Considering the expression of a line and how to obtain it having 2 points, you obtain:
the linear equation giving the sales y in terms of the year x is y=1.012x - 2002.866the sales in 2013 will be $34.29 billion.Linear equation o lineA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x1, y1) and (x2, y2) of a line, the slope m of said line can be calculated using the following expression:
m= (y2 - y1)÷ (x2 - x1)
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.
Linear equation in this caseIn this case, you want to obtaina linear equation giving the sales y in terms of the year x. You know:
In 2011, Tyson foods had sales of $32.266 billion.In 2012, sales were $33.278 billion.So, being (x1,y1)= (2011, 32.266) and (x2,y2)= (2012, 33.278), the slope m can be calculated as:
m= (33.278 - 32.266)÷ (2012 - 2011)
Solving:
m=1.012
Considering point 1 and the slope m, you obtain:
32.266= 1.012×2011 + b
32.266= 2035.132 + b
32.266- 2035.132= b
- 2002.866= b
Finally, the linear equation giving the sales y in terms of the year x is y=1.012x - 2002.866
You can use the equation to predict the sales for 2013 as follow:
y=1.012×2013 - 2002.866
Solving:
y=1.012×2013 - 2002.866
y= $34.29 billion
Finally, the sales in 2013 will be $34.29 billion.
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Please find the slope of line ST
The slope of line ST is 4
How to determine the slope of the line
The formula for determining the slope of a line is expressed as;
Slope = y2 - y1/x2 - x1
It is mostly represented with 'm' and it also known as the gradient of a line.
From the points given , we have that;
y2 = -4y1 = 0x2 = -1x1 = 0Substitute the values into the formula
Slope, m = -4 - 0/ -1 - 0
Slope, m = -4/ -1
Slope, m = 4
Thus, the slope of line ST is 4
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Isaac deposits $2,500 into an account that pays 4.75% interest
compounding continuously. How long will it take to double his
initial investment? Show all work for full credit and round your
answer to two decimal places.
Answer:0.02
Step-by-step explanation:
The key words in this problem is that you are compounding continuously, so that would be a equals p e to the r t power to show you that formula, and so when it says you have 2500 in the account e to the .4 excuse me, 0.0475 t Power is equal to, it says, doubling the investment, and so you just have to think about your doubling the investment you're going to take 2500 times to do it. The first thing i would do, then, is to divide the 2500 over which actually cancels out this 2500 point so you're. Looking at e to the .0475 t, power is equal to 2 right, 4.75 percent, so to solve for t want to natural log, both sides- i forgot my t in there so to solve for t natural log of 2 divided by 0475, so it takes about 14.593 Years or, however, you're supposed around it says: 2 decimals soul be 14.59 years all right, so on number 2, this time they give you the formula for ph is equal to negative log of the hydrogen plus atoms ions. So, basically, what they want you to do is take 1.7 plugging them, for the ph is equal to negative log of let's just call it h, and we have to solve for h now. So the first thing you want to do is to divide that negative 1.7. Over to undo log base 10, this would take 10 to that power and that's your answer not sure exactly where they want you to round says the nearest one hundredth would be .02, so the h plus items is equal to 0.02.
Solve this pls (pls)
Answer:
21-3= 18 18 +18=36 36/6 =6
Step-by-step explanation:
correct 36/6=6
Answer:
This problem is not solvable. So, the correct answer is 21 – 3 + 18 ÷ 6 = 6
Step-by-step explanation:
21 – 3 + 18 ÷ 6 = 6
Hope this still helps! Have an amazing day! Please award me brainliest! :)
Mercury, Venus, and Earth are the three planets closest to the sun. Would their combined distance from the sun be greater or less than the distance from the sun to Neptune? Show your work and justify your answer.
Find following measure.
m RT
When an angle exists encircled by a circle, its measure exists equivalent to the intercepted arc's measure divided by two.
The measure of m RT is 126.
What is meant by inscribed arc?The arc that is inside the inscribed angle and whose endpoints are on the angle is known as the intercepted arc. Anywhere on the circle that the sides of an inscribed angle intersect to produce an intercepted arc can serve as the angle's vertex.
Angles with vertices on a circle and that cross an arc on the circle are said to be inscribed angles. Half of the intercepted arc's length and half of the central angle's length intersecting that same arc make up the measure of an inscribed angle. Congruent inscribed angles are those that intersect the same arc.
According to the Inscribed Angle Theorem, an inscribed angle's measure is equal to half of its intercepted arc's measure. Congruent inscribed angles are those that intersect the same arc.
