If a = \(\frac{2 + \sqrt{5}}{2}\), find the value of \(a^{2} + \frac{1}{a^{2} }\).

Answer:

8 - the sum of 14 = 7=7

8 - 14 = 7+7+7= 21

Step-by-step explanation:

The probability of randomly selecting a home that has at least one of the two systems is 0.84, rounded to two decimal places.

To find the probability of randomly selecting a home that has at least one of the two systems, we can use the principle of inclusion-exclusion.

Let's denote:

P(A) = probability of a home having a security system

P(B) = probability of a home having a fire alarm system

We are given:

P(A) = 0.42 (42% of homes have a security system)

P(B) = 0.54 (54% of homes have a fire alarm system)

P(A ∩ B) = 0.12 (12% of homes have both systems)

To find the probability of at least one of the two systems, we can use the formula:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Substituting the given values:

P(A ∪ B) = 0.42 + 0.54 - 0.12

         = 0.84

Therefore, the probability of randomly selecting a home that has at least one of the two systems is 0.84, rounded to two decimal places.

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First let's make the picture of the movement of the little sister:

The green line represents the first trip and the red line represents the trip back.

Since she traveled 1000m and then came back 300m, we have that:

therefore, the little sister displaced 700 meters and she traveled 1300m

By analyzing the table we conclude that the range is the set R : [0, 7.66] so the correct option is the last one.

For a relation y = f(x), we define the range as the possible values of y.

In this case, y represents the height that the ball takes, in the table, we can see that it starts at 0, then in reaches a maximum value of 7.66, and then it decreases again until it reaches the zero again when the ball returns to the ground.

Then y can take all the values between 0 and 7.66, meaning that the range is:

R : [0, 7.66]

Then the correct option is the last one.

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9514 1404 393

Answer:

a There are n-3 diagonals from each vertex.

b The diagonals from each vertex divide the polygon into n-2 triangles.

c In a regular polygon with n sides, each angle measures (n-2)180/n degrees.

Step-by-step explanation:

You can check to see which answers are true for a 3-sided or 4-sided regular polygon (a triangle or square).

  triangle: 3 sides, 0 diagonals, 1 triangle 60-degree angles

  square: 4 sides, 1 diagonal, 2 triangles, 90-degree angles

The statements that are true for our test cases are ...

  a There are n-3 diagonals from each vertex.

  b The diagonals from each vertex divide the polygon into n-2 triangles.

  c In a regular polygon with n sides, each angle measures (n-2)180/n degrees.

Answer: The Correct answer is 8.2

Explanation: I took the K12 test and got it right

The height of the prism is 8.2 feet.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Volume is a three-dimensional measurement that's used to gauge a solid shape's capacity. It implies that the volume of a closed form determines how much space it can occupy in three dimensions.

We have,

The volume of this right prism is 266.5 ft³.

As, the formula for Volume of Trapezoidal prism is

= 1/2 ( base 1  + base 2) x height x length

So, Volume of prism

266.5 = 1/2 (5 + 8) x 5 x y

266.5 = 32.5 y

y= 8.2

Thus, the height of the prism is 8.2 feet.

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The standard deviation for the binomial distribution with n = 17 and p = 0.20 is approximately equal to 1.649.

Given a binomial distribution with n = 17 and p = 0.20, the standard deviation is 1.87.

The formula for finding the standard deviation of the binomial distribution is: σ= sqrt [npq]

Where; σ = standard deviation of the binomial distribution

n = sample size

p = probability of success

q = probability of failure = 1 - p.

Substituting the given values in the above formula, we have:

σ= sqrt [17 × 0.20 × (1 - 0.20)]

σ= sqrt [2.72]

σ = 1.649.

Therefore, the standard deviation for the binomial distribution with n = 17 and p = 0.20 is approximately equal to 1.649.

The answer is option A) 1.649.

Given a binomial distribution with n = 17 and p = 0.20, the standard deviation is 1.87.

The formula for finding the standard deviation of the binomial distribution is:σ= √[npq]

Where; σ = standard deviation of the binomial distribution

n = sample size

p = probability of success

q = probability of failure = 1 - p.

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Answer:

\((a)\ b = 8\)

\((b)\ T = 3.1\)

Step-by-step explanation:

Given

\(y = 2\sqrt x\)

See attachment

Solving (a): Find b

At point b, \(x = 16\)

So, the value of b is:

\(b = 2 * \sqrt{16\)

\(b = 2 * 4\)

\(b = 8\)

Solving (b): Find T

First, we calculate the value of y at point T

\(y = 2\sqrt x\)

At point T, \(x = 6\)

So:

\(y = 2 * \sqrt 6\)

\(y = 2 * 2.45\)

\(y = 4.9\)

To calculate T, we subtract the calculated height (y) from the value of b

\(T =b - y\)

\(T = 8 - 4.9\)

\(T = 3.1\)

The correct answer among the choices provided is A. 11.48.

Given that side XY of triangle XYZ corresponds to side JK of triangle JKL, we can set up the following proportion:

XY/JK = YZ/LJ

Substituting the given values:

8.7 / 12.18 = 7.8 / LJ

We solve this for LJ:

LJ = (7.8 * 12.18) / 8.7

Calculating that gives us:

LJ ≈ 11.48

So, the correct answer among the choices provided is A. 11.48.

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The value of the definite integral ∫(from 0 to 3) \(e^{(2x)\) dx is \((1/2)(e^6 - 1).\)

To evaluate the definite integral, you'll need to find the antiderivative of the function \(e^{(2x)\) and then apply the limits of integration (0 to 3).

The antiderivative of  \(e^{(2x)\) is \((1/2)e^{(2x)\), since the derivative of \((1/2)e^{(2x)\) with respect to x is \(e^{(2x)\). Now, you can apply the Fundamental Theorem of Calculus:

∫(from 0 to 3) \(e^{(2x)\) dx = \([(1/2)e^{(2x)]\)(from 0 to 3)

First, substitute the upper limit (3) into the antiderivative:

\((1/2)e^{(2*3)} = (1/2)e^6\)
Next, substitute the lower limit (0) into the antiderivative:

\((1/2)e^{(2*0)} = (1/2)e^0 = (1/2)\)

Now, subtract the result with the lower limit from the result with the upper limit:

\((1/2)e^6 - (1/2) = (1/2)(e^6 - 1)\)

So, the exact value of the definite integral is:

\((1/2)(e^6 - 1)\)

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Answer:

90

Step-by-step explanation:

Be sure to use PEMDAS. Begin with parentheses, the move to multiplication, then adding.

20 + 3(7 + 4) + 5 + 2(7+9)

20 + 3(11) + 5 + 2(16)

20 + 33 + 5 + 32

You can add those final four numbers in any order you want, to get a sum of 90.

Answer:

Your answer will be 90

Step-by-step explanation

First you will have to answer what's inside the parentheses

7 + 4 = 11 , 7 + 9 = 16

Then you multiply what is next to the parentheses

3×11 = 33, 2×16 = 32

Finally you will have to add

20 + 33 =53

53 + 5 =58

58 + 32 = 90

The point is doing PEMDAS

P=Parentheses

E= Exponent

M= Multiplication

D= Division

A= Addition

S= Subtraction

Answer: Slope = 3/2 or 1.5

Answer: y= 1.5 x+2 or y=3/2x+2

Step-by-step explanation:Slope (m) =

ΔY

ΔX

=

3

2

= 1.5

θ =

arctan( ΔY )

ΔX

= 56.30993247402°

ΔX = 4 – 2 = 2

ΔY = 8 – 5 = 3

Distance (d) = √ΔX2 + ΔY2 = √13 = 3.605551275464

y = 1.5x + 2

or

y =

3 x

2

+ 2

When x=0, y = 2

When y=0, x = -1.3333333333333

Answer:

2

Step-by-step explanation:

Plug in x=0

p(x)=6x^4+2x^3-x+2 at x=0

p(0)=6(0)^4+2(0)^3-(0)+2

p(0)=2

Answer:

2

Step-by-step explanation:

6×0^4+2×0^3-0+2

=0+0-0+2

=2

Answer:

Calories are transferred to flea beetle = 150 Calories

Calories are transferred to the sparrow = 15 Calories

Step-by-step explanation:

Given:

Calories in grass = 1,500 Calories

Find:

Calories are transferred to flea beetle

Calories are transferred to the sparrow

Computation:

According to food chain level only 10 % of Calorie transferred to the next level.

So,

Calories are transferred to flea beetle = 10% (Calories in grass)

Calories are transferred to flea beetle = 10% (1,500)

Calories are transferred to flea beetle = 150 Calories

Calories are transferred to the sparrow = 10% (Calories are transferred to flea beetle)

Calories are transferred to the sparrow = 10% (150)

Calories are transferred to the sparrow = 15 Calories

Answer:

60th percentile = 23.5

Step-by-step explanation:

Put numbers in order from lowest to highest:

14, 14, 14, 15, 15, 15, 16, 18, 19, 21, 23, 23, 24, 24, 25, 25, 25, 26, 29, 29

Formula:

60th percentile = 60% x Total number of elements

We have 20 scores,

60th percentile = 60% x 20

                          = 0.60 x 20

                          = 12

the 60th percentile is the 12th number on the list

14, 14, 14, 15, 15, 15, 16, 18, 19, 21, 23, 23, 24, 24, 25, 25, 25, 26, 29, 29

The 60th percentile is between 23 and 24

23 + 24 / 2 = 23.5

Step-by-step explanation:

✓44×11

=✓2²×11²

=22

!!!!????!!!!!!

Answer:

22

Step-by-step explanation:

First, multiply 11 and 44

11 × 44 = 484

\(\sqrt{484}\) = 22

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Have a great summer :)

Answer:

2a.) 8 times on blue. 2b.) 18 times on red. 2c. ) 4 times on green.

Step-by-step explanation) the answer for 8 times on blue. is yes The answer for 18 times on red. Is yes. The answer for 4 times on green. Is no

By using the change of base formula, 1.405684 is found to be the solution. Option 2 is the correct answer.

To solve the equation 3x+1 = 15 for x using the change of base formula, we need to first isolate the variable x. We can do this by subtracting 1 from both sides of the equation:

3x = 14

Then we can divide both sides by 3 to get x alone:

x = 14/3

Now we can use the change of base formula to express x in terms of logarithms. Let's use the base 10 logarithm:

log(14/3) = log(14) - log(3)

We can evaluate the logarithms using a calculator:

log(14) ≈ 1.146128

log(3) ≈ 0.477121

So we get:

log(14/3) ≈ 0.669007

Now we can use the given options to find the logarithm that is closest to 0.669007. We can do this by calculating the absolute value of the difference between each option and 0.669007, and choosing the option with the smallest absolute difference:

|log( y / b ) - 0.669007| ≈

-0.594316 : |(-0.594316) - 0.669007| ≈ 1.263323

1.405684 : |(1.405684) - 0.669007| ≈ 0.736677

1.464973 : |(1.464973) - 0.669007| ≈ 0.795966

3.469743 : |(3.469743) - 0.669007| ≈ 2.800736

Therefore, the option that is closest to 0.669007 is 1.405684. This means that:

log( y / b ) ≈ 1.405684

To find y/b, we can rewrite the equation as:

10^1.405684 ≈ y/b

Using a calculator, we get:

y/b ≈ 25.078

Therefore, the answer is approximately:

log(14/3) ≈ log(y/b) ≈ 1.405684

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Answer:

54

Step-by-step explanation:

The total displacement of the car after 5hrs is 0km.

                s =sf– si

where, s = displacement.

In the given graph, there is the change in distance covered with the time that is:

Thus, the displacement will be 0 km as the final point and initial point are the same.

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The equation of  line that passes through the points (-6,-5) and (-4,-4) is  x - 2y = 4 .

The equation of the line passing through the points (x₁,y₁) having slope as m is given by the formula .

y-y₁ = m(x-x₁)

In the question ,

it is given that

the required line passes through the points (-6,-5) and (-4,-4) ,

So , the slope(m) is = (-4 -(-5)/(-4 -(-6))

= (-4+5)/(-4+6)

= 1/2

the equation of the line passing through (-4,-4) and slope as 1/2  is

(y -(-4)) = (1/2)(x -(-4))

y + 4 = (x+4)/2

2y + 8 = x + 4

x - 2y = 8-4

x - 2y = 4

Therefore , The equation of  line that passes through the points (-6,-5) and (-4,-4) is  x - 2y = 4 .

The given question is incomplete , the complete question is

Complete the equation of  line that passes through the points (-6,-5) and (-4,-4) .

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The total distance ran by Johnny after he left the house is D = 31 miles

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as D

Now , the value of D is

Substituting the values in the equation , we get

Let the total distance ran by Johnny be D = ran 2 miles north, 6 miles west, 3 miles north, 10 miles south, 8 miles east, and then 2 miles

So , D = 2 + 6 + 3 + 10 + 8 + 2

On simplifying the equation , we get

D = 31 miles

Hence , the distance is D = 31 miles

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$11.2425 money she save on the purchase of the tires.

The basic way to calculate a discount is to multiply the original price by the decimal form of the given percentage rate. To calculate the sale price of any item, we need to subtract the discount from the original price.

Both bought 2 new tires for her race car

each tire originally cost is $74.95

she received a 15% discount

=74.95 × 15%

=74.95 × 0.15

=11.2425

$11.2425 money she save on the purchase of the tires.

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the cost of a wardrobe is approximately $850. Since the bed costs $250 more than the wardrobe, the cost of a bed would be approximately $850 + $250 = $1,100.

Let's assume the cost of a wardrobe is x dollars. Since the bed costs $250 more than the wardrobe, the cost of a bed would be x + $250.

According to the given information, the total cost of 4 beds and 3 wardrobes is $6,950. We can set up an equation to represent this:

4 * (x + $250) + 3 * x = $6,950

Simplifying the equation:

4x + $1,000 + 3x = $6,950

Combining like terms:

7x + $1,000 = $6,950

Subtracting $1,000 from both sides:

7x = $5,950

Dividing both sides by 7:

x ≈ $850

Therefore, the cost of a wardrobe is approximately $850. Since the bed costs $250 more than the wardrobe, the cost of a bed would be approximately $850 + $250 = $1,100.

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Answer:

y = 2x + 5

Step-by-step explanation:

slope = (-5 - -7) /(-1 - -2) = 2 / 1 = 2

y = mx + b

y = 2x + 5

The equation with an equivalent slope as the table is y = -2x + 5.

Here, we have,

The table shown has the following values:

X Y

-2 -7

-1 -5

0 -3

1 -1

To determine the equation with an equivalent slope, we can observe the change in y-values (vertical change) for each unit change in x-values (horizontal change).

From the table, we can see that for every unit increase in x, the y-value increases by 2.

Therefore, the slope of the table is 2.

Among the given equation options:

A. y = 3x (slope is 3)

B. y=-2/3 x (slope is -2/3)

C. y = -2/3 x +5 (slope is -2/3)

D. y= 2x + 5 (slope is 2)

Option C, y = -2x + 5, has an equivalent slope of -2, which matches the slope of the given table.

So, the equation with an equivalent slope as the table is y = -2x + 5.

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Answer:

35

Step-by-step explanation:

Well if m<YVW = (12x-1) and x=3 then just plug in x

So,

m<YVW = (12(3)-1)

m<YVW = 36-1

m<YVW = 35

Answer:

L = 52°

J = 45°

K = 83°

Step-by-step explanation:

J = L - 7

K = 2L - 21

J + K + L = 180°

∴ (L - 7) + (2L - 21) + L = 180

4L - 28 = 180

4L = 208

L = 52°

J = 52 - 7 = 45°

K = 2 x 52 - 21 = 83°

The statement (a U b) = a U b is true for all symbols a and b, regardless of the set to which they belong, which implies that the statement is true for every alphabet and every symbol that belongs to it. Consequently, the given statement is true for each alphabet and each symbol a that belongs to it.

Yes, the given statement is true for each alphabet and each symbol a that belongs to it.

Let's see why this is true:

A set is a collection of unique elements that is denoted by capital letters such as A, B, C, etc. Elements are enclosed in braces, e.g., {1, 2, 3}.

The union of two sets is a set of elements that belong to either of the two sets. A∪B reads as A union B. A union B is the combination of all the elements from sets A and B.

(A∪B) means the union of sets A and B. It consists of all the elements in set A and all the elements in set B. The elements of set A and set B are combined without any repetition.

A set is said to be a subset of another set if all its elements are present in the other set. It is denoted by ⊆. If A is a subset of B, then B ⊇ A.

The union of a set A with a set B is denoted by A U B, and it contains all elements that are in A or B, or in both. Let a be a symbol belonging to the alphabet set. The given statement is (a U b) = a U b which means the set containing a and b is the same as the set containing b and a, where a and b are elements of an arbitrary set.

Suppose a is an element of set A and b is an element of set B. Then (a U b) means the union of A and B and it contains all the elements of A and all the elements of B. The order of the elements in a set does not matter, so (a U b) = (b U a) = A U B.

The statement (a U b) = a U b is true for all symbols a and b, regardless of the set to which they belong, which implies that the statement is true for every alphabet and every symbol that belongs to it. Consequently, the given statement is true for each alphabet and each symbol a that belongs to it.

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