An equation to model the situation: h = 30000 - 2000t
the altitude of the plane after 5 minutes is 20000 feet
In this question, an airplane 30,000 feet above the ground.
It begins descending at a rate of 2,000 feet per minute.
We need to write an equation to model the situation. Also, we need to find
the altitude of the plane after 5 minutes.
Let h be the altitude of plane after t hours.
So, we get an equation,
h = 30000 - 2000t
For t = 5 minutes,
h = 30000 - 2000(5)
h = 30000 - 10000
h = 20000 feet
Therefore, an equation to model the situation: h = 30000 - 2000t
the altitude of the plane after 5 minutes is 20000 feet
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Each marble bag sold by Debra's Marble Company contains 6 orange marbles for every 5 red marbles. If a bag has 40 red marbles, how many orange marbles does it contain?
left on together, the cold and hot water faucets of a certain bathtub take minutes to fill the tub. if it takes the hot water faucet minutes to fill the tub by itself, how long will it take the cold water faucet to fill the tub on its own?
The cold water faucet will fill the tub on its own in 5.6 minutes.
Let us assume the time taken by cold water faucet to fill the tub be x minutes. Now, the rate of hot water faucet to fill the tub = 1/14
Combined rate of filling by both faucets = 1/4
Rate of filling by hot water faucet + Rate of filling by cold water faucet = Rate of filling of tub by combination of two faucets
1/14 + 1/x = 1/4
1/x = 1/4 - 1/14
1/x = (14 - 4)/(4×14)
1/x = 10/56
x = 56/10
x = 5.6 minutes
Thus, cold water faucet will take 5.6 minutes.
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The complete question is -
Left on together, the cold and hot water faucets of a certain bathtub take 4 minutes to fill the tub. if it takes the hot water faucet 14 minutes to fill the tub by itself, how long will it take the cold water faucet to fill the tub on its own?
8 Ryan is 5½ feet tall. John is,5½ feet tall.
a Who is taller?
b
How much taller?
John is taller then Ryan, John is 0.08 feet taller then Ryan when John is 5 1/3 feet tall, whereas Ryan is 5 1/4 feet.
Given that,
John is 5 1/3 feet tall, whereas Ryan is 5 1/4 feet.
We have to find who is tall and how much is tall.
A fraction that has the numerator higher than or equal to the denominator is said to be improper.
Take the Ryan,
5 1/4 feet
21/4 feet
5.25 feet tall Ryan.
Take the John,
5 1/3 feet
16/3 feet
5.33 feet tall John.
We can see that John is taller then Ryan.
John is 0.08 feet taller then Ryan.
Therefore, John is taller then Ryan, John is 0.08 feet taller then Ryan when John is 5 1/3 feet tall, whereas Ryan is 5 1/4 feet.
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What does y and x stand for in an equation???
Answer: nothing it’s a variable
MODELING REAL LIFE The table represents the time x (in minutes) and the distance y (in miles) you bike.
Time, x 30 40 50 60
Distance, y 6 8 10 12
a. Write an equation in point-slope form that represents distance as a function of time.
b. interpret the slope and y-intercept
c. how far can you bike in 4 hours?
justify your answer
a. The equation in a point-slope form that represents distance as a function of time is (y - 6)= (1/5)(x - 30).
b. The slope and y-intercept are (1/5) and 0 respectively.
c. In 4 hours I can bike for 40 miles.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
We know the equation of a line in point-slope form is (y - y₁) = m(x - x₁).
Given, x represents time in minutes and y represents the distance in miles.
Let us take two ordered pairs (30, 6) and (40, 8).
Slope(m) = (y₂ - y₁)/(x₂ - x₁).
Slope(m) = (8 - 6)/(40 - 30).
Slope(m) = 2/10.
Slope(m) = 1/5.
∴ The equation of the line that represents distance as a function of time
is (y - 6)= (1/5)(x - 30).
Let y = mx + b.
6 = (1/5)30 + b.
6 = 6 + b.
b = 0.
So, y-intercept(b) = 0 and slope(m) is 1/5.
I can bike in 4 hours or (4×60) = 240 minutes is,
y = (1/5)(240) + 0.
y = 48 miles.
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An orange grower harvested oranges from 4 acres of land and collected 720 bushels of oranges. The next day, the farmer harvested oranges from 7 acres of land and collected 1,260 bushels of oranges.
Is there a proportional relationship between the number of bushels of oranges collected and the number of acres harvested over the two days? Explain.
No, it is not proportional because both variables cannot be zero at the same time.
No, it is not proportional because all ratios between the number of bushels collected and the number of acres harvested are not equivalent.
Yes, it is proportional because the farmer collected 18 bushels for every 1 acre harvested.
Yes, it is proportional because the farmer collected 180 bushels for every 1 acre harvested.
Answer:
(d) Yes, it is proportional because the farmer collected 180 bushels for every 1 acre harvested.
Step-by-step explanation:
You want to know if the ratios 4 acres : 720 bushels and 7 acres : 1260 bushels represent a proportional relationship.
ProportionA relationship is proportional if the ratio of the dependent variable to the independent variable is a constant. We can check this for the numbers given:
(720 bu)/(4 ac) = 180 bu/ac
(1260 bu)/(7 ac) = 180 bu/ac
The ratios are the same, 180 bushels for each acre, so the relationship is proportional.
Answer:
(d) Yes, it is proportional because the farmer collected 180 bushels for every 1 acre harvested.
Step-by-step explanation:
I took the exam and got it right
in a distribution with a mean of 100 and a standard deviation of 15, what is the probability that the score will be 120 or higher
0.0912 is the probability that the score will be 120 or higher .
What is probability explain with an example?
The likelihood that something will occur is the foundation of it. The justification for probability serves as the basic foundation for theoretical probability. A coin is tossed, for instance, and the theoretical likelihood of getting a head is 1 in 2.Zlower = X₁ - μ/σ = 120 - 100/15 = 1.33
the probability is compared as
Pr ( X ≥ 120 ) = Pr(X - 100/15 ≥ 120 - 100/15)
= Pr(Z ≥ 120 - 100/15
= Pr( Z ≥ 1.33)
= 0.0912
Since 0.0912 > 0.05 i.e. this IQ score is not unusual and hence I can believe the claim.
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What is the inequality shown?
Answer:
5 is > -4
Step-by-step explanation:
5 is greater than or equal to -4
i think this is the answer
Find the slope of the line graphed below.
Answer:
5/4
Step-by-step explanation:
Count up from the first point to the line where the second point lies, then write that number and count to the side till you reach the second point which would give you 5/4.
An online furniture store sells chairs for $200 each and tables for $600 each. Every day, the store can ship no more than 40 pieces of furniture and must sell no less than $12000 worth of chairs and tables. If xx represents the number of tables sold and yy represents the number of chairs sold, write and solve a system of inequalities graphically and determine one possible solution.
If the minimum 30 chairs were sold , then the minimum number of Tables sold is 10.
Given as :
The cost of each chair = $ 200
The cost of each table = $ 600
The total number of furniture sold per day = 40
The minimum amount of selling per day = $ 12000
Let the total number of chair = C
The total number of table = T
So , according to question
C + T = 40 .......1
200 C + 600 T = 12000 .......2
Solving eq 1 and 2
200 C + 600 T = 12000
200 × ( C + T ) = 40 × 200
i.e 200 C + 200 T = 8000
or, ( 200 C + 600 T ) - ( 200 C + 200 T ) = 12,000 - 8000
Or, 400 T = 4000
i.e T = 10
Put The value of T in eq 2
So, 200 C + 600 × 10 = 12000
or , 200 C + 6000 = 12,000
Or, 200 C = 12000 - 6000
Or, 200 C = 6000
i.e C = 30
The number of chair sold is 30
If the number of chair sold is 10 ,
Then the min number of table sold = 200 × 30 + 600 T = 12000
i.e 600 T = 12000 - 6000
or, 600 T = 6000
∴ T = 10
I.e T = 10
Hence, if the minimum 30 chairs were sold , then the minimum number of Tables sold is 10 .
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What is the area of a rectangle ABCD with vertices at
A(-1, 11)
B(7, 9)
C(10, 13)
D(2, 7)
The Area of the rectangle is 32 square units
Finding the Area of Rectangle with vertices:The area of the rectangle can be defined as 'the region covered by the rectangle in a 2-D plane. The formula for the area of the Rectangle or the Quadrilateral with vertices is given below
Area of Quadrilateral
= (¹/₂) | x₁y₂+ x₂y₃+ x₃y₄ +x₄y₁ - (x₂y₁ +x₃y₂ +x₄y₃ +x₁y₄) |
Where (x₁, y₁); (x₂, y₂); (x₃, y₃) and (x₄, y₄) are vertices of the quadrilateral
Here we have
Vertices of rectangle are A(-1, 11), B(7, 9), C(10, 13) and D(2, 7)
If we draw the given vertice in a graph then the order of the sides will be 'ACBD' [ For more understanding observe the given figure ]
From the above formula,
Area of rectangle
= (¹/₂) | (-1)(13) + (10)(9) + (7)(7) + (2)(11) - [ (10)(11)+(7)(13) +(2)(9) +(-1)(7) ] |
= (¹/₂) | -13 + 90 +49 + 22 - [ 110+ 91 + 18 - 7 ] |
= (¹/₂) | -13 + 90 +49 + 22 - [ 110+ 91 + 18 - 7 ] |
= (¹/₂)(64)
= 32 Square units
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This image would be used for part b.
Question B: During what interval(s) of the domain is the baseball’s height staying the same?
(btw I have to write the question)
Step-by-step explanation:
what does it mean for an object to stay at the same height ?
come on, you cannot tell me you don't understand this.
it means that e.g. the object is at a certain height (e.g. 50 ft above the ground) at the beginning of a time interval. then 1 seconds later it is still at the same height. 1 seconds after that it is still at this height. and so on.
how do you think that shows on a chart that displays height on an up or down scale ? as a flat (horizontal) line.
the chart is simply a rough picture of what the object does in real life.
so, where do we have flat (horizontal) segments in the curve ?
between second 2 and second 6.
and then infinitely after second 12.
in interval notation
[2, 6] and [12, +infinity)
please note the round bracket on the infinity side. it means the indicated end of the interval is not included. that is, because infinity is just a concept and not a number. it can never be reached. and it is therefore not included in the interval itself.
FYI - the flat line between second 2 and second 6 is not possible in real life, unless it rolls on a flat surface or something is holding it steady in place for these 4 seconds.
but a flying ball can never have a pure flat curve regarding height. only when it comes at rest on the ground. gravity would not allow that. not even for a bullet shot by a gun.
x+y=8
Let x=6. What is y?
Answer:
y = 2
Step-by-step explanation:
x + y = 8
6 + y = 8 Subtract 6 from both sides of the equation
y = 2
Which statement explains whether 0.1515 is rational?
A Yes, because 0.1515 is a repeating decimal, so it can be expressed as a ratio of integers.
B Yes, because 0.1515 is a terminating decimal, so it can be expressed as a ratio of integers.
(c) No, because 0.1515 is a repeating decimal, so it cannot be expressed as a ratio of integers.
D No, because 0.1515 is a terminating decimal, so it cannot be expressed as a ratio of integers.
A statement that explains whether 0.1515 is rational: Yes, because 0.1515 is a repeating decimal, so it can be expressed as a ratio of integers.
The correct answer is an option A
We need to select a correct statement that explains whether 0.1515 is rational.
We can observe that 0.1515 is the recurring decimal 0.15
This decimal can be written as a ratio of two integers.
Consider numerator = 5 and the denominator = 33.
So, 5/33 = 0.1515..
This means, 0.1515 can be expressed as p/q where p, q are integers with q ≠ 0
Therefore, a statement that explains whether 0.1515 is rational: Yes, because 0.1515 is a repeating decimal, so it can be expressed as a ratio of integers.
The correct answer is an option A
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The points (0,g) and (2,10) fall on a line with a slope of 6. What is the value of g?
Answer:
rise/run
(10-g)/(2-0) must equal 6
(10-g)/2 = 6
10-g = 12
-g = 2
g = -2
jenelle draws one card from a standard deck of 52 cards. determine the probability of drawing either a queen or a king? write your answer as a reduced fraction. answer
Answer:
18/7
Step-by-step explanation:
check this might work as I simply
(3x² + 15x+14) + (x+4)
Your answer should give the quotient and the remainder.
Answer:
ofco 1+1=2
Step-by-step explanation:
abc that's why
A line has a slope of 1/7 and includes the points (0,–4) and (u,–5). What is the value of u?
Answer:
u : -7
So the points are (0,-4) and (-7,-5)
Slope: 1/7
What’s 55 divided by 50,325?
Answer:
Step-by-step explanation:
0.0010928961748634
but 50,325 divided by 55 is 915
Determine the distance between the points (−6, −3) and (0, 5).
Answer: Total distance 2√10
Step-by-step explanation:
what is the slope of the line?
Answer:
The slope is 2/3
Step-by-step explanation:
y is 4 and x is 6 so it will be 4/6 then divide 2
4:2 = 2
6:2 = 3
2/3
There are 60 books that are either hardcover or softcover. The hardcover books each weigh 26 ounces. The softcover books each weigh 12 ounces. The books weigh 1,056 ounces in all
The number of hardcover books is 24 and the number of the softcover book is 36.
Here we have to find the number of hardcover and softcover.
Here it is given that 60 books are there.
Let x be the number of hardcovers, so the number of software books is 60- x.
The weight of each hardcover is 26 ounces and of softcover is 12 ounces.
The total weight is 1056 ounces.
So we get:
26x + ( 60 -x) 12 = 1056
26x - 12x + 720 = 1056
14x = 336
x = 24
60-x = 60 -24 = 36
Therefore the number of hardcovers is 24 and the number of softcovers is 36.
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The complete question:
There are 60 books that are either hardcover or softcover. The hardcover books each weigh 26 ounces. The softcover books each weigh 12 ounces. The books weigh 1,056 ounces in all. Find the number of hardcover and softcover books are there.
Find the distance from p to line n in the following questions
Line n contains points (–2, 1) and (4, 1). Point p has coordinates (5, 7).
The distance from coordinates p (5, 7) to coordinates (–2, 1) and (4, 1) in line n are 9.21 units and 6.08 units respectively.
What is the distance between two points?The distance between two points is defined as the length of the line segment between two places representing their distance.
The distance from coordinates p (5, 7) to coordinates (–2, 1) in line n will be
⇒ √[(-2-5)² + (1-7)²]
⇒ √[(-7)² + (-6)²]
⇒ √[49 + 36]
⇒ √85
⇒ 9.21 units
The distance from coordinates p (5, 7) to coordinates (4, 1) in line n will be
⇒ √[(4-5)² + (1-7)²]
⇒ √[(-1)² + (-6)²]
⇒ √[1 + 36]
⇒ √37
⇒ 6.08 units
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A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 160 lb and each box of books weighs 60 lbs. The maximum capacity of the elevator is 1110 lb. How many boxes of books can the delivery person bring up at one time?
The number of boxes that the delivery person can carry at a time is less than or equal to 15.
Given,
The weight of the delivery person = 160 lb
The weight of one box of books he carries = 60 lbs
The maximum capacity of the elevator = 1110 lb
We have to find the number of boxes of books can the delivery person bring up at one time;
Let x be the number of boxes;
Then,
The number of boxes that the delivery person can carry at a time;
160 + 60x ≤ 1110
60x ≤ 1110 - 160
x ≤ 950/60
x ≤ 15.8
That is,
The number of boxes that the delivery person can carry at a time is less than or equal to 15.
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Yani buys a certain brand of cereal that cost you $10 per box. Yani changes to a super-saving brand of the same size. The equation shows the price, y, as a function of the number of boxes, x, for the new brand. Y= 7x
Part A: How many more dollars is the price of a box if Yanis original of cereal than the price of a box of super-saving cereal? Show your work.
Part B: how much money does Yani save each month with the change In cereal brand if he buys 5 cereal boxes each month? Show your work.
Answer:
part A= 3
Part B= 15$
Step-by-step explanation:
Part A= 10-7=3
Part B = 5*10 =50 7*5= 35 50-35= 15$
-9 divided by -1 (-9+-2)
how please help
Answer:
-8 and then the second one is -11
Step-by-step explanation:
Answer:
Step-by-step explanation:
it’s negative 3
The perimeter of a playing field is 302 yards. It’s length is 7 yards longer than three times its width. What is the area of the playing field?
The area of the field is 4140 square yards.
What is a rectangle?A rectangle is a quadrilateral with all four interior angles 90°.
Given that, the perimeter of the field is 302 yards.
Let the length and width of the field be l and w respectively.
Given that, the length is 7 yards longer than three times its width, therefore,
l = 7 + 3w
The perimeter of the field is given by:
2(l +w) =302
l + w = 151
w = 151 - l..........(1)
Substitute l = 7+3w into the above equation:
w = 151 - 7 - 3w
w + 3w = 144
4w = 144
w = 36
Substitute w = 36 into equation (1):
36 = 151 - l
l = 151 - 36
l = 115
The area of the field is:
l × w
115 × 36
=4140
Hence, the area of the field is 4140 square yards.
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School rule permit no fewer than 2 teacher per 25 tudent. There are at leat 245 tudent enrolled in the chool. If x repreent teacher and y repreent tudent, which linear inequalitie can be ued to determine the poible number of teacher and tudent at the chool
The linear inequality is y≥ 245 and x ≥ 2y/25.
Linear Inequality:
Linear inequalities are defined as mathematical expressions in which two expressions are compared using the inequality symbol. The expression can be an algebraic expression or numerical expression or a combination of both.
Here it is given that x represents the teacher y represents the student.
It is given that no fewer than 2 teachers per 25 students.
x/y > 2/25
It is given that at least 245 students enrolled in the school.
As per the given condition,
The linear inequality for the students:
y≥ 245
Now the possible number of teachers (x).
As per the condition the required inequality for teachers will be:
x ≥ 2(y/25)
x≥ 2y /25.
Therefore the linear inequalities are y≥ 245 and x ≥ 2y /25.
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In a video game, Shar has to build a pen shaped like a right triangle for her animals. If she needs 9 feet of fence for the shortest side and 15 feet of fence for the longest side, how many feet of fencing is needed for the entire animal pen?
12 feet
16 feet
36 feet
38 feet
The number of feet for the fencing needed for the entire animal pen will be 36 feet. Then the correct option is C.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
In a computer game, Shar needs to construct a pen molded like a right triangle for her creatures. Assuming she wants 9 feet of wall for the most limited side and 15 feet of wall for the longest side.
Then the third side of the triangle is given as,
⇒ √(15² - 9²)
⇒ √(225 - 81)
⇒ √144
⇒ 12 feet
Then the perimeter of the triangle is given as,
P = 9 + 12 + 15
P = 36 feet
The number of feet for the fencing needed for the entire animal pen will be 36 feet. Then the correct option is C.
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Answer: 36
Step-by-step explanation: srry if wrong i used this online calculator
I need help pls this is due soon
30 points pls don't guess I really need help
Answer: x ≈ 2.67
Step-by-step explanation:
To solve, we will isolate the variable with reverse operations.
Given:
[tex]\displaystyle x^2=\frac{521}{73}[/tex]
Square root both sides of the equation:
[tex]\displaystyle x=\sqrt{\frac{521}{73}}[/tex]
Evaluate:
x = 2.6715138 ... ≈ 2.67
