Which situation below represents a 30% decrease?

from 50 to 35 OR from 30 to 27

Answer:

To subtract a number from another number, the sign of the number (which is to be subtracted) should be changed and then this number with the changed sign, should be added to the first number

Step-by-step explanation:

(i) Evaluate (+6) – (+2)

= (+6) + (-2) (charging the sign of the number to be subtracted and then adding)

On subtracting smaller number 2 from bigger number 6; we get 6 – 2 = 4

Since, the sign of bigger number is + (positive)

= +4 or 4

Therefore, (+6) – (+2) = 4

(ii) Evaluate (+5) – (-3)

= (+5) + (+3) (charging the sign of the number to be subtracted and then adding)

We know, to add a positive (+ ve) number to a positive (+ ve) number, the numbers should be added and positive sign should be attached to the sum obtained.

= +8

Therefore, (+5) – (-3) = 8

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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The data value that is an outlier is 67

The dataset is given as:

83, 84, 85, 87, 89, 88, 67, 79, and 81

To determine the outlier, we select the data values that are relatively far from others

In the above dataset, the data element 67 is far from other data values

Hence, the data value that is an outlier is 67

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Neil is growing sugar crystals for his science fair experiment. He wants to find out if the amount of sugar affects the size of the crystal. Neil adds 18 tablespoons of sugar to his first bowl of water. He plans to add less sugar to the second bowl.

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Answer:

12k+8

Step-by-step explanation:

(3k+2)x4

(4x3K)+(4x2)

12k+8

Answer:

12k+8

Step-by-step explanation:

Answer:

Domain : 0 ≤ x ≤ 8

Range : 5450 ≤ f(x) ≤ 6588.65

Step-by-step explanation:

Expression representing the money Samantha collected after x years is,

f(x) = \(5450(1.024)^{x}\)

Time 'x' duration for the investment starts from t = 0 and ends at 8 years, so the domain of the given function will be,

Range : 0 ≤ x ≤ 8

Money collected in the fund from 0 to 8 years is,

f(0) = \(5450(1.024)^{0}\)

     = $5450

f(8) = \(5450(1.024)^{8}\)

     = $6588.6

Therefore, range of the graphed function will be,

Range : 5450 ≤ f(x) ≤ 6588.65

The probability that on a particular Monday, they each suggest a different activity is 0.11.

The probability that in a period of four consecutive Mondays, they all suggest the same activity on exactly two of the four Mondays is 0.0504.

1. Probability that on a particular Monday, they each suggest a different activity:

The probability is calculated using the formula below:

Probability = P(SMC) + P(MCS) + P(CSM)

Probability = (0.4 x 0.55 x 0.5) + (0.3 x 0.2 x 0.3) + (0.3 x 0.25 x 0.2)

Probability = 0.11

2. The probability that in a period of four consecutive Mondays, they all suggest the same activity on exactly two of the four Mondays is determined using the binomial distribution.

Let success be suggesting the same activity on exactly two of the four Mondays.

The probability of success on any Monday is:

P(success) = P(SSNN) + P(NSSN) + P(NNSS)

P(success) = 3 x (0.4 x 0.4 x 0.6 x 0.6)

P(success) = 0.3456

The probability of failure is:

P(failure) = 1 - P(success)

P(failure)= 1 - 0.3456

P(failure) = 0.6544

Choose exactly two Mondays out of four is ⁴C₂

The probability of exactly two successes = ⁴C₂ * P(success)² * P(failure)²

P(exactly 2 successes) = 6 x (0.3456)² x (0.6544)²

P(exactly 2 successes) = 0.0504 or 5.04%

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Answer:

x = 1/2

Step-by-step explanation:

First you want to get rid of the fraction, so you can multiply both sides of the equation by 3.

9 = 2x + 8

Then, subtract 8 from both sides to get x by itself.

1 = 2x

Finally, divide both sides by 2 so you only have one x

1/2 = x

This means that the answer is x = 1/2.

Answer:

x=1/2 or 0.5

Step-by-step explanation:

(2x+8)/3=3

(2x+8)=3x3

(2x+8)=9

2x=9-8

2x=1

x=1/2

x=0.5

1- SHM stands for Simple Harmonic Motion.

In SHM, an object oscillates back and forth about an equilibrium position, with a motion that can be described by a sinusoidal function. The symbols commonly used in SHM are:

y: Displacement from the equilibrium position

t: Time

k: Spring constant or restoring force constant

m: Mass of the object

c₁ and c₂: Constants determined by initial conditions

2- Hooke's law relates the force exerted by a spring to the displacement of the object attached to it. It is represented by the second-order differential equation my" + ky = 0, where m is the mass of the object and k is the spring constant. The solution to this equation is given as y = c₁ cos(√(k/m) * t) + c₂ sin(√(k/m) * t). To determine the values of c₁ and c₂, initial conditions are needed.

3- If the initial conditions are y(0) = 0 and y'(0) = 0, which means the object starts at equilibrium with zero displacement and zero velocity, we can substitute these values into the solution equation and solve for c₁ and c₂. In this case, we find that c₁ = 0 and c₂ = 0.

4- To show that the sum of the solutions c₁ cos(w₀t) and c₂ sin(w₀t) is also a solution of the SHO (Simple Harmonic Oscillator) differential equation, we substitute the sum into the differential equation and demonstrate that it satisfies the equation. By taking the derivatives and substituting, we can show that the sum of the solutions satisfies the equation, thus confirming that it is also a solution.

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Answer:

Length of the string let out by Jim is 156.9 m.

Step-by-step explanation:

From the figure attached,

Jim observes the angle of elevation of the kite = 85°

And Patty observes the angle of elevation of the kite = 40°

Angle formed between the lines joining kite to Jim and Patty = 180° - (85 + 40)° = 55°

Distance between Jim and Patty = 200 m

Let the length of the string between Jim and the kite = x meters

By applying Sine rule in the triangle formed between Jim, Patty and the kite,

\(\frac{\text{Sin}55}{200}=\frac{\text{Sin}40}{x}\)

x = \(\frac{200\times \text{Sin}40}{\text{Sin}55}\)

x = 156.94 m

  ≈ 156.9 m

Therefore, length of the kite string from Jim and the kite is 156.9 m.

Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

The reference angle that has a sin value of 1/2 is π/6 radians or 30 degrees. Therefore, the value of θ is π/6 radians or 30 degrees.

Given that sin θ = 14/28, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 14. This yields sin θ = 1/2.

The value of sin θ equal to 1/2 corresponds to the angle θ being π/6 radians or 30 degrees in the first quadrant.

In general, the trigonometric function sin θ represents the ratio of the length of the side opposite the angle θ to the length of the hypotenuse in a right triangle. For sin θ to be positive, the angle θ must lie in the first or second quadrant. Since we are assuming θ to be an acute angle, it falls within the first quadrant.

In the first quadrant, the reference angle that has a sin value of 1/2 is π/6 radians or 30 degrees. Therefore, the value of θ is π/6 radians or 30 degrees.

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If one of the zeros in the quadratic polynomial is 4, then the value of k is 3.

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x. A polynomial is a mathematical expression that only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are also known as indeterminates in mathematics.

Here,

4 is a root/zero of polynomial

P(x)  =   (k-2) x²  - 2 x  - (k+5)

P(4) = 0

(k - 2) 4²  - 2 * 4 - (k+5)  = 0

15 k - 45 = 0  

k = 3

The value of k if 4 is one of the zeros of the quadratic polynomial is 3.

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Complete question:

If one of the zeros of a quadratic polynomial(k-2)x^2-2x-(k+5) is 4 , find value of k.

Therefore , the solution of the given problem of function comes out to be is that the function approaches negative infinity as x approaches positive or negative infinity.

The mathematics curriculum covers the study of number and their variable as well as our surroundings, architecture, and both actual and hypothetical locations. The link between the amounts of inputs as well as the associated outputs for each is shown graphically by a function. A function is, to put it simply, a group of inputs whose, when combined, result in particular outputs for every input. Each role is assigned a region, locale, or range .

Here,

Given :

f(x) = -x² + 14x³ - 24x⁷ - 10x¹² + 22x⁴ - 18x¹¹ + 4x⁴  +21

To describe the end behavior of the given polynomial function f(x), we only need to consider the term with the highest degree, which is - 10x¹²

Since the degree of the term is even and the coefficient is negative, we know that as x approaches positive or negative infinity, the function will also approach negative infinity.

