danica drove her new car on a trip for a whole number of hours, averaging $55$ miles per hour. at the beginning of the trip, $abc$ miles was displayed on the odometer, where $abc$ is a $3$-digit number with $a\ge1$ and $a b c\le7$. at the end of the trip, the odometer showed $cba$ miles. what is $a^2 b^2 c^2$?

Answer: £102.60

Step-by-step explanation:

79165-78937=228

228x45=10260

10260/100=102.60

[tex]D:\dfrac{4000}{x} > 0 \wedge x\not =0\\D:x > 0\\\\\\\log\left(\dfrac{4000}{x}\right)=3\\\e^3=\dfrac{4000}{x}\\\\x=\dfrac{4000}{e^3}[/tex]

this equation is only valid at the point (a, b) where we found the slope of the normal line. To find the equation of the normal line at a different point, we would need to repeat this process with new values of a and b.

To find the equation of the line normal (perpendicular) to the graph of y = x^3 + 3x^2 + 7x - 1 at a point (a, b), we need to determine the slope of the normal line at that point.

The slope of the tangent line to the curve at (a, b) is given by the derivative:

f'(x) = 3x^2 + 6x + 7

So the slope of the tangent line at x = a is:

m = f'(a) = 3a^2 + 6a + 7

The slope of the normal line is the negative reciprocal of the slope of the tangent line, so:

m_n = -1/m = -1/(3a^2 + 6a + 7)

Now we have the slope of the normal line at (a, b), and we just need to find the equation of the line in point-slope form, using the point (a, b):

y - b = m_n(x - a)

Substituting the expression for m_n, we get:

y - b = (-1)/(3a^2 + 6a + 7)(x - a)

Multiplying both sides by 3a^2 + 6a + 7 to eliminate the fraction, we get:

(3a^2 + 6a + 7)(y - b) = -(x - a)

Expanding and rearranging, we get the equation of the line normal to the graph of y = x^3 + 3x^2 + 7x - 1 at (a, b):

(3a^2 + 6a + 7)y = -x + (3a^2 + 6a + 7)b + a

To know more about slope visit:

brainly.com/question/3605446

#SPJ11

It will cost approximately $1,715.20 to carpet a room with 360 square feet of floor area, assuming the carpet costs $42.88 per square yard.

To calculate the cost of carpeting a room with a floor area of 360 square feet, we need to convert the area into square yards and then multiply it by the cost per square yard.

There are 9 square feet in a square yard (1 square yard = 3 feet x 3 feet = 9 square feet). Therefore, the room's floor area in square yards is:

360 square feet / 9 = 40 square yards

Next, we multiply the area (40 square yards) by the cost per square yard ($42.88) to find the total cost of carpeting the room:

Total cost = 40 square yards * $42.88 per square yard

Calculating this gives us the final result:

Total cost = $1,715.20

Know more about cost here;

https://brainly.com/question/14566816

#SPJ11

Answer:

D. 42

Step-by-step explanation:

y=4x+10

substitute x=8

y=4(8)+10

y=32+10=42

Answer:

The answer is 42 cyclists

Step-by-step explanation:

y=4x+10

where,x=Temperature

y=cyclists

y=4x+10;when x=10

Y=4×8+10

y=32+10

y=42

The quadratic function is defined as follows:

p(x) = 2(x - 3)² - 1.

The quadratic function of vertex(h,k) is given by the rule presented as follows:

y = a(x - h)² + k

In which:

The vertex is the turning point of the quadratic function, where it changes from decreasing to increasing or vice-versa, hence it's coordinates are given as follows:

(3,-1).

Then:

p(x) = a(x - 3)² - 1.

When x = 0, p(x) = 17, hence the leading coefficient a is obtained as follows:

17 = 9a - 1

9a = 18

a = 2.

Hence the equation is:

p(x) = 2(x - 3)² - 1.

More can be learned about quadratic functions at https://brainly.com/question/31895757

#SPJ1

Answer:

I believe it would be 3/10 simplified, 30/100 not simplified

Step-by-step explanation:

because it is 30%, 30% in a fraction form is 3/10, or 30/100

Answer:

8 meters

Step-by-step explanation:

4(16)=64

They have the same area so the area of the square is also 64.

x^2=64

x=8

The statement to be proved is that if (an)[infinity]n=1 is a bounded sequence and (bn)[infinity]n=1 converges to 0, then (anbn)[infinity]n=1 converges to 0 as well.

To prove this statement, we can use the squeeze theorem. Let M be a bound for the sequence (an)[infinity]n=1, i.e., |an| <= M for all n. Since (bn)[infinity]n=1 converges to 0, for any ε > 0, there exists an integer N such that |bn| < ε/M for all n ≥ N.

Now, for any n ≥ N, we have

|anbn| = |an||bn| ≤ M|bn| < ε,

where we used the fact that |an| ≤ M. This shows that (anbn)[infinity]n=1 converges to 0 as well, since the absolute value of each term is bounded by ε for n ≥ N.

In other words, we have shown that for any ε > 0, there exists an integer N such that |anbn - 0| < ε for all n ≥ N. This is the definition of convergence to 0, and so we have proven that (anbn)[infinity]n=1 converges to 0.

To learn more about converges click here, brainly.com/question/29258536

#SPJ11

The value of the interquartile range (IQR) of their scores is,

Interquartile range = 25

Since, WE know that;

A box plot is the 5 -number summary of the set of data.

And, 5 -number summary is name as, the first quartile, median, third quartile, minimum, and maximum.

We have to given that;

The box pot shows the points for the Houston Rockets scored last season.

Now, From given box plot,

First Interquartile = 65

Third Interquartile = 90

Hence, The interquartile range (IQR) of their scores is, difference between Third Interquartile and first Interquartile.

So, We can formulate;

Interquartile range = Third Interquartile - First Interquartile

Substitute the given values, we get;

Interquartile range = 90 - 65

Interquartile range= 25

Therefore, We get;

The interquartile range (IQR) of their scores is,

Interquartile range= 25

Which is difference between Third Interquartile and first Interquartile.

Learn more about  interquartile range ( IQR ) visit:

brainly.com/question/4102829

#SPJ1

Answer:

8.4

Step-by-step explanation:

C^2-B^2=A^2

12.3^2=151.29

9^2=81

151.29-81=70.29

square root of 70.29

is 8.38

Rounded to the nearest tenth is

8.4 or B

Answer:

The additive inverse of A is -A. So, the additive inverse of A = [p q] is -A = [-p -q].

Here's how we can find the additive inverse of a matrix:

Find the additive inverse of each element in the matrix.

Replace each element in the matrix with its additive inverse.

For example, the additive inverse of p is -p. So, the additive inverse of the first element in A is -p.

The additive inverse of q is -q. So, the additive inverse of the second element in A is -q.

Plugging in these values, we get the following:

Additive inverse of A = [-p -q]

Step-by-step explanation:

Mathis's rate of return on his investment of $1,000 in a mutual fund that sold for $1,250, including taxes, inflation, and administrative costs of $8 was 24.2%.

The rate of return represents the percentage of the net gain an investment generates.

The rate of return is determined using the quotient of the division operation between the return and the initial investment.

The return or net return is the difference between the final value and the initial value after taking into account taxes, inflation, and other administrative costs.

The initial investment = $1,000

The final sales value = $1,250

Taxes, inflation, and other costs = $8

Net sales proceeds = $1,242 ($1,250 - $8)

Returns = $242 ($1,242 - $1,000)

Rate of return = 24.2% ($242 ÷ $1,000 x 100)

Learn more about the rate of return at https://brainly.com/question/3578105.

#SPJ1

The domain to plot the growth function is 0 ≤ x < 7

Given that

f(d) = 11(1.01)ᵇ

When the radius is approximately 1179 mm

We have

11(1.01)ᵇ = 11.79

Divide

(1.01)ᵇ = 1.072

Take the logarithm

d = log(1.072)/log(1.01)

Evaluate

d = 6.99

So, the reasonable domain is 0 ≤ x < 7

Here, we have

f(d) = 11(1.01)ᵇ

The y-intercept is 11

This means tha the initial radius of the algae is 11 mm

For the average rate, we have

f(7) = 11(1.01)⁷ = 11.79

f(2) = 11(1.01)² = 11.22

So, we have

Rate  = (11.22 - 11.79)/(2 - 7)

Evaluate

Rate  = 0.114

So, the average rate of change from day 2 to day 7 is 0.114 mm per day

Read more about exponential functions at

https://brainly.com/question/2456547

#SPJ1

Answer:

Step-by-step explanation:

Your welcome

The solution is, in the drop down activity, you should listen to each sentence and determine whether the verb is a form of "ser" or "ir" based on the context and conjugation of the verb.

The verb "ser" means "to be" and is used to describe characteristics, professions, and origins. The verb "ir" means "to go" and is used to indicate movement or direction. To determine whether a verb in a sentence is a form of "ser" or "ir", you should look at the context of the sentence and the conjugation of the verb. If the verb is conjugated in a way that indicates it is a form of "ser", then it is likely a form of "ser". If the verb is conjugated in a way that indicates it is a form of "ir", then it is likely a form of "ir".

For example, in the sentence "Ella es bonita" (She is pretty), the verb "es" is a form of "ser" because it is used to describe a characteristic. In the sentence "Voy a la playa" (I'm going to the beach), the verb "voy" is a form of "ir" because it is used to indicate movement or direction.

In conclusion, to answer the questions in the drop down activity, you should listen to each sentence and determine whether the verb is a form of "ser" or "ir" based on the context and conjugation of the verb.

See more about verb in:

brainly.com/question/1718605

#SPJ1

complete question:

1 - escogerdrop down activity 1 attempt left listen to each sentence and indicate whether the verb is a form of ser or ir. questions

Approximately 32.14% of the renters do not keep a pet.

We know that there are 28 units in the apartment complex. Out of these, 19 renters keep a pet. To calculate the number of renters who do not keep a pet, we subtract the number of renters with pets (19) from the total number of renters (28):

Number of renters without pets = Total number of renters - Number of renters with pets

Number of renters without pets = 28 - 19

Number of renters without pets = 9

Now that we have the number of renters without pets (9), we can calculate the percentage of renters who do not keep a pet. To do this, we divide the number of renters without pets by the total number of renters and multiply by 100:

Percentage of renters without pets = (Number of renters without pets / Total number of renters) × 100

Percentage of renters without pets = (9 / 28) × 100

Percentage of renters without pets ≈ 32.14%

Therefore, approximately 32.14% of the renters in the apartment complex do not keep a pet.

To know more about percentage here

https://brainly.com/question/13729841

#SPJ4

The radius of the cone to the nearest inch is equal to 8.0 inches.

In Mathematics and Geometry, the surface area (SA) of a cone can be calculated by using this mathematical expression:

Surface area (SA) of a cone = πr(l + r)

Where:

By substituting the given parameters into the formula for the surface area (SA) of a cone, we have the following;

364 = 3.14 × r(6.5 + r)

115.92 = 6.5r + r²

r² + 6.5r + 115.92 = 0

By solving the quadratic function, we have:

Radius, r = (-20.41 + √4988.4081)/6.28

Radius, r = 7.9966 ≈ 8.0 inches.

Read more on surface area here: brainly.com/question/27812847

#SPJ1

when k = 4, the function x + k/x will have a relative maximum at x = -2.

To find the value of k that will make x+k/x have a relative maximum at x=-2, we can use the first derivative test.

First, we find the derivative of x+k/x with respect to x:

f'(x) = 1 - k/x^2

Next, we set x = -2 and solve for k to make f'(-2) = 0:

f'(-2) = 1 - k/(-2)^2 = 1 - k/4

1 - k/4 = 0

k = 4

what is derivative?

A derivative is a mathematical concept that represents the rate at which a function changes over time or space. It is the slope of a tangent line to a curve at a particular point.

In other words, the derivative of a function f(x) at a point x=a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim[h→0] [f(a+h) - f(a)]/h

The derivative gives us information about how quickly the function is changing at a specific point.

To know more about derivative visit:

brainly.com/question/29144258

#SPJ11

Answer:

1111 in binary is 10001010111. Unlike the decimal number system where we use the digits 0 to 9 to represent a number, in a binary system, we use only 2 digits that are 0 and 1 (bits).

One possible transformation is a reflection in the x-axis followed by a dilation centered at the origin with a scale factor of 3.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

Before the dilation, the figure was reflected from the first quadrant to the second quadrant, which is a lateral reflection, hence the figure was reflected over the x-axis.

The height of the blue triangle is of 1 unit, while the height of the larger triangle is of 3 units, hence the scale factor is given as follows:

k = 3/1

k = 3.

More can be learned about dilation at brainly.com/question/3457976

#SPJ1

The dimension of the new picture frame is around 51.49 cm by 61.49 cm in size.

Given that,

The measure of rectangular  picture = 20 cm x 30 cm

And the resulting enclosed area = 1064 cm²

Let the length of each side = x

Therefore,

The new rectangular frame will have dimensions = 20 cm + x, 30 cm + x

The new rectangular frame's surface area is:

= (20 + x) x (30 + x).

Since area is given,

So that we can create an equation:  1064 = (20 cm + x) x (30 cm + x)

Increasing the brackets results in: 600 + 50x + x² = 1064

Organizing and making it simpler: x² + 50x - 464 = 0.

By using quadratic formula,

x = (-50 ± 174.96) / 2

Neglecting the undesirable outcome,

x = 62.98 / 2 x = 31.49

Consequently, each side length has increased by around 31.49 cm.

Use this value to determine the new rectangular frame's dimensions:

Length is equal to 20 + 31.49 = 51.49 cm.

Width is equal to 30 + 31.49 = 61.49 cm.

Consequently, the new picture frame is around 51.49 cm by 61.49 cm in size.

Learn more about the rectangle visit:

https://brainly.com/question/2607596

#SPJ1

The coordinates of the point on the graph are (0, -7).

We have,

The concept being used here is the Cartesian coordinate system, which is a system for representing points in a two-dimensional space.

In this system, each point is described by an ordered pair (x, y), where x represents the position along the horizontal x-axis, and y represents the position along the vertical y-axis.

The coordinates are always in an ordered pair.

i.e

(x, y)

Where x is the value of the x-axis and y is the value of the y-axis.

We see that,

The point lies in (0, -7)

Thus,

The coordinates of the point on the graph are (0, -7).

Learn more about coordinates here:

https://brainly.com/question/13118993

#SPJ1

Answer:

 can be written as  without exponent.Given:To find:Write the given expression without exponent.Solution:Formula to be used:Step 1:Write the expanded form of given expression.Step 2:simplifyorThus, can be written as 125×y×y×y without exponent.Learn more:1) Let us simplify some more questions using the exponent rules. (i) (ii) ... brainly.in/question/196047402) find ( 46656)power of -1/6 brainly.in/question/4383230

Answer: 5y³ can be written without using exponents as 5y multiplied by itself three times:

5y × 5y × 5y

Alternatively, we can also write it as:

5 × y × y × y

The inequality is a < 10

Given that a number a is no more than 10, we need to find the inequality, showing the inequality,

Inequalities are the mathematical expressions in which both sides are not equal.

In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

For example = Olivia is selected in the 12U Softball. How old is Olivia? You don't know the age of Olivia, because it doesn't say "equals". But you do know her age should be less than or equal to 12, so it can be written as Olivia's Age ≤ 12.

This is a practical scenario related to inequalities.

So, the inequality will be =

a < 10

Plotting the inequality,

(check the file attached)

Learn more about inequality click;

brainly.com/question/30231190

#SPJ1

The method used to determine the probability that a football team will win the next game is subjective.

The subjective method involves relying on personal judgment, experience, or expert opinion to estimate the probability of an event. In this case, the sports analyst has assessed various factors such as team performance, player injuries, historical data, and other relevant information to form their subjective opinion that the team's probability of winning is 0.37.

This method is based on the analyst's subjective assessment and may vary from one analyst to another. It does not involve any formal calculations or statistical techniques. The probability estimate is derived from the individual's knowledge, expertise, and perception of the situation.

It's important to note that subjective probabilities can be influenced by biases or personal opinions, and they may not always accurately reflect the true probability of an event. However, they can provide valuable insights and serve as a useful starting point for decision-making or further analysis.

Know more about probability here:

https://brainly.com/question/32004014

#SPJ11

To find the point of intersection between the two lines represented by the given equations, we can solve the system of equations simultaneously.

The given equations are:

1) X + Y = 2

2) Y = (1/2)X + 5

We can solve this system by substituting the value of Y from the second equation into the first equation. Let's proceed with the substitution method:

Substitute Y = (1/2)X + 5 into the first equation:

X + (1/2)X + 5 = 2

Combine like terms:

(3/2)X + 5 = 2

Subtract 5 from both sides:

(3/2)X = -3

Multiply both sides by 2/3 to isolate X:

X = -2

Now, substitute the value of X back into the second equation to find Y:

Y = (1/2)(-2) + 5

Y = -1 + 5

Y = 4

Therefore, the lines represented by the given equations intersect at the point (-2, 4).