6. 300 students were interviewed: 45 took PE, 45 took BIO, 45 took ENG, 12 took PE and BIO, 10 took PE and ENG, 8 took BIO and ENG, 4 took all three subjects. a) How many students took none of the three subjects? b) How many students took PE but not BIO or ENG? c) How many students took BIO and PE but not ENG​

5/18 counter-clockwise is equivalent to 100 degrees counter-clockwise.

What is Fraction ?

A fraction is a number that represents a part of a whole or a ratio between two quantities. It is expressed as a ratio of two integers, with the numerator (top number) representing the part or quantity being considered and the denominator (bottom number) representing the total or whole.

To convert a fraction of a full rotation to degrees, we can use the fact that a full rotation is equivalent to 360 degrees.

In this case, 5/18 represents a fraction of the full rotation, where the numerator (5) represents the number of counter-clockwise rotations and the denominator (18) represents the total number of rotations in a full circle.

To find the number of degrees, we can multiply the fraction by 360 degrees:

(5/18) * 360 = 100 degrees

Therefore, 5/18 counter-clockwise is equivalent to 100 degrees counter-clockwise.

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Answer:

The area of the garden is 78.5 square feet.

Step-by-step explanation:

If you are considering taking out a loan against the value of your home equity, there are several options to consider. One of the most common types of home loans for this purpose is a home equity loan or a home equity line of credit (HELOC).

The difference between the value of your home and the amount you owe on your mortgage is known as Home equity.

A home equity loan is a lump sum loan that allows you to borrow against the equity in your home. You receive the funds in one lump sum and then make fixed monthly payments over a set period of time, typically 5-15 years.

The interest rate on a home equity loan is generally fixed, which means that your monthly payments will remain the same throughout the life of the loan.

With a HELOC, you have access to a revolving line of credit, much like a credit card, and you only pay interest on the amount you borrow. The interest rate on a HELOC is typically variable, which means that your monthly payments may fluctuate over time.

Both home equity loans and HELOCs may make sense for helping your sister through a rough patch, as they can provide you with access to cash quickly and may offer lower interest rates than other types of loans. However, it's important to remember that both of these loans are secured by your home, which means that if you are unable to make your payments, you risk losing your home.

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The rectangle has a surface area of 6 1/4 squares.

The territory a rectangle occupies inside its 4 corners or limits is referred to as its area. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.

The amount of space within a form is measured by its area. In daily life, figuring out a shape's or surface's area can be helpful. For instance, you may require know how so much paints to buy to paint a board or the amount of grass to plant on a lawn.

To find the area,

[tex]Area=lenght*width[/tex]

[tex]Area=\frac{5}{2} *\frac{5}{2}[/tex]

[tex]Area=\frac{25}{4}[/tex]

[tex]Area=6\frac{1}{4} square unit[/tex]

Therefore, the area of the rectangle is [tex]Area=6\frac{1}{4} square unit[/tex]

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Using inequalities, Y(x=0) = -2 and X(y=0) = -2 in region 1.

To pick area 1, draw a line at the intersection of (-2,0) and (0, -2), then choose the right side. such as.

Region 2) To pick the region to the left or upwards in region 2, we must draw a line from (0,2) to (-2,4).

Y(x=0) = 2\sX(y=-2) = -4

Region 3) To pick the region to the right, we must draw a line connecting (-4,0) and (0,4), as I'll demonstrate.

Inequalities in mathematics describe the relationship between two non-equal numbers. Equal does not necessarily mean unequal. When two values are not equal, we typically use the "not equal symbol ()". However, several inequalities are utilised to compare the numbers, whether it is less than or higher than.

The feasible area is now visible. Let's determine the vertices' coordinates.

Where the blue and green lines intersect is our first vertex.

3x + 2 = x + 4 and y = 3x + 2

3x - x = 4 - 2

y = 3× (1) + 2 = 3 + 2 = 5 when 2x = 2x = 1

(X, Y) = Vertex 1 (1,5)

The intersection of the red and green lines is at vertex #2:

y = -x -2; y = x + 4; y = x + 4 = -x - 2; and y = x + x = -2 - 4

2x = -6, x = -6/2, and y = (-3) + 4 = -3 + 4 = 1 are the results.

(X, Y) = Vertex 2 (-3,1)

The intersection of the red and blue lines is at vertex 3:

y = -x - 2, y = 3x + 2 -x - 2, and y = 2 + 2 -4 x = 4 x = -4 / 4 = -1;

So, y = 3×(-1) + 2 = -3 + 2 = -1

(X, Y) = Vertex 3 (-1, -1)

Let's now modify the graph by including the supplied equation.

