Two students solved the same multi-step equation. Which student is correct? Explain the error. Student A Student B 2x - 4(3x + 6) = -6(2x + 1) - 4 2x - 4(3x + 6) = -6(2x + 1) - 4 2x - 12x + 6 = -12x + 1 - 4 2x - 12x - 24 = -12x - 6 - 4 -10x + 6 = -12x - 3 -10x - 24 = -12x - 10 2x = -9 2x = 14 x = -4 _1 2 x = 7

The largest rectangle that fits into the triangle with sides x=0, y=0, and x=4, y=6 has an area of 24 square units.

The coordinates of the vertices of the triangle are given by;

x=0 ⇒ (0, 0)

y=0 ⇒ (0, 0)

x=4 ⇒ (4, 0)

y=6 ⇒ (0, 6)

The base of the rectangle will be parallel to the x-axis and the height of the rectangle will be parallel to the y-axis. The vertices will lie along the sides of the triangle with lengths 4 and 6.

The area of the largest rectangle is base × height

where;

base (b) = 4

height (h) = 6

By substituting the values of (b) and (h) in the equation, we get;

Area of the rectangle = 4 × 6

⇒ 24 square units.

Therefore, the largest rectangle that fits into the given triangle has an area of 24 sq. units.

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Given:

There are between 24 and 40 students in a class.

The ratio of boys to girls is 4:7

To find:

The number of students in the class.

Solution:

Let the number of boys are girls are 4x and 7x respectively, where, x must be a positive integer because number of boys and girls is always a positive integer. Then, the total number of students is

\(\text{Total students}=4x+7x\)

\(\text{Total students}=11x\)

It means total number of students is multiply of 11.

Multiples of 11 are 11, 22, 33, 44, ... . So, multiples of 11 between 24 and 40 is 33.

Therefore, the total number of students in the class is 33.

Answer:

\(12w^7 z^6\)

Step-by-step explanation:

\(2w^5 z(6w^2 z^5)=(2)(6)w^5 w^2 z^5 z=12w^7 z^6\)

The case fatality rate is 400 * 100 / 1500 = 26.67 (option d).

For the first scenario, the data determine that there is a difference in average expenditure between the two countries (option c). The P-value of 0.063 suggests that there is a moderate level of statistical significance, indicating that the difference in average expenditure is likely not due to random chance.

In the second scenario, the fact that the 95% confidence interval for the average number of times participants saw their provider per year (3.3) ranges from 0.1 to 6.1 is of statistical use because it provides a range estimate within which the true population means is likely to fall. This interval helps account for the uncertainty associated with the sample estimate and provides a measure of the precision of the estimate (option a).

For the third scenario, the average operating margin is appropriate to use because it is a measure of central tendency that represents the typical financial performance of rural hospitals. The standard deviation provides information about the variability of the operating margins (option d).

In the fourth scenario, the consideration factor that will ultimately contribute to the spread of Ebola is the population density of the affected area (option b). While factors like the influence of non-indigenous people and climatic conditions may play a role, population density is a key determinant in the transmission and spread of infectious diseases.

For the fifth scenario, the case fatality rate is calculated by dividing the number of deaths from the disease (400) by the total reported cases (1500) and multiplying by 100. Therefore, the correct calculation is 400 * 100 / 1500 = 26.67 (option d). This indicates that the case fatality rate is approximately 26.67%.

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Answer: 13.8 m

Step-by-step explanation:

Given

From point A, angle of elevation is \(19^{\circ}\)

From point B which is 18 m closer, it changes to \(32^{\circ}\)

Suppose the height of tree is h

From figure, we can write

\(\Rightarrow \tan 32=\dfrac{h}{x}\\\\\Rightarrow h=x\tan 32^{\circ}\)

Similarly

\(\Rightarrow \tan19^{\circ}=\dfrac{h}{x+18}\\\\\Rightarrow h=(x+18)\tan 19^{\circ}\\\text{Substitute the value of h}\\\Rightarrow x\tan 32^{\circ}=x\tan 19^{\circ}+18\tan 19^{\circ}\\\Rightarrow x(\tan32^{\circ}-\tan 19^{\circ})=18\tan 19^{\circ}\\\\\Rightarrow x=\dfrac{18\tan 19^{\circ}}{\tan32^{\circ}-\tan 19^{\circ}}\\\\\Rightarrow x=22.09\approx 22.1\ m\)

Deduce the value of h

\(\Rightarrow h=22.092\times \tan 32^{\circ}\\\Rightarrow h=13.8\ m\)

Thus, the height of the tree is 13.8 m

The probability that the team will win the sport is 77%.

Given that an area kicker in pro football incorporates a 77% probability of creating a field goal over 40 yards and every attempt field goal is independent.

Probability is how something is likely to happen. The probability of a happening is calculated by the probability formula by simply dividing the favorable number of outcomes by the overall number of possible outcomes.

So, his team will win the sport if he makes a goal otherwise loses.

Therefore, the Probability that his team will win the sport P[E] =P[making a field goal]

P[E]=77%

Hence, the probability that the team will win the sport when making a field goal is 77%.

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Answer:

Step-by-step explanation:

x = 8  ; y = 5/3

\(3z = \dfrac{5}{3}\)

\(\dfrac{1}{4}[x(2y+3z)] =\dfrac{1}{4}[8*(2*\dfrac{5}{3}+\dfrac{5}{3})]\\\\=\dfrac{1}{4}(8*(\dfrac{10}{3}+\dfrac{5}{3})]\\\\=\dfrac{1}{4}(8*\dfrac{15}{3})\\\\=\dfrac{1}{4}*8*5\\\\=2*5\\\\=10\)

The radius of the circle can be found by taking the square root of the area, which is 483.1 square units. The radius of the circle would be approximately 12.4 units, rounded to the nearest tenth.

The area of a circle is calculated by multiplying pi (π) with the radius of the circle squared. In this case, the area of the circle is 483.1 square units. To find the radius of the circle, we need to take the square root of the area. The square root of 483.1 is approximately 21.9, which can be rounded up to 22. To get the radius to the nearest tenth, we need to divide 22 by 2. This gives us a radius of 11. We then round this up to 12.4, which is the radius of the circle to the nearest tenth. Therefore, the radius of the circle with an area of 483.1 square units is 12.4 to the nearest tenth.

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Answer:

25 grams

Step-by-step explanation:

To determine whether the sequence {an} = 5n/4n + 1 is convergent or divergent, we can analyze its behavior as n approaches infinity.

First, let's rewrite the expression for the nth term of the sequence:

an = 5n / (4n + 1)

As n approaches infinity, the denominator 4n + 1 becomes dominant compared to the numerator 5n. Therefore, we can simplify the expression by neglecting the term 5n:

an ≈ n / (4n + 1)

Now, we can consider the limit of the sequence as n approaches infinity:

lim(n→∞) n / (4n + 1)

To evaluate this limit, we can divide both the numerator and denominator by n:

lim(n→∞) (1 / 4 + 1/n)

As n approaches infinity, the term 1/n approaches zero, leaving us with:

lim(n→∞) 1 / 4 = 1/4

Since the limit of the sequence is a finite value (1/4), we can conclude that the sequence {an} = 5n/4n + 1 is convergent.

In other words, as n gets larger and larger, the terms of the sequence {an} get closer and closer to the limit of 1/4. This indicates that the sequence approaches a fixed value and does not exhibit wild oscillations or diverge to infinity. Therefore, we can say that the sequence is convergent.

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Answer:

93º and 87º

Step-by-step explanation:

The amplitude of the function will be 1. Then the correct option is D.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The length between the sine axis and the greatest or lowest value of the sine and cosine operations is described as the amplitude.

From the diagram, the maximum value of the curve from the x-axis will be 1.

The amplitude of the function will be 1. Then the correct option is D.

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Answer:

77 meters

Step-by-step explanation:

For a right triangle, the formula for side length is

a^2 + b^2 = c^2 where c is the hypotenuse (opposite the right angle)

36^2 + b^2 = 85^2

1296 + b^2 = 7225

b^2 = 5,929

find the square root of both sides:

b = 77

Please let me know if you have questions.

Step-by-step explanation:

it's 42.85 percent that you can say 42 or maybe 43

Answer:

y < x + 5

Step-by-step explanation:

at x axis, line crosses at -5

at y axis, line crosses at 5

Answer:

-9a^2+14

Step-by-step explanation:

We find that the radius of the sphere to the nearest thousandth is approximately 4.727 cm.

To find the radius of the sphere, we can use the formula for the volume of a sphere, which is given by:
\(V = (4/3) * π * r^3\)
Here, V represents the volume of the sphere and r represents the radius.

Given that the volume of the sphere is 668 cm^3, we can substitute this value into the formula:
\(668 = (4/3) * π * r^3\)

To solve for the radius, we can isolate r by dividing both sides of the equation by (4/3) * π:
\(r^3\) = (668 / (4/3) * π)

Simplifying the right side of the equation:
\(r^3\) = 501 / π

Now, to solve for r, we can take the cube root of both sides:
\(r = (501 / π)^(1/3)\)

Calculating the value, we find that the radius of the sphere to the nearest thousandth is approximately 4.727 cm.

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The given guy wire forms a right-angled triangle with the ground. Therefore, we can use the trigonometric ratios to find the angle that is formed between the wire and the ground.

A 3.4 guy wire is attached to a tree 3 feet from the ground. To find the angle between the wire and the ground, we can use the trigonometric ratio `tan`.` tan θ = opposite / adjacent `The opposite side is 3.4 feet, and the adjacent side is 3 feet .tan θ = 3.4 / 3The value of θ can be found using an inverse tangent (tan⁻¹) function on both sides.tan⁻¹(tan θ) = tan⁻¹(3.4 / 3)θ = 55.84° (rounded to two decimal places)Therefore, the angle formed between the wire and the ground is 55.84 degrees.

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Answer:

42.8571

Step-by-step explanation:

We would need to divide 150 by 7 and multiply it by 2 to get the answer.

150/7 = 21.42857

21.42857*2 = 42.8571

The total weight of the pineapples and peaches is 8 pounds 6 ounces.

To calculate the weight of the pineapples and peaches, we need to add the weights together. However, since the weights are given in pounds and ounces separately, we first need to convert the ounces to pounds or vice versa.

Converting ounces to pounds:

There are 16 ounces in a pound. Therefore, if we have x ounces, we can convert them to pounds by dividing x by 16.

Adding the weights:

Maria buys 3 pounds 4 ounces of pineapples and 5 pounds 2 ounces of peaches.

Converting the ounces to pounds:

4 ounces / 16 = 0.25 pounds (for pineapples)

2 ounces / 16 = 0.125 pounds (for peaches)

Adding the weights:

Pineapples: 3 pounds + 0.25 pounds = 3.25 pounds

Peaches: 5 pounds + 0.125 pounds = 5.125 pounds

Total weight: 3.25 pounds + 5.125 pounds = 8.375 pounds

To express the weight in pounds and ounces, we can convert the decimal part (0.375) of 8.375 pounds to ounces by multiplying it by 16. This results in 6 ounces.

Therefore, the weight of the pineapples and peaches is 8 pounds 6 ounces.

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Answer:

\(n(x)=x-2\)

Step-by-step explanation:

You can notice that between each of the arithmetic sequence there is a addition of 2. So we know that to add a 2 to get the next value. We can write it as n(x) where n is a function where x is the number:

Answer:

Step-by-step explanation:

To solve the given equation \(\sf x - y = 4 \\\), we can perform the following calculations:

a) To find the value of \(\sf 3(x - y) \\\):

\(\sf 3(x - y) = 3 \cdot 4 = 12 \\\)

b) To find the value of \(\sf 6x - 6y \\\):

\(\sf 6x - 6y = 6(x - y) = 6 \cdot 4 = 24 \\\)

c) To find the value of \(\sf y - x \\\):

\(\sf y - x = - (x - y) = -4 \\\)

Therefore:

a) The value of \(\sf 3(x - y) \\\) is 12.

b) The value of \(\sf 6x - 6y \\\) is 24.

c) The value of \(\sf y - x \\\) is -4.

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Answer:

it's not in a straigt line so ne

Step-by-step explanation:

Answer:

y = 4x + 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 4 and c = 8 , thus

y = 4x + 8 ← equation of line

The equation in slope-intercept form is y = 4x+8

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

Given that, a line has a y-intercept of 8 and a slope of 4.

We know that, the general equation of a line is given by, y = mx+c

where m is slope and c is the y intercept,

Here, m = 4 and c = 8

Therefore, the equation can be, y = 4x+8

Hence, The equation in slope-intercept form is y = 4x+8

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The distance between two opposite corners of the floor is 5 meters.

What is Pythagoras Theorem?

Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Using the Pythagorean theorem, the distance between two opposite corners of the floor can be found by calculating the length of the hypotenuse of a right triangle whose legs are the length and width of the floor. Therefore,

c² = a² + b²

where c is the length of the hypotenuse, a is the length of the floor (3 meters), and b is the width of the floor (4 meters).

Substituting the values, we get:

c² = 3² + 4²

c² = 9 + 16

c² = 25

Taking the square root of both sides, we get:

c = √(25)

c = 5

Therefore, the distance between two opposite corners of the floor is 5 meters.

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Answer:

Step-by-step explanation:

You are given the equation 8x -3 +4x +3 = 180 and asked to simplify it and solve for x.

Collecting terms, we have ...

  (8 +4)x +(-3 +3) = 180

  12x + 0 = 180

Dividing by the coefficient of x gives ...

  x = 180/12 = 15

The value of x is 15.

Answer: 5 * \(x^{2}\) - 7

Answer:

14, 22

Step-by-step explanation:

x+y = 36

2×x - y = 6

=> x = 36 - y

=> 2×(36 - y) - y = 6

72 - 2y - y = 6

-3y = -66

3y = 66

y = 22

=> x = 36 - 22 = 14