Given: Triangle ABC is isosceles with A as the vertex angle and segment AD bisects segment BC,
Prove: Segment AD bisects angle BAC.

1. The students that the academy have per teacher is 18.

2. The students per tutor will be 10.

3. The tutors that the academy need if it has 60 students is 6 tutors.

Given that the arts academy requires there to be 4 teachers for every 72 students and 3 for every 30 students.

The students that the academy have per teacher will be:

= Number if students / Teacher

= 72/4

= 18 students per teacher.

The students per tutor will be:

= 30/3

= 10 students per tutor

The number of tutors for 60 students will be:

= 60 / 10

= 6 tutors.

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Answer:

y={7,10,19,22}

Step-by-step explanation:

3(2)+1 = 6+1 = 7

3(3)+1 = 9+1 = 10

3(6) + 1 = 18+1 = 19

3(7) + 1 = 21+1 = 22

Answer: from generation 19 to 20.

Step-by-step explanation:

The greatest percentage increase will occur  from generation 19 to 20 as the exponential power will be highest.

What is exponential growth?

Exponential growth happens once the larger in size you're the quicker you grow that causes you to even larger in size. it's the expansion characterised by interest, or growth. it's known as exponential growth as a result of it will solely be delineate mathematically by inserting time within the exponent or power of the bottom. Population then is adequate to the population at the current times some discretional range to the facility of the expansion rate times the time. The discretional range is sometimes two then the expansion rates is given because the reciprocal of the doubling time.

Main body:

initial population = 25

Total generation = 20

growth rate = 0.2

General formula of exponential function = aˣ

here a = 25 and x = 0.2

⇒25⁰°²

= 1.9

hence total population = 25+2 = 27

So it is clear that in 19 to 20 generation , growth will be highest.

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Answer:

(Not accurate because I'm estimating amounts) y = ((x-2)/2)^2 + 4

Step-by-step explanation:

Scales horizontally by 2, Shifts up 4, right 2

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

The number of local guests who visited the zoo is 600.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Total number of visitors = 750

The percentage that visited the zoo.

= 100% - 20%

= 80%

Now,

The number of local guests who visited the zoo.

= 80% of 750

= 80/100 x 750

= 600

Thus,

The number of local guests who visited the zoo is 600.

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The distance that each boy ran is as follows:

Donnie = 24 miles

Karim = 12miles

Shawn = 9 mile.

Ratio is defined as an expression that is used to represent the part of a whole entity or structure.

The total distance covered by the three boys = 46miles.

Distance covered by Donnie = 200% of Karim (ratio 4)

That is;

200/100×4 = 8

Now the ratio of the three boys = 8:4:3

To calculate the distance of each boy is by finding the total ratio of the whole boys such as:

= 8+4+3 = 15

For Donnie = 8/15×45 = 24 miles

For Karim = 4/15×45 = 12 miles

For Shawn = 3/15 × 45 = 9 miles

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Answer: 5.76 x 10 to the 5th

An equation with variables on both sides that equal 19 is x - 2 = 17.

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 is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign

Based on the information, the equation will be:

x - 2 = 17

Collect like terms

x = 17 + 2

x = 19

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Answer:

6√3 centimeters

Step-by-step explanation:

This is an isosceles triangle because two of the sides are the same. We can divide this into two triangles to make two right triangles, and use the Pythagorean theorem. The base (a) will be divided by 2.

Pythagorean theorem: a^2 + b^2 = c^2

a and b are the legs of the triangle. c is the hypotenuse.

Let's replace the variables with the given information we know.

The hypotenuse is 6. One of the legs is 3. the other leg is a/2.

3^2 + b^2 = 6^2

9 + b^2 = 36

b^2 = 27

b = √27 = 3√3

Since this was for half of the base, we will multiply it by 2.

3√3 x 2 = 6√3

That is our answer.

I hope this helps.

n=(K+1)^3 the remainder when the positive integer n is divided by the positive integer k, where k > 1

What is Remainder?

The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). The remaining is the name for this amount.

For instance, 10 is not precisely divisible by 3. We can calculate 3 x 3 = 9 because that is the closest value.

As a result, 10 3 3 R 1, where 1 is the remainder and 3 is the quotient.

As we are aware:
Dividend: Divisor x Quotient + Remainder
Therefore,
Dividend - Remainder (Divisor x Quotient)
The formula for the remainder is as follows.

[tex]n=(k+1)^3\\\\=k^3+3k^2+3k+1\\\\=k(k^2+3k+3)+1=(k+1)^3\\\\=k^3+3k^2+3k+1=k(k2+3k+3)+1 \\\\[/tex]

[tex]k(k^2+3k+3)[/tex] is clearly divisible by k, because 1 divided by k gives 1 as the result (since k > 1).

The remainder will be n= (K+1)^3

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By using the formula for sample size, it can be calculated that the sample size is 62

What is sample?

At first it is important to know about population.

Population is the group of items from where samples are taken for study and research and for statistical purpose

A subset of population is called sample.

Here, margin of error E = 2

Value of z for 95 % confidence interval = 1.96

Standard deviation = 8

Sample size  = [tex](\frac{1.96 \times 8}{2})^2[/tex] [tex]\sim[/tex] 62

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Answer:

Geometric Sequence

Finding the sum

The sum of the infinite geometric series 3/4 -9/16+27/64 -81/256+ ...is 3/7.

Solution:

Geometric Series Sum Formula: S = a₁/1 - r

Given: a₁ = 3/4

          a₂ = -9/16

          a₃ = 27/64

          a₄ = -81/256

1. Find the common ratio.

      a_n = a₁r ⁿ ⁻ ¹

       a₂  = a₁r ⁿ ⁻ ¹

  -9/16 = 3/4 r ² ⁻ ¹

  -9/16 = 3/4 r

2. Divide both sides of the equation by 3/4 to find r.

   -9/16/3/4 = 3/4 r/3/4

 (-9/16)(4/3) = r

       -36/48 = r

           -3/4 = r

3. Using r = -3/4, find the sum of the infinite geometric series 3/4 -9/16 +27/64 -81/256+ ...

   S = a₁/1 – r

   S = 3/4/1 – (-3/4)

   S = 3/4/1 + ¾

   S = 3/4/4/4  + 3/4

   S = 3/4/7/4

   S = (3/4)(4/7)

   S = 12/28

   S = 3/7

4. Therefore, the sum of the infinite geometric series 3/4 -9/16+27/64 -81/256+ ...is 3/7.

Definition:

     A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant while the sum of an infinite number of terms in a geometric sequence is called sum to infinity.

Code: 10.3.1.1

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Step-by-step explanation:

Answer:

Step-by-step explanation:

The word "Sum" = addition.

"A number" = the unknown, aka 'x'.

"Is equal to" is =.

Go piece by piece. I will set your equation exactly as it is worded as you read it. Follow along:

4x + (-2) = 5x + (-2)

Imagine there is a "1" infront of the parenthesis around the -2. A positive * a negative always = negative. So.

An equation to represent the value of the car after 1 year is P(t) = 80,000(1 - 0.25)¹.

An equation to represent the value of the car after t years is P(t) = 80,000(1 - 0.25)^t.

Generally speaking, a physical asset that loses its value at specific period of time represent an exponential decay. Therefore, a mathematical model for any physical asset (car) that decreases by r percent per unit of time is an exponential equation of this form:

P(t) = I(1 - r)^t

Where:

Note: 1/4 is equal to 0.25.

For a car that loses 1/4 of its value annually, after 1 year its value is given by;

P(t) = 80,000(1 - 1/4)^1

P(t) = 80,000(1 - 0.25)¹

For a car that loses 1/4 of its value annually, after t year its value is given by;

P(t) = 80,000(1 - 0.25)^t

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Answer: 25 units

Step-by-step explanation:

distance with negatives is still an addition but you have to turn the negative into a positive to get the answer.

Answer:

15%

Step-by-step explanation:

Since the problem is to find how much 69 is as a percent if 60 is 100%, we can use a rule of three, simple, direct proportion to do it:

60 = 100%

68 = x

x = 69x100/60

x = 115

That means 69 is 115% of 60, which means that the error is of:

115 - 100 = 15%

Hope this helps, have a great day! :D

Answer: A = 2(x+3y)+2z=2z+4x+2y

B=2(x+3y)=4x+2y

c=x+3y=2x+y

d=2y=x

Step-by-step explanation:

Answer:

2y=x:D

x+3y=2x+y:C

2(x+3y)=4x+2y:B

2(x+3y)+2z=2z+4x+2y

Step-by-step explanation:

D is the only possibility for 2y=x because it has 3 total. Similarly for C. B only has two different types, so it must be 2(x+3y)=4x+2y.

The slope for the first table will be;

⇒ m = - 4/3

The slope for the second table will be;

⇒ m = 1 / 4

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

There are two table is shown in figure.

Now,

For first table;

Two points are,

⇒ (x, y) = (3, -6)  (0, - 2)

Since, The slope of the line passing through the points  (x₁ , y₁) and

(x₂, y₂) will be;

⇒ m = (y₂ - y₁) / (x₂ - x₁)

Hence, Slope for first table;

⇒ m = (- 2 - (-6)) / (0 - 3)

⇒ m = (- 2 + 6) / (-3)

⇒ m = - 4/3

And, For second table;

Two points are,

⇒ (x, y) = (0, -3)  (4, - 2)

Since, The slope of the line passing through the points  (x₁ , y₁) and (x₂, y₂) will be;

⇒ m = (y₂ - y₁) / (x₂ - x₁)

Hence, Slope for second table;

⇒ m = (- 2 - (-3)) / (4 - 0)

⇒ m = (- 2 + 3) / (4)

⇒ m = 1 / 4

Thus, The slope for the first table will be;

⇒ m = - 4/3

The slope for the second table will be;

⇒ m = 1 / 4

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Answer:

red im pretty sure

Answer: your question is not very clear

Step-by-step explanation:

Answer:D is incorrect

Step-by-step explanation:

D is the only one that is incorrect because D is 9x-81

Answer:

  (d)  9(x -9)

Step-by-step explanation:

You want the expression that is not equivalent to the other three.

The simplified versions of the expressions are ...

The expression not equivalent to the other three is 9(x -9).

<95141404393>

A statement in the form p→q has three related implications that are called converse, inverse, and contrapositive.

A statement in the form p→q has three related implications.

Statement: If p then q (p→q)

Converse: If q then p (q→p)

Inverse: If not p then not q (-p → -q)

Contrapositive: If not q then not p (-q → -p)

For the given implications, its converse, inverse, and contrapositive can be written as.

Given statement:

(a)  If a quadrilateral is a parallelogram, then its opposite sides are congruent then its converse, inverse, and contrapositive are:

Converse: If a quadrilateral has opposite sides that are congruent then it's a parallelogram.

Inverse:  If a quadrilateral is not a parallelogram then its opposite sides are not congruent.

Contrapositive: If a quadrilateral has opposite sides that are not congruent then it's not a parallelogram.

(b) If two lines do not intersect, then they are parallel:

Converse: If the two lines do not intersect in the same plane, then they are parallel.

Contrapositive: If the two lines intersect in the same plane, then they are not parallel.

(c) If the sky does not look blue, then it is not nighttime:

Converse: If it is not nighttime, then the sky looks blue.

Inverse:  If the sky does not look blue then it is nighttime.

Contrapositive:  If it is nighttime then the sky does not look blue.

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The sample size should be 1843 at 99% confidence level with margin of error of 3%.

What is Inferential statistics?

By studying the samples that were drawn from the population data, inferential statistics aids in the development of a solid knowledge of the data. By utilising numerous analytical techniques, it aids in the creation of population-level generalisations.

Given, Margin of error (m) = 0.03

           z (at 99% confidence level)=2.576

We know that, Sample size(n) = (z/m)^2 p (1-p)

In order to find the sample size, we must know the value of proportion.

here, the value of proportion is missing so, in the absence of proportion, we will consider it as 0.5.

Now, we've p = 0.5

∴ Sample size = (z/m)^2 p (1-p)

                        = (2.576/0.03)^2 × 0.5 × (1-0.5)

                        = 1843 (approx).

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Answer: C

Step-by-step explanation: This is because there is no y - intercept. But since there is still a slope an x but be next to the 3/4. Which represents the rate of change.

Solving the equation 8x − 4 = 2(2x + 4) the required integer to make the equation true is 3

The integer required to be found is solved as follows

The given equation is  8x − 4 = 2(2x + 4)

solving for x

8x − 4 = 2(2x + 4)

8x - 4 = 4x + 8

collecting like terms

8x - 4x = 8 + 4

4x = 12

dividing through by 4

x = 3

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We have (123) different possibilities. Therefore, we can derive from the multiplication principle that there are 13(123) ways.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin.

The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half .

According to our question-

Let n be the maximum number of subsets of five elements that can be selected from the first 14 natural numbers,

with at least two of the five numbers being consecutive.

I have made a block of two consecutive numbers (like (1,2),(2,3),(13,14) etc.).

Now we can choose this block in 13 ways. Now we have to choose 3 numbers from the rest 12 numbers.

Hence,  multiplication principle we come to know that there are  13×(123).

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Answer:

y=4x+4

Step-by-step explanation:

slope intercept form is y=mx+b

m is slope

B is y intercept

To find slope we use y2-y1/x2-x1

16-(-4)/3-(-2)

20/5

4 is the slope

We can fill this in

y=4x+b

To find b we fill in any coordinates

-4=4(-2)+b

-4=-8+b

+8. +8

4=b

Now we can fill it in

y=4x+4

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The present age of Sesay is found as the 35 years.

For the stated question;

Let the age of Sesay five years ago be 'x'.

Then, the age of Muskam is twice of Sesay be '2x'.

The sum of their present ages after 5 years  is;

(x + 5) + (2x + 5) = 100

3x + 10 = 100

3x = 90

x = 30 (Age of Sesay 5 years ago)

Present age of Sesay = x + 5 = 30 + 5 = 35 years.

Thus, the present age of Sesay is found as the 35 years.

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If 17% of men are bald, then the probability that at most 140 in a random sample of 900 men are bald, is 0.1335.

In the given question, if 17% of men are bald, then we have to find the probability that at most 140 in a random sample of 900 men are bald.

As given that; 17% of men are bald.

So,p=0.17

Let X=Number of men that are bald

Sample size, n=900

Here X follows binomial distribution with parameters n= 900 and p =0.17

Since np≥5 and n(1-p)≥5, We can use normal approximation to the binomial with continuity correction.

So,Binomial can be approximated to normal with;

mean, μ=np

μ = 900*0.17

μ = 153

Standard deviation, σ = √np(1-p)

σ = √900*0.17*(1-0.17)

σ = √153*0.83

σ = √126.99

σ = 11.269

So, X→Normal (μ = 153, σ = 11.269)

Then, X= (X-μ)/σ

X=(X-153)/11.269

We need to find the probability that at most 140 in a random sample of 900 men are bald i.e. we need to find P(X≤140)

P(X≤140) =P(X<140+0.5)  [using continuity correction factor]

P(X≤140) =P(X<140.5)

P(X≤140) =P(z<(X-153)/11.269)

P(X≤140) =P(z<(140.5-153)/11.269)

P(X≤140) =P(Z<-1.11)  [z score rounded to 2 decimal places]

P(X≤140)  =0.1335

Hence, if 17% of men are bald, then the probability that at most 140 in a random sample of 900 men are bald, is 0.1335.

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