Solve for X. Round your answer to the nearest tenth.

The seventh term of the given binomial expansion is; 15625

The binomial theorem states the expansion of (a + b)ⁿ as the sum of

n + 1 terms given by the binomial expansion formula that has the binomial coefficient as (n, k) = n!/((n - k)!(k!))

We are looking at the expression;

(x - 5)⁶

The objective is to evaluate the 7th term of the expansion.

Using the formula;

t_r + 1 = (n, r) * a^(n - r) * b^(r)

we can calculate the 7th term for n = 6, r = 6, a = x , b = −5.

t₇ = (6, 6) * x⁶⁻⁶ * (-5)⁶

t₇ = 15625

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Answer:

16

Step-by-step explanation:

x/8 = 2

Multiply 8 to both sides:

[x = 16]

Answer:

x = 16

Step-by-step explanation:

Now we have to,

→ find the required value of x.

The equation is,

→ x/8 = 2

Then the value of x will be,

→ x/8 = 2

→ x = 2 × 8

→ x = 16

Hence, the value of x is 16.

Answer:

Given that `x=10`, we can find the value of `a` and `b` by substituting the value of `x` into the given expressions for `a` and `b`.

For `a`, we have: `a = 5x^2/2`. Substituting `x=10`, we get: `a = 5(10)^2/2 = 250`.

For `b`, we have: `b = 2x^2(x-5)/10x`. Substituting `x=10`, we get: `b = 2(10)^2(10-5)/10(10) = 100`.

Therefore, when `x=10`, the value of `a` is 250 and the value of `b` is 100.

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An inequality that repreent is inequality is p≥ 53

Given that, at least 53 people buy food from the food truck. It means minimum 53 people buy the food, and number greater than 53 is quite possible; however, the possibility of people buying food less than 53 is not possible.

Since the number of people is alway 53 or greater than 53 therefore we may represent this condition using the greater and equal sign.

Lets use the variable p for people who buy the food.

Now the inequality can be written as

p≥ 53

Probability is the part of mathematics that discusses the size of the likelihood of something happening in life. Indeed, there are many events that cannot be ascertained to occur or not occur at a later time. but by knowing the measure of the success or failure of the expected event to occur, people can make better and wiser decisions about what should be done. Probability theory provides methods related to uncertainty and is an integral part of the decision-making process.

The concepts of probability are the basis of samples and the inferences about the population that can be made from a sample. After understanding the concept of probability which is the basis of statistics, we will then be given the theory of random variables and their properties, formation of probability distributions, socialization of various discrete and constant random variable probability distributions, and statistical sampling distributions.

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When the L matrix must be unit diagonal, the LU-factorization of the matrix is:

[tex]\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]

A matrix is a rectangular array or table of numbers, symbols, or expressions that are organized in rows and columns to represent a mathematical object or an attribute of such an object in mathematics. For instance, consider a matrix with two rows and three columns. A matrix (plural: matrices) is a rectangular array of numbers, equations, or symbols. This layout is made up of horizontal rows and vertical columns in the order of number of rows x number of columns. They are used to generate graphs and statistics, as well as to compute and perform scientific investigations and research on a wide range of topics. Matrices are also used to illustrate real-world data like population and infant mortality rates.

Here,

[tex]\left[\begin{array}{ccc}1&0\\-2&1\end{array}\right][/tex]

R2=2*R1+R2

[tex]\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]

The  LU-factorization of the matrix when L matrix must be unit diagonal is:  

[tex]\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]

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Answer:

$315.89

Step-by-step explanation:

I = p(1+r/100)^t

 = $215.89

Total = P + I

         = $315.89

Answer:

x = 22.5

<ADE = 67.5

Step-by-step explanation:

Triangle = 180 degrees

180 - 1 right angle (90 degrees) = 90 degrees

90 = 4x

x = 22.5

<ADE is corresponding to <ABC, therefore <ADE is also equal to 3x. Since we know x = 22.5 already:

3 x 22.5 = 67.5

so <ADE = 67.5

The simplest form is -1/2log(9/2).

What is integration?

Integration is a strategy for combining or joining the parts to get at the total. It is a form of differentiation in reverse where we break down functions into their component elements.

Here, we have

Given: ∫⁹₂ 4dx/(9-8x)

We have to find the simplest form in the logarithmic term.

= ∫⁹₂ 4dx/(9-8x)

We let t = (9-8x)

Now, we differentiate w.r.t x and we get

dt = -8dx

dx = -dt/8

Now we put the value of dx in the given equation and we get

= ∫⁹₂ 4(-dt/8)/t

= ∫⁹₂ -1/2t dt

= -1/2[logt]⁹₂

= -1/2[log9 - log2]

= -1/2log(9/2)

Hence, the simplest form is -1/2log(9/2).

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Answer:

Step-by-step explanation:

=92

Answer: About 9.68

2.9 ^ (x + 10) + 3 - 3 = 92 - 3

2.9 ^ (x + 10) = 89

Next, we'll take the logarithm base 2.9 of both sides:

log2.9 (2.9 ^ (x + 10)) = log2.9 89

x + 10 = log2.9 89

Finally, we'll solve for x:

x = log2.9 89 - 10

x ≈ 9.68.

The formula for calculating a histogram is (Number of Data Points in Bin) / (Total Number of Data Points).

A histogram is a graphical representation of data which displays how often certain values occur within a set of data. It is a type of bar graph that displays the number of values within each bin or interval. The bins are usually of equal size, and the height of each bar indicates the frequency of the values within the bin. Histograms are used to display the distribution of data, allowing a quick visual representation of the data.= (Number of Data Points in Bin) / (Total Number of Data Points)

suppose we have a set of data with the following values: 4, 5, 6, 7, 8, 9, 10, 11, 12. To construct a histogram, we would first divide the data into bins of equal size. In this case, we could use bins of size 2, so the bins would be 4-5, 6-7, 8-9, and 10-11. We would then count the number of data points in each bin, resulting in the following: 4-5: 2 data points; 6-7: 2 data points; 8-9: 2 data points; 10-11: 2 data points. To calculate the histogram we would take the number of data points in each bin, and divide it by the total number of data points (8). This would give us the following histogram: 4-5: 2/8; 6-7: 2/8; 8-9: 2/8; 10-11: 2/8.

In summary, a histogram is a graphical representation of data which displays how often certain values occur within a set of data. It is constructed by dividing the data into bins of equal size, and the height of each bar indicates the frequency of the values within the bin. The formula for calculating a histogram is (Number of Data Points in Bin) / (Total Number of Data Points).

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Complete question:

What is a histogram and how is it calculated?

The slice would be in the form of a pentagon.

Parallel lines in geometry are coplanar infinite straight lines that don't intersect anywhere. When two planes in the same three-dimensional space are parallel, they never cross. Curves that maintain a set minimum distance from one another and do not touch or intersect are said to be parallel curves.

Parallel lines are those in a plane that are regularly spaced apart from one another. There is no crossing of parallel lines.

Wendell would need to make a parallel cut to the bases of the pentagons in order to split the doghouse in two.

Consequently, the section will be pentagonal in shape.

Consequently, the slice is pentagonal.

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Answer:

-4

Step-by-step explanation:

Explantion down belowwwww \/

The 5th term of the geometric progression is a₅ = 405

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the 5th term of the geometric progression be a₅

Now , the common ratio of the GP is r = 3

And , a₅ = a + 400   be equation (1)

On simplifying the equation , we get

a₅ = ar⁴

Substituting the value of a₅ in the equation , we get

ar⁴ = a + 400

when r = 3

a ( 3 )⁴ = a + 400

81a = a + 400

Subtracting a on both sides of the equation , we get

80a = 400

Divide by 80 on both sides of the equation , we get

a = 5

Now , the 5th term of the GP is a₅ = ar⁴

On simplifying the equation , we get

a₅ = 5 ( 3 )⁴

a₅ = 5 x 81

a₅ = 405

Hence , the 5th term of the GP is 405

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Natalie is paid more each month this year with £3776.

Salary is a fixed amount of money  paid to an employee by an employer in return for work performed. It is usually paid on a regular basis such as weekly, bi-weekly, or monthly. Salaries are typically based on the employee's job title, level of responsibility and the company's budget and compensation policies.

solution

Melissa's salary this year is £2200 + £2200 * 35/100 = £2970.

Natalie's salary this year is £3200 + £3200 * 18/100 = £3776.

Therefore, Natalie is paid more each month this year with £3776.

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To find out how much candy Vanessa should eat each day, we first need to find the total amount of candy in the box. If the box weighs 1/8 of a pound, we can convert this weight to ounces to get a clearer idea of the quantity of candy. There are 16 ounces in a pound, so 1/8 of a pound is equal to 1/8 * 16 = 2 ounces.

Now that we know the total amount of candy, we can divide this by the number of days that Vanessa wants the candy to last to find out how much she should eat each day. If the candy is meant to last 2 days, she should eat 2 ounces / 2 days = 1 ounce of candy per day.

Answer:

The correct answer is -8yx.

Step-by-step explanation:

To simplify the expression 16yx÷4 + 6yx(-2), we can use the following steps:

Start by computing the expression within the parentheses:
6yx(-2) = -12yx.

Next, divide 16yx by 4 to get 4yx.

Finally, add the two simplified expressions from steps 1 and 2:
4yx + (-12yx) = -8yx.

Hence, the simplified form of the expression 16yx÷4 + 6yx(-2) is -8yx.

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A. Using percentages, if Drew earned 50% of $150 in the first week, the total amount earned is $75.

B. If Drew earned 50% of $75 in the second week, the total amount earned is $37.50.

C. If Drew earned 50% of $37.50 in the third week, the total amount earned is $18.75.

D. The percentage Drew earned in the fourth week is 12.5%.

The percentage refers to a relative size or ratio of one quantity compared to another larger quantity.

The percentage is a fractional value that shows the quotient of a division operation between the numerator and the denominator, which is then multiplied by 100.

A) The total goal for Drew to earn in four weeks = $150

The percentage earned in the first week = 50%

50% of $150 = $75.

B) The remaining part of the goal to be achieved after the first week = $75 ($150 - $75)

The percentage earned in the first week of the remainder = 50%

50% of $75 = $37.50

C) The remaining part of the goal after the second week = $37.50

The percentage of earnings in the third week = 50% of $37.50

= $18.75

D) Total earnings from week 1 to week 3 = $131.25 ($75 + $37.50 + $18.75)

$131.25/$150 x 100 = 87.5%

Remaining percentage = 12.5% (100 - 87.5)

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The probability that the selected ride will be closed because of mechanical is given as follows:

D. 0.675.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

In this problem, the probabilities are given as percentages, which make the calculations easier.

The percentages associated with a closed ride are given as follows:

Hence the probability is given as follows:

p = 0.9 x 0.75 + 0.08 x 0.25

p = 0.675.

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Answer:

-2

Step-by-step explanation:

The slope of a line can be found using the formula m = [tex]\frac{y_2 -y_1}{x_2 - x_1}[/tex], where m is the slope and [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are two points on the line.

From the graph we can see that (-2,1) and (0,-3) are two points on the line, so let's sub these values into our formula to find the slope:

m = [tex]\frac{y_2 -y_1}{x_2 - x_1}[/tex]

m = [tex]\frac{1-(-3)}{-2-0}[/tex]=[tex]\frac{4}{-2}[/tex]=-2

Kari will pay $96 in taxes.

Kari will pay 20% of the $48 interest earned, which is $96.

Kari earned $48 in simple interest on the $1,200 she deposited in a savings account last year. This amount is subject to taxes, which Kari must pay 20% of the interest earned. In this case, Kari will have to pay $96 in taxes on the interest she earned. This means that out of the $48 she earned in interest, she will have to give up $96 to the government in taxes.

Kari must pay $96 in taxes on the $48 in interest she earned on her $1,200 deposit.

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The additive and multiplicative inverse of v{x} are -1 and 1 respectively.

An function in mathematics defines a relationship between one variable (the independent variable, x)  and another variable (the dependent variable, y). Example -

y = f{x} = ax + b

Given is a constant function -

v{x} = 1

We can write the additive inverse of v{x} as -

a⁻¹ (v{x}) = - v{x} = - 1

a⁻¹ (v{x}) = - 1                           ..... { 1 }

and

We can write the multiplicative inverse of v{x} as -

m⁻¹ (v{x}) = 1/v{x} = 1/1 = 1

m⁻¹ (v{x}) = 1                                ...... { 2 }

Therefore, the additive and multiplicative inverse of v{x} are -1 and 1 respectively.

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Answer: 20

Step-by-step explanation:

You divide -915 by -50 and get 18.3 days but you round up to 20 hope it helps

The area of the circle is 113.0 ft²

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

Given that, a circle with diameter 12 feet, we need to find its area,

Diameter = 2 × radius

Radius = 12/2

= 6 ft

Area of a circle = π × (radius)²

Area = 3.14 × 6²

= 3.14 × 36

= 113.04

Hence, the area of the circle is 113.0 ft²

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In exponential functions, the variable is that which is in the exponent and whose base is always greater than zero and different from one.

An exponential function is a mathematical function used to calculate the exponential growth or decay of a given set of data.

We know that a variable in an exponential function is one whose exponent is always larger than zero and whose base is not one.

These limitations are required since 1 increased to any number equals 1. As a result, we would be faced with a regular function rather than an exponential one.

Additionally, because some exponents would result in the function not being defined, the basis of the exponential function cannot be negative or equal to zero.

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It is probably a 90 degree turn then a reflection from the x-axis to the right since you do all corners of Triangle A and do a  90 degree turn, it turns to Triangle B.

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Answer:

reflection

Step-by-step explanation:

A reflects in line y=x

The answer is True. Degrees of freedom are a feature of statistics that are used when we are analyzing a sample rather than the population.

The degrees of freedom (df) refers to the number of independent observations in a sample that can be used to make inferences about a population. The concept of degrees of freedom is used in many statistical methods, including t-tests, ANOVA, and regression analysis.

In simple terms, degrees of freedom can be thought of as the number of data points in a sample that are "free" to vary in order to estimate a population parameter. For example, in a sample of two measurements, only one measurement is "free" to vary since the other measurement is used to calculate the mean. Hence, the degrees of freedom would be 1.

It's important to note that when analyzing a population, there are no degrees of freedom since all of the observations are considered independent and can be used to estimate the population parameters. In contrast, when working with a sample, the degrees of freedom are reduced by the number of constraints that are imposed on the sample in order to make inferences about the population.

In summary, the degrees of freedom are a feature of statistics that reflect the number of independent observations in a sample that can be used to make inferences about the population.

Therefore, The answer is True. Degrees of freedom are a feature of statistics that are used when we are analyzing a sample rather than the population.

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The answer is True. Degrees of freedom are a feature of statistics that are used when we are analyzing a sample rather than the population.

The degrees of freedom (df) refers to the number of independent observations in a sample that can be used to make inferences about a population. The concept of degrees of freedom is used in many statistical methods, including t-tests, ANOVA, and regression analysis.

In simple terms, degrees of freedom can be thought of as the number of data points in a sample that are "free" to vary in order to estimate a population parameter. For example, in a sample of two measurements, only one measurement is "free" to vary since the other measurement is used to calculate the mean. Hence, the degrees of freedom would be 1.

It's important to note that when analyzing a population, there are no degrees of freedom since all of the observations are considered independent and can be used to estimate the population parameters. In contrast, when working with a sample, the degrees of freedom are reduced by the number of constraints that are imposed on the sample in order to make inferences about the population.

In summary, the degrees of freedom are a feature of statistics that reflect the number of independent observations in a sample that can be used to make inferences about the population.

Therefore, The answer is True. Degrees of freedom are a feature of statistics that are used when we are analyzing a sample rather than the population.

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The intersection of two functions f and g occurring midway between x = a and x = b can be calculated using the following formula: (f(x) - g(x)) = 0.

Let f and g be two functions with the domain (a,b). For f and g to intersect midway between x = a and x = b, the x-coordinate of the intersection point must be (a+b)/2. Therefore, the equation to solve is f(x) = g(x) = (a+b)/2. To solve this equation, we must first find the value of f((a+b)/2) and g((a+b)/2). Then, equate these values to each other, and solve for the variable. For example, if f(x) = x2+2x+4 and g(x) = x+7, the equation to solve is (a+b)/2 + 7 = (a+b)2/4 + 2(a+b)/2 + 4. Simplifying this equation, we get a2 - 2b2 + 2ab + 7a - 7b + 11 = 0. This equation can then be solved using the quadratic formula to find the value of a and b.

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Complete question:

Given two functions f and g, and an interval between x = a and x = b, where is the point of intersection between f and g?

Age at natural death is an example of a real-world variable with a left-skewed distribution (heart disease, cancer, etc.). Most of these deaths occur in older people and a minority in younger people.

Salary is an example of a real-world variable with a right-skewed distribution. If there are a few outliers (CEOs, professional athletes, etc.), most individuals have incomes in the low/mid range, with a wide range of higher numbers (a long "tail"). A long left tail indicates that the distribution is skewed to the left. A negatively skewed distribution is similar to a left skewed distribution. This is because the number line has a long tail in the negative direction. The average is also to the left of the peak. The left side of a left-skewed distribution is longer than the right side. That is, a left-skewed distribution has a long tail on the left.

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Answer: This means that Mark spent more on dining out last month than what he had budgeted, and the difference was greater than 20 dollars.

Mark had set aside a specific amount of money each month for dining out expenses. However, last month he exceeded that amount and spent more than what he had budgeted. The difference between the amount he planned to spend and what he actually spent was negative and greater than 20 dollars, indicating that he overspent by more than 20 dollars. This implies that the cost of dining out was higher than expected, and Mark spent more money on it than he had originally intended to.

Step-by-step explanation:

The graph of the function f(x) = –0.5|x + 3| – 2 is best described by: D. graph D.

In Mathematics, the translation a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

In Mathematics, a horizontal translation to the left is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the negative y-direction (downward) is modeled by this mathematical expression g(x) = f(x) - N.

Where:

In this scenario, the function f(x) = –0.5|x + 3| – 2 is translated 3 units to the left and downward by 2 units.

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