A civil engineer is designing a public parking lot for the new town hall. The number of cars in each row should be six less than the number of rows in the lot. The mayor has requested that the new lot should hold twice as many cars as the current parking lot, which has space for 56 cars.

Determine which equation the civil engineer can use to find the number of rows, x, he should include in the new parking lot.

A.
6x2 − 56 = 112
B.
x2 − 6 = 112
C.
x2 − 6x = 112
D.
2x2 − 12x = 112

Answer:

The answer would be 45.

Step-by-step explanation:

5*9=45

Answer:

45

Step-by-step explanation:

First we count how many people he split it between which is 5 and we have to remember the key word here is equal so if he was left with 9 then everybody else did as well. so we multiply 5 times 9 which is 45

From the graph which represents Landon's distance from ground, we can say that the distance from the ground to "first-step" is about 5 inches.

The graph which is representing the "Landon's-distance" from ground as he climb the ladder, is straight line graph,

We observe that, the number of steps is denoted on "x-axis", and

the distance from the ground (in inches) is denoted on the "y-axis";

we have to find the distance from the ground to "first-step"; On observing the graph, we see that when  the number-of-steps is "1", the distance is 5 inches.

Therefore, the required distance is 5 inches.

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The given question is incomplete, the complete question is

The graph represents Landon's distance from the ground as he climbs a ladder. what is the distance from the ground to the first step?

Answer: $43.20

Step-by-step explanation:

Answer:

your answers are correct

the first graph isgeometric

the second graph is arithmeit

Answer:

b

Step-by-step explanation:

1. is perpdicul. 2. is parrell 4. is perpdicul 3. is right angels. 5. is parrell. 6. is right angle

Answer:

2,5 is parallel  3,6 is perpendicular  1,4 is intersecting lines

Step-by-step explanation:

Hope this helps btw feel free to report me if im wrong

Intersecting lines 'intersect' each other, but do not form a right angle. Perpendicular lines ALWAYS form a right angle. Think of these as a 4-way intersection in a big city, such as New York. Parallel lines NEVER intersect each other. Think of these as train tracks.

polynomial p(x) with the real coefficient = 4(x⁴ - 8x³ + 13x² + 32x - 68)

If a polynomial's zeros are known, we may use the equation below to find the polynomial function.

f(x) = (x - a) (x - b) (x - c)

The zeros of the aforementioned function, a third-degree polynomial, are a, b, and c.

Similar to this, if all of the roots are known, we can discover a polynomial, and the degree of the polynomial determines how many zeros there are.

Given data :

The degree of the polynomial = 5

Leading Coefficient = 4

Zeros = 5 (Mulyiplicity 2, 4-i)

One of the zeros of the polynomial is 4-i so, another root will be 4 + i. Similarly, -2 is the polynomial's zero because 2 is also a zero of the polynomial.

f(x) = 4 [x - (4 - i)] [x - (4 + i)] (x + 2) (x - 2)

f(x) =  4 [x - 4 + i] [x - 4 - i] (x + 2) (x - 2)

f(x) =  4 [(x - 4)² + i²] (x)² - (2)²   ⇒   Use identity (a² - b²) = (a+b) (a-b)

f(x) = 4 [x² - 8x + 16 - i²] [x² - 4]

f(x) = 4 [x² - 8x + 16 - (-1)] [x² - 4]     ⇒    Use formula i² = (-1)

f(x) = 4 [x² - 8x + 16 + 1)] [x² - 4]

f(x) = 4 [x² - 8x + 17)] [x² - 4]

Further simplifying it :

f(x) = 4 [x² - 8x + 17)] [x² - 4]

f(x) = 4 [x²(x² - 8x + 17) - 4(x² - 8x + 17)]

f(x) = 4 [x⁴ - 8x³ + 17x² - 4x² + 32x - 68]

f(x) = 4 (x⁴ - 8x³ + 13x² + 32x - 68)

Therefore, the polynomial p(x) with real coefficients =  4 (x⁴ - 8x³ + 13x² + 32x - 68)

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x

2

−3x−10

x

2

−(5x+x)−10

x

2

−5x+2x−10

x(x−5)+2(x−5)

(x−5)(x+2)

x=5

x=−2

sumofzeroes

=αβ=5×−2=−10

α+β=

9

−b

=−

1

(−3)

=3

productofzeroes

=αβ=5×−2=−10

αβ=

a

c

=

1

−10

=−10

proved

________________________

mark me brainliest........proved

Answer:

20

Step-by-step explanation:

Triangle inequality says that the third side can only be 18-3...15, that is bigger than 15.

And 18+3... 21, that is smaller than 21.

If the third side is 21, the 18 and the 3 will just lay right on top of the 21 and not make a triangle. So it has to be 20 in order to be a whole number.

The 98% confidence interval for the true proportion of runners who will need hotel accommodations is (0.434, 0.518)

To construct a confidence interval for the true proportion of runners who will need hotel accommodations, we can use the formula

CI = p ± z × (√(p(1-p)/n))

where

p = sample proportion (441/924 = 0.476)

z = the z-score associated with the desired confidence level (98% = 2.33)

n = sample size (924)

Substituting the values into the formula, we get:

CI = 0.476 ± 2.33 × (√(0.476 × (1-0.476)/924))

CI = 0.476 ± 0.042

The 98% confidence interval for the true proportion of runners who will need hotel accommodations is (0.434, 0.518).

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The given question is incomplete, the complete question is:

Running continues to be a very popular sport in America. At a major race, like the Peachtree Road Race in Atlanta, there may be over 10,000 people entered to run. The race promoters for a road race in the Pacific Northwest took a random sample of 924 runners out of the 5000 runners entered to estimate the number of runners who will need hotel accommodations. There were 441 runners that indicated they would need hotel accommodations. Construct a 98% confidence interval for the true proportion of runners who will need hotel accommodations

Answer: B.Construct a circle of any arbitrary radius.

Step-by-step explanation:

had to complete the question first.

A.Connect every arc along the circle.

B.Construct a circle of any arbitrary radius.

C.Set the compass width to greater than half the diameter of the circle.

D. Set the compass width to the radius of the circle.

Explanation:

when constructing an inscribed square and an inscribed equilateral triangle, the most important step and which turns out to be same for both procedures is the constructio of of a circle of an arbitrary radius. Because it’s is within this circle both the triangle and square would be drawn. Just their method of construction are different.

Answer:

C po

Step-by-step explanation:

sana maka tulong po sayo

Answer:

5/9

Step-by-step explanation:

From the information, 8 are more than 6 feet tall and 7 have good aim.

Therefore, the probability that the coach would randomly pick a player over 6 feet tall or a player with a good aim will be:

= 8/27 + 7/27

= 15/27

= 5/9

If the resulting F-statistic is less than the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the variances are significantly different.

The F-test is a statistical test used to compare the variances of two groups.

In this problem, we will use it to compare the variance of the value added by the manufacturer and the variance of the cost of materials in manufacturing. The F-test is performed by dividing the larger variance by the smaller variance. The resulting F-statistic is then compared to the critical value of an F-distribution with degrees of freedom equal to the sample size minus one for each group.

Before we can perform the F-test, we need to determine which variable will be group 1. Typically, the variable with the smaller mean is designated as group 1. This is because we want to minimize the chance of making a type II error, which is failing to reject the null hypothesis when it is false. If we designated the variable with the larger mean as group 1, we might not detect a significant difference between the groups, even if one exists.

Once we have designated which variable will be group 1, we can perform the F-test. If the resulting F-statistic is greater than the critical value of the F-distribution, we reject the null hypothesis and conclude that the variances are significantly different.

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Answer:

$57.81

Step-by-step explanation:

74/128 = 57.8125, which rounds to 57.81

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:

The percentile rank of someone who earns $75,000 per year is the 85th percentile.

Step-by-step explanation:

Meaning of percentile:

When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.

In this question:

Working population of 10,500

8,925 people earn less than $75,000 per year.

8925/10500 = 0.85

0.85*100 = 85

The percentile rank of someone who earns $75,000 per year is the 85th percentile.

The total number of bacteria in the dish is 31457280

The expression is given as:

Total = (32)^4 * 30

Start by evaluating the exponent

Total = 1048576 * 30

Next, evaluate the product

Total = 31457280

Hence, the total number of bacteria in the dish is 31457280

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Answer:

A (3^8)

Step-by-step explanation:

I have this question on my test. I'm just assuming the person didn't put ^.

(3^2)^4 times 3^0

Answer:

To solve for x, we can start by squaring both sides of the equation:

(√x+3)² = (2√x-2)²

On the left side, we have:

(√x+3)² = x + 6√x + 9

On the right side, we have:

(2√x-2)² = (2√x)² - 2(2√x)(2) + 2² = 4x - 8√x + 4

So now we have:

x + 6√x + 9 = 4x - 8√x + 4

Grouping like terms, we can simplify this to:

10√x - 3x + 5 = 0

Now we can solve for x by isolating the radical term and squaring both sides:

10√x - 3x + 5 = 0

10√x = 3x - 5

(10√x)² = (3x - 5)²

100x = 9x² - 30x + 25

Moving all the terms to one side, we get:

9x² - 130x + 25 = 0

We can now solve this quadratic equation by factoring or using the quadratic formula. Factoring, we have:

(3x - 5)(3x - 5) = 0

So the solution is:

3x - 5 = 0

3x = 5

x = 5/3

Therefore, the solution to the equation √x+3 = 2√x-2 is x = 5/3.

