abigail wanta to find three consecutive even integers whose sum is four times the smallest of those integers. she lets n represent the smallest integer, then writes this equation n + (n + 2) + (n + 4) = 4n

The number of different ways that 11 books can be arranged on a bookshelf is 39,916,800.

To determine the number of ways the 11 books can be arranged on a bookshelf, we can use the formula for permutation, which is given by:

P(n,r) = n!/(n-r)!

Where n is the total number of items and r is the number of items selected. In this case, we have 11 books and we want to arrange them all, so r = 11.

Therefore, the number of different ways the 11 books can be arranged on a bookshelf is:

P(11,11) = 11!/(11-11)! = 11! = 39,916,800.

This means that there are 39,916,800 different possible ways to arrange the 11 books on the bookshelf.

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Triangle AED and triangle BEC have equal areas. The length of AE can be represented as 14 - x (since AC = 14). AE is equal to 10.

To find the length of AE, we can use the fact that triangle AED and triangle BEC have equal areas. Since the areas of two triangles with the same height are proportional to their base lengths, we can set up the following proportion:

Area of triangle AED / Area of triangle BEC = AE / EC

Let's denote EC as x (the length of EC). Then, the length of AE can be represented as 14 - x (since AC = 14).

Now, let's look at the given information about the lengths of the sides of the quadrilateral:

AB = 9

CD = 12

AC = 14

We can use the given information to find the lengths of the other sides of the quadrilateral:

BC = AC - AB = 14 - 9 = 5

AD = AC - CD = 14 - 12 = 2

Next, we can calculate the areas of triangle AED and triangle BEC using the lengths of their sides:

Area of triangle AED = (1/2) * AD * AE

Area of triangle BEC = (1/2) * BC * EC

Since the areas of the two triangles are equal, we can set up the following equation:

(1/2) * AD * AE = (1/2) * BC * EC

Plugging in the values we know:

(1/2) * 2 * (14 - x) = (1/2) * 5 * x

Simplifying the equation:

14 - x = (5/2) * x

Multiplying both sides by 2 to clear the fraction:

28 - 2x = 5x

Adding 2x to both sides:

28 = 7x

Dividing both sides by 7:

x = 4

Therefore, the length of EC is 4.

Since AE = AC - EC, we can calculate AE:

AE = 14 - EC = 14 - 4 = 10

So, AE is equal to 10.

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The complete question is:<Convex quadrilateral ABCD has AB = 9 and CD = 12. Diagonals AC and BD intersect at E, AC = 14 and triangle AED and triangle BEC have equal areas. What is AE?>

Here is an explanation to understand step by step how to do this.

A volume can be determined for any three-dimensional object using formulas that are unique to that item's shape. For instance, the volume of a water bottle indicates how much water it can hold. Understanding an object's volume is crucial since it indicates how much stuff that shape can carry.

Any form or object's volume is directly inversely proportional to the volume of water it displaces when submerged in water because of its link to density. As a result, there are two ways to determine an object's volume: by mathematically calculating it using the formula unique to that shape, or by submerging it in water and measuring the volumetric displacement of the water.

Answer:

C

Step-by-step explanation:

1/18 x³y + 7/18 xy²

1/18 xy (x² + 7y)

1.rs 2.yoy can just put the q with the t and when you subtract it can problabbly go to thr letter a

Answer:

1. R and S

2. Both equidistant from 0

3. Move six spots to the left of T because each spot is 1/4, and 1 1/2 = 6/4, and it is a subtraction problem.

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

A has 9 sig digits. Every digit counts including the 4 zeros, because 3 digits follow them. Even if the 345 were not there, there still are 6 sig digits.

B. Those two trailing zeros mean something. They are guaranteed place holders. This number has 7 sig digs.

D. Depends on who teaches this. 5 without a period at the end means that the number is exactly 5 -- or that's the rule when I was teaching.

The answer is C, believe it or not. Again, those zeros are place holders. They are guaranteed to be accurate. This is a question to look at carefully.

To compute the approximate 95% confidence interval for the difference between the mean foot lengths of men and women, we can use the formula:

Confidence Interval = (mean of men - mean of women) ± (critical value * standard error)

In this case, the mean foot length for men is 28 cm, the mean foot length for women is 23 cm, and the standard error of the difference in sample means is 0.3 cm.

To find the critical value, we need to refer to the t-distribution with (77+111-2) degrees of freedom, which is 185.

Using a t-table or a calculator, we find that the critical value for a 95% confidence interval with 185 degrees of freedom is approximately 1.97.

Now we can calculate the confidence interval:

Confidence Interval = (28 - 23) ± (1.97 * 0.3)

Calculating the confidence interval, we have:

Confidence Interval = 5 ± 0.591

Therefore, the approximate 95% confidence interval for the difference between the mean foot lengths of men and women is (4.4 cm, 5.6 cm).

The interpretation of this interval is: With 95% confidence, we can say that in the population of people represented by the sample, the average foot length for men is greater than the average foot length for women by somewhere between 4.4 cm and 5.6 cm.

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The radius of the circle is approximately 10 (rounded to the nearest whole number).

The radius of a circle can be found using the formula for the length of an arc: arc length = radius × central angle (in radians).

First, we need to convert the given central angle of 225 degrees to radians by multiplying it by π/180: (225 × π)/180 = 5π/4 radian.

We are given that the length of the subtended arc is 39.27.

Now, we can rearrange the formula to find the radius: radius = arc length / central angle (in radians).

Plugging in the given values: radius = 39.27 / (5π/4).

Solving for the radius, we get approximately 9.97.

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Answer:

Let's calculate:

22-5

• Remove minus in the exponent and invert the base:

= (1/22)5

• Expand the multiplication:

= (1/22) * (1/22) * (1/22) * (1/22) * (1/22)

• Find your result:

= 1/5153632 ≈ 0.000000194038

Answer:

10.50x + 15 = y

Step-by-step explanation:

x = amount of hours spent babysitting.

y = total amount of money.

Answer:

The first one is 360 degrees. The second one is 1080.

Step-by-step explanation:

The sum of the interior angles of a quadrilateral are always 360. If you subtract 90 from 360 to get 270. Multiply 270 by 4 to get 1080.

Yes she can use a table with a top that measures 2 1/2 feet long and 1 1/2 feet wide.

Information given in the question

the volume of each case is 1,000 cubic inches

table with a top that measures 2 1/2 feet long and 1 1/2 feet wide

The volume given is in inches and the table top is in feet we convert all to have similar dimensions

long = 2 1/2 feet = 2.5 * 12 = 30 inches

wide = 1 1/2 feet = 1.5 * 12 = 18 inches

volume  = long * wide * height = 1000 cubic inches

area of table top = 30 * 18 = 540 square inches

the height of the table = volume / area

= 1000 / 540

= 1.85 inches

The material will be enough for the table and a remnant of 1.85 inches

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Answer:

parallel

Step-by-step explanation:

3x + 2y = 6 can be written as y = -3/2x +3

4y = -6x -12 can be written as y= -3/2x-3

same slope different y intercept so parallel

When determining the size of a fact table, estimating the number of possible values for each dimension associated with the fact table is equivalent to: determining the number of possible values for each foreign key in the fact table.

The measures, metrics, or facts of a business process are contained in a fact table in data warehousing. In a star or snowflake schema, it sits in the middle, surrounded by dimension tables.

When several fact tables are employed, they are organized according to a fact constellation schema. The two types of columns that make up a fact table are typically those that hold facts and those that serve as a foreign key to dimension tables.

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Answer:

x =56

Step-by-step explanation:

1/4 x - 1 =13

Add 1 to each side

1/4x - 1+1 = 13+1

1/4 x = 14

Multiply each side by 4

1/4x * 4 = 14*4

x =56

In this scenario, the steps that should be taken to calculate the volume of a prism are:

⇒ A, C, D, and E.

Now, Mathematically, the volume of a prism should be calculated by using this formula:

⇒ V = B × H

Where:

H is the height.

B is the base area.

Hence, In conclusion, you should use the triangle-base and height to solve for the area of the base, and the area of the base (B) is one-half of the product of (3.75) and (3), which is,

= 1/2 x 3.75 x 3

= 5.625 m².

Thus, the steps that should be taken to calculate the volume of a prism are:

⇒ A, C, D, and E.

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Answer:

a) 15 divided by 3 which equals 5

b) 21 divided by 21 which equals 1

c) 81 divided by 9 which equals 9

d) 0 divided by 5 which equals 0

To find:-

Answer:-

We are here given two triangles ∆ACB and ∆ECD , and we need to prove them congruent by ASA postulate.

For traingles to be congruent by ASA , two sides of the triangle and the angle between the two sides of the two triangles should be equal.

So , in ∆ACB and ∆ECD , we have;

Also , here

and angle C is between sides AC and BC in ∆ACB and it is between EC and DC in ∆ECD , so BC and DC should be also equal.

Therefore,

BC = DC and ∠C for both traingles needs to be congruent .

Hence option C is correct.

and we are done!

Answer:

\(6(2p + 2) = 120 \\ 2p + 2 = 20 \\ 2p = 18 \\ p = 9\)

Answer:

P = 9

Step-by-step explanation:

6(2P+2) = 120

12P + 12 = 120

      - 12 = -12

      12P = 108

        12 =  12

         P = 9

The height of the tree is 6.4m

the difference is that in one case the shadow of the tree is 60 - 20 = 40 m, and in the other case it is 60 + 20 = 80 m long.

anyway, for a certain angle of the sunlight we know the shadow of the pole is 60 m long, which creates with the 4.8 m height a right-angled triangle, with the line of sight from the top of the pole to the ground end of the shadow being the Hypotenuse or radius for or trigonometric triangle in a circle.

the shadow length (60 m) is sine of the sunshine angle multiplied by the radius.

the height (4.8 m) is cosine of that sunshine angle multiplied also by that radius.

Pythagoras gets us the radius for the pole triangle :

radius² = 60² + 4.8² = 3600 + 23.04 = 3623.04

radius = sqrt(3623.04) = 60.19169378... m

sin(angle) × radius = 60

sin(angle) = 60/radius = 0.996815279...

angle = 85.42607874...°

the sunshine creates with the tree also a right-angled triangle with the same sunshine angle (the sun is so far away, that the tiny, tiny difference is irrelevant, we can simply assume the angles are equal).

but the shadow is of different length (sin(angle)×radius), which means also the radius for the tree triangle has to be different. and that defines the height of the tree (cos(angle)×radius).

but now we know the angle, and we can reverse calculate the side lengths.

but the question is (as mentioned at the beginning) : is the tree shadow 40 m or 80 m long.

we have therefore 2 solutions for the height of the tree.

1. the shadow is 40 m long.

sin(angle) × radius = 40

radius = 40/sin(angle) = 40.12779585... m

tree height = cos(angle)×radius = 3.2 m

2. the shadow is 80 m long.

sin(angle) × radius = 80

radius = 80/sin(angle) = 80.25559171... m

tree height = cos(angle)×radius = 6.4 m

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Answer:

I think the answer is 8 and 11

- They differ by 3

- 8 x 11 = 88

Step-by-step explanation:

Answer:

y=-1/2x+b

Step-by-step explanation:

The equation of line is  y = (-1 / 2)x + b that is perpendicular to the line y = 2x - 8.

When any equation is represented in the y = mx +c form, it is called the slope intercept form of the equation.

Here m is slope and c is constant.

The given equation of line,

y = 2x - 8.

The slope of the given line m₁ = 2.

To find the equation of line that is perpendicular to the given line,

The slope of the required line m₂ = -1 / m = - 1 / 2.

Let the required equation of line is,  

y = m₂ x + b

Substitute the value of m₂ here,

y = (-1/2)x + b

The required equation of line is y = (-1 / 2)x + b.

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Answer: 8 to 5

Step-by-step explanation:

Ratio is referring to the relationship between two things when it is expressed in numbers or amounts. In this case we want to find the smallest amount of one value that equals to another. Think of it as a fraction, you're trying to simplify the numbers to its smallest value. For ratios it's the same but with the extra step that it compares each other.

1) Find the Greatest Common factor between 56 and 35. Answer: 8

2) Divide both 56 and 35 by 8 and your answer should be 8 and 5

3) 8:5 is the the simplest ratio of two circles whose radii are 56:35

The volume of one penny is 0.36 mL if the volume of 50 pennies is 18.0 mL.

To find the volume of one penny if the volume of 50 pennies is 18.0 mL, we use the concept of proportionality as follows:

We can find the volume of one penny by dividing the volume of 50 pennies by 50 since we know that 50 pennies occupy a volume of 18.0 mL.

Therefore, the volume of one penny can be calculated as:Volume of one penny = Volume of 50 pennies / 50= 18.0 mL / 50= 0.36 mL

Hence, the volume of one penny is 0.36 mL if the volume of 50 pennies is 18.0 mL.

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Answer:

c

Step-by-step explanation:

Answer:

n=-5

Step-by-step explanation:

y^5*y^n= y^5+n when multiply , add exponents

y^5+n/y^2= y^(5+n)-2 divide, subtract exponents

y^(5-5-2) =y^-2

Answer:

6 X 10^21

Step-by-step explanation: