The required answers are a) 17.1 km b) 7.1 km, c) 18.6 km away from town A on a bearing of 293°.
How to find the distance and angle?To solve this problem, we can use vector addition to find the displacement vector from town A to the cyclist's destination.
a) To find how far east the cyclist's destination is from town A, we need to find the east component of the displacement vector. We can break down the displacement vector into its north and east components using trigonometry:
[tex]$$\text{East displacement} = 5\text{ km} + 10\text{ km}\cos(45^\circ) = 5\text{ km} + 10\text{ km}\frac{\sqrt{2}}{2} = 10\text{ km} + 5\sqrt{2}\text{ km} \approx 17.1\text{ km}$$[/tex]
So the cyclist's destination is approximately 17.1 km east of town A.
b) Similarly, to find how far north the cyclist's destination is from town A, we need to find the north component of the displacement vector:
[tex]$$\text{North displacement} = 10\text{ km}\sin(45^\circ) = 10\text{ km}\frac{\sqrt{2}}{2} = 5\sqrt{2}\text{ km} \approx 7.1\text{ km}$$[/tex]
So the cyclist's destination is approximately 7.1 km north of town A.
c) To find the distance and bearing of the cyclist's destination from town A, we can use the Pythagorean theorem and trigonometry. The displacement vector is the hypotenuse of a right triangle with legs of length 17.1 km and 7.1 km, so its length is:
[tex]$$\text{Displacement} = \sqrt{(17.1\text{ km})^2 + (7.1\text{ km})^2} \approx 18.6\text{ km}$$[/tex]
To find the bearing of the displacement vector, we can use the inverse tangent function:
[tex]$$\text{Bearing} = \tan^{-1}\left(\frac{\text{East displacement}}{\text{North displacement}}\right) \approx 67^\circ$$[/tex]
However, this angle is measured clockwise from north, so we need to subtract it from 360° to get the bearing measured counterclockwise from north:
[tex]$$\text{Bearing} = 360^\circ - 67^\circ = 293^\circ$$[/tex]
So the cyclist's destination is approximately 18.6 km away from town A on a bearing of 293°.
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Need the answer for A B C
Therefore , the solution of the given problem of percentage comes out to be this amount to the closest dollar, we get $1,042.
What precisely is a percentage?A number or measure that is represented as a proportion of 100 is known as a "a%" in statistics. Additionally, the terms "pct," "pct," and "pc" are not commonly used. However, it is commonly denoted by the symbol "%". There are no dimensions; the percentage total is flat. Since a percentage's numerator is almost always 100, percentages are actually integers. To indicate that a number is a percentage, either the percentage symbol (%).
Here,
a. The formula: can be used to calculate the weekly payment.
=> P = (Ar(1+r)ⁿ) / ((1+r)^n - 1)
A = 9900, r = 0.06/12, and n = 48 in this instance (since there are 4 years or 48 months in total).
Substituting these numbers into the formula, we get:
=> P = (99000.005(1+0.005)⁴⁸) / ((1+0.005)⁴⁸ - 1) ≈ $227.88
Therefore, the monthly payment is roughly $227.88.
=> Overall = P*n = $227.88 * 48 = $10,942.24
We arrive at $10,942 by rounding this sum to the closest dollar.
c. The total interest paid over the course of the loan's four-year term is equivalent to the total amount repaid less the loan balance:
Total interest equals the total sum less A, or $10,942 minus $9,900, or $1,042.
Rounding this amount to the closest dollar, we get $1,042.
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a copper wire of diameter 8mm is wrapped around a cylinder of length 24cm
The length of the wire is 46.218 m and the volume of the wire is 7206.4 cm³.
What is the length of the wire and volume of the cylinder?
To find the length of the wire, we need to calculate the circumference of the cylinder and multiply it by the number of times the wire is wrapped around it.
The circumference of the cylinder is the distance around the circular face, and can be calculated using the formula:
Circumference = π × diameter
where;
π is a constant approximately equal to 3.14.The diameter of the cylinder is 49 cm, so its circumference is:
Circumference = π × diameter = 3.14 × 49 cm = 154.06 cm
The wire is wrapped around the cylinder lengthwise, so the number of times it wraps around the cylinder is equal to the length of the cylinder divided by the diameter of the wire:
Number of wraps = Length of cylinder / Diameter of wire
The length of the cylinder is 24 cm, and the diameter of the wire is 8 mm, or 0.8 cm. So the number of wraps is:
Number of wraps = 24 cm / 0.8 cm = 30
Therefore, the length of the wire is:
Length of wire = Circumference of cylinder × Number of wraps
= 154.06 cm × 30
= 4621.8 cm or 46.218 m (to three decimal places)
To find the volume of the wire, we need to use the formula for the volume of a cylinder:
Volume of cylinder = π × (radius)² × height
Volume of wire = π × (0.4 cm)² × 4618.2 cm
= 7206.4 cm³ (to one decimal place)
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The complete question is below:
A copper wire of diameter 8mm is evenly wrapped over a cylinder of length 24cm and diameter 49cm find the length of the wire and the volume of the wire
Which is Greater? 5^100 or 3^150
It can be concluded that 3¹⁵⁰ is the greater among them.
How to get the solutionThis question can be solved if we use the numerical factorization concepts
Check itFirst, we do the factorization, looking for a number that is common between divisors 3 and 5
[tex]\begin{array}{r|l}\sf 100,150 & \sf 2\\\sf 50,75 & \sf 2\\\sf 25,75 & \sf 3\\\sf 25,25 & \sf 5\\\sf 5,5 & \sf 5\\\sf 1,1&\sf 1\end{array}[/tex]
With this, we can see that the number 25 is common between divisors 3 and 5.
It will be our main exponent, when factoring the exponents 100 and 150.
[tex]\begin{array}{cc}\sf 5^{100}&\sf 3^{150}\\\raisebox{5pt}{$\sf \Big(\big[5^{2}\big]^{2}\Big)^{25}$}&\raisebox{5pt}{$\sf \Big(\big[3^{2}\big]^{3}\Big)^{25}$}\\\raisebox{5pt}{$\sf \big(5^{4}\big)^{25}$}&\raisebox{5pt}{$\sf \big(3^{6}\big)^{25}$}\\\raisebox{5pt}{$\sf 625^{25}$}&\raisebox{5pt}{$\boxed{\bf729^{25}}$}\end{array}[/tex]
Since 729²⁵ > 625²⁵, it follows that 3¹⁵⁰ is the greater of the two
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If you have any question about this solution, you can ask me in the comments :)
I need help with this question.
Answer:
System A: C)infinite answers
System B: B)special answer (x,y)=(3,1)
Step-by-step explanation:
System A:
if we find sum of same variables, we get 5x-5x-y+y=-2+2, it means 0=0 so, this system has infinite answers.
System B:
same thing applied here,
x-x+4y+4y=7+1
8y=8
y=1
so,
x+4*1=x+4=7
x=3
Set A consists of all odd integers between 0 and 10. Set B consists of all prime numbers less than 16 . How many numbers do Set A and Set B have in common?
Set A and Set B have 2 numbers in common: 3 and 7. The intersection of both sets is the set of numbers that appear in both sets.
Set A consists of all odd integers between 0 and 10, which are 1, 3, 5, 7, and 9. Set B consists of all prime numbers less than 16, which are 2, 3, 5, 7, 11, and 13. There are two numbers that Set A and Set B have in common: 3 and 7.
Sets A and B are both subsets of the set of all integers between 0 and 16. Set A is a subset of the set of all odd integers between 0 and 16, while Set B is a subset of the set of all prime numbers between 0 and 16. While Set A and Set B have 2 numbers in common, they are not the same set. Set A includes the numbers 1, 3, 5, 7, and 9, while Set B includes the numbers 2, 3, 5, 7, 11, and 13.
Each set includes a unique set of numbers, and the intersection of Set A and Set B is the set of numbers that appear in both Set A and Set B. In this case, the intersection of Set A and Set B is the set of 2 numbers that both sets have in common: 3 and 7.
In conclusion, Set A and Set B have 2 numbers in common: 3 and 7. While both sets include a unique set of numbers, the intersection of Set A and Set B is the set of numbers that appear in both sets.
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A cylindrical candle has a mass of 200 grams. The candle has a diameter of 3 inches
and a height of 4 inches. What is the density of the candle? Round to the nearest
hundredth
Rounding to the nearest hundredth, the density of the candle is 22.46 grams per cubic inch.
The density of the candle can be found by dividing the mass by the volume of the candle.
The volume of a cylindrical candle can be found using the formula V = πr^2h,
where V is the volume, r is the radius, and h is the height.
First, we need to find the radius of the candle.
The diameter is 3 inches, so the radius is 1.5 inches.
Next, we can plug in the values for r and h into the formula for the volume of a cylinder:
V = π(1.5)^2(4) = 9π
Now, we can divide the mass of the candle by the volume to find the density:
Density = 200 grams / 9π
Density= 22.46 grams per cubic inch
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Jon's parents invested $300 for his college tuition in a savings account when he
was born. The account pays 5% simple interest every year. How much would be
in the account after 18 years if no other money were invested? (1 = Prt)
Jon's parents invested $300 for his college tuition in a savings account when he was born. The account pays 5% simple interest every year. Consequently, if no additional money was invested, the account would be worth $570 after 18 years.
To answer the problem, we must employ the basic interest formula:
Principle x Interest Rate x Time = Simple Interest
where:
Principal = the initial amount invested
Interest Rate = the yearly interest rate expressed in decimal form.
Time = the amount of years the money has been invested for.
The principal in this scenario is $300, the interest rate is 5% (0.05 as a decimal), and the term is 18 years. Thus we may enter the following values into the formula:
Simple Interest = $300 x 0.05 x 18 = $270
As a result, after 18 years, the total money in the account would be:
Total amount = Principal + Simple Interest
=$300 + $270 = $570
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A box contains three blue bulbs, four green bulbs and five red bulbs. Four bulbs were taken out of the box at random and without replacement. What is the probability that a. All the four bulbs are of the same colour
The probability of selecting all four bulbs of the same color is approximately 0.0061.
To calculate the probability that all four bulbs are of the same color, we need to consider the following cases,
1) The probability of selecting the first blue bulb is 3/12 (since there are 3 blue bulbs out of 12 total bulbs). After one blue bulb has been selected, there are 2 blue bulbs left out of 11 total bulbs, so the probability of selecting a second blue bulb is 2/11. Similarly, the probability of selecting the third blue bulb is 1/10, and the probability of selecting the fourth blue bulb is 0/9 (since there are no more blue bulbs left). Therefore, the probability of selecting all four blue bulbs is:
(3/12) × (2/11) × (1/10) × (0/9) = 0
2) Using the same logic as in Case 1, the probability of selecting all four green bulbs is:
(4/12) × (3/11) × (2/10) × (1/9) = 1/495
3) The probability of selecting all four red bulbs is:
(5/12) × (4/11) × (3/10) × (2/9) = 2/495
Therefore, the total probability of selecting all four bulbs of the same color is the sum of the probabilities from Cases 2 and 3
1/495 + 2/495 = 3/495
Simplifying this fraction, we get:
3/495 = 1/165
= 0.0061
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A surveyor wants to know the length of a tunnel built through a mountain. According to her equipment, she is located 212 meters from one entrance of the
tunnel, at an angle of 57° to the perpendicular. Also according to her equipment, she is 119 meters from the other entrance of the tunnel, at an angle of 14° to
the perpendicular, Based on these measurements, fiad the length of the entire tunnel,
Do not round any intermediate computations. Round your answer to the nearest tenth..
Note that the figure below is not drawn to scale.
Answer: Approximately 2 * AC = 737.2 meters. Rounded to the nearest tenth, the answer is 737.2 meters.
Step-by-step explanation: To solve the problem, we can draw a diagram:
A
/|
/ |
/ | x
/ |
/ |
/θ |
/ |
/ |
/ |
/ |
/ |
B-----------C
y
where A and B are the entrances of the tunnel, C is the point in the middle of the tunnel that we want to find, and θ, x, and y are the angles and distances given in the problem. We want to find the length of AC.
Using trigonometry, we can find the distances BC and AB: tan(57°) = x / y => x = y * tan(57°)
tan(14°) = x / (y + 212) => x = (y + 212) * tan(14°)
Setting these two expressions for x equal, we get: y * tan(57°) = (y + 212) * tan(14°)
Solving for y, we get: y = 212 / (tan(57°) / tan(14°) - 1) ≈ 286.5 meters
Now we can use the law of sines to find the length of AC: sin(θ) / AC = sin(14°) / BC = sin(57°) / AB
Solving for AC, we get: AC = AB * sin(θ) / sin(57°) ≈ 368.6 meters
Therefore, the length of the entire tunnel is approximately 2 * AC = 737.2 meters. Rounded to the nearest tenth, the answer is 737.2 meters.
A composite figure is represented in the image.
