Answer:
5 gallons
Step-by-step explanation:
20÷3.50=5.714...
so the answer is 5 gallons
There are 25 pupils in a class who take part in a drinking milk initiative. Pupils have a 210
millilitre glass each. During the break each pupil drinks a full glass of milk. Milk comes in 1000
millilitre bottles. How many bottles of milk are needed?
In order for each of the 25 students in the class to get a full glass of milk during the break, six bottles of milk are required.
Each student in a class of 25 drinks a full 210 millilitre glass of milk, hence the amount of milk consumed overall during the break is:
25 students times 210 millilitres each equals 5250 millilitres.
Milk comes in 1000 millilitre bottles, thus to determine how many bottles are needed, divide the entire amount eaten by the volume of milk in each bottle.
5.25 bottles are equal to 5250 millilitres divided by 1000 millilitres.
We must round up to the nearest whole number because we are unable to have a fraction of a bottle. This results in:
6 bottles in 5.25 bottles
In order for each of the 25 students in the class to get a full glass of milk during the break, six bottles of milk are required.
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_____ is a relative measure of signal loss or gain and is used to measure the logarithmic loss or gain of a signal
Decibel is a relative measure of signal loss or gain and is used to measure the logarithmic loss or gain of a signal.
What is a decibel?
Decibel, also known as dB, is a logarithmic unit that measures the intensity of a sound or the strength of an electrical or electromagnetic signal. A decibel measures the relative amplitude of a sound or signal, rather than its absolute magnitude. Because decibels are logarithmic, they are used to express both large and small differences in amplitude. A difference of 1 decibel corresponds to a power ratio of approximately 1.26 to 1.
Logarithmic measure: A logarithmic scale is a scale that has a constant ratio between successive values. Decibels, for example, are a logarithmic scale. The decibel scale is used to measure the amplitude of sound waves and electrical or electromagnetic signals. Because decibels are logarithmic, they can be used to express a wide range of signal levels, from very weak to very strong.
Relative measure: Relative measure is a measure that compares one value to another. It is used in a variety of fields, including statistics, physics, and engineering. Decibels are a relative measure because they compare one signal to another. They are used to express the relative gain or loss of a signal, rather than its absolute magnitude.
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Exercise 2.4.4: Showing a statement is true or false by direct proof or counterexample. i About Determine whether the statement is true or false. If the statement is true, give a proof. If the statement is false, give a counterexample. (a) If x and y are even integers, then x + y is an even integer. (b) If x + y is an even integer, then x and y are both even integers.
(c) If x2 = y?, then x = y. (d) If x and y are real numbers and x < y, then x2 < y?. (e) If x and y are positive real numbers and x < y, then x2 < y?.
The given statements are True , False, False, True and True.
They are elaborated in points below:
(a) True:
Let x and y be even integers.
Then, by definition, x = 2a and y = 2b for some integers a and b.
Adding these equations, we get x + y = 2a + 2b = 2(a + b), which is an even integer. Therefore, the statement is true.
(b) False:
A counterexample is x = 1 and y = 3. Then x + y = 4, which is even, but neither x nor y is even.
Therefore, the statement is false.
(c) False:
A counterexample is x = -2 and y = 4. Then x² = (-2)²= 4 and y = 4² = 16, but x ≠ y. Therefore, the statement is false.
(d) True:
Since x < y, we have y - x > 0. Multiplying both sides by y + x, we get y² - x² > 0.
Rearranging the terms, we have x² < y².
Since x and y are both non-negative, we can take the square root of both sides to get x < y.
Therefore, the statement is true.
(e) True:
Since x and y are positive, we can take the square root of both sides of the inequality x < y to get √x < √y.
Then, multiplying both sides by √x + √y, we get x + 2√xy + y > x + y.
Since x + y is positive, we can divide both sides by x + y to get 1 + 2√(xy)/(x+y) > 1.
Rearranging the terms, we get √(xy) < (x + y)/2. Squaring both sides, we get xy < (x + y)²/4.
Simplifying, we get x²/4 - xy + y²/4 > 0. Rearranging the terms, we get (x - y/2)² > 0, which is always true since the square of any non-zero number is positive. Therefore, the statement is true.
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Determine whether the function is concave upwards and downwards
x^4 - 2x^3 + 5
The function f(x) = x⁴ - 2x³ + 5 is concave downwards on the interval (0,1) and concave upwards everywhere else.
What is concavity of the function?
To determine the concavity of the function f(x) = x⁴ - 2x³ + 5, we need to find its second derivative f''(x).
f(x) = x⁴ - 2x³ + 5
f'(x) = 4x³ - 6x²
f''(x) = 12x² - 12x
The concavity of the function is determined by the sign of its second derivative.
If f''(x) > 0 for all x, the function is concave upwards.
If f''(x) < 0 for all x, the function is concave downwards.
Let's solve for f''(x) = 12x² - 12x:
12x² - 12x = 0
12x(x - 1) = 0
x = 0 or x = 1
When x < 0, f''(x) > 0, so the function is concave upwards.
When 0 < x < 1, f''(x) < 0, so the function is concave downwards.
When x > 1, f''(x) > 0, so the function is concave upwards.
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Soccer ball specifications require a diameter of 8.65 inches with an allowable margin of error of 0.05 inch.
Use this information to complete these statements.
The equation that can be used to find d, the diameter of a new soccer ball, is
| ____ | = ____
The minimum possible diameter of a soccer ball is ____,
and the maximum possible diameter is ____
The equation that can be used to find d, the diameter of a new soccer ball, is: |d - 8.65| = 0.05
What is diameter ?
Diameter is the distance across a circle passing through its center, and it is defined as the length of a straight line passing through the center of a circle and connecting two points on the circumference of the circle. In the case of a soccer ball, the diameter is the distance between two opposite points on the surface of the ball, passing through its center.
Radius is a term used in geometry to refer to the distance from the center of a circle to any point on its circumference. It is defined as half of the diameter of a circle. In the case of a soccer ball, the radius is the distance from the center of the ball to its surface. The radius is related to the diameter by the formula:
radius = diameter / 2
The minimum possible diameter of a soccer ball is:
d = 8.65 - 0.05 = 8.60 inches
The maximum possible diameter is:
d = 8.65 + 0.05 = 8.70 inches
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Can someone pass help!!:(
Answer:
proofs attached to answer
Step-by-step explanation:
proofs attached to answer
The differential equations depicting the dynamics of four Single-Input-Single-Output (SISO) systems are given below. (iii) \( \dddot{y}(t)+0.25 \dot{y}(t)+1.25 y(t)=u^{2}(t) \)
Therefore, the transfer function of the system is:
G(s) = Y(s) / U(s) = U(s) / (s^3 + 0.25s + 1.25)
In summary, the differential equation depicting the dynamics of a fourth Single-Input-Single-Output (SISO) system is y'''(t) + 0.25y'(t) + 1.25y(t) = u^2(t), and the transfer function of the system is G(s) = U(s) / (s^3 + 0.25s + 1.25).
The differential equation describing the dynamics of a single-input-single-output (SISO) system is given by ddy(t) + ay'(t) + by(t) = cdu(t), where y(t) is the output of the system, u(t) is the input of the system, and d, a, b, and c are constant coefficients representing the system dynamics.
For the given differential equation, which is the dynamics of four Single-Input-Single-Output (SISO) systems, we have:
[tex]y(t) + ay'(t) + by''(t) + cy'''(t) = u(t)[/tex]
Here, we have the third-order differential equatior : [tex]y'''(t) + 0.25y'(t) + 1.25y(t) = u^2(t)[/tex]
The given equation is a third-order, linear, time-invariant (LTI) differential equation. In control theory, a differential equation that relates the input u(t) to the output y(t) of a system is known as the transfer function.
The transfer function of the given system can be found by applying the Laplace transform to the differential equation:
s^3Y(s) + 0.25sY(s) + 1.25Y(s) = U^2(s)
where Y(s) and U(s) are the Laplace transforms of y(t) and u(t), respectively.
Solving for Y(s), we get:
Y(s) = U^2(s) / (s^3 + 0.25s + 1.25)
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A poll agency reports that 38% of teenagers aged 12-17 own smartphones. A random sample of 120 teenagers is drawn. Round your answers to at least four decimal places as needed.a) Find the probability that the proportion of the sampled teenagers who own a smartphone is between 0.35 and 0.45b) Find the probability that less than 45% of sampled teenagers own smartphonesc) Would it be unusual if less than 30% of the sampled teenagers owned smartphones?
The probability of 0.0475 is less than 0.05, so it is unlikely to happen. Hence, it would be unusual if less than 30% of the sampled teenagers owned smartphones.
a) Find the probability that the proportion of the sampled teenagers who own a smartphone is between 0.35 and 0.45b) Find the probability that less than 45% of sampled teenagers own smartphonesc) Would it be unusual if less than 30% of the sampled teenagers owned smartphones?a)Find the probability that the proportion of the sampled teenagers who own a smartphone is between 0.35 and 0.45We know that the proportion of teenagers aged 12-17 who own smartphones is 0.38. Now, we need to find the probability that the proportion of sampled teenagers who own smartphones is between 0.35 and 0.45.The sample size is 120.Let P be the probability that a teenager has a smartphone. The population mean is P = 0.38, while the standard deviation is σ =√((P (1 - P)) /n).P (0.38) and n (120) are given, so σ is calculated as follows:σ=√((P (1 - P)) /n) =√((0.38 (1 - 0.38)) /120) =√((0.38 × 0.62) /120) =0.048Now, let us define the Z scores for both sides, i.e. for 0.35 and 0.45.z1 = (0.35 - 0.38) /0.048 = -0.625z2 = (0.45 - 0.38) /0.048 = 1.458Hence, P(0.35 < p < 0.45) is equal to P(-0.625 < z < 1.458).The probability can be calculated using standard normal tables, which gives 0.5763. Therefore, the probability that the proportion of the sampled teenagers who own a smartphone is between 0.35 and 0.45 is 0.5763.b) Find the probability that less than 45% of sampled teenagers own smartphonesLet P be the probability that a teenager has a smartphone. The population mean is P = 0.38, while the standard deviation is σ =√((P (1 - P)) /n).P (0.38) and n (120) are given, so σ is calculated as follows:σ=√((P (1 - P)) /n) =√((0.38 (1 - 0.38)) /120) =√((0.38 × 0.62) /120) =0.048Now, let us define the Z score as follows:z = (0.45 - 0.38) /0.048 = 1.458We must find the probability that a randomly selected teenager from the sample has less than 0.45 probability of owning a smartphone. This probability can be calculated using a standard normal table. P(z < 1.458) = 0.9265, thus, the probability that less than 45% of sampled teenagers own smartphones is 0.9265.c) Would it be unusual if less than 30% of the sampled teenagers owned smartphones?For this, we need to find the Z-score of 0.30.z = (0.30 - 0.38) /0.048 = -1.667The probability is obtained using a standard normal table. The probability is 0.0475. The probability of 0.0475 is less than 0.05, so it is unlikely to happen. Hence, it would be unusual if less than 30% of the sampled teenagers owned smartphones.
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Problem 4: Find the maximum sustainable yield for a population governed by a Gompertz model and subjected to harvesting (either constant yield or constant effort). Solution. Given that the population is governed by a Gompertz model IN = r Nlog(K)
In the following question, among the conditions given, It can be given by Ymax = H(N*)So the maximum sustainable yield for a population governed by a Gompertz model and subjected to harvesting (either constant yield or constant effort) can be calculated using the above formula.
To find the maximum sustainable yield for a population governed by a Gompertz model and subjected to harvesting (either constant yield or constant effort) we will start with the formula of the Gompertz model that is, IN = r Nlog(K)Solution: Given that the population is governed by a Gompertz model = r Nlog(K)We know that the harvesting term that is responsible for the overexploitation of the resources, hence we can write the Gompertz model as dN/dt = rN[1 - N/K] - H(x)WhereH(x) can be a constant yield or constant effort in the harvesting term.
To find the maximum sustainable yield, we will use the concept of steady-state or equilibrium population level. Steady-state condition:dN/dt = 0Solving this equation gives us the steady-state population level, say N*.Now we need to calculate the maximum amount of resources that can be harvested sustainably. This maximum amount of resources harvested sustainably is called the maximum sustainable yield (MSY). It can be given by Ymax = H(N*)So the maximum sustainable yield for a population governed by a Gompertz model and subjected to harvesting (either constant yield or constant effort) can be calculated using the above formula.
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Find equations of the normal plane and osculating plane of the curve at the given point.
x = 5t, y = t^2
, z = t^3
; (5, 1, 1)
(a) An equation for the normal plane is
O 5x + 2y + 3z = -30
O 30x + 2y + 3z = 30
O 5x + 3y + 2z = 30
O 5x + 2y + 3z = 30
O 5x + 2y - 3z = 30
b) An equation for the osculating plane is
O 3x - 15y + 5z = 5
O 3x - 15y + 5z = -5
O x - 15y + 3z = 5
O 3x - y + 3z= 5
O 3x - 15y + 5z = 15
Answer:
Step-by-step explanation:
To find the normal plane and osculating plane, we first need to find the required derivatives.
x = 5t, y = t^2, z = t^3
dx/dt = 5, dy/dt = 2t, dz/dt = 3t^2
So, the velocity vector v and acceleration vector a are:
v = <5, 2t, 3t^2>
a = <0, 2, 6t>
Now, let's evaluate them at t = 1 since the point (5, 1, 1) is given.
v(1) = <5, 2, 3>
a(1) = <0, 2, 6>
The normal vector N is the unit vector in the direction of a:
N = a/|a| = <0, 1/√10, 3/√10>
Using the point-normal form of the equation for a plane:
normal plane equation = 0(x-5) + 1/√10(y-1) + 3/√10(z-1) = 0
Simplifying this equation we get:
5x + 2y + 3z = 30
The osculating plane can be found using the formula:
osculating plane equation = r(t) · [(r(t) x r''(t))] = 0
where r(t) is the position vector, and x is the cross product.
At t = 1, the position vector r(1) is <5, 1, 1>, v(1) is <5, 2, 3>, and a(1) is <0, 2, 6>.
r(1) x v(1) = <-1, 22, -5>
r(1) x a(1) = <12, -6, -10>
v(1) x a(1) = <-12, 0, 10>
Substituting these values into the formula, we get:
osculating plane equation = (x-5, y-1, z-1) · <12, -6, -10> = 0
Simplifying this equation we get:
3x - 15y + 5z = 5
Therefore, the equations for the normal plane and osculating plane at (5, 1, 1) are:
(a) 5x + 2y + 3z = 30
(b) 3x - 15y + 5z = 5
Un faro se encuentra al borde de un acantilado, tal y como se muestra. Un barco a nivel del mar está a 750 metros de la base del acantilado. El ángulo de elevación entre el nivel del mar y la base del faro mide 24. 7º. El ángulo de elevación entre el nivel del mar y el tope del faro mide
28. 4°. Hallar la altura del faro desde la cima del acantilado
Using trigonometry, the height of the lighthouse from the top of the cliff is approximately 617.38 meters.
Trigonometry is a tool we can utilize to tackle this issue. Let's use "h" to represent the lighthouse's height and "x" to represent the distance between both the boat and the cliff's edge. Next, we have:
tan(24.7º) = h/x (1)
tan(28.4º) = (h + y)/x (2)
where "y" is the height of the cliff.
We want to find "h + y". To eliminate "x", we can use equation (1) to express "x" in terms of "h", and substitute it into equation (2):
x = h/tan(24.7º)
tan(28.4º) = (h + y)/(h/tan(24.7º))
Simplifying and solving for "h", we get:
h = y/tan(28.4º - 24.7º)
Now we can substitute this expression for "h" into equation (1) to find "y":
tan(24.7º) = y/(y/tan(28.4º - 24.7º))
Simplifying and solving for "y", we get:
y = 750 tan(24.7º) / (tan(28.4º - 24.7º))
y ≈ 237.78 meters
Therefore, the height of the lighthouse from the top of the cliff is:
h + y ≈ y/tan(28.4º - 24.7º) + y ≈ 617.38 meters.
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The question is -
A lighthouse is located at the edge of a cliff, as shown. A boat at sea level is 750 meters away from the base of the cliff. The angle of elevation between sea level and the base of the lighthouse measures 24.7º. The angle of elevation between sea level and the top of the lighthouse measures 28.4°. Find the height of the lighthouse from the top of the cliff.
This is the Challenge:
There is a race consisting of 10 individual races in a row. You are able to bet on the racecars for a chance to multiply your money. The potential payout and chances of winning per racer are listed below.
Blue
- 30% Chance of winning
- 2x Payout on winning bids
Red
- 25% Chance of winning
- 2.5x Payout on winning bids
Purple
- 18% Chance of winning
- 3x Payout on winning bids
Yellow
- 10% Chance of winning
- 5x Payout on winning bids
Black
- 8% Chance of winning
- 7x Payout on winning bids
Green
- 5% Chance of winning
- 10x Payout on winning bids
Orange
- 3% Chance of winning
- 15x Payout on winning bids
Pink
- 1% Chance of winning
- 50x Payout on winning bids
At the end of the race, bets placed on the top 3 winning racecars will be paid back to the player depending on the sheep's placement
1st Place: 100% Bet Payout
2nd Place: 40% Bet Payout
3rd Place: 10% Bet Payout
All other bets placed on non top 3 place racecar will be lost
You can safely assume that if one is likely to win but doesn't win then they are statistically most likely to come second and so on
During the 10 rounds, what is the most efficient bets to increase your money?
Calculating the expected value of payout using the probabilities given, we can bet on blue for all 10 races, bet on red for all 10 races and bet on purple for all 10 races
What is the most efficient bets to increase the return?To determine the most efficient bets to increase your money during the 10 rounds, we need to consider the probability and potential payout for each racecar. We can start by calculating the expected value of each racecar's payout:
Blue: 0.3 x 2 = 0.6
Red: 0.25 x 2.5 = 0.625
Purple: 0.18 x 3 = 0.54
Yellow: 0.1 x 5 = 0.5
Black: 0.08 x 7 = 0.56
Green: 0.05 x 10 = 0.5
Orange: 0.03 x 15 = 0.45
Pink: 0.01 x 50 = 0.5
Based on the expected value of payout, the most efficient bets would be on the racecars with the highest expected value. However, we also need to consider the probability of each racecar winning or placing in the top 3.
To maximize our chances of winning, we should bet on the racecars with the highest probability of winning or placing in the top 3, even if their expected payout is not the highest.
Assuming that if one racecar is likely to win but doesn't win, they are statistically most likely to come second, and so on, we can rank the racecars in terms of their probability of winning or placing in the top 3:
1. Blue - 30% chance of winning
2. Red - 25% chance of winning
3. Purple - 18% chance of winning
4. Black - 8% chance of winning
5. Yellow - 10% chance of winning
6. Green - 5% chance of winning
7. Orange - 3% chance of winning
8. Pink - 1% chance of winning
Based on this ranking, the most efficient bets would be as follows:
1. Bet on Blue for all 10 races. The expected payout is not the highest, but the probability of winning is the highest at 30%.
2. Bet on Red for all 10 races. The probability of winning is the second-highest at 25%.
3. Bet on Purple for all 10 races. The probability of winning is the third-highest at 18%.
Betting on these three racecars will give you the highest chance of winning or placing in the top 3, and therefore, the most efficient bets to increase your money. However, keep in mind that gambling always carries risks, and there is no guarantee of winning.
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You are using a broker to purchase stock in company. The broker charges a set free of $7 per transaction. If the shares are worth $7.69/sh and you have $850 to invest,how many shares can you purchase?
A. 111 shares
B.108 shares
C.109 shares
D.110 shares
The answer is option C: 109 shares. If the broker charges a set free of $7 per transaction. If the shares are worth $7.69/sh and you have $850 to invest 109 shares can you purchase.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
To calculate the number of shares you can purchase, you need to subtract the broker's fee from the total amount you have to invest and then divide that by the share price:
$850 - $7 = $843 (the amount available to purchase shares)
$843 ÷ $7.69/share = 109.48
Since you cannot purchase a fraction of a share, you would be able to purchase 109 shares.
Therefore, the answer is option C: 109 shares.
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If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, where will B' be?
Reflection over the y-axis, rotation 90° clockwise, and translation (x + 2, y - 1)
B'( , )
If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, B' would be located at B' (3, 2).
What is a reflection over the y-axis?In Geometry, a reflection over or across the y-axis is represented and modeled by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over or across the y-axis would maintain the same y-coordinate (y-axis) while the sign of the x-coordinate (x-axis) would change from positive to negative or negative to positive.
By applying a reflection over the y-axis to the coordinate of the given point B (-3, 1), we have the following coordinates:
Coordinate B = (-3, 1) → Coordinate B' = (-(-3), 1) = (-3, 1).
Next, we would apply a rotation of 90° clockwise as follows;
(x, y) → (y, -x)
Coordinate B' = (-3, 1) → Coordinate B' = (1, (-3)) = (1, 3)
Lastly, we would apply a translation (x + 2, y - 1) as follows:
Coordinate B' = (1, 3) → (1 + 2, 3 - 1) = B' (3, 2).
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Tom and Peter had 132 stickers. After Peter gave Tom 6 stickers, Peter had 1/3 as many stickers as Tom. How many stickers did Peter have at first?
Answer:
Step-by-step explanation:
42
A farmer sells cows for $350 each and chickens for $75 apiece. At market, he sold 11 animals for a total of $2475. How many of each animal were sold?
Answer:
Let's use algebra to solve this problem.
Let's start by defining some variables to represent the number of cows and chickens the farmer sold. Let c be the number of cows and h be the number of chickens. We know that the farmer sold a total of 11 animals, so:
c + h = 11 (Equation 1)
We also know that the total amount of money the farmer received was $2475. The amount he received from selling cows was $350 times the number of cows, or 350c. The amount he received from selling chickens was $75 times the number of chickens, or 75h. So:
350c + 75h = 2475 (Equation 2)
Now we have two equations with two unknowns. We can solve for one variable in terms of the other in the first equation:
c + h = 11
c = 11 - h
We can substitute this expression for c into the second equation:
350c + 75h = 2475
350(11 - h) + 75h = 2475
Simplifying and solving for h:
3850 - 350h + 75h = 2475
-275h = -1375
h = 5
So the farmer sold 5 chickens. We can substitute this value of h back into the first equation to find c:
c + h = 11
c + 5 = 11
c = 6
Therefore, the farmer sold 6 cows and 5 chickens.
The price of a new car is £12500
It is reduced by £11625
Work out the percentage reduction
To work out the percentage reduction, we need to find the difference between the original price and the reduced price, and express that difference as a percentage of the original price:
Original price = £12500
Reduced price = £11625
Difference = £12500 - £11625 = £875
Percentage reduction = (Difference / Original price) x 100%
= (£875 / £12500) x 100%
= 7%
Therefore, the percentage reduction in the price of the car is 7%.
Answer:
Step-by-step explanation:
Discount [tex]= \pounds12,500 -\pounds11625= \pounds875[/tex]
Percentage reduction [tex]=\frac{875}{12500} \times 100 = 7[/tex]
The price of a new car was reduced by 7%.
Jerry, Jack and Sophie are all hoping to save money! Jerry thinks saving money in a shoe box in his closet every month is a good idea. He decides to start with $125, and then save $50 each month. Jack was given $3520 from his Grandma, and decides to put the money
into an account that has a 6.5% interest rate that is compounded annually. Sophie has earned $3500 working at the movie theater decides to put her money in the bank in an account that has a 7.05% interest rate that is compounded continuously
Part 1: Describe the type of equation that models Jerry’s situation. Create that equation of Jerry’s situation. Using the equation you created, how much money will be in Jerry’s account after 3 years? 10 years?
Think: What do I know and what does it mean? What plan am I going to try?
PLEASE HELP!!!!!
Jerry will have $1825 in his account after 3 years and Jerry will have $6125 in his account after 10 year when compounded.
What is simple interest?Simple interest is computed just using the principle, which is the initial sum borrowed or put into an investment. The interest rate is constant throughout time and solely applies to the principal sum. Short-term loans or investments frequently employ simple interest.
The given situation can be modeled as a linear equation given by:
y = mx + c
For Jerry we have:
y = 50x + 125
For 3 years = 36 months we can substitute x = 36:
y = 50(36) + 125
y = 1825
For x = 10:
y = 50(120) + 125
y = 6125
Hence, Jerry will have $1825 in his account after 3 years and Jerry will have $6125 in his account after 10 year.
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Find the value of each variable
Answer:
y = 90°
x = 63°
Step-by-step explanation:
The unknown y angle is a right angle, meaning it is a 90° angle.
We know a triangle is 180°. We know 2 angles one is 90°, one is 27°, so to find the other missing angle
We Take
180 - (27 + 90) = 63°
So, x = 63° y = 90°
please help me with this savvas question!
Therefore, the compound inequality for the diameter of the washers is: 3.150 ≤ d ≤ 3.240.
What is inequality?In mathematics, an inequality is a statement that compares two values or expressions, indicating that one is greater than, less than, or equal to the other. The symbols used to represent inequalities are:
">" which means "greater than"
"<" which means "less than"
"≥" which means "greater than or equal to"
"≤" which means "less than or equal to"
Inequalities can be solved by applying algebraic techniques, such as adding, subtracting, multiplying, or dividing both sides of the inequality by the same number. The solution to an inequality is a range of values that satisfy the inequality.
Here,
The formula for the circumference of a circle in terms of its diameter is:
C = πd
where π (pi) is approximately 3.14.
We are given that the acceptable range for the circumference of the washer is 9.9 ≤ C ≤ 10.2 centimeters. Substituting C = 3.14d into this inequality, we get:
9.9 ≤ 3.14d ≤ 10.2
Dividing all sides of the inequality by 3.14, we obtain:
3.15 ≤ d ≤ 3.24
Rounding to three decimal places, the corresponding interval for the diameters of the washers is:
3.150 ≤ d ≤ 3.240
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Find the unknown lengths of these isosceles right triangles. (Leave radicals in simplest radical form.) (ASAP!!!!) (it’s urgent!)
The required answers are 19) c = 8√2 units 20) a = b =a = [tex]\frac{\sqrt{10} }{14}[/tex].
What is Right angled triangle?A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangled triangle, is a triangle in which one angle is a right angle, i.e., in which two sides are perpendicular. The relation between the sides and other angles of the right triangle is the basis for trigonometry.
According to question:19) Using Pythagoras theorem
[tex]c^2=a^2+a^2[/tex]
[tex]c^2=\sqrt{a^2+a^2}[/tex]
[tex]c=\sqrt{8^2+8^2}[/tex]
c = 8√2 units
20) It is isosceles triangle,So a = b
Now
[tex]$Sin(45) =\frac{a}{\frac{\sqrt{5}}{7} }[/tex]
a = [tex]\frac{\sqrt{10} }{14}[/tex]
Thus, required answers are 19) c = 8√2 units 20) a = b =a = [tex]\frac{\sqrt{10} }{14}[/tex].
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Let n be a positive integer. If a == (3^{2n}+4)^-1 mod(9), what is the remainder when a is divided by 9?
Let n be a positive integer. We can use the properties of modular arithmetic to calculate this remainder. Let's start with a = (32n + 4)-1 mod 9. We can rewrite this as a = 9 - (32n + 4)-1 because 9 = 0 mod 9.
We can use Fermat's Little Theorem to calculate (32n + 4)-1. This theorem states that (32n + 4)-1 mod 9 = (32n + 4)8 mod 9.
Using the identity (a + b)n mod m = ((a mod m) + (b mod m))n mod m, we can simplify the equation to (32n mod 9 + 4 mod 9)8 mod 9.
32n mod 9 = 0, so (32n mod 9 + 4 mod 9)8 mod 9 = 48 mod 9 = 1.
Finally, a = 9 - 1 = 8 mod 9, so the remainder when a is divided by 9 is 8.
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Melvin borrowed $1,200 for furniture. His monthly payments were $60 for 24 months. Find the total amount repaid.A. $1,200B. $240C. $1,440D. $2,880
The total amount repaid by Melvin was $1,440. Which is option C. $1,440.
Melvin borrowed $1,200 for furniture
His monthly payments were $60 for 24 months
To find the total amount repaid, we can multiply the monthly payment with the number of months. We can write this in mathematical terms as:
The total amount repaid = Monthly payment × Number of months
Using the above formula, let's calculate the total amount repaid by Melvin.
Total amount repaid = $60 × 24= $1,440
Therefore, the total amount repaid by Melvin was $1,440. Therefore, the correct option is C. $1,440.
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three cards are drawn without replacement from an ordinary deck of 52 playing cards. what is the probability that the 3rd card is a heart if the first card was a heart and the second card was a club?
The probability that the 3rd card is a heart if the first card was a heart and the second card was a club is approximately 0.0152. It is the product of the probabilities.
What is the probability?The probability that the 3rd card is a heart if the first card was a heart and the second card was a club when three cards are drawn without replacement from an ordinary deck of 52 playing cards.
There are 13 hearts in a deck of 52 cards.
Therefore, P(1st card is a heart) = 13/52 = 1/4
There are 13 clubs in a deck of 52 cards. Since one heart is already drawn in the first card, there are only 51 cards left in the deck.
Therefore, P(2nd card is a club) = 13/51
There are only 12 hearts remaining in the deck since one heart is already drawn in the first card. There are only 50 cards left in the deck since two cards are already drawn.
Therefore, P(3rd card is a heart) = 12/50 = 6/25
The probability that the 3rd card is a heart if the first card was a heart and the second card was a club is:
P(3rd card is a heart | 1st card is a heart and 2nd card is a club) = P(1st card is a heart) × P(2nd card is a club) × P(3rd card is a heart) = (1/4) × (13/51) × (6/25) = 39/5,775 = 0.0152 (rounded to 5 decimal places)
Therefore, the probability that the 3rd card is a heart if the first card was a heart and the second card was a club is approximately 0.0152.
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/c and /d are vertical angles.if /c is 140, what is the measure of/d?
Coin A is tossed three times and coin B is tossed two times. What is the probability that more heads are tossed using coin A than coin B?
The probability that more heads are tossed using coin A than coin B is 5/16.
The given data is: Coin A is tossed three times and coin B is tossed two times. We have to find the probability that more heads are tossed using coin A than coin B.
P(E) = Number of favorable outcomes/ Total number of possible outcomes
Coin toss:
There are two possible outcomes in a coin toss, Head or Tail. The probability of getting a head in a coin toss is
1/2 = 0.5.
Therefore, the probability of getting a tail in a coin toss is also 1/2 = 0.5.
Let's calculate the possible outcomes when coin A is tossed three times.
There are 2 possible outcomes when one coin is tossed.
Number of possible outcomes when three coins are tossed = 2 * 2 * 2 = 8
Likewise, the possible outcomes when coin B is tossed two times are:
The number of possible outcomes = 2 * 2 = 4
Therefore, the total number of possible outcomes = 8 * 4 = 32
Now, we will find out the cases where the number of heads is more when coin A is tossed three times.
HHH HHT HTH HTT THH THT TTH TTT HHT HTT THT TTT TTH TTT HTT TTT THT TTT TTT TTT
Therefore, the number of times when more heads are obtained when coin A is tossed three times is 10. (We have to exclude the case when there is an equal number of heads.)
Therefore, the required probability is: P = Number of favorable outcomes/ Total number of possible outcomes
P = 10/32P = 5/16
Therefore, the probability that more heads are tossed using coin A than coin B is 5/16.
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what is the solution to the equality shown?
3m+5>2(m-7)
Hello,
3m + 5 > 2(m - 7) =
3m + 5 > 2m - 14
3m - 2m > - 14 - 15
x > - 29
Step-by-step explanation:
3m±2m>-14-5
5m>-19
m>-19/5
m>3.8
Fatoumata is working two summer jobs, making $15 per hour lifeguarding and making $10 per hour tutoring. In a given week, she can work at most 12 total hours and must earn a minimum of $140. Also, she must work at least 8 hours lifeguarding. If � x represents the number of hours lifeguarding and � y represents the number of hours tutoring, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
not sure if this sign � was important did it the best way I could
Step-by-step explanation:
To solve this problem graphically, we will first set up a system of inequalities based on the given information:
x ≥ 8 (Fatoumata must work at least 8 hours lifeguarding)
y ≤ 12 - x (Fatoumata can work at most 12 total hours)
15x + 10y ≥ 140 (Fatoumata must earn a minimum of $140)
To graph these inequalities, we can plot the points (8,0), (12,0), and (0,14) on a coordinate plane and draw lines connecting them. The line between (8,0) and (12,0) represents the constraint on the number of hours Fatoumata can work, while the line between (8,0) and (0,14) represents the constraint on the amount of money she must earn. The shaded region that satisfies all three inequalities is the feasible region.
To find one possible solution, we can pick any point within the feasible region. One such point is (8,6), which represents working 8 hours lifeguarding and 6 hours tutoring. This point satisfies all three inequalities:
x ≥ 8 is true since x = 8
y ≤ 12 - x is true since y = 6 ≤ 12 - 8
15x + 10y ≥ 140 is true since 15(8) + 10(6) = 180 ≥ 140
Therefore, one possible solution is for Fatoumata to work 8 hours lifeguarding and 6 hours tutoring to earn at least $140 while not exceeding 12 total hours worked.
help pls asap ... Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate the slope and y-intercept.
The approximate slope and y-intercept of the line of best fit is y = -0.17x + 33.3.
How to determine an equation of this line?In Mathematics, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁) or [tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex]
Where:
m represent the slope.x and y represent the points.At data point (20, 20), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y - 20 = \frac{(10- 20)}{(80-20)}(x -20)[/tex]
y - 20 = -1/6(x - 20)
y = -x/6 + 20/6 + 20.
y = -x/6 + 200/6
y = -0.17x + 33.3
In this context, we can reasonably infer and logically deduce that a linear function that represent the line of best fit in slope-intercept form is y = -0.17x + 33.3.
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A tin of nuts contains 36 cashews, 14 pecans, 27 peanuts, and 13 pistachios. Find the probability of reaching in and selecting a pecan and then a cashew. Assume the nuts are chosen without replacement. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answer:28/445 or 6.2921 %
Step-by-step explanation:
There are 90 nuts all together. There are 14 pecans so it would be a 14/90 chance. Then since you are not replacing the nut there are 89 nuts. There are 36 cashews which would be a 36/89 chance. Because in the problem it says to find the probability of the selecting a pecan and then a cashew we know it is an and situation. Since it is an and situation you would multiply. You would do 14/90 times 36/89. This gives you 504/8010 which reduced is 28/445 or 6.2921%. Do you have and questions?