Determine if
16
x
2
−
25
y
2
=
1
16
x
2
-
25
y
2
=
1
is a hyperbola and if it is, which type it is. The transverse axis is
what is A and B
Answers
The values of a and b are 1/4 and 1/5 respectively
How to determine the true statement?The function is given as:
16x^2 - 25y^2 = 1
The above function is a horizontal hyperbola.
A horizontal hyperbola that passes through the origin is represented as:
[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]
Rewrite 16x^2 - 25y^2 = 1 as
[tex]\frac{x^2}{1/16} - \frac{y^2}{1/25} = 1[/tex]
By comparison, we have:
[tex]a^2 = \frac{1}{16}[/tex]
[tex]b^2 = \frac{1}{25}[/tex]
Solve for a and b
[tex]a = \frac{1}{4}[/tex]
[tex]b = \frac{1}{5}[/tex]
Hence, the values of a and b are 1/4 and 1/5 respectively
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Related Questions
how do you solve this?
Answers
B. The standard deviation is he square root of variance. The larger the standard deviation the more variation
Answer:
this is quite an easy problem.
Step-by-step explanation:
The problem appears to be asking for the class with the greatest variability of test 1, which merely means that you are looking for the graph that has the most distributed test scores. The graph that shows the largest difference in each test score will be your answer.
A cone of height 9cm has a volume of ncm³ curved surface area of ncm². Find the vertical angle of the cone
Answers
Answer:
Step-by-step explanation:
let the radius be r and the slant height be L
then first of all: L^2 = r^2 + 9^2
= r^2 + 81
Surface area = πrL = n
volume = (1/3)πr^2 (9) = 3πr^2 = n
then 3πr^2 = πrL
3r = L , then in L^2 = r^2 + 81
9r^2 = r^2 + 81
8r^2 = 81
r = 9/√8
L^2 = 81/8 + 81 = 729/8
L = √1458/4
cos(baseangle) = (9/√8) / (√1458/4)
= 1/3
angle of base = appr 70.5°
check my arithmetic
Question 11
Points 2
Mary has four T-shirts-T₁, T2, T3, and T4, and
three pairs of jeans-J1, J2, and J3. The number
of possible ways she can choose her outfit is:
O 12
Answers
The computation shows that the number of possible ways will be 12.
How to calculate the value?From the information given, Mary has four t-shirts-T₁, T2, T3, and T4, and three pairs of jeans-J1, J2, and J3.
Therefore, the number of possible ways that she can choose her outfit will be:
= 4 × 3 = 12
In conclusion, the correct option is 12.
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6. Construct the Truth Table and Determine whether each of the following compound
proposition is a Tautology, Contradiction or Contingency.
Answers
The first expression is Contingency.
The second expression is Tautology.
The third expression is Contingency.
What is Truth table?A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra.
What is Contingency?A sentence is called a contingency if its truth table contains at least one 'T' and at least one 'F. '
What is Contradiction?A statement is called a contradiction if the final column in its truth table contains only 0's.
What is Tautology?A tautology is a statement that is always true.
The first expression is Contingency.
The second expression is Tautology.
The third expression is Contingency.
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The length, l call my a rectangular room is four less than the width, W, of the room. Which expression represents the area of the room.
(I have no options)
Answers
Answer: Either [tex]w(w-4)[/tex] or [tex]w^2 - 4w[/tex]
==================================================
Explanation:
w = width
w-4 = length since it is 4 less than the width
Multiply the length and width to get the area of the rectangle.
area = length*width
area = [tex](w-4)w[/tex]
area = [tex]w(w-4)[/tex]
area = [tex]w^2-4w[/tex]
In the last step, I used the distributive property.
Either expression mentioned above is valid for the area. If you had to pick only one, I'd go for [tex]w^2-4w[/tex]
The height "h" of a ball thrown straight up with a velocity of 88 ft/s is given by h = -16t^2 + 88t where "t" is the time it is in the air. For how many seconds the ball is in the air before it hits the ground?
Answers
Answer:
t=5.5
Step-by-step explanation:
The ball hits the ground when h = 0.
