Answers
Answer:
Option B
Step-by-step explanation:
First identify which options are a match for the hyperbola with a foci of (- 12, 6) and ( 6, 6 ). If there is only one, we can claim that that is the solution. Otherwise we would have to take the vertices into account,
The first option can be eliminated as it is present with a decimal in the denominator, indicating that the foci should also be a decimal. However, the foci of this option should be valuable to us -
[tex]\left(h+c,\:k\right),\:\left(h-c,\:k\right),\\\left(-3+c,\:6\right),\:\left(-3-c,\:6\right),\\c = ( About ) 3.6,\\\\Foci = \left(0.55808 ,\:6\right),\:\left(-6.55808,\:6\right)[/tex]
The second option squares the denominators of the first option, so the foci should be the following -
[tex]Foci = ( - 12, 6 ), ( 6, 6 )[/tex]
Which is the given! The rest of the options are similar to this second option, but are altered, thus don't have the same foci,
Solution = Option B
Related Questions
Jennifer and Stella are cooks at a restaurant that serves breakfast. On a particular day, the two of them tracked the number of pancakes they cooked. The number of pancakes that Jennifer cooked is represented by the following function, where x is the number of hours. The number of pancakes that Stella cooked is shown by the graph below. Who cooked more pancakes in 8 hours?
Answers
Answer:
Stella
Step-by-step explanation:
I guessed and got it right
If f(x) = x² + x - 4, evaluate f(2i).
Can anyone show a step by step process to get the answer?
Answers
Answer:
-6+2i
Step-by-step explanation:
f(2i)=2i^2+2i-4
2i^2 is -2 because i^2 is-1, times 2 is -2.
Therefore, the equation becomes -2+2i-4, leaving the answer of -6+2i.
What are the solutions to log (x2+8)= 1 +log (x)?
Answers
Answer:
Step-by-step explanation:
log(x²+8)=1+log(x)
log(x²+8)-log(x)=1
[tex]log\frac{x^2+8}{x} =1\\\frac{x^2+8}{x} =10^1\\x^2+8=10x\\x^2-10x+8=0\\x=\frac{10 \pm \sqrt{(-10)^2-4*1*8} }{2} \\=\frac{10 \pm \sqrt{100-32} }{2} \\=\frac{10 \pm \sqrt{68} }{2} \\=\frac{10 \pm 2\sqrt{17} }{2} \\=5 \pm \sqrt{17}[/tex]
What is the solution (q, r) to this system of linear equations? 12q + 3r = 15 –4q – 4r = –44
Answers
Answer:
work is shown and pictured
Answer:
(-2, 13)
Step-by-step explanation:
Or b on edge
What is the simplified form of the inequality below? S - 7 < 3
Answers
Answer:
s-7<3
in order to find the value adding 7 on both sides
s-7+7<3+7
s<10
Step-by-step explanation:
i hope this will help you :)
Answer:
s-7<3
in order to find the value adding 7 on both sides
s-7+7<3+7
s<10
Step-by-step explanation:
The weights of college football players are normally distributed with a mean of 200 pounds and a standard deviation of 50 pounds. If a college football player is randomly selected, find the probability that he weighs between 170 and 220 pounds. Round to four decimal places.
Answers
Answer:
0.3811 = 38.11% probability that he weighs between 170 and 220 pounds.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 200, \sigma = 50[/tex]
Find the probability that he weighs between 170 and 220 pounds.
This is the pvalue of Z when X = 220 subtracted by the pvalue of Z when X = 170.
X = 220
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{220 - 200}{50}[/tex]
[tex]Z = 0.4[/tex]
[tex]Z = 0.4[/tex] has a pvalue of 0.6554
X = 170
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{170 - 200}{50}[/tex]
[tex]Z = -0.6[/tex]
[tex]Z = -0.6[/tex] has a pvalue of 0.2743
0.6554 - 0.2743 = 0.3811
0.3811 = 38.11% probability that he weighs between 170 and 220 pounds.
what is the next term in the pattern 2, 3/2, 4/3, 5/4
Answers
Answer:
6/5, 7/6
Step-by-step explanation:
The nth term is (n+1)/n
2/1, 3/2, 4/3, 5/4
Put n as 5 and 6.
