Find the future value (FV) of the annuity due. (Round your answer to the nearest cent.) $180 monthly payment, 6.25% interest, 11 years

[tex]32500[/tex]

[tex]0.00604[/tex]

[tex]2.4 \times 10^6[/tex]

[tex]1.47 \times 10^{-3}[/tex]

Answer:

A) 32500

B) 0.00604

C) [tex]2.4 * 10^6[/tex]

D) [tex]1.47 * 10^{-3}[/tex]

Answer:

[tex] P(0.55 <X<1.1)= F(1.1) -F(0.55) [/tex]

And replacing we got:

[tex] P(0.55 <X<1.1)= (1-e^{-\frac{1}{0.66} *1.1}) -(1-e^{-\frac{1}{0.66} *0.55})[/tex]

[tex] P(0.55 <X<1.1)=e^{-\frac{1}{0.66} *0.55}- e^{-\frac{1}{0.66} *1.1}=0.2457[/tex]

And rounded the answer would be 0.246

Step-by-step explanation:

For this case we can define the random variable X as "The commute time for people in a city" and for this case the distribution of X is given by:

[tex] X \sim exp (\lambda = \frac{1}{0.66}= 1.515)[/tex]

And for this case we want to find the following probability:

[tex] P(0.55 <X<1.1)[/tex]

And we can use the cumulative distribution function given by:

[tex] F(x) =1- e^{-\lambda x}[/tex]

And using this formula we got:

[tex] P(0.55 <X<1.1)= F(1.1) -F(0.55) [/tex]

And replacing we got:

[tex] P(0.55 <X<1.1)= (1-e^{-\frac{1}{0.66} *1.1}) -(1-e^{-\frac{1}{0.66} *0.55})[/tex]

[tex] P(0.55 <X<1.1)=e^{-\frac{1}{0.66} *0.55}- e^{-\frac{1}{0.66} *1.1}=0.2457[/tex]

And rounded the answer would be 0.246

Answer:

Area of the given figure is 51.5 square units.

Step-by-step explanation:

Area of rectangle OCBH = Length × width

                                         = 11 × 8

                                         = 88 square units

Area of trapezoid OGEF = [tex]\frac{1}{2}(b_1+b_2)\times h[/tex]

                                         = [tex]\frac{1}{2}(\text{GE+OF)}\times (\text{OG})[/tex]

                                         = [tex]\frac{1}{2}(3+6)\times 4[/tex]

                                         = 18 units²

Area of trapezoid GCDE = [tex]\frac{1}{2}(\text{GC+DE)}\times (\text{GE})[/tex]

                                         = [tex]\frac{1}{2}(7+2)\times 3[/tex]

                                         = 13.5 units²

Area of triangle AFH = [tex]\frac{1}{2}(\text{Base})\times (\text{Height})[/tex]

                                  = [tex]\frac{1}{2}(5)(2)[/tex]

                                  = 5 units²

Area of polygon ABCDEF = Area of rectangle CBHO - (Area of trapezoid OGEF + Area of trapezoid GCDE + Area of triangle AFH)

                                           = 88 - (18 + 13.5 + 5)

                                           = 88 - 36.5

                                           = 51.5 units²

Therefore, area of the given polygon is 51.5 units²

The correct answer is A

Explanation:

An orthographic drawing shows a three-dimensional figure from different perspectives or sides. Indeed, the orthographic drawing in the question shows how the object looks if you see this the front, side, and top of this. This implies the foundation drawing needs to match the figures of the orthographic drawing.

According to this, the correct figure is A because this is the only one that has a rectangle shape, and due to this, if you look at this from any different sides you will always see a rectangle. For example, the top view shows a rectangle of approximately 2x3 squares, and this view only fits with option A because B and C are not complete rectangles and therefore their top view is not a rectangle.

Answer:

7/54

Step-by-step explanation:

let thenumber be x

then 22/7 /x = -11/27  

= 22x/7 = -11/27

= x = -11*7/27*22 = 7/54

Hope it helps!!

Answer: lower bound, x = 110.5°

              upper bound, x = 113.5°

Step-by-step explanation:

There is no diagram but I am going to assume it is a quadrilateral since it has 4 angles. The sum of the angles of a quadrilateral is 360°.

           Upper       Lower

59°       58.5° ≤ a < 59.5

108°    107.5° ≤ b < 108.5°

81°       80.5° ≤ c < 81.5°  

Total:  246.6° ≤ x < 249.5°

Subtract the lower and upper bound totals from 360° :

                  360.0           360.0          

              -  246.5       - 249.5

x =              1 1 3.5           1 1 0.5

                      ↓                  ↓

                  upper            lower

                 bound            bound

Answer:

(0,7)

Step-by-step explanation:

28

Step-by-step explanation:

Answer:

3/4 or 0.75

Step-by-step explanation:

You have four options available

Lets say P(A) is pick a rocket

P(A) = 2/4 because there are two rockets in the four choices

simplify it to 1/2

P(B) pick a big = 2/4 because there are two bigs and two smalls.

simplify it to 1/2

P(A ∩ B) = Pick a big rocket = 1/4

P(AUB) = P(A)+P(B)- P(A ∩ B)

P(AUB) = 1/2+1/2- 1/4 = 3/4 or 0.75

Answer:

B. AC = 2AB

hope it helps!

Step-by-step explanation:

AC is half of AB

so if the statement says AC is 2AB it suggests that AC is greater than AB

this is definitely false..

Answer:

sin x = 0.998

cosx = 0.046

Step-by-step explanation:

Given that:

tan x = 21

where interval of x is [tex][0,\dfrac{\pi}{2}][/tex].

We know that the trigonometric identity for tan x is:

[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]

Comparing with:

[tex]tan x = \dfrac{21}{1}[/tex]

Perpendicular = 21 units

Base = 1 unit

As per pythagorean theorem:

[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\[/tex]

[tex]\Rightarrow \text{Hypotenuse}^2 = 21^2 +1^2\\\Rightarrow \text{Hypotenuse} = \sqrt{442} = 21.023\ units[/tex]

interval of x is [tex][0,\dfrac{\pi}{2}][/tex] so values of sinx and cosx will be positive because it is first quadrant where values of sine and cosine are positive.

We know that

[tex]sin\theta = \dfrac{Perpendicular}{Hypotenuse}\\cos\theta = \dfrac{Base}{Hypotenuse}[/tex]

So, sine x :

[tex]\Rightarrow sinx =\dfrac{21}{21.023}\\\Rightarrow sinx = 0.998[/tex]

Similarly, value of cos x :

[tex]\Rightarrow cosx =\dfrac{1}{21.023}\\\Rightarrow cosx = 0.046[/tex]

Answer:

369

Step-by-step explanation:

One nickel = 0.05

0.05x=18.45

x=369

Answer:

The volume of all 9 spheres is 301.6 [tex]in^3[/tex]

Step-by-step explanation:

Notice that three of the identical spheres fit perfectly along the 12 in side box, therefore we know that the diameter of each is 12 in/3 = 4 in.

Then the radius of each sphere must be 2 inches (half of the diameter). Now that we know the radius of each sphere, we use the formula for the volume of a sphere to find it:

[tex]V=\frac{4}{3} \pi R^3\\V=\frac{4}{3} \pi (2\,in)^3\\V=\frac{4}{3} \pi\, 8\,\,in^3\\V=\frac{32}{3} \pi\,\,in^3[/tex]

Now, the total volume of all nine spheres is the product of 9 times the volume we just found:

[tex]V_{all \,9}=9\,*\frac{32}{3} \pi\,\,in^3\\V_{all \,9}=96 \pi\,\,in^3\\V_{all \,9}\approx \,301.6\,\,in^3[/tex]

Answer:

Here is an exampls

Step-by-step explanation:

Answer:

Step-by-step explanation:

The claim here is that the brand name aspirin is more consistent in the amount of active ingredient used than the generic aspirin.

This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean amount of active ingredients in brand name aspirin and μ2 be the mean amount of active ingredients in generic name aspirin

The random variable is μ1 - μ2 = difference in the mean amount of active ingredients between the brand name and generic aspirin

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 ≥ μ2 H0 : μ1 - μ2 ≥ 0

The alternative hypothesis is

H1 : μ1 < μ2 H1 : μ1 - μ2 < 0

This is a left tailed test

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

From the information given,

x1 = 325.01

x2 = 323.47

s1 = 10.12

s2 = 11.43

n1 = 200

n2 = 180

t = (325.01 - 323.47)/√(10.12²/200 + 11.43²/180)

t = 1.24

1.237877

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [10.12²/200 + 11.43²/180]²/[(1/200 - 1)(10.12²/200)² + (1/180 - 1)(11.43²/180)²] = 1.53233946713/0.00537245359

df = 285

We would determine the probability value from the t test calculator. It becomes

p value = 0.108

Since alpha, 0.025 < than the p value, 0.108, then we would fail to reject the null hypothesis. Therefore, at 2.5% level of significance, these data support the brand name producers claim

Answer:  b) reflexive property

Step-by-step explanation:

When you are stating that a line is congruent to itself, you are using the Reflexive Property.

a) Associative Property: a + (b + c) = (a + b) + c

b) Reflexive Property: AB = AB

c) Substation Property: not a real property - does not exist

d) Transitive Property: If a = b and b = c, then a = c

Answer:

19272 feet

Step-by-step explanation:

We are given that the distance between the person and peak is 5 miles.

and angle is [tex]47^\circ[/tex] when we look up at the mountain peak.

The given situation is best represented as a right angled triangle as shown in the attached figure.

[tex]\triangle[/tex]IKJ where [tex]\angle K = 90^\circ[/tex]

IK is the mountain.

J is the point where we are standing.

Distance JI = 5 miles

[tex]\angle J = 47^\circ[/tex]

To find: Distance IK = ?

We can use trigonometric identities to find IK.

[tex]sin\theta = \dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]sinJ = \dfrac{IK}{JI}\\\Rightarrow sin47 = \dfrac{IK}{5}\\\Rightarrow IK = sin47^\circ \times 5\\\Rightarrow IK = 0.73 \times 5\\\Rightarrow IK = 3.65\ miles \\\Rightarrow IK = 3.65 \times 5280\ ft\\\Rightarrow IK = 19272\ ft[/tex]

Hence, height of mountain = 19272 ft

Answer:

a.x=39.2

b.Use whole  wire as a circle

Step-by-step explanation:

We are given that

Length of piece of wire=70  units

Let length of wire used to make a square =x units

Length of wire used in circle=70- x

Side of square=[tex]\frac{perimeter\;of\;square}{4}=\frac{x}{4}[/tex]

Circumference of circle=[tex]2\pi r[/tex]

[tex]70-x=2\pi r[/tex]

[tex]r=\frac{70-x}{2\pi}[/tex]

Combined area of circle and square,A=[tex](\frac{x}{4})^2+\pi(\frac{70-x}{2\pi})^2[/tex]

Using the formula

Area of circle=[tex]\pi r^2[/tex]

Area of square=[tex](side)^2[/tex]

a.[tex]A=\frac{x^2}{16}+\frac{4900+x^2-140x}{4\pi}[/tex]

Differentiate w.r.t x

[tex]\frac{dA}{dx}=\frac{x}{8}+\frac{2x-140}{4\pi}[/tex]

[tex]\frac{dA}{dx}=0[/tex]

[tex]\frac{x}{8}+\frac{2x-140}{4\pi}=0[/tex]

[tex]\frac{\pi x+4x-280}{4\pi}=0[/tex]

[tex]\pi x+4x-280=0[/tex]

[tex]x(\pi+4)=280[/tex]

[tex]x=\frac{280}{\pi+4}[/tex]

x=39.2

Again differentiate w.r.t x

[tex]\frac{d^2A}{dx^2}=\frac{1}{8}+\frac{1}{2\pi}[/tex]>0

Hence, the combined area of circle and the square is minimum at x=39.2

b.When the wire is not cut and whole wire used  as a circle . Then, combined area is maximum.

Answer:

  see below

Step-by-step explanation:

We presume you want to simplify ...

  [tex]\dfrac{x^2-9}{x+3}=\dfrac{(x-3)(x+3)}{x+3}=\boxed{x-3}[/tex]

__

The numerator is the difference of squares, so is factored accordingly. One of those factors cancels the denominator.

Answer:

V = 137.2

Step-by-step explanation:

We are given the volume equation. Simply plug in your r into the equation and calculate and you should get 137.189 as your answer.

Answer:

There is enough evidence at the α-: 0.05 level of significance to support the claim that the true population mean market value of houses in the neighborhood where Rebecca works is greater than $250,000.

Step-by-step explanation:

We are given that Rebecca randomly selects 35 houses in the neighborhood and finds that the sample mean market value is $259,860 with a sample standard deviation of $24.922.

Let [tex]\mu[/tex] = population mean market value of houses in the neighborhood.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = $250,000      {means that the population mean market value of houses in the neighborhood where she works is equal to $250,000}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $250,000      {means that the population mean market value of houses in the neighborhood where she works is greater than $250,000}

The test statistics that would be used here One-sample t-test statistics because we don't know about population standard deviation;

                              T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean market value = $259,860

            s = sample standard deviation = $24,922

            n = sample of houses = 35

So, the test statistics  =  [tex]\frac{259,860-250,000}{\frac{24,922}{\sqrt{35} } }[/tex]  ~ [tex]t_3_4[/tex]

                                     =  2.34

The value of t-test statistic is 2.34.

Also, P-value of the test statistics is given by;

            P-value = P([tex]t_3_4[/tex] > 2.34) = 0.0137

Since our P-value is less than the level of significance as 0.0137 < 0.05, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the population mean market value of houses in the neighborhood where she works is greater than $250,000.

Answer:

0.5 gallon

Step-by-step explanation:

let x refer to students

5 = 8x + 1

8x = 4

x= 0.5 gallon

Answer:

Step-by-step explanation:

write down the expression:

x*z-y

lets plug in the variables to evaluate the expression:

8*4.6-(-0.1)

36.8+0.1

36.9

Answer:

Given,

X=8

y=-0.1

z=4.6

Now,

[tex]xz - y \\ = 8 \times 4.6 - ( - 0.1) \\ = 36.8 - ( - 0.1) \\ = 36.8 + 0.1 \\ = 36.9[/tex]

hope this helps..

Good luck on your assignment..

Answer:

23.6

Step-by-step explanation:

Finding AC:

Cos 61 = [tex]\frac{adjacent}{hypotenuse}[/tex]

0.48 × 10 = Adjacent

AC = 4.8

Now, CB:

Cos 29 = [tex]\frac{adjacent}{hypotenuse}[/tex]

0.87 × 10 = CB

CB = 8.8

The perimeter:

=> 10+4.8+8.8

=> 23.6

Answer:

23.6

Step-by-step explanation:

Answer:31

Step-by-step explanation: Since you are trying to find a percentage of a number all you have to do is multiply 242 by 12.9% and because you have to round to the nearest tenth it will be 31

Answer:

The rearranged steps is as follows:

d. procedure last smallest(a1,a2,...,an: integers)

b. min ≔a1 and location ≔1

e. If min >= ai then

c. min ≔ai and location≔i

a. return location

Step-by-step explanation:

The proper steps to perform the task in the question above is dbeca

Here, the procedure (or function) was defined along with necessary parameters

d. procedure last smallest(a1,a2,...,an: integers)

The smallest number is initialized to the first number on the list and its location is initialized to 1

b. min ≔a1 and location ≔1

The next line is an if conditional statement that checks if the current smallest number is greater than a particular number

e. If min >= ai then

If the above condition is true, the smallest value is assigned to variable min; it's location is also assigned to variable location

c. min ≔ai and location≔i

The last step returns the location of the smallest number

a. return location

Answer:

Step-by-step explanation:

12x - y = -4  ----------------------(I)

4x - 3y = -6  ---------------------(II)

Multiply equation (I) by (-3)

(I)*(-3)                -36x + 3y = 12

(II)                       4x    - 3y = - 6  {Add and y will be eliminated}

                           - 32x     = 6

x = 6/-32

x = -3/16

Plugin the value of x in equation (I)

[tex]12*\frac{-3}{16} -y=-4\\\\3*\frac{-3}{4}-y=-4\\\\\frac{-9}{4}-y = -4\\\\-y=-4+\frac{9}{4}\\\\-y=\frac{-4*4}{1*4}+\frac{9}{4}\\\\-y=\frac{-16}{4}+\frac{9}{4}\\\\-y=\frac{-7}{4}\\\\y=\frac{7}{4}\\\\y=1\frac{3}{4}[/tex]

Answer:

The correct answer would be option 4

12x+20

 5y3

Hope that helps.Thank you!!!