The center of the hyperbola is (2, -3)
What is an hyperbola?A hyperbola is a curve that is open and that has two branches and it is symmetrical
How to solve the center of the hyperbola?The equation is given as
(y + 3)²/9 − (x − 2)²/2 = 1
A hyperbola is represented as
(y - k)²/a² − (x − h)²/b² = 1
Where the center of the hyperbola has the coordinates of (h, k)
The values of h and k in the given equation (y + 3)²/9 − (x − 2)²/2 = 1 are
h = 2 and k = -3
This means that:
(h, k) = (2, -3)
So, we have coordinates of the center to be (2, -3)
Hence, the center is (2, -3)
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A software company in Burlington used to bill clients $214.79 per hour for work done by its consultants. The company recently adjusted its rates and now charges the same amount. What was the percent of decrease in the billing rate?
The percent of decrease in the billing rate is 2.37%.
How to calculate the percentage?It should be noted that a percentage decrease is calculated as
= Decrease in value / Initial value × 100
Let's assume the following:
Initial amount = $220
New amount = $214.79
Decrease in amount = $220 - $214.79 = $5.21
The percentage decrease will be:
= 5.21 / 220 × 100
= 2.37%
The question is incomplete and the values were assumptions.
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Solve for x.
3.5x=31.5
Answer:
x = 9
Step-by-step explanation:
x = 31.5 / 3.5
x = 9
Answer:
x = 9
Step-by-step explanation:
since 3.5 is being multiplied by x to get 31.5 to get rid of it and leave x by itself you have to divide both sides by 3.5
(3.5x)/(3.5)= (31.5)/(3.5)
x=9
Express 35 as a fraction of 95. Give your answer in its simplest form.
Answer:
=35/95
=(5 x7)/95
=5 x 7/5 x 19
=7/19
Which statement is true about the given function?fx) > 0 over the interval (-0,3).f(x) > 0 over the interval (-:-).f(x) <0 over the interval (-0,3).f(x) <0 over the interval (- : -).
f(x) means the value of y
The graph has a part down the x-axis which means f(x) < 0
The graph has another part over the x-axis which means f(x) > 0
The value of x for the negative part is from - infinity to 3
Then f(x) < 0 at the interval (-00, 3)
The value of x for the positive part is from 3 to infinity
then f(x) > 0 at the interval (3, 00)
Then the answer is C
Each gallon of paint covers 200 square feet. I have to paint one side of a wall that is 12 meters tall and 80 meters long. If a foot is approximately 0.3084 meters, then what is the smallest whole number of gallons I can buy and have enough paint to cover the whole wall
Answer:
1 ft ≈ 0.3048 m
1 ft2 ≈ 0.09290304 m2
200 ft2 ≈ 18.580608 m2
Step-by-step explanation:
The total surface area to paint = 12 m * 80 m = 960 square meters
1 ft ≈ 0.3048 m
1 ft2 ≈ 0.09290304 m2
200 ft2 ≈ 18.580608 m2
And so one gallon of paint covers about 18.581 square meters.
960 m2 / ( 18.581 m2 per gallon) ≈ 51.67 gallons
So 51 gallons would not be enough... it would take 52 gallons of paint to cover the wall.
Solve 4- 3x = 6 - 5x
X =
Answer:
Step-by-step explanation:
4 - 3 x = 6 - 5 xx
[tex]-3x+4=6-5xx^{2}[/tex]
x = 1
x = - [tex]\frac {2}{5}[/tex]
Answer:
x=1
Step-by-step explanation:
sense x's are on both sides you need to bring one of them over, add 3x to both sides to get 4=6-2x , then subtract 6 from each side to get -2=-2x , then to get x by itself divide both sides by -2 to get 1=x
5. Caleb earns points on his credit card that he can use towards future purchases. He earns four
points per dollar spent on flights, two points per dollar spent at hotels, and one voint per
dollar spent on all other purchases. Last year, he charged a total of $9.480 and earned
14,660 points. The amount of money spent on flights was $140 more than twice the amount
of money spent on hotels. Find the amount of money spent on each type of purchase.
By the concept of linear equation :
$1,500 was spent on flights,
$680 was spent on hotels,
$7,300 was spent on other purchases.
What are linear equations?An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Ax+By=C represents a two-variable linear equation in its standard form. As an illustration, the conventional form of the linear equation 2x+3y=5 It is rather simple to locate both intercepts when an equation is stated in this way (x and y). For the purpose of resolving systems involving two linear equations, this form is also highly helpful.
Given:
Flights: 4 points per dollar
Hotels: 2 points per dollar
Other: 1 point per dollar.
Total spent = $9,480
Points earned = 14,660
Let
x = money spent on flights
y = money spent on hotels
z = money spent on other purchases.
Because the money spent on flights was $140 more than twice the money spent on hotels, therefore
x = 2y + 140 (1)
Total charges were $9,480, therefore
x + y + z = 9480 (2)
Total points earned was 14,660. Therefore
4x + 2y + z = 14660 (3)
Subtract (2) from (3).
4x + 2y + z - (x + y + z)
= 14660 - 9480
3x + y = 5180 (4)
Substitute (1) into (4).
3(2y + 140) + y = 5180
7y + 420 = 5180
7y = 4760
y = 680
From (1), obtain
x = 2y + 140
= 2(680) + 140
= 1500
From (2), obtain
z = 9480 - (x + y)
= 9480 - (1500 + 680)
= 7300
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a builder appoints three construction workers akash, sunil and rakesh on one of his sites. they take 20, 30 and 60 days respectively to do a piece of work. how many days will it take akash to complete the entire work if he is assisted by sunil and rakesh every third day?
It will take 15 days for Akash to complete the entire work if he is assisted by Sunil and Rakesh every third day.
To determine the number of days, we first represent the number of days to do a piece of work by each one of them in fractions as follows;
Fraction of work completed by Akash in 1 day = 1/20
Fraction of work completed by Sunil in 1 day = 1/30
Fraction of work completed by Rakesh in 1 day = 1/60
The total work done in 1 day can be given as;
Total work done by the three in one day = [(1/20) + (1/30) + (1/60)] = 1/10
Work done by Akash in two days = 2 × (1/20) = 2/20 = 1/10
The work done in three days (1 day of all three together + Work done by Akash in two days) = (1/10) + (1/10) = 1/5
Therefore; the total work done in 3 days = 1/5
At this rate, the total number of cycles required to finish the work =
(1) ÷ (1/5) = 5
Since each cycle has three days, the total number of days required to finish the work can be calculated as follows;
5 × 3 = 15 days
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suppose you sell hats for 10 dollars each and sunglasses for 5 dollars each. you know the expected number of hats sold in a day is 10 with standard deviation 1; you know the expected number of sunglasses sold in a day is 20 with standard deviation 2; you know the sale of hats and sunglasses are independent. what is the standard deviation of your revenues in a day? (round to closest dollar)
Answer:
2
Step-by-step explanation:
because average of 1 and 2 is 1.5 rounded is 2
The standard deviation of your revenues in a day is 14.
What is a standard deviation?The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.
Let x be the revenue from hats.
And let y be the revenue from sunglasses.
And z be the total revenue.
Then according to the question:
z = 10x + 5y
You know the expected number of hats sold in a day is 10 with standard deviation 1.
σₓ = 1
σy = 2
Taking squares of both of the equation.
σₓ² = 1² = 1
σy² = 2² = 4
To find the standard deviation of your revenues in a day:
V(z) = (10)²σₓ² + 5²σy²
V(z) = (100)(1) + (25)(4)
V(z) = 200
Standard deviation,
σz² = √(200)
σz² = 10√(2)
σz² = 14.14
σz² ≈ 14
Therefore, the required standard deviation is 14.
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A 21-foot beam is to be cut into three pieces so that the second and third piece are each 3 times the length of the first piece. If X represents represents the length of the first piece find the length of each piece.
The length of the first piece is 3 inches, and the second and third pieces are each 9 inches
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
Given that a 21-foot beam is to be cut into three pieces so that the second and third pieces are each 3 times the length of the first piece.
We have to determine the length of each piece.
Let x represents the length of the first piece
As per the given condition,
x + 3x + 3x = 21
7x = 21
x = 21 / 7
x = 3
Thus, the first piece is 3 inch
So 2nd piece is 3×3 = 9 inches ( 3 times to first piece )
And 3rd piece is 3×3 = 9 inches ( 3 times to first piece )
Therefore, the length of the first piece is 3 inches, and the second and third pieces are each 9 inches
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Find the value of x.
(8x - 11)
5x°
(2x+6)°
Answer: x=37/3
Step-by-step explanation:
8x-11+5x+2x+6=180 ==> three angles of a triangle add up to 180 degrees
8x+5x+2x-11+6=180
13x+2x-5=180
15x-5=180
15x=185
x=185/15
x=37/3
Experimental and theoretical see pic
1) Wrong statement:
The difference between the experimental and theoretical probability is 1/10
Correct statement:
The difference between the experimental and theoretical probability is 3/200
2) Wrong statement:
The difference between the experimental and theoretical probability is 1/10
Correct statement:
The difference between the experimental and theoretical probability is 3/200
Explanation:N(Pennies) = 6
N(Nickels) = 8
N(Dimes) = 4
N(quarters) = 7
N(total) = 6 + 8 + 4 + 7
N(total) = 25
1) The theoretical probability of selecting a dime = 4/25
The experimental probability of selecting a dime = 30/150 = 1/5
B is wrong because theoretical probability is 4/25, not 9/50
Wrong statement:
The theoretical probability of selecting a dime is
Correct statement:
The theoretical probability of selecting a dime is 4/25
2) The experimental probability of selecting a penny = 45/200 = 9/40
The theoretical probability of selecting a penny = 6/25
Difference between experimental and theoretical probability = 6/25 - 9/40
Difference between experimental and theoretical probability = 3/200
Wrong statement:
The difference between the experimental and theoretical probability is 1/10
Correct statement:
The difference between the experimental and theoretical probability is 3/200
given the following expressions1. -5/8+3/52. 1/2+ √23. (√5)×(√5)4. 3×(√49)which expression(s) will result in an irrational number.(1) only 2(2) only 3(3) 1,3,4(4) 2,3,4
1) Only 2
1) Examining the expressions we have
1. -5/8+3/5 =-1/40 Rational Expression
2. 1/2+ √2 Irrational Expression
3.(√5)×(√5)= 5 Rational Expression
4. 3×(√49) = 21 Rational Expression
2) Since √2 is an irrational number √2 = 1.4142.... non-periodic and infinite number, and number added to it will yield an irrational number.
3) So the answer is 1) Only 2
Find the value of x that will make A||B.
X = ?
Answer:
x = 12
Step-by-step explanation:
Since they are opposite exterior angles, they are congruent, so you set them equal to each other
5x = 4x + 12
- 4x - 4x
x = 12
For A and B to be parallel then the angle (4x+12)⁰ and the angle opposite to angle (5x)⁰ should be equal since the two are congruent to each other.
therefore
5x = opposite angle=(4x+12)
=> 5x=(4x+12)
=>5x-4x= 12
therefore
X =12⁰
Given the equation 12.75y = 38.25, determine the value of y.
Answer:
y = 3
Step-by-step explanation:
12.75y = 38.25
To find the value of y, divide each side by 12.75
12.75y/12.75 = 38.25/12.75
y = 3
during a span of 2 hours , lalia played her video games for 50 minutes . what percentage of time was spent on the game
Total time = 2 hours
Time playing video games = 50 minutes
We have to write an equation:
Total time (2hours) multiplied by the percentage in decimal form (x) must be equal to 50 minutes
Time must be in the same unit ( minutes)
since 60 minutes =1 hour
2 hours = 2 (60) =120 minutes
Back with the equation:
120 x = 50
Solving for x
x = 50/120
x = 0.42
In percentage form:
0.42 x 100 = 42%
What is the transformation of both y=-√-4x, and y=√-4x? I've looked everywhere to try and find it, but the internet is not helping!
The transformation that relates the two functions:
f(x) = y = -√(-4x)
g(x) = y = √(-4x)
Is a reflection across the x-axis.
What is the transformation applied?
We define a reflection across the x-axis as a transformation that does a "vertical reflection" along the line y = 0 (which is the x-axis).
For a function f(x), a reflection across the x-axis generaste the new function g(x) that can be written as:
g(x) = -f(x).
In this case the original function is:
f(x) = y = -√(-4x)
And the transformed function is:
g(x) = y = √(-4x)
You can see that the only difference is the sign, such that we can write:
g(x) = -f(x) = -(-√(-4x)) = √(-4x)
So we conclude that the transformation is a reflection across the x-axis.
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Miss Young is bringing cookies and brownies in for one of her classes. She has to bring
a total of 26 desserts. She pays $0.65 for each cookie and $0.90 for each brownie.
Using a system of equations, supposing that she spent $19.65, the amounts are as follows:
Cookies: 15.Brownies: 11.What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the context of this problem.
For this problem, the variables are defined as follows:
Variable x: number of cookies purchased.Variable y: number of brownies purchased.She brought a total of 26 desserts, hence:
x + y = 26.
She spent a total of $19.65, hence, considering the price of each item:
0.65x + 0.9y = 19.65.
From the first equation, we have the following relation:
y = 26 - x.
Hence, replacing in the second, we can solve for x as follows:
0.65x + 0.9(26 - x) = 19.65
0.25x = 3.75
x = 3.75/0.25
x = 15 cookies.
Then the number of brownies is found as follows:
y = 26 - 15 = 11 brownies.
Missing informationWe suppose that she spent $19.65, and that the problems asks for the amounts of cookies and brownies purchased.
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the volume of a rectangular box with a square base remains constant at 1100 cm3 as the area of the base increases at a rate of 10 2/sec. find the rate at which the height of the box is decreasing when each side of the base is 15 cm long. (do not round your answer.)
The height of the box is decreasing at a rate of 2/45 cm/sec.
The volume of a box remains constant at 1100m³ but the area of the base is increasing at a rate of 10 m²/sec.
Since the base of the box is a square, let the sides of the box be a, a, and h. The area of the base can be written as,
A = a²
Differentiate the above equation with respect to t.
dA/dt = 2a(da/dt)
Substitute 10 for dA/dt and 15 for a, to find the rate of change of side of base.
10 = 2(15)(da/dt)
da/dt = 1/3
The volume of the box can be written as,
V = (a)(a)(h) = a²h
Differentiate the above equation with respect to t.
0 = 2a(da/dt) + a² (dh/dt)
dh/dt = -2/a (da/dt)
Substitute 15 for a and 1/3 for da/dt in the above equation, to find the rate of change of height of the box.
dh/dt = -2/15 (1/3)
= -2/45
Thus, the height of the box is decreasing at a rate of 2/45 cm/sec.
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PLEASE HELP QUICK!!!!!!!
Answer:
D
Step-by-step explanation:
Translation 4 units right and 1 unit up
Miguel is going to see a movie and is taking his 5 kids. Each movie
ticket costs $12 and there are an assortment of snacks available to
purchase for $5 each. How much total money would Miguel have to
pay for his family if he were to buy 5 snacks for everybody to share?
How much would Miguel have to pay if he bought a snacks for
everybody to share?
Total cost with 5 snacks:
Total cost with a snacks:
Pls give me a good answer
The total cost for 6 movie tickets and 5 snacks is $97
The total cost for 6 movie tickets and x snacks is $(72 + 5x)
Given,
Miguel is going to see a movie with his 5 kids.
Number of people = 6
Cost for one ticket = $12
Cost of one snack = $5
Number of snacks = 5
We have to find the total cost spend by Miguel:
For tickets and 5 snacks:
For tickets and x snacks:
Now,
Total cost for tickets = 6 × 12 = $72
Cost for 5 snacks = 5 × 5 = $25
Therefore,
Total cost = 72 + 25 = $97
Next,
Cost for x snacks = 5x
Then,
Total cost = 72 + 5x
That is,
The total cost for 6 movie tickets and 5 snacks is $97
The total cost for 6 movie tickets and x snacks is $(72 + 5x)
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A dozen ears of corn for $5. find the unit rate
14#A corporation that maintains a large fleet of company cars for the use of its sales staff is interested in the mean distance driven monthly per salesperson. The following list gives the monthly distances in miles driven by a random sample of 11 salespeople.2482, 2300, 2640, 2085, 2425, 1851, 2346, 1876, 2444, 2153, 2290Send data to calculatorBased on this sample, find a 95% confidence interval for the mean number of miles driven monthly by members of the sales staff, assuming that monthly driving distances are normally distributed. Give the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.
Solution
Given the data set 2482, 2300, 2640, 2085, 2425, 1851, 2346, 1876, 2444, 2153, 2290
The confidence interval formula is
Calculate the standard deviation of the data
The standard deviation is
237.67
Calculate the sample mean
The mean is 2262.91
[tex]\begin{gathered} s=237.67 \\ n=11 \\ mean=2262.909 \\ z=1.96 \end{gathered}[/tex][tex]\begin{gathered} CI=2262.909\pm1.96(\frac{237.67}{\sqrt{11}}) \\ CI=2262.909\pm1.96(71.6602) \\ CI=2262.909\pm140.453992 \\ CI\text{ = 2122.455008 to 2403.362992 to} \end{gathered}[/tex]Thus, the lower limit is
2122.455 ( 3 decimal places)
The Higher limit is 2403.363 ( 3 decimal places)
if the textbook committee makes a histogram of the sample data and it is single-peaked with no outliers, are the conditions of randomness and normality of the population met for this test?
Yes, conditions of randomness and normality of the population met for this test.
The textbook committee made a histogram of the sample data, and it was single peaked with no outliers. The conditions of randomness and normality of the population met for this test, the reason is that it was a random sample, and the plot of the sample data has no outliers.
So, yes, conditions of randomness and normality of the population met for this test.
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7x+12=x-6 please answer
Answer:
x=-3
Step-by-step explanation:
Pls help i domt get this
Answer:
[tex]5^{15}[/tex] × 120 = 30,517,578,125 × 120
Step-by-step explanation:
The admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. On a certain day, 281 people entered the park, and the admission fees collected totaled 684 dollars. How many children how many adults were admitted?
Answer:
176 children and 105 adults.
Explanation:
Let's call x the number of children and y the number of adults.
If 281 people entered the park, we can write the following equation
x + y = 281
If they collected 684 dollars, we can write the following equation
1.5x + 4y = 684
because it cost $1.5 for children and $4 for adults.
Now, we have the following system of equations
x + y = 281
1.5x + 4y = 684
First, we need to solve the first equation for y, so
x + y = 281
x + y - x = 281 - x
y = 281 - x
Then, replace this expression on the second equation
1.5x + 4y = 684
1.5x + 4(281 - x) = 684
1.5x + 4(281) - 4(x) = 684
1.5x + 1124 - 4x = 684
-2.5x + 1124 = 684
Finally, we can solve the equation for x
-2.5x + 1124 - 1124 = 684 - 1124
-2.5x = -440
-2.5x/(-2.5) = -440/(-2.5)
x = 176
So, the value of y is equal to
y = 281 - x
y = 281 - 176
y = 105
Therefore, they admitted 176 children and 105 adults.
someone please help me please
Graph
[tex]-2x+y\ge-2[/tex]
Procedure
find the missing value of x^2+14x+c
The value of missing number is [tex]49[/tex].
The given equation is [tex]x^{2}+14x+c[/tex].
We have to find the missing value of [tex]c[/tex].
We can find the value of [tex]c[/tex] by perfect square trinomial.
A perfect square trinomial is a equation which we can get after the square of binomial expression.
The equation [tex]ax^{2}+bx+c[/tex] said to be a perfect square if and only if it follows the condition [tex]b^{2}=4ac[/tex].
In the equation [tex]ax^{2}+bx+c[/tex], [tex]a,b[/tex] and [tex]c[/tex] are the real numbers.
Now we compare the given equation to [tex]ax^{2}+bx+c[/tex].
After comparing we get
[tex]a=1, b=14, c=c[/tex]
To find the value of [tex]c[/tex] we put the value of [tex]a,b,c[/tex] in expression [tex]b^{2}=4ac[/tex].
[tex](14)^{2}=4\times1\times c[/tex]
[tex]196=4\times c[/tex]
Divide by [tex]4[/tex] on both sides
[tex]\frac{196}{4}=\frac{4\times c}{4}[/tex]
[tex]c=\frac{196}{4} \\c=49[/tex]
Hence, the value of missing number is [tex]49[/tex].
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The weight f a stack of standard 8.5*11 copier paper vs. number of sheets of paper
A. The weight of the copies and the quantity of papers are proportional.
B. There is no proportion between the number of books and their weight.
Given,
A. All versions of the document are 8.5 by 11 inches in size.
We can readily determine the quantity of papers using direct proportion because all the paper has the same dimensions and weight.
As a result, the weight of the copies and the quantity of papers are proportional.
B. Each book has a distinct weight, as we know.
Since each book varies in weight, it is difficult to calculate the quantity of papers using a direct percentage.
Therefore, there is no proportion between the number of books and their weight.
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