ohn drove from Miami to Atlanta, and the trip took him a total of 10 hours.
For 6 hours John’s average speed was 73 mph. His average speed on the remainder of the
trip was 67 mph. What was his average speed on the entire trip?
a) 70.8 mph
b) 70.6 mph
c) 69.4 mph
d) 68.2 mph

We are given:
Initial sound Intensity: 110 dB
Rate of decreasing sound level: 16% every second

Constructing the equation:
Since the Intensity decreases by 16% of it's current value every second.
Intensity(t) = [tex]110 * (\frac{84}{100})^{t}[/tex]               [where t is the time elapsed]
In this equation, we multiply the initial sound intensity by 84% (since 16% was diminished).
because we are multiplying the same value by 84%, it will keep taking that percentage of the new value, which is what we need here because the music's intensity keeps becoming 84% of the previous value.

Time at which sound level falls to 30 dB:
replacing intensity by 30 in the equation we made.
[tex]30 = 110 * (\frac{84}{100})^{t}[/tex]
[tex]\frac{3}{11} = (\frac{84}{100})^t[/tex]
taking log of both sides.
[tex]log(\frac{3}{11}) = t*log(\frac{84}{100})[/tex]
[tex]\displaystyle \frac{log(\frac{3}{11})}{log(\frac{84}{100})} = t[/tex]

t = 7.452 seconds

Answer:

Equation:  [tex]y=110(0.84)^x[/tex]

(where x is the time in seconds, and y is the sound level in decibels)

Answer: The sound level falls below 30 decibels after 7.452 seconds (3 dp)

Step-by-step explanation:

We can model this as an exponential equation.

General form of an exponential equation: [tex]y=ab^x[/tex]

where:

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

If the sound decreases by 16% each second, then the growth (decay) factor will be 100% - 16% = 84%  →  0.84

Given:

Substituting these values into the equation:

[tex]\implies y=110(0.84)^x[/tex]

To find how long until the sound level falls below 30 decibels, set y < 30 and solve for x:

[tex]\begin{aligned}110(0.84)^x & < 30\\\\(0.84)^x & < \dfrac{3}{11}\\\\\ln (0.84)^x & < \ln \left(\dfrac{3}{11}\right)\\\\x \ln (0.84) & < \ln \left(\dfrac{3}{11}\right)\\\\x & > \dfrac{\ln \left(\dfrac{3}{11}\right)}{\ln (0.84)}\\\\x & > 7.452008851\end{aligned}[/tex]

Therefore, the sound level falls below 30 decibels after 7.452 seconds (3 dp)

Answer:12 1/8

Step-by-step explanation:

you add the denomunator in order to get your answer

$0.7

Given sentence:

Writing as an equation:

[tex]\implies 2.4 \ \text{pounds} = \$1.68[/tex]

To obtain the cost per pound of peas, divide 2.4 both sides. This will convert the value on the L.H.S to 1 pound. The value obtained on the R.H.S will be the the cost (answer).

[tex]\implies \dfrac{2.4 \ \text{pounds}}{2.4} = \$\dfrac{1.68}{2.4}[/tex]

[tex]\implies 1 \ \text{pounds}}= \$\dfrac{1.68}{2.4}[/tex]

[tex]\implies 1 \ \text{pound} = \$0.7[/tex]

Answer:

x = 10

Step-by-step explanation:

Both right triangles are similar.

-> Corresponding sides of similar triangles are in proportion.

[tex] \implies \: \frac{x + 6}{16} = \frac{x}{10} \\ \\ \implies \: 10(x + 6) = 16x \\ \\ \implies \: 10x + 60= 16x \\ \\ \implies \: 10x - 16x = - 60 \\ \\ \implies \: - 6x = - 60 \\ \\ \implies \: x = \frac{ - 60}{ - 6} \\ \\ \implies \: x = 10[/tex]

Answer:

x=1

Step-by-step explanation:

1) Distribute 3x+9=12

2) Subtract 9 from both sides 3x=3

3) Divide by three x=1

Step-by-step explanation:

The centroid O cuts every median in the ratio 2:1. The distance between a vertex and the centroid is twice the distance between the centroid and the midpoint of the opposite side.

Therefore: |OB| = 2|OF|

|BF| = |OF| + |OB| = |OF| + 2|OF| = 3|OF|

3x+3=3(2x-8)

3x+3=6x-24

3x=27

x=9

Answer:

  $65,139,000

Step-by-step explanation:

Integration of the given function involves straightforward application of the power rule. It can also be done easily by a modern calculator.

  [tex]\displaystyle \int_{1000}^{1300}{(190x-1370)}\,dx=95(1300^2-1000^2)-1370(1300-1000)\\\\=95(300)(2300)-1370(300)=300(95\cdot2300-1370)\\\\=65\,139\,000[/tex]

Revenue from the sale of those 300 tickets will be $65,139,000.

The Ruiz family using a rounded figure for exchange rate will not give the correct exchange.

Exchange rate:

1 euro = 1.35261 USD

1.35261 rounded to the nearest hundredth = 1.35

If Ruiz family is exchanging 50 euros for instance

Original exchange rate

1 euro = 1.35261 USD

50 euro = 67.6305

Rounded exchange rate:

1 euro = 1.35 USD

50 euro = 67.5 USD

Therefore, the Ruiz family using a rounded figure for exchange rate will not give the correct exchange.

Read more:

https://brainly.com/question/17985441

Answer:

(2, -4)

Step-by-step explanation:

Answer:

(2, -4)

Step-by-step explanation:

The solution to a system of equations is always going to be the point(s) where they intersect. To solve, use substitution and find each variable, x and y. Our final answer will be a set of coordinates (x, y). To plot this system, see the help image attached.

y = -x - 2

2x - y = 8

Substitute y to find x

2x - (-x - 2) = 8

2x + x + 2 = 8

3x = 6

x = 2

Substitute x to find y

y = -(2) - 2

y = -2 - 2

y = -4

Solution: (2, -4)

I hope this helps and God bless!

Typically, linear equations are written in slope-intercept form:

[tex]y=mx+b[/tex]

To find the equation of a line given a point and the slope:

We're given:

[tex]y=mx+b[/tex]

⇒ Plug in the slope, [tex]\dfrac{1}{5}[/tex]:

[tex]y=\dfrac{1}{5}x+b[/tex]

⇒ Plug in the point (-5,-4) and solve for b:

[tex]-4=\dfrac{1}{5}(-5)+b\\\\-4=-1+b\\\\b=-3[/tex]

⇒ Therefore, the y-intercept of the line is -3. Plug this back into our original equation as b:

[tex]y=\dfrac{1}{5}x-3[/tex]

[tex]y=\dfrac{1}{5}x-3[/tex]

Answer:

D. 4.5 and 12 seconds

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

It was correct on the quiz

Answer:

The answer is 3054.8

Step-by-step explanation:

V = 4/3 × 22/7 × 9 × 9 × 9

V = 4 × 22/7 × 3 × 81

V = 4 × 22 × 243/7

V = 21384/7

V = 3054.8

Thus, The answer is 3054.8

Answer:

3054

Step-by-step explanation:

V=4/3 π9³ = 3054

hope it helps

Answer:

75%

Im happy to help you

Answer:

1/8

Step-by-step explanation:

I think so

12-(-8)=20

x axis = 20:2 = 10

The parabolae b, d and f seen in the real coordinate plane have complex roots.

Second order polynomials are algebraic equations of the form:

[tex]y = a\cdot x^{2}+b\cdot x + c[/tex]   (1)

Where:

A value of x is a root of the polynomial for y = 0, which can real or complex but not both according to the discriminant of the quadratic formula. If the polynomial has no real roots, then it does not pass through the x-axis in the real coordinate plane.

Therefore, the parabolae b, d and f seen in the real coordinate plane have complex roots. [tex]\blacksquare[/tex]

To learn more on quadratic functions, we kindly invite to check this verified question: https://brainly.com/question/4119540

Answer:

y<3/2x-5/2

Step-by-step explanation:

You just have to know how to get y on one side and the rest of the problem on the other.

First you would subtract 3x from both sides, which leaves you with -2y>5-3x.

Lastly you would divide both sides by -2.

To get the final answer of y<3/2x-5/2

Answer:

anywhere around 420-450

Step-by-step explanation:

the actual answer is 434, a good estimation would be in that range

Answer:

D. is correct.

[tex]2 * 1 = 2[/tex]

[tex]4 * 1=4[/tex]

[tex]4 + 2 = 6[/tex]

________________________________________________________

The product of answer choice D.(6) is not equal to the product of [tex]\frac{2}{3}[/tex] × 4, because [tex]\frac{2}{3}[/tex] × 4 is actually [tex]2\frac{2}{3}[/tex]

________________________________________________________

We learned how to find whole numbers through an expression with fractions.

Questions related to the topic? Ask me in the comments box.

A two column proof for ΔAEC ≅ ΔDEB  is as shown below.

"Two triangles are congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure."

"These angles formed on the inside of two straight lines when crossed by a transversal."

"It is point which divides a line segment into two equal parts."

"AAS (Angle Angle Side) theorem states that in the two triangles, if two angles and one side of a triangle are congruent to two angles and one side of a second triangle, then the two triangles are congruent."

For given question,

Given that CA is parallel to DB and E is the midpoint of AD.

CA is parallel to DB

CB is transversal.

∠ACB and ∠CBD are alternate interior angles.

We know that when a transversal intersects a parallel line then alternate interior angles formed are congruent.

So, ∠ACB ≅ ∠CBD                       ................(i)

Similarly for CA || DB and AD is transversal.

∠CAD ≅ ∠ADB                             ..................(ii)

Also,  E is the midpoint of AD.

By definition of midpoint,

⇒ AE = ED                                      ..................(iii)

From (i), (ii) and (iii),

By AAS postulate of triangle congruence,

ΔAEC ≅ ΔDEB      

Therefore, a two column proof for ΔAEC ≅ ΔDEB  is as shown below.

Learn more about AAS postulate of triangle congruence here:

https://brainly.com/question/1593616

#SPJ2

Answer: 20v+5

Step-by-step explanation:

5(4v+1)

Use the distributive property to multiply 5 by 4v+1.

20v+5

Answer:

20v+5

Step-by-step explanation:

You would multiply using the distributive property

Distributive property formula examples:

AB=BA

A+B=B+A

(AB)C=A(BC)

(A+B)+C=A+(B+C)

A(B+C)=AB+AC

Answer:

4000

Step-by-step explanation:

Product just means multiply!

40 × 100 = 4000

Answer:

4000

Step-by-step explanation:

40 times 100 is 4000

take the 4 and put the amount of 0's in the equation behind it ( there are 3 in total, 2 from the 100 and 1 from the 40): 4000

Answer:

9/70

Step-by-step explanation:

Given that:

70 students choose to attend one of three after school activities: football, tennis or running.

There are 30 boys. 13 students choose football, of which 9 are girls. 31 students choose tennis. 9 girls choose running.

A student is selected at random.

What is the probability this student chose running?

Since it asking for the probability of this student (randomly select) chose running. And we can see that there are 9 girls choose running.

Therefore, we also know 70 students is the total

Hence, the answer is 9/70

9/70 is in simplest form already.

~lenvy~

Answer:

9/70

Step-by-step explanation:

Important info:

Solution:

Probability of this student (randomly select) chose running. And we can see that there are 9 girls choose running.

Thus, 70 students is the total

Therefore, the answer is 9/70

9/70 can't be simplify.

[RevyBreeze]

Answer:

I dont know

Step-by-step explanation: I hope someone can help you

Answer: 7 hours.

Step-by-step explanation: Randall can assemble 5 race car tracks in an hour and Diggery can assemble 4 race car tracks in an hour.  To see how many hours it takes to make 63 race car tracks, you need to add 5 and 4, since Randall and Diggery are working together.  Both of them combined can make 9 race car tracks in total every hour.  63 can be divided by 9, which is 7.  Therefore, it'll take 7 hours for both of them to make 63 race car tracks.

Let me know if this is right! :)

Answer:

i believe it's 48

Step-by-step explanation:

7x^2 - 3x - 6

7(3)^2 - 3(3) - 6

63 - 9 - 6

54 - 6

48

There would be 413 frozen dinners in the next 16 years.

Let y represent the amount of frozen dinners after x years.

If a certain quantity of money can buy 940 frozen dinners this year, and it decreases by 5% every year, hence:

y = 940(0.95)ˣ

In 16 years:

y = 940(0.95)¹⁶

y = 413.71

There would be 413 frozen dinners in the next 16 years.

Find out more on exponential function at: https://brainly.com/question/12940982

Answer:

D. Graph 4 In an account with 250$ balance that accrues 2% annually, with no deposits or withdrawals, it takes 6 years and 6 months for the balance to be 282$

Step-by-step explanation:

if the balance accrues 2% annually, then that means every year the amount increases by 100% + 2% = 102%

102%= 102/100 = 1.02

if we multiply the balance in the account with 102% or by 1.02 at the beginning of each year we will get the amount accrued at the end of the year

First year: $250 x 1.02 = $260.1

Second year: 260.1 x 1.02 = $265.302

Third year: 265.302 x 1.02 = $270.60802

we can use these points to create a graph that will help us estimate at what year the amount will be 282$

Answer:

D

Step-by-step explanation:

y=6x-20

Hope it helps.

Do comment if you have any query.

Answer:

y = m x + b       is the standard form for a straight line

you have

y = 6 x + b       if m = 6

Now when x = 2, y = -8          this is given

- 8 = 6 * 2 + b       substituting given values

b = -8 - 12 = -20

y = 6 x -20            is the equation requested

Check;

-8 = 6 * 2 - 20      

12 = 12         so this agrees