Answer:
Amanda buy first kind of pen = 3
Amanda buy second kind of pen = 2
Amanda buy third kind of pen = 15
Step-by-step explanation:
Given - Amanda went to the store to purchase ink pens. She found three
kinds of pens. The first cost $4 each; the price of the second kind
was 4 for $1; and the cost for the third kind was 2 for $1. She bought
20 pens and she bought at least one of each kind. (It is possible to
buy only 1 of the pens that are "4 for $1" or "2 for $1".) The cost was
$20.
To find - When she got back to her office, Amanda decided to turn this into
a math problem for me. She asked: how many of each kind did I
buy?
Proof -
Let Amanda buy first kind of pen = x
second kind of pen = y
third kind of pen = z
As given,
She bought total pen = 20
⇒x + y + z = 20 ...............(1)
Now,
As given,
cost for first kind pen = $4 for 1 pen
As she bought x pens of first kind , so
Cost of x pens of first kind = $4x
Now,
The price of the second kind was 4 for $1
⇒Cost of second kind = $[tex]\frac{1}{4}[/tex] for 1 pen
As she bought y pens of send kind , so
Cost of y pens of second kind = $[tex]\frac{1}{4}y[/tex]
Now,
The price of the third kind was 2 for $1
⇒Cost of third kind = $[tex]\frac{1}{2}[/tex] for 1 pen
As she bought z pens of send kind , so
Cost of z pens of third kind = $[tex]\frac{1}{2}z[/tex]
Now,
As given, The cost was $20
⇒4x + [tex]\frac{1}{4}y[/tex] + [tex]\frac{1}{2}z[/tex] = 20
⇒16x + y + 2z = 80 .....................(2)
∴ we get 2 equations
x + y + z = 20 .....................(1)
16x + y + 2z = 80 .....................(2)
Now,
Subtract equation (1) from equation (2) , we get
16x + y + 2z - ( x+ y + z )= 80 - 20
⇒16x + y + 2z - x - y - z = 60
⇒15x + z = 60
⇒z = 60 - 15x
Now,
Put the value of z in equation (1) , we get
x + y + 60 - 15 x = 20
⇒ y - 14x = 20 - 60
⇒y - 14x = -40
⇒14x - y = 40
⇒y = 14x - 40
Now,
we get
z = 60 - 15x
y = 14x - 40
As given
she bought at least one of each kind
it means x > 1, y > 1, z > 1
Now,
If x = 1, then y = 14 - 40 = -26
Not possible
If x = 2 , then y = 14(2) - 40 = -12
Not possible
If x = 3, then y = 14(3) - 40 = 2 and z = 60 - 15(3) = 15
Possible.
If x = 4, then y = 14(4) - 40 = 16 and z = 60 - 15(4) = 0
Not Possible.
If x = 5, then y = 14(5) - 40 = 30 and z = 60 - 15(5) = -15
Not Possible.
∴ we get
x = 3, y = 2, z = 15
Amanda buy first kind of pen = x = 3
Amanda buy second kind of pen = y = 2
Amanda buy third kind of pen = z = 15
Question 11 (1 point)
Evaluate the function.
Given f(x) = x2 - 5x + 5, find f(3).
Answer:
f(3) =-1
Step-by-step explanation:
f(x) = x^2 - 5x + 5
Let x=3
f(3) = 3^2 -5(3) +5
= 9 -15+5
= -6+5
=-1
Find the value of the discriminant of the following equation 10x² + x = 1.
Answer:
41
Step-by-step explanation:
as discriminant is b^2 -4ac
b= 1
a= 10
c = -1
then
1^2 - (4*10*-1) = 1 - (-40) = 1 + 40 = 41
The weekly production cost C of manufacturing x watches is given by the formula C = 6000 + 3x, where the variable C is in dollars.
" (a) What is the cost of producing 1000 watches?
Answer:
therefore, to produce 1000 watches , it would cost 9000 dollars.
Price : 9 dollars a watch
Step-by-step explanation:
C=6000 + 3x
what is the cost of producing 1000 watches?
first do this
C= (1000)= 6000 + 3(1000)
C= (1000)= 6000 +3000
C= 9000
The carnival also offers two magic shows. The morning show is only 20 minutes and it costs $3.75. For the afternoon show, it is 35 minutes and costs $5.25. Which show would give you more for your money?
Answer:
35 min show
Step-by-step explanation:
3.75 / 20 = .1875
5.25 / 35 = .15
you pay less for the 35 min show
can i please get brainliest! :)
Use differences to find a pattern in the sequence.
7, 17, 30, 51, 85, 137, 212
Assuming that the pattern continues, the eighth term should be
Answer:
451
Step-by-step explanation:
7, 17, 30, 51, 85, 137, 212
Differences between Difference between Difference between
numbers in sequence first differences second differences
17 - 7 = 10
30 - 17 = 13 3
51 - 30 = 21 8 5
85 - 51 = 34 13 5
137 - 85 = 52 18 5
212 - 137 = 75 23 5
75 + 28 = 103
212 + 103 = 315 28 5
103 + 33 = 136
315 + 136 = 451 33 5
Bryson has soccer practice for 2 1/4 hours 2 times a week. How much time does Bryson spend at soccer practice in 1 week?
Answer:
15.75
Step-by-step explanation:
Answer number 2 please
Answer:
Its 4
Step-by-step explanation:
Volume is base times wigth times height to 5*4*v has to be 60 so we know v is 4.
200 percent of d is 18 what is d please help this is a question i have been needing help on for a long time
Step-by-step explanation:
what do u mean ??
200 per cent of 8???
If that's so, 200/ 8 * 100 = 2,500
Answer:
9
Step-by-step explanation:
When we calculate percentages, we multiply the numbers divided by 100. Therefore, 200% is the same as ×2.
3. The sum of two numbers is 30 and their difference is 12. Find the two numbers.
Answer:
I don't know is it 12 and 16 I'm not sure
Answer:
The two numbers are 21 and 9
Step-by-step explanation:
Let the two numbers be a and b
The sum of these numbers is 30
a+b=30
The difference between these numbers is 12
a−b=12
―――――――――
I. You can solve this by logic.
If the two numbers were exactly equal, then they would both be 15.
15+15=30
But the difference would be 0, not 12
So if you lowered b by one point, and added that to a, then the two numbers would be 16 and 14, and the difference would be 2.
So you can see that for every point you subtract from b to add to a, you increase the distance between them by 2
So, by logic, you need to subtract 6 points from b and add them to a to create a difference of 12
(15+6) minus (15−6) gives a difference of 12
.m21.....−mm∩9 = 12
Answer:
The two numbers are 21 and 9
―――――――――
II. You can solve this by math
These are simultaneous equations, so you can solve them by math.
.a+b=30
.a−b=12
――――――
2a +0=42
.a =21 ← same answer
A computer game originally sold for $40 but is now on sale for 30% off. What is the sale price of the computer game?
Answer:
28
Step-by-step explanation:
Answer:
28
Step-by-step explanation:
30% of 40 is 12, 40-12=28, the answer is 28.
7
Jackson is creating a rectangular board game that includes a diagonal line from two of the corners of the game. How long is the diagonal if the board game is 10 inches
long by 8 inches wide? Explain your reasoning. Round your answer to the nearest tenth of an inch.
Helppp
Answer:
diagonal = = 12.8 inches (to the nearest tenth of an inch)
Step-by-step explanation:
As shown in the diagram attached to this solution:
Let the Length of the rectangular board = a
Let the width = b
Let the diagonal = d
where:
a = 10 inches
b = 8 inches
d = ?
Triangle ABC in the diagram is a right-angled triangle, therefore, applying Pythagoras theorem:
(hypotenuse)² = (Adjacent)² + (Opposite)²
d² = 10² + 8²
d² = 100 + 64
d² = 164
∴ d = √(164)
d = 12.806 inches
d = 12.8 inches (to the nearest tenth of an inch)
N:B Rounding off to the nearest tenth of an inch is the same as rounding off to 1 decimal place.
Please help thank u i hope u help
It costs $8 per hour to rent a bike. Niko graphs this relationship using x for number of hours and y for total cost in dollars. Write an ordered pair that is a point on the graph of the relationship
Dot plot 1 is the top plot. Dot plot 2 is the bottom plot.
According to the dot plots, which statement is true?
Х
The range of the data in dot plot 1 is less
than the range of the data in dot plot 2.
10
The mean of the data in dot plot 1 is
greater than the mean of the data in data
plot 2.
Х
х
The median of the data in dot plot 1 is
equal to the median of the data in dot plot
2.
The mode of the data in dot plot 1 is less
than the mode of the data in dot plot 2.
Answer:
the answer is b. The mode of the data in dot plot 1 is less than the mode of the data in dot plot 2.
Step-by-step explanation:
In the dot plots 1 and 2, the statement which is true is that the mean of the data in dot plot 1 is greater than the mean of the data in data plot 2.
What is dot plot?The dot plot is the way oif representation of the data. This data is plooted in the form of points or dots over an x-y axis. The dot polt is also known as the strip plot.
Dot plot 1 is the top plot. The value of it are as,
2,3,4,5,5,6,6,6,6,7,7,7,8,8,9,10
Dot plot 2 is the bottom plot. The value of it are as,
1,2,2,3,3,4,4,4,5,5,5,6,6,7,8,9
The options given in the problem are,
The range of the data in dot plot 1 is less than the range of the data in dot plot 2-Range is difference between the highest and lowest value. The range of the first dot plot is,
[tex]r_1=10-2=8[/tex]
The range of the Second dot plot is,
[tex]r_2=9-1=8[/tex]
Range of dot plots are equal.
The mean of the data in dot plot 1 is greater than the mean of the data in data plot 2.Mean of the dot plot one is 6.1875 and mean of the dot plot second is 4.625.
The median of the data in dot plot 1 is equal to the median of the data in dot plotThe median of the data in dot plot 1 is 6 and the median of the data in dot plot is 4.5. Thus they are not equal.
The mode of the data in dot plot 1 is less than the mode of the data in dot plot 2.The mode of the data in dot plot 1 is 6 and the mode of the data in dot plot 2 is 4 and 5. Thus this is not correct option.
Hence, in the dot plots 1 and 2, the statement which is true is that the mean of the data in dot plot 1 is greater than the mean of the data in data plot 2.
Learn more about the dot plot here;
https://brainly.com/question/15853311
Solve for f
-5f +5 < 15
Question 1 options:
f < 8
f > -2
f = 3
f < 2
I NEED HELP ASAP
Step-by-step explanation:
step 1. -5f + 5 < 15
step 2. -5f < 10 (subtract 5 from each side)
step 3. f > -2 (divide both sides by -5 - dont forget to flip arrow when dividing by a negative number).
find the slope of the line
Answer:
-1
Step-by-step explanation:
it goes down 1 per gain of 1 on the x axis
Answer:
-1
rise over run -2/2
slope is -1
Step-by-step explanation:
find the inequality represented by the graph pleasseee help me
Answer:
y≥1/2x is the answer for this problem
A salesperson's commission rate is 5 %. What is the commission from the sale of 32,000 worth of furnaces? Use pencil and paper. Suppose sales would double. What would be true about the commission? Explain without using any calculations. The commission is $ .
Answer: Answer:
Its sad that you have to uses this app to get the right answers.
Have you ever stopped to ponder if someone is trying to scam/Catfish you?
Also I bet that you haven't even tried reading this question.
I know that you can do it yourself!
If not then, Sorry to hear.
Also
The answer is:
Do it yourself, Because if you try..You'll have a better answer then I ever could. Or anyone TBH
Simplify completely''''
Answer:
[tex]\displaystyle \frac{2x + 5}{x - 9}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Terms/CoefficientsFactoringStep-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{2x^2 + 13x + 20}{x^2 - 5x - 36}[/tex]
Step 2: Simplify
[Fraction] Factor numerator: [tex]\displaystyle \frac{(x + 4)(2x + 5)}{x^2 - 5x - 36}[/tex][Fraction] Factor denominator: [tex]\displaystyle \frac{(x + 4)(2x + 5)}{(x - 9)(x + 4)}[/tex][Fraction] Divide: [tex]\displaystyle \frac{2x + 5}{x - 9}[/tex]The median number of part-time employees at fast-food restaurants in a particular city was known to be 18 last year. City officials think the use of part-time employees may be increasing. A sample of nine fast-food restaurants showed that seven restaurants were employing more than 18 part-time employees, one restaurant was employing exactly 18 part-time employees, and one restaurant was employing fewer than 18 part-time employees. Can it be concluded that the median number of part-time employees has increased
Answer:
It can be concluded that the median number of part-time employees has increased hence we will reject the null hypothesis ( H0 : p = 0.5 )
Step-by-step explanation:
Test using α = 0.5 to determine whether the median number of part-time employees has increased
number of restaurants with more than 18 part-time employees = 7 ( + sign )
number of restaurants with less than 18 part-time employees = 1 ( - sign )
number of restaurants with exactly 18 part-time employees = 1
first step : ( state the null and alternate hypothesis )
Null hypothesis : ( H0) : median ≤ 18
Alternate hypothesis : ( Ha ) : median ≥ 18
The size of the sample ( n ) can be considered to be 8 because
number of restaurants with more than 18 part-time employees = 7 ( + sign )
number of restaurants with less than 18 part-time employees = 1 ( - sign )
Hence the actual hypothesis that should be tested will be :
H0 : p = 0.5
Ha : p ≠ 0.5
Next apply the binomial distribution to determine the number of + signs
= nP = 8 ( 0.5 ) = 4 + signs ( right tailed test i.e. upper tail of the binomial distribution )
determine the P ( ≥ 7 ) + signs in order to obtain the p-value of this right tailed test ( using the binomial probability table )
P ( ≥ 7 )+ signs = p(7) +signs + p(8)+signs
= 0.0313 + 0.0039 = 0.0352
Hence the P-value = 0.0352 is < 0.05 hence we will reject the Null hypothesis ( H0 : p = 0.5 )
hence It can be concluded that the median number of part-time employees has increased
The true statement is that, the median number of part-time employees has increased
The given parameters are:
[tex]\mathbf{n_1 = +7}[/tex] ---- restaurants with more than 18 part-time employees[tex]\mathbf{n_2 = -1}[/tex] ---- restaurants with less than 18 part-time employees [tex]\mathbf{n_3 = 1}[/tex] ---- restaurants with exactly 18 part-time employeesUsing a 0.5 test of significance, the null and the alternate hypotheses are:
Null hypothesis : [tex]\mathbf{H_0 : p= 0.5}[/tex]Alternate hypothesis : [tex]\mathbf{H_a : p \ne 0.5}[/tex]The sample size (n) is calculated using
[tex]\mathbf{n =n_1 -n_3}[/tex]
So, we have:
[tex]\mathbf{n =7 --1}[/tex]
[tex]\mathbf{n =8}[/tex]
The mean of the distribution is:
[tex]\mathbf{\bar x = np}[/tex]
This gives
[tex]\mathbf{\bar x = 8 \times 0.5}[/tex]
[tex]\mathbf{\bar x = 4}[/tex]
Using the right tailed test, we calculate the probability that a restaurant has more than 7 part-time employees.
This is calculated as:
[tex]\mathbf{P(x \ge 7+) = P(x = 7+) + P(x = 8+)}[/tex]
Using the binomial probability table, we have:
[tex]\mathbf{P(x \ge 7+) = 0.0313 + 0.0039 }[/tex]
[tex]\mathbf{P(x \ge 7+) = 0.0352}[/tex]
By comparison,
When the p-value is less than the level of significance, then we will reject the Null hypothesis
Hence, it can be concluded that the median number of part-time employees has increased
Read more about probabilities at:
https://brainly.com/question/6476990
what is the speed, if distance is 900 miles and time 300 minutes
Answer:
3 mi/min
Step-by-step explanation:
speed =distance/time
900/300=3
How many tens are in the number 639
Answer:
63 tens are in 639 are in that number
Answer:
There are 63 full tens in 639.
Step-by-step explanation:
639÷10=63.9
Hope this helps! :)
If 3(c+d) = 5 and c = 1, what is the value of c + d?
Answer:
c+d = 5/3
Step-by-step explanation:
3(c+d) = 5
Divide each side by 3
3/3(c+d) = 5/3
c+d = 5/3
Answer:
3(1+d)=5
3×1=3
3×d=3d
:3+3d-5
3d-2
3d=2 (Devide both sides by 3)
d=2/3
Question 2 of 10
If A PQR = ASTU, which statement must be true?
Answer:
PQ = ST
Step-by-step explanation:
..................
Answer:
pq = st
Step-by-step explanation:
PLSS HELP ME TYSMMMMM
Answer:
Picture or question???????
Rob is making a pizza the radius of the pizza is 21 inches what is the circumference of the pizza using 3.14 rounded to the nearest tenth
Answer:
131.9Step-by-step explanation:
C = 2πr
using 3.14 for π, we get C = 2(3.14)(21)
C = 2(65.94)
C = 131.88 or about 131.9
find the circumference of the circle shown below. Remember to use 3.14 for LaTeX: \piπ, and be sure to round your final answer to the nearest hundredth, as needed.
Answer:
62.8 If rounded to the nearest hundredth it is 62.80
Step-by-step explanation:
1. Formula for circumference of a cirlcle is 2 (pi) r where for this problem,
2 =2,
pi= 3.14 and
r= 10 (1/2 of the diameter =radius)
2. 2 x 3.14 x 10
multiply all 3 numbers above, you get 62.8
3. Depending on your teacher or the test,
62.8 is your answer, if it HAS to be to the nearest hunderedth, and it's on a specific program, it might want you to enter the "0" at the end 62.80
R+2 1/4 = 4 1/2 what does r = ?
Answer:
exact form: r= 9/4
decimal form: r=2.25
mixed number form: r= 2 1/4
Step-by-step explanation:
Answer:
R=2 1/4 or 9/4
Step-by-step explanation:
You make the 4 1/2 a 4/24 so it equals 2 1/4
Than you subtract 4 2/4-2 1/4 to get 2 1/4
Hope this helps!!
calcular
a. [1/3+4] =
b. [8-15+4]=
c. 4-√81/ √36=
Answer:
a. 1/7
b. -3
c. -50
Thor made 45 gallons of of punch. The recipe he followed called for 7/9 of the punch to be orange juice. How many gallons of orange juice did Thor use to make the punch
============================================================
Work Shown:
x = orange juice amount
x = (7/9)*(total amount of juice)
x = (7/9)*45
x = (7/9)*(45/1)
x = (7*45)/(9*1)
x = 315/9
x = 35 gallons of orange juice
-------------------------
Another way to approach the problem:
Draw a rectangle and split it into 9 equal slips. If the whole rectangle's area is 45 square units, then each little skinny rectangle is 45/9 = 5 square units.
Shade in exactly 7 of these little rectangular slips. The shaded portion represents 7*5 = 35 square units, which corresponds to the answer of 35 gallons.