Factor completely:
a^n + a^n+1

Answer:

12 students earned B Honor Roll

Step-by-step explanation:

Let A be the number of students who earned A Honor Roll and B the number who earned B.

We are told that A = 24,

and that A = 3B-12  [ . . .were twelve less than three times the number of students who earned B Honor Roll]

Since we know the value of A (24) use the second equation to find B:

A = 3B-12

24 = 3B-12

3B = 36

B = 12

CHECK:

Is 24 12 less than three times B(12)?

 24 = 3*12 - 12?

 24 = 36 - 12?

  24 = 24

 YES

Answer: n = -16

Step-by-step explanation:

1) Distribute

—2(3n +6) = 3(-n + 12)

—6n - 12 =3(-n + 12)

2) Distribute

—6n - 12 = 3(-n + 12)

—6n — 12 = —3n +36

3) Add 12 to both sides

—6n — 12 = -3n +36

-6n = 12+ 12 = - 3n + 36 + 12

4) Simplify

----Add the numbers

—6n = -3n +48

5) Add 3n to both sides

—6n = -3n +48

—6n + 3n = —3n + 48 + 3n

6) Simplify

- Combine like terms

—3n = 48

7) Divide both sides by the same factor

—3n = 48

-3n ÷ -3 = 48 ÷ -3

8) Simplify

- Cancel terms that are in both the numerator and denominator

- Divide the numbers

n = —16

Please give brainliest

Caleb would need to invest $1,764.69 to the nearest cent, for the value of the account to reach $1,900 in 5 years with an interest rate of 6% compounded daily.

What is compound interest?

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It is different from simple interest, which is calculated only on the initial principal.

To find out how much Caleb needs to invest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment

P = the principal or initial investment

r = the annual interest rate (expressed as a decimal)

n = the number of times per year that interest is compounded

t = the number of years the investment will be held

We know that Caleb wants the future value of the investment to be $1,900 in 5 years and interest is compounded daily with an annual rate of 6%. So we can set up the equation as:

A = P(1 + r/n)^(nt)

1900 = P(1 + 0.06/365)^(365*5)

To solve for P, we can use a calculator to get the result:

P = $1,764.69

Hence, Caleb would need to invest $1,764.69 to the nearest cent, for the value of the account to reach $1,900 in 5 years with an interest rate of 6% compounded daily.

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The given equation system has the following solution: (10, 11).

A finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

Given the system of equations below:

2x+3y=53

3x-y=19

From equation 2, y = 3x - 19 .......... 3

Substitute equation 3 into 1 to have;

2x+3y=53

2x + 3(3x - 19) = 53

2x + 9x - 57 = 53

11x = 110

x = 10

Substitute x = 10 into equation 3 to have:

y = 3x - 19

y = 3(10) - 19

y = 30 - 19

y = 11

Hence the solution to the given system of equation is (10, 11).

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The second post is 30 feet tall because the ratio of the shadows is 2:1, meaning that for every 2 feet of shadow, the post is 1 foot tall.

1. ratio of shadows is 2:1, so for every 2 feet of shadow, the post is 1 foot tall

2. 60 feet of shadow divided by 2 is 30 feet tall

3. 24 feet of shadow divided by 2 is 12 feet tall

4. 30 feet tall is the second post

The goal post that casts a 60-foot shadow is 20 feet tall, and the ratio of the shadows is 2:1, meaning that for every 2 feet of shadow, the post is 1 foot tall. To find the height of the second post, we divide the length of the shadow by 2. The second post casts a 24-foot shadow, so when we divide it by 2, the post is 12 feet tall. Therefore, the second post is 30 feet tall. This is because for every 2 feet of shadow, the post is 1 foot tall, so for the 60-foot shadow, the post was 20 feet tall, and for the 24-foot shadow, the post is 12 feet tall. Therefore, the second post is 30 feet tall.

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These identities are not true and cannot be derived from the first identity.

What is trignomentry ?

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right triangles. It is used to study the properties of angles and circles, and to solve problems involving geometric shapes and measurements. Trigonometry is used in many fields such as physics, engineering, and navigation.

The statement "sin 0 + cos 0 = 1" is a correct foundational trigonometric identity. However, it is not possible to derive the identities "1+cot^2(0) = csc^2(0)" or "tan^2(0)+1 = sec^2(0)" by dividing through by cot^2(0) or by tan^2(0) respectively. These identities are not true, and are not a direct consequence of the first identity.

These identities are not true and cannot be derived from the first identity.

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The number of places you put the lens to form a well-focused image of the candle flame on the wall is either we have to move the screen towards the lens or the lens towards the screen.

Here we have given that the lens to form a well-focused image of the candle flame on the wall.

As we all know that if the candle is further from the wall than the focal length of the lens, then there are two places which will result in an image. Here we have know that one of them is just beyond the focal length from the wall.

Here we have given the other is that same distance from the candle.

Then the position near the wall will yield a small image.

Here the position near the candle will produce a large image.

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The radius of the circle is s√3π, which is equal to 3√π. Hence, the answer is option (B).

To calculate the radius of the circle, we need to first calculate the perimeter of the equilateral triangle. The perimeter of an equilateral triangle is equal to 3 times the side length of the triangle. Thus, we can say that the perimeter of the equilateral triangle is 3s.

Now, we need to calculate the area of the circumscribed circle. The area of a circle is equal to π times the square of the radius. Thus, the area of the circumscribed circle is equal to πr2.

Therefore, we can say that 3s = πr2. Solving this equation for r, we get r = s√3π. Thus, the radius of the circle is s√3π, which is equal to 3√π. Hence, the answer is option (B).

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Answer:

DB = 15

Step-by-step explanation:

∠ C and ∠ D are the base angles of Δ BCD

since they are congruent , that is ∠ D = ∠ C

Then the triangle is isosceles with the legs being congruent, so

DB = BC = 15

The solution represents the number of hours of cleaning and cost of two housekeeping services, Premier and Best House Care.

What is algebraic equation ?

An algebraic equation is a mathematical expression containing one or more variables and an equal sign, where the goal is to find the value(s) of the variable(s) that make the equation true. The equation is formed by combining numbers, variables.

PART A:

Let x be the number of hours of cleaning that Premier Housekeeping provides, and let y be the number of hours of cleaning that Best House Care provides. The system of equations representing the housekeeping services is:

Premier Housekeeping: 25 + 65x = cost in dollars

Best House Care: 75y = cost in dollars

PART B:

The solution of this system of equations represents the point (x,y) in the coordinate plane, where x represents the number of hours of cleaning that Premier Housekeeping provides and y represents the number of hours of cleaning that Best House Care provides. The cost in dollars of each service will be given by the corresponding equation: the cost of Premier Housekeeping will be 25 + 65x, while the cost of Best House Care will be 75y.

The solution represents the number of hours of cleaning and cost of two housekeeping services, Premier and Best House Care.

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On solving the provided question, we can say that probability P(B)(1–0.6)=0.3 =>P(B)=3/4= 0.75

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

If two events A and B are independent then,

[tex]P(A n B)= P(A).P(B)\\P(A u B)= P(A)+P(B)-P(A n B)[/tex]

Since A and B are independent, so

[tex]P(A u B)= P(A)+P(B)-P(A).P(B)\\0.9=0.6+P(B)-(0.6 * P(B))\\P(B)(1–0.6)=0.3\\P(B)=3/4= 0.75[/tex]

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When two line segments are of equal length then both the line segments are congruent to each other.

As given in the question,

Therefore, the two line segments with equal lengths they both are congruent to each other.

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The greatest integer that does not exceed S/10 is 2.

1000 can be factored as 1000 = 2^3 * 5^3. The positive divisors of 1000 are the numbers of form 2^i * 5^j, where i and j are non-negative integers and i <= 3, j <= 3.

The sum of all numbers of the form a/b, where a and b are relatively prime positive divisors of 1000, is the sum of all numbers of the form 2^i * 5^j / (2^k * 5^l), where i, j, k, and l are non-negative integers and i, j, k, l are non-negative integers and i <= 3, j <= 3 and (i,j) is not equal to (k,l).

There are total 24 such terms in the sum.

We can evaluate the sum as:

(1/1 + 1/2 + 1/4 + 1/5 + 1/8 + 1/10 + 1/20 + 1/25 + 1/40 + 1/50 + 1/80 + 1/100 + 1/125 + 1/200 + 1/250 + 1/400 + 1/500 + 1/625 + 1/1000 + 2/5 + 4/25 + 8/125 + 16/625)

S = (1 + 0.5 + 0.25 + 0.2 + 0.125 + 0.1 + 0.05 + 0.04 + 0.025 + 0.02 + 0.0125 + 0.01 + 0.008 + 0.005 + 0.004 + 0.0025 + 0.002 + 0.0016 + 0.001 + 0.0004 + 0.0008 + 0.00016 + 0.000064)

S = (2.93120)

Therefore, the greatest integer that does not exceed S/10 is 2.

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The value of x is 7 from the given figure.

What is Triangle ?

Triangle can be defined in which three sides , three angles and the sum of three angles is always is 180 degrees.

From the given triangle ,

Let the triangle be ABC

where A = 60 and B = 30 and C = 90

CA = 7[tex]\sqrt{3}[/tex]

CB = x .

sin60 =  7[tex]\sqrt{3}[/tex]  /x

[tex]\sqrt{3}[/tex] / 2  =  7[tex]\sqrt{3}[/tex]  /x

1/7  = 2 * x

x = 7 * 2

x = 14

In triangle ABC ,

AC^2 + CB ^ 2  = AB ^2

7[tex]\sqrt{3}[/tex]  ^2 + CB^2 = 14*14

CB^2 = 196 - 149

CB^2 = 49

CB = 7

Hence, The value of x is 7  from the given figure.

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The first statement is correct. The 99% confidence interval is (0.3162, 0.5238). We are 99% confident the true proportion of students attending the Winter Formal is between 31.62% and 52.38%. However, the rest of the statements are incorrect.

"There is a 99% chance that a randomly selected student who will attend the Winter Formal lies between 31.62% and 52.38%." is incorrect, this statement is about a probability of a single student, but the confidence interval is about a probability of the whole population.

"Ninety-nine percent of all samples of this size will yield a confidence interval of (0.3162, 0.5238)." is correct, this statement is true, but it doesn't add any additional information.

"The 99% confidence interval is (0.4762, 0.6838)." is incorrect, this value is not the correct confidence interval.

"We are 99% confident that the true proportion of students attending the Winter Formal is between 47.62% and 68.38%." is incorrect, this statement is not true, as the confidence interval is not (0.4762, 0.6838) but (0.3162, 0.5238)

"Ninety-nine percent of all samples of this size will yield a confidence interval of (0.4762, 0.6838)." is incorrect, as this is not the correct confidence interval.

In conclusion, the faculty members at McAdenville High School can be 99% confident that the true proportion of students who will attend the Winter Formal is between 31.62% and 52.38%.

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It is not possible to construct a triangle with 6cm, 9cm, and 17cm.

The sides measure 6 cm, 9 cm, and 17 cm in length.

Only when the third side is greater than the sum of any two sides can a triangle be drawn. This the condition.

Let's verify the rule now.

6 + 9 > 17        Not true

6 + 17 > 9        True

9 + 17 > 6        True

As 6 + 9 > 17 does not satisfy the condition.

Hence, it is not possible to construct a triangle having 6cm, 9cm, and 17cm in length.

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Answer:

j=16.85

s=8.95

Step-by-step explanation:

j=jeans s=shirt

3j+6s=104.25

4j+5s=112.15

working:

3j+6s=104.25 dollars

4j+5s=112.15 dollars

(get j to be the same)

12j+24s=417 dollars

12j+15s=336.45 dollars

(subtract them)

9s=80.55 dollars

s=8.95 dollars

(substitute in)

(3 x j)+(6x8.95)=104.25 dollars

3 x j= 104.25-(6x8.95)

j=50.55/3 (50.55 divided by 3)

j=16.85 dollars

substitute in to double check

(3 x 16.85) + (6 x 8.95) = 104.25 dollars

check with the other equation and it works also, so that must be the values of j and s (jeans and shirt)

(4 x 16.85) + (5 x 8.95)=112.15 dollars

j=16.85

s=8.95

On solving the provide question, we can say that by plotting data they can own 8 to 10 video games.

The most typical approach to display data using a chart is a graph that shows the relationship between two additional variables. Diagrams created by hand or on a computer are also acceptable. Move 2 units to the right after starting at the origin before going 3 units up. The coordinates for the points 2, 3, should be shown on the coordinate plane. Clearly state your points. The pink dot with the letter P thus stands for 2.3. Before creating a line chart, you need first generate a number line for each value in your data collection. Put an X (or dot) over each value of the data on the number line after that. For each instance when a value appears in a record, place an X over the corresponding number.

Here,

We can therefore deduce from the provided number that the cluster owns between 8 to 10 video games.

How do we know the range is 8 to 10 then? In the example figure, the dots are referred to as the cluster.

Based on this, we may deduce that our range is between 8 and 10, the amount of games that are owned as a minimum and maximum, respectively.

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The complete question is " A group of children, 6 to 10 years old, were asked how many video games they owned. The scatter plot shows the results.

What is the range of video games owned for the cluster?"

Answer:

5 4/9

Step-by-step explanation:

7/9 of 7

= 7/9 × 7

= 7/9 × 7/1

Multiply top×top and bottom×bottom

= 49/9

means 49÷9

9 goes into 49, 5 times. And 9 × 5 is 45. 49 - 45 is 4. So

49÷9 is 5 and 4 leftover.

49 ÷ 9

= 5 4/9

Check the picture below.

All of the rectangles together measure 1250 meters in length.

A textile square with a 25 square meter surface area. We are aware that the area of a square is determined by multiplying one side's length by itself. The square root of 25 square meters, or 5 meters, is the length of one side of the square in this instance.

Secondly, we are aware that the fabric is being cut into 50 cm-wide rectangles. We can use the following formula to determine each rectangle's length:

(Rectangle width) x (Square cloth length) / (Width of square cloth)

The equation in this instance is (50 cm) x (25 m) / (5 m) = 2500 cm or 25 meters.

Therefore, each rectangle is 25 meters long.

We divide the square cloth's length by each rectangle's width to get the total number of rectangles.

25m / 0.5m (50cm) = 50 rectangles.

Finally, we multiply the quantity of rectangles by the average length of each rectangle to determine the total length of all the rectangles:

50 m x 25 m = 1250 m

Therefore, a square piece of fabric that is 25 square meters in size and has been divided into 50 rectangles, each measuring 50 cm wide and 25 meters long.

Therefore the rectangles together measure 1250 meters in length.

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The algebraic representation of this dilation is: (x', y') = (-0.9x, -1.5y)

A dilation is a transformation that changes the size of a geometric figure, but not its shape. The center of dilation is a fixed point, and all other points in the figure are expanded or contracted in relation to it. In this case, the center of dilation is the origin, and the original figure is m'n'o'p' and the image figure is mnop.

The algebraic representation of a dilation is given by the equation:

(x', y') = (kx, ky)

Where (x', y') are the coordinates of the image point, (x, y) are the coordinates of the original point and k is the scale factor of the dilation.

We can find the scale factor k by comparing the coordinates of any two corresponding vertices of the figures. For example, if we take the vertex m' and m, we have:

m'(-5, -4) and m(4.5, 6)

Here we can see that the x-coordinate of m' is -5 and the x-coordinate of m is 4.5 and the y-coordinate of m' is -4 and the y-coordinate of m is 6.

So, k = mx/mx' = 4.5/-5 = -0.9 and k = my/my' = 6/-4 = -1.5

We can use this scale factor to find the coordinates of any other point in the image figure.

Therefore, the algebraic representation of this dilation is: (x', y') = (-0.9x, -1.5y)

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As per the ratio proportion, the length of 600 miles freeway is 6 inches on the map.

What is ratio proportion?

Ratio proportion is an equation where two sides of it are equal. A ratio or proportion maintains the equality between two fractions.

Given, 0.5 inches represent 50 miles.

Let, x inches represent 600 miles.

Therefore, as per the ratio proportion, we can write:

0.5 : 50 = x : 600

⇒ 0.5/50 = x/600

⇒ x = (600 × 0.5)/50 = 6.

Therefore, the length of 600 miles freeway is 6 inches on the map.

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Answer:

1.3 * c + 1.5

Step-by-step explanation:

(5.2c-7) + (-3.9c + 8.5)

5.2 * c - 7 - 3.9 * c + 8.5

1. add constants ( - 7 and 8.5)

5.2 * c - 3.9 * c + 1.5

2. add both of the coefficients of c

when a variable is multiplied by a coefficient, we can add another coefficient * variable combination if the variable is the same. for example, 1 * x + 2 * x = 3 * x by adding the 1 and 2 together

similarly, 5.2 * c - 3.9 * c = (5.2 - 3.9) * c = 1.3 * c

1.3 * c + 1.5

The required altitude of the trapezoid ABCD is 2.5 cm.

The Greek roots of the term trapezoid are trapeza, which means "table," and -oeides, which means "formed." A trapezoid is shaped like a table. It has two parallel sides, which are often referred to as the figure's bases. Take the average of the bases and multiply it by the height to determine the area of a trapezoid.

Here, we must utilise the area of a trapezoid formula, which is

where h is the height or altitude and b1 and b2 are the two bases.

[tex]Area =\frac{ (b_{1}+b_{2})h}{2}[/tex]

Given are the values of Area = 7.5, b1 = 1, b2 = 5, and h is unknown.

Then,

7.5 = (1+5)h/2

7.5 = 3h

h = 2.5cm

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The AM = 6 because of Definition of Perpendicular Bisector.

The correct option is A.

Those lines that are perpendicular to each other that means create an angle of 90° at intersecting point are perpendicular lines.

Given:

Kyle is creating a frame for a model car.

He begins by piecing two rods together,

as shown in the attached diagram.

A perpendicular bisector means,

a line intersects another line.

And divide into two same parts.

And angle between two lines is 90°.

Here, the if the one piece of one rod is 6.

Then that means, the rod is divided into 2 equal parts.

Therefore, the definition is the definition of Perpendicular Bisector

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Therefore, 0.4854 to 0.5546 is the 95% confidence range for the percentage of businesses that are anticipated to need greater employee payments for health insurance coverage in 2009.

A. Computation the margin of error

First step is to calculate the Confidence level using this formula

Confidence level= 1 -α

Where,

α=0.95

Let's enter the formula.

Level of confidence = 1-0.95

Level of confidence = 0.05

The following step is to use this formula to get Z.

Zα/2

Let's enter the formula.

Z= 0.05/2

Z=0.025

Finding the Z score of Z=0.025 is the third stage.

Zα/2=1.96

Let's now use this approach to calculating the margin of error.

Margin of error=Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Margin of error=1.96√0.52(1-0.52)/800

Margin of error=1.96√0.52(0.48)/800

Margin of error=1.96√0.2496/800

Margin of error=1.96√0.000312

Margin of error=0.0346

Therefore Margin of error will be 0.0346

B. Calculating the proportion of businesses anticipated to demand greater employee payments for health insurance coverage in 2009 with a 95% confidence interval

computation for the confidence interval's outer limits

p- Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Confidence interval=0.52-1.96√0.52(1-0.52)/800

Confidence interval=0.52-1.96√0.52(0.48)/800

Confidence interval=0.52-1.96√0.2496/800

Confidence interval=-0.52-1.96√0.000312

Confidence interval=0.4854

Computation for the boundaries of confidence interval

Using this formula

p+ Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Confidence interval=0.52+1.96√0.52(1-0.52)/800

Confidence interval=0.52+1.96√0.52(0.48)/800

Confidence interval=0.52+1.96√0.2496/800

Confidence interval=-0.52+1.96√0.000312

Confidence interval=0.5546

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Monetary conversion is essentially the price measure of one currency against another.

A conversion rate is the ratio between two currencies, most commonly used in foreign exchange markets, which designates how much of one currency is needed to exchange for the equivalent value of another currency. Conversion rates fluctuate regularly for all currencies traded in forex markets.

Given here: monetary conversion

Customers exchange their native currency for the currency of the country they are visiting. On the other hand, currency conversions are the process of converting prices to match the customer's native currency.

For example: Suppose you have 40 cents, how many cents would you need to make one dollar!

You can understand this through the following conversion. Since, $1 = 100¢, therefore, we subtract 40 cents from 100 cents. That is 100 cents – 40 cents = 60 cents. Since you already have 40¢, you would need 60¢ more to make it a dollar. This is how we can express 60 cents with different coins.

Hence, Monetary conversion is essentially the price measure of one currency against another.

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1. The  triangles, which are similar to ΔAED  are ΔAFE, ΔEFD, ΔECD, ΔABE

2.  The length of segment FA is, 32/3 units

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is shown here by the symbol "≈"

Given that,

A rectangle ABCD having triangles in it,

1.  ΔAED is a right angle triangle,

all the triangle which are right angle triangle will be similar to  ΔAED

So,  ΔAFE, ΔEFD, ΔECD, ΔABE are similar triangles

2. Now, consider ΔEFD

EF = 8 unit

ED = 10 unit

∠CEB = 53°

∠CEF = 90°

∠DEF = 37°

∠AED = 90°

∠AEF = 53°

tan53° = FA/FE

4/3 = FA/8

FA = 32/3

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Answer: Midpoint

Step-by-step explanation: