8.
A taxi company charges passengers $1.75 for a ride, no matter how long the ride is, and an additional $0.40 for each mile traveled. The rule c = 0.40m + 1.75 describes the relationship between the number of miles m and the total cost of the ride c.
a. What is the charge for a 1-mile ride?
b. What is the charge for a 2.7-mile ride?


A. $2.15; $2.83


B. $0.40; $5.13


C. $0.40; $1.08


D. $1.75; $2.15

Answer:

12

Step-by-step explanation:

Number of outcomes for a coin = 2

Number of outcomes of a die = 6

2*6 = 12

All are technically squares, but if you are referring to just squares, then C and D are squares.

Answer:

choose ypur answer even

Answer:

The distance of two points  = 6 √2 = 8.4852

Step-by-step explanation:

Explanation:-

From the graph

Given points are  A ( 4,2) and B ( -2 , -4)  

The distance formula

       = \(\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1})^{2} }\)

( x₁ , y₁ ) = ( 4,2 )   and (x₂ , y₂) = ( -2 , -4)

The distance formula

       = \(\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1})^{2} }\)

     =\(\sqrt{(-2 -(4))^{2} + (-4 - (2))^{2} }\)

  =   \(\sqrt{36+36} = \sqrt{72} = 6\sqrt{2}\)

Final answer:-

The distance of two points  = 6 √2 = 8.4852

Answer:

20 degrees

Step-by-step explanation:

Angles on the edge of the circle are equal to 1/2 of the arc it forms, so that means angle z is one half of 40 degrees. 1/2 * 40 = 20 degrees.

The independent set in a graph is a set of vertices that contain no edges. So, no neighboring vertices are included. The max independent set problem is to get an independent set of maximum size in graph G.

The solution for this question is discussed below:

a) The integer linear program for the max independent set problem is as follows:

maximize ∑x_i Subject to: x_i+x_j ≤ 1 {i,j} ∈ E;x_i ∈ {0, 1} ∀i. The variable x_i can represent whether the ith vertex is in the independent set. It can take on two values, either 0 or 1.

b) The LP relaxation for the max independent set problem is as follows:

Maximize ∑x_iSubject to:

xi+xj ≤ 1 ∀ {i, j} ∈ E;xi ≥ 0 ∀i. The variable xi can take on fractional values in the LP relaxation.

c) The family of graphs is as follows:

Consider a family of graphs G = (V, E) defined as follows. The vertex set V has n = 2^k vertices, where k is a positive integer. The set of edges E is defined as {uv:u, v ∈ {0, 1}^k and u≠v and u, v differ in precisely one coordinate}. It can be shown that the size of the max independent set is n/2. Using LP, the value can be determined. LP provides a value of approximately n/4. Therefore, the ratio LP-OPT/OPT is at least c/4. Therefore, the ratio is in for a constant c>0.

d) The size of a max-independent set is equivalent to the number of vertices minus the minimum vertex cover size.

e) The 2-approximation algorithm for vertex cover implies a 2-approximation algorithm for the max independent set.

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Answer:

We rotate the point counterclockwise by an angle θ = tan⁻¹ (y/x)

Step-by-step explanation:

If we have the point (x, y), its reflection along the x-axis (x,-y). The reflection of the point (x, -y) along the y - axis is (-x, -y). So, the angle between the initial point (x, y) and the final point (-x, -y) is θ = tan⁻¹ [(-y - y)/(- x -x)] = tan⁻¹ [(-2y/(-2x)] =  tan⁻¹(y/x).

So, the point (x, y) is rotated counterclockwise by an angle of  θ = tan⁻¹ (y/x) to perform both reflections.

Answer:

PF

Step-by-step explanation:

Since the triangles are congruent, meaning they are the same shape, we can just match the lines between the two triangles. In triangle ABC, the line AC is the hypotenuse of the triangle. So, we need to find the hypotenuse of the triangle PDF. Looking, we can see the hypotenuse of the triangle PDF is the line, or side, PF.

Hope this helped!

Answer:

a) 3n + 2 and b) multiply by 4 and add 5

Step-by-step explanation:

a) 3 x n = 3n
3n + 2 = 3n + 2

b) You can see that the 4 has an x next to it, indicating that you need to multiply the x by 4. Then it also has "+ 5" so you also need to add 5 to the 4x. Finally, you get 4x + 5.
(x4, +5)

The coefficient of the squared term in the parabola's equation is 1/25.

In this exercise, you are required to determine the factored form of the given quadratic function that passes through the points (2, -4) and (-3, -3).

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided above, we can determine the value of a as follows:

f(x) = a(x - h)² + k

-3 = a(-3 - 2)² - 4

-3 = 25a - 4

1 = 25a

a = 1/25

Therefore, the required quadratic function is given by:

f(x) = a(x - h)² + k

f(x) = y = 1/25(x - 2)² - 4

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Answer:

10 * 5 / 2 = 25 cm

Step-by-step explanation:

Hope this helps

Answer:

25 cm² is the answer ..... my sister

Answer:

x = 8

Step-by-step explanation:

This question is pretty simple. You already know the value of x, we substitute what x equals and find the number 2 cubed.

2^3 = ?

2x2x2 = 8

Answer:

can't see the equation sorry

Answer:

Subtraction Property of Equality

Step-by-step explanation:

Victor solved this inequality as shown:

Given: 6+3(x+5) = 36

Step 1: 6+3x+15 = 36

Step 2: 3x+21= 36

Step 3: 3x = 15

Step 4: 3x=15

What property justifies the work between step 3, I'm guessing its this question if not message me.

from step 2 to 3 we must use Subtraction Property of Equality since

3x+21 = 36 must subtract 21 both sides

then u get 3x=15

Answer:

Step-by-step explanation:

1.1, 1.112

2x + 17 grows no faster than 3x as x approaches infinity.

To show that 2x + 17 is O(3x), we need to find two positive constants, C and k, such that:

|2x + 17| <= C|3x| for all x > k

We can start by simplifying the left-hand side:

|2x + 17| = 2x + 17 (since x is always non-negative)

Next, we can simplify the right-hand side:

|3x| = 3x

Now, we need to find C and k that satisfy the inequality:

2x + 17 <= C*3x for all x > k

Dividing both sides by 3x, we get:

(2/3) + (17/3x) <= C for all x > k

Since (2/3) is a constant, we only need to find a value of k such that (17/3x) is less than some other constant. Let's choose k = 1, then:

(17/3x) < 6 for all x > 1

So, we can choose C = 6 and k = 1. Therefore, we have shown that:

|2x + 17| <= 6|3x| for all x > 1

This satisfies the definition of 2x + 17 being O(3x), which means that 2x + 17 grows no faster than 3x as x approaches infinity.

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Answer:

Base = 353.55 sq cm

Step-by-step explanation:

10 by 10 triangle = 45 45 90 traingle

hypotenuse = 10√2

A = 10√2 by 25

Answer:

$13.77

Step-by-step explanation:

12.99 x 0.06

0.7794

0.7794+12.99

13.7694

$13.77

Answer:

2.8

Step-by-step explanation:

If you turn the question around (6.7 - 3.9) the answer is 2.8

Hope this helps~

Answer:

see explanation

Step-by-step explanation:

4(x - 1)² - 9(x - 1) =-  2

let t = x - 1 , then rewrite the expression as

4t² - 9t = - 2 ( add 2 to both sides )

4t² - 9t + 2 = 0 ← in standard form

Step 2

consider the factors of the product of the coefficient of the t² term and the constant term which sum to give the coefficient of the t- term

product = 4 ×  2 = 8 and sum = - 9

the factors are - 8 and - 1

use these factors to split the t- term

4t² - 8t - t + 2 = 0 ( factor first/second and third/fourth terms )

4t(t - 2) - 1(t - 2) = 0 ← factor out (t - 2) from each term

(t - 2)(4t - 1) = 0 ← in factored form

equate each factor to zero and solve for t

4t - 1 = 0 ⇒ 4t = 1 ⇒ t = \(\frac{1}{4}\)

t - 2 = 0 ⇒ t = 2

Step 3

Now solve for x using

t = x - 1 ( add 1 to both sides ), then

x = t + 1

t = \(\frac{1}{4}\) , then x = \(\frac{1}{4}\) + 1 = \(\frac{5}{4}\)

x = 2 , then x = 2 + 1 = 3

Given the lengths of the two sides and the angle between them, only one triangle can be created under the given circumstances.

1. Given that angle B is 32.5°, side AB is 37 cm, side AC is 26 cm, etc.

2. Calculate side BC using the Law of Cosines:

BC = (2(AB)(AC)cosB) + (AB)(AC)2

3. Input the values that are known: BC = (37 2 + 26 2 - 2(37)(26)cos32.5°)

4. Condense: BC = (1369 plus 676 minus 1848 cos 32.5 °)

5. Determine BC =. (2095 - 1539.07)

6. Condense: BC = 556.93

7. Determine BC as 23.701 cm.

8. Since the lengths of the two sides and the angle between them are specified, only one triangle can be formed under the current circumstances.

By applying the Law of Cosines, we can determine the length of the third side, BC, given that side AB is 37 cm, side AC is 26 cm, and angle B is 32.5°. In order to perform this, we must first determine the cosine of angle B, which comes out to be 32.5°. Then, we enter this value, together with the lengths of AB and AC, into the Law of Cosines equation to obtain BC.BC = (AB2 + AC2 - 2(AB)(AC)cosB) is the equation. BC is then calculated by plugging in the known variables to obtain (37 + 26 - 2(37)(26)cos32.5°). By condensing this formula, we arrive at BC = (1369 + 676 - 1848cos32.5°). Then, we calculate BC as BC = (2095 - 1539.07), and finally, we simplify to obtain BC = 556.93. Finally, we determine that BC is 23.701 cm. Given the lengths of the two sides and the angle between them.

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The drink costs $1.50. You pay 6% sales tax and leave a $3 tip. You

pay a total of $12.54.The sandwich cost is $34.1 .

Unless the transactions is exempt, every sale, entry, holding, or lease  is taxable. The cost of taxable products or services is increased by the sales tax, which is then charged to the customer at the point of sale.

The right response for Bea's overall price is $34.92

$3.50 + $9.80 + $13.90, or $272, is the total cost of takeaway.

The current sales tax rate is 7%.

and Tip is 20%.

Sales Tax = $27.2 x 7%

$1.90 sales tax

Similar Tip = $5.84 of $27.2 Tip

Tip = $5.84 The overall cost is thus: 

The overall cost is thus: 

Given.

Price in total: $27.2 plus $1.90 Plus $5

A tax rate is the amount at which a company or individual is subject to tax. Tax rates can be shown in a variety of ways, including average, marginal, even effective.

To finance its operations, the government levies fees on citizens based on factors like their income, the worth of the property, etc.

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The variance of a sample or a population cannot be negative. This means that option c, negative, is the correct answer.

Variance is a statistical measure that quantifies the dispersion or spread of data points around the mean. It tells us how much the individual data points deviate from the average. The variance is always a non-negative value because it is calculated by summing the squared differences between each data point and the mean, divided by the total number of data points.
If the variance were negative, it would imply that the sum of the squared differences between each data point and the mean is less than zero. However, this is not possible because squared differences are always positive or zero.
On the other hand, options a, zero, and d, less than 1, are incorrect. The variance can be zero if all the data points in the sample or population are the same, indicating no dispersion. Additionally, the variance can be any positive value, including values less than 1.
To summarize, the variance of a sample or a population cannot be negative, making option c, negative, the correct answer.

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The change in the amount of money that Noah's mother has can be represented by the expression $(17-8) . The expression can be simplified to $9, which shows that Noah still owes $9 to his mother.

The amount of money the Noah borrowed from his mother = $17

The amount of money that he was able to pay back = $8

Therefore the amount of money that is remaining = 17-8 =$9

Therefore, the change in the amount of money that Noah's mother has can be represented by the expression $(17-8) . The expression can be simplified to $9, which shows that Noah still owes $9 to his mother.

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The equation for the quadratic function represented by the table is f(x) = 2x² - 4x + 8.

The quadratic function represented by the given table can be written in the form:

f(x) = ax² + bx + c

Where 'a', 'b' and 'c' are constants that we need to find. To determine these constants, we need to use the values of 'x' and 'y' given in the table.

From the table,

At x = -1, f(x) = 14:

We have: a(-1)² + b(-1) + c = 14

which simplifies to: a - b + c = 14

At x = 0, f(x) = 8:

We have: a(0)² + b(0) + c = 8

which simplifies to: c = 8

At x = 1, f(x) = 6:

we have: a(1)² + b(1) + c = 6

which simplifies to: a + b + c = 6

At x = 2, f(x) = 8:

We have: a² + b(2) + c = 8

which simplifies to: 4a + 2b + c = 8

We now have three equations and three unknowns (a, b, and c), which we can solve simultaneously to find their values.

Substituting c = 8 into the first and third equations, we get:

a - b + 8 = 14

a + b + 8 = 6

Simplifying these equations, we get:

a - b = 6

a + b = -2

Adding the two equations, we get:

2a = 4

Therefore, a = 2.

Substituting a = 2 into either of the previous equations, we get:

b = -4

Hence, we have:

a = 2, b = -4, and c = 8

Plugging into f(x) = ax² + bx + c

We have:

f(x) = 2x² - 4x + 8.

Therefore, the quadratic equation is f(x) = 2x² - 4x + 8.

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We should choose Formulas as X in the given series of clicks to calculate formulas automatically.

File < Options < (A) Formulas < Automatic

We should choose Formulas as X in the given series of clicks to calculate formulas automatically.

Therefore, File < Options < (A) Formulas < Automatic

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The complete question is given below:

What would you choose as X in the given series of clicks to calculate formulas automatically: File < Options < X < Automatic?

a. Formulas

b. Language

c. Proofing

d. Advanced

The function h(x) is decreasing on the interval (3, ∞) (option d).

To determine whether the function h(x) is increasing or decreasing on a given interval, we need to analyze the sign of its derivative. In this case, we have the function h(x) = -2√(x - 3).

To find the derivative of h(x), we can apply the chain rule. Let's denote g(x) = √(x - 3). The derivative of g(x) is given by g'(x) = 1/(2√(x - 3)) * 1 = 1/(2√(x - 3)).

Next, we can find the derivative of h(x) by multiplying the derivative of g(x) by -2. Thus, h'(x) = -2 * 1/(2√(x - 3)) = -1/√(x - 3).

Now, let's analyze the sign of h'(x) to determine the intervals on which h(x) is increasing or decreasing.

When h'(x) < 0, the function h(x) is decreasing. Therefore, we need to find the interval(s) where h'(x) < 0.

h'(x) < 0 can be rewritten as -1/√(x - 3) < 0. Since the square root is always non-negative, we can multiply both sides by √(x - 3) without changing the inequality direction:

-1 < 0.

This inequality holds true for all real numbers. Hence, h'(x) < 0 for all x in the domain of h(x).

Since h(x) is always decreasing, we can conclude that the function h(x) is decreasing on the interval (3, ∞). Therefore, the correct statement is: "The function h(x) is decreasing on the interval (3, ∞)."

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The probability of finding 0 contaminated pieces in  225 g of chocolate is 5.57 X 10⁻⁷.

Here the number of contaminated fragments follows a Poisson process. Hence, let the distribution for the same be X.

Hence we get X ~ Poi(λt)

where λ is the mean no. of contaminated pieces and t is the no. of bars consumed.

For P(X = x) we get [(λt)ˣ  e^(-λt)]/x!

Here λ = 14.4 and t = 1 Hence we will get

P(X = x) = [(14.4)ˣ e⁻¹⁴°⁴]/x!

Here we need to find the probability of the no. of contaminated pieces = 0

Therefore

P(X = 0) = [(14.4)⁰ e⁻¹⁴°⁴]/0!

Hence the probability of finding 0 contaminated pieces in a bar of chocolate is

P(X = 0) =  e⁻¹⁴°⁴

= 5.57 X 10⁻⁷

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The lower bound is 147.5 and the upper bound is 152.5.

Given the weight of an apple 150 g rounded to the nearest 5g.

We have to find lower bound and upper bound.

Lower bound is an element less than or equal to all the elements in a given set.

Upper bound is an element greater than all the elements in a given set.

Lower bound= Number 1- (Number nearest to  which number 1 is rounded)/2

Upper bound=Number 1+(number nearest to which number 1 is rounded)/2

Weight of an apple =150 g

Lower bound=150-5/2

=150-2.5

=147.5

Upper bound=150+5/2

=150+2.5

=152.5

Hence the lower bound is 147.5 and upper bound is 152.5.

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We have:

Total number of cards in a pack = 52

Total number of aces in a pack = 4

The probability of drawing an ace is:

The probability that both are aces is:

Answer: the probability is 1/221