Let x and y be the candy pounds that sells for $0.87 and $1.22 , respectively. Since they both must add up to 9 lb, we have
[tex]x+y=9...(A)[/tex]On the other hand, the mixture should sell for $0.91 per lib, so we can write,
[tex]0.87x+1.22y=9\times0.91[/tex]Or euivalently,
[tex]\begin{gathered} \frac{0.87}{0.91}x+\frac{1.22}{0.91}y=9 \\ that\text{ is, } \\ 0.95604x+1.340659y=9...(B) \end{gathered}[/tex]Then, we need to solve the following system of equations:
[tex]\begin{gathered} x+y=9...(A) \\ 0.95604x+1.340659y=9 \end{gathered}[/tex]Solving by elimination method.
In order to eliminate variable x, we can to multiply equation (A) by -0.95604 and get an equivalent system of equations:
[tex]\begin{gathered} -0.95604x-0.95604y=-8.60439 \\ 0.95604x+1.340659y=9 \end{gathered}[/tex]Then, by adding both equations, we get
[tex]0.384619y=0.39561[/tex]Then, y is given by
[tex]\begin{gathered} y=\frac{0.39561}{0.384619} \\ y=1.02857 \end{gathered}[/tex]Once we have obtained the result for y, we can substitute in into equation (A), that is,
[tex]x+1.02857=9[/tex]then, x is given as
[tex]\begin{gathered} x=9-1.02857 \\ x=7.9714 \end{gathered}[/tex]Therefore, by rounding to two decimal places, the answer is:
$ 0.87 per lb of candy: 7.97 lb
$1.22-per-lb of candy: 1.03 lb
f(x) = 5x2 – 7(4x + 3). What is the value of f(3)?
Given the function:
[tex]f(x)=5x^2-7(4x+3)[/tex]we can find f(3) by making x = 3 and solving for the term f. In this case, we have the following:
[tex]\begin{gathered} f(3)=5(3)^2-7(4(3)+3) \\ =5(9)-7(12+3)=45-7(15)=45-105=-60 \\ \Rightarrow f(3)=-60 \end{gathered}[/tex]therefore, f(3) = -60
Mikel creates the table below to help her determine 40 percent of 70
We want to determine the 40 percent of 70, so we have to multiply 70 by 40%:
[tex]\begin{gathered} 40\text{ percent=}\frac{40}{100} \\ 70\cdot40\text{ percent=70}\cdot\frac{40}{100}=\frac{2800}{100}=28 \end{gathered}[/tex]
Question 3. Y=(1/5)^xSketch the graph of each of the exponential functions and label three points on each graph.
Given exponential function:
[tex]y\text{ = (}\frac{1}{5})^x[/tex]Let us obtain three points including the y-intercept so that we can plot the function y = f(x)
When x =0:
[tex]\begin{gathered} y\text{ = (}\frac{1}{5})^0 \\ =\text{ 1} \end{gathered}[/tex]when x =1:
[tex]\begin{gathered} y\text{ = (}\frac{1}{5})^1 \\ =\text{ }\frac{1}{5} \end{gathered}[/tex]when x =2:
[tex]\begin{gathered} y\text{ = (}\frac{1}{5})^2 \\ =\text{ }\frac{1}{25} \end{gathered}[/tex]We have the points : (0, 1), (1, 1/5), and (2, 1/25)
Using these points, let us provide a sketch of the plot of y =f(x). We have the plot as shown below:
19. We saw 10 ladybugs. We saw 5 butterflies. How many more ladybugs than butterflies did we see?
Given that,
Total ladybugs = 10
Total butterflies = 5
More ladybugs than butterflies are = ladybugs - butterflies
=> 10 - 5
=> 5
Therefore, there will be 5 more ladybugs than butterflies.
4(−5x − 6) = 4(9x + 4)
Answer: X= -5/7
Step-by-step explanation:
4(-5x-6)=4(9x+4)
-20x-24=4(9x+4)
-20x-24=4(9x+4)
-20x-24=36x+16
Then add 24 to both sides:
Can I get a walk through on how this is solved.?
Answer:
1 1/2 quarts of water
Explanation:
If she drinks 1/4 quart of water for every mile, in 6 miles, she will drink 6 times 1/4 quart of water, so
[tex]6\times\frac{1}{4}=\frac{6}{1}\times\frac{1}{4}=\frac{6\times1}{1\times4}=\frac{6}{4}[/tex]Now, we can simplify the fraction dividing the numerator and denominator by 2
[tex]\frac{6}{4}=\frac{6\div2}{4\div2}=\frac{3}{2}[/tex]Now to convert 3/2 to a mixed number, let's divide 3 by 2
Since 1 is the quotient and 1 is the remainder, the mixed number is
[tex]\begin{gathered} \frac{3}{2}=\text{Quotient}\frac{\text{ Remainder}}{2} \\ \frac{3}{2}=1\frac{1}{2} \end{gathered}[/tex]So, the answer is;
1 1/2 quarts of water.
[tex]x + y = - 2 \\ 3x - y = - 2[/tex]draw each line and estimate the solution.
We can draw each line by assuming that x = 0 and y = 0 and solve each case.
In the first equation, we have the following:
[tex]\begin{gathered} x+y=-2 \\ x=0\Rightarrow y=-2 \\ y=0\Rightarrow x=-2 \end{gathered}[/tex]notice that we have a pair of coordinate points (0,-2) and (-2,0). These two points will be useful when we draw the line.
Next, for the second equation we have:
[tex]\begin{gathered} 3x-y=-2 \\ x=0\Rightarrow-y=-2\Rightarrow y=2 \\ y=0\Rightarrow3x=-2\Rightarrow x=-\frac{2}{3} \end{gathered}[/tex]in this case we have the points (0,2) and (-2/3,0). Now, if we draw both lines on the coordinate plane we get the following:
notice that both lines intersect on the point (-1,-1). Thus, the solution of the system of equations is the point (-1,-1)
Points EGNK or midpoints explain how you know figure EGHK is a parallelogram
Solution
Given a triangle FDH with E, G and H the midpoints of the sides of the triangle
Considering the figure EGHK,
Line EG is parallel and equal to line KH
Line, EK is parallel and equal to line GH
This is a feature of a parallelogram i.e two pair of opposite sides of a parallelogram are parallel and equal
∠GEK is equal to ∠GHK and ∠EGH is equal to ∠EKH
This is a feature of a parallelogram i.e
We want to solve the following system of equations.x^2 + y^2 = 1y = 2x + 2One of the solutions to this system is (-1,0).Find the other solution.
Answer:
(-3/5, 4/5)
Explanation:
Given the system of equations:
[tex]\begin{gathered} x^2+y^2=1 \\ y=2x+2 \end{gathered}[/tex]First, we substitute y=2x+2 into the first equation to obtain:
[tex]\begin{gathered} x^2+(2x+2)^2=1 \\ x^2+(2x+2)(2x+2)=1 \\ x^2+4x^2+4x+4x+4=1 \\ 5x^2+8x+4-1=0 \\ 5x^2+8x+3=0 \end{gathered}[/tex]We solve the derived quadratic equation for x,
[tex]\begin{gathered} 5x^2+8x+3=0 \\ 5x^2+5x+3x+3=0 \\ 5x(x+1)+3(x+1)=0 \\ (5x+3)(x+1)=0 \\ 5x+3=0\text{ or }x+1=0 \\ x=-\frac{3}{5}\text{ or -1} \end{gathered}[/tex]We then solve for the corresponding values of y using any of the equations.
[tex]\begin{gathered} \text{When x=-1} \\ y=2x+2 \\ y=2(-1)+2 \\ y=0 \\ When\text{ }x=-\frac{3}{5} \\ y=2(-\frac{3}{5})+2 \\ =\frac{4}{5} \end{gathered}[/tex]Therefore, the solutions o this system are:
(-1,0) and (-3/5, 4/5).
The other solution is (-3/5, 4/5).
QuestionThe following is a data set of the average weekly number of cups of coffee consumed by employees in an office. Find the mean and median and determine if the mean or median is the better measure of central tendency.5,0,5,2,0,10,7,8,10,21,5,8,2,5,3,5Select the correct answer below:Mean = 5, Median = 6The median is the better measure of central tendency.Mean = 5, Median = 6The mean is the better measure of central tendency.Mean = 6, Median = 5The median is the better measure of central tendency.Mean = 6, Median = 5The mean is the better measure of central tendency.
Explanation
we will begin by finding the mean and median of the data set
The mean is simply the average of the set, which will be
[tex]mean=\frac{5+0+5+2+0+10+7+8+10+21+5+8+2+5+3+5}{16}=\frac{96}{16}=6[/tex]The median is
[tex]\begin{gathered} \mathrm{The\:median\:is\:the\:value\:separating\:the\:higher\:half\:of\:the\:data\:set,\:from\:the\:lower\:half.} \\ \mathrm{If\:the\:number\:of\:terms\:is\:odd,\:then\:the\:median\:is\:the\:middle\:element\:of\:the\:sorted\:set} \\ If\:the\:number\:of\:terms\:\:is\:even,\:then\:the\:median\:is\:the\:arithmetic\:mean\:of\:the\:two\:middle\:elements\:of\:the\:sorted\:set \end{gathered}[/tex]Thus, we have the median as 5
To check which is a better measure, we will have to check the skewness
The skew value is 1.51
This means it is positively skewed
Thus
If the distribution is positively skewed then the mean is greater than the median which is in turn greater than the mode.
Therefore, the answer is
Suppose you ride your bicycle to the library traveling at .50 km/min. It takes you 25minutes to get to the library. How far did you travel
Answer:
50km
Step-by-step explanation:
We know that every minute we travel .5 km....
[tex]\frac{1 min}{.50 km}[/tex]
But we want to know how far we traveled in 25 mins
[tex]\frac{25 mins}{? km}[/tex]
So we go and do....
[tex]\frac{1 min}{.50 km} * \frac{25 mins}{? km}[/tex]
Then we have to divide 25 by .50
[tex]\frac{25 mins}{.50 km}[/tex]
Which Gives us
50 so he traveled 50km
Answer:
12.5km
Step-by-step explanation:
Hey! Let's help you with your question here!
We can begin by figuring out what we know!
Known InformationBicycle traveling at .50km/min (0.50km/min)It takes 25 minutes to get to the library.What we don't know and solving for itWhat we don't know is the distance traveled based on the given time. Now, what do we do? Well, we already know that the bicycle is traveling at a distance of .50km per minute and it takes us 25 minutes to get to the library. All we need to do here is take the distance per minute and multiply it by the total amount of minutes it takes to reach the destination. It would look something like this:
[tex]=(0.50km/s)*25[/tex]
[tex]=0.50*25[/tex]
[tex]=12.5[/tex]
Therefore, we can see that if we travel at a distance of .50km/min for 25 total minutes, we get a final distance of 12.5km.
Leah's Cafe has regular coffee and decaffeinated coffee. This morning, the cafe served 5 coffees in all, 20% of which were regular. How many regular coffees did the cafe serve? regular coffees
Let regular coffee be x and decaffeinated be y. If they served 5 coffees in all, and
The cost of a pound of nails increased from $2.03 to $2.19. What is the percent of increase to the nearest whole-number percent?(Type an integer
Hello there. To solve this question, we'll have to remember some properties about percents.
We start with percent of increase: it is the difference between how much a thing is from another and 100%.
Now, to calculate this amount, we take the ratio of the numbers. In this case, the cost of a pound of nails.
Knowing it increased from $2.03 to $2.19, we calculate:
2.19/2.03 = 1.079
Multiply by 100% to find its amount in percent
1.079 * 100% = 107.9%
Now, we simply take the difference:
107.9% - 100% = 7.9%
Rounding this percent to the nearest whole-number percent, we get:
8%
I need help with a homework
Consider the triangle PAM and triangle PBM.
[tex]\begin{gathered} \angle PMA=\angle PMB\text{ (Each angle is right angle)} \\ AM=BM\text{ (M is perpendicular bisector of AB)} \\ PM\cong PM\text{ (Common side)} \\ \Delta\text{PMA}\cong\Delta\text{PMB (By SAS similarity)} \\ PA\cong PB\text{ (Corresponding part of Congurent triangle)} \end{gathered}[/tex]Hence it is proved that,
[tex]PA\cong PB[/tex]A job placement agency advertised that last year its clients, on average, had a starting salary of $39,500. Assuming that average refers to the mean, which of the following claims must be true based on this information?Note: More than one statement could be true. If none of the statements is true, mark the appropriate box.Last year some of their clients had a starting salary of at least $39,500 .Two years ago some of their clients had a starting salary of at least $39,500 .Last year, the number of their clients who had a starting salary of more than $39,500 was equal to the number of their clients who had a starting salary of less than $39,500.Last year at least one of their clients had a starting salary of more than $42,000.Last year at least one of their clients had a starting salary of exactly $39,500.None of the above statements are true.
In the question, it is given that the average salary is $39,500.
In consideration of the first statement
(a) , last year, some of their clients had a starting of atleast $39500 ...this is true
(b) they have mentioned the case of last two years, this is also incorrect.
( c )if the client has lesser than $39,500 salary, and the average salary is $39,500 , then average will be less than $39,500, then statement a is not true..
(d) Last year at least one of their clients had a starting salary of more than $42,000., this is more than the average , but could be true, but it is false as $42000 will be more than the average of $39,500
(e) Last year at least one of their clients had a starting salary of exactly $39,500. ... this is not true, as exactly would not allow the $39,500 to be any less.
• So correct options would be A
P= rt , Solve for t in this literal equation
t = P/r
Explanations:The given equation is:
P = rt
To solve for t by dividing both sides by r
[tex]\begin{gathered} \frac{P}{r}=\frac{rt}{r} \\ \frac{P}{r}=t \end{gathered}[/tex]Therefore:
[tex]t\text{ = }\frac{P}{r}[/tex]For what value of x does f(x) = 1?
Answer Choices:
A. x = 0
B. x= 1
C. x = 5
D. x = -5
A card is selected from a standard deck of cards. What is the probability of selecting a King or an even card?
Given:
A card is selected from a standard deck of cards.
Required:
We need to find the probability of selecting a King or an even card.
Explanation:
The sample space =the total number of cards = 52.
[tex]n(S)=52[/tex]Let A be an event of selection a king.
The number of cards that is king = 4.
The favourable outcomes =The number of the card king
[tex]n(A)=4[/tex]The probability of selecting a king
[tex]P(A)=\frac{n(A)}{n(S)}=\frac{4}{52}[/tex]Let B be an event of selection an even card.
There are 5 even values (2,4,6,8,10) and 4 of each in the deck.
The number of cards that is even card=20.
The favourable outcomes =The number of the even card
[tex]n(B)=20[/tex]The probability of selecting an even card
[tex]P(B)=\frac{n(B)}{n(S)}=\frac{20}{52}[/tex]
The probability of selecting a King or an even card is
[tex]=P(A)+P(B)[/tex][tex]=\frac{4}{52}+\frac{20}{52}=\frac{24}{52}[/tex][tex]=\frac{6}{13}[/tex]Final answer:
The probability of selecting a King or an even card 6/13.
Don'te is sitting on the bus on the way home from school and is thinking about the fact that he has three homeworkassignments to do tonight. The table below shows his estimated probabilities of completing 0, 1, 2, or all 3 of theassignments.Number of Homework Assignments Completed0123Probability162951813What is the probability he will not do exactly 1 assignment?2/9Ob 7/9Ос 7/18Od 1
SOLUTION
Don'te is sitting on the bus on the way home from school and is thinking about the fact that he has three homework assignments to do tonight.
The table below shows his estimated probabilities of completing 0, 1, 2, or all 3 of the
assignments.
Number of Homework
Assignments Completed Probability
0 1/ 6
1 2/ 9
2 5/18
3 1/ 3
What is the probability he will NOT do exactly 1 assignment?
1/ 6 + 5 / 18 + 1/ 3 = 7 / 9 ................. OPTION B
Use inductive reasoning to find the next number in the pattern: 1 / 3 , 2 / 4, 3 / 5, ____.
..
SOLUTION
[tex]\frac{1}{3},\frac{2}{4},\frac{3}{5},...[/tex]The sequence progresses by the addition of 1 to both numberator and denominator.
[tex]\frac{3+1}{5+1}=\frac{4}{6}[/tex]The next number is 4/6.
I need help with this, i dont know what to do
We have given that
[tex]PQ=ST[/tex][tex]QR=TR[/tex]Given that R is the midpoint so
[tex]PR=SR[/tex]Hence
[tex]\Delta PQR\cong\Delta STR[/tex]BY SSS
Brennan puts 600.00 into an account to use for school expenses the account earns 11%interest compounded annually how much will be in the account after 6 years
Here,
P = 600
t = 6
n = 1 (annually)
r = 11% = 0.11
Applying the fromula to calculate compound interest we have,
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{ =600(1+0.11)}^6 \\ \text{ =1122.248} \end{gathered}[/tex]The answer is 1122.248.
Function gis represented by the equation.915) = –18(3) *+ 2Which statement correctly compares the two functions on the interval [-1, 2]?
step 1
Find out the average rate of change function f over the interval [-1,2]
[tex]\frac{f(b)-f(a)}{b-a}[/tex]we have
a=-1
b=2
f(a)=f(-1)=-22
f(b)=f(2)=-1
substitute
[tex]\frac{-1-(-22)}{2-(-1)}=\frac{21}{3}=7[/tex]step 2
Find out the average rate of change function g(x) over the interval [-1,2]
we have
a=-1
b=2
g(a)=g(-1)=-18(1/3)^-1+2=-52
g(b)=g(2)=-18(1/3)^2+2=0
substitute
[tex]\frac{0-(-52)}{2-(-1)}=\frac{52}{3}=17.3[/tex]therefore
17>7
the answer is option A28 Solve. 15 = 4n - 5
We have the next equation
[tex]15=4n-5[/tex]then we need to isolate the n
[tex]\begin{gathered} 4n=15+5 \\ 4n=20 \\ n=\frac{20}{4} \\ n=5 \end{gathered}[/tex]the value of n is 5
Assume the radius of a certain planet is 2460 km and the planet is a sphere. What is its surface area?
Answer:
Explanation:
The surface area of a sphere is calculated using the formula:
[tex]A=4\pi r^2[/tex]Given that the radius of a certain spherical planet, r = 2460 km
[tex]undefined[/tex]consider the relationship between f(x)=2^x and g(x)=log2 x.g is a reflection of f over the line y=x.True or False
the function
[tex]\log _2x[/tex]is the inverse function of
[tex]2^x^{}[/tex]On the graph, the inverse of a function is the reflection of the original function over the line y = x. Then, the statement is true
A data set consists of these points: (2, 4), (4, 7), (5, 12). Malinda found theregression equation to be ŷ = -2.5x - 1.5. Is she correct?A. No. The value for b is incorrect.B. Yes. This is the correct equation.OC. No. Both a and b are incorrect.D. No. The value for a is incorrect.
From the given cooridnate values, we can see that the linear regression model is given by:
the line
[tex]y=2.5x-1.5[/tex]If a and b denote the slope and y-intercept then , by comparing with the given solution, we can note that the slope (a) is incorrect. It must be 2.5 instead of -2.5. Therefore, the answer is option D
My questions are: #1) Determine the account balance at 4 years if $20,000 was invested in an account that compounds daily at 4.5% per year.#2) Determine the account balance at 5 years if $20,000 was invested in an account that compounds continuously at 4.5% per year.#3) A bacterial culture grows from 10 bacteria at 1.5% per minute starting at 7:00 a.m. find bacteria count after 12 hours if continues growth is assumed. (round down to the nearest whole bacterium)
We have the following formula:
[tex]P(t)=10\cdot(1.015)^t[/tex]where t is the amount of minutes we have waited. So in this case we have 12hours, therefore we have waited 12*60=720 minutes
so we have that after 720 minutes the population of bacteria is
[tex]10\cdot(1.015)^{720}=452428.98\approx452429[/tex]so the answer is 452429
write the equation of the line, with the given properties, in slope-intercept form.Slope=-6, through (-8,8)
The given slope is:
[tex]m=-6[/tex]And the point:
[tex](-8,8)[/tex]we label the coordinates as follows:
[tex]\begin{gathered} x_1=-8 \\ y_1=8 \end{gathered}[/tex]And now, we use the slope-point formula, which is:
[tex]y-y_1=m(x-x_1)[/tex]substituting the known values of slope m and the point:
[tex]y-8=-6(x-(-8))[/tex]We need to solve this for y to find the slope intercept form (which is y=mx+b):
[tex]\begin{gathered} y-8=-6(x+8) \\ y-8=-6x-48 \\ y=-6x-48+8 \\ y=-6x-40 \end{gathered}[/tex]The slope-intercept form is:
y = -6x - 40
The quotient of 93 and x
The quotient of ;
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