3. A box contains 36 books and some toys. The ratio of the number of books to the number of toys is 4 : 5.
After some toys are given away, the ratio of the number of books to the number of toys becomes 12:11. Find:

(1) the initial number of toys in the box,

(2) the number of toys that are given away.

Answer:

1) 1.5 meters

2) 75° or (5/12)π radians

3) A = (5/12)πr^2

4) A = (5/12)π(1.5^2)

= 15π/16 square meters

= about 2.95 square meters

The set of inequalities that expresses the given relationships are -6 < -2 and -2 > -4. The correction is second option -6 < -2 and -2 > -4

From the question, we are to determine the set of inequalities that expresses the relationships

From the given information,

The given relationships are:

A score of -6 is lower than a score of -2. A score of -2 is higher than a score of -4.

First, we will write the first relationship as an inequality

A score of -6 is lower than a score of -2

This means that -6 is less than -2.

Using inequalities symbols, we can write that

-6 < -2

Now,

For the second relationship :

A score of -2 is higher than a score of -4

This means, -2 is greater than -4

Using inequalities symbols, we can write that

-2 > -4

Hence,

The inequalities that express the relationships are -6 < -2 and -2 > -4

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The factored form of the equation 4x² + 20x + 200 = 0 is 4(x + (5/2) +-5/2+√7(5/2i))(-5/2+√7(-5/2i))

To factor completely, we can begin by factoring out the greatest common factor of the three terms, which is 4:

4(x² + 5x + 50) = 0

Next, we want to factor the quadratic expression in parentheses.

we can use the quadratic formula, which states that the solutions to the equation ax² + bx + c = 0 are given by:

x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 1, b = 5, and c = 50, so we have:

x = (-5 ± √(5² - 4(1)(50))) / 2(1)

x = (-5 ± √(-175)) / 2

x=-5/2+√7(5/2i)

x=-5/2+√7(- 5/2i)

The factored form of the equation 4x² + 20x + 200 = 0 is:

4(x + (5/2) +-5/2+√7(5/2i))(-5/2+√7(-5/2i))

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Truck B consumed 0.045 mL more diesel than Truck A.

The fuel consumption for each truck is obtained applying the proportions in the context of the problem.

A proportion is applied as we are converting a fraction to decimal, dividing the numerator by the denominator, as follows:

Hence the difference is given as follows:

0.535 - 0.49 = 0.045 mL.

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Answer:sine

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

i got tHAT TEST TRUST ME

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Answer:

the answer is...

Step-by-step explanation:

6d^2 + 10d + 21

The calculated Social Security tax is $ 6621.60 on the maximum taxable earning, that is $106800 on the rate of 6.2% and Medicare tax is  $1812.50 on the annual salary, that is $125,000 on the rate of 1.45%.

Hence option d is the correct option.

The annual salary of an individual is given as  $125,000.

Medicare tax is levied on the annual salary of an individual, that is on $125,000. It is given as 1.45 % on $125,000.

The maximum taxable earnings is $106,800 and Social Security tax is levied on this $106,800. It is given as 6.2% on $106,800.

Thus, applying basic rule of percentage calculation we get,

Earnings from Social Security tax  = $(6.2% of 106800)

= ${(62/100*10)(106800)

= $ 6621.60

Earnings from Medicare tax = $(1.45% of 125000)

=  $(145/100*100)(125000)}

= $1812.50

Hence option d Social Security tax: $6,621.60, Medicare tax: $1,812.50 is the correct option.

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The graphical representation that will be most appreciated for the data would be box plot, because the median can easily be determined from the large set of data. That is option A.

The box plot is a type of graphical representation of data that gIves more than one detail about the data set such as;

Box plots allow you to compare multiple data sets better than others dues to the above listed features that it has.

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Answer:

linear

Step-by-step explanation:

its linear because the data shows a straight line:)

Answer:

Linear

Step-by-step explanation:

linear equation forms a straight line on the graph. A nonlinear equation forms a curve on the graph.

The diameter of the bike's tire is 2.325 inches.

Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of circle defines the region occupied by it.  If we open a circle and make a straight line out of it, then its length is the circumference. It is usually measured in units, such as cm or unit m.

A mountain bike tire completes 15 revolutions and travels 146 feet.

Now,

1 revolution of a tire is equal to the circumference of the tire.

Since we have 15 revolutions, we should take 15C=146

where C=πd where π is pi (use 3.14 or the pi symbol).

Our equation is:

20πd=146.

Then solve for d:

20 × 3.14 × d = 146

62.8d = 146

d = 146/62.8

d = 2.325 inches.

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She needs 74.25 ft² of glass to cover the pyramid.

To obtain the surface area of any prism, we combine the areas of all the parts that compose the prism.

The pyramid in this problem is composed as follows:

The area of the square base is given as follows:

As = 5.5² = 30.25 ft².

The area of the four triangles is given as follows:

At = 4 x 1/2 x 5.5 x 4

At = 44 ft².

Hence the surface area of the pyramid is given as follows:

S = As + At

S = 30.25 + 44

S = 74.25 ft².

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The required amount of stock is of $950 for  both brokers charge the same commission from the linear equation in one variable.

Let the total amount of stock be x (in dollars).

Fierro Brothers charges their customers a $19 flat fee per trade. Whereas, the Sondo Investment House charges 2% as the commission of trade.

Thus the given condition is Fierro Brothers charges equal commission fee on the required amount of stock as Sondo Investment house.

This relation can be shown in terms of linear equation as,

19 = 2% of x

⇒ 19 = (2/100)x

This linear equation is in the form of linear equation in one variable.

⇒ x= 19*(100/2)

⇒ x = 950

Therefore, on single trade of stock of $950 Fierro Brothers charges $19 fee (flat) as their commission which is equal to the commission earned by Sondo Investment House at the rate of 2% on trade.

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Answer: Dude adove is WRONGGG

Step-by-step explanation:

ANSWER IS  540

Answer:

  c. 540°

Step-by-step explanation:

You want to know which angle θ has cos(θ) = -1.

The cosine function is periodic with period 360°. The smallest positive angle θ for which cos(θ) is -1 is 180°. The next such angle is ...

  180° +360° = 540° . . . . . choice D

__

Additional comment

A graph of the cosine function is attached. The horizontal axis is in degrees.

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Answer: 13%

Step-by-step explanation:

10/74 = 0.13513513513

The result of the vector multiplication of a scalar is a vector.

A vector has both magnitude and direction while a scalar has only magnitude and no direction.

When each element of the vector is multiplied by the scalar when a scalar and a vector are multiplied. The resulting vector is multiplied by the scalar, but it still has the same direction as the original vector.  Thus when we multiply the vector by the scalar what we get is a vector as we can see in this question.

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In order to find the upper and lower bounds of a rounded number:

The upper and lower bounds can be found by dividing the degrees of accuracy by 2 and then subtracting and adding with the value to give the lower and upper bounds respectively.

Kindly check the above explanation inorder to know how to calculate the value as your information is incomplete

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How does one find the upper and lower bound of a variable

The missing measures for the triangle are given as follows:

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle B is obtained as follows:

m < B + 73 + 42 = 180

m < B = 180 - 115

m < B = 65º.

Then the relation is:

34/sin(73º) = a/sin(42º) = b/sin(65º).

Then the value of a is obtained as follows:

34/sin(73º) = a/sin(42º)

a = 34 x sine of 42 degrees/sine of 73 degrees

a = 23.8.

The value of b is obtained as follows:

34/sin(73º) = b/sin(65º)

b = 34 x sine of 65 degrees/sine of 73 degrees

b = 32.2.

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The values of following in parallel lines are:

Angle 3 and Angle 6 are an example of corresponding angles. (Option D is the correct answer).

Angle 1 and Angle 5 are an example of corresponding angles. (Option D is the correct answer).

Angle 6 and Angle 7 are an example of alternate interior angles. (Option B is the correct answer).

Angle 28 would not be congruent to the measure of 27. (Option A is the correct answer).

Angle 41 and Angle 23 are an example of corresponding angles. (Option D is the correct answer).

Option B: 23 is not an example of supplementary angles.

Angle 22 is vertical to Angle 27. Therefore, m22 = m27 = 115°.

Angle 23 and Angle 25 are alternate interior angles, so they are congruent. Therefore, m23 = m25 = 63°.

Angle 1 and Angle 26 are corresponding angles, so they are congruent. Therefore, mz1 = mz6 = 57°.

Parallel lines are two or more lines in a plane that never intersect each other, no matter how far they are extended. In other words, they are always at the same distance from each other and never cross.

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Answer: probably  89

Step-by-step explanation: looked it up "you have the wrong picture up"

The hypotenuse of the given right-angled triangle is 89 units.

From the below figure, the base of the triangle AB = 39 units

The height of the triangle AC = 80 units

To know the hypotenuse of the given triangle we have to use the Pythagoras theorem as shown below,

From the given figure,

BC² = AB² + AC²

BC² = 39² + 80²

BC² = 1521 + 6400

BC² = 7921

BC = √7921

BC = 89.

From the above analysis, we can conclude that the hypotenuse of the given right-angled triangle is 89 units.

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Given question is having the wrong picture. I am attaching required correct picture as below,

If three squares have sides that make an acute triangle, then the sum of the areas of the two small squares equals the area of the largest square. This is known as the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two smaller sides is equal to the square of the hypotenuse (the longest side).

2. If three squares have sides that make an obtuse triangle, then the sum of the areas of the two small squares is greater than the area of the largest square. This can be proven using the Law of Cosines, which states that in a triangle with sides a, b, and c and angle C opposite side c, c² = a² + b - 2ab cos(C). For an obtuse triangle, the cosine of the angle opposite the largest side is negative, which makes the right-hand side of the equation larger than c². Therefore, the sum of the squares of the smaller sides is greater than the square of the largest side.

3. If three squares have sides that make a right triangle, then the sum of the areas of the two small squares equals the area of the largest square. This is again the Pythagorean theorem. Let the sides of the squares be a, b, and c, with c being the hypotenuse. Then we have a² + b² = c². The areas of the squares are a², b², and c², respectively, so the sum of the areas of the two small squares is a² + b², which equals the area of the largest square (c²).

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Answer:

6 fewer pizzas

Step-by-step explanation:

The small cafe offers 6 fewer types of pizza than a restaurant. The restaurant offers 18 different types of pizzas and the cafe offers 1/3 as many types of pizzas which means what we have to find 1/3 of 18.

1/3 of 18 is 6 because 6*3 is 18

18 - 6 = 12 which is the number of pizzas the cafe offers but this is slightly irrelevant to the question because the question is asking how many FEWER pizzas the cafe sells than the restaurant

So, the small cafe offers 6 FEWER pizzas than the restaurant.

Hope this helps!

The solution of the given equation 6e/7 = 48 is given by, e = 56.

Equation is a mathematical statement where various numerical values, mathematical variables, mathematical operations, exponents or combination of them related via equal sign.

Given the equation is,

6e/7 = 48

We have to solve this equation and have to find the value of 'e' which satisfy this equation.

Solving the given equation we get,

6e = 48*7 [On multiplying 7 with both sides]

6e = 336

e = 336/6 [On dividing 6 from both sides]

e = 56

Hence the solution of the given equation is, e = 56.

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The solution of the expression is -24/5 < m < 32/5

To solve the absolute value inequality |2 - 5m/2| < 14, we remove the absolute value symbol resulting to two cases which is solved below

Case 1:

2 - 5m/2 < 14

Multiplying both sides by 2

4 - 5m < 28

Subtracting 4 from both sides

-5m < 24

Dividing both sides by -5 and rearranging the equation

m > -24/5

Case 2

2 - 5m/2 < -14

subtracting 2 to both sides

5m/2 < -16

Dividing both sides by -5/2

m < 32/5

Combining the equations

-24/5 < m < 32/5

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the first thing that you're supposed to do is multiply all the given measurements as we know that volume is equal to length times with times height so you have to multiply all the three given measurements the answer that you get after multiplying those three given measurements you have to round your answer to the nearest two decimal places therefore after they'll call my they need to be two numbers just after the coma

Answer:

Since the prism has three rectangular faces, let's call them faces ABCD, ABEF, and CDFH. Without loss of generality, let's assume that the plane goes through points A, B, and C to slice through all three rectangular faces.

First, let's consider the intersection of the plane with face ABCD. Since the plane goes through points A, B, and C, it must contain the line segments AB and AC. Thus, the intersection of the plane with face ABCD is a triangle with vertices A, B, and some point D' on the edge CD.

Next, let's consider the intersection of the plane with face ABEF. Since the line segments AB and AC both lie entirely within face ABEF, their intersection with the plane gives line segments AB' and AC', respectively. Thus, the intersection of the plane with face ABEF is a quadrilateral with vertices A, B', E, and F.

Similarly, the intersection of the plane with face CDFH is a quadrilateral with vertices C, D', H, and F.

To visualize the resulting plane section, imagine unfolding the right triangular prism so that all its faces lie flat. Then the plane section would look something like this:

B'________E

/| / |

A /_|___/' |

| | | |

| D'- -|-----C

| / |____|/

F|/ H

The intersection of the plane with face ABCD is the triangle ABD', and the intersections with faces ABEF and CDFH are the quadrilaterals AB'EF and CD'HF, respectively.

Overall, the resulting plane section has four sides: AB' and B'E from face ABEF, EF and FD' from face CDFH, and D'A from face ABCD. It has one vertex at A and two vertices, B' and D', that lie on the edge CD. The fourth vertex is at some point E on the edge BE. The shape of the resulting plane section depends on the relative positions of points B and D on the edge CD, and point E on the edge BE.

the expected value of the sum of two fair 6-sided dice is 7.

The possible values of the sum of two fair 6-sided dice range from 2 (when both dice show a 1) to 12 (when both dice show a 6). The probability of each possible sum can be calculated using a probability distribution table or by listing all the possible outcomes and counting them.

Here is the probability distribution table:

Sum Number of Outcomes Probability

2 1 1/36

3 2 2/36

4 3 3/36

5 4 4/36

6 5 5/36

7 6 6/36

8 5 5/36

9 4 4/36

10 3 3/36

11 2 2/36

12 1 1/36

The expected value of the sum, denoted E(X), is the sum of each possible value of X multiplied by its probability, or:

E(X) = 2*(1/36) + 3*(2/36) + 4*(3/36) + 5*(4/36) + 6*(5/36) + 7*(6/36) + 8*(5/36) + 9*(4/36) + 10*(3/36) + 11*(2/36) + 12*(1/36)

E(X) = 7

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. A probability of 0.5 (or 50%) means the event is just as likely to occur as it is not to occur.

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The surface area of the triangular prism is approximately calculated as: 361.88 mm².

Surface area of any triangular prism = (Perimeter of the triangular base × Length of the prism) + (2 × Base Area)

= (S1 +S2 + S3)(L) + (bh)

Given the following variables:

S1 = 7.21 mm

S2 = 7.21 mm

S3 = 8 mm

L = 14 mm

b = 8 mm

h = 6 mm

Surface area = (7.21 + 7.21 + 8)(14) + (8 * 6)

Surface area = 361.88 mm²

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The hypotenuse is c and the other leg is b.

Given is a right triangle we need to label the sides,

The sides are =

PR = a

PQ = c

QR = b

Here, a and b are the legs and c is the hypotenuse of the given right triangle.

Hence the hypotenuse is c and the other leg is b.

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