. However, the graph approaches negative infinity as x approaches 3 from the right, indicating a vertical asymptote at x = 3.
To sketch the graph of f(x) = ln(x-3), we start with the x-intercept at (4, 0). We can plot a few more points by choosing values of x greater than 4 and evaluating f(x) using a calculator.
As x approaches 3 from the right, the graph approaches the vertical asymptote at x = 3. The graph will have a horizontal shape, increasing slowly as x increases. Remember to label the axes and indicate the asymptote on the graph.
Learn more about terms
brainly.com/question/28730971
#SPJ11
which is the solution of the system of inequalities? a 0,2 b 0,0 c 1,1 d 2,4
Answers
The solution to the system of inequalities is option C: (1, 1). The system of inequalities typically consists of multiple equations with inequality signs. However, the given options are not in the form of inequalities.
In the given system of inequalities, option d) satisfies all the given conditions. Let's analyze the system of inequalities and understand why option d) is the solution.
The inequalities are not explicitly mentioned, so we'll assume a general form. Let's consider two inequalities:
x > 0
y > x + 2
In option d), we have x = 2 and y = 4.
For the first inequality, x = 2 satisfies the condition x > 0 since 2 is greater than 0.
For the second inequality, y = 4 satisfies the condition y > x + 2. When we substitute x = 2 into the inequality, we get 4 > 2 + 2, which is true.
Therefore, option d) 2,4 satisfies both inequalities and is the solution to the given system.
Learn more about inequalities here:
https://brainly.com/question/30239204
#SPJ11
Hiooo can some help:)
-Boopy❤️
Answers
Consider the following small open economy: с = 200+ 0.69Y I = 80 - 1,000r G = 20 NX = 850.09Ye e = 90 M = 115 YL = 0.5Y - 200r Y = 300 C is consumption spending, I is investment spending, r is the interest rate, G is govern- ment spending, NX is net exports, e is the nominal exchange rate, M is money supply, YL is demand for money, and Y is long-run output. In this economy, the interest rate does not deviate from the foreign interest rate. The price level is fixed and set to one. Note that, in this problem, a decrease in e is synonymous with a depreciation of the nominal exchange rate. 1. Assuming that the economy is in equilibrium, find the value of the interest rate. (6 points) 2. Going from the equilibrium found in Question (1), assuming fixed nominal exchange rates, what is the effect on domestic output if the foreign interest rate increases by 0.05? (6 points) (a) What is the size of the nominal money supply in the new short run equilibrium? (6 points) 3. Going from the equilibrium found in Question (1), assuming flexible exchange rates, what is the effect on domestic output if the foreign interest rate increases by 0.05? (6 points) (a) What is the value of the real exchange rate in the new equilibrium? (6 points)
Answers
The interest rate is 10.89%
1. Given,С = 200+ 0.69YI = 80 - 1,000rG = 20NX = 850.09ee = 90M = 115YL = 0.5Y - 200rY = 300Using the equation for National Saving, we get,National Saving = Investment + Government Saving + Net exports(S – I) + (T – G) + (X – M) = 0T = 0, hence (S – I) + (X – M) = 0(1 – t)Y – C – (I + G) + NX = 0Where t = 0, we get,0.5Y – 200r – 200 – 69/100Y + 80 – 850.09e = 0.5Y – 200r – 970.09e – 120 = 0.5Y – 200r – 970.09e – 120 = 0Therefore, Y = 325.0454 - 0.5r + 4.851eThis is the equation for the IS curve.On the other hand, the equation for the LM curve is given by,Ms / P = YL(i)115 / 1 = 0.5Y - 200rTherefore, Y = 400 + 400rThis is the equation for the LM curve.The interest rate is given by the point of intersection of the two curves. Equating Y from both equations, we get,325.0454 - 0.5r + 4.851e = 400 + 400rSolving the above equation for r, we get r = 0.1089 or 10.89%..
The size of the nominal money supply in the new short-run equilibrium is 121.07.
2. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate.Flexible Exchange Rates:In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output.Real exchange rate will fall.Increase in output will be higher compared to the fixed exchange rate case.Fixed Exchange Rates:In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.Real exchange rate will remain unchanged.Increase in output will be less compared to the flexible exchange rate case.The nominal money supply in the new short-run equilibrium will change in the case of Fixed Exchange Rates. In the fixed exchange rate case, the domestic interest rate will increase, leading to an inflow of capital. This will increase the money supply and the LM curve will shift downwards until it intersects the IS curve at the new equilibrium point.
Real exchange rate will remain unchanged.
3. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate. Flexible Exchange Rates :In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output .Real exchange rate will fall. Value of the real exchange rate in the new equilibrium is 0.891.Fixed Exchange Rates: In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.
Know more about interest rate here:
https://brainly.com/question/28236069
#SPJ11
Create a verbal math expression (using words). (Your verbal expression must contain "a number" so that the algebraic expression contains a variable.)
Answers
Examples of Algebra Word problems and their expressions are;
1) What is 9 increased by a number cubed?
9 + x³
2) What is the product of the sum of a number and five and the difference of a number and 5? (x + 5) * (x - 5)
How to create Algebra Word problems?
Algebraic word problems are defined as questions that require translation of sentences into equations, and after that, we now solve those equations. They usually contain a single variable that depicts an unknown quantity in a real-life scenario.
Examples of Algebra Word problems and their expressions are;
1) What is 9 increased by a number cubed?
9 + x³
2) What is the product of the sum of a number and five and the difference of a number and 5? This is expressed as;
(x + 5) * (x - 5)
Read more about Algebra Word problems at; https://brainly.com/question/13818690
#SPJ1
2^3 + 3(9-5) plz help
Answers
Answer:
The answer is 20
Step-by-step explanation:
Use a linear approximation (or differentials) to estimate the given number. (Do not round your answer). (32. 03)4/5
Answers
Using linear approximation, we estimate that (\(32.03^{4/5}\)) is approximately equal to 31.952. It's important to note that this is only an estimate and may not be exact.
To estimate the value of (\(32.03^{4/5}\)) using linear approximation, we start by finding the differential of the function f(x) = \(x^{4/5}\) at the point x = 32.
\(f(x) = x^{4/5}\)
\(f'(x) = 4/5x^{-1/5}\)
Evaluating \(f'(32)\), we get:
\(f'(32) = (4/5)(32)^{-1/5} = 0.1585\)
Now, using the linear approximation formula:
\(f(x) ≈ f(a) + f'(a)(x - a)\)
where a is the point at which we are estimating the function, we have:
\(f(32.03) = f(32) + f'(32)(32.03 - 32)\)
\(= 32^{4/5} + 0.1585(0.03)\)
\(= 31.952\)
Linear approximation is a useful tool for approximating values of functions near a given point, but it has limitations and may not work well for functions that are highly nonlinear or have discontinuities.
To learn more about linear approximation follow the link: https://brainly.com/question/30881351
#SPJ4
A group of ants in Mauritania, West Africa are building a giant ant hill. Each day they add 5 pounds of dirt to the ant hill. Currently, the ant hill has 68 pounds of dirt. 3 How many pounds of dirt was on the ant hill 2 weeks ago?
Answers
The negative weight for the ant hill shows that two weeks ago there was no dirt on the ant hill .
Pounds of dirt add by ants on ant hill each day = 5 pounds
Pounds of dirt on ant hill = 68 pounds
To determine the number of pounds of dirt on the ant hill two weeks ago,
Calculate the amount of dirt added each day for two weeks and subtract that from the current weight of the ant hill.
There are 7 days in a week, so the ants add 5 pounds of dirt each day for 2 weeks,
which is a total of 5 pounds/day × 14 days = 70 pounds.
Subtracting the 70 pounds of dirt added in the past two weeks from the current weight of 68 pounds, we get,
= 68 pounds - 70 pounds
= -2 pounds.
Therefore, negative weight for the ant hill it is concluded that there was no dirt on the ant hill two weeks ago.
learn more about ant hill here
brainly.com/question/21149627
#SPJ4
Can someone help me with this equation plsss
Answers
Answer:
the answer is -5/3 I guess
hree hundred books sell for 40 dollars each, resulting in a revenue of 12,000 dollars. For each $5 increase in the price, 25 fewer books are sold. Write the revenue R as a function of the number x of $ 5 increases.
Answers
A total of 12,000 dollars is made from the sale of 300 books at a price of $40 each. 25 fewer books are sold for every $5 increase in price. R(x)=(40+5x)(300−25x) R ( x ) = ( 40 + 5 x ) ( 300 − 25 x )
What is the revenue R as a function of number x ?Assumed in this instance is , At a price of 40 dollars apiece, \($(300)(40 \$)=12,000 \$$\) books generate $300 in revenue. The result is that 25 fewer books are sold if we raise the price of each book by $5. That's \($(300-25 x)$\). Due to the fact that the price always rises by five times more than the number of books, the cost is \($(40+5 x)$\).
\($R=(300-25 x) \cdot(40+5 x)$\)
\($R=12000+6000 x-1000 x-125 x^2$\\$R=-125 x^2+5000 x+12000$\\$R=125 x^2-5000 x-12000$\)
The revenue R is expressed as a function of the number x as it approaches 5. R(x)=(40+5x)(30025x) is the necessary revenue function. R(x) = (40 + 5 x)(300 25 x) is the necessary revenue function.
To learn more about revenue refer to :
https://brainly.com/question/2263738
#SPJ4
Suppose that x and y are positive integers such that x^2 * y^3=46656. What is the sum of all possible values of x?
Answers
Answer:
252
Step-by-step explanation:
x² * y³=46656Prime factors of 46656:
46656 = 2⁶3⁶Possible values of x:
(2*3)³= 2163³ = 272³ = 81Sum of them:
216 + 27 + 8 + 1 = 252For all values of x,
f(x) = x/5 + 3
and
g(x) = 10x2 + 5
Work out fg(x).
Give your answer in the form ax2 + b where a and b are integers.
Answers
Answer:
2\(x^{2}\)+4
I would give a step by step explanation but it keeps saying I'm typing inappropriate words so message me if u need
Hence, The value of fg(x) in the form of ax2+b is 2x2+4.
What is composition of functions?Composition of function is an operation in which we combine two or more function to generate a single function. In this question the function g is places in the place of x.
How to solve?
Given f(x)=x/5 +3
g(x)=10\(x^{2}\) + 5
the composition of function ,
fg(x) = g(x)/5 + 3
fg(x) = (10\(x^{2}\) + 5)/5 + 3
= 2\(x^{2}\)+ 1 + 3
= 2\(x^{2}\) + 4
hence, fg(x)= 2\(x^{2}\)+4 where a=2 and b=4
learn more about composition of functions
https://brainly.com/question/10687170
#SPJ2
Which graph represents the linear equation y = −5x − 3?
a graph of a line that passes through the points negative 4 comma 0 and 0 comma negative 3
a graph of a line that passes through the points negative 1 comma 2 and 0 comma negative 3
a graph of a line that passes through the points negative 1 comma 0 and 0 comma negative 5
a graph of a line that passes through the points negative 1 comma 4 and 0 comma negative 2
Answers
Answer: a graph of a line that passes through the points negative 1 comma 2 and 0 comma negative 3.
Step-by-step explanation: the y-intercept is where the line meets the y line which in this case is -3. I used slope formula to find the m of the equation ( slope ) take a look at the attached image to see how I solved it.
Answer:
a graph of a line that passes through the points negative 1 comma 2 and 0 comma negative 3.
Step-by-step explanation:
What is the product of (2i) and (5+3i)?
Group of answer choices
-6 + 10i
10 + 6i
16i
10 - 6i
Answers
The value of the product expression given as product of (2i) and (5+3i) is 10i -6
How to determine the product?The product expression is given as:
product of (2i) and (5+3i)
Rewrite the expression as:
(2i) * (5+3i)
Open the brackets
(2i) * (5+3i) = 10i + 6i^2
Evaluate
(2i) * (5+3i) = 10i + 6(-1)
This gives
(2i) * (5+3i) = 10i -6
Hence, the value of the product expression given as product of (2i) and (5+3i) is 10i -6
Read more about complex numbers at:
https://brainly.com/question/10662770
#SPJ1
112x+3≥7 OR 2x+9>11
anyone know what the answer is
Answers
Answer:
I don't know
Step-by-step explanation:
I don't know
112x greater than equal 7-3
112x ge 4
X ge 4/112
or x ge 1/28
2x+9>11
2x>11-9
2x>2
X>2/2
or x>1
find the perimeter of ABC
state the postulate or theorem that justifies your answer
50 POINTS!!!
Answers
Step-by-step explanation:
BU = AU (Given)
BU = AU = 5 cm
BA = AU + BU
BA = 5 + 5
BA = 10 cm
CT = TA (Given)
CT = TA = 4 cm
AC = CT + TA
AC = 4 + 4 = 8 cm
CV = VB (Given)
CV = VB = 3 cm
CB = CV + VB
CB = 3 + 3 = 6 cm
Now,
Perimeter of ∆ABC = 10 + 8 + 6 = 24 cm
Answer:
24 unitsStep-by-step explanation:
See the statements and reasons below:
BV = VC, AT = CT, BU = AU GivenVU, UT and VT are midsegments of ΔABC Midsegment theoremAC = 2*VU = 2*3 = 6 Definition of midsegmentBC = 2*UT = 2*4 = 8 Definition of midsegmentAB = 2*BU = 2*5 = 10 Definition of midpointP = AB + AC + BC Definition of perimeterP = 10 + 8 + 6 = 24 Substitution property of equality3(x - 5) = 30
I dont know how to solve this
Answers
Answer:
x=15
Step-by-step explanation:
3(x-5)=30
First, you would distribute the three to the x and the negative five.
3x-15=30
Then you would add 15 to the 15 to cancel it and to the 30 to make it even.
3x-15=30
+15=+15=
3x=45
Finally, you would divide 3 into both sides, cancelling out the three and fiving you,
x=15
Hope this helped!
Start by distributing the 3 through the parenthses on the left side.
This gives us 3x - 15 = 30.
Now add 15 to both sides to end up with 3x = 45.
Dividing both sides by 3, we fin that x = 15.
A plane traveled 5525 miles with the wind in 8.5 hours and 4505 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind. The speed of the plane in still air is ____(hours.miles.mph) (Simplify your answer.)
Answers
Answer:
590mph
Step-by-step explanation:
Speed with wind = 5525÷ 8.5
= 650mph
speed against wind = 4505÷8.5
= 530mph
speed without wind = (650mph+530mph)÷2
= 590mph
Write another term using the cosine ratio that is equivalent to cos 75•
Answers
Another term using the cosine ratio that is equivalent to cos 75° is sin 15°.
Using the cosine ratio, we can find the ratio of the adjacent side to the hypotenuse in a right triangle. The cosine ratio of an angle is given as the ratio of the adjacent side to the hypotenuse. The cosine ratio is the reciprocal of the secant ratio.
The cosine ratio of 75° is given as cos 75° = adjacent/hypotenuse.
We know that the cosine of 75 degrees is equal to the sine of 15 degrees.
Therefore, another term using the cosine ratio that is equivalent to cos 75° is sin 15°.This is because of the relationship between complementary angles and the sine and cosine ratios. The sine ratio of an angle is given as the ratio of the opposite side to the hypotenuse.
The sine ratio of the complementary angle is given as the ratio of the adjacent side to the hypotenuse. Since 75° and 15° are complementary angles, their sine and cosine ratios are related by this complementary relationship.
The sine and cosine ratios of complementary angles can be used to find trigonometric values for angles between 0 and 90 degrees.
By using the complementary relationship, we can find equivalent terms for trigonometric functions that involve different angles.
For more such questions on cosine ratio, click on:
https://brainly.com/question/15793827
#SPJ8
Mrs. Claus wants to have a nice meal ready when Santa comes home. She wants to make waffles and she knows that he will be hungry. If each recipe requires ¾ cups of butter and she has 4 ½ cups of butter, how many waffle recipes can she make?
Answers
Answer:
6
Step-by-step explanation:
Each recipe of waffles requires 3/4 cups of butter
Mrs Claus has 4 1/2 cups of butter
Therefore the number of recipes which she will be able to make can be calculated as follows
= 4 1/2 ÷ 3/4
= 9/2 ÷ 3/4
= 9/2 × 4/3
= 6
Hence Mrs Claus can make 6 recipes
Would anyone help With these questions it's the last one I don't know how to do them 1,2,3,4,5 and 6
Answers
Answer:
See below
Step-by-step explanation:
1. Use x to designate the number of hours worked.
Plumber 1 = 35(x) + 25
Plumber 2 = 40(x)
Now you need to find when these two equations are equal to each other.
35(x) + 25 = 40(x)
Solve for x.
25 = 40x - 35x
25 = 5x
5 = x
So when the service call equals 5 hours, both plumbers will charge the same amount of money.
2. Use x to designate the number of months.
Center 1 = 30x
Center 2 = 22x + 80 initiation fee
Now you need to make the two equations equal to each other and solve for x.
30x = 22x + 80
30x - 22x = 80 or 8x = 80
x = 10 months
3. Use x to designate the pounds of the package
Shipper 1 = 14 + 2x
Shipper 2 = 20 + 1.5x
Make the two equations equal to each other.
14 + 2x = 20 + 1.5x
2x - 1.5x = 20 - 14
0.5x = 6
x = 12 pounds
4. Deanna $15 using $0.75 per game. This means she can play a total of 20 games before having $0.
Lise $13 using $0.50 per game. This means she can play a total of 26 games before having $0.
So since both end up with $0, you can see that Deanna would play 20 games and Lise would play 26 games.
5. Use x to designate the call time length.
Hotel 1 = 1 + 0.80x
Hotel 2 = 2 + 0.75x
Make both equations equal to each other.
1 + 0.8x = 2 + 0.75x
0.8x - 0.75x = 2 - 1
0.05x = 1
x = 20
6. Use x to designate semesters.
Duke = 22 + 6x
Kila = 4 + 12x
22 + 6x = 4 + 12x
22 - 4 = 12x - 6x
18 = 6x
3 = x semesters
If u=(4,2) and v=(-3,2) , evaluate |u+v|
Please needs it urgently
Answers
Explanation
Add the components of the vectors
u+v = (4,2) + (-3,2)
u+v = (4+(-3), 2+2)
u+v = (1,4)
Then to evaluate the length of vector u = (a,b), we use this formula
|u| = sqrt(a^2+b^2)
Which is derived from the pythagorean theorem. We're looking for the hypotenuse of the right triangle formed. In this case a = 1 and b = 4.
So,
|u+v| = sqrt(1^2 + 4^2)
|u+v| = sqrt(17)
An apartment complex rents an average of 2.3 new units per week. If the number of apartments rented each week has a Polsson distribution, then the probability of renting exactly three apartments in a week is ....
Answers
The probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.
If the average number of units rented per week is 2.3 and the distribution is Poisson, then the parameter lambda is also equal to 2.3.
The probability of renting exactly three apartments in a week is given by the Poisson probability function:
\(P(X = 3) = (e^(-lambda) * lambda^x) / x!\)
Substituting the values, we get:
\(P(X = 3) = (e^(-2.3) * 2.3^3) / 3!\)
P(X = 3) = (0.09963 * 12.167) / 6
P(X = 3) = 0.2018
Therefore, the probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.
To know more about probability refer to-
https://brainly.com/question/30034780
#SPJ11
how many participants would be needed for a within-subjects experiment comparing four different treatment conditions with a total of 20 scores in each treatment?
Answers
The number of participants that would be needed for a within-subjects experiment is 80.
What is an experiment?An experiment simply means a research that's conducted in order to get information about a particular thing.
In this case, we want to know the number of participants that will be neeed within-subjects experiment comparing four different treatment conditions with a total of 20 scores in each treatment.
This will be:
= Number of scores × Number of treatment
= 20 × 4
= 80
The participants needed are 80.
Learn more about experiments on:
brainly.com/question/17274244
#SPJ1
1. A savings account earns 8 % Interest each year, compounded quarterly (4 times a year). If a person Invests $100 and makes no further deposits or withdrawals, what is the balance inthe account after 3 years?hpA
Answers
So, the formula that we're going to use is:
Compound interest
A = P(1 + r/n)ⁿˣ
Where
A = amount
P = principal = $100
r = rate = 8% = 8 / 100 = 0.08
x = time
In this case, n=4 since it is being compounded quarterly, so:
The answer is $126.82.
halp me this question
Answers
one quarter is 25
one dime is 10
one nickel is 5
one penny is 1
25+25+10+10+5+1=76
Answer: It's 76 cents [insert facepalm here]
Step-by-step explanation:
Honestly, if you are in high school and cannot get this correct then that is just sad, but I guess I'll explain anyway.
2 quarters= 50 cents
2 dimes= 20 cents
1 nickel= 5 cents
1 penny= 1 cent
Total= 76 cents
I really don't see how you got 66 cents out of that but whatever.
How to find out the values of p and q?
Answers
Part a
Comparing the \(\vec{i}\) components, \((p+14)/2=9 \implies \boxed{p=4}\)
Comparing the \(\vec{j}\) components, \((8+q)/2=40 \implies \boxed{q=72}\)
Part B
\(\overrightarrow{OM}=9\vec{i}+40\vec{j} \implies \left|\overrightarrow{OM}\right|=\sqrt{9^2 +40^2}=41\\\\\)
Dividing each of the components of \(\overrightarrow{OM}\) by this magnitude, the unit vector is \(\boxed{\frac{9}{41}\vec{i}+\frac{40}{41}\vec{j}}\).
Please help I if you can thank you do much
Answers
Answer:
A. (Pay as you go) $120 B. (Regular deal) $90 C. (All-in-one price!) $100 D. The "Regular deal" option would be the least expensive for Carl.
Step-by-step explanation:
If Carl does the "Pay as you go" option he would be charged $6 each time. If he works out 20 times a month, we can multiply 20 by 6 to get a total of $120 for that option.
If Carl does the "Regular deal" option he would be charged $50 + an additional $2 for each time he works out. From there, we can get the equation 2x + 50 where x is the amount of time he works out. If we plug in 20 for x (as he works out 20 times a month), we get 2(20) + 50 which equals a total of $90 for that option.
If Carl does the "All-in-one Price!" option he would be charged $100 for the whole month meaning he has unlimited use of the gym with no extra charge besides the $100.
The cheapest option is the "Regular deal" option as it charges $90 compared to the $100 for the "All-in-one Price!" option & the $120 for the "Pay as you go" option.
Solve the inequality for x and identify the graph of its solution.
4|x + 3| < 8
Choose the answer that gives both the correct solution and the correct graph.
A.
Solution: x < 1 or x > 5; graph:
B.
Solution: x < –5 or x > –1; graph:
C.
Solution: x > –5 and x < –1; graph:
D.
Solution: x > –5 and x < –1; graph:
Answers
Answer:
D
Step-by-step explanation:
^^^