What is the measure of MN?

The solution to the equation 8^(2x) = 4096 is x = 2.

To solve the equation 8^(2x) = 4096, we can follow the steps outlined below:

Step 1: Recognize the base

The equation involves the base 8. Since 8 can be written as 2^3, we can rewrite the equation as (2^3)^(2x) = 4096.

Step 2: Apply the power rule

Using the power rule of exponents, we can simplify the equation further. By multiplying the exponents, we have 2^(3 * 2x) = 4096.

Step 3: Simplify the equation

Continuing from Step 2, we simplify the equation to 2^(6x) = 4096.

Step 4: Write 4096 as a power of 2

Since 4096 can be expressed as 2^12, we rewrite the equation as 2^(6x) = 2^12.

Step 5: Apply the exponent rule

Equating the exponents, we get 6x = 12.

Step 6: Solve for x

Dividing both sides of the equation by 6, we find x = 2.

Therefore, the solution to the equation 8^(2x) = 4096 is x = 2.

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Answer:

£16

Step-by-step explanation:

Let's assume the normal price of the coat is represented by the variable "P."

According to the information given, the normal price of the coat is reduced by £12. This can be expressed as:

P - £12

Additionally, in the sale, normal prices are reduced by 25%. This reduction can be calculated by multiplying the normal price by 25% (or 0.25):

0.25P

To find the sale price after the 25% reduction, we subtract the reduction amount from the normal price:

P - 0.25P = £12

Simplifying the equation:

0.75P = £12

To solve for P, we divide both sides of the equation by 0.75:

P = £12 / 0.75

Performing the calculation:

P = £16

Therefore, the normal price of the coat is £16.

The solution to the systems of equations graphically is (8, -1)

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

y = -x + 7

y = 1/4x - 3

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This point is located at (8, -1)

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Question

Solve the following system of equations graphically on the set of axes below.

y = -x + 7

y = 1/4x - 3

Answer: 105 sq.ft

Step-by-step explanation:

Split the soild into 2.

3x5x(7-6) = 15ft

6x3x5= 90ft

90+15=105ft

(I think)

The solution to the inequality √3r + 5 > 1 is r > 16/3.

To solve the inequality √3r + 5 > 1, we can follow these steps:

Subtract 5 from both sides of the inequality:

√3r + 5 - 5 > 1 - 5

√3r > -4

Square both sides of the inequality to eliminate the square root:

(√3r)^2 > (-4)^2

3r > 16

Divide both sides of the inequality by 3 to solve for r:

(3r)/3 > 16/3

r > 16/3

Therefore, the solution to the inequality √3r + 5 > 1 is r > 16/3.

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The  volume of the sphere is calculated as  8,788 cm³.

The volume of the sphere is calculated using the following formulas as shown below;

V = ⁴/₃πr³

where;

The radius of the sphere is given as 13 cm

π is given as 3

The  volume of the sphere is calculated as follows;

V =  ⁴/₃πr³

V = ⁴/₃ x 3 x 13 x 13 x 13

V = 8,788 cm³

Thus, The  volume of the sphere is calculated by using the formula for volume of sphere.

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Answer:

a. geometric series

b. r_n = 100 × (0.75)^n ft

c. 400

Step-by-step explanation:

a.

Start: 100 ft

After 1 hour: 75% of 100ft = 100 ft × 0.75

After 2 hours: 75% of 100ft × 0.75 = 100 ft × 0.75²

After 3 hours: 75% of 100 ft × 0.75² = 100 ft × 0.75³

Notice what is happening to the radius as the hours pass.

With each passing hour, the radius is 0.75 times the previous radius.

Since each new term is the previous term multiplied by a constant, 0.75, this is a geometric series.

b.

At each hour, multiply 100 ft by 0.75 raised to the number of the hour.

a_n = 100 × (0.75)^n ft

The nth term is 100 times 0.75 to the nth power.

c.

The sum of all the radii is the sum of a series that has 100 as its first term, and each subsequent term is 0.75 times the previous term.

r_n = 100(0.75)^n

Since the constant ratio has an absolute value less than 1, the series has a sum.

S = a_1/(1 - r)

S = sum of infinite series

a_1 = first term

r = constant ratio

S = 100/(1 - 0.75)

S = 100/0.25

S = 400

Part A.

The probability of randomly selecting a student who is a girl that prefers the timber wolf is:

19/120

Part B.

The probability of randomly selecting a student who is not a boy that prefers the lion is:

2/3

Probability is the likelihood of a desired event happening. Mathematically:

Probability = Number of occurrence / Number of possible outcomes

Part A.

First, check the value that corresponds to girl and timber wolf in the table. The value is 19.

Also, the total number of students is 120.

Thus, probability of randomly selecting a student who is a girl that prefers the timber wolf is:

19/120

Part B.

The probability of randomly selecting a student who is not a boy that prefers the lion will be:

1 - (probability of randomly selecting a student who is a boy that prefers the lion)

1 - 40/120 = 2/3

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The monthly premium for workers' compensation insurance would be $296.6.

To calculate the monthly premium for workers' compensation insurance for the Variety Store in October, we'll need to know the workers' compensation insurance rate for that specific state and industry. This rate is typically expressed per $100 of payroll.

Let's say the rate is X dollars per $100 of payroll. To calculate the premium, we'll first divide the total payroll of $14,830 by 100. Then, we'll multiply the result by the rate X.

For example, if the rate is $2 per $100 of payroll:

1. Divide the payroll by 100: $14,830 / 100 = 148.3
2. Multiply the result by the rate: 148.3 * $2 = $296.6

Please note that this is just an illustration, and you'll need to find the specific rate for your state and industry to determine the actual premium.

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Answer:

Grapes: 7/15 pound. Cherries: 1/6 pound.

Step-by-step explanation:

The total weight of the fruits is 7/10 of a pound. The weight of the grapes is 2/3 of the total weight. Therefore, the weight of the grapes is 2/3 * 7/10 = 14/30 = 7/15 of a pound. The weight of the cherries is 7/10 - 7/15 = 1/6 of a pound.

The simplified expression of  1/(x-2)(x+3) + 3/(x+3) is (4x-3)/(x-2)(x+3).

Simplification of an algebraic expression can be defined as the process of writing an expression in the most efficient and compact form without affecting the value of the original expression.

The given expression;

1/(x-2)(x+3) + 3/(x+3)

The common denominator for (x-2)(x+3) and x+3 =  (x-2)(x+3).

Simplify with the common denominator as follows

[(1(x+3))/(x-2)(x+3)] + [(3(x-2))/(x-2)(x+3)]

[(x+3)/(x-2)(x+3)] + [(3x-6)/(x-2)(x+3)]

Simplify the expression further as follows;

[(x+3 + 3x-6)/(x-2)(x+3)]

Simplifying the numerator further as follows;

[(4x-3)/(x-2)(x+3)]

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Keegan's error is assuming that the product of the slopes of any two sides of a triangle should be -1 for the triangle to be a right triangle.

To determine if the triangle LMN is a right triangle, Keegan should instead calculate the lengths of the three sides of the triangle and check if they satisfy the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

To correct his approach, Keegan should calculate the lengths of sides LM, MN, and NL using the coordinates of the vertices and then check if the Pythagorean theorem holds true.

If the squared length of one side is equal to the sum of the squares of the other two sides, then the triangle LMN is a right triangle.

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The Area of Square is 81 cm².

let the side of the square which is length for both rectangles be a.

let the width of rectangle be x and y.

So, x+ y= a

sum of perimeters= 54

2 (a +x ) + 2 (a+ y) = 54

2a+ 2x + 2a+ 2y = 54

2a + 2a + 2(x+ y) = 54

4a + 2 (a) = 54

4a + 2a = 54

6a = 54

a= 54/6

a= 9

So, area of square

= 9 x 9

= 81 cm²

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160 packets were there of 500g .

Given,

Sack contains equal number of 250g and 500g packets of sugar

Total mass = 120 kg

Now,

Let the number of packets were x .

Equation:

250g x + 500g x = 120kg

x = 160

Thus there were 160 packets each of 250 gm and 500 gm.

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The expression which would be easier to simplify if the associative property is applied to the grouping is (2 + 5/2) + (-1/2)

The associative property is a mathematical property that states that the grouping of numbers or terms in an addition or multiplication operation does not affect the result.

The expression (2 + 5/2) + (-1/2) would be re-written as follows :

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

A. (2 + 5/2) + (-1/2) can be simplified by associating the terms inside the parentheses differently:

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

This expression allows us to simplify the fractions with equal denominator more easily.

Hence, expression which would be easier to simplify if the associative property is applied to the grouping is (2 + 5/2) + (-1/2)

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The size of the angle between AH and the plane ABCD is approximately 74.4°, rounded to one decimal place.

To find the size of the angle between AH and the plane ABCD in the given cuboid, we can use the concept of three-dimensional geometry.

First, let's consider the right triangle BCA. The given angle BCA is 48°, and we know that the length of AB is 7.3 cm. Using trigonometric functions, we can find the length of BC:

BC = AB * sin(BCA)

BC = 7.3 * sin(48°)

BC ≈ 5.429 cm

Now, let's look at the right triangle BAH. The length of AH is given as 8.1 cm. We can find the length of BH by subtracting BC from AB:

BH = AB - BC

BH ≈ 7.3 - 5.429

BH ≈ 1.871 cm

Next, let's consider the right triangle ABH. We want to find the angle BAH, which is the complement of the angle between AH and the plane ABCD. We can use the cosine function to find the angle BAH:

cos(BAH) = BH / AH

cos(BAH) ≈ 1.871 / 8.1

BAH ≈ arccos(1.871 / 8.1)

BAH ≈ 74.4°

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The actual width of the building is 24 meters.

A scale factor is the size by which a shape is enlarged or reduced. It is used in increasing or reducing the size of a shape, such as triangle, square, rectangle, etc.

We have:

scale = 1:800

That is:

scale = measured : actual

1:800 = 30 : actual

1/800 = 30/actual

actual = 30 * 800

actual = 24000 mm

Since 1000 mm = 1m

actual = 24 m

Therefore, the actual width of the building is 24 meters.

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The possible outcomes in the experiment are {H1, H2, T1, T2}

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

Coin = H and T

Spinner = 1 and 2

The possible outcomes in the experiment are calculated by taking each outcome in the coin and the spinner

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

Outcomes = {H1, H2, T1, T2}

Hence, the possible outcomes are {H1, H2, T1, T2}

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Based on the frequency table given,

a) The minimum number of dogs that could have a mass of more than 26 kg is of: 5.

b) The maximum number of dogs that could have a mass of more than 26 kg is of: 16.

The frequency table displays the number of times each value, or range of values, appears in the data-set.

where 11 weights are between 20 and 30,  and all of the dogs in the interval 20 × 30 have weights less than 26 kg, the lowest number of dogs that might have a mass more than 26 kg is 5.

This  implies that only the dogs in the period 30 x 40 would have a mass greater than 26 kg.

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Answer: The total distance covered by the car is 331 9/16 km.

Step-by-step explanation:

We know that, speed= distance/time taken

Therefore, distance = speed x time taken

= 132 5/8 x 2 1/2

= 5/2 x 1061/8

= 5305/16

= 331 9/16 km

Therefore, total distance is 331 9/16 km.

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The right response is 400%. In other words, Johnny moves at four times the pace of Jane.

We must compare the speeds of Johnny and Jane in relation to one another in order to get their ratio. According to the issue, Jane moves at a pace that is 1/4 that of Johnny. In other words, Jane moves at a speed that is one-fourth that of Johnny.

We may compare the speeds as a fraction to figure out the ratio:

Johnny's speed divided by Jane's speed equals 4/1.

This indicates that Johnny is moving at a speed that is four times that of Jane. We can express Johnny's speed as 400% of Jane's speed in percentage terms.

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The probability that at least one of the two students does not play a sport is:

(D) 88%

Probability is the likelihood of a desired event happening. Mathematically:

Probability = Number of occurrence / Number of possible outcomes

The probability that at least one of the two students does not play a sport is:

1 - (the probability that both students play a sport).

Since 35% of high school students play a sport. The probability that both students play a sport is:

0.35 * 0.35 = 0.1225.

Therefore, the probability that at least one of the two students does not play a sport is:

1 - 0.1225 = 0.8775

                = 87.75%

                ≈ 88%

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a) This data best fits an exponential model.

b) The regression equation would be:

⇒ y = 8385(1.12)ˣ

c) The y-intercept would be the starting value of the account.

d) Yes, the correlation coefficient is 0.9983.

e) If you input 6 into the equation, you will get a value of $16,550.

We have to given that,

Devin invested money into a bank account.

And, The table is the value of Devin’s investment over time.

Now, Let us assume that,

An equation is,

⇒ y = a bˣ

From table x = 2, y = 11,000

⇒ 11,000 = ab²

⇒ a = 11,000 / b²  .. (i)

Put x = 10, y = 25,000

⇒ 25,000 = ab¹⁰

Substitute the value of a in above equation,

⇒ 25,000 = 11,000b¹⁰ / b²

⇒ 25 / 11 = b⁸

⇒ b = 1.12

From (i);

⇒ a = 11,000 / b²

⇒ a = 11,000 / (1.12)²

⇒ a = 8385

Thus, The regression equation would be:

⇒ y = 8385(1.12)ˣ

For 6 years,

⇒ y = 8385 (1.12)⁶

⇒ y = $16,550

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Answer:

1000

Step-by-step explanation:

53*1000-53000 so it is correct answer

Hello!

[tex]\underline{\Large \textbf{Formula:}}\\\\\sf ~a\div~b=c\\\\b = \dfrac{a}{c} \\\\\\\underline{\Large \textbf{Application:}}\\\\ 53000~ \div~x~=~53\\\\x = \dfrac{5300}{53} \\\\x = 100\\\\\\\underline{\Large \textbf{Explanation:}}\\\\\\sf ~a\div~b=c\\\\\sf ~a\div~b~\times~b=c~\times~b\\\\a = c~\times~b\\\\a ~\div~c= c~\times~b~\div~c\\\\b = \dfrac{a}{c}\\\\\\\underline{\Large \textbf{Answer:}}\\\\\boxed{\Large \textbf{the number is 100}}[/tex]

The angle at the center of the circular pizza should be approximately 240.01° to make Neil's piece the same size as Jason's rectangular piece.

