help with number 6 please

The likelihood of  profit and loss in the following week is 18.75%. The Option D is correct.

A probability means the branch of math which deals with finding out the likelihood of the occurrence of an event. Its measures the chance of an event happening.

To get  probability of the company making a profit and then making a loss in two consecutive weeks, we need to multiply the probabilities of each event occurring.

The probability of making a profit in one week is 0.75

The probability of making a loss in the following week will be:

= 1 - 0.75

= 0.25.

So, probability of the company making a profit in one week and then making a loss in the following week is:

= 0.75 * 0.25

= 0.1875

= 18.75%.

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Answer:

3/4

Step-by-step explanation:

(75 divided by 25 / 100 divided by 25) = 3/4

Using the Pythagorean triple formula the numbers 8, 15 and 17 are Pythagorean triple and as such will form a right-angle triangle.

Pythagorean triples are x² = y² + z² where x, y and z are the three positive integers. These triples are represented as (x, y, z). Here, y is the perpendicular, z is the base and x is the hypotenuse of the right-angled triangle.

In this problem, to determine if the given numbers will form a right-angle triangle, we have to check if the numbers are Pythagorean triple.

In doing so, we would use the previous formula given as;

x² = y² + z²

In a Pythagorean triple, the largest side is the hypothenuse.

17² = 8² + 15²

289 = 64 + 225

289 = 289

The numbers are equal and they're Pythagorean triple.

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Answer:

A = 36π units²

Step-by-step explanation:

the area (A) of a circle is calculated as

A = πr² ( r is the radius )

here r = 6 , then

A = π × 6² = 36π units²

The angles that we can determine their measure are ∠1, ∠5, ∠6, and ∠7.

option A is the correct answer.

The measure of the angles of the polygon is calculated as follows;

The following angles were given;

angle 3 = 60⁰

angle 8 = 135⁰

The following angles can be determined as follows;

angle 5 = 180 - 60⁰  ( sum of angles on a straight line )

angle 5 = 120⁰

angle 7 = angle 3 = 60⁰ (corresponding angles )

angle 5 = angle 1 = 120⁰  (corresponding angles )

The value of angle 6 is calculated as;

∠5 + ∠6 + ∠7 + ∠8 = 360 (sum of angles in quadrilateral)

120 + ∠6 + 60 + 135 = 360

315 + ∠6 = 360

∠6 = 360 - 315

∠6 = 45⁰

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If two variables are directly proportional, this means that the ratio of the two variables is constant. In other words, if x and y are directly proportional, then there exists some constant k such that:

y = kx

To find the missing value in the table, we can first calculate the value of k using any set of corresponding values for x and y. For example, we can use the first row of the table:

y = kx 9 = k(-3) k = -3

Now that we know k, we can use it to find the missing value for the second row:

y = kx y = (-3)(-5) y = 15

Therefore, the missing value in the table is 15.

The coordinates of point A' are (4,1) in the given rectangle.

According to the shown figure, the coordinate of the given rectangle can be written as:

The coordinates of vertice A are (4, 3)

As we know that the x-coordinate of the reflected point will be the same as the x-coordinate of the original point.

Therefore, the x-coordinate of point A' will be:

x-coordinate of A' = 4

Here, the y-coordinate of point A is 3, which is 1 unit above the line y = 2. So, the reflection of point A across the line y = 2 will be 1 unit below the line y = 2.

So, the y-coordinate of point A' will be:

y-coordinate of A' = 2 - 1 = 1

Therefore, the coordinates of point A' are (4,1).

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The area of the figure is 183.5 ft².

We have,

The figure has two types of shapes.

Two rectangles and one triangle.

Now,

Area of rectangle = Length x Width

Area of triangle = 1/2 x base x height

Now,

Rectangle 1:

Area = 7 x 5 = 35 ft²

Rectangle 2:

Area = 4 x (4 + 5) = 4 x 9 = 36 ft²

Triangle:

Area = 1/2 x (11 + 4) x 15 = 1/2 x 15 x 15 = 112.5 ft²

Now,

The area of the figure.
= 35 + 36 + 112.5

= 183.5 ft²

Thus,

The area of the figure is 183.5 ft².

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We can conclude that cosθ = sin(90° - θ) for any right triangle with angle θ and its complementary angle (90° - θ).

To prove that cosθ = sin(90° - θ), we can use the properties of right triangles and their angles.
Consider a right triangle ABC, where angle A is θ, angle B is (90° - θ), and angle C is 90°.
According to the definition of trigonometric functions in a right triangle:
- cosθ = adjacent side (AB) / hypotenuse (AC)
- sin(90° - θ) = opposite side (AB) / hypotenuse (AC)
From the given definitions, we can see that both cosθ and sin(90° - θ) have the same ratio of side lengths, which is AB/AC.
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a.) The number of students that took the Algebra 1 for the whole three years = 672

b.) The empirical probability that Sharon will receive an A would be =0.061

For question a.)

To calculate the total number of students that took the Algebra 1 for the 3 years, the students that got the various grades are being added up. That is;

Grade A= 41

Grade B =183

Grade C =265

Grade D =96

Grade F =85

Incomplete = 2

Total = 41+183+265+96+85+2 = 672

For b.)

The probability = possible outcome/sample space

possible outcome = 41/672=0.061

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Step-by-step explanation:

7!  =  7 P 7 = 5040 ways

7 choices for first

6 choices for 2nd

5 choices for 3rd

4 chouces for 4th

3

2

1

           7 x 6 x 5 x 4 x 3 x 2 x 1 = 7!

The spread of the data is not relevant to determining which class used the most paper overall.

Mrs. Potter's class used the most paper overall based on the data displayed because it has a larger median value of 16 pieces of paper. The median value of Mr. Howard's class is 11 pieces of paper.

The spread of the data is not relevant to determining which class used the most paper overall.

Therefore, the correct answer is Mrs. Potter's class; it has a larger median value of 16 pieces of paper.

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An expression that can be used to find the volume of the figure include the following: B. (2 cm × 8 cm × 7 cm) + (1 cm × 6 cm × 8 cm).

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;

Volume of figure = (2 cm × 8 cm × 7 cm) + (1 cm × 6 cm × 8 cm)

Volume of figure = 112 cm³ + 48 cm³

Volume of figure = 160 cm³

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The location of L″ is (-5, 0).

To find the location of L″, we first need to apply the first translation rule to the coordinates of trapezoid JKLM:

J': (x, y) → (x + 3, y - 3) => J'(-2+3, 1-3) = J(1, -2)

K': (x, y) → (x + 3, y - 3) => K'(1+3, 1-3) = K(4, -2)

L': (x, y) → (x + 3, y - 3) => L'(3+3, -2-3) = L(6, -5)

M': (x, y) → (x + 3, y - 3) => M'(-4+3, 2-3) = M(-1, -1)

Now, we need to apply the second translation rule to the coordinates of J', K', L', and M':

J'': (x, y) → (x - 1, y + 1) => J''(1-1, -2+1) = J''(0, -1)

K'': (x, y) → (x - 1, y + 1) => K''(4-1, -2+1) = K''(3, -1)

L'': (x, y) → (x - 1, y + 1) => L''(6-1, -5+1) = L''(5, -4)

M'': (x, y) → (x - 1, y + 1) => M''(-1-1, -1+1) = M''(-2, 0)

Therefore, the location of L″ is (-5, 0).

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Answer:

(5,-4)

Step-by-step explanation:

a. The values of k for which points A, B, and C are collinear are k = 3 and k = -2.

b. The value of k for which AB is parallel to CD is k = 13.

a. slope AB = (k+4-9)/(k+1-0) = (k-5)/(k+1)

The slope of AC is:

slope AC = (k+3-9)/(2k-0) = (k-6)/(2k)

Since A, B, and C are collinear, slope AB = slope AC. Therefore, we have:

(k-5)/(k+1) = (k-6)/(2k)

2k(k-5) = (k+1)(k-6)

2k^2 - 10k = k² - 5k - 6

k = 3 or k = -2

(b)  The slope of AB is:

= (k+4-9)/(k+1-0) = (k-5)/(k+1)

The slope of CD is:

= (k+6-k-3)/(2k+2-2k) = 3/2

Since AB is parallel to CD, slope AB = slope CD. Therefore, we have:

(k-5)/(k+1) = 3/2

2(k-5) = 3(k+1)

k = 13

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Area of the figure is 402.8 ft².

We have,

Rectangle area = Length x Width

Area of sector = π r² x angle / 360

Now,

There are two rectangles and one sector.

So,

Area of one rectangle.

= 8 x 2

= 16 ft²

Area of another rectangle.

= 5 x 2

= 10 ft²

Area of the sector.

= π x r² x {360 - (150 + 90 + 90)}

= 3.14 x 2² x 30

= 376.8 ft²

Now,

The area of the figure.

= 16 + 10 + 376.8

= 402.8 ft²

Thus,

The area of the figure is 402.8 ft².

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The logarithmic expressions when expanded are

1. [tex]\log2^{8yz}[/tex] = 8xyz log(2)

2. [tex]\log9^{81x/y}[/tex] = 81x/y log(9)

3. [tex]\log5^{x^3}[/tex] = x³ log(5)

4. [tex]\log6^{\sqrt[3]{x}}[/tex] = ∛x log(6)

From the question, we have the following parameters that can be used in our computation:

The logarithmic expressions

The logarithmic expressions can be expanded using power rule of logarithm which states that

logaᵇ = b log(a)

Using the above as a guide, we have the following:

[tex]\log2^{8yz}[/tex] = 8xyz log(2)

[tex]\log9^{81x/y}[/tex] = 81x/y log(9)

[tex]\log5^{x^3}[/tex] = x³ log(5)

[tex]\log6^{\sqrt[3]{x}}[/tex] = ∛x log(6)

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Answer:

your answer is c=y=1/6x

Answer:

Step-by-step explanation:

You first do 190cm x 90cm then we divide each dimension by 50

190cm ÷ 50 = 3.8cm

90cm ÷ 50 = 1.8cm

So the scaled size is  3.8cm x 1.8cm

By converting the real measurements of the bed and room into a 1:50 scale, we can draw a floor plan and visualize the possibilities of where the bed can fit.

This question is about scale drawing and understanding measurements in everyday situations. Given the size of the bed (190cm x 90cm) and the scale of the plan (1:50), we first need to translate the actual measurements into the scale for the drawing.

A ratio of 1:50 means that 1cm on the drawing represents 50cm in real life. So, for the bed which is 190cm long and 90cm wide, we have to divide each value by 50. That gives us a bed representation of 3.8cm (190cm/50) by 1.8cm (90cm/50) on the drawing.

Then, we can use the same technique to draw a floor plan. With the room being 3m (300cm) long and 2.5m (250cm) wide, it translates to a drawing of 6cm (300cm/50) by 5cm (250cm/50). By comparing these dimensions, we can see different possibilities of where the bed can fit into the room on the floor plan.

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The probability of randomly choosing two boys is 0.174

If the selection is done at random, then the probability of choosing a boy is equal to the quotient between the number of boys and the total number of people.

There are 12 boys and 16 + 12 = 28 students in total, then the probability is:

P = 12/28

Now, for the second selection the probability is computed in the same way, but now there are 11 boys and 27 students (one was already choosen), then:

P = 11/27

the joint probability (for the two selections) is given by the product between the individual probabilities, we will get:

P = (12/28)*(11/27)

P = 0.174

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The measure of the angles is c = 37. 5 degrees

d = 15 + 37.5 = 52. 5 degrees

To determine the value, we need to know what complementary angles are;

Complementary angles are defined as pair of angles whose sum is equal to 90 degrees

From the information given, we have that;

Angle c and d are both complementary angles

Also, the measure of angle d is 15 degrees greater than the measure of angle c

Then, we have;

d = 15 + c

Substitute the values

c + 15 +c = 90

collect like terms

2c = 90 - 15

2c = 75

Divide both sides by the coefficient

c = 37. 5 degrees

Substitute the value for angles d

d = 15 + 37.5 = 52. 5 degrees

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1.15p is the expression which  represents Daniela's Season 3 pay in terms of p

To find Daniela's Season 3 pay in terms of p, we need to calculate the pay increase for each season.

In Season 2, her pay increases by 5 percent, which means she will receive 105 percent (or 1.05) of her Season 1 pay.

In Season 3, her pay increases by 10 percent from Season 2, so she will receive 110 percent (or 1.10) of her Season 2 pay.

To express Daniela's Season 3 pay in terms of p, we multiply the Season 1 pay (p) by the pay increase factors for Season 2 and Season 3:

Season 2 pay = 1.05p

Season 3 pay = 1.10(1.05p) = (1.10)(1.05)p

Simplifying the expression, we get:

Season 3 pay = 1.155p

Therefore, 1.15p is the expression which  represents Daniela's Season 3 pay in terms of p

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Answer: 60

Step-by-step explanation: If you subtract then you will continue to get 60

The solution of the exponential equation [tex]5^{({\frac{-x}{16})}}= 5[/tex] in terms of logarithms, or correct to four decimal places, is x ≈ -4.4431.

An exponential function is a mathematical function in the form of [tex]f(x) = a^x[/tex], where "a" is a constant and "x" is a variable. The value of the function at a particular value of "x" is found by raising "a" to the power of "x". Exponential functions are characterized by their rapid growth or decay.

We can solve for x by taking the logarithm of both sides with base 5:

[tex]5^{(\frac{-x}{16})} = 5[/tex]

[tex]log_5(5^{(\frac{-x}{16}))} = log_5(5)[/tex]

(-x/16)log₅(5) = 1

-x/16 = 1/log₅(5)

x = -16/log₅(5)

Using a calculator, we get:

x ≈ -4.4431

Therefore, the solution of the exponential equation [tex]5^{({\frac{-x}{16})}}= 5[/tex]  in terms of logarithms, or correct to four decimal places, is x ≈ -4.4431.

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The x-value on the line when y = 100 represents the estimated number of hours a student would need to study to achieve a quiz grade of 100.

We have,

Assuming that the line of best fit represents the trend between the number of hours students study and their quiz grades,

The x-value on the line when y = 100 represents the estimated number of hours a student would need to study to achieve a quiz grade of 100.

In other words,

If a student studies for this amount of time, they are predicted to achieve a quiz score of 100 based on the trend shown by the line of best fit.

Thus,

The x-value on the line when y = 100 represents the estimated number of hours a student would need to study to achieve a quiz grade of 100.

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The graph could be the graph of exponential function of option b)

[tex]F(x) = 2 • (0.5)^{x} [/tex]

The general form of an exponential function is

[tex]f(x) = {ab}^{x} [/tex]

Here, a is the function's starting value and b is its growth factor.

F(x) is an increasing function if b > 1, and if b<1, then f(x) is a decreasing function

The function's initial value is 2 as can be seen from the provided graph. Therefore, a has a value of 2.

Given that the graph indicates that the function is decreasing, b must be less than 1.

It indicates that the necessary function is in the form of

[tex]f(x) = 2(b)^{x} [/tex]

Where it is b<1

By checking option B, b=0.5<1. Hence, option B is the correct answer

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Note that the full question is:

(check the attached image)