An angle's measure exists equivalent to the intercepted arc's measure divided by two when it is surrounded by a circle.
m RT = 2(m ∠S)
m RT = 2(m ∠S) = 126
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The gravitational attraction between two bodies varies inversely as the square of the distance between them: If the force of attraction is 64 pounds when the distance between the bodies is 9 feet, what is the distance between them when the force is 36 pounds?
The distance between them when the force is 36 pounds is 5.06 feet.
According to the statement
We have to find that the distance between two bodies.
So, For this purpose, we know that the
A force is a push or pull upon an object resulting from the object's interaction with another object.
From the given information:
If the force of attraction is 64 pounds when the distance between the bodies is 9 feet
Then
F1 =64 pounds, r1 = 9 ft
F2 = 36 , r2 = ?
The gravitational force of attraction is inversely proportional to the square of distance between the two bodies.
So, F2 / F1 = r1^2 / r2^2
36 / 64 = 9 / r2
r2 = 0.56*9
r2 = 5.06.
So, The distance between them when the force is 36 pounds is 5.06 feet.
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Answer:
12 ft
Step-by-step explanation:
there is less force so the distance is greater
Which expressions are equivalent to -6(b+2)+8−6(b+2)+8minus, 6, left parenthesis, b, plus, 2, right parenthesis, plus, 8 ?
The equivalent expression of -6(b + 2) + 8 is -6b - 4
How to determine the equivalent expression?The expression is given as
-6(b + 2) + 8
Expand
-6b - 12 + 8
Evaluate the like terms
-6b - 4
Hence, the equivalent expression of -6(b + 2) + 8 is -6b - 4
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Cars enter a car wash according to a poisson process at a mean rate of 2 cars per half an hour. what is the probability that, in an hour, at least 4 cars will enter the car wash?
The probability that, in an hour, at least 4 cars will enter the car wash is 0.94.
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:
Cars enter a car wash according to a Poisson process at a mean rate of 2 cars per half an hour.
Here the value of λ is:
λ = 2 cars/half an hour
λ = 4 cars/hour
The probability that, in an hour, at least 4 cars will enter the car wash:
P(x = 4) = 4⁴e⁻⁴/5
After solving:
P(x = 5) = 0.937 ≈ 0.94
Thus, the probability that, in an hour, at least 4 cars will enter the car wash is 0.94.
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The blueprint for Zahra’s new office measures `4` cm long and `2` cm wide.
The scale for the blueprint is `6` cm to `15` ft.
What is the actual area of her office?
Answer:
60 square feet
Step-by-step explanation:
In the blue print, 6 cm represents 15 ft
So 1 cm represents 15/6 feet = 5/2 feet
4 cm long represents 4 x 5/2 = 10'
2 cm wide represents 2 x 5/2 = 5'
Area = 10' x 5' = 60 square feet
Answer:
60 square feet
Step-by-step explanation:
In the blue print, 6 cm represents 15 ft
So 1 cm represents 15/6 feet = 5/2 feet
4 cm long represents 4 x 5/2 = 10'
2 cm wide represents 2 x 5/2 = 5'
Area = 10' x 5' = 60 square feet
State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.
The distance from point X to line q is the length of the segment perpendicular to line q from X .
The statement " The distance from point X to line q is the length of the segment perpendicular to line q from X" is true
Given,
The statement "The distance from point X to line q is the length of the segment perpendicular to line q from X "
From the figure we can say that the distance from point X to line q is the length of the segment perpendicular to line q from X.
So the given statement is true
Hence, the statement " The distance from point X to line q is the length of the segment perpendicular to line q from X" is true
The complete question is:
State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.
The distance from point X to line q is the length of the segment perpendicular to line q from X .
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Dominic is working two summer jobs, making $10 per hour babysitting and making $6 per hour walking dogs. In a given week, he can work no more than 16 total hours and must earn at least $120. If x represents the number of hours babysitting and y represents the number of hours walking dogs, write and solve a system of inequalities graphically and determine one possible solution.
The system of inequalities for this problem is given by:
x + y ≤ 16.10x + 6y ≥ 120.The graphical solution is given at the end of the answer, and one possible solution is 12 hours babysitting and 3 hours walking the dog.
What is a system of inequalities?A system of equations is when two or more variables are related, and inequalities are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: number of hours babysitting.Variably y: number of hours walking dogs.He can work no more than 16 total hours, hence:
x + y ≤ 16.
He must earn at least $120, hence, considering the earnings with each activity:
10x + 6y ≥ 120.
These two inequalities compose the system. The graphical solution is composed by points that:
Are to the left of line y = 16 - x.Are to the right of line -1.67x + 20.Above y = 0, as there are no negative times.The graphical solution is given by the region shaded in blue at the end of the answer.
One possible solution inside the region is:
(12,3).
Meaning that he can work 12 hours babysitting and 3 hours walking the dog.
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Alisa has 10 yellow cars, 7 green cars, 5 red cars, 9 purple cars, 11 blue cars, 26 brown cars, and 44 black cars. How much cars does Alisa have?
Answer:
107 cars
Step-by-step explanation:
Answer:
107 cars
Step-by-step explanation:
10+7+5+9+11+26+44=107
Which equation does NOT represent a direct variation? A. y-3 x=0 B. y+2= (1/2)x C. y/x = 2/3 D. y = x/17
A. y-3 x=0 and B. y+2= (1/2)x are the equation that does not represent a direct variation.
Direct variation is a sort of proportionality in which one quantity fluctuates directly in response to a change in another number.
it is denoted as y = kx (where is the constant)
it is not directly varied if y has two x solution.
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Find the least common multiple of each pair of polynomials.
5 y² - 80 and y + 4
The least common multiple of each pair of the polynomial (5y² - 80) and
(y + 4) is equal to 5(y-4)(y+4).
As given in the question,
Given pair of the polynomial is (5y² - 80) and (y + 4)
Simplify the given polynomial using (a² -b²) = (a-b)(a +b)
(5y² - 80) = 5(y² -16)
⇒(5y² - 80) = 5(y² - 4²)
⇒(5y² - 80) = 5(y -4)(y + 4)
And (y + 4) = (1) (y+4)
Least common multiple = 5(y-4)(y+ 4)
Therefore, the least common multiple of the given pair of the polynomial is 5(y -4)(y+ 4).
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Please help me thanks
Answer:
a). 14 hours a week
b). 10.5 hours a week
Step-by-step explanation:
His time = 42 hours a week
Quarter of his time = one fourth of his time.
Third of his time = one third of his time
So, for dealing with complaints:
42h * 1/3 = 42h / 3 = 14h
On the phone:
42h * 1/4 = 42h / 4 = 10.5h
Answer:
a) 14 hours
b) 10.5 hours
Step-by-step explanation:
42 hours = 1 week
a) 1/3 hours a week dealing with complaints
[tex]\frac{1}{3} *\frac{42}{1} = \frac{42}{3} = 14[/tex]
He spends 14 hours a week dealing with complaints.
b) 1/4 hours a week on the phone
[tex]\frac{1}{4} * \frac{42}{1} = \frac{42}{4} = \frac{21}{2} = 10.5[/tex]
He spends 10.5 hours a week on the phone.
To create their special blend of coffee, the owners of The Café, use 8 pounds of dark beans
that sell for $9.20 a pound and 12 pounds of light beans that sell for $5.50 a pound. Find the price
per pound of this special blend.
Using algebraic expressions, The price per pound of this special blend will be $64.8
Let proportion of 8 pounds = x
8x + (1 - x)9.20 = 1 × 5.50
8x - 9.20x + 9.20 = 5.50
-1.20x+9.20 = 5.50
Lets get rid of the decimals for now and multiply everything by 100
= -120x+920 = 550
x = 3.08
So the proportion of the $5.54 is 1 - 37/12
Determine the weight proportion of each bean type
Price = $64.8
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can sb pls help miiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii
Answer: help is to make it easier for (someone) to do something by offering one's services or resources.
"they helped her with domestic chores"
Step-by-step explanation: hope this helps
Find the percent of the given number. 65 % of 360
A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100.
The percent of the given number 65 % of 360 is 234.
What is meant by percentage?A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100. The term percent comes from the Latin "per centum" which means per hundred. The symbol percentage is used to represent percentage.
Let the equation be 65 % of 360
Percentage = (value/total value) × 100 %.
Since, finding the fraction of a number is same as multiplying the fraction with the number, we have
65 % of 360 = 65/100 of 360
65/100 × 360 = 234
Therefore, the percent of the given number 65 % of 360 is 234.
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2/3 + r =-4/9
What’s the value of r
Answer:
-10/9
Step-by-step explanation:
I made it so that 2/3 a -4/9 had the same denominator which turned 2/3 into 6/9
then I solved normally
Please help 8 through 10
Is 1/10 greater than 0.009
Answer:
yes
Step-by-step explanation:
1/10= 0.1 0.009= something less
Answer:
Yes
Step-by-step explanation:
1/10 (or 1 divided by 10) is .01
find the values of x and y
Answer:
D
Step-by-step explanation:
Similar question to the one on your quiz
help asap please this is timed please make sure your answer is correct
The expression that best represent the given statement is mn + p. The correct option is B. mn + p
Writing an expressionFrom the question, we are to determine the expression that represents the given statement
The given statement is
"the product of quantities m and n increased by p"
The product of m and n can be written as,
m × n = mn
Increased by p means, p was added to the expression.
