There's a roughly linear relationship between the length of someone's femur (the long

leg-bone in your thigh) and their expected height. Within a certain population, this

relationship can be expressed using the formula h = 63. 2 + 2. 31f, where h

represents the expected height in centimeters and f represents the length of the

femur in centimeters. What is the meaning of the h-value when f = 39?

Answer: Roots are real and distinct

Step-by-step explanation:

a = +ve  b = -ve  c = -ve

determinant = +ve

if determinant is positive then roots are real and distinct

Answer:

(x + 11)² + (y - 15)² = 81

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (- 11, 15 ) and r = 9 , then

(x - (- 11) )² + (y - 15)² = 9² , that is

(x + 11)² + (y - 15)² = 81

Answer:

18.7 units

Step-by-step explanation:

In this right-angled triangle, you are provided with:

Two angles (i.e. 36° and 90°)

One side (i.e. Line AC, which is 11 units)

Line AB is known as the 'hypotenuse' of the right-angled triangle, which is what needs to be determined.

On the basis of 36° angle:

The side opposite (i.e. Line AC)  is known as the 'opposite' or 'perpendicular side'

The side adjacent (i.e. Line BC) is known as the 'adjacent' or 'base'

Trigonometric function:

The trigonometric function, which connects an angle, it's opposite side and the hypotenuse is the 'sine function':

sinФ = [tex]\frac{opposite}{hypotenuse}[/tex]

sin36° = [tex]\frac{11}{x}[/tex]

Cross-multiplication is applied:

x needs to be isolated and made the subject of the equation:

xsin36° = 11

≡ x = [tex]\frac{11}{sin36^{o}}[/tex]

∴ x = 18.7 units (Rounded off to 3 significant figures)

By using the data from the bar graph, each of the statistical value are as follows;

Median = 6.

Lower quartile = 4.

Upper quartile = 7.5.

Interquartile range = 3.5

From the information provided in the bar graph above, we can logically deduce the following data set:

Data set = {3, 5, 6, 7, 8}

Median = 6.

For Q₁ of the lower half of the data set, we have:

Lower quartile, Q₁ = {3, 5}

Lower quartile, Q₁ = (3 + 5)/2

Lower quartile, Q₁ = 8/4 = 4.

For Q₃ of the upper half of the data set, we have:

Upper quartile, Q₃ = {7, 8}

Upper quartile, Q₃ = (7 + 8)/2

Upper quartile, Q₃ = 15/2 = 7.5.

Mathematically, interquartile range (IQR) is the difference between lower quartile (Q₁) and upper quartile (Q₃):

IQR = Q₃ - Q₁

IQR = 7.5 - 4

IQR = 3.5

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The correct expansion of the given expression would be = 2x 2x²+2x (-5)+3.2x²+3• (-5). That is option C.

The given expression of equations;

(2x + 3)(2x² - 5). That is the product of 2x+3 and 2x²-5

= 2x *2x² + 2x*(-5) + 3*2x²+3×(-5)

= 4x³ - 10x+ 6x²-15

= 10x⁵ -10x-15.

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Answer:c

Step-by-step explanation:

did it

The required 2 properties to describe the relationship between DE and AC are  1. DE || AC and 2. DC = AC / 2.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
From the figure,
AD = BD and BE = EC

It implies that D and E are the midpoints of the side AB and BC,
So, 1. for the given triangle line joining the midpoints of the triangle always parallel to the third side of the triangle.
DE || AC

And when DE || AC then the measure of DE is equal to half of the measure of AC.
DC = AC / 2

Thus, the required 2 properties are 1. DE || AC and 2. DC = AC / 2.

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The best way is to use the Ratio Test to see that the series = ∑∞ₙ₋₁ n/5ⁿ converges.

In mathematics, convergence definition is the property (some described by myriad series and functions) that it approaches its limit more and more distinctly as the arguments (variables) of the function increase or decrease, or as the number of terms in the series increases.

For example, the function y = 1/x converges to zero as x increases. Even in this case, the final value of x doesn't affect the value of y to actually be zero, and the marginal value of y is zero, since y can be made arbitrarily small by choosing a large enough "x". The line y = 0 (x-axis) is known as the asymptote of the function.

According to the Question:

Let aₙ= n/5ⁿ. If  lim(n→∞)

|an+1|/ |an| <1, the Ratio Test will imply that  

∑∞ₙ₋₁ aₙ = ∑∞ₙ₋₁ n/5ⁿ converges.

Now,

aₙ₊₁ = n + 1/ 5ⁿ⁺¹

    = n + 1 /5.5ⁿ.

Therefore,

since these terms are positive,

    |aₙ₊₁|/|aₙ| = n + 1 /5⋅5ⁿ

⇒ n +1/ 5ⁿ → 1/5 as n→∞

Hence,

∑∞ₙ aₙ = ∑∞ₙ₋₁ n/5ⁿ converges.

Full Question:

How do you test the series (n/5ⁿ ) from n = 1 to infinity for convergence? Determine the values of all positive, for which the series. Determine the values of all positive k for which the series. Express your answer in interval notation will converge. Express your answer in interval notation.

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Answer:

16 = 3x

Step-by-step explanation:

We are here given a equilateral triangle in which each side length measure is " x " .

By perimeter we mean the sum of all the side lengths of the figure.

By question , we have each side length as x ,

So its perimeter would be ,

x + x + x = 3x

But it is given that the perimeter is 16in . So they must be equal .

Hence our required equation is ,

16 = 3x

and if we want to solve out for x , divide both the sides by 3 ,

x = 16/3

and we are done!

a) Sample mean is arithmetic average of data values. The sample mean of provide data values is 10.

b) The five-number summary of the sample is minimum = 4, Q1 = 4.5, median = 9 , Q3 = 15.5 and maximum= 16.

The population mean is denoted by greek letter, μ and sample mean is a random variable; which is written as x-bar and x-bar stands for individual values it takes. The sample mean is a statistic measure obtained by calculating the arithmetic mean of sample values ( values of variable in sample). The sample mean formula is: x-bar = ( Σxᵢ) / n

Now, we have to calculate sample mean of following data values, 12,8,15,16,5,4.

Sum of values, Σ xi = 12 + 8 + 15 + 5 + 4 + 16 = 60

Number of values = 6

So, Sample mean, = ( Σ xi ) / n = 60/6 = 10

The five-number summary includes following :

So, Steps to determine the five-number summary:

Now, the sample set is 12,8,15,16,5,4. Arrange the data values in ascending order, 4,5,6,12,15,16. So, Minimum value

= 4 , Maximum value = 16 ,Median = mean of 6 and 12 = (6 + 12)/2 = 9. The vales written as(4, 5, ) 6, 12, (15, 16 ). The value of first quartile, Q₁ = median of lower ( 4,5) = (4+5)/2

= 9/2 = 4.5. Similarly, Third quartile, Q₃

= (15+16)/2= 31/2 = 15.5. Thus, the five-numer summary is minimum = 4, Q₁

= 4.5, median = 9 , Q₃ = 15.5 and

maximum = 16.

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Complete question:

Consider the sample set 12,8,15,16,5,4 and answer the below questions:

(a)[2 pts] what is the notation of the sample mean? find the sample mean.

(b)[3 pts] find the five-number summary of the sample.

Answer:

Step-by-step explanation:

Based on the information in the tape diagram and table, we can see that the ratio of oil to vinegar in Iara's salad dressing is 8 to 1. This means that for every 8 spoonfuls of oil, she uses 1 spoonful of vinegar.

To calculate the amount of oil and vinegar in the dressing, we can use the following formula:

amount = original ratio * total amount of dressing ÷ (original ratio + 1)

For the oil, the formula would be:

oil amount = 8 * 33 ÷ (8 + 1) = 8 * 33 ÷ 9 = 88 spoonfuls

And for the vinegar, the formula would be:

vinegar amount = 1 * 33 ÷ (8 + 1) = 1 * 33 ÷ 9 = 11 spoonfuls

So the final answer is:

Oil: 88 spoonfuls

Vinegar: 11 spoonfuls

Answer:

6

Step-by-step explanation:

Let x be the vertical height

area of triangle=1/2×6×6=18

1/2×3×x=18/2

1.5x=9

x=6

We have 72-tenths left.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters.

