The following table shows the relationship between weight and calories burned per minute for five people. Weight (in pounds) Calories burnod por minuto
112 725
129 9.15 150 9.85 174 10.25 182 11.75 Mean 149.4 9.65 Standard Deviation 29.51 1.64 Weight is the explanatory variable and has a mean of 149.4 and a standard deviation of 29.51. Calories burned per minute is the response variable and has a mean of 9.65 and a standard deviation of 1.64 The correlation was found to be 0.944. Select the correct slope and y-intercept for the least-squares line. Answer choices are rounded to the hundredths place

A basis for the subspace is {1, [tex]x^2[/tex]}, and the dimension of the subspace is 2.

a. To find a basis for the subspace {a(1 + x) + b(x + x^2) : a, b ∈ R} of P2, we need to find a set of vectors that are linearly independent and span the subspace. We can rewrite the polynomials in the form a + bx + cx^2 and then look for a linearly independent set.

If we set a = 1 and b = 0, we get the polynomial 1 + x, which is in the subspace. If we set a = 0 and b = 1, we get the polynomial x + x^2, which is also in the subspace. These two polynomials are linearly independent since neither is a scalar multiple of the other.

Therefore, a basis for the subspace is {1 + x, x + x^2}, and the dimension of the subspace is 2.

b. To find a basis for the subspace {(a + b(x + x^2)) : a, b ∈ R} of P2, we again need to find a set of vectors that are linearly independent and span the subspace. We can rewrite the polynomials in the form a + bx + cx^2 and then look for a linearly independent set.

If we set b = 0, we get the polynomial a, which is in the subspace. If we set a = 0 and b = 1, we get the polynomial x + x^2, which is also in the subspace. These two polynomials are linearly independent since neither is a scalar multiple of the other.

Therefore, a basis for the subspace is {1, x + x^2}, and the dimension of the subspace is 2.

c. To find a basis for the subspace {p(x) : p(1) = 0}, we need to find a set of polynomials that satisfy the given condition and span the subspace.

A polynomial p(x) that satisfies p(1) = 0 must have a factor of (x - 1). Therefore, we can write any polynomial in the subspace as p(x) = (x - 1)q(x), where q(x) is a polynomial of degree 1 or 0.

If we set q(x) = 1, we get the polynomial x - 1, which is in the subspace. If we set q(x) = 0, we get the zero polynomial, which is also in the subspace. These two polynomials are linearly independent since neither is a scalar multiple of the other.

Therefore, a basis for the subspace is {x - 1}, and the dimension of the subspace is 1.

d. To find a basis for the subspace {p(x) : p(x) = p(-x)}, we need to find a set of polynomials that satisfy the given condition and span the subspace.

A polynomial p(x) that satisfies p(x) = p(-x) must be an even function. Therefore, we can write any polynomial in the subspace as p(x) = a + bx^2, where a and b are constants.

If we set a = 1 and b = 0, we get the polynomial 1, which is in the subspace. If we set a = 0 and b = 1, we get the polynomial x^2, which is also in the subspace. These two polynomials are linearly independent since neither is a scalar multiple of the other.

Therefore, a basis for the subspace is {1, x^2}, and the dimension of the subspace is 2.

To learn more about polynomials visit:

https://brainly.com/question/11536910

#SPJ11

From the given distances and time it is clear that Mrs.Peter arrive before Mr Peter by 5 minute.

Mrs. Peter arrives 5 minutes before Mr. Peter

To find who arrives first we first need to find the speed and time they require to arrive.

Given : From Boston to Worcester

Mr. Peter takes 30 minutes time and speed=60 miles per hour

Mrs. Peter travels with speed 90 miles per hour

We will now calculate Mr.Peters speed

60 miles/h × h/60 = miles/min

We know that, Distance = Speed /Time

Mr.Peters speed is 60 miles per hour

Distance=Miles÷Min /30 minutes

Distance = 30 miles

Similarly, we will now calculate Mrs.Peters speed

90 miles/h h/60 = 1.5 miles per min

Here, Time = 30 / 1.5

= 20 minutes

Here, we know that Mrs.Peter leaves from Boston to Worcester 5 minutes after Mr.Peter so we will add 5 minutes to Mrs. Peters time.