Therefore, we can say:

As x to -∞, f(x)  to - ∞

As x to +∞, f(x) to-∞

So the end behavior of the function

f(x) = -x² + 14x³ - 24x⁷ - 10x¹² + 22x⁴ - 18x¹¹ + 4x⁴  +21

is that the function approaches negative infinity as x approaches positive or negative infinity.

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\(\large\bf{\underline{Given }}\)

__________________________________________

\(\large\bf{\underline{Hence}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎\(\large\bf{⟹£0.14}\)

\(\large\bf{\underline{Total \: time\:he \: talked : }}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\( \large =\frac{8.96}{0.14} \)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large = 64\)

__________________________________________

\(\large\bf{\underline{So,\:he\: talked\: for:}}\)

\(\huge\bf{64 \:minutes}\)

The points D, E, F are not collinear to points A, B, C and are coplanar. (Right choices: 6, 7, 8)

According to Euclidean geometry, three points are coplanar when they are not collinear. Three or more points are coplanar when they are contained by the same plane.

From this perspective, points A, B, C, D, E, F are coplanar, as they are contained by plane π, but points D, E, F are not collinear to points A, B, C, as they are outside the line contained by plane π.

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The total that Mary has initially is:

$6.00

Since the first 30 minutes cost $0.99, after those 30 minutes she will have:

$6.00 - $0.99 = $5.01

So far she has talked for 30 minutes but has $5.01 left.

After 30 minutes, the cost per minute is $0.04. To find the number of minutes that she can talk with those $0.04, we divide 5.01 by 0.04:

Using the remaining amount she can talk for 125.25 minutes more.

Thus, the total of minutes is:

Answer: She can talk for 155.25 minutes.

Let's recalll that:

• 1 mile per hour = 1.46667 feet per second

Therefore:

• 10 miles per hour = 1.46667 * 10 feet per second

• 10 miles per hour = 14.6667 feet per second, Khalil!

The value of g(2) is -1/4, g(0) is undefined, g(1.2) is approximately 1.0833, g(-2) is -1/4, and g(6) is -2/3, where g(x) = 3/x² - 1.

We can evaluate g(x) by substituting the value of x in the expression:

g(x) = 3/x² - 1

a) To evaluate g(2), we substitute 2 for x in the expression:

g(2) = 3/2² - 1

g(2) = 3/4 - 1

g(2) = -1/4

Therefore, the answer is (a) -1/4.

b) To evaluate g(0), we substitute 0 for x in the expression:

g(0) = 3/0² - 1

However, division by zero is undefined, and so g(0) is undefined.

c) To evaluate g(1.2), we substitute 1.2 for x in the expression:

g(1.2) = 3/1.2² - 1

g(1.2) = 3/1.44 - 1

g(1.2) = 1.0833...

Therefore, the answer is (c) approximately 1.0833.

d) To evaluate g(-2), we substitute -2 for x in the expression:

g(-2) = 3/(-2)² - 1

g(-2) = 3/4 - 1

g(-2) = -1/4

Therefore, the answer is (d) -1/4.

e) To evaluate g(6), we substitute 6 for x in the expression:

g(6) = 3/6² - 1

g(6) = 3/36 - 1

g(6) = -8/12

g(6) = -2/3

Therefore, the answer is (e) -2/3.

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Answer:

if its 8 to 5 then 16 is 10

answer: 10 miles

Answer:

10 miles

Step-by-step explanation:

8 km = 5 miles

So, Let's use the unitary method

1 km = \(\frac{5}{8}\) miles

Multiplying both sides by 16, we get

16 km = \(\frac{5}{8} * 16\) miles

16 km = 5 × 2 miles

16 km = 10 miles

The original cost of the tablet is $70.89 in the given algebraic equation.

A mathematical claim containing two equated algebraic expressions is known as an algebraic equation. When P and Q are polynomials, an algebraic equation has the general form P = 0 or P = Q. The term "multivariate equation" refers to an algebraic equation that has more than one variable.

Univariate equations are algebraic equations that only have one variable. Equations in algebra are balanced by definition. Due to this, the right and left sides of the equation will be equal.

Let the original cost be  x

then

15/100 = 24.99.x

x =  166.6

237.49 - 166.6

= $70.89

Thus, the original cost of the tablet is $70.89 in the given algebraic equations.

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Full question?

Lucas bought a tablet that was on sale at a 15% discount on your supra case for $24.99 which is been a total of $237.49. Write an equation to find the original cost of the tablet?

Answer:

length = (x − 8) units and width = (x − 9) units

Step-by-step explanation:

We need to factor

x^2 - 17x + 72

We need two numbers whose product is 72 and whose sum is -17.

The numbers are -8 and -9.

x^2 - 17x + 72 = (x - 8)(x - 9)

Answer: length = (x − 8) units and width = (x − 9) units

Answer:

Step-by-step explanation:

Its right on Edg

Answer:

9 squares

Step-by-step explanation:

An equilateral has three equal sides.  You can have two squares on each side: AB, one in which the triangle, ABC, falls within the square and the other where the square does not contain the triangle, ABC.  You can also have two squares on each side - BC, one in which the triangle, ABC, falls within the square and the other where the square does not contain the triangle, ABC.  Again, you can have two squares on each side - CA, one in which the triangle, ABC, falls within the square and the other where the square does not contain the triangle, ABC.  In addition, AB, BC and CA can be a diagonal of squares.  

TL;DR

In conclusion, you have 9 squares in all - 3 as diagonals of squares and 6 as sides of squares. Brainliest appreciated!

No square shares more than two vertices with the equilateral triangle, so we can find the number of squares having two of their vertices at two given points and triple the result. Given 2 points, 3 squares may be drawn having these points as vertices. The figure below shows a red equilateral triangle with the 3 squares that correspond to one of the sides of the triangle. Therefore, 9 squares share two vertices with the equilateral triangle.

\(\sf Let \ d_1 \ and \ d_2 \ be \ the \ lengths \ of \ the \ sides \ of \ diagonals.\)

\(\sf Given \ that \ d_1=8 \ cm\)

\(\sf And \ d_2=10 \ cm\)

\(\therefore\sf Area \ of \ rhombus=\dfrac{1}{2} (d_1)(d_2)=\dfrac{1}{2}(8)(10)=40 \ cm^2\)

\(\rightarrow\boxed{\sf Area \ of \ rhombus=40 \ cm^2}\)

The value of the function g(x) at g = 4 is 18.

Given is a function g(x) as follows -

g(x) = 3x² - 5(x + 2)

We have the following function as -

g(x) = 3x² - 5(x + 2)

For g(4), we can write -

g(4) = 3 x (4)² - 5(4 + 2)

g(4) = 3 x 16 - 5 x 6

g(4) = 48 - 30

g(4) = 18

Therefore, the value of the function g(x) at g = 4 is 18.

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Answer:

80

Step-by-step explanation:

60 seconds=1 minute

6x10=60

multiply the number of cups with the same number used to multiply 6 with

8x10=80

80 cups per minute

Answer:

Step-by-step explanation:

Part A: 24.50 feet, Part B: 46.68 square feet, I just took the test and got this right!

The perimeter of the figure is \(24.50\) and area of the figure is \(45.68\) square feet.

What is Area of Circle?

In geometry, the area enclosed by a circle of radius r is πr². Here the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159

According to question, the radius of the partial circle with center A is 4 feet.

We have to find the perimeter and area of the figure.

Perimeter of the figure=2πr×\(\frac{3}{4}\) +\(4\sqrt{2}\)

=2×\(3.14\)×\(4\)×\(0.75+4\)×\(1.414\)

\(=24.50\)

Area of figure=\(\frac{3}{4}\) πr²+\(r^{2}\)×\(\frac{1}{2}\)

=\(0.75\)×\(3.14\)×\(16\)\(+16\)×\(0.5\)

\(=37.68+8\)

\(=45.68\)

Hence, we can conclude that the perimeter of the figure is \(24.50\) and area of the figure is \(45.68\) square feet.

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The maximum area of the quadrilateral is achieved when it is a square with a side length of 50cm, resulting in an area of 2500cm².

This is because a square has equal sides and equal angles,

resulting in the most efficient use of the perimeter to enclose the maximum area.

To see why, consider a rectangle with a perimeter of 200cm.

If the rectangle is long and thin, with one side much longer than the others,

then it will have a smaller area than a square with the same perimeter.

This is because the longer sides of the rectangle will be less effective at enclosing area than the shorter sides.

Hence, The maximum area of a quadrilateral with a minimum perimeter of 200cm is achieved when the quadrilateral is a square.

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