HELPPPP!!!!
Which model does the graph represent?

Answer: x > 5

Step-by-step explanation: You need to isolate x. First, distribute the 1/2 into the parentheses. You will get:

4x + x + 2 > 12

Combine like terms.

5x + 2 > 12

Subtract 2 from each side.

5x > 10

Divide by 5 on each side.

X > 2

Since x is by itself, that is the answer.

Answer:

x > 2

Step-by-step explanation:

Distribute 1/2

Distribute 1/2 inside the parentheses

1/2 * 2x = x

1/2 * 4 = 2

Simplify

4x + x + 2 > 12

Combine like terms

5x + 2 > 12

Subtract 2 in both sides

2 - 2 = 0

12 - 2 = 10

5x > 10

Divide 5 in both sides

5x/5 = x

10/5 = 2

Simplify

x > 2

Answer

x > 2

Answer:

C [tex]P(v)=2(v+7)[/tex]

Step-by-step explanation:

Lets say that [tex]P(v)=y[/tex] for simplicity.

In order to find the inverse of a function, we must switch the location of the variable, v, and y. Then we have to solve for y.

As we are already given the inverse, doing the same process again will give us the original function.

First we can set up the equation

[tex]y=\frac{1}{2} v-7[/tex]

Next we can switch the location of the variables

[tex]v=\frac{1}{2} y-7[/tex]

Now we can solve for y

[tex]v=\frac{1}{2} y-7\\\\v+7=\frac{1}{2} y\\\\y=2(v+7)\\\\P(v)=2(v+7)[/tex]

This gives us the function

[tex]P(v)=2(v+7)[/tex]

Answer:

C P(v) = 2(v+7)

Step-by-step explanation:

To find P(v), we need to take the inverse of P^-1 (v)

y = 1/2 v-7

Exchange y and v

v = 1/2 y-7

Solve for y

Add 7 to each side

v+7 = 1/2 y -7+7

v+7 = 1/2y

Multiply each side by 2

2(v+7) = 1/2 y*2

2(v+7) = y

P(v) = 2(v+7)

Answer: 0.0902

Step-by-step explanation:

Given : The average number of phone inquiries per day at the poison control center : [tex]\lambda=2[/tex]

The Poisson distribution function is given by :-

[tex]\dfrac{e^{-\lambda}\lambda^x}{x!}[/tex]

Then ,  the probability that it will receive exactly 4 calls on a given day is  given by (Put [tex]x=4[/tex] and [tex]\lambda=2[/tex]) :-

[tex]\dfrac{e^{-2}2^4}{4!}=0.09022352215\approx0.0902[/tex]

Hence, the required probability : 0.0902

Answer:

The inter-quartile range is 13.

Step-by-step explanation:

   1. Order the data from least to greatest

   2. Find the median  of the data.

   3. Calculate the median of both the lower and upper half of the data.

   4. The inter-quartile range is the difference between the upper and lower medians.

Lower Median: 17

Media: 25.5

Upper Median: 30

Answer:

Renting a vehicle when there are 5 cars, 3 vans, and 10 sports utility vehicles available

Step-by-step explanation:

Creating a stuffed animal when there are 6 animals, 3 fur colors, and 12 clothing themes available

This condition requires multiplication or factorials to determine outcomes

Renting a vehicle when there are 5 cars, 3 vans, and 10 sports utility vehicles available

This situation requires the addition counting principle to determine the number of possible outcomes as there is only one car to be picked so all the numbers 10+5+3 = 18 will be added to get the possible outcomes ..

Answer:

The probability of hitting the bullseye at least once in 6 attempts is 0.469.

Step-by-step explanation:

It is given that a mechanical dart thrower throws darts independently each time, with probability 10% of hitting the bullseye in each attempt.

The probability of hitting bullseye in each attempt, p = 0.10

The probability of not hitting bullseye in each attempt, q = 1-p = 1-0.10 = 0.90

Let x be the event of  hitting the bullseye.

We need to find the probability of hitting the bullseye at least once in 6 attempts.

[tex]P(x\geq 1)=1-P(x=0)[/tex]       .... (1)

According to binomial expression

[tex]P(x=r)=^nC_rp^rq^{n-r}[/tex]

where, n is total attempts, r is number of outcomes, p is probability of success and q is probability of failure.

The probability that the dart thrower not hits the bullseye in 6 attempts is

[tex]P(x=0)=^6C_0(0.10)^0(0.90)^{6-0}[/tex]

[tex]P(x=0)=0.531441[/tex]

Substitute the value of P(x=0) in (1).

[tex]P(x\geq 1)=1-0.531441[/tex]

[tex]P(x\geq 1)=0.468559[/tex]

[tex]P(x\geq 1)\approx 0.469[/tex]

Therefore the probability of hitting the bullseye at least once in 6 attempts is 0.469.

Answer:

more the z-score more will be the extreme. therefore tallest man has high extreme

Step-by-step explanation:

Formula for z-score: [tex]\frac{X-\mu }{\sigma}[/tex]

where

X is height of tallest man

μ mean height

σ is standard deviation

z score for tallest is

z-score = [tex]\frac{ 262 - 175.32}{8.17} = 10.60[/tex]

similarly for shortest man

z-score = [tex]\frac{68.6 - 175.32}{8.17} = - 13.06[/tex]

more the z-score more will be the extreme. therefore tallest man has high extreme

Answer:

The shortest living man's height was more extreme.

Step-by-step explanation:

We have been given that the the tallest living man at one time had a height of 262 cm. The shortest living man at that time had a height of 68.6 cm. Heights of men at that time had a mean of 175.32 cm and a standard deviation of 8.17 cm.

First of all, we will find z-scores for both heights suing z-score formula.

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]z=\frac{68.6-175.32}{8.17}[/tex]

[tex]z=\frac{-106.72}{8.17}[/tex]

[tex]z=-13.06[/tex]

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]z=\frac{262-175.32}{8.17}[/tex]

[tex]z=\frac{86.68}{8.17}[/tex]

[tex]z=10.61[/tex]

Since the data point with a z-score [tex]-13.06[/tex] is more away from the mean than data point with a z-score [tex]10.61[/tex], therefore, the shortest living man's height was more extreme.

Answer:

  (x +8)² +(y +6)² = 100

Step-by-step explanation:

The equation of a circle with center (h, k) and radius r can be written:

  (x -h)² +(y -k)² = r²

For your given values of h=-8, k=-6, r=10, the equation is ...

  (x +8)² +(y +6)² = 100

Answer:

only C

Step-by-step explanation:

Answer:

[tex]\large\boxed{n\leq9\ or\ n>13\to n\in\left(-\infty;\ 9\right]\ \cup\ (13,\ \infty)\to\{x\ |\ x\leq9\ or\ x>13\}}[/tex]

Step-by-step explanation:

[tex]n-12\leq-3\ or\ 2n>26\\\\n-12\leq-3\qquad\text{add 12 to both sides}\\n\leq9\\\\2n>26\qquad\text{divide both sides by 2}\\n>13\\\\n\leq9\ or\ n>13\to n\in\left(-\infty;\ 9\right]\ \cup\ (13,\ \infty)\to\{x\ |\ x\leq9\ or\ x>13\}[/tex]

Answer:

0.07

Step-by-step explanation:

it is given odds in favor of a win is 7 to 93

we have to find the degree of likelihood as a probability

total sample space =7+93=100

so the degree of likelihood as a probability = [tex]\frac{7}{100} =0.07[/tex]

so we can conclude that the probability will be 0.07 which is very less so the chances of win in the casino is very less

The odds 7 to 93, when converted to a probability, gives a value of 0.07. This means there is a 7% chance of winning in this slot machine game.

The question asks to express the odds in favor of winning a casino slot machine game as a probability value between 0 and 1. In this case, the odds given are 7 to 93. This means that for every 100 games, we expect 7 wins and 93 losses.

To convert these odds into a probability, we divide the number of win outcomes by the total number of outcomes. In this case, the probability of winning is 7/(93+7) = 7/100 = 0.07.

So the probability value of winning on this slot machine is 0.07, which is a number between 0 and 1 inclusive.

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Answer:

x = 18.

Step-by-step explanation:

As they are congruent, BC = DC  so

x + 12 = 2x - 6

12 + 6 = 2x - x

x = 18.

Answer:

x=18

Step-by-step explanation:

Because of the SSS criterion, The congruent sides are equal to each other. Meaning, Side AB is congruent to side AD. With this, you can set side BC and side DC equal to each other to solve for x.

x+12=2x-6

You subtract x to both sides;

12=x-6

You then add 6 to both sides to get x alone.

18=x or x=18.

Answer:

The mean of these statistic is 2.18.

Step-by-step explanation:

According to the chart, from 1986-1996, unintentional drug overdose deaths per 100,000 population began to rise.

The given data set is

2, 1, 2, 2, 1, 2, 2, 3, 3, 3, 3

Formula for mean:

[tex]Mean=\frac{\sum x}{n}[/tex]

Using this formula, the mean of the data is

[tex]Mean=\frac{2+1+2+2+1+2+2+3+3+3+3}{11}[/tex]

[tex]Mean=\frac{24}{11}[/tex]

[tex]Mean=2.181818[/tex]

[tex]Mean\approx 2.18[/tex]

Therefore the mean of these statistic is 2.18.

The mean of these statistics is [tex]\large{\boxed{\bold{2.18}}[/tex]

Statistics is a study of a collection, preparation, analysis,presentation/conclusions from some data

Data is a collection of information presented in the form of numbers

Data collection can be done through a sample that represents all data (can be called a population) that is used as research

Data information can be stated in tables, diagrams or graphs

The average value or mean is a measure to provide an overview of a set of data

Mean is the average of a number of data

To determine the mean: the sum of all data divided by the amount of data

General formula

[tex]\large{\boxed{\bold{mean=\frac{\sum_{xi}}{n} }}}[/tex]

xi = data

n = amount of data

The numbers for each year for unintentional drug overdose deaths per 100,000 population are: 2, 1, 2, 2, 1, 2, 2, 3, 3, 3, 3

Total amount of data:

[tex]\displaystyle 2+1+2+2+1+2+2+3+3+3+3=\large{\boxed{24}[/tex]

Amount of data: [tex]\large{\boxed{11}}[/tex]

So the mean value:

[tex]\displaystyle mean=\frac{\sum_{xi}}{n}=\frac{24}{11}=\large{\boxed{\bold{2.18}}}[/tex]

Statistics

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Keywords: mean, statistics, data

Answer:

20%

Step-by-step explanation:

Population of white-tailed deer in 1991 = 25 deer per square mile

Population of white-tailed deer in 1992 = 30 deer per square mile

We have to find the percentage increase in the deer population. The formula for percentage change is:

[tex]\frac{\text{New Value - Original Value}}{\text{Original Value}} \times 100 \%[/tex]

Original value is the population in 1991 and the New value is the population in 1992.

Using the values, we get:

[tex]\frac{30-25}{25} \times 100 \%\\\\ = 20%[/tex]

Thus, the deer population increased by 20% from 1991 to 1992

Final answer:

The deer population in the state park in Indiana increased by 20% from 1991 to 1992.

Explanation:

The question asks by what percentage the deer population increased between 1991 and 1992 in a state park in Indiana. To calculate the percentage increase, we use the formula: Percentage Increase = ((New population - Original population) / Original population) × 100%. Applying this formula to the given numbers, we have:

Original population in 1991 = 25 deer per square mile

New population in 1992 = 30 deer per square mile

Percentage Increase = ((30 - 25) / 25) × 100% = (5 / 25) × 100% = 20%

Therefore, the deer population increased by 20% from 1991 to 1992.

Answer:

  126

Step-by-step explanation:

The number of numbers divisible by 9 is ...

  j = floor(500/9) = 55

The number of numbers divisible by 7 is ...

  k = floor(500/7) = 71

Then the total (j+k) is ...

  j +k = 55 +71 = 126

Answer:

  Reflection across the x-axis

Step-by-step explanation:

The only apparent transformation is negation of the y-coordinate, corresponding to reflection across the x-axis.

Answer:

 Reflection across the x-axis

Step-by-step explanation:

The only apparent transformation is negation of the y-coordinate, corresponding to reflection across the x-axis.

Answer:

160

Step-by-step explanation:

Add the ratios together to get the sum of them is 19.  Since the perimeter is 380, divide 380 by 19 to get 20.  

The shortest side is 3(20) = 60,

the next side is 5(20) = 100, and

the longest side is 8(20) = 160

Answer:

y = 107x + 20

Step-by-step explanation:

The points that represent the number of credits and the cost of those credits in coordinate form are (9, 983) and (13, 1411).

We can use the slope formula to first find the slope of the line containing those 2 points:

[tex]m=\frac{1411-983}{13-9}=\frac{428}{4}=107[/tex]

The slope is 107.  Now we can pick one of the 2 points and use it in the point-slope form of a line to get the equation we are looking for:

[tex]y-983=107(x-9)[/tex] simplifies to

[tex]y-983=107x-963[/tex] so in slope-intercept form:

y = 107x + 20

Answer:

[tex]w=\frac{A}{l}[/tex]

Step-by-step explanation:

The formula to find the area of a rectangle is: [tex]A=w \times l[/tex], where [tex]w[/tex] is width and [tex]l[/tex] is length.

So, if we knoe the area [tex]A[/tex] and the length [tex]l[/tex], we can find the width with the formula

[tex]w=\frac{A}{l}[/tex]

You can get this answer by using the defintion of area, which is the first equation, and isolating [tex]w[/tex].

Remember, when we want to move a factor to the other side of the equalty, we must pass it with the opposite operation. So, in this case, width was multiplying, and it passed to the other side dividing.

Therefore, the answer here is [tex]w=\frac{A}{l}[/tex]

Answer:

  2√13

Step-by-step explanation:

The distance formula is useful for this. One end of the vector is (0, 0), so the measure of its length is ...

  d = √((x2 -x1)² +(y2 -y1)²) = √((6 -0)² +(-4-0)²)

  = √(36 +16) = √52 = √(4·13)

  d = 2√13 = |(6, -4)|

Answer:

I'm not quite sure but I think it's either 21.6 miles or 22 (Mostly 21.6 though, is what i think at least).

Answer:

0.75

Step-by-step explanation:

Total number of people = 400

Number of people who say yes to gun laws being more stringent = 300

Number of people who say no to gun laws being more stringent = 100

The proportion of people who will say yes = Number of people who say yes to gun laws being more stringent / Total number of people

[tex]\text{The proportion of people who will say yes}=\frac{300}{400}\\\Rightarrow \text{The proportion of people who will say yes}=\frac{3}{4}=0.75[/tex]

∴ Proportion in the population who will respond "yes" is 0.75

Answer:

Step-by-step explanation:

This equation is a positive parabola, opening upwards.  Parabolas of this type have a vertex that is a minimum value.  In order to find the year where the population was the lowest, we have to complete the square to find the vertex.  The rule for completing the square is to first set the parabola equal to 0, then next move the constant over to the other side of the equals sign.  The leading coefficient on the x-squared term HAS to be a positive 1.  Ours is a .5, so will factor it out.  Doing those few steps looks like this:

[tex].5(t^2-19.3t)=-100[/tex]

Next we take half the linear term, square it, and add it to both sides.  Don't forget the .5 sitting out front there as a multiplier.  Our linear term is 19.3.  Taking half of that gives us 9.65, and 9.65 squared is 93.1225

[tex].5(t^2-19.3t+93.1225)=-100+46.56125[/tex]

In this process, we have created a perfect square binomial on the left.  Stating that binomial and doing the addition on the right looks like this:

[tex].5(t-9.65)^2=-106.8775[/tex]

Now finally we will divide both sides by .5 then move over the constant again to get the final vertex form of this quadratic:

[tex](t-9.65)^2+106.8775=y[/tex]

From this we can see that the vertex is (9.65, 106.8775) which translates to the year 2009 and 107,000 approximately.

In our situation, that means that the population was at its lowest, 107,000 in the year 2009.

For part b. we will replace the y in the original quadratic with a 200,000 and then factor to find the t values.  Setting the quadratic equal to 0 allows us to factor to find t:

[tex]0=.5t^2-9.65t-199900[/tex]

If you plug this into the quadratic formula you will get t values of

642.02 and -622.72

The two things in math that will never EVER be negative are distances/measurements and time, so we can safely disregard the negative value of t.  Since the year 2000 is our t = 0 value, then we will add 642 years to the year 2000 to get that

In the year 2642, the population in this town will reach 200,000 (as long as it grows according to the model).

Answer:

Step-by-step explanation:

It can be easier to see the answer if you subtract the right side of the equation from both sides, then simplify.

1. 2(x + 2) + 2 = 2(x + 3) + 1

  2(x + 2) + 2 - (2(x + 3) + 1) = 0

  2x +4 +2 -2x -6 -1 = 0

  -1 = 0 . . . . no solution

__

2. 2x + 3(x + 5) = 5(x – 3)

  2x + 3(x + 5) - 5(x – 3) = 0

  2x +3x +15 -5x +15 = 0

  30 = 0 . . . . no solution

__

3. 4(x + 3) = x + 12

  4(x + 3) - (x + 12) = 0

  4x +12 -x -12 = 0

  3x = 0 . . . . one solution, x=0

__

4. 4 – (2x + 5) = (–4x – 2)

  4 – (2x + 5) - (–4x – 2) = 0

  4 -2x -5 +4x +2 = 0

  2x +1 = 0 . . . . one solution, x=-1/2

__

5. 5(x + 4) – x = 4(x + 5) – 1

  5(x + 4) – x - (4(x + 5) – 1) = 0

  5x +20 -x -4x -20 +1 = 0

  1 = 0 . . . . no solution

Answer:

The answer is a,b and e.

Step-by-step explanation:

a. 2(x + 2) + 2 = 2(x + 3) + 1

b. 2x + 3(x + 5) = 5(x – 3)

e. 5(x + 4) – x = 4(x + 5) – 1

i just did this question on my test hope that helps ;) !

Answer:

[tex]\large\boxed{x>-2+\sqrt{14}\ \vee\ x<-2-\sqrt{14}}\\\boxed{x\in(-\infty,\ -2-\sqrt{14})\ \cup\ (-2+\sqrt{14},\ \infty)}[/tex]

Step-by-step explanation:

[tex]x^2+4x>10\\\\x^2+2(x)(2)>10\qquad\text{add}\ 2^2=4\ \text{to both sides}\\\\x^2+2(x)(2)+2^2>10+4\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+2)^2>14\Rightarrow x+2>\sqrt{14}\ \vee\ x+2<-\sqrt{14}\qquad\text{subtract 2 from both sides}\\\\x>-2+\sqrt{14}\ \vee\ x<-2-\sqrt{14}[/tex]

Answer:

The first choice is the one you want.

Step-by-step explanation:

If we plot the point (5, -12) we will be in QIV.  Connecting the point to the origin and then drawing in an altitude to the positive x axis creates a right triangle with side adjacent to the angle being 5 units long, and the altitude being |-12|.  To find the sin of theta, we need the side opposite (got it) over the hypotenuse (don't have it).  We solve for the length of the hypotenuse using Pythagorean's Theorem:

[tex]c^2=12^2+5^2[/tex] and

[tex]c^2=169[/tex] so

c = 13.  

Now we can find the sin of the angle in the side opposite the angle over the hypotenuse:

[tex]sin\theta=-\frac{12}{13}[/tex]

The first choice in your answers is the one you want.

To find the sine of an angle, we use the point given on its terminal side to represent a right triangle. The sine is calculated as the ratio of the opposite side to the hypotenuse. Using the point (5, -12), our calculation gives sin(θ) as -12/13.

The question asks about the value of sin 0 where the point on the terminal side is (5, -12). However, in trigonometry, we more commonly write it as sin(θ) such that θ is the angle being referenced. Specifically, we are being asked to find the value of sin(θ) when a point on the terminal side of the angle is (5, -12).

To figure out what sin(θ) is, we use the mathematical definition of sine which states that sin(θ) = opposite/hypotenuse. In this context, we can treat the point (5,-12) as a representation of a right triangle. The x-coordinate is adjacent to the angle and the y-coordinate is opposite the angle. Accordingly, we can say that sin(θ) = -12/13.

This is because the hypotenuse can be calculated using Pythagoras' theorem, where hypotenuse = √[(x-coordinate)^2 + (y-coordinate)^2] which equals  √[(5)^2 + (-12)^2] = √169 = 13. Hence, sin(θ) = (-12)/13.

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Answer: 15 yards per mistake.

Step-by-step explanation:

Given : A football team had 4 big mistakes in a game.

i.e. the number of big mistakes done by the football team = 4

The total lost of yards because of the big mistakes done by football team = 60 yards

Now, the portion of  team's yardage change per mistake is given by :-

[tex]\dfrac{\text{Total lost of yards}}{\text{Number of big mistakes}}\\\\=\dfrac{60}{4}=15\text{ yards}[/tex]

Hence, the team's yardage changes by 15 yards per mistake.

Answer:

-15 yardage per mistake

Step-by-step explanation:

Answer:

  (x, y, z) = (3, 1, 2)

Step-by-step explanation:

Solving using a calculator, I would enter the coefficients of 1/x, 1/y, 1/z as they are given. The augmented matrix in that case looks like ...

[tex]\left[\begin{array}{ccc|c}\frac{1}{2}&\frac{1}{4}&-\frac{1}{3}&\frac{1}{4}\\1&-\frac{1}{3}&0&0\\1&-\frac{1}{5}&4&\frac{32}{15}\end{array}\right][/tex]

My calculator shows the solution to this set of equations to be ...

So, (x, y, z) = (3, 1, 2).

___

Doing this by hand, I might eliminate numerical fractions. Then the augmented matrix for equations in 1/x, 1/y, and 1/z would be ...

[tex]\left[\begin{array}{ccc|c}6&3&-4&3\\3&-1&0&0\\15&-3&60&32\end{array}\right][/tex]

Adding 3 times the second row to the first, and adding the first row to the third gives ...

[tex]\left[\begin{array}{ccc|c}15&0&-4&3\\3&-1&0&0\\21&0&56&35\end{array}\right][/tex]

Then adding 14 times the first row to the third, and dividing that result by 77 yields equations that are easily solved in a couple of additional steps.

[tex]\left[\begin{array}{ccc|c}6&3&-4&3\\3&-1&0&0\\3&0&0&1\end{array}\right][/tex]

The third row tells you 3/x = 1, or x=3.

Then the second row tells you 3/3 -1/y = 0, or y=1.

Finally, the first row tells you 15/3 -4/z = 3, or z=2.

Answer:

[tex]\tt B. \ \ \ \cfrac{1+\frac{\sqrt{3}}{3}}{1-\frac{\sqrt{3}}{3}}[/tex]

Step-by-step explanation:

[tex]\displaystyle\tt \tan75^o=\tan(45^o+30^o)=\frac{\tan45^o+\tan30^o}{1-\tan45^o\cdot\tan30^o} =\frac{1+\frac{\sqrt{3}}{3}}{1-\frac{\sqrt{3}}{3}}[/tex]

For this case we have to define that:

[tex]tg (x + y) = \frac {tg (x) + tg (y)} {1-tg (x) * tg (y)}[/tex]

So, according to the problem we have:

[tex]tg (45 + 30) = \frac {tg (45) + tg (30)} {1-tg (45) * tg (30)}[/tex]

By definition we have to:

[tex]tg (45) = 1\\tg (30) = \frac {\sqrt {3}} {3}[/tex]

Substituting we have:

[tex]tg (45 + 30) = \frac {1+ \frac {\sqrt {3}} {3}} {1-1 * \frac {\sqrt {3}} {3}}\\tg (45 + 30) = \frac {1+ \frac {\sqrt {3}} {3}} {1- \frac {\sqrt {3}} {3}}[/tex]

Answer:

option B

Answer:

(- 6, 6 )

Step-by-step explanation:

Assuming the centre of dilatation is the origin, then

The coordinates of the image points are 3 times the original points

B = (- 2, 2 ), then

B' = ( 3 × - 2, 3 × 2 ) = (- 6, 6 )