Translate the sentence into an equation.
Twice the difference of a number and 6 is 7.
Use the variable b for the unknown number.

Answer: At equilibrium, the supply and demand are equal, so we can set the two equations equal to each other:

300 + 40x = 9300 - 50x

Simplifying and solving for x:

90x = 9000

x = 100

Now that we know x, we can use either equation to find y:

y = 300 + 40(100) = 4300

So the equilibrium point is when x = 100 and y = 4300.

Step-by-step explanation:

The student's is incorrect because the greatest common factor of 12 and 8 is 2z, so the correct expression is 2x (6x+4).

Expression is the communication of emotion or ideas through words, art, music, or other forms of communication. It is the way in which a person or artist conveys their thoughts and feelings in a creative and meaningful way. Expression can be seen in the form of art, writing, music, dance, and other creative outlets. Expression is a powerful tool that can be used to communicate a message or to evoke a feeling in the audience. Expression can be used to inspire, educate, motivate, and even to heal. Expression is a way to connect people and cultures, and a way to share stories and experiences. It is a way to express oneself in a meaningful and powerful way.

This is because 12z+8 can be written as 2z(6x+4), where the greatest common factor of 12 and 8 (2z) is factored out.

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Complete Question:
The expression 12z+8 is equivalent to the expression a (bx + c), where b and c are constants and have no common factors. A student wrote the answer as 2 (6x+4).

Which statement best explains whether the student's answer is correct or incorrect?

OA. The student's answer is incorrect because the greatest common factor of 12 and 8 is 2z, so the correct expression is 2x (6x+4).

OB. The student's answer is incorrect because the greatest common factor of 12 and 8 is 4z, so the correct expression is 4z (3x+2).

C. The student's answer is incorrect because the greatest common factor of 12 and 8 is 4, so the correct expression is 4 (3x+2).

OD. The student's answer is incorrect because the greatest common factor of 12 and 8 is 8, so the correct expression is 8 (4x+1).

We can use the trigonometric identities to find the exact values of the expressions.

First, we can find cos(alpha) and cos(beta) using the Pythagorean identity:

cos(alpha) = sqrt(1 - sin^2(alpha)) = sqrt(1 - (24/25)^2) = 7/25

cos(beta) = -sqrt(1 - sin^2(beta)) = -sqrt(1 - (15/17)^2) = -8/17 (since beta is in quadrant II, where cosine is negative)

Next, we can use the sum formulas for sine and cosine to find sin(alpha + beta) and cos(alpha + beta):

sin(alpha + beta) = sin(alpha)cos(beta) + cos(alpha)sin(beta) = (24/25)(-8/17) + (7/25)(15/17) = -117/425

cos(alpha + beta) = cos(alpha)cos(beta) - sin(alpha)sin(beta) = (7/25)(-8/17) - (24/25)(15/17) = -24/85

Finally, we can use the quotient identity for tangent to find tan(alpha + beta):

tan(alpha + beta) = sin(alpha + beta) / cos(alpha + beta) = (-117/425) / (-24/85) = 39/85

Therefore, cos(alpha + beta) sin(alpha + beta) = (-24/85)(-117/425) = 936/7225, and tan(alpha + beta) = 39/85.

The value of y is 4, so the answer is option A: y = 4.

What is trigonometric ratios ?

Trigonometric ratios are mathematical relationships between the angles and sides of a right triangle. There are three primary trigonometric ratios: sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.

Using the given diagram, we can use the trigonometric ratios to find the value of y.

First, we can find the length of the side opposite the 30-degree angle by using the sine ratio:

sin(30°) = opposite/hypotenuse

sin(30°) = y/8

y/8 = 1/2

y = 8/2

y = 4

Therefore, the value of y is 4, so the answer is option A: y = 4.

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Answer:

The surface area is 65.94 ft

To the nearest block, Landon's house is at distance of 12 blocks away from Maria's house if Maria could walk in a straight line.

A basic mathematical theorem relating to the sides of a right-angled triangle is known as Pythagoras' theorem. The square of the length of the hypotenuse, the side that faces the right angle, is said to be equal to the sum of the squares of the lengths of the other two sides, known as the legs, in a right triangle.

This can be written in mathematical notation as:

c² = a² + b²

where c is the length of the hypotenuse, and a and b are the lengths of the legs of the right triangle.

In this case, we can consider the straight line between Maria's house and Landon's house as the hypotenuse of a right triangle, with the distances they walked as the other two sides. We can use the distance formula to find the lengths of those sides:

Distance walked by Maria = √(9² + 3²) = √90 ≈ 9.49 blocks

Distance walked by Landon = √(5² + 7²) = √74 ≈ 8.60 blocks

Now we can use the Pythagorean theorem to find the distance between their houses:

Distance between houses = √(9.49² + 8.60²) ≈ 12.46 blocks

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Answer:

59.829787234042556

Step-by-step explanation:

Answer:

40 units

Step-by-step explanation:

a = 8

b = 15

To find c, we can use the formula: [tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]8^{2} +15^{2} =x^{2}[/tex]

64 + 225 = c^2

289 = c^2

c = 17

a + b + c = perimeter

8 + 15 + 17 = 40

Answer:

  40 units

Step-by-step explanation:

You want the perimeter of the triangle shown in the graph.

You can count the grid squares to find the horizontal and vertical dimensions of the triangle. You find they are 8 units and 15 units, respectively.

The length of the slant side is the hypotenuse of a right triangle with sides 8 and 15. If you don't recognize this {8, 15, 17} Pythagorean triple, you can find the hypotenuse using the Pythagorean theorem:

  c² = a² +b²

  c² = 8² +15² = 64 +225 = 289

  c = √289 = 17

The long side of the triangle is 17 units.

The perimeter of the triangle is the sum of the lengths of its sides:

  P = 8 + 15 + 17 = 40

The perimeter is 40 units.

__

Additional comment

A "Pythagorean triple" is a set of three integer side lengths that form a right triangle. The triple is "primitive" if the numbers have no common factor. There are a few Pythagorean triples that regularly show up in algebra, trig, and geometry problems. Some of them are ...

  {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}

You will also see multiples of these, for example, 2·{3, 4, 5} = {6, 8, 10}.

The smallest is {3, 4, 5}, and it is the only set that is an arithmetic sequence (has constant differences between lengths). In every case, the sum of the numbers is even. (A right triangle cannot have integer side lengths and an odd perimeter value.)

I hope this helps you.

The bearing used by the control tower to find the aircraft is N31°E + 79.6° or approximately N110.6°E.

Trigonometric ratios are the ratios of the sides of a right triangle. The sine (sin), cosine (cos), and tangent (tan) are three typical trigonometric ratios.

We may use the principles of bearings and trigonometry to solve this problem.

Let's start by drawing a diagram of the situation below:

Here, A represents the aircraft's original location, and B represents the aircraft's location after it has flown 1 mile to the southeast.

To get the bearing used by the control tower to identify the aircraft, we must first calculate the angle between the initial direction (N31°E) and the ending direction (towards B).

This angle can be calculated using trigonometry as follows:

[tex]\frac{AB}{AC} = tan(theta)\\tan^{-1}(\frac{AB}{AC} ) = theta[/tex]

where AB is the distance between A and B (one mile), AC is the distance between A and the point where the aircraft makes the 90-degree turn (one-quarter mile), and theta is the desired angle.

AB and AC can be calculated as follows:

[tex]AB = \sqrt{((1 mile)^{2} + (1 mile)^{2} )} \\AB = \sqrt{2} miles[/tex]

(1/4) mile = AC

Substituting these values into theta's formula yields:

[tex]\\tan^{-1}(\frac{\sqrt{2} }{\frac{1}{4} } ) = theta[/tex]

evaluate this expression and obtain:

theta ≈ 79.6°

As a result, the bearing used by the control tower to find the aircraft is N31°E + 79.6° or approximately N110.6°E.

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Another way to look at it is to draw the chord UW. Then ΔWZU is an isosceles triangle, and the perpendicular bisector of UW bisects ∠Z and also goes through the circle center. Then the figure is symmetrical about that diameter secant, making WT ≅ UV.

A secant of a circle is known to be a straight line that intersects the circle at two different points. Secant is derived from the Latin secare, meaning "to cut". It can also be understood beyond the circle as an extension of the chord of the circle.

If the secant intersects the circle at two points, you get chords at the two points of intersection. A chord of a circle is a segment whose endpoint lies on an arc.  

Using the secant rule:

ZW × WT = ZU × UV

Substituting for ZT and ZV, you have

ZW × (ZW + WT) = ZU × (ZU + UV)

ZW² + ZW×WT = ZU² + ZU×UV

Substituting ZW for ZU everywhere, we have

ZW² + ZW×WT = ZW² + ZW×UV

Dividing by ZW gives

ZW + WT = ZW + UV

and subtracting ZW leads us to the conclusion

WT = UV

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Answer: Let the two numbers be x and y. We know that:

x*y = 2420 ---(1)

LCM(x, y) = 110 ---(2)

We can write the LCM as:

LCM(x, y) = (x*y)/HCF(x, y)

Substituting the given values, we get:

110 = (x*y)/HCF(x, y)

Multiplying both sides by HCF(x, y), we get:

HCF(x, y) * 110 = x*y

Substituting equation (1), we get:

HCF(x, y) * 110 = 2420

Dividing both sides by 110, we get:

HCF(x, y) = 2420/110

HCF(x, y) = 22

Therefore, the HCF of the two numbers is 22.

Step-by-step explanation:

Answer:

The volume of a cube with a length of 11 meters is 33 m³.

The surface area of the pyramid is 113 cm².

A rectangular pyramid is a type of pyramid where the base is a rectangle and the triangular faces meet at a single point called the apex or vertex. It has five faces, including a rectangular base and four triangular faces, and it is a polyhedron with five vertices and eight edges.

The rectangular pyramid has a base of dimensions 7 cm by 5 cm, and the two large triangular faces have a height of 7.6 cm, while the two small triangular faces have a height of 8 cm.

To find the surface area of the pyramid, we need to find the area of each face and then add them up.

Area of the base:

The base of the pyramid is a rectangle with dimensions 7 cm by 5 cm, so its area is:

Area of base = length × width = 7 cm × 5 cm = 35 cm²

Area of the four triangular faces:

Each of the four triangular faces has a base of 5 cm (the width of the rectangle) and a height of either 7.6 cm or 8 cm. Using the formula for the area of a triangle, we can find the area of each face:

Area of each large triangular face = 1/2 × base × height = 1/2 × 5 cm × 7.6 cm = 19 cm²

Area of each small triangular face = 1/2 × base × height = 1/2 × 5 cm × 8 cm = 20 cm²

There are two large triangular faces and two small triangular faces, so the total area of the four triangular faces is:

Total area of four triangular faces = 2 × area of large triangular face + 2 × area of small triangular face

= 2 × 19 cm² + 2 × 20 cm²

= 78 cm²

Total surface area:

Finally, we can find the total surface area of the pyramid by adding the area of the base to the total area of the four triangular faces:

Total surface area = area of base + total area of four triangular faces

= 35 cm² + 78 cm²

= 113 cm²

Therefore, the surface area of the pyramid is 113 cm²

.

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the probability that the child randomly arranges the letters in the order TIGER is 1/120.

What is Probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

There are 5 blocks with 5 different letters. Since we want the child to arrange the letters in the order TIGER, there is only one way to arrange them correctly out of a total of 5! = 120 possible arrangements.

Therefore, the probability that the child randomly arranges the letters in the order TIGER is 1/120.

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The volume of air passing through the filter is 800 cubic feet per minute. It is calculated by multiplying the air flow speed (100ft/min) by the area of the filter (8ft²).

The volume of air passing through the HEPA filter can be calculated using the formula for the speed of air flow multiplied by area. The speed of the air flow is given as 100ft/min and the area of the filter is given as 4ft x 2ft, which equals 8 square feet. Therefore, the volume of the air passing through the filter can be calculated as 8ft2 x 100ft/min = 800 cubic feet per minute.

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Answer:

147

My teacher has been trying to help me learn this and it has been working.

The approximate distance from the origin to the point (-2, -7, -4) is 8.3 units.

In three-dimensional space, the distance formula is used to calculate the distance between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) in a three-dimensional coordinate system.

The formula is given by:

d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Here we have

The point (-2, -7, -4)

We need to find the distance between the origin to the point

Let (x₁, y₁, z₁) = (-2, -7, -4) and (x₂, y₂, z₂) = (0, 0, 0)

Using the distance formula,

d = √ [(x₂ - x₁)² + (y₂ - y₁)²+ (z₂ - z₁)² ]

d = √ [(0 - (-2))² + (0 - (-7))²+ (0 - (-4))² ]

d = √ [(2)² + (7)²+ (4)² ]

d = √ [4 + 49 + 16 ]

d = √69 = 8.3066

d = 8.3

Therefore,

The approximate distance from the origin to the point (-2, -7, -4) is 8.3 units.

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The probabilities of randomly entering each room in the maze shown at right are:

P(A) = 5/18

P(B) = 1

The probabilities can be determined from the formulas below:

P(A) = 1/3 * 1/2 * 1 + 1/3 * 1/3

P(B) = 1/3 * 1 + 1/3 * 1 + 1/3 *1

To calculate the probabilities, we need to simplify the expressions and do the arithmetic.

Using the formulas you provided:

P(A) = (1/3 * 1/2 * 1) + (1/3 * 1/3) = 1/6 + 1/9 = 5/18

P(B) = (1/3 * 1) + (1/3 * 1) + (1/3 * 1) = 1

Therefore, the probabilities, evaluated to their simplest form, are:

P(A) = 5/18

P(B) = 1

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1. The critical value, according to the z-table, is roughly 2.33. 2. There is enough data to support the alternative hypothesis and reject the null hypothesis.

A null hypothesis is a claim that assumes there is no meaningful difference between two or more variables in a population or that any difference that is detected is the result of chance in statistical hypothesis testing. Typically, it is indicated by H0. A statement that rejects the null hypothesis and assumes that the variables being compared have a substantial difference is known as an alternative hypothesis, or Ha. In contrast to the null hypothesis, which the researcher is attempting to refute, the alternative hypothesis is what the researcher is attempting to prove.

1. We can use a z-table or a calculator to determine the critical value for a right-tailed z-statistic test with a sample size of 100 and a significance level of 0.01. The z-score that equates to the 0.99 probability level, which is the complement of the 0.01 significance level, is the critical value. The crucial value, according to the z-table, is roughly 2.33.

2. We compare the estimated z-statistic value, z = 2.88, to the crucial value, 2.33. The estimated value of z falls in the rejection zone of the null hypothesis because it exceeds the crucial value. As a result, we find that there is enough data to support the alternative hypothesis and reject the null hypothesis.

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Answer: 0.0295

Step-by-step explanation: To solve for r in the equation $425.83=400(1+r)^5$, we can rearrange the equation to isolate the variable.

Dividing both sides by 400 gives $(1+r)^5=1.064575$, and taking the fifth root of both sides gives:

$1+r=\sqrt[5]{1.064575}$.

Subtracting 1 from both sides gives $r\approx 0.0295$.

Therefore, your answer would be 0.0295.

Answer:

a) Let’s assume that the moose population, p, changes linearly with time t (in years since 1991). We can use the given data to find the slope of the line that represents the population change. The slope is (5850-4330)/(1999-1991) = 190 moose/year. The equation of the line is p = 190(t) + 4330.

b) According to this model, the moose population in 2002 would be p = 190(2002-1991) + 4330 = 6490 moose.

Step-by-step explanation:

Answer: 0.0972

Step-by-step explanation:

To find the probability that the first roll is a total of at least 7 and the second roll is a total of at least 10, we need to find the probabilities of each event separately and then multiply them together.

First, let's find the probability of the first roll being a total of at least 7. There are a total of 36 possible outcomes when rolling a pair of dice (6 sides on each die, so 6 x 6 = 36). To get a total of at least 7, the following outcomes are possible:

7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)

8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2)

9: (3, 6), (4, 5), (5, 4), (6, 3)

10: (4, 6), (5, 5), (6, 4)

11: (5, 6), (6, 5)

12: (6, 6)

There are 21 successful outcomes out of the total 36 possibilities. So, the probability of getting a total of at least 7 in the first roll is:

P(at least 7) = 21/36

Next, let's find the probability of the second roll being a total of at least 10. The following outcomes are possible:

10: (4, 6), (5, 5), (6, 4)

11: (5, 6), (6, 5)

12: (6, 6)

There are 6 successful outcomes out of the total 36 possibilities. So, the probability of getting a total of at least 10 in the second roll is:

P(at least 10) = 6/36

Now, to find the probability that both events happen, we multiply the probabilities of each event:

P(first roll at least 7 and second roll at least 10) = P(at least 7) * P(at least 10) = (21/36) * (6/36)

P(first roll at least 7 and second roll at least 10) = 126/1296

So, the probability that the first roll is a total of at least 7 and the second roll is a total of at least 10 is 126/1296, or approximately 0.0972 (rounded to four decimal places).

Step-by-step explanation:

A = π r²

r = 3 inches

A = 3.14 × (3)²

A = 3.14 × 9

A = 28.29 square inches

The percent of those taking this exam had scores between 58.9 and 69.7 is 34.1%

To find the number of standard deviations 58.9 and 69.7 are above and below the mean, find the difference between these two numbers and the mean, then divide by the standard deviation 5.4:

z1 = (58.9 - 64.3) / 5.4 = -0.996

z2 = (69.7 - 64.3) / 5.4 = 1.004

Since the absolute values of the z-scores are almost equal, we can approximate the area between them as half of the total area between -1 and 1 standard deviations.

Therefore, the approximate percentage of those taking the exam with scores between 58.9 and 69.7 is:

68% / 2 = 34%

Therefore, the correct option is D 34.1%.

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the answer to the question is A. 5 hours. This information is essential for accurately modeling the tide using a trigonometric function and predicting the water level at any time in the future or past within the 5-hour cycle

How to solve the question?

The given data represents the variation of water level at Sunny Beach over a period of 5 hours. As Joe arrived at 12:00 p.m., we can assume that the highest tide occurred at that time, and the water level started to decrease until it reached its lowest point after 3 hours. Then, the water level started to increase again until it reached its highest point after 5 hours, completing one full cycle of the tide.

To model this variation of water level over time, we can use a trigonometric function, specifically a sine or cosine function. These functions have a repeating pattern over a fixed period, which makes them suitable for modeling cyclic phenomena such as tides.

The period of a sine or cosine function represents the length of one complete cycle. In this case, the period of the function that models the tide is 5 hours because the tide completes one cycle over a 5-hour period, as observed from the given data.

Therefore, the answer to the question is A. 5 hours. This information is essential for accurately modeling the tide using a trigonometric function and predicting the water level at any time in the future or past within the 5-hour cycle

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Answer: A. He should focus on his student loan debt and give himself a deadline of five years. This statement specifies a particular type of debt and sets a time-bound goal, making it both specific and timely.

Step-by-step explanation:

I hope this helps you .