Based on the calculations, the equation of this hyperbola in standard form is: A. [tex]\frac{x\;-\;7}{16} + \frac{y}{9} = 1[/tex].
How to determine the equation of a hyperbola?Mathematically, the equation of a hyperbola in standard form is given by:
[tex]\frac{x\;-\;h}{a^2} + \frac{x\;-\;k}{b^2} = 1[/tex]
Given the following data:
Center (h, k) = (7, 0)
Vertex (h+a, k) = (7, 4)
Focus = (h+c, k) = (7, 5)
Also, we can deduce that the value of a and c are 4 and 5 respectively.
For the value of b, we would apply Pythagorean's theorem:
c² = a² + b²
b² = c² - a²
b² = 5² - 4²
b² = 9.
Substituting the parameters into the standard equation, we have:
[tex]\frac{x\;-\;7}{4^2} + \frac{y\;-\;0}{3^2} = 1\\\\\frac{x\;-\;7}{16} + \frac{y}{9} = 1[/tex]
Read more on hyperbola here: https://brainly.com/question/3405939
#SPJ1
On the average, five smokers pass acertain street corners every ten minutes, what is the probability that during a given 10 minutes the number of smokers passing will be A. 6 or fewer B. 7 or more C. Exactly 8
Answer:
The answer will be A. 6 or fewer.
The probability that during a given 10 minutes the number of smokers passing will be 6 or fewer.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
Example
Suppose we have to predict about the happening of rain or not. The answer to this question is either "Yes" or "No". There is a likelihood to rain or not rain. Here we can apply probability. Probability is used to predict the outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards.
Terminology of Probability TheoryThe following terms in probability help in a better understanding of the concepts of probability.
Experiment: A trial or an operation conducted to produce an outcome is called an experiment.
Sample Space: All the possible outcomes of an experiment together constitute a sample space. For example, the sample space of tossing a coin is head and tail.
Favorable Outcome: An event that has produced the desired result or expected event is called a favorable outcome. For example, when we roll two dice, the possible/favorable outcomes of getting the sum of numbers on the two dice as 4 are (1,3), (2,2), and (3,1).
Trial: A trial denotes doing a random experiment.
Given:
There are 5 smokers who passes by in every 10 minutes.
So, the probability that during a given 10 minutes the number of smokers passing will be approx 5 or less.
i.e., 6 or fewer.
Learn more about probability here:
https://brainly.com/question/11234923
#SPJ2
find the perimeter.
D. 9.5 cm
To find the perimeter you need to add all the sides.
2.1 + 2.1 + 1 + 3.3 + 1 = 9.5
Help please I need as quick as possible!
Answer: [tex]\sum^{24}_{n=1} (4n+5)[/tex]
Step-by-step explanation:
This is an arithmetic series with a common difference of 4, so we can immediately eliminate the two left-hand options.
To determine which of the two options on the right is correct, we can determine the first term of each sum expanded out.
For the top right, the first term is 4(0)+5=5, which does not match the first term of the given sequence.For the bottom right, the first term is 4(1)+5=9, which does match the first term of the given sequence.Determine whether each set of data can be modeled by an exponential function. If so, find the exponential
function that fits the data.
It can be modeled by an exponential function, f(x) is divided by 3 each time x increases by 1.
This means that the base of the exponential function is 1/3, and since the value of f(x) when x=0 is 81, [tex]f(x)=81\left(\frac{1}{3} \right)^{x}[/tex]
Find the greatest number which divides 6168, 2447, and 3118 leaving the same remainder in each case.
Answer:
Greatest number which divides 6168 is 3084,the greatest number which divides 2447 is1223.5 , and the greatest number which divides 3118 is 1559.
How much would it cost to buy a piece of candy for 50 cents plus tax
Answer:
it depends on which state your in or in your even in the us usually it is either 6% or 4% some times more or less % so im going to do both
50*0.06=53
50*0.04=52
Hope This Helps!!!
Find the slope of every line that is parallel to
the line on the graph
Answer:
[tex] - \frac{1}{6} [/tex]
Step-by-step explanation:
Using the slope formula:
[tex] \frac{ - 1 - 0}{0 - ( - 6)} = - \frac{1}{6} [/tex]
need help i don't know what im doing?
Answer:
X=5
Step-by-step explanation:
f(1)= -1^2+4(1)+12=15
f(2)= -2^2+4(2)+12=16
f(3)= -3^2+4(3)+12=15
f(4)= -4^2+4(4)+12=12
f(5)= -5^2+4(5)+12=7
g(1)=1+2=3
g(2)=2+2=4
g(3)=3+2=5
g(4)=4+2=6
g(5)=5+2=7
so g(5)=f(5)= X=5
Answer:
Step-by-step explanation:
You're suppose to plug in the values 1, 2, 3, 4, 5, and 6 into f(x) and g(x) to find where they're equal to find the solution to f(x) = g(x) (when the column values are equal).
So for example
f(1) = -(1)^2 + 4(1) + 12
f(1) = -1 + 4 + 12
f(1) = 15
g(1) = 1 + 2
g(1) = 3
put these two values in the table for f(1) and g(1)
f(2) = -(2)^2 + 4(2) + 12
f(2) = -4 + 8 + 12
f(2) = 16
g(2) = 2 + 2
g(2) = 4
f(3) = -(3)^2 + 4(3) + 12
f(3) = -9 + 12 + 12
f(3) = 15
g(3) = 3 + 2
g(3) = 5
f(4) = -(4)^2 + 4(4) + 12
f(4) = -16 + 16 + 12
f(4) = 12
g(4) = 4 + 2
g(4) = 6
f(5) = -(5)^2 + 4(5) + 12
f(5) = -25 + 20 + 12
f(5) = 7
g(5) = 5 + 2
g(5) = 7
f(5) = g(5) so the solution is when x=5
f(6) = -(6)^2 + 4(6) + 12
f(6) = -36 + 24 + 12
f(6) = 0
g(6) = 6 + 2
g(6) = 8
If ( 3 y − 9 ) 2 + 7 = 43 , then what is(are) the values of y?
Answer:
y = 5 and y = 1
Step-by-step explanation:
[tex]\textsc {Subtract 7 from each side :}[/tex]
⇒ (3y - 2)² + 7 - 7 = 43 - 7
⇒ (3y - 2)² = 36
[tex]\textsc {take the square root on each side :}[/tex]
⇒ √(3y - 9)² = √36
⇒ 3y - 9 = ±6
[tex]\textsc {When equal to +6, add 9 on each side :}[/tex]
⇒ 3y - 9 + 9 = 6 + 9
⇒ 3y = 15
[tex]\textsc {Divide by 3 on each side :}[/tex]
⇒ 3y/3 = 15/3
⇒ y = 5
[tex]\textsc {When equal to -6, add 9 on each side :}[/tex]
⇒ 3y - 9 + 9 = -6 + 9
⇒ 3y = 3
[tex]\textsc {Divide by 3 on each side :}[/tex]
⇒ 3y/3 = 3/3
⇒ y = 1
The table shows the percentage of students in each of three grade levels who list fishing as their favorite leisure activity
Fishing
6th Grade (38%) 48%
9th Grade (29%) 50%
11th Grade (33%) 32%
Total (100%) (0.38)(0.48) + (0.29)(0.5) + (0.33)(0.32) = 0.433 or 43.3%
Find the probability that a student is a 9th grader, given that fishing is their favorite leisure activity.
Using conditional probability, it is found that there is a 0.3349 = 33.49% probability that a student is a 9th grader, given that fishing is their favorite leisure activity.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.In this problem, we have that the probabilities are given as follows:
[tex]P(A) = 0.433, P(A \cap B) = 0.29 \times 0.50 = 0.145[/tex]
Hence the conditional probability is:
[tex]P(B|A) = \frac{0.145}{0.433} = 0.3349[/tex]
0.3349 = 33.49% probability that a student is a 9th grader, given that fishing is their favorite leisure activity.
More can be learned about conditional probability at https://brainly.com/question/14398287
#SPJ1
answer is equivalent to ?
√16
√49
SA
A.
OB.
O c.
D.
16
49
16
49
316
The solution of the given expression is 9. So the correct answer is option B.
The complete question is given below:-
(√16 - √49 )² The solution of the given equation will be
A. 16
B .9
C .49
D. 316
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The given expression will be calculated as:-
(√16 -√49 )² = (√16)² -2 (√16)(√46) + (√49 )²
= ( 16 - 2(4)(7) + 49 )
= ( 16 - 56 + 49 )
= 9
Therefore the solution of the given expression is 9. So the correct answer is option B.
To know more about expression follow
https://brainly.com/question/723406
#SPJ1
the length of a cell is 2/3 mm. If the area of the cell is 1/12 square mm, whtat is the width of the cell
Answer:
0.125 mm
Step-by-step explanation:
A/L=W
W=0.125
1
Which equation is equivalent to 1/4 + x = -5/4? Select all that apply.
X= 6/4
X= -6/4
X=-1/4=-5/4
X=-3/2
X=-3/4
Answer:
1/4 + x = (-5)/4
x = -5/4 - 1/4
x = (-5)-1 /4
x = (-6)/4
Find the monthly house payment necessary to amortize the following loan. In order to purchase a home, a family borrows $110,000 at 2.9% for 30 yrs. What is their monthly payment? Round the answer to the nearest cent.
The monthly payment for purchasing the home will be $457.85.
What is a monthly payment?The term loan refers to a sort of credit vehicle in which a sum of money is lent to another party in exchange for the value or principal amount being repaid in the future.
Then the formula of monthly payment (MP) will be
[tex]\rm MP = P \times \dfrac{r(1+r)^n}{(1+r)^n - 1}\\[/tex]
In order to purchase a home, a family borrows $110,000 at 2.9% for 30 years.
We have
P = $110,000
r = 0.029 / 12 = 0.0024
n = 30 × 12 = 360
Then the monthly payment will be
[tex]\rm MP = 110,000\times \dfrac{0.0024(1+0.0024)^{360}}{(1+0.0024)^{360} - 1}\\\\[/tex]
On further solving, we have
MP = 110000 × 0.0024 × 1.723
MP = $ 457.85
More about the monthly payment link is given below.
https://brainly.com/question/14064255
#SPJ1
If x = 3, then 3x – 4 = 5. x = 3 law of detatchment
Answer:
3x-4=5
Step-by-step explanation:
it is correct
What is the answer to this question?
Y=x^2-1 with the input as 5
We can see that, when the input is 5, the output is 24.
How to evaluate an equation?
Here we have the equation:
[tex]y = x^2 - 1[/tex]
Where y is the output and x is the input.
We want to evaluate it with the input as 5, so we need to replace the variable x by the number 5, we will get:
[tex]y = 5^2 - 1 = 24[/tex]
Then we can see that, when the input is 5, the output is 24.
If you want to learn more about evaluating functions:
https://brainly.com/question/1719822
#SPJ1
If the price charged for a candy bar is p(x) cents, then x thousand candy bars will be sold in a certain city, where p(x)= 155-(x/10):
a. find an expression for the total revenue from the sale of x thousand candy bars.
b. find the value of x that leads to maximum revenue
c. find the maximum revenue
The expression for the total revenue from x thousand sales is 155,000x - 100x².
The value of x is 775 cents and the maximum revenue is $60,062,500.
What is the maximum revenue?First, come up with an expression for total revenue from x thousand sales:
= (155 - x /10 ) × x × 1,000 units
= 155,000x - 100x²
The value of x would then be:
Derive the function from the total revenue function to give:
0 = 155,000 - 200x
x = 775 cents
The maximum revenue is therefore:
= 155,000(775) - 100(775)²
= $60,062,500
Find out more on finding the maximum revenue at https://brainly.com/question/11829776.
#SPJ1
*Need Help*Match each rational expression to its simplest form.
A manpaid rs 510 as income tax when it was 5 paisa per rupee what was his income?
The income of the man in discuss as in the task content is; rs 10,200.
What is the income of the man?Since, it follows that 100 paisas make one rupee. This insinuates that the income tax rate which corresponds to 5 paisa per rupee is; 5%.
Hence, the amount earned by the man in discuss can be evaluated as follows;
(5/100) × Income = 510
Hence, Income = 510/0.05 = rs 10,200.
Read more on percentages;
https://brainly.com/question/843074
#SPJ1
which has more KE ? a 2 g bee flying at 1 m/s OR a 1 g wasp flying at 2 m/s [tex] \\ [/tex] ty! ~
Answer: Wasp has greater kinetic energy of 0.002 Joules
Given for bee:
mass: 2g = 2 × 10⁻³ kgvelocity: 1 m/sGiven for wasp:
mass: 1 g = 1 × 10⁻³ kgvelocity: 2 m/sFormula:
Kinetic Energy (J) = ½ × mass (kg) × velocity² (m/s)Kinetic energy of bee:
½ × 2 × 10⁻³ × 1² = 1 × 10⁻³ Joules ≈ 0.001 JoulesKinetic energy of wasp:
½ × 1 × 10⁻³ × 2² = 2 × 10⁻³ Joules ≈ 0.002 JoulesFrom this, it is determined wasp has greater kinetic energy.
Urgent help needed algebra 2
replace F with 95:
95 = 9/5C + 32
Subtract 32 from both sides:
63 = 9/5C
Divide both sides by 9/5:
C = 35
answer: 35 Celsius
Find the equation of a line that passes through the point (-2,1) and has a gradient of -3.
Leave your answer in the form
y
=
m
x
+
c
A straight line passing through the point (-2,1) and having a gradient of -3 yields the equation y = -3x - 5.
We know that a straight line is an infinitely long line with no curves on it. A straight line's equation is
y = mx + c...(1), where m is the gradient of the straight line and c is a constant.
Given that the gradient of the given straight line = m = -3.
Putting this value in (1), we get
y = -3x + c ...(2)
Again, the given straight line passes through the point (-2,1). So, we can put x = -2 and y = 1 to get the value of the constant c.
So, 1 = (-3)(-2) + c
i.e. 6 + c = 1
i.e. c = 1 - 6 = -5
(2) can be written as
y = -3x - 5
Therefore the equation of the given straight line is
y = -3x - 5
Know more about straight lines here -
https://brainly.com/question/8085796
#SPJ10
Rewrite the expression as a fraction.
I don't even know Brian tanks
Drag the tiles to the correct boxes to complete the pairs. Match each function to its domain and range.f(x)=5x-3
f(x) is a linear function, so both the domain and the range are the set of real numbers.
find the midpoint of each line segment
Answer:
([tex]\frac{7}{2}[/tex],[tex]\frac{1}{2}[/tex])
Step-by-step explanation:
For this you use the midpoint formula
[tex](\frac{x_{2} +x_{1} }{2} ,\frac{y_{2} +y_{1} }{2} )[/tex]
the points would be (2,1) and (5,2)
The midpoint would be ([tex]\frac{7}{2}[/tex],[tex]\frac{1}{2}[/tex])
Huilan is 8 years older than Thomas. The sum of their ages is 80. What is Thomas's age?
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\texttt {\:Thomas's age = 44 years } [/tex]
[tex]\texttt {\:Hulian's age = 36 years } [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex] \textsf{Assume Thomas's age be ' x ' } [/tex]
[tex] \textsf{and that of Huilan's age be y } [/tex]
[tex] \texttt{we have two conditions :} [/tex]
[tex]\qquad \tt \rightarrow \:y = x + 8[/tex]
it can be simplified as : -
[tex]\qquad \tt \rightarrow \:y - x= 8 \: \: \: \: \: \: \: \: \: - (1)[/tex]
[tex] \texttt{Next condition } [/tex]
[tex]\qquad \tt \rightarrow \:x + y = 80 \: \: \: \: \: \: \: - (2)[/tex]
`` Add both equations ``
[tex]\qquad \tt \rightarrow \:y - x + x + y = 8 + 80[/tex]
[tex]\qquad \tt \rightarrow \:2y = 88[/tex]
[tex]\qquad \tt \rightarrow \:y = 44[/tex]
[tex] \large \textsf{For x :} [/tex]
[tex]\qquad \tt \rightarrow \:y - x = 8[/tex]
[tex]\qquad \tt \rightarrow \:44 - x = 8[/tex]
[tex]\qquad \tt \rightarrow \:x = 44 - 8[/tex]
[tex]\qquad \tt \rightarrow \:x = 36[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
[tex]\fbox {36 years old}[/tex]
Step-by-step explanation:
Let :
⇒ Age of Huilan = x
⇒ Age of Thomas = x - 8
Then :
⇒ x + x - 8 = 80
⇒ 2x = 88
⇒ x = 44
Thomas's age :
⇒ x - 8
⇒ 44 - 8
⇒ 36 years old
Find the number of distinguishable ways the letters of the following word can be arranged. KNICKKNACK
The number of distinguishable ways the letters of the following word can be arranged 'KNICKKNACK' is 37800.
