Better taxi service charges $3.00 for the first mile plus $0.20 for each additional mile. Best
taxi service charges $6.00 for the first two miles plus $0.10 for each additional mile. How
many miles will a person travel in order to spend an equal amount of money using either
service?

Answer:

1) 6r+7=13+7r —> 7r–6r=7–13 —> r = – 6

2) 13–4x=1–x —> 4x–x=13–1 —> 3x=12 —> x=12/3 —> x=4

3)–7x–3x+2=–8x–8 —> –8x+7x+3x=2+8 —> 2x=10 –> x= 10/2 –> x= 5

4)–8–x=x–4x —> –x–x+4x=8 —> 2X=8 —> x= 8/2 —> x= 4

5) –14+6b+7-2b=1+5b —> 5b +2b –6b = –14+7–1 —> b=–8

6) n+2=–14–n —> n+n=–14–2 —> 2n = –16 —> n = – 16/ 2 —> n = – 8

7) n – 3n = 14 –4n —> n –3n + 4n = 14 —> 2n = 14 —> n = 14/ 2 —> n = 7

8) 7a – 3 = 3 + 6a —> 7a – 6a = 3 + 3 —> a = 6

9) 3(1–3x ) =2(–4x+7) —> 3 –9x = –8x+14 —> 9x–8x = 3–14 —> x = –11

10) –10 +x+4–5 =7x –5 —> 7x–x = –10+4–5 +5 —> 6x = –6 —> x= –6/6 —> x = –1

11) –8n +4(1+5n)=–6n–14 —> –8n +4 + 20n = – 6n– 14

20n –8n +6n= –14 –4 —> 18n = – 18 —> n = –18/18 —> n = –1

12) –6n–20=–2n +4(1–3n) —> –6n –20 = – 2n +4 –12n —> 12n +2n –6n = 4 +20 —> 8n =24 —> n = 24/8 —> n =3

I hope I helped you^_^

Answer:

1.

6r + 7 = 13 +7r

6r - 7r = 13-7

-r = 6

r = 6

2.

13 - 4x = 1-x

-4x +x = 1 -13

-3x = -12

x = -12 / -3

x = 4

3.

-7x - 3x + 2 = -8x -8

-10x +2 = -8x -8

-10x +8x = -8 -2

-2x = -6

x = -6 / -2

x = 3

4.

-8 - x  = x- 4x

-8 - x  = -3x

-x + 3x = -8

2x = -8

x = -8 / 2

x = -4

5.

-14 + 6b + 7 -2b = 1 + 5b

-7 + 4b = 1 + 5b

4b - 5b = 1 + 7

-b = 8

b = -8

6.

n + 2 = -14 -n

n + n = -14 -2

2n = - 16

n = -16 / 2

n = -8

7.

n - 3n = 14 -4n

-2n = 14 - 4n

-2n +4n = 14

2n = 14

n = 14 /2

n = 7

8.

7a - 3 = 3 + 6a

7a - 6a = 3 +3

a = 6

9.

3 ( 1 - 3x ) = 2 (-4x + 7)

3 - 9x = -8x +14

-9x +8x  = 14 - 3

-x = 11

x = -11

10.

-10 + x + 4 - 5 = 7x - 5

-10 +x -1 = 7x - 5

-11 + x = 7x - 5

-11 + 5 = 7x -x

-6 = 6x

x = -6/6

x = -1

11.

-8n + 4 ( 1 + 5n ) = -6n -14

-8n + 4 + 20n = -6n -14

12n +4 = -6n -14

12n  + 6n = -14 -4

18n = -18

n = -18/18

n = -1

12.

-6n - 20 = -2n + 4 ( 1 - 3n)

-6n - 20 = -2n + 4 - 12n

-6n - 20 = -14n +4

-20 -4 = -14n +6n

-24 = 8n

n = -24/8

n = -3

A sequence is characterised as one that adheres to a predetermined pattern. The following term is created by increasing or decreasing the previous word by a certain amount.

On occasion, an expression is followed by every term in the series. The general formula for an AP is T n = a + (n - 1) d.

