Mark buys $45 worth of office supplies. He uses a 15% off coupon. What will be the new price?

Answer:

[tex]\text{c)} \quad y=5(2)^x[/tex]

[tex]\text{d)} \quad y=6(2)^x[/tex]

[tex]\text{e)} \quad y=3(7)^x[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

Given points:

Substitute the given (x, y) points into the exponential function formula to create two equations:

[tex]\implies 20=ab^2[/tex]

[tex]\implies 640=ab^7[/tex]

Divide the second equation by the first equation to eliminate a:

[tex]\implies \dfrac{640}{20}=\dfrac{ab^7}{ab^2}[/tex]

[tex]\implies 32=\dfrac{b^7}{b^2}[/tex]

Solve for b:

[tex]\implies 32=b^7 \cdot b^{-2}[/tex]

[tex]\implies 32=b^{7-2}[/tex]

[tex]\implies 32=b^5[/tex]

[tex]\implies b=2[/tex]

Substitute the found value of b into one of the equations and solve for a:

[tex]\implies 20=a \cdot 2^2[/tex]

[tex]\implies 20=4a[/tex]

[tex]\implies a=5[/tex]

Substitute the found values of a and b into the exponential function formula:

[tex]\implies y=5(2)^x[/tex]

---------------------------------------------------------------------------------------

Given points:

As a is the y-intercept, a = 6.

Substitute the point (3, 48) and the found value of a into the  exponential function formula and solve for b:

[tex]\implies 48=6b^3[/tex]

[tex]\implies 8=b^3[/tex]

[tex]\implies b=2[/tex]

Substitute the found values of a and b into the exponential function formula:

[tex]\implies y=6(2)^x[/tex]

---------------------------------------------------------------------------------------

Given points:

Substitute the given (x, y) points into the exponential function formula to create two equations:

[tex]\implies 21=ab^1[/tex]

[tex]\implies 147=ab^2[/tex]

Divide the second equation by the first equation to eliminate a:

[tex]\implies \dfrac{147}{21}=\dfrac{ab^2}{ab^1}[/tex]

[tex]\implies 7=\dfrac{b^2}{b^1}[/tex]

Solve for b:

[tex]\implies 7=b^2 \cdot b^{-1}[/tex]

[tex]\implies 7=b^{2-1}[/tex]

[tex]\implies 7=b^1[/tex]

[tex]\implies b=7[/tex]

Substitute the found value of b into one of the equations and solve for a:

[tex]\implies 21=7a[/tex]

[tex]\implies a=3[/tex]

Substitute the found values of a and b into the exponential function formula:

[tex]\implies y=3(7)^x[/tex]

The Fourier series coefficients for T-2 and A-4 are Ao = 2, B(n-odd) = 0, and B(n-even) = -(4/nπ). The Fourier series for the function is then given by:Y(t) = A0 + ΣB(n)cos(nπt/T) + ΣB(n)

The Fourier series coefficients are used to determine the Fourier series of a given function. The Fourier series is an infinite series of sines and cosines which, when summed, gives an approximation of the original function.

The coefficients are determined by integrating the function over a period and solving for the coefficient of each term.

The coefficients for the function T-2 and A-4 are determined by first calculating the period of the function. The period of the function is T=4. The coefficients are then calculated by integrating the function from 0 to T and solving for each coefficient. The coefficients for T-2 and A-4 are then calculated as follows:

A0= 2

B(n-odd) = 0

B(n-even) = -(4/nπ)

Therefore,

Y(t) = A0 + ΣB(n)cos(nπt/T) + ΣB(n)

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The correct question should be: If T-2 And A-4, Calculate The Fourier Series Coefficients (Integers) Ao B (N-Odd) B (N-Even)- (N-1,2,3,..) Such That: Y(T)-A0 + ?

To the nearest percentage point, Lupita's retirement funds increased by 44% from June to July.

A percentage is a term used in mathematics to describe a value or ratio that may be expressed as a fraction of 100. If we need to calculate a percentage of a number, we should first divide it by 100 before multiplying it by the remainder. Consequently, the percentage refers to a portion per hundred.

Given that Lupita had $115 in her bank account at the beginning of June

The amount Lupita had set aside climbed to $165 in July.

We are expected to calculate the percentage growth in money.

% increase

[tex]= {(165 - 115) / 115 } × 100 = 43.48%. ≈ 44%[/tex]

To the nearest percentage point, Lupita's retirement funds increased by 44% from June to July.

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The equation for the proportional is y= 3x.

The correct option is (B).

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

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

LHS = RHS is a common mathematical formula.

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:

Points taken as (2, 6) and (6, 18).

So, the slope is

slope = (18-6)/ (6-2)

slope = 12 /4

slope= 3

and, the equation of line is

y- 6 = 3(x- 2)

y-6 = 3x - 6

y= 3x

Hence, the equation is y= 3x.

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System Linear equation has no solution , because it is paralell lines but no intersection.

What is system linear equation?

An equation for a line is known as a linear equation. alternatively, y + 0.5x 3.5 = 0 and others. (Note that each linear equation is the same.) When multiple linear equations interact, we get a system of linear equations.

Here the given system linear equations,

[tex]3y=\frac{3}{2}x+6[/tex] -------> 1    and [tex]\frac{1}{2}y-\frac{1}{4}x=3[/tex] --------> 2

Divide by 3  of equation 1 on both sides then,

[tex]y=\frac{1}{2}x+2[/tex]  -----------> 3

Now put 3 into 2 then,

=> [tex]\frac{1}{4}x+1-\frac{1}{4}x=3[/tex]

=> 1=3

Hence the given system equation has no solution , because it is paralell lines but no intersection.

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4.835

(full number)

4.8357033e+24

2^82 = 4.83 We have to add the decimal to fine the real number.

A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.

For example, [tex]= > 3^82 = 1.33[/tex] so:

→ 2^82

→ = 4.83 with a decimal.

Therefore, 2^82 = 4.83 We have to add the decimal to fine the real number.

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If Colah Company purchased $2,000,000 of Jackson, Inc., 6% bonds at par on July 1, 2021. The journal entries for the purchase of the Jackson bonds on July 1 is: Debit Available-for-sale securities $2,000,000

Credit Cash $2,000,000.

Journal entry is used by companies to record their day to day business transaction.

July 1 2021

Debit Available-for-sale securities $2,000,000

Credit Cash $2,000,000

December 31 2021

Debit Cash $60,000

Credit Interest income  $60,000

(6% ×$2,000,000 / 2)

December 31 2021

Debit Available-for-sale securities $300,000

Unrealized Gain - Other comprehensive income $300,000

($2,000,000 - $2,300,000)

June 30 2022

Debit Cash $60,000

Credit Interest income  $60,000

(6% ×$2,000,000 / 2)

The entry necessary upon sale of the Jackson bonds on July 1, 2022 is:

July 1 2022

Debit Available-for-sale securities  $2,300,000

Unrealized Gain-Other comprehensive income account $300,000

Credit Cash $1,800,000

Credit Realized Loss on the sale of Available-for-sale securities $200,000  

[$1,800,000 - $2,000,000= $200,000 (Realized Loss)]

2. Table to show the effect of the Jackson bonds on Colah’s net income,

                             2021                   2022                       Total

Net Income       $60 ,000        ($140,000)              ($80,000)

( 60,000 - $200,000= -$140,000)

OCI                       $300,000                                         $300,000

Comprehensive Income $360,000 ($140,000) $220,000

Therefore the  journal entries for the purchase of the Jackson bonds on July 1 is: Debit Available-for-sale securities $2,000,000

Credit Cash $2,000,000.

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Answer:

14z + 12x is not equivalent to any of the others

2 + (7z + 6x) is not equivalent to any of the others

2(7z + 6x) is equivalent to 14z + 12x

9x + 3(4z + x) + 2z is not equivalent to any of the others

Step-by-step explanation:

14z + 12x is equivalent to itself

2 + (7z + 6x) is equivalent to (7z + 6x) + 2

2(7z + 6x) is equivalent to 14z + 12x

9x + 3(4z + x) + 2z is equivalent to itself.

Answer:

I beleive 4

Step-by-step explanation:

let me know if im wrong

Answer:  

To express the deaths per capita as a decimal, we can divide the number of new construction accidents (deaths) by the population:

4172/11300000 = 0.00037

Rounded to 6 decimal places, the deaths per capita as a decimal is 0.00037

To express the deaths per capita in scientific notation, we can use the decimal value found above and convert it to scientific notation:

3.7 x 10^-4

To express the deaths per capita as a per 100,000 value, we can multiply the decimal value by 100,000:

0.00037 * 100,000 = 37

So the deaths per capita are 37 deaths per 100,000 people.

Step-by-step explanation:

The sum of the interior angles of a decagon is 1440 degrees.

The inner angles of a normal decagon are equal. Every interior angle in a normal decagon is 144° in length because 1440°/10 = 144°. Additionally, each external angle measures 36°.

A decagon is a ten-sided polygon, or ten-gon, in geometry. A basic decagon's inner angles add up to 1440°, and its external angles add up to 360°.

