Answer:
(x+1)²/6 - (y+3)²/12 = 1
Step-by-step explanation:
The standard form of writing the equation of an hyperbola is expressed as;
(x-h)²/a² - (y-b)²/b² = 1 where (h,k) is the centre of the hyperbola.
Given the equation:
6x²-3y²+12x-18y-3 = 0
We are to convert it to the standard form of writing the equation of a hyperbola.
Collecting the like terms will give;
(6x²+12x)-(3y²+18y)-3 = 0
Divide through by 3
(2x²+4x)-(y²+6y)-1 = 0
Completing the square of the equation in parenthesis and adding the constants to the other side of the equation:
(2x²+4x)-(y²+6y+(6/2)²)-1 = 0+(6/2)²
(2x²+4x)-(y²+6y+9)-1 = 9
2x²+4x -{(y+3)²} = 9+1
2x²+4x - (y+3)² = 10
Divide through by 2
x²+2x -(y+3)²/2 = 5
(x²+2x+(2/2)²)-(y+3)²/2 = 5+(2/2)²
(x²+2x+1) - (y+3)²/2 = 5+1
(x+1)²-(y+3)²/2 = 6
Divide through by 6
(x+1)²/6 - (y+3)²/12 = 1
The resulting equation is the required standard form of a hyperbola with centre at (-1, -3)
What is the inverse function of f(x) = x
Answer:
y = x
Step-by-step explanation:
The inverse of f(x) = x is just y = x.
The statewide pass rates for ENGL&101 across Washington state community colleges is 68%. An instructor in the English department at CBC believes rates at CBC may be higher than the state average. This study can be stated as a formal hypothesis test in the following way:
H0 : p=0.68
HA: p > 0.68
To perform his study, he took a random sample of 250 students at CBC that had taken
ENGL&101, and found that 179 had passed the course.
Using your g from the last question, calculate the test statistic for the hypothesis test. Round your answer to two decimal places.
Answer:
The calculated value Z=1.2413 < 1.96 at 0.05 level of significance
Null hypothesis is accepted
An instructor in the English department at CBC believes rates at CBC may be equal to the state average
Step-by-step explanation:
Step(i):-
Given Population proportion
P=68%= 0.68
Sample proportion
[tex]p^{-} =\frac{x}{n} = \frac{179}{250} = 0.716[/tex]
Null hypothesis : H₀ : p = 0.68
Alternative Hypothesis :H₁ : p > 0.68
Step(ii):-
Test statistic
[tex]Z = \frac{p^{-}-P }{\sqrt{\frac{P Q}{n} } }[/tex]
[tex]Z = \frac{0.716-0.68 }{\sqrt{\frac{0.68 X 0.32}{250} } }[/tex]
Z = 1.2413
Level of significance
[tex]Z_{0.05} = 1.96[/tex]
The calculated value Z=1.2413 < 1.96 at 0.05 level of significance
Null hypothesis is accepted
An instructor in the English department at CBC believes rates at CBC may be equal to the state average
Use the Distance Formula to find the distance between the two points in polar coordinates. (Round your answer to one decimal place.) (8, 0.2), (9, 1.7)
Answer:
Distance= 1
Step-by-step explanation:
Distance be points using polar coordinates
Distance= √(8² +9² -2(8)(9)cos(0.2-1.7)
Distance=√(64 + 81-(144)cos(-1.5))
Distance= √(145-143.9506)
Distance=√ 1.0493
Distance= 1.0243
Distance= 1
Only the bottom one please help solve and check
Answer:
3
Step-by-step explanation:
16+5f=31
5f=31-16
5f=15
f=3
CHECK:
16+5(3)=31
16+15=31
31=31
since e=-14 in the first equation, the last one is
-14-3=-17, which is correct
Cuanto es la raíz cuadrada de 25
5. A scientist believes the concentration of radon gas in the air is greater that the established safe level of 4pci or less. The scientist tests the composition for 36 days finding an average concentration of 4.4 pci with a sample standard deviation of 1 pci. a) In testing the scientist's belief, write the appropriate hypotheses at 0.05 level of significance.
Complete Question
A scientist believes the concentration of radon gas in the air is greater that the established safe level of 4 pci or less. The scientist tests the composition for 36 days finding an average concentration of 4.4 pci with a sample standard deviation of 1 pci.
a) In testing the scientist's belief, write the appropriate hypotheses:
[tex]H_o:[/tex] Ha:
b) What decision should be made?
Answer:
a
The null hypothesis is [tex]H_o : \mu \le 4 \ pci[/tex]
The alternative hypothesis is [tex]H_a : \mu > 4 \ pci[/tex]
b
There is sufficient evidence to conclude that the concentration of radon gas in the air is greater that the established safe level of 4pci or less
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 4 \ pci[/tex]
The sample size [tex]n = 36 \ days[/tex]
The sample mean is [tex]\= x = 4.4 \ pci[/tex]
The standard deviation is [tex]\sigma = 1 \ pci[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu = 4 \ pci[/tex]
The alternative hypothesis is [tex]H_a : \mu > 4 \ pci[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{ 4.4 - 4 }{ \frac{ 1}{ \sqrt{36} } }[/tex]
=> [tex]t = \frac{ 4.4 - 4 }{ \frac{ 1}{ \sqrt{36} } }[/tex]
=> [tex]t =2.4[/tex]
The p-value is mathematically represented as
[tex]p-value = P(Z > 2.4 )[/tex]
From the z-table
[tex]P(Z > 2.4 ) = 0.008[/tex]
[tex]p-value =0.008[/tex]
So from this obtained value we see that
[tex]p-value < \alpha[/tex] so we reject the null hypothesis
Hence we can conclude that there is sufficient evidence to conclude that the concentration of radon gas in the air is greater that the established safe level of 4pci or less
Question 1
Solve the equation.
-9h= - 27
Answer:
h=3
Step-by-step explanation:
-9h= - 27
Divide each side by -9
-9h/-9= - 27/-9
h = 3
Answer:
h = 3
Step-by-step explanation:
Step 1: Divide both sides by -9
[tex]\frac{-9h}{-9} =\frac{-27}{-9} \\h=3[/tex]
Therefore the h = 3
Solve application problems using quadratic equations. 1. A positive real number is 4 less than another. When 8 times the larger is added to the square of the smaller, the result is 96. Find the numbers.
Hello, let's note a the positive real number.
A positive real number is 4 less than another.
So, the other number is a - 4
When 8 times the larger is added to the square of the smaller, the result is 96.
So, we need to solve the following equation.
[tex]8a+(a-4)^2=96[/tex]
Let's do it!
[tex]8a+(a-4)^2=96\\\\8a+a^2-8a+16=96\\\\a^2=96-16=80=4^2*5\\\\a=\pm4\sqrt{5}[/tex]
As a is positive, there is only one solution which is.
[tex]\Large \boxed{\sf \bf \ \ a=4\sqrt{5} \ \ }[/tex]
Thank you.
The amount given by the sum of numbers can be presented in an equation
form from which the value of each number can be obtained.
The large number is 4·√5, the smaller number is 4·(√5 - 1)
Reason:
Let x represent the large number, we have;
The smaller number = x - 4
8 × x + (x - 4)² = 96
8·x + (x - 4)² = 96
Required:
The values of the numbers
Solution:
8·x + (x - 4)² = 8·x + x² - 8·x + 16 = 96
8·x - 8·x + x² + 16 = 96
x² + 16 = 96
x² = 96 - 16 = 80
x = ±√(80) = ±4·√5
Given that the numbers are positive, we have;
The large number, x = 4·√5
The smaller number = x - 4 = 4·√5 - 4
The smaller number = 4·√5 - 4 = 4·(√5 - 1)
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A new restaurant, Banana Monkey, has been open for two weeks. The number of diners who have eaten at the restaurant on each of those days is shown in the plot below. Number of diners Stem 7. 8 9 Leaf 6 6 8 9 2 5 5 8 8 9 4 7 7 7 Key 8 7 = 87 How many days did Banana Monkey have more than 85 guests?
Answer:
to much numbers
Step-by-step explanation:
At the dairy farm, two cows produce enough milk to fill 7 equal sized buckets. Each cow produces the same amount of milk. What is the rate per bucket per cow?
Answer:
3.5 buckets per cow
Step-by-step explanation:
Given
[tex]Buckets = 7\ equal\ sized[/tex]
Required
Determine the rate per bucket per each cow
From the question, we understand that both cows produced same quantity of milk;
And since, they're are two cows
Milk produced by each cow is calculated by dividing number of buckets by 2; as follows;
[tex]Each\ cow = \frac{7}{2}\ buckets[/tex]
[tex]Each\ cow = 3.5\ buckets[/tex]
Hence, the rate is 3.5 buckets per cow
Plzzz write all the steps
Answer:
( 2x - 1 ) ( x + 3) / ( 2x - 3 ) ( x + 1 )
Step-by-step explanation:
(x - 2) / (x + 1) - 3(1 - 4x) / ( 2x - 3 ) ( x + 1 )
{ ( x - 2 ) ( 2x - 3) - 3 ( 1- 4x) } / ( 2x - 3 ) ( x + 1 )
{ 2x^2 - 7x - 3 + 12x} / ( 2x - 3 ) ( x + 1 )
{ 2x^2 + 5x - 3 } / ( 2x - 3 ) ( x + 1 )
( 2x - 1 ) ( x + 3 ) / ( 2x - 3 ) ( x + 1 )
Find the odds in favor of rolling the sum of 10 when rolling a pair of dice
A 11 to 1
B 1 to 3
C 1 to 11
D 3 to 1
Answer:
C 1 to 11
Step-by-step explanation:
When rolling 2 dice, there are 36 possible outcomes.
