The size of the standard version is 2.8 megabytes (MB). The size of the high-quality version is 4.3 MB. Yesterday, the high-quality version was downloaded four times as often as the standard version. The total size downloaded for the two versions was 4600 MB. How many downloads of the standard version were there?

The possible locations for the walkway bridge are 1, 5, and 6.

What is factorization?

Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.

Here, we have

Given

The function can model a section of a roller coaster:

F(x) = x⁵ - 5x⁴ - 31x³ + 113x² + 282x - 360.

We have to find the possible locations for the walkway bridge.

Now, we factorize the given function

F(x) = x⁵ - 5x⁴ - 31x³ + 113x² + 282x - 360

F(x) = (x-1)(x+3)(x+4)(x-5)(x-6)

then, x - 1 = 0, x+3 = 0, x+4 = 0, x-5 = 0, x-6 = 0

x = 1, -3, -4, 5, 6, becausex>0

s0, x = 1, 5, 6

Hence, the possible locations for the walkway bridge are 1, 5, and 6.

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The measurement of m∠2 = 47°.

What is an angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Given that m∠PQR = 75° and m∠1 = 28°.

From the figure ∠PQS = m∠1 and ∠SQR = m∠2

The angle ∠PQR can be written as the sum of two angles.

∠PQR = ∠PQS + ∠SQR

∠PQR = m∠1 + m∠2

Putting m∠PQR = 75°  and  m∠1 = 28°:

75° = 28° + m∠2

Subtract 28° from both sides:

m∠2 = 75° - 28°

m∠2 = 47°

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The coefficient of the equation A = 5.4 x 10⁸ is c = 5.4

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the coefficient of the equation be c

A = 5.4 x 10⁸   be equation (1)

On simplifying the equation , we get

Group coefficients together and exponents together to multiply the numbers in the scientific notation

So , A = c x bˣ

where c is the coefficient

Substituting the values in the equation , we get

The value of c = 5.4

Therefore , the value of c is 5.4

Hence , the coefficient is 5.4

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The annual interest rate would have to be about 0.57% in order to earn $1200 in interest in 3.5 years. Rounded to two decimal places, the annual interest rate would have to be about 0.57%.

What is an annual interest rate?

The annual interest rate is the percentage of the principal (the initial amount of money invested or borrowed) that is charged as interest on a loan or earned on an investment over a period of one year. It is used to calculate the amount of interest that will be earned or charged over a given period of time.

To determine the annual interest rate that an account would have to offer in order to earn $1200 in interest in 3.5 years, we need to use the following formula:

rate = (interest / principal) * (1 / time)

Where the rate is the annual interest rate, interest is the amount of interest earned, the principal is the amount of money invested, and time is the length of time in years.

Plugging in the given values, we get:

rate = ($1200 / $60000) * (1 / 3.5)

= 0.02 * (1 / 3.5)

= 0.00571428571

Hence, the annual interest rate would have to be about 0.57% in order to earn $1200 in interest in 3.5 years. Rounded to two decimal places, the annual interest rate would have to be about 0.57%.

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Percentage for each enantiomer is 95%, 5%. Option (d) is Correct.

We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100. A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The symbol "%" is frequently written after the number to indicate percentages. %, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

% ee = % enantiomer A - % ensarstomer B

wheee ee is enantiomeric excess.

ee = 90%.

In the provided options, 90%. the difference is given by subtracting 95%, 5%

95% - 5% = 90%

4th option is 5%, 90% correct.

Percentage of each enantiomer is 95%, 5%.

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The maximum length or width we can increase so that it will not exceed the capacity of AC  is 100 feet.

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel, opposite sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's longer side is its length, while its shorter side is its breadth.

Given:

The volume AC can cool, v = 40000 feet³,

The dimensions of the room are 75 feet × 50 feet × 8 feet.,

Calculate the volume of the room as shown below,

Volume = 75 feet × 50 feet × 8 feet

Volume = 30000 feet³

The remaining margin of volume = 40000 - 30000

The remaining margin of volume = 10000 feet³

Thus, the maximum dimension we can increase in length and width is 100 feet.

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Delilah is baking cupcakes for her brother's birthday party. She has already made 14 cupcakes and is making 2 cupcakes per hour. How many cupcakes will she have in 10 hours? How many hours does it take to make 20 cupcakes?

Lauren’s reasoning does not make sense, as the lcm of 2 and 8 is 8.

In this question we have been given Lauren uses a treadmill every 2 days and the weight machines every 8 days.

She used a treadmill on March 2 and will use the weight machines on March 8.

But she says that the first time she will use both a treadmill and the weight machines in March is March 16 because the LCM of 2 and 8 is 16.

First we find and list multiples of each number until the first common multiple is found. And that would be the least common multiple.

Multiples of 2:

2, 4, 6, 8, 10, 12

Multiples of 8:

8, 16, 24

Therefore, LCM(2, 8) = 8 and Lauren is incorrect.

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The value of a is 133 and b is 999.

A vinculum is a horizontal line that serves a variety of functions in mathematical notation.  In decimal numbers, a bar across one or more consecutive digits indicates that the pattern of digits beneath the bar repeats indefinitely.

Given [tex]0.\overline{1331}[/tex]. This means that 1331 repeats many times in this expression. This expression is the same as 1330/9990.

1, 7, 19, and 133 are factors of 133, and  1, 3, 9, 27, 37, 111, 333, and 999 are the factors of 999. From this, the GCD is found to be 1.

Therefore, by simplifying, we get 1330/9990 = 133/999. The answer to a is 133 and b is 999.

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Answer:

y= 1/2x

Step-by-step explanation:

If y is 2 and x is 4

2= 1/2 (4)

2 = 2

The best description of the distribution is bimodal with a gap.

Here in the plot, we can see that there are two peaks and it implies that there are two modes.

This can be seen in a histogram as a distinct gap between two cohesive groups of bars. When two clearly separate groups are visible in a histogram, you have a bimodal distribution. Literally, a bimodal distribution has two modes, or two distinct clusters of data

We can see that there is a gap between the two modes. So the best description of the distribution is bimodal with a gap.

The following dot-Plot shows the bimodal with a gap.

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To find the z-score for a given systolic blood pressure reading, we need to use the z-score formula:

z = (x - mu) / sigma

where z is the z-score, x is the raw score, mu is the mean, and sigma is the standard deviation.

In this case, we are given that mu = 121 and sigma = 15. We can use this information to find the z-score for each of the given blood pressure readings:

A. For a blood pressure reading of 142, we have:

z = (142 - 121) / 15

= 21 / 15

= 1.4

Therefore, the z-score for a blood pressure reading of 142 is approximately 1.4, to the nearest tenth.

B. For a blood pressure reading of 130, we have:

z = (130 - 121) / 15

= 9 / 15

= 0.6

Therefore, the z-score for a blood pressure reading of 130 is approximately 0.6, to the nearest tenth.

C. For a blood pressure reading of 103, we have:

z = (103 - 121) / 15

= -18 / 15

= -1.2

Therefore, the z-score for a blood pressure reading of 103 is approximately -1.2, to the nearest tenth.

Answer:

The answer is 13 because that is the month that both memberships will cost the same amount of money.

Step-by-step explanation:

First translate the question into equations.

Total Gym:

100+20m

Where "m" equals the amount of months

Fitness Plus Elite

35+25m

Where "m" equals the amount of months

Set the equations equal to each other and solve for m, or the amount of months it takes to get the same price for each membership.

100+20m=35+25m Subtract 35 from both sides.

65+20m=25m Subtract 20m from both sides

65=5m Divide both sides by 5

13=m Both memberships will cost the same amount of money at 13 months. You can substitute this value into the original equations to check your work.

100+20(13)=$360

35+25(13)=$360

The answer is 13 because that is the month that both memberships will cost the same amount of money.

Answer:

Mean, median, mode, and range are all statistical measures that are used to summarize and analyze data. Mean is the arithmetic average of a set of numbers, calculated by adding all the numbers together and dividing by the total number of values. Median is the middle value in a set of numbers, which is the value that divides the data into two equal halves. Mode is the value that occurs most frequently in a set of numbers. Range is the difference between the largest and smallest values in a set of numbers.

Mean is commonly used to calculate the average value of a set of numbers. The Median is commonly used to find the middle value in a set of numbers, especially when the data is not evenly distributed. Mode is commonly used to find the most frequent value in a set of numbers. The range is commonly used to find the difference between the largest and smallest values in a set of numbers.

All of these measures are useful for different purposes, and which measure to use will depend on the data and the question being asked. In general, mean is used when the data is evenly distributed, median is used when the data is not evenly distributed, mode is used when the data is categorical rather than numerical, and range is used to measure the spread of the data.

The probability that the weight of the box less than 27 kilogram is 0.375

The figure shows the probability distribution shows the weights x, in kilograms, of boxes being shipped from a certain factory.

Then a shipped box is randomly chosen

The probability is the ratio of the number of favorable outcomes to the total number of outcome

The probability = Number of favorable outcomes / Total number of outcomes

Number of possible weights = 8 weights

Number weights less than 27 kilogram = 3

Substitute the value in the equation of probability

The probability = 3/8

Divide the numbers

= 0.375

Therefore, the probability is 0.375

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Answer:

A.

Step-by-step explanation:

5 x 14 = 70

x^1 x x^7 = 8

y^0 x y^5 = 5

he provider ordered lactated ringers (lr) to infuse at 75 ml/hr for the next 24 hours. 18.0 liters of lr will infuse with rate of infusion.

First, we need to determine how many milliliters of LR will be infused over 24 hours. So, we need to multiply the rate of infusion (75 mL/hr) by the number of hours (24). This will give us the total number of milliliters that will be infused. In this case, it is 75 x 24 = 1800 mL. To determine the number of liters, we need to divide this by 1000 since there are 1000 mL in 1 L. Therefore, 1800 mL/1000 = 1.8 L. We can round this number up to the tenth (one decimal place), and the answer is 18.0 L.

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Answer:

[tex]2m=45[/tex]

Step-by-step explanation:

He earned twice as much washing cars, which is [tex]2m[/tex]. This is given to be equal to 45.

It would take Laine 20.83 minutes to read 25 pages at the same rate.

Assuming that Laine was able to read 200 pages in 240 minutes at a consistent rate, it would take her 25 minutes to read 25 pages. To figure out how long it would take Laine to read 25 pages, we need to use a proportion.

Let x represent the time it will take Laine to read 25 pages.

200/240 = 25/x

Cross multiply to solve for x:

240x = 5000

Divide both sides by 240:

x = 20.83 minutes

Therefore, it would take Laine 20.83 minutes to read 25 pages at the same rate.

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Answer:

A glide.

Step-by-step explanation:

The image is a shift or a glide.

Reflection is either changes the arrow direction the other direction.

A glide reflection is both.

a) The deviation from the mean for each term is given as follows:

b) The sum of all deviations obtained in part a is of 378.

The deviation from the mean of each term is given by the absolute value of the difference between each term and the mean.

Hence, for example, the absolute deviation of 27 from the mean of 108 is given as follows:

|27 - 108| = |-81| = 81.

(the absolute value of a number is the number without the signal).

For a number greater than the mean of 108, the deviation of 243 from the mean is given as follows:

|243 - 108| = |135| = 135.

Then the sum of all deviations obtained in part a is given as follows:

81 + 63 + 45 + 0 + 54 + 135 = 378.

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Answer:

[tex]223093\pi/187500[/tex]

Step-by-step explanation:

[tex]V=\frac{1}{3}\pi r^2 h=(\pi/3)(1.31^2)(2.08)=223093\pi/187500[/tex]

There are 10240 bacteria after 3 hours.

Initial population = 20

Time period = 3 hours

Time period in minutes = 3 hours x 60 minutes = 180 minutes

Number of doublings = 180 minutes / 20 minutes = 9 doublings

Final population = 20 x 2^9

Final population = 20 x 512

Final population = 10240

Bacteria doubling is the process in which one bacterial cell divides into two identical daughter cells. This process is known as binary fission and is the primary way bacteria reproduce. During this process, a single bacterium first replicates its single chromosome, which is then partitioned into two identical parts. The single cell then divides into two daughter cells, each containing one of the replicated chromosomes. This process is incredibly fast and can occur in as little as twenty minutes.

Bacterial doubling is an important process, as it allows bacteria to rapidly increase in number and spread. In optimal conditions, a single bacterial cell can divide into two daughter cells every twenty minutes, and this can continue for many generations. For this reason, bacteria can quickly become abundant in a given environment and pose a potential threat to human health. Fortunately, antibiotics are often able to help control bacterial doubling and limit the spread of certain bacteria.

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No, The two expression you wrote is not true. Because expression are equivalent when values are substituted in for variables. So, both expression gave same answer. Then we can say equivalent expression.

What is expression?

Expression is a finite of symbols that are formed in accordance with dependent rule. It is a number, a variable and combination of variables or symbols. It can be possible by multiply, divide, subtraction and addition.

What is equivalent expression?

Equivalent expression that always work same but look different. When equivalent expression simplified they give same answer. If all the terms in the two expression are identical then we can expression are equivalent.

NOW we have expression

ax +3b

3b+xc

ax+3b=3b+xc

ax=xc

The two expression can only be equivalent if ax=xc it mean that a is equal to c. which is not true. So, they are not equivalent.

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Answer:

False

Step-by-step explanation:

The first value given is the numerator even if its greater than the denominator.

1) An equation that gives the total cost in dollars, d, of attending the event if you order z ounces of fro-yo is d = $5 + $0.40z

2) 2. If your cup weighs 14 ounces, you would pay $10.6 in total for the evening.

A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts.

Given,

The school jazz band is playing at Sweet Yo's, a frozen yogurt shop. It costs $5 to get in the door for the event and if you'd like to eat fro-yo to eat while listening to their tunes you can fill your cup with yogurt and toppings for $0.40 per ounce.

1) Total cost = d

Total ounces = z

Equation

d = $5 + $0.40z

2) If cup weighs 14 ounces

d = $5 + 0.40(14)

d = $5 + $5.6

Total cost:

d = $10.6

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The measure of each of the other two angles is 72° and 36°.

What is vertex angle?

The angle created by two lines or rays intersecting at a location is known as the vertex angle. The sides of the angle are formed by these two rays. In other terms, vertex angle refers to the angle contained within a certain vertex and is expressed in degrees.

let the vertex angle is 36°

the other two angles are equal

let the angle be x

sum of angle in triangle is 180

x + x + 36 = 180

2x = 180 - 36

2x = 144

x = 144/2

x = 72

largest angle is 72°

smallest angle is 36°

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Answer:

[tex]p+166=249[/tex]; [tex]p=83[/tex] pages

Step-by-step explanation:

The number of pages that need to be read plus the 166 pages already read must add to 249.

Therefore, the margin of error for the 90% confidence interval is 1.32. This means that you can be 90% confident that the true population mean falls within a range of 1.32 around the sample mean.

To find the margin of error for a 90% confidence interval, you can use the following formula:

margin of error = z * standard deviation / sqrt(n)

Where z is the z-score for the desired level of confidence (in this case, 90%), standard deviation is the standard deviation of the sample, and n is the sample size (in this case, 120).

Plugging in the values, you get:

margin of error = 1.645 * 9.1 / sqrt(120)

= 1.645 * 9.1 / 11.1

= 14.72 / 11.1

= 1.32

The middle of the set of values is represented by the mean. This value is the mean of all values in the data collection. In statistics, the middle quantity, referred to as the mean, is known as the average.

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