Review


#9 - 11 Will use the following information:


You work selling food from a food truck at a local park. You want to position your truck so that it is the same distance away from each of the three locations shown on the map below.




9. Is the point of interest the incenter or the circumcenter?


10. Find the point on the map that is equidistant from each of the three locations.


11. How could you fold the map in two places to find the point equidistant from each of the three locations?


#12 - 14 will use the following information:


A new elementary school is to be constructed in your town. The plan is to build the school so that it is the same distance away from each of the three major roads shown in the map below.




12. Is the point of interest the incenter or the circumcenter?


13. Find the point on the map that is equidistant from each of the three roads.


14. How could you fold the map in two places to find the point equidistant from each of the three roads?


16. A sprinkler is being installed in the park. The park is in the shape of a triangle with sidewalks along each side of the park. Draw a diagram to represent this problem and use your knowledge of inscribed circles to determine where the sprinkler should be placed in order to keep the ground wet and the sidewalks dry.

math.ceil(5.5) evaluates to 6.

The CEILING. MATH function rounds a number up to the nearest integer or to the nearest multiple of specified significance. It also specifies whether the number is rounded toward or away from 0 depending on the mode. The ceiling function is a mathematical function that rounds a number up to the nearest integer. It is denoted by the symbol "⌈x⌉" and is also known as the least integer function or the smallest integer not less than x.

The ceiling function of a number x is defined as the smallest integer that is greater than or equal to x. Mathematically, we can express it as:

⌈x⌉ = the smallest integer n such that n ≥ x

For example, the ceiling function of 4.2 is 5, because 5 is the smallest integer that is greater than or equal to 4.2. Similarly, the ceiling function of -1.8 is -1, because -1 is the smallest integer that is greater than or equal to -1.8.

The ceiling function is commonly used in computer programming and engineering to round up values to the nearest integer.

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An statistical question that can result in numerical data is given as follows:

How many hours do the students in your class spend on social media each week?

A question is classified as statistical if it can receive answers of data that vary.

For the question to be classified as numeric, the answers must be numeric instead of labels.

Hence the question in this problem is about the number of hours that the students study, as each study will study a different number of hours.

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Answer:

How many miles do the students in your class run each week? Is the question. Hope it helped

:)

The table for the coefficient of friction and velocity speed square when the radius of the curved path is 40 meters.

Coefficient of static friction         0.1        0.2        0.3        0.4       0.5

(Velocity speed)² ( m²/s² )           40         80        120        140      200

The radius of the curved path is 40 meters.

To provide the friction force necessary for an automobile moving at speed v to navigate a flat curve of radius r, consider the coefficient of static friction of v² = μrg.

When the coefficient of static friction between tires and pavement is μ, the fastest curve of radius r can be traveled is at this speed.

Here g is the acceleration due to gravity g = 10 m/s².

When μ = 0.1,

v² = 0.1 × 40 × 10 = 40 m²/s²

When μ = 0.2,

v² = 0.2 × 40 × 10 = 80 m²/s²

When μ = 0.3,

v² = 0.3 × 40 × 10 = 120 m²/s²

When μ = 0.5,

v² = 0.5 × 40 × 10 = 200 m²/s²

Hence, the complete table is:

Coefficient of static friction         0.1        0.2        0.3        0.4       0.5

(Velocity speed)² ( m²/s² )           40         80        120        140      200

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Answer:

\(\boxed{(x+10)(2x+5)}\)

Step-by-step explanation:

=> \(2x^2+25x+50\)

Using mid-term break formula

=> \(2x^2+20x+5x+50\)

=> 2x(x+10)+5(x+10)

Taking (x+10) common

=> (x+10)(2x+5)

Answer:

(x,y)= (2/15, -(62/15)

Step-by-step explanation:

Answer:

Step-by-step explanation:

no solutions

2x+2y=-4 divide 2

x+y=-2

x+y=3

Answer:

DStep-by-step explanation:

The correct statement about coping strategies is: An effective coping strategy is any strategy that reduces stress.

The correct option is B .

Coping strategies are techniques or actions that individuals use to manage or deal with stressful situations. Different strategies work for different people, so there isn't a one-size-fits-all approach. However, an effective coping strategy is any strategy that successfully reduces or manages stress.

Some examples of effective coping strategies include deep breathing exercises, engaging in physical activity or exercise, seeking support from friends or family, practicing mindfulness or meditation, and engaging in hobbies or activities that bring joy and relaxation.

It's important to note that while ineffective coping strategies may not completely eliminate stress, they can still provide temporary relief or distraction. However, it is generally recommended to focus on developing and using effective coping strategies that can effectively reduce stress and promote overall well-being.

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An effective coping strategy is any strategy that reduces stress.

The true statement about coping strategies is that an effective coping strategy is any strategy that reduces stress.

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Answer:

x/8

Step-by-step explanation:

how I see the problem I just put the 1 over the 8 because you can't really do anything else with the problem

The inverse f'^{-1}x of the given function is x/8

Given the function y = 8x, we are to find the inverse of the function.

Replace y with x

x = 8y

Make y the subject of the formula

x = 8y

Divide both sides by 8\

x/8 = 8y/8

x/8 = y

Swap sides

y = x/8

Hence the inverse f'^{-1}x of the given function is x/8

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5 can be written as 5/1, then:

When multiplying fractions, numerators multiply each other and denominators multiply each other, that is:

This result can be simplified by dividing numerator and denominator by 5, as follows:

7/4 is the final answer

The rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.

What is volume?

Volume refers to the amount of three-dimensional space occupied by an object or a substance.

To find the rate of increase in the volume V of a sphere when the surface area S becomes 100π square inches, we need to use the formulas relating the surface area and volume of a sphere to its radius.

The surface area S of a sphere is given by the formula:

\(S = 4\pi r^2,\)

where r is the radius of the sphere.

The volume V of a sphere is given by the formula:

\(V = (4/3)\pi r^3.\)

To find the rate of increase in volume with respect to time, we need to differentiate the volume formula with respect to time.

Given that the radius r is increasing at a uniform rate of 0.3 inches per second, we can write:

dr/dt = 0.3 inches per second.

Now, let's differentiate the volume formula with respect to time:

\(dV/dt = d/dt [(4/3)\pi r^3].\)

Using the power rule of differentiation, we get:

\(dV/dt = (4/3)\pi * 3r^2 * (dr/dt).\)

Simplifying further, we have:

\(dV/dt = 4\pi r^2 * (dr/dt).\)

Since we want to find the rate of increase in cubic inches per second, we need to express the volume in cubic inches.

Substituting the value of the surface area S = 100π square inches into the surface area formula:

\(100\pi = 4\pi r^2.\)

Dividing both sides by 4π, we get:

\(r^2 = 25.\)

Taking the square root of both sides, we find:

r = 5.

Now, we can substitute the value of r into the rate of increase formula:

\(dV/dt = 4\pi(5^2) * (0.3).\)

Simplifying the expression:

dV/dt = 4π(25) * 0.3.

dV/dt = 30π cubic inches per second.

Therefore, the rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.

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Answer:

A. Total area of Alaska is considerable larger than total area of Connecticut.

B. Population of California is considerably larger that population of Alaska.

Step-by-step explanation:

A. What is the difference in total area of Alaska and Connecticut?

According to the US government, total areas of Alaska and Connecticut are 663,268 square miles and 5,567 square miles, respectively.

The difference between both quantities is:

\(x=6.633 \times 10^{5} mi^{2} -5.567 \times 10^{3} mi^2\\x=6.577 \times 10^{5} mi^2\)

Which means that total area of Alaska is considerable larger than total area of Connecticut.

B. What is the difference in total population of California and Alaska?

According to the US government, total populations of California and Alaska are 39,512,223 people and 710,249 people, respectively.

The difference between both quantities is:

\(x=3.951 \times 10^7 people - 7.103 \times 10^5 people\\x=3.880 \times 10^7 people\)

Which means that population of California is considerably larger that population of Alaska.

Answer:

40billion for the tip question

Answer:

median = 55.5

Step-by-step explanation:

Here we have 10 numbers which is an even number

then the median for the data set is the average of the two middle numbers

firstly ,we have to put the number of the set in order from least to greatest like this :

3 < 12 < 38 < 38 < 46 < 65 < 71 < 78 < 87 < 99

————————                     ————————-

As you can see the middle two numbers are : 46 and 65

Now, we calculate their average :

\(\large \text Median = \frac{46+65}{2}= 55.5\)            

Those two have both two formulas but when dealing with a not-right triangle which is a particular case you use this formula for sines.

\(\frac{SinC}{c} =\frac{SinR}{r}\)

Substitute

Note: the capital letters are for the angles and the small letter are for the sides.

But since we used side R and there is no angle to substitute. you will basically have to find it by adding the two angles given and subtracting it by 180, which is a 100.

\(\frac{Sin(7)}{1.9} =\frac{Sin100}{x}\)

now you do the butterfly method or cross multiplication method.

\(xsin(7)=1.9sin(100)\)

You have to isolate the x

\(\frac{xsin(7)}{sin(7)} =\frac{1.9sin(100)}{sin(7)}\)

now cancel and plug the right side of the equation into your calculator and u get the answer for the missing side.

\(x= 15.35\) or if u want to round it \(15.4\)

<R = 100 and side CK= 15.35 or 15.4

Hope I helped! ^w^

TheOneAndOnlyLara~

Answer:

\(y = - \frac{1}{2} x + 4\)

Step-by-step explanation:

The equation of a line can be written in the form of y=mx+c, where m is the gradient and c is the y-intercept.

This is also known as the slope-intercept form.

\(\boxed{gradient = \frac{y1 - y2}{x1 - x2} }, \\ where \: (x1, y1) \: is \: the \: 1st \: coordinate \: and \: (x2, y2) \: is \: the \: 2nd \: coordinate.\)

Find the value of m using the gradient formula above:

\(m = \frac{4 - 0}{0 - 8} \\ m = \frac{4}{ - 8} \\ m = - \frac{1}{2} \)

Substitute m= -½ into the equation:

y= -½x +c

To find the value of c, substitute a pair of coordinates:

When x= 0, y=4,

\(4 = - \frac{1}{2} (0) + c \\ 4 = c \\ c = 4\)

Thus, the equation of the line is y= -½x +4.

The answer is option D which is the range will be ( -∞, ∞ ).

After substituting the domain, the range of a function is the entire set of all possible values for the dependent variable (often y).

Given function is

u(x) = -2x²+3 and v(x) = ( 1 / x ).

The product of the function will give uv(x).

uv(x) = (-2x²+3 ) x  \(\dfrac{1}{x}\)

uv(x) = \(\dfrac{-2x^2+3}{x}\)

When we plot the graph of the function we found two opposite curved graphs and they are not intersecting at any point so the range will be from negative infinity to positive infinity. The graph of the function is attached with the answer below.

Therefore the answer is option D which is the range will be ( -∞, ∞ ).

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Answer:

Rubi read for 21 minutes longer than Suhani.

Step-by-step explanation:

The least common multiple (LCM) of 4 and 5 is 20.

Rubi read for 3/4 of an hour, which is equivalent to 15/20 of an hour.

Suhani read for 2/5 of an hour, which is equivalent to 8/20 of an hour.

Since 15/20 is greater than 8/20, Rubi read for a longer time.

To find the difference, we can subtract the two fractions:

15/20 - 8/20 = 7/20

So Rubi read for 7/20 of an hour more than Suhani. We can also convert this to minutes by multiplying by 60:

7/20 x 60 = 21 minutes

Therefore, Rubi read for 21 minutes longer than Suhani.

Answer: The IQR is the best measure of variability and it equals 32.

Step-by-step explanation: If you made notes and check your notes you would know that IQR is better than Range, so first you need to order the date in the leaf plot from least to greatest. (No need to do that since it already is in order)  Since it is already created for you, there is no need to create it.  First multiply the IQR by Q1 (the q1 is 17) Don't forget to determine if there are any outliers. Then multiply the Q2 by the IQR The Q2 is 29.5. Then find the Q3, and do the same thing then you would add the Q3 AND Q1 to get the answer of 32.

Hope this helped!

Answer:

k = 4

Step-by-step explanation:

16k = 16(4) = 64 and

64 = 4 × 4 × 4

\(\sqrt[3]{64}\)

= \(\sqrt[3]{4^{3} }\)

= 4

The decibel values for −140 db, −3 db, 20 db, 42 db is 0.00000000000001, 0.501, 100 and 158.49.

Decibels (dB) is a unit of measurement used to express the ratio of two values in terms of power or amplitude. In other words, it is a logarithmic unit of measurement that compares the magnitude of two signals, with one serving as a reference. The decibel scale is logarithmic because the human perception of sound and signal strength is also logarithmic.

To convert decibels to numbers, we use the following formula:

Number = 10^(dB/10)

Calculating it for different values,

For -140dB, 10^(-140/10) = 10^(-14) = 0.00000000000001

For -3 dB, 10^(-3/10) = 0.501

For -20 dB, 10^(20/10) = 100

For -42dB, 10^(42/10) = 158.49

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t3(x)  = f(a) + f'(a)(x-a) + (1/2)f''(a)(x-a)^2 + (1/6)f'''(a)(x-a)^3.

To find t3(x) we need to find the coefficient of polynomials by using the formula for nth degree taylor polynomial.

what is taylor polynomials?

This are approximations of a function, which become generally better as n increases. It is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point.

using the nth degree taylor polynomial formula:

tn(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...... + f^(n)(a)(x-a)^n/n!

where f^(n)(a) is the nth derivative of f evaluated at x=a.

By calculating we get t3(x) as

t3(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3!

       = f(a) + f'(a)(x-a) + (1/2)f''(a)(x-a)^2 + (1/6)f'''(a)(x-a)^3.

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Answer:

Sam has is 7/5 times the reciprocal of the total number of stamps in the new set.

Step-by-step explanation:

Let's start by finding out what fraction of the new set of stamps Sam has after adding 4/5 of the set to his collection.

Let the total number of stamps in the new set be x.

If Sam's collection initially had 3/5 of the new set, then the number of stamps in his collection before adding the new set would be:

3/5 * x = the number of stamps in Sam's collection before adding the new set

After adding 4/5 of the new set to his collection, Sam has:

3/5 * x + 4/5 * x = 7/5 * x

So Sam has 7/5 of the new set of stamps.

However, the problem asks for the fraction of the new set that Sam has, not the fraction of the total number of stamps in the new set.

To find the fraction of the new set that Sam has, we need to divide the number of stamps he has by the total number of stamps in the new set:

(7/5 * x) / x

Simplifying the expression:

(7/5) / 1

We can express this fraction in terms of x by multiplying both the numerator and denominator by 1/x:

(7/5) * (1/x)

Therefore, the fraction of the new set of stamps that Sam has is 7/5 times the reciprocal of the total number of stamps in the new set.

Step-by-step explanation:

which one are you asking for???

The missing values are derived from the graph as follows:

3 ) 7, 14, 21, 28, 35

4) 3, 7, 10, 14, 17

5) 1, 21, 10, 49, 19

In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.

In order to solve for the above values, the best way is to spot the function that exists in the graph which is given as:

F(y) = 3.5x

In the first table, where x = 2

y= 3.5 *2

= 7

This iteration goes on and on and is consistent for all the values.

In the second table,

Where F(y) is known, for example 10.5, then x is derived as:

10.5 = 3.5x (divide both sides by 3.5)

x = 3

This iteration goes on and on and is consistent for all the values.

In the third table, we simply swap the values back and forth using the function F(y) = 3.5x to derive all values.

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Step-by-step explanation:

cos60° = Adjacent/Hypotenuse = a/42.

=> a = 42cos60° = 21.

sin60° = Opposite/Hypotenuse d/42.

=> d = 42sin60° = 42(√3/2) = 21√3.

tan30° = Opposite/Adjacent = d/b.

=> b = d / tan30° = (21√3) / (1/√3) = 63.

sin30° = Opposite/Hypotenuse = d/c.

=> c = d / sin30° = (21√3) / (1/2) = 42√3.

Answer:

Here you go

Step-by-step explanation:

The quadratic formula helps you solve quadratic equations, and is probably one of the top five formulas in math. Then the formula will help you find the roots of a quadratic equation, i.e. the values of x where this equation is solved.

Answer:

1/8

Step-by-step explanation:

\(f( - 2) = 2 \times {4}^{ - 2} \\ = 2 \times \frac{1}{ {4}^{2} } \\ = 2 \times \frac{1}{16} \\ = \frac{1}{8} \)

We can expect that about 45.86% of high-risk drivers will be involved in an accident during the first 80 days of the calendar year.

Let X be the number of days between the beginning of the calendar year and the moment a high-risk driver is involved in an accident. We know that X follows an exponential distribution.

Let λ be the rate parameter of the exponential distribution, which represents the average number of accidents per unit of time. We want to find the probability that a high-risk driver is involved in an accident during the first 80 days of the year, given that the probability of an accident in the first 50 days is 0.3.

We can use the cumulative distribution function (CDF) of the exponential distribution to find this probability:

P(X ≤ 80) = 1 - e^(-λ*80)

To solve for λ, we can use the fact that the probability of an accident in the first 50 days is 0.3:

P(X ≤ 50) = 1 - e^(-λ*50) = 0.3

e^(-λ*50) = 0.7

-λ*50 = ln(0.7)

λ = -ln(0.7)/50

λ ≈ 0.0296

Now we can substitute λ into the expression for P(X ≤ 80):

P(X ≤ 80) = 1 - e^(-0.0296*80)

P(X ≤ 80) ≈ 0.4586

Therefore, we can expect that about 45.86% of high-risk drivers will be involved in an accident during the first 80 days of the calendar year.

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