During a sale, the price of all computers in a store is being reduced by 25%. Albert is interested in a computer with an original cost of $650. Two weeks later, the sale price of this computer is reduced by an additional 5%. Albert thinks he can now get the computer for 30% off the original price. Find the sale price after the double reduction, and then the sale price after a single reduction of 30%. Is the double reduction (25% off and then 5% off) the same as or different than the single reduction (30% off)?

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solution to the equation 4x+2 = 12 using the change of base formula is x = 1.442114.

The given equation is 4x+2 = 12.

To solve for x using the change of base formula, we need to isolate x on one side of the equation. We start subtracting 2 from LHS and RHS:

4x+2-2 = 12-2

4x = 10

Next, we use the change of base formula, which states log base a of b is equal to log base c of b divided by log base c of a. In this case, we want to find x, which is the exponent that 4 is raised to in order to get 10.

Rewrite equation:

x = log base 4 of 10

Use the change of base formula, we can present this as:

x = [tex]log base 10 of 10 / log base 10 of 4[/tex]

Simplifying:

x = 1.442114

Solution to the equation 4x+2 = 12 using the change of base formula is x = 1.442114.

In conclusion, using the change of base formula, the answer to the equation 4x+2 = 12 is roughly 1.442114. This method can be used to solve a variety of problems in the sciences, engineering, and financial sectors, as well as exponential and logarithmic equations.

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Answer: 86

Step-by-step explanation:

let x be the unknown

(84+92+88+ x)

-----------------------   =  87.5

          4

then cross multiply

(84+92+88+ x )= 87.5 times 4

84+ 92+ 88 + x= 350

add the left side

264+ x=350

subtract 264 from both sides

264 - 264 + x= 350 - 264

therefore x= 86.

It will take approximately 58.71 years for the amount in the account to be more than $5000.

We can solve for the number of years it will take for the amount in the account to be more than $5000 by setting the given equation equal to 5000 and solving for t:

5000 = 500 (1.04)^t

Dividing both sides by 500, we get:

10 = (1.04)^t

To solve for t, we can take the logarithm of both sides.

1 = t * log(1.04)

Simplifying, we get:

t = 1/log(1.04)

Evaluate

t ≈ 58.71

Therefore, it will take approximately 58.71 years for the amount in the account to be more than $5000.

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Answer:50%

Step-by-step explanation: Since there are 6 letters in orange, and there are 3 vowels in the word (o,a,e), that would mean there is a 3/6 chance (50%) of selecting a vowel.

Answer:

I think it is not ?

Step-by-step explanation:

You get a remainder at the end when you solve it and that's the opposite of what divisible means

"(of a number) capable of being divided by another number without a remainder."

Answer:

Not divisible

Step-by-step explanation:

5^7  is 78125

5^6 is 15625

15625 + 78125 = 93750

93750/60 = 1562.5

Therefore it is not fully divisible by 60.

Answer:

x < 6/5 and x > 32/5

Step-by-step explanation:

|x| means taking the absolute value, or the distance from 0. This means that  |-8| = 8, because -8 is 8 from 0

if |14-5x|>8, 14-5x > 8, or 14-5x < -8 because the absolute value of any number less than -8 is more than 8

for 14 - 5x > 8, -5x > -6, 5x < 6, x < 6/5

for 14 - 5x < -8, -5x < -32, 5x > 32, x > 32/5

The solution is Option C.

The total amount of earnings of Sondra after 5 years is $ 169,113

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the annual salary of Sandra be A = $ 30,000

Now , the percentage increase in salary = 6 %

So , the equation will be

First year :

The increase in first year =  annual salary of Sandra + percentage increase in salary x annual salary of Sandra

The increase in first year = 30000 + ( 6/100 ) x 30000

                                        = 30000 + 1800

                                        = $ 31,800

Second year :

The increase in second year =  increase in first year + percentage increase in salary x increase in first year

The increase in second year = 31800 + ( 6/100 ) x 31800

                                        = 31800 + 1908

                                        = $ 33,708

Third year :

The increase in third year =  increase in second year + percentage increase in salary x increase in second year

The increase in third year = 33708 + ( 6/100 ) x 33708

                                        = 33708 + 2022.48

                                        = $ 35,730.48

Fourth year :

The increase in fourth year =  increase in third year + percentage increase in salary x increase in third year

The increase in fourth year = 35730.48 + ( 6/100 ) x 35730.48

                                        = 35730.48 + 2143.8288

                                        = $ 37,874.3088

Now , the equation is

The total earnings of Sondra is = First year salary + second year salary + third year salary + fourth year salary

The total earnings of Sondra is = 30000 + 31,800 + 33,708 + 35,730.48 + 37,874.3088

The total amount earnings of Sondra is = $ 169,112.7888

Therefore , the total amount earnings = $ 169,113

Hence , The total amount of earnings of Sondra after 5 years is $ 169,113

Answer:

C)  $199,797

Step-by-step explanation:

Adding 7% of a number to the number is the same as multiplying the number by 1.07

First year: $45,000

Second year: $45,000 × 1.07 = $48,150

Third year: $48,150 × 1.07 = $51,520.50

Fourth year: $51,520.50 × 1.07 = $55,126.94

Total = $199,797.43

Answer: C)  $199,797

Answer:

It will take him 11 hours to mow 12 lawns

Step-by-step explanation:

110/2=55   (meaning it takes him 55 minutes to mow 1 lawn)

55x12=660    (meaning it takes him 660 minutes to mow 12 lawns)

660/60=11   (meaning it takes him 11 hours to mow 12 lawns)

Why 660/60? Because there is 60 minutes in 1 hour.

The unit rate of the given expression through which the relation is satisfied is 300km / 2.5 hrs = 120 km / hr

What about unit rate?

In mathematics, a unit rate is a ratio between two quantities in which one quantity is expressed in terms of one unit of measure. It is commonly used to compare the cost or value of two or more items. For example, if a store charges $4 for 2 pounds of bananas, then the unit rate is $2 per pound of bananas.

The general formula for calculating unit rate is:

Unit rate = Quantity of one item ÷ Cost or value of that item

This formula can be used to find the unit rate of any item or quantity, as long as the quantity and cost or value are known. Unit rate is a useful tool in mathematics, as it allows for easy comparison of different quantities or values, and helps to make complex calculations more straightforward.

According to the given information:

The unit rate = [tex]\frac{Distance}{Time}[/tex]

i.e , unit rate = 300/2.5 = 120

⇒ 120km/hr.

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Answer: Its A

Ive took this test :3

The estimates for the solutions are x = -0.25 and 1.25 when y = 0 and x = -0.5 and 1.5 when y = 2

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

y = 4x² - 4x - 1

When y = 0, we have

4x² - 4x - 1 = 0

From the graph, we can see that

x = -0.25 and 1.25 when y = 0

When y = 2, we have

4x² - 4x - 1 = 2

From the graph, we can see that

x = -0.5 and 1.5 when y = 2

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Answer: You'll have to plug each function into a calculator and match the corresponding ones with each other.

for example Sin45° = B cos 45°

Step-by-step explanation:

Answer:

The value of the vehicle would be $7,242

Step-by-step explanation:

Given,

The original value of the vehicle, P = $29,800,

Rate of depreciation, r = 9% = 0.09

Time, t = 15 years,

Thus, the value of the car after 15 years,

[tex]A=P(1-r)^t[/tex]

[tex]=29800(1-0.09)^{15}[/tex]

[tex]=29800(0.91)^{15}[/tex]

[tex]=7241.64363066[/tex]

[tex]\thickapprox \bold{\$ 7,242}[/tex]

The required in order for Micaela to end up with ,n = 365 , t = 12, P = $360, and A = $670

A relation is any subset of a Cartesian product.

