Marisol claims that the fourth root of x raised to the fourth power is z. Is Marisol correct, and why?

Answer:

5,212.5 rupees

Step-by-step explanation:

If price of 1 kg is 104.25

multiply 50 by 104.25

equals 5,212.5 rupees

Answer:

5212.50 rupees

Step-by-step explanation:

We can use a ratio

1 kg             50 kg

-----------  = ---------------

104.25            x

Using cross products

1x = 50 * 104.25

x =5212.50 rupees

Answer:

34.16

Step-by-step explanation:

42.7

x 0.8

-------

34.16

Answer:

34.16

Step-by-step explanation:  

2 5

42.7

 x

0.8

 =  

43.16

We will have the following:

First, we recall that the equation of a circle with center (h, k) and radius r is given by:

So:

Part A:What is the probability of getting a red jellybean on the first draw?

Given information: Red jellybeans = 12  Yellow jellybeans = 8  Green jellybeans = 4   Total jellybeans = 24                           The probability of getting a red jellybean on the first draw is:

Probability of getting a red jellybean=Number of red jellybeans/Total jellybeans=12/24=1/2=0.5

Decimal: P(1st Red)=0.5 Percent: P(1 st Red )=50%

Part B: Let's say you did get a red jellybean on the first draw.

What is the probability that you will then get a green on the second draw?

Now, the total number of jellybeans is 23, since one red jellybean has been taken out. The probability of getting a green jellybean is: Probability of getting a green jellybean=Number of green jellybeans/Total number of jellybeans=4/23=0.174 Decimal: P(2nd Green | 1st Red )=0.174 Percent: P(2nd Green | 1st Red )=17%

Part C: If you had gotten a yellow on the first draw, would your answer to Part B be different?

Yes, because there is only 1 rotten egg yellow jellybean and if it were chosen in the first draw, it would not be returned back to the container. Therefore, the total number of jellybeans would be 23 for the second draw, and the probability of getting a green jellybean would be:

Probability of getting a green jellybean=Number of green jellybeans/Total number of jellybeans=4/23=0.174

Thus, the answer would be the same as Part B.

Part D: What is the conditional probability of the dependent event "red then green?"

Given that one red jellybean and one green jellybean are selected: Probability of the first jellybean being red is 1/2

Probability of the second jellybean being green given that the first jellybean is red is 4/23

Probability of "red then green" is calculated as follows: Probability of red then green=P(Red) × P(Green|Red)= 1/2 × 4/23 = 2/23  Decimal: P(1st Red and 2nd Green )=2/23  Percent: P(1st Red and 2nd Green )=8.70%

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Fiber optic  type of cable is uses a two-number designator consisting of core and cladding measurements.

What does fiber optics serve?

What methods are used to deploy fiber optics?

Can fiber optics compete with the internet?

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Answer:

Step-by-step explanation:

This problem is based on unit conversion from miles per hour to  meter per second.'

From tables 1 mph= 0.44704 m/s

Given 248 mph to be converted to meters per second.

hence we have

1 mph= 0.44704 m/s

248 mph= x

cross multiplying we have

x= 110.86592 m/s

to the nearest hundreth we have

we can conclude that x = 2.665 is the approximate root of the function f(x) = x^2 - 7 using Newton's method with the initial approximation x0 = 3.

Certainly! Newton's method is an iterative numerical method used to find the roots of a given function. In this case, we want to find the roots of the function f(x) = x^2 - 7 using Newton's method with an initial approximation of x0 = 3.

The iteration formula for Newton's method is given by:

x[n+1] = x[n] - f(x[n]) / f'(x[n])

Where x[n] represents the nth approximation and f'(x) is the derivative of the function f(x).

Let's compute the first 10 iterations:

Iteration 1:

x[1] = x[0] - f(x[0]) / f'(x[0])

= 3 - (3^2 - 7) / (2 * 3)

= 3 - (9 - 7) / 6

= 3 - 2 / 6

= 3 - 1/3

= 8/3

≈ 2.667

Iteration 2:

x[2] = x[1] - f(x[1]) / f'(x[1])

= 8/3 - ((8/3)^2 - 7) / (2 * (8/3))

= 8/3 - ((64/9) - 7) / (16/3)

= 8/3 - (64/9 - 63/9) / (16/3)

= 8/3 - 1/9 / (16/3)

= 8/3 - 1/9 * (3/16)

= 8/3 - 1/48

= 128/48 - 1/48

= 127/48

≈ 2.646

Iteration 3:

x[3] = x[2] - f(x[2]) / f'(x[2])

= 127/48 - ((127/48)^2 - 7) / (2 * (127/48))

= 127/48 - ((16129/2304) - 7) / (254/48)

= 127/48 - (16129/2304 - 7) / (254/48)

= 127/48 - (16129/2304 - 16128/2304) / (254/48)

= 127/48 - 1/2304 / (254/48)

= 127/48 - 1/2304 * (48/254)

= 127/48 - 1/48 * (1/254)

= 127/48 - 1/12192

= 157081/58752

≈ 2.665

Iteration 4:

x[4] = x[3] - f(x[3]) / f'(x[3])

≈ 2.665

Iteration 5:

x[5] = x[4] - f(x[4]) / f'(x[4])

≈ 2.665

Iteration 6:

x[6] = x[5] - f(x[5]) / f'(x[5])

≈ 2.665

Iteration 7:

x[7] = x[6] - f(x[6]) / f'(x[6])

≈ 2.665

Iteration 8:

x[8] = x[7] - f(x[7]) / f'(x[7])

≈ 2.665

Iteration

Iteration 8:

x[8] = x[7] - f(x[7]) / f'(x[7])

≈ 2.665

Iteration 9:

x[9] = x[8] - f(x[8]) / f'(x[8])

≈ 2.665

Iteration 10:

x[10] = x[9] - f(x[9]) / f'(x[9])

≈ 2.665

Based on the calculations so far, it appears that the iterations have converged to approximately x = 2.665. However, since the calculations have stabilized and there is no change in subsequent iterations.

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a. Both projectiles can strike the ground at the same distance from the projection point if the angles θ and (900 - θ) have the same sine value.b. Both projectiles can be in the air for the same time interval if the angles θ and (900 - θ) have the same sine value.

a. The horizontal distance covered by a projectile depends on its initial velocity and the angle at which it is launched. If the angles θ and (900 - θ) have the same sine value, it means that they have the same vertical component of velocity. Since the initial velocities are the same for both projectiles, if they have the same vertical component of velocity, they will have the same time of flight and hence strike the ground at the same distance from the projection point.

b. The time of flight of a projectile depends on its vertical component of velocity and the angle of projection. If the angles θ and (900 - θ) have the same sine value, it means that they have the same vertical component of velocity. Since the initial velocities are the same for both projectiles, if they have the same vertical component of velocity, they will have the same time of flight, allowing them to be in the air for the same time interval.

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Answer:

C. Multiply the bottom equation by 2

Step-by-step explanation:

-2x+ 4y= 10

3x- 2y =-7

We want to multiply the second equation by 2

-2x+ 4y= 10

6x- 4y =-14

------------------

4x +0y = -4

Answer:

C. Multiply the bottom equation by 2

x = - 1

y = 2

Step-by-step explanation:

Multiplying 3x - 2y = - 7 by 2, we get:  

- 2x + 4y = 10

6x - 4y = - 14

____________

4x = - 4

x = - 1

Putting x = - 1 in 3x - 2y = - 7, we get:

3 * (- 1) - 2y = - 7

= - 3 - 2y = - 7

= - 2y = - 7 + 3

= - 2y = - 4

= y = 2

Hope this helps!

Trigonometry is the branch of mathematics that deals with the study of the relationships between the side lengths and angles of triangles.

It is a vital tool for understanding the physical world, as it is used to measure distances, angles and other properties of shapes. Trigonometry can be used for many purposes, such as surveying, navigation, and astronomy. It is a powerful mathematical tool that is used to solve problems involving the relationships between the side lengths and angles of triangles. It is also used in calculus and analytic geometry. Trigonometry is typically taught in high school and college courses, where students learn the formulas and rules of trigonometry in order to solve problems. At its core, trigonometry is the study of the relationships between the side lengths and angles of triangles and how these relationships can be used to solve problems.

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Answer:

x=3

Step-by-step explanation:

1. Simplify the expression

7x-\left(3\cdot\left(x-6\right)\right)=30

Solve by distributing:

7x-\left(3x+3\cdot-6\right)=30

Simplify the arithmetic:

7x-\left(3x-18\right)=30

Expand the parentheses:

7x-3x+18=30

Simplify the arithmetic:

4x+18=30

Answer:

(6,-6)

Step-by-step explanation:

The required coordinates of B is (6,-6).

In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line that is between end points.

Now it is given that,

Midpoint M (x,y) = (2,-7)

Coordinates of A( x₁,y₁) = (-2,-8)

Let the coordinates of B be (x₂,y₂)

Since, midpoint of line segment AB is given as,

{[(x₁+x₂ )/2] , [(y₁+y₂ )/2]}

Therefore,

x = (x₁+x₂ )/2

⇒ 2x = (x₁+x₂)

⇒ x₂ = 2x - x₁

Putting the values we get,

x₂ = 2(2) - (-2)

⇒ x₂ = 4 + 2

⇒ x₂ = 6

Similarly,

y₂ = 2y - y₁

Putting the values we get,

y₂ = 2(-7) - (-8)

⇒ y₂ = -14 + 8

⇒ y₂ = -6

so, the coordinates of B is (6,-6)

Thus, the required coordinates of B is (6,-6).

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Answer:

The slower plane is flying at 175 miles per hour and complete the trip in 10 hours

The faster plane is flying at 250 Miles per hour and complete the trip in 7 hours

Step-by-step explanation:

Let s= speed of the slower plane s+75= speed of the faster plane

The time it takes the slower plane to make the flight = 1750/s

The time it takes the faster plane to make the flight is=1750/(s+75)

The difference in these two times is 3 hours

1750/s - 1750/(s+7)=3

{(s+75) / (s+75) * (1750/s)} - {(s/s) * (1750/s+75)} =3

(1750s+131250 / s^2+75s) - (1750s/s^2+75s) =3

1750s+131,250-1750s / s^2+75d =3

131,250 / s^2+75s = 3

Cross product

131,250=3(s^2+75s)

131,250=3s^2+225s

43,750=s^2+75s

s^2+75s-43,750=0

Solve the quadratic equation

x= -b +or- √b^2-4ac / 2a

a=1

b=75

c= -43750

x= -b +or- √b^2-4ac / 2a

= -75 +or- √(75)^2 - (4)(1)(-43750) / (2)(1)

= -75 +or- √(5625) - (-175,000) / 2

= -75 +or- √180625) / 2

= -75 +or- 425 / 2

x= -75 + 425/2 OR -75- 425/2

=350/2 OR -500/2

x=175 OR -250

We will ignore the negative sign because the planes are not flying Backward

The slower plane is flying at 175 miles per hour and complete the trip in 1750/175= 10 hours

The faster plane is flying at 250 Miles per hour and complete the trip in 1750/250= 7 hours

In a dataset or graph, outliers are extreme values that greatly deviate from the dominant pattern of values.

In order to identify the outlier, search for a value that is significantly greater or smaller than all the other values. Due to its extreme size compared to all other numbers, the number 267 is an outlier.

a value that "lies outside" (i.e., is significantly smaller or substantially bigger) most of the other values in a set of data For instance, both 3 and 85 in the scores 25, 29, 3, 32, 85, 33, 27 and 28 are "outliers".

A data point that is an outlier in a data graph or dataset you are dealing with is one that is extraordinarily high or extraordinarily low in comparison to the nearest data point and the rest of the nearby coexisting values. Outliers in a dataset or graph are extreme values that stand out significantly from the main pattern of values.

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The number of people who become aware of the product at time t is \(p(t) = 5(1 - 0.9^{\frac{t}{10} })\)

The advertising company wants to introduce a new product to a population of 5 million people. They assume that no one was aware of the product at the beginning of the campaign. They also know that after 10 days of advertising, 10% of the people became aware of the product. To find out how many people become aware of the product at time t, they use a function called p(t).

The function p(t) represents the number of people (in millions) who become aware of the product by time t. The company assumes that the rate at which p increases is proportional to the number of people still unaware of the product. This means that the more people who are unaware of the product, the faster the number of people who become aware of it will increase.

To express the proportionality mathematically, we can use the equation:

p'(t) = k [5 - p(t)]

Where p'(t) is the rate of change of p with respect to time t, and k is the proportionality constant that determines the speed of the increase. The quantity (5 - p(t)) represents the number of people who are still unaware of the product at time t. This means that as p(t) gets closer to 5 million, the rate of increase of p(t) will slow down.

To solve this equation, we need to use calculus. Integrating both sides of the equation, we get:

ln|5 - p(t)| = kt + C

Where C is the constant of integration. To determine the value of C, we use the initial condition that p(0) = 0. This means that at the beginning of the campaign, no one was aware of the product. Substituting this into the equation, we get:

ln|5 - 0| = k(0) + C

Simplifying, we get:

C = ln(5)

Substituting this value into the equation, we get:

ln|5 - p(t)| = kt + ln(5)

To find the value of p(t) at a specific time t, we can solve for p(t) by taking the exponential of both sides of the equation:

\(|5 - p(t)| = e^{kt+ln(5)}\)

Simplifying, we get:

\(5 - p(t) = 5e^{kt}\)

Or:

\(p(t) = 5(1 - e^{kt})\)

To find the value of k, we can use the fact that 10% of the people were aware of the product after 10 days of advertising. This means that:

p(10) = 0.1(5) = 0.5

Substituting this into the equation, we get:

\(0.5 = 5(1 - e^{10k})\)

Solving for k, we get:

k = -0.1 ln(0.9)

Substituting this value into the equation for p(t), we get:

\(p(t) = 5(1 - e^{-0.1ln(0.9)t})\)

Simplifying, we get:

\(p(t) = 5(1 - 0.9^{\frac{t}{10} })\)

This is the formula that tells us how many people will become aware of the product at time t.

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Answer:

10% interest

Step-by-step explanation:

150,606.59 - 78,170 = 72,436.59

72,436.59 / 9 = 8,048.51

8,048.51 / 78,170 = 0.1029... = 10%

a) The current ages of his children are: 8 years, 15 years and 17 years

b) In the year when the ages of his three children have doubled, their ages also form a pythagorean triple.

Let x be the age of the youngest child, y represents the age of the middle child and z be the age of oldest child.

The oldest child is nine years older than the youngest.

so, we get an equation,

z = 9 + x

⇒ x = z - 9

and the middle child is two years younger than the oldest.

so, we get an equation,

y = z - 2

The age of his children now form a Pythagorean triple.

⇒ x² + y² = z²

substitute the values for x and y from above two equations.

⇒ (z - 9)² + (z - 2)² = z²

⇒ z² -18z + 81 + z² - 4z +4 = z²

⇒ 2z² -22z + 85 - z² = z² - z²

⇒ z² - 22z + 85 = 0

⇒ (z - 17)(z - 5) = 0

For z = 17:

x = 17 - 9

x = 8

and y = 17 - 2

y = 15

For z = 5, the value of x would be negative which is contradiction.

As is always greater than 0

For x = 8 , y = 15 and z = 17

Consider x² + y²

= 8² + 15²

= 64 + 225

= 289

= 17²

= z²

This means, (8, 15, 17) is a Pythagorean triple.

Thus, their current ages are: 8 years, 15 years and 17 years

If  the ages of his three children have doubled then:

x = 16 , y = 30 and z = 34

Consider x² + y²

= 16² + 30²

= 256 + 900

= 1156

= 34²

= z²

This means, (16, 30, 34) also form a Pythagorean triple.

In the year when the ages of his three children have doubled, their ages will form a pythagorean triple.

Thus, the man is correct.

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We have the following:

In this case, what we must do is calculate the weighted average, as follows:

The mean salary is $28112

Answer:

3. x=8, y=4, (8,4)

x=12,y=6, (12,6)

Step-by-step explanation:

Ratio is 2:1

3. x=8, y= 4 (8,4)

x=12, y=8 (12,8)

4.

Step-by-step explanation:

4.Rule for cookies?

It goes up by 4's.

5.Rule for fruit bars?

It goes up by 2's.

With a sample of 9 tables, the probability that diners would spend fewer than 100 minutes at their table during dinner is \(0.8413\), or around \(84.13\) percent.

The ratio of beneficial results to all beneficial results in the population is a common way to define probability.

Probability has many uses in both analysis and gaming. Probability is used in sectors of real life and business where making predictions is important. The utilisation of probabilistic principles was necessary for forecasting market prices and cricket team performance.

With the values from the problem substituted, we obtain,

\(z = (100 - 97) / (18/\sqrt{9} ) = 1\)

Using a standard normal distribution table or calculator, we find that the probability of getting a z-score less than \(1\) is \(0.8413\).

Therefore tables is \(0.8413\) or approximately \(84.13\)%.

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To find the factors of the expression 12x^2 - 4x - 1, we can use the factor theorem. The factor theorem states that if a polynomial expression evaluates to zero when a certain value is substituted for the variable, then that value is a factor of the polynomial.

To determine if a certain value is a factor of the expression, we can use synthetic division. Synthetic division involves dividing the polynomial expression by the possible factor to check if the remainder is zero. If the remainder is zero, then the value is a factor.

Let's start by checking if x = 1 is a factor of the expression:

    1 | 12 - 4 - 1
      |     12   8
      |____________
       12   8   7

Since the remainder is not zero, x = 1 is not a factor of the expression.

Next, let's check if x = -1 is a factor of the expression:

   -1 | 12 - 4 - 1
      |    -12  16
      |____________
       12 -16  15

Again, the remainder is not zero, so x = -1 is not a factor of the expression.

Now, let's check if x = 2 is a factor of the expression:

    2 | 12 - 4 - 1
      |     24 40
      |____________
       12  20 39

Once again, the remainder is not zero, so x = 2 is not a factor of the expression.

Finally, let's check if x = -2 is a factor of the expression:

   -2 | 12 - 4 - 1
      |    -24 56
      |____________
       12 -28 55

As we can see, the remainder is not zero, so x = -2 is not a factor of the expression.

After checking all the possible factors, we can conclude that none of the values tested (1, -1, 2, -2) are factors of the expression 12x^2 - 4x - 1.

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Answer:

Step-by-step explanation:

Firstly,

According to rational and irrational,

\( \sqrt{15} \: is \: irrational\)

Since,

Natural numbers, Whole Numbers and Integers all come under Rational number.

Hence,

\( \sqrt{15} \)

Is an irrational number.

Answer:

define the unknown quantity as =variable. Then use the given info to write down an equation in terms of the unknown quantity. At the end, solve the equation for the unknown.

Answer: 286 possibilities

Step-by-step explanation:

It's a combination because the order of countries doesn't matter in this scenario.

\(_{n} C_{r} =\frac{n!}{r!(n-r)!}=\frac{13!}{10!(13-10)!}=\frac{13!}{10!(3)!}=\frac{13!}{10!(3)!}\\\\=\frac{6227020800}{3628800(6)}=\frac{6227020800}{3628800(6)}=\frac{6227020800}{21772800}=286\)

I hope this is right

Answer:

the value that belongs there is 26

Step-by-step explanation:

sin56

Since tan56 = -----------

cos56

sin56 = 26/z

cos 56 = x/z

tan56 = 26/x

Answer:

I believe changing -3/4 steepen the slope. For example, y=-1x+2

We can prove this statement using the definition of congruence. According to the definition of congruence, a ≡ b (mod m) means that a - b is divisible by m.

Similarly, c ≡ d (mod m) implies that c - d is divisible by m. Therefore, we can write:

a - b = km
c - d = lm

where k and l are integers. Then we can add the two equations together to get:

a - c = (k + l)m

which implies that a - c is divisible by m, thus a - c ≡ b - d (mod m). This completes the proof.

To show that a − c ≡ b − d (mod m), we need to use the definition of congruence modulo m.
Definition: Two integers a and b are congruent modulo m if and only if there exists an integer k such that a − b = km.
From the given information, we have:
a ≡ b (mod m) → a − b = km for some integer k
c ≡ d (mod m) → c − d = lm for some integer l
Now, we can rearrange the equations and subtract them from each other:
a − b = km → a = km + b
c − d = lm → c = lm + d
a − c = (km + b) − (lm + d) = km − lm + b − d = (k − l)m + (b − d)
Since k − l is an integer, we can let k − l = n, where n is an integer. Then we have:
a − c = nm + (b − d) = (b − d) + nm
This shows that a − c ≡ b − d (mod m), as required. Therefore, if a ≡ b (mod m) and c ≡ d (mod m), then a − c ≡ b − d (mod m).

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Comparing percentages, comparing means, and correlating scores are all different ways of describing results and are used in different contexts.

Comparing percentages is often used when dealing with categorical data or when the response variable is binary. It is a way of summarizing the proportion or percentage of respondents who fall into different categories or have different responses. For example, comparing the percentage of people who prefer Coke over Pepsi or the percentage of people who have a favorable view of a political candidate can be useful in understanding the overall trend in responses.

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