When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.
The number of different permutations of n objects with m₁ repeated items, m₂ repeated items,...,mₙ repeated items can be computed as
m!/(m₁!)(m₂!)...(mₙ!)
Here, the letter 'KNICKKNACK' is a total of 10 letters with 4 K's, 2 N's, 1 I, 2 C's, and 1 A.
So, the number of possible arrangements is
(10!)/(4!*2!*1!*2!*1!) = (10*9*8*7*6*5*4!)/(4!*2*2) = 10*9*7*6*5*2 = 37800
Therefore the number of distinguishable ways the letters of the following word can be arranged 'KNICKKNACK' is 37800.
Learn more about permutations here -
https://brainly.com/question/4301655
#SPJ10
What single transformation was applied to triangle A to get triangle B?
Choose 1 answer:
Translation
Rotation
Reflection
Dilation
d) Suppose you pick one marble from the bag at random. Find the expected value of its number.
(c) Suppose you pick 9 marbles from the bag at random with replacement. Find the probability that you pick at least one purple marble.
C) The probability that you pick at least one purple marble is 98%.
ProbabilityThe question is incomplete, since the number of marbles of each color in the bag is missing: 3 blue, 5 green, and 2 purple marbles.
Now, to answer the questions, the following calculations must be done:
C) 100 - (2/9x9) = X100 - 2 = X98 = XLearn more about probability in brainly.com/question/27656131
#SPJ1
Answer:C) The probability that you pick at least one purple marble is 98%.
Step-by-step explanation:
i need help. Part A: Create a five-number summary and calculate the interquartile range for the two sets of data. (5 points)
Part B: Are there any outliers present for either data set? Justify your answer mathematically. (5 points)
Five number summary and IQR of both the data sets are different.
For school A: Minimum=6, Q₁=6.5, Median= 14, Q₃=16, Maximum=17, IQR=9.5
For school B: Minimum=5, Q₁=8, Median= 12, Q₃=15.5, Maximum=19, IQR=7.5
No, the box plots are not symmetric.
Part A:
The given data sets are
School A : 9,14,15,17,17,7,15,6,6
School B : 12,8,13,11,19,15,16,5,8
Arrange the data in ascending order.
School A : 6,6,7,9,14,15,15,17,17
School B : 5,8,8,11,12,13,15,16,19
Divide each data set into four equal parts.
School A : (6,6),(7,9),14,(15,15),(17,17)
School B : (5,8),(8,11),12,(13,15),(16,19)
For school A:
Minimum=6, Q₁=6.5, Median= 14, Q₃=16, Maximum=17
The interquartile range of the data is
For school B:
Minimum=5, Q₁=8, Median= 12, Q₃=15.5, Maximum=19
[tex]IQR=Q_3-Q_1\\ =Q_3-Q_1\\ =16-6.2\\ =9.5[/tex]
The interquartile range of the data is
[tex]IQR=Q_3-Q_1\\ =Q_3-Q_1\\ =15.5-8\\ =7.5[/tex]
Part B:
The box plots are not symmetric because the data values are different. Five number summary and IQR of both the data sets are different.
To learn more about the symmetric visit:
https://brainly.com/question/1002723
#SPJ1