A 20 litre solution is 85% paint and 15% thinner. Five litres of thinner is added to this solution.

What percentage of the new solution is PAINT?

Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4 using trigonometric ratio.

We know that the point (-3, 4) is on the terminal side of the angle θ, and we can use the Pythagorean theorem to find the value of the hypotenuse:

r² = x² + y²

r² = (-3)² + 4²

r² = 9 + 16

r² = 25

r = 5

Now we can find the values of sin θ, csc θ, and cot θ:

sin θ = y/r = 4/5

csc θ = r/y = 5/4

cot θ = x/y = -3/4

Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4.

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If the loan is a total of $8,465 at 5.9% compounded monthly. at the end of the 12-month repayment period, the student will owe a total of $9246.35 on the loan.

   First, calculate the monthly interest rate by dividing the annual interest rate by 12:

Monthly interest rate = 5.9% / 12 = 0.004917

   Next, calculate the number of months in the repayment period, including the grace period:

Total repayment period = 12 + 6 = 18 months

   Use the formula for calculating the future value of a loan to find the total amount owed at the end of the repayment period:

   FV = PV x (1 + r)^n

   where:

   PV = the present value of the loan (i.e. the amount borrowed)

   r = the monthly interest rate

   n = the number of months in the repayment period

   Plugging in the numbers, we get:

FV = $8,465 x (1 + 0.004917)^18

FV = $9246.35

Therefore, the student will owe a total of $9246.35 on the loan.

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Since 260 is close to 264, our answer of 264 is reasonable.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

The sum of 401-137 can be found by subtracting 137 from 401:

401 - 137 = 264

Therefore, the sum of 401-137 is 264.

To estimate whether this answer is reasonable, we can use rounding. We can round 401 to 400 and 137 to 140, which makes the subtraction easier to estimate mentally:

400 - 140 ≈ 260

Since 260 is close to 264, our answer of 264 is reasonable.

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The figure that represent the triangle described in the question is option (C).

Triangle is a basic geometric shape that consists of three straight sides and three angles.

We can say triangle is a polygon with three sides and three vertices, and is one of the simplest and most fundamental shapes in geometry.

Class of Triangle based on sides

Class of Triangle based on their angles

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If piece of cake has area of 100 in² and sweeps angle of 50°, then the radius of the cake is 15.13 inches.

The area of the piece of cake is given as 100 square inches and

The piece of cake sweeps out an angle of 50 degrees, we have to find the radius of the cake;

We know that "Area" of a sector of a circle is given as : A = (θ/360)πr²,

where A = area of the sector, θ is = angle swept by sector, and r is radius of circle,

We know that area of "piece-of-cake" is = 100 square inches and

The "angle-swept' by the piece is = 50 degrees.

Substituting the values in area of sector formula,

We get,

⇒ 100 = (50/360)πr²,

⇒ r² = (100 × 360)/(50π)

⇒ r ≈ 15.13,

Therefore, the radius of the cake is approximately 15.13 inches.

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Step-by-step explanation:

you remember the priorities of mathematical operations :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

it is irrelevant how close or how far apart the operands are written.

I think, missing operators are multiplications.

so, by writing really everything

(7 × 6) ÷ 2 × [{45 + 3 × (7 × 2 - 15 + 6)} + 4]

we get in a first step :

(42) ÷ 2 × [{45 + 3 × (14 - 15 + 6)} + 4]

second step

21 × [{45 + 3 × (5)} + 4]

third step

21 × [{45 + 15} + 4]

fourth step

21 × [60 + 4]

fifth step

21 × 64

sixth step

1,344

The better prediction for y, when x = 74, based on the scatter plot, can be found to be 57.

Looking at the scatter plot, the better prediction of y when the value of x is 74 can be found by looking for the values of y that have a value of x that is around 74.

From the scatter plot, we see that the value of x of 74, would correspond with the value of y of 57. We can therefore infer that y = 57 is the better prediction for x = 74.

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The height of the pole is approximately 10.2 yards tall.

Let's use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse (the longest side).

In this case, the pole is the vertical side of the right triangle, the ground is the horizontal side, and the rope is the hypotenuse. Let's call the height of the pole "h". Then we have:

h² + 11² = 15²

Simplifying:

h² + 121 = 225

Subtracting 121 from both sides:

h² = 104

Taking the square root of both sides:

h = √104

Simplifying:

h ≈ 10.2

Therefore, the pole is approximately 10.2 yards tall.

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Answer: The answer is D

Answer:

(C) {-3, 2} is the correct answer.

Using the power reducing formulas the expression [tex]5cos^4(x) = 5(1 + cos(2x))^{2/4}[/tex].

We can define higher powers of a trigonometric function in terms of lower powers of the same function using the power-reducing formulas, which are trigonometric identities. Higher powers of cosine can be expressed using this formula in terms of sine and cosine's initial powers. For the other trigonometric functions, such as sine and tangent, there are equivalent formulas. These formulas can be used to solve trigonometric equations and to simplify trigonometric expressions.

The given function is 5cos^4(x).

Now, the power reducing formulas are given by:

[tex]cos(2x) = cos^2(x) - sin^2(x) = 2cos^2(x) - 1\\cos^2(x) = (1 + cos(2x))/2[/tex]

Substituting the value of second equation in 1 we have:

cos(2x) = 2(1 + cos(2x))/4 - 1

[tex]cos(2x) = (2cos^2(x) - 1) = cos^2(x) - sin^2(x)[/tex]

Now we have:

[tex]cos^2(x) = (1 + cos(2x))/2[/tex]

Thus,

[tex]cos^4(x) = (1 + cos(2x))/2)^2[/tex]

Now multiplying by 5:

[tex]5cos^4(x) = 5(1 + cos(2x))^{2/4}[/tex]

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The slope of the line of best fit provides valuable information about the relationship between the two variables being plotted and can be used to make predictions about future data points or to identify patterns and trends in the data.

What is the slope?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

The slope of the line of best fit on a scatter plot represents the rate of change between the two variables being plotted.

In the case of Keilantra's math teacher, the slope of the line of best fit between student grades on weekly quizzes and the number of hours they say they study represents the change in grades for every additional hour of studying.

For example, if the slope is positive (i.e., the line slopes upward from left to right), it indicates that as the number of hours studied increases, the average grade on the quiz tends to increase as well.

On the other hand, if the slope is negative (i.e., the line slopes downward from left to right), it indicates that as the number of hours studied increases, the average grade on the quiz tends to decrease.

Therefore, the slope of the line of best fit provides valuable information about the relationship between the two variables being plotted and can be used to make predictions about future data points or to identify patterns and trends in the data.

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Answer:

Using the Pythagorean theorem, the length of the rope can be found as follows:

c^2 = a^2 + b^2

where c is the length of the rope, a is the height of the fence (8 feet), and b is the distance from the fence to the point where the rope is attached to the ground (6 feet).

Plugging in the values, we get:

c^2 = 8^2 + 6^2

c^2 = 64 + 36

c^2 = 100

c = √100

c = 10

Therefore, the length of the rope is 10 feet.

Answer:

The length of the rope is 10 feet.

Step-by-step explanation:

To find the length of the rope attached to the top of an 8-foot-tall fence and fastened to the ground 6 feet away, we can use the Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In this case, the vertical leg is the height of the fence (8 feet) and the horizontal leg is the distance from the base of the fence to where the rope is fastened (6 feet). Therefore, the length of the rope (the hypotenuse) is given by:

hypotenuse^2 = vertical leg^2 + horizontal leg^2

Substituting the values, we get:

hypotenuse^2 = 8^2 + 6^2

hypotenuse^2 = 64 + 36

hypotenuse^2 = 100

Taking the square root of both sides, we get:

hypotenuse = 10

So the length of the rope is 10 feet.

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Therefore, the expected value of the event P(2k) for 2 ≤ k ≤ 6, given the event E, is 96/1 or simply 96.

Probability theory is widely used in many fields, including mathematics, statistics, physics, engineering, economics, and social sciences. It provides a framework for analyzing and understanding uncertain events and making predictions based on available information. Probability theory is also used in decision-making, risk management, and game theory, among other applications.

Here,

We can start by calculating the probability of each event in the sample space:

P(1) = 1/32

P(4) = 1/8

P(8) = 1/4

P(16) = 1/2

P(32) = 1

P(64) = 1

Next, we can calculate the probability of the event E by summing the probabilities of the individual outcomes in E:

P(E) = P(1) + P(8) + P(32) + P(64)

= 1/32 + 1/4 + 1 + 1

= 33/32

Now, we can calculate the expected value of the event P(2k) for 2 ≤ k ≤ 6:

E[P(2k)] = Σ[2 ≤ k ≤ 6] P(2k) * ΘS(2k)

= P(4)*ΘS(4) + P(8)*ΘS(8) + P(16)*ΘS(16) + P(32)*ΘS(32) + P(64)*ΘS(64)

= (1/8)*4 + (1/4)*8 + (1/2)*16 + (1)*32 + (1)*64

= 4/8 + 8/4 + 16/2 + 32 + 64

= 1/2 + 2 + 8 + 32 + 64

= 106.5

Therefore, the expected value of the event P(2k) for 2 ≤ k ≤ 6, given the event E, is 106.5. However, since the event E has a probability greater than 1, this result does not make sense. So, we need to normalize the probabilities of the events by dividing them by P(E) to obtain the correct expected value:

P'(1) = P(1)/P(E) = (1/32)/(33/32) = 1/33

P'(8) = P(8)/P(E) = (1/4)/(33/32) = 8/33

P'(32) = P(32)/P(E) = 1/(33/32) = 32/33

P'(64) = P(64)/P(E) = 1/(33/32) = 32/33

Now, we can calculate the normalized expected value:

E[P(2k)] = Σ[2 ≤ k ≤ 6] P'(2k) * ΘS(2k)

= P'(8)*ΘS(8) + P'(32)*ΘS(32) + P'(64)*ΘS(64)

=(8/33)*8 + (32/33)*32 + (32/33)*64

= (64/33) + (1024/33) + (2048/33)

= 3136/33

= 96/1

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Answer: 13 units

Step-by-step explanation:

If you look at the corresponding side on the other triangle, it is also 13, and in the question it say the side on the other triangle has the same length as the one you are finding.

Karla will have approximately $11,149 in the account after 5 years, rounded to the nearest dollar.

The formula accrued amount in a compounded interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that:

First, convert R as a percent to r as a decimal

r = R/100

r = 2.2/100

r = 0.022

Plug the given values into the above formula and solve for A.

A = P( 1 + r/n )^( n × t )

A = 10,000( 1 + 0.022/1 )^( 1 × 5 )

A = 10,000( 1 + 0.022 )^( 5 )

A = 10,000( 1.022 )^( 5 )

A = $11,149

Therefore, the accrued amount after 5 years is $11,149.

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The probability that all 3 children will be born with the disease is approximately 0.195 or 19.5%.

We have,

Assuming that the probability of a child being born with the disease is independent of whether or not their siblings are born with the disease, we can use the multiplication rule of probability:

P(all 3 children have the disease)

= P(first child has the disease) x P(second child has the disease) x P(third child has the disease)

Since each child has a 57% chance of being born with the disease:

P(all 3 children have the disease)

= 0.57 x 0.57 x 0.57

Now,

P(all 3 children have the disease)

= 0.195

Therefore,

The probability that all 3 children will be born with the disease is approximately 0.195 or 19.5%.

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The amount that Marcus will receive when he redeems the CD at the end of the 19 years, which is described as the compounded future value, is $37,255.14.

The future value is the present investment or value compounded at an interest rate.

The future value can be determined using the FV formula or an online finance calculator as follows:

N (# of periods) = 228 months (19 years x 12)

I/Y (Interest per year) = 7.5%

PV (Present Value) = $9,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $37,255.14

Total Interest: $28,255.14

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Answer:

The equation x - y = 7 represents a linear equation with two variables, x and y. To find three ordered pairs (x, y) that satisfy this equation, we can arbitrarily choose values for one variable and solve for the other.

Ordered Pair 1:

Let's choose x = 0:

x - y = 7

0 - y = 7 (Substituting x = 0)

y = -7

So, the first ordered pair is (0, -7).

Ordered Pair 2:

Let's choose y = 0:

x - y = 7

x - 0 = 7 (Substituting y = 0)

x = 7

So, the second ordered pair is (7, 0).

Ordered Pair 3:

Let's choose x = 5:

x - y = 7

5 - y = 7 (Substituting x = 5)

y = -2

So, the third ordered pair is (5, -2).

Therefore, three ordered pairs (x, y) that satisfy the equation x - y = 7 are: (0, -7), (7, 0), and (5, -2).

The rectangle with largest area has length 3 and width 3/2, with an area of 9/2.

What is a rectangle?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. As a result, it is sometimes referred to as an equiangular quadrilateral. Because the opposing sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

The equation for the area of a rectangle is length * width. For us here, it would be x * y. We can substitute the equation of the line for y and get

A = x * (6-x)/2

A = 3x - x2/2

To find the maximum of this equation, we first need to find a critical point. So we take the derivative and find the zeros:

A' = 3 - x = 0

x = 3

So we have a critical point at 3, which happens to be the maximum of the area equation. We plug this back into the line equation to get y:

y = (6 - 3)/2 = 3/2

So the rectangle with largest area has length 3 and width 3/2, with an area of 9/2.

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Answer:3/10

Step-by-step explanation:

The ratios of each type are:

1/4 has big beak (BB)

2/4  has big short beak (Bb)

1/4 has short beak (bb)

A Punnett square is a diagram used to predict the possible outcomes of a genetic cross between two individuals.

               B          b

B            BB        Bb

b             Bb        bb

We have 1 BB, this implies that we have one bird with big beak.

We have 2 Bb, this implies that we have two bird with big short beak.

We have 1 bb, this implies that we have one bird with short beak.

The ratios of each type are:

1/4 (i.e. 25%) has big beak (BB)

2/4 (i.e. 50%) has big short beak (Bb)

1/4 (i.e. 25%) has  short beak (bb)

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Answer:

955 11 7 11

3101 thats my answer

Step-by-step explanation:

10 and 3 thank you

The probability of selecting an elm or oak tree is 0.38.

The probability of selecting an elm or oak tree is the sum of the probabilities of selecting an elm and selecting an oak:

P(elm or oak) = P(elm) + P(oak)

P(elm) = 0.04

P(Oak) =0.34

Plug in these values

= 0.04 + 0.34

= 0.38

Therefore, the probability of selecting an elm or oak tree is 0.38.

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The values of x, y and z are given as follows:

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The bases for the triangle in this problem are given as follows:

6 and 19.

Hence the segment x is obtained as follows:

x² = 6 x 19

x = sqrt(6 x 19)

x = 10.68.

Applying the Pythagorean Theorem, the value of y is given as follows:

y² = 6² + 10.68²

y = sqrt(6² + 10.68²)

y = 12.25.

The value of z is given as follows:

z² = 10.68² + 19²

z = sqrt(10.68² + 19²)

z = 21.8.

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Answer:8%

Step-by-step explanation:

you divide 25 by 32 and round to nearest tenth

hope this helps :)

Step-by-step explanation:

slope,   m = ( y1-y2) / (x1-x2)   = ( 6-8) / (12-28) =  -2 / -16 = 1/8