Step-by-step explanation:

Answer:

7/6

Step-by-step explanation:

y2-y1/x2-x1(slope formula)

plug in numbers

12-5=7

8-2=6

hence 7/6

The unit rate of the juice is 0.5 carrot juice per green apple juice

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

This means that

Carrot juice = 2

Green apple juice = 4

Using the above as a guide, we have the following:

Unit rate = Carrot juice/Green apple juice

Substitute the known values in the above equation, so, we have the following representation

Unit rate = 2/4

Evaluate

Unit rate = 0.5

Hence, the unit rate is 0.5 carrot juice per green apple juice

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Answer:

domain -3<x<6

range -2<y<7

it is a function

Answer:

Domain:{3,-3,0,-1,6}

Range:{7,5,4,5,-2}

Since there is one value of  y  for every value of  x , this relation is a function.

The relation is a function.

Step-by-step explanation:

we need 31/2 pounds mirepoix to make 31/2 gallons of soup.

let we need x% (percent) of mirepoix to make 1 gallon of soup

given we have 1 pound of mirpoix which yeilds 1 gallon soup of soup

so total amount of mirepoix that required in the solution is = \(\frac{x}{100} *1 pound\)

so x/100 = 1 gallon / pound

we will use this equation for further calculation

let we need y pounds of mirepoix to make 31/2 gallon of soup  ans we know that x% of mirepoix is required for this solution.

so \(\frac{x}{100} * y = 31/2\)

ans in the above equation x/100 =1 gallon / pound

so  1 * y= 31 /2

and hence y = 31/2 pounds

so we need 31/2 pounds of mirepoix to form requied amount of soup.

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The value of y can be determined by solving the system of equations derived from the given information. The correct equation is y = 2.

Let's assign variables to the unknowns. Let x represent the value of x and y represent the value of y. We can form two equations based on the given information:

The sum of two times x and 3 times y is 5:

2x + 3y = 5

The difference of x and y is 5:

x - y = 5

To find the value of y, we can solve this system of equations. One way to do this is by elimination or substitution. Let's use substitution to solve the system.

From equation 2, we can express x in terms of y:

x = y + 5

Substituting this value of x into equation 1:

2(y + 5) + 3y = 5

2y + 10 + 3y = 5

5y + 10 = 5

5y = -5

y = -1

Therefore, the value of y is -1, which corresponds to option d: y = -1.

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Answer/Step-by-step explanation:

Length of AC:

Given that AB = x + 2, and BC = 7x - 3, therefore,

\( (x + 2) + (7x - 3) = AC \) (segment addition postulate)

Simply the expression for the length of segment AC

\( x + 2 + 7x - 3 = AC \)

Collect like terms

\( x + 7x + 2 - 3 = AC \)

\( 8x - 1 = AC \)

Length of QR:

Given that PQ = 8y + 5, and PR = 13y + 25, therefore,

QR = (13y + 25) - (8y + 5) (PQ + QR = PR)

Simplify the expression to for the length of segment QR

QR = 13y + 25 - 8y - 5

Collect like terms

QR = 13y - 8y + 25 - 5

QR = 5y + 20

Answer:

see below

Step-by-step explanation:

These angles are complementary because you can see the right angle symbol in the picture. Therefore, 2x + 1 + x - 7 = 90.

3x - 6 = 90

3x = 96

x = 32°

Answer: 4/25

Step-by-step explanation:

\((\frac{2}{5}) ^2=\frac{2}{5}\times\frac{2}{5}=\large\boxed{\frac{4}{25} }\)

The probability that the mean of a sample of 55 families will be between 17 and 18 pounds is approximately 71.55%.

σ_sample = σ / sqrt(n)

σ_sample = 2.5 / sqrt(55)

σ_sample ≈ 0.336

Now, we can standardize the values of 17 and 18 pounds using the Z-score formula. This will tell us how many standard deviations away from the population mean these values are:

Z = (X - μ) / σ_sample

Z_17 = (17 - 17.2) / 0.336 ≈ -0.595

Z_18 = (18 - 17.2) / 0.336 ≈ 2.381

Now we will use the standard normal distribution (Z-distribution) to find the probabilities corresponding to these Z-scores. You can use a Z-table, statistical software, or an online calculator to find these probabilities.

P(Z < -0.595) = 0.2760

P(Z < 2.381) = 0.9915

To find the probability that the mean of a sample of 55 families will be between 17 and 18 pounds, we will find the difference between the probabilities corresponding to the two Z-scores:

P(17 < X < 18) = P(Z < 2.381) - P(Z < -0.595)

P(17 < X < 18) = 0.9915 - 0.2760

P(17 < X < 18) ≈ 0.7155

So, the probability that the mean of a sample of 55 families will be between 17 and 18 pounds is approximately 71.55%.

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Answer:

32

Step-by-step explanation:

The horizontal line (5+3) is 8m

and the vertical line (4+4) is also 8m

multiply together 64 (8 x 8)

then divided it by 2 (64/2)

32

Answer:

Step-by-step explanation:

u have to combine like terms

7.2+0.8w B