The answer is 2/5.
There is an 8/20 chance that the next person will receive a window seat. You simplify that probability to get your answer. 8/20 becomes 2/5. So the answer is 2/5.
Match the name of the sampling method descriptions given.
Situations:
1. ask all the students in your math class
2. choosing every 5th person on a list
3. pulling 50 names from a hat
4. randomly select two tables in the cafeteria and survey all the people at those two tables
5. dividing the population by Gender, and choosing 30 people of each gender
Sampling Method:
a. Simple Random
b. Convenience
c. Cluster
d. Systematic
e. Stratified
Enquire οf each pupil in yοur math class. --> b. Cοnvenience
chοοsing every 5th persοn οn a list --> d. Systematic
pulling 50 names frοm a hat --> a. Simple Randοm
Chοοse twο cafeteria tables at randοm, then pοll every patrοn at thοse twο tables. --> e. Stratified
selecting 30 individuals frοm each gender after dividing the pοpulatiοn intο genders. --> c. Cluster
What is the sampling methοd?Samples can be categοrized intο:
Cοnvenient: Sample taken frοm a pοοl that is easily accessible.
Put all the pοssibilities intο a hat, and draw sοme οf them at randοm.
Every kth cοmpοnent is taken in a systematic manner. If yοu wanted tο survey anything οn the street, fοr instance, yοu may interview every fifth persοn.
Cluster: This pοpulatiοn is brοken dοwn intο grοups, οr clusters, and each cluster's cοnstituents are surveyed.
Further divides the peοple intο several grοups. After that, thοugh, just a small percentage οf the grοup gets quizzed.
Thus, cοrrect match οf the sampling methοd are:
enquire οf each pupil in yοur math class. --> b. Cοnvenience
chοοsing every 5th persοn οn a list --> d. Systematic
pulling 50 names frοm a hat --> a. Simple Randοm
Chοοse twο cafeteria tables at randοm, then pοll every patrοn at thοse twο tables. --> e. Stratified
selecting 30 individuals frοm each gender after dividing the pοpulatiοn intο genders. --> c. Cluster
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In ΔSTU, \overline{SU}
SU
is extended through point U to point V, \text{m}\angle STU = (3x+14)^{\circ}m∠STU=(3x+14)
∘
, \text{m}\angle UST = (2x+12)^{\circ}m∠UST=(2x+12)
∘
, and \text{m}\angle TUV = (7x+6)^{\circ}m∠TUV=(7x+6)
∘
. What is the value of x?x?
The value of x from the calculation is given as 10
How to solve for the value of xWe have ∠TUV = ∠STU + ∠UST
(7x+6) = (3x+14) + (2x+12)
open the bracket
7x+6 = 3x+14 + 2x+12
take the like terms
7x + 6 = 3x + 2x + 14 + 12
7x + 6 = 5x + 26
7x - 5x = 26 - 6
2x = 20
Divide through the equation that we have by 2 to get the value of x
2x / 2 = 20 / 2
x = 10
Hence the value of x is given as 10
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A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1534 and the standard deviation was 310. The test scores of four students selected at random are 1940, 1280, 2260, and 1420. Find the z-scores that correspond to each value and determine whether any of the values are unusual.
The first student Z-score= 1.31, the second student= -0.82, the third student = 2.35, the fourth student = -0.37. None of these scores are unusual.
Describe Z-score?In statistics, a Z-score (also known as a standard score) is a measure of how many standard deviations a data point is from the mean of a population or sample. The Z-score is calculated by subtracting the mean from the data point and then dividing by the standard deviation.
A Z-score of 0 indicates that the data point is equal to the mean, while positive Z-scores indicate that the data point is above the mean and negative Z-scores indicate that the data point is below the mean.
Z-scores are often used in statistics to standardize data so that it can be compared across different populations or samples. Z-scores can also be used to identify outliers, which are data points that are unusually far from the mean and may skew the analysis of the data.
To find the z-score for each student, we use the formula:
z = (x - μ) / σ
where x is the student's score, μ is the mean test score, and σ is the standard deviation.
For the first student with a score of 1940:
z = (1940 - 1534) / 310
z = 1.31
For the second student with a score of 1280:
z = (1280 - 1534) / 310
z = -0.82
For the third student with a score of 2260:
z = (2260 - 1534) / 310
z = 2.35
For the fourth student with a score of 1420:
z = (1420 - 1534) / 310
z = -0.37
To determine if any of these values are unusual, we can use the rule of thumb that considers any z-score greater than 3 or less than -3 to be unusual.
None of the z-scores calculated above are greater than 3 or less than -3, so we can conclude that none of these scores are unusual.
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A triangle has the measures of two of its interior angles 48° and 65°, the third interior angle is unknown. What is the value of the exterior angle corresponding to the interior angle whose value is unknown?
a) 123°
b) 131°
c) 113°
d) 128°
e) 118°
Answer:
c) 113°
Step-by-step explanation:
Exterior angle is equal to the sum or the "remote" interior angles, that is the two angles that are not just next to the exterior angle. See image.
So the answer, quickly:
exterior angle
= 65° + 48°
= 113°
This is why:
(skip if you don't care)
The three angles in a triangle add up to 180° But also, a linear pair of angles also add up to 180°
So
x + 65° + 48° = 180°
x + y = 180°
y = 65° + 48°
See image.
determine the length of a plot of land 16 m wide and whose area is 336 m².
Answer:
21
Step-by-step explanation:
The equation to find the area of a space is length x width. Divide the total area by the width to find the length.
Which two consecutive numbers that this number comes between? 2 3/10 + 4 1/2
Two consecutive number between [tex]2 \frac{3}{10}[/tex] and [tex]4 \frac{1}{2}$[/tex] are 3 and 4.
What is a Composite Number?Composite number are those number which follow a particular sequence whether it is normal, even, odd or any other sequence. AP) is the best method to identify whether the number are consecutive or not.
So here, we can write as [tex]\frac{23}{10}=2.3[/t[/tex] ex] and we can write [tex]\frac{1}{2}[/tex] as [tex]frac| {9}{2}=4.5[/tex]
So, two composite number are 3 and 4.
Arithmetic Progression, (AP) A sequence can called in as AP when the difference between them are common which means the each previous is differ from its preceding one by a constant quantity.
[tex]a_n=a_1+(n-1) * d[/tex] where, [tex]a_1=[/tex] first termed= common difference [tex]a_n=[/tex] term in the sequence
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Kids under 16 must be accompanied by an adult. Which inequality describes the age, a, of a kid accompanied?
Group of answer choices
x ≤ 16
x < 16
x > 16
x ≥ 16
Answer:
x < 16
Step-by-step explanation:
geometry question attached
The area of triangle PYR, obtained using the formula for the area of a triangle; A = (1/2)·a·b·sin(C), is about 87.85 square units
What is the formula for the area of a triangle that can be used to find the area of PYR?The area of a triangle is the product of half multiplied by the base length and the height of the triangle. The height of the triangle is the length of a side of the triangle multiplied by the sine of the included angle between two sides of the triangle.
The dimensions in the triangle indicates that we get;
Length of the side PQ = 36
Length of the side PR = 22
PQ = QM + MP (Segment addition postulate)
MQ ≅ MP (Definition of bisected segment PQ)
MQ = MP (Definition of congruent segments)
PQ = MP + MP (Substitution property)
PQ = 2 × MP
PQ = 36
36 = 2 × MP
2 × MP = 36
MP = 36/2 = 18
MP = 18
Length of the segment, MY = 8
The Pythagorean Theorem indicates that we get;
PY = √(18² + 8²) = 2·√(97)
∠MPY = arctan(8/18) ≈ 23.92°
Therefore; ∠YPR ≈ 23.92°
The area, A, of the triangle PYR can be obtained from the formula;
A = (1/2)·a·b·sin(C)
The area of the triangle PYR is therefore;
A ≈ (1/2) × (2·√(97)) × 22 × sin(23.92°) ≈ 87.85
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Which statement is true about the given expression 3x2 -11(2y+1)+4
Answer:
The given expression 3x2 -11(2y+1)+4 is a polynomial expression with two variables, x and y. It can be simplified by distributing the -11 to the terms inside the parentheses and combining like terms:
3x2 -11(2y+1)+4 = 3x2 -22y -11 +4
= 3x2 -22y -7
Therefore, the statement "the expression is a polynomial with two variables" is true, while the statements "the expression is in simplest form" and "the expression has a constant term of 11" are false.
Step-by-step explanation:
To use the method of triangulation you need measurement from at least three locations
The given statement is false. The solution has been obtained by using the concept of triangulation.
What is triangulation?
Based on the principles of trigonometry, triangulation is a technique used to locate a fixed point. According to these principles, it is possible to compute the other two sides and angle of a triangle if just one side and two angles of the triangle are known.
We are given a statement that to use the method of triangulation you need measurement from at least three locations.
The statement is false because for this, we need only two points.
Hence, the given statement is false.
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Question: To use the method of triangulation, you need measurements from at least three other locations.
A.True
B.False
What is -2, 3 reflected over the y- axis?????
I NEED THE ANSWER ASAP
Answer:
2, 3
Step-by-step explanation:
When a point is reflected over the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. Therefore, if you reflect the point (-2, 3) over the y-axis, it will become (2, 3).
(Sorry, I tried to provide a picture but I could not.)
An insurance company offers renters insurance to customers in a certain area. Suppose they charge $ 40 $40dollar sign, 40 for a given plan. Based on historical data, there is a 1 11 in 500 500500 probability that a customer with this plan makes a claim, and in those cases, the average payout from the insurance company to the customer was $ 5 , 000 $5,000dollar sign, 5, comma, 000. Here is a table that summarizes the possible outcomes from the company's perspective: Event Payout Net gain ( X ) (X)left parenthesis, X, right parenthesis Claim $ 5 , 000 $5,000dollar sign, 5, comma, 000 − $ 4 , 960 −$4,960minus, dollar sign, 4, comma, 960 No claim $ 0 $0dollar sign, 0 $ 40 $40dollar sign, 40 Let X XX represent the company's net gain from one of these plans. Calculate the expected net gain E ( X ) E(X)E, left parenthesis, X, right parenthesis. E ( X ) = E(X)=E, left parenthesis, X, right parenthesis, equals dollars
An insurance company's anticipated total profit from a single of these policies is $0.08.
What does the term "insurance" mean?Describe insurance. Insurance is a tool for risk management. You acquire security against unforeseen financial losses when you purchase insurance. If something terrible occurs to you, the insurance company compensates you or someone else of your choosing.
The expected net gain can be calculated as:
E(X) = P(Claim) × Net gain (Claim) + P(No claim) × Net gain (No claim)
P(Claim) = 1/500
P(No claim) = 1 - P(Claim) = 499/500
Net gain (Claim) = -$4960 + $5000 = $40
Net gain (No claim) = $40 - $40 = $0
Therefore,
E(X) = (1/500) × $40 + (499/500) × $0
E(X) = $0.08
So the expected net gain for the insurance company from one of these plans is $0.08.
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Answer:
30 dollars
Step-by-step explanation:
Khan Academy
Can someone explain me how to do this task please? Thank you
12) the common multiples of 3 and 5 up to 50 are: 15, 30, 45.
13) the common multiples of 4 and 6 up to 50 are: 12, 24, 36, 48.
14) the common multiples of 3 and 7 up to 50 are: 12, 42.
15) the equivalent fraction of 3/4 is 6/8
16) the equivalent fraction of 2/3 is 4/6
17) the equivalent fraction of 4/5 is 8/10
18) In its simplest form, 4/12 is 1/3
19) In its simplest form, 6/10 is 3/5
20) In its simplest form, 4/8 is 1/2.
What is the justification for the above response?12) To find the common multiples of 3 and 5 up to 50, we can simply list the multiples of 15 (which is the least common multiple of 3 and 5) that are less than or equal to 50.
Multiples of 15: 15, 30, 45
Therefore, the common multiples of 3 and 5 up to 50 are:
15, 30, 45
13)
To find the common multiples of 4 and 6 up to 50, we can again find the least common multiple of 4 and 6, which is 12, and list its multiples that are less than or equal to 50.
Multiples of 12: 12, 24, 36, 48
Therefore, the common multiples of 4 and 6 up to 50 are:
12, 24, 36, 48
14)
To find the common multiples of 3 and 7 up to 50, we can again find the least common multiple of 3 and 7, which is 21, and list its multiples that are less than or equal to 50.
Multiples of 21: 21, 42
Therefore, the common multiples of 3 and 7 up to 50 are:
21, 42
15)
To write an equivalent fraction of 3/4, we can multiply or divide both the numerator and denominator of 3/4 by the same non-zero number. This will give us a fraction that has the same value as 3/4 but with a different numerator and denominator.
For example, if we multiply both the numerator and denominator of 3/4 by 2, we get:
3/4 * 2/2 = 6/8
Therefore, an equivalent fraction of 3/4 is 6/8.
replicating this logic for 16 and 17, we have:
16) the equivalent fraction of 2/3 is 4/6 and
17) the equivalent fraction of 4/5 is 8/10
18) to get the simplest form of 4/12, we can divide the numerator and denominator by 4 to get
(4/4)/(12/4)
= 1/3
replicate this logic for 19 and 20, and we get:
19) In its simplest form, 6/10 is 3/5
20) In its simplest form, 4/8 is 1/2.
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probability problem algebra 2 please help
The probability that the alumni member is male and did not attend graduate school is (546-206)/1214, or 83.09%.
What is probability?Probability is a measure of how likely an event is to happen. It is expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain. Probability is used to describe the likelihood of something happening and to make decisions when dealing with uncertain situations. Probability theory is the mathematics of predicting the outcomes of events when the exact outcome is unknown.
In conclusion, the probability that the alumni member is female is 8.55%, that the alumni member is male is 16.91%, that the alumni member is female and went on to graduate school is 8.55%, that the alumni member is male and went on to graduate school is 16.91%, that the alumni member is female and did not attend graduate school is 79.60%, and that the alumni member is male and did not attend graduate school is 83.09%.
The probability that the alumni member is female is 104/1214, or 8.55%. The probability that the alumni member is male is 206/1214, or 16.91%. The probability that the alumni member is female and went on to graduate school is 104/1214, or 8.55%. The probability that the alumni member is male and went on to graduate school is 206/1214, or 16.91%. Finally, the probability that the alumni member is female and did not attend graduate school is (668-104)/1214, or 79.60%.
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determine the total amount of money that was utilized on fuel in june 2022.
The Consumer Price Index (CPI) for All Urban Consumers grew by 9.1%. The all items index rose 9.1%, the largest annual increase since the year that ended in November 1981.
What is Consumer Price Index?A consumer price index can be defined as a measure of a market basket of goods and services that households have purchased at a weighted average price. The measured CPI fluctuates(differs) to reflect changes in prices over time.
The CPI is one of the most widely(popularly) used indicators of inflation and deflation.
[tex]Annual\ CPI = \frac{Value\ of Basket\ in \ Current \Year}{Value\ of Basket\ in \ Prior\ Year} *100[/tex]
[tex]Inflation\ Rate = \frac{New \ CPI - Prior\ CPI}{Prior\ CPI} *100[/tex]
It is one of the most used methods for measuring inflation and reveals the state and trajectory of the economy.
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Which statement is in-correct
The statement "The Poisson distribution is always skewed right" is incorrect. Option A
What is Poisson distribution?The Poisson distribution is a discrete probability distribution that is used to model the probability of a given number of events occurring in a fixed interval of time or space, assuming that the events occur independently and at a constant rate.
The key features of the Poisson distribution include:
The distribution is discrete, meaning that it only takes on integer values.The distribution is defined by a single parameter, lambda (λ), which represents the expected number of events that will occur in the interval.The distribution is skewed right, with a long tail on the right-hand side.The mean and variance of the distribution are both equal to λ.The statement "The Poisson distribution is always skewed right" is incorrect.
The Poisson distribution can be skewed left, right, or approximately symmetric depending on the value of its parameter lambda. If lambda is small, the distribution will be skewed right. If lambda is large, the distribution will be approximately symmetric.
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Cuantos minutos tardará en llenarse un depósito de 10.080 litros de capacidad si recibe agua por 3 grifos diferentes que arrojan 60 litros, 70 litros, 80 litros cada minuto?
Answer:
El tanque tardará aproximadamente 48 minutos en llenarse.
Step-by-step explanation:
Podemos encontrar la tasa de llenado del depósito sumando las tasas de flujo de los tres grifos:
Tasa de llenado = 60 + 70 + 80 = 210 litros/minuto
Luego, podemos usar la fórmula:
Tiempo = Volumen / Tasa de llenado
Donde el volumen es 10.080 litros y la tasa de llenado es 210 litros/minuto. Sustituyendo estos valores, obtenemos:
Tiempo = 10.080 / 210 ≈ 48 minutos
Por lo tanto, tardará alrededor de 48 minutos en llenarse el depósito de capacidad 10.080 litros si recibe agua por tres grifos diferentes que arrojan 60 litros, 70 litros, 80 litros cada minuto.
¡Espero que esto ayude! Lo siento si no es así. ¡Si necesitas más ayuda, pregúntame! :]
Which of the following represent dividing 72 by 6?
a. 72 ÷ 6
b. 7/2
c. 6÷72
d. 7/2
a and d
a and c
b and c
Cb and d
Answer:
Step-by-step explanation:
The answer to your question is a.
|a-b|-|c+d| if a=-5, b=4. c=1, d=-3
please help soon!
Answer:-7
Step-by-step explanation:
|-5 - 4| = -9
|1 + -3|= -2
|-9 - -2| = -7
Answer:
Step-by-step explanation:
[tex]|a-b|-|c+d|=|-5-4|-|1+(-3)|=|-9|-|-2|=9-2=7[/tex]
Absolute value is just the distance from 0 and therefore is always positive.
Help please! I need help with my hw!
The area of the shaded portion in the image of right triangle attached is solved to be 401.85 square millimeters
How to find the area of the shaded portionThe area of the shaded portion is solved by subtracting the area of the smaller triangle from the area of the bigger triangle
The area of a triangle is solved using the formula
= 0.5 base * height
Information given in the problem
base1 = 24.8
base2 = 15.9
height1 = 34.2 mm
height2 = 21.9
where
base1 and height1 are for the bigger triangle while
base2 and height2 is for smaller triangle
area of shaded portion = 0.5(24.8 * 34.2) - 0.5(15.9 * 21.9)
area of shaded portion = 418.95 - 174.105
area of shaded portion =401.845
area of shaded portion = 401.85 square millimeters
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The diameter of a circle is 33 cm. Find its area to the nearest whole number.
Answer:
Step-by-step explanation:
The answer is not 855.3^2cm
On Monday, the worker drove a total of 134 work-related and personal miles. She received $32.13 for the work-related miles she drove on Monday. what percent of her total miles driven were work-related on Monday
Answer:
Step-by-step explanation:
If the worker drove a total of 134 miles on Monday, and received $32.13 for the work-related miles, then we can assume that the work-related miles pay rate is constant, and calculate the total pay for all the miles:
Total pay for all miles = Total miles * Pay rate per mile
Since the worker received $32.13 for the work-related miles, and we assume a constant pay rate, we can find the pay rate per mile:
Pay rate per mile = Total pay for all miles / Total miles
= $32.13 / Total work-related miles
Now we can use this pay rate per mile to calculate the percentage of work-related miles:
Percentage of work-related miles = (Pay for work-related miles / Pay rate per mile) / Total miles * 100
Plugging in the given values, we get:
Percentage of work-related miles = (32.13 / (134 - 32.13)) / (134) * 100
= 0.2874 * 100
= 28.74%
Therefore, approximately 28.74% of the worker's total miles driven on Monday were work-related.
A parallelogram has a height of 5 units. One side of the parallelogram is AB⎯⎯⎯⎯⎯. The parallelogram has no right angles.
Draw the parallelogram using the Polygon tool.
Each segment of the grid represents 1 unit.
Keyboard Instructions
Initial graph state
The horizontal axis goes from 1.5 to 12.5 with ticks spaced every 1 unit(s).
The vertical axis goes from 1.5 to 12.5 with ticks spaced every 1 unit(s).
Point with coordinates (2, 3) labelled: A.
Point with coordinates (8, 3) labelled: B.
Parallelogram, In Euclidean geometry, a parallelogram is a simple quadrilateral with two(2) pairs of parallel sides.
What is Parallelogram?A parallelogram is a geometric object with sides that are parallel to one another in two(2) dimensions. It is a form of a polygon with four(4) sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length.
A Quadrilateral is a closed shape and a type of polygon that has four sides, four(4) vertices and four angles. It is formed by joining(connecting) four non-collinear points. The sum of the interior angles of quadrilaterals(4 sides) is always equal to 360 degrees.
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Please I need assistance please help
The length of the diagonal of the television screen is equal to 56 cm to the nearest centimeter using the Pythagoras rule.
What is the Pythagoras rule?The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
we shall represent the length of the diagonal with the letter x so by Pythagoras rule we can write:
x² = 34² + 45²
x² = 1156 + 2025
x² = 3181
x = √3181 {take square root of both sides}
x = 56.4004
Therefore, the length of the diagonal of the television screen is equal to 56 cm to the nearest centimeter using the Pythagoras rule.
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Below is the relative-frequency table of the probability distribution for the discrete random variable X, with X = "the number of cars owned by families in New York."
x P(X = x)
0 0.03
1 0.31
2 0.43
3 0.14
4 0.09
If the expected value is 1.95, what is the standard deviation?
0.93
0.99
0.96
Answer: To calculate the standard deviation of a discrete random variable, we need to know the expected value and the variance. The variance of a discrete random variable X is given by:
Var(X) = Σ [ (x - E(X))^2 * P(X = x) ]
where the summation is taken over all possible values of X, and E(X) is the expected value of X.
We are given that the expected value of X is 1.95. Using the formula for the variance and the probabilities given in the table, we can calculate the variance as follows:
Var(X) = (0 - 1.95)^2 * 0.03 + (1 - 1.95)^2 * 0.31 + (2 - 1.95)^2 * 0.43 + (3 - 1.95)^2 * 0.14 + (4 - 1.95)^2 * 0.09
Var(X) = 1.1429
To find the standard deviation, we take the square root of the variance:
SD(X) = sqrt(Var(X))
SD(X) = sqrt(1.1429)
SD(X) ≈ 1.07
Therefore, the standard deviation of the number of cars owned by families in New York is approximately 1.07. None of the options given match this value exactly, but 0.99 is the closest.
Step-by-step explanation:
If X is a discrete uniform random variable ranging from 0 to 12 find
The calculated value of probability, P(X≥10) is option b) 0.1666
What is probability?Probability refers to possibility. The subject of this mathematical discipline is the occurrence of random events. An event is occur by a chance.
Since the given distribution is uniform, the percentage of data set lying between any two consecutive values of X is given by:
[tex]= \frac{100\ \% }{Maximum \ possible\ X - minimum\ possible\ X}[/tex]
[tex]= \frac{100\ \%}{(12\ -\ 0)}[/tex]
[tex]= \frac{100\ \%}{12}[/tex]
[tex]= 8.33\ \%[/tex]
The probability of X having a value that is greater than or equal to 10 i.e.
P(X≥10) is given by:
[tex]= (12- 10) * Percentage \ of data set \ lying\ between \ any two \ values \ of\ x[/tex]
[tex]=2*8.33\%[/tex]
[tex]=16.66\%[/tex]
[tex]=0.1666[/tex]
The calculated value of probability, P(X≥10) is 0.1666.
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HURRY I WILL GIVE BRAINLIEST TO WHO ANSWERS FIRST
Raymond was riding a zip-cable from the top of a viewing post. The cable is 55 yards long. The viewing post is 44 yards high and forms a right angle with the ground, as shown in the picture below.
Given this information, how far is the bottom of the cable from the base of the viewing post?
Answer: i am pretty sure it is 33
Step-by-step explanation:
1. Write down the first five multiples of:
a) 3
b) 9
c) 14
Answer:
a)3,6,9,12,15
b)9,18,27,36,45
c)14,28,42,56,70
Step-by-step explanation:
multiply each of it with 1,2,3,4 and 5 :)
Answer:
3-3,6,9,12,15
9-9,18,27,36.45
14-14,28,42,56.70
Megan used her bike to go to a friend's house, 10 miles away from her house, and then jogged for 8 miles with her friend. The jogging time was one hour longer than her bike ride, and her biking speed was 4 times the jogging speed. Find the speed of Megan on the bike and while jogging, in mph.
Megan's biking speed was 6.4 mph and her jogging speed was 1.6 mph
What is variable ?A variable is a quantity that may change within the context of a mathematical problem.
Let's use the following variables to represent the unknown speed :
v_bike: Megan's biking speed, in miles per hour (mph)v_jog: Megan's jogging speed, in mphWe know that Megan biked for a certain amount of time, and then jogged for one hour longer. Let's use the variable t to represent Megan's biking time, in hours. Then her jogging time is t + 1 hour.
We can use the formula:
distance = rate x time
To create two equations based on the given information.
For the biking distance of 10 miles, we have:
10 = v_bike * t
For the jogging distance of 8 miles, we have:
8 = v_jog * (t + 1)
We also know that Megan's biking speed was 4 times her jogging speed, so we have:
v_bike = 4 * v_jog
We can substitute this equation into the first equation to get:
10 = 4 * v_jog * t
Simplifying this equation, we get:
t = 2.5 * v_jog
We can substitute this equation into the second equation to get:
8 = v_jog * (2.5 * v_jog + 1)
Simplifying this equation, we get:
8 = 2.5 * v_jog^2 + v_jog
Rearranging the terms, we get:
2.5 * v_jog^2 + v_jog - 8 = 0
We can solve this quadratic equation using the quadratic formula:
v_jog = (-1 ± sqrt(1 + 4 * 2.5 * 8)) / (2 * 2.5)v_jog = (-1 ± sqrt(81)) / 5v_jog = (-1 ± 9) / 5v_jog = 1.6 mph (ignoring the negative solution)Finally, we can use the equation v_bike = 4 * v_jog to find Megan's biking speed:
v_bike = 4 * 1.6 mph = 6.4 mph
Therefore, Megan's biking speed was 6.4 mph and her jogging speed was 1.6 mph
Learn more about variable here : brainly.com/question/29283831
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Given the function of(x) = 2√x +√x³, find f'(3). Express your answer as a
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Answer:
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