Original Problem:

Solve the equation for x.
5³x-2 = 125²x

a. Solve using the change of
base formula:
Log by=log y/ log b

b. Solve using a different
method.

C. Verify your solution(s) by
substituting your value back
into the original equation.

Answer:

The number of large bars of chocolate sold is:

1/4 x 208 = 52

The number of small bars of chocolate sold is:

208 - 52 = 156

The total amount of money earned from selling the large bars of chocolate is:

52 x e1 = e52

The total amount of money earned from selling the small bars of chocolate is:

156 x 60p = £93.60

To convert e52 to pounds, we need to multiply by the exchange rate. Let's assume that the exchange rate is £1 = e1.20.

So, e52 = £52 x 1.20 = £62.40

Therefore, the total amount of money earned from selling all 208 bars of chocolate is: £62.40 + £93.60 = £156

The option representing the solution of the inequality is given as follows:

D) There are no solutions.

The inequality for this problem is defined as follows:

-6x + 14 < -28 and 3x + 28 < 25.

The and operation means that we must solve each inequality, and then obtain the intersection of the two solutions.

The solution to the first inequality is given as follows:

-6x + 14 < -28

6x - 14 > 28

6x > 42

x > 7.

The solution to the second inequality is given as follows:

3x + 28 < 25.

3x < -3

x < -1.

There is no intersection between x > 7 and x < -1, hence the system has no solutions.

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The number of mice needed is given as follows:

a) 10 snakes: 23 mice.

b) 6 snakes: 15 mice.

c) x snakes: (3 + 2x) mice.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For every feeding, she needs three mice and an additional two mice for each snake, hence the slope and the intercept of the function are given as follows:

m = 2, b = 3.

The function is then defined as follows:

y = 2x + 3.

For 10 snakes, the number of mice is given as follows:

y = 2(10) + 3

y = 23 mice.

For 6 snakes, the number of mice is given as follows:

y = 2(6) + 3

y = 15 mice.

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The height of the attic in Mr. Lee's house is 6 1/3

An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.

Mr. Lee's house has two stories and an attic. Therefore:

Height of entire house = height of first floor + height of second floor + height of attic

The first floor is 9½ feet high, the second floor is 8 3/4 feet high, and the entire house is 24 7/12 feet high

9 1/2 = 19/2; 8 3/4 = 27/4; 24 7/12 = 295/12. Let x represent the height of the attic. Substituting:

x + 19/2 + 35/4 = 295/12

x = 19/3

x = 6 1/3

The height of the attic is 6 1/3

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Answer:10 or 25

Step-by-step explanation:

just add both  or times them

5+5 or 5x5

From the given data by doing unit conversion, 250 mL is approximately equal to 8.4535 fluid ounces.

Unit conversion is the process of converting a given quantity from one unit of measurement to another.

To convert milliliters (mL) to fluid ounces (fl oz), you can use the following conversion factor:

1 mL = 0.033814 fl oz

To convert, simply multiply the number of milliliters by 0.033814 to get the equivalent volume in fluid ounces.

For example, if you want to convert 250 mL to fluid ounces, you can use the conversion factor as follows:

250 mL × 0.033814 fl oz/mL = 8.4535 fl oz (rounded to four decimal places)

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Answer:

The answer is: y=4+3x

Step-by-step explanation:

I know this because I believe we are solving for the system of equations or solving by the system of subtraction.

I will say I am not completely sure this is right but I hope I helped out a little :)

Answer:

4 + 0.2 + 0.05

Step-by-step explanation:

A and B are independent events if, the probability of getting a red convertible is 0.10

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, in a video game, the probability of getting a red car is 0.25 (event A), and the probability of getting a convertible is 0.40 (event B).

We need to identify the condition for events A and event B being independent events.

We know that,

The events in probability two are independent if event one does not affect the other one.

The formula for independent events =

P(A∩B) = P(A) x P(B).

So,

P(A) = 0.25 and P(B) = 0.40

P(A∩B) = P(A)xP(B)

= 0.25 x 0.4

= 0.10

Hence, the events A and B are independent events if, the probability of getting a red convertible is 0.10

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Answer:

a ) one by forty fourth

Step-by-step explanation:

1/11 ÷ 4

= 1/11 x 1/4

= 1/44

therefore, the answer is one by forty fourth

Hope it's helpful..

Answer:

Sarah must get between a 67 and 85.

Step-by-step explanation:

69 + 75 + 65 + 83 = 292

70 ≥ 1/8(292 + 4x) ≥ 79

70 ≥ 0.5x + 36.5 ≥ 79

67 ≥ x ≥ 85

The expression [tex](3 \times 5)^4[/tex] is equivalent to 10+5 to the fourth power.

Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.

To find equivalent expressions of some expressions, we can either make it look more complex or simple. Usually, we simplify it.

We need to find the expression into an equivalent form 10+5 to the fourth power

Therefore,

This expression 10+5 to the fourth power could also be given as;

10 + 5 = 15

That is [tex]15^4[/tex]

We can also write as;

[tex](3 \times 5)^4[/tex]

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my brain is playing not smart on me right now

Applying the properties of similar triangles, the other side lengths of ΔDEF are: B. 9 and 12

The ratio of the corresponding sides two triangles that are similar to each other are the same/equal.

here, we have,

Given that ΔABC and ΔDEF are similar triangles, therefore:

Let, a = 6, b = 8, and c = 12 be the sides of ΔABC.

Let, x, y, and z be the sides of ΔDEF.

Let z = 18

Thus:

a/x = b/y = c/z

Substitute

6/x = 8/y = 12/18

Find x using 6/x = 12/18:

6/x = 12/18

Cross multiply

x = 18*6/ 12

x = 9

Find x using 8/y = 12/18:

8/y = 12/18

Cross multiply

x = 18*8/12

x = 12

Therefore, applying the properties of similar triangles, the other side lengths of ΔDEF are: B. 9 and 12

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The gopher’s new elevation relative to the surface of the ground will be

13¹/₄ inches.

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

Given that a gopher is in a hole that is 6¹/₄ in. below the surface of the ground. and, Then digs 7¹/₂ in. deeper.

The gopher’s new elevation relative to the surface of the ground will be calculated as;

⇒  6¹/₄ + 7¹/₂

⇒ 25/4 + 15/2

Make denominators the same as;

⇒ 25/4 + 30/4

⇒ (25 + 30) / 4

⇒ 55 / 4

⇒ 13¹/₄ inches.

Thus, the gopher’s new elevation relative to the surface of the ground will be 13¹/₄ inches.

The complete question is given below,

A gopher is in a hole that is 6 1/4 in. below the surface of the ground. It then digs 7 1/2 in. deeper. What is the gopher’s new elevation relative to the surface of the ground? Show your work.

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In a perfectly symmetrical distribution, the median equals the mean. This means that half of the values in the distribution fall below the mean and half fall above it. So , the correct option is C.

In a perfectly symmetrical distribution, the median equals the mean. This means that half of the values in the distribution fall below the mean and half fall above it. The mean and median are both measures of the central tendency of a distribution and in a symmetrical distribution, they are the same value.

Option (a) is false because the range is the difference between the largest and smallest values in a distribution, whereas the interquartile range is the difference between the first quartile (25th percentile) and the third quartile (75th percentile), which are measures of variability.

Option (b) is false because the interquartile range is always smaller than the mean in any distribution, symmetrical or not.

Option (d) is false because in a symmetrical distribution, the variance and standard deviation may be equal, but this is not always the case.

So , the correct option is c.

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Answer: 9/16

Step-by-step explanation: Also known as (3/4)^2

1. 3x3/4x4

2. 9/4x4

3. 9/16

You can't simplify anymore because it is in the simplest form already.

The apartment can accommodate 24 people if each person requires 5 cubic meters of air space.

Solution:

Given,

Dimension of apartment

l = 8m

b = 5m

h = 3m

So, the volume of the apartment will be,

l*b*h = 8*5*3 = 120 cubic meters

Each person requires 5 cubic meters of air space,

Hence, the total number of persons = 120/5 = 24

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The length of the segment AC is 40 units

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

The quadrilateral ABCD is a rhombus

The diagonals of rhombus bisect each other

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

AC = 2 * EC

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

AC = 2 * 20

Evaluate

AC = 40

Hence, the length is 40 uints

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The length of the shadow of the maple tree will be 15 meters.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

A shadow 30 meters long is cast by a fir tree that is 16 meters tall. If a nearby maple tree is 8 meters tall.

Let 'S' be the shadow of the maple tree. Then the equation is given as,

16 / 30 = 8 / S

0.533 = 8 / S

S = 8 / 0.533

S = 15 meters

The length of the shadow of the maple tree will be 15 meters.

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187/17 is 11, so x = 11. Substituting 11 in for x gives you 93 for the measure of angle Q and 87 for the measure of angle R.

By using the formula that connects the linear velocity to the angular velocity, we may convert metres per second (m/s) to radians per second (rad/s).

Using the formula that connects the linear velocity to the angular velocity, we may convert metres per second (m/s) to radians per second (rad/s).

The equation reads: Radius divided by linear velocity gives you the angular velocity (). (r) where R is in metres, V is in m/s, and is in rad/s.

Direct conversion from m/s to rad/s is not possible if the radius is omitted. The aforementioned formula can be used to determine the missing value and then convert m/s to rad/s if you know the radius or the angular velocity. You can use the formula to determine the angular velocity in rad/s, for instance, if you know the linear velocity v in m/s and the radius r in metres.

ω = v / r

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The value of x is 20 and the property is similar triangle

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Since ∆ ADC and IJH are similar, the ratio of their corresponding sides are equal.

Therefore,1.2/12 = 2/x

1.2x= 12×2

x = 24/1.2

x = 20

Therefore the value of x is 20

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The distance traveled by the ping-pong ball as it rolls forward 6 meters and bounces backward 3 meters is 3 meters.

Distance is a concept that is important to understand in physics and mathematics. It refers to the amount of space between two points. In this scenario, we will be discussing the distance traveled by a ping-pong ball as it rolls forward and bounces backward.

When the ping-pong ball rolls forward, it covers a distance of 6 meters. This can be represented mathematically as d1 = 6 meters.

When the ball bounces backward, it covers a distance of 3 meters. This can be represented as d2 = -3 meters which means the negative sign indicates that it is moving in the opposite direction.

The total distance traveled by the ball can be found by adding the distance traveled in each direction. This can be represented as

=> d = d1 + d2 = 6 + (-3) = 3 meters.

In other words, the total distance traveled by the ball is 3 meters, which is the net distance covered after taking into account both the forward and backward movements.

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The required complete table of heights of teachers is shown in the image attached.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
To calculate the height without heels, we need to subtract 4% of the height with heels from the height with heels. This can be done by multiplying the height with heels by 0.96 (which is equivalent to subtracting 4%):

Height without the heels = Height with the heels x 0.96

Using this formula, we can fill in the chart for each teacher.

Thus, the required complete table has been shown in the image attached.

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Answer:

B.

D.

Step-by-step explanation:

B is actually 141, not 14.1

(204 plus 98) is more than 250.7

This means that multiplying it by 8.3 would not even make it near 250.7

It would actually be 2506.6

Answer: Your answers are B and D.

Since, 01 kilogram is approximately equal to 2.2046226218 lbs.

Therefore, 65 Kilogram is 143.3 lbs.

Pound:

Pound is the name of a series of units of mass ranging from 300 to 600 grams. It refers to an avoirdupois pound (454 grams), most commonly divided by 16 avoirdupois ounces.

Kilogram:

The kilogram or kilogram (symbol: kg) is the basic unit of mass in the SI system. It is defined equal to the mass of the International Prototype in kilograms. It is the only SI base unit that uses prefixes and is still defined in terms of artifacts rather than basic physical properties. A kilogram is equivalent to £2.205 in the English system used in the United States.

According to the Question:

To find how many pounds are in kilograms, you can convert kg to pounds using this formula:

X(lb) = Y(kg) / 0.45359237

Now,

Converting 65 kg to lbs:

To convert 65 kg to pounds:

⇒ X(lbs) = 65(kg) / 0.45359237

⇒ 143.3005 lbs

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Answer:

Step-by-step explanation:

Rf values (retention factor values) are used in thin layer chromatography (TLC) to measure the separation of components in a mixture. They are calculated as follows:

Rf = (distance traveled by the solute) / (distance traveled by the solvent)

The distance traveled by the solute is measured from the origin (the spot where the sample was applied) to the final position of the solute on the TLC plate. The distance traveled by the solvent is measured from the origin to the solvent front (the point where the solvent stops moving up the plate).

It is important to note that Rf values are unique to each solute and are dependent on the solvent used, the type of TLC plate, and the conditions of the experiment (such as the temperature and humidity). To ensure accurate comparison of Rf values, it is necessary to standardize the conditions of the experiment.

Calculating Rf values is a crucial step in the interpretation of TLC data, as it allows for the identification of the components of a mixture based on the unique Rf values of each solute.

The area of the shape for the quilt block is 166.5 in²

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape

Given that, a quilt has blocks of design on it, we need to find the area of the block,

To find the area of the block = sum of the areas of the right triangle and the rectangle,

Area of the block = 16 × 9 + 6 × 7.5 × 1/2 = 166.5 in²

Hence, the area of the shape for the quilt block is 166.5 in²

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The figure is unavailable is the question is solved for the figure attached