Write the correct equation for the following statement and then solve for the given number of
miles.


You decide to rent a limo for prom. The rate is $200 plus $5 per mile
traveled. Write an equation to calculate your total cost (c) at the end of
the evening for a given number of miles (m).




If you travel 45 miles what will be your total bill at the end
of the evening?

Climate change is causing an increase in air temperature, sea surface temperature, sea level, ocean acidity, and snow cover, but not humidity.  

Humidity

Climate change is the long-term change in average weather patterns, and is caused by increased atmospheric concentrations of greenhouse gases. Earth's vital signs that have been on the rise due to climate change include air temperature, sea surface temperature, sea level, ocean acidity, and snow cover. Humidity is not one of these vital signs, and actually is expected to decrease in some areas due to climate change.

Climate change is causing an increase in air temperature, sea surface temperature, sea level, ocean acidity, and snow cover, but not humidity.

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Answer:

  x = 22

Step-by-step explanation:

Two chords are shown at the same distance from the center of the circle, each with its perpendicular bisector. Half the length of one chord is shown; the length of the other chord is wanted.

The length of a chord of a circle will depend on its distance from the center. Chords at the same distance have the same length.

The perpendicular bisector of a chord intersects the center of the circle. A segment drawn from the midpoint of a chord to the circle center will be perpendicular to the chord.

These facts allow us to conclude that the geometry of each of the chords shown is the same. Both segments from the center bisect the chord at right angles. Because those segments are the same length, the chords are the same length.

If the full length of the bottom chord is what is being indicated by x, then ...

  x = 2×11

  x = 22

Answer:

3800 tickets

Step-by-step explanation:

we are given that,

total people seated:266

yet to come:93%

so the percentage of people who have arrived is 100%-93%=7%

and one ticket for each people

therefore,

\( \displaystyle \begin{array}{ccc} \displaystyle \rm7\% \quad \text{People} \implies266 \: \text{tickets} \\ \displaystyle100 \%\: \quad \imath \imath \implies \frac{266}{7\%} \: \: \: \: \imath \imath \\ \\ \qquad \displaystyle \qquad\rm as \: \% = \frac{1}{100} \longleftarrow \frac{266}{ \dfrac{7}{100} } \\ \\ \displaystyle \rm \: by \: simplifying \: complex \: fraction\longleftarrow 266 \times \frac{100}{7} \\ \rm reduce \: fraction \longleftarrow 38 \times 100 \\ \rm simplify \:multiplication \longleftarrow3800\end{array}\)

hence,

3800 tickets were sold for the movie

Answer:

Solutions given:

[100%-97%]=266people

7% =266people

Each people is 1 ticket.

266 people =266tickets

so

7% of people=266ticket

100% of people =266/7×100=3800tickets

3800tickets were sold for the movie

The range of the absolute function will be from 0 to 9. Then the correct option is A.

The absolute function is also known as the mode function. The value of the absolute function is always positive.

If the vertex of the absolute function is at (h, k). Then the absolute function is given as

f(x) = | x - h| + k

The domain means all the possible values of x and the range means all the possible values of y.

From the graph, the range of the absolute function will be from 0 to 9.

Then the correct option is A.

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The complete question is attached below.

If an equilateral triangle has a perimeter of 24 feet. the area of the circle is approximately 50.27 square feet.

Since the perimeter of the equilateral triangle is 24 feet, each side has a length of 8 feet (since all three sides are equal).

The diameter of the circle is equal to the length of one side of the equilateral triangle, which is 8 feet. Therefore, the radius of the circle is half the diameter, which is 4 feet.

The area of a circle is given by the formula:

A = πr^2

where A is the area and r is the radius.

Plugging in the value of the radius, we get:

A = π(4 feet)^2

A = 16π square feet

A ≈ 50.27 square feet (rounded to two decimal places)

Therefore, the area of the circle is approximately 50.27 square feet.

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The length of the sides of triangle ABC are: 6, 8, and 12.

One of the conditions that two triangles are similar is their Three pairs of corresponding sides are proportional.

In the given problem, the ratio of the sides of triangle ABC is 3 : 4 : 6

Another triangle, let's say triangle DEF, is made with its vertices at midpoints of the sides of triangle ABC.

Hence, all three pairs of corresponding sides have the same proportion.

AB/DE = BC/EF = AC/DF = 1/2

Due to similarity, the ratio of the sides of triangle DEF is also 3 : 4 : 6.

ratio f sides : perimeter = 3 : 4 : 6 : 13

Since its perimeter is 13, it means that the length of sides of triangle DEF are: 3, 4, and 6

Length of the sides of triangle ABC = 2 x length of the sides of Δ DEF

Length of the sides of triangle ABC are: 6, 8, and 12.

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Answer:

5 ≤ L ≤ 35

Step-by-step explanation:

Let w represent the width of the rectangle.

The perimeter (P) of the rectangle is given by:

P = 2w + 2L

Where L is the length of the rectangle.

We know that w = 30 cm and that the perimeter is between 100 and 160 cm. We can now set up our compound inequality:

100 ≤ 2(30) + 2L ≤ 160

100 ≤ 90 + 2L ≤ 160

10 ≤ 2L ≤ 70

We can now divide both sides by 2 to solve for L:

5 ≤ L ≤ 35

Therefore, the compound inequality that represents the graph of a rectangle with a width of 30 centimeters and a perimeter of 100 centimeters to 160 centimeters is:  5 ≤ L ≤ 35

Answer:

48 boys

Step-by-step explanation:

Step-by-step explanation:

with ABCD and ABDE being parallelograms, this means a indicated by the marks

AB = ED = CD

and with BD = DF that means that the line segments BF and CE are intersecting each other at their midpoint.

so they represent a pair of diagonals of a parallelogram, which makes BCFE a parallelogram.

Answer:

0.9910 = 99.10% probability that a sample of 170 steady smokers spend between $19 and $21

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 20, standard deviation of 5:

This means that \(\mu = 20, \sigma = 5\)

Sample of 170:

This means that \(n = 170, s = \frac{5}{\sqrt{170}}\)

What is the probability that a sample of 170 steady smokers spend between $19 and $21?

This is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 19.

X = 21

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{21 - 20}{\frac{5}{\sqrt{170}}}\)

\(Z = 2.61\)

\(Z = 2.61\) has a p-value of 0.9955

X = 19

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{19 - 20}{\frac{5}{\sqrt{170}}}\)

\(Z = -2.61\)

\(Z = -2.61\) has a p-value of 0.0045

0.9955 - 0.0045 = 0.9910

0.9910 = 99.10% probability that a sample of 170 steady smokers spend between $19 and $21

(1) x² - 2 x - 8 and Option (2) x² + 2 x - 8 are two polynomials which has been factored.

Given are the polynomials,

1) x² - 2 x - 8

Factors = (x+2)(x-4)

2) x² + 2 x - 8

Factors = (x-2)(x+4)

3) x²-2x-4 = There will be no integral root.

4) x²+2x-4 = There will be no integral root.

Hence the (1) x² - 2 x - 8 and Option (2) x² + 2 x - 8 are two polynomials which has been factored.

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Answer:

9 and 18

Step-by-step explanation:

Let the integers be a and 2a (since one is twice the other).

The reciprocals are 1/a and 1/(2a) respectively.

Difference means tk subtract.

So we have 1/a-1/(2a)=1/18

Multiply both sides by 18:.

18a/a-18a/(2a)=18a/18

Simplify:

18-9=a

Simplify:

9=a

If a=9, then 2a=18

The integers are 9 and 18.

Test:

1/9-1/18

2/18-1/18

1/18

Golden!

Answer:

x > -5, so the correct answer is C.

The rate at which the depth of the liquid is increasing when it reaches one-third of the height of the bowl is (7/3)π cm³/s.

To ascertain the rate at which the liquid's depth rises, let's find the derivative of the depth function with respect to time.

Let;

The rate of change of the volume of the liquid with respect to time is constant and equal to 7π cm³/s.

To determine the height of the bowl, we can evaluate the curve y = [-4 / (8 - x)] - 1 when x = 4 and y = 7.6 and then find the absolute difference between the values.

h = |[-4 / (8 - 4)] - 1 - [-4 / (8 - 7.6)] - 1|

Let's calculate the rate at which the depth rises when it reaches one-third of the bowl's height.

D = depth of bowl

Using this relationship from the question given;

D = (1/3) * h

In order to determine the rate at which D will change with respect to time, let's differentiate both sides of the equation.

dD/dt = (1/3) * dh/dt

Since dh/dt is the rate at which the depth of the liquid is changing, which is constant and equal to 7π cm³/s, we can substitute it into the equation:

dD/dt = (1/3) * (7π)

Simplifying, we have:

dD/dt = (7/3)π cm³/s

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Answer:

w=13

Step-by-step explanation:

15+w=3w-11

+11           +11

26+w=3w

    -w   -w

26=2w

26/2=2w/2

13=w

Answer:

w =13

Step-by-step explanation:

15+w=3w−11

Collect like terms

15+11=3w−w

Simplify

26=2w

Divide both sides of the equationy 2

26/2=2w/2

Simplify

13=w

switch sides

w=13

Step-by-step explanation:

the answer is in the image above

Answer:

12

Step-by-step explanation:

The number of shells collected by Paula is 12 shells

The correct answer is B.

The given expression:

total number of shells collected by the friends, t = 43 shells

number of shells collected by Paula = x

number of shell collected by Bethany = 2x - 3

number of shell collected by Jerrell = \(\frac{x}{2} + 2\)

To find:

The number of shells collected by Paula is calculated as follows:

\(x + (2x-3 ) + (\frac{x}{2} + 2) = 43\\\\3x + \frac{x}{2} - 1 = 43\\\\\frac{6x + x}{2} = 43 + 1\\\\\frac{7x}{2} = 44\\\\7x = 88\\\\x = \frac{88}{7} \\\\x \approx 12 \ shells\)

Thus, the number of shells collected by Paula is 12 shells

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The three consecutive numbers that have a sum of 12 is 3, 4 and 5. The formula for calculation is x + x + 1 + x + 2 = 12.

Let the first number in three consecutive numbers be x. So, the next two numbers will be (x+1) and (x+2). Now, their sum wil be represented as mathematical equation -

x + x + 1 + x + 2 = 12

Performing addition on Left Hand Side of the equation

3x + 3 = 12

Rewriting the equation

3x = 12 - 3

Performing subtraction on Right Hand Side of the equation

3x = 9

x = 9/3

Performing division on Right Hand Side of the equation

x = 3

So, next number = x+1

Second number = 3+1

Second number = 4

Third number = x+2

Third number = 3+2

Third number = 5

Hence, the three consecutive numbers are 3, 4 and 5.

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This means that she made a 20% return on the money she invested in the property. For every dollar she invested, she earned 20 cents in profit.

To calculate Jennifer Aniston's return on investment (ROI), we can use the formula:

ROI = (Net Profit / Initial Investment) * 100

First, let's calculate the net profit. The net profit is the selling price minus the initial investment:

Net Profit = Selling Price - Initial Investment

Net Profit = $2,200,000 - $2,000,000

Net Profit = $200,000

Next, we calculate the ROI:

ROI = (Net Profit / Initial Investment) * 100

ROI = ($200,000 / $1,000,000) * 100

ROI = 0.2 * 100

ROI = 20%

Jennifer Aniston's return on investment for this property is 20%.

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Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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Answer:

Make the -4 exponent in the denominator positive.

Answer:

For the quantity less than one, all the x-values smaller than 4

For the quantity greater than one, all the x-values larger than 4

the value 4 cannot be used at all.

Step-by-step explanation:

According to the description, the quantity in question can be represented by the fraction:

\(\frac{x}{x-4}\)

Notice that since the binomial (x - 4) is in the denominator, in order to prevent a case with undefined quotient, x - 4 cannot be zero, and that is x cannot be 4.

Notice as well that in the case that x is larger than 4, the binomial (x-4) is a positive number, and in the case that x is less than 4, the binomial (x - 4) is a negative number.

Which values result in the quantity greater than one?

We need to solve for x in the inequality:

\(\frac{x}{x-4} >1\)

So, if x > 4 then we can proceed as follows:

\(\frac{x}{x-4} >1\\x>x-4\\0>-4\)

which is a true statement, when x > 4

If x < 4 then:

\(\frac{x}{x-4} >1\\x<x-4\\0<-4\)

where we have used that (x-4) is negative, so multiplying by it would flip the direction of the inequality. As we see, this case results in an absurd , so it is not possible for x < 4 to render the quantity under study larger than one.

We study similarly the case for the quantity in question being smaller than one considering x > 4:

\(\frac{x}{x-4} <1\\x<x-4\\0<-4\)

and we arrive at an absurd. so the quantity cannot be smaller than 1 if x is larger than 4

Now for x smaller than 4:

\(\frac{x}{x-4} <1\\x>x-4\\0>-4\)

we arrive at a true statement. So it is possible to get the quantity in question smaller that one if x is less than 4.

Answer:

D.

Step-by-step explanation:

Answer: 2

Step-by-step explanation:

(x1,y1) = (-1,0)

(x2,y2) = (3,8)

m = (8–0)/(3-(-1))

m = 8/(3+1)

m = 8/4

m = 2

The signature of the Principal Investigator on the final proposal does not imply responsibility for the availability of funding or the financial aspects of the project.

The complete question should be What does the signature of the Principal Investigator on the final proposal NOT imply responsibility for?

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Notice that:

Therefore:

Then a carat is greater.

Now, since:

Then:

Simplifying the above result we get:

Also, since:

then:

Simplifying the above result we get:

Answer:

A carat is greater.

and

and