A building in a city has a rectangular base. The length of the base measures 75 ft less than three times the width. The
perimeter of this base is 810 ft. What are the dimensions of the base?

The volume of the cylindrical tank for refrigerant with an inside diameter of 14 inches and a height of 16 inches is 10,736 cubic inches.

The volume of a cylinder can be calculated using the formula:

\(\[ V = \pi r^2 h \]\)

where V represents the volume, \(\(\pi\)\) is a mathematical constant approximately equal to 3.14159, r is the radius of the cylinder (which is half the diameter), and h is the height of the cylinder.

In this case, the inside diameter of the tank is given as 14 inches, so the radius can be calculated as \(\(r = \frac{14}{2} = 7\)\) inches. The height of the tank is given as 16 inches. Substituting these values into the formula, we get:

\(\[ V = 3.14159 \times 7^2 \times 16 \approx 10,736 \text{ cubic inches} \]\)

Therefore, the volume of the cylindrical tank for refrigerant is approximately 10,736 cubic inches.

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The product of the volume and total surface area of the given right conical frustum is approximately 146520π². To find the product of the volume and total surface area of a right conical frustum, we first need to determine the individual values of volume and surface area.

The volume of a frustum can be calculated using the formula:

V = (1/3)πh(r₁² + r₂² + r₁r₂),

where h is the height of the frustum, r₁ and r₂ are the radii of the larger and smaller bases, respectively.

In this case, we are given that the radii of the larger and smaller bases are 12 and 9 units, respectively. We also know that the two bases are 4 units apart, which means the height of the frustum is 4 units.

Substituting the given values into the formula, we have:

V = (1/3)π(4)(12² + 9² + 12*9)

 = (1/3)π(4)(144 + 81 + 108)

 = (1/3)π(4)(333)

 = (4/3)π(333)

 ≈ 444π cubic units

Now, let's move on to calculating the total surface area of the frustum. The formula for the total surface area is:

A = π(r₁ + r₂)ℓ + πr₁² + πr₂²,

where ℓ is the slant height of the frustum.

Since the frustum is a right frustum, the slant height ℓ can be found using the Pythagorean theorem:

ℓ = √(h² + (r₁ - r₂)²)

Substituting the given values, we have:

ℓ = √(4² + (12 - 9)²)

 = √(16 + 9)

 = √25

 = 5

Now we can calculate the total surface area:

A = π(12 + 9)(5) + π(12²) + π(9²)

 = π(21)(5) + π(144) + π(81)

 = 105π + 144π + 81π

 = 330π square units

Finally, to find the product of the volume and total surface area, we multiply the two values:

VA = (444π)(330π)

  ≈ 146520π²

Therefore, the product of the volume and total surface area of the given right conical frustum is approximately 146520π².

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The surface area of the hexagonal pyramid is 75240 square millimeters to the nearest square millimeter.

The surface area of the hexagonal pyramid can be calculated by finding the sum of the areas of its faces. The hexagonal pyramid has a base with six equal sides of length 44 millimeters, and six identical triangular faces with a height of 95 millimeters.

Each triangular face is an isosceles triangle, with two sides of length 44 millimeters and a base of length equal to the perimeter of the hexagonal base, which is 6 times 44 millimeters, or 264 millimeters.

To calculate the area of each triangular face, we can use the formula for the area of an isosceles triangle, which is (base x height) / 2. Substituting the values we have, we get: Area of each triangular face = (264 x 95) / 2 = 12540 square millimeters

Since the hexagonal pyramid has six identical triangular faces, we can multiply the area of one triangular face by 6 to get the total surface area of the pyramid: Total surface area = 6 x 12540 = 75240 square millimeters.

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The critical t-value is approximately 1.753.

To find the critical value for a 96% confidence interval with a sample size of 15, we need to determine the t-value from the t-distribution table. The t-distribution table is a statistical tool used to determine the probability of a t-value given the degrees of freedom (df) and the desired level of significance (α).

In this case, we have a sample size of 15, which means our degrees of freedom are 14 (n - 1). Looking at a t-distribution table for 14 degrees of freedom and a 96% confidence interval.

This means that if we were to construct a confidence interval from a sample size of 15, the margin of error would be calculated by multiplying the critical t-value of 1.753 by the standard deviation of the sample and dividing by the square root of the sample size. The resulting interval would contain the population mean with 96% confidence.

It's essential to note that the critical value will change as the sample size and confidence level change. Therefore, it's crucial to use the correct table to find the corresponding critical values for a given dataset's sample size and confidence level.

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The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.

Factors are numbers that can be divided evenly into another number without leaving a remainder. In the case of 70, each factor can be divided evenly into 70.

For example, 70 divided by 1 equals 70. 70 divided by 2 equals 35. 70 divided by 5 equals 14. 70 divided by 7 equals 10. 70 divided by 10 equals 7. 70 divided by 14 equals 5. 70 divided by 35 equals 2. 70 divided by 70 equals 1.

When we are looking for the factors of a number, it is important to remember that the number itself is a factor and that every factor is paired with another factor (e.g., 2 and 35). This means that if you know the factors of 70, you also know the factors of all the other numbers in the list.

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Answer:

Solving the quadratic equation \(8v^2+37v=0\) we get: \(\mathbf{v=0\:or\:v=\frac{-37}{8}}\)

Step-by-step explanation:

We need to solve the quadratic equation: \(8v^2+37v=0\)

We can solve the quadratic equation of form \(ax^2+bx+c=0\) using quadratic formula: \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

We need to put values of a , b and c in order to find the solutions of quadratic equations.

In the given equation: \(8v^2+37v=0\) we have, a =8, b=37, c=0

Putting values and finding the values for n:

\(v=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\v=\frac{-37\pm\sqrt{(-37)^2-4(8)(0)}}{2(8)}\\v=\frac{-37\pm\sqrt{(-37)^2-0}}{2(8)}\\v=\frac{-37\pm\sqrt{1369}}{2(8)}\\v=\frac{-37\pm37}{2(8)}\\v=\frac{-37+37}{2(8)}\:or\:v=\frac{-37-37}{2(8)}\\v=\frac{0}{2(8)}\:or\:v=\frac{-74}{2(8)}\\v=0\:or\:v=\frac{-37}{8}\)

So, solving the quadratic equation \(8v^2+37v=0\) we get: \(\mathbf{v=0\:or\:v=\frac{-37}{8}}\)

Answer:

32.25 miles in 43mins

45miles in an hour

Step-by-step explanation:

Divide '2 1/2' by '3 1/3' to find the distance done in a minute: 0.75 miles

Multiply the distance done in a minute(0.75) by 43 to find the distance done in 43 minutes: 32.25miles

Multiply the distance done in a minute(0.75) by 60 to find the distance done in an hour: 45miles

Answer:

the answer is B) 12a+6b

Step-by-step explanation:

3+9=12 so 3a+9a=12a,

7-1=6 so 7b-(1)b=6b

Step-by-step explanation:

calm down ! just breathe.

these are totally simple additions and one also very simple subtraction to make.

you know that you can combine terms based on the same variable, right ?

3a + 9a = 12a

7b - b = 6b

the result is then

12a + 6b, so B is the right answer.

this bases already on the same principle of actual numbers.

2×3 + 5×3 = 7×3 because this is also

(2 + 5) × 3

or

6×5 + 6×3 = 6×8 because this is also

6 × (5 + 3)

or

7×8 - 4×8 = 3×8 because this is also

(7 - 4) × 8

and so on.

second one is correct

mark me brainlist

Answer

\(168in^{2}\)

Step-by-step explanation:

SA=2(wl+hl+hw)

2·(6·2+9·2+9·6)

=168

Answer:

h= -10

Step-by-step explanation:

Basically you’re finding out what h is equal to because h can’t be a real number i guess i would say. It is but it also isn’t if that makes sense. Basically just subtract 8 on both sides ands you get your answer. Hope this helped :)

Answer:

75000, 112500, 62500

Step-by-step explanation:

To find 1% of 250000:

1/100 x 250000 = 2500 (1% of total)

Son 1: 30x2500 = 75000 (30% of lawyers money)

Son 2: 45x2500 = 112500 (45% of lawyers money)

Son 3: 25x2500 = 62500 (25% of lawyers money)

The number that represents the total debt is 303 if the group pre-orders 9 tickets for a sightseeing tour, even though they don't have the money to pay for them yet.

It is defined as the amount one party needs to pay to another party as the first party borrowed an amount that will be credited by the second party. Debt occurs when one party cannot be able to purchase something under normal circumstances.

We have:

Each ticket costs 32 dollars, so the debt for one ticket is -$32. The tour company adds a 15-dollar fee for the entire order.

A group of 9 pre-orders 9 tickets for a sightseeing tour.

Total cost of 9 tickets = 9×32 = $288

As this group doesn't have money

The debt for the tickets will be = $288

The tour company adds a $15 fee for the entire order.

The total debt for this tour = $15 + $288 = $303

Thus, the number that represents the total debt is 303 if the group pre-orders 9 tickets for a sightseeing tour, even though they don't have the money to pay for them yet.

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Right Triangles

Right triangles can be identified because they have one internal angle of 90°.

Right triangles have two shorter sided called the legs and one larger side called the hypotenuse.

The relationship between the side lengths and the angles are called the trigonometric ratios.

For example, the angle of 42° as shown in the figure has one adjacent side (35) one opposite side (x) and the hypotenuse (y).

It's required to find the value of x, knowing the value of the side (45) and the angle 42°.

The trigonometric ratio that relates the opposite leg and the adjacent leg is called the tangent.

Substituting:

Solving for x:

x = 35 tan 42°

Calculating:

x = 35 * 0.9004

x = 31.51

Answer:

4w-  4

Step-by-step explanation:

The equivalent expression of (-69.3x + 81y) + (29.1x - 86y) in standard form is -40.2x - 5y.

To find the equivalent expression of (-69.3x + 81y) + (29.1x - 86y) in standard form, we need to simplify and combine like terms.

(-69.3x + 81y) + (29.1x - 86y)

To combine like terms, we can add the coefficients of x and y separately:

-69.3x + 29.1x + 81y - 86y

Combining the x terms gives us:

(-69.3 + 29.1)x + 81y - 86y

Simplifying further, we have:

-40.2x - 5y

Therefore, the equivalent expression of (-69.3x + 81y) + (29.1x - 86y) in standard terms is -40.2x - 5y.

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Answer:

1.5 meters tall / 150cm

Step-by-step explanation:

1.6 meters - 10cm

= 160 cm - 10cm

= 150cm

The number of organisms (n) at any time is proportional to the initial number organisms (n0) is True.

The equation for growth of bacterial cells after n number of generations is -

N = No 2n

Where N = final number of cells.

No = initial number of cells

n = number of generations

As clear from the equation, the value of N depends on the initial number of cells in a population. Or we can say, N is directly proportional to No. Therefore, the statement is true.

Given that the population of bacteria has grown from 2.2*104 CFU/g to 2.2*107 CFU/g in a week (7 days).

The number of generations passed after 7 days can be calculated as -

N = No 2n

Putting values, we get

2.2*107 = 2.2*104 * 2n

2n = 103

Taking log of both sides,

n log 2 = log 103

n = 3/0.3

n = 10

S, after one week, 10 generations are passed.

Now we need to take final population of bacteria after one week to be 2.2*105 CFU/g.

Putting values in equation, the initial number of cells can be calculated as -

2.2*105 = No *210

No = 2.2*105 / 1024

No = 177,419.

Therefore, we need to keep initial population of 177,419 CFU/g to increase the shelf life of food.

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Complete question:

1. The number of organisms (N) at any time is proportional to the initial number organisms (No)? a. True b. False 2. Your first job out of college is working for Ricky's Risky Ready-To-Eat Foods. As a microbiologist for the company, you are tasked with extending the shelf-life of the company's leafy greens salad mixes. You find that a salad mix has an initial total plate count of 2.2 x 104 CFU/g (colony forming units per gram). After one week of refrigerated storage, the count reaches an unacceptable level of 2.2 x 107 CFU/g. You decide that an acceptable level of 2.2 x 105 CFU/g could be achieved if the initial count were lower. What starting level of bacteria would you need to achieve this goal?

With a 16% prevalence of spam emails, a filter that has a 64% true positive rate and a 28% false positive rate would correctly flag 10.24% of emails as spam and incorrectly flag 19.12% of non-spam emails as spam.

In this scenario, the prevalence of spam emails is 16%, or 0.16. A filter that has a 64% true positive rate and a 28% false positive rate means that, out of every 100 spam emails, 64 will be correctly flagged as spam and 36 will be missed, and out of every 100 non-spam emails, 28 will be incorrectly flagged as spam and 72 will not.

To calculate the probability that an email flagged by the filter is actually spam (the positive predictive value), we can use Bayes' theorem:

P(Spam | Flagged) = P(Flagged | Spam) * P(Spam) / P(Flagged)

P(Flagged | Spam) is the true positive rate of the filter, or 0.64. P(Spam) is the prevalence of spam emails, or 0.16. To find P(Flagged), we need to consider the probability of two mutually exclusive events: either the email is spam and is correctly flagged, or the email is not spam and is incorrectly flagged.

P(Flagged) = P(Flagged | Spam) * P(Spam) + P(Flagged | Not Spam) * P(Not Spam) = 0.64 * 0.16 + 0.28 * 0.84 = 0.2688

Therefore, the probability that an email flagged by the filter is actually spam is:

P(Spam | Flagged) = 0.64 * 0.16 / 0.2688 = 0.381

This means that the filter correctly identifies 38.1% of the spam emails that it receives. To find the false positive rate (the probability that a non-spam email is incorrectly flagged as spam), we can use the complement rule:

P(False Positive) = 1 - P(True Negative)

P(True Negative) is the probability that a non-spam email is not flagged, which is:

P(True Negative) = 1 - P(Flagged | Not Spam) = 1 - 0.28 = 0.72

Therefore, the false positive rate is:

P(False Positive) = 1 - 0.72 = 0.28

This means that the filter incorrectly flags 28% of non-spam emails as spam. Overall, the filter correctly flags 10.24% of emails as spam (0.16 * 0.64), and incorrectly flags 19.12% of non-spam emails as spam (0.84 * 0.28).

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The shapes of the curves in the AS/AD (Aggregate Supply/Aggregate Demand) model are based upon the relationship between the price level and the output level in an economy.

The AD curve shows the relationship between the overall price level and the quantity of goods and services demanded by all buyers in an economy. It has a negative slope, indicating that as the price level increases, the quantity of goods and services demanded decreases.

The AS curve shows the relationship between the overall price level and the quantity of goods and services that firms are willing and able to supply. In the short run, the AS curve is upward sloping, indicating that as the price level increases, firms are willing to supply more output due to higher profits. In the long run, the AS curve becomes vertical, indicating that the level of output is determined by the factors of production and technology, not the price level.

Thus, the shapes of the curves in the AS/AD model are based on the behavior of buyers and sellers in an economy and their response to changes in the overall price level.

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Answer:

168

Step-by-step explanation:

Area = Length * Width

Area = 14 * 12

Area = 168

Detailed multiplication:

14

* 12

-------

28

+ 140

---------

168

Answer:

Step-by-step explanation:

Width =  w units

Length = ( w + 13 ) units

Perimeter of rectangle = 38 units

2* (length + width) = 38

2*(w +13 + w )= 38            {Use distributive property: a*(b+c)=(a*b) +(a*c)

2* ( 2w + 13)   = 38  

2*2w + 2*13   = 38

     4w + 26   = 38              {Subtract 26 from both sides}

              4w   = 38 - 26

              4w =  12       {Divide both sides by 4}

                w = 12/4

w = 3 units

Length = 3 + 13 = 16 units

Answer:

\(=\frac{62}{49}\)

Step-by-step explanation:

Given: \(8\frac{6}{7} /7\)

First, convert the mixed fraction to an improper fraction:

\(8\frac{6}{7}\) = \(\frac{62}{7}\)

Then to divide, turn the division sign to a multiplication and turn 7/1 around:

\(\frac{62}{7} *\frac{1}{7}\)

= \(\frac{62}{49}\)

Answer:

62/49

Step-by-step explanation:

To divide a mixed number by a whole number, you need to convert the mixed number into an improper fraction and then divide it by the whole number. What you want to do first is convert 8 6/7 into an improper fraction by multiplying the whole number 8 by the denominator 7 and then adding the numerator 6. This gives you 62/7. Next you want to divide 62/7 by 7 by multiplying 62/7 by the reciprocal of 7, which is 1/7. This gives you (62/7) x (1/7) = 62/49. Now simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 1. This gives you 62/49 as the simplest form.

So, 8 6/7 divided by 7 is 62/49.  

Hope this helps :)

Answer:

2(50 + 30)

130 is the hypotenuse

After executing this code, the object "stats" will contain the vector of odd numbers: 21, 23, 25, 27, 29.

To assign a vector of odd numbers between 20 and 30 to an object called "stats" in a programming language like R, you can use the following code:

stats <- seq(21, 29, 2)

Here's how this code works:

seq() is a function in R used to generate a sequence of numbers.

We specify the starting point as 21 (the first odd number between 20 and 30).

The endpoint is set to 29 (the last odd number between 20 and 30).

The third argument, 2, indicates the step size. By setting it as 2, we ensure that only odd numbers are included in the sequence.

The resulting sequence of odd numbers between 20 and 30 is then assigned to the object called "stats" using the assignment operator <-.

After executing this code, the object "stats" will contain the vector of odd numbers: 21, 23, 25, 27, 29.

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A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

The constant for this problem is given as follows:

k = y/x

k = 16/7.

Hence the equation is:

y = 16x/7.

The outputs for the given inputs are given as follows:

When y = 22, the input is given as follows:

22 = 16x/7

x = 22 x 7/16

x = 77/8.

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Answer:

h=0.8

Step-by-step explanation:

Steps

$h+\frac{6}{5}=2$

$\mathrm{Subtract\:}\frac{6}{5}\mathrm{\:from\:both\:sides}$

$h+\frac{6}{5}-\frac{6}{5}=2-\frac{6}{5}$

Show Steps

$\mathrm{Simplify}$

$h=\frac{4}{5}$

Answer:

The answer would be 2h

Step-by-step explanation:

please let this be helpful

Rejecting the null hypothesis implies that we have evidence to support the alternative hypothesis, which suggests that there is a significant difference between the proportions of vaccinated and unvaccinated people who develop COVID-19.

However, if it turns out that the proportion of those who are vaccinated and develop COVID-19 is the same as the proportion of those who are not vaccinated and develop COVID-19 when the Moderna vaccine is distributed to the entire population, this would be an unexpected result, which means that our earlier decision to reject the null hypothesis was incorrect.

In hypothesis testing, we use the null hypothesis to make a decision about whether there is sufficient evidence to support the alternative hypothesis. In this case, the null hypothesis assumes that the proportion of vaccinated and unvaccinated people who develop COVID-19 is the same. We reject the null hypothesis when our test statistic is larger than the critical value, which means that the difference between the observed proportions is too large to be explained by chance alone.

However, if we later discover that the proportions are actually the same, this means that our initial rejection of the null hypothesis was incorrect. It's important to note that hypothesis testing does not prove that the alternative hypothesis is true, but rather, it provides evidence in favor of it. In this case, if we were to observe equal proportions of COVID-19 cases among vaccinated and unvaccinated individuals in the entire population, this would indicate that the Moderna vaccine is not effective in preventing COVID-19.

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