A decagon is a polygon with ten sides, ten internal angles, and ten vertices, or points where the sides meet. There are 10 equal-length sides and 10 equal-sized interior angles in a normal decagon. The sum of all the angles, each of which is 144°, is 1,440°.

A decagon is a polygon having 10 sides.

The sum of interior angles of a polygon having 'n' sides is (2n- 4) × 90°.

sum of interior angles of a decagon= (204) × 90°

= 16 x 90°

= 1440°

Therefore, the sum of the interior angles of a decagon is 1440 degrees.

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Answer:

are the capital letter formed by three line segments.

40

.

.

.

.

.

.

.

........

.

.

.

.

.

.

.

.

.

Answer:

Step-by-step explanation:

its 40

When w=12 and x=1/2, the value of the given equation 13-0.75w +8x is 8.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The product of 8 and 3 equals 11. 8 + 3 is an expression.

Here,

given expression,

=13-0.75w +8x

x=1/2

w=12

=13-0.75*12 +8*1/2

=8

The value of given expression 13-0.75w +8x when w=12 and x=1/2 is 8.

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The equation when Chris and Josh have saved the same amount is given as by substituting the value of y in equation 1 in equation 2 9x + 50 = 15x + 20.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the conventional form Ax + By = C.

Let us suppose the number of hours = x.

Let us suppose the total amount saved = y

Given that:

Chris makes $9 per hour at Chicken Express and already has $50 in his savings account. The equation for Chris is:

y = 9x + 50

Josh makes $15 per hour at amazon and already has $20 in his savings account. The equation for John is:

y = 15x + 20

The equation when Chris and Josh have saved the same amount is given as by substituting the value of y in equation 1 in equation 2.

9x + 50 = 15x + 20

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Answer:

3.75 cm²

Step-by-step explanation:

Area of a triangle = 1/2bh = 1/2(2.5)(3) = 3.75 cm²

The point on the graph is given by the coordinate Q ( 4 , 4 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be represented as P

The coordinates of point P = P ( 12 , 11 )

Now , the point P movers 8 units left

So , the new coordinates of the position is ( 12 - 8 , 11 )

The new coordinates is ( 4 , 11 )

And , the it moves 7 units down ,

So , the coordinates of the point Q be Q ( 4 , 11 - 7 )

On simplifying , we get

The coordinates of point Q = Q ( 4 , 4 )

Hence , the coordinate is Q ( 4 , 4 )

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The numerical expression which shows the diference between how many planes Fiona made and Gary mmade is (12 - 8) - (3 - 1).

The correct answer choice is option A

Morning Afternoon 12 3 8 1

Fiona. 12 3

Gary. 8 1

The diference between how many planes Fiona made and Gary made;

Morning = 12 - 8

Afternoon = 3 - 1

The difference between how many planes Fiona made and Gary made for both morning and afternoon = (12 - 8) - (3 - 1)

= 4 - 2

= 2

Therefore, the expression which represents the difference between how many planes Fiona made and Gary made is (12 - 8) - (3 - 1)

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The volume of this cone is equal to: A. 2,411.5 cm³.

Mathematically, the volume of a cone can be calculated by using this formula:

V = 1/3 × πr²√(l² - r²)

Radius = diameter/2 = 24/2 = 12 cm.

Substituting the given parameters into the volume of a cone formula, we have;

Volume of a cone, V = 1/3 × 3.142(12)²√(20² - 12²)

Volume of a cone, V = 1/3 × 3.142(144)×√(400 - 144)

Volume of a cone, V =  2,411.5 cubic cm.

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the bisectors of two supplementary angles are perpendicular to each other is proved along with the given diagram.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

Here, we have,

from the given diagram we get,

∠BOP=x  &   ∠AOP=180-x

and, ∠NOP=x/2   &   ∠MOP=(90-x/2)

Now,

∠MON=∠MOP+∠NOP

          =90-x/2 + x/2

          =90

Hence, it is proved that  the bisectors of two supplementary angles are perpendicular to each other.

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The greatest possible error of 4700 is equal to 2,350.

In Mathematics, precision can be defined as a quality which is independent of accuracy because it only describes how close together are numerical values that are obtained in a series of measurements.

In Mathematics, the greatest possible error (GPE) of a measurement can be defined as one-half of the value of a given smallest measuring unit, or one-half of a given precision.

This ultimately implies that, the greatest possible error (GPE) of a measurement can calculated by dividing the precision by two and this is represented by this mathematical expression;

Greatest possible error (GPE) = precision/2

Greatest possible error (GPE) = 4700/2

Greatest possible error (GPE) = 2,350.

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Answer:

2 3/4

Step-by-step explanation:

11-4=7-4=3 there is 4 twice and 3 remaining making 2 and 3/4

Answer: 2 3/4

Step-by-step explanation: To convert 11/4 in a mixed fraction, we will divide 11 by 4.

When 11 is divided by 4, the quotient is 2, the remainder is 3 and the divisor is 4.

After getting the new numerator, simplify and the fraction that will give us the final answer in the mixed number form.

Hence, 11/4 can be written as a mixed number, 2 3/4.

Answer:

Brand Z

Step-by-step explanation:

Set up all of them up as a fraction x/y where x is the fluid ounces and y is the cost.

Next, find the values of all the fractions and note them down.

Brand Z had the highest cost per fluid ounce of 2, and therefore is the correct answer.

Answer:

Brand w.

Step-by-step explanation:

First thing you want to do is divide your fluid ounces by your given cost. Which ever is greatest is your answer.

Brand w: 20/12.00 = 1.66

Brand x: 15/11.25 = 1.33

Brand y: 10/6.50 = 1.53

Brand z: 5/2.50 = 2.00

Brand w has the greastest price per fluid ounce compared to the rest of the brands.

The statement that is true about the ratios comparing the width and length of each painting is:

The paintings' width to length ratios are equal because the ratio 4 to 6 is equal to the ratio 2 to 3.

A ratio is a fraction which compares the values of two numbers. Such that they can be expressed as a ratio of one to the other. Example is the ratio of a to b which can be expressed as; a:b or a/ b.

From the first dimension of the canvas size, we have;

length = 6 feet

width = 4 feet

So that,

the ratio comparing the width and length = 4/ 6

                                                       = 0.6667

From the second dimensions of the canvas size, we have;

length = 3 feet

width = 2 feet

the ratio comparing the width and length = 2/ 3

                                                        = 0.6667

Therefore, the statement that is true about the ratios comparing the width and length of each panting is; The paintings' width to length ratios are equal because the ratio 4 to 6 is equal to the ratio 2 to 3.

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Answer:

I think the answer is 288.

Step-by-step explanation:

Answer:

add 500 and 50 together then multiple that number my 20 then do the same but multiple by 50

One solution of the following system is:

A. (–6, 0)

The above mathematical expression requires that we use the substitution formula to obtain the correct value.

2y - 2x = 12     ... 1

x² + y² = 36     ... 2

For equation 1

2y = 12 + 2x

          2

y = 6 + x           ... 3

Now we substitute equation 3 in equation 2

x² + (6 + x)² = 36

= x² + 36 + 12x + x² = 36

2x² + 12x = 36 -36

2x² + 12x = 0

2x (x + 6) = 0

x = 0, -6

When we substitute x for 0 in the third equation, we will have

y = 6 + 0 = 6

If we substitute x to be -6 in the third equation, we will arrive at

y = 0.

Therefore, the two solutions that can be obtained are (0,6) and (-6,0) as seen in the first option.

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Answer:

D) y = 5/3x - 7

A) 5/3

Step-by-step explanation:

5x - 3y = 21   Subtract 5x from both sides

5x - 5x - 3y = -5x + 21

-3y = -5x + 21  Divide all the way through by -3

[tex]\frac{-3y}{-3}[/tex] = [tex]\frac{-5}{-3}[/tex] x + [tex]\frac{21}{-3}[/tex]

y = [tex]\frac{5}{3}[/tex] x = 7

The slope is the number before the x 5/3

The next year population is 61500

step1

present population=60,000

increment per year=2.5%

next year population = 60000 + 2.5 % of 60,000

2.5% of 60000 =60000*2.5%

=60000*2.5/100

=1500*2.5

=3750

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Answer:

58500

Step-by-step explanation:

100

%

−

2.5

%

=

100%−2.5%=

97.5

%

97.5%

Whole population before decrease = 100%, then subtract decrease

97.5% of the current population means

97.5

100

of it.

97.5% of the current population means  

100

97.5

​

 of it.

"Percent" literally means "out of 100."

97.5

100

=

100

97.5

​

=

0.975

0.975

To find 97.5% of the current population, multiply by

0.975

:

To find 97.5% of the current population, multiply by 0.975:

60000

×

0.975

=

60000×0.975=

58500

58500

​

Method 2

Find the decrease, 2.5% of 60000:

Find the decrease, 2.5% of 60000:

2.5

100

=

100

2.5

​

=

0.025

0.025

60000

×

0.025

=

60000×0.025=

1500

1500

Subtract the decrease from the current pop:

Subtract the decrease from the current pop:

60000

−

1500

=

60000−1500=

58500

58500

​

population

percent

58500

97.5%

60000

100%

1500

current pop

current pop - decrease

2.5% decrease

Your Solution:

58500