Step-by-step explanation:
im sorry but i need more info or a picture or something to actually anwser the question...
The graph of a quadratic function with vertex (0, 4) is shown in the figure below.
Find the domain and the range.
Write your answers as inequalities, using X or y as appropriate.
Or, you may instead click on "Empty set" or "All reals" as the answer.
Answer:
See below
Step-by-step explanation:
The domain of the quadratic equation is going to be [tex]\mathbb{R}[/tex] (all reals), since you can set x to be any real number and get a real value of y.
I can't see the graph, but the range of the quadratic is going to be y ≥ 4 (if the graph opens upwards) or y ≤ 4 (if the graph opens downwards).
Test the claim that the proportion of men who own cats is smaller than 70% at the 0.05 significance level. The null and alternative hypothesis would be:
Answer:
the null hypothesis would be: p = 70%/0.7
The alternative hypothesis would be: p < 0.7
Step-by-step explanation:
The null hypothesis is most of the time always the default statement while the alternative hypothesis is tested against the null and is its opposite.
In this case study the null hypothesis would be: the proportion of men who own cats is 70%: p = 0.7
The alternative hypothesis would be: the proportion of men who own cats is smaller than 70% : p < 0.7
what is the y-intercept of the function f(x) equals 4-5x
Answer: 4
Step-by-step explanation:
f(x)=4-5x is the same as y = -5x + 4 (Slope-intercept form). Thus, the y-intercept is 4.
Hope it helps <3
Answer: 4
Step-by-step explanation:
in the eq f(x) = 4 - 5x,
putting x=0 we get
f(x) = 4 - 0 = 4
hence y intercept = 4
PLEASE ANSWER FAST PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! The point (1, −1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.
Answer:
sin = -√2 / 2
cos = √2 / 2
tan = -1
Step-by-step explanation:
Θ is in quad IV
sin = -√2 / 2
cos = √2 / 2
tan = -1
A bag contains a collection of distinguishable marbles. The bag has two red marbles, three green ones, one lavender one, two yellows, and two orange marbles. HINT [See Example 7.] How many sets of four marbles include exactly two green marbles
Answer:
63
Step-by-step explanation:
Given that;
The bag has two red marbles, n(red) =2
three green ones marbles, n(green) = 3
one lavender one marbles, n(lavender) = 1
two yellows marbles, n(yellow ) = 2
two orange marbles. n(orange) = 2
number of non green marbles = 2+1+2+2 = 7
The objective is to find out how many sets of four marbles include exactly two green marbles
Since sets of four marbles contain exactly two green marbles, then N(select 2 from 3 marbles and 2 from 7 marbles)
= [tex]^3C_2 \times ^{7}C _2[/tex]
= [tex]\dfrac{3!}{2!(3-2)!} \times \dfrac{7!}{2!(7-2)!}[/tex]
= [tex]\dfrac{3*2!}{2!} \times \dfrac{7*6*5!}{2!(5)!}[/tex]
= [tex]3 \times 7\times 3[/tex]
= 63
Your PI claims that the proportion of Morpho butterflies in a population that are blue is 0.3 .A sample is independently obtained from this population. Of 200 sampled Morphos, 50 turn out to be blue.Given only this information, carry out a hypothesis test to evaluate the claim. What is closest to the p-value that you obtain?
Complete Question
Your PI claims that the proportion of Morpho butterflies in a population that are blue is 0.3 .A sample is independently obtained from this population. Of 200 sampled Morphos, 50 turn out to be blue.Given only this information, carry out a hypothesis test to evaluate the claim. What is closest to the p-value that you obtain?
A 0.019
B 0.038
C 0.070
D 0.139
Answer:
The correct answer is D
Step-by-step explanation:
From the question we are told that
The population proportion of blue butterflies is [tex]p = 0.3[/tex]
The sample size is [tex]n = 200[/tex]
The sample mean is [tex]\= x = 50[/tex]
The Null Hypothesis is mathematically represented as
[tex]H_o : p = 0.3[/tex]
The Alternative Hypothesis is mathematically represented as
[tex]H_a : p \ne 0.3[/tex]
Now the sample proportion is mathematically represented as
[tex]\r p = \frac{\= x}{n}[/tex]
substituting values
[tex]\r p = \frac{50 }{200 }[/tex]
[tex]\r p = 0.25[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\r p - p }{\sqrt{\frac{p(1-p)}{n } } }[/tex]
substituting values
[tex]z = \frac{ 0.25 - 0.3 }{\sqrt{\frac{0.3(1-0.3)}{200 } } }[/tex]
[tex]z = -1.54[/tex]
The p-value for a two-tailed test is mathematically represented as
for lower -tail test
[tex]p-value = P(Z \le z | H0\ is \ true) = cdf(z )[/tex]
for higher-tail test
[tex]p-value = P(Z \ge z | H0\ is \ true) = 1- cdf(z )[/tex]
for this test i assumed a 0.05 level of significance
Now
[tex]cdf(z)[/tex] is the cumulative distribution function for test statistics under the null hypothesis
Which can be calculated using MInitab (A statistics calculator )
for lower-tail test
The p-value is not significant
for higher-tail test
p-value is
[tex]1- cdf(-1.54) = 0.125[/tex]
2 mechanics worked on a car. the 1st mechanic charged $75 per hour, and the 2nd charged $95. They worked a combined 20 hours and charged a total of $1800. How many hours did each mechanic work?
Answer:
1. set up the equations:
a. total cost: 75x + 95y = 1800
b. total hours: x + y = 20
2. use substitution:
a. x + y = 20 → x = 20 - y
3. plug in value of x:
a. 75(20 - y) + 95y = 1800
4. distribute (75).
1500 - 75y + 95y = 1800
5. combine like terms:
20y = 300
6. divide:
y = 15
7. plug in y to other equation to get x:
x + 15 = 20
8. solve:
x = 5
1st mechanic (x) worked 5 hours
2nd mechanic (y) worked 15 hours
hope this helps :)
Answer:
The first mechanic worked 5 hours and the second worked 15
Step-by-step explanation:
Let h = hours for first mechanic
j = hours for second mechanic
h+j = 20
75h + 95 j = 1800
Multiply the first equation by -75
-75(h+j = 20)
-75h -75j = -1500
Add this to the second equation to eliminate h
75h + 95 j = 1800
-75h -75j = -1500
----------------------------
0 + 20j = 300
Divide by 20
20j/20 = 300/20
j = 15
Now gind h
h+j = 20
h +15 = 20
h = 5
(x*129)-3=126 what is x
Answer:
x should equal 1
Step-by-step explanation:
(1*129)-3=126
129-3=126
126=126
Answer:
x=1
Step-by-step explanation:
We can start by adding 3 to both sides to get rid of the -3
That leaves us with 129x=129
It ends up working out really evenly because by dividing both sides by 129, we are left with x=1
WHICH EXPRESSION IS NOT EQUIVALENT?
Answer:
C
Step-by-step explanation:
First, factor the original expression:
[tex]2x^2+10x+12\\2(x^2+5x+6)\\2(x+3)(x+2)[/tex]
As we can see, D is the same as above. Eliminate D.
Go through each of the answer choices.
A:
[tex](2x+4)(x+3)\\=2(x+2)(x+3)[/tex]
This is equivalent to what we factored. Eliminate A.
B:
[tex](2x+6)(x+2)\\=2(x+3)(x+2)[/tex]
This is again equivalent to what we factored. Eliminate B.
C:
[tex](2x+3)(x+4)\\[/tex]
This cannot be simplified and it is not equivalent to what we have previously. C is not the equivalent expression.
Answer:
The expression that is not equivalent to 2x²+ 10x + 12 is c)
Step-by-step explanation:
Hello!
To resolve these equations you have to do the following steps:
For example, you have (a+b)(c+d) you have to multiply the first term included in the first parenthesis with the terms of the second parenthesis and add them:
a*c + a*d
Then do the same with the second term:
b*c + b*d
Finally, you add them
ac+ad+bc+bd
If there are common terms, you have to add them.
a)
(2x+4)(x+3)
First you multiply 2x by the terms contained in the second parenthesis.
2x*x + 2x*3= 2x²+6x
Then you do the same with 4
4*x + 4*3= 4x + 12
Now you put it all together:
2x²+6x + 4x + 12
and add common terms 6x + 4x= 10x
2x²+ 10x + 12
b)
(2x+6)(x+2)= 2x²+4x +6x +12= 2x²+ 10x + 12
c)
(2x+3)(x+4)= 2x²+8x + 3x + 12= 2x² + 11x + 12
d)
2(x+3)(x+2)
In this case you have three terms in the equation "2" "(x+3)" and "(x+2)"
First you have to resolve the multiplication between the parenthesis and then you can multiply it by two
First:
(x+3)(x+2)= x*x+x*2+3*x+3*2= x²+2x+3x+6= x²+ 5x + 6
Now you can multiply it by two:
2(x²+ 5x + 6)= 2*x²+ 2*5x + 2*6= 2x² + 10x + 12
The expression that is not equivalent to 2x²+ 10x + 12 is c)
I hope this helps!
