Answer:
e) Shamika= 224 balloon, Crystal= 112 balloon, Aliya= 114 Balloon.
f) We know,Crystal sold "b" balloon
Aliya sold (b+2) balloon
Shamika sold 2b balloon.
As per data given in question part c that each balloon cost $2 and Total cost of balloon is $900.
Now, solving to find how much each student sold balloon at school´s winter dance.
As we know total cost is $900 and each balloon cost is $2.
∴ Total cost= [tex]Total\ quantity \times cost\ of\ each\ unit[/tex]
Total quantity= [tex]{b+(2+b)+2b}[/tex]
∴ [tex]\$ 900= {b+(2+b)+2b}\times \$ 2[/tex]
Once we solve, we will get the value of b as 112 balloon, which is the number of balloon sold by Crystal.
Substituting the value of b in the equation of Aliya and Shamika, we will get the number of balloon sold by them.
Which is 114 and 224 respectively.
Step-by-step explanation:
Given: Crystal sold "b" balloon
Aliya sold (b+2) balloon
Shamika sold 2b balloon.
As per data given in question part c that each balloon cost $2 and Total cost of balloon is $900.
Now, solving to find how much each student sold balloon at school´s winter dance.
As we know total cost is $900 and each balloon cost is $2.
∴ Total cost= [tex]Total\ quantity \times cost\ of\ each\ unit[/tex]
Total quantity= [tex]{b+(2+b)+2b}[/tex]
∴ [tex]\$ 900= {b+(2+b)+2b}\times \$ 2[/tex]
Opening the parenthesis.
⇒[tex]\$ 900= (b+2+b+2b)\times \$ 2[/tex]
⇒[tex]\$ 900= 2+4b \times 2[/tex]
Dividing both side by 2
⇒ [tex]\$ 450= 2+4b[/tex]
Subtracting both side by 2
⇒ [tex]\$ 448= 4b[/tex]
Cross multiplying
∴[tex]b= \frac{448}{4} = 112[/tex]
∴ b= 112.
Hence, we can say Crystal have sold 112 balloons.
Next subtituting the value of "b" in the equation for Aliya and Shamika to get number of balloon they have sold.
We know, Aliya sold b+2 balloons
∴ Aliya sold= [tex]112+2= 114\ balloon[/tex]
Aliya sold 114 balloon.
We know, Shamika sold 2b balloons
∴[tex]2\times 112= 224 balloon.[/tex]
Shamika sold 224 balloon.
The area of a trapezium is 34 cm and the length one of its parallel side is
10.4cm and its height is 4cm.Find the length of the other parallel side.
Answer:
6.6 cm.
Step-by-step explanation:
The area of a trapezium A = (h/2)(a + b) where h = the height, a and b are the length of the parallel sides.
So substituting the given values in this formula:
34 = (4/2)(10.4 + b)
34 = 2(10.4 + b
34 = 20.8 + 2b
2b = 34 - 20.8 = 13.2
b = 6.6 cm.
Select the correct answer.
Does the equation below represent a relation, a function, both a relation and a function, or neither a relation nor a function?
y = 3:2 – 93 + 20
A.
neither a relation nor a function
B. both a relation and a function
C.
function only
D.
relation only
Answer:
A
Step-by-step explanation:
neither a relation nor a function
Answer:
NOTE: This is the answer for the equation (y=3x^2-9x+20) Both a Relation and a Function
Step-by-step explanation:
Because a Relation can be represented as a verbal descriptions, graphs, mapping diagrams, equations, list ordered pairs, and tables. Which in this case is an equation so its a RELATION.
A function is a type of relation in which every x-value in the domain is paired with exactly one y-value. Which in this case every x-value is paired with one Y-value.
Let me know if this helps. :)
What is an equivalent expression for 1.5(3x + 4) + 0.25(6x + 8)?
Answer:
6x+8
Step-by-step explanation:
To answer this question we just simply use the distributive property to get rid of the parenthesis.
1.5*3x=4.5x
1.5*4=6
So the first parenthesis cancelled out would be : 4.5x+6
Now, onto the second:
0.25*6x=1.5x
0.25*8=2
So the second one is : 1.5x+2
Not that we have distributed both things, we add these.
4.5x+6+1.5x+2 we combine like terms
4.5x+1.5x=6x
6+2=8
So, the answer is 6x+8
Answer:
6x+8
Step-by-step explanation:
Took the question
Robert has seven more than five times the number of video games Sam has. All together they have 25 video games. How many video games does Robert have?
Answer:
Step-by-step explanation:
r = 5s + 7
r + s = 25
5s + 7 + s = 25
6s + 7 = 25
6s = 25 - 7
6s = 18
s = 18/6
s = 3 <=== sam has 3 video games
r = 5s + 7
r = 5(3) + 7
r = 15 + 7
r = 22 <=== robert has 22 video games
simplify 3(2x- 3xy) + 5x-5xy
Answer:
11x-14xy
Step-by-step explanation:
3(2x- 3xy) + 5x-5xy
=6x-9xy+5x-5xy
=11x-14xy
Answer: The answer is 11x-14xy
Step-by-step explanation:
3(2x- 3xy) + 5x-5xy
6x-9xy+5x-5xy
6x+5x-9xy-5xy
11x-14xy
how do you solve for x on this problem?
3x=7.5
Answer:X=2.5
Step-by-step explanation:
Divide both sides by 3
3 over 3 cancels out and 7.5 over 3 equals 2.5
Answer:
x= 2.5
Step-by-step explanation:
divide both sides by 3
Tracy deposited $59 into a bank account that earned 3.5% simple interest each year.
If no money was deposited into or withdrawn from the account, how much money was in the account after 112 years?
Round your answer to the nearest cent.
Enter your answer in the box.
$
/second questoin Vanessa deposited money into a bank account that earned 1.25% simple interest each year. After 12 year, she had earned $5.00 in interest on the account.
If no other money was deposited into or withdrawn from the account, how much was her initial deposit?
Enter your answer in the box.
$
Answer:
Step-by-step explanation:
1) Tracy:
P =$ 59 ; r =3.5% ; T = 12 years
SI = PrT/100
= 59 * 3.5 * 12 /100
= $24.78
Amount Tracy that will be after 12 years in her account = $ 59 +$24.78
= $83.78
Find the constant of proportionality if y is directly related to x when y = 12 and x = 6
Answer:
2
Step-by-step explanation:
Please see attached picture for full solution.
if 42 butterflies were seen in 3 hours at that rate how many butterflies were seen per hour
Answer: 14 butterflies per hour
Step-by-step explanation: "Per hour" means in 1 hour so we can rewrite the given statement using fractions.
42 butterflies over 3 hours = ___ butterflies per hour.
I have attached my work in the image provided.
To find out what goes in the blank, notice that we have a 1 in the denominator of our second fraction. So we want to find a fraction that is equivalent to 42/3 that has a 1 in the denominator.
If we divide the numerator and denominator of 42/3 by 3, we get the equivalent fraction 14/1 or 14 butterflies over 1 hour. So now we have 14 butterflies over 1 hour = ___ butterflies per hour.
Now we can easily see that a 14 must go in the blank which means that the unit rate for 42 butterflies in 3 hours is 14 butterflies per hour.
Decide whether the two events are disjoint and tell why or why not:
• randomly drawing a jack from a standard deck of cards
• randomly drawing an ace from a standard deck of cards
Disjoint, because the events can occur at the same time.
Not disjoint, because the events can occur at the same time.
Not disjoint, because the events cannot occur at the same time.
Disjoint, because the events cannot occur at the same time.
Answer:
Disjoint, because the events cannot occur at the same time.
Step-by-step explanation:
disjoint events are mutually exclusive events.
if a and b are two events then a intersection b will be 0 . they cannot occur at the same time.
here in the given problem let the event A be randomly drawing a jack from a standard deckn of card and evnt B be randomly drawing an ace from a standard deck of card.
since in a same card jack and ace cannot occur they are disjoint events.
therefore randomly drawing a jack from a standard deck of cards and randomly drawing an ace from a standard deck of cards are disjoint events because the events cannot occur at the same time.
The two events are disjoint because a card from a standard deck cannot be both a jack and an ace at the same time. That is, these events cannot occur simultaneously.
Explanation:In the given scenario, the two events - randomly drawing a jack from a standard deck of cards and randomly drawing an ace from a standard deck of cards - are disjoint. This is because these are separate and distinct events which cannot occur simultaneously. In terms of probability theory, two events are considered disjoint if the occurrence of one event excludes the possibility of the occurrence of the other event. In a standard deck of cards, a card cannot be both a jack and an ace at the same time.
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after placing an equation into his calculator Rob got the following table. He then determine that X=6 when f (x) = -4 is he correct? explain
x | f(x)
——————
-4 | 6
——————
-2 | 3
——————
0 | -1
——————
2 | -4
Answer:
f(6) = - 4 is incorrect.
Step-by-step explanation:
In the given table the values of x and corresponding values of f(x) are given.
The ordered pairs are (-4,6), (-2,3), (0,-1) and (2,-4).
Now, we have to determine the function y = f(x) from any two of the given ordered pair.
The equation of the function is
[tex]\frac{y - 6}{6 - 3} = \frac{x - (- 4)}{- 4 - (- 2)}[/tex]
⇒ -2(y - 6) = 3(x + 4)
⇒ 2y + 3x = 0 ........... (1)
Now, putting x = 6 in the above equation (1), we get y = - 9
Therefore, f(6) = - 9
Hence, f(6) = - 4 is incorrect. (Answer)
Hii:) is this the simplest form or can it be further simplified? Thanks :)!
Step-by-step explanation:
[tex](12 + 3 \sqrt{2 } - 2 \sqrt{5} )(2 + 3 \sqrt{2} + 2 \sqrt{5} ) \\ = 24 + 36 \sqrt{2} + 24 \sqrt{5} + 6 \sqrt{2} + 18 + 6 \sqrt{10} - 4 \sqrt{5} - 6 \sqrt{10} - 20 \\ = 22 + 42 \sqrt{2} + 20 \sqrt{5} [/tex]
if an object has an acceleration of 7 m/s, and a mass of 3 kg, what is its force?
Answer:
force = 21 kg m/s^2 = 21 N
Step-by-step explanation:
If an object has mass (m) 3 kg, and its acceleration (a) is 7 m/s^2, its force is given by Newton's second law of motion: Force = M * a
Force = 3 kg * 7 m/s^2= 21 kg * m/s^2
This combinations of units (kg * m/s^2) is defined as Newtons in physics and abbreviated "N".
So we can say that the force on this object is of magnitude 21 N
rearrange the equation so u is the independent variable. 4u+8w=-3u+2w
The equation in terms of u as independent variable is w = (-7/6)u
What is an Independent Variable ?A variable upon which another variable depends is called an Independent variable , On changing the value of the independent variable , the dependent variable changes .
The equation given is
4u +8w = -3u+2w
8w -2w = -3u - 4u
6w = -7u
w = (-7/6) u
Therefore the equation in terms of u as independent variable is w = (-7/6)u.
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Answer:
the equation rearranged with [tex]\( u \)[/tex] as the independent variable is:
[tex]\[ u = -\frac{6}{7}w \][/tex]
Step-by-step explanation:
To rearrange the equation so that [tex]\( u \)[/tex] is the independent variable, we need to isolate [tex]\( u \)[/tex] on one side of the equation.
Starting with the given equation:
[tex]\[ 4u + 8w = -3u + 2w \][/tex]
First, add [tex]\( 3u \)[/tex] to both sides to get all the [tex]\( u \)[/tex] terms on one side:
[tex]\[ 4u + 3u + 8w = -3u + 3u + 2w \][/tex]
[tex]\[ 7u + 8w = 2w \][/tex]
Next, subtract [tex]\( 8w \)[/tex] from both sides to get all the [tex]\( w \)[/tex] terms on the other side:
[tex]\[ 7u + 8w - 8w = 2w - 8w \][/tex]
[tex]\[ 7u = -6w \][/tex]
Finally, divide both sides by [tex]\( 7 \)[/tex] to solve for [tex]\( u \)[/tex]:
[tex]\[ \frac{7u}{7} = \frac{-6w}{7} \] \[ u = -\frac{6}{7}w \][/tex]
So, the equation rearranged with [tex]\( u \)[/tex] as the independent variable is:
[tex]\[ u = -\frac{6}{7}w \][/tex]
This is the final answer, with [tex]\( u \)[/tex] isolated on one side of the equation.
a moving walkway at an airport moves at a pace of 1.75 feet per second
if you stand on the walkway as it moves how long will it take to transport you 280 feet
Answer:
The time taken to move distance of 280 feet at the speed of 1.75 feet per second is 160 seconds
Step-by-step explanation:
Given as :
The speed of the moving walkway at an airport = s = 1.75 feet per second
The distance cover on the walkway = d = 280 feet
Let The time taken to move 280 feet = t sec
Now, According to question
Time = [tex]\dfrac{\textrm distance}{\textrm speed}[/tex]
t = [tex]\dfrac{\textrm d}{\textrm s}[/tex]
t = [tex]\dfrac{\textrm 280 feet}{\textrm 1.75 ft per sec}[/tex]
t = 160 seconds
So, The time taken to move distance of 280 feet at the speed of 1.75 feet per second = t = 160 seconds
Hence, The time taken to move distance of 280 feet at the speed of 1.75 feet per second is 160 seconds . Answer
the binomial 8x+6 is equivalent to
Using the Distributive Property
The answer would be 3.
2 *4x = 8x and 2 * 3 = 6, to get 8x 6
When a company dropships its products to customers following a Web-based purchase, they _____.
do not keep products in inventory; rather an order is sent to the manufacturer or distributor who then fills the order and sends it to the customer
maintain a fleet of aircraft and delivery vehicles that they use to ship worldwide overnight, dropping off the package to the consumer by 10:00 AM
drop or fail to fill the order
None of the above
Answer: on oddysey its
A) do not keep products in inventory; rather an order is sent to the manufacturer or distributor who then fills the order and sends it to the customer
Step-by-step explanation:
HELP PLEASE!!
What is a line segment?
Step-by-step explanation: To understand what a line segment, we first need to introduce the most basic figure in geometry which is called a point. A point in usually labeled with a capital letter. For example, .A.
When we have two points such as points X and Y, we can introduce our next figure in geometry which is called a line segment. For example, segment XY. A line segment is defined as a figure that's composed of two points which are called the endpoints and all the points in between.
Segment XY can be represented as XY with a segment drawn over it like I have attached in in the image provided.
Find the slope of the line passing through the points (2,3) and (2,-4)
Answer:
Undefined
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-4-3)/(2-2)
m=-7/0
undefined
Answer:
UndefinedStep-by-step explanation:
[tex]\bold{METHOD\ 1:}\\\\\text{The first coordinates of the points (abscissa) are the same.}\\\text{Conclusion: This is a vertical line.}\\\text{The vertical line has the equation x = a (here x = 2). It has no slope.}\\\\\boxed{\text{Answer: unde}\text{fined}}[/tex]
[tex]\bold{METHOD\ 2:}\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{Substitute the coordinates of the given points}\ (2,\ 3)\ \text{and}\ (2,\ -4).\\\\m=\dfrac{-4-3}{2-2}=\dfrac{-7}{0}\\\\\text{The denominator must be different from 0.}\\\text{The expression}\ \dfrac{-7}{0}\ \text{ has no numerical sense.}\\\\\boxed{\text{Conclusion and naswer: unde}\text{fined}}[/tex]
g is the centroid of triangle abc what is the length of gf
Answer:
26
Step-by-step explanation:
The length of GF if, G is the centroid of the triangle ABC is 26.
What is triangle?
Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric shapes, it is represented by the symbol and consists of three connected vertices.
Given:
G is the centroid of the triangle ABC,
The line segment BD can be written as,
40 is 2x as long as 9x+2
The equation can be written as for the above statement.
40 = 2(9x + 2)
40 = 18x + 4
36 = 8x
x = 2
Put the value of x = 2 in 19X + 14, and divide that answer by 2, because GF is 2x smaller than AG
19x + 14
19 (2) + 14
52
Thus, the length of GF = 52 / 2 = 26.
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if 2.1x+4.2y=14.7 and
−5.7x−1.9y=−11.4
what is x and what is y?
Answer:
Step-by-step explanation:
another 10second challenge is wich expresion has a lesser value?
Answer:
Therefore
Greater Value Expression is Expression ( 2 ) i.e [tex]3\times (492 - 166)\\[/tex]
Lesser Value Expression is Expression ( 1 ) i.e [tex]\frac{1}{3}\times (492 - 166)\\[/tex]
Step-by-step explanation:
Given:
[tex]\frac{1}{3}\times (492 - 166)\\[/tex] ............Expression ( 1 )
[tex]3\times (492 - 166)\\[/tex] ............Expression ( 2 )
To Find:
Which Expression has a lesser value ?
Solution:
First we will solve Expression ( 1 ) we get
[tex]\frac{1}{3}\times (492 - 166)=\frac{1}{3}\times 326=108.66[/tex]
Now we will solve Expression ( 2 ) we get
[tex]3\times (492 - 166)=3\times 326=978[/tex]
Therefore
Greater Value Expression is Expression ( 2 ) i.e [tex]3\times (492 - 166)\\[/tex]
Lesser Value Expression is Expression ( 1 ) i.e [tex]\frac{1}{3}\times (492 - 166)\\[/tex]
88511, 16351, ?, 10251
Complete the sequence
Answer:
73155
Step-by-step explanation:
To find sequence, we need to find the pattern of number.
88511= [tex]8 + 8, 8-5, 5\times 1, \frac{1}{1} = 16351[/tex]
16351= [tex]1+6,6-3,3\times 5,\frac{5}{1} = 73155[/tex]
73155= [tex]7+3, 3-1, 1\times 5, \frac{5}{5} = 10251[/tex]
10251
The missing number in the sequence '88511, 16351, ?, 10251' is 60809, as the pattern in this sequence is to subtract 77160 from the previous number and take its absolute value.
Explanation:This is an example of a number sequence problem. Let me explain how we can find the missing number in the sequence '88511, 16351, ?, 10251'. To solve this, we need to identify the pattern used to generate this sequence. In this case, it appears the number 77160 (88511 - 16351) is subtracted to get the next number.
So if we subtract 77160 from 16351, we get -60809. But given the pattern of the sequence, all numbers are positive. Therefore, we need to take the absolute value of the result to fit the sequence. So our missing number would then be 60809.
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What is the final price with discount off 25% off $30
Answer:
$22.50
Step-by-step explanation:
25% of $30 is 22.5
Answer:
$22.50
Step-by-step explanation:
25% of 30 is 22.5
find the exact values of sin θ/2 and cos θ/2 for sin θ = 3/4 on the interval 0° ≤ θ ≤ 90°
Answer:
Step-by-step explanation:
If our interval is between 0 and 90 degrees, that means that our angles are first quadrant angles. Since the formulas for the half angles of sin and cos consider both the positive and negative roots, knowing that we are in QI leaves us using only the principle, or positive, root.
Also, if we know that the sin of angle is 3/4, we can set up a right triangle in QI and find the missing side of that triangle using Pythagorean's Theorem. Sin of an angle is the ratio opposite side/hypotenuse. That means that, according to Pythagorean's Theorem,
[tex]4^2=3^2+b^2[/tex] and
[tex]16-9=b^2[/tex] and
[tex]b=\sqrt{7}[/tex]
Now for the forula for the sin of a half-angle:
[tex]sin(\frac{\theta}{2})=\sqrt{\frac{1-cos\theta}{2} }[/tex]
Referring to the right triangle we created and found the missing side for, we see that the cosine of that same triangle is [tex]\frac{\sqrt{7} }{4}[/tex]
Filling in the formula then:
[tex]sin(\frac{\theta}{2})=\sqrt{\frac{1-\frac{\sqrt{7} }{4} }{2} }[/tex]
Get a common denominator on the upper fraction:
[tex]sin(\frac{\theta}{2})=\sqrt{\frac{\frac{4-\sqrt{7} }{4} }{2} }[/tex]
Bring up the 2 as 1/2 to multiply and get:
[tex]sin(\frac{\theta}{2})=\sqrt{\frac{4-\sqrt{7} }{8} }[/tex]
When you do the exact same thing to find the cos of the half angle, you are using a + sign instead of a - sign under the radical. That gives you as your exact value:
[tex]cos(\frac{\theta}{2})=\sqrt{\frac{4+\sqrt{7} }{8} }[/tex]
You are helping a coworker with a presentation and he has asked you to print out memos on a variety of colored paper. 60 will be attending and he needs 60% of the memos to be blue, 20% to be red, 15% to be green, and 5% to be yellow. How many green memos do you need to print
Answer:
Step-by-step explanation:
60 will be attending......15% of the memos are green
so u need to print : 15% of 60.....turn ur percent to a decimal...." of " means multiply
0.15(60) = 9 <==== u need to print 9 green memos
The number of green memos is 9.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The number of green memos is calculated as:-
60 will be attending and 15% of the memos are green
print: 15% of 60.
0.15 x (60) = 9
The number of green memos will be 9.
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8. In 1986, an accident at the Chernobyl nuclear power reactor led to widespread
contamination of Cesium-137, a highly radioactive, man-made isotope of Cesium. It has a
half-life of 30.17 years, which means it decays at a rate of 2.3% per year. It is estimated
that nearly 191,500 kBq/m² was leaked during the disaster. How much of the material is
still radioactive now, 25 years later?
Answer:
79,342.061650646
Step-by-step explanation:
if 1/2 9f life is 30.17
complete life is 60.34
KE= 1/2 mvsquared
for v
Answer:
v=sqrt(2KE/m), -sqrt(2KE/m)
Step-by-step explanation:
KE=1/2mv^2
v^2=KE/(1/2m)
v^2=KE/(m/2)
v^2=KE(2/m)
v^2=2KE/m
v=sqrt(2KE/m), -sqrt(2KE/m)
What is the value of 5 ^ 3 * i ^ 9
Answer:
Step-by-step explanation:
5 ^ 3 = 5 * 5 *5 = 125
i⁹ = i⁴ * i⁴ * i = 1 * 1 * i = i
5 ^ 3 * i ^ 9 = 125 * i = 125i
5 ^ 3 * i ^ 9
Answer: 125i
Step-by-step explanation:
An engineer is planning a new water pipe installation. The circular pipe has a diameter of d=20\text{ cm}d=20 cmd, equals, 20, start text, space, c, m, end text.
What is the area AAA of the circular cross section of this pipe?
Give your answer in terms of pi.
Area of circular pipe in terms of pi is found as [tex]100 \pi[/tex] square centimeter
Solution:
Given that an engineer is going to install a new water pipe. The diameter of this circular pipe is, d = 20 cm
We have to find the area 'A' of the circular cross-section of the pipe.
Given, diameter of the circular section is:
diameter = 20 cm
Let us find the radius
[tex]radius = \frac{diameter}{2}\\\\r = \frac{20}{2} = 10[/tex]
Thus radius = r = 10 cm
The area 'A' of the circular cross-section of the pipe measn we can use the area of circle formula
The area of circle is given as:
[tex]area = \pi r^2[/tex]
Where "r' is the radius of circle
We have to find area in terms of pi
[tex]area = \pi (10)^2\\\\area = \pi \times 10 \times 10\\\\area = 100 \pi[/tex]
Thus area of circular pipe in terms of pi is found as [tex]100 \pi[/tex] square centimeter