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Week 5 Assignment: Mixture Problems and Systems of Equations
Due Sunday by 11:59pm
Points 10
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Solve interest applications using a system of equations
Question
Matthew invested $3,000 into two accounts. One account paid 3% interest and the other paid 8% interest. He earned 4%
interest on the total investment. How much money did he put in each account?
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3% amount: S 600
8% amount: S 2400
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Answer:

[tex]\boxed{x=1}[/tex] and [tex]\boxed{x=7}[/tex]

Step-by-step explanation:

This quadratic is already factored down to its factors (x - 1) and (x - 7).

Set these equal to zero and solve for x by adding 1 or 7 to both sides of the equation.

[tex]x-1=0\\\\\boxed{x=1}[/tex]

[tex]x-7=0\\\\\boxed{x=7}[/tex]

Answer:

A. 1/4

Step-by-step explanation:

We know that before the 1st bounce, the height of the ball is 512 inches.

Say the fraction is x.

Then, after the first bounce, the height of the ball is 512 * x = 512x.

After the second bounce, the height is now x * 512x = 512x².

By similar reasoning, the height after the third bounce is 512x³ and after the fourth bounce, it is [tex]512x^4[/tex].

We also know that after the fourth bounce, the height is 2 inches. So, set 2 equal to [tex]512x^4[/tex]:

2 = [tex]512x^4[/tex]

Divide both sides by 512:

[tex]x^4=2/512[/tex][tex]x^4=2/512=1/256[/tex]

Take the fourth root of both sides:

[tex]x=\sqrt[4]{1/256} =1/4[/tex]

Hence, the answer is A.

~ an aesthetics lover

Answer:

A. 1/4.

Step-by-step explanation:

This is exponential decay so we  have , where x = the fraction:

512(x)^4 = 2

x^4 = 1/256

x= 1 / (256)^0.25

= 1/4

Answer:

UAE is in the Gulf Standard Time zone.

It is GMT + 4

Breakfast: 7 am; GMT 3 am

School time 8 am: GMT 4 am

Lunch time: 12:30 pm; GMT 8:30 am

Step-by-step explanation:

UAE is in the Gulf Standard Time zone.

It is GMT + 4

Breakfast: 7 am; GMT 3 am

School time 8 am: GMT 4 am

Lunch time: 12:30 pm; GMT 8:30 am

Answer:

a. 539.54

b. No, the result from part (a) could not be the actual number of adult who said that secondhand smoke are very harmful because a count of people must result into a whole number.

c. 540

d. 25.54%

Step-by-step explanation:

Given that:

A polling company reported that 53​% of 1018 surveyed adults said that secondhand smoke is "very harmful."

Complete parts​ (a) through​ (d) below.

a. What is the exact value that is 53​% of 1018​?

The 53% of 1018 is :

=[tex]\dfrac{53}{100} \times 1018[/tex]

= 0.53 × 1018

= 539.54

b. Could the result from part​ (a) be the actual number of adults who said that secondhand smoke is ''very harmful"? Why or why​ not?

No, the result from part (a) could not be the actual number of adult who said that secondhand smoke are very harmful because a count of people must result into a whole number.

c. What could be the actual number of adults who said that secondhand smoke is secondhand smoke "very harmful"?

Since, a count of people must result into a whole number, the actual number of adults who said that secondhand smoke is secondhand smoke "very harmful" can be determined from the approximation of the exact value into whole number which is 539.54 [tex]\approx[/tex] 540.

d. Among the 1018 ​respondents, 260 said that secondhand smoke is  is "not at all harmful.''  What percentage of respondents said that secondhand smoke is  "not at all harmful"?

Since 260 respondents out of 1018 respondents said that the second hand smoke is not harmful, then the percentage of the 260 respondents is :

= [tex]\dfrac{260}{1018} \times 100 \%[/tex]

= 25.54%

Answer:

see explanation

Step-by-step explanation:

(43)

3[tex]x^{5}[/tex] - 75x³ ← factor out 3x³ from each term

= 3x³(x² - 25) ← this is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , thus

x² - 25 = x² - 5² = (x - 5)(x + 5)

Thus

3[tex]x^{5}[/tex] - 75x³ = 3x³(x - 5)(x + 5)

(44)

81c² + 72c + 16 ← is a perfect square of the form

(ac + b)² = a²c² + 2abc + b²

Compare coefficients of like terms

a² = 81 ⇒ a = [tex]\sqrt{81}[/tex] = 9

b² = 16 ⇒ b = [tex]\sqrt{16}[/tex] = 4

and 2ab = 2 × 9 × 4 = 72

Thus

81c² + 72c + 16 = (9c + 4)²

1. 3x^5 -75x³

=3x³(x²-25)

=3x³(x²-5²)

=3x³(x-5)(x+5)

2. 81c²+72c+16

=81c²+36c+36c+16

=9c(9c+4)+4(9c+4)

=(9c+4)(9c+4)

=(9c+4)²

Answer:

a) 0.36

b) 0.3

c) Yes

Step-by-step explanation:

Given:

Probability of no traffic delay in one period, given no traffic delay in the preceding period = P(No_Delay) = 0.9

Probability of finding a traffic delay in one period, given a delay in the preceding period = P(Delay) = 0.6

Period considered = 30 minutes

a)

Let A be the probability that for the next 60 minutes (two time periods) the system will be in the delay state:

As the Probability of finding a traffic delay in one period, given a delay in the preceding period is 0.6 and one period is considered as 30 minutes.

So probability that for the next two time periods i.e. 30*2 = 60 minutes, the system in Delay is

P(A) = P(Delay) * P(Delay) =  0.6 * 0.6 = 0.36

b)

Let B be the probability that in the long run the traffic will not be in the delay state.

This statement means that the traffic will not be in Delay state but be in No_Delay state in long run.

Let C be the probability of one period in Delay state given that preceding period in No-delay state :

P(C) =  1 - P(No_Delay)

        = 1 - 0.9

P(C) = 0.1

Now using P(C) and P(Delay) we can compute P(B) as:

P(B) = 1 - (P(Delay) + P(C))

      = 1 - ( 0.6 + 0.10 )

      = 1 - 0.7

P(B) = 0.3

c)

Yes this assumption should be questioned for this traffic problem because it implies that  traffic will be in Delay state for the 30 minutes and just after 30 minutes, it will be in No_Delay state. However, traffic does not work like this in general and it makes this scenario unrealistic. Markov process model can be improved if probabilities are modeled as a function of time instead of being presented as constant (for 30 mins).

Answer:69

Step-by-step explanation:

Answer:

distance from the flying object to

the ground

= 7.2 melo(unit of measurement)

Step-by-step explanation:

The distance between the robot and Jo is 5 melo( unit Of measurement)

Let the distance between the flying object and the ground= y

Let's the remaining length of the closest between robot and Jonny and the ground be x.

Y/(x+5)= tan 29.... equation 1

Y/x= tan 42.... equation 2

Equating the value of y

Tan 29(x+5) = tan42(x)

Tan29/tan 42 = x/(x+5)

0.61562(x+5)= x

3.0781= x- 0.61562x

3.0781= 0.38438x

3.0781/0.38438= x

8.008= x

8= x

Y/x= tan 42

Y/8= 0.9004

Y= 7.203

Y= 7.2 melo (unit of measurement )

Answer:

Supplementary

Step-by-step explanation:

When the sum of 2 angles equal 180°, they are called supplementary angles. And they also form a straight line together.

<AOB (40°) and <BOC (140°) are not equal angles.

<AOB (40°) and <BOC (140°) are not complementary angles. Complementary angles add up to equal 90°.

<AOB (40°) and <BOC (140°) are not vertical angles. Vertical angles are opposite angles formed when two lines intersect.

<AOB (40°) and <BOC (140°) are supplementary angles. They add up to equal 180°.

Answer: (3x^2-1)(4x-3)

============================

Work Shown:

Use the factor by grouping method

12x^3-9x^2-4x+3

(12x^3-9x^2)+(-4x+3)

3x^2(4x-3)-1(4x-3)

(3x^2-1)(4x-3)

Answer:

The two missing sides are : 79.54m and 58.62m

Step-by-step explanation:

first we look for the missing angle in the triangle

so now we use sine rules:

Let us make:

so :

so the side facing 35° = 79.54m

To find the area of this triangle

Step-by-step explanation:

To find this inverse of a graph you have to multiply the current equation by -1.

-1(2x-3)

f(x)=-2x+3.

This graph will start at the point (0,3). Then according to the slope the rest of the points will go down two than right one. So the next two point will be (1,1) and (2,-1).

Answer:

it should be 308,608. the comma is after every three in this scenario.

Step-by-step explanation:

Answer:

[tex]\bold{4\sqrt3 + i4}[/tex]

Step-by-step explanation:

Given complex number is:

[tex][2(cos10^\circ + i sin10^\circ)]^3[/tex]

To find:

Answer in rectangular form after using De Moivre's theorem = ?

i.e. the form [tex]a+ib[/tex] (not in forms of angles)

Solution:

De Moivre's theorem provides us a way of solving the powers of complex numbers written in polar form.

As per De Moivre's theorem:

[tex](cos\theta+isin\theta)^n = cos(n\theta)+i(sin(n\theta))[/tex]

So, the given complex number can be written as:

[tex][2(cos10^\circ + i sin10^\circ)]^3\\\Rightarrow 2^3 \times (cos10^\circ + i sin10^\circ)^3[/tex]

Now, using De Moivre's theorem:

[tex]\Rightarrow 2^3 \times (cos10^\circ + i sin10^\circ)^3\\\Rightarrow 8 \times [cos(3 \times10)^\circ + i sin(3 \times10^\circ)]\\\Rightarrow 8 \times (cos30^\circ + i sin30^\circ)\\\Rightarrow 8 \times (\dfrac{\sqrt3}2 + i \dfrac{1}{2})\\\Rightarrow \dfrac{\sqrt3}2\times 8 + i \dfrac{1}{2}\times 8\\\Rightarrow \bold{4\sqrt3 + i4}[/tex]

So, the answer in rectangular form is:

[tex]\bold{4\sqrt3 + i4}[/tex]

Answer:

Since the calculated value of t= 2.249 does not  falls in the rejection region we therefore accept  the null hypothesis at 5 % significance level . On the basis of this we conclude that the  bonus plan has not  increased sales significantly.

Step-by-step explanation:

The null and alternative hypotheses as

H0: μd=0    Ha: μd≠0

Significance level is set at ∝= 0.05

n= 6

degrees of freedom = df = 6-1 = 5

The critical region is t  ( base alpha by 2 with df=5) ≥ ± 2.571

The test statistic under H0 is

t = d/ sd/ √n

Which has t distribution with n-1 degrees of freedom

Sales                                      Difference

Person      After      Before   d = after - before      d²

1                   94          90                4                      16

2                  82          84               -2                       4

3                  90          84               6                       36

4                  76           70               6                       36

5                  79           80               -1                        1

6                  85          80                 5                       25  

∑                                                       18                   118

d`= ∑d/n= 18/6= 3

sd²= 1/6( 118- 18²/6) = 1/6 ( 118 - 54) = 10.67

sd= 3.266

t= 3/ 3.266/ √6

t= 2.249

Since the calculated value of t= 2.249 does not  falls in the rejection region we therefore accept  the null hypothesis at 5 % significance level . On the basis of this we conclude that the  bonus plan has not  increased sales significantly.

Answer:

[tex]-[ln(x^2-yx-y^2)] = K\\[/tex]

Step-by-step explanation:

Given the differential equation [tex](x+2y)y'=2x-y[/tex], this can also be written as;

[tex](x+2y)\frac{dy}{dx} =2x-y[/tex]

On simplification

[tex](x+2y)\frac{dy}{dx} =2x-y\\\\\frac{dy}{dx} = \frac{2x-y}{x+2y} \\\\let \ y = vx\\\frac{dy}{dx} = v+x\frac{dv}{dx}[/tex]

The differential equation becomes;

[tex]v+x\frac{dv}{dx} =\frac{ 2x-vx}{x+2vx}\\\\v+x\frac{dv}{dx} = \frac{ x(2-v)}{x(1+2v)}\\\\v+x\frac{dv}{dx} = \frac{2-v}{1+2v}\\\\x\frac{dv}{dx} = \frac{2-v}{1+2v} - v\\\\x\frac{dv}{dx} = \frac{(2-v)-v(1+2v)}{1+2v}\\\\x\frac{dv}{dx} = \frac{2-v-v-2v^2}{1+2v}\\\\x\frac{dv}{dx} = \frac{2-2v-2v^2}{1+2v}[/tex]

[tex]\frac{dx}{x} = \frac{1+2v}{2-2v-2v^2}dv\\\\integrating\ both \ sides\\\\[/tex]

[tex]\int\limits \frac{dx}{x} = \int\limits \frac{1+2v}{2-2v-2v^2}dv\\\\lnx = \frac{1}{2} \int\limits \frac{1+2v}{1-v-v^2}dv\\\\lnx + C = -\frac{1}{2}ln(1-v-v^2)[/tex]

[tex]C = -\frac{1}{2}ln(1-v-v^2) - lnx \\\\ -ln(1-v-v^2) - 2lnx = 2C\\\\-[ln(1-v-v^2) + lnx^2] = 2C\\\\-[ln(1-v-v^2)x^2] = 2C\\since\ v = y/x\\\\- [ln(1-y/x-y^2/x^2)x^2] = K\\\\-[ln(x^2-yx-y^2)] = K\\[/tex]

Hence the solution to the differential equation is [tex]-[ln(x^2-yx-y^2)] = K\\[/tex]

Answer:

Simplify:

[tex]-4^2-5(1^3)[/tex]

So you get:

[tex]-21\\[/tex]

Answer:

[tex]\huge\boxed{-21}[/tex]

Step-by-step explanation:

-x²-5y³

Given that x = 4, y = 1

[tex]-(4)^2-5(1)^3[/tex]

[tex]-16-5(1)\\-16-5\\-21[/tex]

Answer:

Infinite amount of solutions

Step-by-step explanation:

Parallel lines have no solution

Same lines have infinite solutions

Intersecting lines have 1 solution

Step 1: Write out equation

-14(x - 5) = -14x + 70

Step 2: Distribute -14

-14x + 70 = -14x + 70

Here we see that we have 2 exact same lines. Therefore, we have infinite amount of solutions.

Alternatively, we can plug in any number x and it would work. So then we would have infinite amount of solutions as well.

Answer:

The fraction [tex]\displaystyle \frac{55}{22}[/tex] is indeed a rational number.

Step-by-step explanation:

A number [tex]x[/tex] is rational if and only if there exist two integers [tex]p[/tex] and [tex]q[/tex] (where [tex]q \ne 0[/tex]) such that [tex]x = \displaystyle \frac{p}{q}[/tex].

[tex]\displaystyle \frac{55}{22}[/tex], the number in question here is already written in the form of a fraction. The two integers [tex]p = 55[/tex] and [tex]q = 22[/tex] ([tex]q \ne 0[/tex]) meet the requirement that [tex]\displaystyle \frac{55}{22} = \frac{p}{q}[/tex]. Therefore, [tex]\displaystyle \frac{55}{22}\![/tex] is indeed a rational number.

Side note: the [tex]p[/tex] and [tex]q[/tex] here ([tex]q \ne 0[/tex]) don't have to be unique. For example:

because [tex]\displaystyle \frac{55}{22} = \frac{5 \times 11 }{2 \times 11} = \fraac{5}{2}[/tex], both of the following pairs could satisfy [tex]\displaystyle \frac{55}{22} = \frac{p}{q}[/tex]:

Answer:

4th multiple = 24

Step-by-step explanation:

Given

Let the two numbers be represented by m and n

Required

Find the 4th common multiple of the numbers.

From the question, we understand that the first common multiple of m and n is 6.

This can be represented as:

m * n * 1 = 6

mn = 6

Their fourth common multiple can be represented as: m * n * 4

4th multiple = m * n * 4

4th multiple = 4 * mn

Substitute 6 for mn

4th multiple = 4 * 6

4th multiple = 24

Hence, the 4th multiple of both numbers is 24.

Answer:

16x^2 - 64

Step-by-step explanation:

(4x − 8)(4x + 8)

We recognize that this is the difference of squares

(a-b) (a+b) = a^2 - b^2

                 =(4x)^2 - 8^2

                 =16x^2 - 64

Answer:

3 mL

Step-by-step explanation:

The fluid level is called the concave meniscus. The adhesive force causes it to crawl up on the sides, but you should ignore that while reading the level.

Answer:

7/10 mi

Step-by-step explanation:

The total distance is 3 miles = 30/10 miles.

The other distances added gives 7/10+7/10+9/10 = 23/10

Therefore the last hop from Kingwood to Silvergrove is 30/10 - 23/10 = 7/10

Answer:

5 miles away

Step-by-step explanation:

If you walked north 8 miles, then west 4 miles, then south 5 miles, you have, in total, travelled 4 miles west and [tex]8-5=3[/tex] miles north.

This creates a triangle, in which we can find the the length of the hypotenuse to find how far away you are now.

We can use the Pythagorean theorem since this is a right triangle.

[tex]a^2+b^2=c^2\\3^2+4^2=c^2\\9+16=c^2\\25=c^2\\c=5[/tex]

Hope this helped!

Answer:

5 miles away

Step-by-step explanation:

Answer:

113.04 cm^2

Step-by-step explanation:

The area of a circle is

A = pi r^2

We know the radius is 6 cm

A = 3.14 * 6^2

A = 3.14 * 36

A =113.04

Answer

A. 720 ways

B. 240 ways

C. 6 ways

There are 720 ways they can be seated in a row together, 120 ways can the people be seated together in a row with the doctor in an aisle seat, and 6 ways can the six be seated together in a row.

A permutation is defined as a mathematical process that determines the number of different arrangements in a set of objects when the order of the sequential arrangements.

It is assumed that six people will attend the theater together and sit in a row of six.

The following are the various ways they can be seated in a row together:

⇒ 6!

⇒ 6 × 5 × 4 × 3 × 2 × 1

⇒ 720

If the doctor sits in the aisle seat, the remaining 5 persons can sit in the remaining 5 seats 5! ways

The total possibilities are as follows:

⇒ 5 × 4 × 3 × 2 × 1

= 120

Consider that the six persons are made up of three married couples.

In addition to the aforementioned, divide the six chairs into three groups of two seats each.

There is one choice in each block for the husband to be placed on the left and the wife to be positioned on the right and the 3 couples can be seated in the 3 blocks in 3! ways.

⇒ 3 × 2 × 1

The required answer is 6.

Thus, there are 720 ways they can be seated in a row together, 120 ways can the people be seated together in a row with the doctor in an aisle seat, and 6 ways can the six be seated together in a row.

Learn more about permutation here:

brainly.com/question/1216161

#SPJ2

Answer:

6 glasses

I hope this helps!

Answer:

28/5

Step-by-step explanation:

looked up on khan

Answer:

[tex]Area = 5a - a^2[/tex] [tex]inches\²[/tex]

[tex]Perimeter = 10\ inches[/tex]

Step-by-step explanation:

Given

Length = a

Width = 5 - a

Required

Determine the Area and Perimeter;

Calculating Area

Area is calculated as thus;

[tex]Area = Length * Width[/tex]

Substitute values for Length and Width

[tex]Area = a * 5 - a[/tex]

[tex]Area = a * (5 - a)[/tex]

Open Bracket

[tex]Area = 5a - a^2[/tex]

Calculating Perimeter

Perimeter is calculated as thus;

[tex]Perimeter = 2 (Length + Width)[/tex]

Substitute values for Length and Width

[tex]Perimeter = 2 (a + 5 - a)[/tex]

Collect Like Terms

[tex]Perimeter = 2 (5 + a- a)[/tex]

[tex]Perimeter = 2 (5)[/tex]

Open Bracket

[tex]Perimeter = 10\ inches[/tex]

Answer:

equal value and function

Step-by-step explanation: