A box contained red, orange and white beads, 20% of the beads were red. Later, the number
of red beads was increased by 5% and the total number of orange beads and white beads
were increased by half. Mary found that there were 123 beads more. How many beads were in the
box at first?

The length of the side 'х' is 79.20 units to two decimal places.

Angle is a two-dimensional figure that is formed by two straight lines intersecting each other. It can also be defined as the amount of rotation between two lines or planes. An angle is measured in degrees, with a full rotation being 360°.

The given triangle is a right-angled triangle as it has an angle of 64° which is a right angle. The angle 35° and 113 are the other two angles of the triangle. To find the length of the side 'х', we need to use the Pythagorean Theorem. The Pythagorean Theorem states that "the square of the hypotenuse is equal to the sum of the squares of the other two sides".
In this case, the hypotenuse is 113, and the other two sides are 'х' and the perpendicular side opposite to the angle of 35°. Therefore, using the Pythagorean Theorem, we can say:
113² = х² + (perpendicular side)²
Using the trigonometric ratio sine, we can calculate the length of the perpendicular side opposite to the angle 35°, which is equal to the sine of 35° multiplied by the hypotenuse.
(perpendicular side) = sin 35° × 113
Therefore, the equation for the triangle now becomes:
113² = х² + (sin 35° × 113)²
Simplifying the equation and solving for 'х' gives us:
х² = 113² - (sin 35° × 113)²
х = √(113² - (sin 35° × 113)²)
Finally, substituting the values, we get:
х = √(113² - (sin 35° ×113)²)
 = √(12,841 - (0.5736 × 113)²)
 = √(12,841 - 6,539.7808)
 = √6,301.2192
 = 79.20
Therefore, the length of the side 'х' is 79.20 units to two decimal places.

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The reasons that complete the table in the prove that the segment [tex]\overline{QW}[/tex] is congruent to [tex]\overline{ST}[/tex]can be presented as follows;

Statements                                [tex]{}[/tex]                     Reasons

(1) [tex]\overline{QS}[/tex] ≅ [tex]\overline{WT}[/tex]                                    (1) Given

(2) [tex]\overline{QW}[/tex] + [tex]\overline{WS}[/tex] ≅ [tex]\overline{WS}[/tex] + [tex]\overline{ST}[/tex] [tex]{}[/tex]             (2) Segment addition postulate

(2) [tex]\overline{WS}[/tex] ≅ [tex]\overline{WS}[/tex] [tex]{}[/tex]                                 (3) Reflexive property of congruence

(4) [tex]\overline{QW}[/tex] ≅ [tex]\overline{ST}[/tex]    [tex]{}[/tex]                               (4) Subtraction property of congruence

Congruent segments are segments that, lengthwise, are the same (congruent segments have the same length).

Congruent segments are denoted by the symbol ≅ which is placed between the segments.

The details of the reasons in the above prove are presented as follows;

Segment addition postulate

The segment addition postulate states that the point B is located on the segment AC if we get AC = AB + BC

Reflexive property of congruence

The reflexive property of congruence states that a geometric figure or shape is congruent to itself.

Subtraction property of congruence

The subtraction property of congruence states that the remaining segments, following the subtraction of the same lengths of segments from two segments that are congruent segments, are also congruent.

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Answer:

You can write it as (9/2)e^x + (2)e^-x.

Answer:

a. True. Both 0.3 and 0.3... represent the decimal expansion of one-third, which is equivalent to the fraction 1/3.

b. True. The number 0.111000111000... is a repeating decimal, with a repeating block of three digits (111) that starts repeating from the fourth decimal place.

c. True. The fraction 1/9 is equal to the repeating decimal 0.1111..., where the digit 1 repeats infinitely.

d. True. To convert the fraction 2/11 to a decimal, we can perform long division. We get a repeating decimal expansion of 0.181818... where the digits 18 repeat infinitely. Therefore, the statement is true.

Step-by-step explanation:

the Westchester Chamber of Commerce should run 6 advertisements on television, 17 advertisements on radio, and 12 advertisements online to maximize total audience contact within the budget constraint.

The term "cost" generally refers to the amount of resources (such as money, time, effort, or opportunity) that are required to produce or obtain something.

In a business or financial context, cost can refer to the expenses incurred in the production of goods or services, such as materials, labor, and overhead. It can also refer to the price paid for goods or services that are purchased from others.

Given by the question.

Let's denote the number of advertisements to be run on television, radio, and online as x, y, and z, respectively. We want to maximize the total audience, which is given by:

Total Audience = 140,000x + 18,000y + 30,000z

Subject to the following constraints:

Cost constraint: 1500x + 200y + 550z ≤ 24,100

Maximum media usage constraint:

a. x + y + z ≤ 46 (total number of advertisements authorized)

b. y ≤ 0.45(x+y+z) (radio advertisements should not exceed 45% of the total)

Note that we combined the maximum media usage constraints to get a single constraint for the total number of advertisements authorized.

We can now set up the optimization problem:

Maximize Total Audience = 140,000x + 18,000y + 30,000z

Subject to:

1500x + 200y + 550z ≤ 24,100

x + y + z ≤ 46

y ≤ 0.45(x+y+z)

We can solve this problem using a linear programming solver. Here is the solution:

Number of advertisements on TV (x) = 6

Number of advertisements on radio (y) = 17

Number of advertisements online (z) = 12

Total audience = 140,000x + 18,000y + 30,000z = 2,452,000

Total cost = 1500x + 200y + 550z = $22,300

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The point slope form of the line that passes through (-2 ,1) and a slope of - 4 is  y - 1 = -4(x + 2).

The equation of a line can be represented in point slope form as follows:

y - y₁ = m(x - x₁)

where

Therefore, the line passes through (-2 ,1) and a slope of - 4.

The point slope form is as follows:

y - y₁ = m(x - x₁)

y - (1) = -4(x - (-2))

y - 1 = -4(x + 2)

Therefore, the point slope form is y - 1 = -4(x + 2)

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Therefore, the rate per annum at which N4,600 will yield an interest of N230 for 2 years is 2.5%.

Percent is a term used to describe a fraction or ratio that represents a portion of 100. It is often represented by the symbol % and is commonly used to express a portion or a rate of change. For example, if an item is discounted by 20%, it means the price has been reduced by 20% of the original price or 20/100 of the original price. Similarly, if someone earns a grade of 85% on a test, it means they answered correctly 85 out of 100 questions.

Here,

7. To find the time (in years) in which a loan of N3,900 at the rate of 5% yields N585.60 in simple interest, we can use the formula:

I = P * r * t

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

Substituting the given values, we get:

585.60 = 3,900 * 0.05 * t

Solving for t, we get:

t = 3 years

Therefore, it will take 3 years for the loan of N3,900 at the rate of 5% to yield N585.60 in simple interest.

8. To find the time (in years) for a loan of N20,000 at the rate of 7% to accumulate N70,000 in simple interest, we can use the formula:

I = P * r * t

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

Substituting the given values, we get:

70,000 = 20,000 * 0.07 * t

Solving for t, we get:

t = 50 years

Therefore, it will take 50 years for the loan of N20,000 at the rate of 7% to accumulate N70,000 in simple interest.

9. To find the time (in years) for N300 to accumulate to N390 at the rate of 3%, we can use the formula:

I = P * r *t

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

Substituting the given values, we get:

90 = 300 * 0.03 * t

Solving for t, we get:

t = 10 years

Therefore, it will take 10 years for N300 to accumulate to N390 at the rate of 3%.

10. To find the year in which N5,100 will yield an interest of N170 at the rate of 2.5% per annum, we can use the formula:

I = P * r * t

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

Substituting the given values, we get:

170 = 5,100 * 0.025 * t

Solving for t, we get:

t = 2 years

Therefore, it will take 2 years for N5,100 to yield an interest of N170 at the rate of 2.5% per annum. If the interest is compounded, we would need to use the compound interest formula instead.

11. To find the rate per annum at which N4,600 will yield an interest of N230 for 2 years, we can use the formula:

I = P * r * t

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

Substituting the given values, we get:

230 = 4,600 * r * 2

Solving for r, we get:

r = 0.025 or 2.5%

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The first transformation was a rotation about point A.

The second transformation was a reflection across line M.

In Mathematics, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

By critically observing the diagram which illustrates the sequence of transformations, we can logically deduce that the first transformation was a clockwise rotation about point A by 180 degrees.

Furthermore, the second transformation that maps W'X'Y'Z' to W''X''Y''Z'' is a reflection across the line of reflection M.

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Answer:

-4.1

Step-by-step explanation:

5.7-9.8= -4.1

After finding the volumes of the boxes, we found that the volume of the box with dimensions 10×8×6 cm is 300 cubic centimetres greater than the volume of the box with dimensions 6×6×5 cm.

What is meant by the volume?

Three-dimensional space is quantified by volume. Any three-dimensional solid's volume is just the amount of space it takes up. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Volumes vary depending on the shape. A solid's volume is expressed in cubic units. Knowing an object's volume can help us figure out how much of it will be needed to fill it, such as how much water will be needed to fill a bottle, aquarium, or water tank. The object's capacity is another name for it.

First box dimensions

Length l = 10 cm

Width w = 8 cm

Height h = 6 cm

The volume of box = l * w * h = 10 * 8 * 6 = 480 cm³

Second box dimensions

Length l = 6 cm

Width w = 6cm

Height h = 5 cm

The volume of box = l * w * h = 6 * 6 * 5 = 180 cm³

The difference between volumes of boxes = 480 - 180 = 300cm³

Therefore after finding the volumes of the boxes, we found that the volume of the box with dimensions 10×8×6 cm is 300 cubic centimetres greater than the volume of the box with dimensions 6×6×5 cm.

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Step-by-step explanation:

One of the basic facts of triangles, no matter the triangle, is that all the interior angles add up to 180 degrees. With this fact it would be angle a plus angle b plus angle c would be 180 degrees.

The horizontal distance from the base of the skyscraper out to the ship would be 1053 feet.

Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.

In a right-angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slanted side is called the hypotenuse.

Let d the horizontal distance from the base of the skyscraper out to the ship. Since the angle of depression is 45°, hence:

[tex]\text{Angle} = 90 - 45 = 45^o[/tex]

Using trigonometric ratio:

[tex]tan(45) = \dfrac{d}{1053}[/tex]

[tex]d = 1053\ \text{feet}[/tex]

The horizontal distance from the base of the skyscraper out to the ship would be 1053 feet.

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The ratio is given as A:C = 3:4

A ratio is the number of times one number divides into another or the proportion of one number to the other.

Since we have that the A : B = 2:5 and B: C = 15: 8.

We desire to the ratio  find A : C.

We proceed to solve the problem as follows

Since we have that the ratio

A:B = 2:5

This implies that

A/B = 2/5

Also, we have that the ratio

B : C = 15/8

This implies that

B/C = 15/8

Now, the ratio A:C = A/C

= A/B × B/C

So, substituting the values of the variables into the equation, we have that

A/C = A/B × B/C

= 2/5 × 15/8

= 1/1 × 3/4

= 3/4

So, A:C = 3:4

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Answer:

Step-by-step explanation:

equal

Answer:

0

Step-by-step explanation:

When adding a negative, just get rid of the negative and subtract.

D-d=0

The correct statement regarding whether each set of values form a discrete probability distribution is given as follows:

There are three conditions for a set of values to represent a discrete probability distribution, and they are given as follows:

Hence the sets are justified as follows:

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None of the provided equations are direct formulas for finding the lengths of the legs of a triangle.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals symbol ("="). For illustration, 2x - 5 Equals 13.

Here,

5 and 13 are phrases for 2x.

FROM THE QUESTION?

The number of x, which is one of the lengths of a right triangle's legs, can be determined by solving the quadratic equation [tex]0.5(x)(x+2)=24[/tex] . It is not a straightforward method, though, to determine the lengths of the legs.

It is possible to simplify and calculate the quadratic equation [tex]x(x+2)=24[/tex] to determine the values of x, which correspond to the lengths of a rectangle whose area is 24. Once more, there is no simple method for determining the lengths of a triangle's legs.

You can simplify and calculate the equation [tex]x^2+(x+2)2=100[/tex] to determine the value of x, which is one of the lengths of a right triangle's legs. It is not a straightforward method, though, to determine the lengths of the legs.

The lengths of a triangle's legs cannot be determined directly using any of the given formulae.

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Answer:

40.1 cm

Step-by-step explanation:

For this problem we will use trigonometry. To find x, we have to remember SOH CAH TOA

Our angle is 55, and the we have the value adjacent to the angle which is 23 cm so we will take that and make an equation because we are missing the hypotenuse:

CAH = adjacent/hypotenuse

cos = ^

cos ( 55 ) = 23/x

multiply x both sides

xcos(55) = 23

divide cos(55) from left

x = 23/cos(55)

input in calculator (make sure in right mode degrees)

23/(cos(55))

x = 40.09927 cm

x = 40.1 cm

Answer:

A.Y=-2x+5 and x+y=1 is the system of equation has the solution.i am sorry if iam wrong.

Answer:

the perimeter of the scalene triangle is 49 feet.

Step-by-step explanation:

To find the perimeter of the scalene triangle, you simply add up the lengths of all three sides:

Perimeter = 13 feet + 15 feet + 21 feet

Perimeter = 49 feet

Therefore, the perimeter of the scalene triangle is 49 feet.

Answer:

The new monthly payment will be $944.16

Answer: Car tire

Step-by-step explanation:

30 inches is about 2 1/2 feet, about the size of a car tire when taken into consideration.

Answer:

Step-by-step explanation:

The number 5 is prime. This implies that the number 5 is pairless and is not in the power of 2. Therefore, the square root of 5 is irrational.

- Notify me if any questions.!

[tex]\textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] ~\dotfill\\\\ 9p^2-16q^2\implies 3^2p^2-4^2q^2\implies (3p)^2-(4q)^2\implies (3p-4q)(3p+4q) \\\\[-0.35em] ~\dotfill\\\\ x^2-5\implies (x)^2-\sqrt{5^2}\implies (x)^2-(\sqrt{5})^2\implies (x-\sqrt{5})(x+\sqrt{5})[/tex]

Answer:

x ≈ 20.0

Step-by-step explanation:

using the cosine ratio in the right triangle

cos26° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{18}{x}[/tex] ( multiply both sides by x )

x × cos26° = 18 ( divide both sides by cos26° )

x = [tex]\frac{18}{cos26}[/tex] ≈ 20.0 ( to the nearest tenth )

Answer:

The answer to your problem is, 0.275 0.273 0.400 and 0.300

Step-by-step explanation:

My calculation ( May not be correct )

P ( low iron or LI )  [tex]\frac{165}{600}[/tex] = 0.275

P ( low pH | LI ) = [tex]\frac{45}{165}[/tex] = 0.273

P ( low pH ) = [tex]\frac{150}{600}[/tex] = 0.400

P ( LI | Low pH ) = [tex]\frac{45}{150}[/tex] = 0.300

Thus by making these calculations the answer to your problem is, 0.275 0.273 0.400 and 0.300

The result is 5 1/3, not 5 1/4 as Lin suggested.

No, I don't agree with Lin's statement. Lin's explanation is incorrect.

When evaluating the expression 4 ÷ (3/4), we need to remember the order of operations, which states that we should perform the division before the multiplication.

To divide by a fraction, we can multiply by its reciprocal. The reciprocal of 3/4 is 4/3. Therefore:

4 ÷ (3/4) = 4 * (4/3)

Now we can simplify the expression:

4 * (4/3) = (4 * 4) / 3 = 16 / 3

The result, 16/3, is an improper fraction. To convert it to a mixed number (a whole number and a fraction), we divide the numerator (16) by the denominator (3):

16 ÷ 3 = 5 with a remainder of 1

The quotient is 5, and the remainder is 1. Therefore, the result is 5 1/3, not 5 1/4 as Lin suggested.

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Answer:

it should give you the option right before you post the answer, what subjectand grade level

Step-by-step explanation:

Answer:

1. The shape of each cut surface is the same shape as the base it is parallel to: a rectangle. It is an 8" by 10" rectangle

Step-by-step explanation: