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Question 29
Juan invests $5,000 at 11% simple interest for 1 year. How much is in the account at the end of the 1 yea
period?
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Answer:

The possible arrangement= 18 ways

Step-by-step explanation:

Six identical coin are tossed.

Coin has only a tail and a head.

In how many possible ways can the arrangement be 3 head and 3 tail.

The possible arrangement= (3! * 3!)/2

The reason for dividing by two because coin has two face.

The possible arrangement= (3! * 3!)/2

The possible arrangement=( 6*6)/2

The possible arrangement= 36/2

The possible arrangement= 18 ways

Answer:

A. Perimeter of segment = 49 in.

B. Area of segment = 52 in².

Step-by-step explanation:

Data obtained from the question include:

Radius (r) = 24 in.

Angle at the centre (θ) = 60°

Perimeter of segment =.?

Area of segment =.?

A. Determination of the perimeter of the segment.

Perimeter of segment = length of arc + length of chord

Length of arc = θ/360 x 2πr

Length of chord = 2r x sine (θ/2)

Pi (π) = 3.14

Length of arc = θ/360 x 2πr

Length of arc = 60/360 x 2 x 3.14 x 24

Lenght of arc = 25.12 in

Length of chord = 2r x sine (θ/2)

Length of chord = 2 x 24 x sine (60/2)

Length of chord = 24 in

Perimeter of segment = length of arc + length of chord

Perimeter of segment = 25.12 + 24

Perimeter of segment = 49.12 ≈ 49 in.

B. Determination of the area of the segment.

Area of segment = Area of sector – Area of triangle.

Area of sector = θ/360 x πr²

Area of triangle = r²/2 sine θ

Area of sector = θ/360 x πr²

Area of sector = 60/360 x 3.14 x 24²

Area of sector = 301.44 in²

Area of triangle = r²/2 sine θ

Area of triangle = 24²/2 x sine 60

Area of triangle = 249.42 in².

Area of segment = Area of sector – Area of triangle.

Area of segment = 301.44 – 249.42

Area of segment = 52.02 ≈ 52 in²

​

Answer:

adult=18$ and children=13$

Step-by-step explanation:

a= adult. and. c= children

first change the statement into linear equation

3a+4c=106

2a+3c=75

then it just solving for a and y

3a+4c=106. a= 75-3c.

2

3(75-3c)+ 4c=106. solve for c

2

c=13

then find c by substituting the value you got into a . you can you either 3a+4c=106

or 2a+3c=75 to find the answer but the value of a is the same.

2a+3c=75. c=13

2a+3(13)=75

2a=75 -39

2a= 36

a=18

Answer:

Adults Ticket = $18

Child's Ticket = $13

Step-by-step explanation:

Let A denote the price of an adult's ticket

Let C denote the price of a child's ticket

It is given that the three adults and four children must pay $106.

Mathematically,

[tex]3A + 4C = 106 \:\:\:\:\:\:\:\:\:\:\: eq. 1[/tex]

It is also given that the two adults and three children must pay $75.

Mathematically,

[tex]2A + 3C = 75 \\\\2A = 75 - 3C[/tex]

[tex]$ A = \frac{(75 - 3C)}{2} \:\:\:\:\:\:\: eq\:. 2 $[/tex]

Substitute eq. 2 into eq. 1

[tex]3A + 4C = 106[/tex]

[tex]$ \frac{3(75 - 3C)}{2} + 4C = 106 $[/tex]

Simplify,

[tex]$ \frac{3(75 - 3C)}{2} + 4C = 106 $[/tex]

[tex]$ \frac{225 - 9C}{2} + 4C = 106 $[/tex]

[tex]$ \frac{225 - 9C + 2(4C)}{2} = 106 $[/tex]

[tex]$ \frac{225 - 9C + 8C}{2} = 106 $[/tex]

[tex]$ 225 - 9C + 8C = 2(106) $[/tex]

[tex]$ 225 - C = 212 $[/tex]

[tex]C = 225 - 212[/tex]

[tex]C = \$13[/tex]

Substitute the value of C into eq. 2

[tex]$ A = \frac{75 - 3(13)}{2} $[/tex]

[tex]$ A = \frac{75 - 39}{2} $[/tex]

[tex]A = \$18[/tex]

Therefore, the price of the​ adult's ticket is $18 and the price of a​ child's ticket is $13

Answer:

[tex]\large \boxed{\sf \ \ x=0, \ \ y=-5 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

We have two equations:

(1) -2x - 4y = 20

(2) -3x + 5y = -25

5*(1)+4*(2) gives

   -10x - 20y -12x + 20y = 100 - 100 = 0

   -22x = 0

   x = 0

I replace in (1)

   -4y = 20

   y = -20/4 = -5

There is one solution x = 0, y = -5

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

The two equations are

-2x-4y=20

-3x+5y=-25

multiply equation 1 by 5 and equation 2 by 4

-10x-20y=100

-12x+20y=-100

-22x=0

x=0

Substitute value in either equation

y=-5

So,option 1 is correct only one solution

Answer:  B) 10 three-point questions and 14 five-point questions

Step-by-step explanation:

x represents three-point questions

y represents five-point questions

3x + 5y = 100  →  1(3x + 5y = 100)  =  3x + 5y = 100

 x  +  y  = 24   → -3(x  +  y  = 24)   = -3x  -3y  = -72

                                                                  2y = 28

                                                                    y = 14  (five-point questions)

x +  y = 24

x + 14 = 24

     x = 10  (three-point questions)

Answer:

1

Step-by-step explanation:

=> [tex]\sqrt[3]{3375} - \sqrt[4]{38416}[/tex]

Factorizing 3375 gives 15 * 15 * 15 which equals 15^3 and factorizing 38416 gives 14 * 14 * 14 * 14 which equals 14^4

=> [tex]\sqrt[3]{15^3} - \sqrt[4]{14^4}[/tex]

=> 15 - 14

=> 1

Answer:

Step-by-step explanation:

[tex] \sqrt[3]{3375} - \sqrt[4]{38416} [/tex]

Calculate the cube root

[tex] \sqrt[3]{ {15}^{3} } - \sqrt[4]{38416} [/tex]

Calculate the root

[tex] \sqrt[3]{ {15}^{3} } - \sqrt[4]{ {14}^{4} } [/tex]

[tex] {15}^{ \frac{3}{3} } - {14}^{ \frac{4}{4} } [/tex]

[tex]15 - 14[/tex]

Subtract the numbers

[tex]1[/tex]

Hope this helps...

Answer:

x = -1.964636

Step-by-step explanation:

Given equation;

eˣ = 4 - x²

This can be re-written as;

eˣ - 4 + x² = 0

Let

f(x) = eˣ - 4 + x²    -----------(i)

To use Newton's method, we need to get the first derivative of the above equation as follows;

f¹(x) = eˣ - 0 + 2x

f¹(x) = eˣ + 2x         -----------(ii)

The graph of f(x) has been attached to this response.

As shown in the graph, the curve intersects the x-axis twice - around x = -2 and x = 1. These are the approximate roots of the equation.

Since the question requires that we use the negative root, then we start using the Newton's law with a guess of x₀ = -2 at n=0

From Newton's method,

[tex]x_{n+1} = x_n + \frac{f(x_{n})}{f^1(x_{n})}[/tex]

=> When n=0, the equation becomes;

[tex]x_{1} = x_0 - \frac{f(x_{0})}{f^1(x_{0})}[/tex]

[tex]x_{1} = -2 - \frac{f(-2)}{f^1(-2)}[/tex]

Where f(-2) and f¹(-2) are found by plugging x = -2 into equations (i) and (ii) as follows;

f(-2) = e⁻² - 4 + (-2)²

f(-2) = e⁻² = 0.13533528323

And;

f¹(2) = e⁻² + 2(-2)

f¹(2) = e⁻² - 4 = -3.8646647167

Therefore

[tex]x_{1} = -2 - \frac{0.13533528323}{-3.8646647167}[/tex]

[tex]x_{1} = -2 - \frac{0.13533528323}{-3.8646647167}[/tex]

[tex]x_{1} = -2 - -0.03501863503[/tex]

[tex]x_{1} = -2 + 0.03501863503[/tex]

[tex]x_{1} = -1.9649813649[/tex]

[tex]x_{1} = -1.96498136[/tex]         [to 8 decimal places]

=> When n=1, the equation becomes;

[tex]x_{2} = x_1 - \frac{f(x_{1})}{f^1(x_{1})}[/tex]

[tex]x_{2} = -1.96498136 - \frac{f(-1.9649813)}{f^1(-1.9649813)}[/tex]

Following the same procedure as above we have

[tex]x_{2} = -1.96463563[/tex]

=> When n=2, the equation becomes;

[tex]x_{3} = x_2 - \frac{f(x_{2})}{f^1(x_{2})}[/tex]

[tex]x_{3} = -1.96463563- \frac{f( -1.96463563)}{f^1( -1.96463563)}[/tex]

Following the same procedure as above we have

[tex]x_{3} = -1.96463560[/tex]

From the values of [tex]x_2[/tex] and [tex]x_3[/tex], it can be seen that there is no change in the first 6 decimal places, therefore, it is safe to say that the value of the negative root of the equation is approximately  -1.964636 to 6 decimal places.

Newton's method of approximation is one of the several ways of estimating values.

The approximated value of [tex]\mathbf{e^x = 4 - x^2}[/tex] to 6 decimal places is [tex]\mathbf{ -1.964636}[/tex]

The equation is given as:

[tex]\mathbf{e^x = 4 - x^2}[/tex]

Equate to 0

[tex]\mathbf{4 - x^2 = 0}[/tex]

So, we have:

[tex]\mathbf{x^2 = 4}[/tex]

Take square roots of both sides

[tex]\mathbf{ x= \pm 2}[/tex]

So, the negative root is:

[tex]\mathbf{x = -2}[/tex]

[tex]\mathbf{e^x = 4 - x^2}[/tex] becomes [tex]\mathbf{f(x) = e^x - 4 + x^2 }[/tex]

Differentiate

[tex]\mathbf{f'(x) = e^x +2x }[/tex]

Using Newton's method of approximation, we have:

[tex]\mathbf{x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}}[/tex]

When x = -2, we have:

[tex]\mathbf{f'(-2) = e^{(-2)} +2(-2) = -3.86466471676}[/tex]

[tex]\mathbf{f(-2) = e^{-2} - 4 + (-2)^2 = 0.13533528323}[/tex]

So, we have:

[tex]\mathbf{x_{1} = -2 - \frac{0.13533528323}{-3.86466471676}}[/tex]

[tex]\mathbf{x_{1} = -2 + \frac{0.13533528323}{3.86466471676}}[/tex]

[tex]\mathbf{x_{1} = -1.96498136}[/tex]

Repeat the above process for repeated x values.

We have:

[tex]\mathbf{x_{2} = -1.96463563}[/tex]

[tex]\mathbf{x_{3} = -1.96463560}[/tex]

Up till the 6th decimal places,

[tex]\mathbf{x_2 = x_3}[/tex]

Hence, the approximated value of [tex]\mathbf{e^x = 4 - x^2}[/tex] to 6 decimal places is [tex]\mathbf{ -1.964636}[/tex]

Read more about Newton approximation at:

https://brainly.com/question/14279052

Answer:

The correct answer is option a.

a. 5( √3+ 1 )

Step-by-step explanation:

Given that the angle changes from 45° to 60° in 10 minutes.

This situation can be represented as right angled triangles [tex]\triangle[/tex]ABC (in the starting when angle is 45°)and [tex]\triangle[/tex]ABD (after 10 minutes when the angle is 60°).

AB is the tower (A be its top and B be its base).

Now, we need to find the time to be taken to cover the distance D to B.

First of all, let us consider [tex]\triangle[/tex]ABC.

Using tangent property:

[tex]tan\theta =\dfrac{Perpendicular}{Base}\\\Rightarrow tan 45=\dfrac{AB}{BC}\\\Rightarrow 1=\dfrac{h}{BC}\\\Rightarrow h = BC[/tex]

Using tangent property in [tex]\triangle[/tex]ABD:

[tex]\Rightarrow tan 60=\dfrac{AB}{BD}\\\Rightarrow \sqrt3=\dfrac{h}{BD}\\\Rightarrow BD = \dfrac{h}{ \sqrt3}\ units[/tex]

Now distance traveled in 10 minutes, CD  = BC - BD

[tex]\Rightarrow h - \dfrac{h}{\sqrt3}\\\Rightarrow \dfrac{(\sqrt3-1)h}{\sqrt3}[/tex]

[tex]Speed =\dfrac{Distance }{Time}[/tex]

[tex]\Rightarrow \dfrac{(\sqrt3-1)h}{10\sqrt3}[/tex]

Now, we can say that more distance to be traveled to reach the base of tower is BD i.e. '[tex]\bold{\dfrac{h}{\sqrt3}}[/tex]'

So, more time required = Distance left divided by Speed

[tex]\Rightarrow \dfrac{\dfrac{h}{\sqrt3}}{\dfrac{(\sqrt3-1)h}{10\sqrt3}}\\\Rightarrow \dfrac{h\times 10\sqrt3}{\sqrt3(\sqrt3-1)h}\\\Rightarrow \dfrac{10 (\sqrt3+1)}{(\sqrt3-1)(\sqrt3+1)} (\text{Rationalizing the denominator})\\\Rightarrow \dfrac{10 (\sqrt3+1)}{3-1}\\\Rightarrow \dfrac{10 (\sqrt3+1)}{2}\\\Rightarrow 5(\sqrt3+1)}[/tex]

So, The correct answer is option a.

a. 5( √3+ 1 )

Answer: A).  A Blue, then a Red.

     = 4/8 * 1/7

     = 1/14

B). A Red, then a White.

     = 1/7 * 3/8

     = 3/56

C). A Blue, then a Blue, then another Blue.

   = 4/8 * 3/7 * 2/6

   = 1/14

Step-by-step explanation:

had to complete the question first.

Find the following probabilities of Derek drawing the given marbles from the bag if the first marble(s) is(are) not returned to the bag after they are drawn.

(a) A Blue, then a Red =  

(b) A Red, then a White =  

(c) A Blue, then a Blue, then a Blue =  

given data:

blue marble = 4

white marble = 3

red marble = 1

total marble = 8

solution:

probability of drawing

A).  A Blue, then a Red.

     = 4/8 * 1/7

     = 1/14

B). A Red, then a White.

     = 1/7 * 3/8

     = 3/56

C). A Blue, then a Blue, then another Blue.

   = 4/8 * 3/7 * 2/6

   = 1/14

Answer:

1/4

Step-by-step explanation:

There are 80 students.

25 are girls and 55 are boys.

10 are foreigners and 70 are Nepalese.

62.5% are Nepalese boys.

This means that the number of Nepalese boys is:

62.5/100 * 80 = 50

There are 50 nepalese boys and so there are 20 nepalese girls.

The probability of selecting a Nepalese girl is therefore:

20 / 80 = 1/4

Answer: Use calculations for population standard deviation.

Step-by-step explanation:

The population standard deviation is defined as

A sample standard deviation is defined as

Since, data set represents the heights of all students in the middle school with 600 students which is population here.

So, we do calculations to find population standard deviation.

Answer:

$1387.4

Step-by-step explanation:

Total cost for the computer will be sum of down payments and monthly installments.

____________________________________

Given

down payment = $200

monthly installment value = $98.85

no. of installments = 12

total value of monthly installments = 12*98.95 = $1187.4

Total cost of computer system = $200+  $1187.4 = $1387.4

Answer:

y = -(1/2)x+1

Step-by-step explanation:

-2Y - X = -2

Add x to both sides:

-2Y = X - 2

Divide both sides by -2:

Y = -(1/2)x+1

You could also use the shortcuts:

For Ay+Bx=C, the slope is -B/A and the y-intercept is C/A.

Slope = -B/A = -(-1)/(-2) = 1/-2 = -(1/2)

Y-intercept = C/A = (-2)/(-2) = 1

y = mx + b ---> y = -(1/2)x + 1

Answer:

y = -1/2x +1

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

-2y -x = -2

Solve for y

Add x to each side

-2y = x-2

Divide by -2

-2y/2- = x/-2 -2/-2

y = -1/2x +1

Answer:

The expression that fits into the box is x¹⁵⁸

Step-by-step explanation:

Let the empty box be y

(x¹²)⁵ × (x⁻²)⁹ × y = (x⁴⁰)⁵

Here, we will apply the laws of indices.

The laws of indices gives the answer for the expressions

1) xᵏ × xˢ = xᵏ⁺ˢ

2) xᵏ ÷ xˢ = xᵏ⁻ˢ

3) (xᵏ)ˢ = xᵏ•ˢ

So,

(x¹²)⁵ = x⁶⁰

(x⁻²)⁹ = x⁻¹⁸

(x⁴⁰)⁵ = x²⁰⁰

(x¹²)⁵ × (x⁻²)⁹ × y = (x⁴⁰)⁵

Becomes

x⁶⁰ × x⁻¹⁸ × y = x²⁰⁰

x⁶⁰⁻¹⁸ × y = x²⁰⁰

x⁴² × y = x²⁰⁰

y = x²⁰⁰ ÷ x⁴²

y = x²⁰⁰⁻⁴² = x¹⁵⁸

Hope this Helps!!!

Answer:

20b^3+12b^2

Step-by-step explanation:

v=(2b)^2 (5b+3) = 4b^2 (5b+3) = 20b3+12b^2

Answer:

0.38

Step-by-step explanation:

The area under the probability density curve is equal to 1.

The width of the rectangle is 2, so the height of the rectangle must be ½.

The probability that X is between 0.68 and 1.44 is therefore:

P = ½ (1.44 − 0.68)

P = 0.38

Using the uniform distribution, it is found that there is a 0.38 = 38% probability that X is between 0.68 and 1.44.

-----------------------

Uniform probability distribution:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

In this problem:

The probability that X is between 0.68 and 1.44 is:

[tex]P(0.68 \leq X \leq 1.44) = \frac{1.44 - 0.68}{2 - 0} = 0.38[/tex]

0.38 = 38% probability that X is between 0.68 and 1.44.

A similar problem is given at https://brainly.com/question/13547683

Answer: $34.18

Step-by-step explanation:

Let the cost of the Jacket = $x and

The cost of the sweater. = $y

Now total price. = $71.55.

So, $x + $y. = $71.55 -- 1

From the second statements, the price of the sweater was $3.19 less than the price of the jacket. Transforming that into equation

y = ( x - $3.19 )

Now substitute for y in the equation (1) above.

x + ( x - 3.19 ) = 71.55

Now solve the equation

x + x - 3.19 = 71.55

2x - 3.19. = 71.55

2x = 71.55 + 3.19

2x. = 74.74

x = 74.74/2

= $37.37. cost of the jacket

Now to determine the cost of the sweater,

$71.55 - $37.37 = $34.18

The cost of the sweater = $34.18.

Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

From the question

Slope / m = 5

Equation of the line passing through point (2 , 10) is

y - 10 = 5(x - 2)

y - 10 = 5x - 10

y = 5x - 10 + 10

Hope this helps you

Answer:

b, c, e

Step-by-step explanation:

the reasons have to include an angle from both of the parallel lines. by using process of elimination it is b, c, e. I also got it right

Answer:

B. a=d

C. c=d

E. b + d=180°

Step-by-step explanation:

Got Correct On MyPath.

Answer:

A. 1 4/6 cups of blueberries

Step-by-step explanation:

1 -- 2/3                      

Proportion, Batches to Blueberries

1*(2 1/2) -- (2/3)( 2 1/2)              

Because we are now multiplying the 1 batch to 2 1/2 batches. So to keep the proportion balanced/equal we are using the same operation on the right side of the proportion

2 1/2 -- (2/3)( 5/2 )      

2 1/2 -- 5/3

2 1/2 -- 1 2/3

Simplify

On the right side shows the blueberries for 2 1/2 batches. 1 2/3 = 1 4/6    

Hope that helps! Tell me if you need more info

Answer:

Aquarium dimensions:

x = 3,106 m

h = 6,22 m

C(min) = 1277,62 $

Step-by-step explanation: (INCOMPLETE QUESTION)

We have to assume:

The shape of the aquarium  (square base)

Let´s call "x" the side of the base, then h ( the heigh)

V(a) = x²*h          h = V(a)/x²      

Cost of Aquarium   C(a) = cost of the base (in stones) + 4* cost of one side (in glass)

C(a) = Area of the base *120 + 4*Area of one side*30

Area of the base is x²

Area of one side  is   x*h   or  x*V(a)/x²  

Area of one side is V(a)/x

C(x) = 120*x² + 4*30*60/x

C(x) = 120*x² +  7200/x

Taking derivatives on both sides of the equation we get

C´(x) = 2*120*x  - 7200/x²

C´(x) = 0 means    240 *x  - 7200/x² = 0

240*x³ - 7200 = 0

x³ = 7200/240

x = 3,106 m   and  h = 60 /x²     h =   6,22 m

and C (min) = 120*(3,106)³ - 7200 / 3,106

C(min) =  3595,72 - 2318,1

C(min) = 1277,62

Answer:

m<1 = 50

Step-by-step explanation:

We can first find the angle next to 140, by doing 180 - 40 = 40.

Now that we know that one of the triangles angle is 40, we also know that there's a 90 degree angle, so we can do:

180 - 90 - 40 = 50

So m<1 = 50

Answer:

0.8390

Step-by-step explanation:

From the question,

Z score = (Value-mean)/standard deviation

Z score = (150.2-160.5)/10.4

Z score = -0.9904.

P(x>Z) = 1- P(x<Z)

From the Z table,

P(x<Z) = 0.16099

Therefore,

P(x>Z) = 1-0.16099

P(x>Z) = 0.8390

Hence the probability that a person weighs more than 150.2 pounds = 0.8390

Answer:

-1

Step-by-step explanation:

since m=4

we substitute in eqn which is 2(5-(1/2m))

2(5-(1/2(4)))

2(5-2)-7

=-1

536 children = 4 months

536/4 children = 4/4 months ... divide both sides by 4

134 children = 1 month

The clinic treated 134 children in 1 month. This is assuming that every month was the same number of patients.

Step-by-step explanation:

Solution,

Number of children treated in 4 months = 536

Now, let's find the number of children treated in one month:

[tex] = \frac{total \: number \: of \: childrens \: }{total \: month} [/tex]

Plug the values

[tex] = \frac{536}{4} [/tex]

Calculate

[tex] = 134 \: [/tex] childrens

Therefore, A clinic treated 134 childrens in one month.

Hope this helps...

Best regards!!

Answer:

52 dimes and 54 nickels

Step-by-step explanation: 52 dimes is $5.20 and 54 nickels is $2.70

Total coins 106 total $7.90

Answer:

A. 70 dimes, 30 quarters

Step-by-step explanation:

Only options A and B create a total of 100 coins. It cannot be option B because 80 quarters by itself, is already over $14.50.

Answer:

13°

Step-by-step explanation:

The trigonometric ratio formula can be used in calculating the angle of elevation (x°) of the sun, as the person makes a right angle with the ground.

The height of the person would be the opposite length = 6 ft, the shadow of the person would be the adjacent length = 26 ft

Therefore, according to the trigonometric ratio formula, we would calculate angle of elevation (x°) as follows:

[tex] tan x = \frac{opposite}{adjacent} [/tex]

[tex] tan x = \frac{6}{26} [/tex]

[tex] tan x = 0.2308 [/tex]

x = tan-¹(0.2308)

x = 12.996

x ≈ 13° (to the nearest whole degree)

The angle of elevation of the sun = 13°

Answer:

y = 4x -5

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = 4x -5