Answer:
[tex]-2[/tex]
Step-by-step explanation:
Just substitute -3 for all instances of x.
[tex](-3)^{2} + 4(-3) + 1\\\\[/tex]
[tex]9 - 12 + 1[/tex]
[tex]-2[/tex]
Nuts Galore sells a trail mix containing dried banana chips, roasted almonds, and chocolate chips that sells for $6.52 per pound. The dried banana chips costs $4 per pound, the roasted almonds cost $8 per pound, and the chocolate chips cost $6 per pound. The amount of roasted almonds used is three times the amount of chocolate chips used. If they plan to make 100 pounds of this trail mix, how many pounds of each ingredient should be used
Answer:
[tex]x = 28[/tex] ----- Banana
[tex]y = 54[/tex] ----- Almonds
[tex]z = 18[/tex] ---- Chocolate
Step-by-step explanation:
Let
[tex]x \to[/tex] banana
[tex]y \to[/tex] almonds
[tex]z \to[/tex] chocolate
So, we have:
[tex]x + y + z = 100[/tex] --- total used
[tex]4x + 8y + 6z = 652[/tex] -- i.e. 6.52 * 100 --- total sales from 100 pounds
[tex]y = 3z[/tex]
Required
The number of pounds of each (i.e. x, y and z)
Substitute [tex]y = 3z[/tex] in [tex]x + y + z = 100[/tex]
[tex]x + 3z + z = 100[/tex]
[tex]x + 4z = 100[/tex]
Make x the subject
[tex]x = 100 - 4z[/tex]
Substitute [tex]y = 3z[/tex] in [tex]4x + 8y + 6z = 652[/tex]
[tex]4x + 8 * 3z + 6z = 652[/tex]
[tex]4x + 24z + 6z = 652[/tex]
[tex]4x + 30z = 652[/tex]
Substitute [tex]x = 100 - 4z[/tex]
[tex]4(100 - 4z) + 30z = 652[/tex]
[tex]400 - 16z + 30z = 652[/tex]
Collect like terms
[tex]- 16z + 30z = 652-400[/tex]
[tex]14z = 252[/tex]
Divide by 14
[tex]z = 18[/tex]
Substitute [tex]z = 18[/tex] in [tex]x = 100 - 4z[/tex]
[tex]x = 100 - 4 * 18[/tex]
[tex]x = 100 - 72[/tex]
[tex]x = 28[/tex]
To calculate y, we have:
[tex]y = 3z[/tex]
[tex]y = 3 * 18[/tex]
[tex]y = 54[/tex]
Solve by using matrices. 2x – y +2 + w = -3 x + 2y – 3z + w = 12 3x - y - + 2w = 3 -2x + 3y + 2 – 3w = -3
Some symbols and numbers are missing. I assume the system is supposed to read
2x - y + 2z + w = -3
x + 2y - 3z + w = 12
3x - y - z + 2w = 3
-2x + 3y + 2z - 3w = -3
In matrix form, this is
[tex]\begin{bmatrix}2&-1&2&1\\1&2&-3&1\\3&-1&-1&2\\-2&3&2&-3\end{bmatrix}\begin{bmatrix}x\\y\\z\\w\end{bmatrix}=\begin{bmatrix}-3\\12\\3\-3\end{bmatrix}[/tex]
which we can strip down to the augmented matrix,
[tex]\left[\begin{array}{cccc|c}2&-1&2&1&-3\\1&2&-3&1&12\\3&-1&-1&2&3\\-2&3&2&-3&-3\end{array}\right][/tex]
Now for the row operations:
• swap rows 1 and 2
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\2&-1&2&1&-3\\3&-1&-1&2&3\\-2&3&2&-3&-3\end{array}\right][/tex]
• add -2 (row 1) to row 2, -3 (row 1) to row 3, and 2 (row 1) to row 4
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&-7&8&-1&-33\\0&7&-4&-1&21\end{array}\right][/tex]
• add 7 (row 2) to -5 (row 3), and row 3 to row 4
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&16&-2&-24\\0&0&4&-2&-12\end{array}\right][/tex]
• multiply through rows 3 and 4 by 1/2
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&8&-1&-12\\0&0&2&-1&-6\end{array}\right][/tex]
• add -4 (row 4) to row 3
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&0&3&12\\0&0&2&-1&-6\end{array}\right][/tex]
• swap rows 3 and 4
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&2&-1&-6\\0&0&0&3&12\end{array}\right][/tex]
• multiply through row 4 by 1/3
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&2&-1&-6\\0&0&0&1&4\end{array}\right][/tex]
• add row 4 to row 3
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&2&0&-2\\0&0&0&1&4\end{array}\right][/tex]
• multiply through row 3 by 1/2
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]
• add -8 (row 3) and row 4 to row 2
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&0&0&-15\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]
• multiply through row 2 by -1/5
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&1&0&0&3\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]
• add -2 (row 2) and 3 (row 3) and -1 (row 4) to row 1
[tex]\left[\begin{array}{cccc|c}1&0&0&0&-1\\0&1&0&0&3\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]
Then the solution to the system is (x, y, z, w) = (-1, 3, -1, 4).
11. Which point is not on the graph of 2x + 3y - Z - 12 = 0?
(6, 0, 0)
(3,3,3)
(0, 4,0)
(1, 1, 7)
PLEASE HELP ASAP !! WILL MARK BRAINLIEST
I think it might be the 3rd option
Step-by-step explanation:
A 19 in. monitor has a length of 16 in. What is its width?
10.25 in.
14.64 in.
16.51 in.
18.91 in.
Which of these figures has rotational symmetry?
Hello!
The answer is a.
Good luck! :)
9 friends are lining up. Joe, Susan, John, and Meredith must be beside each other. How many ways can they line up?
This is one single number slightly over 17 thousand.
You may need to erase the comma when typing the answer in.
=========================================================
Explanation:
Let's say that another person steps in for Joe, Susan, John, and Meredith. I'll refer to this person as the teacher (perhaps these 9 friends are students on a field trip).
The 9 friends drops to 9-4 = 5 people when those four named people leave the group temporarily. Then it bumps up to 5+1 = 6 people when the teacher steps in. Wherever the teacher is located, the four friends that left will replace the teacher. This guarantees that those four friends stick together.
There are 6! = 6*5*4*3*2*1 = 720 ways to arrange those 6 people. The exclamation mark is a factorial symbol.
Within any of those 720 permutations, we have 4! = 4*3*2*1 = 24 ways to arrange those group of named people when they come back to replace the teacher.
So overall the answer is 4!*6! = 24*720 = 17,280
You may need to erase the comma when typing the answer in.
-------------
Side note: There are 9! = 362,880 ways to arrange all nine friends regardless if those four mentioned people stick together or not. We see that they stick together roughly (17,280)/(362,880) = 0.0476 = 4.76% of the time.
What is the domain of D(t) as it applies in this situation?
Answer:
t could be all real numbers.
Step-by-step explanation:
The function D(t) is given by:
[tex]D(t)=-1.5t+12[/tex]
The domain is all the posible x-values for which the function is defined.
In our case, t could be all real numbers.
The answer is the first option.
I hope it helps you!
what is the measure of angle X in degrees
Answer:
If you are working with equilateral triangles, divide 180 by three to find the value of X. All of the angles of an equilateral triangle are equal. Solve for X in interesting lines by finding the value of one adjacent angle and subtracting it from 180 degrees.
Step-by-step explanation:
There are 4 contestants in a beauty pageant. How many results are possible for the first, second, and third place?
Explanation:
There are 4 choices for first place, 3 choices for second place, and 2 choices for third place. Overall, there are 4*3*2 = 24 permutations.
What is the range of g?
y
--
.
9
7.
6+
5+
4+
3+
2+
1+
.
3
{4}}
-7 -6 -5 -4 -3 -2
+++
2 3 4 5 6 7
-2
-3
-4+
-5
-6+
7
7
Answer:
y 9 5 473648
Step-by-step explanation:
The function y=5(1/2)^x Models the number of grams of radioactive material, y, left in a container after x days. Sketch the graph of this function below
Answer:
see graph
Step-by-step explanation:
solve the system of equations using substitution or graphing.
Step-by-step explanation:
I think substitution would be the easiest since you already have one of the variables solved for.
[tex]y=-x^2+4x+5\\y=x+1\\x+1=-x^2+4x+5\\x^2-3x-4=0\\(x-4)(x+1)=0\\x-4=0\\x=4\\x+1=0\\x=-1[/tex]
(You can just set the equations equal to each other since they both equal y).
Now, to get the points, plug in x = 4 and x = -1 into one of the equations (I'm going to plug them into y = x+1 because that one is much simpler)
[tex]y(4)=4+1\\y(4)=5\\y(-1)=-1+1\\y(-1)=0[/tex]
So, your final points are:
(4,5) and (-1,0)
Answer: A
Step-by-step explanation:
We can use substitution to solve this problem. Since we are given y=-x²+4x+5 and y=x+1, we can set them equal to each other.
-x²+4x+5=x+1 [subtract both sides by x]
-x²+3x+5=1 [subtract both sides by 1]
-x²+3x+4=0
Now that we have the equation above, we can factor it to find the roots.
-x²+3x+4=0 [factor out -1]
-1(x²-3x-4)=0 [factor x²-3x-4]
-1(x+1)(x-4)=0
This tells us that x=-1 and x=4.
We can narrow down our answer to A, but let's plug in those values to be sure it is correct.
-(-1)²+4(-1)+5=(-1)+1 [exponent]
-1+4(-1)+5=-1+1 [multiply]
-1-4+5=-1+1 [add and subtract from left to right]
0=0
-------------------------------------------------------------------------------------------
-(4)²+4(4)+5=(4)+1 [exponent]
-16+4(4)+5=4+1 [multiply]
-16+16+5=4+1 [add and subtract from left to right]
5=5
Therefore, we can conclude that A is the correct answer.
6v^2x^3y^7 and 20v^8x^5
Answer:
LCD????
[tex]2v^2x^3[/tex]
Step-by-step explanation:
As part of a classic experiment on mutations, 10 aliquots of identical size were taken from the same cul-ture of the bacterium E. coli. For each aliquot, the number of bacteria resistant to a certain virus was determined. The results were as follows:
14 15 13 21 15
14 26 16 20 13
Construct a frequency distribution of these days and display it as a histogram.
Determine the mean and the median of the dad and mark their locations on the histogram.
Answer:
a. See the attached excel file for the frequency distribution table, and the attached photo for the histogram.
b. We have:
Mean = 16.7
Median = 15
Note: See the attached photo for the locations of Mean and Median on the histogram.
Step-by-step explanation:
a. Construct a frequency distribution of these days and display it as a histogram.
Note: See the attached excel file for the frequency distribution table, and the attached photo for the histogram.
b. Determine the mean and the median of the dad and mark their locations on the histogram.
From the attached excel file, we have:
Total of F = 10
Total of FX = 167
Therefore, we have:
Mean = 167 / 10 = 16.7
Median is the middle number after arranged the data in ascending or descending order. Using the ascending order, we have:
13 13 14 14 15 15 16 20 21 26
Since 15 and 15 are in the middle, their average are the median which is calculated as follows:
Median = (15 + 15) / 2 = 15
Note: See the attached photo for the locations of Mean and Median on the histogram.
if a x + B Y is equal to a square minus b square and b x + A Y is equal to zero find the value of x + Y
9514 1404 393
Answer:
a-b
Step-by-step explanation:
Add the two equations together:
(ax +by) +(bx +ay) = (a² -b²) +(0)
x(a +b) +y(a +b) = (a +b)(a -b)
x + y = a - b . . . . . divide by (a+b), assuming a+b ≠ 0
Helppp and explain!!!
In how many ways could nine people be divided into two groups of two people and one group of five people?
Nine people could be divided into two groups of two people and one group of five people ways.
(Type a whole number.)
Answer:
your can only divide then up in that specific sequence one time
g A two-factor study with 3 levels of factor A and 3 levels of factor B uses a separate sample of 10 participants in each treatment condition. How many participants are needed for the entire study
Answer:
the total number of participants required is 90
Step-by-step explanation:
Given the data in the question;
Factor A has three levels
Factor B has three levels
sample size n; ten participants
we have two Way ANOVA involving Factor A and Factor B.
Now,
{ Total # Participants Required } = { #Levels factor A } × { #Levels factor B } × { Sample size of each level }
we substitute
{ Total # Participants Required } = 3 × 3 × 10
{ Total # Participants Required } = 9 × 10
{ Total # Participants Required } = 90
Therefore, the total number of participants required is 90
HELP PLEASE QUICK
use the graphs of f and g to describe the transformation from the graph of f to the graph of g.
f(x)=2x+3
g(x)=f(x)-2
Answer:
2x - 1
Step-by-step explanation:
that is the procedure above
Ngân hàng rơi vào tình trạng vỡ nợ khi nào
Answer:
.
Step-by-step explanation:
.
2. H = 5 cm
W= 4 cm
L= 8 cm
V= L×W×H
=___×___×___
=______cm3
Answer:
160cm^3
Step-by-step explanation:
5 x 4 x 8 = 160cm^3
Simultaneous equations 5x-4y=19
x+2y=8
Answer:
x = 5 and y = 1.5
Step-by-step explanation:
hope this helps please like and mark as brainliest
jenny has 3 cherry candies and 3 orange candies. She takes out 2 candies without looking.What is the probability in fractions that both are cherry?
its
A bag contains 5 green candies and 7 blue candies.
A piece of candy is selected at random, put back into the bag, and then
another piece of candy is chosen.
What is the probability that both pieces are green?
Answer:
[tex]P(Green\ and\ Green) = \frac{25}{144}[/tex]
Step-by-step explanation:
Given
[tex]Green=5[/tex]
[tex]Blue = 7[/tex]
Required
[tex]P(Green\ and\ Green)[/tex]
This is calculated as:
[tex]P(Green\ and\ Green) = P(Green) * P(Green)[/tex]
Since, it is a probability with replacement, we have:
[tex]P(Green\ and\ Green) = \frac{Green}{Total} * \frac{Green}{Total}[/tex]
So, we have:
[tex]P(Green\ and\ Green) = \frac{5}{12} * \frac{5}{12}[/tex]
[tex]P(Green\ and\ Green) = \frac{25}{144}[/tex]
suppose y varies inversely with X, and y = 48 when x = 3. What is the value of x when y = 24?
NO LINKS OR ANSWERING YOU DON'T KNOW.
a. 3
b. 12
c. 6
d. 24
Answer:
C. 6
Step-by-step explanation:
Recall that inverse variation is given by:
[tex]\displaystyle y=\frac{k}{x}[/tex]
Where k is the constant of variation.
We know that y = 48 when x = 3. Substitute:
[tex]\displaystyle (48)=\frac{k}{(3)}[/tex]
Solve for k:
[tex]k=3(48)=144[/tex]
Hence, our equation is:
[tex]\displaystyle y=\frac{144}{x}[/tex]
We want to find x when y = 24. Substitute:
[tex]\displaystyle \frac{24}{1}=\frac{144}{x}[/tex]
Cross-multiply:
[tex]24x=144[/tex]
Divide both sides by 24. Hence:
[tex]x=6[/tex]
Our answer is C.
what is the value of x? 4/5x-1/10=3/19
Answer:
x=[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Hi there!
We are given the following equation:
[tex]\frac{4x}{5}[/tex]-[tex]\frac{1}{10}[/tex]=[tex]\frac{3}{10}[/tex]
and we need to find the value of x
To do this, we need to isolate the value of x with a coefficient of 1 (1x) on one side. The value of x, or everything else is on the other side
So let's get rid of [tex]\frac{1}{10}[/tex] from the left side by adding [tex]\frac{1}{10}[/tex] to both sides (-[tex]\frac{1}{10}[/tex]+[tex]\frac{1}{10}[/tex]=0).
[tex]\frac{4x}{5}[/tex]-[tex]\frac{1}{10}[/tex]=[tex]\frac{3}{10}[/tex]
+[tex]\frac{1}{10}[/tex] +[tex]\frac{1}{10}[/tex]
___________
[tex]\frac{4x}{5}[/tex]=[tex]\frac{3}{10}[/tex]+[tex]\frac{1}{10}[/tex]
as the fractions on the right side both have the same denominator, we can add them together
[tex]\frac{4x}{5}[/tex]=[tex]\frac{4}{10}[/tex]
Now we need to have the value of 1x. Currently we have [tex]\frac{4x}{5}[/tex].
In order to get x with a coefficient of 1, multiply both sides by the reciprocal of [tex]\frac{4}{5}[/tex], which is [tex]\frac{5}{4}[/tex]
[tex]\frac{5}{4}[/tex]×[tex]\frac{4x}{5}[/tex]=[tex]\frac{4}{10}[/tex]*[tex]\frac{5}{4}[/tex]
which simplifies down to
x=[tex]\frac{20}{40}[/tex]
Now reduce the fraction by dividing the numerator and denominator both by 20
x=[tex]\frac{1}{2}[/tex]
Hope this helps!
If you select a random sample of 6 people, what is the probability that all but one of them are using Chrome as their browser? (show all work - use data below)
Use the data provided below:
Chrome: 52.57%
Safari: 31.17%
Firefox: 4.29%
Edge: 2.91%
IE: 2.47%
Samsung: 2.36%
Answer:
0.1143 = 11.43% probability that all but one of them are using Chrome as their browser
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they use Chrome, or they do not. The probability of a person using Chrome is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Chrome: 52.57%
This means that [tex]p = 0.5257[/tex]
Sample of 6 people
This means that [tex]n = 6[/tex]
What is the probability that all but one of them are using Chrome as their browser?
5 using Chrome, so:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{6,5}.(0.5257)^{5}.(1-0.5257)^{1} = 0.1143[/tex]
0.1143 = 11.43% probability that all but one of them are using Chrome as their browser
What is the graph of x=1
Answer:
Slope: Undefined
Step-by-step explanation:
Since x=1
is a vertical line, there is no y-intercept and the slope is undefined.
y-intercept: No y-intercept
So i have a puppy that im bottle feeding because the momma died. I have to feed him 4 ounces a day every 3 hours. I'm using a syringe that goes up to 3ML. There are 29MLs in an ounce so that means i would fill up my syringe 9 times for an ounce. There are 8 feeding sessions in 24hours and I'm trying to figure out how many MLs to feed every 3 hours. I know this is simple math but I haven't slept in 4 days since I've had the puppy and my brain hurts from the lack of sleep.. Pleae help!!
Answer:
116ML every 3 hours, 928ML a day
Step-by-step explanation:
You said it yourself if there is 29ML in one once and you need 4 ounces every 3 hours then 29 x 4 = 116.
