Use this information to answer the questions.
You are helping plan your sister's wedding. You decide to help set up a night to prepare the decorations and gift bags, but worry it all won't get done and you will be stuck doing the rest by yourself. Use the information below to help you know how long it will take to get everything done.
Question 1: You plan to have 2 people work on each task. How would you pair them up to complete each task in the shortest amount of time? Explain using rational expressions.
Question 2: What is the shortest amount of time it would take to complete all the tasks? If you know people have to leave your house by 9pm, what time should they come over to get started? Explain using rational expressions.
The best pairing to complete the task in the shortest amount of time is You and Aunt 1 and it would take them 30 minutes.
What is the Shortest Amount of Time?This represents the fastest time it takes for a person to execute a task.
The time needed for all tasks for You is:
2.5 + 5 + 1.5 = 9 hours
The time needed for all tasks for Aunt 1 is:
1.5 + 4 + 3= 8.5 hours.
9 - 8.5 = 0.5 hours
= 30 minutes
The shortest amount of time to complete all tasks is 8.5 hours by Aunt 1
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Ivan bought a suit on sale for $152. This price was 60% less than the original price.
What was the original price?
Work Shown:
x = original price in dollars
x - 60% of x = x - 0.60x = 0.40x = sale price in dollars
0.40x = 152
x = 152/0.40
x = 380
A delicatessen makes a roast-beef-on-sourdough sandwich for which you can choose from eight condiments. a. How many different types of roast-beef-on-sourdough sandwiches can the delicatessen prepare? b. What is the minimum number of condiments the delicatessen must have available if it wishes to offer at least 1000
different types of roast-beef-on-sourdough sandwiches?
Analyzing the information, it is clear that to find the solutions of the problems it is necessary to perform the calculation of mathematical arrangements.
What are arrangements?Correspond to a case of permutations, they are groupings that are formed with a number p of elements from a set of n elements. The elements of p must occupy ordered positions, where p ≤ n. The formula is:
A = n!/(n-p)!So, to solve the problems we do the following calculations:
A) 2^n =
2^8 = 256
B) We must pay attention to the statement, which asks for the minimum number of condiments required to prepare 1000 different sandwiches, so:
2^n [tex]\geq[/tex] 1000
n = 3
2^3 = 8
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The area of a rectangle is 1,036 cm and its length is 74 cm.
Find (i) its breadth (ii) its perimeter
Answer:
(i) Breadth = 14 cm
(ii) Perimeter = 176 cm
Step-by-step explanation:
Given,
Area of a rectangle = [tex]1036[/tex] cm²Length = [tex]74[/tex] cm(i) Breadth = ?
We know that, Area of a rectangle = length × breadth.
Then,
[tex]1036 = 74 \times Breadth\\1036 \div 74 = Breadth\\\boxed{\bf\:14 \:cm = Breadth }[/tex]
(ii) Perimeter of a rectangle = 2 (length + breadth)
Then,
[tex]Perimeter = 2(74 + 14)\\Perimeter = 2(88)\\\boxed{\bf\: Perimeter = 176 \: cm}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
Need help for this please
Answer:
The area of the circle is approximately 154 square meters
Step-by-step explanation:
Area of a circle formula: [tex]A = \pi r^{2}[/tex]
given:
- diameter = 14m
- pi = 22/7
[tex]radius (r) = diameter/2 = 14/2 = 7\\A = 22/7*(7)^2\\A = 22/7*(49)\\A = 154[/tex]
Find the domain in the following
Y=2x+5
Answer
All real numbers or (-∞, ∞)
Step-by-step explanation:
There aren't any X values that can make this linear equation output an invalid results, so we can deduce that the domain is all x values.
Answer:
All Real Numbers
Step-by-step explanation:
The Domain for a function simply is all the possible x values.
When graphing this function, you'll realize that it's continuous and passes all x values.
Additionally, when looking at it, you'll realize you can input any number of your choosing.
When trying to evaluate the domain of other functions, you can look at if any values of x will create an undefined value.
For example, some functions may have x in the denominator, and since the denominator can not be 0, there will be a discontinuity.
Other examples where the domain wouldn't be all real numbers would be if x was under a square root and couldn't be negative, or if the function was a vertical line.
Hope that helps, please let me know if you have any queries.
A recipe of chocolate chip cookies need 28 oz of oil for every 44 cups of flower. Approximately how many ounces of oil do you need for 89 cups of flower?
Type your answer to the nearest whole ounce
Answer:
57 ounces
Step-by-step explanation:
He needs 28 oz of oil for every 44 cups. Multiply both to get 56 oz of oil for 88. Since there is one more cup of flour, you will need one more ounce of oil.
A cylinder has a base diameter of 6 cm and a height of 18 cm. What is its volume in cubic centimeters to the nearest tenths place?
Answer:
108 cm that my answer
sana makatulong
The answer is 508.9 cubed
108cm cubed is wrong
The first three terms of an arithmetic progression are 2x, x+4, 2x - 7 respectively.
a. Find the value of x
b. Find the three terms
(6 m
c. What is the common difference?
Answer:
a) x = 7.5
b) 15, 11.5, 8
c) -3.5
Step-by-step explanation:
As there is a common difference between consecutive terms of an arithmetic progression, then:
[tex]a_3-a_2=a_2-a_1[/tex]
Given:
[tex]a_1=2x[/tex][tex]a_2=x+4[/tex][tex]a_3=2x-7[/tex]Therefore:
[tex]\implies a_3-a_2=a_2-a_1[/tex]
[tex]\implies (2x-7)-(x+4)=(x+4)-2x[/tex]
[tex]\implies 2x-7-x-4=x+4-2x[/tex]
[tex]\implies x-11=-x+4[/tex]
[tex]\implies 2x=15[/tex]
[tex]\implies x=7.5[/tex]
Inputting the found value of x into the term expressions to find the three terms of the arithmetic progression:
[tex]a_1=2(7.5)=15[/tex][tex]a_2=(7.5)+4=11.5[/tex][tex]a_3=2(7.5)-7=8[/tex]The common difference (d) is the difference between each consecutive term. To find the common difference, subtract one term from the next term:
[tex]\implies d=a_3-a_2= 8 - 11.5 = -3.5[/tex]
[tex]\implies d=a_2-a_1= 11.5-15 = -3.5[/tex]
Therefore, the common difference is -3.5
three times the sum of x and y is increased by 5
Answer:
Here is the answer .Please mark as brainliest plshope its help you
Step-by-step explanation:
3(x+y)+5=0
3x+3y+5=0
or,3x+3y= -5
Answer:
3*(x+y) + 5
Step-by-step explanation:
This is an mathematical expression....it isi NOT an equation...the question does NOT say this is equal to zero (or anything else)
it is this 3 (x+y) + 5 or 3x + 3y + 5
Find the volume of a cylinder 9in 9in
Answer:
2290.22
Step-by-step explanation:
Formula: V=pi*r^2*h
Plug in the values:
V=pi*81*9
81*pi=~254.469
~254.469 * 9 = 2290.22
you take out a cash advance of
Answer:
$0
Step-by-step explanation:
Since there is no useful data in this question, we will fill in the blanks with what we know:
Amount of cash taken: $0
Therefore, you have taken a cash advance of $0
LOL
Helllppppppp I can’t figure this out
Answer:
Step-by-step explanation:
2x^2 + 9x + 4=0
2x^2+8x+x+4=0
2x(x+4) +1 (x+4) =0
2x+1 = 0
x+ 4 =0
2x= -1
x= -1/2
x=-4
Therefore x = -4 and x = -1/2
Suppose that y varies inversely with x where x=4 and y=5. Solve for the constant
k and find the value of y when x=11
A cylinder has a diameter of 5 centimeters and a height of 50 millimeters. Which of the following steps should be done
first in order to find the surface area of the cylinder?
O multiply the circumference of the circle by the height of the cylinder
o calculate the circumference of the circle
convert the diameter and the height to the same unit
o determine the radius and multiply by 2
NEXT QUESTION
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Answer:
convert the diameter and the height to the same unit
Step-by-step explanation:
Answer: convert the diameter and the height to the same unit
Step-by-step explanation:
The surface area of a cylinder can be found with A = 2πrh + 2πr². To use this formula, all units of measurement must be the same.
This can be converting 5 centimeters to millimeters or converting 50 millimeters to 5 centimeters.
Masud rode his bike 48 miles in 6 days. He rode the same number of miles
each day. How many miles did he ride each day?
A 7
B 8
C 9
D 42
What is the value of x
Answer:
x = 25
Step-by-step explanation:
The measure of an inscribed angle in a circle is half the measure of the arc it subtends. The acute angles in a right triangle are complementary.
__
Inscribed angle CAD is half the measure of arc CD, so is 80°/2 = 40°.
Acute angle 2x° is the complement of angle CAD in the right triangle shown, so we have ...
2x° = 90° -40° = 50°
x = 25 . . . . . . . . . . . . divide by 2°
What is the radius of a cone that has a lateral area of 70TT and a total surface area of 120TT?
A)50 units
B)50TT units
C)7.1 units
D)7.117 units
Step-by-step explanation:
the lateral area of the cone is, well, the lateral area.
the total surface area of the cone is the lateral area plus the area of base circle.
so, the difference between both is the area of the base circle :
120pi - 70pi = 50pi
the area of a circle is
pi×radius²
and that is in our case
pi×radius² = 50pi
radius² = 50
radius = sqrt(50) = 7.071067812... ≈ 7.1 units
therefore, C is the right answer.
Find the perimeter of the figure below
Perimeter=
In the whole number 70,819 the place value of the digit 1 is
Step-by-step explanation:
a number is a sequence of digits with every position being multiplied by increasing powers of 10.
and the whole number is then the sum of of these little multiplications.
the first position left of the decimal point is for 10⁰ (1). the second position is 10¹ (10). the third position for 10² (100). and so on.
the given number is therefore just the short version of
7×10⁴ + 0×10³ + 8×10² + 1×10¹ + 9×10⁰
and therefore, the digit 1 in this number has the value 1×10¹ = 10, which is also the place value, 10¹ = 10.
Select the correct answer.
If the graphs of the linear equations in a system are the same line, what does that mean about the possible solution or solutions of the system?
A. There is exactly one solution.
B. There is no solution.
C. There are infinitely many solutions.
D. The lines in a system cannot graph as the same line.
Answer:
c! :))
Step-by-step explanation:
i cant exactly remember how to explain it step by step, but all i remember is that i took a similar test not too long ago that had the same question!
Answer:
C. There are infinetly many solutions.
Step-by-step explanation:
A system of linear equations has infinite solutions when the graphs are the exact same line.
Evaluate 52+[x divided3] when x=15
Answer: A. 30
Step-by-step explanation:
We will plug the value of x, 15, into the given expression. Then, we will use the order of operations, also known as PEMDAS. View attached if you need a review.
5² + (x / 3)
5² + (15 / 3)
25 + (5)
30
A. 30
If there are 12 people, and each person has 3 coins, there are ____ times as many coins as people
Answer:
Step-by-step explanation:
What is 75% of 99. Round your answer to the nearest hundredths.
Answer: 74.25
Step-by-step explanation:
75% ÷ 100 = 0.75
0.75 * 99
= 74.25
Help !!!
Geometry and the circle
Answer:
Look at the explanation.
Step-by-step explanation:
To begin with, the center of a circle is obviously the point in the middle of the circle and it has the same distance where ever you distance the center point from a point on the edges. Hope this makes sense so far. The diameter is from one point of the circle to another point of the circle and the diameter is in the middle meaning if you folded the circle upon the diameter it should be half and half. Radii are half of the diameter. Chords of a circle are "the line segment joining any two points on the circumference of the circle".
So now:
Center is Point F, Radii could be segments FU or Segment KF, Diameter is KU, Chords of the circle could be Segment, VL, GL, or DX. I hope this is correct and hope it helps....
Answer:
Step-by-step explanation:
Center
Which point is the center is just a guess. You are intended to say F.
Radii
KF FUA radius is a line that goes from the center of a circle to the circumference.
Chord
A chord is a line segment that joins two points on the circumference. Believe it or not, the diameter of a circle is a chord.
KUDKVLGLDiameter
KU
In October 2017 a pound of apples cost $1.55, while oranges cost $1.19. Two years earlier the price of apples was only $1.34 a pound and that of oranges was $1.05 a pound. What was the annual compound rate of growth in the price of apples
The annual growth rate in the price of the apple will be 7.83%.
What is the growth rate?
The growth rate is defined as the increment of any quantity over a period of time.
Given that:-
In October 2017 a pound of apples cost $1.55, while oranges cost $1.19.Two years earlier the price of apples was only $1.34 a pound and that of oranges was $1.05 a pound.The growth rate will be calculated as::-
Growth rate = Cost in 2017 / Cost in 2015
Growth rate = 1.55 / 1.34 = 1.15
The growth rate will be 15.67% for the apple in 2 years so for 1 year it will be
15.67 / 2 = 7.8%
Therefore the annual growth rate in the price of the apple will be 7.83%.
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Need Help please 3rd time posting this.
What is the equation of the circle with a radius of 7 and center at (6, -5)?
A (x + 6)2 + (y - 5)2 = 49
B (x - 6)2 + (y + 5)2 = 7
C (x + 6)2 + (y - 5)2 = 7
D (x - 6)2 + (y + 5)2 = 49
Answer:
D is the equation of the circle
Find the equation of the perpendicular line, to the line: y=2x+4
Answer:
y = -1/2 x + 4
Step-by-step explanation:
y = 2x + 4
Since this equation is in slope-intercept form, the slope of the line is 2. Perpendicular lines have slopes that are negative reciprocals of each other. Thus, the slope of a line perpendicular to this line would be -1/2.
So, any equation of the form y = -1/2 x + b
it does not matter what the y-intercept of either line is. They will remain perpendicular as long as their slopes are negative reciprocals.
suppose y is directly proportional to x and y=40 when x=10 find y if x=16
Answer:
64
Step-by-step explanation:
16/10=1.6 and 1.6x40=64
Answer: y = 64
Step-by-step explanation:
[tex]$$Given, \\$y$ is directly proportional to $x$ \\$\Rightarrow y \propto x$ (Note: ' $\alpha$ ' be proportion/various sign) \\$\Rightarrow y=k x$ ( $k$ be the constant) \\$\therefore y=k x-$ (1)[/tex]
[tex]$$Given $y=40$ when $x=10$.So, substitute $y=40 \ \& \ x=10$ in (1) we get,$$\begin{aligned}&\Rightarrow 40=k(10) \\&\Rightarrow 10 k=40 \\&\Rightarrow k=\frac{40}{10} \text { (divide '10' both sides) } \\&\Rightarrow k=4\end{aligned}$$[/tex]
[tex]$$Put $k=4$ in (1) we get,$$y=4 x$$We substitute $x=16$ in (2) we get$$\begin{aligned}y &=4(16) \\\Rightarrow y &=64 \\\end{aligned}$$[/tex]