Answer:
12
Step-by-step explanation:
Alright so we are asked to find the intersection of y=(x-8)^2 and y=36.
So plug second equation into first giving: 36=(x-8)^2.
36=(x-8)^2
Take square root of both sides:
[tex]\pm 6=x-8[/tex]
Add 8 on both sides:
[tex]8 \pm 6=x[/tex]
x=8+6=14 or x=8-6=2
So we have the two intersections (14,36) and (2,36).
We are asked to compute this length.
The distance formula is:
[tex]\sqrt{(14-2)^2+(36-36)^2}[/tex]
[tex]\sqrt{14-2)^2+(0)^2[/tex]
[tex]\sqrt{14-2)^2[/tex]
[tex]\sqrt{12^2}[/tex]
[tex]12[/tex].
I could have just found the distance from 14 and 2 because the y-coordinates were the same. Oh well. 14-2=12.
Solve the compound inequality.
n-12<=-3 or 2n>26
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]
Write the equation for the circle with center at (-8,-6) and radius of 10
(x•8)2 + (y + 5)2 - 10
(x+8)2 + (y + 6) 2 - 100
(4-8)2 + (y - 6)2 -100
d
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
Which situation requires the addition counting principle to determine the number of possible outcomes?
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 ..
Could I solve this inequality by completing the square? How would I do so?
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]
A mechanical dart thrower throws darts independently each time, with probability 10% of hitting the bullseye in each attempt. The chance that the dart thrower hits the bullseye at least once in 6 attempts is:
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.
Four hundred people were asked whether gun laws should be more stringent. Three hundred said "yes," and 100 said "no". The point estimate of the proportion in the population who will respond "yes" is:
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
URGENT
WILL GIVE BRAINLIEST ANSWER
ANSWER
C, D, and E
EXPLANATION
The given ellipse has been translated therefore the center is no longer at the origin.
Option A is not correct.
The major axis is the horizontal axis. Its length is 8 units.
Option B is also not correct.
The vertices are where the major horizontal axis intersected the ellipse. They are indeed 4 units to the right and left of the center.
Option C is correct.
The foci can be found using
[tex] {a}^{2} - {b}^{2} = {c}^{2} [/tex]
a=4 is the distance from the center to the vertex and b=2 is the distance from the center to the co-vertex.
[tex] {4}^{2} - {2}^{2} = {c}^{2} [/tex]
[tex]16 - 4 = {c}^{2} [/tex]
[tex]12 = {c}^{2} [/tex]
[tex]c = \pm \sqrt{12} [/tex]
[tex]c = \pm 2\sqrt{3} [/tex]
Option D is also correct.
The directrices are parallel to the semi-minor axis therefore they are vertical lines.
Option E is also correct.
HELP MEEE!!
Select the correct answer.
Which of the following is not an identity for ?
Answer:
only C
Step-by-step explanation:
What is the value of sin 0 given that (5, -12) is a point on the terminal side of 0 ?
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.
Explanation: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.
Learn more about sin(θ) here:https://brainly.com/question/35502722
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ΔABC is congruent to ΔADC by the SSS criterion. What is the value of x?
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.
According to the chart, from 1986-1996, unintentional drug overdose deaths per 100,000 population began to rise. The numbers for each year are, roughly, 2, 1, 2, 2, 1, 2, 2, 3, 3, 3, 3. What is the mean of these statistics? hope
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]
Further explanationStatistics 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
Tables are usually in the form of frequency tables that show the frequency distribution of dataDiagrams can be in the form of bar charts, pie charts, line charts or pictogramsThe 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]
Learn moreStatistics
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Keywords: mean, statistics, data
***********************(((((((((((((((((((((((Can i get some help?())))))))))))))))))))))))))))))))))))))************
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
Inter-quartile range: 30 - 17 = 13I don't know why it is faced that way but help plz
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
A hat contains slips of paper with the names of the 26 other students in Eduardo's class on them, 10 of whom are boys. To determine his partners for the group project, Eduardo has to pull two names out of the hat without replacing them.
What is the probability that both of Eduardo's partners for the group project will be girls?
Answer:
[tex]\frac{24}{65}[/tex]
Step-by-step explanation:
Total number of students in the class = 26
Number of boys in the class = 10
Number of girls in the class = 26 - 10 = 16
The formula for probability is :
[tex]\text{Probability}=\frac{\text{Favorable Outcomes}}{\text{Total Outcomes}}[/tex]
In this case the favorable outcomes would be the number of girls in the class and total outcomes would be the total number of students in the class.
Eduardo has to pull out two names from the hat. Since there are 16 girls in the class of 26, the probability that the first name will be of the girl will be = [tex]\frac{16}{26}[/tex]
After picking up the 1st name, there would be 25 names in the hat with 15 names of girls as one of the girl is already been chosen. So,
The probability that the second name would belong to a girl = [tex]\frac{15}{25}[/tex]
The probability that both the partners will be girls will be equal to the product of two individual probabilities as both the events are independent.
Therefore,
The probability that both of Eduardo's partners for the group project will be girls = [tex]\frac{16}{26} \times \frac{15}{25} = \frac{24}{65}[/tex]
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. Which of these two men had the height that was more extreme?
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.
The ratio of the side lengths of a quadrilateral is 3:3:5:8, and the perimeter is 380cm. What is the measure of the longest side?
20 cm
160 cm
60 cm
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
A football team had 4 big mistakes in a game. Because of these mistakes, the team lost a total of 60 yards. On average, how much did the team's yardage change per mistake?
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:
The average number of phone inquiries per day at the poison control center is 2. Find the probability that it will receive exactly 4 calls on a given day
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
[20 points+Brainliest] Solve the system of equations. Please give an explanation with your answer, please! A detailed answer will get Brainliest. :)
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 ...
1/x = 1/31/y = 11/z = 1/2So, (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.
if j is the number of integers between 1 and 500 that are divisible by 9 and k is the number of integers between 1 and 500 that are divisible by 7, what is j + k?
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
Which of these equations have no solution? Check all that apply. 2(x + 2) + 2 = 2(x + 3) + 1 2x + 3(x + 5) = 5(x – 3) 4(x + 3) = x + 12 4 – (2x + 5) = (–4x – 2) 5(x + 4) – x = 4(x + 5) – 1
Answer:
2(x + 2) + 2 = 2(x + 3) + 12x + 3(x + 5) = 5(x – 3)5(x + 4) – x = 4(x + 5) – 1Step-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 ;) !
You have recorded your car mileage and gasoline use for 5 weeks Estimate the
number of miles you can drive on a full 15-gallon tank of gasoline,
Number of miles 198 115 154 160 132
| Number of gallons
9 5 7 8 6
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).
What set of transformations are applied to parallelogram ABCD to create A'B'C'D'?
Parallelogram formed by ordered pairs A at negative 4, 1, B at negative 3, 2, C at negative 1, 2, D at negative 2, 1. Second parallelogram transformed formed by ordered pairs A prime at negative 4, negative 1, B prime at negative 3, negative 2, C prime at negative 1, negative 2, D prime at negative 2, negative 1.
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.
The population of a city is modeled by P(t)=0.5t2 - 9.65t + 100,where P(t) is the population in thousands and t=0 corresponds to the year 2000. a)In what year did the population reach its minimum value? How low was the population at this time?b)When will the population reach 200 000?
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).
For a certain casino slot machine comma the odds in favor of a win are given as 7 to 93. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
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.
Explanation: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.
Learn more about Probability here:https://brainly.com/question/32117953
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HELP PLEASE!!
Select the correct answer.
What is the exact value of tan 75°?
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
NEED HELP WITH A MATH QUESTION
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 )
What is the magnitude of the position vector whose terminal point is (6, -4)?
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)|
The Department of Natural Resources determined that the population of white-tailed deer in one of Indiana's state parks was 25 deer per square mile in 1991. By 1992, the population had increased to 30 deer per square mile. By what percentage does the deer population increase in this time frame?
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.
A ladder leans against the side of a house. The angle of elevation of the ladder is 70 when the bottom of the ladder is 14ft from the side of the house. Find the length of the ladder. Round your answer to the nearest tenth.
Check the picture below.
make sure your calculator is in Degree mode.
The length of the ladder is 30.83 ft
What are trigonometry ratios?Trigonometric ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
various ratios are:-
sin=perpendicular/hypoteneusecos=base/hypotenusetan=perpendicular/base (tan30°)=5/bcot=base/perpendicularsec=hypotenuse/basecosec= hypotenuse/perpendicularThe ratios of sides of a right-angled triangle with respect to any of its acute angles are known as trigonometric.
CALCULATIONS:-
The angle of elevation is 70°
using the height and distance formula
cos∅ = base/hypotenuse
cos 70°= 0.454
cos∅ = base/hypotenuse
0.454 =14/hypotenuse
hypotenuse(length of ladder)= 14/0.454
length of ladder= 30.83 ft
Learn more about trigonometry here:-https://brainly.com/question/24349828
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