Factor 2x^4-5x^3+6x^2-15x completely over the set of integers

Answer: 4x^2(7x+1)

Step-by-step explanation: Divide by the common divisible of 4x^2 and you will get your answer/.

Answer:4x^2(1+7x)

Step-by-step explanation:

4x^2(1+7x)

Solution

Given series is [tex]$5+11+17+\ldots .+95$.[/tex]

Thus,

[tex]$\mathrm{a}=5, \mathrm{~d}=11-5=6,1=95$$$\begin{aligned}& \mathrm{n}=\frac{1-a}{d}+1 \\& =\frac{95-5}{6}+1 \\& =\frac{90}{6}+1=15+1=16\end{aligned}[/tex]

Therefore, [tex]$\mathrm{S}_{\mathrm{n}}=\frac{\mathrm{n}}{2}(\mathrm{a}+1)$$$\begin{aligned}& =\frac{16}{2}(5+95) \\& =8(100) \\& =800\end{aligned}$$[/tex]

What is arithmetic series?

The total of the terms in an arithmetic sequence with a predetermined number of terms is known as an arithmetic series. Here is a straightforward formula for calculating the sum: Formula 1: If the sum of an arithmetic series of terms is represented by S n, then The first and last terms' values, as well as the total number of terms, are needed for this formula.

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Answer:

m=30

Step-by-step explanation:

The expression that represents the amount of money Angel would have savings in w weeks is 30+8w

The total amount of money saved after 5 weeks is $70

Which algebraic expression is required for Angel's total savings?

Total savings=30+8w

Now by substituting 5 , the number of weeks for w, we can determine total savings after 5 weeks

total savings=30+(8*5)

total savings=30+40

Total savings=$70

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Answer: The total amount of overdraft fees that Lewis will pay is {$1149.28}.

Step-by-step explanation:

To find out how much Lewis will pay in overdraft fees, we need to calculate the total amount of his overdrafts. We can do this by subtracting the sum of his checks from his account balance on June 5. This gives us:

overdraft = 932.77 - (791.29 + 340.50 + 208.35 + 428.61 + 113.3)

         = 932.77 - 2082.05

         = -1149.28

Since the bank charges a $31-per-check overdraft protection fee, Lewis will have to pay $31 for each check that he overdraws his account. Since he overdraws his account by $1149.28 in total, he will have to pay $31 * (1149.28 / 31) = $1149.28 in overdraft fees.

Therefore, the total amount of overdraft fees that Lewis will pay is {$1149.28}.

The minimum sample size is needed to be 90% confident that the sample mean is within 5 minutes of the true population mean is 40.

In frequentist statistics, a confidence interval is a range of estimates for an unknown parameter.

We have that to find our α level, that is the subtraction of 1 by the confidence interval divided by 2.

α = (1 - 0.90)/2 = 0.05.

Now, we have to find z in the Ztable as such z has a p-value of 1 - α.

So it is z with a pvalue of  1 - 0.05 = 0.95 = 1.96.

Now, find the margin of error M as such,

M = z×(sigma/√n).

5 = 1.96×(16/√n).

5√n = 31.36.

n = 39.9.

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The side lengths of each triangle are given as follows:

D. [tex]DE = \sqrt{13}, PQ = \sqrt{13}, EF = 2\sqrt{5}, QR = \sqrt{26}, DF = \sqrt{29}, PR = \sqrt{13}[/tex]

The side lengths of each triangle are given by the distances between the vertices.

These vertices are in the coordinate plane, hence the distance between them is found using the equation for the distance between two points.

Suppose two points in the coordinate plane with notation given as follows:

[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Then the distance between them is given by the equation presented as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Thus the side lengths are given as follows:

Meaning that option D is correct.

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Area or a circles given by the formula = radius , r

What is area?

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.

For the circle or area given by the formula is radius ,r.

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The cost of driving Jenna's car is $0.341/mile

From the question, we are to determine the cost of driving Jenna's car in $/mile

From the given information

The formula used to find Jenna's cost to drive her own car for work is

J = g/22 + 0.146

We are to find the cost of driving when the price of gas, g, is $4.29/gallon

Substitute g = 4.29 in the formula

J = 4.29/22 + 0.146

J = 0.195 + 0.146

J = 0.341

Hence, the cost is $0.341

Here is the complete question:

Recall the formula used to find Jenna's cost to drive her own car for work:

J = g/22 + 0.146

In this formula, J = Cost of driving Jenna's car in $/mile, and g = Cost of gas in $/gallon.

Find the cost of driving Jenna’s car (J) in $/mile when the price of gas is $4.29/gallon

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The inverse sine trig function would be used to solve for angle Z .

In the right angle triangle the ratio of the opposite to the hypotenuse of any acute <A is called the sine of < A

The inverse of the sine function, also known as the arcsine function, returns the angle's value when the sine function's opposite side and hypotenuse ratio are equal. It produces the angle's value.

The opposite of the sine function is the inverse sine function, also known as arcsine. Due to the fact that the sine of an angle (or sine function) is equal to the ratio of the opposite side to the hypotenuse, the sine inverse of this ratio will provide the angle's measurement.

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Step-by-step explanation:

12.93 is the answer of this question.

The probability that the total time taken by a random sample of 52 customers is less than 180 minutes is 0.02%.

μ=Population mean=4

σ=Population standard deviation=2

n=Sample size=50

The sampling distribution of the sum S is roughly normal if the sample size is big (30 or more), according to the central limit theorem.

The central limit theorem tells us that the sampling distribution of the sum S is about normal because the sample size of 50 is at least 30.

The sum S's sample distribution has a mean and standard deviation of n and n, respectively.

The z-score is the value decreased by the mean, divided by the standard deviation

z = ( x -μS ) / √σS

= 150 - 50(4) / √ 50(2)

= 3.54

Using the appendix's normal probability table, get the relevant probability,

P(S < 150 ) = P(Z< -3.54)

= 0.0002

=0.02%

The term "standard deviation"  refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

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True, the given function f has an inverse.

A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y.  Inverse functions f and g result in f(x) = y if and only if g(y) = x.

Under the given condition, we can define the function g on the set of the images  {b | b = f(a), a belongs to A}  in a way

   g(b) = a,   if f(a) = b.

This function is defined correctly on this set and is the inverse function to f.

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By using the distance formula, the length of the interval AC 10.8, After rounding it will be 11 units.

The distance formula is given as:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Give the example of two decimal rounding off.

Here are two examples of rounding off to two decimal places:

12.3456 rounded to two decimal places is 12.35

0.678 rounded to two decimal places is 0.68

Plugging in the coordinates of the two points, we get:

Distance = sqrt((5 - (-1))^2 + (4 - 13)^2)

= sqrt(6^2 + (-9)^2)

= sqrt(36 + 81)

= sqrt(117)

= approximately 10.8

Therefore, the distance between the points (-1,13) and (5,4) is approximately 10.8.

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Answer:

first do criss cross the it will be like this : 2(a-3)=4*5 . Now do like as given in the picture.

well, the total amount is really "x", which oddly enough is the 100%, but we also know that 32% of that is 8, hmmmm

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 8& 32 \end{array} \implies \cfrac{x}{8}~~=~~\cfrac{100}{32} \\\\\\ \cfrac{ x }{ 8 } ~~=~~ \cfrac{ 25 }{ 8 }\implies 8x=200\implies x=\cfrac{200}{8}\implies x=25[/tex]

The maximum area is 12.25 square feet

From the question, we have the following parameters that can be used in our computation:

Perimeter = 14 feet

This means that

P = 2(l + w)

So, we have

2(l + w) = 14

Divide by 2

l + w = 7

Make l the subject

l = 7 - w

The area is calculated as

A = lw

So, we have

A = (7 - w)w

Expand

A = 7w - w²

Differentiate and set to 0

7 - 2w = 0

So, we have

w = 3.5

Substitute w = 3.5 in A = (7 - w)w

A = (7 - 3.5) * 3.5

Evaluate

A = 12.25

Hence, the area is 12.25 square feet

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Complete question

There is 14 feet of fencing available to enclose a rectangular region. For what value of area is the area maximum

Option 1: An initial investment of $5 that increases by 50% every year

as after 20 years, it amounts to a greater value.

An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference

d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.

In a geometric sequence numbers are written in the same constant ratio(r).

It means every next number is a multiple of a common constant and the previous number.

r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.

The given situations can be modeled as a geometric sequence.

Option A :

a₁ = 5, r = 1.5.

We know Sₙ = a₁(rⁿ - 1)/(r -1).

Sₙ = 5(1.5ⁿ - 1)/(1.5 - 1).

Sₙ = 5(1.5ⁿ - 1)/(0.5).

Let us see for n = 20, 20th year.

S₂₀ = 5(1.5²⁰ - 1)/(0.5).

S₂₀ = 5(3324.25)/(0.5).

S₂₀ = 33242.5.

Option B :

a₁ = 0.01 and r = 2.

Sₙ = 0.01(2ⁿ - 1)/(1).

S₂₀ = 0.01(2²⁰ - 1)/(1).

S₂₀ = 10,485.75

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The square root of 40 is approximately 6.324555320336759. This is the width of the rectangle.

What is a rectangle?

It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral. It occupies area in two-dimensional planner geometry.

The area of a rectangle is given by the formula A = lw,

where A is the area, l is the length, and w is the width.

We are told that the length of the rectangle is twice the width, so we can write the formula as follows:

A = 2w * w

We are also told that the area of the rectangle is 80 square inches, so we can substitute this value into the formula:

80 = 2w * w

We can rearrange this equation to solve for w:

80 = 2w²

w² = 40

The square root of 40 is an irrational number, so the width of the rectangle is an irrational number.

Hence,  To express this number in decimal form, the square root of 40 is approximately 6.324555320336759. This is the width of the rectangle.

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Answer: If 30% of the fruits in the box are apples, then 100% - 30% = 70% of the fruits in the box are not apples. Of these non-apple fruits, 25% are pears, so the remaining fruits, 100% - 25% = 75% are oranges. Since 75% of the fruits in the box are oranges, and the total number of fruits in the box is 160, then the number of oranges in the box is 75/100 * 160 = <<75/100*160=120>>120. Answer: \boxed{120}.

The following statements which must be true is [tex]\lim_{x \to \1} _1[/tex] f ( x ) = ∞.

Given :

the values f ( x ) of a function f can be made arbitrarily large by taking x sufficiently close to 1 but not equal to 1.

Function :

In simple words, a function is a relationship between inputs where each input is related to exactly one output.

Every function has a domain and a co - domain.

x sufficiently close to 1 means x → 1

but x ≠ 1.

so function = [tex]\lim_{x \to \1} _1[/tex] f ( x ) = ∞

Therefore the following statements which must be true is [tex]\lim_{x \to \1} _1[/tex] f ( x ) = ∞.

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Answer:

the range of the graph would move down by 4 units.

Step-by-step explanation:

f(x) is the original/basis equation

g(x) is the translation equation

-4 does not have any x's attached to it, so it would affect the range, or the y of the equation

for example:

f(x) = 2x + 8

if you subtracted 4 from that it would be:

f(x) = 2x - 4, so the range would be affected

Answer:

44.8

Step-by-step explanation:

Volume = Length * Height * Width

Volume = 10 * 1.5 * 3.2

Volume = 44.8cm

a) The values are given as follows:

b) The solution of the equation is of: -0.25410169644.

The equation in this problem is given as follows:

y = (x³ - 1)/4.

The solution is obtained using a iterative solution method, until the difference between previous iterations is less than 10^-6, as the solution is exact to 6 decimal places.

Then the values are given as follows:

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Answer:

13

Step-by-step explanation:

The box plot ends at 13.

Box plots show the average score of the data. It shows the minimum, median and maximum. The line inside the box is the median. The minimum, in this case is 0 and the max is 13.

Answer:

3/10

Step-by-step explanation:

please mark me brainliest if this is right

The equation which model the relationship between the weeks and the viewers is;

f(x) = 2160(1.5)ˣ

The distance between each number in a geometric series is known as the common ratio. The ratio between two consecutive numbers, or a number divided by the number before it in the sequence, is known as the common ratio since it is the same for all numbers or common.

Given that the expression f(x) = abˣ

Here, b is the common ratio.

Now to find the common ratio b;

To check for first and second term, 3240 / 2160 = 1.5

To check for second term and third term, 4860 / 3240 = 1.5

To check for third term and forth term, 7290 / 4860 = 1.5

To check for forth and fifth term, 10935 / 7290 = 1.5

Therefore the common ratio b is 1.5.

now to find a,

let x =0 and f(x) = 2160

Then, 2160 = a (1.5)°

a = 2160

Therefore, the equation which model the relationship between the weeks and the viewers is;

f(x) = 2160(1.5)ˣ

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The value of r(x) approaches as x approaches Infinity is; 0

Limit is defined as the value that a function approaches for the given input value.

We have been given a function;

r (x) = Start Fraction a x Superscript b Baseline + 8 Over c x Superscript d Baseline End Fraction

We can rewrite this function as;

r(x) = (axᵇ + 8)/(cx^d)

where a, b, c, and d are positive integers and b < d.

We need to find the value of r(x) approach as x approaches Infinity.

This means, we need to find the value of the limit [tex]\lim_{x \to \infty} r(x)[/tex]

Now, we find the value of limit for given function;

[tex]\lim_{x \to \infty} \frac{ax^b + 8 }{cx^d}[/tex]

This simplifies to;

[tex]\lim_{x \to \infty} \frac{8 }{cx^d}[/tex] (since d > b)

Thus;

[tex]\lim_{x \to \infty} r(x) = 0[/tex]

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Using Triangle inequality theorem Angle C of triangle CBT will be the biggest angle.

Triangle inequality. A theorem in Euclidean geometry that states that the sum of any two sides of a triangle is greater than or equal to the third side. In symbol a + b ≥ c. Basically, the theorem states that the shortest distance between two points is a straight line.

In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides of it must be greater than or equal to the length of the remaining sides.

In the given triangle CBT , CB = 24 cm BT = 35 cm CT = 30 cm

We know angle opposite to larger side will be greatest therefore, angle C of triangle CBT will be the biggest angle

.

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