Terick ran 2 3of a mile in 8 minutes. It took Chad 40 minutes to run 3 1 4miles. a. If Terick runs at that speed, how long will it take him to run one mile?

The resultant value of x for the given quadratic equation 9x² − 16 = 0 is x = ±4/3.

Any equation in algebra that can be written in standard form where x stands for an unknown value, where a, b, and c stand for known values, and where a 0 is true is known as a quadratic equation.  

An algebraic equation of the second degree in x is a quadratic equation.

The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

So, we have the quadratic equation:

9x² − 16 = 0

Now, solve as follows:

a = 9

b = 0

c = -16

Now,

c = -0 ± √0² - 4-9(-16)/2*9

x = ±4/3

Therefore, the resultant value of x for the given quadratic equation 9x² − 16 = 0 is x = ±4/3.

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Jayden needs no fewer than 90 tiles to cover the entire floor of his bathroom during the renovation. This means that he needs at least 90 tiles to complete the project.

It is important for Jayden to accurately measure the size of his bathroom floor and calculate the number of tiles he will need to ensure that he has enough to cover the entire area. If he does not have enough tiles, he may need to purchase additional tiles to complete the project. It is also important for Jayden to consider the size and shape of the tiles he will be using, as this will impact the number of tiles he will need to cover the floor. By accurately measuring and calculating the number of tiles needed, Jayden can ensure that he has enough materials to complete the renovation of his bathroom floor.

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Options a, b, d, and g are the correct conditions for a Binomial Distribution.

The four conditions necessary for X to have a Binomial Distribution are:

a. There are n set trials: In a binomial distribution, the number of trials, denoted as "n," must be predetermined and fixed. Each trial is independent and represents a discrete event.

b. The trials must be independent: The outcomes of each trial must be independent of each other. This means that the outcome of one trial does not influence or affect the outcome of any other trial. The independence assumption ensures that the probability of success remains constant across all trials.

d. There can only be two outcomes, a success and a failure: In a binomial distribution, each trial can have only two possible outcomes. These outcomes are typically labeled as "success" and "failure," although they can represent any two mutually exclusive events. The probability of success is denoted as "p," and the probability of failure is denoted as "q," where q = 1 - p.

g. The probability of success, p, is constant from trial to trial: In a binomial distribution, the probability of success (p) remains constant throughout all trials. This means that the likelihood of the desired outcome occurring remains the same for each trial. The constant probability ensures consistency in the distribution.

The remaining options, c, e, and f, are not conditions necessary for a binomial distribution. Option c, "Continue sampling until you get a success," suggests a different type of distribution where the number of trials is not predetermined. Options e and f, "You must have at least 10 successes and 10 failures" and "The population must be at least 10x larger than the sample," are not specific conditions for a binomial distribution. The number of successes or failures and the size of the population relative to the sample size are not inherent requirements for a binomial distribution.

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Answer:

63.8

Step-by-step explanation:

63.77 so you look at the hundredths 5 or higher round up

63.8 is the required answer

The given number is 63.7786879082, we have to round to the nearest tenth

How to round nearest 10th?

To round the decimal number to its nearest tenth, look at the hundredth number. If that number is greater than 5, add 1 to the tenth value.

63.7786879082

We can see that 100th number i. e 7 is greater than 5, so add 1 to the tenth value

So we get 63.8

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Answer:

id say A

because its an opened circle, and when its opened its usually not with the little dash and there's no negative number (that i know of)

Answer:

2(7+y)

Step-by-step explanation:

if you need more explanation lmk

Answer:

Answer = (7+y)2

.......

Answer:

a cycle is a sequence of non-repeated vertices and the degree of a graph is the number of neighbors the vertex has.

Applying law of sine and law of cosine, the unknown values x and y are 16.2 units and 37.1 degrees respectively.

To determine the value of x and y in the given triangle, we can use law of sine or law of cosine depending on the variables available and what we need to determine.

Applying law of cosine;

x² = 15² + 10² - 2(15)(10)cos78

x² = 225 + 100 - 300cos78

x² = 225 + 100 - 62.4

x² = 262.6

x = √262.6

x = 16.2 units

From this, we can apply law of sine to determine y;

x / sin X = y / sin Y

Substituting the values into the formula above;

16.2 / sin78 = 10 / sin y

Cross multiply both sides and solve for y;

16.2siny = 10sin78

sin y = 10sin78 / 16.2

sin y = 0.6038

y = sin⁻¹ (0.6038)

y = 37.14°

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The variable gets eliminated, then the equation has no solution.