Time = 20+5 =15 minutes

Therefore,

Learn more about the average speed here:

brainly.com/question/9834403.

#SPJ1

Answer:

I'm pretty sure the answer is 80.

Step-by-step explanation:

5 × 8 × 2 = 80

The probability that a senator is under 70 years old given that he or she is at least 50 years old is 0.75.

To answer this question, we need to use conditional probability. Let A be the event that a senator is under 70 years old, and let B be the event that a senator is at least 50 years old. We want to find the probability of A given B, denoted as P(A|B).

Using Bayes' theorem, we have:

P(A|B) = P(B|A) * P(A) / P(B)

where P(B|A) is the probability that a senator is at least 50 years old given that they are under 70 years old (which is 1), P(A) is the probability that a senator is under 70 years old (which we do not know yet), and P(B) is the probability that a senator is at least 50 years old (which we also do not know yet).

To find P(A), we need more information. Let's assume that we know the following:

The total number of senators is 100.

The number of senators who are under 70 years old is 60.

The number of senators who are at least 50 years old is 80.

Using this information, we can calculate P(A) and P(B) as follows:

P(A) = number of senators under 70 / total number of senators = 60/100 = 0.6

P(B) = number of senators at least 50 / total number of senators = 80/100 = 0.8

Now we can plug these values into Bayes' theorem:

P(A|B) = P(B|A) * P(A) / P(B)

P(A|B) = 1 * 0.6 / 0.8

P(A|B) = 0.75

Therefore, the probability that a senator is under 70 years old given that he or she is at least 50 years old is 0.75.

Learn more about probability

brainly.com/question/11234923

#SPJ11

The given representation is a quadratic function.

The given table can be represented in the form of equation as,

y = x²

When x = 0, y = 0

When x = 1, y = 1

When x = 2, y = 2² = 4

When x = 3, y = 3² = 9

When x = 4, y = 4² = 16

This can be written as,

y = x² + 0x + 0

This is a quadratic function.

Hence the given representation is a quadratic function.

Learn more about Quadratic Functions here :

https://brainly.com/question/18958913

#SPJ1

The value of the variables are x = 2 and y = 1

From the information given, we have the simultaneous equations are;

y = 6x -11

-2x - 3y = -7

Now, substitute the value of y in equation 1 to equation 2, we get;

-2x - 3(6x -11) = -7

expand the bracket

-2x - 18x + 33 = -7

collect the like terms

-2x - 18x = -7 - 33

Add the values

-20x = -40

Make 'x' the subject

x = 2

Substitute the values

y = 6x -11

y = 6(2) - 11

y = 1

Learn about simultaneous equations at: https://brainly.com/question/16863577

#SPJ1

The number of moles for the first equation is 1.8 and the number of moles for the second equation is 0.0240.

The balanced chemical equation is 4Al + 3O² → 2Al₂O₃. The molar ratio of Al to O₂ is 4:3. Therefore, if 1.35 moles of O₂

4 moles Al/₃ moles O₂ = x moles Al/1.35 moles O₂

x = 1.8 moles of Al

The balanced chemical equation is N + 2H₂O → NaOH + H₂. The molar ratio of N to H₂ is 1:1. Therefore, if 0.0240 moles of N is used, then the number of moles of H₂ produced would be:

1 mole N/1 mole H₂ = 0.0240 moles N/x moles H₂

To know more about chemical reactions follow

https://brainly.com/question/31681528

#SPJ1

True. Seasonality refers to a regular, repeating pattern in the data that takes longer than one year to complete. It can occur in various forms such as monthly, quarterly, or even weekly patterns.

These patterns are usually associated with external factors such as weather, holidays, or other events that influence consumer behavior. By identifying seasonality in the data, businesses can use it to predict future trends and adjust their strategies accordingly. This information can be valuable in a range of industries such as retail, tourism, and agriculture.

Overall, understanding the repeating patterns in data is essential for making informed decisions and staying ahead of the competition.

Learn more about pattern here:

https://brainly.com/question/14720576

#SPJ11

The full answer is 1101000. So, 104 in base 10 is equivalent to 1101000 in base 2.  When converting 104 from base 10 to base 2 using repeated division by 2.

The quotient obtained from the third division is as follows:

1. 104 ÷ 2 = 52 (remainder: 0)
2. 52 ÷ 2 = 26 (remainder: 0)
3. 26 ÷ 2 = 13 (remainder: 0)

After the third division, the quotient is 13. The full answer for converting 104 to base 2 will require a few more divisions:

4. 13 ÷ 2 = 6 (remainder: 1)
5. 6 ÷ 2 = 3 (remainder: 0)
6. 3 ÷ 2 = 1 (remainder: 1)
7. 1 ÷ 2 = 0 (remainder: 1)

Reading the remainder from bottom to top, the full answer is 1101000. So, 104 in base 10 is equivalent to 1101000 in base 2.

Learn more about base here:

https://brainly.com/question/14291917

#SPJ11

The area of the diagram ABDC is 625cm2.

We are given that;

RQ is parallel to ST, which implies that ∆PRQ and ∆PST are similar by the AA criterion (angle-angle). We are also given that ST = 4 cm, RP = 10 cm, and PT = 5 cm;

Now,

we can use the fact that RP = 10 cm and PT = 5 cm to find PQ by using the Pythagorean theorem. PQ is the hypotenuse of the right triangle PRT, so we get:

PQ2 = RP2 + PT2 PQ2 = 102 + 52 PQ2 = 100 + 25 PQ2 = 125 PQ = √125 PQ ≈ 11.18 cm

Now we can use PQ and ST as corresponding sides to find the scale factor. We get:

Scale factor = PQ / ST Scale factor ≈ 11.18 / 4 Scale factor ≈ 2.795

ii. To find |RQ|, we can use the scale factor and multiply it by |ST|. We get:

|RQ| = Scale factor * |ST| |RQ| ≈ 2.795 * 4 |RQ| ≈ 11.18 cm

b. Find the area of ∆PST if the area of ∆PRQ is 80 cm2.

To find the area of ∆PST, we can use the fact that the ratio of the areas of similar triangles is equal to the square of the scale factor. We get:

Area of ∆PST / Area of ∆PRQ = (Scale factor)2 Area of ∆PST / 80 = (2.795)2 Area of ∆PST / 80 = 7.812 Area of ∆PST = 7.812 * 80 Area of ∆PST ≈ 625 cm2

Therefore, by the area the answer will be 625cm2.

Learn more about the area;

https://brainly.com/question/1658516

#SPJ1

The gradient of the line is 2

[tex]Distance AB = \sqrt{[(5-(-3))^2 + (2-4)^2]}= \sqrt{68} \\Distance AC = \sqrt{[(-3-0)^2 + (4-(-3))^2]} = \sqrt{58} \\Distance BC = \sqrt{[(5-0)^2 + (2-(-3))^2]}= \sqrt{50}[/tex]

mAB = (2 - 4) / (5 - (-3)) = -1/2

This is the slope of AB

-1 / (-1/2) = 2

we have to find the point that is perpendicular to AB

(-3 + 5) / 2 = 1

(4 + 2) / 2 = 3

1 , 3 are  perpendicular to AB

y - 3 = 2(x - 1)

y - 3 = 2x - 2

y = 2x + 1

There fore the gradient of the line is 2

Read more on gradient here:https://brainly.com/question/23016580

#SPJ1

The range of brain volume is 572 cm^3.

To obtain the range, simply subtract the minimum value from the maximum.

Range equals High minus Low:

Range = 1484 cubic centimeters minus 912 cubic centimeters,

producing a difference of 572 cubic centimeters.

Thus, the range for brain volume is verified at exactly 572 cm³.

The range of a set of data in statistics is the difference between the largest and smallest values, calculated by subtracting the sample maximum and minimum. It is given in the same units as the data.

Read more about range here:

https://brainly.com/question/26098895

#SPJ1

Given that the brain volume varies from a low of 912 cm^3 to a high of 1484 cm^3, what is the range of brain volume?

Answer: The exponential function that models the population growth of the city over time is:

y = 350,000 * (1 + 0.044)^t

where t is the number of years since the start of the study, y is the city's population, and 0.044 is the annual growth rate expressed as a decimal.

The function is an example of exponential growth, where the population is increasing at a constant rate over time.

Step-by-step explanation:

The polygon VWXY is reflection across y = 2. Therefore, option D is the correct answer.

Given that, polygon VWYZ with vertices V at (-11, 2), W at (-11, 0), Y at (-5, 0) and Z(-5, 2).

A second polygon V' at (7, 2), W' at (7, 0), Y'(1, 0) and Z'(1, 2).

We know that, the reflection of point (x, y) across the y-axis is (-x, y).

The polygon VWXY is reflection across y = 2

Therefore, option D is the correct answer.

To learn more about the reflection over y-axis visit:

https://brainly.com/question/15175017.

#SPJ1

The linear regression equation is y = 41,461.54 + 2,714.46x.

The correlation coefficient is 0.992180617.

The type of correlation is a positive linear correlation.

Yes, the correlation is strong because the correlation coefficient approximately equals to 1.

The employee's income for his 15th year of work is $82,178.

In this scenario, the years (x) would be plotted on the x-axis of the scatter plot while the income (y) would be plotted on the x-axis of the scatter plot.

By critically observing the scatter plot (see attachment) which models the relationship between the years (x) and the income (y), an equation for the linear regression is given by:

y = 41,461.54 + 2,714.46x

Next, we would predict this employee's income for his 15th year of work as follows;

y = 41,461.54 + 2,714.46(15)

y = 41,461.54 + 40,716.9

y = $82,178.44 ≈ $82,178

In conclusion, there is a strong correlation between the data because the correlation coefficient (r) approximately equals to 1;

0.7＜|r| ≤ 1   (strong correlation)

Read more on positive correlation here: brainly.com/question/3753830

#SPJ1

The required, 4.5 × 10⁵ as an ordinary number is 450,000.

An ordinary number is a number that is expressed in the usual way, using digits 0-9 without any exponent notation or other mathematical symbols.

4.5 × 10⁵ means 4.5 multiplied by 10 raised to the power of 5. To write this as an ordinary number, we simply need to perform this multiplication:

4.5 × 10⁵ = 4.5 × 100,000 = 450,000

Therefore, 4.5 × 10⁵ as an ordinary number is 450,000.

Learn more about ordinary numbers here:

https://brainly.com/question/7244720

#SPJ1

The correct answer would be

B) half of her classmates have a sibling and half do not

Add totals for classmates who have chores and those who do not have chores for each group.

7 + 8 = 15

9 + 6 = 15

Therefore, the correct answer would be

B) half of her classmates have a sibling and half do not

Based on the fact that the total for the classmates that have chores and those that don't have are equal which is 15, we can conclude that option B is correct.

Read more about algebra here:

https://brainly.com/question/22399890

#SPJ1

So the vector form of the quadratic function y = x² + 4x + 3 is: y = (x + 2)² - 1.

To change from standard form to vertex form, we need to complete the square.

First, we group the x-terms together and factor out any common coefficient of x², giving:

y = x² + 4x + 3

y = 1(x² + 4x) + 3

Next, we need to add and subtract a constant inside the parentheses to complete the square. To determine this constant, we take half of the coefficient of x (4) and square it:

(4/2)² = 4

So we add and subtract 4 inside the parentheses:

y = 1(x² + 4x + 4 - 4) + 3

Now we can factor the quadratic expression inside the parentheses as a perfect square:

y = 1[(x + 2)² - 4] + 3

Simplifying and rearranging terms, we get:

y = (x + 2)² - 1

To know more about vector,

https://brainly.com/question/20426452

#SPJ11

The margin of error for this estimate is 0.8853 MB/s. Your answer is option 1) 0.8853.

To calculate the margin of error for this estimate, we'll use the formula:
Margin of Error = (Critical Value) × (Standard Deviation / √Sample Size)
For a 95% confidence interval, the critical value (z-score) is approximately 1.96. The standard deviation is 1.62 MB/s, and the sample size is 11.
Margin of Error = 1.96 × (1.62 / √11) ≈ 0.8853

Learn more about margin of error here:

https://brainly.com/question/30633768

#SPJ11

The area of the quadrilateral is 176.6 square meters, rounded to one decimal place.

Triangle ABC is approximately 14.1 meters tall.

Triangle ACD is roughly 2.6 meters tall.

We can now calculate the area of triangle ACD:

Area(ACD) = (1/2) * AD * height Area(ACD) = (1/2) * 7.8 * 2.6 Area(ACD) = (1/2) * 7.8 * 2.6

Finally, we may sum the areas of the two triangles to get the quadrilateral's area:

Area(quadrilateral) equals Area(ABC) + Area(ACD).

166.5 + 10.1 = 176.6

The area of the quadrilateral is roughly 176.6 square meters, rounded to one decimal place.

Learn more about area on

https://brainly.com/question/25292087

#SPJ1

An equation of the line in point-slope form, using the coordinates of the labeled point is y + 3 = 0.8(x + 2).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

At data point (-2, -3) and a slope of 0.8, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-3) = 0.8(x - (-2))  

y + 3 = 0.8(x + 2)

Read more on point-slope here: brainly.com/question/24907633

#SPJ1

Therefore, there are 8820 groups of 9 that contain 5 women and 4 men using combination formula.

To solve part (b)(i), we need to use the combination formula. The number of ways to choose 5 women out of 9 is given by the combination C(9,5), which is:

C(9,5) = 9! / (5! * 4!)

= 126

Similarly, the number of ways to choose 4 men out of 8 is given by the combination C(8,4), which is:

C(8,4) = 8! / (4! * 4!)

= 70

To get the total number of groups of 9 that contain 5 women and 4 men, we need to multiply these two numbers:

126 * 70 = 8820

To know more about combination,

https://brainly.com/question/20211959

#SPJ11

Answer: A

Step-by-step explanation:

A.  this is correct, to find your IQR, interquartile range, you break up the numbers into 4 even groups listed in numerical order

16    40    49   130    200     210

         |           |              |

The lines under the numbers represent the 4 even groups

The IQR is the upper quartile(where last line is) - lower quartile (where last line is(where first line is)

IQR=200-40=160

B. is wrong, range is last number - first  (210-16)=194 not 160

C. is wrong, we found the IQR to be 160 not 194

D. is wrong,  MAD, mean absolute deviation, is the average of the distance from the mean

mean/average of all = 107.5  I added all and divided by how many (6)

MAD means subtract each number from the average and divide by how many  

= [(107.5-16)+(107.5-40)+(107.5-49)+(130-107.5)+(200-107.5)+(210-107.5)]/6

=72.5

Ernesto travels a distance of 94.9 feet after the 20 swings.

For our initial arc, the length was 16 ft. Subsequent arcs had lengths that were 90% of their preceding element in succession

Therefore, the first 10 arcs' lengths respectively calculate as follows:  16 ft, 14.4 ft, 12.96 ft, 11.664 ft, 10.4996 ft, 9.44784 ft, 8.503056 ft, 7.6527504 ft, 6.88747536 ft and 6.198727824 ft; cumulatively amounting to a distance of roughly 94.86ft traversed by Ernesto after his 10 swings.

Learn more about word problem on

https://brainly.com/question/21405634

#SPJ1

To find the top 10% salaries of workers at the company, we need to use the standard normal distribution table. First, we need to find the z-score that corresponds to the top 10% of the distribution, which is 1.28 (found using the table).

Next, we can use the formula:

z = (x - mean) / (standard deviation / sqrt(sample size))

We know the mean is $60,000, the standard deviation is $9,000, and the sample size is 36. We can solve for x:

1.28 = (x - 60,000) / (9,000 / sqrt(36))

1.28 = (x - 60,000) / 1,500

1.28 * 1,500 = x - 60,000

1,920 + 60,000 = x

x = $61,920

Therefore, the top 10% salaries of workers at the company is $61,920 or more.
To find the top 10% salary for workers at this company, we need to first determine the z-score that corresponds to the 90th percentile. This is because 100% - 10% = 90%.

Step 1: Look up the z-score for the 90th percentile in a standard normal distribution table. You will find a z-score of approximately 1.28.

Step 2: Use the z-score formula to find the salary corresponding to this z-score:
X = μ + Z * σ / √n
where X is the salary, μ is the mean, Z is the z-score, σ is the standard deviation, and n is the sample size.

Step 3: Plug in the given values:
X = $60,000 + 1.28 * $9,000 / √36

Step 4: Simplify the equation:
X = $60,000 + 1.28 * $9,000 / 6

Step 5: Calculate the result:
X = $60,000 + $1,920 = $61,920

The top 10% of salaries for workers at this company is $61,920 or more, rounded to the nearest dollar.

To learn more about standard deviation : brainly.com/question/23907081

#SPJ11

The critical numbers in increasing order, we have:

x = 0, 4/9, 4

At x = 0, the function has a local minimum.

At x = 4/9, the function has a local maximum.

At x = 4, the function has neither a local maximum nor minimum.

To find the critical numbers of the function f(x) = [tex]x^8(x - 4)^7[/tex]:

We need to take the derivative of the function and set it equal to zero.

f'(x) = [tex]8x^7(x - 4)^7 + 7x^8(x - 4)^6(-1)[/tex]
Setting f'(x) = 0 and solving for x, we get:

x = 0 or x = 4/9

To describe the behavior of f at these critical numbers:

At x = 0, the function has a local minimum.

This is because the derivative changes sign from negative to positive at this point, indicating a change from decreasing to increasing behavior.

At x = 4/9, the function has a local maximum.

This is because the derivative changes sign from positive to negative at this point, indicating a change from increasing to decreasing behavior.

At x = 4, the function has neither a local maximum nor minimum.

This is because the derivative is zero at this point, but does not change sign. Instead, the behavior of the function changes from decreasing to increasing to decreasing again as we move from left to right around x = 4.

Listing the critical numbers in increasing order, we have:

x = 0, 4/9, 4

To know more about Critical Numbers:

https://brainly.com/question/30000833

#SPJ11

The height of the ball will be 16.94 feet. Then the baseball travels over the fence.

Given that:

Distance at time t, x = 140t

Height at time t, y = 3.1 + 40t − 16t²

Height, h = 10 feet

Distance, x = 320 feet

The time is calculated as,

320 = 140t

t = 320/140

t = 16/7

The height at t = 16/7 is calculated as,

y = 3.1 + 40(16/7) − 16(16/7)²

y = 3.1 + 97.43 - 83.59

y = 16.94 feet

y > 10 feet

The height of the ball will be 16.94 feet. Then the baseball travels over the fence.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ1

There will be $530.68 in the account at the end of 2 years, if Arianna deposits $500 in an account that pays 3% interest, compounded semiannually.

The formula accrued amount in a compounded interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Principal P = $500

Compounded semi annually n = 2

Time t = 2 years

Interest rate r = 3%

Accrued amount A = ?

First, convert R as a percent to r as a decimal

r = R/100

r = 3/100

r = 0.03

Plug the values into the above formula:

A = P( 1 + r/n )^( n × t )

A = $500( 1 + 0.03/2 )^( 2 × 2 )

A = $500( 1 + 0.015 )^( 4 )

A = $530.68

Therefore, the accrued amount is $530.68.

Learn more about compound interest here: brainly.com/question/27128740

#SPJ1