Find the time required for an investment of 5000 dollars to grow to 6700 dollars at an interest rate of 7.5 percent per year, compounded quarterly.Your answer is t= how many years?

Therefore, according to the given information, The formulas to find the area of a circle are\(\pi r^2 and (d/2)^2\pi or r^2\pi\).

The area of a circle is given by the formula A = πr², where r is the radius of the circle.

The area of a circle can be found using either of the following formulas:

\(\pi r^2\), where π (pi) is a mathematical constant approximately equal to 3.14159 and r is the radius of the circle.

\(A = (d/2)^2π,\) where d is the diameter of the circle. This formula can also be written as \($A = r^2\pi$\), where r is the radius of the circle and A is the area.

Both formulas are equivalent and can be used interchangeably, depending on the given information about the circle.

Therefore, according to the given information, The formulas to find the area of a circle are\(\pi r^2 and (d/2)^2\pi or r^2\pi\).

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Answer:

35) 352.14

36) 329.8

37) 339.4

38) 319.4

Answer:

Step-by-step explanation:

29

Option(A) is the correct answer is A. 1,335 birds.

To calculate the number of birds that will be left after 20 years, we need to consider the annual decline rate of 2%.

We can use the formula for exponential decay:

N = N₀ * (1 - r/100)^t

Where:

N is the final number of birds after t years

N₀ is the initial number of birds (2,000 in this case)

r is the annual decline rate (2% or 0.02)

t is the number of years (20 in this case)

Plugging in the values, we get:

N = 2,000 * (1 - 0.02)^20

N = 2,000 * (0.98)^20

N ≈ 2,000 * 0.672749

N ≈ 1,345.498

Rounded to the nearest whole number, the number of birds that will be left after 20 years is 1,345.

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Answer:

The second one A = 1/2 bh

Step-by-step explanation:

Answer: x = -30

Step-by-step explanation:

y = -20 by using process of elimination substitute y as -20 in either of the equations you get -30 for x

The solution to the system of equations is x = 390 and y = 50. The value of x is equal to 390.

To find the value of x, solve the system of equations using the method of  substitution . Let's use the method of elimination:

Given equations:

x - 12y = -210                      (1)

x - 6y = 90                          (2)

To eliminate x, we can subtract equation 2 from equation 1:

(x - 12y) - (x - 6y) = (-210) - 90

Simplifying the equation:

x - 12y - x + 6y = -210 - 90

-6y = -300

Divide both sides of the equation by -6:

y = -300 / -6

y = 50

Now, substitute the value of y back into either equation:

x - 6(50) = 90

Simplify the equation:

x - 300 = 90

Add 300 to both sides of the equation:

x = 90 + 300

x = 390

Therefore, the solution to the system of equations is x = 390 and y = 50.

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Answer:

(Given m∠DCB = 105, m∠DAB = 75) m∠ADC=75, m∠AXY=105, m∠DYX=105, m∠BXY=75, m∠CYX=75, m∠ABC=105

Step-by-step explanation:

Definition of consecutive interior angles

Answer:

Step-by-step explanation:

The value of \(m\angle B=125^o-\sin^{-1}1.8441\).

In the given question,

\(m\angle A=55^o,AB=27,BC=12\).

We have to find the value of \(m\angle B\).

To find the value of \(m\angle B\) we used sine rule.

Sine Rule

The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal.

The ratio of the side length to the sine of the opposing angle is how the law of sines is typically defined. It is true for all three triangle sides, regardless of their sides and angles.

The formula for the Law of Sine Rule is

\(\frac{\sin A}{BC}=\frac{\sin B}{CA}=\frac{\sin C}{AB}\)

From the given question

\(\angle A=55^o\), \(AB=27\), \(BC=12\)

Now putting the value in the formula

\(\frac{\sin A}{BC}=\frac{\sin C}{AB}\)

\(\frac{\sin 55^o}{12}=\frac{\sin C}{27}\)

Multiply by \(27\) on both side

\(\frac{\sin 55^o}{12}\times27=\frac{\sin C}{27}\times27\)

\(\frac{\sin 55^o}{12}\times27=\sin C\)

\(\sin C=\frac{\sin 55^o}{12}\times27\)

From the calculator \(\sin55^o=0.8192\)

\(\sin C=\frac{0.8192}{12}\times27\)

\(\sin C=0.0683\times27\)

\(\sin C=1.8441\)

Now taking the inverse of sin to find the value of \(C\).

\(C=\sin^{-1}1.8441\)

Now finding the value of \(m\angle B\).

The sum of angle in triangle is \(180^o\).

So, \(\angle A+\angle B+\angle C=180^o\)

So \(\angle B=180^o-\angle A-\angle C\)

We know that \(\angle A=55^o\) and \(C=\sin^{-1}1.8441\)

Now putting the value

\(\angle B=180^o-55^o-\sin^{-1}1.8441\)

\(\angle B=125^o-\sin^{-1}1.8441\)

Hence, the value of \(m\angle B=125^o-\sin^{-1}1.8441\).

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Answer:

176.71 in square inches

Answer:

모 ⃢ ⃢ Heres The Link To The Answer: https://vm.answersheet.com/ZMeSy4nH1/

Step-by-step explanation:

Payback b*tch!!!

Answer:

D) 56

Step-by-step explanation:

\(\displaystyle \frac{8!}{(8-2)!}=\frac{8!}{6!}=\frac{8*7*6*5*4*3*2*1}{6*5*4*3*2*1}=8*7=56\)

Answer:

144 is the perimeter

Step-by-step explanation:

48 times 3= 144

The person is approximately 8.43 miles from home, and they need to walk in the direction of approximately 26.6 degrees east of north to head directly home.

To determine the distance from home, we can use the concept of vector addition. The person walks 4 miles west, which can be represented as a vector (-4, 0) in a coordinate plane. Then, they walk 5 miles southwest, which can be represented as a vector (-3.54, -3.54) since southwest is a combination of west and south. Adding these two vectors together gives us (-7.54, -3.54).

To find the magnitude or distance from home, we use the Pythagorean theorem. The distance is given by sqrt((-7.54)^2 + (-3.54)^2) = 8.43 miles (approximately).

To determine the direction to head directly home, we need to find the angle between the vector (-7.54, -3.54) and the positive x-axis. We can use trigonometry to find this angle. The tangent of the angle is given by the ratio of the y-coordinate to the x-coordinate, which is -3.54 / -7.54. Taking the inverse tangent of this value gives us approximately 26.6 degrees.

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Answer:

Step-by-step explanation:

12q + 3r = 15

-12q - 12r = -132

-9r = -117

r = 13

12q + 3(13) = 15

12q + 39 = 15

12q = -24

q = -2

(-2, 13)

b is the answer

Answer:

(-2,13)

Step-by-step explanation:

i took the test and can confirm its 100% on edge

Answer:

Sports is beneficial to physical health and well-being

as well as for growth and development, it decreases chances of contracting diseases and illnesses such as cardiovascular disease, lowers fat - intake as well as improves memory and relieves stress.

Answer:

5, 6

Step-by-step explanation:

Answer:

Los números son:

6 y 5

Step-by-step explanation:

Planteamiento:

a * b = 30

a + b = 11

Desarrollo:

De la segunda ecuación del planteamiento:

a = 11-b    

Sustituyendo esta última ecuación en la primer ecuación del planteamiento:

(11-b)*b = 30

11*b + b*-b = 30

11b - b² - 30 = 0

-b² + 11b - 30 = 0

b = {-11±√((11²)-(4*-1*-30))} / (2*-1)

b = {-11±√(121-120)} /-2

b = {-11±√1} / -2

b = {-11±1} / -2

b₁ = {-11-1} / -2 = -12/-2 = 6

b₂ = {-11+1} / -2 = -10/-2 = 5

Comprobación:

6*5 = 30

6+5 = 11

The expression in the options which is equivalent to the given expression is D. (22x + 48) / (x² - 36).

Given expression is,

[15 / (x - 6)] + [7 / (x + 6)]

Cross multiplying the two fractional expressions,

= [15 (x + 6) + 7 (x - 6)] / [(x - 6) (x + 6)]

= [15x + 90 + 7x - 42] / [x² - 6²]

= (22x + 48) / (x² - 36)

Hence the equivalent expression is D.

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Answer:

shifted left 7 & shifted down 3

Step-by-step explanation:

The payment made for apprentice plumbers is $36.

Given that,

Based on the above information, the calculation is as follows:

\(= 60\% \times \$60\)

= $36

Therefore we can conclude that the payment made for apprentice plumbers is $36.

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Answer: The equation of a line perpendicular to 2x + 2y = - 10 that passes through the point (6, 2) is y = x - 4

The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

Given that;

The sequence is,

11, 13, 15, 17, ....

Here, Common difference is,

13 - 11 = 2

15 - 13 = 2

Hence, Sequence is in Arithmetic sequence.

So, the nth term of 11,13,15,17 is,

⇒ T (n) = a + (n - 1)d

⇒ T (n) = 11 + (n - 1) 2

⇒ T (n) = 11 + 2n - 2

⇒ T (n) = 9 + 2n

Thus, The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

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Answer:

2sqr3, the first option

Step-by-step explanation:

Answer:

6 3/16 in²

Step-by-step explanation:

Area of rectangle = width x length

Given:

width = 2 3/4 in

length = 2 1/4 in

⇒ area = 2 3/4 × 2 1/4 = 11/4 × 9/4 = 99/16 = 6 3/16 in²

Answer:

\(x^{2} + 2x - 1\)

Step-by-step explanation:

We are solving for :

\(\frac{x^{3}+ 5x^{2} + 5x - 3 }{x + 3}\)

Factor \(x^{3} + 5x^{2} + 5x - 3 : (x + 3)(x^{2} + 2x - 1)\)

\(\frac{(x + 3)(x^{2} + 2x - 1)}{x + 3}\)

= \(x^{2} + 2x - 1\)

A local minimum or a local maximum are both examples of local extremums.

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Hello!

It's a division.

17  I  6

-12 I   2

  5

the dividende = 17

the divider = 6

the quotient = 2

the rest = 5

17 = 2 x 6 + 5

Answer:

The 95 % confidence interval of the mean of the time playing video games. is

        \(15.67< \mu <17.52\)

Step-by-step explanation:

From the question we are told that

      The sample size is \(n = 35\)

        The sample mean is \(\= x = 16.6\)

       The standard deviation is  \(\sigma = 2.8\)

The confidence level is  95%  hence the level of significance is mathematically represented as

     \(\alpha = 100 - 95\)

     \(\alpha = 5\)%

      \(\alpha = 0.05\)

Now the critical value of half of this level of significance obtained from the normal distribution table is  

       \(Z_{\frac{\alpha }{2} } = 1.96\)

The  reason for the half is that we are considering the two tails of the normal distribution curve which we use to obtain the interval

Now the standard error of the mean is mathematically evaluated as

       \(\sigma _{\= x} = \frac{\sigma }{\sqrt{n} }\)

substituting values  

     \(\sigma _{\= x} = \frac{2.8 }{\sqrt{35} }\)

      \(\sigma _{\= x} = 0.473\)

the 95 % confidence interval of the mean of the time playing video games.

is mathematically evaluated as

    \(\= x - (Z_{\frac{\alpha }{2} } * \sigma_{\= x }) < \mu < \= x - (Z_{\frac{\alpha }{2} } * \sigma_{\= x })\)

substituting values

    \(16.6 - (1.96 * 0.473) < \mu < 16.6 + (1.96 * 0.473)\)

     \(15.67< \mu <17.52\)

The image of the triangle ABC after the rotation of 90 degrees clockwise is located in the 4th quadrant.

Given that,

A triangle ABC in the XY coordinate plane.

It is rotated 90 degrees clockwise about the origin to form triangle A'B'C'.

Coordinates of ABC are,

A(2, 1), B(3, 3) and C(5, 2)

A point (x, y) after rotated 90 degrees clockwise changes to (y, -x).

Using this rule, coordinates of A'B'C' are,

A'(1, -2), B'(3, -3) and C'(2, -5)

A triangle with these coordinates having positive x value and negative y values is located in the fourth quadrant.

Hence the correct answer is 4.

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The x-intercepts are (4,0)(5,0) of the following graph.

In the context of a graph, an x-intercept is a point where a curve or line crosses the x-axis. It is the point at which the value of y is zero. In other words, the x-intercept is the value of x when the function or equation crosses the x-axis.

To find the x-intercepts of a function, you can set y equal to zero and solve for x. The resulting values of x will be the x-intercepts.

In the context of a graph, a y-intercept is a point where a curve or line crosses the y-axis. It is the point at which the value of x is zero. In other words, the y-intercept is the value of y when the function or equation crosses the y-axis.

To find the y-intercept of a function, you can set x equal to zero and solve for y. The resulting value of y will be the y-intercept.

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