Answer:
Isabelle spent $52.50 more on Erasers than rulers.
Step-by-step explanation:
Step 1
Find the quantity of each stationery bought in fraction
Let us represent the total fraction of what Isabelle bought as: x
1/3x = quantity of pencils bought
5/8 of the remainder = quantity of erasers bought
The remainder = x - 1/3x = 2/3x
5/8 of 2/3x = 5/8 × 2/3x = 5/12x
Hence, 5/12x = quantity of erasers bought
The rest is rulers
1 - (1/3 + 5/12)
1 - (4 + 5/12)
1 - 9/12
1 - 3/4
= 1/4x
Hence, 1/4 = quantity of rulers bought.
Step 2
We find the number of stationeries that Isabelle bought.
The cost of the stationery is
a Pencil: $1.20
an eraser: $1
a ruler: $0.50.
Total amount spent on stationery = 169.50
We have this equation
1.20 × 1/3x + 1 × 5/12x + 0.50 × 1/4x = 169.50
0.4x + 0.4166666667x + 0.125x =
169.50
0.9416666667x = 169.50
x = 169.50 /0.9416666667
x = 179.99999999
Approximately , the number of stationeries that Isabelle bought = x = 180
Step 3
Find the number and the amount spent on each stationery that Isabelle bought
a) i) Quantity of pencils bought = 1/3 x
x = 180
= 1/3 × 180
= 60 pencils
ii) Amount spent on pencils
If 1 pencil = $1.20
60 pencils =
60 × 1.20 = $72
b) i) Quantity of Erasers bought = 5/12x
x = 180
= 5/12 × 180
= 75 pencils
ii) Amount spent on Eraser
If 1 pencil = $1
75 pencils =
75 × 1 = $75
c) i) Quantity of rulers bought = 1/4 x
x = 180
= 1/4 × 180
= 45 pencils
ii) Amount spent on pencils
If 1 pencil = $0.50
45 pencils =
45 × 0.50 = $22.50
Step 4
We were asked to calculate how much more did she spend on erasers than rulers.
In step 3, the amount spent on Erasers = $75
the amount spent on ruler = $22.5
The difference in the amount spent = $75 - $22.5
= $52.5
Therefore, Isabelle spent $52.50 more on Erasers than rulers.
Gisele has $5.90 in quarters and nickels. If Gisele has 16 more nickels than quarters, how many quarters does she have? [I don't want the answer I just want to know how to set the problem up please]
Answer: There are 17 quarters.
Step-by-step explanation:
Let x = Number of quarters and Number of nickels =x+16
∵ 1 nickel = $0.05, 1 quarter = $0.25
value of x quarters = 0.25 x
value of x+16 nickels = 0.05(x+16)
Then, as per given,
[tex]0.05(x+16)+0.25 x= 5.90 \\\\\Rightarrow\ 0.05x+0.8+0.25x=5.90\\\\\Rightarrow\ 0.30x=5.9-0.8\\\\\Rightarrow\ 0.30x=5.1\\\\\Rightarrow\ x=\dfrac{5.1}{0.30}=\dfrac{51}{3}\\\\\Rightarrow\ x=17[/tex]
Hence, there are 17 quarters.
Plot the value(s) on the number line where this function is equal to zero: f(x) = (x + 5)(x − 1).
Answer:
Step-by-step explanation:
Hope this Helps ;)
Finding which number supports the idea that the rational numbers are dense in the real numbers.
Answer:A terminating decimal between -3.14 and -3.15.
Step-by-step explanation:
A natural number includes non-negative numbers like 5, 203, and 18476.
It is encapsulated by integers, which include negative numbers like -29, -4, and -198.
Integers are further encapsulated by rational numbers, which includes terminating decimals like 3.14, 1.495, and 9.47283.
By showing a terminating decimal between -3.14 and -3.15, you are showing that rational numbers include integers (because integers include negative numbers.
How many times does 5 go into 1,200??
240 times.
Explanation:
24 times because,
If you divide 5 with 12k that's,
= 1200/5
= 240
Hence proved, 240 times.
Emergency help will mark brainliest answer
Answer:
Step-by-step explanation:
Use the formula
[tex]A(t)=P(1+r)^t[/tex] where P is the initial investment, r is the interest rate in decimal form, and t is the time in years. Filling in what we are given:
[tex]A(t)=5000(1+.05)^6[/tex] and simplifying a bit:
[tex]A(t)=5000(1.05)^6[/tex] and a bit more:
A(t) = 5000(1.340095641) so
A(t) = 6700.48
A___has a regular polygon base and a vertex over the center of the base.
A. Regular pyramid
B. Prism
C. Pyramid
D. Right Prism
Answer:
A. Regular pyramid
Step-by-step explanation:
If it has a vertex over the centre of the base, it has to be a pyramid.
Also, since the base is a regular polygon, the solid is a regular pyramid.
Answer:
The correct answer is
Step-by-step explanation:
Regular pyramid: A regular pyramid has a regular polygon base and a vertex over the center of the base.
Hope this helps....
Have a nice day!!!!
Chen is baking muffins and banana bread for a brunch buffet. He needs 3 and one-fifth cups of flour to make the muffins and 3 and two-thirds cups of flour to make the banana bread. Which is the best estimate of the number of cups of flour that Chen needs to bake both recipes?
Options :
A. 6 cups of flour
B.7 cups of flour
C.8 cups of flour
D.9 cups of flour
Answer:
B.7 cups of flour
Step-by-step explanation:
Given the following :
Cups of flour required to make muffins = 3 1/5
Cups of flour required to make banana = 3 2/3
Number of cups of flour required to make both recipe :
(cups of flour required to make muffins + cups of flour required to make bread)
(3 1/5 + 3 2/3) = 3+3+(1/5 + 2/3)
= 6 + (1/5 + 2/3) = (3 + 10)/15 = 6 + (13/15)
6 13/15 = 6.8666666
The best estimate is to round to the nearest whole number = 7
Answer: The answer is 7
Step-by-step explanation:
I got it right in my quiz! Hope this helps (:
solve the equation: csc(4x)-2=0
Step-by-step explanation:
csc(4x) − 2 = 0
csc(4x) = 2
sin(4x) = 1/2
In radians:
4x = π/6 + 2kπ, 5π/6 + 2kπ
x = π/24 + kπ/2, 5π/24 + kπ/2
In degrees:
4x = 30° + 360°k, 150° + 360°k
x = 7.5° + 90°k, 37.5° + 90°k
PLEASE HELP I PUT THE PROBLEM AS A PICTURE PLEASE ANSWER WILL GIVE 30 POINTS SHOW WORK
Answer:
[tex]\huge\boxed{9}[/tex]
Step-by-step explanation:
[tex]\sf (2^8 * 3^{-5} * 6^0)^{-2 } (\frac{3^{-2}}{2^3} )^4*2^{28}[/tex]
Rule of exponents [tex]a^0 = 1[/tex] , [tex]1/a^m = a^{-m}[/tex]
=> [tex]\sf 2^{8*-2} * 3 ^{-5*-2} * 3 ^{-2}* 2^{-3*4} * 2^{28}[/tex]
=> [tex]\sf 2 ^ {-16} * 3^{10} * 3^{-8} * 2 ^{-12}* 2^{28}[/tex]
Combining same bases
=> [tex]\sf 2 ^ {-16} * 2 ^{-12}* 2^{28}* 3^{10} * 3^{-8}[/tex]
When bases are same , powers are to be added
=> [tex]\sf 2 ^{-16-12+28} * 3^{10-8}[/tex]
=> [tex]\sf 2^{-28+28} * 3^2[/tex]
=> [tex]\sf 2^0 * 3^2[/tex]
=> [tex]\sf 3^2[/tex]
=> 9
Write an equation of the line that passes through the point (5, –8) with slope 5. A. y−5=5(x+8) B. y+8=−5(x−5) C. y−5=−5(x+8) D. y+8=5(x−5)
Answer:
D
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = 5 and (a, b) = (5, - 8 ), thus
y - (- 8) = 5( x - 5), that is
y + 8 = 5(x - 5) → D
MATHEMATICS
Algebra
Simultaneous Equations
1. 5u + 2v=7
2u - 2v=7
2. 3x - 4y=19
4x - 5y=23
Answer:
1. u = 2, v = -1.5
2. y = -7, x = -3
Step-by-step explanation:
1) For the following simultaneous equation, we have;
5·u + 2·v = 7....................(1)
2·u - 2·v = 7......................(2)
Adding equation (1) to equation (2), gives;
5·u + 2·v + 2·u - 2·v = 14
5·u + 2·u + 2·v- 2·v = 14
7·u = 14
u = 14/7 = 2u = 2
u = 2
From equation (1), we have;
5·u + 2·v = 7 substituting u = 2 gives;
5×2 + 2·v = 7
2·v = 7 - 5×2 = 7 - 10 = -3
v = -3/2 = -1.5
v = -1.5
2.
3·x - 4·y = 19....................(1)
4·x - 5·y = 23.......................(2)
Multiplying equation (1) by 4 and equation (2) by 3 gives;
For equation (1)
4 × (3·x - 4·y) = 4 ×19
12·x - 16·y = 76...........................(3)
For equation (2)
3 × (4·x - 5·y) = 3 × 23
12·x - 15·y = 69...........................(4)
Subtracting equation (3) from equation (4) gives;
12·x - 15·y - (12·x - 16·y) = 69 - 76 = -7
12·x - 15·y - 12·x + 16·y = 69 - 76 = -7
12·x - 12·x - 15·y + 16·y = -7
y = -7
Substituting the value of y = -7 in equation (1), we have;
3·x - 4·y = 19 = 3·x - 4×(-7) = 19
3·x - 4×(-7) = 19
3·x + 28 = 19
3·x = 19- 28 = -9
x = -9/3 = -3
x = -3.
Based on the graph what are the solutions to ax^2 + bx+c=0 Select all that apply
A. X=-2
B. X=10
C. X=5
D. X=8
Answer:
x=-2 and x = 5
Step-by-step explanation:
The solutions to the equation are where the graph crosses the x axis
We can see that the graph crosses at x=-2 and x = 5
Answer:
x = -2
x = 5
Step-by-step explanation:
The answer is found when the graph crosses the x-axis
Hope this helps :D
2( -4n+ 2)
6n = 4(-2 - 2n)
Answer:
(n^(2)+6n-4)(2n-4)
witch numbers are domain -3 ,-2 ,-3 ,0 ,-1 ,2 ,1 ,2
Correct Presentation of Question
Which numbers are domain? (-3,-2) (3,0)(-1,2)(1,2)
Answer:
Domain = {-3,-3,-1,1}
Step-by-step explanation:
Given
(-3,-2) (3,0)(-1,2)(1,2)
Required
Determine which numbers are domain
A function is always represented as thus (x,y) in this format (domain, range);
Tabulate the given data
x || y
-3 || -2
3 || 0
-1 || 2
1 || 2
The values under the x column are the domain;
Hence, the domain are {-3,-3,-1,1}
I am on a farm with pigs and horses. The ratio of pigs to horses is 4:1. The ratio of adult pigs to piglets is 1:5. The ratio of adult horse to foal is 3:1. What fraction of the farm are babies (foals and piglets)?
Answer:
EAT THIS ANDAD Which polynomial has (3x + 2) as a binomial factor?
6x3 + 3x2 + 4x + 2
12x2 + 15x + 8x + 10
18x3 – 12x2 + 9x – 6
21x4 + 7x3 + 6x + 2
Step-by-step explanation:
the volume of a cube is 125cm cubed. The area of a square is 64cm squared. How does the length of one edge of the cube compare to the length of one side of the square? Explain
Answer:
One edge of the cube is 5 cm, one edge of the square is 8 cm, so the edge of the cube is 3 cm shorter than the edge of the square.
Step-by-step explanation:
The volume of the cube is found by the formula
V = s³,
where s is the side length (called the edge in this problem)
Since V = 125 cm³, we can take the cube root of 125 to find the edge length.
The cube root of 125 is 5, ( 5³ = 125)
So the edge of the cube is 5 cm
The are of a square is found by the formula
A = s² ,
where s is the side length (called the edge in this problem)
Since A = 64 cm², we can take the square root of 64 to find the edge length.
The square root of 64 is 8 (8² = 84)
So the edge of the square is 8cm
Comparing the two edges tells us that the edge of the cube is 3cm shorter than the edge of the square.
Look at the picture and answer the question
Answer:
b
Step-by-step explanation:
Answer:
80 degrees
Step-by-step explanation:
m∠4 is the same as m∠2
I measured it with a protracter
( plz mark me as brainliest, that would be most appreciated! )
zero of the function f(x)=3x/x2-9
Answer:
It should equal zero or seven. I think is zero
April typed a 5 page report in 50 mintues. Each page had 500 words at what rate is April typing
Answer:
Amy types at a rate of 50 words per minute
Step-by-step explanation:
In this question, we are interested in calculating the rate at which April is typing.
From the question, we can deduce that she typed a 5 page report, with each page having a total of 500 words.
Now, if each page has 500 words, the total number of words in all of the pages will be 5 * 500 = 2,500 words
Now, from here, we can see that 2,500 words were typed in 50 minutes.
The number of words per minute will be ;
Total number of words/Time taken = 2500 words/50 minutes
That will give a value of 50 words per minute
Simplify the following expression 5(y + 3) + 7(y − 5) + 6
Answer:
12y-14
Step-by-step explanation:
we expand first and doing that we get
5y+15+7y-35+6
12y-14
2(6y-7)
Step-by-step explanation:
5(y+3) + 7(y-5) +6
5y+15+7y-35+6
5y+7y+15-35+6
12y-14
y= -14-12
y= +26
HELP DOES ANYONE KNOW THIS
Answer:
10x
Step-by-step explanation:
The height on the left is the same as the height on the right:
(2x -y) +(y) = (2x)
2x = 2x . . . . . not particularly helpful
The width across the top is the same as the width across the bottom:
3x = (y) +(4x -2y)
y = x . . . . . . . . add y-3x to both sides
The perimeter is the sum of side lengths. Working clockwise from the top, that is ...
P = 3x +2x +(4x-2y) +y +y +(2x -y) = 11x -y = 10x
The perimeter is 10x. (or 10y, if you like)
Kari bought 3 boxes of cookies to share with a book club. Each box contains 12 cookies. The expression StartFraction 36 over p EndFraction represents the number of cookies that each person, p, can have if the cookies are divided equally. Which evaluations of the expression are correct? Select three options. If p = 5, then each person would get 6 cookies, with 4 cookies left over. If p = 7, then each person would get 5 cookies, with 1 cookie left over. If p = 8, then each person would get 4 cookies, with 3 cookies left over. If p = 10, then each person would get 3 cookies, with 6 cookies left over. If p = 11, then each person would get 3 cookies, with 3 cookies left over.
Answer:
i). If p = 7, then each person would get 5 cookies, with 1 cookie left over.
ii). If p = 10, then each person would get 3 cookies, with 6 cookies left over.
iii). If p = 11, then each person would get 3 cookies, with 3 cookies left over.
Step-by-step explanation:
First option is wrong because 5 dividing 36 is 7, not 6. It would remain 1, not 4.
Second option is correct because 36 divided by 7 would give you 5 remaining 1.
Third option is correct because 8 dividing 36 is 4, but will remain 4, not 3.
Fourth option is correct because 36 divided by 10 is 3, then will remain 6.
Fifth option is correct because 36 divided by 11 is 3, remaining 3.
Answer:
B,D,E
Step-by-step explanation:
edge
Adding
ing and Multiplying Rati
What type of answer would you expect from the problem below? Expla
answer
DONES
need help right now please
its 4
x=4
[tex]4^{2}[/tex]-2x4
16-8
=8
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's solve your equation step-by-step.
[tex]x^2 - 2x = 8[/tex]
Step 1: Subtract 8 from both sides.
[tex]x^2 - 2x - 8 = 8 - 8\\x^2 - 2x - 8 = 0[/tex]
Step 2: Factor left side of equation.
[tex]( x+2) ( x - 4) = 0[/tex]
Step 3: Set factors equal to 0.
[tex]x + 2 = 0[/tex] or [tex]x - 4 = 0[/tex]
[tex]x = -2[/tex] or [tex]x = 4[/tex]
Answer : -2 , 4
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
5/9 of a piece of metal has a mass of 7 kg. What is
the mass of the piece of metal?
No wrong answer or else I will report
Answer:
The mass of the metal is 12.6 kgStep-by-step explanation:
Let the mass of the metal be x
From the question
5/9 of the metal is 7kg
That's
[tex] \frac{5}{9} x = 7[/tex]
Multiply through by 9
We have
5x = 7 × 9
5x = 63
Divide both sides by 5
[tex] \frac{5x}{5} = \frac{63}{5} [/tex]
We have the final answer as
x = 12.6 kg
The mass of the metal is 12.6 kgHope this helps you
You want to borrow three rock CDs from your friend. She loves math puzzles and she always makes you solve one before you can borrow her stuff. Here's the puzzle: Before you borrow three CDs, she will have 39 CDs. She will have half as many country CDs as rock CDs, and one-fourth as many soundtracks as country CDs. How many of each type of CD does she have after you borrow three rock CDs?
Answer:
Rock CD's=21
Country CD's=12
Soundtrack CD's=3
Step-by-step explanation:
let
r= rock CD's
c = country CD's
s = soundtrack CD's
Total CD's=r + c + s =39
2c=r
c/4=s
2c+c+c/4=39
8c+4c+c=156
13c=156
c=12
Substitute c=12 into 2c=r
2c=r
3(12)=r
24=r
r=24
Substitute c=12 into c/4=s
c/4=s
12/4=s
3=s
s=3
Therefore, she has
c=12
s=3
r=24
before she borrowed you 3 rock CD's
Sha has
r=21
s=3
c=12
after you borrowed 3 rock CD's
On a distant planet, a ball is thrown upwards from ground level, reaching a maximum height of 12m and hitting the ground again in eight seconds. Determine a quadratic equation in the form ax^2 + bx^2+c = 0 that could be used to calculate when the ball is at a height of 3m. Do not solve the equation.
Answer:
(-3 ÷ 4)x^2 + 6x
Step-by-step explanation:
Data mentioned in the question
Maximum height = 12m
Number of seconds = 8
Height = 3m
Depend on the above information, the quadratic equation is shown below:
As it took 8 seconds to hit the maximum altitude and it reverted to the ground floor, this graph also reflects the motion in parabola after 4 seconds, so that the a must be negative
Now it is given that
a × x ^ 2 + bx + c =0
We can considered that
x = 0
x = 8
As {0.8} are intercepts of x
When x = 0, then it is
a × 0 ^ 2 + b(0) + c = 0 .................... (i)
Hence 0 = 0
Now x = 8, it is
a × 8 ^ 2 + b(8) + c = 0
Hence a(8)^2 + b(8) + c = 0 ..................(ii)
As it can be seen that in the first equation c must be zero
Whereas the second equation is
64a + 8b = 0
i.e.
8a = -b or a = -b ÷ 8
Now according to the quadratic function, it presented
(-b ÷8)x^2 + bx + 0
So, the parabola vertex is (4, 12)
Now place this in the place of a
(-b ÷ 8)(4)^2 + b(4) = 12
And for calculating this b, all terms must be multiplied by 8
That appears
-b(16) + 32b = 96
16b = 96
So, b = 6.
As a = -b ÷8
a = -6 ÷ 8
a = -3 ÷4
So, the equation is
= (-3 ÷ 4)x^2 + 6x
Hence, this is the equation
A student finds the slope of the line between (8,17,) and (1,4) she writes 17-4/1-8 What mistake did she make?
The first mistake is that she didn't use parenthesis to indicate we're dividing all of one thing (numerator) over all of another expression (denominator)
slope = rise/run = numerator/denominator
So she should write (17-4)/(1-8) to indicate all of "17-4" is divided over all of "1-8"
However, there's another error that your teacher is probably more focused on. Note how 17-4 represents subtracting the y coordinates from left to right. We start with the left point y coordinate 17 and subtract off the right point y coordinate 4
left y - right y = 17 - 4
But then the student swaps the order when they wrote 1-8. Instead it should be 8-1
-----------------
Here's what they should have written (17-4)/(8-1)
This is the same as (4-17)/(1-8)
We can subtract in any order as long as it stays consistent between the numerator and denominator
At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 16 computer chips is taken. What is the probability of thesample mean
THIS IS COMPLETE QUESTION
computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.2 centimeters. A random sample of 16 computer chip is taken. What is the probability that the sample mean will be below 0.95?
Answer:
the probability is P=0.045
Step-by-step explanation:
We were given mean of computer chips as 1 centimeter and a standard deviation of 0.1 centimeter
We were given
σ=0.1
n=16
We calculate:
Z=(0.95-1)/0.1 √16
Z=-0.125
Using the standard z- tables. to get the probability we have
P(X<0.95)=P(z<-0.115)=0.045
Therefore, probability is P=0.045
Marta esta poniendo sus libros en una estantería. Le faltan 7 libros para poder poner 12 en cada estante; sin embargo, si pone 10 libros en cada estante, se quedan 5 libros sin poner. ¿Cuantos es antes tiene la estantería?
Answer:
x = 6 la cantidad de estantes
y = 65 cantidad de libros
Step-by-step explanation:
LLamemos "x" la cantidad de estantes que tiene Marta, y llamaremos "y" la cantidad de libros.
La primera condición que se debe cumplir es que cuando Marta coloca 12 libros en cada estante entonces le faltan 7, esto lo expresamos así:
y + 7 = 12*x (1)
La segunda condición establece que si Marta coloca los libros en número de 10 por estante le quedan 5 sin colocar, luego esto en lenguaje matemático se expresa así:
y - 5 = 10*x (2)
Ahora hemos obtenido un sistema de dos ecuaciones con dos incógnitas que se resuelve por cualquiera de los métodos conocidos, usaremos el método de sustitución.
Despejamos y en la primera ecuación y lo sustituimos en la segunda, de esa forma obtendremos el valor de x
y = 12*x - 7
(12*x - 7 ) - 5 = 10*x
2*x -12 = 0
2*x = 12
x = 6 la cantidad de estantes, y
y = 12*x -7
y = 72 - 7
y = 65 cantidad de libros
