Seventy-five 6th- grade students chose to watch a movie on the last day of school. This is 25% of the 6th-grade class. How many total students are in the 6th grade?

Answer:

p≥35

Step-by-step explanation:

because you have done 15 so you subtract 15 from 50 giving you 35 and then you would say p is greater than or equal to 35 cause 50 pages is your minimum

The simplification of the given expression is equal to 192524.3.

The expression is equal to,

√2 × √6 × √110 × √120 × √450 × √520

Simplify this expression by first simplifying the square roots under the radical signs,

√2 = √(2 × 1)

     = √2 × √1

√6 = √(2 × 3)

     = √2 × √3

√110 = √(2 × 5 × 11)

        = √2 × √5 × √11

√120 = √(2 × 2 × 2 × 3 × 5)

        = 2√2 × √3 × √5

√450 = √(2 × 3² × 5²)

         = √2 × (3 × 5)²

         = 15√2

√520 = √(2³ × 5 × 13)

        = 2√2 ×√5 × √13

Substituting these simplifications back into the original expression, we have,

√2 × √6 × √110 × √120 × √450 × √520

= √2 × √2 × √3 × √2 × √5 × √11 × 2√2 × √3 × √5 × 15√2  ×  2√2 ×√5 × √13

= 2⁵ × 3² × 5²√(5 × 11  × 13)

= 7200√715

= 192524.3

Therefore, the simplification value of √2 × √6 × √110 × √120 × √450 × √520 is equal to 192524.3.

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The above question is incomplete, the complete question is:

Simplify

√2 × √6 × √110 × √120 × √450 × √520

The solution in the equation is x = 12.

We have,

To solve the logarithmic equation log (x − 2) = 1,

We can use the definition of logarithm which states that log base b of x equals y if and only if b to the power of y equals x, where b is the base of the logarithm.

In this case, the base is not specified, so we assume it is 10, which is the common base used in most calculators and mathematical applications

Using the exponential form, we have:

log (x - 2) = 1

10^1 = x - 2

10 = x - 2

x = 12

Therefore,

The solution is x = 12.

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The rate of change for the cab ride is A = $3 per mile

Given data ,

Change in cost = $55 - $40 = $15

Change in distance = 15 miles - 10 miles = 5 miles

Now, we can divide the change in cost by the change in distance to get the rate of change or cost per mile:

Rate of change or cost per mile = Change in cost / Change in distance

A = $15 / 5 miles

A = $3 per mile

Hence , the rate of change or cost per mile for the cab ride is $3 per mile

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If the radius of Jasmine's swimming pool is 4.2 meter, then it's circumference is 26.4 meters.

The "Circumference" of a circle is known as the distance around the boundary of a circle.

The circumference of a circle is given by the formula : 2 × π × radius,

where π (pi) is a mathematical constant approximately equal to 3.14,

We are given that Jasmine's swimming pool has a radius of 4.2 meters.
So, we can calculate the circumference of the pool as :

⇒ Circumference = 2 × 3.14 × 4.2 meters,

⇒ Circumference ≈ 26.4 meters,

Therefore, the circumference of Jasmine's swimming pool is 26.4 meters.

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The values of the variables x and y are;

1, x = -y and y = 5. Option D

2. x= 1 and y = -1. Option A

Using the substitution method of solving simultaneous equations, we have;

4x + 7y = 19

y - x = 9

Now, make 'y' the subject from equation 2

y = 9 + x

Substitute the equation into equation 1

4x + 7(9 + x)= 19

expand the bracket, we have;

4x + 63 + 7x = 19

collect the like terms

11x = -44

x = -4

then,

y = 9 - 4 = 5

-3x + y = -4

4x + 3y = 1

make y' the subject from equation 1

y =-4 + 3x

Substitute the value

4x + 3(-4 + 3x) = 1

expand the bracket

4x - 12 + 9x = 1

13x = 13

x = 1

Substitute the value

y = -4 + 3

y = -1

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Step-by-step explanation:

a) 11*5=55

15*5=75

8*5+5=45

b) No, because (55+75+45=175°) and the perimeter of a triangle is 180°

The radius is 5.316 cm, height is 10.362 cm and Maximum volume is  

60.583 cm³.

We have,

Surface area of sphere = 36 cm²

4πr² = 36

πr² = 9

r = 3√π

r= 5.316

Now, Volume spherical cap

= 1/3 πh² (3R- h)

= 1/3π (10.362) (3 (5.316) - 10.362)

= 1/3 π (57.882132)

= 60.583 cm³

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The expected joint frequencies are

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

The table of values

Also, we have

People = 160

This means that

Male and Drama = 12.5% * 160

Male and Drama = 20

Male and Comedy = 25% * 160

Male and Comedy = 40

Female and Drama = 46.9% * 160

Female and Drama = 75

Female and Comedy = 15.6% * 160

Female and Comedy = 25

In conclusion, we have

Because the expected and the joint frequencies are not the same, gender is not independent of movie type

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-63.63 m/s is the rate of change of the distance between the plane and the car when both are maximum speed and the plane is ahead by 70m?

Let's use the Pythagorean theorem to relate the distance between the car and the plane to their individual distances traveled. Let d be the distance traveled by the car, then the distance traveled by the plane is d + 70 (since the plane is ahead by 70m). Then, the distance between them is given by:

distance = [tex]\sqrt{d^{2}+500^{2} }[/tex] (using Pythagorean theorem)

Now, let's differentiate both sides with respect to time (t) to find the rate of change of the distance between the car and the plane:

d(distance)/dt = (1/2)[tex](d^{2} +500^{2} )^{(-1/2)}[/tex] * (2d/dd)(dd/dt)

where the first term on the right side is the derivative of the square root expression and the second term is the derivative of d with respect to time.

Now we need to find d in terms of t, given the maximum speeds of the car and the plane. Let's assume that they both start at time t = 0 and are racing for a time of T. Then, we can write:

d = 200T (distance traveled by the car)

d + 70 = 300T (distance traveled by the plane)

Solving for T, we get:

T = 70/100 = 0.7 hours = 42 minutes

Substituting T back into the expressions for d, we get:

d = 200(0.7) = 140 km

d + 70 = 300(0.7) = 210 km

Now we can substitute these values into the expression for the rate of change of the distance between the car and the plane:

d(distance)/dt = (1/2)[tex](d^{2} +500^{2} )^{(-1/2)}[/tex]  * (2d/dd)(dd/dt)

d(distance)/dt = (1/2)[tex](140^{2} +500^{2} )^{(-1/2)}[/tex] * (2*140/60)(300 - 200)

d(distance)/dt = -63.63 m/s

Therefore, the rate of change of the distance between the car and the plane when both are at maximum speed and the plane is ahead by 70m is approximately -63.63 m/s. Note that the negative sign indicates that the distance between them is decreasing, since the plane is ahead of the car.

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The equation will have the solution in the form of an imaginary number "i" as: x = (3 ± 2i)/2

In a quadratic equation, an imaginary number is a complex number that can arise when trying to take the square root of a negative number.

We shall solve for x in the equation as follows:

(2x + 3)² - 2 = -6

add 2 to both sides

(2x + 3)² = 2 - 6

(2x + 3)² = -4

2x + 3 = √(-4) {taking square root of both sides}

subtract 3 from both sides

2x = 3 ± √(-4)

divide through by 2

x = [3 ± √(-4)]/2

note that: √(-4) = √(1-) × √4 where √(-1) = I, so;

x = (3 ± 2i)/2.

Therefore, the equation will have the solution in the form of an imaginary number "i" as: x = (3 ± 2i)/2

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Step-by-step explanation:

Arithmetic sequence with  d = 2    a1 = -6

a20 = -6 + 2(20-1) = 32

Answer:

16

Step-by-step explanation:

24 divided by X(3) is equal to 8, then 8+8 equals 16 (EASY)

The instantaneous velocity of the train at t = 9 seconds is approximately 6.8 m/s

To estimate the instantaneous velocity of the train at t = 9 seconds, we can consider the average velocities over several small intervals of time that include the point t = 9. This is an approximation of the slope of the tangent line to the curve s(t) at t = 9, which is the instantaneous velocity.

We can calculate the average velocity over each interval by dividing the change in displacement by the change in time:

Average velocity from [8.5, 9] = (s(9) - s(8.5)) / (9 - 8.5) = (8√9 + 1 - 8√8.5 + 1) / 0.5 = 6.34 m/s (approx.)

Similarly, we can calculate the average velocities over the other intervals:

[8.7, 9]: 6.48 m/s (approx.)

[8.9, 9]: 6.60 m/s (approx.)

[8.99, 9]: 6.66 m/s (approx.)

[9, 9.01]: 6.67 m/s (approx.)

[9, 9.1]: 6.74 m/s (approx.)

[9, 9.3]: 6.87 m/s (approx.)

[9, 9.5]: 7.00 m/s (approx.)

As we consider smaller intervals closer to t = 9, the average velocities approach a limit, which is the instantaneous velocity at t = 9. In this case, we see that the average velocities are increasing as we approach t = 9, indicating that the instantaneous velocity at t = 9 is also increasing.

Based on these calculations, we can estimate that the instantaneous velocity of the train at t = 9 seconds is approximately 6.8 m/s (averaging the average velocities from [8.99, 9] to [9, 9.5]).

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Answer:

  3/23 or 0.1304 or 13%

Step-by-step explanation:

Given 3 students have a brother and sister, and 20 students have only a brother, you want the probability that a student who has a brother also has a sister.

The conditional probability formula is ...

  P(A | B) = P(A&B)/P(B)

Here, this means ...

  P(has a sister | has a brother) = P(has both)/P(has a brother)

  = 3/(3 +20)

  = 3/23 ≈ 0.1304 ≈ 13% . . . . . probability of a sister if has a brother

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To determine what percentage of working adults in your neighborhood regularly ride the bus to work, the best sampling method and survey question are D. Enter the names of all adults in your neighborhood into a computer program to randomly select a sample and ask, "Do you ever ride the bus to work?"

The best sampling method involves random sampling of the population.

A random sample gives each member of the population an equal chance of being selected as a participant in the survey.

It is also described as a probability sampling method.

Thus, in this instance, the correct option is D.

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Answer: the answer is E

Step-by-step explanation:

Remember that the coordinates (5,−2π3) tell us the radius r=5 and the angle θ=−2π3. So the point should be on the circle labeled 5 and form an angle of −2π3 with the positive x-axis. Point E is the correct point.

Answer:

Step-by-step explanation:

Remember that the coordinates (5,−2π/3) tell us the radius r=5 and the angle θ=−2π/3. So the point should be on the circle labeled 5 and form an angle of −2π/3 with the positive x-axis. Point E is the correct point.

The system of inequalities that represents this real-world scenario is:

x + y ≤ 450  (The total people cannot be greater than 450)

7x + 4y ≤ 1150  (total price cap of $1,150)

A group of two or more simultaneously true inequalities is referred to as a system of inequalities. A system of inequalities can be solved by finding the set of values that satisfies every one of the inequalities in the system.

Therefore, The system of inequalities that represents this real-world scenario is:

x + y ≤ 450 (The total people cannot be greater than 450)

7x + 4y ≤ 1150 (total price cap of $1,150)

Where x is the number of adults and y is the number of campers.

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The values of c that satisfy Rolle's Theorem is 2.15 or -0.15.

The value of c that satisfies Roll's theorem is calculated as follows;

y = x³ - 3x² - x; [-1, 3]

Based on Roll's theorem conditions, since the function is a polynomial it is continuous.

The derivative is also a polynomial.

y' = 3x² - 6x - 1

The final condition;

y(-1) = (-1)³ - 3(-1)² - (-1)

y(-1) = -1 - 3 + 1

y(-1) = -3

y(3) = (3)³ - 3(3)² - 3

y(3) = 27 - 27 - 3

y(3) = -3

The three conditions of Rolle's theorem is statisfied,  so there exists at least one value of c in the interval (-1, 3) such that y'(c) = 0.

y' = 3x² - 6x - 1

y'(c) = 3c² - 6c - 1

3c² - 6c - 1 = 0

Solve the quadratic equation using formula method;

a = 3, b = -6, c = -1

c = 2.15 or - 0.15

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The time it will take the bird to travel 1.4 m is 0.5738 seconds.

In Science and Mathematics, velocity can be defined as the distance covered by an object per unit of time in a specific direction. This ultimately implies that, velocity is a vector quantity because it has both magnitude and direction.