The outcomes that have a sum of 10 are:
4, 6
5, 5
6, 4
There are 3 outcomes of 10 and 33 outcomes of not 10.
Odds of outcome of 10:
3:33 = 1:11
1 to 11 is the odds in favor of rolling the sum of 10 when rolling a pair of dice option (C) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
A standard dice is rolled:
The total number of outcomes(two dice are rollling) = 6x6 = 36
The outcomes that have a sum of 10 = ({4, 6}, (5, 5), (6, 4)}
The total number of outcomes = 3
Total outcomes(after removing 3 outcomes that have a sum of 10)
= 36 - 3 = 33
Odds of outcomes = 3
The odds in favor = 3/33 = 1/11 or 1 to 11
Thus, 1 to 11 is the odds in favor of rolling the sum of 10 when rolling a pair of dice option (C) is correct.
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Compute the following probabilities:
A. If Y is distributed N (-8,9), Pr (Y≤-12) = —— . (Round your response to four decimal places.)
B. If Y is distributed N (-4,9), Pr (Y>-1) = ——. (Round your response to four decimal places.)
C. If Y is distributed N (40,25), Pr (34≤Y≤44) = ——. (Round your response to four decimal places.)
D. If Y is distributed N (−3,4), Pr (Y>−4) = _____ (Round your response to four decimal places.)
Answer:
a) P [ Y ≤ -12 ] = 0,32997 or P [ Y ≤ -12 ] = 32,99 %
b) P [ Y > -1 ] = 0,3707 or P [ Y > -1 ] = 37,07 %
c) P [ 34 ≤ Y ≤ 44] = 0,1585 or P [ 34 ≤ Y ≤ 44] = 15,85 %
d) P [ Y > -4 ] = 0,59871 or P [ Y > -4 ] = 59,87 %
Step-by-step explanation:
Normal Distribution: N ( -8 ; 9 )
a) P [ Y ≤ -12 ] = ( - 12 - (-8))/9
P [ Y ≤ -12 ] = - 4/9 = - 0,44
From z-table for the z score -0,44 we get:
P [ Y ≤ -12 ] = 0,32997 or P [ Y ≤ -12 ] = 32,99 %
b) Normal Distribution: N ( - 4 ; 9 )
P [ Y > -1 ] = 1 - P [ Y ≤ -1 ]
P [ Y ≤ -1 ] = ( - 1 - ( - 4 ) ) / 9
P [ Y ≤ -1 ] = 3 / 9 = 0,3333
From z-table for the z score 0,33 we get:
P [ Y ≤ -1 ] = 0,6293
P [ Y > -1 ] = 1 - P [ Y ≤ -1 ] = 1 - 0,6293
P [ Y > -1 ] = 0,3707 or P [ Y > -1 ] = 37,07 %
c) Normal Distribution: N ( 40 ; 25 )
P [ 34 ≤ Y ≤ 44]
P [ 34 ≤ Y ≤ 44] = P [ Y ≤ 44] - P [ Y ≤ 34 ]
P [ Y ≤ 44] = ( 44 - 40 ) / 25 = 0,16
From z-table for the z score 0,16 we get:
P [ Y ≤ 44] = 0,5636
P [ Y ≤ 34 ] = ( 34 - 40 ) / 25 = - 6 / 25 = - 0,24
From z-table for the z score -0,24 we get:
P [ Y ≤ 34 ] = 0,40517
Then
P [ 34 ≤ Y ≤ 44] = P [ Y ≤ 44] - P [ Y ≤ 34 ]
P [ 34 ≤ Y ≤ 44] = 0,5636 - 0,40517
P [ 34 ≤ Y ≤ 44] = 0,1585 or P [ 34 ≤ Y ≤ 44] = 15,85 %
d) Normal Distribution: N ( -3 ; 4 )
P [ Y > -4 ] = 1 - P [ Y ≤ -4 ]
P [ Y ≤ -4 ] = ( - 4 - ( -3))/4 = - 1/4 = - 0,25
From z-table for the z score -0,25 we get:
P [ Y ≤ -4 ] = 0,40129
P [ Y > -4 ] = 1 - 0,40129
P [ Y > -4 ] = 0,59871 or P [ Y > -4 ] = 59,87 %
Is the number 25/9 irrational?
Answer:
Step-by-step explanation:
No; it is rational. 25/9 is the ratio of two integers.
Explanation:
We have a fraction of two integers, so 25/9 is rational. A rational number is any fraction of two integers (as long as the denominator is not zero).
Something that is irrational would be pi = 3.14159... where we cannot write it as a fraction of two integers. We can get approximations such as 22/7, but we cannot land exactly on pi with a fraction like this. Another irrational value is sqrt(2).
Something like sqrt(25) is rational though because sqrt(25) = 5 = 5/1.
Meghan is making fruit salads and fruit smoothies. The salad recipe calls for 1/6 cup of strawberries, and the smoothie recipe calls for 2/3 cup strawberries. If Meghan wants to make 2 fruit salads and 2 fruit smoothies, how many cups of strawberries does she need?
Answer:
5/3 cup(s)
Step-by-step explanation:
Meghan needs 5/3 cups of strawberries to make 2 fruit salads and 2 fruit smoothies.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Need of cup of strawberries for making one fruit salad recipe = 1/6,
And need of cup of strawberries for making one fruit smoothie recipe = 2/3.
To make 2 fruit salads,
Need of cup of strawberries = 2 x 1/6 = 1 / 3
To make 2 fruit smoothies,
Need of cup of strawberries = 2 x 2/3 = 4/3
Total number of cups of strawberries = 1/3 + 4/3 = 5/3
Meghan needs 5/3 cups of strawberries.
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If there were 1,000 cars in a line with an average car length of 10.8 feet, how long would the line be in feet? Assume that the cars are lined up bumper-to-bumper.
Answer:
10,800 feet
Step-by-step explanation:
1000 * 10.8 because there are 1000 cars each 10.8 feet long
Solve the equation. 5/7p - 2/7p + 12 = 6
Answer:
p = -14
Step-by-step explanation:
5/7p - 2/7p + 12 = 6
Combine like terms
3/7 p +12 = 6
Subtract 12 from each side
3/7p + 12-12 = 6-12
3/7p = -6
Multiply each side by 7/3
7/3 * 3/7p = -6*7/3
p = -14
Answer:
p = - 14
Step-by-step explanation:
5/7p - 2/7p + 12 = 6
subtract 12 both sides
5p/ 7 - 2p/7 + 12 = 6 - 12
simplify
5p/7 - 2p/7 = -6
multiply both side by 7
5p/7 * 7 - 2p/7 * 7 = -6 * 7
simplify
5p - 2p = -42
p = -42 / 3
p = - 14
Y A chemist can purchase a 10% saline solution in 500 cubic centimeter containers, a 20% saline solution in 500 cubic centimeter containers, and a 50% saline solution in 1,000 cubic centimeter containers. He needs 12,000 cubic centimeters of 30% saline solution. How many containers of each type of solution should he purchase in order to form this solution
Step-by-step explanation:
ultimately you need to end up with 30% solution
with 10%, 20%, and 50%, you are forced to tamper with the various percentages to reach the desired goal.
Since it is an even 12,000 (i.e. no 12500) and you have no hard container volumes to deal with, therefore find the easiest combination to reach 30%. In this case, (10%+50%)/2 = 30%
So therefore you need 12000 cubic centimeters of liquid, half of it being 50% and half being 10%.
12000/2 = 6000 cubic centimeters each
for 50%, each container is 1,000 cubic centimeters, so 6000/1000 =6 containers for 10% each container is 500 cubic centimeters, so 6000/500 = 12 containers
Therefore, you need 6 containers of 50% solution and 12 containers of 10% solution.
19. In each of the following ligures, find the values of x and y
Answer:
x and y is 115 exterior angle property
Answer:
[tex]\boxed{x = 65, y=50}[/tex]
Step-by-step explanation:
→ We know that angles on a straight line add up to 180° so we can use that to work out angle x
x + 115° = 180°
⇒ Minus 115° from both sides to isolate x
x = 65°
→ We can see that there are 2 angles labelled x so we can use that to find the value of y
65° × 2 = 130°
→ We utilise the angle fact that angles in a triangle add up to 180°
130° + y = 180°
⇒ Minus 130° from both sides to isolate y
y = 50°
Landon usually eats two slices of pizza from a 12 inch pizza cut into 6 slices. I make homemade pizza on a rectangular cookie sheet that is 10 inches by 15 inches and I cut it into 8 rectangular pieces. How many slices of this homemade pizza will Landon proabably eat
Answer:
He will eat 0.233 of one slice
Step-by-step explanation:
If Landon eats only two slices of pizza from a 12 inch pizza cut into 6
It means each slice has 2 inch pizza and Landon eats 2 of these
So Landon eats 2*2 = 4 inch pizza
So a rectangular pizza of 10 by 15
= 10*15
= 150 inch pizza
Cut into 8 slices
= 150/8
.= 18.75 inch per slice
4/18.75 = 0.233
He will eat 0.233 of one slice
A rectangular bird feeder costs $18.00. A cylindrical bird feeder costs $24.00. The expected cost to keep the rectangular bird feeder filled is $3.00 per week. The expected cost the keep the cylindrical bird feeder filled is $2.00 per week. The equation below models the break-even point. 18 + 3x = 24 + 2x What does x represent? the total cost to fill the rectangular bird feeder after any number of weeks the total cost to fill the cylindrical bird feeder after any number of weeks the number of weeks the bird feeders are filled the number of bird feeders purchased each week
Answer:
the number of weeks the bird feeders are filled
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Just took the review
A university law school accepts 6 out of every 11 applicants. If the school accepts 552 students find how many applicants they received
Answer:
1012
Step-by-step explanation:
The ratio of student / applicant is 6 /11
So for 552 students, the applicants number is:
6/11 = 552/xx = 552*11/6 x= 1012Number of applicants is 1012
A line has the equation y = 3x + 4.
(a) This line has slope 3/1
(b) Any line parallel to this line has slope
(c) Any line perpendicular to this line has
Answer:
b. 3/1 c. -1/3
Step-by-step explanation:
When a line is parallel to another they don't intersect and instead go in the same direction. Therefore they have the same slope
b. 3/1
When a line is perpendicular it has to be the negative reciprocal. This means that it you have to flip the numbers in the fraction and make it negative (unless it is already negative, then it becomes positive)
c. -1/3
Sara bought a pair of shoes that were $64 but were on sale for $46. Sales tax is 6%. How much did she pay for the shoes?
Answer:
$48.76
Step-by-step explanation:
So, Sara bought the pair of shoes for $46 due to a discount.
Sales tax was 6% or 0.06. In other words, she had to pay 0.06(46)=2.76 for tax.
Thus, the total amount Sara paid for the shoes is $46+$2.76=$48.76
Marcus bought w childrens's movie tickets for $5 each and n adult's movie tickets for $11 each. Write an algebraic expression for total amount Marcus spent.
Answer:
5w+11n
:D
Hope this helped!
My regards
Find the range of the given data set. 5/8, 3/4, 1 1/8, 1 1/4 A)5/8 B)3/4 C)1 1/8
Answer:
A)5/8
Step-by-step explanation:
The range of a set of data is the difference between the highest and lowest values in the set.Given data set:
5/8, 3/4, 1 1/8, 1 1/4Rewriting the data set in the same denominator to compare:
5/8, 6/8, 9/8, 10/8As we see the smallest value is 5/8 and the highest value is 10/8, so the difference:
10/8 - 5/8 = 5/8So, the range of the given data set is 5/8
Correct choice is: A)5/8
What is the value of x that makes the given equation true? x−3x=2(4+x)
the answer to your question is x= -2
Write a decimal expansion for 2/9. Chose the correct decimal notation.
Answer:
This is the answer
2/9=0.222222222.
Answer:
.2222 ( repeating)
Step-by-step explanation:
Which of the following numbers is not a
prime number?
A. 2
C. 11
B. 3
D. 27
Answer:
27, it is divisible by 1, 3, 9, and 27
Step-by-step explanation:
pls answer asap!! will mark brainliest giving 50 points ty ily <3
Answer:
56
Step-by-step explanation:
Keep the order of opperations in mind when doing this (PEMDAS). First, solve what is inside the parentheses (6-1). Then, solve the exponent and the multiplication (6² and 5×5). Finally, finish adding and subtracting to get the answer.
Answer:
56
Step-by-step explanation:
Hello!
We have to follow the order of PEMDAS
Parenthesis, Exponents, Multiplication and Division, Addition and Subtraction
5 x 5 - (6 - 1) + [tex]6^{2}[/tex]
Parenthesis First
[tex]5 x 5 - (5) + 6^2[/tex]
Exponents next
[tex]5x5 - (5) + 36[/tex]
Multiplication and Divsion from left to right
25 - (5) + 36
Addition and Subtraction from left to right
20 + 36
56
The answer is 56
Hope this Helps!