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Which of the following tables represents a linear relationship that is also proportional?
x 2 34
y -303
O
x 4 20
y-2 -1 0
X-214
У 0 12
x012
y-404

The inequality is |x-9| ≥ 4, and its solution set is (5,13).

An Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The inequality of the form |x-a| ≥ k means that the distance between x and a is greater than or equal to a certain value, k.

If the solution set is (5,13), it means that x is a number between 5 and 13, but not including 5 or 13. In other words, 5 < x < 13.

To find the value of a and k, we need to look for the midpoint of the solution set, which is (5+13)/2 = 9.

The distance between 9 and either endpoint (5 or 13) is 4, which is the value of k.

Thus, the inequality is |x-9| ≥ 4, and its solution set is (5,13).

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a)

The total number of possible 3​-card poker hands is 22100

b)

The number of possible black flushes is 2600

c)

The probability of being dealt a black flush is 0.1176

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of cards = 52

Number of cards in hand = 3

Combination formula.

[tex]^nC_r[/tex] = n! / r! (n -r)!

a)

The total number of possible 3​-card poker hands.

= [tex]^{52}C_3[/tex]

= (52 x 51 x 50) / (3 x 2)

= 22100

b.

Number of black cards (spades and clubs) = 13 + 13 = 26

The number of possible black flushes.

= [tex]^{26}C_3[/tex]

= (26 x 25 x 24) / (3 x 2)

= 2600

c.

The probability of being dealt a black flush.

From (a) and (b)

= 2600/22100

= 0.1176

Thus,

The total number of possible 3​-card poker hands = 22100

The number of possible black flushes = 2600

The probability of being dealt a black flush = 0.1176

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Answer:

D

Step-by-step explanation: I did it

Answer:

1

Step-by-step explanation:

f(x)=x3+2x2-x-2

...................

The Roots of the given polynomials shown below f(x) = x^3+2x^2-x-2 are -1, 1, -2.

They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and nonnegative exponentiation of variables involved.

Example: x² + 3x + 3 is a polynomial.

Since, The given polynomials is,

f(x) = x³ + 2x²-x-2

Now, Solve as;

f(x) = x³ + 2x²-x-2

f (x) = x² (x + 2) - 1 (x + 2)

f (x) = (x² - 1) (x + 2)

Hence, The Roots of the polynomials : -1, 1, -2

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Answer:

Step-by-step explanation:

To put a ratio in its lowest terms, we need to divide both terms of the ratio by their greatest common divisor (GCD). The GCD of 1500 and 1200 is 300, which is the largest number that divides both numbers evenly.

Dividing both terms of the ratio by 300, we get:

1500 / 300 : 1200 / 300 = 5 : 4

So, the ratio 1500:1200 in its lowest terms is 5:4.

The required equation of the line representing line CD is y = x + 2. Option C is correct.

The equation of the line passing through two points is given by the equation,

y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)  - - - -- -(1)

Here,
Line CD passes through points (0, 2) and (4, 6)
Let (0, 2) and (4, 6) equal to (x₁, y₁) and (x₂, y₂) respectively.
Substitute this point in equation 1 to get the equation of the line representing CD,

So,
y - 2 = (6 - 2)/(4-0) (x - 0)
y = x + 2

Thus, the required equation of the line representing line CD is y = x + 2. Option C is correct.

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Answer:

29 feet by 40 feet to get a viable dimension for the goats pen

If X and Y are independent and identically distributed uniform random variables on (0, 1), then the joint density of

(a) U = X + Y, V = X/Y is u/v² for v > 1 and 0 ≤ u ≤ 1.

(b) U = X, V = X/Y is 1/v for v > 1 and 0 ≤ u ≤ 1.

(c) U = X + Y, V = X/(X+Y) is v/(1+v)² for v > 0 and v/(1+v) ≤ u ≤ 1.

In probability theory, joint density is a mathematical function that describes the probability distribution of two or more random variables. It represents the probability of occurrence of different values of those variables in a particular region of space. In this problem, we have to calculate the joint density of U and V, where U and V are functions of X and Y.

(a) For U = X + Y and V = X/Y, we can find the joint density as follows:

First, we need to find the distribution of U and V separately. Since X and Y are independent and identically distributed uniform random variables on (0, 1), their individual probability density functions are f(x) = 1 for 0 ≤ x ≤ 1.

To find the density of U, we can use the convolution formula, which states that the density of the sum of two independent random variables is the convolution of their individual densities. Thus,

fU(u) = ∫ fX(u - y)fY(y) dy

= ∫ 1 dy

= u for 0 ≤ u ≤ 1.

Next, to find the density of V, we need to transform X and Y using the change of variables formula. Let Z = X/Y, then

fV(v) = fZ(z)|dz/dv|

= fX(vz)/(z²) |z|

= 1/(v²) for v > 1.

Therefore, the joint density of U and V is given by the product of their individual densities:

fUV(u,v) = fU(u) fV(v)

= u/v² for v > 1 and 0 ≤ u ≤ 1.

(b) For U = X and V = X/Y, we can similarly find the joint density as:

fUV(u,v) = fX(u) fV(v)

= 1/v for v > 1 and 0 ≤ u ≤ 1.

(c) For U = X + Y and V = X/(X+Y), we can use the same method as in (a) to find the individual densities of U and V:

fU(u) = u for 0 ≤ u ≤ 1,

fV(v) = v/(1+v)² for v > 0.

Then, the joint density of U and V is given by:

fUV(u,v) = fU(u) fV(v) |du/dx|

= v/(1+v)² for v > 0 and v/(1+v) ≤ u ≤ 1.

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According to the given function net change and average rate of change between the given values of the variable.

A. 2

B. 2/a

A rate of change's integral is taken into account by the net change theorem. According to this, a quantity's new value equals its initial value plus the integral of its rate of change whenever it changes. There are two methods to formulate the equation. The second is more widely known and is just the definite integral.

The (definite) integral of a function's derivative, in other words, represents the overall change in a function. In specifically, the integral of velocity is the net distance travelled (final position minus initial position). The integral of acceleration is the difference between the final velocity and the starting velocity.

g(x) =2/x

x = 1

x = a

A.

g(x) =2/x

g(1) =2/x

g(1) =2

B.

g(x) =2/x

g(a) =2/x

g(a) =2/a

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Answer:

Step-by-step explanation:

Step 1: Understand the formula for the circumference of a circle

The formula for the circumference of a circle is given by:

C = 2 * π * r

where C is the circumference of the circle, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle. This formula expresses the relationship between the radius and the circumference of a circle.

Step 2: Substitute the radius of the circle for "r" in the formula

Let's say the radius of the circle is "r". Substitute "r" for "r" in the formula for the circumference:

C = 2 * π * r

Step 3: Divide the circumference by the radius

Now that you have the formula for the circumference, divide the circumference by the radius:

C/r = 2 * π

Step 4: Simplify the expression

The expression on the right side of the equation can be simplified to 2 times pi:

C/r = 2 * π

C/r = 2 * 3.14 = 6.28

Step 5: Conclusion

Therefore, it would take 6.28 radii laid end to end to fit exactly around the circumference of the circle.

Note: This answer is only an approximation, as the value of π is an irrational number that cannot be expressed exactly as a fraction or a decimal.

f(x) is discontinuous.

Since LHS ≠ RHS ≠ f(x).

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = x + 1, for x ≤ 2

f(x) = 2x - 1, for 1 < x < 2

f(x) = x - 1, for x < 1

Now,

A x = 1

LHS of f(x) = [tex]\lim_{x\to1^-}[/tex] f((h - 1)) = [tex]\lim_{h \to 0}[/tex] (h - 1 - 1) = 0 -2 = -2

RHS of f(x) = [tex]\lim_{x\to1^+}[/tex] f(h + 1) = [tex]\lim_{h \to 0}[/tex] (2(h + 1) - 1) = 2h + 2 - 1 = 0 + 1

f(1) = x + 1 = 1 + 1 = 2

We see that,

LHS ≠ RHS ≠ f(x)

So,

f(x) is not continuous, it is discontinuous.

Thus,

f(x) is discontinuous.

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The complete question.

Show that the following functions are continuous or discontinuous at x = 1.

f(x) = x + 1, for x ≤ 2

f(x) = 2x - 1, for 1 < x < 2

f(x) = x - 1, for x < 1

Answer:

Below

Step-by-step explanation:

So you have this:

4x + 16 = 35       subtract 16 from both sides of the equation

4x = 19   Divide by 4

x = 19/4

Answer:

The value of x is

[tex]x = 4.75[/tex]

Step-by-step explanation:

Greetings!!!

Thus, the value of y is given as 35, substitute known value of y in expression and solve for x.

[tex]4x + 16 = 35[/tex]

Move the constant to the right

[tex]4x = 35 - 16 \\ 4x = 19[/tex]

Divide both sides of the expression by 4

[tex] \frac{4x}{4} = \frac{19}{4} [/tex]

solve

[tex]x = \frac{19}{4} [/tex]

or

[tex]x = 4 \frac{3}{4} [/tex]

or

[tex]x = 4.75[/tex]

Hope it helps!!!

Answer:

Below

Step-by-step explanation:

Center (h,k)   is - 2, -2     radius is   1

Equation for a circle with center (h,k) and radius r    is  :

       (x-h)^2 + (y- k )^2 = r^2   <====you have to learn/remember this

 Plug in the values above to get

(x+2)^2  + (y+2)^2 = 1

Answer:

(x+2)^2+(y+2)^2=0.5625

Step-by-step explanation:

trust

Step-by-step explanation:

Here is it. I hope it will help

7 is not included and hence it is depicted on the number line using an open dot. Hence, solution to the inequality is option B.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

The given inequality is:

x + 8 > 15

Subtracting 8 on both sides of the equation:

x + 8 - 8 > 15 - 8

x > 7

Here, 7 is not included and hence it is depicted using an open dot.

Hence, option B is the correct answer.

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Answer:

35y^(10)z^(4)

Step-by-step explanation:

Solution Given:

(-5y^(4)z)(-7y^(6)z³)

Here while opening bracket

If their is like terms they can be multiplied ,divided,subtracted as well as added.

So

Here

opening bracket and keeping in serially

-5*-7*y^(4)*y^(6)*z*z^(3)

here if their is like terms their power is added.

And solving remaining one.

35y^(4+6)z^(1+3)

Here -5*-7=35

Again

Solving it.

35y^(10)z^(4)

Answer:

[tex]35y^{10}z^4[/tex]

Step-by-step explanation:

Given expression:

[tex](-5y^4z)(-7y^6z^3)[/tex]

Apply the rule:  (-a) · (-b) = ab

[tex]\implies 5y^4z \cdot 7y^6z^3[/tex]

Multiply the numbers:  5 · 7 = 35

[tex]\implies 35y^4zy^6z^3[/tex]

Collect like terms:

[tex]\implies 35y^4y^6z^3z[/tex]

[tex]\textsf{Apply exponent rule:} \quad a^b \cdot a^c=a^{b+c}[/tex]

[tex]\implies 35y^{(4+6)}z^{(3+1)}[/tex]

Simplify the exponents:

[tex]\implies 35y^{10}z^4[/tex]

It's important to work through the problems yourself to improve your understanding and problem-solving skills.

For the unit 3 homework on parallel and perpendicular lines, you should have learned about the slope of lines, how to find the slope of a line given two points, and the relationship between parallel and perpendicular lines.

To find the slope of a line given two points, you can use the slope formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.

To determine if two lines are parallel, you can compare their slopes. Parallel lines have the same slope.

To determine if two lines are perpendicular, you can use the fact that the product of their slopes is -1. That is, if m1 and m2 are the slopes of two lines, and m1 * m2 = -1, then the lines are perpendicular.

It's important to practice working through problems using these concepts and formulas to develop your skills and understanding. Additionally, you can seek assistance from your teacher or tutor if you have specific questions or concerns.

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The exact value of cosine is 4/5

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

(8,-6) be a point on the terminal side of an angle

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

Cos(angle) = x/(√x² + y²)

In this case

x = 8 and y = -6

substitute the known values in the above equation, so, we have the following representation

Cos(angle) = 8/(√8² + (-6)²)

So, we have

Cos(angle) = 8/10

Simplify

Cos(angle) = 4/5

Hence, the value is 4/5

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Answer:

12 blue chips 8 red chips.

Step-by-step explanation:

Let's call the number of blue chips "b" and the number of red chips "r". We know that 2 blue chips for every 3 red chips, so we can set up the following equation:

2b = 3r

And we know that there are 20 total chips, so:

b + r = 20

Now we can use substitution to find the value of b. We'll substitute the expression for r from the first equation:

2b = 3(20 - b)

Expanding the right side:

2b = 60 - 3b

Combining like terms:

5b = 60

And finally, solving for b:

b = 12

So there are 12 blue chips and 20 - 12 = 8 red chips.

56.7 cubic feet of acetylene gas will be needed to make 27 brackets.

What is Total price?

In order to calculate the total price of something is by using this formula. Purchase Price = Cost Price + Margin.

To find out how much gas will be needed to make 27 brackets, we need to multiply the amount of gas required for making one bracket by the number of brackets to be made.

So, the total amount of gas needed to make 27 brackets would be:

2.1 cu ft * 27 = 56.7 cu ft

Therefore, 56.7 cubic feet of acetylene gas will be needed to make 27 brackets.

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The store with the best deal is given as follows:

Store D.

The store with the best deal is obtained applying the proportions in the context of the problem.

The best deal is the store with the lowest cost per hour, and the cost per hour is obtained dividing the total cost by the number of hours.

Hence the hourly cost for each store is obtained as follows:

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Answer:

PR and SQ have the same midpoint.

Step-by-step explanation:

PR and SQ have the same midpoint.

The location of the points for quadrilateral KLMN have been plotted in the graph shown in the image attached below.

In Geometry, there are different types of quadrilateral and these include the following:

Next, we would use an online graphing calculator to construct (plot) quadrilateral KLMN on a cartesian coordinate based on the given vertices. Also, you should enter the value for each vertices of quadrilateral KLMN on the x-coordinate and y-coordinate respectively as shown in the table.

By critically observing the graph of quadrilateral QRST, we can reasonably infer and logically deduce that it represents a parallelogram.

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Answer:

R207

Step-by-step explanation:

R180 times 15% =27

27+180=207, therefore, R270 ir correct

Answer:

120

Step-by-step explanation:

The total number of medals won is 150, and the circle graph shows that the proportion of medals won as gold is 20 percent, as silver is 30 percent, and as bronze is 50 percent.

To find the number of gold and bronze medals won, we need to calculate the total number of medals won in each category by multiplying the total number of medals by the proportion of medals won in each category.

Gold medals: 150 * 20% = 30

Bronze medals: 150 * 50% = 75

So, a total of 30 + 75 = 105 medals were won as gold and bronze.

Answer:

384 cm

Step-by-step explanation:

The number of bags of sand that has to be used would be 92

diameter = 30 yards

width of path = 5 yards

diameter with path

30 + 2 * 5

= 40 Yd

area of path = area of garden with path - ara of garden

= 3.14 * 40² / 4 - 3.14 * 30² / 4

= 1256 - 706.5

= 549.5

area covered by bag = 549.5 / 6

= 91.58

= 92 bags

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On solving the provided question we can say that equations are = .60x + .85y = .75(180)

A mathematical equatiοn is a formula that joins two statements and uses the equal symbol (=) tο indicate equality. A mathematical statement that establishes the equality of twο mathematical expressiοns is known as an equation in algebra. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart.

The relationship between the twο sentences on either side of a letter is described by a mathematical formula. Often, there is οnly one variable, which also serves as the symbοl. for instance, 2x – 4 = 2.

t x = the number of ounces of Sοlution A

y = the number of ounces of Sοlution B

x + y = 180    

y = 180 - x

Solving equation -

0.60 + 0.85y = 0.75(180)

0.60 + 0.85y = 135

60x + 85y = 13500

60x + 85(180-x) = 13500

60x + 15300 - 85x = 13500

-25x = -1800

x = 72ounces

y = 180 - 72

y = 108 ounces        

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