Answer:
El saldo que el Sr. Rodríguez debe pagar cuando vence el pagaré es de $ 370
Step-by-step explanation:
Los parámetros dados del préstamo son;
El monto principal del préstamo, P = $ 675
La duración del préstamo, T = 8 meses = 2/3 años
La tasa de interés aplicada al préstamo, R = 10%
La cantidad que paga el Sr. Rodríguez en el segundo mes = $ 150
La cantidad que paga el Sr. Rodríguez en el cuarto mes = $ 200
Interés simple = P · R · T / 100 = 675 × 10 × 2/3/100 = 45
El interés simple del préstamo, I = $ 45
La cantidad total que el Sr. Rodríguez tiene que pagar, A = P + I = 675 + 45 = 720
La cantidad de reembolso que realiza el Sr. Rodríguez, R = 150 + 200 = 350
El saldo que debe pagar el señor Rodríguez, B = 720 - 350 = 370
El saldo que el señor Rodríguez debe pagar cuando el pagaré no vence, B = $ 370
Al vencerse el pagaré el señor Rodríguez deberá pagar $370.
Dado que el señor Rodríguez firma un pagaré por $675 a 8 meses de plazo y al 10%, si efectúa dos pagos antes del vencimiento, uno por $150 a los 2 meses, y otro por $200 a los 4 meses, para determinar cuál es el saldo que debe pagar al vencerse el pagaré se debe realizar el siguiente cálculo:
10/12 x 8 = 6.666(675 x 1.06666) - 150 - 200 = X720 - 350 = X370 = XPor lo tanto, al vencerse el pagaré el señor Rodríguez deberá pagar $370.
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Ravi works as a tutor for an hour and as a waiter for an hour. This month, he worked a combined total of hours at his two jobs. Let be the number of hours Ravi worked as a tutor this month. Write an expression for the combined total dollar amount he earned this month.
The expression for his total earnings can be derived by multiplying the number of tutoring hours by the tutoring rate and adding it to the product of the number of waiter hours and the waiter rate.
Let's assume the hourly rate for Ravi's tutoring job is "t" dollars and the hourly rate for his waiter job is "w" dollars.
Since Ravi worked as a tutor for "x" hours this month, he earned a total of x * t dollars from his tutoring job.
Similarly, as he worked as a waiter for 1 hour each day this month, he earned a total of 1 * w dollars from his waiter job.
To calculate the combined total dollar amount he earned this month, we can express it as x * t + 1 * w, which represents the earnings from his tutoring job plus the earnings from his waiter job.
This expression provides the total dollar amount Ravi earned based on the given hourly rates and the number of tutoring hours.
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What are the step to the Quadratic Formula?
The steps to solve a quadratic formula include:
Combine all of the like terms and move them to one side of the equationFactor the expressionSet each set of parenthesis equal to zero as separate equationsSolve each "zeroed" equation independentlyWhat is a quadratic equation?In algebra, a quadratic equation is a equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0.
A quadratic equation is an equation that could be written as ax² + bx + c = 0
when a 0. The factoring method is illustrated:
To solve a quadratic equation by factoring, put all terms on one side of the equal sign, leaving zero on the other side.
Set each factor equal to zero.
Solve each of these equations.
Check by inserting your answer in the original equation.
Example 1
Solve x² – 6 x = 16.
Following the steps,
x² – 6 x = 16 becomes x² – 8x + 2x – 16 = 0
Factor.
( x – 8)( x + 2) = 0
Therefore, x = 8 and -2.
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(01.08 mc) a high school's student council wants to purchase spirit shirts for its upcoming homecoming event. purchases of 25 shirts or less cost $20 per shirt, plus $20 shipping and handling. when more than 25 shirts are ordered, the price is $15 per shirt, plus $15 shipping and handling. if $720 was spent on shirts, how many shirts did the student council order?
When more than 25 shirts are ordered, the price is $15 per shirt, plus $15 shipping and handling. If $720 was spent on shirts, the student council ordered 47 shirts.
Let x be the number of shirts ordered. We can set up an equation based on the given information:
If x ≤ 25, then the cost of the shirts is 20x + 20.
If x > 25, then the cost of the shirts is 15x + 15.
