Stephen's current average weekly net pay is $354.76. The van he wants to purchase has monthly payments of $325.00. Which inequality correctly shows the comparison between 15% of Stephen's average monthly net pay and the monthly van payment? (4 points)
$212.86 ≥ $325.00
$212.86 ≤ $325.00
$230.59 ≤ $325.00
$230.59 ≥ $325.00

The appropriate Taylor series for an infinite series with the first four nonzero terms equal to ln(5/3) is 0/1!, 0/2!, 0/3!, and 0/4! .......

An infinite sum of words that are expressed in terms of a function's derivatives at a single point is known as the Taylor series or Taylor expansion of a function in mathematics. Near this point, the function and the sum of its Taylor series are equivalent for the majority of common functions. The polynomial or function of an infinite sum of terms is the Taylor series. The exponent or degree of each succeeding term will be greater than the exponent or degree of the one before it.

The formula is:

∑​n=0​ to ∞(fⁿ(a)(x-a)ⁿ)/n!

Here,

∑​n=0​ to ∞(fⁿ(a)(x-a)ⁿ)/n!

at n=1,

=0/1!

at n=2,

=0/2!

at n=3,

=0/3!

at n=4,

=0/4!

Appropriate taylor series for first four nonzero terms of an infinite series that is equal to ln(5/3) is 0/1!, 0/2!, 0/3!, 0/4!.......

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If log₁₀2=0.3010, the value of  log₂10 will be 3.3×10⁻⁴.Logarithm identity is used to find the value of the log₂10.

It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

[tex]\rm a^b = c\\log_ac =b[/tex]

It is given that, log₁₀2=0.3010

We have to find the log₂10

The following logarithm identity is used as,

logₐn=logₙa

log₂10 =1/ log₁₀2

log₂10 =1/ 0.3010

log₂10 =3.3×10⁻⁴

Thus, if log₁₀2=0.3010, the value of  log₂10 will be 3.3×10⁻⁴. Logarithm identity is used to find the value of the log₂10.

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The inequality that the graph represent is y < -x + 1. The correct option is B. y < –x + 1

From the question, we are to determine the inequality that represents the given graph.

From the given information,

The line is passing through the coordinates (1, 0) and (-1, 2).

Using the formula for the equation of a line,

Using the formula,

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

Then,

(y - 0)/(x - 1) = (2 - 0)/(-1 - 1)

y/(x-1) = 2/-2

y/(x -1) = -1

y = -1(x -1)

y = -x + 1

Since the line is dotted and the shaded region is below the line, the inequality becomes

y < -x + 1

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Answer:

  a.  $3155.19

  b.  $1,135,868.40

  c.  $705,868.40

  d.  interest

Step-by-step explanation:

You want to find the monthly payment, total repaid, and finance charge on a 30-year mortgage for $430,000 at the rate of 8%.

You can use a spreadsheet, financial calculator, app, or the amortization formula to find the payment amount.

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

where P is the principal amount of the loan, r is the annual interest rate, and t is the number of years.

  A = 430,000(0.08/12)/(1 -(1 +0.08/12)^(-12·30)) ≈ 3155.19

The monthly payment is $3,155.19.

The total of the 12·30 = 360 payments is ...

  360 · $3155.19 = $1,135,868.40

It will take about $1,135,868.40 to pay off the loan.

The finance charge is the difference between the amount repaid and the original loan amount:

  $1135868.40 -430000 = $705,868.40

The finance charge is $705,868.40.

The finance charge at $706k is considerably greater than the original cost of the home, $430k.

The finance charge is greater.

Ty's visibility if out the upper window of a building with an altitude of 1,602 feet is 49.

What is altitude?

The height of an object in relation to a planet's or a natural satellite's surface, like sea level or land. the degree to which a celestial body is elevated above the horizon.

Here, we have

Given

The formula V = 1.225 √a is used to estimate how far a person can see on a clear day, where V is the visibility in miles and A is the altitude in feet.

