Joshua's mail truck travels 14 miles every day he works


and is not used at all on days he does not work. At the


end of his 100th day of work the mail truck shows a


mileage of 76,762. Model Joshua's truck mileage as a


function of the number of days he has worked. When


will he reach 100,000 miles?

The explicit formula for this sequence 6, 12, 24, 48, 96, .. is equal to aₙ = 6 * 2ⁿ⁻¹.

The sequence shown above is a geometric sequence because each term is obtained by multiplying the previous term by 2. To find the explicit formula for this sequence, we can use the formula:

aₙ = a₁ * rⁿ⁻¹

where:

aₙ = the nth term of the sequence

a₁ = the first term of the sequence

r = the common ratio between terms

n = the position of the term in the sequence

In this case, a₁ = 6 and r = 2, so the formula becomes:

aₙ = 6 * 2ⁿ⁻¹

Using this formula, we can find any term in the sequence by plugging in the value of n. For example, to find the 7th term, we would plug in n = 7:

a₇ = 6 * 2⁷⁻¹ = 6 * 2⁶ = 384

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Answer:

rectangle

Step-by-step explanation:

a shoe box is a rectangle

Answer:

1) b⁵⁴

2) 7⁷

Step-by-step explanation:

When you have an exponent raised to an exponent, like in #1, you simply multiply the exponents.

When you are dividing two numbers with exponents and they have the same base, like in #2, you subtract the denominator exponent from the numerator exponent.

Answer:

each tube costs $1.5 so put it the point in between 1 and 2

thank you

Step-by-step explanation:

The probability that you choose exactly 30 cents is 1/3.

To find the probability of choosing exactly 30 cents, we would first find the probability of choosing just a quarter and a nickel. This would be gotten this way:

4/9 * 3/8

= 12/72

= 1/6

The probability of choosing a nickel and a quarter would be:

3/9 * 4/8

= 12/72

= 1/6

Now we add up the probabilities to get the chance of choosing exactly 30 cents and this is:

1/6 + 1/6

= 2/6

=1/3

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The type of manufacturing process used to create the world's largest pizza can be classified as batch processing. Considerations such as ingredient sourcing, logistics, equipment capacity, and coordination among multiple teams were likely made during the planning stage. The process would change when planning the manufacturing process for a pizza available at Pie Craft or a pizza in the frozen section of a supermarket, with a shift towards more standardized and automated production methods.

World's Largest Pizza:

The manufacturing process for the world's largest pizza was a massive undertaking due to its size and quantity of ingredients. It involved batch processing, where a specific quantity of the product was produced at one time. During the planning stage, considerations were made regarding ingredient sourcing, logistics, equipment capacity, and coordination among multiple teams.

Pizza at Pie Craft:

If planning the manufacturing process for a pizza available at Pie Craft, a more standardized and streamlined approach would be adopted. The emphasis would be on consistency and quality. This would involve creating standardized recipes, portion control, and training staff to follow specific procedures. Some manual steps might still be involved, but automation could be introduced to streamline processes such as dough mixing and ingredient assembly.

Frozen Supermarket Pizza:

For a pizza in the frozen section of a supermarket, the manufacturing process would undergo significant changes. It would be highly automated and designed for mass production. The emphasis would be on consistency, convenience, and shelf life. The dough would be mechanically mixed, shaped, and portioned, while ingredients would be applied using automated systems. Packaging and freezing processes would also be optimized to maintain product quality.

In summary, the manufacturing process for the world's largest pizza was a massive undertaking, involving batch processing and careful planning regarding ingredient sourcing, logistics, and equipment capacity. For a pizza at Pie Craft, a more standardized approach would be adopted with a balance of manual and automated processes. In contrast, a frozen supermarket pizza would undergo a highly automated process to achieve consistency, convenience, and extended shelf life.

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Answer:

6141 - 89 = The 68th multiple (6052)

Answer:.

Step-by-step explanation:

Therefore, The Outdoor Furniture Corporation should produce 120 benches and 175 picnic tables to obtain the largest possible profit of $4,015.

Explanation:The given problem can be expressed in the form of a mathematical equation as: Maximize P = 9x + 20ySubject to constraints

:4x + 6y <= 120010x + 35y <= 35004x + 10y <= 12003x + 5y <= 1200x >= 0, y >= 0

Where, x = Number of Benchesy = Number of Picnic TablesFirst, we need to plot all the constraints on a graph. The shaded region in the figure below represents the feasible region for the given problem. Feasible region\(P = 9x + 20y = Z\)The feasible region is bounded by the following points:

A (0, 60)B (120, 175)C (70, 80)D (300, 0)

We need to calculate the profit at each of these points. Profit at

A(0, 60) = 0 + 20(60) = $1200Profit at B(120, 175) = 9(120) + 20(175) = $4,015

Profit at C(70, 80) = 9(70) + 20(80) = $1,630Profit at D(300, 0) = 9(300) + 20(0) = $2,700

From the above calculations, we can see that the maximum profit of $4,015 is obtained at point B (120, 175). Hence, the number of benches and tables that Outdoor Furniture should produce to obtain the largest possible profit are 120 and 175, respectively.

Therefore, The Outdoor Furniture Corporation should produce 120 benches and 175 picnic tables to obtain the largest possible profit of $4,015.

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Answer:

Step-by-step explanation:

The the terms be x and y

The sum of the terms = x+y

Difference of terms = x-y

Product of the sun and differences will be expressed as:

(x-y)(x+y) = x²-xy+xy-y²

(x-y)(x+y) = x²-y²

Hence the product of the terms is equivalent to the difference of two squares of the terms

Answer:

2 rocks

Step-by-step explanation:

2 crates + 2 rocks = 1 crate + 4 rocks

2 crates + 2 rocks = 2 crates + 8 rocks

Hence, 1 crate = (8-4)÷2

= 2 rocks

The number of friends in the group is 13

What is the appropriate function for $2771 spent in total?

The total cost function would consider all expenses, the one-time convenience fee of $15, the ticket cost per person  multiplied by the number of persons in the group and the fee for ride of $27 multiplied by number of friends going together

Let x represents the number of friends  going to the championship

Total cost=15+185x+27x

total cost=2771

2771=15+185x+27x

2771-15=212x

2756=212x

x=2756/212

x=13

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All of these statements are correct.

When describing categorical data, several methods can be used to provide meaningful insights and summarize the data.

Counts and proportions: Counting the number of observations in each category can provide information about the distribution and frequency of different categories. Proportions, also known as percentages, can be calculated by dividing the count in each category by the total count, allowing for a comparison of the relative frequencies of different categories.

Measures of center, spread, and shape: Although measures of center, spread, and shape are commonly associated with numerical data, they can also be used to describe certain aspects of categorical data. For example, the mode represents the most frequent category, which can be considered a measure of center. Measures of spread, such as the range or interquartile range, may not be applicable to categorical data. However, bar graphs and pie charts can visually depict the distribution and shape of categorical variables.

Box plots: Box plots are graphical representations primarily used for numerical data. They display the median, quartiles, and any potential outliers. While box plots are not commonly used for categorical data, they can be adapted by representing the frequency or proportion of categories instead of numerical values.

In summary, when describing categorical data, counts and proportions are commonly used to present the frequency and relative frequency of categories. Measures of center, such as the mode, can provide insights into the most frequent category. Measures of spread and shape may not be applicable, but graphical representations like bar graphs and pie charts can be used to visualize the distribution and shape of the categorical data. Box plots are not typically used for categorical data, as they are more suitable for numerical variables.

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The ordered pairs for the system of equations f(x) = x^2 -2x + 3 and f(x) = -2x + 12 are (3, 6) and (-3, 18)

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term(a ≠ 0)

f(x) = x^2 -2x +3 and f(x) = -2x + 12

which means

x^2 -2x +3  = -2x + 12

x^2 -2x +3  + 2x - 12 = 0

x^2 -9 = 0

by factorizing we have

(x-3)(x+3) = 0

x = 3 or -3

when x = 3

f(x) = -2x + 12

f(3) = -2(3) + 12 which is 6

when x = -3

f(-3) = -2(-3) + 12 which is 18

ordered pairs are (3, 6) and (-3, 18)

In conclusion, (3, 6) and (-3, 18) are the ordered pairs

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36ft^2 square feet of outdoor carpet we will need for this hole.

Big square: Length = 6 ft ; Width = 4 ft

Small square: Length = 6 ft ; Width = 2 ft

Area = L x W

Big square: 6 * 4 = 24 ft^2

Small square: 6 * 2 = 12ft^2

On adding both, we get

Total area = 24 + 12 = 36ft^2

36ft^2 square feet of outdoor carpet we will need for this hole.

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The true statement is "Causation implies correlation.."

From the question, we have the following parameters that can be used in our computation:

The list of options

As a general rule, causation means that there is a cause-and-effect relationship between variables.

A correlation doesn't imply causation, but causation always implies correlation

Correlation can occur without causation, meaning that two variables can be statistically related without one causing the other.

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When E is the region bounded by the spheres then the answer to the triple integral is -π/2 (e⁻¹ - e⁻¹⁶)

To evaluate the triple integral using spherical coordinates, we need to express the volume element dV in terms of spherical coordinates and determine the limits of integration.

In spherical coordinates, the volume element dV is given by:

dV = ρ² sin(φ) dρ dφ dθ

where ρ represents the radial distance, φ represents the polar angle (measured from the positive z-axis), and θ represents the azimuthal angle (measured from the positive x-axis in the xy-plane).

The given region E is bounded by the spheres x² + y² + z² = 1 and x² + y² + z² = 16. These can be expressed in terms of ρ as:

1 ≤ ρ ≤ 4

To determine the limits of integration for φ and θ, we consider the spherical symmetry of the problem. Since the region is bounded by spheres, the limits for both φ and θ will be the full range of [0, π] and [0, 2π], respectively.

Now, let's evaluate the triple integral:

∭E e(-x² - y² - z²) / √(x² + y² + z²) dV

= ∫₀²π ∫₀ᴨ ∫₁⁴ e(-ρ²) / ρ ρ² sin(φ) dρ dφ dθ

= ∫₀²π ∫₀ᴨ ∫₁⁴ e(-ρ²) ρ sin(φ) dρ dφ dθ

Since the integrand does not depend on θ, we can simplify the triple integral:

= ∫₀²π ∫₀ᴨ [-e(-ρ²) cos(φ)]₁⁴ sin(φ) dφ dθ

= ∫₀²π [-e(-ρ²) cos(φ) sin(φ)]₁⁴ dθ

= ∫₀²π [-e(-ρ²) / 4] dθ

= -e(-ρ²) / 4 [θ]₀²π

= -e(-ρ²) / 4 (2π - 0)

= -π/2 (e(-ρ²))

Now, we need to evaluate this expression within the limits of ρ:

= -π/2 ∫₁⁴ e(-ρ²) dρ

To solve this integral, we can use the substitution u = -ρ², which gives du = -2ρ dρ. The limits of integration transform accordingly:

u = -1, u = -16

∫ eu du = eu [u]_{-1}{-16} = e⁻¹ - e⁻¹⁶

Please note that the above expression represents the numerical value of the triple integral.

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Answer:

g=3.1

Step-by-step explanation:

If you want to do the math all you have to do is divide 7.13 by 2.3 and you get the answer

Please mark brainlest

Answer:

g=31/10

Step-by-step explanation:

To ensure that smooth curves have no cusps, we need to require that z'(t) never vanishes. This condition ensures that the tangent line to the curve changes smoothly and continuously as we move along the curve, without any abrupt changes in direction that would create cusps.

To understand why the condition that z'(t) never vanishes is necessary to ensure that smooth curves have no cusps, we first need to understand what a cusp is. A cusp is a point on a curve where the tangent line changes direction abruptly, creating a sharp point or corner in the curve.

Now, let's consider the curve traced by the parametrization z(t) = t^2it^3 with -1 ≤ t ≤ 1. To determine whether this curve has any cusps, we need to calculate the derivative of z(t) with respect to t:

z'(t) = 2it^3 + 3t^2i

If we set z'(t) equal to zero and solve for t, we get:

2it^3 + 3t^2i = 0
t^2(2i t + 3i) = 0

This equation has two solutions: t = 0 and t = -3/2i. These are the points on the curve where z'(t) vanishes.

At t = 0, the curve passes through the origin, which is a smooth point. However, at t = -3/2i, the curve has a cusp. To see why, we can look at the behavior of z(t) near this point.

As t approaches -3/2i from either side, the magnitude of t^2 increases without bound, while the magnitude of t^3 remains constant. This means that z(t) approaches infinity along a straight line with slope -3/2i. In other words, the curve has a sharp corner or cusp at this point.

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The given expression \(\log_3 x^6\) can be rewritten as \(6 \log_3 x\) using the property of logarithms. The values for \(A\) and \(B\) in the expression \(A \log_3 B\) are \(A = 6\) and \(B = x\).

The given expression is \(\log_3 x^6\). To rewrite it in the form \(A \log_3 B\), we can use the property of logarithms that states \(\log_a (x^n) = n \log_a x\). Applying this property, we have:

\(\log_3 x^6 = 6 \log_3 x\)

Here, \(A\) represents the coefficient of the logarithm, which is 6 in this case, and \(B\) represents the base of the logarithm, which is \(x\). Therefore, we can say that \(A = 6\) and \(B = x\).

In conclusion, the values for \(A\) and \(B\) in the expression \(A \log_3 B\) are \(A = 6\) and \(B = x\).

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Answer: 4.95

Step-by-step explanation:

54.25÷6.2−3.8=

54.25/6.2−3.8=

8.75-3.8=

8.75-3.80=

8-3+0.75-0.80=

5-0.05=4.95

The Probability that Robert randomly pulls out a black sock is 1/5  .

In the question ,

it is given that

Total number of socks in sock drawer = 30 socks

number of white socks in the drawer = 16 socks

number of black socks in the drawer = 6 socks

number of red socks in the drawer = 2 socks

number of yellow socks in the drawer = 6 socks

So , the probability that he randomly pulls out a black sock = (number of black socks in the drawer) / ( total number of socks in the drawer )

= 6 / 30

= 1/5

Therefore , The Probability that Robert randomly pulls out a black sock is 1/5  .

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Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

x

≥

9

Interval Notation:

[

9

,

∞

)

Step-by-step explanation:

There is enough data to draw the conclusion that Lakeville North has a higher percentage of low-income kids than Lakeville South.

X₁ = 42, n₁ = 130

X₂ = 35, n₂ = 160

Samples proportion:

P'₁ = X₁/n₁ = 42/130 = 0.3231

P'₂ = X₂/n₂ = 35/160 = 0.2188

Pooled proportion :

P = (X₁ + X₂)/(n₁ + n₂) = (42+35) /(130+160) = 0.2655

Claim: Lakeville North has a higher percentage of low-income kids than Lakeville South.

a) Hypothesis test :

The null and alternative hypothesis is

H(0) : p₁ = p₂

H(a) : p₁ > p₂.... (Claim)

b) Test statistic :

z = (P'₁ - P'₂)/√(P(1 - P)(1/n₁ + 1/n₂))

z = (0.3231 - 0.2188)/√(0.2655(1 - 0.2655) (1/130 + 1/160))

z = 0.1043/√(0.2655 * 0.7345 * (0.0077 + 0.00625))

z = 0.1043/√(0.2655 * 0.7345 * 0.01395)

z = 0.1043/√0.0027

z = 0.1043/0.052

z = 2.00

Test statistic is 2.00

P-value :

P-value = P(Z > 2.00) = 0.0227

P-value = 0.0227...( from z table)

c) We reject the null hypothesis since the P-value is less than the significance level of 0.05.

H(0) is to be rejected as the null hypothesis.

Conclusion: There is enough data to draw the conclusion that Lakeville North has a higher percentage of low-income kids than Lakeville South.

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Answer:

You could use 3.14 or 22/7

Step-by-step explanation:

It should be what you're asking, if not, tell me and I'll give you another answer.

:)

Answer:

use 22/7 or 355/133, but 355/133 is not very commonly used and is unwieldy.

Step-by-step explanation:

The temperature after a "very long time" in the heat conduction model on a metal circular ring of radius 1, with an initial temperature of 2δ(θ - 4π), approaches a constant value of zero.

The heat equation describes the behavior of temperature distribution over time in a conducting medium. In this case, we have a metal circular ring with a radius of 1, and the initial temperature is given by 2δ(θ - 4π), where δ represents the Dirac delta function and θ is the angular coordinate.

To solve the heat equation for this scenario, we need to consider the boundary conditions, which include the initial temperature distribution and the properties of the ring. The initial temperature distribution indicates a temperature spike at θ = 4π and zero temperature elsewhere.

As time progresses, the heat conduction in the metal ring will cause the temperature to equalize throughout the ring. Since the heat is continuously dissipating to the surroundings, the temperature will tend towards a steady-state condition. In the case of a "very long time," the temperature will approach a constant value of zero.

This result can be understood by considering the heat diffusion process. As time increases, the heat will flow from regions of higher temperature to regions of lower temperature until equilibrium is reached. In this case, since the initial temperature is concentrated at a single point and dissipates continuously, the temperature will eventually reach a state where it is uniformly distributed and approaches zero.

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Answer:

45%

Step-by-step explanation:

\( \frac{27}{60} \times 100 = 45\%\)

Answer:

Step-by-step explanation:

We know that:

Solution:

Hence, the percentage mark of Mary is 45%.

The cost of 1 liter for the small and medium cans is 4.4 and 2.4.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

As,  

Small can: A 200 ml can costs £0.88.

Medium can: A 500 ml can costs £1.32.

Large can: A 1 litre can costs £3.60.

Now, 200 ml = 0.2 l

500 ml = 0.5 l

For 0.2 l = 0.88

For 1 l= 0.88/0.2

For 1 liter = 4.4

For 0.5l medium can = 1.32

For 1 l medium can= 1.32/0.5

For 1 l medium can = 2.4

Hence, cost of 1 liter for the small can is £ 0.88 the cost of 1 liter for the medium can is £ 2.4.

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Answer:

See the attached histogram.

Step-by-step explanation:

Answer:

0.8679.

Step-by-step explanation: