The equation for the linear model in the scatter plot is Y = -2x + 56.
To calculate this equation, we need to find the slope (m) and the y-intercept (b). The slope is calculated with the formula m = (y2 - y1) / (x2 - x1), where x and y represent the coordinates of two points on the graph.
The two points closest to the line in the scatter plot are (2, 48) and (4, 52). Substituting these values into the formula gives us m = (52 - 48) / (4 - 2) = 4/2 = 2.
The y-intercept is the point where the line crosses the y-axis. To find it, we need to substitute the slope and one point's coordinates into the equation y = mx + b. For our equation, we will use the coordinates (2, 48). Substituting these values into the equation gives us 48 = 2x + b, and solving for b gives us b = 48 - 2(2) = 44.
Therefore, the equation for the linear model in the scatter plot is Y = -2x + 56.
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Kendra used 6 loaves of bread on an 8 day hiking trip. She wants to know how many loaves of bread she should pack for a 12 day hiking trip if she eats the same amount of bread each day.
Answer:
9 loaves of bread
Step-by-step explanation:
We know
8 days = 6 loaves of bread
1 day = 0.75 loaves of bread
12 days = 0.75 x 12 = 9 loaves of bread
So, she should pack 9 loaves of bread for a 12-day hiking trip.
Answer: Kendra will need to back 9 loaves of bread for a 12 day hiking trip.
Step-by-step explanation:
Alright, the first step to solve any math problem is to take a look at the information we have. We know that Kendra has eaten through 6 loaves over the course of 8 days. We want to know how much bread she needs if she takes a 12 day hiking trip.
Because she's eating the same amount of bread each day, we need to find out how much of a loaf she eats daily. In order to find that number, we have to divide. In this case, it would be 6/8. (Amount of bread she has/Time taken to eat that bread).
This gives us 0.75. This means that Kendra eats 0.75 of a loaf of bread daily. In order to find out how much bread she needs for a 12 day hiking trip, all we have to do is multiply by 12.
0.75 * 12 = 9.
Kendra will need to back 9 loaves of bread for a 12 day hiking trip.
P.S. You could also do this with fractions by simplifying 6/8 to 3/4 (divide the numerator and denominator by 2, as they're both divisible by 2), and then multiply like 12 in the same way. They both yield the same answer, so it's a matter of preference. I used decimals as I found them easier to work with!
Select the interval where the graph h is negative.
Answer: C
Step-by-step explanation:
Based on the graph, we know that it is negative if it is under the x-axis. It is also indicated by the negative labels.
A: incorrect
Looking at choice A, it says the interval is from -3<x<-2. This means we have to find x=-3 and x=-2. On the graph, that interval is above the x-axis, so it is positive, not negative.
B: incorrect
Looking at choice B, it says the interval is from 2<x<3. This means we have to find x=2 and x=3. On the graph, that interval is above the x-axis, so it is positive, not negative.
C: correct
Looking at choice C, it says the interval is from 4<x<5. This means we have to find x=4 and x=5. On the graph, that interval is under the x-axis, so it is negative.
Therefore, C is the correct answer.
15. Find the lengths of the sides of the kite KITE. (Answer in simplest radical form and show work)
The lengths of the sides of the kite LM is 13√2.
How does Pythagoras' rule work?According to the Pythagorean theorem, the hypotenuse of a right-angled triangle's other two sides add up to a square whose length equals the hypotenuse's.
The hypotenuse (longest side) of a right-angled triangle's square is equal to the sum of its other two sides, according to the Pythagoras theorem (base and perpendicular). Hypotenuse2 = Base2 + Perpendicular2 is how this is expressed. A2 + B2 = C2 is the formula for the hypotenuse.
According to question:-
LM = 13√2
Hypotenuse = Base 2 + Perpendicular 2.
So,
LM = √7² + 17²
LM = √49 + 289
LM = √338
LM = 13√2.
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I dont know how to prove the equation below...pls help prove it with clear steps, i have no clue how does sin^2x can go into 1+cosx
Answer:
Answer:
Foci: (±5, 0)
Vertex: ( ±4 , 0)
Eccentricity: e = 5/4
Step-by-step explanation:
Hyperbola:
Write the equation of hyperbola in the form,
\boxed{\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1}
a
2
x
2
−
b
2
y
2
=1
9x² - 16y² = 144
Divide the entire equation by 144,
\begin{gathered}\sf \dfrac{9x^2}{144}-\dfrac{16y^2}{144}=\dfrac{144}{144}\\\\\\ \dfrac{x^2}{16}-\dfrac{y^2}{9}=1\\\\\\\dfrac{x^2}{4^2}-\dfrac{y^2}{3^2}=1\end{gathered}
144
9x
2
−
144
16y
2
=
144
144
16
x
2
−
9
y
2
=1
4
2
x
2
−
3
2
y
2
=1
a = 4 and b =3
Eccentricity: e
\boxed{e=\sqrt{1+\dfrac{b^2}{a^2}}}
e=
1+
a
2
b
2
\begin{gathered}\sf = \sqrt{1+\dfrac{9}{16}}\\\\=\sqrt{\dfrac{16}{16}+\dfrac{9}{16}}\\\\=\sqrt{\dfrac{25}{16}}=\sqrt{\dfrac{5*5}{4*4}}\\\\\\=\dfrac{5}{4}\end{gathered}
=
1+
16
9
=
16
16
+
16
9
=
16
25
=
4∗4
5∗5
=
4
5
Foci:
(ae, 0) & (-ae , 0)
\begin{gathered}\sf \left(4*\dfrac{5}{4},0 \right) \ ; \ \left( -4*\dfrac{5}{4},0 \right)\\\\\\(5, 0) \ ; \ (-5,0)\end{gathered}
(4∗
4
5
,0) ; (−4∗
4
5
,0)
(5,0) ; (−5,0)
Vertex of hyperbola:
The vertex of the hyperbola is a point where the hyperbola cuts the axis. (-a , 0) ; (a , 0)
Vertex : (-4 , 0) ; (4 , 0)
If it takes 9 hours to travel from North Carolina to Florida driving an
average speed of 55 mph, about how long will it take to travel from North
Carolina to Florida driving an average speed of 70 mph?
Time taken to travel from North Carolina to Florida driving an average speed of 70 mph is 7 hours.
What is the typical speed?Calculating average speed involves dividing the total distance traveled by the total time it took to cover that distance.
Given,
Time taken to travel = 9hours
average speed =55 mph
distance between North Carolina to Florida = speed x distance
distance= 55 x 9
distance= 495 miles
if driving at speed of 70 mph
time taken = distance/speed
time taken=495/70
time taken=7 hours
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How many times smaller is 2.7 x 10^3 than 5.481 x 10^5?
Function: This means that 2.7 x 10^3 is about 201.593 times smaller than 5.481 x 10^5. This can also be expressed as 0.049 or 4.9%.
What is function?A function is a mathematical relation between two sets of values, usually between an input and an output. It can be thought of as a machine that takes a certain input and produces a certain output.
2.7 x 10^3 is about 0.049 times smaller than 5.481 x 10^5.
To determine this, we can divide the two numbers. 5.481 x 10^5 divided by 2.7 x 10^3 equals about 201.593.
This means that 2.7 x 10^3 is about 201.593 times smaller than 5.481 x 10^5. This can also be expressed as 0.049 or 4.9%.
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What is the value of the polynomial 5x − 4x^2 3 at x =- 1?
The value of the polynomial "5x - 4x^2 + 3" at x =- 1 is -6.
The polynomial is 5x - 4x^2 + 3, and it is required to find its value at x = -1,
Now solve the polynomial by putting the value of x equal to -1:
5(-1) - 4(-1)^2 + 3 , x = - 1
-5 - 4 ( 1 ) + 3 , squaring -1 gives + 1
minus 5 minus 4 plus 3
( - 9 + 3)
( - 6 )
Hence, is shown that the value - 6 is obtained when the given polynomial "5x - 4x^2 + 3" is solved for x = -1.
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What is the ratio of sin t?
Sine of an angle is defined as the ratio of the side opposite (perpendicular side) to that angle divided by hypotenuse of the triangle.
sin is a trigonometric ratio.
If θ is one of the acute angles in a triangle, then the sine of theta is the ratio of the opposite side to the hypotenuse.
sin Q = perpendicular / hypotenuse.
sin Q is the base of the trigonometry ratios and it is one of the ratio.
sine is an acute angle.
some formula of sine angle are ,
1- sine Q = 1/ cosec Q .
2- sin ^2 Q = 1- cos^2 Q .
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One bottle holds 67.34 onces and another bottle holds 48.5 onces combined how much do they hold?
After combine they hold 115.84 ounces.
What is Addition?A process of combining or adding two or more numbers is called addition.
We have to given that;
One bottle holds 67.34 ounces and another bottle holds 48.5 ounces.
So, After combine, we get;
Both bottle hold = 67.34 ounces + 48.5 ounces
= 115.84 ounces
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A traffic study has shown that the probability that 5 cars will pass over a small bridge in a 4-minute period is 0.16.
What are the odds against exactly 5 cars passing over the bridge in that time?
Answer: The odds against an event occurring are the ratio of the probability that the event will not occur to the probability that the event will occur. To find the odds against an event, you can use the formula:
Odds against = (1 - probability of event occurring) / probability of event occurring
In this case, the event is that exactly 5 cars will pass over the bridge in a 4-minute period. The probability that this event will occur is 0.16. Therefore, the odds against this event occurring are:
Odds against = (1 - 0.16) / 0.16
= 0.84 / 0.16
= 5.25
So, the odds against exactly 5 cars passing over the bridge in a 4-minute period are 5.25 to 1.
It means that there are 5.25 times more likely that it will not happen compare to happen.
Step-by-step explanation:
How do you prove inverse?
To prove the inverse :
In the equation expressing the function, swap out f(x) for y.Swap out x and y. To put it another way, swap out every x for a y and vice versa.Solve for y.Change y to [tex]f^{-1}[/tex] (x).You assemble the functions (that is, insert x into one function, plug that function into the suggested inverse function, then simplify) and check that you end up with simply "x" to establish (or refute) that two functions are the inverses of one another. The functions are inverses if you get x; otherwise, they are not.
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(6) (Bonus) A rectangular tank with a bottom and sides but no top is to have volume 500 cubic feet. Determine the dimensions (length, width, height) with the smallest possible surface area.
The dimensions length is 10 feet, width is 10 feet and height is 5 feet and the smallest possible surface area is 300 square feet.
Volume=lbh
lbh=500 cubic feet
h=500/lb
Surface area S=lb+2bh+2lh...(1) {rectangular tank has no top}
S=lb+2b(500/lb)+2l(500/lb) {substituting the value of h in 1}
S=lb+1000/l+1000/b { partially differentiating S with respect to l and b}
for S to be minimum dS/dl=0 and dS/db=0
dS/dl= b-1000/l^2
dS/dl=0
b=1000/l^2...(2)
dS/db= l-1000/b^2
dS/db=0
l=1000/b^2
l=1000/(1000/l^2)^2 {substituting the value of b from 2}
l=(1000 x l^4)/(1000000)
1000000/1000=l^4/l
1000=l^3
l=10 feet
b=1000/l^2
b=1000/100=10 feet
lbh=500
h=500/(10x10(
h=5 feet
S=10x10+2x5x10+2x10x5
S=300 square feet
Length is 10 feet, width is 10 feet and height is 5 feet and the smallest possible surface area is 300 square feet of the rectangular tank.
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Is this right?
If not please help me understand or tell me the answer.
=========================================
Explanation:
L = 6 inches = length
W = 3 inches = width
H = 5 inches = height
----------------------
V = volume
V = L*W*H
V = 6*3*5
V = 90 cubic inches is the volume
----------------------
SA = Surface Area
SA = 2*(LW + LH + WH)
SA = 2*(6*3 + 6*5 + 3*5)
SA = 126 square inches is the surface area
-----------------------
Unfortunately there isn't enough information to know the material cost. Please post the full problem, and any other relevant information connected to this question.
5) If it takes 4 men 6 hours to repair a road, how long will it take 7 men to do the job if they work at the same rate
By fraction , 3 3/7 will it take 7 men to do the job if they work at the same rate.
What is fraction in maths?
In mathematics, the portion or component of the complete item is represented by a fraction. It stands for the proportionate pieces of the whole.
The denominator and numerator are the two components of a fraction. The top number is referred to as the numerator, and the bottom number is referred to as the denominator.
per person per hour
1/4*6 = 1/24
7 men per hour
1/24 * 7 = 7/24
total times
1 ÷ 7/24 = 1 * 24/7
= 3 3/7
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Tickets for all of the described charity raffle games cost $2 per ticket .identify the games in which a person who buys a ticket for each game every day for the next 400 days could expect to lose less than a total of $200
Answer: To determine the games in which a person who buys a ticket for each game every day for the next 400 days could expect to lose less than a total of $200, we need to find the games in which the probability of winning is greater than the probability of losing.
Since the tickets for all of the games cost $2 per ticket, the probability of winning any given game is equal to the prize money divided by the ticket cost. For example, if the prize money for a game is $10, the probability of winning is $10/$2 = 1/2.
If the probability of winning a game is greater than the probability of losing, the expected value of the game is positive, which means that the person can expect to win more than they lose over time. On the other hand, if the probability of winning is less than the probability of losing, the expected value of the game is negative, which means that the person can expect to lose more than they win over time.
Therefore, to determine which games the person could expect to lose less than $200 in total, we need to find the games in which the prize money is greater than $2 per ticket.
Step-by-step explanation:
GIVING BRAINLIEST AND MANY POINTS FOR ANSWER I BEG PLEASE PLEASE
1. Use the Distributive Property to simplify the expression.
6(5 - q)
Group of answer choices
11 - 6q
11 - q
30 - 6q
1 - q
3.
Use the Distributive Property to simplify the expression.
(d + 2)(-7)
Group of answer choices
-7d - 14 OR -7d + -14
7d - 2 OR 7d + -2
d - 14 OR d + -14
d - 5 OR d + -5
4. Use the Distributive Property to simplify the expression.
-4(x - 6y)
Group of answer choices
4x + 24y
-4x + 24y
4x - 1.5y
-4x - 10y
5. Use the Distributive Property to simplify each expression.
a) -3(5 + b)
=
[ Select ]
+
[ Select ]
b
b) 3(-4x + 8)
=
[ Select ]
x +
[ Select ]
6. The table shows different prices of items at a movie theater.
Item Cost ($)
box of candy 2.25
drink 3.25
popcorn 4.50
ticket 7.50
Suppose Mina and her two friends want to go to the movies.
Which expression could be used to find the total cost if each of them buy one of each item?
[ Select ]
What is the total cost for all three people?
$
[ Select ]
Answer:
1. 30 − 6q
3. −7d − 14 OR -7d + -14
4. = −4x + 24y
5. a) −3b − 15 b)−12x + 24
6. For the first answer to this question: 3x + 3y OR 3x = t
For the second answer to this question: 3x = t and it costs 15 dollars in total with x = 5.
MATH PLEASE I NEED ANSWER
Please just write the numerical value of the volume of the prism.
I really need an answer for this FAST so if anybody can answer id really appreciate it :)
The volume of the prism in the attached figure is calculated to be
672 m³
How to find the volume of the prismIn the given problem, the formula used for volume of prism is
= area of base * height
Assuming a triangular base
area of triangular base = 1/2 * base * height
where
base = 12 m
height = 14 m
area of triangular base = 1/2 * 12 * 14
area of triangular base = 84 m²
The volume of the prism with a triangular base
volume of the prism = area of triangular base * height
where
area of triangular base = 84 m²
height = 8 m
volume of the prism = 84 * 8
volume of the prism = 672 m³
The volume of the prism is solved to be 672 m³
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Tlaloc pumped up 565656 ball. He pumped up 555 dodge ball for every 999 other ball. Complete the table. Original ratio Number Tlaloc pumped up
Dodge ball 555
Other ball 999
Total ball
5656
20 dodgeballs have been pumped up by Ttaloc.
Ttaloc has 36 additional pumped-up balls.
The complete ball's original number is 14.
The relationship between two or more numbers is expressed by the ratio. It displays the frequency of how often one value is encapsulated by another value (s).
The number of dodgeballs Ttaloc pumped up = (5/14) x 56 = 20
The number of other balls Ttaloc pumped up = (9/14) x 56 = 36.
A ratio in mathematics demonstrates how many times one number is present in another.
A ratio can have any number of quantities, such as counts of people or things or measurements of length, weight, time, etc. Both numbers must be positive in most situations.
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Select all the expressions that are equivalent to 0.3(9n + 22).
–2.7n – 6.6
2.7n + 6.6
2.7 + 6.6n
6.6 + 2.7n
6.6 – 2.7n
Answer:
2.7n + 6.6 or 6.6 + 2.7n
Step-by-step explanation:
Algebraic ExpressionsAlgebraic Expressions are just like Numerical Expressions but instead of numbers, alphabets are used, these alphabets can also be used as variables. (BODMAS rule applies to Algebraic Expressions as well.)
Eg. 45x + 31x(2) = 45x + 62x = 107x
SolutionGiven from the question:
[tex]0.3(9n + 22) \\ = 2.7n + 6.6 \: or \: 6.6 + 2.7n[/tex]
What is the smallest four-digit palindrome that is divisible by 4? (A palindrome is a number that reads the same forwards and backwards, like 61216.)
Answer:
1004 is the smallest four-digit palindrome that is divisible by 4.
Which graph represents the function?
f(x)=3√x + 2
Radicals
How do I Simplify
(4√5-3)(√5-2)
Answer:
26 - 11√5
Step-by-step explanation:
(4√5-3)(√5-2)
= 4√5 (√5-2) -3 (√5-2)
= 4√5 √5 + 4√5 ⋅ -2 -3 (√5-2)
= 4√5 √5 + 4√5 ⋅ -2 -3√5 -3 ⋅ -2
= 26 - 11√5
If you can, please give me a Brainliest; thank you!
solve for g here
[tex]55g + 25 = 625 \div 25[/tex]
Answer:
0
Step-by-step explanation:
625 / 25 = 25
55g + 25 = 25
55g = 25 - 25
55g = 0
g = 0/55
g = 0
Answer:
[tex] \sf \: g = 0[/tex]
Step-by-step explanation:
Given equation,
→ 55g + 25 = 625 ÷ 25
Now the value of g will be,
→ 55g + 25 = 625 ÷ 25
→ 55g + 25 = 25
→ 55g = 25 - 25
→ g = 0 ÷ 55
→ [ g = 0 ]
Hence, the value of g is 0.
Which of the following sets of ordered pairs represents a function? {(-8,-14), (-7,-12), (-6,-10), (-5,-8)} {(-4,-14), (-9,-12), (-6,-10), (-9,-8)} {(8,-2), (9,-1), (10,2), (8,-10)} {(-8,-6), (-5,-3), (-2,0), (-2,3)}
The correct answer is A. {(-8,-14), (-7,-12), (-6,-10), (-5,-8)} which sets of ordered pairs represents a function.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
Here, we have,
sets of ordered pairs represents a function are,
{(-8,-14), (-7,-12), (-6,-10), (-5,-8)}
{(-4,-14), (-9,-12), (-6,-10), (-9,-8)}
{(8,-2), (9,-1), (10,2), (8,-10)}
{(-8,-6), (-5,-3), (-2,0), (-2,3)}
Now, we know that,
A function has no repeated values of the independent variable.
So, we have now,
Only choice A meets that requirement.
And,
B: (-9, 12) and (-9, 8) both have -9 as a first value; not a function.
C: (8, -2) and (8, -10) both have 8 as a first value; not a function.
D: (-2, 0) and (-2, 3) both have -2 as a first value; not a function.
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Name the property that is shown by each equation.
A. 6a + 4 = 4 + 6a
B. 30 + 60 = 15(2 + 4)
C. 3(8x + 4) = 3(4 + 8x)
D. 4(6a) = (4 · 6)a
A. Commutative property of addition
B. Distributive property
C. Commutative property of addition
D. Associative property of multiplication
What is a 3 variable system?
The three variable system is written as (x, y, z).
Here we have to find the definition of three variable system.
basically a solution of a system in three variables is an ordered triple (x, y, z) that makes all three equations true.
On the other hand it is what they all three have in common.
Where as the solution to a system of three equations in three variables (x, y, z) is called an ordered triple.
In order to solve these one we have to do the following:
First we have to pick any two pairs of equations from the system.
And then we have to eliminate the same variable from each pair using the Addition/Subtraction method.
Final step is to solve the system of the two new equations using the Addition/Subtraction method.
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Write an exponential function to describe the given sequence of numbers,
10, 60, 360, 2160, 12960,.
The exponential function to describe the given sequence of numbers, 10, 60, 360, 2160, 12960, ... is aₙ = 10 × [tex]6^{n-1}[/tex].
The given series 10, 60, 360, 2160, 12960, ... is a geometric progression.
a = 10
The common difference r = 60/10 = 6
As we know the general formula of the nth term of a geometric series is
aₙ = a × [tex]r^{n-1}[/tex]
Now, put the values of a = 10, r = 6 and n in the general formula,
aₙ = 10 × [tex]6^{n-1}[/tex]
Therefore, the required exponential function to describe the given sequence of numbers, 10, 60, 360, 2160, 12960, ... is aₙ = 10 × [tex]6^{n-1}[/tex].
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Of the 360 members of the kennel club who were
surveyed, 190 said they would try a new dog food.
If the kennel club has 2,100 members, how many
could be expected to try the new dog food?
A rental car company charges a fixed fee of $30 + 0.05 per mile. Let’s see represent the total cost of renting a car and driving a.m. miles right in equation that could be used to find the total cost of the renting car and driving it any number of miles
Answer:
C = $30 + $0.05M
Step-by-step explanation:
We know that renting the car will cost $30, regardless of whether you drive it any where or not
So far
C = $30
On the end of this equation, we want to be able to add another value, that can vary depending on the quantity of M (number of miles)
The second value is $0.05 multiplied by how many miles are travelled
Also expressed as $0.05M
Finally, just fix the two parts together
Answer:
Step-by-step explanation:
We know that renting the car will cost $30, regardless of whether you drive it any where or not
So far
C = $30
On the end of this equation, we want to be able to add another value, that can vary depending on the quantity of M (number of miles)
The second value is $0.05 multiplied by how many miles are travelled
Also expressed as $0.05M
Finally, just fix the two parts together
C = $30 + $0.05M