We have to find Ty's visibility out the upper window of a building with an altitude of 1,602 feet.

We know that

V = 1.225 √a

a = 1,602 feet.

V = 1.225 √1602

V = 49

Hence, Ty's visibility out the upper window of a building with an altitude of 1,602 feet is 49.

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Answer:

x + y = 87

1.5x + 0.5y = 78.50

Step-by-step explanation:

Let x be the number of nachos sold and y be the number of sodas sold

x nachos will cost 1.50x dollars
y sodas will cost 0.50y dollars

So total sales = 1.5x + 0.5y and we know he made $78.50

so one equation is
1.5x + 0.5y = 78.50

Total sold = x + y and we know that this number is 87

So the second equation is

x + y = 87

B. There is no function rule

s = 1, x = 0, y = 3 and s = 1, x = 2, y = 0 produce an image congruent to its pre-image so option C and D are correct

What is dilation?

Dilation is the increase or decrease in the size of a figure by a scale factor. Rigid transformations preserve the shape of a figure. Examples of rigid transformation are reflection, rotation and translation.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation. The phrase "scale factor" describes this transition.

Dilation is said to be a rigid transformation if the scale factor is equal to one.

Therefore the dilation by a scale factor of one produce an image congruent to its pre-image.

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The vertex labels of Δ QRT are : ∠2 label is Q, ∠8 label is T and the remaining vertex label is R. The vertex labels for ΔSTR are: ∠5 label is S, ∠9 label is R and the remaining label is T.

The polygon having three sides and three vertices are known as triangle.

If we separate the two triangles as shown in the figure. We can find the vertex labels with the help of the angles marked in the figure.

For Δ QRT, the vertex labels are:

∠2 is Q, ∠1 is R and ∠8 is T

Similarly. for ΔSTR, the vertex labels are:

∠5 is S, ∠6 is T, and ∠9 is R

Hence,  For Δ QRT, we can label as ∠2 is Q, ∠1 is R and ∠8 is T and for ΔSTR we can label as  ∠5 is S, ∠6 is T, and ∠9 is R.

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Answer:

88.75% is the percentage Tami earned.

The revenue function of Patrice Bergeron earnings is R(x) = (50 + 5x)(20 -x)

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

Charges  = $50

Students = 20

Also, we have:

For every $5/hr he increases the price, he loses one student.

This means that

Charges  = 50 + 5x

Students = 20 - x

So, the revenue equation is

R(x) = Charges * Students

Substitute the known values in the above equation, so, we have the following representation

R(x) = (50 + 5x)(20 -x)

Hence, the function is R(x) = (50 + 5x)(20 -x)

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Complete question

Whenever he is injured and unable to play, Patrice Bergeron likes to earn a little extra cash by doing some tutoring. He currently charges $50/hr and has 20 students that he works with. He has discovered that for every $5/hr he increases the price, he loses one student.

What is the revenue function

The information that we need to come up with her demand curve for milk is D how much milk she buys at each price point

A demand curve is a graph that shows the relationship between a commodity's price and the amount that is desired at that price. Demand curves can be applied to the price-quantity relationship for either a specific consumer or for every consumer in a given market.

Individual demand curves and market demand curves are the two types of demand curves. It shows a graphic depiction of the demand schedule. It should be noted that based on the information, the quantity is needed. The correct option is D.

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In linear equation, 96 is the quotient.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                             Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

f(x) =  6x^3-+18x^2-18x+12

x - 2 = 0

x = 2

f( x) = 6 * 8 + 18 * 4 - 18 * 2 + 12

     =  48 + 72 - 36 + 12

      = 132 - 36

      = 96

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Answer:

Parabola

Step-by-step explanation:

A conic section is a curve obtained by the intersection of a plane with the surface of a (double-napped) cone, When the plane is parallel to the edge of one cone.

Thus, The intersection is a parabola.

Answer: degenerate hyperbola

Step-by-step explanation:

degenerate hyperbola because its the thickest of the plane so it can be formed.

