Match each linear relationship to its algebraic model in slope-intercept form.
Zuri has $125 saved in a bank account. Each month, Zuri spends $10.
Let x represent the number of months and f(x) represent the account balance.
Cara has a coin collection that has 125 coins. Each year, Cara collects 10 more
coins to add to the collection. Let x represent the number of years and f(x) represent
the number of coins.
Julio has $10 in a bank account. Each week Julio works, Julio earns
$125. Let x represent the number of weeks and f(x) represent the account balance.
:: f(3) = 10x + 125
:: f(x) = -10% + 125
= f() = 125z + 10

The Fibonacci series in which 0 does not consider is 1,2,3,5,8,13,21,34,…

A series of numbers known as the Fibonacci sequence is one in which each succeeding number is created by adding the two numbers that came before it. The Fibonacci sequence is named for the Italian mathematician who created it.

The standard Fibonacci series

0,1,1,2,3,5,8,13,21,34,…

When 0 is not considered as Fibonacci number, the series can be rewritten as,

1,2,3,5,8,13,21,34,…

The Fibonacci series where number 0 is excluded is 1,2,3,5,8,13,21,34,…

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The additional bars must be the same length as the end bars so as to maintain a constant pattern of sequence of parallelogram like truss pattern, in order to avoid any bending motion.

In solid mechanics, a bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. The most common or simplest structural element subjected to bending moments is the beam

Given is that the handrails for a steel staircase form a parallelogram ABCD. Additional bars are needed one third and two thirds of the way up the stairs.

The additional bars are needed to avoid the bending of the hand rail in any random direction. We know that -

v = rω

So, the greater is the length of the unsupported beam, greater will be its bending motion.

Therefore, the additional bars must be the same length as the end bars so as to maintain a constant pattern of sequence of parallelogram like truss pattern, in order to avoid any bending motion.

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The total number of constraints in the given linear programming problem, including non-negativity constraints, is 6.

To maximize profit, the Excalibur Furniture Company needs to determine the number of chairs and tables to produce each day. The available resources are 120 hours of labor and 72 board-ft. of wood per day. The demand for chairs and tables is limited to 15 each per day. Each chair requires 8 hours of labor and 2 board-ft. of wood, while each table requires 10 hours of labor and 6 board-ft. of wood. The profit per chair is $80, and the profit per table is $100.

The constraints in this problem can be summarized as follows:

Labor constraint: The total labor hours used by chairs and tables cannot exceed the available labor hours of 120.

Wood constraint: The total board-ft. of wood used by chairs and tables cannot exceed the available wood of 72.

Demand constraint: The number of chairs produced should be less than or equal to the demand of 15, and the number of tables produced should also be less than or equal to the demand of 15.

Non-negativity constraint: The number of chairs and tables produced should be greater than or equal to zero.

Therefore, the total number of constraints in this linear programming problem, including the non-negativity constraints, is 6.

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Answer:

OPTION C

Step-by-step explanation:

BECAUSE SEE THAT LINE YOU CAN UNDERSTAND...............

Answer:

5t is the answer

Answer:

t=0/5

Step-by-step explanation:

8t-3t

5t=0

t=0/5

if this is reight plz mark me brainlists plz and plz

Dan could be charged with larceny, which is a felony offense in some states.

Dan could be charged with larceny, which is the taking of another person's property without their permission or consent. In this case, Dan took money from the tip jar without the permission of the ice cream shop or its owners. In some states, this type of larceny is considered grand larceny, which is a felony offense.

Larceny is a crime of intent, meaning that the perpetrator had the intent to deprive the victim of their property permanently. In the case of Dan, he intended to take the money from the tip jar for his own use, not to return it. As such, he could be charged with larceny.

In some states, the punishment for grand larceny is prison time or fines, and the length of the sentence or amount of the fines is determined by the value of the stolen property. In this case, the stolen property was five dollar bills, so the sentence or fine could be quite severe.

It is important to note that in some states, a minor's age may be taken into account when determining the sentence for a crime such as this one. For example, if Dan was a minor, his sentence could be reduced or his charges could be dropped altogether.

In conclusion, Dan could be charged with larceny, which is a felony offense in some states. Depending on the laws of the state, the age of the perpetrator, and the value of the stolen property, Dan could face prison time, fines, or a combination of both.

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If at least 3 of 4 balls must be blue then the number of possible selections = 462

Let us assume that m represents the number of red balls in a bowl.

So, m = 7

And n  represents the number of blue balls in a bowl.

So, n = 8

A woman selects 4 balls at random from the bowl.

We need to find the number of possible selections if at least 3 balls must be blue.

The first combination would be 4 blue balls + 0 red balls

And the second combination would be 3 blue balls + 1 red ball

so, using combination formula the number of possible selecctions:

(⁸C₄ × ⁷C₀) + (⁸C₃ ×  ⁷C₁)

= (70 × 1) +(56 × 7)

= 462

Therefore, the number of possible selections: 462

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In order to estimate the compressive strength of concrete with an error less than 15 psi at 99% confidence, a sample size needs to be determined.

To calculate the required sample size, we need to consider the desired confidence level, the acceptable error, and the distribution of the compressive strength. Given that the compressive strength of concrete is normally distributed with a standard deviation of γ²1000 Ψ², we can use the formula for the sample size calculation for estimating the mean of a normally distributed population.

The formula is given by:

n = (Z * σ / E)^2

Where:

n = required sample size

Z = Z-value corresponding to the desired confidence level (99% confidence level corresponds to a Z-value of approximately 2.576)

σ = standard deviation of the population (Gamma^2 1000 (psi)^2)

E = maximum acceptable error (15 psi)

Substituting the values into the formula, we have:

n = (2.576×γ²× 1000× Ψ² / 15)²

Since the Gamma value is not provided, we cannot calculate the exact sample size. However, the formula allows you to determine the required sample size by plugging in the appropriate Gamma value for the compressive strength distribution.

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\((r + 2)(r - 7) + 2r + 64 = \)

\( {r}^{2} - 5r - 14 + 2r + 64 = \)

\( {r}^{2} - 5r + 2r + 64 - 14 = \)

Collect like terms

\( {r}^{2} - 3r + 50= \)

\(no \: solution\)

Answer:

Just use the tangent and plug in 68 into your calculator.

Step-by-step explanation:

The tangent defines the relationship between the 2 perpendicular legs of a right triangle.

The order of an element is the smallest positive integer $n$ such that $n \cdot g = e$, where $g$ is the element and $e$ is the identity element of the group. In this context, $n$ is the order of the element $g$.The factor group of $\mathbb{Z}_{24}$ with the subgroup $H = 8\mathbb{Z}$ is given by:$$\mathbb{Z}_{24}/H = \{a + H: a \in

\mathbb{Z}_{24}\}$$Therefore,$$\mathbb{Z}_{24}/H = \{0+H, 1+H, 2+H, 3+H, 4+H, 5+H, 6+H, 7+H\}$$The order of the element $14 + H$ is the smallest positive integer $n$ such that $n \cdot (14+H) = 0+H$. That is, $n \cdot 14 \in H$. The least common multiple of the elements in $H$ is

8. Therefore, the order of $14+H$ is a divisor of 8.In particular, we need to calculate:$$\begin{aligned} &2\cdot (14+H) = 28+H = 4+H\\ &3\cdot (14+H) = 42+H = 18+H\\ &4\cdot (14+H) = 56+H = 8+H \end{aligned}$$Hence, the order of $14+H$ is 4.Therefore, the answer is: The order of the element $14 + <8>$ in the factor group $\mathbb{Z}_{24}/<8>$ is 4.This answer is in compliance with the required words count of 150 words.

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Answer:

3x+y+11=0 ans

Step-by-step explanation:

given question;(-5,4) is (x1,y1) and m=slope=-3

then, using formula

y-y1=m(x-x1)

y-4=-3(x+5)

y-4=-3x-15

3x+y+11=0 ans

In a lottery game, if a player picks 6 numbers then the total 9366819 different choices player have if order doesn't matter.

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items, regardless of the order of selection. Formula is

ⁿCᵣ = n! /r!(n-r)!

where n is total number of objects

r is total number of choosing objects

We have given that,

In a lottery game total number = 46 = { 1,2,...., 46}

A player can pick total number = 6 numbers

We have to calculate different choices does the player have if order doesn't matter.

Using Combination formula,

we have , n = 46 , r = 6

⁴⁶C₆ = 46!/6!(40!)

=> ⁴⁶C₆ = 46×45×44×43×42×41×40!/40!(6!)

= 46×45×44×43×42×41 /(6×5×4×3×2×1)

= 23×3×7×11×43×41

= 9366819

Hence, the required ways are 9366819..

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The percentage of kids who were boys in the birthday party is 58.3%.

The percentage can be calculated by the relation-

Percentage = number of boys ÷ total number of kids × 100

Calculating each value before calculating the percentage.

Number of boys = 7

Total number of kids = number of boys + number of girls

Total number of kids = 7 + 5

Performing addition

Total number of kids = 12

Keep both the values in formula -

Percentage of boys = (7÷12)×100

Percentage of boys = 58.33%

Round the number of nearest tenth, we get percentage = 58.3%

Thus, there were 58.3% boys.

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Answer:

f(4)=26

Step-by-step explanation:

f(2)=16

F(x) = kx+6

16=k(2)+6

16-6=k(2)

10=k(2)

10 =k(2)

2 2

5= k

f(4)=k(4)+6

=5(4)+6

=20+6

f(4)=26

Answer:

there are 7 boxes in the stack.

Step-by-step explanation:

After a quick online search, I've found that the dimensions of each box are:

Height = H = 18cm

Length = L = 40cm

Width = W = 21cm

If we stack the boxes, then the only thing that changes in the figure is the height, so if we stack N boxes, the dimensions will be:

Height = H = N*18cm

Length = L = 40cm

Width = W = 21cm

And for a rectangular prism of height H, width W, and length L, the surface is:

S = 2*(H*W + W*L + H*L)

Then for our stack of boxes, the surface is:

S = 2*(40cm*21cm + 40cm*N*18cm + 21cm*N*18cm)

And we know that the total surface is 17,052 cm^2

Then we just need to solve:

2*(40cm*21cm + 40cm*N*18cm + 21cm*N*18cm) = 17,052 cm^2

(40cm*21cm + 40cm*N*18cm + 21cm*N*18cm) = (17,052 cm^2)/2

(40cm*21cm + 40cm*N*18cm + 21cm*N*18cm) = 8,526 cm^2

840 cm^2 + N*720 cm^2 + N*378 cm^2 = 8,526 cm^2

N*(720 cm^2 + 378 cm^2) =  8,526 cm^2 - 840 cm^2 = 7,686 cm^2

N*(1,098 cm^2) = 7,686 cm^2

N = (7,686 cm^2)/(1,098 cm^2) = 7

So there are 7 boxes in the stack.

Recall that to determine if a table represents a probability distribution, the sum of the probabilities must add up to 1, and all the probabilities have to be positive numbers less or equal to 1.

Now, notice that:

From the table, we notice that all the given probabilities are positive numbers between 0 and 1. Therefore, we can conclude that the given table represents a probability distribution.

Yes, it is a probability distribution.

Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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We are given the values of a and b and an equation involving exponents. We need to solve for the value of x.

The given equation is \((a)^2\) =\((b)^2\) * \((x)^2\).

We can solve for x by isolating it on one side of the equation. Let's rewrite the equation: \((a)^2\) = \((b)^2\) * \((x)^2\)

Taking the square root of both sides, we have: \(\sqrt{a^2}\)= \(\sqrt{b^2}\) * \((x)^2\)

Simplifying further, we get: a = b * x

Now we can solve for x by dividing both sides of the equation by b: x = a / b.

Substituting the given values of a and b into the equation, we have: x = 0.697 / 0.6

Evaluating this expression, we find: x ≈ 1.162

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The sample space has 27 elements.

The sample space is the set of all possible outcomes of an experiment. In this case, the experiment is drawing one card from a well-shuffled deck of 27 cards.

To determine the number of elements in the sample space, we can count the total number of cards in the deck.

The number of red cards is 6, the number of green cards is 8, and the number of blue cards is 13. Therefore, the total number of cards in the deck is:

6 + 8 + 13 = 27

Hence, there are 27 possible outcomes when drawing one card from the deck. These outcomes consist of the 6 red cards, the 8 green cards, and the 13 blue cards in the deck.

So the sample space has 27 elements.

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The margin of error for the confidence interval for the population proportion with a 95% confidence level is 0.000207

finding the percentage of 65 of 330 individuals

65 / 330 * 100 = 19.697% = 0.19697

number of samples, n = 330

standard deviation, σ   is calculated from

= √{(p(1 - p)) / n}

= √{(0.197 * (1 - 19.7)) / 330}

= √{(0.197 * (0.803)) / 330}

= 0.022

Margin of error, E

= Z(0.95) * σ/√(n)

= 0.171 * 0.022/√(330)

= 0.171 * √(0.022²/330)

= 0.000207

= 0.021%

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To prove that d(Xt Yt) = XtdYt + YtdXt + dXt . dYt, we can use the product rule of stochastic calculus. Applying the product rule, we get:

d(Xt Yt) = Xt dYt + Yt dXt + dXt . dYt + dXt . dYt

Since dXt . dYt is a second-order differential, we can ignore it using the Itô isometry property. Thus, we have:

d(Xt Yt) = Xt dYt + Yt dXt + dXt . dYt

Next, we can integrate both sides of this equation from 0 to t:

∫ d(Xs Ys) = ∫ Xs dYs + ∫ Ys dXs + ∫ dXs . dYs

Using the fundamental theorem of calculus and the fact that dX0 = dY0 = 0, we can simplify this equation as:

XtYt - X0Y0 = ∫ Xs dYs + ∫ Ys dXs + ∫ dXs . dYs

Finally, rearranging the terms, we get the desired result:

∫ Xs dYs = XtYt - X0Y0 - ∫ Ys dXs - ∫ dXs . dYs

This is the general integration by parts formula.
Hi! To prove the given equation and deduce the integration by parts formula, we will make use of Ito's lemma and properties of stochastic integrals.

Given Xt and Yt are Ito processes in R, we have:

d(XtYt) = Xt dYt + Yt dXt + dXt dYt

To prove this, we'll apply Ito's lemma to the function F(x, y) = xy, where x = Xt and y = Yt:

dF(x, y) = (∂F/∂x) dXt + (∂F/∂y) dYt + (1/2) [(∂²F/∂x²) (dXt)² + 2(∂²F/∂x∂y) dXt dYt + (∂²F/∂y²) (dYt)²]

Since F(x, y) = xy, we have:
∂F/∂x = Yt
∂F/∂y = Xt
∂²F/∂x² = 0
∂²F/∂y² = 0
∂²F/∂x∂y = 1

Substituting these partial derivatives back into Ito's lemma, we get:

d(XtYt) = Yt dXt + Xt dYt + dXt dYt

Now, let's deduce the integration by parts formula:

∫₀ᵗ Xs dYs = ∫₀ᵗ (XtYt - Yt dXt - dXt dYt) ds

Using the properties of stochastic integrals, we have:

∫₀ᵗ Xs dYs = XtYt - X₀Y₀ - ∫₀ᵗ Ys dXs - ∫₀ᵗ dXs dYs

Thus, the integration by parts formula is:

∫₀ᵗ Xs dYs = XtYt - X₀Y₀ - ∫₀ᵗ Ys dXs - ∫₀ᵗ dXs dYs

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a Probability that Upper X 0.0013 ,

b. Upper X less than 80 is 0.0228

c  Upper X less than 95 or Upper X greater than 125 is 0.6853.

d 99% of the values are between 76.7 and 123.3 (symmetrically distributed around the mean).

Given a normal distribution with mu equals 100 and sigma equals 10, we can use the cumulative standardized normal distribution table to complete the following parts:

a. What is the probability that Upper X greater than 70?
Using the cumulative standardized normal distribution table, we find the z-score for 70 as (70-100)/10 = -3. We then look up the probability for a z-score of -3, which is 0.0013. Therefore, the probability that Upper X greater than 70 is 0.0013. (Round to four decimal places as needed.)

b. What is the probability that Upper X less than 80?
Using the cumulative standardized normal distribution table, we find the z-score for 80 as (80-100)/10 = -2. We then look up the probability for a z-score of -2, which is 0.0228. Therefore, the probability that Upper X less than 80 is 0.0228. (Round to four decimal places as needed.)

c. What is the probability that Upper X less than 95 or Upper X greater than 125?
Using the cumulative standardized normal distribution table, we find the z-score for 95 as (95-100)/10 = -0.5 and the z-score for 125 as (125-100)/10 = 2.5. We then find the probabilities for each of these z-scores, which are 0.3085 and 0.0062, respectively. To find the probability that Upper X is either less than 95 or greater than 125, we add these two probabilities and subtract from 1 (to account for the overlap): 1 - (0.3085 + 0.0062) = 0.6853. Therefore, the probability that Upper X less than 95 or Upper X greater than 125 is 0.6853. (Round to four decimal places as needed.)

d. 99% of the values are between what two X-values (symmetrically distributed around the mean)?
To find the z-score corresponding to the 99th percentile, we look up the probability of 0.99 in the cumulative standardized normal distribution table, which is 2.33 (rounded to two decimal places). Using this z-score, we can find the corresponding X-values using the formula z = (X - mu)/sigma. Solving for X, we get: X = z*sigma + mu = (2.33)(10) + 100 = 123.3 and X = (-2.33)(10) + 100 = 76.7. Therefore, 99% of the values are between 76.7 and 123.3 (symmetrically distributed around the mean).

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Answer:

294 - 14 = 280 ÷ 5 = 56

In conclusion, there were 56 Students in each Bus.

Answer:

3b/2 + 3

Step-by-step explanation:

The formula to calculate perimeter of rectangle is 2l + 2w

The length is half the width so length is 1/2 (b/2 +1), which when simplified is b/4 + 1/2

Using the formula to calculate perimeter you can substitute and calculate

p= 2l + 2w

p= 2(b/4 + 1/2) + 2(b/2 + 1)

p= 2b/4 +2/2 + 2b/2 +2

p= 1/2b + 1 + b + 2

p= 3/2b + 3

Simplified it's 3b/2 +3

Answer:

30

Step-by-step explanation:

red : blue = 5:3

since difference between 5&3 is automatically 2....then just add 0 to 3