Line l passes through the points, (6,-14) and (2,-4) . If line m is parallel to line l, the slope of the line m is equal to

We are given that a bag contains 1 gold marble, 6 silver marbles, and 21 black marbles. First, we need to determine the total number of marbles. The number of marbles of each color is:

The total number is then:

Substituting the values:

Therefore, there are a total of 28 marbles. Now we determine the probability of getting each of the marbles by determining the quotient of the number of marbles of a given color over the total number of marbles. For the gold marbles we have:

For silver we have:

For the black marbles:

Now, to determine the expected value we need to multiply each probability by the value that is gained for each of the colors. We need to have into account that is it is a gain we use a positive sign and if it is a lose we use a negative sign:

Solving the operations we get:

Therefore, the expected value is -$0.21.

The given expression is

(4 + 3i) - (2 - i)

We would simplify the terms inside the parentheses. The negative sign(- 1) outside the second parentheses would be used to multiply each term inside. We have

4 + 3i + - 1 * 2 + - 1 * - i

4 + 3i - 2 + i

By collecting like terms, we have

4 - 2 + 3i + i

2 + 4i

Thus, the answer in a + bi form is

2 + 4i

Using the slope intercept equation, the equation of the line in fully simplified slope intercepted form is y=4x−4.

In the given question we have to write the equation of the line in fully simplified slope intercepted form.

As we know that slope intercept form of equation of line is given by

y=mx+c

where m=slope

c=intercept of the line (i.e point where line cut y-axis )

From graph we can easily find two point of the line that is (1,0)(0,−4).

From the point x(1)=1, y(1)=0, x(2)=0, y(2)=−4

Slope (m)=(y(2)−y(1))/(x(2)−x(1))

m=(−4−0)/(0−1)

m=-4/−1

m=4

As we know that c is a point where line cut y axis so c=−4

Hence, slope-intercept form of equation is y=4x−4.

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The equation of consideration is:

Since two unknowns ( x and y) are given in just one equation, to get each set of the solutions, we are going to choose a value of x and get a corresponding value of y

Let x = 0, to get the value of y at point x = 0, substitute this value of x into the given equation:

The first set of solutions is therefore:

To get the second set of solution, let us choose x = 3 and substitute this value into the given equation:

The second set of equation is:

The above is the graph showing the two sets of solutions

In order to solve by subdtitution, first, solve the second equation for x:

x - 2y = 4 add 2y both sides

x = 4 + 2y

next, replace the previous expression for x into the first equation and solve for y:

4x + 2y = -14 replace x=4+2y

4(4 + 2y) + 2y = -14 apply distribution property

16 + 8y + 2y = -14 subtract 16 both sides

8y + 2y = -14 - 16 simplify like terms both sides

10y = -30 divide by 10 both sides

y = -30/10

y = -3

next, replace y=-3 into x = 4 + 2y

x = 4 + 2y = 4 + 2(-3) = 4 -6 = -2

x = -2

Hence, the solution to the given system of equations is:

x = -2

y = -3

SOLUTION:

Case: Matrices multiplication

Given:

Two matrices can always be multiplied if they have the same dimensions.

Method:

From the image above, if and only if the number of items of columns matches the number of items of the columns, then it is possible to multiply.

Final answer:

True,

Two matrices can always be multiplied if they have the same dimensions

Using the pythagoras theorem,

Given:

Sample Size (n) = 425

No. of Success = 121

Find: estimate the proportion of the population

Solution:

Let's calculate first the success proportion in the sample by dividing no. of success over the total number of people then multiply it by 100.

Our sample proportion p = 28.47%.

Then, for the margin of error, the formula is:

where z = critical value, p = sample proportion, and n = sample size.

For our z-value, since we are using a 95% confidence interval, the value of z = 1.645.

Then, solve.

Let's multiply the MOE by 100%.

Therefore, about 28.47% ± 3.6% or between 24.87% to 32.07% of the population would be able to successfully reproduce the rhythm.

Given the numbers : 7 1/2 and 1 1/8

We will divide them

so,

The wholesale price for a pillow is $4.50 .

The store marks up the wholesale price by 90%.

That is, 90% of $4.50 has been aadded with the wholesale price as the store price (SP).

Therefore we have, '

Thus, the store price is $8.55

Hello there. To solve this question, we'll need to remember some properties on geometry and areas of figures.

First, the area of a square is equal to the square of its side length.

The area of a circle is given by pi * the square of its radii, being this radii half of the diameter:

In this case, the side of the square is 1.5' and the diameter of the circle is 5.8'.

Finding the radii of the circle:

r = d/2 = 5.8'/2 = 2.9'

Calculating the area of the square and the circle

Asquare = 1.5² = 2.25 and Acircle = pi * 2.9² = pi * 8.41

The area of the shaded region is calculated by the difference between the area of the circle and the square

Ashaded = Acircle - Asquare

Ashaded = 8.41pi - 2.25

This is the area of the region we've been looking for.

Answer to part A :

The school that gets the award for the highly consistent attendance among its students is school B . Because its range is the smallest that is there exists a smaller variation in the highest and the lowest value and also because the interquartile range is the smallest means that the data is spread out the least.

Answer to part B :

The school that gets the award for the highest average attendance among its students is High school A . This is because its mean and median are the highest which means that there are more kids attended school on average.

We have the expression:

We can apply logarithm to both sides. We would use it in order to get "4d+1". Then, we would apply logarithm with base c. This is beacuse of the definition of logarithm:

If we apply this to our expression, we get:

If we rearrange both sides, we get the expression in Option B (we have to switch the sides):

Answer: Option B

The probability that among these 11 people, the number passing the test is between 2 and 4 inclusive is 0.0665

What is Probability?

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.

Now

Binomial distribution of probability will be used

Here, n = 11, p = 0.63,

P(X = x) = [tex]{n\choose x} p^x(1-p)^{n-x}[/tex]

P(X= 2) = [tex]{11\choose 2} 0.63^2(1-0.63)^{11-2}[/tex]

            = 0.0028

P(X = 3) = [tex]{11\choose 3} 0.63^3(1-0.63)^{11 - 3}\\[/tex]

             = 0.0144

P(X = 4) = [tex]{11\choose 4} 0.63^4(1-0.63)^{11 - 4}\\\\[/tex]

             = 0.0493

The probability that among these 11 people, the number passing the test is between 2 and 4 inclusive =  0.0028 + 0.0144 + 0.0493

                                                = 0.0665

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From the given question

There are given that the equation:

Now,

For finding the value of a, first, add b in both sides of the equation

So,

Then,

Divide by m on both sides the above equation

Hence, the value of a is z + b.

Answer

Use the distributive property to remove the parenthesis

Now , Given

The final answer

Remember that the domain is the data set of all possibles values of x and the range is the data set of all possibles values of y

so

Looking at the graph

Domain is the interval for x

[-5,8}

All real numbers greater than or equal to -5 and less than or equal to 8

Range is the interval for y

[-3,2]

All real numbers greater than or equal to -3 and less than or equal to 2

GIVEN:

We are given the details of an investment as follows;

Initial investment = $19,400

Interest rate = 3.16%

Period of investment = 9 years and 6 months

Required;

To use the information given to calculate

(a) The maturity value at the end of the term

(b) The amount of compound interest earned.

Step-by-step solution;

The formula applied in calculating the maturity value is as follows;

Where the variables are;

However, for an investment whose interest is compounded at different intervals within 1 year, the formula becomes modified as shown below;

Where the variable n is the number of times interest is compounded annually. For an investment whose interest is compounded quarterly, that is, four times a year, the formula becomes;

We can now calculate as follows;

We can now determine the amount of compound interest earned by deducting the initial amount invested from the maturity value. Thus we have;

Therefore,

ANSWER:

As we see in the figure, BD bisects the right angle ABC and thus, we find out that ∠ABD = 60° and ∠CBD = 30°. Thus, option 1 is correct.

From the given figure, we have

∠ABD = 4x° ---- (1)

∠CBD = 2x° ---- (2)

∠ABC = 90° ---- (3)

We have to find out the values of the ∠ABD and ∠CBD.

As given in the figure, we can see that BD bisects ∠ABC into ∠ABD and ∠CBD. So, we can say that -

∠ABD + ∠CBD = ∠ABC

=> 4x° + 2x° = 90° [From equation (1), (2), (3)]

=> 6x° = 90°

=> x° = 15° ---- (4)

Substituting equation (4) in equations (1) and (2), we get

∠ABD = 4x° and ∠CBD = 2x°

=> ∠ABD = 4*15° and ∠CBD = 2*15°

=> ∠ABD = 60° and ∠CBD = 30°

Since BD bisects the right angle ABC, we find out that ∠ABD = 60° and ∠CBD = 30°. Thus, option 1 is correct.

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Weare asked to use the "point-slope" form of a line that has slope -5 and goes though the point (1, -7) on the plane.

Therefore we use the form:

y - yp = m (x - xp)

where "m" is the slope, and xp and yp are the coordinates of the point on the plane the line goes through. So in our case we have:

y - (-7) = -5 (x - 1)

now we proceed to remove parenthesis using distributive property:

y + 7 = -5 x + 5

and finally express the equation in slope-intercept form by isolating "y" on the left:

Subtract 7 from both sides and combine:

y = -5 x + 5 - 7

y = -5 x - 2

The definition of the inverse function is

In our case,

Then,

We need to verify this result using the other equality as shown below

Therefore,

The inverse function is f^-1(x)=(x+1)/2.

We say that a relation is a function if, for x in the domain of f, there is only one value of f(x).

In our case, notice that for any value of x, there is only one value of (x+1)/2=x/2+1/2.

The function is indeed a function, it is a straight line on the plane that is not parallel to the y-axis.

The inverse f^-1(x) is indeed a function

Two perpendicular lines have reciprocal and opposite slopes.

First we have to write the given line in the slope-intercept form:

Where m is the slope and b is the y-intercept.

We have this equation:

To write it in the slope-intercept form we have to clear y:

The slope is 1/4 and the y-intercept is -5.

The slope of the perpendicular line will be the opposite and reciprocal of 1/4, that's -4.

For now we have the perpendicular line's equation:

There are a lot of lines that are perpendicular to the given line, but only one that passes through (2, -5). We use this point to find the y-intercept by replacing x = 2 and y = -5 into the expression above and solving for b:

The y-intercept of the perpendicular line is 3.

The equation of a line perpendicular to the given line that passes through the point (2,-5) is

The second polynomial [tex]f(x) = (x - 3)(x+4)(x+2)^2[/tex]  has roots 3, -4 and a double root at -2.

What is root of polynomial?

The values of a variable for which the provided polynomial equals zero are referred to as a polynomial's roots. P(a) = 0 if an is the polynomial's root for x.

Since, if x is a root of the polynomial then x is a zero of the polynomial.

That means f(x) = 0

Consider, the first polynomial, [tex]f(x) = (x+3)(x-4)(x-2)^2[/tex]

plug x = 3,  [tex]f(3) = (9)(-1)(1)^2 = -9[/tex] ≠ 0

Plug x = -4, [tex]f(-4) = (-1)(-8)(36) = 368[/tex] ≠ 0

Plug x = -2, [tex]f(-2) = (1)(-6)(16) = -96[/tex] ≠ 0

Therefore, 3, -4 and -2 are not the roots of the first polynomial.

Now consider the second polynomial,  [tex]f(x) = (x-3)(x+4)(x+2)^2[/tex]

Plug x = 3,  [tex]f(3) = 0[/tex]

Plug x = -4, [tex]f(-4) = 0[/tex]

Plug x = -2, [tex]f(-2) = 0[/tex]

Therefore, x = 3, -4, -2 are the roots of the second polynomial.

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areAs given by the question

There are given that the profit function

Now,

The zeros are the x values where the graph intersects the x axis.

Then,

To find the zeroes, replace P(x) with 0 and solve for x.

Then,

The zeroes of the given function is:

Hence, the zeroes of the function is 0, 12, 5.

The volume of a sphere is given by

where V denotes the volume and r the radius. In our case,

Then, by substituting this value into the formula, we have

which gives

By taking Pi as 3.14, we get

So , by rounding to the nearest tenth, the answer is 14.1 cubic inches.

We know that the equation of the line that pass through the pair of points (3, 3) and (-5, -5) is x = y, so the slope of a paralell line is 1 and a perpendicular line is -1.

So the answe is C. 1, -1.

The Solution:

Given:

Required:

To determine the interval in which the function is decreasing.

From the given graph, the interval in which the function is decreasing is:

Therefore, the correct answer is (-2.5, 1)

A standard deck of cards consists of 52 cards with 4 aces.

The probability of getting an ace in a pack of the standard deck is;