Use this table to answer the following questions.If the number of gallons of gas is known, can you find the number of gallons consumed? Explain how this value would be calculated.

Answer:

(a)  D = 72.05 dB  (2 d.p.)

(b)  I = 2.51 W/m²  (2 d.p.)

Step-by-step explanation:

Given function:

[tex]\boxed{D(I)=10 \log_{10}(I)+120, \quad I\geq 0}[/tex]

where:

Given:

Substitute the given value of I into the given function and solve for D:

[tex]\begin{aligned}\implies D(1.6 \times 10^{-5}) & =10 \log_{10}(1.6 \times 10^{-5})+120\\& = 10 \log_{10}(0.000016)+120\\& = 10 (-4.795880017)+120\\& = -47.95880017+120\\&=72.04119983\\&=72.04\; \sf dB\;(2\:d.p.)\end{aligned}[/tex]

Given:

Substitute the given value of D into the given function and solve for I:

[tex]\begin{aligned}\implies 124 & =10 \log_{10}(I)+120\\4 & =10 \log_{10}(I)\\10 \log_{10}(I)&=4\\\log_{10}(I)&=0.4\\10^{\log_{10}(I)}&=10^{0.4\\I&=2.511886432\\I&=2.51\; \sf W/m^2\; (2\:d.p.)\end{aligned}[/tex]

The order of the numbers from least to greatest will be 97%, 1.74, 2 4/5, and 18/5.

I rewrite the numbers in equivalent forms, this was illustrated in decimals to make it easier.

From the information, the data set includes the following numbers: eighteen over 5, two and four fifths, 97%, and 1.74. This will be:

18/5 = 3.6

2 4/5 = 2.8

97% = 0.97

1.74

The arrangement will be 97%, 1.74, 2 4/5, and 18/5.

Therefore, it should be noted that rewriting then in decimal is important to effectively convey the information better.

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Answer:

3

Step-by-step explanation:

Question:Two families went to a baseball game. The first family bought 5 pretzels and 4 sodas, which totaled $22. The second family bought 6 pretzels and 6 sodas, which totaled $30. How much did one soda cost? 

first family bout 5 PRETZELS  and 4 SODAS and the second family bought 6 PRETZELS and 6 SODAS
So immanently 5 is wrong because that would be too much and not fit the amount that the families spent
4 is also incorrect because the price is not reasonable it’s to high and out of budget for both of the families

3 is the only right answer also 2 is wrong (wrote this in rush)

Answer:

Step-by-step explanation:

equation: 2x-8=5x

x=-8/3

Main Answer:

Explanation:

Given that,

[tex]\frac{dA}{dt}[/tex] = -4

The surface area of the snow ball = 4π[tex]r^{2}[/tex]

Let the surface area = A

If A denotes the surface area and D the diameter then,

A = 4π[tex]r^{2}[/tex] = 4π[tex](\frac{D}{2} )^{2}[/tex]

⇒ A = π[tex]D^{2}[/tex]

Differentiate with respect to r,

[tex]\frac{dA}{dD}[/tex] = 2πD

By using chain rule,

[tex]\frac{dA}{dD}[/tex] = [tex](\frac{dA}{dt})[/tex][tex](\frac{dt}{dD})[/tex] = [tex]\frac{\frac{dA}{dt}}{\frac{dD}{dt}}[/tex]

⇒ 2πD = [tex]-\frac{4}{\frac{dD}{dt}}[/tex]

∴ [tex]\frac{dD}{dt}[/tex] = [tex]-\frac{4}{2\pi\\D}[/tex]

when D = 9,

[tex]\frac{dD}{dt}[/tex] = [tex]-\frac{4}{18\pi}[/tex]

∴ [tex]\frac{dD}{dt}[/tex] = [tex]-\frac{2}{9\pi}[/tex]

so, the diameter is decreasing at a rate of [tex]\frac{2}{9\pi}[/tex] .

The   BEST advice you can offer so that he can maximize interest is : b Deposit your money as early as possible in an account with the highest interest rate possible.

Compound interest can be defined as the interest a person earn on the money they saved in their account as well as the money earn on the interest the bank gives them which implies that a person tend to earn interest on the money saved and the interest giving on the money saved.

A person can tend to earn more interest when they deposit their money earlier into an account that pay more interest rate as this will enables them to accumulate more interest.

Therefore the correct option is b.

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The complete question is:

Tyreke has $5000 to put into an account that earns compound interest. Which of the following is the BEST advice you can offer so that he can maximize interest?

a. It's ok to open an account with a low interest rates as long as you deposit your money early

b. Deposit your money as early as possible in an account with the highest interest rate possible

c. Wait for interest rates to rise above 5%, otherwise compounding doesn't have any effect

d. Compound interest will not have any effect at such a low dollar amount. Find different opportunities to earn interest on your savings.

Answer:

[tex]\frac{y^{2}}{2x}[/tex]

Step-by-step explanation:

a) simplify

[tex]\frac{y^{2} }{2x}[/tex]

Answer:

ez y² /2x

Step-by-step explanation:

Answer:x+y=36

xy=256

x=256/y

256/y + y = 36

256/y + y²/y = 36y/y

y² - 36y +256 = 0

use the quadratic formula to get 18+2√17 and 18-2√17. ugly numbers but they work!

Step-by-step explanation:

The change to the amount of money she has = $10

what is amount ?

Amount is defined as to add up to a total .the bill for four people at a restaurant that is 50 dollars is an example of the costs of four meals that amount to 50 dollars.

A amount is a number, or quantity of something

she made 6 payments of $4each = 6(4) =$ 20 spent

she got $ 10 back  = 20-10 =$10

the change to the amount of money she has is -$10 because

she has $10 less than she started with

so the change to the amount of money she has $10

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The average speed of the car which travels 3.5 miles in 5 minutes is 42 miles per hour.

Speed is simply referred to as distance traveled per unit time. It is expressed mathematically as;

Speed = Distance ÷ time.

Given the data in the question;

First, we convert unit of the elapsed time from minutes to hours.

Time = 5 min = ( 5/60 )hr = 5/60hr

Now, plug the given values into the speed formula and solve for speed.

Speed = 3.5 ÷ 5/60

Speed = 3.5 × 60/5

Speed = 210/5

Average speed = 42 mph

Therefore, the average speed of the car 42 mph.

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The fraction of the teacups that are either teal or red is 5/6.

Given:

Fraction of teal teacups = 1/6

Fraction of red teacups = 2/3

Fraction of the teacups are either teal or red = Fraction of teal teacups + Fraction of red teacups

= 1/6 + 2/3

= (1+4)/6

= 5/6

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When considering their desire to go outside of their state, 6.94% of people say they would like to attend a festival.

A percentage is what?

A percentage of 100 is represented as a number or ratio known as a percentage.

We've got

Take in a performance Attend a concert and a festival

Remain in state 214 and 186

Travel outside of state 391 and 59

The amount of groups planning to visit a state while attending a concert=214

The amount of groups planning to leave the state to attend a concert=391

The amount of groups planning to visit a state while attending a festival=186

The amount of groups planning to leave the state to attend a festival=59

The proportion of festival-goers that desire to travel outside of their state:

= Total number of groups from all four conditions/ Number of groups wishing to attend an event while remaining outside the state.

= 59 / ( 214 + 391 + 186 + 59 ) x 100

= 59 / 850 x 100

= 6.94%

Therefore, When considering their desire to go outside of their state, 6.94% of people say they would like to attend a festival.

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The expression 1/(2x²) - 7y is not a polynomial because it has a negative exponent

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

A polynomial is an expression that involves only the operations of addition, subtraction, multiplication, and positive exponent powers of variables. If the expression has a negative exponent, it is not a polynomial.

Given:

1/(2x²) - 7y = 0.5x⁻² - 7y

1/(2x²) - 7y is not a polynomial

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Answer: A.)

Step-by-step explanation: if you start at 7 and take 8 away your left with a negative

A is correct purple line to 7 and red line to -1

Hope this helps

6x+26x-10=8(4x+10) quadratic equation has no solution.

First, Simplify the equation:

6x + 26x + (-10) = 8(4x + 10)

Now, reorder the terms:

(-10) + 6x + 26x = 8(4x + 10)

Combine the like terms:

6x + 26x = 32x

-10 + 32x = 8(4x + 10)

Then, reorder the terms:

-10 + 32x = 8(10 + 4x)

-10 + 32x = (10 × 8 + 4x × 8)

-10 + 32x = (80 + 32x)

Add '-32x' to each side of the equation.

-10 + 32x + -32x = 80 + 32x + -32x

Again, Combine like terms:

32x + -32x = 0

-10 + 0 = 80 + 32x + -32x

-10 = 80 + 32x + -32x

Repetitively, Combine like terms:

32x + -32x = 0

-10 = 80 + 0

-10 = 80

After Solving,

-10 = 80

Thus, there is no further variable to solve.

∴ This equation is invalid, the left and right sides are not equal, therefore there is no solution.

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The value of the z-score for the sample mean is estimated as 0.5.

As per the stated question;

The formula for calculating the z-score is;

z = (x - μ)/σ

x = sample size

μ = population mean

σ = standard deviation population.

The vales given in the question;

Substitute the value in the z-score.

z = (35 - 25)/20

z = 10/20

z = 0.5

Thus, the value of the z-score  for the sample mean is estimated as 0.5.

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The correct question is-

Suppose you have a population with mean 25 and standard deviation 20. You take samples of size 100 and consider the distribution of the means of those samples. What is the z-score for the of the sample means for the sample less than 35?.

drebra and William Pierce is hosting a reception at a nearby reception hall to commemorate their 20th anniversary. The number of people are invited in the reception are 104.

Given that,

drebra and William Pierce is hosting a reception at a nearby reception hall to commemorate their 20th anniversary. $3,500 has been set aside for their reception. If the prison's recreation center charges $70 for cleanup and $33 per person.

We have to determine how many guests they can invite while staying inside their budget.

The total budget of the party = $3500

Reception hall charges for clean up =$70

Extra fee per person =$33

Let us assume that the number of people are invited  in the reception are be x.

Given in the question the  be the clean up charge and $33  be fee per person.

We know,

The equation become

⇒ 70 +33x = 3500

33x = 3500-70

33x = 3430

x = 3430/33

x=104

Therefore, The number of people are invited in the reception are 104.

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Answer:

8840

Step-by-step explanation:

10^2=100;

(6.8*100)*(1.3*10)

680*13

8840

Answer:

8.84 × 10³

Step-by-step explanation:

(6.8 × 10²) (1.3 × 10)

(6.8 × 1.3) (10² × 10) = (8.84) (10³)

8.84 × 10³

The length of a diagonal will be 109 cm.

What is Rectangle?

A rectangle is a quadrilateral that has parallel sides equal to each other and all the four angles are equal to 90 degrees.

Given that;

Length of a rectangle = 60 cm

Width of a rectangle = 91 cm

Now,

Since, We know that;

Diagonal of a rectangle (D) = √Length² + Width²

Substitute all the values we get;

Diagonal of a rectangle (D) = √Length² + Width²

                                         = √60² + 91²

                                         = √3600 + 8,281

                                         = √11,881

                                         = 109

So, Diagonal of a rectangle = 109 cm.

Thus, The length of a diagonal will be 109 cm.

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Moving counterclockwise around the rectangle, the labels and coordinates of the other  vertices are; E'(6, 8), C'(10, 10), T'(0, 10)

I have drawn an image of the given triangle RECT and attached it.

The length is 10 units and width is 6 units.

From the image of the triangle, we see that the coordinates are;

R(0, 0), E(10, 0), C(10, 6), T(0, 6)

Now, we are told that moving counterclockwise around the rectangle, and after rotation, we will now have the transformations as;

R'(0, 0), E'(6, 8), C'(10, 10), T'(0, 10)

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-1/16 meters per minute is the rate of change of an edge.

So, the Volume of the cube: V = r³

Differentiate with respect to t (time) as follows:

dV/dt = -3 : Cubic meters per minute

Now, substitute the values:

Therefore, -1/16 meters per minute is the rate of change of an edge.

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Answer:

A. {2.82, √8, √11, 3 1/2}

Step-by-step explanation:

A. {2.82, 2.83, 3.32, 3.5}

√8 = 2.82842712475 or 2.83 when rounded to the nearest hundredth.

√11 = 3.31662479036 or 3.32 when rounded to the nearest hundredth.

To find the square root you multiply a factor of a number by itself in order to get that number.

3 1/2, or 7/2 = 3.5

To convert a fraction into a decimal you divide the numerator by denominator.

B. {2.24, -2.45, 2.5, -3}
√5 = 2.2360679775 or 2.24 when rounded to the nearest hundredth.

-√6 = -2.44948974278 or -2.45 when rounded to the nearest hundredth.

2 1/2, or 5/2 = 2.5

C. {-4, -4.12, -4.24, -4.36}

-√16 = -4

-√17 = -4.12310562562 or -4.12 when rounded to the nearest hundredth.

-√18 = -4.24264068712 or -4.24 when rounded to the nearest hundredth.

-√19 = -4.35889894354 or -4.36 when rounded to the nearest hundredth.

D. {3.16, 4, 2, 1.5}
√10 = 3.16227766017 or 3.16 when rounded to the nearest hundredth

√4 = 2

Answer:

Step-by-step explanation:

Answer:

a,b,coeiiggjfj

jrjjunr

Answer:

Yeah

Step-by-step explanation:

but i can also do it in opposite

The rate of the area of the circle, expressed in terms of the circumference C, is 0.1C square centimeters per second.

What is known as a circle?

C=2πr

A=πr²

dA/dr=2πr=C

dr/dt=-0.1 cm/sec

      dA/dt

= dA/dr * dr/dt

= 2πr (-0.1) cm²/s

= -0.1C cm²/s

As a result, a circle's radius is reducing at a steady rate of 0.1 centimeters each second. The rate of the area of the circle, expressed in terms of the circumference C, is 0.1C square centimeters per second.

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Answer:

13, 21, 34, 55, 89 are the next five numbers in the sequence.

Step-by-step explanation:

It's known as the Fibonacci sequence. Every term is the sum of the previous two. If you add the terms of the sequence then the result of each of the sums will form a sequence as well. For this sequence 1+1=2, 2+3=5, 5+3=8, 8+5=13, 13+8=21, 21+13=34, 34+21=55, 55+34=89 and so on.