What is the total area of the figure?
75 m2
63 m2
61.5 m2
45 m2
Step-by-step explanation:
area of rectangle= 9×4=36m^2
9-3=6 which is the base of the triangle
6×3=18
18÷2=9m^2
36+9=45m^2
answer: 45m^2
14. What is the Kaplan-Meier estimator used for? Estimating the probability density function of a continuous random variable. Estimating the mean of a discrete random variable. Estimating the survival function from right-censored data. Estimating the cumulative distribution function of a continuous random variable.
It is used to calculate the probabilities of random variables being less than or equal to a specific value
The Kaplan-Meier estimator is used to estimate the survival function from right-censored data.What is the Kaplan-Meier estimator?The Kaplan-Meier estimator is a non-parametric statistic that estimates the survival function from right-censored data. It is frequently utilized in clinical research and other fields of study where the time-to-event outcome is crucial to the analysis.What is the probability density function of a continuous random variable?The probability density function (PDF) of a continuous random variable is a function that specifies the probability distribution of that random variable. It provides the likelihood of observing a particular value within a particular interval of values.What is a continuous random variable?A continuous random variable is a type of random variable that can take on any numerical value in a given range of values. It can be any value on a continuous range of values rather than just taking on certain values.What is the cumulative distribution function?The cumulative distribution function (CDF) is a function that gives the probability that a random variable is less than or equal to a certain value. It is used to calculate the probabilities of random variables being less than or equal to a specific value.
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What is the answer of :20y=-42
Step by step
Answer:
y=-21/10
Step-by-step explanation:
20y=-42
20y/20=-42/20
y=-42/20
y=-21/10
Calculate the rate of power drainage per hour if the capacity of the cell phone is 3 600 mAh?
The rate οf pοwer drainage per hοur is 13.32 watts per hοur οr 13.32 Wh (watt-hοurs) per hοur.
What is the basic mathematical οperatiοns?The fοur basic mathematical οperatiοns are Additiοn, subtractiοn, multiplicatiοn, and divisiοn.
Tο calculate the rate οf pοwer drainage per hοur, we need tο knοw the pοwer cοnsumptiοn οf the cell phοne. Let's assume that the pοwer cοnsumptiοn οf the phοne is cοnstant and equal tο P watts.
The capacity οf the cell phοne battery is 3,600 mAh, which means that it can supply a current οf 3,600 mA (milliampere) fοr οne hοur. Using Ohm's law, we can express the pοwer cοnsumptiοn in terms οf the current and vοltage:
P = I × V
where I is the current and V is the vοltage.
The vοltage οf a typical cell phοne battery is arοund 3.7 vοlts. Therefοre, the current drawn by the phοne is:
I = 3,600 mA = 3.6 A
t = 1 hοur
The pοwer cοnsumptiοn οf the phοne is:
P = I × V = 3.6 A × 3.7 V = 13.32 W
Hence, the rate οf pοwer drainage per hοur is 13.32 watts per hοur οr 13.32 Wh (watt-hοurs) per hοur.
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50 POINTS!
Set L contains all the integers from -4 through 12, inclusive. Set M contains the absolute values of all the numbers in Set L. How many numbers are in the intersection of sets L and M?
Answer:
The intersection of sets L and M has 13 numbers.
Question content area top
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 14 people took the trip. She was able to purchase coach tickets for 120$ and first class tickets for 1030$. She used her total budget for airfare for the trip, which was 6230$. How many first class tickets did she buy? How many coach tickets did she buy?
Sarah bought 5 first class tickets for 1030$ each and 9 coach tickets for 120$ each.
Let's use variables C and F to denote the quantity of coach and first class tickets purchased.
We may deduce from the problem:
C + F = 14 (because Sarah is one among the 14 persons)
The overall cost of the tickets is as follows:
120C + 1030F = 6230
The first equation may be used to solve for one of the variables in terms of the other:
C = 14 - F
When we plug this into the second equation, we get:
120(14 - F) + 1030F = 6230
When we simplify this equation, we get:
1680 - 120F + 1030F = 6230
910F = 4550
F = 5
So Sarah purchased five first-class tickets. The first equation may be used to calculate the number of coach tickets:
C + 5 = 14
C = 9
As a result, Sarah purchased nine coach tickets.
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The expression −290+15m represents a submarine that began at a depth of 290 feet below sea level and ascended at a rate of 15 feet per minute. What was the depth of the submarine after 8 minutes?
Select the correct answer below and, if necessary, fill in the answer box to complete your choice.
A) The submarine was (enter answer here) feet below sea level after 8 minutes.
B) The submarine will have reached sea level after 8 minutes.
Answer: A,
Step-by-step explanation:
it will be -170 feet after 8 min
i need help look at attachment
Answer: [tex]a=\frac{1}{3}[/tex]
Step-by-step explanation:
Determine the voltage dropped across
The answer of the given question based on the Voltage drop the answer is , the voltage dropped across R3 is 277.11 V.
What is Ohm's law?Ohm's law is fundamental principle in electrical engineering and physics that describes relationship between voltage, current, and resistance in electrical circuit. It states that current through conductor between two points is directly proportional to voltage across two points, and inversely proportional to resistance between them.
To determine the voltage dropped across R3, we need to use Ohm's law and Kirchhoff's circuit laws. First, we can calculate the total resistance in the circuit:
Rtotal = R1 + R2 || R3
R2 || R3 = (R2 * R3) / (R2 + R3) (parallel resistance formula)
Rtotal = R1 + (R2 || R3)
Rtotal = 152 + ((18 * 362) / (18 + 362))
Rtotal = 149.89 Ω (rounded to 2 decimal places)
Next, we can use Ohm's law to calculate the current flowing through the circuit:
I = ET / Rtotal
I = 120 / 149.89
I = 0.8004 A (rounded to 4 decimal places)
Finally, we can use Kirchhoff's voltage law to determine the voltage dropped across R3:
ET = IR1 + IR2 || IR3 + IR3
ET = I(R1 + R2 || R3) + IR3
ET - I(R1 + R2 || R3) = IR3
R3 = (ET - I(R1 + R2 || R3)) / I
R3 = (120 - (0.8004 * (152 + ((18 * 362) / (18 + 362))))) / 0.8004
R3 = 277.11 V (rounded to 2 decimal places)
Therefore, the voltage dropped across R3 is 277.11 V.
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Please help me
Conditional probability question
The conditional probabilities are are (a) P(A/B) = 0.69 b) P(A/B) = 31/100
How to determine the conditional probabilities?You should recall that Probability is the chance that a given event will occur; the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes;
The conditional probability P(A|B) is calculated using:
P(A/B)
P(A/B) = P( A and B) / P(B)
P(A/B) = (18/26 * 8/26)/ 8/26
P(A/B) = (0.69 * 0.31)/ 0.31
P(A/B) = 0.69
P(A/B) = 69/100
b) Using the same formula
P(B/A) = P( B and A) / P(A)
P(A/B) = (8/26 * 18/26) / 18/26
P(A/B) = (0.31 * 0.69)/0.69
P(A/B) = 0.31
P(A/B) = 31/100
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Determine the total number of kilograms from 15 boxes if 1 sachet is 4g
Answer:
50
Step-by-step explanation:
To determine the total number of kilograms from 15 boxes, we need to know the weight of one box. Let's assume that one box contains 50 sachets (this is just an assumption, the actual number may vary). Then the weight of one sachet is 4 grams or 0.004 kilograms.
the weight of one box is:
50 sachets x 0.004 kg/sachet = 0.2 kg
the total weight of 15 boxes is:
15 boxes x 0.2 kg/box = 3 kg
the total weight of 15 boxes is 3 kilograms.
to determine whether the 15 boxes will be enough to last for a year, we need to know how many sachets a person uses in a day. Let's assume that a person uses one sachet per day.
then the total number of sachets used in a year is:
1 sachet/day x 365 days = 365 sachets
the total number of sachets in 15 boxes is:
15 boxes x 50 sachets/box = 750 sachets
since 750 sachets is greater than 365 sachets, 15 boxes will be enough to last for a year.
to determine the number of sachets that will make one box, we need to know the weight of one box and the weight of one sachet. Let's assume that one box weighs 0.2 kg and one sachet weighs 4 grams or 0.004 kg.
then the number of sachets in one box is:
number of sachets = weight of box / weight of one sachet
number of sachets = 0.2 kg / 0.004 kg
number of sachets = 50 sachets
therefore, one box contains 50 sachets.
A rocket is shot off from a launcher. The accompanying table represents the height of the rocket at given times, where x is time, in seconds, and y is height, In feet. Write a quadratic regression equation for this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the height, to the nearest foot, at a time of 15-3 seconds.
The height at a time of 15.3 seconds ≈ 729.2562 feet.
Finding the best-fit equation for a set of data with a parabola-like form is the goal of quadratic regression.
Making a scatter plot is the first stage in the regression process. You should generally consider a quadratic equation as the best fit for your data if your scatter plot has a "U" shape, either concave up (like the letter U) or concave down (). You can have only a portion of a quadratic "U" shape, like a quarter or a third.
The general form of the quadratic regression equation is y = A + Bx + Cx²
The quadratic regression formula is given as follows;
[tex]B=\frac{S_{xy}S_{x'x'}-S_{x'y}S_{xx'}}{S_{xx}S_{x'x'}-(S_{xx'})^2}\\\\\\C=\frac{S_{xy}S_{x'x'}-S_{x'y}S_{xx'}}{S_{xx}S_{x'x'}-(S_{xx'})^2}\\\\\\A=y'-Bx'-Cx^2\\\\[/tex]
Solving using an online quadratic regression calculator, gives;
A = 2.5643259\
B = 246.6374865
C = -15.41986006
Substituting gives;
y = 2.5643259 + 246.6374865·x -15.41986006·x²
When time, x = 15.3, we have;
y = 2.5643259 + 246.6374865×15.3 -15.41986006×15.3²≈ 729.2562 feet
The height at a time of 15.3 seconds ≈ 729.2562 feet.
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11. College women who play have had more success than others with using social media to benefit from their name, image, and likeness (NIL).
Cοllege wοmen whο play have had mοre success than οthers with using sοcial media tο benefit frοm their name, image, and likeness. (False)
Why is it false?Female cοllege athletes and their success in using sοcial media tο mοnetize their name, image, and likeness which is false.
This statement means that female cοllege athletes whο participate in spοrts have been mοre successful in leveraging their name, image, and likeness fοr financial gain thrοugh sοcial media platfοrms than their nοn-athlete peers.
In οther wοrds, female athletes whο engage in spοrts don't have an advantage in mοnetizing their sοcial media presence and using it tο prοmοte their persοnal brand, cοmpared tο female cοllege students whο dο nοt participate in spοrts.
Therefore, it is false that college women who play have had more success than others with using social media to benefit from their name, image, and likeness
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Complete question:
True or False:
11. College women who play have had more success than others with using social media to benefit from their name, image, and likeness (___).
find the answer in terms of pie
Answer:
SA = 56π cm²
Step-by-step explanation:
the surface area (SA) is calculated as
SA = area of 2 circular ends + area of curved surface
= 2πr² + 2πrh ( r is the radius and h the height )
here r = 4 and h = 3 , then
SA = 2π × 4² + 2π × 4 × 3
= 2π × 16 + 2π × 12
= 32π + 24π
= 56π cm²
the circumference of earth is 24,902 miles (1 mile is 5280 feet). imagine a rope tied tightly to the circumference. if you added 3 ft of rope and kept its circular shape, how high above the ground would the rope be?
The rope would be about 4,285,082.98 feet high above the ground.
Answer: The circumference of the earth is 24,902 miles. We have to add 3 ft of rope and keep its circular shape. We must determine how high the rope would be from the ground.To determine the length of the rope, we must first determine the length of the circumference of the circle.Circumference of the circle = πd = π * 8000 miles = 25132 miles (taking radius of earth as 4000 miles).1 mile is 5280 feet, which implies that the distance around the circle is 25132 * 5280 = 132712960 feet.
The length of the rope will be equal to the distance around the circle, plus 3 feet.Length of the rope = 132712963 feet.Now, to determine how high the rope would be from the ground, we need to use the Pythagorean theorem.Height of the rope = √(length of the rope² - radius of earth²) = √(132712963² - 4000²) = √17602394294769 = 4,285,082.98 feet (approx.)The rope would be about 4,285,082.98 feet high above the ground.
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colton is skiing on a circular ski trail that has a radius of 0.6 km. colton starts at the 3-o'clock position and travels 2.5 km in the counter-clockwise direction. how many radians does colton sweep out? radians how many degrees does colton sweep out? degrees when colton stops skiing, how many km is colton to the right of the center of the ski trail? km when colton stops skiing, how many km is colton above the center of the ski trail? km
1. 4.167 radians does colton sweep out.
2. 238.1° degrees does colton sweep out.
3. 0.344 km is colton to the right of the center of the ski trail.
4. 0.139 km is colton above the center of the ski trail.
Question analysis Colton is skiing on a circular ski trail with a radius of 0.6 km.
Colton starts at the 3-o'clock position and travels 2.5 km in the counterclockwise direction.
There are four parts to this question: How many radians does Colton sweep out.
Radians refer to the distance covered by the object in circular motion around the circumference.
We can determine this using the formula:
θ = s / r
Where θ is the angle in radians, s is the length of the arc, and r is the radius of the circle.
Substituting the given values,θ = 2.5 km / 0.6 km= 4.167 radians.
Degrees does Colton sweep out:
We know that 180° = π radians
So, we can convert radians to degrees by multiplying it by
180° / πθ = 4.167 radians x (180° / π) ≈ 238.1°
When Colton stops skiing, how many km is Colton to the right of the center of the ski trail.
The displacement of the skier from the center is the same as the horizontal distance.
We can use trigonometry to calculate this distance.
From the given position, we know that Colton has travelled 2.5 km along the circumference of the circle.
This is equivalent to the angle swept by Colton (4.167 radians) multiplied by the radius of the circle (0.6 km).Using trigonometry, we can determine the horizontal distance as:
d = r cos(θ)
Where d is the horizontal distance, r is the radius, and θ is the angle swept by Colton.
d = 0.6 km x cos(4.167)≈ 0.344 km.
When Colton stops skiing, how many km is Colton above the center of the ski trail?The vertical distance from the center of the circle can be calculated using trigonometry.
We can use the same method as above to calculate the vertical distance as:
v = r sin(θ)
Where v is the vertical distance, r is the radius, and θ is the angle swept by Colton.
v = 0.6 km x sin(4.167) ≈ 0.139 km
Colton sweeps out 4.167 radians ≈ 238.1°.
When Colton stops skiing, he is to the right of the center of the ski trail by ≈ 0.344 km.
When Colton stops skiing, he is above the center of the ski trail by ≈ 0.139 km.
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Elijah invested $94,000 in an account paying an interest rate of
4. 125% compounded quarterly. Kayden invested $94,000 in an account paying an interest rate of 4. 25% compounded daily. After 7 years, how much more money would Kayden have in his account than Elijah, to the nearest dollar?
Kayden would have $1,110.45 more in his account than Elijah after 7 years, to the nearest dollar when compounded daily.
What is Compound interest?The interest that is accrued on both the principle and any prior interest is known as compound interest. This implies that the interest received in succeeding periods rises as the interest is added to the principle. Compound interest is a crucial idea in personal finance that may be utilised in calculations for both savings and loans.
The compound interest is given by the formula:
[tex]A = P(1 + r/n)^{(nt)}[/tex]
For Elijah substituting the values we have:
[tex]A = $94,000(1 + 0.04125/4)^{(4*7)} = $129,852.94[/tex]
For Kayden substituting the values we have:
[tex]A = $94,000(1 + 0.0425/365)^{(365*7)} = $130,963.39[/tex]
The difference between the two amounts is:
$130,963.39 - $129,852.94 = $1,110.45
Therefore, Kayden would have $1,110.45 more in his account than Elijah after 7 years, to the nearest dollar.
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Answer:$1286 when rounded. Got it right
Step-by-step explanation:
The graph of the parent quadratic
function f(x) = x2 and that of a second function
of the form g(x) = ax2 are shown. What
conclusion can you make about the value of a in the equation of the second function?
The correct answer is D. The value of a in the equation of the second function is greater than 1.
Describe Quadratic Function?A quadratic function is a type of function in algebra that can be written in the form f(x) = ax² + bx + c, where a, b, and c are constants (coefficients) and x is the independent variable. The graph of a quadratic function is a parabola, which is a U-shaped curve.
The coefficient a determines whether the parabola opens upwards (if a > 0) or downwards (if a < 0). The point where the parabola changes direction is called the vertex, which is located at the point (-b/2a, f(-b/2a)).
The coefficient b determines the horizontal position of the vertex, and c determines the vertical position of the vertex.
We know that the parent quadratic function f(x) = x² is a U-shaped curve with its vertex at the origin (0,0).
If the graph of a second function g(x) = ax² intersects the graph of f(x) at exactly one point, then this point must be the vertex of g(x), since the vertex of f(x) is already fixed at the origin.
In order for g(x) to intersect f(x) at exactly one point, the vertex of g(x) must lie on the x-axis (since it cannot be above the x-axis, or else there would be two points of intersection). Therefore, the y-coordinate of the vertex of g(x) is 0.
The vertex of a quadratic function of the form ax² + bx + c has x-coordinate -b/2a and y-coordinate c - b²/4a. Since the y-coordinate must be 0 in this case, we have:
0 = c - b²/4a
Solving for c, we get:
c = b²/4a
Therefore, the vertex of g(x) is (0, b²/4a).
We can see from the graph that the vertex of g(x) is to the right of the origin, so its x-coordinate is positive. This means that the coefficient a must be positive, since otherwise the parabola would open downwards and the vertex would be below the x-axis.
We also know that the vertex of g(x) is above the x-axis, so its y-coordinate (which is b²/4a) must be positive. This means that b^2 and a have the same sign.
Putting this information together, we can conclude that:
If a > 0, then b²/4a > 0, which means that b² and a have the same sign. This means that the parabola opens upwards, and the vertex is above the x-axis. From the graph, we can see that this is the case, so we can eliminate options B and C.
If a < 1, then the parabola is narrower than the parent function f(x) = x², and the vertex is closer to the y-axis. This is not the case from the graph, so we can eliminate option A.
Therefore, the correct answer is D. The value of a in the equation of the second function is greater than 1.
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The complete question is:
Find any rational number between -5,25 and -5,26.
Answer:
ANSWER: -5,2.55
Step-by-step explanation:
I got it right
4) At the end of each quarter year, Rod makes a $500 payment into Lanagham Mutual Fund. If his investments earn 7.88% annual interest compounded quarterly, what will be the value of Rod's annuity in 20 years?
5) Bubba contributes $50 per month into the Vanguard National Bond Fund that earns 7.26% annual interest compounded monthly. What is the value of Bubba's investment after 25 years?
6) Ursula is considering opening an account with Crab Key Bank at 5.15% annual interest compounded quarterly. What is the equivalent APY?
7) How can you tell the difference if one bank offers an investment earning 8.75% annual interest compounded quarterly versus one earning 8.7% compounded monthly?
The value of each investment scenario based on the given interest compounded will be:
Rod's annuity after 20 years will be $30,904.95.Buba's investment value after 25 years will be $41,438.55.Ursula equivalent APY will be 5.25%.The different between an investment earning annual investment compounded ed quarterly and one earning compounded monthly is the number of times the interest is compounded each year.Let's discuss each scenario we have.
4) At the end of each quarter year, Rod makes a $500 payment into Lanagham Mutual Fund. If his investments earn 7.88% annual interest compounded quarterly, what will be the value of Rod's annuity in 20 years?The value of Rod's annuity after 20 years will be $30,904.95. This is calculated by using the formula A = P((1+r/n)^(nt)), where P is the payment, r is the annual interest rate (7.88%), n is the number of times compounded per year (quarterly, or 4), and t is the number of years (20).
5) Bubba contributes $50 per month into the Vanguard National Bond Fund that earns 7.26% annual interest compounded monthly. What is the value of Bubba's investment after 25 years?The value of Bubba's investment after 25 years will be $41,438.55. This is calculated by using the formula A = P((1+r/n)^(nt)), where P is the payment, r is the annual interest rate (7.26%), n is the number of times compounded per year (monthly, or 12), and t is the number of years (25).
6) Ursula is considering opening an account with Crab Key Bank at 5.15% annual interest compounded quarterly. What is the equivalent APY?The equivalent APY for the account at Crab Key Bank with an annual interest rate of 5.15% compounded quarterly is 5.25%. This is calculated by using the formula APY = (1+r/n)^n - 1, where r is the annual interest rate (5.15%), and n is the number of times compounded per year (quarterly, or 4).
7) How can you tell the difference if one bank offers an investment earning 8.75% annual interest compounded quarterly versus one earning 8.7% compounded monthly?The difference between an investment earning 8.75% annual interest compounded quarterly and one earning 8.7% compounded monthly is the number of times the interest is compounded each year. An investment earning 8.75% compounded quarterly has an interest rate of 8.75% that is compounded four times per year, while an investment earning 8.7% compounded monthly has an interest rate of 8.7% that is compounded twelve times per year.
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30POINTS
Factor completely.
3x^5 - 75x^3 =
Answer:
3x3 (x+5) (x - 5)
Step-by-step explanation: