solve for x

7x/2+5=8

o x=6/7

o x=26/7

o x=21/2

o x=91/2​

The third approximation to 63 using Newton's method with initial approximation x = 3 is equal to 8.625.

Use Newton's method to find the root of a function,

Follow these steps,

Choose an initial approximation x_0.

Calculate the function value f(x_0) and the derivative f'(x_0).

Use the formula,

x_1 = x_0 - f(x_0)/f'(x_0)

To calculate a new approximation x_1.

Repeat steps 2 and 3 with x_1 as the new initial approximation,

until we obtain the desired accuracy.

For this problem, we want to find the square root of 63,

which is equivalent to finding the root of the function f(x) = x^2 - 63.

Starting with x_0 = 3, we have,

f(x) = x^2 - 63

⇒f'(x) = 2x

At x_0 = 3,

f(x_0) = 3^2 - 63

         = -54

f'(x_0) = 2×3

          = 6

Using the formula for Newton's method, we get,

x_1 = x_0 - f(x_0)/f'(x_0)

      = 3 - (-54)/6

      = 3 + 9

      = 12

So, the second approximation to the square root of 63 is 12.

To obtain the third approximation, we repeat the process with x_1 as the new initial approximation,

At x_1 = 12,

f(x_1) = 12^2 - 63

        = 81

f'(x_1) = 2× 12 = 24

Using the formula for Newton's method, we get,

x_2 = x_1 - f(x_1)/f'(x_1)

= 12 - 81/24

= 8.625

Therefore, the third approximation to the square root of 63 using Newton's method, rounded to five decimal places, is Xs = 8.625.

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Answer:

the acorn is 32 feet from the base of the tree.

Answer:

The acorn is 32 feet from the base of the tree.

Step-by-step explanation:

This is an problem where the Pythagorean Theroem.

The formula is \(a^2+b^2=c^2\) where a & b are the legs and c is the hypotenuse.

In this problem, we are given the height, which is a and the hypotenuse, which the flying squirrel glides, which is c.

We can substitute the values and solve for b which is the distance from the base to the acorn.

The new equation would be \(60^2+b^2=68^2\)

We can simplify the exponents and we get: \(3600+b^2=4624\).

Now, we have to solve for b.

1. Subtract 3600 on both sides: \(b^2=1024\)

2. Take the square root of both sides: \(\sqrt{b^2} =\sqrt{1024}\)

3. Since the exponent and the radical cancel each other, we are left with just b. The square root fo 1024 is 32, which is the value of b.

So the distance from the acorn to the base of the tree is 32 feet.

Answer:

35 students total

Step-by-step explanation:

if there is 20 girls and 3 boys for every 4 girls, all you need to do is 20/4=5, then do 5*3=15, there is 15 boys and 20 girls, so do 15+20=35, or at least i think

The peak runoff rate (ft 3/s) for a storm that is likely to occur once every 5 years is approximately 34.08 ft3/s.

Here's how to solve the problem:

Given: Watershed area (A) = 296 ac Weighted curve number (C) = 73Time of concentration (tc) = 2.7 hr. Return period (T) = 5 years

Solution: First, use the formula for the average rainfall intensity (i) during the 5-year storm event: i = (0.2/T)^0.8 x C x (10 / (t c + 10))^(0.5)where i is in inches/hour.

Substitute the values :i = (0.2/5)^0.8 x 73 x (10 / (2.7 + 10))^(0.5)i = 0.784 in/hr.

Next, calculate the rainfall volume (V) for the 5-year storm event: V = A x i where A is in acres and i is in inches/hour. Convert the area from acres to square feet: A = 296 ac x 43,560 ft^2/ac A = 12,893,760 ft^2

Substitute the values: V = 12,893,760 ft^2 x (0.784 in/hr / 12 in/ft)V = 849,581 ft^3. Now, calculate the peak runoff rate (Q) using the formula :

Q = (C x V) / (3600 x t c )where Q is in ft3/s and t c is in seconds.

Convert the time of concentration from hours to seconds: t c = 2.7 hr x 3600 sec/hr = 9,720 sec.

Substitute the values :Q = (73 x 849,581 ft^3) / (3600 sec/hr x 9,720 sec)Q = 23.692 ft^3/s

Finally, adjust the peak runoff rate for the 5-year storm event using the formula:Q5 = Q x 1.21where Q5 is the peak runoff rate for the 5-year storm event.

Substitute the value:Q5 = 23.692 ft^3/s x 1.21Q5 = 28.68 ft^3/s

Rounding to two decimal places, the answer is approximately 34.08 ft3/s.

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We must find the flowerbed's area in order to calculate the suggested mulch coverage for a flowerbed with a 20-foot radius. Given that the function's vertex is located at the coordinates (0, 0.5), it is likely a quadratic function with the vertex form y = a(x - h)2 + k, where (h, k) stands for the vertex coordinates.

We may enter these values into the vertex form equation given that the vertex is at (0, 0.5):

y = a(x - 0)^2 + 0.5

y = ax^2 + 0.5

Since the area of the flowerbed is represented by this equation, we may evaluate it for the specified radius of 20 feet:

area = a(20)^2 + 0.5

We circle the area to the closest inch to determine the recommended amount of mulch.

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The line representing the equation 7x1 + 4x2 \(\leq\) 28 goes through the following two points: (0,7) and (4,0).

Hence, option (c) is the correct choice.

The constraint equation is g(x,y)=c, and we state that x and y are constrained by g(x,y)=c.

Constrained maximum and constrained minimum points are locations (x,y) that are maxima or minima of f(x,y) with the condition that they meet the constraint equation g(x,y)=c.

As per the data given,

We have,

The equation of the constraint: 7 x_1+4 x_2\(\leq\) 28

7 x_1+4 x_2 \(\leq\) 28

So, putting the value of x_2=0

We will get the above expression as:

7 x_1=28

=>x_1=4

So, the points will be (4,0)

Now, putting the value of x_1=0

Thus, we will get:

4 x_2=28

=>x_2=7

So, the points will be (0,7)

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y=8x+b, b being any number, is parallel to y=8x+4.

For example:

y=8x+2

y=8x+(1/2)

y=8x+937382

y=8x-4

The value of each of the softball mitts which were sold by Quinn at the thrift mart as described in the task content is; $10.

It follows from the task content that Quinn sold 3 softball mitts.

On this note, let the value of each of the softball mitts sold by Quinn be; x.

Since she sold, the total money she realises would be; 3x. Therefore the equation which correctly represents the situation of her spendings and the remainder is as follows;

3x - 23 = 7

Add 23 to both sides of the equation so that we have;

3x = 7 + 23

3x = 30

Divide both sides of the equation by; 3;

x = $10.

Ultimately, the value of each of the softball mitts which were sold by Quinn at the thrift mart as described in the task content is; $10.

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Answer:

Don't know

Step-by-step explanation:

The probability of finding 0 contaminated pieces in  225 g of chocolate is 5.57 X 10⁻⁷.

Here the number of contaminated fragments follows a Poisson process. Hence, let the distribution for the same be X.

Hence we get X ~ Poi(λt)

where λ is the mean no. of contaminated pieces and t is the no. of bars consumed.

For P(X = x) we get [(λt)ˣ  e^(-λt)]/x!

Here λ = 14.4 and t = 1 Hence we will get

P(X = x) = [(14.4)ˣ e⁻¹⁴°⁴]/x!

Here we need to find the probability of the no. of contaminated pieces = 0

Therefore

P(X = 0) = [(14.4)⁰ e⁻¹⁴°⁴]/0!

Hence the probability of finding 0 contaminated pieces in a bar of chocolate is

P(X = 0) =  e⁻¹⁴°⁴

= 5.57 X 10⁻⁷

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The equation of the horizontal parabola with vertex (2, -1) that passes through the point (5, 0) is: y + 1 = (1/9)(x - 2)^2

The equation of a horizontal parabola can be written in the form:

(y - k) = a(x - h)^2

where (h, k) represents the vertex of the parabola.

Given that the vertex is (2, -1), we have h = 2 and k = -1.

Substituting these values into the equation, we have:

(y - (-1)) = a(x - 2)^2

Simplifying, we get:

y + 1 = a(x - 2)^2

To find the value of 'a' and complete the equation, we can use the fact that the parabola passes through the point (5, 0).

Substituting x = 5 and y = 0 into the equation, we have:

0 + 1 = a(5 - 2)^2

1 = 9a

Solving for 'a', we get:

a = 1/9

Substituting this value of 'a' back into the equation, we have:

y + 1 = (1/9)(x - 2)^2

Therefore, the equation of the horizontal parabola with vertex (2, -1) that passes through the point (5, 0) is:

y + 1 = (1/9)(x - 2)^2

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Answer:

80

Step-by-step explanation:

1234567891011121314

Answer:

-21z-35t+21g

Step-by-step explanation:

-7x3z=-21z

-7x5t=-35t

-7x-3g=21g

Answer:

5v is an equivalent expression for 6v + -1 ?

Answer:

5v is equivalent expression for 6v + -1

Answer:

Step-by-step explanation:

Difference of 2 and q:  2 - q

Expression: (2 - q)⁸

The ratios of\(4\):\(5\) and \(40\):\(3\) are not equal, the initial ratios of \(12\):\(15\) and \(200:15\)are not proportionate.

When two or more numbers or values are compared, the outcome is the ratio, which is expressed as a fraction or a colon. It is used to describe how the relative magnitudes of two or more objects correlate. Ratios can be used to evaluate quantities of the same unit or of different units.

For instance, a ratio of \(3:1\) is used to compare three units to four, while a ratio of \(2:1\) is used to compare two units to one. Ratios can be expressed or simplified in a variety of methods.

The ratio \(6:9\) will become\(2:3\) if both parts are multiplied by\(3\). Ratios can also take the shape of decimals or percentages.

\(12:15 =200:15\)

multiplying both the left side  by\(3\) and right side by \(5\) we get

\(4:5= 40:3\)

Hence it shows that they are not equal so they are not proportionate

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Answer:  1/4

Step-by-step explanation: The coin is fair, the probabilities of getting a head and a tail are equal to 12 . The probability of getting an even number on a die is 36=12 because among 6 results there are 3 even numbers

Answer:

150

Step-by-step explanation:

p/5=30

p=30*5

p=150

By using the formula for expectation, it can be calculated that-

Expectation of b = 1.79

What is expectation?

At first it is important to know about probability of an event.

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Suppose x is a random variable with the probability function f(x). suppose  \(x_1, x_2, ... ,x_n\) are the values corrosponding to the actual occurance of the event and \(p_1, p_2,...,p_n\) be the corrosponding probabilities.

Expectation is given by the formula

\(p_1x_1+p_2x_2+....+p_nx_n\)

Here, the table is

Number of Books                 Probability

0                                                 0.35

1                                                  0.20

2                                                 0.15

3                                                 0.10

4                                                 0.07

5                                                 0.08

6                                                 0.04

7                                                  0.01

Expectation of b = 0 \(\times\) 0.35 + 1 \(\times\) 0.20 + 2 \(\times\) 0.15 + 3 \(\times\) 0.10 + 4 \(\times\) 0.07 + 5 \(\times\) 0.08 + 6 \(\times\) 0.04 + 7 \(\times\) 0.01

                          = 1.79

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Complete Question

The table is as follows

Number of Books                 Probability

0                                                 0.35

1                                                  0.20

2                                                 0.15

3                                                 0.10

4                                                 0.07

5                                                 0.08

6                                                 0.04

7                                                  0.01

Answer:

Step-by-step explanation:

\((3y-1)\)

\((3y-1)*(3y-1)*(3y-1)*(3y-1)*(3y-1)\)

\(243y^5-405y^4+270y^3-90y^2+15y-1\)

Answer:

Q is the point (3, 4).

Step-by-step explanation:

The formulae for the coordinates of a point (h, k) which divides a line  joining the points (x1, y1) and (x2, y2) in the ratio m : n is:

h = (mx2 + nx1) / (m + n), k = (my2 + my1)/(m+n)

Now we have S = (x1, y1) = (-2, -6) and T = (x2, y2) = (5, 8) and

m = 5 and n = 2.

So here, for point Q:

h = (5*5) + 2*-2)/(2+5)

    = 21/7

     = 3.

k = (5*8 + (-6*2) / 7

   = 28/7

    = 4.

Answer:

Oy > 2x - 3

Step-by-step explanation:

because it has > so with will be on the left side

I also recommend Desmos because it helps you with these questions.

and that's what I used.

The inequality represented by the graph below is y > 2x - 3.

Option B is the correct answer.

An inequality is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

We have,

To graph an inequality, you need to identify the equation of the line or boundary that separates the two regions defined by the inequality.

This boundary can be a line, a curve, or even a plane in three dimensions.

Next, you need to determine which region to shade, based on whether the inequality symbol is less than (<), greater than (>), less than or equal to (≤), or greater than or equal to (≥).

If the inequality symbol is less than (<) or greater than (>), the boundary line should be drawn as a dashed line since the points on the line are not included in the solution set.

Then, shade the region above the line if the symbol is greater than (>), or below the line if the symbol is less than (<).

If the inequality symbol is less than or equal to (≤) or greater than or equal to (≥), the boundary line should be drawn as a solid line since the points on the line are included in the solution set.

Then, shade the region above the line if the symbol is greater than or equal to (≥), or below the line if the symbol is less than or equal to (≤).

Finally, label the shaded region as the solution set and write the inequality symbol next to it.

From the given graph we see that,

y > 2x - 3 has the same graph.

Thus,

The inequality represented by the graph below is y > 2x - 3.

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Answer:

2.41401985483

Step-by-step explanation:

Distance/Rate

Traveling 250 miles at 103.5617 mph would take time approximately 2.41 hours.

A mathematical number known as distance measures "how much ground an object has traveled" while moving. Distance is defined as the product of speed and time.

The information is given in the question following as:

Distance | Rate

250 miles | 103.5617 mph

We have to determine the time based on the information given.

To find the time it takes to travel a certain distance at a certain rate, you can use the formula time = distance/rate.

Plugging in the values from the given information, you get:

time = 250 miles / 103.5617 mph

Apply the division operation,

time = 2.41 hours

This means it would take time approximately 2.41 hours to travel 250 miles at a rate of 103.5617 mph.

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Answer:

Values of y are:

2 1 -1

2 -1 -4

How long the meeting last = End time - Starting time

                =  10:25 - 9:30

                =  9:85 - 9:30   [I converted 10:25 to make it easier to see the

                                           subtraction. This is posibble because 1hr = 60mins]

                = 55 mins

The probability of winning the lottery by selecting the correct five numbers in the same order they were drawn can be determined by calculating the ratio of the favorable outcomes (winning combination) to the total number of possible outcomes.

In this particular lottery, there are 39 possible numbers to choose from, and the winning combination consists of five numbers. Since the order of the numbers matters, the probability of selecting the correct numbers in the correct order is calculated by dividing the number of favorable outcomes (1) by the total number of possible outcomes.

The total number of possible outcomes can be calculated using the concept of permutations. The formula for the number of permutations of n objects taken r at a time is nPr = n! / (n - r)!, where n! denotes the factorial of n.

In this case, we have 39 choices for the first number, 38 choices for the second number, 37 choices for the third number, 36 choices for the fourth number, and 35 choices for the fifth number. Therefore, the total number of possible outcomes is 39P5.

To calculate the probability of winning, we divide the number of favorable outcomes (1) by the total number of possible outcomes (39P5). This gives us the probability of winning the lottery by selecting the correct five numbers in the same order they were drawn.

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The solution set for the given graph is (2,1). The solution has been obtained using linear equations.

What is a linear equation?

It is a linear equation that has the greatest degree of one. In a linear equation with an exponent greater than one, this indicates that there are no variables. A straight line is produced on the graph by this equation.

We are given two lines on the graph

The points of the red line are (3,0) and (0,3)

So, the equation of the line comes out to be

y=−x+3      ...(1)

The points of the blue line are (3,2) and (-1,-2)

So, the equation of the line comes out to be

y=x−1     ...(2)

To find the solution set, we need to solve the equations

Substituting (1) in (2), we get,

⇒−x+3 = x−1

⇒−2x = -4

⇒x = 2

So, y = 1

Hence, the solution set for the given graph is (2,1).

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