We know that the total cost of the shirts is $720. So, we can write:
20x + 20 if x ≤ 25
15x + 15 if x > 25
Setting these equal to each other, we get:
20x + 20 = 15x + 15
5x = 5
x = 1
This doesn't make sense, because the number of shirts ordered must be greater than 1. Therefore, we know that the student council ordered more than 25 shirts.
Using the equation 15x + 15 = 720, we can solve for x:
15x + 15 = 720
15x = 705
x = 47
To check, we can calculate the cost of the shirts:
If 47 shirts are ordered, then the cost is 15(47) + 15 = $720.
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I need a bit of help please
Answer: x= 1
Step-by-step explanation:
a wodden plnk 15
\( \sqrt{3} \)
m long rests on a wall in such a way that it mskes an angel with ground at 15m away from the foot of the wall. find the angle made by the plank with the ground
Step-by-step explanation:
when you look at that right-angled triangle that is created by the plank as Hypotenuse (the side opposite of the 90° angle), and the distance on the ground from the wall and the height on the wall (from ground to the plank) as the legs, we know that the Hypotenuse (the plank) is the radius of the trigonometric circle we can draw there, and the 15 m ground distance from the wall is
cos(our angle) × radius
15×sqrt(3) × cos(our angle) = 15
cos(our angle) = 1/ sqrt(3) = 0.577350269...
our angle = 54.73561032...°
Compute the z score for the applicant. Applicant's score 21.0; Mean 18.0; Standard Deviation - 3.0 O2.0 O-10 10 O-20 O None of these
To compute the z-score for the applicant, we can use the formula:
z = (x - μ) / σ
Where:
x is the applicant's score
μ is the mean
σ is the standard deviation
Given that the applicant's score is 21.0, the mean is 18.0, and the standard deviation is -3.0, we can substitute these values into the formula to calculate the z-score.
z = (21.0 - 18.0) / (-3.0)
z = 3.0 / -3.0
z = -1.0
Therefore, the z-score for the applicant is -1.0.
The correct option is O-10.
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help me solve this please
What is the dividend on £320.80 at 15p per £?
a = , b = , c =
HELP ASAP!WILL MARK BRAINLIEST AND WORTH 23 POINTS!
Answer:
a = 2
b = 3
c = 2³ or 8
Step-by-step explanation:
Exponent Rule: \(\frac{b^m}{b^n} =b^{m-n}\)
log₂(4) = 2 or 2² = 4
2⁵/2² = 2³
2³ = 8
Answer:
a=2
b=3
c=8
Step-by-step explanation:
a=2, 2^a must equal 4
b=3, 2^b must equal 8 which is answer to 2⁵/4
c=8, the answer to 2⁵/4, and
he line y =-x passes through the origin in the xy-plane, what is the measure of the angle that the line makes with the positive x-axis?
The line y = -x, passing through the origin in the xy-plane, forms a 45-degree angle with the positive x-axis.
The slope-intercept form of a linear equation is y = mx + b, where m represents the slope of the line. In this case, the equation y = -x has a slope of -1. The slope indicates the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.
To determine the angle between the line and the positive x-axis, we need to find the angle that the line's slope makes with the x-axis. Since the slope is -1, the line rises 1 unit for every 1 unit it runs. This means the line forms a 45-degree angle with the x-axis.
The angle can also be determined using trigonometry. The slope of the line (-1) is equal to the tangent of the angle formed with the x-axis. Therefore, we can take the inverse tangent (arctan) of -1 to find the angle. The arctan(-1) is -45 degrees or -π/4 radians. However, since the line is in the positive x-axis direction, the angle is conventionally expressed as 45 degrees or π/4 radians.
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a man has 32 coins in his pocket, all of which are dimes and quarters. if the total value of his change is 620 cents, how many dimes and how many quarters does he have? your answer is
If the total value of his change is 620 cents, the man has 12 dimes and 20 quarters in his pocket.
Let's assume that the man has x dimes and y quarters in his pocket. We know that he has 32 coins in total,
x + y = 32.
We also know that the total value of his change is 620 cents, which can be expressed as
10x + 25y = 620.
To solve for x and y, we can use either substitution or elimination. Let's use substitution. Solving the first equation for x, we get
x = 32 - y.
Substituting this into the second equation, we get
10(32 - y) + 25y = 620
Simplifying this equation, we get
320 - 10y + 25y = 620
which yields
15y = 300.
Therefore, y = 20, and x = 32 - 20 = 12.
So the man has 12 dimes and 20 quarters in his pocket. We can check that this is correct by verifying that
12(10) + 20(25)
= 120 + 500
= 620.
In summary, we can solve the problem by setting up a system of equations, either using substitution or elimination to solve for the variables, and then checking our answer to make sure it is correct.
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HELP ASAPPPP!!!!! The table shows the deer population in a forest over a 15-year period. Find the rate of change for each time period to the nearest hundredth. Identify the time period during which the population increased at the fastest rate.
Answer:Hope fully this helps please mark me brainliest :)
Step-by-step explanation:
Find the are n circumference of each circle above
The area and circumference of the circles are solved
Given data ,
Let the area and circumference be represented as A and C
Now , the circles are
Circumference of circle = 2πr
Area of the circle = πr²
a)
Radius = 7 m
C = 2 ( π ) ( 7 )
C = 43.98 m
A = π ( 7 )²
C = 153.938 m²
b)
Diameter = 30 feet
C = 2 ( π ) ( 15 )
C = 94.24 feet
A = π ( 15 )²
C = 706.858 feet²
c)
Radius = 10.2 inches
C = 2 ( π ) ( 10.2 )
C = 64.088 inches
A = π ( 10.2 )²
C = 326.85 inches²
d)
Diameter = 9 mm
C = 2 ( π ) ( 4.5 )
C = 28.274 mm
A = π ( 4.5 )²
C = 63.617 mm²
Hence , the circles are solved
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Planes x = 2, y = 4 and z =4, respectively, carrying charges of 14nC/m², 17nC/m² and 22nC/m². If the line charges of 10nC/m, 15nC/m and 20nC/m at x = 10, y = 5; y=6, z = 5 and x 9, z = 6, respectively. Calculate the total electric flux density at the following locations: a. P1(2, 2, 5)
The total electric flux density at P1(2, 2, 5) is 66,102.3 Nm²/C.
To calculate the total electric flux density at P1(2, 2, 5), we'll use Gauss's law: ΦE = q/ε₀. Where ΦE represents the total electric flux, q is the net charge inside the closed surface, and ε₀ is the permittivity of free space. We'll need to first determine the total charge enclosed by the Gaussian surface at P1(2,2,5).
Here are the steps to do so:
Step 1: Define the Gaussian surface
We'll define a Gaussian surface such that it passes through P1(2, 2, 5), as shown below: \(\vec{A}\) is the area vector, which is perpendicular to the Gaussian surface. Its direction is pointing outward.
Step 2: Calculate the net charge enclosed by the Gaussian surfaceThe Gaussian surface passes through the three planes x=2, y=4 and z=4, which carry charges of 14nC/m², 17nC/m² and 22nC/m², respectively. The Gaussian surface also passes through four line charges: 10nC/m, 15nC/m, 15nC/m, and 20nC/m.
We'll use these charges to find the total charge enclosed by the Gaussian surface.q = Σqinwhere qin is the charge enclosed by each part of the Gaussian surface. We can calculate qin using the surface charge density for the planes and the line charge density for the lines.
For example, the charge enclosed by the plane x = 2 isqin = σA
where σ = 14nC/m² is the surface charge density and A is the area of the part of the Gaussian surface that intersects with the plane. Since the Gaussian surface passes through x = 2 at y = 2 to y = 4 and z = 4 to z = 5, we can find A by calculating the area of the rectangle defined by these points: A = (4-2) x (5-4) = 2m²
Therefore,qx=2 = σxA = 14nC/m² x 2m² = 28nC
Similarly, the charge enclosed by the planes y = 4 and z = 4 are qy=4 = σyA = 17nC/m² x 2m² = 34nC and qz=4 = σzA = 22nC/m² x 2m² = 44nC, respectively.
