Below are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both the number of births x per one thousand people in the population and the female life expectancy y (in years) are given.
Birthrate, x Female life expectancy, y
15.2 72.1
45.8 58.0
18.6 71.6
35.2 66.0
23.9 74.1
39.5 64.8
16.2 74.6
49.9 55.5
50.3 60.0
25.7 72.3
50.8 58.9
31.8 62.7
The value of the sample correlation coefficient r for these data is approximately -0.935. Answer the following. Carry your intermediate computations to at least four decimal places, and round your answers as specified below.
a). What is the value of the slope of the least-squares regression line for these data? Round your answer to at least two decimal places.
b). What is the value of the y-intercept of the least-squares regression line for these data? Round your answer to at least two decimal places.

Answer:

B

Step-by-step explanation:

Two negatives is a positive, and you want your outcome to be a positive x, therefore b is the correct answer.

Answer:

second one

A negative multiplied by a negative is a positive.

- (-x) is multiplication.

The circulation of the vector field G = xy i + z j + 3y k around a square centered at the origin and lying in the yz-plane, with a counterclockwise orientation from the positive x-axis.the total circulation of G around the square is 3(s^2/8).

To evaluate the circulation, we need to compute the line integral of G along the boundary of the square. The square lies in the yz-plane and is centered at the origin, with side length s. Since the square is oriented counterclockwise from the positive x-axis, its boundary can be parametrized as follows:

Top side: r(t) = (0, t, s/2), for t ranging from -s/2 to s/2.

Right side: r(t) = (0, s/2, t), for t ranging from s/2 to -s/2.

Bottom side: r(t) = (0, t, -s/2), for t ranging from s/2 to -s/2.

Left side: r(t) = (0, -s/2, t), for t ranging from -s/2 to s/2.

Next, we calculate the dot product of G and the tangent vector along each side of the square, and then integrate over each side. The circulation is given by the sum of these line integrals. The dot product of G and the tangent vector along each side simplifies to the following:

Top and bottom sides: G · dr = (t)(dy) + (3y)(dz) = (t)(dt) + 3y(dy) = t dt + 3yt dy.

Right and left sides: G · dr = (3y)(dy) = 3y dy.

Integrating over each side, we find:

Circulation along the top and bottom sides = ∫(t dt + 3yt dy) = 0 (since the integral of t dt over a symmetric interval is zero, and y(dy) is zero at the endpoints).

Circulation along the right and left sides = ∫(3y dy) = 3 ∫(y dy) = 3(y^2/2) evaluated from -s/2 to s/2 = 3(s^2/8).

Hence, the total circulation of G around the square is 3(s^2/8).

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The ratio of the probability of flipping a tail to the probability of flipping a head when the probability of getting three heads is the same as the probability of getting exactly two tails in three flips is 1/3.

Let p be the probability of flipping a head and q be the probability of flipping a tail.

The probability of getting three heads in three flips is \((p)^3.\)

The probability of getting exactly two tails in three flips is 3pq².

Given that these probabilities are equal, we have:

\((p)^3\)= 3pq²

Simplifying this equation gives:

p = 3q

Dividing both sides by q gives:

p/q = 3

Therefore, the ratio of the probability of flipping a tail to the probability of flipping a head is 1/3.

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Answer:

18x4-30x3+66*2-40x+56

Step-by-step explanation:

( 6 x 2 + 8 ) ( 3 x 2 − 5 x + 7 ) Expand ( 6 x 2 + 8 ) ( 3 x 2 − 5 x + 7 ) by multiplying each term in the first expression by each term in the second expression. 6 x 2 ( 3 x 2 ) + 6 x 2 ( − 5 x ) + 6 x 2 ⋅ 7 + 8 ( 3 x 2 ) + 8 ( − 5 x ) + 8 ⋅ 7 Simplify terms. Tap for more steps... 18 x 4 − 30 x 3 + 66 x 2 − 40 x + 56

Answer: x = 6

Step-by-step explanation:

(7x+3)+85+50 = 180

(7x+3)+135 = 180

7x+3 = 180 - 135 = 45

7x = 45-3 = 42

x = 42 / 7 = 6

x = 6

Answer:

Step-by-step explanation:

milk: 3 *\(\frac{14}{15} = \frac{14}{5}\) ;

flavors: 3*\(\frac{1}{15} = \frac{1}{5}\);

The amount of milk is (14/5) and the quantity of flavours will be 1 / 5 litre.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that the vanilla milkshake is made by mixing milk and flavours in a ratio of 14:1 . The quantity required to make 3 litres of the milkshake will be calculated as,

Ratio = 14: 1

Let the constant term between the ratio is x. From the equation,

14x + x = 3

15x = 3

x = 1 / 5

The quantity of milk = 14x = 14 x (1/ 5 ) = 14 / 5 liters

The quantity of flavors = x = 1 / 5 liters

Therefore, the amount of milk is (14/5) and the quantity of flavours will be 1 / 5 litre.

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The required values are x = 12 and y = -3 solution to the given system of equations.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The system of equations is given as:

2x + 7y = 3 ....(i)

x = -4y    ....(ii)

Substitute the value of x = -4y in the equation (i), and solve for y

2( -4y) + 7y = 3

-8y + 7y = 3-y = 3

y = -3

Substitute the value of y = -3 in equation (ii), and solve for x

x = -4(-3)

x = 12

Thus, the solutions are x = 12 and y = -3.

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Answer:

A is 1/2 and the answer for B is 2/3

The expression equal to the given expression is \(\frac{y^{20} }{z^{20} }\) . The solution has been obtained by using exponents.

What is an exponent?

Exponents, which are used to express numbers, reveal a number's multiplicity. For instance, the term 2³ represents multiplying the number 2 three times. The number has been raised to 2 * 2 * 2. Exponents are also referred to as a number's power. You can use a decimal, whole number, fraction, or even a negative value.

We are given an expression as \((\frac{y^{-2}z^{7}}{z^{-3}y^{8} } )^{-2}\) .

Now, we know that base with power to power are multiplied.

So, we get

⇒ \(\frac{y^{4}z^{-14}}{z^{6}y^{-16} }\)

Now, powers having same base are added.

So, from this we get,

⇒ \(\frac{y^{4 + 16}}{z^{6 + 14} }\)

⇒ \(\frac{y^{20} }{z^{20} }\)

Hence, the expression equal to the given expression is \(\frac{y^{20} }{z^{20} }\) .

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a) 100%
b) 19/50 or 38%

Answer: a= (4x-1)(6x+9)

Step-by-step explanation:

area= length x width

Answer:

below

Step-by-step explanation:

24 x 2 + 30 x − 9

Using the properties of trigonometric functions, we can find the exact value of the expression tan 25º and cot 25º. The exact values are tan 25º = √3 - 2 and cot 25º = 1/(√3 - 2).

To find the exact value of tan 25º, we can use the tangent function's property: tan(x) = sin(x)/cos(x). We know that sin 25º = √3/2 and cos 25º = 1/2. Therefore, tan 25º = sin 25º / cos 25º = (√3/2) / (1/2) = √3 - 2.

To find the exact value of cot 25º, we can use the cotangent function's property: cot(x) = 1/tan(x). Since we already found tan 25º = √3 - 2, we can substitute it into the cotangent expression: cot 25º = 1 / (√3 - 2) = 1/(√3 - 2).

So, the exact value of tan 25º is √3 - 2, and the exact value of cot 25º is 1/(√3 - 2).

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The probability that a card drawn at random from an ordinary deck of 52 playing cards is: (a) An ace is 1/13. (b) A jack of hearts is 1/52. (c) A three of clubs or a six of diamonds is 1/26. (d) A heart is 1/4. (e) Any suit except hearts is 3/4. (f) A ten or a spade is 4/13. (g) Neither a four nor a club is 10/13.

We will find the probability of the given situations.

a) An aceThere are 4 aces in the deck.

Therefore, the probability of drawing an ace is given by

P(Ace) = 4/52 = 1/13

b) A jack of hearts

There is only one jack of hearts in the deck.

Therefore, the probability of drawing a jack of hearts is given by

P(Jack of hearts) = 1/52

c) A three of clubs or a six of diamonds

There is one three of clubs and one six of diamonds in the deck.

Therefore, the probability of drawing a three of clubs or a six of diamonds is given by

P(Three of clubs or six of diamonds) = 2/52 = 1/26

d) A heart

There are 13 hearts in the deck.

Therefore, the probability of drawing a heart is given by

P(Heart) = 13/52 = 1/4

e) Any suit except hearts

There are 39 cards that are not hearts in the deck.

Therefore, the probability of drawing any suit except hearts is given by

P(Any suit except hearts) = 39/52 = 3/4

f) A ten or a spade

There are 16 cards that are either tens or spades.

Therefore, the probability of drawing a ten or a spade is given by

P(Ten or spade) = 16/52 = 4/13

g) Neither a four nor a club

There are 12 cards that are either fours or clubs.

Therefore, the probability of drawing neither a four nor a club is given by

P(Neither four nor club) = 40/52 = 10/13

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The range for this data is 17, and the IQR is 13.

From the question, we have the following parameters that can be used in our computation:

The values of 41, 43, 49.5, 56, and 58 are all marked by the box plot.

These values are the five number summary of the box plot and it means that

So, we have

Range = 58 - 41

Range = 17

Also, we have

IQR = 56 - 43

IQR = 13

Hence, the range is 17, and the IQR is 13.

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Answer: false

Step-by-step explanation:

1. FALSE. If X and Y are independent, then P(X=x, Y=y) = P(X=x)*P(Y=y). So, the value is not 0 in general. In fact, it holds value if at least one of P(X=x) and P(Y=y) posses value 0. 2. TRUE. An event and its complement event constitutes the total s

True, for any two random variables x and y, -1 < p < 1.

The value p represents the correlation coefficient between two random variables x and y. The correlation coefficient measures the strength and direction of the linear relationship between the variables. The range of p is between -1 and 1. If p is closer to -1, it implies that there is a strong negative correlation between x and y, meaning that as x increases, y decreases. If p is closer to 1, it implies that there is a strong positive correlation between x and y, meaning that as x increases, y also increases. If p is 0, it implies that there is no correlation between x and y.

Therefore, for any two random variables x and y, -1 < p < 1, as the correlation coefficient p must fall within this range.

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Answer:

0.125 is the answer of 1/8

Hey there!

“ -1 over 8”

= -1/8

= -1 ÷ 8

= -0.125

Therefore, your answer is: -0.125

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Guide:

2 negatives = positive

1 negative & 1 positive = negative

2 positives = positive

1 positive & 1 negative = negative

Answer:

Step-by-step explanation:

18/24=3/4

Answer:

8% chance out of 19 marbles

Step-by-step explanation:

Answer: 0.0016

Step-by-step explanation:

5^3 = 125

5^-7 = 0.0000128

125 * 0.0000128 = 0.0016

No, the standard deviation of a data set can never be negative. The standard deviation is a measure of the dispersion or spread of data points from the mean.

It is calculated by taking the square root of the variance, which is the average of the squared differences between each data point and the mean.

Since the variance involves squaring the differences, it ensures that all values are positive. Taking the square root of the positive variance yields a positive value, which is the standard deviation. Thus, the standard deviation is always non-negative.

Similarly, the Interquartile Range (IQR) cannot be negative. The IQR is a measure of statistical dispersion that represents the range between the first quartile (25th percentile) and the third quartile (75th percentile) of a dataset. It provides insights into the spread of the central 50% of the data.

Like the standard deviation, the IQR involves calculating the difference between specific percentiles. Since percentiles represent ordered values in a dataset, the difference between them is non-negative, ensuring that the IQR is also non-negative.

In summary, both the standard deviation and the IQR are measures of dispersion that involve calculating differences between values in a dataset, ensuring that they cannot be negative.

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A repeating decimal or recurring decimal is the decimal representation of a number with periodic digits and an indefinitely repeated component that is not zero.

When a collection of decimal terms must be repeated uniformly, it is known as repeating decimals.

The decimal representation of a number with periodic digits and an infinitely repeated component that is not zero is called a repeating decimal or recurring decimal. Only when a number's decimal representation repeats or terminates can it be demonstrated that the number is rational.

Decimal values that repeatedly occur are known as recurring decimals (also known as repeating decimals). The customary behavior when a decimal expires and so ceases is not the case here. Therefore, 0.75 would be a repeating decimal since it would proceed indefinitely up to 0.755555 rather than ending at 0.75 like the previous example.

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Answer:

2=100

3=100

4=80

5=80

6=100

7=80

8=100

Step-by-step explanation:

If 1 is equal to 80 than 2 must be equal to 100. 180-80=100.

Using the z rule you can find that 2 and 4 are equivalent and 1 and 4 are equivalent. You can also find that 1 and 5 are adjacent using the z rule (add up to 180). So 5 is is  80. Using the same steps as on the a line you can find 6,7,8.

• ,Plan A :

Initial fee = 48

Cost per mile = 0.09

Cost A = 48 + 0.09x

Where x is the number of miles driven.

• Plan B

Initial fee = 57

Cost per mile = 0.07

Cost B = 57 + 0.07x

If both costs are the same:

Cost A = Cost B

48+0.09x = 57+0.07x

Solve for x

0.09x - 0.07x = 57 - 48

0.02x = 9

x = 9 / 0.02x

x= 450

Number of miles = 450

Cost = 48+0.09 (450) = $88.5

By applying dilatation and congruency theorem, it can be concluded that the distance between points R and R' is 3 units (option A).

Dilation is a transformation of a geometric shape, either becoming larger or smaller, without changing the original shape using a certain scale factor.

Two shapes are said to be congruent if a pair of corresponding sides have the same ratio and the corresponding angles have the same measure.

From the problem we obtained the following information:

QR is dilated to create Q'R' ⇒ QR // Q'R'

The dilatation factor is 1.5 ⇒ Q'R'/QR = 1.5

Now we look at the ΔTRQ and ΔTR'Q':

QR // Q'R'

∠TRQ = ∠TR'Q'

So ΔTRQ is congruent to ΔTR'Q' and TR'/TR = Q'R'/QR

Now we can calculate y using this equation:

   TR'/TR = Q'R'/QR

(6 + y) / 6 = 1.5

      6 + y = 9

            y = 3

Thus, the distance between points R and R' is 3 units.

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Answer:

-641.

Step-by-step explanation:

hope that helps:))

According to elementary algebra, time t has values of 3 and 1 seconds, respectively.

Polynomial equations are those created by combining variables, exponents, and coefficients. The higher exponent, known as the degree of the equation, might have several exponents.

A polynomial expression equal to 0 is the basis of a polynomial equation. For instance, since 3x² - 5 is a polynomial expression, 3x² - 5 = 0 is a polynomial equation.

Quadratic equations are two-variable, degree-two polynomial equations of the form f(x) = \(ax^{2}\) + bx + c = 0 and with the variables a, b, c, and R R and a = 0.

With "a" denoting the leading coefficient and "c" denoting the absolute term of f, it is a quadratic equation in its general form (x).

Knowing that h = 15 m, we can enter that number into the equation to find t:

15 = 20t - \(5t^{2}\)   Let's set the equation equal to 0 to solve

-\(5t^{2}\) + 20t - 15 = 0 Let's factor out a -5 to simplify the equation

-5(t2 - 4t + 3) = 0  0/-5 is still 0

\(t^{2}\) - 4t + 3 = 0   Let's find factors for this solution

(t -3)(t - 1) = 0   We have 2 solutions for this equation

t = 3, t = 1

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Answer:

8-x=2

-x=2-8

-x=-6

x=6

if 8 is subtract from 6answer is 2

The volume of the cone is approximately 37.7 cubic units

What is volume?

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.

To find the volume of a cone, we use the formula:

V = (1/3) * π * r² * h

where π is the constant pi, r is the radius of the base of the cone, and h is the height of the cone.

Plugging in the given values, we get:

V = (1/3) * 3.14 * 3² * 4 ≈ 37.7

Therefore, the volume of the cone is approximately 37.7 cubic units (rounded to the nearest tenth).

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The profit margins (return on sales) for each division are approximately :Division A = 10.85%,Division B = 9.11% and The calculations for the year would be:Net Income = $85,428,Return on Assets = 18.9%.

To compute the profit margins (return on sales) for each division, we divide the profit by the sales and multiply by 100 to express the result as a percentage.

For Division A:

Profit Margin = (Profit / Sales) * 100

Profit Margin = ($230,000 / $2,120,000) * 100

Profit Margin ≈ 10.85%

For Division B:

Profit Margin = (Profit / Sales) * 100

Profit Margin = ($34,700 / $381,000) * 100

Profit Margin ≈ 9.11%

To calculate the net income and return on assets for Polly Esther Dress Shops Inc., we use the given information.

Net Income = Profit Margin * Sales

Net Income = 7% * $1,220,400

Net Income = $85,428

Return on Assets = Profit Margin * Asset Turnover

Return on Assets = 7% * 2.7

Return on Assets = 18.9%

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If an auditorium has 20 rows of seats. there are 20 seats in the first row, 21 seats in the second row, 22 seats in the third row, and so on. then,  there are 39 seats present in the 17th row.

The given data is as follows:

Number of rows of seats = 20

Number of seats in the first row = 20

Number of seats in the second row = 21

Number of seats in the third row = 22 and so on.

Let's calculate the common difference between the seats,

common difference = 21-20 = 1 or 22-21 = 1

Therefore common difference = 1

Then the number of the seats in 17th row will be

The number of the seats = 20 + (20 - 1)* 1

The number of the seats= 39 seats.

Therefore, there are a total of 39 seats present in the 17th row.

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