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
Can someone please help me and explain I’ll mark brainliest
Part (a)
Answer: x = -8------------------
Work Shown:
2(x-1) = 3(x+2)
2x-2 = 3x+6 .... distribute
2x = 3x+6+2 .... adding 2 to both sides
2x = 3x+8
2x-3x = 8 .... subtracting 3x from both sides
-x = 8
x = -8 ..... multiply both sides by -1
===========================================================
Part (b)
Answer: x = 5/11------------------
Work Shown:
-4(2x-2) = 3(x+1)
-8x+8 = 3x+3 ..... distribute
-8x = 3x+3-8 .... subtract 8 from both sides
-8x = 3x-5
-8x-3x = -5 ... subtract 3x from both sides
-11x = -5
x = -5/(-11) .... divide both sides by -11
x = 5/11
In decimal form, this is approximately equal to 5/11 = 0.4545
solve the following system of equations using the substitution method
x=2y
2x+5y=9
Answer:
y=1
x=2
(2,1)
Step-by-step explanation:
x=2y
2x+5y=9
2(2y)+5y=9
4y+5y=9
9y=9
y=1
x=2(1)
x=2
(2,1)
If x ≠ 2y, then
eq1aIf Dave drove one-third of the distance of his trip on the first day, and 60 miles on the second day, he figured out that he still had 1/2 of the trip to drive. What was the total length, in miles, of his trip?
360
180
120
60
90
2(x-2y)
2y-x
1
0
-2
I need help with this whoever can get it right I will mark you brainlest
2 and 3? I need help please
Answer:
2: 7:10 3: 6:14
Step-by-step explanation:
There are 7 blue marbles and 10 are green
There are 6 circles and 14 hearts
HELPP PLZZZZZZZZZZ tand thanks
I NEED HELP ON THIS ASAP!! GIVING 75 POINTS TO WHOEVER CAN HELP ME WITH THIS!!!
Answer:
288pi
904.3
1648.5
33493.3
Step-by-step explanation:
1.
volume = 6^2 * 8 * pi = 288pi
= 904.32
2.
5^2*21*3.14 = 1648.5
3.
4/3 * 20^3 * 3.14 = 33493.3
I need help fasttttt! Helpppppp
Answer:
r>12 or r<−4
Step-by-step explanation:
PLEASE I ONLY AHEB 5 minutes left
Jean deposits $730 in an account that pays 2.8% simple interest. He neither adds
more money nor withdraws any money from his account. What amount will be in
Jean's account after 5 years? Show your work.
Answer:
hyujd6dssgshfjf kryaydfhfvjmbnno vfifufiigbff
PLEASE HELP ITS URGENT
DONT GUESS
WILL MARK BRAINLIEST (make sure to use yd² and yd³)
Answer:
Perimeter: 210[tex]yd[/tex]
Area: 2106[tex]yd^{2}[/tex]
good luck, hope this helped :)
The school spent $504 on calculators. How
many did the school buy?
Answer:
where is the rest of the question, how much was each calculator?
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
The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation.
Answer:
Rate of change = $25 per day
Step-by-step explanation:
Since, rate of change of the data given in the table is constant graph will be a linear graph.
Rate of change of the line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
Rate of change = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
From the table given,
Graph passes through two points (3, 75) and (4, 100)
Rate of change = [tex]\frac{100-75}{4-3}[/tex]
= 25
Here rate of change defines the change in cost per day.
The product of -13 and K
Answer:
- 13 × k = -13k
good luck, hope this helps :)
Plz answer i will gibe brainiest
If I understand this right:
3/4=24
24/3=8
8*4=32
You divide the number by the numerator, and then multiply that number by the denominator.
If you mean you want 3/4 of 24 then you divide 24 by 4, which equals 6. And then multiply 6 and 3, which equals 18
PLEASE HELP ITS URGENT DONT GUESS ILL MARK BRAINLIEST IF YOU GET IT RIGHT
Answer:
circumference = 301.44
area =7,234.56
Step-by-step explanation:
The circumference of a circle can be found by multiplying pi ( π = 3.14 ) by the diameter of the circle.
96 x 3.14 = 301.44
area = 3.14r^2
radius = d/2
radius = 48
3.14(48^2)
area =7,234.56
A taxi company charges £5 standing charge and £1.50 per mile for a journey
Aman travels in a taxi for 12.2 miles.
What is the cost of his journey?
Answer:
I believe its £18.30. If not sorry.
Step-by-step explanation:
Distributive property
9(2n/1)
To distribute, multiply 9 times 2n plus 9 times 1.
9*2n+9*1
18n+9 is your final answer.
Step-by-step explanation:
Find the value of x that makes triangle CDE ~triangle FGH
Answer: 5
Step-by-step explanation:
4x + 10- 25
John bought a video game that was 20% off. THe game was originally $50. How much money DID HE SAVE by getting it on sale?
A glass contains 0.75 liters of solution. John uses 0.9 of the solution for his experiment
The graph of function gis the graph of function f (x) = 2x2 + 5 after a
vertical stretch by a factor of 3. What is the function rule for function g?
Answer: g(x) = 6*x^2 + 15
Step-by-step explanation:
Suppose that we have a function y = f(x)
A vertical stretch by a factor of K is written as:
g(x) = K*f(x).
In this case, we have f(x) = 2*x^2 + 5.
And we know that g(x) is a f(x) after a stretch by a factor of 3.
Then we get:
g(x) = 3*f(x) = 3*(2*x^2 + 5) = 3*2*x^2 + 3*5 = 6*x^2 + 15
g(x) = 6*x^2 + 15
e Michael is working on the roof of his house. Michael is on the ground, standing 5 feet away from the house. A ladder touches the house at a point 20 feet above the ground, and the ground at Michael's feet. What is the approximate distance between Michael and the point where the ladder touches the house?
Answer:
Step-by-step explanation:
25
sb pls answer this lollllllll!?
Answer:
y = 1.5x
Step-by-step explanation:
We are to find the equation of the line
The equation is expressed as y = MX+c
m is the slope
c is the intercept
Get the slope
Using the coordnate (10, 15) and (20, 30)
m = 30-15/20-10
m = 15/10
m = 1.5
Get the intercept
Substitute m = 1.5 and (10, 15) into y = mx+c
15 = 1.5(10) + c
15 = 15+c
c = 0
Get the equation
y = mx+c
y = 1.5x+0
y = 1.5x
Hence the required equation is y = 1.5x
Answer:
y=1.5x
Step-by-step explanation:
Simplify.
(5v2-3v – 4)+(7v?-v+6)
Answer:
35 v 3 ? − 21 v 2 ? − 5 v 3 − 28 v ? + 13 v 2 − 2 v − 8
What is the area of the parallelogram?
Step-by-step explanation:
to find the area of a parallelogram multiply the base by the height. multiply so 8x4= 32. but thats not it, ill come back when i get it or ask a tutor
Answer:
A=bh
Step-by-step explanation:
Write the exponent for 4^? = 64 What number is the question mark? *
What is the sum of
1
2
+
1
4
? Use the fraction strip to help.
One whole fraction strip is equal in length to one one-half fraction strip combined with two one-fourth fraction strips. One-whole fraction strip is also equal to eight one-eighth fraction strips.
Answer:
Step-by-step explanation:
3/4
Answer:
3/8
Step-by-step explanation:
first find a good denominators then multiply the numerators by how many times it took you to get the denominator then add 1/8+ 2/8 which equals 3/8
What is 63x13
Me give brainliest
And thanks in advance
Answer:
819
Step-by-step explanation:
Help me with my math
Answer:
The first one is correct
Step-by-step explanation:
-3<1-1 - 3<0 correct
-3>1 it is not correct