Understanding the underlying pattern or rule that creates the sequence is necessary for formulating the general term an of the sequence. Finding a formula for the overall term of a series can be done in a number of ways, including:

1) Finding a pattern: In some cases, a pattern can be found by examining the terms of the sequence and looking for a common ratio or difference. For instance, the formula for the general term can be written as a = a1 + (n - 1)d, where a1 is the first term and d is the common difference, assuming the terms of a sequence are rising by a constant amount.

2) Recurrence relations are used to characterise some sequences. These relations define the nth term in terms of the phrases that came before it. If the recurrence relation, for instance, is a = an-1 + an-2, then the general term's formula can be discovered by resolving the recurrence relation.

3) Making use of generating functions: Sequences can be represented mathematically using generating functions. A formula for the general term of a sequence can be discovered by fiddling with the generating function.

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Answer:

$12

Step-by-step explanation:

$144 = 12 mangoes

Divide both sides by 12

$12 = 1 mango

(a) Correct answer is Approximately normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis greater than or equals 10.

(b) The value of P (X ≥ 770) is 0.0143.

(c) The value of P (X ≤ 720) is 0.0708.

Let X = number of elements with a particular characteristic.

The variable p is defined as the population proportion of elements with the particular characteristic.

The value of p is:

p = 0.74.

A sample of size, n = 1000 is selected from a population with this characteristic.

(a)

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

               μ = p

The standard deviation of this sampling distribution of sample proportion is:

                  σ = \(\sqrt \frac{p(1-p)}{n}\)

The sample selected is of size, n = 1000 > 30.

Thus, according to the central limit theorem the distribution of  is Normal, i.e. .

p~ N(μ = 0.74, σ =0.0139)

Thus the correct option is (A).

(b) We need to compute the value of P (X ≥ 770).

Apply continuity correction:

P (X ≥ 770) = P (X > 770 + 0.50)

                  = P (X > 770.50)

Then,

   p > 770.5/1000 = 0.7705

Compute the value of  P( p > 0.7705) as follows:

P( p > 0.7705) = P(p -μ/σ > 0.7705 - 0.74/0.0139)

                       = P( Z > 2.19)

                       = 1 - P( Z< 2.19)

                       = 1 - 0.98574

                       = 0.01426

                       ≈ 0.0143

Thus, the value of P (X ≥ 770) is 0.0143.

(c)

We need to compute the value of P (X ≤ 720).

Apply continuity correction:

P (X ≤ 720) = P (X < 720 - 0.50)

                  = P (X < 719.50)

Then

Compute the value of  as follows:

P( p < 0.7195) = P(p -μ/σ > 0.7705 - 0.74/0.0139)

                       = P(Z < - 1.47)

                       = 1 - P(Z < 1.47)

                       = 1 - 0.92922

                       = 0.07078

                        ≈ 0.0708

Thus, the value of P (X ≤ 720) is 0.0708.

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If the HRM Cafe expects to generate $120,000 in annual-revenue, renting space with a monthly cost of 5% of sales which is variable cost would be the cheaper option.

To determine which option costs less for the HRM Cafe, we need to compare the total costs of each option.
Option 1: Fixed costs of $5,000 per month.
This means that the monthly rent will always be $5,000 regardless of how much revenue the cafe generates.
Annual rent cost = $5,000 x 12 months = $60,000
Option 2:Variable costs: 5% of monthly sales.
This means that the monthly rent will be a percentage of the cafe's monthly sales.
Monthly rent cost = 5% x $120,000 (annual revenue) / 12 months = $500
Annual rent cost = $500 x 12 months = $6,000
Comparing the two options, we can see that option 2 (5% of monthly sales) costs less at an annual rent cost of $6,000 compared to option 1's annual rent cost of $60,000.
The variable rent option, which is 5% of monthly sales, costs less for HRM Cafe's second location.

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Answer:

Step-by-step explanation:

You didn't add the answers but here are some things that are approximately 100 centimeters (or 1 meter)
1 meterstick (of course)

Most guitars

Some or most golf sticks

Answer:  See below.

