If a trader Gaines 15% interest by selling an article for 1560.00 what is the cost price for the article

The answer would be C - "Cheetah B has a higher ratio of miles per minute than Cheetah A because 17 over 8 is less than 56 over 20."

also "get it right please" ?! how rude

Answer:

Hope this helps ^^

Step-by-step explanation:

Part A: To determine the values where the pogo stick's spring will be equal to its non-compressed length, we set the function equal to zero:

f(θ) = 2cos(θ) + √3

To find the values of θ that satisfy this equation, we solve:

2cos(θ) + √3 = 0

Subtracting √3 from both sides:

2cos(θ) = -√3

Dividing by 2:

cos(θ) = -√3/2

Using the unit circle, we can find the angles where cosine is equal to -√3/2. These angles are π/6 and 11π/6.

Therefore, the values where the pogo stick's spring will be equal to its non-compressed length are θ = π/6 and 11π/6.

Part B: If the angle θ is doubled, that is, θ becomes 2θ, we substitute 2θ into the original function:

f(2θ) = 2cos(2θ) + √3

Using the double angle formula for cosine:

f(2θ) = 2(2cos²(θ) - 1) + √3

Expanding and simplifying:

f(2θ) = 4cos²(θ) - 2 + √3

Comparing this to the original function f(θ), we see that the new function has the same form but with different coefficients. The solutions for f(2θ) in the interval [0, 2π) will be the same as the solutions for f(θ), but they will occur at double the angles. In other words, if θ is a solution for f(θ), then 2θ will be a solution for f(2θ).

Part C: To find the times when the lengths of the springs from the original pogo stick and the toddler's pogo stick are equal, we set the two functions equal to each other:

f(θ) = g(θ)

2cos(θ) + √3 = 1 - sin²(θ) + √3

Rearranging the equation:

sin²(θ) + 2cos(θ) = 0

Using the Pythagorean identity sin²(θ) = 1 - cos²(θ), we substitute:

1 - cos²(θ) + 2cos(θ) = 0

Rearranging and simplifying:

cos²(θ) - 2cos(θ) + 1 = 0

Factoring:

(cos(θ) - 1)² = 0

Taking the square root:

cos(θ) - 1 = 0

cos(θ) = 1

This occurs when θ is a multiple of 2π.

Therefore, the lengths of the springs from the original pogo stick and the toddler's pogo stick are equal at θ = 2πn, where n is an integer.

1. Statement 1 is false because the + sign in logarithm laws stands for multiplication

2. The value of x is not a solution

3. In logarithmic form we can write; log10 0.0001 = -4

A set of guidelines called the laws of logarithms governs how to work with and simplify logarithmic expressions. These principles are useful for performing numerous mathematical operations involving logarithms as well as for solving logarithmic equations and simplifying complex logarithmic statements.

1. log3(a + b) ought to be the same as log3(a * b)

2. We have that;

[tex]3^{2x - 5} = 27[/tex]

Writing in the same base;

[tex]3^{2x - 5 } = 3^3[/tex]

2x - 5 = 3

2x = 3 + 5

2x = 8

x = 4

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Answer:

the length of C is 6, the length of D is 9,

Step-by-step explanation:

The expected value for this game, when you pay $1 to play, is -$4.00. This means that, on average, you can expect to lose $4.00 per game in the long run.

To calculate the expected value for the game, we need to multiply each outcome by its respective probability and then sum them up.

Let's calculate the expected value for each outcome:

Outcome 1: Roll a 1 and receive $55.

The probability of rolling a 1 on a fair die is 1/6.

Expected value = (1/6) × $55 = $9.17

Outcome 2: Roll a 2 and receive $10.

The probability of rolling a 2 on a fair die is 1/6.

Expected value = (1/6) × $10 = $1.67

Outcome 3: Roll a 3 and win nothing.

The probability of rolling a 3 on a fair die is 1/6.

Expected value = (1/6) × $0 = $0

Outcome 4: Roll a 4 or 5 and pay Señor Rick $35.

The probability of rolling a 4 or 5 on a fair die is 2/6 or 1/3.

Expected value = (1/3) × (-$35) = -$11.67 (negative because you have to pay)

Outcome 5: Roll a 6 and pay Señor Rick $25.

The probability of rolling a 6 on a fair die is 1/6.

Expected value = (1/6) × (-$25) = -$4.17 (negative because you have to pay)

Now, let's sum up the expected values:

Expected value = $9.17 + $1.67 + $0 - $11.67 - $4.17

= -$4.00

The expected value for this game, when you pay $1 to play, is -$4.00. This means that, on average, you can expect to lose $4.00 per game in the long run.

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From the vertices provided, the area of the parallelogram is 42cm².

The area of a parallelogram remain

Area = base×height

we need to start by creating two vectors using the given vertices. We can use LM and LN.

Vector LM = M - L = (-12, -2, -4) - (-5, -2, -4) = (-7, 0, 0)

Vector LN = N - L = (-12, -8, -10) - (-5, -2, -4) = (-7, -6, -6)

LM x LN = (0×(-6) - 0×(-6), 0×(-7) - (-7)×0, -7×(-6) - 0×0)

= (0, 0, 42)

Area = ||LM x LN|| =√(0² + 0² + 42²) = √(0 + 0 + 1764)

= √(1764) = 42 cm²

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a. The rate of change of the relation is 2.

b. The value of n is 14.5.

In Mathematics and Geometry, the rate of change (slope) of any straight line can be determined by using this mathematical equation;

Rate of change (slope) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change (slope) = rise/run

Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the rate of change (slope) of a line, we have the following;

Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)

Rate of change (slope) = (10 + 1)/(3.5 + 2)

Rate of change (slope) = 11/5.5

Rate of change (slope) = 2

Part b.

Next, we would determine the value of n as follows;

2 = (43 - 32)/(20 - n)

2(20 - n) = 11

40 - 2n = 11

2n = 29

n = 14.5

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Answer:2.381 cm.

Step-by-step explanation:

The volume of the gold bar can be calculated using the formula for the volume of a rectangular prism:

Volume = Length x Width x Height

We know the length and width of the bar, so we can substitute those values:

Volume = 23.5 cm x 28 cm x Height

We can then solve for the height by rearranging the equation:

Height = Volume / (Length x Width)

To find the volume, we can use the density of gold and the mass of the bar:

Density = Mass / Volume

Volume = Mass / Density

Substituting the values we have:

Volume = 43,892.5 g / 27.2 g/cm³

Volume = 1610.049 cm³

Now we can substitute the volume into the equation we derived earlier to solve for the height:

Height = 1610.049 cm³ / (23.5 cm x 28 cm)

Height = 2.381 cm

Therefore, the height of the gold bar is approximately 2.381 cm.

Answer:

Step-by-step explanation:

let m = mean

s= standard deviation

to find zscore = (value-m)/s

1.)

((m-1.5s)-m)/s = -1.5

in fact, if it's n standard deviations ABOVE the mean, your zscore is n

if it's n standard deviations BELOW the mean, your zscore is -n

2.)

((m+1.7s)-m)/s= 1.7

3.)

(m-m)/s= 0

Answer:

Step-by-step explanation:

Set h=0 for ground height, then solve for t

-16t^2 -20t +240 = 0

divide by -4

4t^2 +5t - 60 = 0

use the quadratic formula

t= -5/8 + or - (1/8)square root of (25 +4(4)(60)).  Ignore the negative square root

 =-5/8 + (1/8)sqr(960+25)

= -5/8 + (1/8)sqr(985)

 =-5/8 + (1/8)sqr(5(197))= slightly less than -5/8 +(10/8)(sqr10) = about -5/8 +32/8 = 27/8 = 3.3 seconds

the ball's initial velocity is negative, meaning the ball was thrown downward. Then add the effect of gravity, and it should hit the ground in a short time, even when thrown from an initial height of 240 feet.

plug t=2 into the original equation for height.  You should get slightly above ground, near zero

-16(2)^2 -20(2) +240 = -64 -40+240 = 136

try t=3

-16(9) -20(3) +240 = -144 -60 +240 = 36

try t=4

-16(16) -20(4) +240 =-256 -80 +240 =-96

the time to hit ground should be between t=3 and 4, but closer to t=3, maybe about 3 1/3 seconds

By using the given graph of the function​ f, the key features include the following:

​(a) the​ y-intercept is (0, 10).

​(b) its domain is [-∞, ∞] and the range is [0, ∞].

​(c) it is​ increasing over the interval [-∞, ∞].

​(d) The function is​ even.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

Based on the graph, we would calculate the value of a and b as follows;

f(x) = a(b)^x

10 = a(b)⁰

a = 10

Next, we would determine value of b as follows;

12 = 10(b)¹

12 = 10b

b = 12/10

b = 1.2

Therefore, the required exponential function is given by;

[tex]y = 10(1.2)^x[/tex]

Part a.

When x = 0, the y-intercept can be determined as follows;

[tex]y = 10(1.2)^0[/tex]

y = 10(1)

y = 10.

Part b.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-∞, ∞].

Range = [0, ∞] or {y | y ≥ 0}

Part c.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce that the exponential function is always increasing over the interval [-∞, ∞].

Part d.

In conclusion, this exponential function is an even function because it is symmetric with respect to the y-coordinate (y-axis).

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The height of cuboid is 5.412 unit.

TSA of cuboid is 96 unit².

Volume of Cuboid is 61.704 unit³

We have,

LSA of cuboid = 72 square unit

width = 3

length = 4

So, LSA of cuboid = 72 square unit

2h(l+b) = 72

2h(4+3) = 72

14h = 72

h = 72/14

h= 5.142

Now, TSA of cuboid

= 2(lw + wh + lh)

= 2 (12 + 20.568 + 15.426)

= 95.988

= 96 unit²

Now, Volume of Cuboid

= l w h

= 4 x 3 x 5.142

= 61.704 unit³

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The area of the region that lies inside both curves is 11π/3 - 9√3/2 square units.

The area of the region that lies inside both curves first need to find the points of intersection.

The two equations equal to each other and solve for θ:

6sin(2θ) = 6sin(θ)

Dividing both sides by 6 get:

sin(2θ) = sin(θ)

The identity sin(2θ) = 2sin(θ)cos(θ) can rewrite this as:

2sin(θ)cos(θ) = sin(θ)

Dividing both sides by sin(θ) we get:

2cos(θ) = 1

Solving for θ we get:

θ = π/3, 5π/3

The area of the region by integrating the function r with respect to θ from θ = π/3 to θ = 5π/3:

A = ∫[π/3, 5π/3] 1/2 r² dθ

r = 6sin(2θ) when 0 ≤ θ ≤ π and r = 6sin(θ) when π ≤ θ ≤ 2π.

Substituting the appropriate values of r and integrating, we get:

A = ∫[π/3, π] 1/2 (6sin(2θ))² dθ + ∫[π, 5π/3] 1/2 (6sin(θ))² dθ

= ∫[π/3, π] 27sin²(2θ) dθ + ∫[π, 5π/3] 18sin²(θ) dθ

= [9θ - 3/4 sin(4θ)]π/3π + [6θ - 9/2 cos(2θ)]π/5π

= (π/3)[9π/2 - 3√3] + (2π/3)[5 - 9√3/2]

= 11π/3 - 9√3/2

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The calculated number of miles run is 24 miles

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

The graph (see attachment)

The graph is a proportional graph with the points

(x, y) = (10, 1)

So, the equation of the graph is

y = x/10

At 4 hours, the value of x is

x = 4 * 60

So, we have

y = 4 * 60/10

Evaluate

y = 24

Hence, the number of miles run is 24 miles

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We can see that (a^2+b^2)(x+y) - (a^2y+b^2x) simplifies to zero, which means the expression is true. Therefore, the polynomial identity (a^2+b^2)(x+y) - (a^2y+b^2x) holds.

To verify the polynomial identity (a^2+b^2)(x+y) - (a^2y+b^2x), we need to simplify the expression on both sides and show that they are equal.

Expanding (a^2+b^2)(x+y) using the distributive property, we get:

(a^2+b^2)(x+y) = a^2x + a^2y + b^2x + b^2y

Expanding (a^2y+b^2x), we have:

(a^2y+b^2x)

Now, let's subtract (a^2y+b^2x) from (a^2x + a^2y + b^2x + b^2y):

(a^2x + a^2y + b^2x + b^2y) - (a^2y+b^2x)

We can observe that the terms involving 'x' and 'y' cancel each other out:

(a^2x - b^2x) + (a^2y - a^2y) + (b^2y - b^2y)

= 0 + 0 + 0

= 0

We can see that (a^2+b^2)(x+y) - (a^2y+b^2x) is being simplified to zero, which means that the expression is true. Therefore, the polynomial identity (a^2+b^2)(x+y) - (a^2y+b^2x) holds.

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Answer:

third option represents a function.

Step-by-step explanation:

for the ordered pairs to represent a function.

each value of x must only map to one unique value of y

in the first option

(- 2, 0 ) and (- 2, 2 )

the same x- coordinate maps to 2 different values of y

thus not a function.

in the second option

every value of x = - 5 maps to 5 different values of y

thus not a function.

in the third option

each value of x maps to a unique value of y.

thus a function.

in the fourth option

(- 6, - 3 ) and (- 6, - 2 )

the same x value maps to 2 different values of y

thus not a function.

Answer:

1.57ft

Step-by-step explanation:

The circumference is twice the radius times pi.

C=2πr

C=2·π·5

C=10π

C=31.4159265359

We know that KL is 18° of that (180-162).

So we get the formula

31.4159265359÷360x18=1.57

The simplified expression is [tex]-2x^2 - 2x - 5.[/tex]

To simplify the expression, combine like terms:

[tex]3x^2 + 5x - 7x - 3 - 5x^2 - 2[/tex]

Combine the [tex]x^2[/tex] terms:

[tex](3x^2 - 5x^2) + 5x - 7x - 3 - 2[/tex]

Simplify the [tex]x^2[/tex] terms:

[tex]-2x^2 + 5x - 7x - 3 - 2[/tex]

Combine the x terms:

[tex]-2x^2 - 2x - 3[/tex]

This is the simplified form of the expression.

Therefore, the simplified expression is [tex]-2x^2 - 2x - 5.[/tex]

We have grouped the terms with similar variables together and performed the necessary arithmetic operations to obtain the simplified form.

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24-gon is the regular polygons has a perimeter that would be closest to circumference of a circle with the same radius

The closer a regular polygon's range of facets is to infinity, the closer its perimeter will be to the circumference of a circle with the identical radius.

Therefore, the answer is the 24-gon, which has greater facets than the octagon and the dodecagon but fewer facets than the 15-gon.

This makes the 24 - gon the most appropriate answer isnce it has more faces

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The regular polygons which has a perimeter that would be closest to the circumference of a circle with same radius is a; 24-gon.

It follows from the task content that the regular polygon which would have a perimeter closest to circumference of a circle with the same radius is to be determined.

By observation, the greater the number of sides of a regular polygon, the greater is its perimeter and the closer is its perimeter to the circumference of a circle with same radius.

Therefore, the answer choice which is correct is; 24-gon.

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The length of the other diagonal of the kite is: 50 cm

We want to find the area of the given kite but It should be noted that:

The hypotenuse is usually the slanted line part in a triangle.

Area of a kite = pq/2

where:

p and q are diagonals

We are given:

Area of Kite = 180 cm²

Length of diagonal = 16 cm

Thus:

16q = 180

q = 180/16

q = 50 cm

This gives us the length of the other diagonal of the kite

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Answer:

A = (1/2)Pa = Pa/2 You can multiply both sides by 2 to eliminate the fraction on the right side: 2A = 2 (Pa/ 2) = Pa Then divide both sides by a (or multiply both sides by 1/a) to leave P alone on the right side: (2A) (1/a) = 2A/a = (P a) (1/ a) = P

Step-by-step explanation:

have a nice day.

Answer:

if you make 413 dollars a second, in 30 minutes you would make 743,400 dollars.

Step-by-step explanation:

If you make 413 dollars a second, in 30 minutes you would make:

30 minutes = 30 x 60 = 1800 seconds

So, the amount of money you would make in 30 minutes can be calculated as follows:

1800 seconds x 413 dollars/second = 743,400 dollars

Answer:

Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Which of these could be a step to prove that BC2 = AB2 + AC2?

Step-by-step explanation:

Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Which of these could be a step to prove that BC2 = AB2 + AC2?

Answer:

Step-by-step explanation:

here is the solution of your problem i hope u enjoy

The values of x for the lengths of the similar shapes are: (3). x = 10, (4). x = 6, (6). x = 35, and (7). x = 60

Similar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other.

(3). PN/PR = PM/PQ

(x + 8)/(3x - 9) = 24/28

28(x + 8) = 24(3x - 9) {cross multiplication}

72x - 28x = 224 + 216 {open brackets and collect like terms}

44x = 440

x = 440/44

x = 10

(4). FE/BD = FG/BC

(5x - 2)/42 = (4x + 2)/39

39(5x - 2) = 42(4x + 2) {cross multiplication}

195x - 168x = 84 + 78 open brackets and collect like terms}

27x = 162

x = 162/27

x = 6

(6). DE/AB = EF/BC

25/x = 20/28

x = (25 × 28)/20 {cross multiplication}

x = 35

(7). YZ/RS = ZW/SP

32/x = 40/75

x = (32 × 75)/40 {cross multiplication}

x = 69

Therefore, the values of x for the lengths of the similar shapes are: (3). x = 10, (4). x = 6, (6). x = 35, and (7). x = 60

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In a right angled triangle, the base is 17 and the angle between base and hypotenuse is 29°, then the hypotenuse x is equal to 19.4 after rounding off to the nearest tenth.

From the given figure, we have to find the missing length x

In the figure we can see that,

For the angle, θ = 29°

Base = 17

and, hypotenuse = x

We know that by the cosine of the angle in the given triangle can be written as,

cos θ = [tex]\frac{base}{hypotenuse}[/tex]

⇒ cos 29° = [tex]\frac{17}{x}[/tex]

⇒ x = [tex]\frac{17}{cos \ 29\textdegree}[/tex]

⇒ x = 19.437

Rounding to the nearest tenth, x = 19.4

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The city's popuation grew by approximately 2.56% from 2010 to 2020

Considering the percentage in bits

From 2010 to 2015

Population growth = 7.4% of 175 000 = 0.074 * 175,000 = 12,950

New population in 2015 = 175 000 + 12,950 = 187,950

From 2015 to 2020

population decrease = 4.5% of 187 950 = 0.045 * 187,950 = 8,462.75

new population in 2020 = 187 950 - 8,463 = 179,487

overall percent change in the population

Percent change = (New population - Initial population) / Initial population * 100

Percent change = (179,487 - 175,000) / 175,000 * 100

Percent change = 4,487 / 175,000 * 100

Percent change ≈ 2.56

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The probability that exactly three of their seven children will have the given trait is 0.073.

To solve this problem, we can use the binomial probability formula. The probability of exactly k successes in n trials, where the probability of success is p, is given by:

P(X = k) = C(n, k) . [tex]p^k[/tex] . (1 - [tex]p)^(n - k)[/tex]

In this case, the probability of a child having the trait is p = 3/4, and we want to find the probability of exactly 3 children having the trait out of 7 children, so k = 3 and n = 7.

Using the formula:

P(3) = 7! / 4! 3! x (3/4)³ x (1-3/4)⁴

P(3) = 35 x 27/64 x 1/256

P(3) ≈ 0.073

Therefore, the probability that exactly three of their seven children will have the given trait is 0.073.

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The location of L″ is (-5, 0).

To find the location of L″, we first need to apply the first translation rule to the coordinates of trapezoid JKLM:

J': (x, y) → (x + 3, y - 3) => J'(-2+3, 1-3) = J(1, -2)

K': (x, y) → (x + 3, y - 3) => K'(1+3, 1-3) = K(4, -2)

L': (x, y) → (x + 3, y - 3) => L'(3+3, -2-3) = L(6, -5)

M': (x, y) → (x + 3, y - 3) => M'(-4+3, 2-3) = M(-1, -1)

Now, we need to apply the second translation rule to the coordinates of J', K', L', and M':

J'': (x, y) → (x - 1, y + 1) => J''(1-1, -2+1) = J''(0, -1)

K'': (x, y) → (x - 1, y + 1) => K''(4-1, -2+1) = K''(3, -1)

L'': (x, y) → (x - 1, y + 1) => L''(6-1, -5+1) = L''(5, -4)

M'': (x, y) → (x - 1, y + 1) => M''(-1-1, -1+1) = M''(-2, 0)

Therefore, the location of L″ is (-5, 0).

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Answer:

(5,-4)

Step-by-step explanation: