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An athlete burns 14 calories per minute running and 8 calories per minute lifting weights. Write an objective function z=f(x,y) that represents the total
number of calories burned by running for x minutes and lifting weights for y minutes.


The function is z=

Answer:

a) Three ways of describing the representative or typical temperatures are the mean, median, and mode.

The mean = 5.  This is the average temperature.  It is calculated by adding up the varying temperatures each year and dividing by 10.

Median = 5.5.  This is the middle value in the temperature table.  There are two middle numbers (5 and 6) in the dataset.  They are added and divided by two.

Mode = 6.  This is the value that occurs more than other values in the dataset.  The value 6 occurred twice more than other values.

b) The two ways of describing the variation of temperatures are the variance and the standard deviation.

Variance = 7. This is a measure of how spread out a data set is. It is calculated as the average squared deviation of each number from the mean of a dataset.

Standard Deviation = 2.65.  The standard deviation measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.

Step-by-step explanation:

a) Data and Calculations:

Noon Temperatures (in degrees Celsius) in a particular Canadian City on Thanksgiving Day:

Year    Degree  Difference     Squared

           Celsius                       Difference

2002        0          -5                     25

2003        3          -2                       4

2004        6           1                        1

2005        8           3                       9

2006        2          -3                       9

2007        9           4                      16

2008        7           2                       4

2009        6           1                        1

2010         4          -1                        1

2011          5          0                       0

Sum       50                                  70

Mean =    5 (50/10)

Variance =                                    7 (70/10)

Standard Deviation = 2.65 (Square root of variance)          

Median =  0, 2, 3, 4, 5, 6, 6, 7, 8, 9 (the values are arranged numerically.)

= (5 + 6)/2 = 5.5

Mode = 6 (occurred twice more than other values)

Answer:

approximately 254.5

btw area of circle= pi multiplied by radius

Step-by-step explanation: I got you bro

Answer: Circle area = π * r² = π * 81 [inch²] ≈ 254.47 [in²]

but because it asks for nearest tenth

254.5 in²

this is your real answer

Answer:

H0: μc ≤ μs    Ha :μc > μs    

Step-by-step explanation:

The null and alternate hypotheses can be stated as

H0: μc ≤ μs    Ha :μc > μs    one tailed test

Where

μc =  Mean of college students watching movies in a month

μs  =  Mean of school students watching movies in a month

For one tailed test of α =0.05   the value of Z= ± 1.645

The critical region will be Z >  ± 1.645

It is of importance to note that by rejecting the null hypothesis and accepting the alternate hypothesis we are automatically rejecting all values of mean that are greater than 7.1

if 40 miles is is 80 percent of her goal and 40 is 80 percent of 50 then her goal for how many miles she wants to run by the end of the month is 50 miles.

Answer:

\( \boxed{\tt\orange{x > 10 }}\)

Step-by-step explanation:

Let's solve the inequality step-by-step.

2x+3>23

Step 1: Subtract 3 from both sides.

2x+3−3>23−3

2x>20

Step 2: Divide both sides by 2.

\( \bf \bold {\frac{2x}{2} } > \frac{20}{2} \)

Result:

\( \boxed{\tt \: x > 10 }\)

Answer:

here

Step-by-step explanation:

2.000.000.099

The probability that the hacker guesses the password on their first try is extremely low.

What is the probability that the hacker guesses the password on his first try?

There are 26 lowercase letters, 26 uppercase letters, and 10 numerical digits, for a total of 62 possible characters for each position in the password. Since the password is 9 characters long, there are \(62^{9}\) possible passwords.

The probability that the hacker guesses the password on their first try is 1 out of the total number of possible passwords:

Probability = 1 / (\(62^{9}\))

Using a calculator, this can be simplified to approximately 1.2 x \(10^{-16}\)

Therefore, the probability that the hacker guesses the password on their first try is extremely low.

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Answer:

  $28

Step-by-step explanation:

Each round trip will be double the price of a one-way trip, so will be ...

  2 × $3.50 = $7.00

Diego and his 3 friends will require a total of 4 round-trip tickets for a cost of ...

  4 × $7.00 = $28.00

Option D is the correct answer.

From the graph, we can conclude that,

1. The two lines are continuous lines and not broken lines. So, the inequality sign should be either ≤ or ≥.

2. The points on the lines of the shaded region are also included in the solution.

The only option that matches with the above conditions is option D. So, option D is the correct answer.

Let us verify it.

Now, let us consider a point that is inside the shaded region and also on any one line.

Let us take (0, 2).

Plug in 0 for x and 2 for y in each of the options and check which inequality holds true.

Considering the inequalities,

y ≥ 3x - 2

x + 2y ≤ 4

Solving we get,

2 ≥ 3(0) - 2

2 ≥ -2

x + 2y ≤ 4

0 + 2(2) ≤ 4

4 ≤ 4

Here, both inequalities are correct.

So, option D is the correct answer.

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The complete question is =

Which system of linear inequalities is graphed?

A. y < 3x-2

x + 2y ≥ 4

B. y < 3x - 2

x + 2y > 4

C. y > 3x - 2

x + 2y < 4

D. y ≥ 3x - 2

x + 2y ≤ 4

Account Compounding Interest after 6 years

1 quarterly

A1 = -$1798.42

2 monthly $

A2 = -$1798.01

3 daily $

A3 =  -$1797.96

1) An account with quarterly compounding: After 6 years, the formula to calculate the interest is:

Interest = Principal \(\times\)(1 + (rate / \(n))^{(n * t)}\) - Principal

Substituting the given values:

Principal = $2200

Rate = 3% = 0.03

n = 4 (quarterly compounding)

t = 6 years

Interest = $2200 \(\times\) (1 + (0.03 / \(4))^{(4 \times 6)}\) - $2200

Interest = $2200 \(\times\)\((1.0075)^{(24)}\) - $2200

Interest ≈ $401.58 - $2200

Interest ≈ -$1798.42 (rounded to two decimal places).

2) An account with monthly compounding: After 6 years, the formula remains the same, but the compounding frequency changes:

   Principal = $2200

   Rate = 3% = 0.03

   n = 12 (monthly compounding)

   t = 6 years

Interest = $2200 \(\times\)(1 + (0.03 / \(12))^{(12 \times 6)}\) - $2200

Interest = $2200 \(\times\)\((1.0025)^{(72)}\) - $2200

Interest ≈ $401.99 - $2200

Interest ≈ -$1798.01 (rounded to two decimal places)

3) An account with daily compounding: Using the same formula with the compounding frequency:

   Principal = $2200

   Rate = 3% = 0.03

   n = 365 (daily compounding)

   t = 6 years

Interest = $2200 \(\times\)(1 + (0.03 / \(365))^{(365 \times 6)}\) - $2200

Interest = $2200 \(\times\)\((1.000082)^{(2190)}\) - $2200

Interest ≈ $402.04 - $2200

Interest ≈ -$1797.96 (rounded to two decimal places)

In all three cases, the interest earned is negative, indicating that the accounts would have lost money rather than gained interest.

This suggests that there might be an error in the calculations or the provided interest rates. It's important to verify the given information to ensure accurate calculations and resolve any discrepancies.

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Answer: C; 5.32

Step-by-step explanation: If you are short $5.32, then that is represented as -5.32. The opposite of -5.32 is +5.32 or just 5.32. I hoped this helped!

Answer:

c

Step-by-step explanation:

i search it up

Answer:

C

Step-by-step explanation:

Answer:

3.5 feet

Step-by-step explanation:

You see, the question states that the distance it travels is always 3.5 minutes per foot traveled. Therefore, 3.5 is the answer.

Answer:

Step-by-step explanation:

The equation is a proportional one. This is the kind of question you sort of have to look at twice.

d = 3.5 m

m = 1 minute

d = 3.5 * 1

d = 3.5 feet per minute.

Answer:

25 option

have a nice day ahead

Step-by-step explanation:

well I don't know the correct answer

The cosine equation of the function shown is f(x) = 4cos(x) + 3

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

The graph

From the graph, we can see that the function is shifted up

Next, we enter the points in a graphing calculator to determine the function

From the graph, we have

f(x) = 4cos(x) + 3

Hence, the equation is f(x) = 4cos(x) + 3

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From the given distributions, the distribution that would have the least variation is weights of 20-year-old women. (Option A)

A variation refers to a relation between a set of values of one variable and a set of values of other variables. Hence, in a distribution, variability indicates how far apart points lie from each other and from the center of a distribution or a data set. Variability is also referred to as spread, scatter, or dispersion. There are many ways to describe variability or spread including range, interquartile range (IQR), and variance and standard deviation. The variance is defined as the sum of the squared distances of each term in the distribution from the mean (μ), divided by the number of terms in the distribution (N). The distributions which will have least variation would be weights of 20-year-old women, as due to smaller range, the difference between the values and the mean would be smaller as well. Hence, the variance would be least for this distribution.

Note: The question is incomplete. The complete question probably is: From the following distributions, which distributions would have the least variation. (A) Weight of 20-year-old woman (B) Weight of all adult men (C) Weight of all adults (D) Weight of 20 year old.

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A is either 45° or 135°.

To prove the given statement, let's assume that the points B and C lie on a coordinate plane, with the origin (0, 0) as the common vertex of the right angles at points B, C, and A. Let the coordinates of points B and C be (x₁, y₁) and (x₂, y₂) respectively.

Using the distance formula, we have:

AB² = x₁² + y₁²

AC² = x₂² + y₂²

According to the given equation, +b4+c4 = 20² (b²+c²), we can rewrite it as:

(x₁² + y₁²) + (x₂² + y₂²) = 20² [(x₁² + y₁²) + (x₂² + y₂²)]

Expanding and simplifying the equation, we get:

x₁² + y₁² + x₂² + y₂² = 20² (x₁² + y₁² + x₂² + y₂²)

This equation can be further simplified to:

(x₁² + y₁²) + (x₂² + y₂²) = (20² - 1) (x₁² + y₁² + x₂² + y₂²)

Since the left side represents the sum of the squares of the distances from the origin to points B and C, and the right side is a constant multiplied by the same sum, we can conclude that the points B and C must lie on a circle centered at the origin.

In a circle, the sum of angles subtended by two perpendicular chords at the center is either 180° or 360°. Since the given problem involves right angles, we consider the sum of angles to be 180°.

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Answer:

the loan was 1000

Step-by-step explanation:

Take the tuition and multiply by 5/6

1200 *5/6

1200/6 *5

200 *5

1000

Answer:

$1000

Step-by-step explanation:

In order to find 5/6 of the tuition, we just need to multiply the 2 values together.

5/6*1200

Note that 1200 = 1200/1

5/6*1200/1

When multiplying fractions, we can multiply the numerators together, and the denominators together.

5*1200/6*1

6000/6

Divide.

1000

Therefore, the loan was $1000.

Answer:

120° and 60°

Step-by-step explanation:

The sum of the exterior angle of a polygon is 360°, then

exterior angle = 360° ÷ 3 = 120°

The exterior and interior angle sum to 180°, then

interior angle = 180° - 120° = 60°

Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

The correct expression is 5/a = 1. There is no need to introduce an additional variable "x".

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.

The error in the reasoning is that it assumes that multiplying the second fraction by "x" will result in an equivalent expression to 5/a. However, this is not necessarily true.

To correct the error, we can use the property of reciprocals, which states that if a/b = c/d, then b/a = d/c. Using this property, we can rewrite the given equation as:

a/5 = b/3

5/a = 3/b (multiplying both sides by 5/a)

5/a = (b/3) * (3/b) (multiplying both sides by the reciprocal of b/3)

5/a = 1

Therefore, the correct expression is 5/a = 1. There is no need to introduce an additional variable "x".

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Answer:

Step-by-step explanation:

Remaining fraction:

1/5 of books are encyclopedia

Answer:

Let the total fraction of books be 1, then;

\(1 - ( \frac{1}{10} + \frac{2}{10} + \frac{1}{2} ) \\ 1 - ( \frac{(1 + 2 + 5)}{10} ) \\ (1 - \frac{8}{10}) = \frac{(10 - 8)}{10} \\ \frac{2}{10} = \boxed{ \frac{1}{5} }\)

I am just not sure if I did this properly. My professor hasn't really gone over when to use the range equation but I would assume range would equal the distance traveled therefore can be used for this problem. If not the how would I go about solving this? I did 1/6*9.8=1.63 for g on the moon Then used R=(Vi^2sin2theta)/g so on the moon R=((28^2)sin2*35)/1.63=452m

Please Brainliest..? thx

Answer:

Step-by-step explanation:

Given that:

t          0           1              2          3            4            5           6            7

A'(t)    0.91       0.83       0.76     0.69       0.62      0.58      0.48      0.44

a)  \(\Delta x = \dfrac{5-0}{5}\)

\(\Delta x = 1\)

\(L_ 5= \Delta x ( (A'(0)+A'(1)+A'(2)+A'(3)+A'(4)) \\ \\ = 1 (0.91 + 0.83+ 0.76 +0.69 + 0.62 ) \\\\ L_5 =1( 3.81) \\ \\ \mathbf{L_5 = 3.81}\)

\(R_ 5= \Delta x ( (A'(1)+A'(2)+A'(3)+A'(4)+A'(5)) \\ \\ = 1 ( 0.83+ 0.76 +0.69 + 0.62 +0.58) \\\\ R_5 =1( 3.48) \\ \\ \mathbf{R_5 = 3.48}\)

The true statement:

\(Since, R_5 = 3.48 \ and \ L_5 = 3.81; \\ \\ Then : R_5 \le \int \limits ^5_0 A'(t) dt \le L_5\)

Answer:

its 6.

hope it helps.. its 6.

EXPLANATION

Since we have the given polynomial, multiplying terms:

Multiplying terms:

Removing the parentheses:

The marginal frequency of students who chose dancing is 37.

The correct answer to the given question is option 3.

The marginal frequency of students who chose dancing can be calculated by adding up the number of students who chose dancing in each row or column. In this case, we need to add up the number of art students who chose dancing (22) and the number of music students who chose dancing (15), which gives us a total of 37. This is the marginal frequency of students who chose dancing.

Based on the survey results, it appears that a slightly higher percentage of art students prefer dancing (41.5%) compared to music students (31.9%). However, both groups of students seem to be fairly evenly split between dancing and playing sports, with a slight preference for playing sports overall.

It's worth noting that cardiovascular activity is important for overall health and well-being, and both dancing and playing sports can provide great opportunities for exercise and physical activity. Additionally, both activities can also be enjoyable and provide a sense of community and social connection, which is important for middle school students who are still developing their social skills and relationships. Ultimately, the choice between dancing and playing sports will depend on individual interests, preferences, and abilities.

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The coupon rate of the bonds by King of Diamonds Industries would be 7 %.

The formula for the bond price shows the coupon payment and so can be used to find the coupon rate:

= (Coupon payment  x ( 1 - ( 1 + r ) ^ ( - number of years till maturity ) ) ) / r + Face value /  (1  + rate )^ number of years

1,482.01 = (C x (1 - (1 + 0.07 )^ (- 14) ) ) / 0.07 + F / (1 + 0.07 ) ^ 14

103.7407 - 0.07 x (F / (1 + 0.07) ^14 ) = C x  (1 - ( 1 + 0.07) ^ ( - 14) )

Using a calculator, C is $ 70.

This means that the coupon rate is:

= 70 / 1, 000

= 7 %

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