[tex]-16t^2 + 88t = 0 \\ \\ 2t^2 - 11t =0 \\ \\ t(2t-11)=0 \\ \\ t=0, 5.5[/tex]
However, as the answer must be positive, t=5.5
Which system of equations has a solution of (0,1,2),
A.) 3x - y = -1
2y - z = 4
X- y + z = -1
B.) 2x + 4y = 4
y - 5z = 9
x+y+z=2
C.) -2x + 2y = 2
y + 7z = 13
1-y-z=0
D.) I + 3y - z = 1
4x + 2y = 2
5y - 2z = 1
Answers
Answer:
D
Step-by-step explanation:
well, you can simply put the arguments where belong and if you check choice D
5(1)–2(2)=1
so that will be the answer
Which is not a method for solving a system of equations?
A. Graphing
B. Substitution
C. Fundamental Theorem of Arithmetic
D. Linear combination
Answers
Fundamental Theorem of Arithmetic is not a method for solving a system of equations.
What are system of equation?A system of equations is a collection of two or more equations with a same set of unknowns.
The system of equation can be solved using the following method.
Graphing methodSubstitution methodLinear combinationThe graphing involves using graph to find the intersection of the system of equation.
Substitution method involves substituting one variable to another.
Therefore, Fundamental Theorem of Arithmetic is not a method for solving a system of equations
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If f(x) = 3x + 2, what is f(5)?
Answers
Answer:
17
Step-by-step explanation:
f(5) means replacing any x in the equation with 5, so that would give you 3*5 + 2
in order of operations, 3*5 = 15 + 2 = 17
hope this helped! :)
he Golfing Emporium had a set of 10 golf clubs that were marked on sale for $780. This was a discount of 30% off the original selling price.
Step 2 of 4 : If the golf clubs cost The Golfing Emporium $620, what was their profit? Follow the problem-solving process and round your answer to the nearest cent, if necessary.
Answers
The profit for the Golfing Emporium is $160.
How to get the profit?
We know that profit is defined as the difference between the revenue and the cost.
Here, we know that on the sale, the Golfing Emporium sells the set of clubs at $780 (this is the already discounted price).
While when they buy the set, the pay $620 for it.
Then the profit is given by:
P = $780 - $620 = $160
The profit for the Golfing Emporium is $160.
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Consider a population that grows according to the recursive rule
P
n
=
P
n
−
1
+
25
, with initial population
P
0
=
30
.
Then:
P
1
=
P
2
=
Find an explicit formula for the population. Your formula should involve
n
(use lowercase n)
P
n
=
Use your explicit formula to find
P
100
P
100
=
Answers
The explicit formula for the arithmetic sequence is: [tex]P_n = 30 + 25n[/tex]
Using the formula, we have that [tex]P_{100} = 2530[/tex].
What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term.
From the recursive formula, we have that:
[tex]a_1 = 30 + 25 = 55, d = 25[/tex]
Hence the explicit formula is:
[tex]P_n = 55 + 25(n-1)[/tex]
[tex]P_n = 30 + 25n[/tex]
Then, when n = 100:
[tex]P_{100} = 30 + 25(100) = 2530[/tex]
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The two dot plots represent a sample of the number of people in households in two towns. Which statements are true about the data sets?
Answers
The true statement ae:
Both have the same number of data points.
Both means are between 3 and 4.
Westwood has less variability than Middleton.
What are the true statements?A dot plot is made up of dots which represents the frequency of the values in the data set and a numberline.
The total number of data points for both dot plots is 20.
The range of Middleton is : 9 -1 = 8
The range of Westwood is: 6 - 2 = 4
Middleton has more variability than Westwood.
Mean sum of numbers / total numbers
Middleton = (1+ 2+ 2 + 2 + 2 + 3 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 4 + 5 + 5 + 5, 5 + 6 + 9) / 20 = 3.75
Westwood = ( 2 + 2 + 2 + 2 + 3 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 5 + 6 + 6 + 6) / 20 = 3.85
Here is the complete question:
The two dot plots represent a sample of the number of people in households in two towns. Which statements are true about the data sets?
Check all that apply.
Both have the same number of data points.
Both means are between 3 and 4.
Both have the same median.
Both have the same range.
Westwood has less variability than Middleton.
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A survey found that women's heights are normally distributed with mean 62.7 in, and standard deviation 2.8 in. The survey also found that men's heights are normally distributed with mean
69.3 in. and standard deviation 3.9 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 55 in, and a maximum of 62 in. Complete
parts (a) and (b) below.
a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement park?
The percentage of men who meet the height requirement is %.
(Round to two decimal places as needed)
Answers
Using the normal distribution, we have that:
The percentage of men who meet the height requirement is 3.06%. This suggests that the majority of employees at the park are females.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation of men's heights are given as follows:
[tex]\mu = 69.3, \sigma = 3.9[/tex].
The proportion of men who meet the height requirement is is the p-value of Z when X = 62 subtracted by the p-value of Z when X = 55, hence:
X = 62:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{62 - 69.3}{3.9}[/tex]
Z = -1.87
Z = -1.87 has a p-value of 0.0307.
X = 55:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55 - 69.3}{3.9}[/tex]
Z = -3.67
Z = -3.67 has a p-value of 0.0001.
0.0307 - 0.0001 = 0.0306 = 3.06%.
The percentage of men who meet the height requirement is 3.06%. This suggests that the majority of employees at the park are females.
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PLEASE HELP LOOK AT IMAGE FOR ANSWER I WILL MAKE YOU BRAINLISET PLEASE HELP
Answers
Answer:
c
Step-by-step explanation:
Help I'm confused with this question
Answers
so short answer is: 46, 57, 68
Since 35 + 11 = 46, 46 is our next number in the ID.
Since 46 + 11 = 57, 57 is our next number in the ID.
Since 57 + 11 = 68, 68 is our next number in the ID.
Your final answer: In the first blank, we added by 11 and got 46. In the second blank, we added by 11 and got 57. In the third blank, we added by 11 and got 68. Combining these numbers with all of the other numbers, the ID of one customer would be 2132435465768. If you need extra help, let me know and I will gladly assist you.
Find the value(s) of x in the function f(x) = |-2x – 3| when f(x) = 5. (Separate multiple answers with a comma.)
Answers
Answer:
x = -4, 1
Step-by-step explanation:
Since we have a absolute value function here, we can tell there is goning to be multiple values.
First we will find x with the original function since we know |5| = 5.
Given f(x) = 5 = -2x-3,
[tex]2x-3 = 5 \\
-2x-3+3 = 5 + 3 \\
-2x = 8 \\
x = \frac{8}{ - 2} \\ = - 4[/tex]
Now we also know that |-5| = 5 as well (absolute value)
Given |-2x-3| = |-5|,
[tex] - 2x - 3 = - 5 \\ - 2x - 3 + 3 = - 5 + 3\\ - 2x = - 2 \\ x = \frac{ - 2}{ - 2} \\ = 1[/tex]
You can verifiy these 2 values by substituting them into the equation.
f(-4) = |-2(-4)-3|
= |8-3|
= |5|
= 5
f(1) = |-2(1)-3|
= |-2-3|
= |-5|
= 5
A modulus function is defined as a function that gives positive value for either a negative or positive argument. The values of x for given condition are -4 and 1.
What is a Modulus function?A function in the form of f(x) = |x| is known as a modulus function. The graph of a modulus function is symmetric about y-axis.
The function is given as,
f(x) = |-2x-3|
which implies that f(x) = -2x - 3 for x > 0 and f(x) = -(-2x - 3 )for x < 0
As per the question ,
Substitute the value of f(x) = 5, for both the cases to get the value of x as,
-2x - 3 = 5 and -(-2x - 3 ) = 5
=> x = -4 and x = 1.
Hence, the values of x obtained for the given condition are x =-4 and x = 1.
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#280 at the
Nader plans to buy a car. He can afford to pay
end of each month for 3 years. The best interest rate
he can find is 9.8% la, compounded monthly.
for this interest rate, the most he could spend on a car
is $8702.85,
Determine the amount he could spend on the
purchase of the car if the interest rate is 9.8%.la,
Compounded annually.
Answers
Based on the amount that Nader can pay per month, and the interest rate as well as the period, the amount he could spend if the rate was annual is $8,385.33.
How much could Nader spend on the car?If Nader can pay $280 per month, the amount he can pay per year i:
= 280 x 12
= $3,360
The amount that he can spend on the car is the present value of these yearly payments:
= 3,360 x (1 - (1 + 9.8%)⁻³) / 9.8%
= 3,360 x 2.49563439768461
= $8,385.33
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use venn diagram to find the elements in each set A'
Answers
Based on the Venn diagram, the elements in set A can be found to be 2, 3 ,5, 7,and 9.
What are the elements in set A?The elements in set A would be those which are in A alone and in set B as well.
The numbers in set A alone are:
7, 3, 5, 9
The number in set B and A is 2.
The elements in set A is therefore:
2, 3 , 5, 7,and 9
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write an equation of a line in standard form
passes through (35,42) and (15,-2)
Answers
Answer:
[tex]y=\frac{11}{5}x-35[/tex]
Step-by-step explanation:
The equation of a line is y=mx+b
Plug in the points
35m+b=42 (1)
15m+b=-2 (2)
(1)-(2)
20m = 44
m = 11/5
33+b=-2
b=-35
[tex]y=\frac{11}{5}x-35[/tex]
Write the equation of the line that is parallel to the line y=−74x−2 through the point (4,-2).
Answers
Parallel lines have the same slope, so since the slope of the given line is -74, the slope of the line we want to find is also -74.
Substituting into point-slope form,
[tex]y+2=-74(x-4)\\\\y+2=-74x+296\\\\\boxed{y=-74x+294}[/tex]
Which equation could be used to find the length of the hypotenuse
Answers
Answer:
first equation
Step-by-step explanation:
The product of w and 6
Answers
Answer:
w x 6
Because W is a variable and we don't know what W so it the equation is gonna be a open sentance
Write −1.2 as a ratio of two integers.
Answers
Answer: (-6:5)
Step-by-step explanation:
6/5 = 1.2
-1 * 6 = -6
-6/5 = -1.2
thus...
Ratio = (-6:5)
Cedrick is going to meet his mother for dinner at a restaurant halfway between his house and hers. On a coordinate grip map, Cedrick’s house is at (–51, –26) and his mom lives at (2, –4).
Where is the best restaurant for them to meet?
Greek restaurant at (–25, –15)
French restaurant at (–27, –11)
Mediterranean restaurant at (–28, –12)
Thai restaurant at (–38, –1)
Answers
Using the mid-point concept, the best restaurant for them to meet is given by:
Greek restaurant at (–25, –15).
What is the midpoint concept?The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.
For the midpoint between his house and his mom's, the coordinates are given as follows:
x = (-51 + 2)/2 = -49/2 = -24.5.y = (-26 - 4)/2 = -30/2 = -15.Hence the Greek restaurant is the best option, as it is closest.
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5. Ellie's street address is a prime number greater than 10 and less than 19. Which of the following could be Ellie's street address?
Answers
We want to find a prime number greater than 10 and less than 19.
* What is a prime number?
Prime number is a number that cannot be divided by any number other than 1 and itself
There are so many possibilities:
Ellie's street address could be 11, 13 or 17
Hope it helps!
Here's the work I've done. Is it right?
V=πr^2h
π(0.375)^2(0.80)
=0.4m^3 (smallest cylinder)
π(0.625)^2(0.80)
=1.0m^3 (middle cylinder)
0.70+0.80
=1.5m (height for big cylinder)
π(1.5)^2(1.5)
=10.6m^3
10.6m^3+0.4m^3+1.0m^3
=12.0m^3
The spa will fit 12.0m^3 of water
Answers
Answer: [tex]6.67m^3[/tex]
Step-by-step explanation:
For hemisphere...
diameter (d1) = 3m
radius (r1) = (3/2)m
The total volume of the hemisphere
[tex]v1=\frac{2}{3} \pi (r1)^3[/tex]
[tex]=\frac{2}{3} \pi (\frac{3}{2} )^3[/tex]
[tex]=\frac{9}{4} \pi[/tex]
-----------------------------------------------------------------------
For smaller cylinder
diameter (d2) = 0.75
radius (r2) = 0.75/2m
height (h2) = 0.80m
Volume of smaller cylinder
(V2) = [tex]\frac{1}{3} \pi (r2)^2h2[/tex]
[tex]=\frac{1}{3} \pi (\frac{0.75}{2} )^2*0.80[/tex]
[tex]=\frac{3}{80} \pi[/tex]
------------------------------------------------------------------------
For bigger cylinder
Volume of bigger cylinder =
[tex]V3=\frac{1}{3} \pi (\frac{1.25}{2} )^2*0.70[/tex]
[tex]=\frac{35}{384} \pi[/tex]
-----------------------------------------------------------------------
Volume of water = [tex](v1 - v2 - v3) =\frac{9}{4} \pi -\frac{3}{80} \pi -\frac{35}{384} \pi = 6.67 m^3[/tex]
What is the angle of rotation for the following figure?
Answers
Answer:
Angle rotation 120 ,90,60,45
What is the slope of a line parallel to the line whose equation is3x−4y=8?
−43
−34
34
43
Answers
Answer:
The parallel slope for this equation is going to be [tex]\frac{3}{4}[/tex] hope that helps and can you mark me as brainlist please.
In major league baseball, a no-hitter is a game in which a pitcher, or pitchers, doesn't give up any hits throughout the game. No-hitters occur at a rate of about three per season. Assume that the duration of time between no-hitters is exponential. What is the probability that an entire season elapses with a single no-hitter? If an entire season elapses without any no-hitters, what is the probability that there are no no-hitters in the following season? What is the probability that there are more than 3 no-hitters in a single season?
Answers
Using the Poisson distribution, it is found that:
There is a 0.0498 = 4.98% probability that an entire season elapses with a single no-hitter.If an entire season elapses without any no-hitters, there is a 0.0498 = 4.98% probability that there are no no-hitters in the following season.There is a 0.3528 = 35.28% probability that there are more than 3 no-hitters in a single season.What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.The average rate is of 3 no-hitters per season, hence:
[tex]\mu = 3[/tex].
The probability that an entire season elapses with a single no-hitter is P(X = 0), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}3^{0}}{(0)!} = 0.0498[/tex]
There is a 0.0498 = 4.98% probability that an entire season elapses with a single no-hitter.
Seasons are independent, hence:
If an entire season elapses without any no-hitters, there is a 0.0498 = 4.98% probability that there are no no-hitters in the following season.
The probability that there are more than 3 no-hitters in a single season is P(X > 3) given as follows:
[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]
In which:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
Then:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}3^{0}}{(0)!} = 0.0498[/tex]
[tex]P(X = 1) = \frac{e^{-3}3^{1}}{(1)!} = 0.1494[/tex]
[tex]P(X = 2) = \frac{e^{-3}3^{2}}{(2)!} = 0.2240[/tex]
[tex]P(X = 3) = \frac{e^{-3}3^{3}}{(3)!} = 0.2240[/tex]
Then:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0498 + 0.1494 + 0.2240 + 0.2240 = 0.6472[/tex]
[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.6472 = 0.3528[/tex]
There is a 0.3528 = 35.28% probability that there are more than 3 no-hitters in a single season.
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Please help with this question if you can
Answers
Line AE is NOT parallel to line BD. This is because the intercepts made by the lines and the transversals are not proportional
Parallel lines theoremIn the given diagram,
If
[tex]\frac{|AB|}{|ED|} =\frac{|AC|}{|EC|}[/tex]
Then,
Line AE is parallel to line BD
From the given information,
|AB| = x = 9
|ED| = 5
|AC| = 9 + 11 = 20
|EC| =5 + 7 = 12
Thus,
[tex]\frac{9}{20}=\frac{5}{12}[/tex]
20 × 5 = 9 × 12
100 ≠ 108
∴ The lines are not parallel
Hence, line AE is NOT parallel to line BD. This is because the intercepts made by the lines and the transversals are not proportional
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