Identify the recursive formula for the following sequence. 8, 16, 32, 64, ...

Answer:

140.085

Step-by-step explanation:

Answer:

140.08

Step-by-step explanation:

Hope it helped!

Answer: A=12

Step-by-step explanation:

Shoe Sizes:                            Frequency:
3                                              11
4                                              A
5                                              7

The frequency is how many people have the shoe sizes. For example, 11 people have shoe size 3, and 7 people have shoe size 5. Since 30 people's shoe sizes were recorded, 30 - (11+7) will be the answer.

30 will be from the 30 people whos shoe sizes were recorded. The 11 will be from the people with shoe size 3, and the 7 will be from the people with shoe size 5. So, 30 - 18 = 12.

12 people have shoe size 4.

Answer:

Here the value is similar to the value of pi (\(\pi\))

Step-by-step explanation:

22 / 7 = \(\pi\)

22 / 7 = 3.14159

So it is based on a multiple on the divisor 7

Answer:

3a + (5b + 7c)

Step-by-step explanation:

The answer cannot be 3a(5b +7c) because when the number is immediately before the brackets, it signifies multiplication. therefore the 3a(5b+7c) would be equivalent to 15ab+21ac

the answer cant be 7c(5b+3a) because of the same explanation as the one above, therefore 7c(5b+3a) would be equivalent to 35cb+21ca

the answer finally cant be 8ab+7c because it means that one added 3a and 5b giving you 8 but it cannot be ab because ab is equivalent to a×b, hence, one cant put a multiplied algebraic expression with an added number

The equation equivalent to the the expression (3a + 5b) + 7c is 3a + (5b+7c). Hence, the first option is the correct one.

In mathematics, expressions are assertions that must contain at least two words with variables or terms with numbers in them, or both, and connect them with an operator. It is possible for the mathematical operators to be addition, subtraction, multiplication, or division.

For instance, the equation x + y has the terms x and y with an addition operator in between. Numerical expressions, which just contain numbers, and algebraic expressions, which also include variables, are the two types of expressions used in mathematics.

The first option is correct because it does not affect the main equation rest are not the same as the equation.

For example, let's take the second equation :

3a (5b + 7C)

After solving this option we get 15ab + 21 ac so it is incorrect because it changed the main expression.

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Answer:

20

Step-by-step explanation:

Given: F = 11, C = 11, E=?

By Euler's formula, we have:

\(F + V - E = 2 \\ \therefore \: 11 + 11 - E = 2 \\ \therefore \:22 - E = 2 \\ \therefore \:22 - 2 = E \\ \huge \red{ \boxed{\therefore \: E = 20}}\)

Hence, the solid will have 20 edges.

There are 22 edges for a solid with 11 faces and 11 vertices.

It is concerned with the geometry, region, and density of various 2D and 3D shapes.

Given data;

Faces,F = 11

Vertices,V = 11

Edge,E = ?

From Euler's formula;

F+V-E = 2

11+11-E =2

22-2 =E

E=20

Hence there are 22 edges for a solid with 11 faces and 11 vertices.

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Using trigonometric function the value of x is 51.3°.

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here Let us take the given right triangle as ABC.

∠A = x , ∠B = 90° and AB = 25 , AC= 40

Now using Cosine ratio then

Cos  A = \(\frac{adjacent}{hypotenuse}\)

=> cos x = \(\frac{25}{40}\)

=> cos x = \(\frac{5}{8}\)

=> x = \(cos^{-1}\frac{5}{8}\)

=> x = 51.3°

Hence the value of x is 51.3°.

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The amount of yoghurt used in 800 ml salad dressing is 300 ml.

Let the amount of yoghurt and mayonnaise used be 3x and 5x. So, forming the equation based on total amount.

3x + 5x = 800

Performing addition on Left Hand Side of the equation

8x = 800

x = 800 ÷ 8

Performing division on Right Jand Side of the equation

x = 100

So, the amount of yoghurt required = 3x

The amount of yoghurt = 3 × 100

Performing multiplication

The amount for yoghurt = 300 ml

Hence, the amount of yoghurt is 300 ml.

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Answer:

Step-by-step explanation:

\(\bf Step-by-step~explanation:\)

Keep in mind: The entire line segment (VX) is equal to 14.

\(\bf Step~1:\)

Let's see how the line segment looks like first.

Line segment VX is 14 units long.

             14

______________

V                         X

W is on the line segment somewhere, and VW is equal to 3.

     3              ?

______________

V           W           X

\(\bf Step~2:\)

We have to solve for the ?. Let's put ? as x. So now we are solving for x.

We have to set up our equation like this:

x + 3 = 14

Since our unknown value plus 3 is equal to 14, we have to subtract 3 from 14 to get our answer.

14 - 3 = 11

   3               11

______________

V           W           X

\(\large\boxed {\bf Our~final~answer: ~WX=11}\)

On solving the provided query we have Therefore, assuming that order equation counts, there are 20,736 different ways to arrange 12 different books on four shelves.

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

Using the permutation formula with repetition, we can determine how many different ways there are to arrange 12 books on 4 shelves.

\(n^r\)

where r is the number of empty spaces to be filled (in this example, 4 shelves) and n is the number of options to select from (12 distinct books in this case).

\(12^4 = 20,736\)

Therefore, assuming that order counts, there are 20,736 different ways to arrange 12 different books on four shelves.

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The proportional relationship between the price and quantity of ears of corn can be represented using a table or a graph, showing how the price and quantity vary in a consistent manner.

One way to represent the proportional relationship between the price and quantity of ears of corn is by using a table:

Price (in dollars) Quantity (in ears of corn)

             2             5

             4             10

This table shows the corresponding values of the price and quantity.

As we can observe, when the price is $2, the quantity is 5 ears of corn, and when the price is $4, the quantity is 10 ears of corn.

The relationship is proportional because as the price doubles, the quantity also doubles.

Another representation of this proportional relationship is through a graph.

We can plot the points (2, 5) and (4, 10) on a coordinate plane, where the x-axis represents the price and the y-axis represents the quantity.

By connecting these two points with a straight line, we can visualize the proportional relationship.

The line will pass through the origin (0, 0) since zero price corresponds to zero quantity.

The slope of the line will indicate the rate of change between price and quantity.

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The scale of measurement being used to classify the students in the introductory art class as art majors and non-art majors is nominal.

Nominal scales are used for categorical data, where the items being measured can be placed into categories or labels, but no order or ranking is implied. In this case, the students are being classified into two categories: art majors and non-art majors.

The students are being classified into two categories: art majors and non-art majors. These categories are mutually exclusive and exhaustive, meaning that every student in the class falls into one and only one of the two categories. There is no inherent order or ranking to the categories, and it is not meaningful to say that one category is greater or smaller than the other. This type of data classification is an example of nominal scale measurement.

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Answer:

With What?

Step-by-step explanation:

Therefore , the solution of the given problem of function comes out to be  f(x) = 2871 thousands.

A science called mathematics studies numbers, its variations, arithmetic and the local tissue, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function. A function is a collection of inputs that together produce a single, recognizable output with each input. A city, municipality, or scope—often referred to as a realm—is assigned to each function. Usually, the letter f is used to represent functions (x). The input has an x in it.

Here,

Given :

=>  f(x) = 225(1.29)×

After 10 year number of years x =10

=> f(x) = 225(1.29)¹⁰

=> f(x) = 12.76 * 225

=>  f(x) = 2871 thousands.

Therefore , the solution of the given problem of function comes out to be  f(x) = 2871 thousands.

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Answer:

okay wait lemme answer it first

Sample mean of 2.4% or higher is somewhat unlikely to occur by chance alone, and may indicate that the true mean childhood asthma prevalence in the sampled cities is higher than the Population mean of 2.16%.

We can use the Central Limit Theorem (CLT), which states that the sample mean of a sufficiently large sample size from a population with any distribution will be approximately normally distributed. The mean of the sampling distribution of the sample mean will be the same as the population mean, and the standard deviation of the sampling distribution of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

In this problem, we are given that the population standard deviation sigma is 1.27%, the population mean mu is 2.16%, and the sample size n is 34. Therefore, the standard error of the sample mean is:

standard error = sigma / sqrt(n) = 1.27% / sqrt(34) = 0.218%

The probability that the sample mean is greater than 2.4%, we need to standardize the sample mean using the formula:

z = (x - mu) / standard error

where x is the sample mean. Substituting the given values, we get:

z = (2.4% - 2.16%) / 0.218% = 1.10

Using a standard normal table or calculator, we find that the probability of a standard normal random variable being greater than 1.10 is approximately 0.1379. Therefore, the probability that the sample mean is greater than 2.4% is 0.1379, or about 13.79%.

Interpreting this probability, we can say that if we take many random samples of size 34 from the population of 43 cities and compute the sample mean for each sample, about 13.79% of these sample means will be greater than 2.4%. This suggests that a sample mean of 2.4% or higher is somewhat unlikely to occur by chance alone, and may indicate that the true mean childhood asthma prevalence in the sampled cities is higher than the population mean of 2.16%.

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The fraction is 1/6 is less than 2/6.

Less than is the answer

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole.

From the image, the fraction to the left is 1/6 and the fraction to the right is 2/6.

You can think of 1/6 as having a pizza divided into 6 equal portions and you are to pick 1 out of the 6 whereas in the case of 2/6 you are to pick 2 out of the 6. You will notice that you have less pizza in 1/6 than 2/6.

Thus, 1/6 is  less than 2/6

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The probability that a student owns a car or a computer is 0.82.

To calculate this, we can use the principle of inclusion-exclusion. The probability of owning a car is 0.67, the probability of owning a computer is 0.72, and the probability of owning both is 0.57.

To find the probability of owning a car or a computer, we add the probabilities of owning each individually and subtract the probability of owning both to avoid double-counting.

Therefore, the probability is calculated as:

0.67 + 0.72 - 0.57 = 0.82.

In summary, the probability that a randomly selected student owns a car or a computer is 0.82. This is obtained by adding the probabilities of owning each item individually and subtracting the probability of owning both to avoid counting it twice.

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Answer: slope = 3x , y intercept = 5

Step-by-step explanation: use the formula : y2 - y1 / x2 - x1 to find slope. y intercept is shown on graph

Answer:

30 yards of string will remain unused

Step-by-step explanation:

Ok, there are a lot of conversions going on here.

1 yard = 3 feet,

so 50 yards • 3ft per yard = 150 feet of string on the spool

1 foot = 12 inches,

so 150 feet • 12in per foot = 1800 inches of string on the spool

There are 24 students and they each get 30 inches, multiply 24 • 30 to see how much string is used:

24 • 30 = 720 inches of string used

Find how many inches of string is left by subtracting what is used from the original amount:

1800 - 720 = 1080 inches of spool left

To make this faster, instead of dividing by 12 inches per foot and then dividing by 3 feet per yard, I'm just dividing by 36 inches per yard.

1080 ÷ 36 = 30 yards of string remaining

There are 30 yards of the string that will be leftover.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operation is called the arithmetic operator.

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

We have been given that Trisha gives 30 inches of string to each student.

∵ 1 yard = 3 feet,

∴ 50 yards = 150 feet of string on the spool

∵ 1 foot = 12 inches,

∴ 150 feet = 1800 inches of string on the spool

There are 24 students and they each get 30 inches,

So used inches of string :

⇒ 24×30 = 720

Now subtract the used string from the original amount:

⇒ 1800 - 720 = 1080 inches of spool left

So yards of string remaining = 1080/36 = 30.

Hence, there are 30 yards of the string that will be leftover.

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The value of the error for Z, where x = 5.9 +/- 0.5 and y = 2.1 +/- 0.2, with one decimal place is 4.

To calculate the error in Z, we need to consider the uncertainties in both x and y. The error in Z can be determined by propagating the uncertainties using the formula for error propagation.

In this case, Z is given by the equation Z = x/y. To propagate the uncertainties, we use the formula for relative error:

ΔZ/Z = sqrt((Δx/x)^2 + (Δy/y)^2)

Given the uncertainties Δx = 0.5 and Δy = 0.2, and the values x = 5.9 and y = 2.1, we substitute these values into the formula:

ΔZ/Z = sqrt((0.5/5.9)^2 + (0.2/2.1)^2) = sqrt(0.0089 + 0.0181) ≈ 0.134

Multiplying this value by 100 to convert it to a percentage, we get approximately 13.4%. Rounding to one decimal place, the value of the error is 4.

Therefore, the value of the error for Z, with one decimal place, is 4.

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(a) The inverse of matrix A, denoted as A^(-1), can be computed by finding the transpose of A and then dividing it by the determinant of A. The inverse matrix A^(-1) is obtained by taking the transpose of A and dividing it by the determinant of A.

(b) The transformation of vector v under the inverse transformation A^(-1) is given by A^(-1)v. It effectively rotates the vector counterclockwise by 45 degrees, reversing the effect of the original transformation A.

(a) To compute A^(-1), find the transpose of matrix A by interchanging its rows and columns. If A = [a11, a12; a21, a22], then the transpose of A is [a11, a21; a12, a22]. Next, calculate the determinant of matrix A, given by det(A) = a11 * a22 - a12 * a21. Finally, divide the transpose of A by the determinant of A to obtain A^(-1).

(b) The transformation of vector v under the inverse transformation A^(-1) is represented by A^(-1)v. This operation rotates the vector counterclockwise by 45 degrees, effectively reversing the effect of the original transformation A. It can be computed by multiplying the inverse matrix A^(-1) with the vector v.

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Answer:

y=1/4x+3

Step-by-step explanation:

To determine Emma's federal income tax (FIT) withholding, we need to consider her annual salary, pay frequency, filing status, and the standard withholding allowances.

Given that Emma earns an annual salary of $84,400 and is paid biweekly, we can calculate her gross biweekly salary by dividing the annual salary by the number of pay periods in a year. Assuming there are 26 pay periods in a year for biweekly payments:

Gross biweekly salary = Annual salary / Number of pay periods

                    = $84,400 / 26

                    = $3,246.15 (rounded to two decimal places)

Next, we need to determine Emma's withholding allowances based on her filing status. Since she selected "married filing jointly" and is using the standard withholding, the default number of allowances for this status is usually higher compared to single or married filing separately. However, the specific number of allowances can vary based on personal circumstances.

As of my knowledge cutoff in September 2021, the standard withholding allowances for married filing jointly were as follows:

First allowance: $4,300

Additional allowances: $4,400

Please note that tax laws can change, and it's advisable to consult the latest IRS guidelines or use an online tax calculator to get accurate withholding information.

To calculate Emma's FIT withholding, we'll subtract her allowances from her gross biweekly salary and apply the appropriate tax rates. For simplicity, let's assume Emma has one withholding allowance:

Total allowances = First allowance + Additional allowances

               = $4,300 + $4,400

               = $8,700

Taxable income = Gross biweekly salary - Total allowances

             = $3,246.15 - $8,700

             = -$5,453.85 (negative because allowances exceed the salary)

Since the taxable income is negative, Emma's FIT withholding should be $0. In this case, no federal income tax will be withheld from her biweekly paychecks. However, please note that Emma may still owe taxes when filing her annual tax return if her other sources of income or deductions are not accounted for in her withholding calculations.

As per Mental hypothesis, the statistical inference procedures that we should use Chi-square test for goodness of fit.

Hypothesis

In probability, an idea or explanation that you then test through study and experimentation is known as hypothesis.

Given,

Here we have given that, an experiment involving peas results in 580 offspring, 152 of which peas have yellow pods. Mendel claimed that the proportion of peas with yellow pods should be 25%. we want to know if these data are consistent with Mendel's hypothesis.

And we need to find in which statistical inference procedures should we use.

According to the definition of Chi-square test for goodness of fit, the claim is that the proportion of peas with yellow pods should be 25%. And then here the researcher wants to check that the experimental and observed counts of yellow offspring peas shows significant difference or not.

So, the statistical procedure used to study this case is Chi-square test for goodness of fit . Hence, option (1) is correct.

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Answer:

45

Step-by-step explanation:

Answer:

It equals 0

Step-by-step explanation:

Hope it helps!

Answer: C

Step-by-step explanation:

Answer: I think the answer is A.

Step-by-step explanation:

The value οf x is 3

A variety οf issues are resοlved by algebraic calculatiοns that treat variables like explicit integers in a single cοmputatiοn. The quadratic fοrmula, fοr instance, can be used tο sοlve any quadratic equatiοn by exchanging the variables in the quadratic fοrmula fοr the numerical values οf the cοefficients in the equatiοn.

A variable in mathematical lοgic is either a symbοl fοr an undefined term οf the theοry (a meta-variable), οr it is a fundamental οbject οf the theοry that is changed withοut cοnsidering any pοtential intuitive meaning.

Given

8x+17 = 41

Sοlving fοr variable 'x'

Add '-17' tο each side.

17 + -17 + 8x = 41 + -17

Or, 8x=24

Divide each side by '8'

Or, x=3

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