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The equivalent expression to the given expression [tex]2^{3x}[/tex] - 4  is equal to 8ˣ - 4.

The expression is equal to,

[tex]2^{3x}[/tex] - 4

Simplify the expression using the law of exponent we get,

yᵃᵇ = (yᵃ)ᵇ

Here  in the expression the value of y = 2,

Value of a = 3

and the value of b = x

Substitute the value in the formula we get,

= ( 2³ )ˣ - 4

value of the exponent 2³ = 2 × 2 × 2

                                          = 8

This implies the equivalent expression is,

= 8ˣ - 4

Therefore, the value of the given expression is equivalent to 8ˣ - 4.

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The tangent at any point of a circle is perpendicular to the radius through the point of contact by showing that line PQ coincides with the radius OP.

Let us assume that we have a circle with center O and radius r.

Let P be any point on the circle .

And let Q be the point of intersection of the tangent to the circle at P and the radius OP,

To prove that PQ is perpendicular to OP.

First, we observe that OP is a radius of the circle and therefore its length is r.

Since PQ is tangent to the circle at point P,

It is perpendicular to the radius drawn from the center of the circle to point P.

As the tangent to a circle is perpendicular to the radius drawn to the point of contact.

This implies, angle QOP is a right angle.

Next, triangle OPQ is a right triangle with right angle at Q.

By the Pythagorean Theorem, we have,

OP²= OQ² + PQ²

Substituting r for OP and noting that OQ = r since Q is on the radius. we have,

⇒ r² = r²+ PQ²

Subtracting r² from both sides, we get,

⇒ PQ² = 0

This implies that PQ = 0,

In other words, that point Q coincides with point P.

PQ is a line that coincides with the radius OP.

And since angle QOP is a right angle, we can conclude that PQ is perpendicular to OP.

Therefore, it is proved that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

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The above question is incomplete, the complete question is:

Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

Answer:

y = 1/2x + 5

Step-by-step explanation:

hope this helps :)

Answer:

y= 1/2x +5

Step-by-step explanation:

3x-6y=-30

-3x -3x

-6y = -3x -30

/-6 /-6 /-6

y = 1/2 +5

Answer:

(a) 15 students

(b) 3 minutes (by 4 students)

(c) 2 students

(d) 7 students

(e) Ordering this data from least to greatest:

0, 1, 2, 2, 3, 3, 3, 3, 5, 5, 7, 7, 9, 9, 11

The median number is 3.

The monthly payment required to made for the balance on credit card of $2400 with 13.5% of compound interest is given by $114.66.

Balance on credit card = $2,400

Rate of interest = 13.5%

Time period = 2 years

Let us consider monthly payment be 'M' required to pay off a balance 'B'.

Time period of time 'n' with monthly interest rate 'r' .

Use the formula of monthly compounding is ,

M = r ×  B / (1 - (1+r)⁻ⁿ )

Here, the balance is B = $2,400,

The interest rate is r = 0.135/12 = 0.01125 since the interest is compounded monthly.

And the period of time is n = 2 years ×  12 months/year

                                             = 24 months.

Plugging in these values, we get,

M = 0.01125 × $2,400 / (1 - (1+0.01125)⁻²⁴)

Simplifying this expression, we get,

⇒ m = 27 /(1 - (1.01125)⁻²⁴)

⇒ m = 27 / ( 1- 0.7645 )

⇒ m = $114.66

Therefore, the monthly payment required to pay off the $2,400 balance with compound interest in two years is $114.66.

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The situation that could represent the probability distribution table is

Considering the given probability distribution table:

X : P(X)

A = 1/10

B = 3/5

C = 3/10

Let there be 40 cards each labeled A, B, and C.

The probabilities are aclculated as follows:

Four of the cards are labeled A;

Hence, P(A) = 4/40 or 1/10

24 of the cards are labeled B;

Hence, P(B) = 24/40 or 3/5

12 of the cards are labeled C;

Hence, P(C) = 12/40 or 3/10

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Answer:

Step-byHow do I calculate the mean?

The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of value

-step explanation:

46+57+66+63+49+52+61+68= 462/8 the total number of observation

the answer 57

To calculate the number of different meals available when selecting an appetizer, an entrée, and a dessert, we need to multiply the number of choices for each course.

Using the multiplication principle of counting, we can find the total number of meal options as follows:

Total number of meal options = number of appetizer choices x number of entrée choices x number of dessert choices

Total number of meal options = 5 x 13 x 4

Total number of meal options = 260

Therefore, there are 260 different meals available when you select an appetizer, an entrée, and a dessert from the given choices.

The two numbers whose geometric mean is 5√3 is 3 and 25

Given data ,

Let the geometric mean of the numbers be A = 5√3

Now , the first number is a = 3

Let the second number be b

And , the equation for the geometric mean as:

√(b x 3) = 5√3

To solve for "b", we can square both sides of the equation

(√(b * 3))² = (5√3)²

b x 3 = 75 (since (√a)² = a)

Now, we can divide both sides of the equation by 3

b = 75 / 3

b = 25

Hence , the other number is 25

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Answer:

Step-by-step explanation:

23/40 = 0.575

75% of students of a class answered Question No. 1 correct and 55% answered Question No. 1 correct and 20% answered neither question correctly . 50 is the percentage of students who only answered one question

A percentage is a quantity or ratio that is expressed as a fraction of 100. It is symbolised by the '%' percentage sign. 'pct' or 'pc' are the acronyms used to indicate the percentage. In sense, the percentage is measured in terms of 100 and is defined as the amount of one quantity that is made up of another.

Students answer Q.1 or Q.2 or both correctly = ( 100 - 20) = 80%

x% students answered both correctly

( 75 - x) + ( 55 - x) + x = 80

130 - x = 80

x = 50

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Your question is incomplete but most probably your full question was,

75% of students of a class answered Question No. 1 correct and 55% answered Question No. 1 correct and 20% answered neither question correctly . What percent of students answered both question correctly ?

The length of the hypotenuse of the given right angled triangle is √113.

Three given side lengths of a triangle a, b and c are said to be the sides of the right angled triangle if -

a² = b² + c²

The above theorem is known as the Pythagoras theorem.

Now, we can write that -

(hypotenuse)² = (base)² + (perpendicular)²

(hypotenuse)² = (7 x 7) + (8 x 8)

(hypotenuse)² = 49 + 64

(hypotenuse)² = 113

(hypotenuse) = √113

So, the length of the hypotenuse of the given right angled triangle is √113.

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The probability of at least covering the transportation costs and additional fee is 0.9888.

To estimate the probability of at least covering the transportation costs and additional fee, we can use the binomial distribution.

The binomial distribution models the probability of success or failure in a fixed number of independent trials.

The probability of success is 0.28 (choosing a brand on premium shelf space), and we want to calculate the probability of at least 40 successes out of 200 trials (customers).

We can use the binomial probability formula to calculate this probability:

P(X ≥ 40) = 1 - P(X < 40)

Where:

P(X≥ 40) is the probability of at least 40 successes

P(X < 40) is the probability of less than 40 successes

P(X < 40) = sum of binomial probabilities for x = 0 to 39

P(X < 40) = sum [from x = 0 to 39] (200 C x) × (0.28ˣ)×(0.72²⁰⁰⁻ˣ)

P(X < 40) = 0.0112

Therefore,

P(X ≥ 40) = 1 - P(X < 40)

P(X ≥ 40) = 1 - 0.0112

P(X≥ 40) = 0.9888

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The area of each of the bottom fret markers using given dimensions is equal to 364 square millimeters.

Base of the fret marker = 45.5mm

Height of the fret marker = 8mm

Attached image.

The area of a parallelogram can be found by multiplying the base by the height.

Here, the base of each of the 3 bottom fret markers is 45.5mm and the height is 8mm.

So, the area of each fret marker is,

Area = base x height

Substitute the value of base and height we have,

⇒ Area = 45.5mm x 8mm

⇒ Area = 364 mm²

Therefore, the area of each of the 3 bottom fret markers is 364 square millimeters.

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The above question is incomplete, the complete question is:

Raymond applies the pearl guitar fret markers to his fret board as shown. Each fret marker is in the shape of a parallelogram. Each of the 3 bottom fret markers has a base that measures 45.5mm and a height of 8mm. What is the area of each of the bottom fret​ markers?

Attached image.

The equation in polar form is r^2 + 6r * cos(θ) - 2r * sin(θ) = 0

x = r * cos(θ)

y = r * sin(θ)

The given equation is:

(x + 3)² + (y - 1)² = 10

Substitute x and y with the polar coordinate expressions:

(r * cos(θ) + 3)² + (r * sin(θ) - 1)² = 10

Expand and simplify:

(r^2 * cos^2(θ) + 6r * cos(θ) + 9) + (r^2 * sin^2(θ) - 2r * sin(θ) + 1) = 10

Combine like terms:

r^2 * (cos^2(θ) + sin^2(θ)) + 6r * cos(θ) - 2r * sin(θ) + 9 + 1 - 10 = 0

Since cos^2(θ) + sin^2(θ) = 1, we can simplify further:

r^2 + 6r * cos(θ) - 2r * sin(θ) = 0

Now, the equation is in polar form:

r^2 + 6r * cos(θ) - 2r * sin(θ) = 0

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The value of x would be equal to 36.

We are given that mLDFB = (4x)°.

Since angle DFB = 144°.

So, we can say that

144 = 4x

x = 144/4

x = 36

The value of x is 36.

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Answer:

45

Step-by-step explanation:

10!/(10-2)!*2!

10!=1*2*3*4*5*6*7*8*9*10=3628800

8!=1*2*3*4*5*6*7*8=40320

2!=1*2=2

3628800/40320*2

3628800/80640=45

The length of the side of the square is given as follows:

20 cm.

In the figure, there are two expressions used to give the side length to each square, as follows:

In a square, all the four side lengths have the same length, hence the value of x is obtained as follows:

6x - 1 = 4x + 6

2x = 7

x = 3.5 cm.

Then the side length of the square is obtained as follows:

6(3.5) - 1 = 20 cm.

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JL = 4x = 12 units.

Step-by-step explanation:

Since JKLM is an isosceles trapezoid, we know that parallel sides JK and LM are congruent. Additionally, since the diagonals intersect at point R, we know that angles JRM and KRL are congruent.

To find m∠JKL, we can use the fact that the sum of the angles in a quadrilateral is 360 degrees. We know that angle LMK is 78 degrees, angle KJM is 27 degrees, and JRM and KRL are congruent. So, m∠JKL = 360 - 78 - 27 - 2x, where x is the measure of angle KRL.

To find angle KRL, we can use the fact that JRL and KRM are congruent (since they are opposite angles formed by intersecting lines). We also know that JRL + KRL = 180 degrees (since they form a linear pair). Therefore, JRL = KRL = (180 - 27 - 78) / 2 = 37.5 degrees.

Plugging this into our equation for m∠JKL, we get:

m∠JKL = 360 - 78 - 27 - 2(37.5) = 197 degrees

To find m∠KJM, we can simply use the given measure:

m∠KJM = 27 degrees

To find JL, we can use the Pythagorean theorem on right triangles JRL and KRL. We know that JRL is a 3-4-5 right triangle (since 3, 4, 5 is a Pythagorean triple), so JR = 3x and RL = 4x for some value of x. Similarly, we know that KRL is a 7-24-25 right triangle (since 7, 24, 25 is another Pythagorean triple), so KR = 7y and RL = 24y for some value of y.

Since JR = 39 and KR = 42, we can set up two equations:

3x + 24y = 39

4x + 7y = 42

Solving for x and y using any method (substitution, elimination, etc.), we get:

x = 3, y = 2

Therefore, JL = 4x = 12 units.

The solution of the differential equation is y + e²ˣ = Ceˣ, if Ceˣ > 0

or -y - e²ˣ = Ceˣ, if Ceˣ < 0.

The solution of the differential equation is calculated as follows;

dy/dx = e²ˣ + y

Apply the method of separating viables;

dy/dx = e²ˣ + y

dy/(y + e²ˣ) = dx

Integrate both sides;

∫ dy/(y + e²ˣ) = ∫ dx

ln|y + e²ˣ| = x + C

To solve for y, we need to exponentiate both sides;

|y + e²ˣ| = e^(x+C) = Ceˣ

The final solution becomes;

y + e²ˣ = Ceˣ, if Ceˣ > 0

or

-y - e²ˣ = Ceˣ, if Ceˣ < 0

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The equivalent logarithmic value of the given expression log 3  + log 6 is equal to logarithm of 18.

The expression is equal to,

log 3  + log 6

By using the law of multiplication we have,

Log A + Log B = Log ( A × B )

Using the properties of logarithms, we can simplify the expression and get the equivalent logarithm number ,

Substitute the value of A = 3 and value of B = 6 in the formula we have,

log 3 + log 6

= log (3 × 6)

= log 18

Therefore, the expression log 3 + log 6 is equivalent to the logarithm of 18.

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The value of the identities are;

sin X= 3/√34

tan Y = 3/5

Option A

To determine the value, we need to take note of the different trigonometric identities. These identities are;

From the information given, we have that;

the hypotenuse side = √34

The opposite of X is 3

the opposite of Y is 5

Using the sine identity;

Substitute the opposite and the hypotenuse in the fraction order

sin X = 3/√34

Using the tangent identity, we have;

tan Y = 3/5

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The value of the product is  -6i² + 37ij - 6j²

Algebraic expressions are simply described as expressions that are composed of coefficients, their variables, constants, terms, and factors.

Also note that algebraic expressions are expressions that consists of mathematical or arithmetic operations.

These operations are listed thus;

From the information given, we have;

Then, the product is;

vw = (6i - j)(-i + 6j)

expand the bracket

= -6i² + 36ij + ij - 6j²

add the like terms

= -6i² + 37ij - 6j²

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The length of the screen would be 182.2 meters and the width would be 30.2 meters.

Let's assume that the width of the screen is w. The length of the screen is 5 meters more than 6 times its width, which can be expressed as:

length = 6w + 5

The viewable area of the screen is given as 5,550 square meters. We know that the area of a rectangle is given by:

Solving the quadratic equation:

Therefore, the width of the screen is approximately 30.2 meters. Now, let's find the length:

length = 6w + 5 ≈ 6(30.2) + 5 ≈ 182.2

In other words, the length of the screen is approximately 182.2 meters and the width of the screen is approximately 30.2 meters.

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If 30% children travelling by bus is represented by 360 children, then total number of students who attended the school are 1200.

The "Percent" is a way of expressing a fraction or proportion as a number out of 100. It is a unit of measurement used to represent the relative size or amount of something compared to the whole.

If 30% of the children at a particular school travel by bus and this represents 360 children, we use this data to find total number of children who attend the school.

Let "X" be = total number of children at the school.

We know that 30% of X represents 360 children, so we can write an equation:

⇒ 30% of X = 360,

⇒ 30% × X = 360,

⇒ 0.3 × X = 360,            ...because 30% = 0.3,

⇒ X = 360/0.3 = 1200,

Therefore, there are 1200 students who attend the school.

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Answer: x=14 y=10

Step-by-step explanation:

The box and whisker plot that has the greatest interquartile range is option 3..

The interquartile range of a data set can be found by finding the difference of the data at the beginning and end of the edges of the rectangular box in a box and whisker plot.

It is also the difference between the third and first quartile.

The box and whisker plot in option 3 has the greatest interquartile range because the difference of the Q3 and Q1 is close to 9, which is the highest compared to the other data.

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Answer:

Therefore, you need 2600 pounds of 35% supplement and 1300 - 2600 = -1300 pounds of 10% ration.

Step-by-step explanation:

The unknown variable is x, which is the amount of 35% supplement needed. The other expressions are derived from the given information and the fact that the total amount of solution is 1300 pounds.

The equation from the fourth column is:

0.35x + 0.10(1300 - x) = 0.25(1300)

Solving for x, we get:

x = (0.25(1300) - 0.10(1300)) / (0.35 - 0.10) x = 650 / 0.25 x = 2600