Graph the equation y=4x+1 by plotting points.
Look at the attached image (credit to Desmos graphing calculator)
To graph the equation y=4x+1, we just find two points that exist, plot them, and draw a straight line that goes through them.
Let's try x=0:
[tex]y=4(0)+1=1[/tex]
One point on the line is (0,1)
Let's try x=1:
[tex]y=4(1)+1=5[/tex]
Another point is (1,5).
Now, plot these two points and draw a line through them.
The graph of the equation represents that straight line connecting the points (0, 1), (1, 5), and (-1, -3) on a coordinate plane.
What is the equation?The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.
To plot the graph of the equation y=4x+1 by plotting points, we need to choose some values of x and then calculate the corresponding values of y using the equation.
Let's choose some values of x and calculate the corresponding values of y:
When x = 0, y = 4(0) + 1 = 1, so one point on the graph is (0, 1).
When x = 1, y = 4(1) + 1 = 5, so another point on the graph is (1, 5).
When x = -1, y = 4(-1) + 1 = -3, so another point on the graph is (-1, -3).
We can continue this process to find more points, or we can use these three points to draw a straight line through them.
Thus, the graph of the equation represents that straight line connecting the points (0, 1), (1, 5), and (-1, -3) on a coordinate plane.
Learn more about the equation here:
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Which of the following can be used to find the area of a circle?
A.
B.
C.
D.
Answer:
option B
hope it was useful for you
stay at home stay safe
pls mark me as brain.....
Answer:
[tex]\boxed{Option \ B}[/tex]
Step-by-step explanation:
Area of a circle = [tex]\pi r^2[/tex]
Finding the area of the circle, we need to know what the radius of the circle is. So, We would get the area of the circle.
An HR manager would like to test the hypothesis that the proportion of agenda-less meetings is more than 45%. Based on the information below, choose the correct conclusion for this hypothesis test. To test this, he randomly selected minutes from 100 past meeting, and found that 65 of them had no agenda. The following is the setup for this hypothesis test: H0:p=0.45 Ha:p>0.45 The p-value for this hypothesis test is 0.025. At the 5% significance level, should he reject or fail to reject the null hypothesis? Select the correct answer below: Reject the null hypothesis because 0.45>0.05. Fail to reject the null hypothesis because 0.45>0.05. Reject the null hypothesis because the p-value =0.025 is less than the significance level α=0.05. Fail to reject the null hypothesis because the p-value =0.025 is less than the significance level α=0.05.
Answer: Reject the null hypothesis because the p-value =0.025 is less than the significance level α=0.05.
Step-by-step explanation: Trust me
A mechanic's tool set is on sale for $204 after a markdown of 40% off the regular price. Find the regular price.
Answer:
$340
Step-by-step explanation:
From the information given we know that $204 is the price after a 40% discount is applied which means that this value represents 60% of the regular price and you can find the answer using the rule of three:
204 → 60%
x ← 100%
x=(204*100)/60=340
According to this, the answer is that the regular price of the product is $340.
340*0.4= 136
340-136=204
Please I need your help, if i get wrong will get f in class, just one question
Answer:
(D) 56
Step-by-step explanation:
x/y = 2/7
x = 2/7 y
S = x + y
S = 2/7 y + y
S = 9/7 y
y is a multiple of 7, so S is a multiple of 9.
So S cannot be 56.
PLZZZ HELP FAST FIRST ONE GETS THE BRAINIEST!!!!!!!!!!! Gina has borrowed 100 songs from her friend. She plans to download an equal number of songs on her music player each week for 5 weeks. The graph shows the number of songs left to download, y, for a certain number of weeks, x: A graph titled Song Downloading shows Number of Weeks on x-axis and Number of Songs Left to Download on y-axis. The x-axis scale is shown from 0 to 5 at increments of 1, and the y-axis scale is shown from 0 to 140 at increments of 20. A straight line joins the ordered pairs 0, 100 and 1, 80 and 2, 60 and 3, 40 and 4, 20 and 5, 0. Part A: What is the rate of change and initial value of the function represented by the graph, and what do they represent in this scenario? Show your work to find the rate of change and initial value. (6 points) Part B: Write an equation in slope-intercept form to model the relationship between x and y. (4 points)
Answer:
Step-by-step explanation:
The rate of change is equal to (y2-y1)/(x2-x1) where (x1,y1)=((0,150) and (x2,y2)=(5,0). Therefore the rate of change equals (0-150)/((5-0)=-30 songs/week. This is equal to the slope of the line that goes through these two points. The initial value is the y coordinate of the point when x=0 which is 150. The equation of the line is y=-30x+150, and this is the slope-intercept form (y=my+b) where m is the slope of the line and b is the y-intercept.
Which of the following can be calculated using the formula c=2r ?
A.
Area of a circle
B.
Circumference of a circle
C.
Arc length of a circle
D.
Diameter of a circle
Answer:
B. Circumference of a circle
Step-by-step explanation:
The circumference of a circle can be found using formula 2πr where r is the radius of circle.
What is the circumference of a circle?A circle's or an ellipse's circumference is its perimeter. The circumference would be the length of the circle's arc, if the circle were opened up and straightened out to a line segment, in other words.
Here, we have,
Suppose the radius of a circle is 5cm
So, we can find the circumference by using formula 2πr
Circumference = 2 × π × 5 = 10π cm.
Hence, The circumference of a circle can be found using formula 2πr where r is the radius of circle.
To learn more about Circumference and Perimeter,
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complete question;
The circumference of a circle can be found using the formula c 2r
a cylinder has a diameter 14cm and height of 11cm calculate the curved surface area of the cylinder (take pi=22/7 up
Answer:
484 cm^2.
Step-by-step explanation:
The length of the circumference = diameter * pi
= 14 * 22/7
The area of the curved surface = circumference * height
= 14 * 22/7 * 11
= 484.
cos(0)=√2/2, and 3π/2<0<2π, evaluate sin(0) and tan(0). Sin(0)?
Answer:
Option (2)
Step-by-step explanation:
In this question we have to find the values of Sinθ and tanθ where [tex]\frac{3\pi}{2}<x<2\pi[/tex].
Cosθ = [tex]\frac{\sqrt{2}}{2}[/tex] ⇒ θ = [tex]\frac{7\pi }{4}[/tex]
[Since [tex]\text{Cos}\frac{7\pi }{4}=\text{Cos}(2\pi-\frac{\pi}{4})[/tex]
[tex]=\text{Cos}\frac{\pi }{4}[/tex]
[tex]=\frac{\sqrt{2} }{2}[/tex] ]
Since Cosine of any angle between [tex]\frac{3\pi}{2}[/tex] and 2π is positive and Sine is negative in nature,
[tex]\text{Sin}\frac{7\pi }{4}[/tex] = [tex]-\frac{\sqrt{2}}{2}[/tex]
Since, tanθ = [tex]\frac{\text{Sin}\theta}{\text{Cos}\theta}[/tex]
tanθ = [tex]\frac{\frac{-\sqrt{2} }{2} }{\frac{\sqrt{2} }{2} }[/tex]
= [tex]-\frac{\sqrt{2}}{2}\times \frac{2}{\sqrt{2}}[/tex]
= -1
Therefore, Option (2) will be the answer.
Answer:
Step-by-step explanation:
option 2 is the correct answer
A car is purchased for $16,500. After each year, the resale value decreases by 35%. What will the resale value be after 3 years?
round your answer to the nearest dollar.
Answer: 16500(.65)^3 =4531.31
Step-by-step explanation:
Need help solving hi
Answer:
See below.
Step-by-step explanation:
[tex]2 \ln(x+2)=6[/tex]
[tex]\ln (x+2)=3[/tex]
[tex]e^{\ln(x+2)}=e^3[/tex]
[tex]x+2=e^3[/tex]
[tex]x=e^3-2[/tex]
[tex]x\approx 18. 09[/tex]
Jill put 53 buttons in a box. Marci put 17 buttons in an other box. Jarrod says Marci has 33 fewer buttons than Jill. He thinks 53-20 is easier to subtract than 53-17. He subtracts 53-20 and gets 33. Do you agree or not agree with Jarid's thinking?
Answer:I do not agree
Step-by-step explanation:he needs to take away 17 if he takes away 20 not 17 he needs to return 20-17=3 so in easier words you do 53-20+3=36
Find the average rate of change of the function from x=1 to x=2. f(x)=−6/x^2
Answer:
4.5.
Step-by-step explanation:
f(x) = −6 / x^2
f(1) = -6 / (1)^2 = -6 / 1 = -6.
f(2) = -6 / (2)^2 = -6 / 4 = -3 / 2 = -1.5.
Now, you have two sets of coordinates: (1, -6), and (2, -1.5).
You need to find the slope, which is the average rate of change.
(-1.5 - (-6)) / (2 - 1) = (-1.5 + 6) / 1 = -1.5 + 6 = 4.5
Hope this helps!
The average rate of change of the function from x=1 to x=2 is 4.5
The average rate of change of a function is given by:
Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Hence, the average rate of change of the function from x=1 to x=2. f(x)=−6/x² is:
f(2) = -6/2² = -1.5
f(1) = -6/1² = -6
[tex]Average\ rate\ of\ change=\frac{f(2)-f(1)}{2-1}=\frac{-1.5-(-6)}{2-1}=4.5[/tex]
Hence the average rate of change of the function from x=1 to x=2 is 4.5
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Michelle Duncan wants to know what price home she can afford. Her annual gross income is $45,000. She owes $790 per month on other debts and expects her property taxes and homeowners insurance to cost $340 per month. She knows she can get an 10.00%, 30-year mortgage so her mortgage payment factor is 8.78. She expects to make a 20% down payment. What is Michelle's affordable home purchase price? (Round your answer to the nearest dollar amount.)
Group of answer choices
$43,870
$635
$655
$41,999
$39,784
Answer:
$41,999
Step-by-step explanation:
Annual income = 45000
monthly income = $45000/12 months = $3750
mandatory expense at 38% rule = $3750 x 0.38 = 1425
other debt = 790
tax and insurance = 340
= 1425 - 790 - 340
= 295
balance left = 295
mortgage payment = (295/8.78) x 1000
= $33,599
purchase price = monthly payment/ 1- % of down payment
= $33599/1 - 0.20
= 33599/0.80
= $41,999
Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of the test statistic that would result in rejection of the null hypothesis. We wish to compare the means of two populations using paired observations. Suppose that d=3.125, sd=2.911, and n=8, and that you wish to test the hypothesis below at the 10% level of significance. What decision rule would you use? H0: μd=0 against H1: μd>0
Answer:
If the value of our test statistics is less than the critical value of t at 7 degrees of freedom at a 10% level of significance for the right-tailed test (which is 1.415), then we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
If the value of our test statistics is more than the critical value of t at 7 degrees of freedom at a 10% level of significance for the right-tailed test (which is 1.415), then we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Step-by-step explanation:
We are given that the means of two populations using paired observations. Suppose that [tex]\bar D[/tex] = 3.125, [tex]s_D[/tex] = 2.911, and n = 8, and that you wish to test the hypothesis below at the 10% level of significance.
Let D = difference between the two paired observations.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_D[/tex] = 0
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_D[/tex] > 0
The test statistics that would be used here is Paired t-test for dependent samples;
T.S. = [tex]\frac{\bar D-\mu_D}{\frac{s_d}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar D[/tex] = 3.125, [tex]s_D[/tex] = 2.911, and n = 8
The decision rule for rejecting the null hypothesis in the given hypothesis test would be;
If the value of our test statistics is less than the critical value of t at 7 degrees of freedom at a 10% level of significance for the right-tailed test (which is 1.415), then we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.If the value of our test statistics is more than the critical value of t at 7 degrees of freedom at a 10% level of significance for the right-tailed test (which is 1.415), then we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.ghvhhhhcycycugvuviggggggvvvggfgffgfggyg
Answer:
fortnite
Step-by-step explanation:
winwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwinwin
Answer:
Yes
Step-by-step explanation:
Yes
Question 16 (5 points)
Given the recursive formula shown, what are the first 4 terms of the sequence?
Answer:
i think its b
???
Step-by-step explanation:
im sorry if im wrong im not very confident on my answer :(
Answer:
D
Step-by-step explanation:
Most logical looking if you look at the formula, the last number has to be smaller than the one before, so.
answer asap, please :)
Answer:
[tex]\boxed{\sf 4.41}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
We can solve using trigonometric functions.
[tex]\sf cos(\theta)=\frac{adjacent}{hypotenuse}[/tex]
[tex]\sf cos(25)=\frac{4}{?}[/tex]
[tex]\sf ?=\frac{4}{cos(25)}[/tex]
[tex]\sf ?= 4.41351167...[/tex]
I made a square frame for my favorite bird picture from four wooden pieces. Each piece is a rectangle with a perimeter of 24 inches. What is the area and perimeter of the picture and frame, together?
Answer:
Perimeter of the picture and frame = 38.4inches
Area of the picture and frame = 92.16inches²
Step-by-step explanation:
A square frame is made up of 4 different pieces. The shape of each piece = Rectangle
The perimeter of the rectangle = 24
Perimeter of the rectangle = 24 inches
The perimeter of a rectangle = 2L + 2W
The Width of a Rectangle is always on her than the length hence.
24 = 2L + 2W
24 = 2( L + W)
24/2 = L + W
12 = L + W
Because the width is always longer than the length
W > L
Width of wooden frame = 4 × Length
Therefore;
4 × L = W
Which gives
L + W = 12 inches
4 × L + L = 12 inches
L×(4 + 1)
= 5L = 12 inches
L = 12/5 = 2.4 inches
W = 4 × L = 4 × 12/5
W = 48/5 = 9.6 inches
Side length of wooden frame, L =9.6
The perimeter of the picture frame = 4 × L= 4 × 9.6= 38.4 inches
The area of the picture frame = L²
= L × L
= 9.6 × 9.6 = 92.16inches².
doreen schmidt Is a chemist. She needs to prepare 36 ounces of a 16% hydrochloric acid solution. Find the amount of 18% solution and the amount of 9% solution she should mix to get this solution
Please help.
Answer:
Mixing two concentrations for known amount of mixture
Step-by-step explanation:
Let x = amount (ounces) of 18% solution
then
36-x = amount (ounces) of 9% solution
0.18x + 0.09(36-x) = .16(36)
0.18x + 3.24-.09x = 5.76
0.09x + 3.24 = 5.76
0.09x = 2.52
x = 28 ounces of 18% solution
amount of 9% solution:
36-x = 36-18 = 18 ounces
"prepare 36 ounces", means mass or weight.
Let u = ounces of 16%
Let v = ounces of 18%
(16u + 18v)/36=9
and u + v = 36
based on the above findings....
Mixing two concentrations for known amount of mixture
Nakashima Gallery had the following petty cash transactions in February of the current year. Nakashima uses the perpetual system to account for merchandise inventory. Feb 2 Write a $400 check to establish a petty cash fund. Feb 5 Purchased paper for the copier for $14.15 that is immediately used. Feb 9 Paid $32.50 shipping charges (transportation in) on merchandise purchased for resale, terms FOB shipping point. These costs are added to merchandise inventory. Feb 12 Paid $7.95 postage to deliver a contract to a client Feb 14 Reimbursed Adina Sharon, the manager, $68 for mileage on her car. Feb 20 Purchased office paper for $67.77 that is immediately used. Feb 23 Paid a courier $20 to deliver merchandise sold to a customer, terms FOB destination. Feb 25 Paid $13.10 shipping charges (transportation in) on merchandise purchased for resale, terms FOB shipping point. These cost are added to merchandise inventory. Feb 27 Paid $54 for postage expenses Feb 28 The fund had $120.42 remaining in the petty cashbox. Sorted the petty cash receipts by accounts affected and exchanged them for a check to reimburse the fund for expenditures. Feb 28 The petty cash fund amount is increased by $100 to a total of $500
Answer:
1. Debit Petty cash for $400; and Credit Cash for $400.
2. Total petty cash payment = $270.57
3(a) Cash reimbursement is $279.58; and Cash over and short is $9.01.
3(b) Debit Petty cash for $100; and Credit Cash for $100.
Step-by-step explanation:
Note: This question is not complete. The full complete question is therefore provided before answering the question. See the attached pdf file for the full question.
The explanations to the answers are now given as follows:
1. Prepare the journal entry to establish the petty cash fund.
Note: See the journal entry in the attached excel file
2. Prepare a petty cash payments report for February with these categories: delivery expense, mileage expense, postage expense, merchandise inventory (for transportation-in), and office supplies expense. Sort the payments into the appropriate categories and total the expenditures in each category.
Note: See the petty cash payments report in the attached excel file.
3. Prepare the journal entries for required 2 to both (a) reimburse and (b) increase the fund amount.
Note: See the journal entries (a) and (b) in the attached excel file
3(a) Reimburse Workings:
w.1: Calculation of Cash reimbursement
Cash reimbursement = Petty cash fund - Petty cash fund balance = $400 - $120.42 = $279.58
w.2: Calculation of the Cash over and short
Cash over and short = Cash reimbursement – Total expenses = $279.58 - $270.57 - $120.42 = $9.01