Which is equivalent to 4(x - 1)?
A. X - 4
B. 4x - 1
C. 4x - 3
D. 4x - 4​

Step-by-step explanation:

31 + 6x + x + 16 = 180

7x + 47 = 180

7x = 180 - 47

x = 133/7

x = 19

Answer:

2,472

Step-by-step explanation:

Each room needs 24 new desks. To get the answer multiply the total number of rooms by the number of desks needed.

24 x 103 = 2,472

The number of hydrogen atoms present in the sculpture of earth if the mass of earth is 829 kg is 4.145 × 10²⁹.

Given that,

Mass of the sculpture of the earth = 829 kg

We know that,

Mass of an hydrogen atom = 2 × 10⁻²⁷ kg

Number of hydrogen atoms = Mass of earth / Mass of hydrogen atom

                                              = 829 / 2 × 10⁻²⁷

                                              = 414.5 × 10²⁷

                                              = 4.145 × 10²⁹

Hence the required number of atoms is 4.145 × 10²⁹.

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Out of 69 students in the art class, around 23 are expected to fail the mathematics test, assuming the probability of passing given is 2/3.

To determine how many students are likely to fail mathematics in the art class, we need to use the given probability of passing the mathematics test, which is 2/3.

First, let's find the probability of failing the mathematics test. Since passing and failing are complementary events (i.e., if the probability of passing is p, then the probability of failing is 1 - p), we can calculate the probability of failing as 1 - 2/3, which simplifies to 1/3.

Now, let's consider the art class, which has a total of 69 students. If the probability of failing mathematics is 1/3, then approximately 1/3 of the students in the art class are likely to fail the mathematics test.

To find the number of students likely to fail, we multiply the probability of failing (1/3) by the total number of students in the art class (69).

(1/3) * 69 ≈ 23

Therefore, approximately 23 students are likely to fail mathematics in the art class of 69 students based on the given probability of passing the mathematics test.

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We show that at n = 1 the basis step works, but the inductive step fails.

Let consider the Inequality

\(\frac{1}{2}\cdot\frac{3}{4}\dots\dots\frac{2n-1}{2n} < \frac{1}{\sqrt{3n}}\)

We must demonstrate that while the fundamental step of mathematical induction proves the aforementioned inequality, the inductive step does not.

Mathematical induction is a method of proof used in mathematics to prove that a statement is true for all natural numbers.

It involves proving that a statement holds true for a base case (typically zero or one), and then proving that, if it holds true for any given natural number, it must also hold true for the next natural number.

This process is repeated until the statement has been shown to be true for all natural numbers.

Basic Step: n = 1

1/2 < 1/√3, which is true.

Hence we proved that at n = 1  the basic steps of mathematical induction works.

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The complete question is:

Suppose that we want to prove that

\(\frac{1}{2}\cdot\frac{3}{4}\dots\dots\frac{2n-1}{2n} < \frac{1}{\sqrt{3n}}\)

for all positive integers n.

Show that if we try to prove this inequality using mathematical induction, the basis step works, but the inductive step fails.

Answer:

what do you mean by land ?

The intensity of sound is proportional to the square of its amplitude.

Thus, if I9 and I8 are the intensities of sounds at 9 decibels and 8 decibels respectively, then:

I9/I8 = (10^(9/10))/(10^(8/10))

I9/I8 = 10^(0.1)

I9/I8 = 1.2589

Therefore, the relative intensity of 9 decibels is approximately 1.26 times higher than that of 8 decibels.

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The vertical displacement is of 2 units down, the correct option is B.

Remember that for a function f(x), a vertical displacement of N units is written in general form as:

g(x) = f(x) + N

If N > 0, the translation is upwards.

if N < 0, the translation is downwards.

Here we assume that we start with the parent cosine function:

y = cos(x)

And the transformed function is:

y = -2 - cos(x - π)

So we have some transformations, but the vertical translation is of 2 units down. So the correct option is B.

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We have to calculate the mean, median and mode (or modes) of the data.

The size of the sample is n = 18.

We can start by sorting the data:

[1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 8]

We can calculate the mean as:

NOTE: we use the frequency of each value to save space, but we could have just add each value individually and get the same result.

We now will identify the median.

As we have an even sample size, the median will be the average between the 9th value and the 10th value.

Both values are 3, so the median is also 3.

The mode is the most frequent value in the dataset. In this case, the mode is 2, with a frequency of 5.

Both the mean and the median represent the data correctly as central measures. As the median is more robust than the mean, we can select the median as the best representation of the data.

Answer:

Mean = 3.5

Median = 3

Mode = 2

The median is a robust representation of the data.

Answer: - 21/16 = 15/16 (simplified)

= - 1.3125 convert decimal to fraction

= - 13125/10000

= - 21/16 = 15/16  (simplified)

The equation that represents a quadratic relationship is y = 4x^2. Option A.

A quadratic relationship is a mathematical relationship where the variable y is a function of the variable x raised to the power of 2. In other words, it is an equation in which the highest power of the variable is 2.

Let's analyze the given equations:

1. y = 4x^2: This equation represents a quadratic relationship because the variable x is raised to the power of 2. The term 4x^2 indicates that the relationship between x and y is quadratic.

2. y = 4x^4: This equation represents a quartic relationship, not a quadratic relationship. The variable x is raised to the power of 4, which indicates a higher degree relationship than quadratic.

3. y = 4x^3: This equation represents a cubic relationship, not a quadratic relationship. The variable x is raised to the power of 3, indicating a higher degree relationship.

4. y = 4: This equation represents a linear relationship, not a quadratic relationship. It is a constant equation where y is always equal to 4, regardless of the value of x. In a quadratic relationship, the variable x should have a power of 2. Option A.

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Answer:

david

Step-by-step explanation:

david=30000

alexia=2000

alexia make 2000

david make 30000

A table of values for g(x) has been completed below;

x            f(x)          g(x)

-2           3             8

0             1             7

1             -4             1

3            -2             3

In Mathematics and Geometry, the translation a geometric figure upward simply means adding a digit to the value on the positive y-coordinate (y-axis) of the pre-image;

g(x) = f(x) + N

Since the parent function f(x) was translated 5 units up, we have the following transformed function;

g(x) = f(x) + 5

Therefore, the table of values should be completed as follows;

x            f(x)          g(x)

-2           3             8

0             1             7

1             -4             1

3            -2             3

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Answer:

151.5 cm = 1.515 m

151.5 cm = 1515/1000 m

The range for boys is 12 and the range for girls is 6. The mean for boys is 3.7 hours and the mean for girls is 3.8 hours.

The range is the difference between the maximum and minimum values in a data set. Looking at the line plot, the maximum value for boys is 12 and the minimum value is 0. For girls, the maximum value is 8 and the minimum value is 2. Therefore, the range for boys is 12 - 0 = 12 and the range for girls is 8 - 2 = 6.

The mean is the average of a set of numbers. To find the mean, we add up all the values and divide by the total number of values. For boys, the total hours spent reading is 5 + 1 + 2 + 3 + 4 + 10 + 12 = 37. Since there are 10 boys, the mean is 37/10 = 3.7 hours. For girls, the total hours spent reading is 8 + 8 + 3 + 4 + 2 + 6 + 7 = 38. Since there are 10 girls, the mean is 38/10 = 3.8 hours.

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The complete question:

The line plot shows the results of a survey of 10 boys and 10 girls about how many hours they spent reading for pleasure the previous week. Select from the drop-down menus to complete each statement. The range ___. The mean___ . Two line plots one above the other, both are labeled from zero to twelve by ones. The top line plot is labeled Boys with four Xs over five and one X over zero, two, three, four, ten, and twelve. The bottom line plot is labeled Girls with three Xs above eight, two Xs above three and four, and one X above two, six and seven.

Answer:

1364

Step-by-step explanation:

1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364

a1+a2 = a3, a2+a3=a4 etcetera..

1+3 =4

3+4 =7

4+7=11

.

.

a13+a14 = a15

521+843 = 1364

so, 1364 is the answer

Answer: To calculate the dividends per share for preferred and common stock for each year, we need to divide the total dividends by the number of shares for each type of stock.

20Y1:

Preferred Stock: $30,000 / 15,000 shares = $2.00 per share

Common Stock: $6,000 / 50,000 shares = $0.12 per share

20Y2:

Preferred Stock: $30,000 / 15,000 shares = $2.00 per share (cumulative preferred stock means that if the company misses a dividend, they still have to pay it in the future, so the dividends per share remain the same)

Common Stock: $45,000 / 50,000 shares = $0.90 per share

20Y3:

Preferred Stock: $30,000 / 15,000 shares = $2.00 per share

Common Stock: $0 (there is no information about dividends for the common stock in 20Y3)

So, the dividends per share for each year would be:

20Y1:

Preferred Stock: $2.00 per share

Common Stock: $0.12 per share

20Y2:

Preferred Stock: $2.00 per share

Common Stock: $0.90 per share

20Y3:

Preferred Stock: $2.00 per share

Common Stock: $0.00 per share

Step-by-step explanation:

Answer:

33,44,55,66,77,88

Hope this helps!!!!!!!

Answer: It is a reflection of Reflections of You (second location) in the x-axis.

Step-by-step explanation: Based on the given information, the relationship between the new location (The Gridiron) and the previous locations can be determined.

The correct answer is:

   It is a reflection of Reflections of You (second location) in the x-axis.

The coordinates of the first three checkpoints of The Gridiron (A''(0,−5), B''(9,−5), and C''(4,−5)) indicate that they have the same y-coordinate (-5) as the corresponding checkpoints in the second location, Reflections of You. However, there is no indication of a reflection in the y-axis or any transformation related to the first location, Transformation Fitness Studios. Therefore, the correct answer is that The Gridiron is a reflection of Reflections of You in the x-axis.

Answer: 4 1/6

Step-by-step explanation:

Answer:

vv

Step-by-step explanation:

10.1(3) + 9.5(4) = 30.3 + 38.0

                        = 68.3

Answer:

9 6/7

This is the answer

Answer:

6(3+7)

Step-by-step explanation:

The factors of 18 are 1, 2, 3, 6, 9, 18.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42.

The greatest common factor is six.

To put it in distributive form, divide both by 6:

6(3+7)

Cutting squares with side length approximately 3.8 inches from each corner will result in a box with the maximum volume.

To determine the value of x that will maximize the volume of the box, we can start by visualizing the box and expressing its volume in terms of x.

When we cut out squares with side lengths x from each corner of the rectangular cardboard, the resulting shape, when folded, will form the box without a top. The height of the box will be equal to the side length of the squares, which is x. The length and width of the base of the box will be the dimensions of the cardboard after the squares are cut out, which will be (30 - 2x) and (10 - 2x) respectively.

The volume of the box can be calculated by multiplying the dimensions of the base and the height:

V(x) = (30 - 2x)(10 - 2x)x.

To find the value of x that maximizes the volume, we can take the derivative of V(x) with respect to x, set it equal to zero, and solve for x.

dV/dx = 0.

Let's calculate the derivative of V(x):

dV/dx = [(30 - 2x)(10 - 2x)]'x + (30 - 2x)(10 - 2x) * 1.

Simplifying and setting it equal to zero:

[(30 - 2x)(10 - 2x)]'x + (30 - 2x)(10 - 2x) = 0.

Solving for this;

x = 3.8 inches

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Answer:

Solving the equation \(x^2+6x-8=0\) by completing the square method we get \(\mathbf{(x+3)^2=17}\)

Option B is correct option.

Step-by-step explanation:

We need to solve the equation \(x^2+6x-8=0\) by completing the square method.

For completing the square method: we need to follow: \(a^2+2ab+b^2=(a+b)^2\)

We are given:

\(x^2+6x-8=0\)

Solving by completing the square

\(x^2+2(x)(?)+(?)^2-8=0\)

We need to find ? in our case ? is 3 because 2*3= 6 and our middle term is 6x i,e 2(x)(3)=6x.

So, adding and subtracting (3)^2

\(x^2+2(x)(3)+(3)^2-8-(3)^2=0\\(x+3)^2-8-9=0\\(x+3)^2-17=0\\(x+3)^2=17\)

So, solving the equation \(x^2+6x-8=0\) by completing the square method we get \(\mathbf{(x+3)^2=17}\)

Option B is correct option.

Answer:b

Step-by-step explanation:

Explanation:

We are told SP is parallel to RQ. So we would apply similar triangles theorem

Ratio of the corresponding sides of the triangles are equal

Ratio of the corresponding sides of small to big triangle

NS/NR = NP/NQ

NS=12, SR=78, and NP=2

NR = NS + SR

NR = 12 + 78

NR = 90

12/90 = 2/NQ

Answer:

60%

Step-by-step explanation:

21/35 = 3/5

= 0.6

=60%

The equation to find the cost of each chicken so that Tom can make $50 is option C: 4c + 5 = 50. The price at which each chicken should be sold is $11.25.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The number of chickens Tom has = 4

The amount of money Tom has = $5

The amount of money Tom wants to get = $50

Let the cost of selling each chicken be = c.

Then the cost of 4 chickens will be = 4c.

The equation to find the cost of each chicken will be -

4c + 5 = 50

Combine all the like terms -

4c = 50 - 5

4c = 45

Use the arithmetic operation of division -

c = 45/4

c = 11.25

Therefore, the cost of each chicken is $11.25.

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Answer:

yes it does

17 is the longest side.

Iff  Iff 17%5E2+=+8%5E2+%2B+15%5E2 it's a right triangle.  it's a right triangle.

Ps "iff" means if and only if

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