Which of these expressions is equivalent to log (128)?
OA. log (8) - log (12)
OB. 8 log (12)
OC. log (8) + log (12)
OD. log (8) log (12)

The statement that is true after dilation is: B. Lines FG and F'G' are parallel to each other.

The form of transformation that enlarges or reduces the size of a figure by a scale factor is referred to as Dilation. After dilation, the new figure is similar to the original. If a line is dilated by any scale factor, the new line formed is similar to the original line, which means that they must be parallel to each other.

Since lines FG and F'G' are similar, therefore, the statement that is true is: B. Lines FG and F'G' are parallel to each other.

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Answer:

B. Lines FG and F'G' are parallel to each other.

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

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Answer:

Its 7 I took the test

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There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

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Answer:

an estimate would be 2000/4 so it would be 500

Step-by-step explanation:

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Answer:

Initial temperature = 20° C

Temperature after 18 minutes = 4° C

Step-by-step explanation:

Function representing the relation in the temperature of the soda and time has been given as,

T(x) = \(-8+28e^{-0.045x}\)

Here x = number of minutes since the can was placed in the cooler

For initial temperature of the soda,

x = 0,

T(0) = \(-8+28e^{(28\times 0)}\)

      = -8 + 28(1)

      = 20° C

For the temperature after 18 minutes,

x = 18,

T(18) = \(-8+28.e^{-0.045\times 18}\)

       = \(-8+28.e^{(-0.81)}\)

       = \(-8+12.456\)

       = 4.456 C

       ≈ 4° C

Answer:

Rate of the plane in still air: 940km/h

Rate of the wind: 1440km/h

Step-by-step explanation:

We want to find the rates of travel in km/h, so we will put kilometers over hours.

Rate of plane against wind: 3760km/4hrs

3760/4 = 940

The rate of the plane against the wind is 940km/h

Rate of plane with wind: 11,520km/8hrs

11,520/8 = 1440

The rate of the plane with the wind is 1440km/h

The solution to the inequality expression 3x + 4 > 16 is x > 4

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

3x + 4 > 16

Subtract 4 from both sides of the expression

So, we have the following representation

3x > 12

Divide by 3

x > 4

Hence, the solution is x > 4

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The probability that a randomly selected point within the square falls in the red shaded square is 1/16

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event to occur is 1 and it is 100% in percentage.

Probability = sample space /total outcome

sample space is the area of the red shaded square and the total outcome is the big square.

Area of red shaded square = 1 × 1 = 1unit²

area of the big square = 4 × 4 = 16 units²

Therefore the probability that a point selected falls on the red shaded square

= 1/16

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The x-intercepts of the graph of 4x² + 25x - 21 are 3/4 and -7. the correct option is b. Three-fourths, negative 7

From the question, we are to sketch the graph of the given quadratic expression

The given quadratic expression is

4x² + 25x - 21

The graph of 4x² + 25x - 21 is shown in the image below

From the graph,

We can observe that the graph cuts the x - axis the points x = -7 and x = 3/4

∴ The x - intercepts of the given quadratic are -7 and 3/4

Hence, the x-intercepts of the graph of 4x² + 25x - 21 are 3/4 and -7. the correct option is b. Three-fourths, negative 7

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Answer:

The 96th term of the arithmetic sequence is -1234.

Step-by-step explanation:

first term (a)=1

second term (t2)=-12

common difference (d)= t2-a

d=-12-1

d=-13

96th term (t96)=?

We know that,

t96=a+(n-1)d

t96=1+(96-1)(-13)

t96=1+95(-13)

t96=1-1235

t96=-1234

The limiting reactant in the reaction between 35.2 grams of Ca(OH)₂ and 20.7 grams of H₂SO₄ is H₂SO₄. This was determined by calculating the moles of each reactant and comparing them to the stoichiometric ratio of the reaction.

To determine the limiting reactant, we need to calculate the amount of product that can be formed from each reactant.

First, let's write the balanced chemical equation for the reaction between Ca(OH)₂ and H₂SO₄

Ca(OH)₂ + H₂SO₄ → CaSO₄ + 2H₂O

Next, let's calculate the amount of product that can be formed from each reactant

For Ca(OH)₂:

Molar mass of Ca(OH)₂ = 74.09 g/mol

1 mole of Ca(OH)₂ reacts with 1 mole of H₂SO₄ to produce 1 mole of CaSO₄

Moles of Ca(OH)₂ = 35.2 g / 74.09 g/mol = 0.475 mol

Moles of H₂SO₄ = 20.7 g / 98.08 g/mol = 0.211 mol

Moles of CaSO₄ that can be formed from Ca(OH)₂ = 0.475 mol

Moles of CaSO₄ that can be formed from H₂SO₄ = 0.211 mol

For H2SO4

Molar mass of H₂SO₄ = 98.08 g/mol

Moles of CaSO₄ that can be formed from H2SO4 = 0.211 mol

Since the amount of CaSO₄ that can be formed from Ca(OH)₂ is greater than the amount that can be formed from H₂SO₄, Ca(OH)₂ is the excess reactant and H₂SO₄ is the limiting reactant.

Therefore, H₂SO₄ is the limiting reactant

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Answer:

ANSWER

Step-by-step explanation:

Without knowing the specific function w(x), it is impossible to determine the domain of the inverse function w^-1(x). However, in general, the domain of an inverse function is the range of the original function, and vice versa.

If we assume that w(x) is a one-to-one function (which is necessary for it to have an inverse function), we can determine the range of w(x) and use it to find the domain of w^-1(x).

For example, if we know that w(x) is a function that takes all real numbers except x=2, then the range of w(x) is (-∞,2) U (2,∞). The domain of w^-1(x) is then the same as the range of w(x), which is (-∞,2) U (2,∞). Therefore, the domain of w^-1(x) is x ≠ 2.

Without more information about w(x), we cannot determine the domain of w^-1(x) more precisely.

Answer: 300 ft

Step-by-step Explanation: You start by multiplying 4 by 3 to get 12 because each second is split into 3 parts. From there you just have to multiply 12 by 25 for foot per second to get 300.

The tables which shows a proportional relationship between x and y are table 3 and table 4.

Using ratio to find the proportional relationship

Table 1

x : y = 8 : 8

= 1 : 1

x : y = 12 : 10

= 6 : 5

Not proportional

Table 2:

x : y = 2 : 3

x : y = 3 : 8

Not proportional

Table 3:

x : y = 5 : 3

x : y = 10 : 6

= 5 : 3

Proportional

Table 4:

x : y = 4 : 1

x : y = 16 : 4

= 4 : 1

Proportional

Ultimately, table 3 and table 4 shoes a proportional relationship between x and y.

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The probability of rolling a total of 9 is 1/9.

The probability of rolling a total of 10 is 1/12.

The probability of rolling a total of 11 is 1/18.

We have,

To calculate the probabilities of rolling specific totals with a pair of dice, we need to consider all possible combinations of numbers on each die.

Probability of rolling a total of 9:

There are four combinations that can result in a total of 9: (3, 6), (4, 5), (5, 4), and (6, 3).

Since each die has six sides, there are 6 * 6 = 36 equally likely outcomes when rolling two dice.

The probability of rolling a total of 9 is 4/36, which can be simplified to 1/9.

Probability of rolling a total of 10:

There are three combinations that can result in a total of 10: (4, 6), (5, 5), and (6, 4).

The probability of rolling a total of 10 is 3/36, which can be simplified to 1/12.

Probability of rolling a total of 11:

There are two combinations that can result in a total of 11: (5, 6) and (6, 5).

The probability of rolling a total of 11 is 2/36, which can be simplified to 1/18.

Thus,

The probability of rolling a total of 9 is 1/9.

The probability of rolling a total of 10 is 1/12.

The probability of rolling a total of 11 is 1/18.

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Let's make y the subject of the equation.

The correct option is A

Answer:

11

Step-by-step explanation:

GIVEN

x = 6

y = 2

STEPS

(4x - 12) + (1/3xy - 5 )

(4(6) - 12 ) + ( 1/3(6x2) - 5)

(24 - 12) + ( 1/3(12) - 5)

12 + (4 - 5)

12 + (-1)

(12 - 1)

11

Answer:

As a whole, the piece first measured 38 inches. No matter how many times you cut it, all of the pieces will still add up to 38 inches. You know that 19 inches is the length of one of the two pieces, so all you need to find is the other unknown piece. Add the two together, with m being the unknown length.

19+m=38

If you want to solve the equation, just subtract 19 from both sides.

19+m=38

m=19

The median age of the 120 people seated in the first five rows of the concert was 31.

Value is an important concept in economics and business. It is the worth of goods, services, or assets that is determined by the market or by an individual. It can be measured in terms of money, time, or effort. Value is also used to describe a person’s sense of worth or importance. Values can be seen as the principles, standards, or goals that guide an individual’s actions and decisions. Ultimately, value is subjective and is held by each person and can change over time.

The box and whisker plot provided by the sponsor shows the ages of the 120 people seated in the first five rows of the concert. The box and whisker plot shows a minimum value of 18, a maximum value of 45, a median of 31, a first quartile of 24, and a third quartile of 37. This indicates that 50% of the 120 people in the first five rows had an age of 31 or below, and 50% of the 120 people had an age of 37 or above. The median age of the 120 people seated in the first five rows of the concert was 31.

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One angle measure provided (27 degrees), to determine the lengths of the sides or the measures of the other Angles.

The triangle, we need more information about the triangle, such as the lengths of the sides or the measures of other angles. The given information, "27 degrees," only specifies one angle of the triangle, but it is not sufficient to solve the triangle completely.

To solve a triangle, we typically need at least three pieces of information, which can include side lengths, angle measures, or a combination of both. With only one angle measure provided (27 degrees), we are unable to determine the lengths of the sides or the measures of the other angles.

To fully solve the triangle, we would need additional information such as the lengths of the sides or measures of at least two more angles. Without this additional information, it is not possible to provide a complete solution or determine the lengths of the sides or the measures of the other angles in the triangle.

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A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.

The symbols W and L are variables.

The symbol P is a constant.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + W)

52 = 2(12 + 14)

52 = 2(26)

52 feet = 52 feet.

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The baker's total sales is a function of the number of boxes of cookies she sells will be y = 5x.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A pastry specialist sells boxes of treats for $5 each. She has a sum of 20 boxes of treats to sell, and each crate contains 12 treats.

Let 'x' be the number of boxes of cookies and 'y' be the total cost. Then the equation is given as,

y = 5x

The baker's total sales is a function of the number of boxes of cookies she sells will be y = 5x.

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Approximately 99.7% of scores lie in the shaded region.

We have,

The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.

According to this rule:

Approximately 68% of scores lie within 1 standard deviation of the mean.

Approximately 95% of scores lie within 2 standard deviations of the mean.

Approximately 99.7% of scores lie within 3 standard deviations of the mean.

Now,

In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.

This encompasses the area within 3 standard deviations of the mean.

And,

Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.

Therefore,

Approximately 99.7% of scores lie in the shaded region.

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Answer:

There are 9 people in the class.

Step-by-step explanation:

Sean received the 5th highest grade in his class meaning that there are 4 people in front of him who got a higher grade. This also means that Sean has 4 people behind him who have lower grades. So,

4+4+1 (Sean himself) = 9 people

The number of students in the class is given by the sum of the frequency

of each score.

Reasons:

When the class scores are arranged in increasing order, we have;

Sean's position = 5 th = The fifth lowest score

Therefore;

When the scores are arranged in decreasing order, we have;

Sean's position = 5 th = Fifth highest score

Therefore;

Given that two or more students can have the same score, the frequency

of each score, determines the number of students in the class, we have;

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Answer:

Step-by-step explanation:

To determine the resistance and series inductance or capacitance for the impedance 4+j7 ohms at a frequency of 50 Hz, we can use the following equations:

Resistance (R) = Re(Z)

Series Inductance (L) = Im(Z) / (2πf)

Series Capacitance (C) = -1 / (2πfIm(Z))

where Z is the complex impedance and f is the frequency.

Given the impedance is 4+j7 ohms at 50 Hz, we have:

Resistance (R) = 4 ohms

Series Inductance (L) = Im(Z) / (2πf) = 7 / (2π×50) ≈ 0.022 Henrys

Series Capacitance (C) = -1 / (2πfIm(Z)) = -1 / (2π×50×7) ≈ -0.0018 Farads

Note that the negative sign in the formula for series capacitance arises because the imaginary part of the impedance is positive, indicating a net inductive behavior. This means that to counteract the inductive behavior and achieve a purely resistive impedance, a capacitance must be added in series.

The expression sin²x/(1+cosx) can be simplified to 1-cosθ

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Recall that sin²x = 1 - cos²x. Thus, we have:

sin²x/(1+cosx) = (1-cos²x) / (1+cosx)

                      = (1²-cos²x) / (1+cosx)

                      = (1+cosx)(1-cosx) / (1+cosx)

                      = 1-cosx

                      = 1-cosθ        (If x = θ)

Note: Using difference of two squares, 1²-cos²x = (1+cosx)(1-cosx)

Therefore, the expression sin²x/(1+cosx) can be simplified to 1-cosθ

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Answer:

(25a2c - 15a2d - 10cb + 6db)

Step-by-step explanation:

Equation at the end of step 1: (((75•(a2))•c)-((32•5a2)•d))-30cb)+18db

STEP 2:Equation at the end of step2:  ((((3•52a2) • c) -  (32•5a2d)) -  30cb) +  18db

STEP3:

STEP 4:Pulling out like terms

4.1     Pull out like factors :

  75a2c - 45a2d - 30cb + 18db  =

 3 • (25a2c - 15a2d - 10cb + 6db)

Answer:

-7.5

Step-by-step explanation:

Answer:

What value of v makes the equation 3.1v + 1 = 2.5v – 3.5 TRUE? Show your work.

Step-by-step explanation:

Answer:

Option 3

Step-by-step explanation:

\(\frac{5}{3}=\frac{AD}{7-AD} \\ \\ 35-5AD=3AD \\ \\ 35=8AD \\ \\ AD=4 \frac{3}{8}\)