Write an exponential decay function in the form f(x)=ab^x for each of Car A and Car B. Explain how you determined the value of b for each function.

Answer: 41 miles per gallon

Step-by-step explanation: Divide 256 by 6 and you get 41

The solution for y and x in the expressions given as 2/5(10y-5) =2y + -10 and x − 3.28 = −5.34 are y = 6 and x = -2.06, respectively

Variable y

From the question, the algebraic expression is given as

2/5(10y-5) =2y + -10

Open the brackets

This gives

4y - 2 = 2y + -10

Collect the like terms in the above equation

So, we have the following representation

4y - 2y = 10 + 2

Evaluate the like terms

2y = 12

Divide by 2

y = 6

Variable x

Here, we have

x − 3.28 = −5.34

There is a constant to add to or subtract from the expression

So, we add 3.28 to both sides

x = 3.28 − 5.34

Evaluate the like terms

x = -2.06

Hence, the solution is x = -2.06

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a) Refer to the attachment for graph:

The ellipse in counter clockwise direction starting from the point (1,0)

b) Cartesian equation for a curve that contains the parametrized curve is

  x²+ y/4=1

What are trigonometric expressions?

Trigonometric identities are, by definition, reciprocal. These formulas show the connections between the sine/cosine functions and tangents.

a) Given: x= cost , y= 2 sin t,  0<t≤2π

y= 2 sin t,

sin t= y/2

we know that,

cos²t + sin²t=1

x²+ y/4=1

b)  The point (x,y) moves on the ellipse x²+ y/4=1

   t increases from 0 to 2π.  The point (x,y)  moves around the ellipse around the ellipse in counter clockwise direction starting from the point (1,0)

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Step-by-step explanation:

The lengths of the sides of the rectangular field should be 40 ft (smaller value) and 60 ft (larger value) respectively.

Let L = length of rectangle area and W = width of rectangle area.

Let the length of the side that divides the area be parallel to the width of the area.

The total length of fencing F = 2L + 2W + W

F = 2L + 3W

Since the area is a rectangle, its area is A = LW

Since the area = 2400 square feet,

LW  = 2400 ft²

So, L = 2400/W

Substituting L into F, we have

F = 2L + 3W

F = 2(2400/W) + 3W

F = 4800/W + 3W

To find the value at which F is minimum, we differentiate F with respect to W.

So, dF/dW = d(4800/W + 3W)/dW

dF/dW = -4800/W² + 3

Equating dF/dW to zero, we have

-4800/W² + 3 = 0

-4800/W² = - 3

W² = -4800/-3

W² = 1600

W = √1600

W = 40 ft

To determine if this is a value that gives minimum F, we differentiate F twice to get

d²F/dW² = d(-4800/W² + 3)/dW

d²F/dW² = 14400/W³ + 0

d²F/dW² = 14400/W³

substituting W = 40 into the equation, we have

d²F/dW² = 14400/(40)³

d²F/dW² = 14400/64000

d²F/dW² = 0.225

Since d²F/dW² = 0.225 > 0, W = 40 is a minimum point for F

Since L = 2400/W

So, L = 2400/40

L = 60 ft

So, the lengths of the sides of the rectangular field should be 40 ft (smaller value) and 60 ft (larger value) respectively.

Step-by-step explanation:

for every x change by +1, y changes by -3.

so, the slope is

-3/1 = -3

Answer:

-3

Step-by-step explanation:

I hope it helps :]

Answer: florist a is cheaper than florist b

Step-by-step explanation: the price of florist B's flowers are 5.20$ more than florist A's

The equation which represents the population, P after t months is:

y = 1600(1+ 0.25)^t.

Given,

A population of beetles grows by 25% every month.

the beetle population starts with 1,600 beetles,

we are asked to determine the equation which represents the population, P after t months.

The equation for the population is:

Pf = Pi(1-r)^t

where pf = final value

pi = initial value

r = growth factor

t = time in years.

substitute the values in the equations.

let y represent the final population after t years.

r = 25%

convert percentage to decimal.

r = 0.25

y = 1600(1+ 0.25)^t

Hence we get the required answer.

