use the data below make a frequency table take a picture of you frequency table and attach it to your answer marathon time

the given expression is

-14 + (-8/9)

so,

so the answer is -14 8/9 or -134/9

see explanation below

Explanation:

To find the point slope form of an equation, we will apply the formula:

Given two points, we will be able to find the slope = m

for example: (1, 2), (2, 4)

m = slope = change in y/ change in x

m = (4-2)/(2-1)

m = 2/1

m = 2

Then, we will pick any of the points and insert into the formula for the point slope.

Let's assume we are using point (1, 2) = (x1, y1)

inserting into the formula together with the slope gives:

y - 2 = 2(x - 1)

The above is a point slope for the points given.

STEP - BY - STEP EXPLANATION

What to do?

Graph each equation on the same set of axis.

Determine the mass that makes the spring the same length.

Determine the length of that mass.

Write a sentence comparing the two springs.

Given:

f(m) = 18 + 0.4m and g(m) = 11.2 + 0.54m

Step 1

Find the x and y-intercept of both function.

f(m) = 18 + 0.4m

f(0) = 18+0.4(0) = 18

0 = 18 + 0.4m

0.4m = -18

m=-45

The x and y -intercept of the function f(m) are (0, 18) and (-45, 0) respectively.

g(m) = 11.2 + 0.54m

g(0) = 11.2 + 0.54(0)

g(0) = 11.2

0 = 11.2+ 0.54m

0.54m = -11.2

m=20.7

The x and y - intercepts are (0, 11.2) and (20.7, 0).

Step 2

Graph the function.

Below is the graph of the function.

Observe from the graph that that the mass that makes the spring the same length is approximately 48.5 grams.

The length at that point is 37.4 centimeters.

Comparison between the two strings.

The string with the function f(m) started out longer, but does not stretch as quickly as the other spring with the function g(m).

ANSWER

b) 48.6 grams

c) 37.4 centimeters

d) The string with the function f(m) started out longer, but does not stretch as quickly as the other spring with the function g(m).

y= x+ 1/4 x

Y = dependent variable

x= independent variable

Jenny has a bank account. In the first month, she deposits a certain amount of money (x), and in the month after she deposits 1/4 of that amount.

Find the total amount of money deposited (y).

Answer:

∠ FAE = 120°

Step-by-step explanation:

4x and 2x are a linear pair and sum to 180° , that is

4x + 2x = 180

6x = 180 ( divide both sides by 6 )

x = 30

then

∠ FAE = 4x = 4 × 30 = 120°

The probability of a 6 being drawn in one pick is

For 4 drawings, the probability would be

The most appropriate choice for polynomial will be given by

1) Zeroes of P(x) = 2, [tex]\frac{2 + \sqrt{2}i}{3}[/tex], [tex]\frac{2 - \sqrt{2}i}{3}[/tex]

where [tex]i = \sqrt{-1}[/tex]

2) Zeroes of P(x) = 3, 2i, -2i

3) Roots are 2i, -2i, [tex]\frac{3}{2}[/tex]

4) Roots are 0, 1, [tex]2 + \sqrt{5}[/tex], [tex]2 - \sqrt{5}[/tex]

What is a polynomial?

An algebraic expression of the form [tex]a_0 + a_1x +a_2x^2 + a_nx^n[/tex] is called a polynomial of degree n.

[tex]1) P(x ) = 3x^3 -10x^2 + 10x -4\\P(2) = 3(2)^3 - 10(2)^2 +10(2) - 4\\[/tex]

        [tex]= 24 -40 + 20 -16\\= 0[/tex]

(x - 2)  is a factor of P(x)

[tex]P(x) = 3x^2(x - 2) -4x(x - 2) +2(x-2)\\[/tex]

        = [tex](x - 2)(3x^2 - 4x + 2)[/tex]

        [tex]=(x-2)(x -a)(x - b)[/tex]

where,

[tex]a = \frac{-(-4)+\sqrt{(-4)^2 - 4\times 3\times 2}}{2\times 3}\\a =\frac{ 4 + \sqrt{-8}}{6}\\a = \frac{4 + 2\sqrt{2} i}{6}\\a = \frac{2(2 + \sqrt{2}i)}{6}\\a = \frac{2 + \sqrt{2}i}{3}[/tex]

[tex]b = \frac{-(-4)-\sqrt{(-4)^2 - 4\times 3\times 2}}{2\times 3}\\b =\frac{ 4 -\sqrt{-8}}{6}\\b = \frac{4 - 2\sqrt{2} i}{6}\\b = \frac{2(2 - \sqrt{2}i)}{6}\\b = \frac{2 - \sqrt{2}i}{3}[/tex]

Zeroes of P(x) = 2, [tex]\frac{2 + \sqrt{2}i}{3}[/tex], [tex]\frac{2 - \sqrt{2}i}{3}[/tex]

where [tex]i = \sqrt{-1}[/tex]

[tex]2) P(x) = x^3 - 3x^2+4x-12\\P(3) = (3)^3 - 3(3)^2 +4(3) -12\\ P(3) = 0[/tex]

(x - 3) is a factor of P(x)

[tex]x^2(x - 3) + 4(x - 3)\\(x - 3)(x^2 + 4)\\(x - 3)(x -a)(x-b)\\[/tex]

where,

[tex]a = \sqrt{-4}\\a = 2i[/tex]

[tex]b = -\sqrt{-4}\\a = -2i[/tex]

Zeroes of P(x) = 3, 2i, -2i

[tex]3) 2x^3 - 3x^2 +8x-12= 0\\[/tex]

x = 2 satisfies the equation

[tex]2x^2(x -\frac{3}{2}) + 8(x-\frac{3}{2})=0\\(2x^2+8)(x - \frac{3}{2}) = 0\\[/tex]

[tex]2x^2 + 8 = 0[/tex] or [tex]x - \frac{3}{2} = 0[/tex]

[tex]x^2 = -\frac{8}{2}[/tex] or [tex]x = \frac{3}{2}[/tex]

[tex]x^2 = -4[/tex] or [tex]x = \frac{3}{2}[/tex]

[tex]x = \sqrt{-4}[/tex] or [tex]x = \frac{3}{2}[/tex]

[tex]x = 2i[/tex] or [tex]x = -2i[/tex] or [tex]x = \frac{3}{2}[/tex]

Roots are 2i, -2i, [tex]\frac{3}{2}[/tex]

4)

[tex]x^4 - 5x^3 +3x^2 +x = 0\\x(x^3 -5x^2 + 3x +1) = 0\\[/tex]

[tex]x = 0[/tex] or [tex]x^3 -5x^2+3x +1 = 0[/tex]

For  [tex]x^3 -5x^2+3x +1 = 0[/tex]

x = 1 satisfies the equation

[tex]x^2(x -1) -4x(x-1)-1(x-1) = 0\\(x - 1)(x^2 - 4x -1) = 0\\[/tex]

[tex]x -1 = 0[/tex] or [tex]x^2 - 4x -1 = 0[/tex]

Roots are x = 1 or x = a or x = b

where,

[tex]a = \frac{-(-4) + \sqrt{(-4)^2 - 4\times 1 \times(-1)}}{2\times 1}\\a = \frac{4+\sqrt{20}}{2}\\a = \frac{4 + 2\sqrt{5}}{2}\\a = \frac{2(2 + \sqrt{5})}{2}\\a = 2 + \sqrt{5}[/tex]

[tex]b = \frac{-(-4) - \sqrt{(-4)^2 - 4\times 1 \times(-1)}}{2\times 1}\\b = \frac{4-\sqrt{20}}{2}\\b = \frac{4 - 2\sqrt{5}}{2}\\b = \frac{2(2 - \sqrt{5})}{2}\\b = 2 - \sqrt{5}[/tex]

Roots are 0, 1, [tex]2 + \sqrt{5}[/tex], [tex]2 - \sqrt{5}[/tex]

To learn more about polynomial, refer to the link-

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For the vertical asymptotes, we set the argument of the logarithm to be zero. Therefore,

The domain of the function can be found below

Given data:

The given time taken by Tin to type 720 words is t=15 min.

The given expression can be wriiten as,

720 word=15 min

720 words= 15(60 sec)

720 words= 900 sec

1 word = 900/720 sec

=1.25 sec

Multiplying the above equation with 864 on both sides .

864 words= 864(1.25) sec

= 1080 sec

=1080/60 min

= 18 min.

Thus, the time taken bby Tine to type 864 words is 18 min.

Given the following function:

Both θ and y are functions of the time (t)

We will find the derivatives of θ and y with respect of the time (t) as follows:

Now, we will find dy/dt when θ = π/6 and dθ/dt = π/12

First, we need to find the value of y when θ = π/6

so, we will substitute the values to find dy/dt as follows:

Rounding to 2 decimal places

So, the answer will be:

The given function is

The domain is all real numbers, but the range would be all the real numbers greater than 2 because the function approximates to y = 2.

The given equation is expressed as

x + 3 = 2x - 18

Subtracting x from both sides of the equation, it becomes

x - x + 3 = 2x - x - 18

3 = x - 18

Adding 18 to both sides of the equation, it becomes

3 + 18 = x - 18 + 18

21 = x

x = 21

Since there is only one value for x, the correct option is

a. A single solution

The resulting expression using the distributive property of multiplication over subtraction is 3(12) - 3(10).

The distributive property of binary operations extends the distributive law, which states that in elementary algebra, equality is always true.

For instance, given the expression;

A(B - C)

We will have to distribute A over B and C to have;

A(B - C) = AB - AC

Applying the rule to the given expression

3 (12 - 10)

3(12) - 3(10)

This shows that the given expression can also be written as 3(12) - 3(10)

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Remember that the sum of the interior angles is 180. Then, we have the following equation:

This is equivalent to:

solve for M-angle:

Then, te correct answer is :

The Solution:

The given expression is

Rationalizing the expression with the conjugate of the denominator, we have

This becomes

Thus, the correct answer is

In order to have grade A, the score needs to be in the top 9%.

Since the scores are normally distributed, the top 9% scores correspond to 91% of the area under the normal curve. That means we need to find a value of z in the z-table that corresponds to the value 0.91 (that is, 91%).

Looking at the z-table, the value of z for a probability of 0.91 is z = 1.34.

Now, to find the score that this value of z represents, we can use the formula below:

Rounding to the nearest whole number, the minimum score for grade A is 79.

the channel that devoted more time was channel 8, because since 6<8 then it follows thay 1/6>1/8 (the inequiality changes), channel 8 devoted

Explanation

we need to solve for n

Step 1

cross multiply

Step 2

subtract 4n in both sides

Step 3

subtract 14 in both sides,

Step 4

Finally, divide both sides by 3

I hope this helps you

Answer:

The length of the base is:

The resulting quadratic is

Step-by-step explanation:

Base = x

Height = 4x

Area, A = 1/2* base * Height

           A = (1/2) * (x) * (4x)

          A = 2x²           (1)

But,    A = 6              (2)

Since (1) = (2);

2x²= 6

x²= 3

Resulting quadratic:

x² - 3= 0

For the difference between 2 squares:

a² - b² = (a-b)(a+b)

Using that identity, we can factorize our quadratic:

(x-3)(x+3) = 0

So, we have 2 roots:

x = 3 and x = -3

Now, noting that length must take a positive value, we go for the first:

x = 3

The length of the base is:

The resulting quadratic is

Part 1:

The probability that a single randomly selected value is greater than 231.1 equals one minus the probability that it is less or equal to 231.1:

P(x > 231.1) = 1 - P(x ≤ 231.1)

Now, to find P(x ≤ 231.1), we can transform x in its correspondent z-score, and then use a z-score table to find the probability:

x ≤ 231.1 => z ≤ (231.1 - 203.6)/35.5, because z = (x - mean)/(standard deviation)

z ≤ 0.775 (rounding to 3 decimal places)

Then we have:

P(x ≤ 231.1) = P( z ≤ 0.775)

Now, using a table, we find:

P( z ≤ 0.775) ≅ 0.7808

Then, we have:

P(x > 231.1) ≅ 1 - 0.7808 = 0.2192

Therefore, the asked probability is approximately 0.2192.

Part 2

For the next part, since we will select a sample out of other samples with size n = 16, we need to use the formula:

z = (x - mean)/(standard deviation/√n)

Now, x represents the mean of the selected sample, which we want to be greater than 231.1. Then, we have:

z = (231.1 - 203.6)/(35.5/√16) = 27.5/(35.5/4) = 3.099

P(x > 231.1) = 1 - P(x ≤ 231.1) = 1 - P(x ≤ 231.1) = 1 - P( z ≤ 3.099) = 1 - 0.9990 = 0.0010

Therefore, the asked probability is approximately 0.0010.

Start to see the possible options

The first digit will have 10 possible numbers to choose from 0 to 9, however in the second digit since it cannot repeat there will be only 9 possible to choose from. As for ther third number 0 is not an option meaning that there are 9 to choose as well.

SOLUTION:

Step 1:

In this question, we are given the following:

Explain the behavior of :

when x=a.

Give values to x and a such that:

Step 2:

The graph of the function:

are as follows:

Explanation:

From the graph, we can see that the function:

is a horizontal translation, shift to the right of its parent function,

Find the volume of a pyramid with a square base, where the side length of the base is

19.3 ft and the height of the pyramid is 16.2 ft. Round your answer to the nearest

tenth of a cubic foo

Remember that

the volume of the pyramid is equal to

where

B is the area of the base

h is the height

step 1

Find out the area of the base

B=19.3^2

B=372.49 ft2

h=16.2 ft

substitute the given values in the formula

To find the solution of the system by graphing we need to plot each line in the plane and look for the intersection.

First we need to write both equations in terms of y:

now we need to find two points for each of this lines. To do this we give values to the variable x and find y.

For the equation 2x-y=-1, if x=0 then:

so we have the point (0,1).

If x=1, then:

so we have the point (1,3).

Now we plot this points on the plane and join them with a straight line.

Now we look for two points of the second equation.

If x=0, then:

so we have the point (0,-3)

If x=1, then:

so we have the point (1,-1).

We plot the points and join them wiith a line, then we have:

once we have both lines in the plane we look for the intersection. In this case we notice that the lines are parallel; this means that they wont intersect.

Therefore the system of equations has no solutions.

Probability of selecting a black three or a red jack = 1/13

There are a total of 52 cards in a deck of cards

Total number of ways of selecting one card from 52 cards = 52C1 = 52 ways

There are two red jacks in a deck of cards

Number of ways of selecting a red jack = 2C1 = 2 ways

There are two blacks 3s in a deck of cards

Number of ways of selecting a black three = 2C1 = 2 ways

Probability of selecting a black three or a red jack = (1/26) + (1/26)

Probability of selecting a black three or a red jack = 2/26 = 1/13

We have the residuals of each function graphed.

They represent the distance, taking into account the sign, of each data point to the line of best fit.

A good fit will have residuals that are close to the x-axis. Also, the distribution for the residuals should not have too much spread, meaning that all the points should have approximately the same residual in ideal conditions.

In this case, we see that Function A has most residuals around the horizontal axis. Except for one of the points, that may be considered an outliert.

In the case of Function B there is a clear pattern (a quadratic relation between x and the residual) that shows that the degree of the best fit function is not the adequate (maybe two degrees lower than what should be).

This results in residuals that have a wide spread depending on the value of x.

Then, we can conclude that Function A has a better fit because the points are clustered around the x-axis.

Answer: Function A has a better fit because the points are clustered around the x-axis [Third option]

we have that

triangle ABD is a right triangle , because AD is a tangent

so

Apply the Pythagorean Theorem

DB^2=AB^2+AD^2

we have

AB is a diameter (two times rhe radius)

AB=2*295,000=590,000 km

AD=203,000 km

substitute

DB^2=590,000^2+203,000^2

Given

Let the total number of fare be f and total number of miles be m.

Therefore, the total fare f is given by:

Substitute f = 16.30 into the equation:

Therefore, the required number of miles is 3.