On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite
direction. The number b varies directly with the number a. For example b = 22 when a = - -2 Which equation
represents this direct variation between a and b?

The solution to the set {2x < 6} n {x - 5 > -4} is {x | 1 < x < 3 }

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

{2x < 6} n {x - 5 > -4}

Divide both sides of 2x < 6 by 2

So, we have

{x < 3} n {x - 5 > -4}

Add 5 to both sides of x - 5 > -4

So, we have

{x < 3} n {x > 1}

The above set when combined is

1 < x < 3

This means that the solution to the set is {x | 1 < x < 3 }

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The probability that the teacher chooses a girl with glasses is 3/16, and the probability that the teacher chooses a boy with glasses is 1/4.

Let's calculate the probability that the teacher chooses a student with glasses.
a) A girl with glasses: There are 6 girls in the class, and 3 of them wear glasses. There are a total of 16 students (6 girls + 10 boys).
Probability = (Number of girls with glasses) / (Total number of students)
Probability = 3 girls with glasses / 16 total students
Probability = 3/16
b) A boy with glasses: There are 10 boys in the class, and 4 of them wear glasses.
Probability = (Number of boys with glasses) / (Total number of students)
Probability = 4 boys with glasses / 16 total students
Probability = 1/4
So, the probability that the teacher chooses a girl with glasses is 3/16, and the probability that the teacher chooses a boy with glasses is 1/4.

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Answer:

√3/2

Step-by-step explanation:

Easy Method

The equation above is in the forms of sin(a)cos(b) - cos(a)sin(b), which is sin(a-b) according to the trig identities. sin(75-15) = sin(60) = √3/2

Harder Method

Find sin75 with equation sin(a+b) = sin(a)cos(b) + cos(a)sin(b)

sin75°

= sin(45° + 30°)

= [sin45°cos30° + cos45°sin30°]

= [√2/2 * √3/2 + √2/2 * 1/2]  <-- unit circle known values

= [(√6 + √2)/4]

Find cos75 with the equation: cos(a+b) = sin(a)sin(b) - cos(a)cos(b)

cos75°

= cos(45° + 30°)

= [cos45°cos30° - sin45°sin30°]

= [√2/2 * √3/2 - √2/2 * 1/2]  <-- unit circle known values

= [(√6 - √2)/4]

Find sin15 with the equation: sin(a-b) = sin(a)cos(b) - cos(a)sin(b)

sin15°

= sin(45° - 30°)

= [sin45°cos30° - cos45°sin30°]

= [√2/2 * √3/2 - √2/2 * 1/2]  <-- unit circle known values

= [(√6 - √2)/4]

Find cos15 with the equation: cos(a-b) = sin(a)sin(b) + cos(a)cos(b)

cos15°

= cos(45° - 30°)

= [cos45°cos30° + sin45°sin30°]

= [√2/2 * √3/2 + √2/2 * 1/2]  <-- unit circle known values

= [(√6 + √2)/4]

Now plug in all the solved values, we get: {[(√6 + √2)/4] * [(√6 + √2)/4]} - {[(√6 - √2)/4] * [(√6 - √2)/4]} = √3/2

Answer: 27[tex]\pi[/tex]

Step-by-step explanation:

Use the circle area formula: r²[tex]\pi[/tex]...

6²[tex]\pi[/tex] = 36[tex]\pi[/tex]

And since a quarter of the circle is removed(aka [tex]\frac{1}{4}[/tex]), divide 36 by [tex]\frac{3}{4}[/tex]...

= 27[tex]\pi[/tex]

The diameter of the basketball is 16 cm given the volume of 268 [tex]cm^{3}[/tex]

Sphere is a three-dimensional object that is round in shape. It  is an object that is completely round in shape like a ball.

How to determine this

When a basketball has a volume of 268[tex]cm^{3}[/tex]

The volume of a sphere = 4/3 * π * [tex]r^{3}[/tex]

Where π = 3.14

Radius, r = ?

Volume of basketball = 4/3 * 3.14 * [tex]r^{3}[/tex]

268[tex]cm^{3}[/tex] = 4/3 * 3.14 * [tex]r^{3}[/tex]

268[tex]cm^{3}[/tex] = 12.56/3 * [tex]r^{3}[/tex]

Cross multiply

268 * 3 = 12.56 * [tex]r^{3}[/tex]

804 = 12.56 * [tex]r^{3}[/tex]

divides through by 12.56

804/12.56 = 12.56[tex]r^{3}[/tex]/12.56

64.01 = [tex]r^{3}[/tex]

cube both sides

∛64.01 = r

r = 4 cm

So, the radius = 4 cm

To find the diameter of basketball

When the radius = 4 cm

And diameter = 2(r)

Diameter = 2 * 4 cm

Diameter = 8 cm

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The pH level of the pool is determined as 8.6.

The pH of a solution is a measure of its acidity or basicity. The pH scale ranges from 0 to 14, with a pH of 7 being neutral, less than 7 is acidic and above 7 is alkaline.

The pH of a solution can be calculated using the formula;

pH = -log[H₃O⁺]

where;

Using the measured [H₃O⁺] concentration of 2.40 x 10⁻⁹ moles/liter, we can calculate the pH of the swimming pool as follows;

pH = -log(2.40 x 10⁻⁹)

pH = 8.62

Therefore, the pH of the swimming pool is 8.6, rounded to the nearest tenth.

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Answer:

A''(3, 0); B''(3, 2); C''(1, 1); D''(1, -1)

Step-by-step explanation:

Approximately 99.4% of people have an IQ score between 55 and 145.

The empirical rule, also known as the 68-95-99.7 rule, is a statistical rule that applies to data that is normally distributed. It states that:

- Approximately 68% of data falls within one standard deviation of the mean.

- Approximately 95% of data falls within two standard deviations of the mean.

- Approximately 99.7% of data falls within three standard deviations of the mean.

In this case, we are given that IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. To find the percentage of people with an IQ score between 55 and 145, we need to find the number of standard deviations away from the mean that these scores are.

For an IQ score of 55, we have:

z = (55 - 100) / 15 = -3

For an IQ score of 145, we have:

z = (145 - 100) / 15 = 3

So, we can see that an IQ score of 55 is 3 standard deviations below the mean, and an IQ score of 145 is 3 standard deviations above the mean.

According to the empirical rule, approximately 99.7% of data falls within three standard deviations of the mean. Therefore, the percentage of people with an IQ score between 55 and 145 is approximately:

99.7% - (0.15% + 0.15%) = 99.4%

(Note that we subtracted the percentage of data that falls more than 3 standard deviations away from the mean, which is approximately 0.15% on either side.)

So, approximately 99.4% of people have an IQ score between 55 and 145.

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We cannot conclude that 95% of the population agrees that there is no difference in Taste between Coke and Pepsi.

To calculate the probability that 95% of the population agrees that there is no difference in taste between Coke and Pepsi, we can use the binomial distribution formula.

Let X be the number of students who say there is no difference in taste, and n be the total number of students in the sample. Then, X follows a binomial distribution with parameters n and p, where p is the true proportion of students who say there is no difference in taste.

The point estimate of p is 7/10 = 0.7. The standard error of the proportion can be calculated as the square root of p(1-p)/n = sqrt(0.7*0.3/10) = 0.23.

Using a normal approximation to the binomial distribution, the 95% confidence interval for p is given by:

0.7 +/- 1.96*0.23 = (0.24, 1.16)

Since the interval includes 0.5, which represents the point where the proportion of agreement and disagreement is equal, we cannot conclude that 95% of the population agrees that there is no difference in taste between Coke and Pepsi.

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Total length of the two sides of the triangle is 2x² + 4x + 4 and  length of the third side of the triangle is 5x³ - 5x² + 3x - 12.

The total length of the two sides of the triangle is the sum of Side 1 and Side 2:

(3x² - 4x - 1) + (4x - x² + 5)

2x² + 4x + 4

The total length of the two sides of the triangle is 2x² + 4x + 4.

The length of the third side of the triangle can be found by subtracting the sum of Side 1 and Side 2 from the perimeter of the triangle:

Perimeter - (Side 1 + Side 2)

(5x³ - 2x² + 3x - 8) - (3x² - 4x - 1 + 4x - x² + 5)

Combining like terms

5x³ - 5x² + 3x - 12

The length of the third side of the triangle is 5x³ - 5x² + 3x - 12.

The polynomials are closed under addition and subtraction by part A and part B because when we added Side 1 and Side 2, and when we subtracted their sum from the perimeter of the triangle, the resulting expressions were still polynomials with real coefficients.

Therefore, the sum and difference of polynomials with real coefficients are also polynomials with real coefficients.

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Inverse variation is a relationship between two variables where one variable increases as the other variable decreases, and vice versa.

This means that as one variable doubles, the other variable will decrease by half, or vice versa.

The following are situations that depict inverse variation:

1. When you are traveling at a constant speed, the time it takes to cover a given distance is inversely proportional to the distance. This is because the distance will decrease as the speed increases.

2. If you have a light source, the intensity of the light decreases as you move further away from the source. This is because the distance between the source and the object increases as the intensity of the light decreases.

3. The force of gravity between two objects is inversely proportional to the square of the distance between them. This is because the force of gravity will decrease as the distance between the objects increases.

4. When the temperature of a gas decreases, its pressure increases. This is because the volume of the gas remains constant as the temperature decreases, which causes the pressure to increase according to the gas laws.

5. The period of a pendulum is inversely proportional to the square root of its length. This is because the length of the pendulum will decrease as the period increases.

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Answer:

X=20

Step-by-step explanation:

khan academy :))

Answer:

a) 2/25. b) 3/100. c) 1/20. d) 11/50.

Step-by-step explanation:

there are 3 + 6 + 4 + 12 = 25 markers

a) p(red) = 4/25. then p(blue) = 12/24.

4/25 X 12/24 = 2/25

b) p(yellow) = 6/25. then p(green) = 3/24.

6/25 X 3/24 = 3/100

c) p(yellow) = 6/25. p(2nd yellow) = 5/24

6/25 X 5/24 = 1/20

d) p(blue) = 12/25. p(2nd blue) = 11/24

12/25 X 11/24 = 11/50

The calculated value of the missing side length of the triangle is 13.96 units

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

The triangle

The missing side length of the triangle can be calculated using the law of sines

The law of sines states that

a/sin(A) = b/sin(B) = c/sin(C)

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

x/sin(61) = 15/sin(70)

Cross multiply

x = sin(61) * 15/sin(70)

Evaluate

x = 13.96 units

Hence, the missing side length of the triangle is 13.96 units

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The function that corresponds to the parabola Graph is f(x) = -3(x + 1)² + 2, which is option B.

The graph represents a downward open parabola that rises from (-2.4,-4) to (-1,2) and then declines through (0.4,-4) on the x-y coordinate plane.

To determine the function that corresponds to this graph, we need to consider the key features of a parabolic function, including its vertex and axis of symmetry.

The vertex of a parabola in the form f(x) = a(x-h)² + k is (h,k), and the axis of symmetry is x = h

From the graph, we can see that the vertex of the parabola is at (-1,2), which means that h = -1 and k = 2.

We also know that the parabola opens downward, which means that a < 0.

Therefore, we can eliminate options A and D since they both have a positive value of "a."

Next, we can test options B and C.

Option B has the form f(x) = -3(x + 1)² + 2, which means that the vertex is at (-1,2) and the parabola opens downward due to the negative coefficient of (x+1)².

To confirm if option B is correct, we can check if the point (0.4,-4) lies on the parabola:

f(0.4) = -3(0.4+1)² + 2 = -3(1.4)² + 2 = -5.88

Since the y-coordinate of the point (0.4,-4) is -4, which is equal to -5.88, we can see that the point lies on the parabola.

Therefore, the function that corresponds to the graph is f(x) = -3(x + 1)² + 2, which is option B.

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Answer:

Step-by-step explanation:

You probably should check for silly mistakes.

The sum of the equation 3y/y²+7y+10 + 2/y+2 is 5/(y + 5).

In order to find the sum, we have to first find a common denominator for the two fractions:

3y/y² + 7y + 10 + 2/y + 2 = (3y/(y + 5)(y + 2)) + (2(y + 5)/(y + 5)(y + 2))

Next, we join the two fractions by adding their numerators:

= (3y + 2(y + 5))/((y + 5)(y + 2))

Then, we simplify the numerator:

= (3y + 2y + 10)/((y + 5)(y + 2))

= (5y + 10)/((y + 5)(y + 2))

= 5(y + 2)/((y + 5)(y + 2))

= 5/(y + 5)

Therefore, the sum of 3y/y²+7y+10 + 2/y+2 = 5/(y + 5).

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Answer:

----------------

The line that is perpendicular to x = 8 has a form of:

Since it has a point (-3, - 2), the value of a is the y-coordinate of this point. Therefore the line is:

The expression with the greatest value when a = 5 is:

a + 9 × 8 ÷ 7, with 9 in the first box, 8 in the second box, and 7 in the third box.

To create the expression with the greatest value when a = 5, we want to choose the largest possible numbers to fill in the missing parts.

Since each whole number can only be used once, we should choose the three largest numbers from 1 to 9.

The three largest numbers from 1 to 9 are 9, 8, and 7. So we can fill in the expression as follows:

a + 9 × 8 ÷ 7

When a = 5, this expression evaluates to:

5 + 9 × 8 ÷ 7 = 5 + 72 ÷ 7 = 15.2857...

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Using a trigonometric relation we can see that the distance between the base and the wall is 26.76ft

In the image at the end you can see a diagram for this problem.

We have a right triangle where we want to find the value of d, which is the adjacent cathetus to the known angle.

Then we can use the trigonometric relation:

cos(a) = (adjacent cathetus)/hypotenuse

Where:

a = 48°

hypotenuse = 40ft

adjacent cathetus = d

Replacing that we will get:

cos(48°) = d/40ft

Solving that for d, we will get:

40ft*cos(48°) =d

26.76ft = d

That is the distance between the base and the wall.

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Answer:

Final Expression:

3.095D + $10

Step-by-step explanation:

Let's represent the Monthly Rent by "D" dollars

The amount Dave is expected to pay before renting the apartment is the Sum of All the Fees he has been quoted:

Application Fee:

1.5% of 1 month's rent = 0.015D

Credit Application Fee:

$10.00

Security Deposit:

1 Month's rent =  D

Last Month's rent:

1 Month's Rent = D

Broker's Fee:

9%

Thus, The algebraic expression that represents the amount Dave is expected to pay before renting the apartment is:

0.015D + $10  +  D  +  D + 1.08D

Simplify Expression:

3.095D  + $10

Hence, The final expression is:

Answer:  3.095D + $10

Answer:

x=5,1

Step-by-step explanation:

have a great day and thx for your inquiry :)

Answer: x = 5, 1

Step-by-step explanation:

Take the root of both sides and solve

Answer:

Step-by-step explanation:

D

The length FE is 6 units and the arc AE is 64 degrees

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

The circle

Given that the lengths from the center to either chords are equal

This means that

FE = 6 units

For the other circle, we have

BC = 58 degrees

AB = ED

The arc AE is calculated as

AE = 180 - BC - ED

Where

AB = ED = BC = 58 degrees

So, we have

AE = 180 - 58 - 58

Evaluate

AE = 64

Hence, the arc AE is 64 degrees

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Answer:

22 = 2 × 11

40 = 2 × 2 × 2 × 5

LCM of 22 and 40 = 2^3 × 5 × 11 = 440

y=3(5)ˣ is the equation of the function represented by the table

We can see that as x increases, y increases exponentially.

To determine the specific form of the exponential function, we can take the ratio of successive y-values:

(3/5)/(3/25) = 5/1

(3)/(3/5) = 5

(15)/(3) = 5

(75)/(15) = 5

This shows that the ratio of successive y-values is constant at 5. Therefore, the function represented by the table is an exponential function of the form:

y = a(b)ˣ

To find a and b, we can use any two pairs of (x,y) values.

Let's use (0,3) and (1,15):

3 = a(b)⁰

15 = a(b)¹

3 = a

Now we get b =5

Hence, y=3(5)ˣ is the equation of the function represented by the table

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Answer:

The polygons are similar. They are similar in the way that the larger polygon is 3 times the size of the smaller one.

Answer:

GJ ≈ 31.42 units

Step-by-step explanation:

the arc length GJ is calculated as

GJ = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{30}{180}[/tex] ( r is the radius )

the radius HJ = 30 , then

GJ = 2π × 30 × [tex]\frac{1}{6}[/tex]

     = 60π × [tex]\frac{1}{6}[/tex]

     = 10π

     ≈ 31.42 units ( to the nearest hundredth )

Answer:

Step-by-step explanation:

We know that the cosine of an angle is the reciprocal of the secant of the same angle, and the cotangent of an angle is the reciprocal of the tangent of the same angle. Therefore, we can use these relationships to find the value of the secant of an angle when the cotangent of the same angle is given.We are given that cot(o) = 13/6. Using the definition of the cotangent function, we know that:cot(o) = adjacent side / opposite sideWe can use the Pythagorean theorem to find the hypotenuse of a right triangle with adjacent side 13 and opposite side 6:h^2 = 13^2 + 6^2

h^2 = 169 + 36

h^2 = 205

h = sqrt(205)Now we can use the definitions of the secant and cosine functions to find the value of sec(o):sec(o) = hypotenuse / adjacent side

sec(o) = sqrt(205) / 13Therefore, the value of sec(o) is:sec(o) = sqrt(205) / 13 ≈ 1.5276