To determine the angle that should be made at the center of the circular pizza to obtain a piece the same size as Jason's rectangular piece, we need to compare the areas of the two shapes.

The area of Jason's rectangular piece is given by length times width, which is 10 cm × 15 cm = 150 cm².

The area of Neil's circular piece is given by the formula for the area of a circle, which is π times the square of the radius (A = πr²). Since the diameter is 30 cm, the radius is half of that, which is 15 cm. Thus, the area of Neil's piece is π × (15 cm)² =225π cm².

To make Neil's piece the same size as Jason's, we set up the equation:

150 cm² = 225π cm²

Now we solve for π:

π = 150 cm² / (225 cm²)

π ≈ 0.6667

To find the angle, we use the relationship between angles and the fraction of the circle's circumference they cover. Since π represents the fraction of the circumference, the angle is:

Angle = π × 360° ≈ 0.6667 × 360° ≈ 240.01°

Therefore, the angle at the center of the circular pizza should be approximately 240.01° to make Neil's piece the same size as Jason's rectangular piece.

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Hello!

x = the intersection

5x + 3 = 2x + 15

5x - 2x = 15 - 3

3x = 12

x = 12/3

x = 4

Answer: X=4

Step-by-step explanation: 5x + 3 and 2x + 15 are congruent. sub tract 3 from each side, 5x and 2x + 12 are equal. Subtract 2x from each side, 3x and 12 are equal. Divide each side by 3 and get X=4

The shape that can tessellate without leaving gaps is the hexagon (option A).

The shapes that can tessellate without leaving gaps are shapes that can be repeated to completely cover a flat surface without any overlaps or gaps. Among the options provided, the shape that will tessellate without leaving gaps is the hexagon (option A).

A hexagon is a six-sided polygon with equal sides and angles. It is a regular polygon, which means all of its sides and angles are equal. A regular hexagon can be arranged and repeated in a pattern to fill a plane without any gaps or overlaps. Bees' honeycombs are a real-world example of hexagonal tessellation.

On the other hand, octagons (option B) and pentagons (option C) do not tessellate by themselves without gaps. While they can be used in combination with other shapes to create tessellations, they cannot tessellate on their own.

A circle (option D) cannot tessellate without leaving gaps. A circle is a curved shape, and it cannot form a repeating pattern that completely covers a flat surface without overlaps or gaps.

In summary, the shape that can tessellate without leaving gaps is the hexagon (option A).

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The vertical asymptotes are at x = 3 and x = -3

To find the vertical asymptotes, we need to find the values of x such that the denominator is zero and the numerator isn't.

The denominator is:

x² - 9

It is zero when:

x² - 9 = 0

x² = 9

x = ±√9

x = ±3

Now let's evaluate the numerator there:

the numerator is:

x² + 8x + 12

When x = 3

3² + 8*3 + 12 = 45

when x = -3

(-3)² + 8*-3 + 12 = -3

So both of these are vertical asymptotes.

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None of the options A), B), C), or D) is the correct answer for this system of equations.

To find the solution to the given system of equations, we need to find the values of x and y that satisfy both equations simultaneously. We can do this by setting the two equations equal to each other and solving for x.

-1/2x - 2 = -3/2x + 2

To get rid of the fractions, we can multiply both sides of the equation by 2:

-2(x) - 4 = -3(x) + 4

Now, let's simplify the equation

-2x - 4 = -3x + 4

To isolate x, we can add 3x to both sides and add 4 to both sides:

x = 8

Now that we have the value of x, we can substitute it into either of the original equations to find the value of y. Let's use the first equation:

y = -1/2(8) - 2

y = -4 - 2

y = -6

Therefore, the solution to the system of equations is x = 8 and y = -6.

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The force of the rock as it hits the river is 17.15 N.To find the force of the rock as it hits the river, we need to use the formula F=ma (force equals mass times acceleration).

For the first part of the question, when Camille throws the rock at the tree with an acceleration of 2.45 m/s2, we can plug in the given values to get:

F = (1.75 kg) x (2.45 m/s2)
F = 4.29 N

So the force of the rock as it hits the tree is 4.29 N.

For the second part of the question, when Camille drops the rock from the bridge with an acceleration 4 times greater than her throw, we can calculate the acceleration by multiplying 2.45 m/s2 by 4, which gives us 9.8 m/s2 (the acceleration due to gravity).

Then, using the same formula, we can find the force when the rock hits the river:

F = (1.75 kg) x (9.8 m/s2)
F = 17.15 N

So the force of the rock as it hits the river is 17.15 N.

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