In Mathematics and Science, the velocity of any a physical object can be calculated by using this formula;

Velocity = distance/time

244 cm/s to m = 244/100 = 2.44 cm/s

By making time the subject of formula, we have:

Time = distance/velocity

Time = 1.4/2.44

Time = 0.5738 seconds.

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Answer:

2(5(11) + 5(2.5) + 11(2.5))

= 2(55 + 12.5 + 27.5) = 2(55 + 40) = 2(95)

= 190 square centimeters

Answer:

The answer to your problem is, 7

Step-by-step explanation:

First you can either convert;

ml to liter

liter to ml

I will use liter to ml.

1.75 liters in ml is 1750 ml

So we can then divide, 1750 / 250 = 7

Which is the answer

Thus the answer to your problem is, 7

The value of y for this ordered pair is 7.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of line AC;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-2 + 8)/(-4 + 8)

Slope (m) = 6/4

Slope (m) = 3/2

At data point (-4, -2) and a slope of 3/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 2 = 3/2(x + 4)  

y = 3x/2 + 4

When x = 2, the y-value is given by;

y = 3(2)/2 + 4

y = 7.

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Answer:

Me: 60

Zayn and Attia: 6

Step-by-step explanation:

12 = 2 × 2 × 3

20 = 2 × 2 × 5

LCM of 12 and 20 = 2 × 2 × 3 × 5 = 60

My number is 60.

Zayn's and Attia's numbers are 6.

The measure of angle C is given as follows:

m < C = 44º.

To obtain the measures of the angles in this problem, we must consider that the sum of the measures of the internal angles of a triangle is of 180º.

Considering that the sum of the measures of the internal angles of a triangle is of 180º, and angles C, D and E, the value of x is obtained as follows:

4x - 16 + 6x - 1 + 4x - 13 = 180

14x - 30 = 180

14x = 210

x = 210/14

x = 15.

Hence the measure of angle C is obtained as follows:

m < C = 4 x 15 - 16 = 44º.

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After two years, Swathu will pay back the debt in full, which comes to Rs. 105287.27.

To find the total amount Swathu will pay back after 2 years on a loan of Rs. 90,000 with an interest rate of 8% per annum compounded half-yearly, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^{nt[/tex]

where:

A = the total amount Swathu will pay back

P = the principal amount borrowed (Rs. 90,000)

r = the annual interest rate (8%)

n = the number of times the interest is compounded per year (2 times, since it is compounded half-yearly)

t = the time period (2 years)

Substituting these values into the formula, we get:

[tex]A = 90,000(1 + 0.08/2)^{2*2}\\\\A = 90,000(1 + 0.04)^4\\\\A = 90,000(1.04)^4\\\\A = 90,000(1.16985856)\\[/tex]

A = 105287.27 (rounded to the nearest tenth)

Therefore, Swathu will pay back a total of Rs. 105287.27 after 2 years on the loan.

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Answer:

The union of sets A and B is:

A U B = {1, 2, 3, 4, 6, 8}

The solution to the equation is x = 10 or x = -2.

An equation refers to a mathematical expression showing that two expressions are equal.

It must have variables (e.g. a, c, x, y), constants (like 1, 13, 50, etc), and mathematical operations (like +, -, *, /).

To solve for x, we shall start with the given equation:

x + 6 = √(2x + 29) + 9

Subtract 9 from both sides:

x - 3 = √(2x + 29)

Square both sides:

[tex](x - 3)^2[/tex] = 2x + 29

Expand the left side:

[tex]x^2[/tex] - 6x + 9 = 2x + 29

We then subtract 2x and 9 from both sides:

[tex]x^2[/tex] - 8x - 20 = 0

Next, actor the quadratic equation:

(x - 10)(x + 2) = 0

Therefore, the equation x = 10 or x = -2

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The next number in the series would be 31 so the complete series is 101, 001, 66, 31.

The first thing we observe is that 101 equals 100 plus one. The second term, 001, equals 0 plus 1. Now consider the distinctions between consecutive terms:

101 - 001 = 100

001 - 66 = -65

When we look at the disparities (100, -65), we can see a pattern. The difference between 100 and 65 is a factor of 35. We can now apply this distinction to the final term in the series:

66 - 35 = 31

So the next number in the series is 31, completing the sequence: 101, 001, 66, 31.

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