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Explanation:
Roy spends 1/4 of his money on 3 pens and 6 notebooks. That means 3/4 of it is leftover.
2/3 of 3/4 = (2/3)*(3/4) = 1/2 of his money is spent on buying some unknown number of additional pens. We'll come back to this later.
---------------
In terms of cost,
1 pen = 3 notebooks
which is another way of saying 1 pen is the same price as 3 notebooks.
Multiply both sides by 2 to get
2 pens = 6 notebooks
Therefore, saying "3 pens + 6 notebooks" is the same as "3 pens + 2 pens = 5 pens" when just thinking about costs.
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In short, Roy buying 3 pens and 6 notebooks is the same as him buying 5 pens. He spends 1/4 = 25% of his money on getting these 5 pens.
Multiply those two values by 2 to find that 50% = 1/2 of his money would allow him to get 10 pens.
--------------
Recall that at the end of the first section, we concluded that Roy spent 1/2 of his money on buying those unknown additional number of pens. Then the previous section mentioned that 1/2 of his money gets him 10 pens. Therefore, he must have bought 10 additional pens on top of the original 3 mentioned in the instructions.
Overall, he purchased 3+10 = 13 pens
Answer:
13 pens
Step-by-step explanation:
If a pen costs 3 times the cost of a notebook, then the cost of 3 notebooks will equal the cost of a pen. The 6 notebooks that Roy bought are equivalent in cost to 2 pens, so 1/4 of Roy's money is the cost of 3+2 = 5 pens.
After the first purchase, Roy has (1 -1/4) = 3/4 of his money remaining. If he spends 2/3 of that on more pens, he will have spent ...
(2/3)(3/4) = 2/4
of his money on more pens. We've already seen that 1/4 of his money buys 5 pens, so 2/4 will buy 10 more pens.
Roy bought 3 +10 = 13 pens altogether.
a cookie recipe included 2/3 cups of sugar for 12 cookies, how many cups of sugar will you need if you wanted to make 42 cookies
Answer:10/6 cups of sugar is the answer to this equation being the correct answer.
Step-by-step explanation:
What is the "theoretical yield" of cookies from each of the "reactants?"
Express the following as mathematical statements or phrases. 1. Twice the product of the number 2. Seven less than a number 3. The sum of three consecutive numbers 4. The sum f two consecutive even numbers is 42 5. The sum of a number and 5 times its reciprocal 6. Four more than twice a number 7. The square of a number increase by five 8. The sum of two numbers is equal to four more than their difference 9. Rian's age four years from now 10. Clara's age 10 year from now
Answer:
See belowStep-by-step explanation:
Let x or y be the variable in each case.
1. Twice the product of the numbers ... x and y (just a guess, its incomplete):
2xy2. Seven less than a number:
x - 73. The sum of three consecutive numbers:
x + (x + 1) + (x + 2)4. The sum of two consecutive even numbers is 42:
2x + 2x + 2 = 425. The sum of a number and 5 times its reciprocal:
x + 5*(1/5)6. Four more than twice a number:
4 + 2x7. The square of a number increase by five:
x² + 58. The sum of two numbers is equal to four more than their difference:
x + y = 4 + (x - y)9. Rian's age four years from now:
x + 410. Clara's age 10 year from now:
x + 10Step-by-step explanation:
1. Let, Number = x
2x
2. Let, Number = x
x - 7
3. Let,
Consecutive numbers = x, x + 1 and x + 2
x + x + 1 + x + 2
3x + 3
4. Let,
Consecutive numbers = a and a + 2
a + a + 2 = 42
2a + 2 = 42
5. Let, Number = x
Reciprocal = 1/x
x + 5/x
6. Let, Number = y
2y + 4
7. Let, Number = y
(x + 8)²
x² + 16x + 64
8. Let,
First number = x
Second number = y
x + y = 4 + (x - y)
9. Let,
Rian's age = y
y + 4
10. Let,
Clara's age = y
y + 10
Can somebody please help me with this true or false algebra 1 question?
A relation that pairs each input with exactly one output is a function.
True or False
I'll help.
The answer to your question is True!!
find the equivalent fraction 2/6= __ 2/5= ___
Question 8 Tasha noticed that bags are not selling quite well. She reduced the original price of $300 by 20%. After, three months the bags were still not selling.She reduced the price again by 40%. A, What was the total percent of decrease? Show your work.
Answer:
84% decrease
Step-by-step explanation:
100 - 80 = 20%
80% = 4/5
300 * 4/5 = 240
100 - 40 = 60%
60% = 3/5
240 * 3/5 = 48
48/300 = 4/25 = 16%
100 - 16 = 84%
3. Twenty-five percent of Santa's elves
decorated the North Pole. If 150 elves
decorated, how many total elves live in
the North Pole?
A line includes the points (-7, 1) and (7, -1). What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y=-1/7x
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-1-1)/(7-(-7))
m=-2/(7+7)
m=-2/14
simplify
m=-1/7
--------------------
y-y1=m(x-x1)
y-1=-1/7(x-(-7))
y-1=-1/7(x+7)
y=-1/7x-7/7+1
y=-1/7x-1+1
y=-1/7x
Marty is 54 years old, and his niece is 6. How many times older is Marty than his niece? Choose the answer that has the correct equation AND the correct solution to the equation.
6x = 54; x = 8 times older
54 + x = 6; x = 48 times older
6x = 54; x = 9 times older
54x = 6; x = 9 times older
Answer:
6x = 54; x = 9 times older
Step-by-step explanation:
Which of the following situations can be modeled by the expression 5 - (-3)?
Kylie is three years younger than Tyler, and Claire is five years older than Kylie. How many years separate Tyler and Claire?
Kylie is three years younger than Tyler, and Claire is five years older than Tyler. How many years separate Kylie and Claire?
None of the above.
Kylie is three years younger than Tyler, and Claire is five years younger than Tyler. How many years separate Kylie and Claire?
Answer:the first option
Step-by-step explanation:
25 Points please help!!!
Answer:
The one you clicked on in the picture is correct
Step-by-step explanation:
By elimination you can tell that it is the bottom two answers (+3 is inverse of -3). And it is the answer you selected because it cube roots whats in parentheses. So you are correct with the answer you have selected right now
Using the unit circle, determine the value of sin 450°
Answer:
To find the value of sin 450 degrees using the unit circle, represent 450° in the form (1 × 360°) + 90° [∵ 450°>360°] ∵ sine is a periodic function, sin 450° = sin 90°.
Answer:
1
Step-by-step explanation:
To find the value of sin 450 degrees using the unit circle, represent 450° in the form (1 × 360°) + 90° [∵ 450°>360°] ∵ sine is a periodic function, sin 450° = sin 90°.
Rotate ‘r’ anticlockwise to form a 90° or 450° angle with the positive x-axis.
The sin of 450 degrees equals the y-coordinate(1) of the point of intersection (0, 1) of unit circle and r.
Hence the value of sin 450° = y = 1
List all the factors of 42 from least to greatest. Enter your answer below,
using a comma to separate each factor.
Answer Here
SUBMIT
Answer:
Factors of 42: 1, 2, 3, 6, 7, 14, 21 and 42.
Step-by-step explanation:
:)
Activity 3.
Direction. Name the ratio as a fraction in simplest form.
1. P5.00 to P60.00
2. 1 hour to 40 minutes
3. 2 weeks to 4 days
4. Eight out of 30 passengers are tourist. Give the ratio of tourist to passengers.
5. For every 45 passengers, 9 are foreigners. Write the ratio of foreigners to
passengers.
Please answer please help me
Answer:
see explanation
Step-by-step explanation:
(1)
[tex]\frac{5}{60}[/tex] ( divide numerator/ denominator by 5 )
= [tex]\frac{1}{12}[/tex] ( in simplest form )
(2)
both quantities must have the same units
1 hour = 60 minutes , then
[tex]\frac{60}{40}[/tex] ( divide numerator/ denominator by 20 )
= [tex]\frac{3}{2}[/tex] ( in simplest form )
(3)
1 week = 7 days then 2 weeks = 2 × 7 = 14 days , so
[tex]\frac{14}{4}[/tex] ( divide numerator/ denominator by 2 )
= [tex]\frac{7}{2}[/tex] ( in simplest form )
(4)
[tex]\frac{8}{30}[/tex] ( divide numerator/ denominator by 2 )
= [tex]\frac{4}{15}[/tex] ( in simplest form )
(5)
[tex]\frac{9}{45}[/tex] ( divide numerator/ denominator by 9 )
= [tex]\frac{1}{5}[/tex] ( in simplest form )
4y^3-9y=0 solve by factoring
Answer:
[tex]y_1=0,y_2=\frac{3}{2},y_3=\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]4y^3-9y=0[/tex]
[tex]y(4y^2-9)=0[/tex]
[tex]y(2y-3)(2y+3)=0[/tex] <-- Difference of squares
[tex]y_1=0,y_2=\frac{3}{2},y_3=\frac{3}{2}[/tex]
Find the value of x need help
If A=−2x+8 and B=2x−4, find an expression that equals 2A+B in standard form.
Answer: -2x + 12
Step-by-step explanation:
2A + B = 2(-2x + 8) + (2x - 4) = -4x + 16 + 2x - 4 = -2x + 12
Complete the equation of the line through (-10,3)(−10,3)left parenthesis, minus, 10, comma, 3, right parenthesis and (-8,-8)(−8,−8)left parenthesis, minus, 8, comma, minus, 8, right parenthesis.
Answer:
[tex] y = -\dfrac{11}{2}x - 52 [/tex]
Step-by-step explanation:
Line through points (-10, 3) and (-8, -8).
slope = (-8 - 3)/(-8 - (-10)) = -11/2
y = mx + b
y = (-11/2)x + b
-8 = (-11/2)(-8) + b
-8 = 44 + b
b = -52
y = (-11/2)x - 52
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the line passing through (-10,3) and (−8, -8) is y=(-11/2)x-52.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
The slope fo the line passing through (-10,3) and (−8, -8) is
Slope, m = (-8-3)/(-8+10) = -11/2
Now, equate a point in the equation,
3 = -10(-11/2) + C
3 = 55 + C
c = -52
Hence, the equation of the line passing through (-10,3) and (−8, -8) is y=(-11/2)x-52.
Learn more about Equation of Line:
https://brainly.com/question/21511618
#SPJ2
The width of a rectangle is 7ft less than the length. The area of the rectangle is 228 square feet. Find the length and width
Set up figure, side length x, and width x-7. Set equation up
[tex]228 = (x)(x - 7) \\ 228 = {x}^{2} - 7x \\ {x}^{2} - 7x - 228 = 0 \\ (x - 19)(x + 12) = 0 \\ x = - 12 \\ x = 19[/tex]
Since the value x, cannot be negative, x is equal to 19. Therefore the length is 19, width 12 (19-7)
How many yards is 24 feet
Answer:
8 yards
Step-by-step explanation:
1 yard is equal to 3 feet, so we just do 24/3 = 8 yards
Answer:
8
Step-by-step explanation:
1 feet is 3 yards so 24 yards is 8
Help help math math math please
Answer:
-2) -14
0) -8
2) -2
4) 4
Step-by-step explanation:
Plug in each input for x, and solve for y
Answer: 2) -140) -82) -24) 4
Step-by-step explanation:
Some one help me? ill give 50 points
Answer:
v=[tex]\frac{(w+v)/t}{2}[/tex]
Step-by-step explanation:
just inverse operations and you will always get your answer :)
557.59 in terms of pi
combine the like terms in the equation : 2s-4w+5+6s
To combine like terms, you have to add the same variables and all
First You have to find if the Numbers are positive or Negative
2s is positive
4w is Negative because i has Minus sigh before it
5 is Positive because it has added sigh
6s s Positive because it has added sign
Second you have to find the Like terms
2s+6s=8s
so, the new equation is
8s-4w+5.
That is the simplest
If you have questions just ask me I went through it pretty fast
you went to a coffee house with 2 friends and ordered an iced coffee and dessert which came to $12.96 how much is the tip if the rate is 15%
Answer:
its 1.944
Step-by-step explanation:
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. The formula used to calculate percentage is: (value/total value)×100%.
Marcie bought a 50-foot roll of packing tape. She used 8 5/6 foot lengtss. How much tape is left on the roll?
Answer:
22.40 feeds
Step-by-step explanation:
multiply it
1.5kg : 350g solve the ratio
Step-by-step explanation:
convert kg into grams
1kg=1000g
1.5kg/350g=1.5×1000g/350
1500/350=300/70
=30/7
ratio will be 30:7
answer is 4.2g
The answer to the ratio is:
4.2g
First of all, we need to convert the kg to g
This can be done by multiplying the Kg by 1000
1.5kg x 1000= 1500g
Next, we solve the ratio since they are in the same parameters
This would be 1500g:350g
1500/350= 30/7.
Therefore, the ratio would be 30:7
Finally when further broken down, it would be 4.2g
Read more about ratio here:
https://brainly.com/question/13513438
Help please
(1/5 x 5) to the 5th power =
Answer:
(1/5 x 5) to the 5th power = 1
16. Which of the following situations is represented by the graph?
A conversion of inches to yards
B conversion of feet to inches
c conversion of miles to feet
d conversion of yards to feet
HELP
Answer:
B. conversion of feet to inches
Step-by-step explanation:
there are 12 inches in one foot.
If a = 0.3 and b =0.5, what is the value of a+b?
A. [tex]\frac{8}{10}[/tex]
B. [tex]\frac{8}{9}[/tex]
C. [tex]\frac{80}{99}[/tex]
D. [tex]\frac{88}{100}[/tex]
Answer=
D
Step-by-step explanation
because of the dot/line at the top of the number it means it is a continuous same number
for example, 0.3 with a dot/line on top means it is 0.333333...
so 0.55...+0.33...=0.88...
and as it is a decimal that is in the range of 1-100 its like a percentage so it is 88/100
At a school 60% of students buy a school lunch. Only 10% of students buy lunch and dessert. What is the probability that a student who buys lunch also buys dessert?
Answer:
1/6
Step-by-step explanation:
P(A) = probability a student buys lunch = 60% = 0.6
P(B) = probability a student buys lunch and dessert = 10% = 0.1
We are looking at the probability that a student buys lunch and dessert on the condition that they already bought lunch. Therefore, we are looking at a conditional probability.
P(B given A) = P(A and B) / P(A)
= 0.1 / 0.6
= 1/6 ≈ 0.167