Given is the direct relationship between number of produced straws and the hours of operating machine.
Given that 20,000 straws are produced in 8 hours of machine's operation.
Let's assume that 'x' straws are produced in 50 hours of machine's operation.
Using the concept of proportions, x straws in 50 hours would be proportional to 2000 straws in 8 hours.
[tex] \frac{X \;straws}{50 \;hours} =\frac{20,000 \;straws}{8 \;hours} \\\\\frac{X \;straws}{20,000 \;straws} =\frac{50 \;hours}{8 \;hours} \\\\\frac{X}{20,000} =\frac{50}{8} \\\\Cross \;multiplying \\\\8*X = 50*20000 \\\\8X = 1,000,000 \\\\\frac{8X}{8} =\frac{1,000,000}{8} \\\\X=125,000 \;straws [/tex]
Hence, total 125,000 straws would be produced in 50 hours.
for the function f(x)= -(x + 1)^2 + 4 identify the vertex, domain, and range
Answer:
Vertex = (-1, 4)
Domain = All real numbers i.e. R
Range = (-∞, 4)
Step-by-step explanation:
The vertex of the quadratic equation:
f(x) = a(x - h)² + k
Here, Vertex = (h,k)
Thus, Vertex = (-1, 4)
Domain = All real numbers i.e. R
Range = All real numbers less than or equal to 4 i.e. (-∞, 4) or f = ≤ 4.
Further, the possible values of x are called Domain.
And, the possible output we get as y is called Range.
I don't understand this question. Could anyone excplain to me what it wants me to do and what the answer is?
What is the diameter of a sphere that has a surface area of 1041 square inches?
A) 9.1
B) 22.5
C) 40.3
D) 18.2
The length of a rectangle is 4 inches less than twice its width. If the area of the rectangle is 70 square inches, what are its demensions
Easy math problem, please help.
O is the center of the circle. Assume that lines appear to be tangent are tangent. What is the value of x?
A. 34
B. 36.5
C. 73
D. 107
Answer:
Option C. 73
Step-by-step explanation:
In the given figure Δ OPQ is the right angle triangle because radius is always perpendicular to the tangent drawn on the circle from an external point.
Here OQ is radius and PO is tangent.
So ∠OQP = 90°
Now sum of all angles of a triangle is 180°
Therefore, ∠OPQ + ∠OQP + ∠POQ = 180°
17° + 90° + x° = 180°
107 + x = 180
x = 180 - 107
x = 73°
Option C. 73
Give an exact answer in simplified form. 5y+3 > -7y + 13 5y+3>−7y+13 (see pic
Th answer to the inequality will be evaluated as follows:
5y+3>-7y+3
putting like terms together we obtain:
5y+7y>3-3
2y>0
dividing both sides by 2 we get:
(2y)/2>0/2
thus
y>0
Carlos swam the perimeter of a rectangular pool seven times. If the length of the pool is 21 ft and the width of the pool is 9 ft, how many feet did Carlos swim?
The total length did Carlos swim is 420 feet.
To find the perimeter.
What is rectangle?A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees.
Given that:
Let the perimeter of rectangular swimming pool be x metres.
Then, its length =21 feet.
The width of the pool = 9 feet
The Perimeter of a rectangle =2(Length+Breadth)
According to the given condition, we have
Perimeter of a rectangle =2(Length+Breadth)
Perimeter of a rectangle=2(21+9)
Perimeter of a rectangle=2*30
Perimeter of a rectangle=60 feet
But, carlos swam the perimeter of a rectangular pool seven times.
Old perimeter=7*60=420 feet
Thus ,the total length did Carlos swim is 420 feet.
Learn more about rectangle here:
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Find the x-intercepts for the parabola defined by the equation below. y=2x^2-6x+4
What is the distance between point (3, 2) and line y = 1/4x-9
What is the length of the unknown side of the right triangle? (1 point) A right triangle with hypotenuse x and legs 5 and 12 13 17 25 60
Which equation represents a parabola with a focus at (0,-2) and a directrix of y=6?
Hey there!!
First, let's learn the parabola formula when the focus and the directrix is given.
Formula :
[tex]y = \frac{( x - a ) ^{2} }{ 2 ( b - k ) } + \frac{( b + k ) }{2}[/tex]
We have ,
Focus : ( 0 , -2 )
Hence, a = 0 and b = -2
And k = 6
Now, we will just have to plug in the values and find out the equation.
[tex]y = \frac{( x - 0 )^{2} }{2 ( - 2 - 6 )} + \frac{( - 2 + 6 ) }{2}[/tex]
[tex]y = \frac{x^{2} }{-16}+ 2[/tex]
The final equation would be :
[tex]y = \frac{-x^{2} }{16} + 2[/tex]
Hope my answer helps!!
The equation of a parabola is given. y=−16x2+7x−80 What is the equation of the directrix of the parabola?
Melissa pulls the pep club to see which sport they like. She finds that 45 students like soccer only, 35 students like football only, and 15 students like soccer and football. There is no one who doesn't like at least one of the two sports mentioned. Which venn diagram would be an appropriate model for the data melissa collected
The length of a rectangle is 7 cm less than twice its width. if the area of the rectangle is 39 cm2, find the dimensions of the rectangle.
2/3 - 4x + 7/2 = -9x + 5/6
What is the surface area of a sphere with the given dimension? Express your answer to nearest hundredth. Use 3.14 for pi. Radius = 5cm.
please help!!!
Write an expression for the volume of a cylinder with a height 7in. greater than the radius.
