The equation R= -0.028t +20.8 can be used to predict the world record in the 200 meter​ dash, where R stands for the record in seconds and t for the number of years since 1920. In what year did the record become 19.68 ​seconds?

Answer:

1. 3.767

2. 0.145

Step-by-step explanation:

Let X be the exam scores and Y be the number of drinks.

X     Y   X-Xbar    Y-Ybar   (X-Xbar)(Y-Ybar)    (X-Xbar)²       (Y-Ybar)²    

75    5    -2.3          2.3          -5.29                      5.29              5.29

92    3     14.7         0.3           4.41                       216.09           0.09

84    2     6.7         -0.7           -4.69                     44.89             0.49

64    4     -13.3        1.3           -17.29                     176.89           1.69

64    2     -13.3       -0.7           9.31                       176.89           0.49

86    7     8.7           4.3           37.41                     75.69            18.49

81     3     3.7           0.3           1.11                         13.69             0.09

61     0    -16.3        -2.7           44.01                     265.69          7.29

73    1      -4.3         -1.7            7.31                        18.49             2.89

93    0    15.7         -2.7           -42.39                    246.49          7.29

sumx=773, sumy=27, sum(x-xbar)(y-ybar)= 33.9 , sum(X-Xbar)²= 1240.1 ,sum(Y-Ybar)²= 44.1

Xbar=sumx/n=773/10=77.3

Ybar=sumy/n=27/10=2.7

1.

[tex]Cov(x,y)=sxy=\frac{Sum(X-Xbar)(Y-Ybar)}{n-1}[/tex]

Cov(x,y)=33.9/9

Cov(x,y)=3.76667

The the sample co-variance between the exam scores and the number of energy drinks consumed is 3.767

2.

[tex]Cor(x,y)=r=\frac{Sum(X-Xbar)(Y-Ybar)}{\sqrt{Sum(X-Xbar)^2sum(Y-Ybar)^2} }[/tex]

[tex]Cor(x,y)=r=\frac{33.9}{\sqrt{(1240.1)(44.1)} }[/tex]

Cor(x,y)=r=33.9/233.85553

Cor(x,y)=r=0.14496

The sample correlation coefficient between the exam scores and the number of energy drinks consumed 0.145.

Calculate sample covariance and correlation coefficient between exam scores and energy drinks consumed by students.

Sample Covariance:
1. Calculate the mean of exam scores (77.3) and number of drinks (2.7).
2. Subtract the mean from each score and drink value to get the deviations.
3. Multiply the deviations of exam scores and drinks for each student, sum them up, and divide by 10 to get the sample covariance of approximately -22.6.

Sample Correlation Coefficient:
1. Calculate the standard deviations of exam scores (12.15) and number of drinks (2.51).
2. Divide the sample covariance by the product of the standard deviations to get the correlation coefficient of around -0.79.

Answer:

96 ft/s

Step-by-step explanation:

We can start by deriving the equation of the velocity, which is the derivative of the position equation:

[tex]v(t) = \frac{ds}{dt} = (-16t^2)' + 800' = -32t[/tex]

After 3 seconds, the wrench would achieve a speed of

v(3) = -32t = -32*3 = -96 ft/s

So it's falling at the rate of 96 ft per second after 3 s

Final answer:

To calculate the velocity of the falling wrench after 3 seconds, the first derivative of the position function s(t) is taken to get v(t) = -32t. By substituting t with 3, the velocity at three seconds is -96 feet per second.

Explanation:

To find how fast the wrench will be falling after 3 seconds, we need to calculate the first derivative of the position function s(t) to get the velocity function v(t). The position function given is s(t) = −16t² + 800. Differentiating this with respect to t gives v(t) = d/dt (-16t² + 800) = -32t.

To find the velocity after 3 seconds, we substitute t = 3 into the velocity equation, which gives v(3) = -32(3) = -96 feet per second.

Therefore, the wrench will be falling at a velocity of -96 feet per second after 3 seconds.

Answer:

Mean speed is 55.7 mph.

Step-by-step explanation:

The provided frequency distribution is:

Speed Cars

30-39 4

40-49 19

50-59 50

60-69 15

70-79 12

The formula to compute the mean for the grouped data is:

[tex]\bar{X} =\frac{\sum(mf)}{\sum(f)}[/tex]

Here, m is mid point and f is frequency.

The mean speed can be computed as:

Thus, the mean speed is 55.7 mph.

To find the mean of data from a frequency table, multiply each speed by its frequency, sum those products, and then divide by the total number of items. This produces a weighted average that reflects the frequency of each speed value in the dataset.

To calculate the mean from a frequency table, we should multiply each speed by its frequency to get the 'combined speed' for each group. Add those combined speeds together, then divide by the total number of cars (or the sum of the frequencies).

For example, suppose we had 5 cars with a speed of 60 mph and 10 cars with a speed of 70 mph. We multiply each speed by its frequency (5*60 + 10*70), then sum these values to get the total combined speed. Divide this total combined speed by the total number of cars (5 + 10) to get the mean speed.

This method averages out the impact of each speed, weighted by how frequently each occurs in the dataset.

https://brainly.com/question/31994405

Answer:

Sampling Frame

Step-by-step explanation:

If you are finding the representation of this style than it isHilton Honors membership list represents the Sampling frame

Explanation:

A yard is a larger unit of measure than an inch, so it takes fewer yards to equal the distance of a larger number of inches.

__

As it happens, 1 yard is exactly the same as 36 inches (by definition). So the measurement that is 36 inches will be a measurement that is 1 yard.

Final answer:

Josh's desk appeared to have different measurements because of the change in units from inches to yards; 1 yard is equal to 36 inches, so the desk's height didn't actually decrease.

Explanation:

The question seems to contain a typo. Assuming the question should read as 'Josh's desk is 36 inches tall, when he measured the desk using a yard stick, it was 1 yard tall,' the discrepancy in numbers is because of the different units used to measure the desk. There was no actual decrease in size; it is merely a difference in the units of measurement. Inches and yards are both units used to measure length or height, with 1 yard being equivalent to 36 inches. When Josh used a yard stick, he measured the desk in yards, which is a larger unit compared to inches. This is why the number appears to be smaller (1 instead of 36), even though the height of the desk remained the same.

Explanation:

It isn't clear what the elements of your flowchart are supposed to look like. In general, the proof would go like this:

1. List the "givens": PQ=6=TS; ∠P=120°=∠T; ∠PRQ and ∠TRS are vertical angles.

2. Note that the vertical angles are congruent

3. Claim ΔPRQ ≅ ΔTRS by the AAS congruence postulate since two corresponding adjacent angles and the corresponding sides not between them have been shown to be congruent.

Answer: y = 3x - 5

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

c = intercept

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

y = -1/3x + 2

Comparing with the slope intercept form, slope = - 1/3

If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. Therefore, the slope of the line passing through

(2, 1) is 3/1 = 3

To determine the intercept, we would substitute m = 3, x = 2 and y = 1 into y = mx + c. It becomes

1 = 3 × 2 + c = 6 + c

c = 1 - 6 = - 5

The equation becomes

y = 3x - 5

Answer:

x=16

Step-by-step explanation:

Since triangle DGH is parallel to trianle DBN, the corresponding sides are also proportional.

We have [tex]\frac{DN}{DH}=\frac{DB}{DG}[/tex]

This implies that:

[tex]\frac{40}{40+x}=\frac{30}{42}[/tex]

We cross multiply to get;

[tex]30(40+x)=42*40[/tex]

This implies that:

[tex](x+40)=14*4[/tex]

[tex]x+40=56[/tex]

[tex]x=56-40[/tex]

[tex]x=16[/tex]

soo this may seem a little awkwark but it still should provide the same resault however its faster :)

so we have

(48x^5-16x^3+40x)/8x

What we are going to be doing is factoring out any and all possibilities for

(48x^5-16x^3+40x)

first factor

(8x(6x^4-2x^2+5))/8x

when we get to this step simplify 8x

we are left with 6x^4-2x^2+5

in order to get an answer that would often be used by long devision just get rid of the +5

This is just a remainder using long devision your instructer may ask for

6x^4-2x^2

Hope it helps

Answer:

6x⁴ - 2x² + 5

Step-by-step explanation:

[48x⁵ - 16x³ + 40x] ÷ 8x

[8x(6x⁴ - 2x² + 5)] ÷ 8x

6x⁴ - 2x² + 5

Check:

(6x⁴ - 2x² + 5)(8x)

= 48x⁵ - 16x³ + 40x (verified)

Answer:

The length of the rope between the boat and the dock is of 30 feet.

Step-by-step explanation:

Given:

tan(40) ≈ 0.839

Angle of depression = 40 (deg)

Distance between boat and the floor of the ocean = 25.17 feet

If we look into the diagram we can see that,they form 2 right angled triangle.

Where we can say that :

Distance between boat and dock  = Rope's distance = Base of the triangle.

Let the length of the rope be 'x' feet.

Considering the dotted triangle:

[tex]tan\ (40) =\frac{opposite}{adjacent}[/tex]

⇒ [tex]tan\ (40) =\frac{25.17}{x}[/tex]

⇒ [tex]tan\ (40)\times x =\frac{25.17}{x}\times x[/tex]

⇒ [tex]tan\ (40)\times x =25.17[/tex]

⇒ [tex]\frac{tan\ (40)\times x}{tan\ (40)} =\frac{25.17}{tan\ (40)}[/tex]

⇒ [tex]x =\frac{25.17}{0.839}[/tex]

⇒ [tex]x= 30[/tex]

Length of the rope between the boat and the dock is 'x' = 30 feet.

Answer:

[tex]\angle ACD=124\°\\\\\angle CED=64\°[/tex]

Step-by-step explanation:

To solve this exercise you need to remember:

1. The sum of the Interior angles of a triangle is 180 degrees.

2. Straight angles are those angles that measure 180 degrees.

3. Supplementary angles are those angles whose sum is 180 degrees.

4. Vertical angles are angles that share the same vertex and they are opposiste to each other. They are congruent.

Knowing the above, you can set up the following equation:

[tex]31\°+93\°+\angle ACB=180\°[/tex]

Solving the equation, you get:

[tex]\angle ACB=180\°-124\°=56\°[/tex]

Since [tex]\angle ACB[/tex] and [tex]\angle DCE[/tex] are Vertical angles:

[tex]\angle ACB=\angle DCE=56\°[/tex]

Knowing the measure of [tex]\angle DCE[/tex]  , you can write the following equation to find [tex]\angle CED[/tex]:

[tex]56\°+60\°+\angle CED=180\°[/tex]

Solve the equation:

[tex]\angle CED=180\°-116\°=64\°[/tex]

As you can observe in the figure, the angles [tex]\angle DCE[/tex] and [tex]\angle ACD[/tex] are Supplementary. Then:

[tex]\angle ACD+\angle DCE=180\°\\\\\angle ACD+56\°=180\°[/tex]

Solving for [tex]\angle ACD[/tex], you get:

[tex]\angle ACD=180\°-56\°=124\°[/tex]

Answer:

Triangle DEF is not a right triangle ; possible lengths are 20 & 15

Step-by-step explanation:

For right triangle;

the sum of the square of the two adjacent sides must equal the square of the hypotenus.

Therefore, (6^2)+(11^2)≠(13^2).

the possible length are 20 & 15 because

(20^2)+(15^2)=(25^2)

Triangle DEF with sides lengths of 6, 11, and 13 units is not a right triangle as the Pythagorean theorem is not satisfied. To find the lengths of the legs of a right triangle with a hypotenuse of 25, one can use the Pythagorean theorem to find whole number pairs that satisfy the equation.

To determine whether triangle DEF is a right triangle with sides of lengths 6, 11, and 13 units, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c².

Let's check if the sides of triangle DEF satisfy this condition:

Since 157 does not equal 169, triangle DEF is not a right triangle.

For the second part of the question, we are given that a right triangle has a hypotenuse with a length of 25 units and we need to find the lengths of the legs which are whole numbers. We can use the Pythagorean theorem to find pairs of integers (a and b) that satisfy the equation a² + b² = 25² = 625. Some possible pairs of legs that meet this criterion include (7, 24), (15, 20), and (9, 24). Note that there are multiple correct answers to this question.

Answer:

[tex]C(x) = 45x + 75\\\text{where x is the width of rectangular pen}[/tex]

Step-by-step explanation:

We are given the following in the question:

The length of the pen will be 5 feet more than twice as long as the width of the pen.

Let y be the length and x be the width. Thus, we can write:

[tex]y = 2x +5[/tex]

Fencing = Perimeter of rectangular pen

[tex]\text{Perimeter of rectangle} = 2(\text{length} + \text{width})\\ P = 2(y+x)\\P=2(2x+5+x)\\P= 2(3x+5)\\P = (6x + 10)\text{ feet}[/tex]

The cost of the pen will be $7.50 per foot of fencing.

Total Cost of fencing =

[tex]\text{Cost of fencing}\times \text{Perimeter}\\C(x) = 7.50\times (6x+10)\\C(x) = 45x + 75\\\text{where x is the width of rectangular pen}[/tex]

is the required cost function.

Final answer:

The cost function for fencing a rectangular pen, given the width x and a cost of $7.50 per foot, is c(x) = 45x + 75, representing the total cost as a function of the width x.

Explanation:

The student is asking for a function that represents the cost of fencing a rectangular pen when the width is given. Let x be the width of the pen. The length of the pen, according to the problem, is 5 feet more than twice the width, so it can be expressed as 2x + 5 feet.

The cost of the fencing is $7.50 per foot. To find the total cost of the pen, we have to calculate the perimeter of the rectangular pen, which is 2 times the width plus 2 times the length. Hence, the perimeter P(x) can be represented as P(x) = 2x + 2(2x+5).

Multiplying through and simplifying gives us the cost function c(x) = 7.50 * P(x). Therefore, c(x) = 7.50 * (2x + 2(2x + 5)) = 7.50 * (6x + 10) = 45x + 75. This function represents the cost of fencing the pen as a function of its width x.

Answer:

8

Step-by-step explanation:

Hi,

When we divide 5655 by N, we get remainder of 11, which means that 5655-11 is a multiple of N.

5655 - 11 = 5644 is a multiple of N.

Similarly, 5879-14 should be a multiple of N.

5879 - 14 = 5865 is a multiple of N.

Because 5644 and 5865 are both multiples of N, their difference must be a multiple of N.

5865 − 5644 = 221 then 221 is a multiple of N.

We have three number of which N can be a multiple of, however we choose to factorize the smallest possible number amongst these three, which is 221. (This is only for simplification of the solution, smaller the number, less the factors)

221 : 1, 13, 17, 221.

There are only two two - digit factors: 13 and 17.

We divide 5865 and 5644 by both numbers.

[tex]\frac{5865}{13} = 451.15 \\\frac{5865}{17} = 345 \\\frac{5644}{13} = 434.15 \\\frac{5644}{17} = 332\\[/tex]

Looking at these results, we know only 17 divides all three numbers.

Hence N=17.

The sum of both digits will be: 1 + 7 = 8

Subtract the two given numbers excluding their identical remainders to find a multiple of the divisor N. By then finding a two-digit factor of this multiple that can divide both numbers, we get N = 28. The sum of its digits is 10.

When a number is divided by a divisor and leaves the same remainder, the difference between these numbers is a multiple of that divisor. Therefore, as given, when 5655 is divided by a positive two-digit integer N, the remainder is 11, and also when 5879 is divided by N, the remainder is 11. To find N, we subtract the two numbers before considering the remainder, which will give us a number that is a multiple of N: 5879 - 5655 = 224.

So, N divides 224 perfectly. The factors of 224 that are two-digit numbers are 14, 16, and 28. However, since the remainder when dividing both 5655 and 5879 by N is identical and equal to 11, we need to make sure that both 5655-11 and 5879-11 are divisible by N equally, thus 5644 and 5868 should be divisible by N. The correct N which fulfills this condition is 28.

The sum of the digits of N or 28 is: 2 + 8 = 10.

Answer:

[tex]7\frac{29}{36}\ hours[/tex]

Step-by-step explanation:

Given:

Time spent on Monday (M) = [tex]4\frac{1}{4}\ hours[/tex]

Time spent on Tuesday (T) = [tex]3\frac{5}{9}\ hours[/tex]

Now, the total combined time spent on study is equal to the sum of the times spent on Monday and Tuesday.

So, we need to add both the times to get the combined time spent on studying.

The combined study time is given as:

Total time spent = Time spent on Monday + Time spent on Tuesday

[tex]Total\ time=4\frac{1}{4}+3\frac{5}{9}\\\\Total\ time = \frac{4\times 4+1}{4}+\frac{3\times 9+5}{9}\\\\Total\ time = \frac{17}{4}+\frac{32}{9}\\\\\textrm{Taking LCD of 9 and 4 as 36, we get:}\\\\Total\ time = \frac{17\times 9}{4\times 9}+\frac{32\times 4}{9\times 4}\\\\Total\ time = \frac{153}{36}+\frac{128}{36}\\\\\textrm{Since the denominators are same, we add the numerators.}\\\\Total\ time = \frac{153+128}{36}\\\\Total\ time = \frac{281}{36}\ hours[/tex]

Divide 281 by 36. The quotient is the whole number part, the remainder is the numerator part and the denominator remains the same.

So, on dividing, we get 7 as quotient and 29 as remainder. So, converting to mixed fractions, we get:

[tex]Total\ time = 7\frac{29}{36}\ hours[/tex]

Therefore, the  the combined time he spent studying is [tex]7\frac{29}{36}\ hours[/tex]

Answer:

  86 °F = 30 °C

Step-by-step explanation:

Put the given number in the equation and solve for C.

  86 = 9/5C +32

  54 = 9/5C

  (5/9)54 = C = 30

The equivalent is 30 degrees Celsius.

Final answer:

To convert 86 degrees Fahrenheit to Celsius, use the formula T°C = 5/9 (86 - 32). Subtracting 32 from 86 and then multiplying by 5/9 gives a result of 30 degrees Celsius.

Explanation:

The question asks how to find the Celsius equivalent of 86 degrees Fahrenheit using the formula to convert degrees Fahrenheit to degrees Celsius. The formula is T°C = 5/9 (T°F - 32), where T°C is the temperature in degrees Celsius and T°F is the temperature in degrees Fahrenheit.

To convert 86°F to Celsius, substitute 86 for T°F in the formula:

T°C = 5/9 (86 - 32)

First, subtract 32 from 86, which gives 54. Then, multiply 54 by 5/9 to get the final result:

T°C = 5/9 × 54

T°C = 30

Therefore, 86 degrees Fahrenheit is equivalent to 30 degrees Celsius.

Answer:

Step-by-step explanation:

The slope intercept form equation of a straight line is expressed as

y = mx + c

Where

m represents slope

c represents y intercept.

Comparing the given equations with the slope intercept form equation,

2) y = 4x + 14 is in the slope intercept form. Its slope is 4 and the intercept is 14.

3) y = -4x + 14 is in the slope intercept form. Its slope is - 4 and the intercept is 14.

4) y = 2x + 7 is in the slope intercept form. Its slope is 2 and the intercept is 7.

5) y = -2x + 7 is in the slope intercept form. Its slope is - 2 and the intercept is 7.

Answer:

the answer would be: y = 2x + 7 .

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

y = mx + c

y = -½x + 1

Final answer:

To solve for the distance, velocity, and acceleration of a hammer dropped from a hovering helicopter, calculations based on the given formula s(t) = 1818t^2 are used, yielding a fall of 29128 feet in 4 seconds, a velocity of 14512 feet/sec at 4 seconds, and a constant acceleration of 3636 feet/sec^2.

Explanation:

When an object is dropped on a certain earth-like planet, the distance it falls in t seconds, assuming that air resistance is negligible, is given by s(t) = 1818t2, where s(t) is in feet. To solve the problem involving a medic's reflex hammer dropped from a hovering helicopter:

(a) To find how far the hammer falls in 4 seconds, substitute t = 4 into the equation: s(4) = 1818(4)2 = 29128 feet.

(b) The velocity of the hammer after 4 seconds can be found using the derivative of s(t), v(t) = 2×1818×t. Substituting t = 4, v(4) = 2×1818×4 = 14512 feet/sec.

(c) The acceleration of the hammer is constant and equal to 2×1818 feet/sec2 = 3636 feet/sec2, which is twice the coefficient in the equation for s(t).

These calculations demonstrate the principles of kinematics, specifically how position, velocity, and acceleration relate to one another for an object in free fall on an earth-like planet with negligible air resistance.

Answer:

Step-by-step explanation:

Let "o" and "s" represent the number of pounds of orange slices and strawberry leaves in the mix, respectively. We want ...

  o + s = 13 . . . . . . . . . . . . . . . total weight

  1.29o +1.79s = 19.27 . . . . . .total cost

Solving the first equation for o, we can substitute that result into the second equation to get ...

  o = 13 -s

  1.29(13 -s) +1.79s = 19.27

  0.50s +16.77 = 19.27 . . . . eliminate parentheses

  0.50s = 2.50 . . . . . . . . . . . subtract 16.77

  s = 5 . . . . . . . . . . . . . . . . . . multiply by 2

  o = 13 -5 = 8

5 pounds of strawberry leaves should be mixed with 8 pounds of orange slices to get the desired mixture.

To find out how many pounds of both orange slices and strawberry leaves are needed for the mixture, we need to solve a system of equations involving weight and total cost.

The question involves solving a system of linear equations to determine how many pounds of orange slices and strawberry leaves should be mixed to achieve a 13-pound mixture that totals $19.27. Let's define two variables:

We have two equations based on the weight and cost of the mixture:

Solving this system will provide us with the values for x and y that satisfy both equations.

Answer: the combined time he spent studying is 281/36 hours

Step-by-step explanation:

The first step is to convert all mixed numbers to improper fraction.

On Monday Billy spent 4 1/4 hour study. Converting 4 1/4 hours to improper fraction, it becomes 17/4 hours.

On Tuesday he spent another 3 5/9 hour study. Converting 3 5/9 hours to improper fraction, it becomes 32/9 hours.

The combined time he spent studying answer as a mixed number would be

17/4 + 32/9 = (153 + 128)/36

= 281/36 hours

Answer: Let the Number of hours Enzo sleeps on average per day while School is in session be Y

Y = SS/115% = SS/1.15

Step-by-step explanation:

Given in the question:

- While on vacation, Enzo sleeps 115% as much as he sleeps when school is in session.

- Enzo sleeps SS hours per day during vacation

Mathematically, SS = 115% of Y

SS = 115% × Y

115% × Y = SS

Y = SS/115%

But 115% = 115/100 = 1.15

Therefore,

Y = SS/1.15

Solved!

Answer:

Option B.

Step-by-step explanation:

The given vertices of the polygon are (-6,-2),(-5,1),(-1,4),(1,1),(5,3),(1,-2).

We need to find the area of the polygon.

Plot the given vertices and on a coordinate plane and draw the polygon. Divide the polygon in 4 parts as shown below.

Area of rectangle is

[tex]A=length\times width[/tex]

Area of triangle is

[tex]A=\dfrac{1}{2}\times base\times height[/tex]

Area of each figure is

[tex]A_1=\dfrac{1}{2}\times 1\times 3=1.5[/tex]

[tex]A_2=\dfrac{1}{2}\times 6\times 3=9[/tex]

[tex]A_3=\dfrac{1}{2}\times 4\times 3=6[/tex]

[tex]A_4=6\times 3=18[/tex]

Area of polygon is

[tex]A=A_1+A_2+A_3+A_4[/tex]

[tex]A=1.5+9+6+18=34.5[/tex]

The area of polygon is 34.5 units².

Therefore, the correct option is B.

Answer:

20 percent

Step-by-step explanation:

Percentage score = [tex]\frac{actual score}{total score}[/tex] × 100

                              = [tex]\frac{6}{30}[/tex] × 100

                               = 20 percent

The 6th value in a sequence is -26.

Step-by-step explanation:

an = -2n-14

⇒ a6 = -2(6)-14

⇒ a6 = -12-14

⇒ a6 = -26

∴ The 6th value in a sequence is -26.

The space left inside the tree is 300 cubic feet.

David and Karen have to paint 275 square feet on the outside.

Explanation:

It is given that the length of the tree house is 7.5 feet

The width of the tree house is 8 feet

The height of the tree house is 5 feet

The tree house is in the shape of a rectangular prism.

The volume of the rectangular prism is given by

[tex]\text {Volume}=\text {length } \times \text {width} \times \text {height}[/tex]

Substituting the values, we have,

[tex]Volume$=7.5 \times 8 \times 5$\\Volume $=300$[/tex]

Thus, the volume of the rectangular prism is 300 cubic feet

Hence, the space left inside the tree is 300 cubic feet.

The area they have to paint on the outside can be determined using the formula for surface area of the prism .

[tex]Area=2(w l+h l+h w)[/tex]

Substituting the values, we get,

[tex]Area=2[(8*7.5)+(5*7.5)+(5*8)][/tex]

Multiplying the terms within the bracket, we get,

[tex]Area=2(60+37.5+40)[/tex]

Adding the terms, we have,

[tex]Area=2 \times 137.5[/tex]

Multiplying, we get,

[tex]Area =275[/tex]

Thus, David and Karen have to paint 275 square feet on the outside.

V= L x W x H

Leight x with x height = V

5 x 8 x 7.5= V

=300feet2

Step-by-step explanation:

Hope it helps

Answer:

The answer to your question is   y = 1/12 (x - 5)²

Step-by-step explanation:

Data

directrix   y = -3

focus       (5, 3)

Process

1.- Graph the directrix and focus to determine if the parabola is vertical or horizontal.

From the graph we know that it is a vertical parabola with equation

                  (x - h)² = 4p(y - k)

2.- From the graph we know that p = 3 because the distance from the focus to the directrix is 6 and p = 6/2.

3.- The vertex (5, 0)

4.- Substitution

                 (x - 5)² = 4(3)(y - 0)

5.- Simplification

                (x - 5)² = 12y

6.- Result

                y = 1/12 (x - 5)²

Answer:

y = 1/12 (x - 5)²

Step-by-step explanation:

Answer:

Step-by-step explanation:

concentration = amount of salt/solution

A) Initial concentration= 90/1000 = 0.09

Q = quantity of salt

Q(0) = 90 kg

Inflow rate = 8 l/min

Outflow rate = 8 l/min

Solution = 1000 L at any time t.

Salt inflow = 0.045 * 8 per minute

= 0.36 kg per minute

This is mixed and drains from the tank.

Outflow = [tex]\frac{Q(t)}{1000}[/tex]

Thus rate of change of salt

Q'(t) = inflow - outflow = [tex]0.36-\frac{Q(t)}{1000} \\=\frac{360-Q(t)}{1000}[/tex]

Separate the variables and integrate

[tex]\frac{1000dQ}{360-q(t)} =dt\\-1000 ln |360-Q(t)| = t+C\\ln |360-Q(t)| = -0.001+C'\\360-Q(t) = Ae^{-0.001t} \\Q(t) = 360-Ae^{-0.001t}[/tex]

Use the fact that Q(0) = 90

90 = 360-A

A = 270

So

[tex]Q(t) = 360-270e^{-0.001t}[/tex]

B) Q(t) = 360-270e^-0.004  = 91.07784

C) When t approaches infinity, we get

Q(t) tends to 360

So concentration =360/1000 = 0.36

Final answer:

a) The initial concentration of the solution in the tank is 0.09 kg/L. b) The amount of salt in the tank after 4 hours is 3.6 kg. c) The concentration of salt in the solution in the tank approaches 0.045 kg/L as time approaches infinity.

Explanation:

a) To find the concentration of the solution in the tank initially, we need to calculate the total mass of salt and water in the tank. The concentration is the mass of salt divided by the volume of water. Since 1 liter of water weighs 1 kg, the initial concentration of the solution in the tank is 90 kg of salt divided by 1000 kg of water, which is 0.09 kg/L.

b) To find the amount of salt in the tank after 4 hours, we need to calculate the amount of salt entering the tank and the amount of salt leaving the tank in that time. The amount of salt entering the tank is the concentration of the incoming solution (0.045 kg/L) multiplied by the rate of flow (8 L/min) and the time (4 hours = 240 minutes). This gives us 0.045 kg/L × 8 L/min × 240 min = 86.4 kg. The amount of salt leaving the tank is the concentration of the solution in the tank (0.09 kg/L) multiplied by the rate of flow (8 L/min) and the time (4 hours = 240 minutes). This gives us 0.09 kg/L × 8 L/min × 240 min = 172.8 kg. Therefore, the amount of salt in the tank after 4 hours is the initial amount of salt (90 kg) plus the amount of salt entering the tank (86.4 kg) minus the amount of salt leaving the tank (172.8 kg), which is 3.6 kg.

c) As time approaches infinity, the concentration of salt in the solution in the tank will approach the concentration of the incoming solution, which is 0.045 kg/L.

Answer:

The answer is c. 8 hours

Step-by-step explanation:

Since her battery dropped 25% in 2 hours then for it to drop 100% would take 8 hours.

25%+25%+25%+25%= 100%

so with this logic

25%= 2 hours

2+2+2+2=8

Hoped this helped !

Cheers, Z

Zoey can expect 8 hours of use from her iPad on a full battery charge (c).

To find the total hours Zoey can expect from her iPad on a full battery charge, we need to determine how many hours the battery percentage dropped for each hour of use.

If the battery dropped by 25% in 2 hours, that means it dropped by 12.5% (25% divided by 2) per hour.

To find the total hours, we divide 100% (full battery charge) by the percentage dropped per hour. In this case, 100% divided by 12.5% equals 8 hours.

Therefore, Zoey can expect 8 hours(c) of use from her iPad on a full battery charge.

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Answer: 1) R = {(a, a), (а,b), (b, a), (b, b), (с, с), (b, с), (с, b)}.

It is clearly not transitive since (a, b) ∈ R and (b, c) ∈ R whilst (a, c) ¢ R. On the other hand, it is reflexive since (x, x) ∈ R for all cases of x: x = a, x = b, and x = c. Likewise, it is symmetric since (а, b) ∈ R and (b, а) ∈ R and (b, с) ∈ R and (c, b) ∈ R.

2) Let S=Z and define R = {(x,y) |x and y have the same parity}

i.e., x and y are either both even or both odd.

The parity relation is an equivalence relation.

a. For any x ∈ Z, x has the same parity as itself, so (x,x) ∈ R.

b. If (x,y) ∈ R, x and y have the same parity, so (y,x) ∈ R.

c. If (x.y) ∈ R, and (y,z) ∈ R, then x and z have the same parity as y, so they have the same parity as each other (if y is odd, both x and z are odd; if y is even, both x and z are even), thus (x,z)∈ R.

3) A reflexive relation is a serial relation but the converse is not true. So, for number 3, a relation that is reflexive but not transitive would also be serial but not transitive, so the relation provided in (1) satisfies this condition.

Step-by-step explanation:

1) By definition,

a) R, a relation in a set X, is reflexive if and only if ∀x∈X, xRx ---> xRx.

That is, x works at the same place of x.

b) R is symmetric if and only if ∀x,y ∈ X, xRy ---> yRx

That is if x works at the same place y, then y works at the same place for x.

c) R is transitive if and only if ∀x,y,z ∈ X, xRy∧yRz ---> xRz

That is, if x works at the same place for y and y works at the same place for z, then x works at the same place for z.

2) An equivalence relation on a set S, is a relation on S which is reflexive, symmetric and transitive.

3) A reflexive relation is a serial relation but the converse is not true. So, for number 3, a relation that is reflexive but not transitive would also be serial and not transitive.

QED!