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

The equation is given below.

(10x - 4) + ( -7 + x) = (10x + 2) + (-4 + x)

Simplify the equation, then we have

(10x - 4) + ( -7 + x) = (10x + 2) + (-4 + x)

10x - 4 - 7 + x = 10x + 2 - 4 + x

11x - 11 = 11x - 2

11x - 11x = 9

The variable gets eliminated, then the equation has no solution.

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The correct equation is given below.

(10x - 4) + ( -7 + x) = (10x + 2) + (-4 + x)

there are n(n-1)(n-2)/2 simple paths of nonzero length in a tree with n vertices, where two simple paths are regarded as the same if they have the same edges.

In a tree with n vertices, there are (n-1) edges, since a tree is a connected acyclic graph.

To count the number of simple paths of nonzero length in the tree, we can consider each vertex as a starting point for a path and count the number of possible paths from that vertex.

Starting from any vertex, there are at most (n-1) paths that can be formed by moving to any of the neighboring vertices. From each of these neighboring vertices, there are at most (n-2) paths that can be formed by moving to a new neighboring vertex (excluding the vertex that was just visited).

This process can be continued until there are no more vertices to visit. However, to avoid counting the same path twice, we should only consider paths that do not backtrack on themselves.

Therefore, the total number of simple paths of nonzero length in the tree is the sum of all simple paths that start from each vertex:

(number of paths starting from vertex 1) + (number of paths starting from vertex 2) + ... + (number of paths starting from vertex n)

Using the reasoning above, we can see that the number of paths starting from each vertex is at most (n-1) * (n-2), since each path can visit at most (n-2) additional vertices after the starting vertex, and there are at most (n-1) vertices to choose from as the next vertex on the path.

Therefore, the total number of simple paths of nonzero length in the tree is at most n(n-1)(n-2).

However, we have counted each simple path twice (once in each direction), so the actual number of distinct simple paths of nonzero length is half of this maximum value, which is:

n(n-1)(n-2)/2

So, there are n(n-1)(n-2)/2 simple paths of nonzero length in a tree with n vertices, where two simple paths are regarded as the same if they have the same edges.

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Answer:

5/9

Step-by-step explanation:

we add all of the values and divide by the total number in this case 9, all of them add to make 5 so we do 5÷9 to get 5/9

Answer:

No, i dont think so

Step-by-step explanation:

10 1/2 divided by 3/8:

KCF (keep, change the sign, flip the fraction)

·21/2×8/3=168/6

168/6=28

12/2×8/3=16

therefore they are not equal so it is not true

Hope this helped ;)

Answer:

well lets solve this:

10 1/2-->21/10

21/10 dvided by 3/8-------> to divide fractions we do this: 10/21 x 3/8 (swap the denom and num of the firs fraction then multiply by the sec)

10/21x3/8=30/168 = 3/56

12/2 x 8/3 = 6x 8/3= 6/1x8/3=48/3

48/3 simplified is 16/1 =16

3/56x16/1 = 48/56

48/56=24/28=12/14=6/7

Step-by-step explanation:

Therfore this is false

-hope this helps

At the end of the year, Achley Company's owner's equity is $4,685,000 and can be calculated by starting with the beginning owner's equity, adding the revenues, subtracting the expenses, and subtracting the owner's withdrawals.

To calculate Achley Company's owner's equity at the end of the year, we start with the beginning owner's equity of $5,175,000. We then add the revenues of $225,000 and subtract the expenses of $165,000. This gives us the net income, which is the difference between revenues and expenses, and represents the increase in owner's equity.

So, net income = revenues - expenses = $225,000 - $165,000 = $60,000. Next, we subtract the owner's withdrawals of $550,000 from the net income. Owner's withdrawals are personal expenses or cash withdrawals made by the owner and reduce the owner's equity.

Owner's equity at the end of the year = Beginning owner's equity + Net income - Owner's withdrawals.Owner's equity at the end of the year = $5,175,000 + $60,000 - $550,000. Calculating the above expression, we find that Achley Company's owner's equity at the end of the year is $4,685,000.

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Answer:

1st choice

Step-by-step explanation:

(r² -4r + 5 - r² -2r + 8) / (r - 4)

= (-6r + 13) / (r - 4)

The line plot that shows Sonia's data will be line plot A.

A line plot, also known as a dot plot or a scatter plot, is a graphical representation of data that displays individual data points as dots or markers on a number line. The line plot is used to show the distribution of a set of data and to identify any patterns or trends that may be present.

Line plots are particularly useful for displaying small to medium-sized data sets with discrete values. They are commonly used in the fields of statistics, mathematics.

In this case, the correct option is A.

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a) 26 × 0.02584 = 0.67384 ≈ 0.67

b) 15.3 ÷ 1.1 = 13.9090909... ≈ 13.9

c) 782.45 − 3.5328 = 778.9172 ≈ 779

d) 63.258 + 734.2 = 797.458 ≈ 800

a) To determine the result of 26 × 0.02584, multiply the numbers and round the answer to the appropriate number of significant figures. Since 26 has two significant figures and 0.02584 has four significant figures, the answer should have two significant figures. Multiplying the numbers gives 0.67384, which is rounded to 0.67.

b) To find the result of 15.3 ÷ 1.1, divide 15.3 by 1.1 and round the answer to the appropriate number of significant figures. Both 15.3 and 1.1 have three significant figures, so the answer should also have three significant figures. Dividing the numbers gives 13.9090909..., which is rounded to 13.9.

c) To calculate 782.45 − 3.5328, subtract the second number from the first and round the answer to the appropriate number of significant figures. Both 782.45 and 3.5328 have five significant figures, so the answer should also have five significant figures. Subtracting the numbers gives 778.9172, which is rounded to 779.

d) To find the sum of 63.258 and 734.2, add the numbers together and round the answer to the appropriate number of significant figures. Both 63.258 and 734.2 have four significant figures, so the answer should also have four significant figures. Adding the numbers gives 797.458, which is rounded to 800.

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Answer:

It will take 56 hours to make 8 airplanes

Step-by-step explanation:

Given that,

Carson builds 3 airplanes in 1 3/4 hours i.e. 7/3 hours.

We need to find the time it would take him to make 8 airplanes.

We know that,

3 airplanes = 7/3 hours.

1 airplane = (7/3)×3 hours

= 7 hours

To make 8 airplanes, the required time will be :

T = 8×7

= 56 hours

Hence, it will take 56 hours to make 8 airplanes.

The expected number of people who will drop out due to either relapse or moving away is 10 + 6 = 16. However, taking into account the standard deviations, it is 16 +/- 5.

To find the expected number of people who will drop out due to either relapse or moving away, we need to add the expected number of people who will drop out due to relapse (10) and the expected number of people who will drop out due to moving away (6).

Expected number of people who will drop out due to either relapse or moving away = 10 + 6 = 16.

However, we also need to take into account the standard deviations for each of these groups. To do this, we can use the square root of the sum of the variances (SD squared) for each group, squared.

Variances:
- Relapse: 4 squared = 16
- Moving away: 3 squared = 9

Square root of the sum of the variances:
- sqrt(16 + 9) = 5

Therefore, the expected number of people who will drop out due to either relapse or moving away, taking into account the standard deviations, is 16 +/- 5.

This means that we can expect anywhere between 11 and 21 people to drop out due to either relapse or moving away during the two-year cohort study.

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The function in variable w giving the cost C (in dollars) of constructing the box is C(w) = 30w² + 270/w. The result is obtained by using the formula of volume and area of the box.

We have a rectangular storage container without a lid.

The formula of volume of the box is

V = l × w × h

Where

So, the height is

10 = 2w × w × h

10 = 2w² × h

h = 10/2w²

h = 5/w²

To find the total cost, calculate the area of base and sides of the box!

See the picture in the attachment!

The base area is

A₁ = 2w × w = 2w² m²

The sides area is

A₂ = 2(2wh + wh)

A₂ = 2(3wh)

A₂ = 6wh

A₂ = 6w(5/w²)

A₂ = 30/w m²

The total cost is

C = $15(2w²) + $9(30/w)

C = $30w² + $270/w

The function of the total cost is

C(w) = 30w² + 270/w

Hence, the function of constructing the box is C(w) = 30w² + 270/w.

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Answer:

a = 10.5 feet

Step-by-step explanation:

Given that,

The area of a square room, A = 110.25 ft²

We need to find the side length of the living room. Let the side be x.

We know that,

The area of a square, \(A=a^2\)

So,

\(a=\sqrt{110.25} \\\\a=10.5\ ft\)

So, the side length of the living room is equal to 10.5 feet.

Answer: 1130 grams.

Step-by-step explanation:

She has 1130 grams remaining after converting 1.6kg to grams (160 0grams).

Answer:

Step-by-step explanation:

convert into grams

multiply 1000 by 1.6

Now substract 470g from it

subtract 470 from 1600

convert the g back into kg

divide 1130 by 1000

Answer:

A. 28

Step-by-step explanation:

Recall that the sum of all of the angle of a triangle must be 180 degrees. As we have 2 of the angles, we can subtract these angles from 180 to find the missing angle

\(180-95-57=28\)

Answer:

Option A is correct

Step-by-step explanation:

    x + 95 + 57 = 180 deg (sum of 3 angles in triangle)

=> x = 180 - 95 - 57

=> x = 28

Hope this helps!

Answer:

403.625

Step-by-step explanation:

Online calc cuz nobody knows how to do long division no more

Answer:

Step-by-step explanation:

Saying that each glass is 8 ounces if you drink 6.5 glasses a day your drinking 52 ounces a day. Seven days are in a week 52 ounces times 7 days gives you 364 ounces a week 364 ounces divided by 8 ounces per glass gives you 45.5 glasses in a full week

When factoring a tricky trinomial with a leading coefficient greater than 1, and you have more than one pair of factors for a term, it is usually best to try the pair of factors that multiplies to give the constant term first.

This is because when factoring a trinomial with a leading coefficient greater than 1, the first term will always have fewer factors than the last term, and it can be easier to find the correct pair of factors for the constant term than for the first term.

If the correct pair of factors for the constant term is found first, it can be easier to use that information to deduce the correct pair of factors for the first term.

In addition, once you have found one pair of factors for the trinomial, you can use the factoring by grouping technique to factor the trinomial completely. This involves grouping the terms of the trinomial in pairs, factoring out the greatest common factor of each pair, and then factoring out the greatest common factor of the resulting expressions.

Overall, when factoring a tricky trinomial with a leading coefficient greater than 1, it can be helpful to start by trying the pair of factors that multiplies to give the constant term first, and then using the factoring by grouping technique to factor the trinomial completely.

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A bicycle repair shop that offers two service packages: a tune-up and a complete overhaul.

The shop operates for 60 hours per week and receives an average of 180 bicycles each week. To analyze the capacity and utilization of the process, we need to consider the time taken at each stage and the demand for each service option. We'll break down the problem into multiple parts and provide a detailed explanation using mathematical terms.

a) Creating the Demand Matrix:

To create a demand matrix, we need to determine the number of bicycles going through each stage of the process. Let's denote the demand for tune-up as T and the demand for additional services as A.

Given that the average number of bicycles received per week is 180 and 25% of customers opt for additional services, we can calculate the demands as follows:

Demand for tune-up (T) = Total demand - Demand for additional services

T = 180 - (0.25 * 180)

T = 180 - 45

T = 135

Demand for additional services (A) = 0.25 * Total demand

A = 0.25 * 180

A = 45

Now, we can create a demand matrix based on the demand for each service option:

Demand Matrix:

Tune-up Additional Services Wheel Balancing

Tune-up  [135  0  0]

Additional [0  45  0]

Services

Total [ 135  45  0 ]

The demand matrix shows the number of bicycles flowing through each stage of the process.

b) Daily Capacity at Each Stage:

To calculate the daily capacity at each stage, we need to consider the time taken for each service option. Given that the shop operates for 60 hours per week, we can calculate the daily capacity at each stage:

Tune-up technician time per bicycle (\(T_{tuneup}\)) = 75 minutes

Additional services technician time per bicycle (\(T_{additional}\)) = 72 minutes

Wheel balancing specialist time per bicycle (\(T_{balancing}\)) = 20 minutes

Daily Capacity (C) = (60 hours * 60 minutes) / (\(T_{tuneup}\) + \(T_{additional}\) + \(T_{balancing}\))

Substituting the given values:

C = (60 * 60) / (75 + 72 + 20)

C = 21600 / 167

C ≈ 129.34 bicycles per day

Therefore, the daily capacity at each stage of the process is as follows:

Tune-up: 129 bicycles per day

Additional Services: 129 bicycles per day

Wheel Balancing: 129 bicycles per day

c) Implied Utilizations:

To find the implied utilizations, we need to compare the demand and the capacity at each stage of the process. Utilization can be calculated as the demand divided by the capacity.

Implied Utilization (U) = Demand / Daily Capacity

For the Tune-up stage:

\(U_{tuneup}\) = 135 / 129 ≈ 1.05

For the Additional Services stage:

\(U_{additional}\) = 45 / 129 ≈ 0.35

For the Wheel Balancing stage:

\(U_{balancing}\) = 0 / 129 = 0

The implied utilizations show how efficiently each stage of the process is being utilized. Utilization values greater than 1 indicate that the stage is operating beyond its capacity.

d) Weekly Capacity of the Process:

To calculate the weekly capacity of the process, we multiply the daily capacity by the number of days the shop is open per week:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Given that the shop is open for 60 hours per week, the number of days the shop is open per week can be calculated as follows:

Number of days shop is open per week = 60 hours / 24 hours per day = 2.5 days

Therefore, the weekly capacity of the process is:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Weekly Capacity = 129 bicycles per day * 2.5 days

Weekly Capacity = 322.5 bicycles per week

e) Flow Rate and Constraint Analysis:

To determine if the flow rate of the process is capacity-constrained or demand-constrained, we compare the weekly capacity to the demand for each service option.

Demand for Tune-up (\(T_{demand}\)) = 135 bicycles per week

Demand for Additional Services (\(A_{demand}\)) = 45 bicycles per week

Comparing the demands with the weekly capacity:

\(T_{demand}\) < Weekly Capacity (135 < 322.5)

\(A_{demand}\) < Weekly Capacity (45 < 322.5)

Since both the demands for tune-up and additional services are less than the weekly capacity, the flow rate of the process is demand-constrained. This means the shop has the capacity to handle the current demand without operating beyond its limits.

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Answer:

>

Step-by-step explanation:

Answer:

You would use >

Step-by-step explanation:

-1/4 is greater. When you divide -1/4 you get -0.25. In negatives, the number that's the CLOSEST to 0 is greater. Since -0.25 is closer to 0 than -0.42, the answer is that -1/4 is GREATER than -0.42.

Hope this helps!

he function f(z) = (2z + 1)/(z(z² + 1)) has singular points at z = 0 and z = ±i. The function is not analytic at these singular points due to the presence of poles in some terms of the function. However, it is analytic everywhere else in the complex plane.

To determine the singular points of the function f(z) = (2z + 1)/(z(z² + 1)), we need to find the values of z for which the function is not defined or becomes infinite.

The singular points of f(z) occur at the values of z that make the denominator of the fraction equal to zero. Let's find these points:

1. z = 0: At z = 0

the denominator becomes zero, which makes the function undefined. Therefore, z = 0 is a singular point.

2. z² + 1 = 0:

Solving this equation,

we find z = ±i, where i is the imaginary unit. At these points, the denominator becomes zero, and the function is undefined.

Hence, z = ±i are also singular points.

Now, let's analyze why the function is analytic everywhere except at these singular points:

1. At z = 0: The function is not defined at z = 0 because it leads to a division by zero.

Near z = 0, we can factorize the function as

f(z) = (2z + 1)/(z(z² + 1))

= 1/z² + 2/z + 1/(z² + 1).

The first term 1/z² is not analytic at z = 0 since it has a pole of order 2. However, the other terms, 2/z and 1/(z² + 1), are both analytic at z = 0. Therefore, the function is not analytic at z = 0 due to the pole in the first term, but it is analytic everywhere else.

2. At z = ±i:

the function is not defined at z = ±i due to division by zero.

However, near these points, we can factorize the function as

f(z) = (2z + 1)/(z(z² + 1))

= 1/z + 2/(z² + 1) + 1/z(z² + 1).

The first term, 1/z, is not analytic at z = ±i since it has a simple pole. The second term, 2/(z² + 1), is also not analytic at z = ±i because it has simple poles at z = ±i. However, the last term, 1/z(z² + 1), is analytic at z = ±i.

Therefore, the function f(z) = (2z + 1)/(z(z² + 1)) has singular points at z = 0 and z = ±i.

The function is not analytic at these singular points due to the presence of poles in some terms of the function. However, it is analytic everywhere else in the complex plane.

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Given question is incomplete, the complete question is below

Determine the singular points of the function. In each case, determine the singular points of the function and state why the function is analytic everywhere except at those points:

f(z)=(2z+1)/z(z²+1)

The single-precision floating point representation of 0.5625 in hexadecimal is: 0x3E100000.

Identify the sign bit. In this case, the number is positive, so the sign bit is 0.

Convert the decimal number to binary. The decimal number 0.5625 (or 9/16) can be converted to binary as follows: 0.1001.

Convert the 32-bit binary number to hexadecimal. To do this, group the binary number into blocks of 4, from right to left, and convert each block into its hexadecimal equivalent:

0000 -> 0

0000 -> 0

0000 -> 0

0000 -> 0

0000 -> 0

0001 -> 1

0000 -> 0

0111 -> 7

1110 -> E

0 -> 0

So, the single-precision floating point representation of 0.5625 in hexadecimal is: 0x3E100000.

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