MATH!!! HELP!! MULTIPLE QUESTIONS (because they're all connected) BUT WORTH LOTS OF POINTS.

requirements in last attachment

Answer:B

Step-by-step explanation:

Answer:

no noob

Step-by-step explanation:

Answer:

infinite number of solutions

Step-by-step explanation:

6(x + 7) = 6x + 42 ← distribute parenthesis on left side

6x + 42 = 6x + 42

Since the expressions on both sides are the same then any value of x will be a solution, that is

The equation has an infinite number of solutions

Answer: To find the ratio of the dimensions of the actual room to that of the scale model, we can divide the dimensions of the actual room by the dimensions of the scale model.

The dimensions of the actual room are 15m by 9m by 12m, and the dimensions of the scale model are 5m by 3m by 4m.

Therefore, the ratio of the dimensions of the actual room to that of the scale model is:

length: 15m / 5m = 3 : 1

width: 9m / 3m = 3 : 1

height: 12m / 4m = 3 : 1

So, the ratio of the dimensions of the actual room to that of the scale model is 3:1 for all dimensions (length, width, and height)

The ratio of the dimensions of the scale model to that of the actual object is 1:16

so to find the length and width of the actual object, you can use this relation

length = scale model length * 16 = 2.416 = 38.4m

width = scale model width * 16 = 1.816 = 28.8m

So the length and width of the actual object are 38.4m and 28.8m respectively.

Step-by-step explanation:

Thus, the probability that the focus group will have two males and two females is 0.3.

To determine the total number of possible ways to select four members from a department of 10. This is known as the sample space and is calculated using the combination formula, which is:
n C r = n! / r! (n - r)!

where n is the total number of individuals (in this case, 10) and r is the number of individuals being selected (in this case, 4).

So, the sample space for selecting four members from a department of 10 is:
10 C 4 = 10! / 4! (10 - 4)! = 210

Next, we need to determine the number of ways to select two males and two females from a department with 7 males and 3 females.

This is calculated using the multiplication principle, which states that the total number of ways to perform a sequence of events is equal to the product of the number of ways to perform each individual event.

So, the number of ways to select two males and two females from a department with 7 males and 3 females is:
(7 C 2) x (3 C 2) = 21 x 3 = 63

Finally, we can calculate the probability of selecting a focus group with two males and two females by dividing the number of ways to select two males and two females by the total number of possible ways to select four members:
63 / 210 = 0.3

Therefore, the probability that the focus group will have two males and two females is 0.3. The answer is d.

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translating phrases and sentences into expressions, equations, and inequalities is an important skill in mathematics. It involves identifying key words and phrases that indicate mathematical operations and relationships. By understanding these key words, we can represent real-world problems using mathematical language and symbols, making it easier to solve and analyze them.

translating phrases and sentences into expressions, equations, and inequalities

When solving mathematical problems, it is often necessary to translate phrases and sentences into mathematical expressions, equations, and inequalities. This process involves identifying key words and phrases that indicate mathematical operations and relationships.

For example, let's consider the following sentence:

'The sum of a number and 5 is equal to 12.'

In this sentence, the key words 'sum,' 'number,' 'equal to,' and '12' indicate that we need to perform addition and find the value of the unknown number. We can represent this sentence as the following equation:

x + 5 = 12

Here, 'x' represents the unknown number.

Similarly, let's consider the following sentence:

'Twice a number decreased by 7 is greater than 15.'

In this sentence, the key words 'twice,' 'decreased by,' 'greater than,' and '15' indicate that we need to perform multiplication, subtraction, and comparison. We can represent this sentence as the following inequality:

2x - 7 > 15

Here, 'x' represents the unknown number.

By understanding key words and phrases, we can effectively translate real-world problems into mathematical language and solve them using expressions, equations, and inequalities.

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1) An inequality to represent the given phrase is 5q>30.

2) An equation to represent the given phrase is 2b²=8.

1) The given phrase is "The product of 5 and q is greater than 30."

Here, the product of 5 and q = 5×q

= 5q

Now, the product is greater than 30.

Thus, 5q>30

q>30/5

q>6

2) The given phrase is "Twice the square of b is equal to 8."

Here, the square of b = b×b

= b²

Twice the square of b = 2b²

So, the product is equal to 8.

That is. 2b²=8

b²=4

b=±2

Therefore,

1) An inequality to represent the given phrase is 5q>30.

2) An equation to represent the given phrase is 2b²=8.

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"Your question is incomplete, probably the complete question/missing part is:"

Translate phrases and sentences into expressions, equations and inequalities.

1) The product of 5 and q is greater than 30.

2) Twice the square of b is equal to 8.

35.45 N is the tension in the wire on either side of the pulley.

A wheel on an axle or shaft known as a pulley is used to transfer power from the shaft to the cable or belt or to sustain movement and direction change of a taut cable or belt.

So, we know that:
Block A's (M1) weight is 12 kg.

Block B's weight (M2) is 5 kg.

Pulley's mass (M) is 2.10 kg.

Pulley's diameter is 0.560 meters.

Pulley's radius is 0.28 meters.

Now, find the wire tension on both sides of the pulley.

This relationship can be used to calculate the tension in the wire on both sides.

T₁ = m₁* a

T₁ = ( 12 * 2.71 )

T₁ = 32.52 N

And

T₂ (strain on the wire's reverse side)

T₂ = ( m₂ * g ) - m₂* a

T₂ = ( 5 * 9.8 ) - ( 5 * 2.71 )

T₂ =  35.45 N

Therefore, 35.45 N is the tension in the wire on either side of the pulley.

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Complete question:
A 12.0-kg box resting on a horizontal, frictionless surface is attached to a 5.00-kg weight by a thin, light wire that passes over a frictionless pulley (Fig. E10.16).

The pulley has the shape of a uniform solid disk of mass 2.10 kg and diameter of 0.560 m.

After the system is released, find the tension in the wire on both sides of the pulley.

Answer:

8√57/57

Step-by-step explanation:

a² + b² = c²

a² + 8² = 11²

a² + 64 = 121

a² = 57

a = √57

For angle Θ, opp = 8, adj = √57, hyp = 11.

tan Θ = opp/adj = 8/√57 = 8√57/57

Answer:

4

Step-by-step explanation:

1/2 goes into 1/8 4 times.

Answer:

Step-by-step explanation:

area = pi x 4sq. = 50.3

circumfrence 2 x pi x 4 = 25,1

Answer:

$855.00

Step-by-step explanation:

85.50 x 15 = 1,282.50

2,137.50 - 1,282.50 = 855.00

1. The number of students that the art academy has per teacher is 16.

2. The number of students that the art academy has per tutor is 9.

3. With 108 students, the art academy requires 12 tutors, given the student-to-tutor ratio of 9:1.

In this situation, we can use the mathematical operation of division to state the ratio of students to either teachers or tutors.

The parts of the division operation include the dividend, the divisor, and the quotient, which is the result of applying the divisor to the dividend.

The number of teachers for 80 students = 5

1. The number of students per teacher = 16 students (80/5)

The number of tutors for 36 students = 4

2. The number of students per tutor = 9 students (36/4)

3. If the students are 108, the number of tutors = 12 tutors (108/9)

Thus, after determining the quotients, we can relate the number of students to teachers and tutors using ratios.

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An arts academy requires there to be 5 teachers for every 80 students and 4 tutors for every 36 students.

Answer:

\(3\)

Step-by-step explanation:

\(\mathrm{The\ slope\ of\ a\ line\ passing\ through\ the\ points\ (x_1,y_1)\ and\ (y_2,y_1)\ is\ given\ by:}\\\mathrm{Slope(m)=\frac{y_2-y_1}{x_2-x_1}}\\\\\mathrm{According\ to\ the\ question,}\\\mathrm{(x_1,y_1)=(0,-2)}\\\mathrm{(x_2,y_2)=(-2,-8)}\)

\(\mathrm{Therefore\ the\ slope=\frac{-8-(-2)}{-2-0}=\frac{-8+2}{-2}=3}\)

The value of cos2x when sine of x equals negative 15 over 17 and cos x > 0 is -161/289.

