A new taxi company, Littleton Cabs, just opened in town. A cab ride for m miles costs 8.5+2m dollars. Polly took a 14-mile cab ride to the airport. What price did Polly pay for her cab ride?

74-p

20-q

I think this is right

Answer:

David, 20%

Step-by-step explanation:

Anna saves 19%.

Laura spends 17/20 , or, 85/100=> Laura saves 15/100; 15%.

amount of salary David saves : amount of salary he spends = 2:8,

or, 20/100 : 80/100

=> David saves 20/100;  20%.

David saves the most, (20%).

David saves more money than Laura and Anna and this can be determined by using the given data and converting that data into percentages.

Given :

Let the total amount of money Anna, Laura, and David each earn be 'x'.

Now, according to the given data Anna saves 19% of her salary and spends the rest of it. So, the amount of money Anna saved is:

= 19%

It is also given that Laura spends 17/20 of her salary and saves the rest of it. So, the amount of money Laura saved is:

\(=\dfrac{3}{20}\)

= 15%

It is given that amount of salary David saves : amount of salary he spends = 2:8. So, it can be written as 20/100:80/100. So, the amount of money David saved is:

= 20%

David saves more money than Laura and Anna.

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Answer:

3y+7

Step-by-step explanation:

6+7.2y+−4.2y+1

(7.2y+−4.2y)+(6+1)

3y+7

Answer:

It's: A

Step-by-step explanation:

Answer:

from the origin of the graph(which is the center) go right 3 then mark a point( should be a little before the number 4, then from the origin again go up to the number 4 and mark another point. then run a line connecting the two dots you made

Step-by-step explanation:

The length of the rectangle is 19 cm.

The formula for the area of a rectangle,

Area = Length x Width

Given that the area is 336 cm squared.

So, we can set up an equation,

⇒ 336 = (w + 5)w

where w represents the width of the rectangle.

Expanding this equation,

⇒ 336 = w² + 5w

Moving all terms to one side:

⇒ w² + 5w - 336 = 0

This is a quadratic equation that we can solve using the quadratic formula,

⇒ w = (-5 ± √(5² - 4(1)(-336))) / (2(1))

⇒ w = (-5 ± 23) / 2

We'll take the positive value,

⇒ w = 14

So, the width of the rectangle is 14 cm.

We also know that the length is 5 cm more than the width,

Therefore,

⇒ l = w + 5

⇒ l = 14 + 5

⇒ l = 19

Therefore, the length of the rectangle is 19 cm.

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Conclusion
Therefore, for some natural number N, n ≥ N and n ∈ N implies |(p - q)/n| < ε.

To show that for some natural number N, n ≥ N and n ∈ N implies |p/n - q/n| < ε, we'll use the Archimedean property of real numbers. The Archimedean property states that for any positive real numbers a and b, there exists a natural number n such that n*a > b.

Let's consider the inequality we want to prove: \(|p/n - q/n| < ε.\)

Step 1: Rewrite the inequality
First, we can rewrite the inequality as |(p - q)/n| < ε, since we are allowed to combine the fractions.

Step 2: Apply the Archimedean property
By the Archimedean property, we know that for any ε > 0, there exists a natural number N such that N > (p - q)/ε.

Step 3: Rearrange the inequality
We can rearrange the inequality from step 2 to get\( N*ε > p - q. \)

Step 4: Divide by N
Now, divide both sides of the inequality by N to get \(ε > (p - q)/N.\)

Step 5: Relate this to our original inequality
We want to show that |(p - q)/n| < ε for some n ∈ N, where n ≥ N. Since n ≥ N, and ε > (p - q)/N, we have ε > (p - q)/n for n ∈ N and n ≥ N

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Answer:

x=8

Step-by-step explanation:

(2x + 1)² = x² + (2x - 1)² = x² + (2x - 1)(2x - 1)

(2x + 1)(2x + 1) = x² + 4x²-2x-2x+1

4x²+2x+2x+1 = 5x²-4x+1

4x²+4x+1 = 5x²-4x+1

0= 5x²-4x²-4x-4x+1-1

0= x²-8x

x²-8x=0

x²=8x

x=8

Answer:

b= -10

Step-by-step explanation:

Divide -10 from both sides to get b alone

hope this helps :)

Answer:

b=-10

Step-by-step explanation:

divide each term by -10 to get your answer

The estimated probability that the sum of five dice will be 26 is 0.0053

Estimated Probability: Estimated probability is an approximation, or estimate, of theoretical probability. The larger the number of trials, the more accurate we expect this approximation to be. If E consists of a single outcome s, we refer to P(E) as the probability of the outcome s, and write P(s) for P(E)

N = Number of Repeated Process = 10,000

n = Number of times the sum of the five tosses equaled 26 = 53

The estimated probability that the sum of the five dice will be 26 = n/N

Where n = 53

And N = 10,000

Using the above formula, we have the following:-

n/N becomes

n/N = 53/10,000

n/N = 0.0053

Hence, the estimated probability that the sum of five dice will be 26 is 0.0053

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Answer:

504

Step-by-step explanation:

take 163 and subtract 142 then times by 24

The complete triangle congruence statement are:

a) ∠A ≅ ∠Y, ∠B ≅ ∠Z, ∠C ≅ ∠X

b) AB ≅ YZ, AC ≅ XY, BC ≅ XZ

c) ΔABC ≅  ΔXYZ.

What is the congruent triangle?

The triangles are congruent regardless of how they are rotated or flipped. The symbol “≅” is frequently used to express the congruence of two items. In the diagram given, ΔABC ≅  ΔXYZ.

The corresponding angles and the sides of the triangles are also congruent with each other.

We have given,

all the corresponding congruent angles and sides. Then the triangle congruence statement.

a)

∠A ≅ ∠Y

∠B ≅ ∠Z

∠C ≅ ∠X

b)

AB ≅ YZ

AC ≅ XY

BC ≅ XZ

c)

ΔABC ≅  ΔXYZ.

Therefore, the complete triangle congruence statement are:

a) ∠A ≅ ∠Y, ∠B ≅ ∠Z, ∠C ≅ ∠X

b) AB ≅ YZ, AC ≅ XY, BC ≅ XZ

c) ΔABC ≅  ΔXYZ.

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Based on the given scale of 1.5 inches to 2 miles on the map, an ant's 8-inch walk in Apollo Beach corresponds to a distance of 10.67 miles for a real person.

To determine the distance a real person would walk in Apollo Beach, we can use the given scale of 1.5 inches to 2 miles on the map. Since the ant walked 8 inches on the map, we need to calculate the equivalent distance in miles.

First, we can set up a proportion to find the conversion factor:

1.5 inches / 2 miles = 8 inches / x miles

To solve for x, we can cross-multiply:

1.5 inches * x miles = 2 miles * 8 inches

Simplifying the equation, we have:

1.5x = 16

Dividing both sides by 1.5, we find:

x ≈ 10.67 miles

Therefore, a real person would walk approximately 10.67 miles in Apollo Beach.

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Answer:

there both 0.8

Answer:

wait who is that again?

Step-by-step explanation:

Answer:

 Yes, I am a fan.

Step-by-step explanation:

;)

Answer:

x = 71.5 in

Step-by-step explanation:

Remember the SOHCAHTOA rule

Soh...

Sine = Opposite / Hypotenuse

...cah...

Cosine = Adjacent / Hypotenuse

...toa

Tangent = Opposite / Adjacent

In this case, we use: CAH.

cos(52) = 44/x

x = 44/cos(52)

x = 71.5 inches

Hey there! I'm happy to help!

LINE SEGMENT 1

To find the x value of the midpoint, you add the x values and divide by 2.

-1/3+4/3=1

1/2=1/2

For the y value, you add the y values and divide by 2.

7/5+5/2= 3 9/10

3 9/10÷2=1 19/20 or 39/20.

So, our midpoint is (1/2, 39/20).

LINE SEGMENT 2

X-Values

5+(-1)=5-1=4

4/2=2

Y-Values

√3+5√3=6√3

6√3÷2=3√3

So, our midpoint is (2, 3√3).

Have a wonderful day! :D

The midpoint of a line segment divides the line segment into 2.

\(\mathbf{(a)\ (-\frac 13, \frac 75)\ and\ (\frac 43, \frac 52)}\)

The midpoint is calculated as follows:

\(\mathbf{(x,y) = (\frac{-1/3 + 4/3}{2}, \frac {7/5 + 5/2}{2})}\)

\(\mathbf{(x,y) = (\frac{3/3}{2}, \frac {39/10}{2})}\)

\(\mathbf{(x,y) = (\frac{1}{2}, \frac {39}{20})}\)

Hence, the midpoint of \(\mathbf{(-\frac 13, \frac 75)\ and\ (\frac 43, \frac 52)}\) is \(\mathbf{(\frac{1}{2}, \frac {39}{20})}\)

\(\mathbf{(b)\ (5 \sqrt 3)\ and\ (-1, 5\sqrt 3)}\)

The midpoint is calculated as follows:

\(\mathbf{(x,y) = (\frac{5 - 1}{2}, \frac {\sqrt 3 + 5\sqrt 3}{2})}\)

\(\mathbf{(x,y) = (\frac{4}{2}, \frac {6\sqrt 3}{2})}\)

\(\mathbf{(x,y) = (2, 3\sqrt 3)}\)

Hence, the midpoint of \(\mathbf{(5 \sqrt 3)\ and\ (-1, 5\sqrt 3)}\) is \(\mathbf{(2, 3\sqrt 3)}\)

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The Hermite curve with four control points P0(0,0), P1(1,1), P2(2,-1), and P3(3,0) has tangent vectors P0'(1,1) and P3'(1,1) at the endpoints. To determine the intermediate points on the curve at t = 1/3 and t = 2/3, we can use the Hermite interpolation formula.

The Hermite interpolation formula allows us to construct a curve based on given control points and tangent vectors. In this case, we have four control points P0, P1, P2, and P3, and tangent vectors P0' and P3'.

To find the intermediate point at t = 1/3, we use the Hermite interpolation formula:

P(t) = \((2t^3 - 3t^2 + 1)P0 + (-2t^3 + 3t^2)P3 + (t^3 - 2t^2 + t)P0' + (t^3 - t^2)P3'\)

Substituting the given values:

\(P(1/3) = (2(1/3)^3 - 3(1/3)^2 + 1)(0,0) + (-2(1/3)^3 + 3(1/3)^2)(3,0) + ((1/3)^3 - 2(1/3)^2 + (1/3))(1,1) + ((1/3)^3 - (1/3)^2)(1,1)\)

Simplifying the equation, we can find the coordinates of the intermediate point at t = 1/3.

Similarly, for t = 2/3, we use the same formula:

\(P(2/3) = (2(2/3)^3 - 3(2/3)^2 + 1)(0,0) + (-2(2/3)^3 + 3(2/3)^2)(3,0) + ((2/3)^3 - 2(2/3)^2 + (2/3))(1,1) + ((2/3)^3 - (2/3)^2)(1,1)\)

Calculating the equation yields the coordinates of the intermediate point at t = 2/3.

In this way, we can use the Hermite interpolation formula to determine the intermediate points on the Hermite curve at t = 1/3 and t = 2/3 based on the given control points and tangent vectors.

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Answer: it takes 4 seconds

Step-by-step explanation: solve values of t when h(t) = 0.

-3t² + 12t= 0 when t(-3t+12)= 0, t= 0 (start) or t=4

The derivative of the function 4 / x - 1 / y = 3 is equal to y' = 4 / (4 - 3 · x)².

In this problem we must use two differentiation methods in a function to obtain its first derivative. These methods are (i) explicit differentiation and (ii) implicit differentiation. Each procedure is described below:

Explicit differentation

Implicit differentiation

Explicit differentiation

Step 1

4 / x - 1 / y = 3

1 / y = 4 / x - 3

1 / y = (4 - 3 · x) / x

y = x / (4 - 3 · x)

Step 2

y' = [(4 - 3 · x) - x · (- 3)] / (4 - 3 · x)²

Step 3

y' = 4 / (4 - 3 · x)²

Implicit differentiation

Step 1

- 4 / x² + [1 / (y²)] · y' = 0

Step 2

(1 / y²) · y' = 4 / x²

Step 3

y' = 4 · y² / x²

Step 4

y' = 4 · [x / (4 - 3 · x)]² / x²

y' = 4 / (4 - 3 · x)²

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The likelihood that a randomly chosen bundle of steel rods would have an average length larger than 184.1 cm is 0.9319.

Here we use the Central Limit Theorem,

Which states that when the sample size is large enough (in this case, 6 steel rods), the sampling distribution of the sample mean will be approximately normal.

The mean of the sampling distribution of the sample mean is equal to the population mean, which is 185.5-cm.

The population standard deviation divided by the square root of the sample size gives the standard deviation of the sampling distribution of the sample mean.

which is 2.3/ √(6) = 0.94cm.

So we want to find the probability that the sample mean is greater than 184.1 cm.

We can standardize this value by subtracting the population mean and dividing by the standard deviation of the sampling distribution,

⇒ (184.1 - 185.5) / 0.94 = -1.49.

Using a standard normal distribution table,

we can find that the probability of a z-score being less than -1.49 is 0.0681.

Thus, the likelihood that the average length of a bundle of steel rods chosen at random is larger than 184.1 cm,

⇒ 1 - 0.0681 = 0.9319, or 93.19%.

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Answer:

\(\displaystyle \cos (G)=\frac{36}{85}\)

Step-by-step explanation:

Recall that cosine is the ratio of the adjacent side to the hypotenuse:

\(\displaystyle \cos(G)=\frac{\text{adjacent}}{\text{hypotenuse}}\)

The hypotenuse is always the side opposite to the right angle. In this case, it is

85.

The adjacent side to G is 36.

Therefore:

\(\displaystyle \cos (G)=\frac{36}{85}\)

For your other question, remember that in a right triangle, cosine is the ratio of the adjacent side to the hypotenuse.

As you know, the hypotenuse is always the longest side in a right triangle.

Therefore, the ratio of the adjacent side to the hypotenuse will never be greater than 1.

Since 85/77 is greater than 1, it is undefined.

The same applies to sine as well.

Answer:

graph B is the correct solution

Answer:

tan G = 2.4

Step-by-step explanation:

Step-by-step explanation:

when numbers are negative, the bigger the number looks the smaller it is therefore

-6 is smaller than -5

but 6 is bigger than 5

however, the numbers are;

-5.99, -3, -6, -5.9, -1, -5.999, -5 ,2

The answer are: a. Total outflows: $2,007,901, b. Total inflows: $827,080, c. Net present value: $824,179, d. Should the old issue be refunded with new debt? Yes

To determine whether the old bond issue should be refunded with new debt, we need to calculate the present value of total outflows, the present value of total inflows, and the net present value (NPV). Let's calculate each of these values step by step: Calculate the present value of total outflows. The total outflows consist of the call premium, underwriting cost on the old issue, and underwriting cost on the new issue. Since these costs are one-time payments, we can calculate their present value using the formula: PV = Cash Flow / (1 + r)^t, where PV is the present value, Cash Flow is the cash payment, r is the discount rate, and t is the time period.

Call premium on the old issue: PV_call = (7% of $22 million) / (1 + 0.1)^16, Underwriting cost on the old issue: PV_underwriting_old = $530,000 / (1 + 0.1)^16, Underwriting cost on the new issue: PV_underwriting_new = $680,000 / (1 + 0.1)^16. Total present value of outflows: PV_outflows = PV_call + PV_underwriting_old + PV_underwriting_new. Calculate the present value of total inflows. The total inflows consist of the interest savings and the tax savings resulting from the interest expense deduction. Since these cash flows occur annually, we can calculate their present value using the formula: PV = CF * [1 - (1 + r)^(-t)] / r, where CF is the cash flow, r is the discount rate, and t is the time period.

Interest savings: CF_interest = (12% - 10%) * $22 million, Tax savings: CF_tax = (40% * interest expense * tax rate) * [1 - (1 + r)^(-t)] / r. Total present value of inflows: PV_inflows = CF_interest + CF_tax.  Calculate the net present value (NPV). NPV = PV_inflows - PV_outflows Determine whether the old issue should be refunded with new debt. If NPV is positive, it indicates that the present value of inflows exceeds the present value of outflows, meaning the company would benefit from refunding the old issue with new debt. If NPV is negative, it suggests that the company should not proceed with the refunding.

Now let's calculate these values: PV_call = (0.07 * $22,000,000) / (1 + 0.1)^16, PV_underwriting_old = $530,000 / (1 + 0.1)^16, PV_underwriting_new = $680,000 / (1 + 0.1)^16, PV_outflows = PV_call + PV_underwriting_old + PV_underwriting_new. CF_interest = (0.12 - 0.1) * $22,000,000, CF_tax = (0.4 * interest expense * 0.4) * [1 - (1 + 0.1)^(-16)] / 0.1, PV_inflows = CF_interest + CF_tax. NPV = PV_inflows - PV_outflows.  If NPV is positive, the old issue should be refunded with new debt. If NPV is negative, it should not.

Performing the calculations (rounded to the nearest whole dollar): PV_call ≈ $1,708,085, PV_underwriting_old ≈ $130,892, PV_underwriting_new ≈ $168,924, PV_outflows ≈ $2,007,901,

CF_interest ≈ $440,000, CF_tax ≈ $387,080, PV_inflows ≈ $827,080.  NPV ≈ $824,179.  Since NPV is positive ($824,179), the net present value suggests that the old bond issue should be refunded with new debt.

Therefore, the answers are:

a. Total outflows: $2,007,901

b. Total inflows: $827,080

c. Net present value: $824,179

d. Should the old issue be refunded with new debt? Yes

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Answer:

a

Step-by-step explanation:

The Volume of the Pyramid=19.19in³

Surface Area of  the Pyramid=48.65in²

Volume is a unit of measurement for the area occupied in three dimensions. It is widely quantified and measured using SI-derived units, alternative imperial units, or US standard units (such as the gallon, quart, cubic inch). Volume and length (cubed) have a similar meaning.

First, volume was calculated using naturally occurring vessels with a similar shape, and then using standardized containers. Calculating the volume of numerous common three-dimensional forms is made simple by arithmetic formulas. The volumes of increasingly complicated shapes can be calculated using integral calculus.

Given that,

Height of the pyramid =4.7

Pyramid's slant height= 5.2

Base of pyramid is a square with side=3.5

Volume of the pyramid=(1/3)(3.5×3.5)×(4.7)

=19.19 in³

The surface area of a pyramid=((1/2)×(4×3.5)×5.2)+(3.5×3.5)

=18.65in²

Therefore, the volume of the pyramid=19.19 in³

And the surface area of the pyramid=18.65in²

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The probability that you are correct by making a random guess is 1/5.

According to the given question.

On a multiple choice test, each question has 5 possible answers.

As we know that probability, is a measure of the likelihood of an event to occur. It is calculated by taking the ratios of favorable outcomes to the total number of outcomes.

Here, it is given that there are 5 possible answers of one question.

⇒ Total number of outcomes = 5

Also, only one answer will correct out of 5 possible answers.

Which means, total number of favorable outcomes = 1

Therefore, the probability that you are correct by making a random guess

= favorable outcomes/total number of outcomes

= 1/5

Hence, the probability that you are correct by making a random guess is 1/5.

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