For the lines, we'll use the line charge density and the length of the part of the line that intersects with the Gaussian surface. For example, the charge enclosed by the line at x = 10, y = 5 isqin = λlwhere λ = 10nC/m is the line charge density and l is the length of the part of the line that intersects with the Gaussian surface. The part of the line that intersects with the Gaussian surface is a straight line segment that goes from (2, 5, 5) to (10, 5, 5), which has a length of l = √((10-2)² + (5-5)² + (5-5)²) = 8m
Therefore,qx=10,y=5 = λl = 10nC/m x 8m = 80nC
Similarly, the charges enclosed by the other lines are:qy=6,x=10 = λl = 15nC/m x 8m = 120nCqy=5,x=9 = λl = 15nC/m x 8m = 120nCqz=6,x=9 = λl = 20nC/m x 8m = 160nCTherefore, the total charge enclosed by the Gaussian surface is:q = qx=2 + qy=4 + qz=4 + qy=5,x=10 + qy=6,x=10 + qy=5,x=9 + qz=6,x=9= 28nC + 34nC + 44nC + 80nC + 120nC + 120nC + 160nC = 586nC
Step 3: Calculate the total electric flux density at P1(2, 2, 5)We can now use Gauss's law to find the total electric flux density at P1(2, 2, 5).ΦE = q/ε₀ε₀ = 8.85 x 10^-12 F/mΦE = (586 x 10^-9 C)/(8.85 x 10^-12 F/m)ΦE = 66,102.3 Nm²/C
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Q1) 4a + 7b +5a - b
Q2) 6c + 4d - c - 7 d
Answer:
4a+5a+7b-b
the first thing is to put the like terms together
Step-by-step explanation:
then add or subtract as given after pairing.
Therefore;
our answer is; 9a+6b
since it is factorisable we can further write it this way; 3(3a+2b)
q2) 6c+4d-c-7d
we first put the like terms together
6c-c+4d-7d
we then add and subtract
5c-3d
since our answer is not factorisable we leavem;
5c-3d as our final answer
Hilda's personal information is shown below:
Age
Time at address
Age of auto
Car payment
None
None
Housing costs
$700
Checking and Both
savings
accounts
Finance
company
reference
Major credit
cards
Ratio of debt to
income
Age
Time at address
Age of auto
Car payment
Declared
bankruptcy
According to the following table, what is her hypothetical credit score?
Under 25
2-29
20
48
<1 yr
36
None
0
None
72
Housing costs
35
6 months
No
Major credit cards
Ratio of debt Income
2
Declared bankruptcy
No debts
Never
Checking and savings accounts
Finance company reference
<$274
0
Both
60
Yes
0
None
0
No debts
164
Never
102
1 yr
0
0-1 yrs
48
<$125
24
$275-$399
40
Checking only
8-8300
No
60
30-34
0
20
2-3 yrs
20
2 yrs
64
$1265-$150
4
$400 +
48
Savings only
8
2 or more
60
1%-5%
6%-15%
80
64
In the last 10 yrs Over 10 yrs ago
0
24
35-39
4
40-44
72
6-9 yrs
4-5 yrs
0
3-4 yrs
52
$151-$199
16
Owns clear Lives w/ relatives
5-7 yrs
12
$200 +
0
96
48
Neither
0
16% over
0
20
45-49 50 or over
124
88
10+ yrs
48
8+yrs
0
Hilda's personal information is provided below:0-1 yrs242010+ yrs8+yrs0Hilda is a woman whose personal information is displayed above. It is possible that she is of any age, but it is clear that she has spent zero to one year in a particular task or domain, according to the first component. Hilda has spent 24 years in a different sector or field, according to the second component. According to the third part, Hilda has spent ten years in another field or area. Hilda has spent eight years in another subject or area, according to the fourth component. There are no years available in the last component. It can be noticed that these pieces of information may indicate how Hilda has gained experience over time in a variety of fields or domains.
Someone
Help me please
The solution for the system of equations 2x - 3y = 50 and 7x + 8y = -10 by elimination are x = 10, y = -10
How to evaluate for the solutions of the equations by eliminationwe shall write the equations as:
2x - 3y = 50...(1)
7x + 8y = -10...(2)
multiply equation (1) by 7 to get equation (3) and equation (2) by 2 to get equation (4)
7(2x - 3y) = 7 × 50
14x - 21y = 350...(3)
2(7x + 8y) = 2 × -10
14x + 16y = -20...(4)
subtract equation (3) from (4) to eliminate x
14x + 16y - 14x + 21y = -20 - 350
37y = -370
divide through by 37
y = -10
put the value -10 for y in equation (1) to get x
2x - 3(-10) = 50
2x + 30 = 50
2x = 50 - 30 {subtract 30 from both sides}
2x = 20
x = 20/2 {divide through by 2}
x = 10
Therefore, the solution for the system of equations 2x - 3y = 50 and 7x + 8y = -10 by elimination are x = 10, y = -10
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You are buying a pair of shoes online. The price of the
shoes is $29.99. You have to pay a shipping fee of 6.5%.
How much will you pay for shipping? (Round to the nearest
cent)
Answer:
Ok so I think I know the answer.
Since there is a 6.5% shipping fee I am pretty sure you have to divide 6.5% of 29.99 which would be 1.94. Hope this Helps!
Answer: $1.94 shipping fee
Step-by-step explanation:
Triangle A B C is shown. Angle A C B is a right angle. The length of hypotenuse A B is 12 and the length of B C is 6. Angle A B C is 60 degrees and angle B A C is 30 degrees.
What is the value of tan(60°)?
One-half
StartRoot 3 EndRoot
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
StartFraction 1 Over StartRoot 3 EndRoot EndFraction
Answer: 2 is the answer
Step-by-step explanation:
did it on ed
The value of tan 60° in the triangle ABC is √3
Right angle triangle:Right angle triangle have one of its angles as 90 degrees. The sides are called hypotenuse, adjacent and opposite side base on the angles.
Therefore,
ΔABC
∠C = 90°
AB = 12
BC = 6
∠B = 60°
∠A = 30°
Therefore,
tan 60° = opposite / adjacent
AC = √12² - 6² = √108 = 6√3
tan 60° = AC / BC
tan 60° = 6√3 / 6
tan 60° = √3
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Help with pre calc question
Therefore , the solution of the given problem of angles comes out to be k can be any number, so θ = 0 + k180 or θ = 180 + k180
An angle meaning is what?A tilt is a form in Euclidean geometry made up of two lines, or conical faces, that divide at the structure's centre and apex. At their junctions, two rays may combine to form an angle. Angle is another outcome of two entities interacting. Dihedral shapes best describe them. A two-dimensional curve can be created by arranging two line beams in various configurations at their ends. The term "angle" was first used in the Latin term "angulus," which is translated as "horn" in English.
Here,
The solution can be factored to begin with:
=> tanθ(tanθ + 3) = 0
Either
=> tanθ = 0 or tanθ + 3 = 0
will result in the satisfaction of this equation.
When sin = 0, can be any integer multiple of 180 degrees, including zero.
We can find tan by solving for 3 when tan + 3 = 0.
=> tanθ = -3
There are no answers to this problem because there isn't any angle whose tangent is -3.
As a result, the following are the answers to the equation
tan²θ + 3tanθ = 0 :
k can be any number, so θ = 0 + k180 or θ = 180 + k180
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What is the percent decrease from 100 to 82
Percent decrease from 100 to 82 is 18% decrease.
Calculating the % decrease from 100 to 82,
\(\frac{82-100}{100}\)×100%
\(\frac{-18}{100}\)×100%
on simplifying we get,
-18%
here, negative sign indicates that there is a decrease of percentage.
Hence, we get 18% decrease from 100 to 82.
How to calculate Percent decrease?
Do the % growth and reduction calculations. By dividing the new number by the initial value, the percentage is computed.
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Match the information on the left with the appropriate equation on the right.
Answer:
See attachment below
Step-by-step explanation:
For the first option, we are given m = - 2 / 3, b = 3. This is likely in the point - slope form y = mx + b, where m = slope and b = y - intercept. Thus, the equation of the line in point - slope form given this information, should be y = - 2 / 3x + 3. It seems as if none of the following equations match this form, so let us interchange the equation a bit,
y = - 2 / 3x + 3,
y + 2 / 3x = 3,
2x + 3y = 9 - Option C
_______________________________________________________
Next we are given m = - 3 / 2, and that this line passes through the point ( 4, - 1 ). Substitute m as - 3 / 2, x as 4, y as - 1, knowing point ( 4, - 1 ), into the form y = mx + b - solving for b.
- 1 = ( - 3 / 2 )( 4 ) + b,
b = 5,
Thus the equation in point - slope form should be y = - 3 / 2x + 5. None of the choices match this, so let us again alter the equation,
y = - 3 / 2x + 5,
2y = - 3x + 10,
- 2y = 3x - 10 - Option A
_______________________________________________________
( 6, 3 ) and ( 3, 1 ) is given to lie on this line. The slope of the line should be as follows,
Slope = 3 - 1 / 6 - 3 = 2 / 3
Now let us determine the y - intercept ( b ) by substitute one of the points, say ( 6, 3 ). In this case x = 6, and y = 3,
3 = ( 2 / 3 )( 6 ) + b,
b = - 1,
y = 2 / 3x - 1 = Option D
Take a look at the attachment below for further help;
in a random sample of 100 ucla students, 35 have travelled outside the us. estimate the true population proportion of ucla students who travelled outside the us using a 99% confidence interval. find the most reasonable formula to find the interval.
The most reasonable formula to find the interval is
0.35 ± 2.576 (√ (0.35 × 0.65)/100).
The subset chosen from the larger set to make assumptions is known as a random sample. A range of values is a confidence interval.
According to the given problem, n =100 and x = 35
To estimate the true population of students who travelled outside the US using a 99% confidence interval:
p = x / n
= 35 / 100
p = 0.35
At 99% confidence,
α = 1 - 0.99
α = 0.01
α/2 = 0.01/2
α/2 = 0.005
∴ z(α/2) = \(z_{0.005}\) = 2.576
99% confidence interval (CI) is,
CI = p ± z(α/2) * √(p(1-p)/n)
= 0.35 ± 2.576 * \(\sqrt{\frac{0.35(1-0.35)}{100} }\)
= 0.35 ± 2.576 * \(\sqrt{\frac{0.35(0.65)}{100} }\)
= 0.35 ± 2.576 * \(\sqrt{\frac{0.2275}{100} }\)
= 0.35 ± 2.576 * \(\sqrt{0.002275}\)
= 0.35 ± 2.576 * 0.0476969600
= 0.35 ± 0.122867391
= ( 0.35 - 0.1229,0.35 + 0.1229 )
CI = ( 0.2271,0.4729 )
Therefore, the most reasonable formula to find the interval is,
0.35 ± 2.576 × \(\sqrt{\frac{0.35 * 0.65}{100} }\)
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If x - 10 is a factor of x2 - 8x - 20, what is the other
factor?
Answer:
(x + 2)
Step-by-step explanation:
x² - 8x - 20
consider the factors of the constant term (- 20) which sum to give the coefficient of the x- term (- 8)
the factors are - 10 and + 2 , since
- 10 × + 2 = - 20 and - 10 + 2 = - 8 , then
x² - 8x - 20 = (x - 10)(x + 2)
Answer:
(×+ 2)
Step-by-step explanation:
just did that trust me
Helppppppppppppppppp
Answer:
I couldn't read the full problem but I could read the first problem.
Step-by-step explanation:
The hourly rate is 8 dollars because $52-$44 is $8. $44-$36 is also $8. So $36- (the amount for 2 hours) $28 is $8. so in one hour the cost to rent a bicycle is $8.
Given g(c) = -x + 5, solve for x when g(x) =
-2
Answer:
x=7
Step-by-step explanation:
The population of an island was 2 million in 1950. The population grew in an exponential trend for 63 years and became 6.5 million in 2013. It is estimated that the carrying capacity of the island is 10 million. Assuming the population growth rate in the future remains the same as in the last 50 years, what will be the population of the island in 2050? (Assume constant carrying capacity and consumption/capita.)
The population of an island in 1950 was 2 million. The population grew exponentially for 63 years and reached 6.5 million in 2013. The carrying capacity of the island is estimated to be 10 million.
If the population growth rate in the future is similar to the last 50 years, what will the population be in 2050
The population is given to be increasing exponentially, which means it will follow the equation:
\($P(t) = P_0 e^{rt}$\)Here,\($P(t)$\) is the population after a period of time \($t$, $P_0$\) is the initial population, $r$ is the annual growth rate (which we are given is the same as the growth rate of the last 50 years), and \($t$\) is the time.
We can find the annual growth rate $r$ using the formula:\($$r = \frac{\ln{\frac{P(t)}{P_0}}}{t}$$\)
We know\($P_0 = 2$ million, $P(t) = 6.5$ million, and $t = 63$\) years. Substituting these values, we get:
\($r = \frac{\ln{\frac{6.5}{2}}}{63} = 0.032$\) (rounded to 3 decimal places)
Since the carrying capacity of the island is 10 million, we know that the population will not exceed this limit.
Therefore, we can use the logistic model to find the population growth over time. The logistic growth model is:
\($$\frac{dP}{dt} = r P \left(1 - \frac{P}{K}\right)$$\)
where $K$ is the carrying capacity of the environment. This can be solved to give:\($P(t) = \frac{K}{1 + A e^{-rt}}$\)
where \($A = \frac{K-P_0}{P_0}$. We know $K = 10$ million, $P_0 = 2$ million, and $r = 0.032$\). Substituting these values, we get:\($A = \frac{10-2}{2} = 4$\)
Therefore, the equation for the population of the island is:\($P(t) = \frac{10}{1 + 4 e^{-0.032t}}$\)
To find the population in 2050, we substitute\($t = 100$\) (since 63 years have already passed and we want to find the population in 2050, which is 100 years after 1950):
\($P(100) = \frac{10}{1 + 4 e^{-0.032 \times 100}} \approx \boxed{8.76}$ million\)
Therefore, the estimated population of the island in 2050, assuming constant carrying capacity and consumption per capita, is approximately 8.76 million.
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On a coordinate plane, a square has points A (negative 5, 2), B (1, 2), C (negative 4, 1), and D (negative 5, negative 4). If a translation of is applied to square ABCD, what is the y-coordinate of B'?
Answer:
The y coordinates of B' is: 8
Step-by-step explanation:
Given
\(A = (-5,2)\)
\(B =(1,2)\)
\(C = (-4,1)\)
\(D = (-5,-4)\)
Translation of (x, y) → (x + 6, y – 10) ---Missing from the question
Required
Determine the y coordinates of B'
We have:
(x, y) → (x + 6, y – 10)
And
\(B =(1,2)\)
So the translation from B to B' is:
\(B (1,2) \to B'(1+6,2-10)\)
\(B (1,2) \to B'(7,-8)\)
So, we have:
\(B' = (7,-8)\)
The y coordinates of B' is: 8
Answer:
-2
Step-by-step explanation:
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suppose a baseball pitcher throws fastballs 80% of the time and curveballs 20% of the time. suppose a batter hits a home run on 8% of all fastball pitches, and on 5% of all curveball pitches. what is the probability that this batter will hit a home run on this pitcher’s next pitch?
The probability that this batter will hit a home run on this pitcher's next pitch is approximately 0.074, or 7.4%.
To determine the probability that the batter will hit a home run on the pitcher's next pitch,
we need to consider the probabilities of the pitcher throwing a fastball and a curveball, as well as the probabilities of hitting a home run on each type of pitch.
Given that the pitcher throws fastballs 80% of the time and curveballs 20% of the time, we can calculate the probability of the batter facing each type of pitch:
- Probability of facing a fastball = 80% = 0.8
- Probability of facing a curveball = 20% = 0.2
Now, we need to determine the probability of hitting a home run on each type of pitch:
- Probability of hitting a home run on a fastball = 8% = 0.08
- Probability of hitting a home run on a curveball = 5% = 0.05
To find the overall probability of hitting a home run on the pitcher's next pitch, we can use the following formula:
Overall probability = (Probability of facing a fastball * Probability of hitting a home run on a fastball) + (Probability of facing a curveball * Probability of hitting a home run on a curveball)
Plugging in the values we have:
Overall probability = (0.8 * 0.08) + (0.2 * 0.05)
Overall probability = 0.064 + 0.01
Overall probability = 0.074
Therefore, the probability that this batter will hit a home run on this pitcher's next pitch is approximately 0.074, or 7.4%.
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