Susan Marciano invested part of her $19000 bonus in a fund that paid a 12% profit and invested the rest in stock that suffered a %4 loss. Find the amount of each investment if her overall net profit was $520

Answer:

x=3

Step-by-step explanation:

the answer is 3 because 3*12=36 and 4*12=48

The length of b = √36 = 6 cm.

Length is a measurement of size and it can be measured in a variety of waste including inches sentiment of metres feet miles and more. Playing these an important concept in mathematics, science and engineering and many others build it to used to calculate the dimensions of this area. And more it is also used to measure the time it takes to travel.


Triangle ABC is a right triangle with angle B = 90°.

If a = 8 cm and c = 10 cm, we can use the Pythagorean Theorem to find the missing length, b.

The Pythagorean Theorem states that a2 + b2 = c2.

Therefore, b2 = c2 – a2 = 102 – 82 = 100 – 64 = 36.

The length of b = √36 = 6 cm.
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Refer to the attached image.

Both expressions 0.5 + 2(0.25x) + 0.75(3-x) and 2 - 2(0.75x) - 3(0.25x) are equivalent to 0.5x + 1.5, and they satisfy the condition that each term is used only once.

One possible solution is:

0.5 + 2(0.25x) + 0.75(3-x) = 0.5x + 1.5

Simplifying this expression:

0.5 + 0.5x + 0.5x + 2(0.25x) + 2.25 - 0.75x = 0.5x + 1.5

0.5x + 0.5x - 0.75x = 1.5 - 0.5 - 2.25

0.25x = -0.25

x = -1

Substituting x = -1 into 0.5x + 1.5:

0.5(-1) + 1.5 = 0.5 + 1.5 = 2

Therefore, another equivalent expression is:

2 - 2(0.75x) - 3(0.25x) = 0.5x + 1.5

Simplifying this expression:

2 - 1.5x = 0.5x + 1.5

2 - 1.5x - 0.5x = 1.5

-2x = -0.5

x = 0.25

Substituting x = 0.25 into 0.5x + 1.5:

0.5(0.25) + 1.5 = 0.125 + 1.5 = 1.625

Therefore, both expressions 0.5 + 2(0.25x) + 0.75(3-x) and 2 - 2(0.75x) - 3(0.25x) are equivalent to 0.5x + 1.5, and they satisfy the condition that each term is used only once.

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Answer:

the answer is 21.56

Step-by-step explanation:

have a nice day.

The maximum height of the ball from the maximum compression of the spring is 13.39 m

Maximum height is the highest displacement of the object.

Since a spring of spring constant 504 N/m is compressed 7.66 cm by a ball of mass 11.2 g. If the ball is shot straight into the air, we desire the maximum height of the ball.

Using the law of conservation of energy, the elastic potential energy lost by the spring, E equals the gravitational potential energy gained by the ball, E'

So, E = E'

1/2kx² = mgh where

Making h subject of the formula, we have that

h = kx²/2mg

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

h = kx²/2mg

h = 504 N/m × (0.0766 m)²/(2 × 0.0112 kg × 9.8 m/s²)

= 504 N/m × 0.00586756 m²/(2 × 0.0112 kg × 9.8 m/s²)

= 2.95725024 Nm/(0.21952 kgm/s²)

= 13.47 m

So, the maximum height from the springs compression is H = h - x = 13.47 - 0.0766 m

= 13.3934 m

≅ 13.39 m

So, the maximum height is 13.39 m

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Answer:

Step-by-step explanation:

Let's simplify the given expression by combining like terms:

3x + 6 + x - 2 + 8(x - 3) - 4 - 4 + x + 1 - 2(x + 2) + 6 + 7x - 8x

First, let's simplify the expression inside the parentheses:

8(x - 3) = 8x - 24

Now we can combine like terms:

3x + x + x + 7x - 8x + 6 - 2 - 4 - 4 + 1 + 6 - 2( x + 2) + 8x - 24

Simplifying further:

6x - 2 - 4 - 4 + 8x - 2(x + 2) - 17

6x + 8x - 2x - 2(2) - 25

12x - 4 - 25

12x - 29

Therefore, the answer to the given expression is 12x - 29.

Answer:

hope this helps!!

Step-by-step explanation:

The probability of throwing 3 shots is 100% and the sample space is set of all possible real number.

Probability is the measure of the likelihood that a given event will occur. In this case, the event is a basketball player making a shot from the free throw line.

Since the player has a 40% success rate, we can calculate the probability of him making x number of shots, where x is the number of shots that he throws.

Since the shots are independent of each other, the sample space for x is the set of all possible numbers of shots that he can make, from 0 to the total number of shots (3 in this case).

Therefore, the sample space for x is {0, 1, 2, 3}, which means that the player has a 0% probability of making 0 shots, a 40% probability of making 1 shot, an 80% probability of making 2 shots, and a 100% probability of making all 3 shots

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The Pseudocode is discussed below.

Java is a high-level, class-based, object-oriented programming language that is designed to have as few implementation dependencies as possible.

Given is to write a Pseudo code.

Therefore, the Pseudocode is discussed above.

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His estimated monthly income should be $480.

The length of CG is approximately 5.4 units.

A triangle is a closed geometric figure that is formed by connecting three straight line segments called sides. These sides meet at three points called vertices. Triangles are one of the simplest and most fundamental shapes in geometry and can be found in many natural and man-made objects.

Triangles can be classified into different types based on their sides and angles.

By sides:

Equilateral triangle: all three sides are equal in length.

Isosceles triangle: two sides are equal in length.

Scalene triangle: all three sides are different in length.

By angles:

Acute triangle: all three angles are acute (less than 90 degrees).

Right triangle: one angle is a right angle (exactly 90 degrees).

Obtuse triangle: one angle is an obtuse angle (greater than 90 degrees).

Triangles have many properties and are used in various fields such as architecture, engineering, physics, and mathematics. They are also commonly used in trigonometry to solve problems involving angles and distances.

We can use the property of similar triangles to solve this problem.

First, let's label the intersection point of FG and BC as point H. Also, let's label the length of CG as x.

Since FG is parallel to AC, we can use the property of similar triangles to find that triangles ABF and HBG are similar.

Therefore, we can set up the proportion:

AB/FB = HG/GB

Plugging in the given values, we get:

10/63 = (x + 57)/57

Solving for x, we get:

x = 5.4

Therefore, the length of CG is approximately 5.4 units.

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Therefore, the expansion of log(7x²) using the properties of logarithm is

log 7 + 2log x, expressed in terms of log x.

The mathematical idea of a logarithm illustrates the opposite of a power. It follows that the exponential that must be multiplied by bc to get the value of a number, x, is equal to its ground logarithm. As an illustration, 1000 = 103, so log10 = 3 is 1000's base-10 logarithm, which is 3. As an example, the square of ten is now only one twentieth of the base-10 exponential of ten, which is two. Log 100 = 2. Mathematicians use the logistic (or log) notion to respond to problems like these.

Here,

Using the product rule of logarithms, we can write:

log(7x²) = log 7 + log(x²)

Using the power rule of logarithms, we can write:

log(7x²) = log 7 + log(x²) = log 7 + 2log x

Therefore, the expansion of log(7x²) using the properties of logs is:

log 7 + 2log x, expressed in terms of log x.

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The tables that show a valid probability density function, are tables 1 to 3

From the question, we have the following parameters that can be used in our computation:

Table of values

For a table to show a valid probability density function, the following must be true

Sum of P(X = x) = 1

Using the above as a guide, we have the following:

Table 1: Sum = 0.37  + 0.06 + 0.01 + 0.56 = 1

Table 2: Sum = 3/8 + 3/8 + 1/4 = 1

Table 3: Sum = 1/8 + 1/8 + 1/8 + 3/8 + 1/4 = 1

Table 4: Sum = 0.03 + 0.01 + 0.61 + 0.31 + 0.21 = 1.17

Table 5: Sum = 1/10 + 3/10 + 4/5 + 1/5 = 1.4

Hence, the tables are tables 1 to 3

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The required angle 1 between the side and diagonal of a square is approximately 45 degrees.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
Let's assume that the length of one side of the square is 'a'.

Then the length of the diagonal of the square is given by the Pythagorean theorem:

d² = a² + a² = 2a²

d = a * √(2)

To find the angle between the side and the diagonal, we can use the cosine function:

cos(Ф) = adjacent/hypotenuse = a / (a * √(2))

cos(Ф) = 1 / √(2)

Ф= cos⁻¹(1/√(2))

Ф≈ 45°

Therefore, the angle between the side and diagonal of a square is approximately 45 degrees.

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Answer:

Step-by-step explanation:

50% of 366 is 183, therefore your answer is 366.

Answer: The formula D = R * T relates the distance traveled (D) to the rate of speed (R) and the time elapsed (T). Using the given values, we can substitute R = 20 km/h and T = 1.6 h to find:

D = R * T = 20 km/h * 1.6 h = 32 km

Therefore, the bicyclist traveled a total distance of 32 kilometers.

Step-by-step explanation:

Answer:

Step-by-step explanation:

here are the steps to solve this problem:

Draw a line segment MO and a point N on it, such that N is between M and O. Label the length of MN as 2x, the length of NO as x-2, and the length of MO as 2x-9.

Write the equation that relates the lengths of MN, NO, and MO. This equation is MO = MN + NO, since MO is the sum of MN and NO.

Substitute the given expressions for MN, NO, and MO into the equation from step 2. We get:

2x-9 = 2x + (x-2)

Simplify the equation by combining like terms. We get:

2x-9 = 3x-2

Bring all the x terms to one side of the equation and all the constant terms to the other side. We get:

-x = 7

Divide both sides of the equation by -1 to isolate x. We get:

x = -7

Check the solution by plugging it back into the original equation. We get:

2(-7)-9 = -23

2(-7) + (x-2) = -16

The two sides of the equation are not equal, so x = -7 is not a valid solution.

Recheck the original problem to see if there was an error in the given values, or if the problem was written incorrectly. We notice that the values of MN, NO, and MO are all positive, so x cannot be negative. Therefore, we assume that there was an error in the given solution for MO, and that it should be 2x+9 instead of 2x-9.

Rewrite the equation from step 2 with the corrected value for MO. We get:

2x+9 = 2x + (x-2)

Simplify the equation by combining like terms. We get:

2x+9 = 3x-2

Bring all the x terms to one side of the equation and all the constant terms to the other side. We get:

x = 11

Check the solution by plugging it back into the original equation. We get:

2(11) + (x-2) = 22 + 9 = 31

2(11) + (11-2) = 20 + 9 = 29

The two sides of the equation are not equal, so x = 11 is not a valid solution.

Recheck the original problem to make sure there are no other errors. We notice that the length of MN is given as 2x, but we haven't yet found the value of x. This means we need to solve the equation from step 11 for the value of 2x:

2x = 2(11) = 22

Therefore, the numerical length of MN is 22.

Answer:

the original list price of the grinder was $147

Step-by-step explanation:

If the sale price is 20% off the original price, then the sale price is 100% - 20% = 80% of the original price. We can set up the equation:

Sale price = 0.8 * original price

We know the sale price is $117.60, so we can substitute and solve for the original price:

117.60 = 0.8 * original price

original price = 117.60 / 0.8

original price = 147

Therefore, the original list price of the grinder was $147.

5 - 1/4 in simplest form is 19/4.

The phrase "expressing a number, fraction, or statement in its simplest form" has a mathematical meaning. This signifies that further simplification or reduction of the result would cause a change in the result's value.

By dividing the numerator and denominator by their 4 greatest common factors, for instance, the fraction 4/8 can be made simpler. In its simplest form, this gives us 1/2. A different number, such as 0.5, which is not in its simplest form, results from additional simplification.

To simplify 5 - 1/4, we need to find a common denominator and combine the terms. The common denominator is 4, so we can write:

5 - 1/4 = 20/4 - 1/4

= (20 - 1)/4

= 19/4

Therefore, 5 - 1/4 in simplest form is 19/4.

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Using the arithmetic operation the value for x in the equation (x – 7)2 = 36 is obtained as 25.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The given equation is (x – 7)2 = 36.

Use the arithmetic operation of multiplication -

2x - 14 = 36

Collect all the like terms -

2x = 36 + 14

Use the arithmetic operation of addition -

2x = 50

Use the arithmetic operation of division -

x = 50/2

x = 25

Therefore, the value is 25.

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1. The probability the project will be finished in 62 weeks or less is 0.6915. 2.The probability the project will be finished in longer than 65 days is 0.8944.

The standard score in statistics is the amount of standard deviations that a raw score (i.e., an observed value or data point) deviates from or exceeds the mean of the thing being observed or measured. Standard scores are positive for raw scores above the mean and negative for raw scores below the mean.

It is determined by deducting the population mean from a given raw score, then dividing the result by the population standard deviation. Standardizing or normalising is the process of transforming a raw score into a standard score.

Given that,

mean = 60 weeks

SD = 4 weeks

1. P (p ≤ 62) = P(z ≤ 62)

The z-score is given by:

z-score = x - mean / SD

Substituting the values we have:

z-score = 62 - 60/4 = 2/4 = 0.5

P(z ≤ 0.5) = 0.6915 (Using the z -table)

Hence, the probability the project will be finished in 62 weeks or less is 0.6915.

Similarly,

2. P(z > 65) = P(z > 1.25) = 0.8944

Hence, the probability the project will be finished in longer than 65 days is 0.8944.

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Answer:

The largest possible whole-number length for the third side of a triangle with two sides of length 7 and 10 is 13. This is due to the fact that the two given lengths must be added together, and then subtracted from the third side in order to create a valid triangle. Therefore, the third side must be at least 13 in order to create a triangle.

The distance from Megan to the point on the ground directly below the kite would be = 80yd

To calculate the distance, the Pythagorean formula should be used such as follows;

c² = a² + b²

a = 60yd

C= 100yd

b = ?

That is;

100² = 60² + b²

make b the subject of formula;

b² = 10,000 - 3600

b² = 6400

b= √6400

b = 80yd

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Answer:

B

Step-by-step explanation:

urheheyfthxhzhditoiytdyifxzydzyfuyrzuysriduyrsute

The fractional equivalent of the repeating decimal is 15/99

What does division of fractions mean?

A fraction is divided into additional equal pieces when it is divided into fractions. For instance, if you had three-fourths of a pizza remaining and divided each slice into two pieces, you would have received six slices, which would be equivalent to six-eighths of the entire pizza.

n = 0.1515...-------(1)

multiply n by 100 =10²

The reason we multiply x by 100 is because 0.1515... has 2 repeating digits and 100 has two zeros.

100n=15.15......--------(2)

Subtract (1) from (2)

100n=15.15...

n = 0.1515....

___________

99n=15

=> n=15/99

The fractional equivalent of the repeating decimal is 15/99

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The six trigonometric functions' values for angle B in this right triangle are as follows: Tan(B) = 8/15 CSC(B) = 17/8 Sin(B) = 8/17 Cos(B) = 15/17 Tan(B) = 8/15 (rationalized denominator)

cot(B) = 15/8 sec(B) = 17/15.

[tex]c2 equals a2 + b2; c2 equals 82 + 152; c2 equals 64 + 225^2 = 289 \sc = √289 \sc = 17[/tex]

Thus, the hypotenuse's length is 17.

We must first get the measure of angle B before we can determine the values of the six trigonometric functions for that angle. Since angle C is a right angle and the total of the angles in a triangle is 180 degrees, we can calculate angle B's measure as follows:

angle B is equal to 90 times angle A, or 90 times angle B.

For now, since we lack sufficient data to estimate the size of angle A, angle B will be specified in terms of an unknowable angle. We are still able to calculate the six trigonometric functions for angle B using the ratios of the triangle's side lengths.

B = opposite/hypotenuse = a/c = 8/17;

B = adjacent/hypotenuse = b/c = 15/17;

B = opposite/adjacent = a/b = 8/15;

B = hypotenuse/opposite = c/a = 17/8;

B = cos(B) = (rationalized denominator)

Hypotenuse/nearby = c/b = 17/15; adjacent/opposite = b/a = 15/8; sec(B) = c/b = 17/15; cot(B) = b/a = 15/8.

For angle B in this right triangle, the values of the six trigonometric functions are as follows:

sin(B) = 8/17

cos(B) = 15/17

tan(B) = 8/15

csc(B) = 17/8 (rationalized denominator)

sec(B) = 17/15

cot(B) = 15/8

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Answer:

The width of the patio is 15 feet

Step-by-step explanation:

We can start by using the formula for the area of a rectangle:

Area = length x width

In this case, we know that the area of the patio is given by:

16x^2 + 20x square feet

And we also know that the length of the patio is x + 5 feet. So we can substitute these values into the formula to get:

16x^2 + 20x = (x + 5) x width

Simplifying the right-hand side by multiplying x + 5 by width, we get:

16x^2 + 20x = width x^2 + 5x

To solve for the width, we can move all the terms with width to the left-hand side and all the other terms to the right-hand side:

width x^2 - 16x^2 + 20x - 5x = 0

Simplifying the left-hand side by combining like terms, we get:

width x^2 - 16x^2 + 15x = 0

Factoring out x, we get:

x (width x - 16x + 15) = 0

Now we can solve for the width by setting each factor equal to zero and solving for x:

x = 0 or width x - 16x + 15 = 0

Since the length and width of the patio must be positive values, we can disregard the solution x = 0. So we are left with:

width x - 16x + 15 = 0

We can factor this quadratic equation by finding two numbers whose product is 15 and whose sum is -16. These numbers are -1 and -15, so we can write:

(width x - 1)(x - 15) = 0

Setting each factor equal to zero and solving for x, we get:

width x - 1 = 0 or x - 15 = 0

width x = 1 or x = 15

Since the length of the patio is x + 5, which is 20 feet, we know that x = 15 is the correct solution. So we can substitute x = 15 into the expression for the width:

width x = 1, x = 15, so we choose x = 15

width x - 16x + 15 = (15) x - (16)(15) + 15 = 15 feet

Therefore, the width of the patio is 15 feet.

Using the loan rates we know that the maximum loan amount Tyresa needs to pay for 4 years which is 48 months is $330.81 for the new car.

The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal or the loaned amount.

Typically, a loan's interest rate is expressed as an annual percentage rate, or APR (APR).

The annual cost of a loan to a borrower is referred to as the interest rate and is indicated as a percentage.

APR represents the total yearly cost of a loan to the borrower, including all fees.

The APR is stated as a percentage, just like an interest rate.

Thus, we discover that using the present value formula:

Pv = C[(1-(1+i)n/i)]

Now, calculate for the new car as follows:

Pv = 350[(1-(1+2.79%/12)2.79%/12)]

Pv = $15879.04

Loan amount each month: 15879.04/48 months = $330.81

Similarly, calculate for the old car as follows:

Pv = 350[(1-(1+3.29%/12)3.29%/12)]

Pv = $15721.34

Loan amount each month: 15721.34/48 months = $327.52

Therefore, using the loan rates we know that the maximum loan amount Tyresa needs to pay for 4 years which is 48 months is $330.81 for the new car.

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The exponential function that is represented by the graph is f(x) = 2(2x).

This is because the graph shows a function with a base of 2 and an exponent of x. The function f(x) = 2(2x) has a base of 2 and an exponent of x, so it matches the graph.

To verify this, we can plug in some values of x into the function and see if they match the points on the graph. For example, when x = 0, the function gives us f(0) = 2(2^0) = 2(1) = 2, which matches the point (0, 2) on the graph. Similarly, when x = 1, the function gives us f(1) = 2(2^1) = 2(2) = 4, which matches the point (1, 4) on the graph.

Therefore, the correct answer is f(x) = 2(2x).

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The missing term in the sequence 5, 11, 17, ?, 31, 41 is B. 23.

We have been given the series 5, 11, 17, ?, 31, 41. We need to find the missing number out of the given sequence.

Let us write the prime numbers upto 50.

2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47.

By looking into the above prime numbers we can make out our sequence. The series is formed by the alternate prime numbers. Thus we can complete the given sequence as,

5, 11, 17, 23, 31, 41.

Thus we got the missing number as 23 in the sequence 5, 11, 17, 23, 31, 41.

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Find the missing term in the sequence 5, 11, 17, ?, 31, 41.