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Answer:

Step-by-step explanation:

or

Answer:

[tex]\left(\dfrac{12}{5}\right)^2=\left(2\frac{2}{5}\right)^2[/tex]

Step-by-step explanation:

Given mixed number:

[tex]5 \frac{19}{25}[/tex]

Rewrite the given mixed number as an improper fraction:

[tex]\implies 5 \frac{19}{25}=\dfrac{5 \times 25+19}{25}=\dfrac{125+19}{25}=\dfrac{144}{25}[/tex]

Rewrite 144 as 12² and 25 as 5²:

[tex]\implies \dfrac{144}{25}=\dfrac{12^2}{5^2}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^c}{b^c}=\left(\dfrac{a}{b}\right)^c:[/tex]

[tex]\implies \dfrac{12^2}{5^2}=\left(\dfrac{12}{5}\right)^2[/tex]

Convert 12/5 to a mixed number:

[tex]\implies \left(\dfrac{12}{5}\right)^2=\left(\dfrac{10+2}{5}\right)^2=\left(\dfrac{10}{5}+\dfrac{2}{5}\right)^2=\left(2\frac{2}{5}\right)^2[/tex]

The expression that can be used to find the change in temperature each hour would be 27 h.

It is given that the temperature dropped 27°F in h hours. The temperature dropped the same number of degrees each hour.

We have to find the change in temperature each hour.

We can express this mathematically:

27 h

Then the equation would be 27 h.

Therefore, The temperature dropped the same number of degrees each hour would be 27 h.

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Using the concepts of Application of derivative, we got that 1657.92inches³/sec rate  of the  volume of the cone changing when the radius is 40 inches and the height is 40 inches for a right circular cone.

We know that volume of right circular cone is given by =(1/3πr²h)

We are given rate of change of radius(dr/dt) and rate of change of the height(dh/dt)

Therefore ,differentiating the volume with respect to time and applying the chain rule.

dV/dt = [(1/3)πr²×(dh/dt)+ (1/3)π·2·r·(dr/dt)·h]

=>dV/dt=[(1/3)× π×r × [(r×dh/dt)+2h×(dr/dt)]]

We are given that dr/dt=2inc/sec and dh/dt= -5inc/sec

So, on putting the values, we get

=>dV/dt=[ ( (1/3)×3.14×40)×[40×(-5)+2×40×2]]

=>dV/dt=[0.33×3.14×40×[-200+160]

=>dV/dt=[0.33×3.14×40×(-40)]

=>dV/dt= -1657.92inches³/sec(negative sign denote volume is decreasing)

Hence, if the radius of a right circular cone is increasing at the rate of 2 inches per second and its height is decreasing at the rate of 5 inches per second.  the rate of  the volume of the cone changing when the radius is 40 inches and the height is 40 inches is 1657.92inches³/sec.

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The perimeter of the rectangle is 16 feet.

The correct answer is an option (C)

In this question, the length of the rectangle is,

l = 1 yard 2 feet 1 inch

l = 3 feet + 2 feet + 0.0833 feet

l = 5.0833 feet

And the width of the rectangle is,

w = 2 feet 11 inches

w = 2 feet + 0.9167 feet

w = 2.9167 feet

So, the perimeter of the rectangle would be,

P = 2(l + w)

P = 2 * (5.0833 + 2.9167)

P = 16 feet

Therefore, the perimeter of the rectangle is 16 feet.

The correct answer is an option (C)

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If the chemistry club wants to spend at most $88.20 on renting the meeting room. The possible amounts of time for which they could rent the meeting room is 8.

Let t represent  the number of hours the meeting room is rented

Formulate an inequality and use the inequality to find the time

37 + 6.40t < 88.20

Combine like terms

6.40t < 88.20 - 37

6.40t < 51.20

Divide both side by 6.40t

t = 51.20 /6.40

t < 8

Therefore the time is 8.

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Answer: maybe

12

Step-by-step explanation:

the answer is 12

Answer:

Step-by-step explanation:

Its the last two and the first one

Answer:

5

Step-by-step explanation:

Answer:

The answer for the question is five!

The probability that a pupil selected uses the tennis courts only is the fraction 11/50 or 0.22

The probability of an event occurring is the ratio of the number of required outcome divided by the total number of possible outcomes.

From the question,

The pupils that uses only tennis courts = 92 - (30+19+10) { where 30 is the number of pupils that uses all three, 19 is the number of pupils that uses only swimming pool and 10 is the number of pupils that uses only gym and tennis court}

The pupils that uses only Tennis courts = 92 - 59

The pupils that uses only Tennis courts = 33

The probability of selecting a pupil who uses only the tennis court = 33/150

Therefore by simplification, the probability that only a pupil selected uses only the tennis court is the fraction 11/50

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The probability the mean of his sample will be between $45.00 and $65.00 is 0.6826.

Given:

A delivery driver has an average daily gasoline expense of $55.00. the standard deviation is $10.00. the owner takes a sample of 54 bills.

n = 54

standard error = 10/[tex]\sqrt{54}[/tex]

= 2.205

when x = 45,

z score = 45 - 55 / 10

= -10/10

= -1

probability at z = -1 is 0.3413

z score for x = 65

z = 65 - 55 / 10

= 10/10

= 1

probability at z = 1 is 0.3413

Total probability = 0.3413+0.3413

= 0.6826

Therefore the probability the mean of his sample will be between $45.00 and $65.00 is 0.6826.

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Answer:

Step-by-step explanation:

m just means measure. So the question is asking you what is the MEASURE of the ANGLE AEB.

Since angles AEB and CED are vertical angles, you can set the two expressions equal to each other and solve for X.

1) 3x + 54 = 7x - 30

2) 54 = 4x - 30

3) 84 = 4x

4) x = 21

3(21) + 54 = 117

m∠AEB = 117°

Raja can make 7 perfume samples from a 2.8 ounce bottle of perfume.

According to the question,

We have the following information:

Raja manages a perfume store. She makes 0.4-ounce samples from a 2.8- ounce bottle of perfume.

So, we have the following expressions:

1 bottle of perfume sample = 0.4 ounce

Total ounces of perfume in the bottle = 2.8 ounce

Now, we can easily find the number of perfume samples that can be made from this perfume by dividing the total ounces of perfume in bottle by the ounces of perfume sample.

Number of perfume samples = 2.8/0.4

Number of perfume samples = 7

Hence, Raja can make 7 perfume samples from a 2.8 ounce bottle of perfume.

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The equation of the transformed function is f(x)= -1/3[tex]\sqrt{2(x-6)}[/tex] -3.

Given that,

The f(x) = square root of X base function is transformed by a reflection in the x-axis, a vertical stretch by a factor of 3, a horizontal compression by a factor of 1/2, a vertical translation by a factor of 3, a vertical translation by a factor of 3 down, and then a horizontal translation by a factor of 6 right.

We have to verify the changed function's equation.

Take the function

f(x)=√x

The function reflection in the x-axis,

f(x)=-√x

The function is vertical stretch by a factor of 3.

f(x)= -1/3√x

The function is horizontal compression by a factor of 1/2.

f(x)= -1/3[tex]\sqrt{2x}[/tex]

The function is vertical translation by a factor of 3 down,

f(x)=  -1/3[tex]\sqrt{2x}[/tex] -3

The function is horizontal translation by a factor of 6 right.

f(x)= -1/3[tex]\sqrt{2(x-6)}[/tex] -3

Therefore, The equation of the transformed function is f(x)= -1/3[tex]\sqrt{2(x-6)}[/tex] -3.

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The value of the expression will be;

⇒ 4

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 2 - [(2 + 10(−1) ÷ 2) + 1]

Now,

Solve the expression by using BODMAS rule as;

The expression is,

⇒ 2 - [(2 + 10(−1) ÷ 2) + 1]

⇒ 2 - [ (2 - 10 ÷ 2) + 1 ]

⇒ 2 - [(2 - 5) + 1 ]

⇒ 2 - [ - 3 + 1 ]

⇒ 2 - { - 2 ]

⇒ 2 + 2

⇒ 4

Thus, The value of the expression will be;

⇒ 4

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The equivalent expression to 17g-2g will be (17-2)g.

According to the question,

We have the following expression:

17g-2g

Now, we can simplify this expression easily to find the equivalent expression.

So, our first step will be to take g as a common factor from both the terms. Now, we have the following expression:

(Note that the common factor means that the variable or the number taken as a common factor should be able to divide the terms given in the expression.)

(17-2)g

Now, this can be solved further because 2 can be subtracted from 17 because they both are integers without any variable.

Hence, the correct option is C.

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The annual interest rate is 1.2%

The principal amount = $425

The total interest her earned = $10.20

The final amount = 425 + 10.20

= $435.2

Time period = 2 years

The simple interest

A = P(1 + rt)

Where A is the final amount

P is principal amount

r is the interest rate

t is the time period

Substitute the values in the equation

435.2 = 425(1 + r×2)

1 + 2r = 435.2 / 425

Divide the terms

1 + 2r = 1.024

2r = 1.024 - 1

2r = 0.024

r = 0.024/2

Divide the terms

r = 0.012

Then the percentage will be

r = 1.2%

Hence, the annual interest rate is 1.2%

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Answer:x=5, y=-4

Step-by-step explanation:2x+9y = -26

-3x-7y = 13

Multiply the first equation by 3

3(2x+9y = -26)

6x +27y = -78

Multiply the second equation by 2

2(-3x-7y = 13)

-6x -14y = 26

Add these two equations together

6x +27y = -78

-6x -14y = 26

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

13y = -52

Divide by 13

13y/13 = -52/13

y = -4

Now we need to find x

2x+9y = -26

2x+9(-4) = -26

2x-36=-26

Add 36 to each side

2x-36+36 = -26+36

2x=10

Divide by 2

2x/2 =10/2

x=5

The evaluation of the inverse of the function, f(x) = -0.086·x + 2.92 are;

a. The inverse of the function is f⁻¹(x)  = -11.63·x + 33.95

B. The inverse function gives the number of year after 2000 when the percentage of children taking antidepressants is equal to x

b. The percentage of children taking antidepressant is 2.3% in 2007

The inverse of a function is a function that gives the input from the output such that it undoes the function's effect.

The function that indicates the percentage of children taking that take antidepressants from from the year 2004 to the year 2009 is presented as follows;

f(x) = -0.086·x + 2.92

x = The number of years after the year 2000

The inverse of the function can be obtained by making x the subject of the function formula as follows;

f(x) = -0.086·x + 2.92

f(x) - 2.92 = -0.086·x

x = (f(x) - 2.92)/(-0.086) ≈ -11.63·f(x) + 33.95

x  ≈ -11.63·f(x) + 33.95

Which through plugging in f⁻¹(x) = x, and f(x) = x,

Indicates;

f⁻¹(x) = -11.63·x + 33.95

In the inverse function, the argument is the percentage, while the output is the number of years, f⁻¹(x)

When x = 2.3,

f⁻¹(2.3) = -11.63×2.3 + 33.95 ≈ 7.2

The inverse when the percentage is 2.3% is 7.2 years

a. The inverse function is f⁻¹(x) = -11.63·x + 33.95

The output of the inverse function represents the number of years since 2000 when the percentage of the children taking antidepressants is x. The correct option is option B

b. The year in which the number of children taking antidepressant equals 2.3% is 2,000 + 7 = 2007

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Answer:30

Step-by-step explanation:6 times 4 is24 and to the nearest 100 it will be 30

According to the given standard deviation, the bag that the student brought has more than 1 gram of potato chip than the average chip bag.

Standard deviation:

Standard deviation refers the measure of how scattered the data is in relation to the mean.

Given,

The student wanted to know if the bags of potato chips they were buying contained the correct weight of chips compared to the listed weight on the bag of 42.5 grams.

And the student collected a sample of 30 bags of chips and weighed each bag. Here the average weight of the bags they collected was 41 grams with a standard deviation of 1.6 grams. assume a 95% level of confidence.

Now, we have to find the confidence interval for this situation.

From, the given details, we have obtained the following things,

Bag weight = 42.5 gram

Number of samples = 30

Average weight = 41 grams

Standard deviation = 1.6 grams

Confidence level = 95%

So, according to the formula of confidence interval,

The value of it is calculated as,

=> CI = x ±  Z × s / √n

When we apply the values on the formula, then we get,

=> CI = 41 ± 1.9600 × 1.6 / √30

=> CI = 41 ± 0.573

Therefore, Confidence Interval 41 ±0.573 (±1.4%) [40.427 – 41.573].

While we compare this one with the given bag weight we get the difference of,

=> 42.5 - 41.5

=> 1

Therefore, the bag that the student brought has more than 1 gram of potato chip than the average chip bag.

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Answer:

4: The factors had the same sign

Step-by-step explanation:

They are both positive (i think)

1. The first figure posses the SSS property.

2. The second figure posses the ASA property.

3. The third figure posses the hypotenuse length property.

4. The fourth figure posses the SAS property.

Given:

1. The first figure shows the SSS property.

Side-Side-Side criterion is referred to as the SSS criterion. According to this standard, two triangles are congruent if their respective triangles' three sides are equal to one another.

hence the two triangles are congruent.

2. The second figure posses the ASA property.

Angle-Side-Angle criterion is also known as ASA criterion. According to the ASA criterion, two triangles are congruent if any two of their included sides and related angles are equivalent in size to those of the other triangle.

hence the two triangles are congruent.

3. The third figure posses the hypotenuse length properety.

RHS criterion stands for right angle-hypotenuse-side congruence criterion. Under this criterion, two triangles are congruent, if the hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle.

hence the two triangles are congruent.

4. The fourth figure posses the SAS property.

Side-Angle-Side criterion is referred to as the SAS criterion. According to this standard, two triangles are said to be congruent if their matching sides and included angles are the same on each side of each other.

hence the two triangles are congruent.

Hence we get the required answer.

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