Answer: A

Step-by-step explanation:

From the statement.

Times = Multiplication

The sum of a number and 18.3 = (r + 18.3)

Equals = 27.9

Therefore,

-6 x (r + 18.3) = 27.9

Bearing is a topic that deals with angles and distance. Thus, the required answers to the given question are:

i. Distance of 1034.2 miles

ii. Bearing of [tex]158^{o}[/tex]

The speed of an object is the rate of movement of the object with time.

speed = [tex]\frac{distance}{time}[/tex]

So that:

distance = speed x time

i. In the given question; let the initial distance covered be represented by d, so that:

d = 250 x 2

  = 500 miles

ii. Let the second distance covered by the pilot be represented by D, so that:

D = 300 x 2

   = 600 miles

iii. Thus let the distance to the starting point be represented by x. From Cosine rule, we have:

[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2abCos C

[tex]x^{2}[/tex] = [tex]500^{2}[/tex] + [tex]600^{2}[/tex] - 2(500 x 600)Cos [tex]140^{o}[/tex]

   = 250000 + 360000 - 600000(-0,7660)

   = 610000 + 459600

   = 1069600

x = [tex]\sqrt{1069600}[/tex]

  = 1034.22

x = 1034.2 miles

Using the Sine rule to determine the required internal angle, we have:

[tex]\frac{a}{Sin A}[/tex] = [tex]\frac{c}{Sin C}[/tex]

[tex]\frac{500}{Sin A}[/tex] = [tex]\frac{1034.22}{Sin 140}[/tex]

Sin A = [tex]\frac{500*0.6428}{1034.22}[/tex]

         = 0.3108

A = [tex]Sin^{-1}[/tex] 0.3108

   = 18.11

A = [tex]18^{o}[/tex]

To determine angle B, we have:

140 + 18 + B = 180 (sum of angles in a triangle)

158 + B = 180

B = 180 - 158

  = 22

B = [tex]22^{o}[/tex]

Thus, the required bearing is 180 - 22 = 158

Therefore the distance and bearing required to fly to starting point are 1034.2 miles and [tex]158^{o}[/tex] respectively.

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If a graph G has an Euler path, then it must include precisely two odd vertices. Or, to put it another way, G cannot have an Euler path if the number of odd vertices is less than 2.

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The line passes through Y=5. Correct option is A.

Two lines are perpendicular to each other if they are at right angle

to each other.

Given, line is perpendicular to Y-axis and passes through (-4,5).

Therefore, the given line is parallel to X-axis and passes Y-axis at y=5.

Hence, the given line passes through Y=5.

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For many of the rolls die, the long run relative frequency of a number less than 3 landing face up is 1/3.

What is relative frequency?

The proportion of outcomes where a specific event occurs to all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.

Given that, Only two integers (1 and 2) are smaller than 3, hence their relative frequency will be 2/6=1/3.

The best way to interpret the data is thus,

For many rolls of the die, the long- run relative frequency of a number less than three landing face up is1/3.

Hence option A is correct which is for many of the rolls die, the long run relative frequency of a number less than 3 landing face up is 1/3.

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Answer:

[tex]\huge{\boxed{\text{A) move the decimal point one place to the right}}}}[/tex]

Step-by-step explanation:

Think about the following scenarios

4.00 * 10

529.00 * 10

4 * 10 = 40 (4.00 * 10 =  40.0)

529 * 10 = 5290 (5290.00 * 10 =  5290.0)

As you can see, the decimal point is moving one space to the right when multiplying by ten.

In the decimal system, moving the decimal point one place to the right multiplies by ten, while moving the decimal point one place to the left multiplies by 1/10.

Hope it helps :) and let me know if you want me to elaborate.

Answer: x=3√14

Step-by-step explanation:

Answer: 9 because 45% of 20 is 9

Answer:

c or b

Step-by-step explanation:

Difference in interest paid = $82,740.52

Total interest paid for 25 year loan interest - Total interest paid for 20 year loan interest

According to the given information

A.

Monthly payment for 20 year mortgage [tex]& $=$ PMT $\left(6.5 \% / 12,20^* 12,-312500^* 0.8\right)$ & $=$ PMT $($ rate, nper, $-$ pv $)$ \[/tex]\

Monthly payment for 25 year mortgage [tex]& $=$ PMT $\left(7 \% / 12,25^* 12,-312500^* 0.8\right)$ & $=$ PMT(rate,nper,-pv) \\[/tex]

B

Total cost of interest for 20 year mortgage [tex]& $=(\mathrm{B} 2 * 20 * 12)-(312500 * 0.8)$ \\[/tex]

Total cost of interest for 25 year mortgage [tex]$=(\mathrm{B} 3 * 25 * 12)-(312500 * 0.8)$ &[/tex]

C.

Difference in interest paid [tex]& $=\mathrm{B} 7-\mathrm{B} 6$ &[/tex] = Total interest for 25 year loan-total interest for 20 years

A.

Monthly payment for 20 year mortgage [tex]& $\$ 1,863.93$ & $=$ PMT(rate,nper,-pv) \\[/tex]

Monthly payment for 25 year mortgage [tex]& $\$ 1,766.95$ & $=$ PMT(rate,nper,-pv) \\[/tex]

B.

Total cost of interest for 20 year mortgage = [tex]& $\$ 197,343.88$ & $=$[/tex]  total monthly payments-loan taken

Total cost of interest for 25 year mortgage = [tex]& $\$ 280,084.40$ & $[/tex] = total monthly payments-loan taken

C.

Difference in interest paid = $82,740.52

Total interest paid for 25 year loan interest - Total interest paid for 20 year loan interest

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Answer:

  $348.79

Step-by-step explanation:

You want to know Sandy Sellers' net weekly pay if she earns $15 per hour for 30 hours' work and has deductions of ...

Sellers' net pay will be her gross pay, less the taxes. Those taxes are all percentages of her gross pay.

  gross pay = (hourly rate) × (hours worked)

  gross pay = ($15.00/hour) × (30 hours) = $450

The deductions from her pay total ...

  12% +2.84% +6.2% +1.45% = 22.49% . . . . of her gross pay

The dollar amount of the deductions is ...

  0.2249 × $450 = $101.205 ≈ $101.21

Then Sellers' net pay is ...

  net = gross - deductions

  net = $450 -101.21 = $348.79

Sandy Sellers' take-home pay each week is $348.79.

If the midpoint of AB is at (0,4). and A = (3,0) then B is at point (-3, 8)

The formula to determine the center point of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.

The formula is of the form

X= (x₂ - x₁)/2

Y = (y₂ - y₁)/2

solving for B (x₂, y₂)

0 = (x₂ + 3)/2

0 = x₂ + 3

x₂ = -3

4 = (y₂ + 0)/2

8 = y₂ + 0

y₂ = 8

point B = (-3, 8)

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Answer:

Step-by-step explanation:

First find the hourly rate Carmen makes. You can find it by dividing the amount she made by the number of hours she worked

209 / 11 = 19

Now multiply that rate by the amount of hours you want to figure out.

19 * 8 = 152

Answer: $152

Step-by-step explanation:

Divide 209 by 11 to find how much money she gets for 1 hour of work ($19) then multiply that value by 8.

Answer:155m

Step-by-step explanation:GK is congruent to HI

The coordinates of the endpoints after the transformation is (c) (7, 3) and (1, 5)

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

Segment with endpoints at (1, 5) and (7, 3)

Also from the question, we have:

The points are reflected the segment about a vertical line through the segment’s own midpoint

When this is done, this means that the points would swap positions

So, we have the following representations

(1, 5) and (7, 3) ⇒ (7, 3) and (1, 5)

Hence, the coordinates of the endpoints is (c) (7, 3) and (1, 5)

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