Find the sum of the arithmetic series where n = 50, a = 9, and t50 = 331.

The given 4th degree polynomial is ,[tex]f(x)=(x+5)(x+1)^2(x-2)[/tex] zeroes of the equation are -5,-1,2

A fourth-degree polynomial, or quartic function, is one that has a variable raised to the fourth power as its highest order term.

If the highest order term is positive or negative, a fourth-degree polynomial's graph will frequently resemble a M or a W.

The function will reach infinity on both sides if the leading term's coefficient, a, is positive.

The function will extend to minus infinity on both sides if the coefficient an is negative.

The function's y-intercept, or the point at which the function crosses the y-axis, is indicated by the word a0. The x-intercepts are revealed by the function's roots.

Inflection Points are roots of double derivate equation.

Given;

From the graph, x-intercepts are -5,-1,2.

That gives us (x+5),(x+1),(x-2) are factors of the function;

As at [tex]x=-1[/tex] graph touches x axis (x+1) is a double factor of f(x)

That leaves us with [tex](x+5),(x+1)^2,(x-2)[/tex] as factors of f(x);

[tex]f(x)=(x+5)(x+1)^2(x-2)[/tex];

From graph inflections points are -2.686,0.186;

That gives [tex]f^|^|(x)=(x+2.686)(x-0.186)[/tex]

The given 4th degree polynomial is ,[tex]f(x)=(x+5)(x+1)^2(x-2)[/tex] zeroes of the equation are -5,-1,2

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The amount of money left on the gift card, in term of the number of cups, a Lauren has bought is represented by the equation would be A = 10 - 2a.

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given that from the task content that the total amount of money Lauren has initially is $10.

Hence, each cup of coffee costs $2.

Since the amount of money Lauren has left each time,

That is related to the number of coffee cups bought by the equation;

A = 10 -2a.

where a ranges be between 0 and 5.

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Answer:

Step-by-step explanation:

Well, there are the same amount of numbers in each equation. You can take the a from both equations, raise it to the second power, then do the same to the b. The addition sign will automatically disappear because you've added the two components together. You'll use subtraction to get your answer. I think.

Using monthly payment formula, the principal of the facility paying a monthly payment of $8750 for 25 years at a rate of 5.50% is $1,424,878.39

The monthly payment is the amount paid per month to pay off the loan in the time period of the loan. When a loan is taken out it isn't only the principal amount, or the original amount loaned out, that needs to be repaid, but also the interest that accumulates.

The formula to calculate the monthly payment of a facility is;

A = P[(r(1 + r)ⁿ] / [(1 + r)ⁿ - 1]

Substituting the values into the formula and solving for p

P = $1,424,878.39

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Answer:

D. 0.53

Step-by-step explanation:

California = 90

Total of those who prefer Brand A = 170

To find the percentage, you do:

90/170 × 100 = 52.941...

However you have to round it to two decimal points, hence you do:

52.941 ≈ 53%

53% = 0.53

This is due to 53% representing 53/100 = 0.53

Therefore, the probability that the person that likes brand A is from California is 0.53

:)

Answer: x=5

Step-by-step explanation:

isolate x

8x-4+4=36+4

8x=40

x=5

Answer:

x=5

Step-by-step explanation:

You would first want to add 4 to both sides. Then divide 40 and 8 by 8 and you get x=5.

Answer:

Step-by-step explanation:

a. The equation for the cost of AT&T would be $100 + $15n, where n is the number of phones on the account. The equation for the cost of Sprint would be $200.

We can graph these equations on a coordinate plane with the x-axis representing the number of phones on the account and the y-axis representing the monthly cost. The graph for the cost of AT&T would be a straight line starting at the point (0,100) and going through the point (1,115), (2,130), etc. The graph for the cost of Sprint would be a horizontal line at the y-coordinate of 200.

b. In order to determine which company would be cheaper for Carly's family, we can simply plug in the number of phones they have (5) into each of the equations we derived in part a. This would give us a cost of $200 for AT&T and $200 for Sprint. In this case, both companies would be equally cheap for Carly's family.

Alternatively, we could graph the equations and see which company's line is lower on the y-axis for the given number of phones (5). This would also show that both companies would be equally cheap for Carly's family in this case.

On solving the given equation y=(x+4)(x-1) the point on the graph are as follows:

(-4,0), (-1,0), (2,6), (-3,-4) &(0,-4)

What is a graph?

A relation is a specific instance of a function graph. A function is truly equivalent to its graph in set theory and the current mathematical underpinnings.

It is frequently more helpful to think about functions as mappings, which include the sets that constitute the domain and the codomain in addition to the relationship between input and output. For instance, the codomain should be considered while determining if a function is onto (surjective) or not. The codomain of a function is not determined by the graph alone.

It is typical to use the phrases function and graph of a function interchangeably since, although referring to the same thing, they suggest distinct ways of looking at it.

1)

let   y=0

0=(x+4)(x-1)

i.e. x = -4 and -1

2)

Let x =0

y=(0+4)(0-1)

y=-4

3)

Let x = 2

y=(2+4)(2-1)

y=6

4)

Let x = -3

y=(-3+4)(-3-1)

y=-4

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The values which are less than -7 on the number line makes the value true.

b≤-6

-7≤-6

-9≤-6

-256≤-6

only in the case where b = -6 satisfy only equality condition not less than condition. Other than this remaining other values which are less than -7 on the number line including rational numbers , decimal numbers, all negative numbers which are less than -6 satisfy.

The values which are less than -7 on the number line makes the value true

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Question what makes the value Inequality b≤-6 is true for what values of b?

T is not a function of G as they don't have a constant of proportionality.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It should be noted that the constant of proportionality simply means the ratio that relates two given values in what is known as a proportional relationship. In this case, other names for the constant of proportionality are the constant ratio, constant rate, unit rate, constant of variation, or the rate of change

Since the parking garage charges $5 for the first hour, $10 for up to two hours, and $12 for the entire day. This implies that they don't have a constant of proportionality.

In this case, the time doesn't have an effect on amount paid.

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When the temperature is 30° in Celsius, the temperature in Fahrenheit is 86.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given equation to find the temperature,

C= 5/9(F-32)          (1)

Here, C represents the temperature in Celsius,

And F represents the temperature in Fahrenheit.

To find the temperature in Fahrenheit, when C = 30°,

Substitute C = 30° in equation (1),

30 = 5/9(F - 32)

6 x 9 = F - 32

54 = F - 32

F = 86

The temperature in Fahrenheit is 86.

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The solution is, the following expressions are equivalent to 4⁻³ / 4⁻⁸

A.  4^8/4^3

D. 4⁵

An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.

here, we have,

We have to calculate to find the result -

The expression is = 4^(-3)/4^(-8)

According to the indices rule, the power will be deducted if it is a division.

Therefore, a^m/a^n = a^(m-n)

Using that formula,

4⁻³ / 4⁻⁸

= 4⁸ / 4³

= 4⁽⁸⁻³⁾

=4⁵

Therefore, the answer choice D is the option, and the answer is 4^5.

Option A is also correct.

Because we can find 4^5 with the help of that option.

Alternative way,

4^(-3)/4^(-8)

= 4^(-3+8)

= 4^(8-3)

= 4^8/4^3

In the is way, we can also find option A is correct.

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complete question:

Which of the following expressions are equivalent to 4^-3/4^-8?

Step-by-step explanation:

[tex] {x}^{2} - 14x = 164[/tex]

[tex] {x}^{2} - 14x + 49 = 213[/tex]

[tex](x - 7) {}^{2} = 213[/tex]

[tex](x - 7) = \sqrt{213} [/tex]

[tex](x - 7) = - \sqrt{213} [/tex]

[tex]x = 7 + \sqrt{213} [/tex]

[tex]x = 7 - \sqrt{213} [/tex]

The number of possible paint jobs that can be done on the 4 cars can be determined by permutation (15,4). That is option B.

Permutation is defined as the various number of ways a data set can be arranged to arrive at a definite value.

the number of colours offered by the paint shop = 15

The number of cars the need a new paint job = 4

To find the possible number of colour that can be used permutation (15,4) is carried out.

That is,

= 15!/(15-4)!

= 15!/11!

= 15×14×13×12×11×10×9×8×7×6×5×4×3×2×1/11×10×9×8×7×6×5×4×3×2×1

or 15×14×13×12×11!/11!

= 15×14×13×12

= 32,760

Therefore, there would be 32,760 possible paint jobs that can be carried out on the 4 cars.

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Answer:

250 meters per minute.

Step-by-step explanation:

1 km = 1000 m

15 km = 15*1000 = 15000 m

1 hour = 60 min

Then:

15km/h = 15000km/60minutes

= 250 meter per minute

Answer:250 meters / minute

Step-by-step explanation:1 km/h = 16.66667 m/min

The option that shows that Wesley will save enough money for his vacation is D. Multiply 30 × 12 to get 360. Then divide 360 ÷ 7 to get 51 R3. Wesley will have $51 for each.day plus $3 left over.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this situation, Wesley wants to have at least $50 to spend each day of his 7-day vacation. He plans to save $30 each month for 12 months.

This will be illustrated thus:

(30 × 12) / 7

= 51 R 3

This shows that he'll have enough money. The correct option is D.

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Answer:

not possible

Step-by-step explanation:

Answer:

[tex]493.039 \;in^3[/tex]

Step-by-step explanation:

If each side of the cube is [tex]a[/tex] then the volume of the cube is given by [tex]a^3[/tex]

If Volume is [tex]V[/tex] then each side [tex]a = \sqrt[3]{V}[/tex]

Here we are given the volume of the smaller cube as [tex]85\; in^3[/tex]

So each side of this cube = [tex]\sqrt[3]{85} = 4.396 \approx 4.4 \;in[/tex]

and each side of the larger cube [tex]= 4.4 + 3.5 = 7.9\;in[/tex]

Volume of larger cube [tex]= 7.9^3 = 493.039 \; in^3[/tex]

A has the larger standard devlation.

What is standard devlation?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

We are given two plots of normal distributions A and B.

The mean of a normal distribution is located at the center of the plot.

Since the centers of both of the normal distributions A and B seems to be aligned, therefore, they both seems to have equal means.

The standard deviation basically determines the shape of the distribution.

As you can see, the normal distribution A is more spread out and thus has a larger standard deviation than normal distribution B.

Therefore, the two correct options are

• The means of A and B are equal.

• A has larger standard deviation.

Complete question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.

Select all that apply:

A has the larger mean.

B has the larger mean.

The means of A and. Q jual.

A has the larger standard devlation.

B has the larger standard deviation.

The standard deviations of A and B are equal.

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Answer:

Below

Step-by-step explanation:

From the data , the miles per gallon is  

199.2 mi  / 6 gal       or      265.6 mi / 8 gal      or     863.2 / 26    

   = 33.2 mi/gal

for 50 gallons this would be

    33.2 mi / gal   *  50 gal = 1660 mi

The values of x where f(x) is 0 to determine a function's zeros.

The set of all x for which the f(x) graph crosses the x-axis is the solution of f(x) = 0. The set of all x for which the graph of f is strictly above the x-axis is the solution of f(x) > 0

In general, finding the zeros of the function f(x) involves setting the function to zero. The zeroes of the function are the values of x that correspond to the set equation. Find the values of x where f(x) = 0 to determine a function's zeros.

f ( x)=- 3 is a horizontal line that connects to the x-axis, hence there is no x-intercept and the y-intercept is ( 0, -3).

The y-intercept is ( 0, -3)

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are NOT true for binary search algorithm.

Now, According to the question:

Options 1, 3 are NOT true for binary search algorithm

Hence, Binary search algorithm can be used for any arrays.

and, The worst-case time complexity of binary search is greater than sequential search

are NOT true for binary search algorithm.

In the question:

Which of the following statement(s) is/are NOT TRUE for binary search algorithm? (select all that apply]

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The slope of AB -3

The slope of BC 1/3

The slope of AC -1/2

△ABC a right triangle because two lines are perpendicular shown by a negative reciprocal slope -3 and 1/3

The slope is represented as m, The slope by definition is the ratio change of the output values to the input values

The slope, m using the points A(-2, 4), and B(-1, 1)

m = (y₀ - y₁) / (x₀ - x₁)

m = (4 - 1) / (-2 - -1)

m = (3) / (-1)

m = -3

The slope, m using the points B(-1, 1), and C(2, 2)

m = (1 - 2) / (-1 - 2)

m = (-1) / (-3)

m = 1/3

The slope, m using the points A(-2, 4), and C(2, 2)

m = (4 - 2) / (-2 - 2)

m = (2) / (-4)

m = -1/2

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Equation for each option to model the value A of the account after x years is 5+ 5/nⁿ and 2ˣ 0.01.

What is an equation?

In arithmetic,an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main body:

for option 1

initial investment is $5 after 1 year investment is

5+5/2

after 2 year 5+5/2+(5+5/2)/2=5+5/2+5/2²

continuing this way we get the formula

5+ 5/nⁿ

for option 2

after 1 year money becomes 2*0.01

after 2 year money becomes 2²*0.01

after x year money becomes 2ˣ 0.01

Hence the forumla for each option is as provided.

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The baby is 105.6  ounces or 6.96 pounds lighter than an average baby.

Weight is the measurement of Gravitational force on an object. It can be zero as in the space.

We are given in the question that A baby weighed only 14.4 ounces at birth the weight of an average baby is 7lb 8 ounces.

1 lb = 16 ounce

Therefore an average baby weight = 7 x 16 + 8 = 120 ounces

The baby weight is just 14.4 ounces

Hence, the baby is 120 - 14.4 = 105.6 ounces lighter than an average baby.

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Answer:

£ 178.34 tax amount

Step-by-step explanation:

A computer costs £ 964. A tax of 18.5% is then added to the cost of the computer. Work out the amount of tax that is added to the cost of the computer.

18.5% tax = 0.185 tax rate

0.185 tax rate * £ 964 = £ 178.34 tax amount

You can make a chart in PowerPoint or Excel. If you have lots of data to chart, create your chart in Excel, and then copy it into your presentation. This is also the best way if your data changes regularly and you want your chart to always reflect the latest numbers. In that case, when you copy and paste the chart, keep it linked to the original Excel file.

To create a simple chart from scratch in PowerPoint, click Insert > Chart and pick the chart you want.

1. Click Insert > Chart.

2.Click the chart type and then double-click the chart you want.

3.In the worksheet that appears, replace the placeholder data with your own information.

4.When you insert a chart, small buttons appear next to its upper-right corner. Use the Chart Elements Chart Elements button button to show, hide, or format things like axis titles or data labels. Or use the Chart Styles Customize the Look of Your Chart button button to quickly change the color or style of the chart.

What is excel ?

Excel is a spreadsheet program from Microsoft and a component of its Office product group for business applications. Microsoft Excel enables users to format, organize and calculate data in a spreadsheet.

The main uses of Excel include: Data entry. Data management. Accounting.

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By using the formula for slope, it can be calculated that

The slope of the given line is 10

What is slope of a line?

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m =  [tex]tan \theta[/tex]

If the line passes through [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex], slope is calculated by the formula

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

Here, the line passes through (2, 3) and (3, 13)

Slope = [tex]\frac{13 - 3}{3-2}[/tex]

Slope = 10

So the slope of the given line is 10

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Answer:

Solve for x

by simplifying both sides of the inequality, then isolating the variable.

Inequality Form: x>10.4

Interval Notation: (10.4,∞)

Step-by-step explanation:

A linear equation to find p, Laredo's population for any year after 1990 is 5441t + 123000.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Here, we have

Given:

t = the number of years after 1990.

So, for 1990, t = 0. So the coordinate is (0, 123000).

For 2007, t = 17. So the coordinate is (17, 215500).

Slope = (215500 - 123000)/17

Slope = 5441

P = 5441t + b,

b = 123000

P = 5441t + 123000

Hence,  a linear equation to find p, Laredo's population for any year after 1990 is 5441t + 123000.

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