(5+1)/5
= 6/5
(6+1)/6
= 7/6
Two spheres of the same outer diameter, one solid and the other hollow, are completely immersed in the water. We can affirm:
a) The hollow receives less push
b) The hollow receives more push
c) Both receive the same push
d) The solid receives less push
Answers
Answer:
c) Both receive the same push
Step-by-step explanation:
The buoyancy force is equal to the weight of the displaced fluid:
B = ρVg
where ρ is the density of the water, V is the volume of displaced water, and g is the acceleration due to gravity.
Since both spheres displace the same amount of water, they have equal buoyancy forces.
A soccer team sold raffle tickets to raise money for the upcoming season. They sold three different types of tickets: premium for $6, deluxe for $4, and regular for $2. The total number of tickets sold was 273, and the total amount of money from raffle tickets was $836. If 118 more regular tickets were sold than deluxe tickets, how many premium tickets were sold?
Answers
Answer:
45 premium tickets were sold
Step-by-step explanation:
p = premium
d = deluxe
r = regular
p+d+r = 273
6p+4d + 2r = 836
118+d = r
Replace r with 118+d
p+d+118+d = 273
p +2d = 273-118
p+2d = 155
6p+4d + 2(118+d) = 836
6p+4d + 236+2d = 836
6p +6d = 836-236
6p + 6d = 600
Divide by 6
p+d = 100
d = 100-p
Replace d in p +2d= 155
p +2(100-p) = 155
p+200-2p = 155
-p = 155-200
-p =-45
p =45
45 premium tickets were sold
Answer:
Step-by-step explanation
We get three linear equations from the information given, where
p= number of premium tickets
d = number of deluxe tickets
r = number of regular tickets:
[tex]\left \{ {{p+d+r=273} \atop \\{6p+4d+2r=836} \right.[/tex]
and the applying third r=118+d, we get
[tex]\left \{ {p+d+118+d=273} \atop {6p+4d+2d+236=836}} \right.[/tex]
[tex]\left \{ {{p+2d=115} \atop {6p+6d=600}} \right.[/tex]
Now we get from the upper one
p=115-2d
solving the another equation gives us
6*115-12d+6d=600,
hence d=15
and by replacing
p=115-2*15=85.
85 premium tickets were sold
7x-14=3x+12
Solve for x!
Answers
Answer: x = 6.5
Step-by-step explanation:
[tex]7x-14=3x+12\\\\Add(14)\\\\7x=3x+26\\\\Subtract(3x)\\\\4x=26\\\\Divide(4)\\\\x=6.5[/tex]
Hope it helps <3
Answer:
x=26/4 (simply to 13/2)
Step-by-step explanation:
Add 14 to both sides to cancel out the negative 14
7x=3x+26
Subtract 3x from both sides to cancel the 3x
4x=26
x=26/4 or 13/2
What is a square root
Answers
Write the inverse of g(x)=x²-7
Answers
Answer:
[tex]\± \sqrt{x + 7}[/tex]
Step-by-step explanation:
y = x² - 7
Add 7 to both sides.
y + 7 = x²
Take square root on both sides.
±√(y + 7) = x
Switch variables.
±√(x + 7) = y
Not sure how I would find what axis
Answers
Answer:
Quad 1
Step-by-step explanation:
How many 3-digit numbers can be formed if repetition is
allowed?
Answers
Answer: up to 999
Step-by-step explanation: Now, if you consider repetition allowed, all the numbers from 100 to 999 are 3 digit numbers. How many numbers are formed ? count numbers starting from 100 up to 999. Hence, 900 numbers are formed.
How much of salt would you get if you evaporate all water from 20g of a 17% salt solution?
Answers
Answer:
3.4 grams
Step-by-step explanation:
The water 20g has salt solution of 17%.
If you were to evaporate all the water.
17% × 20
0.17 × 20 = 3.4
You would get 3.4 grams of salt.
The amount of salt extracted when evaporating 20g of a 17 % salt solution is 3.4 grams of salt
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the percentage of salt solution be = 17 %
The total amount of solution = 20g
The amount of salt while evaporating the solution is =
percentage of salt solution x total amount of solution
So , the equation will be
The amount of salt while evaporating the solution is = ( 17 / 100 ) x 20
The amount of salt while evaporating the solution is = 0.17 x 20
The amount of salt while evaporating the solution is = 3.4 grams
Therefore , the value is 3.4 grams
Hence , The amount of salt extracted when evaporating 20g of a 17 % salt solution is 3.4 grams of salt
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A card is drawn randomly from a standard 52-card deck. Find the probability of the given event.
(a) The card drawn is a king.
(b) The card drawn is a face card.
(c) The card drawn is not a face card.
Answers
Answer:
(a) [tex]\frac{1}{13}[/tex]
(b) [tex]\frac{3}{13}[/tex]
(c) [tex]\frac{10}{13}[/tex]
Step-by-step explanation:
The probability of an event B occurring is given by;
P(B) = [tex]\frac{n(E)}{n(S)}[/tex]
Where;
P(B) = probability of the event B
n(E) = number of favourable outcomes
n(S) = total number of events in the sampled space.
From the question, the card is drawn randomly from a standard 52-card deck. The probability of
(a) drawing a "king" card is analyzed as follows.
Let the event of drawing the "king" card be B.
In a standard 52-card deck, the number of cards that are of type king is 4. i.e 1 from the diamond pack, 1 from the spade pack, 1 from the heart pack and 1 from the club pack.
Therefore, the number of favourable outcomes is 4, while the total number of events in the sampled space is 52.
The probability of drawing a "king" card, P(B) is;
P(B) = [tex]\frac{4}{52}[/tex]
P(B) = [tex]\frac{1}{13}[/tex]
(b) drawing a "face" card is analyzed as follows.
Let the event of drawing the "face" card be B.
In a standard 52-card deck, a face card can either be a Jack, Queen or a King. There are 4 Jack cards, 4 Queen cards and 4 King cards in the deck. The number of cards that are of type face is 12.
Therefore, the number of favourable outcomes is 12, while the total number of events in the sampled space is 52.
The probability of drawing a "face" card, P(B) is;
P(B) = [tex]\frac{12}{52}[/tex]
P(B) = [tex]\frac{3}{13}[/tex]
(c) drawing a card that is not a "face" is analyzed as follows;
The sum of the probability of drawing a face card and the probability of not drawing a face card is always 1.
Let the event of drawing a "face" card be B and the event of not drawing a "face" card be C.
P(B) + P(C) = 1
P(C) = 1 - P(B)
From (b) above, the P(B) = [tex]\frac{3}{13}[/tex]
Therefore,
P(C) = 1 - [tex]\frac{3}{13}[/tex]
P(C) = [tex]\frac{10}{13}[/tex]
Complete the following proof. Given: Points R, S, T, Q on circle O Prove: m \overarc R S + m \overarc S T + m \overarc T Q = m \overarc R Q
Answers
Answer:
Answer is below.
Step-by-step explanation:
Points R, S, T, Q on Circle O - Given
m (arc) RS + m (arc) ST = m (arc) RT , m (arc) RT + m (arc) TQ = m (arc) RQ - Arc addition
m (arc) RS + m (arc) ST + m (arc) TQ = m (arc) RQ - Substitution
Hope this helps.
The proofing is as follows:
Given that,
Points R, S, T, Q on Circle O -Now
m (arc) RS + m (arc) ST = m (arc) RT , m (arc) RT + m (arc) TQ = m (arc) RQ - Arc addition
And,
m (arc) RS + m (arc) ST + m (arc) TQ = m (arc) RQ - Substitution
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PLEASE QUICK!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Which number completes the system of linear inequalities represented by the graph? y > 2x – 2 and x + 4y > -12 -3 4 6
Answers
Answer:
-12
Step-by-step explanation:
Edge 2021
what it 17.15 in 12hour clock
Answers
Answer:
Step-by-step explanation:
Hello friend
The answer is 5:15 in 12 hour clock
Answer:
5:15 PM
Step-by-step explanation:
12:00 + 5:00
17:00 in 12 hour clock is 5:00 PM.
15 minutes + 5:00 PM
⇒ 5:15 PM
What is the output of the following function for x = -4?
F(x) = 3x^5 + 4x^3 -x +11
Answers
Answer:
-3313
Step-by-step explanation:
3x^5 + 4x^3 - x +11
Put x as -4 and evaluate.
3(-4)^5 + 4(-4)^3 - (-4) + 11
-3072 + - 256 + 4 + 11
= -3313
solve for x.
x/3 < -6
Answers
Answer: x < -18
Step-by-step explanation:
Simply multiply both sides by three to get x < -18
Step-by-step explanation:
x/3 < - 6
x < - 18
This should be the answer
a sample of 49 observations is taken from a normal population with a standard deviation of 10. the sample mean is 55. Determine the 99% confidence interval for the population mean.
Answers
Answer:
55+/-3.69
= (51.31, 58.69)
Therefore, the 99% confidence interval (a,b)= (51.31, 58.69)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x =55
Standard deviation r = 10
Number of samples n = 49
Confidence interval = 99%
z-value (at 99% confidence) = 2.58
Substituting the values we have;
55+/-2.58(10/√49)
55+/-2.58(1.428571428571)
55+/-3.685714285714
55+/-3.69
= (51.31, 58.69)
Therefore, the 99% confidence interval (a,b)= (51.31, 58.69)
researchers are interested in the average size of a certain species of mouse. They collect the length and gender of each mouse. What is the parameter likely estimated and the sample statistic
Answers
Answer:
E. The parameter is μmale - μfemale and the statistic is xmale - xfemale.
Step-by-step explanation:
The sample statistic is a piece of information about the individuals or objects that were selected from a given population. The sample is just a fraction of the total population. Since it is a herculean task studying an entire population, the sample forms a manageable size that allows us to have an insight into the entire population. The sample statistics are now the piece of information about the sample being studied such as the average, mean, median, or mode. The sample statistics have to be as specific as possible of the factors being measured. In the question, we would have to obtain the mean of both the male and female genders. This gives us an insight into the population under study.
The parameter, on the other hand, is a description of the entire population being studied. For example, we might want to determine the population mean. That is the factor we seek to measure. It is represented by the sign mu (μ).
Describe the possible echelon forms of a nonzero 2 x 2 matrix.
Answers
Answer:
we approach the issue by taking note of that a 2 x 2 matrix can either have 1 0r 2 pivot columns. If the matrix has no pivot columns then every entry in the matrix must be zero.
-> if our matrix has two pivot columns then : [tex]\left(\begin{array}{rr}-&*&0&-\end{array}\right)[/tex]
-> if our matrix has one pivot column then we have a choice to make. If the first column is pivot column then: [tex]\left(\begin{array}{rr}-&*&0&0\end{array}\right)[/tex]
->otherwise, if the pivot column is the second column then: [tex]\left(\begin{array}{rr}0&-&0&0\end{array}\right)[/tex]
Eight times the difference between a number and six is equal to four times the number. What’s the number?
Answers
Answer:
12
Step-by-step explanation:
Given:
Let the number be x.
According to the question,
8(x-6)= 4 x
8 x-48=4 x
8 x-4 x= 48
4 x=48
x=48/4
x=12
Thank you!
find the length of side A
Answers
Answer:
First option: 3
Step-by-step explanation:
To solve for side 'a', use the Pythagorean Theorem
a² + b² = c²
where "c" is always the longest side called the hypotenuse,
"a" and "b" are the two shorter sides called legs.
Substitute c = 5 (hypotenuse) and b = 4
a² + b² = c²
a² + (4)² = (5)²
Square the numbers you know
a² + 16 = 25
Subtract 16 on both sides to isolate 'a'
a² = 25 - 16
a² = 9
Find the square root on both sides
a = √9
a = 3
The answer is option A. ( i.e 3)... answer.
What is the slope of this line?
Answers
Answer:
3/2
Step-by-step explanation:
We can find the slope of this line by using two points
(1,-3) and (3,0)
m = (y2-y1)/(x2-x1)
= (0- -3)/(3 -1)
= (0+3)/(3-1)
= 3/2
A girl walks 800 m on a bearing of 129°.
Calculate how far: a east b south she is from
her starting point.
Answers
Answer: a) 503.2m
b) 621.6m
Step-by-step explanation:
The diagram representing the scenario is shown in the attached photo.
A represents her starting point.
CD = x = how far east she is from her starting point
BC = y = how far south she is from her starting point
Angle BAC = 180 - 129 = 51°
Angle ACD = angle BAC = 51° because they are alternate angles
To determine x, we would apply the cosine trigonometric ratio
Cos 51 = x /800
x = 800Cos51 = 800 × 0.629 = 503.2m
To determine y, we would apply the sine trigonometric ratio
Sin 51 = y /800
y = 800Sin51 = 800 × 0.777 = 621.6m
Find the coordinates of the point on a circle with radius 4 at an angle of 2pi/3
{Please help!!}
Answers
Answer:
The coordinates of the point on a circle with radius 4 at an angle of [tex]\frac{2\pi}{3}[/tex] radians are x = -2 and y = 3.464.
Step-by-step explanation:
This problem ask us to determine the rectangular coordinates from polar coordinates. The polar coordinates of the point in rectangular form is expressed by the following expression:
[tex](x,y) = (r\cdot \cos \theta, r\cdot \sin \theta)[/tex]
Where [tex]r[/tex] and [tex]\theta[/tex] are the radius of the circle and the angle of inclination of the point with respect to horizontal, measured in radians. If [tex]r = 4[/tex] and [tex]\theta = \frac{2\pi}{3}\,rad[/tex], the coordinates of the point are:
[tex](x,y) = \left(4\cdot \cos \frac{2\pi}{3},4\cdot \sin \frac{2\pi}{3} \right)[/tex]
[tex](x,y) = (-2, 3.464)[/tex]
The coordinates of the point on a circle with radius 4 at an angle of [tex]\frac{2\pi}{3}[/tex] radians are x = -2 and y = 3.464.
The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 3.3 hours. If 1 gram of this isotope is present initially, how long will it take for 95% of the lead to decay?
Answers
Answer:
[tex] N(t) =N_o (\frac{1}{2})^{\frac{t}{t_{1/2}}}[/tex]
Where [tex]t_{1/2}= 3.3 hr[/tex] represent the half life and the intial amount would be [tex] N_o = 1[/tex]
And we want to find the time in order to have a 95% of decay so we can set up the following equation:
[tex] 0.05 = 1 (0.5)^{t/3.3}[/tex]
If we apply natural log on both sides we got:
[tex] ln(0.05) = \frac{t}{3.3} ln (0.5)[/tex]
And solving for t we got:
[tex] t= 3.3 *\frac{ln(0.05)}{ln(0.5)}= 14.26[/tex]
So then would takes about 14.26 hours in order to have 95% of the lead to decay
Step-by-step explanation:
For this case we can define the variable of interest amount of Pb209 and for the half life would be given:
[tex] N(t) =N_o (\frac{1}{2})^{\frac{t}{t_{1/2}}}[/tex]
Where [tex]t_{1/2}= 3.3 hr[/tex] represent the half life and the intial amount would be [tex] N_o = 1[/tex]
And we want to find the time in order to have a 95% of decay so we can set up the following equation:
[tex] 0.05 = 1 (0.5)^{t/3.3}[/tex]
If we apply natural log on both sides we got:
[tex] ln(0.05) = \frac{t}{3.3} ln (0.5)[/tex]
And solving for t we got:
[tex] t= 3.3 *\frac{ln(0.05)}{ln(0.5)}= 14.26[/tex]
So then would takes about 14.26 hours in order to have 95% of the lead to decay