in a proof what is the reason that justifies this statement: segment bp is congruent to segment bp.

The area of rectangular region r is = 12.

Given:

each diagonal of r has length 5. the perimeter of r is 14.

Let l and b be the length and breadth of a rectangle.

we know that

perimeter of rectangle = 2 ( l + b )

2 ( l + b ) = 14

divide by 2 on both sides

( l + b ) = 14/2

l + b = 7

l = 7 - b

l^2 + b^2 = d^2

( 7 - b )^2 + b^2 = 5^2

7^2 + b^2 - 2 * 7 * b  + b^2 = 25

49 + 2b^2 - 14b = 25

2b^2 - 14b + 24 = 0

on solving b = 4,3

Take any one value

b = 4

l = 7 - 4

l = 3

Area of rectangle = l * b

= 4 * 3

= 12

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Ms. Cole have the 8 pieces of string.

Given,

In the question:

A number line going from 0 to 4. numbers 0, 1, 2, 3, and 4 are marked on the line. marks divide the spaces between each number into 2 equal parts. Ms. Cole has 4 yards of string. she cuts the string into pieces that are each 1 2 yard long.

To find the how many pieces of string does Ms. Cole have?

Now, According to the question:

Total yards of string = 4

Length in yard of each string = 1/2 yards

Number of pieces of string Ms. Cole has :

Total. Yards of string / length in yard of each string

=> 4 / (1/2)

=> 4 * (2 /1)

=> 8/1

=> 8 pieces of string.

Hence, Ms. Cole have the 8 pieces of string.

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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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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

We can say that there is sufficient evidence that revenue and the number of downloads are linearly related.

What is the null hypothesis?

The null hypothesis is a common statistical theory that asserts that no statistical relationship or significance exists between two sets of observed data and measured phenomena based on a single observed variable.

Hypothesis:

[tex]H_0:\rho_1=0\\H_1:\rho\neq0[/tex]

Test statistic:

[tex]t=r\times\sqrt{\frac{n-2}{1-r^2} }\\\\ t=(0.8691)\times\sqrt{\frac{30-2}{(1-0.8691)^2} } \\\\t=9.2974[/tex]

D.F. = n - 2 = 28

P-value = P-value at t = 9.2974, ∝=0.05, 28 d.f. is

        P-value = 0.000

Conclusion: Since. P-value < ∝=0.05, so we have to reject the null hypothesis.

Hence, we can say that there is sufficient evidence that revenue and the number of downloads are linearly related.

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The 90% confidence interval for the mean height of students at UH is (5.885,5.915) feet.

We have given that, an srs of 28 students at UH gave an average height of 5.9 feet and a standard deviation  of 0.1 feet.

i.e n = 28

x = 5.9 feet

s = 0.1 feet

and we have to construct a 90% confidence interval for the mean height of students at UH.

The level of significance, α = 1 - 0.9 = 0.1

The value of 0.9 in z-table is 0.816.

The formula for confidence interval is,

CI = x ± z* (s/[tex]\sqrt{n}[/tex])

Substituting the values,

CI = 5.9 ± (0.816) (0.1/√28 )

   = 5.9 ± (0.816)(0.1/5.291)

   = 5.9 ± (0.816)(0.0189)

CI = 5.9 ± 0.015

CI = 5.9 + 0.015 = 5.915

CI = 5.9 - 0.015 = 5.885

Therefore 90% confidence interval for the mean height of students at UH is 5.885 feet to 5.915 feet.

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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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Answer:

1. The GCF is 15 and the LCF is 1.

There are 4 common factors: 1, 3, 5, 15

2. The GCF and LCF is 1. This is the only common factor.

Step-by-step explanation:

To find common factors, think about what two numbers you can multiply to get the desired values. The numbers that are the same for both desired values are going to be factors.

Answer: 5.76 x 10 to the 5th

Answer: The relationship between points R , S , and T is that the sum of the RS and RT will be equal to  RT that is RT=RS+ST

Step-by-step explanation:

The result of the following: [tex]\left(\frac{\mathrm{h}}{\mathrm{g}}\right)(x)[/tex] is (x+2)/( 4x+3).

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the following function:

[tex]f(x)=x^2-8x+4;\;g(x)=4x+3;\;and\;h(x)=x+2.[/tex]

We need to find the result of the following: [tex]\left(\frac{\mathrm{h}}{\mathrm{g}}\right)(x)[/tex]

Therefore,

g(x)=4x+3

h(x)=x+2

[tex]\left(\frac{\mathrm{h}}{\mathrm{g}}\right)(x)[/tex] =(x+2)/( 4x+3)

Hence, the result of the following: [tex]\left(\frac{\mathrm{h}}{\mathrm{g}}\right)(x)[/tex] is (x+2)/( 4x+3).

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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=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

Hopes this helps please mark brainliest

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.

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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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: 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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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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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.

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: 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.

Answer: your question is not very clear

Step-by-step explanation:

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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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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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:

red im pretty sure

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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