Dilations and Partitions
A segment AB is partitioned as shown.
A
P
Complete the statement.

Based on the complete question, the Normal Distribution Graph will resemble the one in the figure attached.  

Also, note that using the 68-95-99.7 rule, the proportion of runners between 48.7 and 67.9 kg is 0.8385.

The 68-95-99.7 rule, also known as the empirical rule, is a statistician's shorthand for remembering the percentage of values in a normal distribution that fits within an interval estimate: 68%, 95%, and 99.7% of the variables lie within one, two, and three standard deviations of the mean, correspondingly.

To compute the proportion of runners whose body weight is between 48.7 and 67.9 kg with the help of the 68-95-99.7 rule:

We know given that:

The mean = 63.1 and

the standard deviation (SD) = 4.8.

Where the weight is 67.9kg, we know that the distance between this and the mean is 4.8, that is;

67.9 - mean

= 67.9 - 63.1

= 4.8 [1*SD]

In the same way,
48.7 corresponds to 48.7-63.1 = -14.4 [ -3*SD]

Hence, based on the rule,

= 83.85%

= 0.8385.

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Full Question:

A study of elite distance runners found a mean body weight of 63.1 Kilograms (kg), with a standard deviation of 4.8kg.

The time that both gongs will strike together again after striking simultaneously at 12 noon is 2 : 34 pm.

The time the gongs will strike together again can be determined by calculating the least common multiple of 22 and 77. The multiple of a number is the product of a number and another number. For example, a multiple of 2 is 10. The least common multiple is the smallest multiple that is common to two or more numbers.

The least common multiple would be determined using the prime factorisation method.

Prime factors of 22 = 2 x 11

Prime factors of 77 = 7 x 11

The least common multiple = 2 x 7 x 11 = 154

The next time both gongs would strike at the same time is 154 minutes or 2 hours 34 minutes

12 noon + 2 hours + 34 minutes = 2 : 34 pm

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The variable y has a value of 72 when x equals 9

The variation statement is given as

x and y are in direct proportion

This means that

y = kx

Where k represents the constant of variation

Using the values given from the question, we have

(x, y) = (7, 56)

This gives

56 = 7k

Divide both sides by 7

k = 8

So, we have

y = 8k

The value of y when x = 9 is calculated as

y = 8 * 9

Evaluate the products

y = 72

Hence, the value of y is 72

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The original price of the sweater is $48.

Given that, Kate used a 30% off coupon to purchase a sweater.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The cost of sweater is $33.60

Let the original price of the sweater be x

Now, x-30% of x=33.60

⇒ x-30x/100 = 33.60

⇒ x -3x/10 =33.60

⇒ 7x/10 =33.60

⇒ 7x=336.0

⇒ x=48

Therefore, the original price of the sweater is $48.

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Answer: Following the pattern, the prediction for the next numbers is as follows:

Confirmation by calculator use:

Therefore the predicted numbers are the correct one.

Answer:

$43071

Step-by-step explanation:

Commission = 5.6%

So $2,412 represents 5.6% of total value of sold vacation packages

Image the numbers as ratios:

$2,412 : 5.6%

X : 100%

To get from 5.6% to 100% you can divide by 5.6 and then multiply by 100

So to find X you do:

(2,412 / 5.6)*100 = 43071.428…

Now round the answer to nearest dollar:

43071.428… = $43071 (to nearest dollar)

The total number of pages in the book is 180.

Total number of pages:

It refers the number of pages in the prescribed book.

And if we want to find the total number of pages, then we have to add the read pages and the remaining pages.

Given,

Jimmy read 2/15 of a book on Monday, 1/3 on Tuesday, 2/9 on Wednesday and 3/4 of the remainder on Thursday. If he still had 14 pages left to read on Friday.

Here we need to find the total number of pages in the book.

Let us consider x be the number of pages in the book.

The portion of book read by Jimmy on Monday is 2/15

The portion of book read by Jimmy on Tuesday is 1/3

The portion of book read by Jimmy on Wednesday is 2/9

The portion of book read by Jimmy on Thursday is 3/4

And the remaining pages to read on Friday is 14

So, the total of all is:

=> x (2/15 + 1/3 + 2/9)

=> x (6 + 15 + 10)/45

=> 31x/45

So, for Thursdays, he reads 3/4 of the remainder of the book.

He has (1 - 31/45)x left that is 14x/45.

So, he reads 3/4 of this; which is

=> 3/4(14x/45) = 42/180x.

Therefore, until Thursday he has read

=> 31/45x + 42/180x.

We know that here 180 would be a common denominator;

Now we have to convert these fractions,

Then we have,

124/180x + 42/180x = 166/180x

Up to this point, he has 14 pages left;

Therefore, this means he has read 14 pages less than x, the total number of pages.

Then the given equation is written as,

166/180x = x-14

0 = 14/180x - 14

Adding 14 to each side gives us, then we get,

14 = 14/180x

14(180)/14 = x

180 = x

Therefore, there are 180 pages in the book.

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Answer: You can only bring 5 people maximum.

Step-by-step explanation:

1) Set up the equation

(>= greater than or equal to)

134.50 >= 24x +14.5

We set up the equation here with 24x as x is the amount of people. 14.5 is the starting value as it never changes. 134.50 is the amount that they can't overspend.

2) Solve the equation

134.50 >= 24x +14.5

120>= 24x

5>= x

3) Solve

You can only bring 5 people maximum.

Answer:$9.695

Step-by-step explanation:

1/4 is 0.25 so this means Allison is paying 25% of the bill. Then all you have to do is times 38.78 with 0.25 and you get $9.695 or $9.70.

Answer:

$9.70

Step-by-step explanation:

You can do this question several way on a calculator:

1/4 × 38.78

OR

.25 × 38.78

OR (I like this one)

38.78 ÷ 4

All these calculations will give you the result 9.695

Since this is a real-world money problem, we would round this number to 9.70.

Allison paid $9.70.

Answer:

8v - 42

Step-by-step explanation:

Distributive property: a* (b + c) = (a*b) + (a*c)

3(4v - 6) - 4(v + 6) = (3*4v) + (3*(-6) ) + (-4*v + (-4)*6) )

                             = 12v - 18 - 4v - 24

                              = 12v - 4v - 18 - 24

Combine like terms [ 12v & (-4v) ] and combine constants [ (-18) & (-24)]

                             = 8v - 42

a) The mean of this distribution is 7 min

b) The standard deviation is 4.0414 min

a) The mean is the midpoint between the ends or 7 min

variance is (b-a)^2/12 or 196/12 or 16.3333 min

b) standard deviation is sqrt(V)= 4.0414 min

the complete question is

a bus comes by every 14 minutes. the times from when a person arives at the bus stop until the bus arrives follows a uniform distribution from 0 to 14 minutes. a person arrives at the bus stop at a randomly selected time. round to 4 decimal places where possible.

a) The mean of this distribution is

b) The standard deviation is

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Answer: 1.c   2.a   3.c

Step-by-step explanation:

Answer:

first picture

1 and 2 are congruent because they are a pair of corresponding angles

second picture

A = B

This is because they are alternate exterior angles and they equal the same thing

third picture

angle 5

it is also an alternate interior angle

The mistake is that, what we have to prove is taken as a known fact.

A theorem is a statement that can be proved or has already been proved true by a logical argument.

"there is no smallest negative integer" is taken as a fact

but it is the part of the theorem that we have to prove,

Therefore, we can conclude that the mistake in the given proof is what we have to prove is taken as a known fact.

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Answer:

five blocks away

Step-by-step explanation:

because 4 +1 =5

please if it is wrong let me know so I can correct

The answer to the given expression 2⁴· [(2²·2⁴)⁻³/2¹⁴] would be 2⁻²⁸ which is determined by the laws of the exponents.

The product rule is an exponent rule that states that when you multiply similar bases, the add exponents.

For example, (a²)·(a³) = a²⁺³ = a⁵

In the power rule, elevating one exponent to a second multiplies the exponents.

For example, (a²)³ = a²ˣ³ = a⁶

The given expression would be as

⇒ 2⁴· [(2²·2⁴)⁻³/2¹⁴]

As per the laws of the exponents, the solution would be as :

⇒ 2⁴· [(2²⁺⁴)⁻³/2¹⁴]

⇒ 2⁴· [(2⁶)⁻³/2¹⁴]

⇒ 2⁴· (2⁻¹⁸/2¹⁴)

⇒ 2⁴· (2⁻¹⁸⁻¹⁴)

⇒ 2⁴· (2⁻³²)

⇒ 2⁴⁻³²

⇒ 2⁻²⁸

Therefore, the answer would be 2⁻²⁸.

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Answer:

5x-8

Step-by-step explanation:

7x-14-2x+6

-14+6=-8

7x-2x=5x

Answer:

Step-by-step explanation:

ŷ = − 2.6s + 1.1.

residual value = Measured value - Predicted value

Measured value = actual y-coordinate of the point, y

Predicted value = value of y from the equation, y1

residual value = (actual y-coordinate of the point, y) - (value of y from the equation, y1)

residual value = y - y1

For s = 1.3

     y  = 1.2

value of y from the equation, y1:

y1 = -2.6*(1.3) + 1.1

y1 = -3.38 + 1.1

y1 = -2.28

residual value = y - y1

residual value = 1.2 -  -2.28

residual value = 1.2 + 2.28

Since the predicted value is far less than the observed value, the line of best fit underpredicts the temperature change.

Answer:

3.48; The line of best fit underpredicts the temperature change.

Step-by-step explanation:

i took the test :)

The notebook's length in centimeters is 27.94 cm.

Since we are provided that

The  desk's width is 25 inches.

Convert into cm.

There is a stated measurement of 25 inches = 63.5 cm.

As previously stated, a measurement in inches differs directly from a measurement in centimeters.

As a result, we have said that

If the notebook's length is 11 inches

Let 'x' be the length of the notebook in cm.

As a result of the question,

[tex]\frac{25}{63.5} = \frac{11}{x}[/tex]

[tex]x=\frac{698.5}{25}[/tex]

x = 27.94 cm

Hence the length of note book is 27.84 cm.

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Answer:

2x44/7

Step-by-step explanation:

Answer:

Step-by-step explanation:

well it very confusing to some but,...31.7142857143 and i don't know the other one :) ;).

Answer:

Step-by-step explanation:

There are 9 squares filled halfway, and 5 squares filled completely.

9 x 0.5 = 4.5

4.5 + 5 = 9.5

There are 25 squares in the shape.

9.5  / 25 = 0.38

38% of the square is shaded.

the product of negative 1/3 ⁵⁰

The expression is :

Since the product of negative to negative is positive

and negative x negative x negative = negative

Thus, if we multiply the negative upto odd number times the resultant will be negative

if we multiply the negative upto even number times the resultant will be positive

In the given expression we multiply (-1/3) upto 50 times

50 is the even number so the the resultant value will be positive

Answer : Positive

becasue if we multiply the negative upto odd number times the resultant will be negative & if we multiply the negative upto even number times the resultant will be positive

Answer:

Step-by-step explanationFrom your home, the route to the store tat passes the beach is 2 miles shorter than the route to the store that passes the park. What is the length of each route.:

Answer: y = -3x - 2

Step-by-step explanation:

slope intercept form: y=mx+b

Rounding off to nearest ten thousand gives the most accurate answer as 240,000 cans.

Given that, the number of cans collected during September = 32,537 and the number of cans collected during October = 207,492.

Rounding numbers means adjusting the digits (up or down) to make rough calculations easier. The result will be an estimated answer rather than a precise one.

a) Now, the number of cans were collected during September and October = 32537+207492 = 240,029

To the nearest thousand is 240,000

b) Rounding 32,537 to the nearest thousand is 32000 and rounding 207,492 to the nearest thousand is 207,000

Sum = 32000+207000 = 239,000

Rounding 32,537 to the nearest ten thousand is 30000 and rounding 207,492 to the nearest ten thousand is 210,000

Sum = 30000+210,000 = 240,000

Therefore, rounding off to nearest ten thousand gives the most accurate answer as 240,000 cans.

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Answer:

Let b represent the number of hours babysitting, and let l be the number of hours landscaping. We have this system of equations:

[tex]7b + 8l = 134[/tex]

[tex]b = l + 2[/tex]

The value of k is -1 of tangent over the parabola.

Equation of a line: y = (2 + x - k) ÷ 2, in line form of y = mx + c.

Equation of the parabola: x² = (y - 6x - 3) ÷ 2

Given,

y = (x ÷ 2) + (1) - (k ÷ 2)

where, m = 1 ÷ 2 and c = (1 - k) ÷ 2

For parabola equation in parabola form,

y = 2x² + 6x - 3

y = 2(x² + 3x - n) - 3

n = (b ÷ 2)²

n = (6 ÷ 2)²

n = 9

y = 2(x² + 3x - 9 + 9) - 3

y = 2(x² + 3x + 9) - 9 - 3

y = 2(x² + 3x + 9) - 12

y = 2(x + 3)² - 12, Hence the parabola equation is in vertex form.

Now, comparing the above vertex form with the parabola equation,

x² = 4ay

(x + 3)² = (y ÷ 2) + 6

where a = 1 ÷ 2

Now using the condition of tangency c = a ÷ m

c = (1 - k) ÷ 2

m = 1 ÷ 2

a = 1 ÷ 2

(1 - k) ÷ 2 = (1 ÷ 2) ÷ (1 ÷ 2)

1 - k = 2

k = -1

Therefore, the value of k is -1.

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