Step-by-step explanation:

We'll assume the top and bottom lines are parallel.  That means angles 4 and 5 are 90 degrees since the line coming down is perpendicular to the parallel line.  The sum of angles 1 and 2 is also 90°.  The interior angles of a triangle must add to 180°. So far we have two:  90° and 60°.  The third must therefore be 30°(angle 2).  Angle 3 must be 120° since it shares a straight line with the 60° angle and the straight line is 180° from one side to the other.  Angle 1 must be (90°- angle 2), which makes it 60°.  

1.  60°

2. 30°

3.  120°

4.  60°

5.  90°

We are given that the distribution of maximum oxygen uptake for elite athletes is approximately normal with mean 69 and standard deviation 7.6.

To find the probability that an elite athlete has a maximum oxygen uptake of at least 84.2 ml/kg, we need to standardize the value using the formula:

z = (x - μ) / σ

where,

x = the value of 84.2 ml/kg

μ = the mean of 69 ml/kg

σ = the standard deviation of 7.6 ml/kg.

Plugging in the values, we get:

z = (84.2 - 69) / 7.6

    = 2.03

Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being greater than or equal to 2.03 is 0.0217. Therefore, the probability that an elite athlete has a maximum oxygen uptake of at least 84.2 ml/kg is 0.0217.

z = (58.36 - 69) / 7.6

   = -1.36

Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being less than or equal to -1.36 is 0.0869. Therefore, the probability that an elite athlete has a maximum oxygen uptake of at most 58.36 ml/kg is 0.0869.

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The correct answer is option  C. The first example represents reflected-appraisal; the second example represents social comparison.

Given that: When Abe was young, he learned that he could lighten the mood with humor. Others laughed at his jokes, and he began to see himself as the 'life of the party'.
In the first example, Abe's sense of humor is positively reinforced by others laughing at his jokes, leading to an enhanced self-image. This is an example of reflected appraisal, where one's self-concept is shaped by the feedback received from others.

Also given that:Abe sometimes wishes he could be more studious and serious like his peers.
In the second example, Abe is comparing himself to his peers and wishing to be more like them. This is an example of social comparison, where individuals evaluate their own abilities and attributes by comparing themselves to others.
C. The first example represents reflected appraisal; the second example represents social comparison.

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Answer:

Explanation:

To find the area of the triangle, we must multiply 1/2 x base x altitude to get the answer. But first, we need to simplify the height. We are given the base and the altitude.

Solution:

Hence, the area of the triangle is 27x³ + 27x² - 4 meters².

Answer:

I think the answer is B. $12.55

Step-by-step explanation:

14.50 - 6.95 = 7.55

7.55 + 5 = 12.55

Hi!

your answer would be: B

Reason being: If you subtract $6.95 from $14.50 you get $7.55 (which is what she had leftover after she bought the ticket). She needed $5 more to get snacks, so add $5 to $7.55 and you get $12.55.

Hope this helps!

50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that a punch recipe calls for 1(¹/₂) quart of sparkling water and 3/4 of a quart of grape juice.

The ratio of sparkling water to grape juice is,

1(¹/₂) : (3/4 quarts) = (3/2) : (3/4) =  2 : 1

The amount sparkling water in the total volume is 2 : (2+1) = 2/3 of the total volume. For a volume of 100 quarts, the sparkling water content is

2/3 · 75quarts = 50 quarts

Then the grape juice content is,

1/3 · 75 quarts = 25 quarts

Therefore, 50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.

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Suppose that a point (X_1, X_2, X_3) is chosen at random, in the given set S, which represents a three-dimensional unit cube, we need to calculate the probabilities of two events:

(a) To calculate P((X_1−1/2)² + (X_2−1/2)² + (X_3−1/2)² ≤ 1/4), we need to determine the volume of the region enclosed by the equation. The given equation represents a sphere centered at (1/2, 1/2, 1/2) with a radius of 1/2. Since the region lies within the unit cube, the probability is equal to the ratio of the volume of the sphere to the volume of the cube. The volume of the sphere can be calculated using the formula for the volume of a sphere, and the volume of the cube is simply 1. By dividing the volume of the sphere by the volume of the cube, we obtain the probability.

(b) P(X_1² + X_2² + X_3² ≤ 1) represents the probability of a point lying within or on the unit sphere centered at the origin. Since the given set S is a unit cube, we need to find the ratio of the volume of the unit sphere to the volume of the unit cube to calculate the probability. Again, the volume of the sphere can be calculated using the formula, and the volume of the cube is 1. By dividing the volume of the sphere by the volume of the cube, we obtain the probability.

To provide specific numerical values for the probabilities, the calculations based on the formulas mentioned above need to be performed.

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Explanation:

I'm assuming the rope is fully taut and connects the top of the flag pole with the tip of the shadow.

Draw a right triangle that has a horizontal leg of 5 feet and a hypotenuse of 13 feet. I'll call these a = 5 and c = 13.

Use the pythagorean theorem to find b

\(a^2 + b^2 = c^2\\\\5^2 + b^2 = 13^2\\\\25 + b^2 = 169\\\\b^2 = 169-25\\\\b^2 = 144\\\\b = \sqrt{144}\\\\b = 12\)

The vertical leg of the right triangle is 12 feet, which is the height of the flag pole. We have a 5-12-13 right triangle.

Answer:

C

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

r = \(\frac{5}{8}\) t - 9 ← is in slope- intercept form

with y- intercept c = - 9

Function 2 has the ordered pair (0, - 9 )

This indicates that when t = 0 , r = - 9

This is the y- intercept at - 9

Thus both functions have the same y- intercept

The coefficient of determination given the correlation coefficient is 0.81.

Correlation is used to measure the linear relationship between two variables. When the correlation coeffienient is negative, it means that the variables have a negative correlation. This means that the two variables move in opposite directions.

The coefficient of determination is used to measure the variation between the two variables being measured.

The coefficient of determination = correlation coeffienct²

-0.9² = 0.81

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The volume of water in the cone-shaped paper cup is 25.12 cubic centimeters.

To calculate the volume of water in the cone-shaped paper cup, we can use the formula for the volume of a cone:

V = (1/3) * π * r^2 * h

Given:

Height of water (h) = 6 cm

Diameter of the top surface of water (2r) = 4 cm

First, we need to find the radius (r) of the top surface of the water. Since the diameter is given as 4 cm, the radius is half of that:

r = 4 cm / 2 = 2 cm

Now we can substitute the values into the volume formula and calculate the volume of water:

V = (1/3) * 3.14 * (2 cm)^2 * 6 cm

V = (1/3) * 3.14 * 4 cm^2 * 6 cm

V = (1/3) * 3.14 * 24 cm^3

V = 25.12 cm^3.

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Answer:

1. The percentage change is 74% and it is a percentage decrease

2. The percentage change is 15% and it is a percentage decrease

3. The percentage change is 20% and it is a percentage decrease

4. The percentage change is 43% and it is a percentage increase

5. The percentage change is 40% and it is a percentage decrease

6. The percentage change is 39% and it is a percentage decrease

Step-by-step explanation:

Given

\(1.\ Original = 5; New = 1.3\)

\(2.\ Original = 160; New = 136\)

\(3.\ Original = 15; New = 12\)

\(4.\ Original = 7; New = 10\)

\(5.\ Original = $30; New = $18\)

\(6.\ Original = 9.6; New = 5.9\)

Required

Determine the percentage change and state whether it's an increase or decrease

Percentage change is calculated as:

\(\%Change = \frac{New - Original}{Original} * 100\%\)

\(1.\ Original = 5; New = 1.3\)

\(\%Change = \frac{1.3 - 5}{1.3} * 100\%\)

\(\%Change = \frac{-3.7}5} * 100\%\)

\(\%Change = \frac{-3.7 * 100\%}{5}\)

\(\%Change = \frac{-370\%}{5}\)

\(\%Change = -74\%\)

The percentage change is 74% and it is a percentage decrease

\(2.\ Original = 160; New = 136\)

\(\%Change = \frac{136 - 160}{160} * 100\%\)

\(\%Change = \frac{-24}{160} * 100\%\)

\(\%Change = \frac{-24 * 100\%}{160}\)

\(\%Change = \frac{-2400\%}{160}\)

\(\%Change = -15\%\)

The percentage change is 15% and it is a percentage decrease

\(3.\ Original = 15; New = 12\)

\(\%Change = \frac{12- 15}{15} * 100\%\)

\(\%Change = \frac{-3}{15} * 100\%\)

\(\%Change = \frac{-3* 100\%}{15}\)

\(\%Change = \frac{-300\%}{15}\)

\(\%Change = -20\%\)

The percentage change is 20% and it is a percentage decrease

\(4.\ Original = 7; New = 10\)

\(\%Change = \frac{10- 7}{7} * 100\%\)

\(\%Change = \frac{3}{7} * 100\%\)

\(\%Change = \frac{3* 100\%}{7}\)

\(\%Change = \frac{300\%}{7}\)

\(\%Change = 43\%\) -- (approximated)

The percentage change is 43% and it is a percentage increase

\(5.\ Original = $30; New = $18\)

\(\%Change = \frac{18- 30}{30} * 100\%\)

\(\%Change = \frac{-12}{30} * 100\%\)

\(\%Change = \frac{-12* 100\%}{30}\)

\(\%Change = \frac{-1200\%}{30}\)

\(\%Change = -40\%}\)

The percentage change is 40% and it is a percentage decrease

\(6.\ Original = 9.6; New = 5.9\)

\(\%Change = \frac{5.9- 9.6}{9.6} * 100\%\)

\(\%Change = \frac{-3.7}{9.6} * 100\%\)

\(\%Change = \frac{-3.7* 100\%}{9.6}\)

\(\%Change = \frac{-370\%}{9.6}\)

\(\%Change = -39\%\) -- (approximated)

The percentage change is 39% and it is a percentage decrease

Answer:

  20 km/hr

Step-by-step explanation:

The boat's still-water speed is the average of its speeds against and with the current:

  (15 +25)/2 = 20 . . . km/hr

__

If you want to write equations, you can let b and c represent the speeds of the boat and current in km/hr.

  b - c = 15 . . . . upstream speed

  b + c = 25 . . . . downstream speed

Add these two equations, and you get ...

  (b -c) +(b +c) = (15) +(25)

  2b = 40

  b = 20 . . . . divide by 2

The speed of the boat in still water is 20 km/hr.

Answer:

20 km/hr

Step-by-step explanation:

To solve this, you have to find the average speed it is going. To find this, you just add up all of the speeds mentioned and divide it by the number of speeds you added.

15 +25=40

40/2=20

20km/hr!!!

Good luck on what you are doing I hope you do well! Brainliest would be great :)

Answer:

That would be 14 miles ÷ 6 hours which would be 2.3333 or 2 and 1/3

Answer:

I believe 6/7 times 3/4 in the simplest form is 9/14 because you aren't able to put anything in both of those numbers

Step-by-step explanation:

The value of x in the equation (6/7) × (3/4) = x is 9/14.

To find the value of x in the equation (6/7) × (3/4) = x.

We can simply multiply the two fractions together.

Multiplying the numerators and denominators gives us:

(6 × 3) / (7 × 4)

= 18/28

The fraction 18/28 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2.

(18/2) / (28/2)

= 9/14

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The relationship between a statistic and a parameter is the same as the relationship between , Option(A) a sample and a population

The Population is defied as an entire group of individuals that we are interested in studying, while a sample is a subset of that population that we actually observe and collect data from.

A Parameter is defined as a numerical characteristic of a population, such as its mean or variance, whereas a statistic is a numerical characteristic of a sample, such as its sample mean or sample standard deviation.

The relationship between a sample and a population is similar to the relationship between a statistic and a parameter because a sample is used to estimate  information about the population, and a statistic is used to estimate  information about a parameter.

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Answer:

Option (4)

Step-by-step explanation:

Vertices of ΔABC are,

A → (-9, 3)

B → (-9, 6)

C → (0, 3)

If the given triangle is rotated 180° about the origin image triangle will have the vertices as,

Rule for the rotation,

(x, y) → (-x, -y)

A' → (9, -3)

B' → (9, -6)

C' → (0, -3)

If a point (x, y) is dilated by a scale factor of 'k',

Rule for the dilation,

(x, y) → (kx, ky)

Since, ΔA"B"C" is smaller than ΔABC,

Therefore, dilating ΔA'B'C' by a scale factor = \(\frac{1}{3}\)

Image triangle ΔA"B"C" will be,

A" → (3, -1)

B" → (3, -2)

C" → (0, -1)

Therefore, Option (4) is the correct option.

Answer:

the guy above me is wrong the correct option is the second option

Step-by-step explanation:

i just got it wrong & it showed me the answer

___________________________

___________________________

___________________________

___________________________

These are parallel and equal lines.

Mark as brainliest.❤️

\({\huge{\purple{\underline{\underline{\bf{\pink{\mathfrak{Thanks}}}}}}}}\)

The sequence {an} = {\(8n^4 + n + 1\)} is not convergent. It diverges to infinity as n approaches infinity.

To determine whether the sequence {an} = {\(8n^4 + n + 1\)} is convergent, we need to examine the behavior of the terms as n approaches infinity.

The sequence {an} is said to be convergent if there exists a real number L such that the terms of the sequence get arbitrarily close to L as n approaches infinity.

To investigate convergence, we can calculate the limit of the sequence as n approaches infinity.

lim(n→∞) \((8n^4 + n + 1)\)

To evaluate this limit, we can look at the highest power of n in the sequence, which is \(n^4.\) As n approaches infinity, the other terms (n and 1) become insignificant compared to n^4.

Taking the limit as n approaches infinity:

lim(n→∞) \(8n^4 + n + 1\)

= lim(n→∞) \(8n^4\)

Here, we can clearly see that the limit goes to infinity as n approaches infinity.

Therefore, the sequence {an} = {\(8n^4 + n + 1\)} is not convergent. It diverges to infinity as n approaches infinity.

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Answer:

Hi there!

Your answer is:

996 students were apart of this survey!

Step-by-step explanation:

3 out of 4 students means that 75% of students prefer the assemblies be held on Friday.

If 75% = 747 students then:

/75

1% = 9.96 students

×100

100% = 996 students

I hope this makes sense!

Answer:

2/3&1/6

2/3- 1/6

the LCM for 3 and 6 is 6

=(2x6)/(3x6) -(1x6)/(6x6)

=4/6-1/6

=(4-1)/6

find the difference

= 3/6

=1/2

2/3-1/6= 1/2

By using LCM method, 1/2 is the equivalent fraction by subtracting 1/6 from 2/3.

2/3&1/6

2/3- 1/6

cross multiply

2x6-1x3/3x6

simplify

12-3/18

=9/18

= 1/2

2/3-1/6 = 1/2

By using cross multiplication method, 1/2 is the difference between two fractions 2/3 and 1/6.

Step-by-step explanation:

hope that helps>3

The correct options for the values of a and b in the equation are a = 2 and b = -3/4

We shall use the negative sign before the bracket at the left hand side of the equation to open bracket as follows;

-(-2 + 3/3) = (- × -2) + (- × 3/4)

-(-2 + 3/3) = (+2) +(-3/4)

so the equation becomes;

7/8 -(-2 + 3/3) = (+2) +(-3/4) + 7/8.

Therefore, the correct options for the values of a and b in the equation are a = 2 and b = -3/4

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Sarah used 30 scoops of drink mix per gallon of water. Since the proportions of the ingredients remained the same for each container, we can calculate the ratio between the scoops of drink mix and gallons of water.

The table shows the number of scoops of powdered drink mix and gallons of water Sarah used to fill three containers. The question asks for the proportion of scoops of drink mix per gallon of water.

Since the proportions of the ingredients remained the same for each container, we can calculate the ratio between the scoops of drink mix and gallons of water. From the given information, we see that for each gallon of water used, Sarah used 30 scoops of drink mix.

This means that the ratio of scoops of drink mix to gallons of water is 30:1. For every gallon of water, 30 scoops of drink mix are used. This ratio remains consistent across all the containers Sarah filled.

Therefore, the answer is that Sarah used 30 scoops of drink mix per gallon of water.

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