Legs have length of 4 find the length of the hypotenuse

The equivalent of the expression 2³/2⁷ using the law of indices is (a) 1/2⁴

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

2³/2⁷

The above expression can be solved using the law of indices

When the law of indices is applied, we have the following representation

2³/2⁷ = 2(³ ⁻ ⁷)

Remove the bracket in the above expression

So, we have the following representation

2³/2⁷ = 2³ ⁻ ⁷

Evaluate the difference

This gives

2³/2⁷ = 2⁻⁴

Rewrite as

2³/2⁷ = 1/2⁴

Hence, the solution is (a) 1/2⁴

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Answer:

The line and the parabola cross at x = -4 and x = 1

Step-by-step explanation:

Set f(x) = g(x)

[tex]x-1 = (x+2)^2-9\\x - 1 = x^2+4x+4-9\\x = x^2 + 4x - 4\\0 = x^2 + 3x - 4\\Factor\\0 = (x - 1) (x + 4)\\x = 1, -4[/tex]

a) A minimum number of dogs that could have a mass of more than 24 kg is 6.

b) The maximum number of dogs that could have a mass of more than 18 kg is 20.

We will rearrange the function using fundamental algebraic concepts to process the value of x when the derivative equals 0. This response gives  us the x-coordinate of the function's vertex, which is the point that  the maximum or minimum will occur. To find the minimum or maximum, we will start by rewriting the solution into the original function.

From the given parameters, we can see that the minimum of the values present in the interval 20 to 40 is 6

From the given parameters, we can see that the maximum of the values present in the interval 20 to 40 is;

(12 + 6) = 18

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An equation for the line in slope-intercept form is y=(6/5)x+8

The same number is given for every two different points on the same line when the ratio is stated as a quotient ("rise over run"). On a falling line, there is a negative "rise." In a diagram that depicts a roof or a road as a description or a design, the line may be practical as established by a road surveyor.

The steepness, incline, or grade of a line can be approximated by the slope's absolute value. The slope of a line determines how steep it is.

From the graph,

The line passes through the points (0,8) and (5, 14)

Slope m=(14-8)/(5-0)

m=6/5

(0, 8) passes through the line y=mx+c

So, 8=6(0)/5+c

Then, c=8

An equation for the line in slope-intercept form is y=(6/5)x+8.

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Probability of winning a grand prize is 1/10

Probability of winning a basic prize is 11/20

What is the probability of two independent events?

If A and B are two independent events, then P(A and B) = P(A) * P(B).

If Events A and B are independent, the probability that either Event A or Event B occurs is: P(A or B) = P(A) + P(B) - P(A and B).

Solution:

P(A) = no. of A / total possibility

      = 4/10

P(B) = no. of 1's/total possibility

      = 3/12

     =  1/4

Now,

To win a grand prize you need an "A" and "1" .

∴ P(A and B) = P(A) × P(B)

                    = 4/10 × 1/4

         P(A and B) = 1/10

Now ,

To win a basic prize you need to spin an "A" or a "1"

∴ P(A or B) = P(A) + P(B) - P(A and B)

                  = 4/10 + 1/4 - 1/10

                  = 3/10 + 1/4

∴ P(A or B)=  11/20

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Probability of winning a grand prize is 1/10

Probability of winning a basic prize is 11/20

If A and B are two independent events, then P(A and B) = P(A) * P(B).

If Events A and B are independent, the probability that either Event A or Event B occurs is: P(A or B) = P(A) + P(B) - P(A and B).

P(A) = no. of A / total possibility

    = 4/10

P(B) = no. of 1's/total possibility

     = 3/12

    =  1/4

Now,

To win a grand prize you need an "A" and "1" .

∴ P(A and B) = P(A) × P(B)

                   = 4/10 × 1/4

        P(A and B) = 1/10

Now ,

To win a basic prize you need to spin an "A" or a "1"

∴ P(A or B) = P(A) + P(B) - P(A and B)

                 = 4/10 + 1/4 - 1/10

                 = 3/10 + 1/4

∴ P(A or B)=  11/20

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The equation of the ellipse is x²/8² + y²/(2√15)² = 1.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

Foci: (-2, 0) and (2, 0)

Length of major axis: 8

The equation of an ellipse.

x²/a² + y²/b² = 1

Where a is the major axis and b is the minor axis.

Now,

b² + c² = a²

c = 2

a = 8

b² = a² - c²

b² = 64 - 4

b² = 60

b = √60

b = √(4 x 15)

b = 2√15

Now,

x²/a² + y²/b² = 1

x²/8² + y²/(2√15)² = 1

Thus,

The ellipse equation is x²/8² + y²/(2√15)² = 1.

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The amount of diesel required to create slash burn fuel is = 112 gallons

The amount of gas required to create slash burn fuel = 28 gallons

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

Given data ,

The total amount of slash fuel = 140 gallons

The ratio of diesel to gas in slash fuel is = 8 : 2

Let the amount of diesel required to create slash burn fuel be = 8x

Let the amount of gas required to create slash burn fuel be = 2x

So , the equation of proportion is given by

Total amount of slash fuel = amount of diesel required to create slash burn fuel + amount of gas required to create slash burn fuel

Substituting the values in the equation , we get

Total amount of slash fuel = 8x + 2x

8x + 2x = 140

10x = 140

Divide by 10 on both sides of the equation , we get

x = 14 gallons

Substituting the value of x in the above expressions , we get

Amount of diesel required to create slash burn fuel = 8x

Amount of diesel required to create slash burn fuel = 8 x 14

Amount of diesel required to create slash burn fuel = 112 gallons

And ,

Amount of gas required to create slash burn fuel = 2x

Amount of gas required to create slash burn fuel = 2 x 14

Amount of gas required to create slash burn fuel = 28 gallons

Hence ,

The amount of diesel required to create slash burn fuel is = 112 gallons

The amount of gas required to create slash burn fuel = 28 gallons

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[tex] \huge{ \bold{ \color{purple}{Solution }}}[/tex]

Let a be the first term and r be the common ratio

Now,

[tex] \large{ \sf{T _3 = 4}}[/tex]

[tex] \large{ \sf{ {ar}^{2} = 4}}[/tex]

[tex]\large{ \sf{ \therefore \: product \: of \: first \: 5 \: term \: = a _1 \times a_2 \times a_3 \times a_4 \times \: a _5}}[/tex]

[tex] \large{ \sf{ = a(ar)( {ar}^{2} )( {ar}^{3} )( {ar}^{4} ) = {a}^{5} r {}^{10} }}[/tex]

[tex] \large{ \sf{ \red{(ar {}^{2} ) {}^{5} = {4}^{5} }}}[/tex]

[tex] \rule{150pt}{5pt}[/tex]

Answer:

y = 3x - 8

Step-by-step explanation:

Answer:

Making a fraction is the easiest way to do this.

The x-intercepts give solutions to a problem that equals zero.

The vertical asymptotes are values x cannot be, in a fraction the denominator can not be zero.

Horizontal asymptotes are the values y approaches. This can be accomplished by making the leading term have a coefficient of 6

Step-by-step explanation:

The equation of a line that is parallel to -x + 3y = 6 and passes through the point (3,5) is y = 1 / 3 x + 5

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the equation of a line that is parallel to -x + 3y = 6 and passes through the point (3,5) can be found as follows:

Parallel lines have the same slope.

-x + 3y = 6

3y = x + 6

y = 1  / 3 x + 2

Therefore, the slope is 1 / 3. Let's find the y-intercept using (3, 5).

y = 1 / 3 x + b

5 = 1 / 3 (3) + b

b = 5

Therefore, the equation is y = 1 / 3 x + 5

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The coordinates point C of the given line segment AC is C(0, -2) whose midpoint is at B.

To calculate the midpoint of a line segment, find the average for the coordinates of the endpoints of the line segment. I.e.,

Consider a line segment AC, B is its midpoint.

So, the coordinates of B are (Where we have A(x1, y1) and C(x2, y2))

B(x, y) = [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2})[/tex]

It is given that, B is the midpoint of a line segment AC.

Where A has coordinates as (-3, 4) and B has coordinates as (-1 1/2, 1).

So, the coordinates of the other end point C of the given line segment are calculated as

B(x, y) = [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2})[/tex]

⇒ (-1.5, 1) = [tex](\frac{-3+x2}{2}, \frac{4+y2}{2})[/tex]

⇒ -1.5 = (-3 + x2)/2 and 1 = (4 + y2)/2

⇒ -3 = -3 + x2 and 2 = 4 + y2

⇒ x2 = 0 and y2 = 2 - 4 = -2

Therefore, point C has coordinates as (0, -2).

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Answer:

[tex] 2 \sqrt[3] {60}~mm [/tex]

Step-by-step explanation:

The volume of a cube is the side cubed, so each edge is the cubic root of the volume.

V = 480 mm³

[tex] s = \sqrt[3] {V} [/tex]

[tex] s = \sqrt[3] {480~mm^3} [/tex]

[tex] s = \sqrt[3] {2^3 \times 2^2 \times 3 \times 5~mm^3} [/tex]

[tex] s = \sqrt[3] {2^3} \times \sqrt[3] {2^2 \times 3 \times 5~mm^3} [/tex]

[tex] s = 2 \sqrt[3] {60}~mm [/tex]

The greatest common factor of 40 and 24 would be; 8.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We can rewrite this expression for distribution using the amount of times 8 goes into both numbers as;

8(5 + 3)

Using the distributive property, we get:

8(5) + 8(3) = 40 + 24.

Threfore,

The greatest common factor of 40 and 24 would be; 8.

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The ratio of 27 feet to 8 yards is 9/8 while converting feet to yards and the ratio is also 9/8 while converting yards to feet.

Yards and feet are units use to measure the length of geometrical shapes.

1 foot equal to 0.333 yards and similarly 1 yard equal to 3 feet. There is proportional relationship between them.

We got the same fraction value from the ratio of two units which implies that the two units are proportional.

1 foot =0.333 yard so

27 feet = 9 yards

similarly, 1 yard = 3 feet

so, 8 yard = 24 feet

hence, the ratio is 9/8

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The inequality Fx + Wy > R written with x isolated to the left sides is

Inequality refers to a way of representing relationships between variables at the left hand side of equation to the variables to the right hand side of an equation.

The signs used in inequality are of 4 types namely

The given inequality in the problem has greater than sign and it is written as Fx + Wy > R

rearranging the inequality gives

Fx + Wy > R

Fx > R - Wy

divide through by F

Fx / F> R/F - Wy/F

x > (R - Wy) / F

isolating x to the left side gives  x > (R - Wy) / F

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The measure of angle ABC is 90° and the the measure of angle BDC is 45°.

Square ABCD is given.

A square is a quadrilateral with four equal sides. There are many objects around us that are in the shape of a square. Each square shape is identified by its equal sides and its interior angles that are equal to 90°.

Diagonals bisects the angles in square and intersect each other at right angle.

Now, ∠ABC=90°

∠AED=90°

∠BAC=45°

∠DBC=45°

∠BDC=45°

Hence, the measure of angle ABC is 90° and the the measure of angle BDC is 45°.

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Answer:

x = 3

Step-by-step explanation:

You want to solve for x, so you want to get x on one side of the equation. To do this, you can add the -12.18 to both sides of the equation (you add since it's negative).

2.14x - 12.18 = -5.76

2.14x = 6.42

Then you want to get x by itself, without the 2.14 in front of it. To do this, you can divide both sides of the equation by 2.14.

This will give you,

x = 3

In the simple random sample, the probability that at least half of the students have brown eyes is 0.400

Probability is defined as the chance of occurrence of an event.

Probability is defined as follows:

P(E)=[tex]\frac{no of required outcome}{total of possible outcomes}[/tex]

The given parameters are:

The sample size= 30 students

Number with brown eye=40%

40% x 30 = [tex]\frac{40}{100} * 30[/tex]

=12

This means that there 12 students out of 30 that have brown eyes.

Applying the probability formula

[tex]\frac{12}{30}[/tex]= 2/5

In conclusion 0.400 of the students have brown eyes.

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(a) For positive Linear Regression , Y score will be above mean .

(b) For negative Linear Regression , Y score will be below the mean .

What is Linear Regression ?

The term Linear regression analysis is used to predict the value of one  variable based on the value of another variable.

Part(a)

when the relationship of regression between two variables is positive then if one variable increase the other variable also increases ,

So , if the the x score is above the mean then the Y score will be also above the mean .

Part(b)

when the relationship of regression between two variables is negative then if one variable increase the other variable decreases ,

So , if the the x score is above the mean then the Y score will be below the mean .

Therefore , (a) Y score will be above the mean .

(b) the Y score will be below the mean .

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The equivalent expression is  2x² - 7x + 7

Option A is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example:

2 + 3x + 4y = 7 is an expression.

2x + 6 - 9 is an expression.

3x = 9 is an expression.

We have,

(3x² - 2x + 2) - (x² + 5x - 5)

Remove the parenthesis.

3x² - 2x + 2 - x² - 5x + 5

Add like terms.

2x² - 2x + 2 - 5x + 5

Add like terms

2x² - 7x + 7

Thus,

The final expression is 2x² - 7x + 7

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Answer:

On average, the football club sells 1,058,000 tickets per season.

Step-by-step explanation:

[tex]23000[/tex] × [tex]46 = 1058000[/tex]

The sample size needed is at least 311.17.

We have that to find our α level, that is the subtraction of 1 by the confidence interval divided by 2. So:

α = [tex]\frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of 1-α

So it is z with a p-value of , so

1-0.025 = 0.975, so z = 1.96

Now, find the margin of error M as such

[tex]M = z*\frac{sd}{\sqrt{n} }[/tex]

where sd = σ = standard deviation

At least n, in which N is found when M= 0.06 and σ = 0.54. So

 [tex]M = z*\frac{sd}{\sqrt{n} } \\0.06 = 1.96 * \frac{0.54}{\sqrt{n}} \\\sqrt{n} = \frac{1.96*0.54}{0.06} \\\sqrt{n} = 17.64\\n = 311.1696\\[/tex]

Rounding off to the nearest integer, we get n = 311.17.

Thus, the sample size needed is at least 311.17.

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With the mid segment of the triangle MNP as M (-1, 3), N (4, 0), P (-2, -2) the coordinates of the triangle are

The coordinates is calculated from the midsegment using the formula

X= (x₂ + x₁)/2

Y = (y₂ + y₁)/2

Vertex 1 and 2: point  M  (-1, 3),  

X

-1 = (x₂ + x₁)/2

-2 = x₂ + x₁

Y

3 = (y₂ + y₁)/2

6 = y₂ + y₁

Vertex 2 and 3:  point N (4, 0)

X

4 = (x₂ + x₃)/2

8 = x₂ + x₃

Y

0 = (y₂ + y₃)/2

0 = y₂ + y₃

Vertex 1 and 3:  point P(-2, -2)

X

-2 = (x₃ + x₁)/2

-4 = x₃ + x₁

Y

-2 = (y₃ + y₁)/2

-4 = y₃ + y₁

The equations

X

-2 = x₂ + x₁

8 = x₂ + x₃

-4 = x₃ + x₁

Y

6 = y₂ + y₁

0 = y₂ + y₃

-4 = y₃ + y₁

from -2 = x₂ + x₁, we find x₁ = -2 - x₂

plugging in x₁ = -2 - x₂ to -4 = x₃ + x₁ gives

-4 = x₃ + -2 - x₂

-2 = x₃ - x₂

then we have

8 = x₂ + x₃

-2 = x₃ - x₂

solving simultaneously

x₃ = 3, x₂ = 5 then x₁ = -2 - x₂ = -7

from 0 = y₂ + y₃, we find that y₂ = -y₃

plugging in y₂ = -y₃ into 6 = y₂ + y₁ gives

6 = -y₃ + y₁

then we have

-4 = y₃ + y₁

6 = -y₃ + y₁

solving simultaneously gives

y₁ = 1, y₃ = -5, then y₂ = -y₃ = -(-4) = 5

The vertex of the triangle are

(-7, 1), (5, 5), and (3, -5)

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Answer:

-16n-41

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

3x - 2y = 10 → (1)

2y = 3x - 16 → (2)

substitute 2y = 3x - 16 into (1)

3x - (3x - 16) = 10

3x - 3x + 16 = 10

16 = 10 ← not possible

this indicates the system has no solution.

There is no solution to this system. Therefore, option D is the correct answer.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given that the system of linear equations are

3x - 2y = 10 -------(i)

2y = 3x - 16

3x-2y=16 -------(ii)

Subtract equation (ii) from equation (i), we get

3x-2y-(3x-2y)=10-16

0≠4

Therefore, option D is the correct answer.

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Answer: $11.94

Step-by-step explanation: 4 x 0.99 = $3.96 and then 2 x $3.99 = $7.98 now $7.98 + $3.96 = $11.94

Answer:

Factorization

Step-by-step explanation: