Your car averages about 27 miles per gallon on highways. With gasoline priced at $2.599 per gallon, how much will
you expect to spend on gasoline during your 500-mile trip?
$192.38
b. $18.51
C $70.17
d. $48.13

Answer:

1649.33 units³

Step-by-step explanation:

Let the height and the radius be known as "h" and "r" respectively.

Formulae(s):

Clearly, we can see that the volume of the cylinder is three times greater than the volume of the cone as,

Determining the volume of the cylinder;

Therefore, the volume of the cylinder is 1649.33 units³.

The probability of the random variable Z being less than -3.10 is obtained using the Standard Normal Distribution table.

a) To find the probability (P(Z < -3.10)) for a standard normal random variable Z, we can use a standard normal distribution table or a calculator.

Using a standard normal distribution table, we look up the value -3.10 and find the corresponding probability. The table typically provides the cumulative probability up to a given value. Since we want (P(Z < -3.10)), we need to find the probability for -3.10 and subtract it from 1.

The probability (P(Z < -3.10)) is approximately 0.000968.

b) To find the probability (P(Z < 1.28)) for a standard normal random variable Z, we can again use a standard normal distribution table or a calculator.

Using a standard normal distribution table, we look up the value 1.28 and find the corresponding probability. This probability represents (P(Z < 1.28)) directly.

The probability (P(Z < 1.28)) is approximately 0.89973.

c) The probability (P(Z > 0)) for a standard normal random variable Z represents the area under the standard normal curve to the right of 0.

Since the standard normal distribution is symmetric around 0, the area to the left of 0 is 0.5. Therefore, the area to the right of 0 is also 0.5.

Hence, (P(Z > 0)) is 0.5.

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Answer:

20

Step-by-step explanation:

Total no of plants in a garden = 36

The ratio of tomato plants to cucumber plants to be 4:5.

Let tomato plants are 4x and cucumber plants is 5x.

ATQ,

4x+5x=36

9x = 36

x = 4

For cucumber plant, 5x = 5(4) = 20

So, there are 20 cucumber plants will be in Reggie's garden

Answer:

-3a-21

Step-by-step explanation:

Answer:

27a-21

Step-by-step explanation:

12a-3(7+5a)

distribute the 3

3x7=21

3x5a=15a

12a-21+15a

12a+15a=27a

27a-21

6y² - 13y + 6 is the product of 2y -3 and 3y - 2.

Given the following linear expression

(2y-3)(3y-2)

We need to expand the expression to get a quadratic function as shown below:

(2y-3)(3y-2) = 2y(3y) - 2(2y) - 3(3y) -3(-2)

(2y-3)(3y-2) = 6y² - 4y - 9y + 6

(2y-3)(3y-2) = 6y² - 13y + 6

Hence the product of 2y - 3 and 3y - 2 is equivalent to 6y² - 13y + 6

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When choosing a bank, consider fees for services such as ATM transactions and debit card usage, as well as factors such as availability of free checking, customer service, and rewards/interest rates.

First State Bank:

Total check fees = 5 checks x $1/check = $5

Total ATM fees = 3 ATM transactions x $1/transaction + 2 nonbank ATM transactions x $2/transaction = $7

Total debit card fees = 8 debit card transactions x $0/debit card transaction = $0

Total monthly fees = $12.50

Total fees = $5 + $7 + $12.50 = $24.50

National Bank:

Total check fees = 5 checks x $1/check = $5

Total ATM fees = 3 ATM transactions x $0/transaction + 2 nonbank ATM transactions x $2/transaction = $4

Total debit card fees = 8 debit card transactions x $0/debit card transaction = $0

Total monthly fees = $0

Total fees = $5 + $4 + $0 = $9

Third City Bank:

Total check fees = 3 checks x $0/check = $0

Total ATM fees = 3 ATM transactions x $0/transaction + 2 nonbank ATM transactions x $3/transaction = $6

Total debit card fees = 8 debit card transactions x $0.75/debit card transaction = $6

Total monthly fees = $0

Total fees = $0 + $6 + $6 + $0 = $12

When choosing which of the three banks to use for making debit purchases, you might consider factors such as the availability of free checking, the fees for nonbank ATM transactions, the fees for debit card transactions, and the level of customer service provided by each bank. Additionally, you might consider the interest rates and rewards offered by each bank for maintaining a checking account with them.

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Answer:

16/22, 24/33, and 40/55

or

72.7272...% = Percentage form

0.7272... = Decimal form

Hope this helps :)

Pls brainliest...

For a bag with total 28 marbles ( 10 - yellow , 18- teal). The probability that both randomly chosen marbles are teal is equals to the 2.4706.

We have a opaque bag which contains a number of marbles.

Number of yellow marbles in bag = 10

number of teal marbles in a bag = 18

Total number of marbles in a bag

= 10 + 18 = 28

Randomly, two marbles are chosen from the bag at the same time. We have to determine the probability that both marbles are teal.Probability is used to measure the chances of occurrence of an event. It is calculated by dividing the favourable response or outcomes for event to the total possible outcomes. Let us consider an event E such that both choosen marbles are teal. Now, total possible outcomes = 28

Number of ways to draw 2 marbles from bag = ²⁸C₂ = 27 × 14

= 378

Number of ways to draw 2 teal marbles from bag = ¹⁸C₂

= 9× 17 = 153

The probability that both marbles are teal, P(E) = 153/378 = 2.470588

Hence, required probability is 2.4706.

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Question:

Solution:

According to the statement of the problem, we get the following scheme:

According to this scheme, we get the following equation:

this is equivalent to:

Putting Like Terms Together, we get:

this is equivalent to:

solving for x, we obtain:

So that, we can conclude that the correct answer is:

Answer:

4, x-1

Step-by-step explanation:

The first piece of this function goes from -1 to 1. Since that part of the function is a horizontal line at y=4, and has no slope, this first part is just 4.

The second piece of this function goes from 3 to 5. This piece does have a slope that you can either solve or just from reading the graph will give you a slope of 1. Since one of the points is (3, 2), we can figure out that the y-intercept is -1. (You can also just extend the line across the y-axis). When putting this equation together we get x-1 being the second part.

The solution is:

The graph represents the piecewise function:

f(x)= { 4, if -1 ≤ x ≤ 1;

         (x - 1), if 3 ≤ x ≤ 5 }

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

The first piece of this function goes from -1 to 1.

Since that part of the function is a horizontal line at y=4, and has no slope, this first part is just 4.

so, we have,

The second piece of this function goes from 3 to 5.

This piece does have a slope that you can either solve or just from reading the graph will give you a slope of 1.

Since one of the points is (3, 2), we can figure out that the y-intercept is -1. (You can also just extend the line across the y-axis).

When putting this equation together we get x-1 being the second part.

Hence, The solution is:

The graph represents the piecewise function:

f(x)= { 4, if -1 ≤ x ≤ 1;

         (x - 1), if 3 ≤ x ≤ 5 }

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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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Data:

Cheese: c

People: p

Sarah:

c=2.5 cups

p=10

Arun:

c=1.6 cups

p=8

To find the number of cups of cheese that Arun need to a serving you divide the 1.6 cups into 8 (8 servings):

Answer:

El polinomio ordenado de forma ascendente y con relación a \(x\) es \(p(x,y) = y^{5}+6\cdot y^{4}\cdot x -7\cdot y^{3}\cdot x^{2}-y^{2}\cdot x^{3}+x^{4}\cdot y -5\cdot x^{5}\).

Step-by-step explanation:

El polinomio está en términos de dos variables: \(x\), \(y\). Puesto que necesitamos ordenar el polinomio con relación a

\(p(x, y) = \Sigma\limits_{i = 0}^{n} \,c_{i} (y)\cdot x^{i}\) (1)

Where:

\(i\) - Índice i-ésimo del polinomio asociado al polinomio i-ésimo.

\(c_{i}(y)\) - Coeficiente i-ésimo en función de \(y\).

\(x, y\) - Variables independientes.

\(p(x,y)\) - Variable dependiente.

\(n\) - Grado del polinomio.

A partir de esto y comparando (1) con la expresión del enunciado, encontramos que el último está formado por seis monomios y tiene grado 5. Al aplicar las propiedades algebraicas correspondientes tenemos que:

\(p(x,y) = y^{5}+6\cdot y^{4}\cdot x -7\cdot y^{3}\cdot x^{2}-y^{2}\cdot x^{3}+x^{4}\cdot y -5\cdot x^{5}\)

Answer:

$1053

Step-by-step explanation:

If we have that £1 = $1.62, then we can multiply both sides by 650 in order to get £650 on the left side of the equality. We must multiply the right side also by 650, and so we get £650=$1.62 * 650.

To do this multiplication, we can break 1.62 down  simply into $1.00 +$0.6+$0.02

650*$1.00=$650, 650*$0.6=650*6/10=65*6=$390, and 650*$0.02=650*2/100=6.5*2=$13.

When we add these three products together, we get $650+$390+$13=$1053. And so, £650=$1053

To find a decimal approximation of the radical expression using the given notation, you can use the following steps:
1. Identify the function f'(x) as the derivative of the original function f(x).
2. Find the value of Δx, which is the change in x.
3. Apply the formula f'(x)Δx to approximate the change in the function value.

For example, let's say f(x) is the radical expression, which could be represented as f(x) = √x. To find f'(x), we need to find the derivative of f(x) with respect to x:
f'(x) = 1/(2√x)
Now, let's say we want to approximate the value of the expression at x = 103. We can choose a small value for Δx, such as 0.001:
Δx = 0.001
Now, we can apply the formula f'(x)Δx:
Approximation = f'(103)Δx = (1/(2√103))(0.001)
After calculating the expression, we get:
Approximation = 0.049 (rounded to three decimal places)
So, the value found using f'(x)Δx for the radical expression at x = 103 is approximately 0.049.

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(a) E(X) = ∫x fx(x) dx = ∫x ex dx from -∞ to 0

= [-e^x] from -∞ to 0 = 1

(b) Variance(X) = E(X^2) - [E(X)]^2

= ∫x^2 fx(x) dx - 1^2

= ∫x^2 ex dx from -∞ to 0 - 1

= [-x^2e^x] from -∞ to 0 + 2[∫xe^x dx from -∞ to 0] - 1

= 0 + 2(-1) - 1 = -3

(c) E(e^(1/2 X)) = ∫e^(1/2 x) fx(x) dx = ∫e^(1/2 x) ex dx from -∞ to 0

= [-2e^(-x/2)] from -∞ to 0

= 2

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A system having ΔG equal to zero means that the system is at equilibrium at standard conditions. This is option c. In a chemical reaction, ΔG represents the change in Gibbs free energy, which is a measure of the energy available to do work.

When ΔG is equal to zero, it indicates that the system is balanced, with the forward and reverse reactions occurring at the same rate. At equilibrium, the concentrations of reactants and products remain constant over time. For example, consider the reaction A ⇌ B. Initially, if we have more A than B, the forward reaction will be favored until equilibrium is reached. At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction, and the concentrations of A and B remain constant. In this case, ΔG is zero.

It is important to note that while a ΔG of zero indicates equilibrium, it does not provide information about whether the reaction is spontaneous or nonspontaneous. The spontaneity of a reaction is determined by the sign of ΔG. If ΔG is negative, the reaction is spontaneous, while a positive ΔG indicates a nonspontaneous reaction.

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Answer:

f(x) = 9x - 18

Step-by-step explanation:

Moving the graph to the left or right involves directly manipulating the "x" value. When you want to shift the graph to the right, you need to subtract the desired value directly from "x". This would make the equation look like this:

f(x) = 9(x - 2)

However, this can be simplified by multiplying 9 by each term in the parentheses.

f(x) = 9x - 18

Answer:

the answer is-

Step-by-step explanation:

42.5% and the estimation is 43%

Answer:

42.5%

Step-by-step explanation:

17/40 = 0.425

Move decimal to the tenths place.

0.425 --> 42.5

a. the probability of getting a positive result is approximately 0.5658 or 56.58%. b. the chance of having breast cancer given a positive result is approximately 0.9174 or 91.74%.

(a) To calculate the probability of getting a positive result, we need to consider both the sensitivity and the prevalence of the disease.

The sensitivity of the test is given as 86.9%, which means that the test correctly identifies 86.9% of the positive cases.

The prevalence of breast cancer in the population is 60%, which means that 60% of individuals have the disease.

To calculate the probability of getting a positive result, we can use Bayes' theorem:

P(Positive) = P(Positive | Cancer) * P(Cancer) + P(Positive | No Cancer) * P(No Cancer).

Given that the specificity is the complement of the false positive rate (1 - specificity), we can determine P(Positive | No Cancer) as 1 - specificity = 1 - 0.889 = 0.111.

Plugging in the values, we have:

P(Positive) = (0.869 * 0.60) + (0.111 * 0.40) = 0.5214 + 0.0444 = 0.5658.

Therefore, the probability of getting a positive result is approximately 0.5658 or 56.58%.

(b) If a positive result is obtained, we want to calculate the chance of having breast cancer. This is the conditional probability of having cancer given a positive result.

To calculate this probability, we can use Bayes' theorem again:

P(Cancer | Positive) = (P(Positive | Cancer) * P(Cancer)) / P(Positive).

From part (a), we have already calculated P(Positive) as 0.5658, P(Positive | Cancer) as 0.869, and P(Cancer) as 0.60.

Plugging in the values, we have:

P(Cancer | Positive) = (0.869 * 0.60) / 0.5658 = 0.9174.

Therefore, the chance of having breast cancer given a positive result is approximately 0.9174 or 91.74%.

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A regular pyramid has a polygonal base and a vertex directly above the center of the base. The specific name of the regular pyramid depends on the number of sides in its base polygon.

A regular pyramid has a polygonal base and a vertex directly above the center of the base. The base of a regular pyramid can be any regular polygon, meaning all its sides are equal in length and all its angles are equal. The number of sides in the base determines the name of the regular pyramid.

For example:

- A regular pyramid with a triangular base is called a tetrahedron.

- A regular pyramid with a square base is called a square pyramid.

- A regular pyramid with a pentagonal base is called a pentagonal pyramid.

- A regular pyramid with a hexagonal base is called a hexagonal pyramid.

- And so on, based on the number of sides in the base polygon.

In summary, a regular pyramid has a polygonal base and a vertex directly above the center of the base. The specific name of the regular pyramid depends on the number of sides in its base polygon.

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Answer:

brrrrrrrrrrrr

Step-by-step explanation:

Answer:

I believe its A.

Step-by-step explanation:

The expression that represents the perimeter of the other shape is 9x + 6y.

Option(b) is the correct one.

Expressions in mathematics are mathematical statements that comprise at least two terms that contain numbers, variables, or both, and are joined by an operator. Addition, subtraction, multiplication, and division are all examples of mathematical operators.

Given:

Expression for the sum of the perimeter of two shapes = 13x + 4y

Expression for the perimeter of one shape = 4x - 2y

Expression for the perimeter of the other shape is,

(13x + 4y) - (4x - 2y)

= 13x - 4x + 4y + 2y (combine the like terms and solve)

= 9x + 6y

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Answer:

35742

Step-by-step explanation:

Answer:

ill give my honest opinion i dont know

Step-by-step explanation:

The technique used by an aerodynamic particle sizer to measure the amount of particles in the air is laser diffraction. Option A is answer.

Laser diffraction is a commonly employed technique in aerosol science and particle analysis. It works by passing a laser beam through a sample containing airborne particles. As the laser beam interacts with the particles, it undergoes diffraction, resulting in scattering patterns. These scattering patterns are then analyzed to determine the size distribution of the particles.

By measuring the intensity and angle of the scattered light, the aerodynamic particle sizer can calculate the size of the particles and provide information about their concentration in the air.

Option A is answer.

""

laser diffraction

laser refraction

laser reflection

laser diversion

""

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