Thus,
The statement, the product of quantities m and n becomes
mn + p
Hence, the expression that best represent the given statement is mn + p. The correct option is B. mn + p
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1. Estimate the average rate of change of y over the interval -10≤x≤-8. Show your work
below.
Answer:
average rate of change = 4
Step-by-step explanation:
the average rate of change of f(x) in the closed interval [a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here [ a, b ] = [ - 10, - 8 ] , then
f(b) = f(- 8) = 8 ← point on graph (- 8, 8 )
f(a) = f(- 10) = 0 ← point on the graph (- 10, 0 )
average rate of change = [tex]\frac{8-0}{-8-(-10)}[/tex] = [tex]\frac{8}{-8+10}[/tex] = [tex]\frac{8}{2}[/tex] = 4
Identify the hypothesis and conclusion of conditional statement.
If you are a teenager, then you are at least 13 years old.
The hypothesis is the phrase following the word if = "you are a teenager"
The conclusion is the phrase following the word then = "you are at least 13 years old."
What is hypothesis?A specific, verifiable prediction of what the researcher(s) believe the study's results will be is known as a hypothesis (plural: hypothese). It is stated at the outset of the investigation.
Most often, this entails speculating on a potential correlation between two variables: the independent variable (what the researcher modifies) and the dependent variable (what the research measures).
The null hypothesis and the alternative hypothesis (known as the experimental hypothesis when the technique of examination is an experiment) are traditionally written as two separate forms of the hypothesis in research.
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Find the equation of the axis of symmetry of the following parabola algebraically.
y=2x^2-24x+86y
The equation of the axis of symmetry is x = 6
How to find the equation of the axis of symmetry?The equation of the parabola is given as:
y = 2x^2 - 24x + 86
Differentiate the equation of the parabola
So, we have
y' = 4x - 24
Set the differentiated equation of the parabola to 0
So, we have
4x - 24 = 0
Add 24 to both sides of the differentiated equation of the parabola
4x = 24
Divide both sides of the differentiated equation of the parabola by 4
x = 6
This represents the the axis of symmetry
Hence, the equation of the axis of symmetry is x = 6
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A football field is about 100 m long.
One of the players can run the full
distance in 25 seconds. How fast was
the player running?
Answer:
The player is running about 4 yards a second
Step-by-step explanation:
Answer:
2.5m a second
Step-by-step explanation:
What is the value of z in the solution of the system? y = -2x + 10 , -x + y - 2z=-2 , 3x - 2y + 4z = 7.
For the following system of equations: y = -2x + 10 , -x + y - 2z = -2 , and 3x - 2y + 4z = 7, the value of z in the solution is 3/2.
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using the substitution method, given three equation of three variables,
y = -2x + 10 (equation 1)
-x + y - 2z = -2 (equation 2)
3x - 2y + 4z = 7 (equation 3)
Using equation 1, substitute the value of y to equation 2 and 3.
-x + y - 2z = -2 (equation 2)
-x + (-2x + 10) - 2z = -2
-3x - 2z = -12
3x + 2z = 12 (equation 4)
3x - 2y + 4z = 7 (equation 3)
3x -2(-2x + 10) + 4z = 7
7x + 4z = 27 (equation 5)
Rewrite equation 4 as an equation of x in terms of z.
3x + 2z = 12 (equation 4)
3x = 12 - 2z
x = 4 - 2/3z (equation 4)
Substitute the new equation 4 to equation 5 and solve for z.
7x + 4z = 27 (equation 5)
7(4 - 2/3z) + 4z = 27
28 - 14/3z + 4z = 27
-2/3 z = -1
z = 3/2
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what 10982 to the nearest hunder
What rationale could Judy have provided
Using the condition needed for a graph to represent a function, it is found that:
a) It can be noticed that these graphs do not represent functions.
b) The rationale is that they have vertically aligned points.
When does a graph represents a function?A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y.
For this problem, we have that each graph has vertically aligned points, that is, they have values of x mapped to multiply values of y, hence they do not represent functions.
Examples of the vertically aligned points are given by:
In graph D, the values of x inside the circle are mapped to two values of y.In graph K, values of x > 0 are also mapped to two values of y.In graph O, in the vertical line, the coordinate of x is mapped to infinite values of y.More can be learned about graphs and functions at https://brainly.com/question/12463448
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