The ratio of the neighboring side's length to the longest side, or hypotenuse, in a right triangle is known as the cosine. Let's say that the hypotenuse of a triangle ABC is written as AB, and the angle between the hypotenuse and base is written as.

It's interesting to see that cos's value varies depending on the quadrant. As observed in the above table, cos 0°, 30°, etc. have positive values while cos 120°, 150°, and 180° have negative values. Cos will have a good value in the first and fourth quadrants.

Given that, sin x equals negative 15 over 17.

Using the Pythagoras theorem we have:

(17)² = (- 15)² + y²

y = 8

The value of cos x = 8/17

Then the value of cos2(x) is calculated using the formula:

cos2x = cos²x - sin²x

cos2x = (8/17)² - (15/17)²

cos2x = -161/289

Hence, the value of cos2x when sine of x equals negative 15 over 17 and cos x > 0 is -161/289.

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The five-number summary first need to sort the data in ascending order. Then we can find the minimum value is the smallest data point and the maximum value is the largest data point.

Generally, the five-number summary is a set of descriptive statistics that summarizes a dataset.

It includes the minimum value the first quartile (Q1) the median (Q2) the third quartile (Q3) and the maximum value.

These statistics divide the dataset into four equal parts with the median being the middle value.

Q1 is the value below which 25% of the data falls and Q3 is the value below which 75% of the data falls.

The median is the middle value of the dataset or the average of the two middle values if the dataset has an even number of values.

Q1 is the median of the lower half of the dataset and Q3 is the median of the upper half of the dataset.

Once you provide the table or data I can help you find the five-number summary that matches the data.

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Answer:

x= 2

Step-by-step explanation:

please study its simple

Answer:

  x =2

Step-by-step explanation:

   11x=22

11x/11=22/11

      x =2

Hope you got it

If you have any question just ask me

Answer:

movment and breath

Step-by-step explanation:

Answer:

Similarities:

You work out

They are both a form of dance

Differences:

One is made up while the other isn't

One is for workout while the other for fun

Step-by-step explanation:

I do hope I was able to help! :)

we can calculate the center and radious using this form of the equation of the circle

Where D is -2, E is 16 and F is 61

Center is

where a is

and b is

Radious

radious is 2 units

the line segment after a 90 counterclockwise rotation about the origin is attached accordingly.

A rotation is a sort of transformation  that rotates each point in a figure a specific number of degrees around a particular  point.

To do a 90-  degree counterclockwise rotation about  the origin, we can use the following rotation  formula

x ' = x *  cos( θ) - y * sin(θ)

 y' =  x * sin(θ )+ y * cos( θ)

where   (x, y) are the original coordinates and (x ', y') are the coordinates after the rotation.

Applying this

For   point A (- 5, -3) we have

x' = (-5) * cos(90°) - ( -3) * sin(90 °) = 3

y' = (-5) * sin(90°)+ (-3) * cos(90°) =  -5

So the new coordinates after the 90-degree counterclockwise rotation about the origin for point A are (3, -5).

 point B (1  , -2)

x' =  (1 ) * cos(90°) - (-2) * sin(90°) = 2

y ' = (1 ) * sin ( 90°) + ( - 2) * cos (90 °) = 1

So the new coordinates after the 90-degree counterclockwise rotation about the origin   for point B are (2, 1).

The line segment after a 90-degree counterclockwise rotation about the origin would connect point A' (3, -5) to point B' (2, 1).

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The sketch of the function y = \(x^{2}\) - x - 3 for -3 <= x <= 3 reveals a parabolic curve that opens upwards. The turning point of the parabola, also known as the vertex, can be identified as (-0.5, -3.25).

To sketch the graph of y = \(x^{2}\) - x - 3, we consider the given domain of -3 <= x <= 3. The function represents a parabola that opens upwards. By calculating the coordinates of the turning point, we can locate the vertex of the parabola.

To find the x-coordinate of the turning point, we use the formula x = -b/2a, where a and b are the coefficients of the quadratic equation. In this case, a = 1 and b = -1. Substituting these values, we have x = -(-1)/2(1) = -0.5.

To find the y-coordinate of the turning point, we substitute the x-coordinate (-0.5) into the equation y = \(x^{2}\) - x - 3. Evaluating this expression, we get y = \(-0.5^{2}\) - (-0.5) - 3 = -3.25.

Therefore, the turning point of the parabola is approximately (-0.5, -3.25).

From the sketch, we can estimate the approximate solutions to the equation \(x^{2}\)- x - 3 = 0 by identifying the x-values where the graph intersects the x-axis. These solutions are approximately x ≈ -2.5 and x ≈ 1.5.

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Answer:

0.3 (3 repeating)

Step-by-step explanation:

Hope this helps!!

Answer:

0.33333333333333333333333333333333

Step-by-step explanation:

The dimensions of impulse are (M¹L¹T⁻¹).

Impulse is equal to force multiplied by time, or can be formulated as:

P = FT

where:

P = impulse

F = force

T = time

The dimensions of force and time are:

Dimension of Force: (M¹L¹T⁻²)

dimensions of Time: (T).

When you multiply these two quantities together, you get :

P = FT

P = (M¹L¹T⁻²) * (T)

P = (M¹L¹T⁻¹).

Therefore, the dimensions of impulse are (M¹L¹T⁻¹).

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Trigonometric functions are real functions that relate the angle of a right triangle to the length rates of two sides.

Trigonometric ratios are rates that we can use to find the missing sides or angles of a right triangle.

The particle stays in the box and the surge function is nonstop, the value of ψ( X) must be zero on each side. This means that the value of ψ( X) must be zero for X = 0 and X = L.

But the value of the cosine function is 1 at X = 0, so a function like Acos( LX) isn't a suitable result for a flyspeck in a one- dimensional box.

The boundary conditions for patches present in a one- dimensional box are given below.

1. A dribble is always confined to being only inside the box and can not live outside the box.

2. The overall probability of chancing a flyspeck in a box is always one.

3. The surge function must be nonstop.

Consider the expression of the surge function as follows

ψ() = Acos{ nπ/ L x}, is a surge function.

A = is constant.

x = is any point along the length of the box.

L =  length

Since the flyspeck stays in the box and the surge function is nonstop, the value of ψ( x) should be zero on either side.

This means that the value of ψ( x) must be zero for x = 0 and x = L. But the value of the cosine function is 1 at x = 0. hence a function of type Acos( Lx) isn't a suitable result for a flyspeck in a one- dimensional box.

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Answer:

-5

Step-by-step explanation:

Answer:

The coefficient is the number before the variable. In this, they are asking for the first term which is -5m. The coefficient is -5.

Step-by-step explanation:

The total increase in the population between the 1st and 6th year is 6100

Given,

Rate of increase in the population of cattle = 800 + 60t, Where t is the number of years. From the above statement, it is evident that the given population increases every year. We need to find how much the population has increased between the first and the sixth year.

First we need to find the increase in the population between 1st year and 6th year.

Using the rate, we can say;

Rate of increase in the first year = 800 + 60(1)

= 860

Rate of increase in the second year = 800 + 60(2)

= 920

Rate of increase in the third year = 800 + 60(3)

= 980

Rate of increase in the fourth year = 800 + 60(4)

= 1040

Rate of increase in the fifth year = 800 + 60(5)

= 1100

Rate of increase in the sixth year = 800 + 60(6)

= 1160

Total increase in the population between 1st and 6th year = 860 + 920 + 980 + 1040 + 1100 + 1160

= 6100

Therefore, we found out that the total increase in the population between the 1st and 6th year is 6100.

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The determinant of matrix A is 23 and using an inverse matrix, the system of linear equations is solved as x = (1/23) [9, -10].

Given that a sequence is defined by an=7+8(n−1), for n≥1.

The above sequence is in the form of an arithmetic sequence. The general formula for the nth term of an arithmetic sequence is given by an=a1+(n−1)d where a1 is the first term and d is the common difference.

The first term, a1 is 7 and the common difference, d is 8.

The 15th term is T15=7+8(15−1)

=115.

The last term of the sequence is 599. Hence the total number of terms is n=599.

Using the formula for the sum of n terms of an arithmetic sequence:

Sn=(n2)[2a1+(n−1)d].

Here, the first term a1=7, the common difference d=8, and the total number of terms n=599.

Therefore, sum of all terms of the sequence =115(1+599)2

=34770.

The system of linear equations is:

2x1​−5x2​=9−3x1​+4x2​

=−10  

We can write this as a matrix equation Ax=b by writing the coefficient matrix and the variable matrix as follows:

2−5−34x1x2=9−10

Ax=b

The determinant of matrix A is given by

|A|=2(4)−(−3)(−5)

=23

We can find the inverse of matrix A as follows:

A−1=23 4−5−3−2

Using the inverse of matrix A, we can solve the system of equations Ax=b as follows:

A−1Ax=A−1

b⇒x=A−1

b=23 4−5−3−2 9

10=1−23

Thus, T15 is 115, the total number of terms is 599, and the sum of all the terms of the sequence is 34770.

The system of linear equations in matrix form is Ax=b where A is a coefficient matrix, x is a variable column matrix and b is a column matrix. The determinant of matrix A is 23 and using an inverse matrix, the system of linear equations is solved as x = (1/23) [9, -10].

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Step-by-step explanation:

The equation is   sinθ * cosθ - sinθ = 0

θ = 0 + 2kπ

θ = 2kπ where k is any integer

The solutions to the equation are: {0 degree, 180 degree, 360 degree, 360 degree + 180 degree n, where n is any integer}

Hence, the correct option is C.

The given equation is:

sin theta × cos theta - sin theta = 0

We can factor out the sine theta:

sin theta (cos theta - 1) = 0

This means that either sin theta = 0 or cos theta - 1 = 0.

If sin theta = 0, then theta = 0, 180 degrees, 360 degrees, etc.

If cos theta - 1 = 0, then cos theta = 1, which means that theta = 0 degrees and 360 degrees.

Therefore, the solutions to the equation are:

{0 degree, 180 degree, 360 degree, 360 degree + 180 degree n, where n is any integer}

So the answer is C.

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The area of the swimming pool cover is approximately 159.27 square feet, rounded to the nearest hundredth.

To find the area of the swimming pool cover, we can calculate the area of the rectangle and the area of the semicircle separately.

Area of the rectangle:

The length of the rectangle is 12 feet and the width is 10 feet. The formula to calculate the area of a rectangle is:

Area_rectangle = length × width

Area_rectangle = 12 × 10

Area_rectangle = 120 square feet

Area of the semicircle:

The radius of the semicircle is half the distance between the parallel lines, which is 10/2 = 5 feet. The formula to calculate the area of a semicircle is:

Area_semicircle = (π × radius²) / 2

Area_semicircle = (π × 5²) / 2

Area_semicircle = (π × 25) / 2

Area_semicircle ≈ 39.27 square feet

The total area of the swimming pool cover:

To find the total area, we add the area of the rectangle and the area of the semicircle:

Total_area = Area_rectangle + Area_semicircle

Total_area = 120 + 39.27

Total_area ≈ 159.27 square feet

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Answer:

\(\huge\boxed{\sf (x*4) + (x*5) = 54}\)

Step-by-step explanation:

\(\sf x(4+5) = 54\\\\Applying \ distributive \ property\\\\(x*4) + (x*5) = 54\\\\Distributive\ Property\ is:\\\\A(B+C) = (A*B)+(A*C)\\\\\rule[225]{225}{2}\)

Hope this helped!