The possible equation of the parabola is y = (x - 5)^2 - 4
How to determine the possible equationfrom the question, we have the following parameters that can be used in our computation:
Vertex = (5, -4)
The vertex form of a parabola is given by:
y = a(x - h)^2 + k
where (h, k) is the vertex of the parabola and "a" is a constant that determines the shape of the parabola.
We are given that the vertex of the parabola is (5,-4). Substituting these values into the vertex form, we get:
y = a(x - 5)^2 - 4
Let a = 1
So, we have
y = (x - 5)^2 - 4
Hnce, the possible equation is y = (x - 5)^2 - 4
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If x=3. what is y=?
Y=
X: -3 0 3 6
Y: -5 -4 -3 -3
Answer:
Step-by-step explanation:
y = -3
How do we rewrite 10^ -1 without using negative exponents?
Answer:
[tex]\frac{1}{10}[/tex]
Step-by-step explanation:
which is a true statement about two numerical sets of data that have negative association
Answer:
Option D.
Step-by-step explanation:
Negative correlation also called an " inverse correlation " is a relation between 2 variables where-by they behave in opposite manner. When one variable moves ---> in an increasing /\ direction, the other variable moves in a decreasing \/ direction.
Thus, Option D.
A sample, sized 5, was taken with the following measurements: 5, 10, 2, 7, and 6.
What is the point estimate of the population mean?
The point estimate of the population mean is 6
What is the point estimate of the population mean?From the question, we have the following parameters that can be used in our computation:
Measurements: 5, 10, 2, 7, and 6.
Sample size = 5
The point estimate of the population mean is the sample size of the mean
Using the above as a guide, we have the following:
Sample mean = Sum/Count
substitute the known values in the above equation, so, we have the following representation
Sample mean = (5 + 10 + 2 + 7 + 6)/5
Evaluate
Sample mean = 6
Hence, the estimate is 6
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Find the distance the point P(3, 1, 7), is to the plane through the three points
Q(5, 0, 3), R(0, -1, 7), and S(7, 5, 0).
The distance between the point P and the plane through the points Q, R, and S is 60/23.
How did we get the value?The distance of a point P(x1, y1, z1) from a plane that passes through the points Q(x2, y2, z2), R(x3, y3, z3), and S(x4, y4, z4) can be found using the following formula:
d = |(A * x1 + B * y1 + C * z1 + D) / sqrt(A^2 + B^2 + C^2)|
Where A, B, and C are the coefficients of the plane's normal vector and D is the constant term in the equation of the plane. The normal vector can be found by taking the cross product of the vectors Q-R and Q-S:
n = (Q-R) x (Q-S)
The coefficients of the normal vector can be found using the following equations:
A = n1
B = n2
C = n3
D = -(A * x2 + B * y2 + C * z2)
Substituting the values of Q, R, and S, we have:
Q-R = (5-0, 0-(-1), 3-7) = (5, 1, -4)
Q-S = (7-5, 5-0, 0-3) = (2, 5, -3)
The cross product of Q-R and Q-S is:
n = (1 * -3 - 5 * -4, -3 * 5 - 2 * -4, -2 * 1 - 5 * 5) = (-23, 29, 17)
So,
A = -23
B = 29
C = 17
D = -(A * x2 + B * y2 + C * z2) = -(-23 * 5 + 29 * 0 + 17 * 3) = -109
Finally, substituting the values of x1, y1, and z1:
d = |(A * x1 + B * y1 + C * z1 + D) / √(A^2 + B^2 + C^2)|
= |(-23 * 3 + 29 * 1 + 17 * 7 + -109) / √(-23^2 + 29^2 + 17^2)|
= |(-69 + 29 + 119 -109) / √(-23^2 + 29^2 + 17^2)|
= |60 / √(-23^2 + 29^2 + 17^2)|
= |60 / √(529)|
= 60 / 23
So the distance between the point P and the plane through the points Q, R, and S is 60/23.
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The length of the dashed line in the circle
The length of the dotted line would be 7.922 ft.
What is the diameter of the circle?
The diameter of a circle is the distance across the circle through its center. It is equal to twice the length of the radius, which is the distance from the center of the circle to any point on the circle.
In mathematical terms, if d represents the diameter of a circle, and r represents its radius, we have the formula:
d = 2r
In the given circle, for finding the inner diameter we have to remove the thickness of the circle from outer diameter, we get
q = 17.708 - 4.893 - 4.893
By solving this, we get
q = 7.922
Hence, the length of the dotted line would be 7.922 ft.
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Circle the pair of like fractions 4/6and5/6and1/2and3/4and1/3and2/6 and1/10and2/100
The required pair of the like fraction among the given fraction is given as 1/3 and 2/6.
What is the fraction?A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers.
Here,
For pairs of fraction area given we have to determine that fair of like fraction,
So we have to simplify the fraction given in the pair,
1. 4/6 and 5/6 = 2/3 and 5/6which not like pair of fraction, Similarly pairs [1/2 and 3/4] and [1/10and2/100] are not like fractions.
Now,
3. pair 1/3and2/6 is like fractions because 1/3 = 2/6 (=1/3)
Thus, the required pair of the like fraction among the given fraction is given as 1/3 and 2/6.
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Find the image of the given point
under the given translation.
P(12, 8)
T(x, y) = (x-8, y - 12)
P(12,8)
Move 8 units to the left (X) and 12 units down(Y).
P'(12-8, 8-12)
P'(4, -4)
If you don't how to do translation try plotting (12,8).
The sum of the digits in a two-digit number is 14. If you reverse
and double the original number, and then add the result to the
original number, the sum is 222. Find the original number. Please help me.
Answer:
The original number is 86.
Step-by-step explanation:
The only two-digit numbers whose digits sum to 14 are:
5968778695If we reverse and double the original number:
59 reversed is 95 → 95 × 2 = 19068 reversed is 86 → 86 × 2 = 17277 reversed is 77 → 77 × 2 = 15486 reversed is 68 → 68 × 2 = 13695 reversed is 59 → 59 × 2 = 118If we add the result of reversing and doubling the original number to the original number:
59 + 190 = 24968 + 172 = 24077 + 154 = 23186 + 136 = 22295 + 118 = 213As the sum of adding the result of reversing and doubling the original number to the original number is 222, the original number must be 86.
10 inches in 6 hours
80 inches in 2 days
The relation is a direct variation
How to determine if the relation is a direct variationFrom the question, we have the following parameters that can be used in our computation:
10 inches in 6 hours
80 inches in 2 days
Convert 2 days to hours
So, we have the following representation
10 inches in 6 hours
80 inches in 72 hours
For the relation to be a direct variation, the following must be equal
6/10 = 72/80
Evaluate
0.6 = 0.6
Hence, the relation is a direct variation
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Complete question
Determine if the following relation represents a direct variation
10 inches in 6 hours
80 inches in 2 days
Add Decimals-Instruction - Level E
June makes slime using 1.5 liters of white glue and 0.72 liter of a starch and water mixture.
Find the total volume of the slime.
Are there enough hundredths to make a tenth?
➡ There are ? hundredths. That is
enough to make a tenth.
✓is
is not
➡ There are 22 hundredths. That is enough to make a tenth.
What is the arithmetic operations?
Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms,[disputed – discuss] which are highly important to the field of mathematical logic today.
The four basic mathematical operations are Addition, subtraction, multiplication, and division.
To find the total volume of the slime, we need to add 1.5 and 0.72:
1.5 + 0.72 = 2.22
There are 22 hundredths, which is enough to make a tenth.
Hence, the answer is:
➡ There are 22 hundredths. That is enough to make a tenth.
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suppose you are one of 19 people at a dinner party. Find the probability that at least one of the other guests has the same birthday as you and that some pair of guests share the same birthday assume there are 365 days in the year
The probability that at least one other guest shares your birthday is approximately?
The probability that some pair of guests share the same birthday is approximately?
The solution is 0.3486 or 34.86%, chance that exactly one other guest has the same birthday as you.
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.
here, we have,
For each guest, the probability that they share a birthday with you is 1 in 365. Aside from you, there are 499 guests.
Therefore, this problem can be modeled by a binomial probability model with probability of success 1/365.
The probability of exactly 1 success in 499 trials is given by:
P(x=1) = 0.3486
There is a 0.3486 or 34.86% chance that exactly one other guest has the same birthday as you.
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Charles and some friends ate at the Winterfield Café. Their bill was $50.00$ They paid $60.00. What percentage gratuity did they pay?
The percentage of gratuity paid is 20%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Amount for the bill = $50
Amount paid = $60
The amount of gratuity.
= 60 - 50
= $10
Now,
The percentage of gratuity.
= 10/50 x 100
= 20%
Thus,
The percentage of gratuity is 20%.
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help help help help help help help help help help help help help help help
What is the number of sides of a regular polygon in which each interior angle has a measure of 165°?
Answer:
the answer is 24 sides
explanation
Please help will mark Brainly
Answer:
P=10x^2+38y
Step-by-step explanation:
its the answer
PLSSSS HELP ME ASAP I DONT UNDERSTAND THIS
Jon filled up the tank of his semitruck with 240 gallons of fuel and set out to deliver a shipment of vegetables. His truck uses an average of 0.15 gallons of fuel for each mile he drives. You can use a function to approximate the amount of fuel in Jon's tank after he drives x miles.
Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)^x.
The equation for the function is [tex]y=-0.15x+240[/tex].
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, occasionally referred to as a "linear equation of two variables."
It is given that the amount of fuel filled up in Jon's semi truck is 240 gallons.
It is also given that for 1 mile the truck uses 0.15 gallons of fuel.
So, for "x" miles, the truck uses 0.15*x gallons of fuel.
So, the remaining fuel in the tank will be 240-0.15x.
Let the remaining fuel be "y".
This can be written as:
[tex]y=240-0.15x\\y=-0.15x+240[/tex].
Therefore the remaining fuel in the tank after Jon drives x miles will be a linear equation [tex]y=-0.15x+240[/tex]
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The price (in S) of a cookbook is determined by the number of cookbooks x demanded by consumers and supplied by the publisher.
Supply: p=0.003.x
Demand: p= -0.008x+330
(a) Solve the system of equations defined by the supply and demand models.
(b) What is the equilibrium price?
(c) What is the equilibrium quantity?
The system of equations defined by the supply and demand models solved for equilibrium price is $9 and equilibrium quantity is 3000 units
How to solve system of equation?Supply:
p=0.003x
x = p/0.003
x = 1/0.003p
Demand:
p= -0.008x+330
-0.008x = p - 330
x = (p - 330)/-0.008
Equilibrium price
Equate supply and demand price
0.003x = -0.008x+330
0.003x + 0.008x = 330
0.011x = 330
x = 330/0.11
x = 3,000
Substitute into
p=0.003x
p = 0.003(3000)
p = $9
Consequently, the equilibrium quantity and price is 3000 units and $9
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The accompanying data represent the miles per gallon of a random sample of cars with a three-cylinder, 1.0 liter engine.
(a)
Compute the z-score corresponding to the individual who obtained miles per gallon. Interpret this result.
(b)
Determine the quartiles.
(c)
Compute and interpret the interquartile range, IQR.
(d)
Determine the lower and upper fences. Are there any outliers?
a) The value of z-score is -0.299.
c) The IQR value is measure of spread of data, IQR = 4.25.
d) There is outliers since observations are not less than 30.375 and greater than 47.375.
What is z- score?The z-score is an example of a standardised score. The standard deviation of a data point's divergence from the mean of the distribution is calculated using a z-score.
Given:
Sample Data = 31.5, 36.0, 37.8, 38.5, 40.1, 42.2, 34.2, 36.2, 38.1, 38.7, 40.6, 42.5, 34.7, 37.3, 38.2, 39.5, 41.4, 43.4, 35.6, 37.6, 38.4, 39.6, 41.7, 49.3
(a) The value of z-score is calculated as follows,
μ = [tex]\sum _{i=1}^n[/tex]/ n = 933.1 /24 = 38.88
σ = 3.61
So, z = X - μ / σ
= 37.8 - 38.88/3.61
= − 0.299
(b) Quartile:
Q₁ = ( n+1/4)th value
= (24+1/4)th
= 6.25th
= 36.2 + 0.25 x ( 37.3 − 36.2 )
= 36.47
and, M = ( n+1/2)th value
= (24+1/2)th
= (24+1/4)th
= 12.5 t h
= 38.4 + 38.5/2
= 38.45
Q₃ = 3( n+1/4)th
= 3(24+1/4)th
= 18.75 t h
= 40.6 + 0.75 x ( 41.4 − 40.6 )
= 41.2
(c) Interquartile range
= Q ₃ − Q ₁
= 41.2 − 36.47
= 4.25
(d) Lower fences = Q₁− 1.5 ( I Q R )
= 36.75 − 1.5 ( 4.25 )
= 30.375
Upper fences = Q ₃+1.5
= 41 + 1.5( 4.25 )
= 47.375
Hence, there is outliers since observations are not less than 30.375 and greater than 47.375.
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To find 15+32,
Kayla adds the ones.
Then she adds the tens.
Then she adds the ones and tens.
5+2=7
1+3=4
7+4=11
Do you agree with Kayla? Yes or No.
Explain by showing your thinking using drawings, numbers, or
words.
Answer:
no
Step-by-step explanation:
15+32 you would first add the tens
5+2=7
then the ones
1+3 =4
you're answer would then be 47 as the ones come before the tens
what is statistics?
Statistics is referred to as a discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
What is Data?This is referred to as information that has been translated into a form that is efficient for movement or processing.
Statistics involves using information that has been translated into a form that is efficient for movement or processing through different tools such as mean standard deviation etc.They help to provide more details about a set of data which makes it use very important.
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Write the sentence as an equation.
242 fewer than the quantity 193 times n equals 131
I think this is it
252-(193×n) =131
verify the
identity algebraically.
Step-by-step explanation:
[tex] \frac{1}{ \sin(x ) } - \frac{1}{ \csc(x) } = \csc(x) - \sin(x) [/tex]
[tex] \frac{ \csc(x) - \sin(x) }{ \csc(x) \sin(x) } [/tex]
[tex] \csc(x) - \sin(x) = \csc(x) - \sin(x) [/tex]
6.88 + 3w= 17.98 find w
Answer:
3w= 17.98-6.88
3w=11.1
w =3.7
Step-by-step explanation:
After subtracting divide both side by 3
Answer:
w = 3.70
Step-by-step explanation:
Given that,
6.88 + 3w= 17.98 ..........(1)
Now subtracting both sides by 6.88 in equation (1), We have
6.88 + 3w - 6.88 = 17.98 - 6.88
or, 3w + 0 = 11.1
or, 3w = 11.1
Again dividing both sides by 3 in the above equation, We have
[tex]\frac{3w}{3}=\frac{11.1}{3} = 3.70[/tex]
Hence the required answer is w = 3.70
Find the area of a rectangle with side lengths 5/8ft. and 1/3 ft.
A. 5/11
B. 1 11/12
C. 6/11
D. 5/24
The area of a rectangle with side lengths 5/8ft. and 1/3 ft is: D. 5/24 ft².
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.W represents the width or base of a rectangle.L represents the length or height of a rectangle.Substituting the given points into the area of rectangle formula, we have the following;
Area of rectangle = 5/8 × 1/3
Area of rectangle = 5/24 square feet.
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6 3/14 divided by 250 + 5 2/7 divided by 250
Answer:
The solution is 23/500 or 0,046
Step-by-step explanation:
6 3/14÷250+5 2/7÷250
= 6 3/14×1/250+5 2/7×1/250
= (87/14×1/250)+(37/7×1/250)
= (87/3500)+(37/1750)
= 87+37(2)/3500
= 87+74/3500
= 161/3500
= 161÷7/3500÷7
= 23/500
= 0,046
How many solutions does the system have? { � = 5 � + 1 � = − 2 � − 8 ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ y=5x+1 y=−2x−8
The given system of linear equations has a unique solution.
What are linear equations?A linear equation is an algebraic equation in which each term has an exponent of 1 and when graphed, the result is always a straight line.
Given that, a system of linear equations, y = 5x+1 and y = -2x-8, we are asked to find how many solutions do they have,
The rule for a system of linear equations, a₁x+b₁y+c₁ = 0 and a₂x+b₂y+c₂ = 0 are :-
When the system has a unique solution :-a₁ / a₂ ≠ b₁ / b₂, and the lines intersect at one only point.
When the system has a no solution :-a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂, and the lines are parallel.
When the system has infinite solution :-a₁ / a₂ = b₁ / b₂ = c₁ / c₂, and the lines overlaps.
Checking for the given equations,
y = 5x+1 and y = -2x-8
Converting into standard form of the linear equations,
5x-y +1 = 0 and 2x+y+8 = 0
5/2 ≠ -1
The equation is following the rule of unique solution, also the graph is intersecting at one point, [graph is attached]
Hence, the given system of linear equations has a unique solution.
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Answer:
One solution
Step-by-step explanation:
Write 15*15*15*15 using an exponent
Answer:
15^4
Step-by-step explanation:
An exponent refers to the number of times a number is multiplied by itself,
so 15 multiplied 3 more times by itself (15 * 15 * 15 * 15) its 15^4.
[tex]15^{4} .[/tex]
Step-by-step explanation:1. General concept about exponents.When working with positive non fractional exponents, we state that a number A elevated to the n power is that number A in a multiplication of itself n times. For example, when we write [tex]7^{3}[/tex] we're stating that the seven is being multiplied 3 times: [tex]7*7*7[/tex].
2. Use the rule to rewrite the expression.As you may see, the expression "15*15*15*15" is just the number 15 being multiplied by itself four times. Hence, we could say that the number 15 to the power of 4. Thus, we can rewrite it as:
[tex]15^{4} .[/tex]
Solve the triangle. Round to the nearest tenth.
In the given triangle, ∠F=29°, d>15 and e<15.
What exactly is a triangle?
Triangles are polygons in geometry that have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle. The triangle is classified into six forms based on its sides and angles.
A triangle is categorised into three categories based on its sides, namely:
Scalene Triangle - Each side has a distinct length.
Isosceles Triangle - A triangle with two sides of equal length and one side of a different length.
Equilateral Triangle - A triangle has three sides that are of the same length.
A triangle is categorised into three categories based on its angles, namely:
Acute Angle Triangle - A triangle with all of its angles smaller than 90°.
Obtuse Angle Triangle - A triangle with one of its angles larger than 90°.
Triangle with a Right Angle - A triangle with one of its angles equal to 90°.
Now
As sum of all angles of triangle=180°
∠F+127°+24°=180°
∠F=180-151
∠F=29°
and In a triangle Largest angle is opposite to largest side and smallest angle is opposite to smallest side.
Then the sides e and d will be as following d>15 and e<15.
hence,
In the given triangle, ∠F=29°, d>15 and e<15.
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carrie is cutting sheets of stickers to put in 4 gift bags Each bag will contain the same number of stickers . if each sheet contains 22 stickers then what is the fewwer number of sheets carrie can use so there are no stickers left over
Carrie is slicing sticker sheets to fit four present bags. There will be an equal quantity of stickers in each bag.
What is fewer number?The word "fewer" is represented by the Greek letter "," which denotes that one thing is less than another. Any number bigger than another is indicated by the sign >. In this case, 6 10 demonstrates that 6 is less than 10. According to this, 6 is less than 10 in size.A rule concerning fewer and less is frequently cited. As an example, "fewer options" and "fewer issues" relate to the quantity or amount among things that are counted, whereas "less time" and "less work" refer to the quantity or amount among things that are measured. Lesser simply indicates "not as many."To learn more about fewer number refer to:
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Suppose that 71% of the surface of the Earth is covered in water, and a random number generator uses latitude and longitude to select a random location on the Earth. If 7 such locations are generated, what is the probability that the first 5 locations are in water and the last 2 locations are on land?
A. 0.0010
B. 0.0152
C. 0.0910
D. 0.9090
Answer:
0.0152 is the probability that the first 5 locations are in water and the last 2 locations are on land.
