The table shows the functions representing the height and base of a triangle for different values of x.
Height
Base
f(x)=x² + 3
g(x) = 2x
4
1
7
4
3
12
6
4
19
8
The area of the triangle when x = 2 is 14. Which equation can be used to represent the area of the triangle, A(x)?

The amplitude of a sine function is the absolute value of the coefficient multiplying the sin(x) term.

In this case, the coefficient is -2. Since the amplitude is always positive, we take the absolute value of -2, which gives us an amplitude of 2.

The period of a sine function is given by the formula 2π/b, where b is the coefficient multiplying the x variable. In our equation, the coefficient is 1 (since sin(x) has an implied coefficient of 1), so the period is 2π/1 = 2π.

The phase shift of a sine function is determined by the value inside the parentheses. In this case, there is no value inside the parentheses, so there is no phase shift. The function remains centered around the origin (x = 0).

The vertical shift of a function is the constant term added or subtracted from the trigonometric function. In this equation, the constant term is -3, which means the graph is shifted downward by 3 units.

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When a house is sold for $73,400.00 with a commission rate of 5 1/2 %, the agent's earnings would be $2,220.35.

To calculate the agent's earnings, we need to determine the total commission earned from the sale of the house and then calculate 55% of that amount.

First, we need to calculate the total commission earned from the sale of the house. The commission rate is given as 5 1/2 %, which can be written as a decimal as 0.055.

The total commission can be found by multiplying the sale price of the house ($73,400.00) by the commission rate (0.055):

Total Commission = $73,400.00 * 0.055

= $4,037.00

Now, we need to determine the agent's earnings, which is 55% of the total commission. We can calculate this by multiplying the total commission by 55% or 0.55:

Agent's Earnings = $4,037.00 * 0.55

= $2,220.35

Therefore, when a house is sold for $73,400.00 with a commission rate of 5 1/2 %, the agent's earnings would be $2,220.35.

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Answer:

37.7 feet

Step-by-step explanation:

The circumference of a circle can be calculated using the formula: Circumference = 2 * π * radius, where π (pi) is approximately 3.14159.

For example, if we have a circle with a radius of 3 feet, its circumference would be approximately 18.85 feet (rounded to five decimal places).

When we double the radius to 6 feet, the circumference also doubles. In this case, the circumference would be approximately 37.70 feet (rounded to five decimal places).

In summary, when the radius of a circle doubles, the circumference also doubles, maintaining a direct proportional relationship between the two measurements.

Answer:

Step-by-step explanation:

\[y={5x,x \n I\]

={...,-10,-5,0,5,10,...}

[tex]{\Large \begin{array}{llll} y=\{5x; ~~ x\in \mathbb{Z}\} \end{array}} \qquad \textit{integers multiples of 5}[/tex]

The angle 7 is the alternative interior angle to angle 2.

Given that,In the diagram a || bWe need to find the alternate interior angle to <2 .Alternate interior angles are the angles that are formed when a transversal crosses two parallel lines.

They are the angles that are on opposite sides of the transversal and inside the two parallel lines.

Thus, in the given diagram, the angle that is opposite to angle <2 and is inside the two parallel lines a and b is the alternate interior angle to angle <2.

We can see that the alternate interior angle to angle <2 is <7. Therefore, the alternate interior angle to angle <2 is <7.

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Liz table that shows her compounded interest should be completed the following way;

Original Principal                                                                               $2,000  

Interest for First Quarter        $2,000.00 x 8% ×1/4 =  $40  = + $  40            

Amount/End of First Quarter  $2,000.00+ $40.00 = $2040 = + $ 2040

Interest for Second Quarter  $ 2040 × 8% ×1/4 = $ 40.8  =  + $ $ 40.8

Amount/End of Second Quarter 2040  + 40.8 = $ 2080.8 = + $  2080.8

Interest for Third Quarter 2080.8  × 8% ×1/4 = $ 41.616 = + $ 41.616

Amount/End Third Quarter 2080.8+41.616 = $2122.416 = + $ 2122.416

Interest/Fourth Quarter 2122.416  × 8% ×1/4 = $ 42.4483 = + 42.4483

Amount/ End of Fourth Quarter $2122.416 + $42.4483 = 2164.8643

Quarterly compound interest is a type of interest that is calculated and paid out four times in a year. This means that the interest earned in one quarter is added to the principal amount, and then interest is calculated on the new, larger principal amount in the next quarter.

Quarterly compound interest is more profitable than annual compound interest in many cases, however, it depends on the percentage increase.

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The volume of blood that passes through the cross-section per unit time is approximately 0.1532 cm^3/s.

Poiseuille's Law describes the flow of fluid through a cylindrical tube. It can be used to calculate the volume of blood that passes through a cross-section per unit time. The formula for Poiseuille's Law is as follows:

Q = (π * ΔP * r^4) / (8 * η * L)

Where:

Q is the volume flow rate,

ΔP is the pressure difference across the tube,

r is the radius of the tube,

η is the viscosity of the fluid, and

L is the length of the tube.

Given information:

Viscosity (η) = 0.0010

Radius (r) = 0.030 cm

Length (L) = 3 cm

Pressure difference (ΔP) = 1000 dynes/square cm

First, we need to convert the radius and length to meters, as the SI unit system is typically used in scientific calculations:

Radius (r) = 0.030 cm = 0.030 * 0.01 m = 0.0003 m

Length (L) = 3 cm = 3 * 0.01 m = 0.03 m

Now, we can calculate the volume flow rate (Q) using Poiseuille's Law:

Q = (π * ΔP * r^4) / (8 * η * L)

= (π * 1000 * (0.0003)^4) / (8 * 0.0010 * 0.03)

= (3.1416 * 1000 * 0.000000000027) / (0.024)

= 0.0036756 / 0.024

≈ 0.1532 cm^3/s

Therefore, the volume of blood that passes through the cross-section per unit time is approximately 0.1532 cm^3/s.

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Answer:

[tex]9\frac{2}{3}[/tex]

Step-by-step explanation:

[tex]\displaystyle 1\frac{1}{4}+\biggr(3\frac{2}{3}+5\frac{3}{4}\biggr)\\\\1\frac{3}{12}+3\frac{8}{12}+5\frac{9}{12}\\\\(1+3+5)+\biggr(\frac{3}{12}+\frac{8}{12}+\frac{9}{12}\biggr)\\\\9+\frac{20}{12}\\\\9+1\frac{8}{12}\\\\9+\frac{2}{3}\\\\9\frac{2}{3}[/tex]

Again, least common denominator is 3*4=12

Step-by-step explanation:

1 1/4 + ( 3 2/3 + 5 3/4)

First change them from mixed fractions to normal fractions.

= 5/4 + ( 11/3 + 23/4)

Then Find the LCM(lowest common factor) of 4 and 3 which is 12 so we'll multiply both 4 and 3 to the number so the answer would be 12. and also if we multiply the denominator we do the same to the numerator.

= 5/4 + (44/12 + 69/12)

add them.

= 5/4 + (44 + 69/12)

now find their LCM and do the same to them since 4 is a factor of 12 we'll multiply it by 3 to get 12 as a denominator to add.

= 5/4 + 113/12

= 15/4 + 113/12

= 15 + 113/12

add them.

= 128/12

Divide both numerator and the denominator by the LCM.

= 64/6

= 32/3

Answer: 32/3 or in mixed fraction: 10 2/3

Answer:

No

Step-by-step explanation:

[tex]A=Pe^{rt}\\20000\stackrel{?}{\leq}15000e^{0.045(3)}\\20000\nleq17168.05[/tex]

Therefore, Oliver will not be able to pay for his son's college tuition of $20,000 after 3 years. He'll be short by about $3000.

The length of the curve described by the function x = (y - 5)² where 0 ≤ y ≤ 1, is approximately A. 7.982.

Substituting the values back into the arc length formula, we have:

L = ∫√(dx/dt)² + (dy/dt)² dt

L = ∫√(2(t - 5))² + 1² dt

L = ∫√(4(t - 5)² + 1) dt

Now, let's integrate this expression over the given range 0 ≤ y ≤ 1:

L = ∫[0,1]√(4(t - 5)² + 1) dt

Approximating the integral with the midpoint rule:

L ≈ ∑[i=0 to n-1] √(4(t_i+1 - 5)² + 1) Δt

Let's choose n = 1000 for a reasonably accurate result. Thus, Δt = (1 - 0) / 1000 = 0.001.

Calculating the sum:

L ≈ ∑[i=0 to 999] √(4(t_i+1 - 5)² + 1) * 0.001

Performing this calculation, we find that L ≈ 7.982.

Therefore, the length of the curve described by the function x = (y - 5)² where 0 ≤ y ≤ 1, is approximately 7.982.

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Answer:

To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:

8x = x + 9

Solving for x, we get:

x = 1.5

Therefore, AB = 8x = 8(1.5) = 12.

To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:

AB^2 + BD^2 = AD^2

Substituting the values, we get:

12^2 + BD^2 = (1.5 + 9)^2

Simplifying, we get:

BD^2 = 56.25

Taking the square root of both sides, we get:

BD = 7.5

Hence, the length of AB is 12 and the length of BD is 7.5.

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Answer:

(a) Decision rule: reject null hypothesis if [tex]t < -1.753[/tex] or [tex]t > 1.753[/tex], and fail to reject null hypothesis if [tex]-1.753\leq t\leq 1.753[/tex]

(b) [tex]s_{p}^{2}=18.214[/tex]

(c) [tex]t=-1.902[/tex]

(d) Reject [tex]H_{0}[/tex]

(e) The p-value is between 0.1 and 0.05

Step-by-step explanation:

The explanation is attached below.

Answer:

C) [tex]x^2+y^2=16[/tex]

Step-by-step explanation:

[tex](x-h)^2+(y-k)^2=r^2\\(x-0)^2+(y-0)^2=4^2\\x^2+y^2=16[/tex]

Therefore, C is correct

Answer:

option C:

x² + y² = 16

Step-by-step explanation:

general equation of a circle is,

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the center of the circle

           r is the radius of the circle

according to the question the circle is centered at the origin so h and k will be 0

and r = 4

by substituting the values in the equation,

(x - 0)² + (y - 0)² = 4²

x² + y² = 16

The probability that exactly seven claims will be filed during the next week is approximately 0.1038 or 10.38%.

To determine the probability of exactly seven claims being filed during the next week, we need to use the Poisson distribution. The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space when the events occur with a known average rate and independently of the time since the last event.

In this case, we are given that the average number of claims filed per week is seven. This average rate is also the parameter λ (lambda) of the Poisson distribution.

The probability mass function (PMF) of the Poisson distribution is given by:

P(X = k) = (e^(-λ) * λ^k) / k!

Where X is the random variable representing the number of claims filed, k is the specific number of claims we are interested in (in this case, k = 7), e is the base of the natural logarithm (approximately 2.71828), and k! represents the factorial of k.

Substituting the given average rate of seven claims per week into the equation, we have:

P(X = 7) = (e^(-7) * 7^7) / 7!

Calculating this expression will give us the probability of exactly seven claims being filed during the next week.

P(X = 7) ≈ 0.1038

Therefore, the probability that exactly seven claims will be filed during the next week is approximately 0.1038 or 10.38%.

This means that, on average, we can expect approximately 10.38% of weeks to have exactly seven claims filed based on the given average rate of seven claims per week.

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The cost of the car is $59,711.4.

Since,  A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100.

Given here:

Price of the car = $46,890.00,

percent down: 26%,

finance cost: $792.00 per month for 60 months

Thus Total cost= $46,890.00×0.26+60×792

                        = $12191.4 + $47520

                        = $59,711.4

Hence, The cost of the car is $59,711.4

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Step-by-step explanation:

for the first one the sales on table is going downn while the days are increasing

for the second one the arrow going up signifies that the sales are going up according to days

Your lab regularly runs tests on mice, resulting in several bags of leftover mouse food sitting in your storage closet, the lab will need more food around day 116 of the year.

To determine if the lab's reserve of mouse meals will hold up for the entirety of subsequent year, we need to research the fee at which the food reserves are reducing.

Let's calculate the common day by day decrease in meals reserves:

Average daily decrease = (Initial food reserves - Final food reserves) / (Number of days)

Initial food reserves = 112.6 kg

Final food reserves = 109.1 kg

Number of days = 8 (from December 13 to December 21)

Average daily decrease = (112.6 kg - 109.1 kg) / 8 ≈ 0.4375 kg/day

Number of days until food reserves reach zero = Final food reserves / Average daily decrease

Number of days until food reserves reach zero = 109.1 kg / 0.4375 kg/day ≈ 249.14 days

Thus, the lab will need more food approximately 365 - 249.14 = 115.86 days into the year. Round it up to the nearest whole number, and the lab will need more food around day 116 of the year.

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The amount to be remitted when paying the invoices together on December 8 is $2,477.19.

To calculate the amount that must be remitted when paying the invoices together on December 8, we need to consider the available discount periods and the due date.

Let's break down the information provided:

Invoice No. 312 dated November 2 for $923.00

Invoice No. 429 dated November 14 for $784.00

Invoice No. 563 dated November 30 for $873.00

Given the terms 5/10, 2/30, n/60, this means that a 5% discount is offered if payment is made within 10 days, a 2% discount is offered if payment is made within 30 days, and the net amount is due within 60 days.

To calculate the amount to be remitted, we need to consider the applicable discount periods. For payments made on or before December 8, the following discounts apply:

Invoice No. 312: 5% discount if paid within 10 days

Invoice No. 429: 5% discount if paid within 10 days

Invoice No. 563: 2% discount if paid within 30 days

To calculate the remitted amount, we subtract the applicable discount from each invoice amount and sum them up:

Invoice No. 312: $923.00 - (5% of $923.00) = $923.00 - ($46.15) = $876.85

Invoice No. 429: $784.00 - (5% of $784.00) = $784.00 - ($39.20) = $744.80

Invoice No. 563: $873.00 - (2% of $873.00) = $873.00 - ($17.46) = $855.54

Total amount to be remitted = $876.85 + $744.80 + $855.54 = $2,477.19

Therefore, the amount to be remitted when paying the invoices together on December 8 is $2,477.19.

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The producer surplus is approximately $663.772.

To find the producer surplus, we need to calculate the area between the supply curve and the selling price line.

The supply curve is given by the equation:

[tex]s(x) = 180 + 0.3x^{(3/2)[/tex]

where x is the product quantity.

Let's set the selling price to $250.

We want to find the quantity (x) at which the selling price intersects the supply curve. So, we can set:

[tex]250 = 180 + 0.3x^{(3/2)[/tex]

Now, let's solve this equation to find the value of x:

[tex]250 - 180 = 0.3x^{(3/2)[/tex]

[tex]70 = 0.3x^{(3/2)[/tex]

Divide both sides by 0.3:

[tex]x^{(3/2)} = 70 / 0.3[/tex]

[tex]x^{(3/2)} = 233.33[/tex]

Now, we can solve for x by raising both sides to the power of 2/3:

[tex]x = (233.33)^{(2/3)[/tex]

x ≈ 24.88

So, the quantity (x) at which the selling price intersects the supply curve is approximately 24.88.

To calculate the producer surplus, we need to find the area between the supply curve and the selling price line from 0 to x.

The formula for the producer surplus is:

Producer Surplus = ∫[0 to x] (s(x) - Selling Price) dx

Using the given supply curve [tex]s(x) = 180 + 0.3x^{(3/2)[/tex] and the selling price of $250, we can evaluate the integral:

Producer Surplus = ∫[0 to 24.88] ([tex]180 + 0.3x^{(3/2)[/tex]) dx

Calculating the integral we get,

= 663.772

Therefore, the producer surplus is approximately $663.772.

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The scale factor that was used to create triangle D' include the following: C. Scale factor of 1/2

We have,

In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Compare the corresponding sides of triangle D and triangle D':

Side DE in triangle D corresponds to side D'E in triangle D'.

Side EF in triangle D corresponds to side E'F in triangle D'.

Side FD in triangle D corresponds to side F'D in triangle D'.

Determine the ratios of the corresponding sides:

The ratio of side D'E to DE is 2:1.

The ratio of side E'F to EF is 2:1.

The ratio of side F'D to FD is 2:1.

Scale factor = Dimension of image (new figure)/Dimension of pre-image (original figure)

By substituting the given dimensions into the formula for scale factor, we have the following;

Scale factor = Dimension of image/Dimension of pre-image

Scale factor = 8/16 = 6/12 = 10/20

Scale factor = 1/2.

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Answer:

Amanda has 8 cousins

Step-by-step explanation:

Let C be the number of cousins Caleb has, A be the number of cousins Amanda has, and R be the number of cousins Ruby has:

[tex]C=2A\\R=5\\R=C-11\\\\R=C-11\\5=C-11\\16=C\\\\C=2A\\16=2A\\8=A[/tex]

Therefore, Amanda has 8 cousins.

Answer:

Amanda has 8 cousins.

Step-by-step explanation:

Let's use algebraic variables to solve the problem.

Let's assume the number of cousins Amanda has is represented by 'A'.

Since Caleb has twice as many cousins as Amanda, the number of cousins Caleb has is '2A'.

And Ruby has 5 cousins, which is 11 less than what Caleb has, so the number of cousins Caleb has is '5 + 11 = 16'.

Equating the two expressions for the number of cousins Caleb has:

2A = 16

Now we can solve for 'A', the number of cousins Amanda has:

Divide both sides of the equation by 2:

A = 16 / 2

A = 8

Therefore, Amanda has 8 cousins.

The multiplicative rate of change of the function is,

⇒ 0.5

We have to given that,

The curve through the ordered pairs (0, 10), (1, 5), and (2, 2.5) can be represented by the function,

⇒ f(x) = 10(0.5)ˣ

Now, For the multiplicative rate of change of the function,

Let two values, of points are x = 1 and x = 0

Put x = 1 in function,

⇒ f(1) = 10(0.5)¹

⇒ f(1) = 10(0.5)

⇒ f(1) = 5

Put x = 0;

⇒ f(0) = 10(0.5)⁰

⇒ f(0) = 10

Hence, The ratio is,

⇒ f (1)) / f (0)

⇒ 5 / 10

⇒ 0.5

Thus, the multiplicative rate of change of the function is,

⇒ 0.5

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Answer:

∡C=53°

∡F=102°

AB=11

DF=27

Step-by-step explanation:

Similar triangles have the same shape but not necessarily the same size. If two triangles are similar, their corresponding angles are equal and their corresponding sides are proportional.

Some of the properties of similar triangles:

For the question:

In ΔABC and ΔEFD

Since the respective corresponding angles are equal.

so,

∡A=∡E=25°

∡B=∡F=102°

∡C=∡D=53°

so, ΔABC  [tex]\sim[/tex]  ΔEFD

Again

Since their corresponding sides are proportional.

First, we need to find the ratio of their respective side:

DE: CA=63:14=9:2 when compared to big triangle to small triangle.

CA: DE=14:63=2:9 when compared to big triangle to small triangle.

AB=2/9*EF=2/9*49.5=11

DF=9/2*CB=9/2*6=27

Answer:

Step-by-step explanation:

[tex]P(blue)=\frac{3}{10} \\[/tex]

For sample of 500 jellybeans:

   [tex]E(blue)=\frac{3}{10}\times500=150[/tex]

Solution: 150 blue jellybeans.

Answer:

60 in.²

Step-by-step explanation:

A = (B + b)h/2

A = (14 in. + 6 in.)(6 in.)(1/2)

A = 60 in.²

Answer:

60 in^2

Step-by-step explanation:

solution Given:

Area of the shaded region or trapezoid = Area of Rectangle ABCD - Area of triangle CDE

we have

Area of Rectangle ABCD= length* breadth =BC*AB=14*6=84 in^2

Area of Triangle CDE= 1/2* base*height=1/2*DE*CD=1/2*8*6=24 in ^2

Now

Area of the shaded region or trapezoid = Area of Rectangle ABCD - Area of triangle CDE

=84 in^2-24in^2

=60 in^2

Similarly, we have another way to calculate the area of the trapezoid;

Area = 1/2*h*(side1*side2)

=1/2*AB*(AE+BC)

=1/2*6*(6+14)

=60 in^2

Answer:

x = 12.85714286 (as a decimal)

x = [tex]\frac{90}{7}[/tex] (as a fraction)

Step-by-step explanation:

These 2 triangles are similar.

[tex]\frac{20}{x} = \frac{20 + 8}{x + 18}[/tex]

20(x + 18) = x(20 + 8)

20x + 360 = 20x + 8x

20x + 360 = 28x

360 = 28x

x = 12.85714286 or x = [tex]\frac{90}{7}[/tex]

I believe the correct anwser is 45

Answer:

a is -13

b is 31

c is 24

Step-by-step explanation:

To maximize profit, the factory should manufacture 8 bicycles and 12 motorcycles.

Let us assume the number of bicycles as 'x'

Let us assume the number of motorcycles as 'y'.

The time constraint on machine A can be expressed as: 5x + 4y ≤ 120

The time constraint on machine B can be expressed as: 4x + 8y ≤ 144

To maximize profit, we need to maximize the objective function:

P = 40x + 50y

By graphing the constraints and finding the feasible region, we can determine the optimal solution.

Graphing the constraints:

For 5x + 4y ≤ 120:

Let's solve for y in terms of x: y ≤ (120 - 5x) / 4

For 4x + 8y ≤ 144:

Let's solve for y in terms of x: y ≤ (144 - 4x) / 8

The feasible region will be the intersection of the shaded regions:

y ≤ (120 - 5x) / 4

y ≤ (144 - 4x) / 8

Now, we will find the corner points of the feasible region:

When x = 0, y = 0

When x = 24, y = 0

When x = 8, y = 12

Substituting values into objective function P = 40x + 50y:

When x = 0, y = 0:

P = 40(0) + 50(0)

P = 0

When x = 24, y = 0:

P = 40(24) + 50(0)

P= 960

When x = 8, y = 12:

P = 40(8) + 50(12)

P = 1360.

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