Hello! 5/6 2/5 in simplest form

It took about 4.04 years for the number of students to reach 365.

The correct option is D.

The logarithm is the opposite of exponentiation. This shows that the logarithm of x to the base of b is the exponent to which b must be raised in order to reach the number x.

Given:

There were 240 students enrolled in Birchwood Elementary School during its first academic year.

The number of students grew significantly throughout the course of each of the ensuing ten years.

We may use logarithms to find n, the number of years.

By multiplying both sides of the equation by their logarithms, we obtain:

log(240(1.15)ⁿ) = log(365)

Using the rule of logarithms that says log(ab) = log(a) + log(b) and the fact that log(1.15) is a constant,

we can simplify the left side of the equation:

log(240) + nlog(1.15) = log(365)

Subtracting log(240) from both sides, we get:

nlog(1.15) = log(365) - log(240)

Using the rule of logarithms that says log(a/b) = log(a) - log(b), we can simplify the right side of the equation:

nlog(1.15) = log(365/240)

nlog(1.15) = log(1.52083)

Dividing both sides by log(1.15), we get:

n = log(1.52083) / log(1.15)

n ≈ 4.04

Therefore, n = 4 years.

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The response to the given question would be that As a result, there is a probability 1.3% chance (or about 0.013) that a random sample of 50 seniors will have a mean score of no higher than 415.

Calculating the chance that an event will occur or a statement will be true is the subject of probability theory, a branch of mathematics. A risk is a number between 0 and 1, where 1 denotes certainty and a probability of about 0 denotes the likelihood that an event will occur. The likelihood that an event will take place is mathematically expressed as probability. Probabilities can also be expressed as percentages ranging from 0% to 100% or as integers between 0 and 1. the proportion of equally plausible possibilities that actually happen in relation to all possible outcomes when a certain event occurs.

The sample mean's sampling distribution may be approximated using the central limit theorem as having a mean of 425 and a standard deviation of[tex]80\sqrt(50) = 11.31.[/tex]

z is equal to (x - mu) / (sigma / sqrt(n))

where n is the sample size, x is the sample mean, mu is the population mean, sigma is the population standard deviation.

When we enter the values, we obtain:

[tex]z = (415 - 425) / (80\sqrt(50)) = -2.23[/tex]

As a result, there is a 1.3% chance (or about 0.013) that a random sample of 50 seniors will have a mean score of no higher than 415.

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Answer: 6 cups of flour = 4 cups of sugar

              9 cups of flour = 6 cups of sugar

             12 cups of flour = 9 cups of sugar

Step-by-step explanation:

Well, if Kurt uses 3 cups of flour for every 2 cups of sugar, than for every 6 cups of flour, he would need 4 cups of sugar. With 9 cups of flour, he would need 6 cups of sugar. For 12 cups of flour, he would need 9 cups of sugar.

By answering the above question, we may infer that The equation's answer is B) 60 ft.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

What is the distance between the bases on a softball field

A) 50 ft

B) 60 ft

C) 70 ft

D) 80 ft

The answer is B) 60 ft.

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The supply of the supply of eggs is changing at 10.7¢ per carton per week

The equation of the function is given as

625p^2 - x^2 = 100

When the supply is 37000, we have

x = 37

So, the equation becomes

625p^2 - 37^2 = 100

Evaluate

625p^2 - 1369 = 100

This gives

625p^2 = 1469

Divide by 625

p^2 = 2.3504

Take the square roots of both sides

x = 1.53

The supply rate is then calculated as

Rate = 7¢ * 1.53

Evaluate

Rate = 10.7¢

Hence, the supply is changing at 10.7¢ per carton per week

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Patrick bought 4 times the number of beans in each bag.

What is expressions ?

An expression is a combination of one or more numbers, variables, and operations. It can contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division. Expressions can be evaluated to obtain a numerical result or simplified by combining like terms or using mathematical rules.

To find an expression that shows how many beans Patrick bought, you can multiply the number of bags by the number of beans in each bag.

So, if Patrick bought 4 bags of beans, and there are b beans in each bag, then the expression would be:

4b

This means that Patrick bought 4 times the number of beans in each bag.

Therefore, Patrick bought 4 times the number of beans in each bag.

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Answer:

64%

Step-by-step explanation:

Convert a fraction to a decimal and move the decimal point to make a percent

Answer:42

Step-by-step explanation: 42x0=42

Answer:

21 miles per gallon

Step-by-step explanation:

find the gradient of the line:

change in y = 105 - 21 = 84

change in x = 5 - 1 = 4

gradient is change in y/ change in x

= 84/4 = 21

Answer:

(4,1)

Step-by-step explanation:

(4,1) is the answer

Answer:

What is the unit price of each battery in each package?

To find the unit price of each battery in each package, we need to divide the total cost of each package by the number of batteries in each package.

For the package of 8 count AA batteries:

Total cost: $6.16

Number of batteries: 8

Unit price = Total cost / Number of batteries = $6.16 / 8 = $0.77 per battery

For the package of 20 count AA batteries:

Total cost: $15.20

Number of batteries: 20

Unit price = Total cost / Number of batteries = $15.20 / 20 = $0.76 per battery

Therefore, the unit price of each battery in the package of 8 count AA batteries is $0.77, and the unit price of each battery in the package of 20 count AA batteries is $0.76.

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Step-by-step explanation:

To find the unit price of each battery in each package, we need to divide the total cost of each package by the number of batteries in each package.

For the package of 8 count AA batteries:

Total cost: $6.16

Number of batteries: 8

Unit price = Total cost / Number of batteries = $6.16 / 8 = $0.77 per battery

For the package of 20 count AA batteries:

Total cost: $15.20

Number of batteries: 20

Unit price = Total cost / Number of batteries = $15.20 / 20 = $0.76 per battery

Therefore, the unit price of each battery in the package of 8 count AA batteries is $0.77, and the unit price of each battery in the package of 20 count AA batteries is $0.76.

Using arithmetic operation, the statement that is true is -

A: The 20-count pack of AA batteries has a lower unit price of $0.78 per battery.

D: The 8-count pack of AA batteries has a lower unit price of S0.77 per battery

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

To find the unit price per battery, we divide the cost of each package by the number of batteries in the package.

For the 8-count pack -

Use the arithmetic operation of division.

Unit price per battery = $6.16 / 8 batteries = $0.77 per battery

For the 20-count pack -

Use the arithmetic operation of division.

Unit price per battery = $15.60 / 20 batteries = $0.78 per battery

Therefore, the statements A and D are correct.

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The value of x that makes the equation true is 2.25.

A mathematical model is an abstract, mathematically based description of a physical system. Mathematical modelling is the process of creating a mathematical model. Both applied mathematics and the natural sciences employ mathematical models. The area of operations research is largely concerned with using mathematical models to resolve issues in commercial or military operations.

Using the figure we see that, for the left model we have:

3 (-x) = -3x.

Also, we have 10(1) = 10

Thus the left model has the equation:

-3x + 10

For the right model we have:

5x - 8

Equate the two models:

-3x + 10 = 5x - 8

18 = 8x

x = 2.25

Hence, the value of x that makes the equation true is 2.25.

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Answer:

It seems like there is a mistake in the variable provided. The variable mentioned is "Gender" but the data provided is about "Age" and "f" (frequency). Assuming that "f" is the frequency of participants at each age, here are the answers to your questions:

For the variable "f", the most appropriate measure of central tendency would be the mode, which represents the most frequently occurring value. For the variable "Age", the most appropriate measure of central tendency would be the median, as it is less affected by outliers than the mean.

Mode = 8; Median = 11; Mean = 10.11 (rounded to two decimal places)

Range = 15 - 7 = 8; Variance = 8.99 (rounded to two decimal places); Standard deviation = 2.99 (rounded to two decimal places)

To calculate the age range that reflects 68% of the sample, we need to find the mean age and the standard deviation. The mean age is 10.11, and the standard deviation is 2.99. 68% of the data falls within one standard deviation of the mean. Using the empirical rule, we can say that the ages of participants that reflect 68% of the sample are between (10.11 - 2.99) and (10.11 + 2.99), which is between 7.12 and 13.10.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since the variable Gender is not given in the data, we cannot compute any measure of central tendency for it. For the variable Age, the most appropriate measure of central tendency would be the mode, since all the observations have the same value for this variable.

To calculate the mode, median and mean for Age, we can first arrange the data in ascending order of age:

7, 2

8, 2

9, 0

10, 1

11, 1

12, 1

13, 1

14, 1

15, 1

The mode is the most frequently occurring value, which is 1 for all ages. The median is the middle value when the data is arranged in ascending order. Since there are 9 observations, the median is the average of the 5th and 6th values, which are 12 and 13. So, the median is (12+13)/2 = 12.5. The mean is the sum of all the values divided by the number of observations, which is:

(72 + 82 + 90 + 101 + 111 + 121 + 131 + 141 + 15*1) / 9 = 11.44 (rounded to two decimal places)

Therefore, the mode is 1, the median is 12.5 and the mean is 11.44.

To calculate the range, variance and standard deviation for Age, we can use the following formulas (assuming the data is a population):

Range = maximum value - minimum value = 15 - 7 = 8

Mean = 11.44 (computed in step 2)

Variance = Σ(x - μ)^2 / N, where μ is the mean, x is each value, and N is the number of observations. Plugging in the values, we get:

Variance = [(7-11.44)^2 + (8-11.44)^2 + (9-11.44)^2 + (10-11.44)^2 + (11-11.44)^2 + (12-11.44)^2 + (13-11.44)^2 + (14-11.44)^2 + (15-11.44)^2] / 9 = 5.72 (rounded to two decimal places)

Standard deviation = square root of variance = √5.72 = 2.39 (rounded to two decimal places)

Therefore, the range is 8, the variance is 5.72, and the standard deviation is 2.39.

Since the data is approximately normally distributed, we can use the empirical rule to estimate the ages that reflect 68% of the sample. According to the empirical rule, 68% of the data falls within one standard deviation of the mean. So, we can compute the lower and upper limits of this range by subtracting and adding one standard deviation from the mean, respectively:

Lower limit = mean - standard deviation = 11.44 - 2.39 = 9.05 (rounded to two decimal places)

Upper limit = mean + standard deviation = 11.44 + 2.39 = 13.83 (rounded to two decimal places)

Therefore, the ages of participants that reflect 68% of the sample are between 9.05 and 13.83 years old.

The area of the resulting figure is 4 times smaller than the area of the original figure.

And, When the side lengths are multiplied by 2, the perimeter is 2 times the original perimeter.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. And, Opposite sides of the rectangle are equal and parallel to each other.

We know that;

When two figures are similar, then ratio of its areas is also equal to the scale factor squared.

Hence, We can assume that the figure is a rectangle or a triangle;

Let

z = the scale factor

x = Area of the resulting figure

y = Area of the original figure

So, We get;

z² = x/y

Since, we have;

z = 1/2

Hence, We can substitute;

⇒ (1/2)² = x/y

⇒ x/y = 1/4

⇒ x = y/4

Therefore, The area of the resulting figure is 4 times smaller than the area of the original figure.

And, If the side lengths are multiplied by 2.

We get;

Perimeter = 2 (L + W)

                = 2 (2L + 2W)

                = 2 (2L + 2W)

Thus, When the side lengths are multiplied by 2, the perimeter is 2 times the original perimeter.

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Answer:

[tex] \frac{25}{2} [/tex]

Step-by-step explanation:

Given 15 ÷6/5

[tex]15 \div \frac{6}{5} \\ = > 15 \times \frac{5}{6} \\ = > 5 \times \frac{5}{2} \\ = > \frac{25}{2} \\ therefore \: the \: answer \: is \: \frac{25}{2} \\ this \: is \: because \: it \: cannot \: be \: broken \: down \: into \: lowest \: term \: again[/tex]

The diagram shows the quantity x is 13.

A tape diagram, also known as a bar model or a strip diagram, is a visual representation of a problem or situation that helps students to organize and solve mathematical problems. It involves drawing a rectangular strip or bar to represent a quantity or a value, and then dividing or labeling the strip to represent different parts of the problem.

The full completed question is related to an equation as shown in the below diagram (Check it).

Given equation is x+4 = 17

If we select part 'a' the diagram is shown in the below diagram, see it.

For part 'b' the quantity x can be represent by:

x+4 = 17

x = 17 - 4

x = 13

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The better deal is 12 donuts for $10 because the unit rate is $0.83.

Generally speaking, a unit price can be defined as the price that is being charged by a seller for the sale of a single unit of product.

In order to determine the unit price, we would determine the unit price for number of donuts by using the following mathematical expression;

Unit price = Cost of donuts/Number of donuts

Substituting the given parameters into the unit price formula, we have the following;

Unit price = $10/12

Unit price = $0.83.

For the second deal, we have:

Unit price = $6/6.99

Unit price = $0.86.

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Answer:

Ignore my handwriting loll

Step-by-step explanation:

Hope this helps! :)

Answer: Marginal cost is the added cost to produce an additional good or the increase in production costs generated by the production of additional product units

Step-by-step explanation:  It is calculated by taking the total change in the cost of producing more goods and dividing that by the change in the number of goods produced.

Answer:

So it's basically the cost added by producing one extra unit of a product or service. I hoped this helped and if you need a better explanation let me know!

Answer: 164

Step-by-step explanation: (16 X 8) + (6 X 5)+ (^^triang)+ 164

The cardinality of B and (A ⋂ C) will be n(B) = 3 and n(A ⋂ C) = 1.

In mathematics, cardinality refers to the size or number of elements in a set. It is a concept used to compare the sizes of sets, regardless of their specific elements. For instance, the cardinality of the set {1, 2, 3} is 3, while the cardinality of the set {2, 4, 6, 8, 10} is 5. Cardinality is typically denoted using vertical bars, such that |S| represents the cardinality of set S.

Now,

The symbol "n(S)" represents the cardinality

Given sets:

A = {1, 2, 3, 4, 5}

B = {1, 3, 5}

C = {4, 6}

To find the cardinality of the sets:

n(B) = 3

Set B has three elements: 1, 3, and 5.

n(A ⋂ C) = 1

The intersection of sets A and C is the set of elements that are in both A and C. Since A and C only have one element in common (the number 4), the cardinality of the intersection set A ⋂ C is 1. Therefore, n(A ⋂ C) = 1.

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The magnitude of resultant of the two forces is 104pounds and angle of resultant is 37°

The resultant is the vector sum of two or more vectors. It is the result of adding two or more vectors together. If displacement vectors A, B, and C are added together, the result will be vector R.

using parallelogram law of vectors

R² = 64² +68²+2(64)(68)cos 76

R² = 8720 + 8704cos 76

R² = 8720+2105.7

R² = 10825.7

R = √ 10825.7

R = 104pounds( nearest pounds)

represent resultant angle by x

using sine rule

64/sinX = 104/sin(180-76)

64/sinX = 104/sin104

104sinX = 64sin 104

104sinX = 62.1

sinX = 62.1/104

sinX = 0.597

X = sin^-1(0.597)

X = 37°( nearest degree)

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Answer:

20/125 is the answer

Step-by-step explanation:

The value of area of triangle ABC is found as 11.42 sq. unit.

Area of a triangle = ½ × base × height.

From the given data:

Using trigonometric function.

tan 25 = 7 / AC

AC  = 7*tan 25

AC = 3.26

Area of  triangle ABC = ½ × 7× 3.26

Area of  triangle ABC = 11.42

Thus, the value of  area of triangle ABC is found as 11.42 sq. unit.

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S = 30 - 0.15(30) or S = 0.85 can be used to calculate the sale price S of an oil change (30).

By resolving this equation, we find that the value of the variable x is 7. An equation is a mathematical formula that states that two quantities or values are equal, as in the example 6 x 4 = 12 x 2.

S will serve as a stand-in for the sale price of the oil change.

Mr. Allen has a 15% off voucher, and the oil change normally costs $30. The reduction can be shown as 15% of the standard price, or:

0.15 * $30 = $4.50

We can deduct the discount from the list price to determine the oil change's selling price:

S = $30 - $4.50

S = $25.50

As a result, S = 30 - 0.15 can be used to calculate the sale price S of an oil change (30)

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Answer:

The answer is  s=0.85*30=22.50(final sale price)  which will be 15 % of the 30 dollars

Step-by-step explanation:

Answer:

The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.

Step-by-step explanation:

o find the equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) using implicit differentiation, we can follow these steps:

Differentiate both sides of the equation with respect to x:

cos(x+y) * (1 + dy/dx) = 4 - 4dy/dx

Simplify by grouping the terms with dy/dx on one side and the rest on the other side:

cos(x+y) * (1 + dy/dx) + 4dy/dx = 4

Substitute x = π and y = π, since we want to find the equation of the tangent line at the point (π,π):

cos(2π) * (1 + dy/dx) + 4dy/dx = 4

Simplify:

-5dy/dx = 4 - cos(2π)

dy/dx = -4/5

Use the point-slope form of the equation of a line to write the equation of the tangent line:

y - π = (-4/5)(x - π)

Simplify:

y = (-4/5)x + (8/5) + π

The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.

The full expression is 6n+1. We can find the solution of the given sequence in the following manner.

First take the differences: 13–7 = 19–13 = 25–19 = 31–25 = 6. So, we know there is a 6n in the expression. Then subtract 6n from each term: 7–6 = 13–12 = 19–18 = 25–24 = 31–30 = 1.

Reduce the size, number, or amount of something else by taking (something) away from it is called subtraction. Subtraction is the activity or procedure of determining the difference between two amounts or numbers. The phrase "taking away one number from another" is also used to describe the act of subtracting one number from another. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process since it is the number from which we subtract another integer in a subtraction phrase.

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Set D ∈ {76, 90, 92, 94, 96}

Sets are groups of clearly defined objects or elements in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.

As per the given data:

Set D consists of positive two-digit even numbers greater than 74 without the digit 8 in them.

For writing set D in the roster form:

For greater than 74:

{76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98}

Without the digit 8:

{76, 90, 92, 94, 96}

Hence, Set D ∈ {76, 90, 92, 94, 96}

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The function which has the same zeros as h(x) = (x² - 4)(x² - 9) is f(x) = (x - 2)(x + 2)(x - 3)(x + 3).

To determine which function has the same zeros as h(x) = (x² - 4)(x² - 9), we need to first find the zeros of h(x).

The zeros of h(x) are the values of x that make h(x) equal to zero.

h(x) = (x² - 4)(x² - 9)

h(x) = 0 if and only if (x² - 4) = 0 or (x² - 9) = 0

Solving for x, we get -

x² - 4 = 0 -> x = ±2

x² - 9 = 0 -> x = ±3

So, the zeros of h(x) are x = ±2 and x = ±3.

Now, we need to find the function that has the same zeros.

A function that has the same zeros will have the same factors of (x - 2), (x + 2), (x - 3), and (x + 3).

One such function is -

f(x) = (x - 2)(x + 2)(x - 3)(x + 3)

Therefore, this function has the same zeros as h(x) = (x² - 4)(x² - 9).

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Answer:

Step-by-step explanation: