which equation has an infinite number of solutions?

Which Equation Has An Infinite Number Of Solutions?

Answers

Answer 1

The equation 8(x-9)=6(2x-12)-4x (option C) has an infinite number of solutions.

How to check for infinite number of solutions?

Let's simplify the given equation and solve for x:

8(x-9) = 6(2x-12) - 4x

8x - 72 = 12x - 72 - 4x // Distributing 6

8x - 72 = 8x - 72 // Simplifying

We can see that both sides of the equation are equal, and there is no variable 'x' present. This means that the equation is an identity and it will hold true for any value of x.

Therefore, this equation has an infinite number of solutions, since any value of x will satisfy the equation.

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Related Questions

If m/P = (4x - 1)° and m/R = (12x - 27), find mQPS.​

Answers

The arc angle QPS is 258 degrees.

How to find the angles of a cyclic quadrilateral?

A cyclic quadrilateral is a four sided shape(quadrilateral) that can be inscribed into a circle. The sum of angles in a cyclic quadrilateral is 360 degrees.

The opposite angles of a cyclic quadrilateral have a total of. 180 ° . In other words, the opposite angles of a cyclic quadrilateral is supplementary angles.

Therefore,

m∠P = 4x - 1

m∠R = 12x - 27

Hence,

4x - 1 + 12x - 27 = 180

16x - 28 = 180

16x = 180 + 28

16x = 208

x = 208 / 16

x = 13

m∠R = 12(13) - 27

m∠R = 156 - 27

m∠R = 129 degrees

Therefore,

m∠R = 1 / 2 (QPS)

129 = 1 / 2 × x

x = 129 ×2

x = 258 degrees

Hence,

mQPS = 258 degrees

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To use the method of triangulation you need measurement from at least three locations

Answers

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

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°

Answers

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.

If X is a discrete uniform random variable ranging from 0 to 12 find

Answers

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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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

Answers

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:

|a-b|-|c+d| if a=-5, b=4. c=1, d=-3
please help soon!

Answers

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.

Which statement is true about the given expression 3x2 -11(2y+1)+4

Answers

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:

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?

Answers

Answer:    i am pretty sure it is 33

Step-by-step explanation:

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.

Answers

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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Given the function of(x) = 2√x +√x³, find f'(3). Express your answer as a
single fraction in simplest radical form.

Answers

Answer:

Here is the answer for the following question:

determine whether f (x) x^2-2x-3/x^2+3x+2 has any holes. if it does, give coordinates

Answers

Answer:

hole at (- 1, - 4 )

Step-by-step explanation:

If f(x) has terms that cancel , on the numerator/ denominator then a discontinuity  corresponding to that factor is removable and there is a hole.

f(x) = [tex]\frac{x^2-2x-3}{x^2+3x+2}[/tex] ← factor numerator and denominator

    = [tex]\frac{(x-3)(x+1)}{(x+2)(x+1)}[/tex] ← cancel (x + 1) on numerator/ denominator

   = [tex]\frac{x-3}{x+2}[/tex]

this indicates that x + 1 = 0 ( or x = - 1) is a removable discontinuity and the graph has a hole in it.

substitute x = - 1 into the remaining f(x) for y- coordinate of hole

f(- 1) = [tex]\frac{-1-3}{-1+2}[/tex] = [tex]\frac{-4}{1}[/tex] = - 4

coordinates of hole are (- 1, - 4 )

Answer:

Yes, this function has one hole

This occurs at [tex](-1, -4)[/tex]

Step-by-step explanation:

Definition of hole
A hole on a rational function represents the fact that the function approaches the point, but is not actually defined on that precise x value.

To identify holes first factor out the numerator and denominator. If there is a common factor in the numerator and denominator then there is a holeCancel the common factor from both numerator and denominatorSet the common factor = 0 and find the corresponding value for xUse this x value in the factored function to determine the y-value for the hole

Given function
[tex]f(x) = \dfrac{x^2-2x\:-3}{x^2+\:3x\:+\:2}\\[/tex]

Factor the numerator:
[tex]x^2 - 2x - 3 = (x+1)(x - 3)[/tex]

Factor the denominator:
[tex]x^2+\:3x\:+\:2 = (x + 1)(x + 2)[/tex]

Hence

[tex]\begin{aligned}f(x) & = \dfrac{x^2-2x\:-3}{x^2+\:3x\:+\:2}\\\\& = \dfrac{ (x+1)(x - 3)}{(x + 1)(x + 2)}\\\\ &= \dfrac{x - 3}{x+2} \end{aligned}[/tex]

The common factor is   [tex](x + 1)[/tex]

Set this = 0 to find the hole:
[tex]x + 1 = 0 = > x = -1[/tex]

So at[tex]x = -1[/tex] there is a hole.

Substitute this value of x in the factored function to get the y value for the hole

We have
[tex]f(x) = \dfrac{x - 3}{x+2}[/tex]

[tex]\begin{aligned}f(2) &= \dfrac{-1 - 3}{-1 + 2}\\& = \dfrac{-4}{1}\\&= -4\end{aligned}[/tex]

So the hole occurs at   [tex](-1, -4)[/tex]

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

Answers

Answer:

Step-by-step explanation:

The answer to your question is a.

Can someone explain me how to do this task please? Thank you

Answers

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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Which statement is in-correct

Answers

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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determine the total amount of money that was utilized on fuel in june 2022.

Answers

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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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

Answers

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.

geometry question attached

Answers

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

The area of the triangle PYR is about 87.85 square units

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li
People can pick strawberries on a farm.
The pay for the strawberries they pick.
Brian picks 4 ½ kg of strawberries.
He pays a total of £15.75.
Sue wants 500 grams of strawberries.
Brian says she can buy them from him for the same price he paid.
How much should Sue pay Brian for 500 grams of strawberries?
Answer:
Question 10
Not yet answered
Marked out of 1.00
Robert packs potatoes into bags.
He then packs bags into boxes to sell to shops.
Robert has these orders.
P Flag question
Browns
25 hoxes

Answers

Brian will receive £[tex]1.75[/tex] from Sue buying [tex]500[/tex] grams of berries.

What is grams vs. kg?

The metric measure for a tiny amount of mass and weight is the gram (g). It weighs the same as one milliliter (or one cubic centimeter) of water. 1,000 grams make to one kilogram (kg). One liter liquid water weighs exactly one kilogram (kg).

How should I weigh a gram?

Using a scale is the most accurate technique to measure in grams. Kitchen spoons and cups, for example, offer an approximate approximation. Moreover, always have a conversion tool or chart on available so you can estimate grams without a scale.

Brian paid a total of £[tex]15.75[/tex] for [tex]4\frac{1}{2}[/tex] kg of strawberries. To find out the price per gram, we can divide the total cost by the total weight:

Price per gram [tex]=[/tex]Total cost / Total weight

Total weight of strawberries [tex]= 4.5 kg = 4500 grams[/tex]

Price per gram [tex]=[/tex] £[tex]15.75 / 4500[/tex] grams

Price per gram [tex]=[/tex] £[tex]0.0035[/tex] per gram

So, Brian paid £[tex]0.0035[/tex] for every gram of strawberries he picked.

Cost of [tex]500[/tex] grams [tex]=[/tex] [tex]500 grams *[/tex] £[tex]0.0035/gram[/tex]

Cost of [tex]500[/tex] grams [tex]=[/tex] £[tex]1.75[/tex]

Therefore, Sue should pay Brian £[tex]1.75[/tex] for [tex]500[/tex] grams of strawberries.

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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

Answers

Answer:

x < 16

Step-by-step explanation:

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.

Answers

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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determine the length of a plot of land 16 m wide and whose area is 336 m².

Answers

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.

The correct answer to this particular question would be 21

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?

Answers

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! :]

Classify the events as independent or not independent. Events A and B where P(A) = 0.7, P(B) = 0.8, and P(A and B) = 0.56

Answers

The given events A and B are two independent events.

Independent and Non-independent events:

In probability, independent events are those events where the occurrence of one event does not affect the probability of the other event occurring.  

On the other hand, non-independent events are those events where the occurrence of one event affects the probability of the other event occurring.

If A and B are two independent events then

                       P(A and B) = P(A) * P(B)  

Here we have

A and B are two events

where P(A) = 0.7, P(B) = 0.8, and P(A and B) = 0.56

Using the above formula,

=> P(A and B) = (0.7) (0.8) = 0.56

=> P(A and B) = 0.56

From the data, P(A and B) = 0.56

Therefore,

The given events A and B are two independent events.

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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.

Answers

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 mph

We 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

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Which two consecutive numbers that this number comes between? 2 3/10 + 4 1/2

Answers

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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The diameter of a circle is 33 cm. Find its area to the nearest whole number.

Answers

The Area is 855.3 cm^2

Answer:

Step-by-step explanation:

The answer is not 855.3^2cm

Use the long division to divide f(x) =b^4 + 3b^3-35b^2-46b+28 by d(x)= b+7 remember to show all your work cleary steps by steps and express your final answer in the from f(x)= q(x)d(x) +r(x)

Answers

The final function is f(x) =  ( [tex]b^3-4b^2[/tex]+[tex]63b[/tex]-487b)(b+7)+3021.

What is function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Here the given function f(x)=[tex]b^4 + 3b^3-35b^2-46b+28[/tex] and d(x)=b+7.

Now using long division then,

=>           [tex]b^3-4b^2[/tex]+[tex]63b[/tex]-487b

    [tex]\\b+7)\overline{b^4 + 3b^3-35b^2-46b+28 }\\\\[/tex]

    (-)      [tex]{b^4+7b^3}[/tex]

                  [tex]\overline{-4b^3+35b^2+46b-28}[/tex]

    (-)           [tex]-4b^3-28b^2[/tex]

                             [tex]\overline{63b^2-46b+28}[/tex]

     (-)                     [tex]63b^2+441b[/tex]

                                     [tex]\overline{-487b-28}[/tex]

     (-)                             [tex]\underline {-487b-3049}[/tex]

                                                3021

Quotient q(x) =   [tex]b^3-4b^2[/tex]+[tex]63b[/tex]-487b

Remainder r(x) = 3021

Hence the final function is f(x) =  ( [tex]b^3-4b^2[/tex]+[tex]63b[/tex]-487b)(b+7)+3021.

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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

Answers

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

Help please! I need help with my hw!

Answers

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 portion

The 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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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?

Answers

The value of x from the calculation is given as 10

How to solve for the value of x

We 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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