How do you factor this equation

3n³+9n²-10n

(1) One of the six countries sent 41 representatives to the congress --> obviously x6=41x6=41 --> x1+x2+x3+x4+A=34x1+x2+x3+x4+A=34.

Given: x1<x2<x3<x4<A<x6x1<x2<x3<x4<A<x6 and x1+x2+x3+x4+A+x6=75x1+x2+x3+x4+A+x6=75. Q: is A≥10A≥10

Can A≥10A≥10? Yes. For example: x1=2x1=2, x2=3x2=3, x3=8x3=8, x4=10x4=10, A=11A=11 --> sum=34sum=34 (answer to the question YES);

Can A<10A<10? Yes. For example: x1=4x1=4, x2=6x2=6, x3=7x3=7, x4=8x4=8, A=9A=9 --> sum=34sum=34 (answer to the question NO).

(2) Country A sent fewer than 12 representatives to the congress --> A<12A<12.

The same breakdown works here as well:

Can 12>A≥1012>A≥10? Yes. For example: x1=2x1=2, x2=3x2=3, x3=8x3=8, x4=10x4=10, A=11A=11, x6=41x6=41 --> sum=75sum=75 (answer to the question YES);

Can A<10A<10? Yes. For example: x1=4x1=4, x2=6x2=6, x3=7x3=7, x4=8x4=8, A=9A=9, x6=41x6=41 --> sum=75sum=75 (answer to the question NO).

(1)+(2) The given examples fit in both statements and A in one is more than 10 and in another less than 10. Not sufficient.

X= 54

hope it helps

Answer:

Step-by-step explanation:

(3b)/5-1/2=1/4

(3b)/5=1/4+1/2

(3b)/5=1/4+(1/2)(2/2)

(3b)/5=1/4+2/4

(3b)/5=3/4

3b=15/4

b=5/4

b=1.25

Answer:

$84.8

Step-by-step explanation:

Amount of discount

\( = 40 \% \: of \: 212 \\ \\ = 0.4 \times 212 \\ \\ = \$ 84.8\)

Answer: $84.8

Step-by-Step:

212x.4

It should give you 84.8

So the amount of the discount is $84.80

There are initially 750 bacteria. There are approximately 2.11 x 10^49 bacteria after 15 minutes. It takes approximately 0.111 minutes for the number of bacteria to double.

a. The initial number of bacteria (when t=0) can be found by plugging t=0 into the equation A(t) = 750e^(6.25t). So, A(0) = 750e^(6.25*0) = 750e^0 = 750*1 = 750. Thus, there are initially 750 bacteria.

b. To find the number of bacteria after 15 minutes, plug t=15 into the equation: A(15) = 750e^(6.25*15). A(15) ≈ 2.11 x 10^49. So, there are approximately 2.11 x 10^49 bacteria after 15 minutes.

c. To find the time it takes for the number of bacteria to double, set A(t) equal to twice the initial amount, 2 * 750 = 1500: 1500 = 750e^(6.25t). Solve for t by dividing both sides by 750, then taking the natural logarithm: ln(2) = 6.25t. Finally, divide by 6.25: t ≈ 0.111. Thus, it takes approximately 0.111 minutes for the number of bacteria to double.

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Based on the information, the only prediction that is justified is that the speed of the fish will be greater than 40 mph, and the speed of the mammal will be less than 50 mph.

Therefore option B  is  correct.

Based on the given information above, we were able to deduct that about 75% of the fish were faster than 40 mph and about 75% of the mammals were slower than 50 mph.

We can go ahead and use this information to make predictions about the speeds of one additional fish and one additional mammal.

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There are 8 different trips that can be made from City X to City Z, passing through City Y.

To find the number of different trips that can be made from City X to City Z, passing through City Y, we can use the multiplication principle of counting.

First, we need to choose one of the 2 major roads from City X to City Y. Then, for each of these roads, there are 4 major roads from City Y to City Z, and we need to choose one of these roads.

By the multiplication principle of counting, the total number of different trips from City X to City Z, passing through City Y, is the product of the number of choices at each stage. Thus, we get:

Number of different trips = Number of roads from City X to City Y x Number of roads from City Y to City Z

= 2 x 4

= 8

This calculation shows how the multiplication principle of counting can be used to find the total number of possible outcomes in a multi-stage process where the number of choices at each stage is known.

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Complete question is:

Automobile Trips. There Are 2 Major Roads From City X To City Y And 4 Major Roads From City Y To City Z. How Many Different trips can be made from City X to City Z, passing through City Y?

The final grade you will have using a mixture word problem is 85%.

The mixture word method or mixture word problem is a method in mathematics to solve the problem when creating a mixture of two or more different things. This method will solve the problem of determining the quantity of mixture result.

In the question, we will mix two grades. So,

= (current grade * current worth grade) + (final exam grade * final exam worth grade)

= (85% * (100%-10%)) + (85% * 10%)

= 76.5% + 8.5%

= 85%

Thus, your final grade doesn't change if you get 85% on a final exam.

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Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

Answer:

216 cm^2

Step-by-step explanation:

A cube has 6 congruent, square faces.

Each face has side length of 6 cm.

The total surface area is the sum of the surface areas of the 6 faces, but since all faces are congruent, the total surface area is

SA = 6s^2

where s = side length

SA = 6 * (6 cm)^2

SA = 6 * 36 cm^2

SA = 216 cm^2

1 teaspoon equal to 4.93 mL .

A teaspoon (symbol: tsp) is a unit of volume based on an item of cutlery. The United States customary teaspoon is equal to exactly 4.928922 mL. The metric teaspoon is equal to 5 mL.

A milliliter is basically a unit that is used to measure the volume that is sustainable in the framework of the International System of Units or a SI. The abbreviation used for a milliliter is ‘ML’. A milliliter is equivalent to one cubic centimetre or 1/1000L & 1,000,000 cubic meters or also m3.

1 teaspoon (US) = 4.9289215938 mL

1 mL = 0.2028841362 teaspoon (US)

Example: convert 15 teaspoon (US) to mL:

15 teaspoon (US) = 15 × 4.9289215938 mL = 73.9338239063 mL

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The sum of the measures of the exterior angles of any polygon, including a triangle, is always 360 degrees.

We have,

An exterior angle of a polygon is formed by extending one of its sides outward.

In the case of a triangle, when we extend each side, we create three exterior angles.

These exterior angles are located outside the triangle.

The key concept to understand is that the sum of the exterior angles of any polygon is always 360 degrees.

This property holds true for all polygons, regardless of their shape or size.

To visualize this, imagine starting at any vertex of a triangle and moving along its sides while measuring the exterior angles.

As you move around the triangle, the sum of the exterior angles will always add up to 360 degrees.

This is because, at each vertex, the exterior angle supplements the interior angle to form a straight angle of 180 degrees.

In a triangle, each interior angle measures less than 180 degrees.

So, when we extend each side to create the exterior angles, they collectively compensate for the deficiency of the interior angles, resulting in a sum of 360 degrees.

Therefore,

The sum of the measures of the exterior angles of a triangle is always 360 degrees.

This principle holds true for all polygons, making it a fundamental property of geometry.

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The interest generated in Pauls savings account is $4.68

The amount generated in Larissa's savings account is $5015.80

Compound interest is interest that builds up over a certain length of time on both principal and interest. The principle is also used to account for the interest that has accrued on a principal over time. Furthermore, the cumulative principal value is used to calculate interest for the subsequent time period. The new way of calculating interest now utilized in all international financial and commercial operations is known as compound interest. When we look at the compound interest values that have built over various time periods, the power of compounding is clearly apparent.

The interest that is paid on both principle and interest and is compounded on a regular basis is known as compound interest. The interest is calculated for the new principal at regular intervals when the accumulated interest and the current principal are combined. The initial principal plus the interest that has already accrued make up the new principal.

The initial principal(p) of Paul is $1000

rate(r) is 5.5%

Number of days(t) = 20th March to 20th April = 31 days = 31/365 years

So the Amount generated =\(p * (1 + \frac{r}{365})\x^{365*t}\)

⇒ A = \(1000* (1 + \frac{5.5}{100*365})\x^{31} = 1000*1.00468 = 1004.68\)

The interest generated = 1004.68 - 1000 = $4.68

Similarly for Larissa

time = 24th Feb to 17th March = 21 days = 21/365 years

So the Amount generated =\(p * (1 + \frac{r}{365})\x^{365*t}\)

⇒ A = \(5000* (1 + \frac{5.5}{100*365})\x^{21} = 5000*1.00317 = 5015.80\)

The amount generated is $5015.80

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Answer:

Reason 1. Given

Statement 2. <CAD is congruent to <BAD

Reason 2. Definition of angle bisector

Statement 3. Segment AD is congruent to segment AD

Reason 4. All right angles are congruent

Reason 5. ASA

Answer:

Step-by-step explanation:

Those angle markings indicate the angles are equal. Which means the sides opposite them are equal as well.

5x-2=33

5x=35

x=7

Answer:

The axis of symmetry for the graph of y = -2x² + 16x - 7 will be:

x = 4

Hence, the last option i.e. x = 4 is the correct option.

Step-by-step explanation:

Given the equation

\(y\:=\:-2x^2\:+\:16x\:-\:7\)

For a parabola in standard form y = ax² + bx + c

The axis of symmetry is the vertical line that goes through the vertex x = -b/2a

so

The axis of symmetry for y = ax² + bx + c is x = -b/2a

In our case,

\(a=-2,\:b=16\)

Therefore,

x = -16/2(-2)

x = -16 /-4

x = 16/4

x = 4

Therefore, the axis of symmetry for the graph of y = -2x² + 16x - 7 will be:

x = 4

Hence, the last option i.e. x = 4 is the correct option.

The regular octagon has an area of 10.15 cm² and side lengths of 1.45 cm. To find the measure of the apothem, rounded to the nearest hundredth of a centimeter, we can use the formula for the area of a regular octagon. The measure of the apothem is 1.75 cm.

The area of a regular octagon can be calculated using the formula A = (2 + 2√2) * s², where A is the area and s is the length of each side. In this case, the area is given as 10.15 cm² and the side length is 1.45 cm.

We can rearrange the formula to solve for the apothem. The formula for the area of a regular octagon can also be expressed as A = (2n * a * ap)/2, where n is the number of sides, a is the side length, and ap is the apothem.

Substituting the given values, we have 10.15 cm² = (2 * 8 * 1.45 * ap)/2. Simplifying further, we get 10.15 cm² = 8.72 * ap.

Dividing both sides by 8.72, we find that ap = 1.165. Rounded to the nearest hundredth of a centimeter, the measure of the apothem is 1.75 cm.

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Answer:

265

Step-by-step explanation:

First, find 8^3. 8^3 is equivalent to 8*8*8=64*8=512

Now you have 9+512/2

Divide 512 by 2, which is 256.

9+256=265

Answer:

1/3x+1/2

Step-by-step explanation:

Answer:

10 & 4

Step-by-step explanation:

Let the numbers are a and b.

Their average = 7

= > ( a + b ) / 2 = 7

= > a + b = 2 * 7 = 14 ...( 1 )

Also,

= > 3 times of difference between a and b = 18

= > 3( a - b ) = 18

= > a - b = 6 ... ( 2 )

adding ( 1 ) & ( 2 ) :

= > ( a + b ) + ( a - b ) = 14 + 6

= > 2a = 20

= > a = 10

Thus,

= > a + b = 14 → 10 + b = 14

= > b = 14 - 10 = 4

A process of analysing, purifying, manipulating, and modelling data in order to find relevant information, come to conclusions, and enhance decision-making is known as data analytics.

It entails posing queries and providing answers utilising quantitative and statistical methods for explanatory and prescriptive analysis. Descriptive, diagnostic, predictive, and prescriptive analytics are the four basic categories of data analysis.

Diagnostic analytics is used to determine the reason why something occurred, whereas descriptive analytics is used to report what has already occurred.

The use of predictive analytics, on the other hand, enables the prediction of likely future events. Last but not least, prescriptive analytics is employed to decide what steps should be taken in order to accomplish a particular result or goal in light of the knowledge gleaned from descriptive, diagnostic, and predictive analytics.

By using these different types of analytics, individuals will be able to gather and analyze data to better understand trends, identify problems, and make informed decisions.

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x = 95/11 lmk if it’s wrong.

Answer: 15 ft

Step-by-step explanation:

You basically add all the sides:

3 + 3 + 3 + 3 +3 = 15 ft

And if you have to add 12 ft then the answer should be 27 ft in total.

I hope this helped!

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$120000\\ r=rate\to 11.5\%\to \frac{11.5}{100}\dotfill &0.115\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &7 \end{cases}\)

\(A=120000\left(1+\frac{0.115}{1}\right)^{1\cdot 7} \implies A \approx 257101.92 \\\\\\ \underset{earned~interest}{\stackrel{257101.92 - 120000}{\text{\LARGE 137101.92}}}\hspace{10em}\underset{adjusted~balance}{\stackrel{257101.92 - 25000}{\text{\LARGE 232101.92}}}\)

Answer:5/6

Step-by-step explanation:

simplify

Based on the dimensions of the rectangle, the number of square inches that are in the rectangle are 23,040 inches ²

x

First, convert the units of the rectangle from feet to inches so that it is easier to find the area.

Length of rectangle in inches:

= 16 x 12 inches per ft

= 192 inches

Width of rectangle:

= 10 x 12 inches per ft

= 120 inches

The area is:

= 192 x 120

= 23,040 inches ²

In conclusion, there are 23,040 square inches in the rectangle.

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First, we solve the product using the rule of signs:

then, the answer is 10+12=22