=========================================================
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.
---------------
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.
Help me with this plzzzzzzzzz
Dalvin has a toy car collection of 200 toy cars. He keeps 194 of the toy cars on his wall. What percentage of Dalvin's toy car collection does he keep on his wall?
Answer: 97%
Step-by-step explanation:
what is 194 out of 200 ? 97%
AND IM SO SORRY ABOUT RED DEV!L
Read in equality quality for the graph shown below use ask for your beard
Answer:
x<-3
Step-by-step explanation:
What kind of taxes are likely to pay for universities and police?
а
local taxes
b. state taxes
C federal taxes
d income taxes
Answer: I'd say the best answer is b.
Step-by-step explanation:
[tex]prove that\ \textless \ br /\ \textgreater \ \frac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } = \frac { 1 + \sin \theta } { \cos \theta }[/tex]
pls i want the answwr as fast u can
ASAP !
MisterBrainly Answer Please :((((
0r any top user
who will answer correctly he will be a good user
plz answer
[tex] \large \bigstar \frak{ } \large\underline{\sf{Solution-}}[/tex]
Consider, LHS
[tex]\begin{gathered}\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } \\ \end{gathered}[/tex]
We know,
[tex]\begin{gathered}\boxed{\sf{ \:\rm \: {sec}^{2}x - {tan}^{2}x = 1 \: \: }} \\ \end{gathered}
\\ \\ \text{So, using this identity, we get}
\\ \\ \begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - ( {sec}^{2}\theta - {tan}^{2}\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}[/tex]
We know,
[tex]\begin{gathered}\boxed{\sf{ \:\rm \: {x}^{2} - {y}^{2} = (x + y)(x - y) \: \: }} \\ \end{gathered} \\ [/tex]
So, using this identity, we get
[tex]\begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - (sec\theta + tan\theta )(sec\theta - tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}[/tex]
can be rewritten as
[tex]\begin{gathered}\rm\:=\:\dfrac {(\sec \theta + tan\theta ) - (sec\theta + tan\theta )(sec\theta -tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac {(\sec \theta + tan\theta ) \: \cancel{(1 - sec\theta + tan\theta )}} { \cancel{ \tan \theta - \sec \theta + 1} } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:sec\theta + tan\theta \\\end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1}{cos\theta } + \dfrac{sin\theta }{cos\theta } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1 + sin\theta }{cos\theta } \\ \end{gathered}[/tex]
Hence,[tex]\begin{gathered} \\ \rm\implies \:\boxed{\sf{ \:\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } = \:\dfrac{1 + sin\theta }{cos\theta } \: \: }} \\ \\ \end{gathered}[/tex]
[tex]\rule{190pt}{2pt}[/tex]
Find the exact value of sin^-1(-√3/2)
Answer:
-60°
Step-by-step explanation:
Your calculator and/or your knowledge of trig function values can find this for you.
The arcsine function has a range of -90° to +90°. Positive angles 240° and 300° will also have the sine value -√3/2.
arcsin(-√3/2) = -60° = -π/3 radians
A newborn child receives a $6000 gift toward a college education from her grandparents. How much will the $6000 be worth in 18 years if it is invested at 7.6% compounded quarterly?
Answer:
333.333333333
Step-by-step explanation:
you have to divide
pls help anyone know dis
Answer:
1st one:5≥x>-infinity
2nd one :5<x<+infinity
3rd one :5>x>- infinity
2-6² +4 2
please help it's review for my finals
Answer: I don’t know :(
Step-by-step explanation:
Answer:
8
Have an amazing day!
If one of the factors of r ^ 2 + 21r + 98 is r + 7 , what is the other factor?
Answer:
i think factor the expression (r+7)(r+14) is answer
Step-by-step explanation:
Answer:
(r + 14)
Step-by-step explanation:
When factoring a trinomial in the form of:
[tex]ax^2+bx+c[/tex]
you need to find 2 numbers that multiply to make ac and add to make b. Here, we need to find 2 numbers that multiply to 98 and add to 21. First, list the factors of 98:
1, 98
2, 49
7, 14
and the reverse of all of those is also true.
Now find factors that add to 21. In this case, those are 7 and 14. You need to break the middle term in the trinomial into those 2 numbers:
[tex]r^2+21r+98\\r^2+7r+14r+98[/tex]
Finally, you can factor each half of this individually.
[tex](r^2+7r)+(14r+98)\\r(r+7)+14(r+7)\\(r+14)(r+7)[/tex]
We were already given (r + 7), so the answer is (r + 14).
B. Analyze the problem below and answer the questions that follow. a monthly salary of Php 18.500 Complete the table below which shows the deductions on Bianca has her payslip Name Bianca Ramos Assistant For the month of September 2020 Basic Salary 18,500 00 Position Financial Allowances Total Earnings 18.500 00 DEDUCTIONS Description SOCIAL SECURITY SYSTEM MEDICARE (PHILHEALTH) PAGIBIG (FUND) BIR (WITHHOLDING TAX) Amount of Deduction (11) (12) (13) (14). Total Deductions (15) NET PAY (16)
The completed table showing Bianca Ramos's tax deduction and NET PAY
is presented as follows;
SOCIAL SECURITY SYSTEM = Php 1,147
MEDICARE (PHILHEALTH) = Php 268.25
PAGIBIG (FUND) = Php 370
BIR (WITHHOLDING TAX) = Php 5,509.19
Total deductions = Php 7,294.44
NET PAY = Php 11,205.56
Reasons:
Based on online search, the tax rate for the items on the table are as follows;
SOCIAL SECURITY SYSTEM = 6.20% of earnings
MEDICARE (PHILHEALTH) = 1.45% of earnings
PAGIBID (FUND) = 2% of salary
BIR (WITHOLDING TAX) = P1,342.47 + 32% over P5,479
Bianca Ramos's basic salary = 18,500.00
Which gives the deduction amount as follows;
SOCIAL SECURITY SYSTEM = 0.062 × 18,500.00 = 1,147
MEDICARE (PHILHEALTH) = 0.0145 × 18,500.00 = 268.25
PAGIBIG (FUND) = 0.02 × 18,500.00 = 370
BIR (WITHHOLDING TAX) = 1,342.47 + 0.32×(18,500 - 5,479) = 5,509.19
Total deductions = 1,147 + 268.25 + 370 + 5,509.19 = 7,294.44
NET PAY = 18,500 - 7,294.44 = 11,205.56
Her net pay = Php 11,205.56
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Shown is a pentagon, with the size of
each angle shown. Work out the largest angle.
Answer:
160°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
Here n = 5 , then
sum = 180° × 3 = 540°
sum the interior angles and equate to 540
x + 10 + 2x + 10 + x + 10 + 2x+ x + 20 = 540 , that is
7x + 50 = 540 ( subtract 50 from both sides )
7x = 490 ( divide both sides by 7 )
x = 70
Then
largest angle = 2x + 10 = 2(70) + 10 = 140 + 10 = 150°
The solution is : the largest angle is 150°.
What is the polygon?A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. Thus, the line segments of a polygon are called sides or edges.
here, we have,
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
Here n = 5 , then
sum = 180° × 3 = 540°
sum the interior angles and equate to 540
x + 10 + 2x + 10 + x + 10 + 2x+ x + 20 = 540 , that is
7x + 50 = 540 ( subtract 50 from both sides )
7x = 490 ( divide both sides by 7 )
x = 70
Then
largest angle = 2x + 10
= 2(70) + 10
= 140 + 10
= 150°
Hence, The solution is : the largest angle is 150°.
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A movie theater is splitting
cups 30 of popcorn into 18
bags. How much popcorn
will each bag holde
Answer:
30/18=1 2/3 cups of popcorn in each bag
Hope This Helps!!!
find the value of x {0<x<(π/2)} satisfying (cos x / cosec x + 1) + (cos x / cosec x-1) = 2
In attachment I have answered this problem.
The value of x {0 < x < (π/2)} satisfying (cos x / cosec x + 1) + (cos x / cosec x-1) = 2 is x = π/4.
Since cos x /(cosec x + 1) + cos x /(cosec x - 1) = 2
Taking the L.C.M (cosecx + 1)(cosecx - 1), we have
[cosx(cosecx - 1) + cosx(cosecx + 1)]/(cosecx + 1)(cosecx - 1) = 2
[cosxcosecx - cosx + cosxcosecx + cosx]/(cosec²x - 1²) = 2
[cosx/sinx - cosx + cosx/sinx + cosx]/(cosec²x - 1²) = 2
[cotx - cosx + cotx + cosx]/(cosec²x - 1) = 2
collecting like terms, we have
[cotx + cotx + cosx - cosx ]/(cosec²x - 1) = 2
[2cotx + 0]/(cosec²x - 1) = 2
2cotx/(cosec²x - 1) = 2
cotx/(cosec²x - 1) = 1
Since cot²x + 1 = cosec²x ⇒ cot²x = cosec²x - 1
So, cotx/(cosec²x - 1) = 1
cotx/cot²x = 1
1/cotx = 1
tanx = 1
Taking inverse tan of both sides, we have
x = tan⁻¹(1)
x = 45°
x = 45 × π/180
x = π/4
So, the value of x {0 < x < (π/2)} satisfying (cos x / cosec x + 1) + (cos x / cosec x-1) = 2 is x = π/4.
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please help I am so lost rn
(please put step by step if you can)
thanks!
Answer:
x=-5 and y= 4
Step-by-step explanation:
To eliminate x, add up both equations
9y= 36
divide both sides by 9
y=36/9
y= 8
To eliminate y, multiply the first equation by 8
-16x + 8y = 112
2x+ 8y= 22
Subtract equation 2 from equation 1
-18x = 90
Divide both sides by -18
x= 90/-18
x= -5
what decimal represents the fraction 1/4
Answer:
0.25
Step-by-step explanation:
1/4 is equal to 1.00 split into 4 equal parts. 0.25*4 = 1.00 , meaning that each 1/4 is equal to 0.25
Answer:
0.25.
Step-by-step explanation:
We divide 1 by 4:
4) 1. 00
0.25
Molly went to play miniature golf on Monday, when it cost $7 to rent the club and ball, plus $1 per game. Sharon went Thursday, paying $2 per game, plus rental fees of $4. By coincidence, they played the same number of games for the same total cost. How much did each one spend?
Answer:
Molly played 4 games
0.15% of what number is 10.5
Answer:
70
Step-by-step explanation:
10.5/0.15 = 70
Check:
70 · 0.15 = 10.5
A.
x y
0 3
1 5
2 7
3 9
4 11
B.
x y
0 0
1 6
2 12
3 18
4 24
C.
x y
0 0
1 -3
2 -6
3 -9
4 -12
D.
x y
0 1
1 3
2 6
3 10
4 15
Which table(s) show x and y in DIRECT PROPORTION?
A)A and B only
B)B and C only
C)C and D only
D)D and A only
Answer:)
Step-by-step explanation:
If line segment AB represents 25%, what is the length of a line segment that is 100%?
In a group of workers, 16 belonged to a lottery syndicate and 4 did not.
What fraction of the workers did not belong to the syndicate?
1: 4/16
2: 1/5
3: 1/4
4: 3/4
Answer:
HI THEREthe answer is number 1 !!
• correct me if I'm wrong
Three Snickers bars and two Butterfinger bars contain a total of 23 grams of protein. One Snickers bar and one Butterfinger bar contain a total of 10 grams of protein. How much protein does one Snickers bar contain?
Answer:
.
Step-by-step explanation:
What number group includes only the counting number and 0
Answer:
Integers
The set of numbers including all the whole numbers and their opposites (the positive whole numbers, the negative whole numbers, and zero)
point w is graphed at (n,1)
Answer:
find the vertical asymptote of the graph of f(×) = (×+3) +2.
What amount of a 40% acid solution must be mixed with 200 mL 10% solution to produce a 20% solution?
Answer:
Step-by-step explanation:
(x + 200)20 = 200(10) + x(40)
20x + 4000 = 2000 + 40x
2000 = 20x
X = 100 mL
The price of gas on Wednesday was 52.03/gallon. On Friday, the price of gas was $2.26. What is the percent change in the price of gas?
Answer:
Percent change in the price of gas is [tex]9.85\%[/tex]
Step-by-step explanation:
Percentage change equals the change in value divided by the absolute value of the original value, multiplied by .
[tex]\text { Percentage Change }=\frac{\Delta V}{\left|V_{1}\right|} \times 100[/tex]
Here
[tex]\Delta V=2.26-2.03\\\\=0.23\$/gallon[/tex]
[tex]V_{1}=2.03\$/gallon[/tex]
The percent change in the price of gas
[tex]=\frac{0.23}{2.03} \times100\\\\=9.85\%[/tex]
Percent change in the price of gas is [tex]9.85\%[/tex]
solve using system of equations by using elimination method for -5x+4y=2 ; 9x-4y=6
Answer:
y = 3
x = 2
Step-by-step explanation:
-5x + 4y = 2
9x - 4y = 6
Sum both eq.
-5x + 9x = 4x
+4y - 4y = 0
2 + 6 = 8
then:
4x + 0 = 8
4x = 8
x = 8/4
x = 2
from the first eq.
-5x + 4y = 2
-5*2 + 4y = 2
-10 + 4y = 2
4y = 2 + 10
4y = 12
y = 12/4
y = 3
Check:
from the second eq.
9x - 4y = 6
9*2 - 4*3 = 6
18 - 12 = 6
1) A museum borrows $2,000,000 at simple annual interest to purchase new exhibits. Let x represent the amount borrowed at 7%, y represent the amount borrowed at 8.5%, and z represent the amount borrowed at 9.5%. Set up a system of linear equations to determine how much is borrowed at each rate given that the total annual interest is $169,750 and the amount borrowed at 8.5% is four times the amount borrowed at 9.5%. Then write the system in matrix form. You do not have to solve the system.
Based on the information the amount borrowed at each rate is:
Z=9.5%=$350,000Y= 8.5%=$1,400,000X=7% =$250,000Let x=9.5%
Let 4x= 8.5%
Let 7% =$2,000,000 - 5x
Formulate
0.095x + 0.085(4x) + 0.07(2,000,000-5x) = 169,750
Collect like terms
0.095x + 0.34x + 140,000 - 0.35x = 169,750
Divide both side by 0.085x
0.085x = 29,750
x=29,750/0.085
x =$350,000
Amount borrowed at each rate:
Z=9.5% =$350,000
Y= 8.5% =$350,000×4
Y= 8.5% =$1,400,000
X=7% =$2,000,000 - 5($350,000)
X=7%=$2,000,000-$1,750,000
X=7% =$250,000
Matrix form
Z $350,000
Y $1,400,000
X $250,000
Inconclusion the amount borrowed at each rate is: $350,000; $1,400,000; $250,000.
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Find the value of x need help
Answer:
x = 13
Step-by-step explanation:
180-52=10x-2
130=10x
13=x
A statistics teacher has a large container of beads that she says contains 60% blue beads. A student randomly selects
50 beads. Let p = the true proportion of blue beads in the container. If the true proportion of blue beads is 0.60, which
value of ô is least likely to occur?
O 0.50
0.60
O 0.70
0.80
Answer:
0.80
Step-by-step explanation:
its the farthest away from 0.60