As an illustration, a subset of is referred to as a "binary connection from

A binary relation from A to B is made up of these ordered pairs (a,b),

A to B," and more specifically, a "relation on A."

A binary relation from A to B is made up of these ordered pairs (a,b), here the first component is from A and the second component is from B.

Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).

A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).

Every function, as you can see from these definitions, is a relation from X.

According to our question-

r=7.5%

Thus, 7.5% would be required in order for Micaela to end up with $670.

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Answer:

34.56 in

Step-by-step explanation:

2.4*2.4*6=34.56

The set A.{x | x R, x < 5} would have a graph with an open circle on 5 and a ray pointing left on the number line.

What exactly is a set?

In mathematics, a set is a collection of distinct objects or elements, which are considered as a single entity. The objects or elements in a set can be anything, such as numbers, letters, people, animals, or other things, depending on the context.

Now,

The set  A.{x | x R, x < 5}  would have a graph with an open circle on 5 and a ray pointing left on the number line.

This is because the symbol "<" means "less than," so the set A includes all real numbers less than 5. The open circle on 5 indicates that 5 is not included in the set, so the graph will have an open circle on 5. The ray pointing left indicates that the set extends infinitely to the left of 5.

In contrast, set B.{x | x R, x > 5} would have an open circle on 5 and a ray pointing to the right, since it includes all real numbers greater than 5. Set C.{x | x R, x ≤ 5} would have a closed circle on 5 and a ray pointing to the left, since it includes all real numbers less than or equal to 5.

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Answer:

(-2,4) is quadrant 2, (8,4) is quadrant 1, (6,-2) is quadrant 4

Step-by-step explanation:

Therefore, the reaction is first-order with respect to the concentration of "A".

In mathematics, an equation is a statement that asserts the equality of two expressions. It typically contains one or more variables, which are placeholders for unknown values, and constants, which are known values. The goal in solving an equation is to find the values of the variables that satisfy the equation, that is, make it true. Equations can be linear or nonlinear, and they may involve one or more variables. Some common types of equations include polynomial equations, trigonometric equations, exponential equations, and logarithmic equations.

Here,

1. Table completion:

Time (s) [A] (M)

0 1.0

50 0.81

100 0.65

150 0.53

200 0.43

250 0.35

300 0.28

350 0.23

400 0.19

450 0.15

500 0.12

2. To determine the reaction order with respect to the concentration of "A", we need to manipulate the above equation for the different orders of the reaction and re-plot the tabulated numbers to determine the order.

For zero-order: [A]t = [A]o - kt

Taking the natural logarithm on both sides:

ln [A]t = ln [A]o - kt

This gives a straight line equation of the form y = mx + b, where y = ln[A]t, x = t, m = -k, and b = ln[A]o.

For first-order: ln [A]t = ln [A]o - kt

Taking the reciprocal on both sides:

1/[A]t = kt + 1/[A]o

This gives a straight line equation of the form y = mx + b, where y = 1/[A]t, x = t, m = k, and b = 1/[A]o.

For second-order: 1/[A]t = 1/[A]o + kt

This gives a straight line equation of the form y = mx + b, where y = 1/[A]t, x = t, m = k, and b = 1/[A]o. We can then plot the given data in Excel with the appropriate equation and check which equation gives us the best straight line fit. The slope of the line will give us the reaction order. Using Excel, we find that the first-order equation gives the best straight line fit with a slope of -0.0077.

3. To calculate the rate constant 'k', we can use the slope of the straight line fit obtained above.

From the equation ln [A]t = ln [A]o - kt, we have k = -slope.

Therefore, k = 0.0077 s⁻¹.

To estimate the half-life of "A", we can use the equation for the half-life of a first-order reaction:

t1/2 = ln 2/k

Substituting the value of k obtained above, we get:

t1/2 = ln 2/0.0077 s⁻¹

= 89.9 s

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Answer:

Step-by-step explanation:

that would be 5 miles bc 3+2 is 5

The distance between Mary's and Roger's houses is approximately 3.6 miles.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

We can use the Pythagorean theorem to find the distance between Mary's and Roger's houses since they form a right triangle with the school at the vertex:

Let A be the school (0, 0), B be Mary's house (0, 2), and C be Roger's house (-3, 0).

Then the length of AB is 2 miles and the length of AC is 3 miles.

The distance between Mary's and Roger's houses is the length of the hypotenuse BC.

Using the Pythagorean theorem, we have[tex]BC^2 = AB^2 + AC^2 = 2^2 + 3^2 = 13.[/tex]

Taking the square root of both sides, we get[tex]BC = \sqrt{(13)} = 3.6[/tex] miles.

Therefore, Between Mary and Roger's homes, there are roughly 3.6 miles.

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The proportion of red gumballs in the random sample is 0.4, meaning 40% of the 200 gumballs are red. To estimate the number of red gumballs in the entire population of 200 gumballs, we multiply the proportion of red gumballs by the total number of gumballs, 0.4 x 200 = 80.

Proportion in mathematics refers to the equality of two ratios. It asserts that two ratios are comparable. A ratio is a fractional comparison of two numbers or quantities, such as a/b or c/d.

To estimate how many of the 200 gumballs are red, we can use the proportion of red gumballs in the random sample and apply it to the entire population of 200 gumballs.

The proportion of red gumballs in the random sample is:

10/25 = 0.4

This means that 40% of the gumballs in the random sample are red.

To estimate the number of red gumballs in the entire population of 200 gumballs, we can multiply the proportion of red gumballs by the total number of gumballs:

0.4 x 200 = 80

Therefore, we can estimate that there are approximately 80 red gumballs in the machine.

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Step-by-step explanation:

Triangle a) is half of an equilateral triangle therefore the height divides the base into two equal parts, same thing for triangle b), triangle c) instead is half square, therefore congruent catheti.

a)

n = 6 : 2

n = 3

m = √(6²+3²)

m = √45

b)

x = 10 x 2 = 20

y = √(20²-10²)

y = √300

c)

a = √(5²+5²)

a = √50

The car has actually travelled 1745 miles, even though the odometer reads 2005. This is because the odometer skips the digit 4, so the number of valid readings must be counted and subtracted from the odometer reading.

We can approach this problem by counting the number of valid readings on the odometer between 3000 and 5000. We can then subtract the number of invalid readings (i.e., readings that contain the digit 4) to determine the actual number of miles the car has travelled.

The valid readings between 3000 and 5000 are: 3001, 3002, 3003, 3005, 3006, 3007, 3008, 3009, 3010, ..., 4997, 4998, 4999, 5000.

There are a total of 2001 valid readings in this range.

However, we need to subtract the number of invalid readings, which are the readings that contain the digit 4. Since the odometer skips the digit 4, we can think of each valid reading as having four possible digits (0, 1, 2, or 5) for each of its four places. Therefore, the number of invalid readings is 4 x 4 x 4 x 4 = 256.

So the actual number of miles the car has travelled is 2001 - 256 = 1745.

Therefore, the car has actually travelled 1745 miles.

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Answer: O

Step-by-step explanation: if the bag is only filled with the letters in OUTCOME then there are more O’s than the rest

Answer:

a. 4

b. -2

c. 0,5

Step-by-step explanation:

1. 4

2.2

3.0,5

IT IS SAYING TO WORK OUT WHAT THAT LINE REPRESENTS

Answer: 10sec 660 feet, 20sec = 1320 feet, 30 sec = 1980 feet.

Step-by-step explanation:

It states that a car moves 660 feet in 10sec.

10sec = 660 feet

20sec: 660+660=1320f

30sec: 660+660+660=1980f