To divide 80 tenths by 9 ones, we first convert the 9 ones to tenths. 9 ones is equivalent to 90 tenths.

Next, we divide 80 by 90:

80 / 90 = 0.8888... (rounded to four decimal places)

To multiply, we multiply 0.8888... by 9:

0.8888... * 9 = 8

Finally, to subtract, we subtract 8 from 80:

80 - 8 = 72

So, we have 72-tenths left.

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It is not possible to determine the probability of survival on the second try if the cylinder is not spun, as the outcome of the first try has no bearing on the outcome of the second try if the cylinder is not spun.

The cylinder serves to randomly distribute the bullet among the chambers, so if the cylinder is not spun, the bullet will remain in the same chamber, and the outcome of the second try will be determined by the initial placement of the bullet in the cylinder.

In a typical scenario where a revolver with a single bullet is used, the probability of survival on the first try is 1/6, and the probability of survival on the second try (assuming the cylinder is spun) is also 1/6. However, without spinning the cylinder, the outcome of the second try is fixed and cannot be determined probabilistically.

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The value of the expression for the given condition is 4.2.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's bis as follows:

Expression: (Math Operator, Number/Variable, Math Operator)

Given expression,

0.7d - 2.1f

and d = 15, f = 3

substitute the values,

0.7d - 2.1f

=> 0.7(15) - 2.1(3)

=> 10.5 - 6.3 = 4.2

Hence the value of the expression is 4.2.

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Answer:

-67

Step-by-step explanation:

- 203 - (-136)

The 2 minuses cancel out each other, turning it into a plus sign.

-203 + 136 = -67

Basic addition

Step-by-step explanation:

Because there is a double negative in between 203 and 136 that would turn into a positive

So

-203+136

Now because 203 is negative you would take 203 and subtract 136 to get 67

Because 136 is less then 203 it would still be negative

So

The answer is -67

Liters of water (w) it would take to water 40 flower pots, if it took 9 liters of water to water 24 flower pots when assuming same amount of water is used on each pot is 15.

Therefore the answer is 15.

To find the amount of water Vito would need to water 40 flower pots, we can use the following formula:

w = (9 liters) * (40 pots) / (24 pots)

Simplifying:

w = 15 liters

So, Vito would need 15 liters of water to water 40 flower pots, assuming he uses the same amount of water on each pot.

--The question has some errors, answering to the question below--

"Vito uses 9 liters of water to water 24 flower pots. He is wondering how many liters of water (w) it would take to water 40 flower pots. He assumes he'll use the same amount of water on each pot."

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Answer:

two plus two equals five

Step-by-step explanation:

The maximum amount of space that the teacher can reserve on her bulletin board using the 40-inch long roll of string is 400 square inches.

A rectangle is a two-dimensional shape with four sides and four right angles. It is characterized by having two equal sides that are parallel to each other and two equal sides that are perpendicular to the first two sides.

First, let's consider the perimeter of the rectangle. The perimeter is the total length of the four sides of the rectangle.

So, if we use the entire 40-inch long roll of string to form the border, it will equal the perimeter of the rectangle. We can represent the length and width of the rectangle using variables "l" and "w", respectively.

The perimeter of the rectangle can be calculated using the formula: P = 2l + 2w.

Now, we can set the perimeter equal to 40 inches and solve for l and w.

P = 40

2l + 2w = 40

l + w = 20

Next, we want to find the maximum area of the rectangle. The area of a rectangle can be calculated using the formula: A = l * w.

