2. Thom is training to run a 5K. In August he can complete a 5K in 50 minutes. InSeptember, after a month of training, he has managed to cut down his time by20%. At the race in October he manages to cut 20% off of his new time. After therace Thom gets lazy and does not run for six months. In April, he attemptsanother 5K and finds that his time has increased by 40% since October.Find Thom's 5K time in September.Find Thom's 5K time in October.Find Thom's 5K time in April.Find the overall percentage change in Thom's 5K time (from August untilApril).

Humanity would achieve a life expectancy of 110 years in approximately 60 years.

To calculate the number of years it would take for humanity to achieve a life expectancy of 110 years, we need to determine the number of decades required to reach this goal based on the given rate of increase.

In 2009, the life expectancy was about 80 years. From that point, we need to calculate the difference between the current life expectancy and the target life expectancy of 110 years.

110 years - 80 years = 30 years

Since the rate of increase is 5.3 years every decade, we can divide the difference by the rate to determine the number of decades required:

30 years / 5.3 years per decade ≈ 5.66 decades

Since we can't have a fraction of a decade, we need to round up to the nearest whole number. Therefore, it would take approximately 6 decades for humanity to achieve a life expectancy of 110 years.

To calculate the number of years, we multiply the number of decades by 10:

6 decades * 10 years per decade = 60 years

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x² + 3x - 2

(5)² + 3 × 5- 2

25 + 15 - 2

40 - 2

38...

Answer: 13 + 2x = 63 and the cost of one ticket is $25 (x=25)

Step-by-step explanation:

Build the equation from what it tells you.

The entire trip costs $63

The concert ticket that is included costs $13

Two passes cost the same amount, use x for what you don't know, 2x.

So,  13 + 2x = 63.

Find x = cost one pass.

13 + 2x = 63

-13.          -13

      2x= 50

    2x/2= 50/2

     x= 25

Solving the given logarithmic equation, it is found that the horn is 100 times more intense compared to the weakest sound heard to the human ear.

The equation is given by:

\(d = 10\log{\frac{p}{p_0}}\)

In which:

In this problem, we have that d = 20, and we have to solve the logarithmic equation for p to find how many times more intense the sound is:

\(d = 10\log{\frac{p}{p_0}}\)

\(20 = 10\log{\frac{p}{p_0}}\)

\(\log{\frac{p}{p_0}} = 2\)

The logarithm is inverse of the function \(10^x\), hence we apply the function to both sides to find the ratio.

\(\frac{p}{p_0} = 10^2\)

\(\frac{p}{p_0} = 100\)

Hence, the horn is 100 times more intense compared to the weakest sound heard to the human ear.

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In the "Tally" column, a vertical line is used to represent each occurrence of the reason, and the total number of tallies for each reason is counted and entered in the "Frequency" column.

Frequency refers to the number of times a particular value or observation occurs in a dataset. It is often used to summarize categorical or discrete data, such as the number of times a certain response was given in a survey or the number of times a particular event occurred in a given time period. Frequencies are often displayed in a frequency table or chart to make it easier to visualize patterns and trends in the data.

Here,

Reasons for Taking a Gap Year:

Reason Tally Frequency

Traveling  

Working  

Volunteering  

Studying  

Personal Development

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Complete question:

Frequency table where you tally five reasons for taking gap year. Mention 5 reasons specifically for this gap year.

Answer:

a)    distance = (rate) x (time)   or do they want    rate = distance / time

Step-by-step explanation:

the rate is 420 km / 3 hr       =  140 km/hr

Answer:

The answer is "2.2 h"

Step-by-step explanation:

Speed of Train B:

\(= \frac{3}{2} \times 70 \ mph \\\\= 105 \ mph\)

Train B is then moving on:

\(= \frac{200 \ miles}{ 105 \ mph} \\\\= 1.905 \ h\\\)

Then it takes Train A to the left:

\(\to 1.905\ h + 20 \ min \\\\= 1.905 \ h +0.333 \ h \\\\= 2.238 \ h\)

To get train B to the reference point of train A = 2.2 h    

Answer:

Step-by-step explanation:

Two sides and the angle between are marked as congruent. That immediately tells you that the Side-Angle-Side (SAS) theorem of congruence applies.

The angle is a right angle, which makes the adjacent sides be "legs" of the right triangle. Then the Leg-Leg (LL) theorem of congruence for a right triangle also applies.

Appropriate choices are ...

  SAS, LL

It will take 3.5 hours for the two cars to be 280 miles apart.

To determine the time it takes for the two cars to be 280 miles apart, we can use the concept of relative velocity.

Since the cars are traveling in opposite directions, their velocities can be added together to find their relative velocity:

Relative velocity = Velocity of car traveling east + Velocity of car traveling west

Relative velocity = 60 mph + 20 mph

Relative velocity = 80 mph

The relative velocity of the cars is 80 mph, which means that they are moving away from each other at a combined speed of 80 mph.

To find the time it takes for them to be 280 miles apart, we can use the formula:

Time = Distance / Speed

Plugging in the values, we have:

Time = 280 miles / 80 mph

Time = 3.5 hours

Therefore, it will take 3.5 hours for the two cars to be 280 miles apart.

During this time, the car traveling east would have covered a distance of 60 mph × 3.5 hours = 210 miles, while the car traveling west would have covered a distance of 20 mph × 3.5 hours = 70 miles.

The sum of these distances is indeed 280 miles, confirming the result.

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This is given by the limit

\(\displaystyle \lim_{x\to1} \frac{f(x) - f(1)}{x - 1} = \lim_{x\to1} \frac{(2x^2 - 5x+1) - (-2)}{x - 1} = \lim_{x\to1} \frac{2x^2 - 5x + 3}{x - 1}\)

Observe that \(2x^2-5x+3=0\) when \(x=1\), and factorizing gives

\(2x^2 - 5x + 3 = (x - 1) (2x - 3)\)

so that

\(\displaystyle \lim_{x\to1} \frac{f(x) - f(1)}{x - 1} = \lim_{x\to1} (2x-3) = 2\cdot1 - 3 = \boxed{-1}\)

(A)

The probability that the student chosen at random was male OR got an "A" is 31/58.

To find the probability that the student was male OR got an "A," we need to calculate the probability of each event separately and then add them together.

Let's calculate the probability of the student being male:

Total number of males = 11

Total number of students = 58

Probability of the student being male = Number of males / Total number of students = 11/58

Now, let's calculate the probability of the student getting an "A":

Total number of students who got an "A" = 20

Probability of the student getting an "A" = Number of students who got an "A" / Total number of students = 20/58

To find the probability of the student being male OR getting an "A," we add the two probabilities together:

Probability (Male OR A) = Probability (Male) + Probability (A) = 11/58 + 20/58 = 31/58

Therefore, the probability that the student chosen at random was male OR got an "A" is 31/58.

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Answer:

Step-by-step explanation:

poor paper

An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.

An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.

This function is one-to-one because for every element x in P, there is a unique element 2x in Q. It is onto because every element y in Q has a preimage x in P such that f(x) = y (e.g., y/2 = x).

Furthermore, this function preserves the group structure between P and Q, as it satisfies the properties of an isomorphism. In this case, the group structure is addition, and the function f preserves addition: f(x + y) = 2(x + y) = 2x + 2y = f(x) + f(y) for all x, y in P.

Therefore, the function f: P -> Q defined as f(x) = 2x is an example of a one-to-one function that is an isomorphism between sets P and Q.

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Answer: 7 inches

Step-by-step explanation:

l x w = a

16 x w = 112

w = 112/16

w = 7

Answer:

\(a(1) = 144\)

\(a(n) = 144{( - \frac{1}{6} )}^{n - 1} \)

\(a(n) = - \frac{1}{6} a(n - 1)\)

Answer:

(-2, -4)

Step-by-step explanation: because its going backwards it should be a negative slope :)

I'm sorry if I'm wrong  but i hope this helps :)

Answer: its the second one

Step-by-step explanation: hope this helps

The piece-wise linear functions can be written as follows:

A linear function is modeled by:

y = mx + b

In which:

For x less than 5, the y-intercept is of b = 3 and the function also gos through (2,2), hence the slope is:

m = (2 - 3)/(2 - 0) = -0.5.

Hence the rule is:

\(f(x) = -0.5x + 3, x < 5\).

When x = 5, the function is constant at -5, hence:

\(f(x) = -5, x = 5\)

For x less than 5, the function goes through points (6,3) and (7,2), hence the slope is:

m = (2 - 3)/(7 - 6) = -1.

Then:

y = -x + b

When x = 6, y = 3, hence the y-intercept is given as follows:

3 = -6 + b

b = 9.

Hence the rule is:

\(f(x) = -x  + 9, x > 5\).

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Answer:

D

Step-by-step explanation:

When rounding, the number 5 is rounded up. So the number 387.352 will be rounded up 387.4. Other options are not suitable. Correct answer is "D"

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The angle of depression at which Beatrice sees the boat is 83.35°.

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Check the attached image for the sketch of triangle ABC.

From the sketch, the angle of depression is represented with x:

tan x = 600/70   (tan = opposite/adjacent)

x = tan⁻¹(600/70)

x = 83.35°

Therefore, the angle of depression at which Beatrice sees the boat is 83.35°.

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Answer:

105

Step-by-step explanation:

Answer:

105

Step-by-step explanation:

Decimal calculation steps
(1101001)₂ = (1 × 2⁶) + (1 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (0 × 2²) + (0 × 2¹) + (1 × 2⁰) = (105)₁₀

For the given triangles:

(1) x = 5.4

(2)  x  =  √23

(3) θ = 25.84 degree

(4)   x = 9.5

(5) n = 41

(1) In the given triangle,

One angle = 16 degree

Perpendicular = x

Hypotenuse    = 20

Since we know that

Sinθ = opposite side of θ/hypotenuse

Therefore,

⇒ sin 16 = x/20

⇒   0.27 = x/20

⇒         x = 5.4

(2)  In the given triangle,

Hypotenuse = 12 km

Base = 11 km

perpendicular = x

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (12)²= (x)² + (11)²

⇒ 144 = (x)² + 121

⇒   x² =  23

Taking square root both sides we get,

Hence,

⇒   x  =  √23

(3) In the given,

Base = 20

Perpendicular = 42

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (Hypotenuse)² =  (42)² + (20)²

⇒ (Hypotenuse)² =  2164

Taking square root both sides,

⇒ (Hypotenuse)  = 46.51

⇒ cosθ = Adjacent/hypotenuse

             = 42/46.51

             = 0.90

Taking inverse of cosθ,

⇒ θ = 25.84 degree

(4) In the given triangle,

One angle = 30 degree

Base = x

Hypotenuse    = 11

Since we know that

cosθ = Adjacent/hypotenuse

Therefore,

⇒ cos 30  = x/11

⇒   √3/2 = x/11

⇒         x = 9.5

(4) In the given triangle,

Base = 40

Perpendicular = 9

Hypotenuse = n

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒  n² = 9² + 40²

⇒  n² = 81 + 1600

⇒  n² = 1681

⇒  n = 41

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Answer:

a rigt angle is a total of 90 degrees so subtratct 51 from 90 and you get 39 degrees.

Answer:A. x= .100

Step-by-step explanation:because of the distance in miles

The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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The solution of the given algebraic expression is: ⁷/₁₂ + ⁴/₆q

We are given the algebraic expression as:

¹¹/₁₂ - ¹/₆q + ⁵/₆q - ¹/₃

Combining Like terms gives us:

(¹¹/₁₂ - ¹/₃) + (⁵/₆q - ¹/₆q)

Solving both brackets individually gives us:

((11 - 4)/12) + ⁴/₆q

= ⁷/₁₂ + ⁴/₆q

Thus, we conclude that is the solution of the given algebraic expression problem

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Answer:

48in

Step-by-step explanation:

6 x 4 x 4

96

divide it by 2

48

Answer:

48

Step-by-step explanation:

grhgbfjsbrvgjxbwifbcozbwicovbsnw

Answer:

Point slope form: y − 7 = 3 4 ( x − 3 ) Slope intercept form: y = 3 4 x + 19 4 or y = 3 4 x + 4 3 4

Step-by-step explanation:

hope this helps, have a nice day/night! :D

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Answer:

Slope = 1

Step-by-step explanation:

Slope = change in y / change in x

Slope = 6 - (-4)/7 - (-3)

Slope = 10/10

Slope = 1

-Chetan K