At 8:30 A.M., a coroner was called to the home of a person who had died during the night. In order to estimate the time of death, the coroner took the person's temperature twice. At 9:00 A.M. the temperature was 85.7°F, and at 11:00 a.m. the temperature was 82.8°F. From these two temperatures, the coroner was able to determine that the time elapsed since death and the body temperature were related by the formula t=-10 lnT-70/98.6-70 where t is the time in hours elapsed since the person died and T is the temperature (in degrees Fahrenheit) of the person's body. Assume that the person had a normal body temperature of 98.6°F at death, and that the room temperature was a constant 70°F. (This formula is derived from a general cooling principle called Newton 's Law of Cooling.) Use the formula to estimate the time of death of the person.

The best answer would be 213.

Assuming that the sign denotes summation, we are adding from k=4 to k=9.

To get, we change k=4 to k=9.

We simplify obtaining,

To simplify means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

Summarizing mainly entails entering the values k=4, 5, 6, 7, 8, and 9 into the formula section 5K+3 and adding them all together.

So, the result is:

(5(4)+3)+(5(5) + 3) + (5(6) + 3) + (5(7) +3) + (5(8) + 3) + (5(9) + 3) 23+28+33 +38+43 + 48

= 213

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Answer:

e=9.14

Step-by-step explanation:

e²=a²+b²-2abcosФ

e²=36+25-2(30)cos112

e=√36+25-2(30)cos112

e=9.14

Answer:

b. 22

Step-by-step explanation:

1.6 x 14 = 22.4

22.4 rounded is 22

Answer:

D. 483.84 ft^2.

Step-by-step explanation:

we have 2 triangles and 7 rectangles, 5 of which are 8.4*8.4 squares.

Area = 2 * 1/2 * 4 * 8.4 + 2*5.8*8.4 + 5 * 8.4^2

= 33.6 + 97.44 + 352.8

= 483.84 ft^2.

Answer:

See Explanation

Step by step Explanation:

The question is incomplete as the plots that show the distance traveled is not given.

So, I will answer the question with the attached plots.

The number of dots on each day represents the number of miles travelled on that day.

From Elizabeth's plot, the shortest is 1 mile on day 4 (i.e. 1 dot on day 4)

From Izak's plot, the shortest is 2 miles on day 3 (i.e. 2 dots on day 3)

Calculate the difference between both distances

\(d = 2\ miles - 1\ mile\)

\(d = 1\ mile\)

Hence, the shortest distance travelled by Izak is 1 mile more than the shortest by Elizabeth

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation: The slope of a line is rise over run. Learn how to calculate the slope of the line in a graph  by  finding  the change  in y and the change in x.

Answer:

130 degrees is your answer

Step-by-step explanation:

The measurement of angle C is given by the expression 180° – 25° – 25°. So, angle C measures 130°.- answer from edmentum

To determine the change in angular momentum (ΔL) of a cylinder from t = 0 to t = t0, a student can use the equation:

ΔL = I * Δω

where ΔL is the change in angular momentum, I is the moment of inertia of the cylinder, and Δω is the change in angular velocity.

To calculate Δω, the student needs to know the initial and final angular velocities, ω0 and ωt0, respectively. The change in angular velocity can be calculated as:

Δω = ωt0 - ω0

Once Δω is determined, the student can use the moment of inertia (I) of the cylinder to calculate ΔL using the equation mentioned earlier.

The moment of inertia (I) depends on the mass distribution and shape of the cylinder. For a solid cylinder rotating about its central axis, the moment of inertia is given by:

I = (1/2) * m * r^2

where m is the mass of the cylinder and r is the radius of the cylinder.

By substituting the known values for Δω and I into the equation ΔL = I * Δω, the student can calculate the change in angular momentum (ΔL) of the cylinder from t = 0 to t = t0.

It's important to note that this method assumes that no external torques act on the cylinder during the time interval. If there are external torques involved, the equation for ΔL would need to include those torques as well.

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The correlation coefficient between x and f(x) is approximately 0.39. This suggests a weak positive correlation between the cost per seat and the profit the airline makes.

The precise metric used in a correlation analysis to quantify the strength of the linear relationship between two variables is the correlation coefficient.

To calculate the correlation coefficient between x and f(x), we need to calculate several quantities first:

mean of x:

\($\overline{x}\) = {50+35+60+65+70+75+80}{7} = {435}/{7}

= 62.14

mean of f(x):

\($\overline{f(x)}\)= {1,272 + 1,884.5 + 2,322 + 2,584.5 + 2,672 + 2,584.5 + 2,322}/{7}

= 2,112.86

and, standard deviation of x:

\($s_x\)=\(\sqrt{\frac{\sum_{i=1}^n (x_i - \overline{x})^2}{n-1}}\)

= \(= \sqrt{\frac{(50-62.14)^2 + (35-62.14)^2 + (60-62.14)^2 + (65-62.14)^2 + (70-62.14)^2 + (75-62.14)^2 + (80-62.14)^2}{6}} \\\approx 17.27$\)

and, standard deviation of f(x):

\($s_{f(x)} = \sqrt{\frac{\sum_{i=1}^n (f(x_i) - \overline{f(x)})^2}{n-1}}\)

= (1,272-2,112.86)² + (1,884.5-2,112.86)² + (2,322-2,112.86)² + (2,584.5-2,112.86)² + (2,672-2,112.86)²+  (2,584.5-2,112.86)² + (2,322-2,112.86)²}/ 6

= 385.09

Now, covariance of x and f(x):

\($cov(x,f(x)) = \frac{\sum_{i=1}^n (x_i - \overline{x})(f(x_i) - \overline{f(x)})}{n-1}\)

= {(50-62.14)(1,272-2,112.86) + (35-62.14)(1,884.5-2,112.86) + (60-62.14)(2,322-2,112.86) + (65-62.14)(2,584.5-2,112.86) + (70-62.14)(2,672-2,112.86) + (75-62.14)(2,584.5-2,112.86) + (80-62.14)(2,322-2,112.86)} / 6

= 762.36

Using these values, we can calculate the correlation coefficient:

\($r = \frac{cov(x,f(x))}{s_x s_{f(x)}} = \frac{762.36}{17.27 \cdot 385.09} \approx 0.39$\)

Therefore, the correlation coefficient between x and f(x) is approximately 0.39. This suggests a weak positive correlation between the cost per seat and the profit the airline makes.

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Answer: 68

Step-by-step explanation: 32 + 2=34 34*2 + 68 2 because a person naturaly has 2 feets  

The domain will be all real numbers and the range will be all real numbers greater than or equal to 1.

The domain of a function is the set of all possible input values that can be used as arguments for the function. In this case, there are no restrictions on the input values of x, so the domain is all real numbers.

Domain: All real numbers

Range:

To find the range of the function, we can complete the square to rewrite the function in vertex form:

f(x) = x^2 + 10x + 26

f(x) = (x + 5)^2 + 1

Since the square of a real number is always nonnegative, the minimum value of the function is 1, which occurs when x = -5. Therefore, the range of the function is all real numbers greater than or equal to 1.

Range: All real numbers greater than or equal to 1.

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Answer:

\(y = 4 {ax}^{2} \\ by \: comparison \: with \: y = 1.5 {x}^{2} \\ 4a = 1.5 \\ a = \frac{1.5}{4} \\ a = \frac{3}{8} \\ vertex = \frac{3}{8} \: \: o r\: \: 0.375\)

Answer:

(0,0)

Step-by-step explanation:

The vertex of the parabola is the minimum ( or maximum) point

Since this is an open upwards parabola, it is the minimum point

The minimum is (0,0) so that is the vertex

Answer:

Javier walks more steps than ebony given the same minutes

Step-by-step explanation:

Javier records a walk of 6000 steps in 50 minutes.

Ebony describes her step rate with the equation y=118x

Where,

y = number of steps

x = number of minutes she walks

Javier and Ebony each walk a total of 5 hours. Who walks more steps?

5 hours = 5 × 60 minutes

= 300 minutes

Javier records a walk of 6000 steps in 50 minutes.

6000 : 50 minutes = x : 300 minutes

6000/50 = x / 300

Cross product

6000 * 300 = 50 * x

1,800,000 = 50x

x = 1,800,000 / 50

= 36,000

x = 36,000

Javier walks 36,000 steps

Ebony describes her step rate with the equation y = 118x

x = 300 minutes

y = 118(300)

= 35,400

y = 35,400

Ebony walks 35,400 steps

Therefore,

Javier walks more steps than ebony given the same minutes

ANSWER

First quadrant

EXPLANATION

Those two trigonometric functions are the reciprocal of the sine and cosine functions:

Therefore:

sinθ is greater than zero for the first and second quadrants.

Also:

cosθ is greater than zero for the first and fourth quadrants.

Hence, for cscθ>0 and secθ>0, angle θ lies in the first quadrant.

The cost of the wall paper per square feet is 0.72 dollars.

The wall paper is rectangular in shape. The dimension of the wall paper is 42 feet by 25.5 feet.

The total cost of the wall paper is 771.12 dollars. Therefore, let's find the cost per square ft.

Hence,

area of the wall paper = 42 × 25.5

area of the wall paper = 1071 ft²

Therefore,

1071 ft² =  771.12 dollars

1 ft² = ?

Hence,

cost per square feet = 771.12  / 1071

cost per square feet = 0.72 dollors

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Answer:

i don't know but i try

Step-by-step explanation:

Answer:

D. x^2-x-9-12/x-2

Step-by-step explanation:

We can use synthetic division to divide (x^3 - 3x^2 - 7x + 6) by (x - 2). First, we set up the division as follows:

    2 |   1   -3   -7    6

       |______2___-2__-18

       | 1   -1   -9  -12

The numbers on the bottom row of the synthetic division table represent the coefficients of the quotient polynomial. Therefore, the quotient is x^2 - x - 9, and the remainder is -12.

So, we have:

(x^3 - 3x^2 - 7x + 6) / (x - 2) = x^2 - x - 9 + (-12 / x - 2)

Therefore, the correct option is D: x^2 - x - 9 - 12/(x - 2).

Answer:

d. 18^2 + 15^2 = c^2. 23.4

Step-by-step explanation:

Right triangle: c^2 = a^2 + b^2

with c is the hypotenuse, a and b are the other sides

c^2 = 18^2 + 15^2

c^2 = 324 + 225

c^2 = 549

c = 23.4

Answer:

\(New\ Lengths = (14,21)\)

\(New\ Scale\ Factor = \frac{1}{7}\)

Step-by-step explanation:

Given

Rectangle:

Length = 2 in

Width = 3 in

Scale Factor = 7

Solving (a):

The side lengths of the new scale is calculated as follows;

New Lengths = Old Lengths * Scale Factor

\(New\ Lengths = (2,3) * 7\)

\(New\ Lengths = (2 * 7,3* 7)\)

\(New\ Lengths = (14,21)\)

Solving (b): To go back to the original length

Given that the initial scale factor is 7;

The new scale factor is the reciprocal of the old factor;

Hence;

\(New\ Scale\ Factor = \frac{1}{7}\)

Answer:

(x + 4)(x + 2)

Step-by-step explanation:

x^2 + 6x + 8

If this can be factorised, then we end up with

x^2 + 6x + 8 = (x + ___)(x + ___)

To fill in the blanks, we need two numbers whose product is 8 and whose sum is 6.

The numbers are 4 and 2.

x^2 + 6x + 8 = (x + 4)(x + 2)

Answer:

(x+4)(x+2)

Step-by-step explanation:

To factorize:

two number that your sum = 6

two number that your multiplication = 8

The numbers are:

4 and 2

then:

x² + 6x + 8 = (x+4)(x+2)

when your friend was born, your friend's parents deposited $2000 in an account paying 4.5% interest compounded yearly. Then the account balance be after 18 years is 4416.96

Initial amount deposited into the account is $2000 This means that the principal,

P = 2000

It was compounded yearly. This means that it was compounded once in a year. So

n = 1

The rate at which the principal was compounded is 4.5%. So

r = 4.5/100 = 0.045

It was compounded for 18 years. So

t = 18

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount in the account at the end of t years. Therefore

A = 2000(1 + 0.045/1)^ 1× 18

A = 2000(1 + 0.045)^18

A= 4416.96

Hence , the amount becomes after 8 years is 4416.96

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Answer:

y=1/4·x+-2 1/4

Step-by-step explanation:

Answer: D. 6

Step-by-step explanation: 7 + 7 = 14

30 - 4 - 14 = 12

12/2 = 6

In this question, i first went to see what the total amount is, which, when subtracting the change from the money paid (30-4) is $26

Next, i went to see the rings cost. Since she bought 2 rings for the price of 7 each, i multiplied 2 with the cost (2 x 7) which is $14

That brought me to the equation:

\(26 - 14= 12\)

The cost of the earring together is $12, but since we want to find out how much each pair costs, i divided 12 by 2 (12/2) and got the answer:

$6 per pair of earring (Letter D)

thank you! btw can u please give me brainly :3

Answer:

2/13

Step-by-step explanation:

Ratio: 4/26

Simplest form : 2/13

Answer:

462 paths from A to B

Step-by-step explanation:

The question is incomplete. However, a possible question is to determine the number of possible paths on the grid map.

The first step is to represent the grid map itself. (See attachment 1)

From the question, we understand that:

There are a several number of ways to navigate through. However, one possible way is in attachment 2

In attachment 2,

And we have:

\(R = 5\)     and    \(U = 6\)

The number of possible paths (N) is then calculated as:

\(N = \frac{(N + U)!}{N!U!}\)

Substitute values for N and U

\(N = \frac{(5 + 6)!}{5!6!}\)

\(N = \frac{11!}{5!6!}\)

\(N = \frac{39916800}{120 * 720}\)

\(N = \frac{39916800}{86400}\)

\(N = 462\)

Hence, there are 462 possible paths from A to B

Answer: 19

Step-by-Step explanation:

So I am assuming that you should divide 114 divided by 6 which will leave you with the answer of 19.

Answer:

22

Step-by-step explanation:

2-4i and i=6

2-4(6)

=22