So, to find the maximum area, we need to maximize the product of l and w. This can be done by setting l and w equal to half of the perimeter, or 20 inches each.

l = w = 20

A = l * w

A = 20 * 20

A = 400 square inches

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Answer:

141

Step-by-step explanation:

First, you need to identify the pattern. As we have 3 terms, the pattern is +18 then +30. So, we can determine the next term is +18. 75 + 18 = 93. 93 is the 4th term. We can also determine the next term is +30. 93 + 30 = 123. 123 is our 5th term. Based off of what we know, we can determine the next term will be +18. 123 + 18 = 141. This proves our 6th term is 141.

I hope this helped. If this isn't correct, I apologize. This is based off of the 3 terms shown. If this helped, leave a heart and leave stars.

Her average speed for the entire trip, in kilometers per hour, is equal to 2d / (7.1 * 3600) * 3600 km/h

Let's assume that the total distance of the round trip is d kilometers and that she drove at a constant speed of v km/h for the entire trip. The time it takes for her to travel the entire distance at speed v is given by t = d/v.

Since she drove back home using the same path she took out to the university, her average speed for the entire trip must be equal to her speed on the way out and back. Therefore, the total time it took for her to complete the round trip is 2t = 2d/v.

Since the total time it took for her to complete the round trip is 7.1 hours, we can set up an equation:

2d/v = 7.1 hours

Converting hours to seconds and solving for v, we have:

v = 2d / (7.1 * 3600) km/s

Finally, converting to km/h, we get:

v = 2d / (7.1 * 3600) * 3600 km/h

Therefore, her average speed for the entire trip, in kilometers per hour, is equal to 2d / (7.1 * 3600) * 3600 km/h

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It should be noted that the amount based on the information will be $1600.00.

From the information, the state government gives property owners a tax rebate with the anticipation that each property owner will spend approximately p% of the rebate, and in turn each recipient of this amount will spend p% of what he or she receives, and so on.

We've been given the rebate as well.

Sum of an infinite Geometric Series = A/(1-r)  

Rebate A $400.00

Rate 75.00%

Sum of an infinite Geometric Series = $400/(1-75%)

= $1600.00

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Based on the Tuesday rate, $100 United States dollars is equal to 843.64 French francs.

1. From the tables, the Tuesday rate is 0.119 US dollars to 1 French franc.

2. To find the exchange rate, multiply the number of US dollars by the exchange rate: 100 x 0.119 = 11.90.

3. To find the amount in French francs, divide the US dollars by the exchange rate: 11.90 / 0.119 = 843.64 French francs.

Therefore, $100 United States dollars is equal to 843.64 French francs based on the Tuesday rate.

At the Tuesday exchange rate, one hundred United States dollars is equal to eight hundred and forty-three point sixty-four French francs. This means that for every one hundred US dollars, you can get eight hundred and forty-three point sixty-four French francs in exchange.

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Answer:

Step-by-step explanation:

To correct the error, Lonnie should write 3 3/4 instead of three and three over four.

A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers. In a fraction, the top number is referred to as the numerator, while the bottom number is referred to as the denominator.

Here,

Lonnie has made a mistake in writing the number of packages of pasta. The correct way to write the amount of pasta is 3 3/4 packages. The fraction 1/3 of a fourth package of pasta means that Lonnie has 1/3 of the fourth package and the three whole packages, making it a mixed number, which is a whole number and a fraction combined. To correct the error, Lonnie should write 3 3/4 instead of three and three over four.

Thus, to correct the error, Lonnie should write 3 3/4 instead of three and three over four.

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A. The linear relationship can be expressed by the equation, 3y = 5x + 10

B. For  25 kg, the height is 45 cm

   For  52 kg, the height is 90 cm

C. For 60 cm, the mass is 34

    For 80 cm, the mass is 46

The equation of a straight line is a relationship between x and y coordinates, The two point form of the equation of a straight line is,

y-y₁ =  (y₂-y₁)/(x₂-x₁)*(x-x₁)

Given that,

The scatter plot,

which shows the linear relationship,

And passes through the points,

(10, 20), (40, 70)

the equation of line can be written as,

y - 20 =  (70-20)/(40-10)*(x-10)

y - 20 = 50/30*(x-10)

y - 20 = 5/3*(x-10)

3y - 60 = 5x - 50

3y = 5x + 10

A. The linear relationship,
3y = 5x + 10

B.    If x = 25, we can substitute this value into the equation to find the corresponding value of y:

3y = 5 x 25 + 10

3y = 125 + 10

3y = 135

Dividing both sides of the equation by 3:

y = 45

So, if x = 25, then y = 45.

similarly,  the value of y for x = 25 is, 90

In the same manner,

when,

For y = 60 x will be 34

And for y = 80 x will be 46

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It's impossible to say Sean should base his decision on the marginal cost and marginal benefit of creating another table. The marginal cost of making a table is not the same as the average cost of making a table. As a result, there is insufficient information to determine what Sean should do.

The opportunity cost of an activity is the value of what must be sacrificed in order to engage in the activity (plus the cost). A cost that cannot be recovered at the time a decision must be made.

The science of decision-making is often used as a crude definition of economics. This stems from the fact that economics is frequently concerned with making the best decision in the most efficient manner. One way to quantify this is to consider total costs and total benefits.

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so your problem is 2x+y=18 and y=4x+6

solution

solve for the first variable in one of the equations then substitute the result into the other equation

point form:

(2,14)

equation form

x=2, y=14

Option A is the correct answer. The expression is (x+3)(x+7).

The given equation is x²+10x+21

we have to find the roots of the equation

x²+10x+21 =0

x²+3x+7x+21

x(x+3)+7(x+3)

(x+3),(x+7)

Now, we need to remember to factorize the given expression, x²+10x+21, and have to choose two numbers when you add them you get "10" and when you multiply them you get "21".

These numbers are:

7 and 3

Because:

7+3=10

7*3=21

Therefore, you get that the factorization of the expression  is the following:

(x+3)(x+7)

We can conclude that this factorization matches the first option.

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Answer:

a) See attached image

b) AA (or AAA) similarity; either one is correct

c) The statue is 22 meters tall

Step-by-step explanation:

Let's assume the height of the statue is h (to be determined)

a) First let's create a diagram to model this scenario. See attached image
 One of the properties of a mirror reflection is that the angle of incidence i.e. the angle at which light strikes the mirror = angle of reflection i.e. the angle at which the light reflects off the mirror

These angles are shown as α and β in the diagram

The two triangles we choose to solve this problem are
ΔABC and ΔCED

Given that ∠BCA is a complementary angle to angle of reflection and ∠ECD is complementary to the angle of incidence, it follows that

m∠BCA = m∠CED

m∠BAC of ΔABC = m∠ECD of ΔECD = 90°

Therefore the third angles of both triangles are also equal

b) By the AA (or AAA) or Angle-Angle Similarity theorem, the two triangles are similar

Therefore the ratio of the sides must be the same for corresponding sides

Therefore
[tex]\dfrac{AB}{DE} = \dfrac{AC}{CD} \\\\Given AD = 12, CD = 3\\\\\dfrac{AD}{CD} = \dfrac{12}{3}= 4\\\\\therefore \\\\\dfrac{AB}{ED} = 4\\\\[/tex]

Since ED is the height of the girl = 5.5 meters and AB = height of the statue = h

we get
[tex]\dfrac{h}{5.5} = 4\\\\h = 4 \times 5.5\\\\h = 22\\\\[/tex]

Answer (c) height of statue = 22 meters

The best prediction of the number of tagged salmon in a sample of 2000 is 100.

The best prediction of the number of tagged salmon in a sample of 2000 returning salmon can be estimated using the proportion of tagged salmon in the sample of 400.

The proportion of tagged salmon in the sample of 400 is [tex](\frac{20}{400} )=(\frac{1}{20} )[/tex].

We can use this proportion:

To estimate the number of tagged salmon in a sample of 2000:

Tagged salmon in a sample of 2000 = [tex](\frac{1}{20}) * 2000[/tex] = 100

Therefore, the best prediction of the number of tagged salmon in a sample of 2000 is 100.

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