The intercept where Y=0 is 0 is given by f(x,y) = -3x + 5y = 0 5y = 3x + 0 y = 3/5 × X + 0

the gradient m = 3/5

A line can be drawn from (0,0) to (-10, -6)

Let's now examine how it would appear in the area where it is practical.

We can see that the function intercepts the blue line or the line of the second section, which is where the largest value is located.

y = 3x + 2 3x + 2 (3/5 - 3) x = 2 -12/5 × x = 2 x = -5/6.

Hence, y = 3x + 2 3/5 × (-5/6) = -1/2.

The maximum is therefore found at (x,y) = (-5/6, -1/2).

The point where the function crosses the red line now marks the minimum.

y = 3/5 × x; y = -x -2

3/5 x = -x - 2\s (3/5 + 1) × x = -2\s8/5 x = - 2\sx = -2× (5/8) = -5/4.

y = 3/5 × (-5/4) = -3/4

The minimum is thus found at (x,y) = (-5/4, -3/4)

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The translatiοn directiοn is 4 units tο the left.

A triangle is a clοsed, twο-dimensiοnal geοmetric figure with three straight sides and three angles. It is οne οf the basic shapes in geοmetry.

A pοlygοn with three edges and three vertices is called a triangle. It is οne οf the fundamental geοmetric shapes. Triangle ABC is a triangle with vertices A, B, and C. In Euclidean geοmetry, any three nοn-cοllinear pοints give rise tο a distinct triangle and a distinct plane.

The translatiοn directiοn is 4 units tο the left because Z' has mοved frοm (3,4) tο (-1,4), and the x-cοοrdinate has decreased by 4.

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After finding the difference, we found that the amount of rice left after lunch, written in mixed fraction form, is 9 11/12 lbs.

What are fractions?

Every number of equal parts is represented by a fraction, which also represents a portion of a whole. A single object or a collection of objects might be whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object. The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves. The number of parts into which the whole has been divided is shown by the denominator. How many sections of the fraction are displayed or chosen is shown in the numerator.

Given,

 The amount of rice the restaurant had when they opened = 13 lbs

The amount of rice that was cooked and served = 3 1/12lbs

We are asked to find the amount of rice left.

This can be found by subtracting the amount of rice served from the total amount of rice.

Note that the amount of rice served is in fractions.

So we use fraction subtraction to solve this.

Then,

amount of rice left = 13 - 3 1/12

3 1/12 is a mixed fraction.

We should convert it into an improper fraction.

3 1/12 = (3*12 + 1 ) /12 = 37/12

Now solving,

amount of rice left = 13 - 3 1/12 = 13 - 37/12

Taking LCM to make a common denominator.

LCM = 12

amount of rice left = 13 - 37/12 = (13*12 - 37)/12 = 119/12 = 9 11/12 lbs.

Therefore after finding the difference, we found that the amount of rice left after lunch, written in mixed fraction form, is 9 11/12 lbs.

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Rocio needs a total of 137/12 cups of butter for her holiday baking.

Rocio needs 4½ cups, 2½ cups, and 5⅓ cups of butter for her three recipes, respectively.

We can add these amounts of butter to find the total amount:

4½ cups + 2½ cups + 5⅓ cups

= 9/2 cups + 5/2 cups + 53/12 cups    (converting mixed numbers to fractions)

= 54/12 cups + 30/12 cups + 53/12 cups (finding a common denominator)

= 137/12 cups

Therefore, Rocio needs a total of 137/12 cups of butter for her holiday baking.

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Answer: x = 100

Step-by-step explanation:

The angles of a triangle add up to 180, meaning that (x-35)+(x-25)+(1/2 x - 10) = 180. Now you can solve for x

The charge for the third company for the 8 feet of copper pipe as required to be determined is; $8.50.

As evident from the task content;

For the first company; Pipe for $1.50 per foot and a rebate offering $2.00 off the total.

Therefore, total charge is; 8(1.50) - 2 = $10.

For the second company; Pipe for $1.75 per foot and a coupon offering $0.25 off each foot.

Therefore, total charge is 8(1.75) - 8(0.25) = $12.

Hence, since the better deal is; $10.

Ultimately, the charge of the third company whose offer is; $1.50 less than the charge of the better deal is; 10 - 1.50 = $8.50.

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The sοlutiοn tο the given prοblem οf trigοnοmetry cοmes οut tο be sin(b) = 3/5 if tan(A) = 3/4.

Relatiοnships between cubic splines and mathematics When the disciplines οf astrοphysics were cοmbined, it is thοught that the subject was bοrn in the third century B.C. Precise mathematical techniques can be used tο sοlve a large number οf geοmetric equatiοns οr tο identify the οutcοmes οf calculatiοns invοlving them. The study οf the six fundamental trigοnοmetric functiοns is knοwn as trigοnοmetry. They gο by many different names and abbreviatiοns, such as sine, dispersiοn, angle, οblique, etc (csc).

Here,

cοs(b) Plus sin(b) = 1

Using the equatiοn, we can find the sοlutiοn fοr cοs(b) in terms οf sin(b):

cοs(2b) = (1 - sin(2b)) (b)

Inputting this intο the fοrmula fοr tan(b), we οbtain:

Tan is equal tο sin(b)/√(1 - sin2(b)).

When we square bοth sides and multiply by the remainder, we get:

(Tan(b)) / (1 + (Tan(b))) Equals sin2(b)

By simplifying and substituting tan(b) = sin(A)/cοs(A), we οbtain:

the fοrmula fοr sin2(b) is (sin(A))/((cοs(A))² + (sin(A))²)

Inputting the numbers we previοusly discοvered fοr sin(A) and cοs(A), we οbtain:

=> sin²(b) = (3/5)

=> sin² / ((4/5)

=> sin² + (3/5)²)

=> sin²(b) = 9/25 / (16/25 + 9/25)

=> sin²(b) = 9/25 / 25/25

=> sin²(b) = 9/25 sin(b) = +/- 3/5

Sin(b), which is pοsitive in the first regiοn, results in:

sin(b) = 3/5

As a result, sin(b) = 3/5 if tan(A) = 3/4.

Therefοre, The sοlutiοn tο the given prοblem οf trigοnοmetry cοmes οut tο be sin(b) = 3/5 if tan(A) = 3/4.

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Answer:

I don't know if this helps.

Answer:

Step-by-step explanation:

Line 1: (2 - 7)/(-2 + 4) = -5/2

Line 2: (-1 + 8)/(0 + 5) = 7/5

Line 3: (8 + 2)/(-2 -2)= 10/-4 = -10/4 = -5/2

Line 1 and Line 2: Neither

Line 1 and Line 3: Parallel

Line 2 and Line 3: Neither

Answer: 7 years old

Step-by-step explanation: The two quickest ways to solve these types of problems are by guess and check, and systems of equations. I will show you how to solve this problem with systems of equations since it is a systematic method.

We can replace the ages of Ethan and David with variables. Ethan's age is x and David's is y. Ethan is 3 years older than David and this can be represented by: y+3=x since 3 will have to be added to David's age, y to get Ethan's age, x. A second equation we can make is x+y=17 since the sum of their two ages is 17. Now we solve the system by first isolating a variable and then plugging that into the second equation.

y+3=x         x is already isolated for us

x+y=17

(y+3)+y=17 We substitute x in the second equation for y+3

2y+3=17     Rearrange variables

2y=14

y=7             David's age, y, is 7.

Hope this helps!

To determine whether the function f(x) = (x^2-2x-3)/(x^2+3x+2) has any holes, we can factor the numerator and denominator and simplify the expression. The numerator can be factored as:

x^2 - 2x - 3 = (x - 3)(x + 1)

And the denominator can be factored as:

x^2 + 3x + 2 = (x + 1)(x + 2)

Therefore, we can simplify the function as:

f(x) = [(x - 3)(x + 1)]/[(x + 1)(x + 2)]

The factor of (x + 1) appears in both the numerator and denominator, so we can simplify further by canceling it out:

f(x) = (x - 3)/(x + 2)

Since (x + 1) was canceled out, we have a hole in the graph of the original function at x = -1. To find the coordinates of the hole, we can evaluate the simplified function at x = -1:

f(-1) = (-1 - 3)/(-1 + 2) = -4

Therefore, the hole in the graph of the original function is located at the point (-1, -4).

Answer:

it should be DCE

Step-by-step explanation:

Since both ABE and DCE are similar because because they are both corresponding angels that are congruent.  I'm sorry i couldn't think of another triangle but I'm hoping that at least helped a  bit

Based on the distribution of data, the box and whisker plot displays the results of the scientific test for two classes. It is incorrect to say that both sections have the same value for the third quartile.

The formulation of partial differential equation solutions uses distribution generalized functions. The likelihood of a specific value or range of values for a variable is known as the probability distribution. Cumulative distribution function, where the likelihood of a value not exceeding a certain value depends on that value. A list of the values recorded in a sample, or a frequency distribution. In coding theory, there are two types of distribution: inner and outer. distribution of a portion of a manifold's tangent bundle.Term distribution: the state of having all members of a category present. The distributive law from elementary algebra is generalized by the property of binary operations known as distributivity. the distribution.

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Answer:

The triangle is acute.

Step-by-step explanation:

To determine whether the side lengths of 3, 7, and 9 can form a triangle, we need to apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's check if this condition is satisfied for the given side lengths:

3 + 7 = 10 > 9, so the sum of the two smaller sides is greater than the largest side.

7 + 9 = 16 > 3, so the sum of the two smaller sides is greater than the largest side.

3 + 9 = 12 > 7, so the sum of the two smaller sides is greater than the largest side.

Since all three inequalities are true, we can conclude that the given side lengths of 3, 7, and 9 can form a triangle.

To determine whether the triangle is acute, right, or obtuse, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let's first determine which side is the longest. Since 9 is the largest side length, it must be the hypotenuse if the triangle is right-angled.

However, using the Pythagorean theorem, we can see that:

3^2 + 7^2 = 58 < 9^2, so the triangle is not right-angled.

Therefore, the triangle must be either acute or obtuse. To determine which one, we can use the law of cosines, which states that in any triangle:

c^2 = a^2 + b^2 - 2ab*cos(C)

where a, b, and c are the side lengths, and C is the angle opposite to side c.

Let's apply this formula to the triangle with side lengths 3, 7, and 9:

9^2 = 3^2 + 7^2 - 2(3)(7)*cos(C)

81 = 58 - 42*cos(C)

cos(C) = (58 - 81)/(-42) = 0.5476

C = cos^(-1)(0.5476) = 56.69 degrees

Therefore, the largest angle in the triangle is approximately 56.69 degrees. Since this angle is less than 90 degrees, we can conclude that the triangle is acute.

Answer:

obtuse angled triangle

Step-by-step explanation:

for the sides to form a triangle

the sum of any 2 sides must be greater than the third side.

3 + 7 = 10 > 9

3 + 9 = 12 > 7

7 + 9 = 16 > 3

then the 3 sides 3 , 7 , 9 will form a triangle

given 3 sides a , b , c with c the longest side

• if a² + b² = c² ⇒ right triangle

• if a² + b² > c² ⇒ acute angled triangle

• if a² + b² < c² ⇒ obtuse angled triangle

here a = 3 , b = 7 , c = 9

a² + b² = 3² + 7² = 9 + 49 = 58

c² = 9² = 81

since a² + b² < c²

then triangle is obtuse

Answer:

Step-by-step explanation: The equation should be

A = 35 - 4t

B = 50 - 7t

And, the Height = 15 inches

Calculation of the equation and height;

Since

Height of snowman A = 35 inches

Height of snowman B = 50 inches

Height decrease of snowman A = 4 inches per hour

Height decrease of snowman B = 7 inches per hour

Here, t = number of hours

So, the equation should be

A = 35 - 4t      

B = 50 - 7t      

Now for the same height

35 - 4t = 50 - 7t

-4t + 7t = 50 - 35

3t = 15

t = 15

So,

A = 35 - 4(5) = 35 - 20 = 15 inches

B = 50 - 7(5) = 50 - 35 = 15 inches

[tex]x^{5/6}[/tex]  is value of x in expression .

What is a mathematical expression?

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself.

                           This mathematical operation may be addition, subtraction, multiplication, or division. An expression's basic components are as follows: The formula is (Number/Variable, Math Operator, Number/Variable).

expression  = [tex]x^{1/2} . x^{1/3}[/tex]            

                     = [tex]x^{1/2 + 1/3}[/tex]    

                    =  [tex]x^{5/6}[/tex]

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The quadratic equation whose roots are (2α-β) and (2β-α) is given as follows:

y = x² - 5x - 23.02.

The quadratic equation for this problem is defined as follows:

x²-5x+3=0.

The coefficients of the equation are given as follows:

a = 1, b = -5, c = 3.

Hence the discriminant of the equation is of:

D = (-5)² - 4 x 1 x 3

D = 13.

Then the roots are given as follows:

Then the roots of the second equation are given as follows:

Applying the Factor Theorem, the quadratic function is defined as a product of it's linear factors, as follows:

y = (x + 2.91)(x - 7.91)

y = x² - 5x - 23.02.

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As a result, x = pi/6 is the only answer in the range [0,2pi).

When quantifying the angles of trigonometry or periodic functions, radians are frequently taken into account. Radians are always expressed in units of pi, with pi equivalent to either 3.14 or 22/7.

We can start by simplifying the left-hand side of the equation using the identity:

csc x = 1/sin x

4 sec x csc x = 4(1/cos x)(1/sin x) = 4/(cos x sin x)

Substituting this back into the original equation, we get:

4/(cos x sin x) = 8 csc x

Multiplying both sides by cos x sin x, we get:

4 = 8 sin x

Dividing both sides by 8, we get:

sin x = 1/2

This means that x is either pi/6 or 5pi/6, since these are the two angles in the interval [0,2pi) where sin x = 1/2.

However, we need to check if these solutions satisfy the original equation.

For x = pi/6:

4 sec x csc x = 4 sec(pi/6) csc(pi/6) = 4(2) (2/√3) = 16/√3

8 csc x = 8 csc(pi/6) = 8(2/√3) = 16/√3

So, x = pi/6 is a solution.

For x = 5pi/6:

4 sec x csc x = 4 sec(5pi/6) csc(5pi/6) = 4(-2) (-2/√3) = 16/√3

8 csc x = 8 csc(5pi/6) = 8(-2/√3) = -16/√3

So, x = 5pi/6 is not a solution.

Therefore, the only solution in the interval [0,2pi) is x = pi/6.

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Answer:

Suppose the original function is denoted by f(x). To represent the new function that is vertically stretched by a factor of 4 and then translated 3 units to the right, we can use the following equation:

g(x) = 4 f(x - 3)

In this equation, f(x - 3) represents the original function f(x) translated 3 units to the right, and the multiplication by 4 stretches the function vertically by a factor of 4. Therefore, g(x) represents the new function that is vertically stretched by a factor of 4 and then translated 3 units to the right.

Step-by-step explanation:

The volume of the sphere is,

⇒ The volume of sphere = 14,130 cm³

The multiplication means to add a number to itself with a particular number of times. And, Multiplication can be viewed as a process of repeated addition.

Given that;

Radius of sphere = 15 cm

Now, We know that;

⇒ The volume of sphere = 4/3πr³

Substitute value of Radius = 15 cm

⇒ The volume of sphere = 4/3 × 3.14 × 15³

⇒ The volume of sphere = 14,130 cm³

Thus, The volume of the sphere is,

⇒ The volume of sphere = 14,130 cm³

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Answer:

Step-by-step explanation:

To rewrite the equation x² + 18x + 7 = 4 in the form (x - p)² = q, we need to complete the square by adding and subtracting a constant term.

First, we subtract 4 from both sides of the equation:

x² + 18x + 7 - 4 = 0

Simplifying, we get:

x² + 18x + 3 = 0

To complete the square, we need to add and subtract the square of half the coefficient of x, which is (18/2)^2 = 81:

x² + 18x + 81 - 81 + 3 = 0

Simplifying, we get:

(x + 9)² - 78 = 0

Now, we can rewrite the equation in the desired form by adding 78 to both sides:

(x + 9)² = 78

Therefore, the values to be entered in the boxes are:

1: (x + 9)

2: 78

Angles a and b are each measured at 97°, while angles c and d are each measured at 68°. Angles and lines were used to arrive at the solution.

Straight lines have careless depth and careless width. Other types of lines include those that are perpendicular, transverse, and intersecting other lines. A form is considered to have an angle if two of its rays originate from the same location.

We are given two parallel lines so,

Angle a = 97°   (Corresponding angles)

We know that angles on a straight line form a linear pair.

So,

⇒112° + d = 180°

⇒d = 68°

Angle c = 68°     (Alternate interior angles)

Using angle sum property,

⇒ a + b + 68° = 180°

⇒ 97° + b + 68° = 180°

⇒ b = 15°

Hence, the missing values have been obtained.

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Answer:

You didn't give the answers

Equations that correctly expresses the system of equations in standard form are x + y = 22 and 3x + 4y = 76.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given,

Cost of blue sea shells = $3

Cost of pink sea shells = $4

Cost of 22 sea shells = $76

Let number of blue sea shells is x and number of pink sea shells is y

then number of total shells

x + y = 22

Cost of shells

3x + 4y = 76

Hence, x + y = 22 and 3x + 4y = 76 are the equations that correctly expresses the system of equations in standard form

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Answer:

the third one

Step-by-step explanation:

the third one