Which of the following best describes the following set of numbers? 6 + 8 + 10 + 12 + ... + (4 + 2n) + ...
answers:
Arithmetic SequenceGeometric SeriesGeometric SequenceArithmetic Series
Answer:
The term that best describes the given set of numbers is:
Arithmetic Series.
Step-by-step explanation:
We are given a series of numbers as:
6 + 8 + 10 + 12 + ... + (4 + 2n) + ...
Clearly as wee could see that each term in the given expression is separated by a plus sign, Hence, the given expression is a series and not a sequence.
Also as we could see that each in the series is more than the preceding term by 2 i.e. the common difference of the term is 2.
( Since, the set of numbers is given as:
[tex]a_0+a_1+a_2+a_3+....[/tex]
where,
[tex]a_n=2n+4[/tex]
[tex]when,n=0\\\\a_1=4\\\\when,n=1\\\\a_1=6\\\\and\ so\ on[/tex]
Also,
[tex]a_0-a_1=2\\\\Simialrly\\a_2-a_1=2\\\\and\ so\ on[/tex]
Hence, the common difference is 2. )
Hence, the given series is an Arithmetic series.
find the volume of the specificed cone. Use 3.14 for pie, and round your answer to the nearest whole number.
Radius=9 in., Height=8 in.
a. 1017 cu. in.
b. 151 cu. in.
c. 678 cu. in.
d. 1356 cu. in.
Write an equation to match each graph:
Write an equation to match each graph.
Solution:
The first graph is V shaped graph centered at origin, (0,0) and the graph is not shifted or translated. So, the equation of first graph is,
y=|x|
The second graph is V shaped graph centered at (1,0) and y=|x| is horizontally shifted right by 1 unit. So, the equation of second graph is,
y=|x-1|
The third graph is also V shaped but, it is inverted V graph centered at (0,1) . As, the graph is inverted V So, the graph must have y=-|x|. But, as the center is (0,1). So, the graph is shifted up by 1 unit. So, the equation of the third graph is,
y=-|x|+1
The fourth graph is shifted V graph, whose center is (1,-1). So, y=|x| is shifted right by 1 unit and down by 1 unit. So, the equation of fourth graph is,
y=|x-1|-1
The center of fifth graph is (-1,0), So, y=|x| graph is shifted left by 1 unit. So, the equation of fifth graph is
y=|x+1|
Someone please help
Roger goose had a 500-yard head start on willa. if willa's speed was 40 yards per second and roger's speed was only 20 yards per second, how long did it take willa to catch up
Greg wants to move out of his dormitory and into an apartment near his college. His parents agreed, on the condition that the rent is no more than 25% of the cost of dorm living. To get an idea of rent amounts for one-bedroom apartments, Greg looks at listings in a local newspaper and on an Internet site.
Which answer best describes the sample and population?
A. Sample: listings in a local newspaper and on an Internet site
Population: all available apartments near the college
B. Sample: all available apartments near the college
Population: all available dormitories near the college
C. Sample: all available dormitories near the college
Population: all available apartments near the college
D. Sample: all available apartments near the college
Population: listings in a local newspaper and on an Internet site
If you can buy 1⁄4 pizza for 5 dollars, how much can you purchase for 8 dollars? Write your answer as a fraction.
(08.05 HC) The work of a student to solve a set of equations is shown: Equation A: y = 15 − 2z Equation B: 3y = 3 − 4z Step 1: −3(y) = −3(15 − 2z) [Equation A is multiplied by −3.] 3y = 3 − 4z [Equation B] Step 2: −3y = 15 − 2z [Equation A in Step 1 is simplified.] 3y = 3 − 4z [Equation B] Step 3: 0 = 18 − 6z [Equations in Step 2 are added.] Step 4: 6z = 18 Step 5: z = 3 In which step did the student first make an error?
Answer:
STEP 2
Step-by-step explanation:Simplifying
-3(y) = -3(15 -2z)
should yield
-3y = -45 +6z
URGENT PLEASE HELP
Suppose 20% of all widgets produced at a factory are defective.
A simulation is used to model widgets randomly selected and then recorded as defective or working.
Which simulation best models the scenario?
Place 50 equally sized pieces of paper in a hat. Of the 50, 5 read “defective” and the rest read “working”.
Place 25 equally sized pieces of paper in a hat. Of the 25, 5 read “defective” and the rest read “working”.
Place 20 equally sized pieces of paper in a hat. Of the 20, 5 read “defective” and the rest read “working”.
Place 100 equally sized pieces of paper in a hat. Of the 100, 5 read “defective” and the rest read “working”.
What is the measure of BAC
50
80
100
130
Pete is purchasing an mp3 player for 199.90 he gives the sales clerk 2 fifty dollar bills, 4 twenty dollar bills and 4 five dollar bills how much should he receive back
Which expression is equivalent to mc003-1.jpg?
Answer:
Option A is correct
The expression which is equivalent to [tex](f\cdot g)(5)[/tex] is [tex] f(5) \cdot g(5)[/tex]
Step-by-step explanation:
Using the formula:
[tex](f \cdot g)(x) = f(x) \cdot g(x)[/tex] .....[1]
Given the expression:
[tex](f\cdot g)(5)[/tex]
Substitute the value of x = 5 in [1]
we get;
[tex](f \cdot g)(5) = f(5) \cdot g(5)[/tex]
Therefore, the expression which is equivalent to [tex](f\cdot g)(5)[/tex] is [tex] f(5) \cdot g(5)[/tex]
Solve a(x - b) - 2k = l for k
. Stephen deposited $1800 into a savings account for which interest is compounded weekly at a rate of 3.2%. How much interest will he earn after 10 years?
58.81
678.59
2478.59
im just putting this up to see if my answer was write. i did the math and unless i messed up writing i got the second answer