barbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. she wrote an equation to find the number of bottles she needs to sell to earn $100. 1.25x 1.49
she would need to sell at least 37 bottles to reach her earnings goal.
Let's assume that Barbara needs to sell x bottles to earn $100. The total revenue she generates from selling water can be calculated by multiplying the number of water bottles (x) by the price per water bottle ($1.25). Similarly, the total revenue from selling iced tea can be calculated by multiplying the number of iced tea bottles (x) by the price per iced tea bottle ($1.49).
To earn $100, the total revenue from selling water and iced tea should sum up to $100. Therefore, we can set up the following equation:
(1.25 * x) + (1.49 * x) = 100
Combining like terms, the equation becomes:
2.74 * x = 100
To find the value of x, we can divide both sides of the equation by 2.74:
x = 100 / 2.74
Evaluating the right side of the equation, we find:
x ≈ 36.50
Therefore, Barbara needs to sell approximately 36.50 bottles (rounded to the nearest whole number) of water and iced tea combined to earn $100.
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n divide 10 and 2 exponent = 0.123
n = _______
The complex numbers z and w are graphed. Which expression represents z + w? (2 + i) + (3 + i) (2 – i) + (3 + i) (2 – i) + (3 + 2i) (2 + i) + (3 + 2i)
Answer:
(2 - i) + (3 + 2i)
Step-by-step explanation:
got it right on edge 2020
Answer:
C. (2 – i) + (3 + 2i)
Step-by-step explanation:
3. solve - 7 - 6 = k
1
-13
13
-1
Answer:
k=-13...............
whats the percent? ............
Answer: 32%
Step-by-step explanation: add up the total and divide 16 by the total number of all people surveyed
Determine whether each ordered pair is a solution or not a solution to this system of inequalities.
y< −x
2x+y>2
The ordered pair that is the solution of the given system of inequalities is (2, -2)
What is inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given is a system of inequalities, y < -x and 2x+y > 2, we need to determine solution set of the given system of inequalities,
The inequalities are,
y < -x....(i)
2x+y > 2
y < 2-2x...(ii)
To find the ordered pair, put y = -x in equation Eq(ii) and replace < by =
-x = 2 - 2x
x = 2
y = -2
Therefore, the ordered pair, is (2, -2) {look at the graph attached}
Hence, the ordered pair that is the solution of the given system of inequalities is (2, -2)
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Which of these tables represents a function
Answer:
Z.
Step-by-step explanation:
A function must pass the Vertical Line Test. No 2 y-values can have the same x-values. Since the first 3 graphs fail to pass the vertical line test, our answer is Z.
Given line m is parallel to line n. What theorem or postulate justifies the statement? ∠1 ≅ ∠4
Answer:
corresponding angles postulate
Step-by-step explanation:
just took the test ;)
f (x) = 5x8 - 25x7
What is the degree of f
The degree of the polynomial defined by the function; f (x) = 5x⁸ - 25x⁷ as required in the task content is; eight, 8.
What is the degree of the polynomial defined by the function; f (x) = 5x⁸ - 25x⁷ as required in the task content?It follows from the task content that the degree of the polynomial in discuss is to be determined as required in the task content.
First, it is noteworthy to know that the degree of a polynomial is the greatest power of a variable present in the polynomial.
On this note, it follows that the degree of the function in this scenario is; 8.
Ultimately, The degree of the polynomial defined by the function; f (x) = 5x⁸ - 25x⁷ as required in the task content is; eight, 8.
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What is the quotient of (2x4 – 3x3 – 3x2 7x – 3) ÷ (x2 – 2x 1)?
The quotient of (2x4 – 3x3 – 3x2 7x – 3) ÷ (x2 – 2x 1) is 2x² + x – 3.
What is Quotient ?A quotient is a quantity produced by the division of two numbers.
The quotient is most frequently encountered as two numbers, or two variables, divided by a horizontal line. The words "dividend" and "divisor" refer to each individual part, while the word "quotient" refers to the whole.
For example when 8 is divided by 2, the result obtained is 3. Thus, the quotient is 4.
To determine the quotient when (2x4 – 3x3 – 3x2 + 7x - 3) is divided by (x2 - 2x + 1), we'll apply the long division method as shown below:
2x² + x – 3
x² - 2x + 1|2x⁴ – 3x² – 3x² + 7x - 3
–(2x⁴ – 2x³ + 2x²)
x³ – 5x² + 7x – 3
–(x³ – 2x² + x)
–3x² + 6x – 3
–(3x² + 6x – 3)
0
Thus, the quotient is 2x² + x – 3.
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Which of these steps will eliminate a variable in this system?
6x - 3y = 8
23 + 6y = 16
A. Multiply the first equation by 2. Then subtract the second equation
from the first
B. Multiply the second equation by 3. Then add the equations.
C. Multiply the second equation by 2. Then add the equations.
D. Multiply the second equation by 3. Then subtract the second
equation from the first.
Answer:Multiply the second equation by 3. Then subtract the second equation from the first.
Step-by-step explanation:
HELP ASAP
HELP ASAP
HELP ASAP
Find the values of m and n.
Determine the slope and the y-intercept of the line
Which system of inequalities with a solution point is represented by the graph? y > 2x – 2 and y < Negative one-halfx – 1; (3, 1) y > 2x – 2 and y < Negative one-halfx + 1; (–3, 1) y > 2x + 2 and y < Negative one-halfx – 1; (3, 1) y > 2x + 2 and y < Negative one-halfx + 1; (–3, 1)
The correct system of inequalities with a solution point represented by the graph is:
y > 2x – 2 and y < Negative one-half x + 1; (–3, 1)
To see why, we can plot the points given in each of the answer choices and see which one matches the graph:
Choice 1: (3, 1) is not on the shaded region of the graph, so this is not the correct answer.
Choice 2: (–3, 1) is on the shaded region of the graph, so this is a possible solution.
Let's check the other inequality to make sure it's also true: -1 < (-1/2)(-3) - 1. Simplifying, we get -1 < 2.
This is true, so we have a detailed solution.
Choice 3: (3, 1) is not on the shaded region of the graph, so this is not the correct answer.
Choice 4: (–3, 1) is on the shaded region of the graph, but the other inequality y > 2x + 2 is not true at that point. 1 is not greater than 2(-3) + 2 = -4, so this is not the correct answer.
Therefore, the detailed solution is: y > 2x – 2 and y < Negative one-half x + 1; (–3, 1)
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Find the value of f(3) for the function
f(x) = - 7 (x + 5)
f(3)=
Evaluate ∣∣256+y∣∣ for y=74. A. 225 B. 315 C. 345 D. 4712
The value of ∣∣2 5/6 + y∣∣ is 55/12 or 4 7/12/ The Option D.
What is the value of ∣∣2 5/6 + y∣∣ for y = 7/4?To evaluate the expression, substitute y = 7/4 into the given expression:
∣∣2 5/6 + (7/4)∣∣
Simplify expression inside the absolute value:
= 2 5/6 + 7/4
= (12/6 + 5/6) + (21/12)
= 17/6 + 21/12
To add the fractions, we need a common denominator:
17/6 + 21/12 = (2 * 17)/(2 * 6) + 21/12
= 34/12 + 21/12
= 55/12
Take absolute value of 55/12:
∣55/12∣ = 55/12
∣55/12∣ = 4 7/12.
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Consider the ordered bases B = {1,x,x²} and C = {1, (2-1), (x - 1)²} for P2. (a) Find the transition matrix from C to B. ge 2 of 1 (b) Find the transition matrix from B to C. pages after page (c) Write p(x) = a + bx + cx² as a linear combination of the polynomials in C.
a) The transition matrix from C to B is [1 0 0], [0 1 0], [0 0 1] b) The transition matrix from C to B is [1 0 0], [0 1 0], [0 0 1] c) p(x) = a + bx + cx² as a linear combination of the polynomials in C can be defined as p(x) = a + b + c(x - 1)²
(a) Finding the transition matrix from C to B
To find the transition matrix from C to B, we need to express the vectors in the basis C as linear combinations of the vectors in basis B.
Let's express each vector in basis C in terms of basis B
1 = 1(1) + 0(x) + 0(x²)
(2 - 1) = 0(1) + 1(x) + 0(x²)
(x - 1)² = 0(1) + 0(x) + 1(x²)
The coefficients of the linear combinations are the entries of the transition matrix from C to B. Thus, the transition matrix is
[1 0 0]
[0 1 0]
[0 0 1]
(b) Finding the transition matrix from B to C:
To find the transition matrix from B to C, we need to express the vectors in the basis B as linear combinations of the vectors in basis C.
Let's express each vector in basis B in terms of basis C
1 = 1(1) + 0(2 - 1) + 0((x - 1)²)
x = 0(1) + 1(2 - 1) + 0((x - 1)²)
x² = 0(1) + 0(2 - 1) + 1((x - 1)²)
The coefficients of the linear combinations are the entries of the transition matrix from B to C. Thus, the transition matrix is
[1 0 0]
[0 1 0]
[0 0 1]
(c) Writing p(x) = a + bx + cx² as a linear combination of the polynomials in C
To write p(x) = a + bx + cx² as a linear combination of the polynomials in C, we need to express the polynomial p(x) in terms of the basis C.
We have the basis C = {1, (2 - 1), (x - 1)²}
p(x) = a + bx + cx² = a(1) + b(2 - 1) + c((x - 1)²) = a + b(2 - 1) + c((x - 1)²)
Thus, the polynomial p(x) = a + bx + cx² can be written as a linear combination of the polynomials in C as
p(x) = a + b(2 - 1) + c((x - 1)²)
Simplifying further
p(x) = a + b + c(x - 1)²
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In a class of 38 students, the mean score on a statistics exam is 70, with a standard deviation of 9. Estimate the maximum score in the class.
The maximum score in the class is approximately 97. To estimate the maximum score in the class, we can use the concept of the normal distribution and z-scores.
Since the mean and standard deviation are given, we can assume that the scores on the statistics exam are normally distributed.
To estimate the maximum score, we need to determine how many standard deviations above the mean corresponds to the maximum score. In a normal distribution, approximately 99.7% of the data falls within three standard deviations of the mean. We can use this information to estimate the maximum score.
First, we calculate the z-score corresponding to the desired percentile (99.7%). The z-score formula is given by:
z = (X - μ) / σ
Where:
X is the maximum score
μ is the mean score
σ is the standard deviation
Rearranging the formula to solve for X, we have:
X = z * σ + μ
Substituting the values we have:
X = 3 * 9 + 70
X = 27 + 70
X ≈ 97
Therefore, we can estimate that the maximum score in the class is approximately 97.
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Enter the value of 12x-2 when x = 3.
Answer:
34
Step-by-step explanation:
12(3)-2
36-2
34
Answer:
im sorry if this is wrong but i think its 2
If (2, 5) is a solution of the equation 2x + 3y = m, find the value of m
Work Shown:
2x + 3y = m
m = 2x + 3y
m = 2(2) + 3(5)
m = 4 + 15
m = 19
The idea is to replace x with 2 and y with 5. Then use PEMDAS to simplify. When it comes to ordered pairs, the x coordinate is always listed first.
In inferential statistics, the objective is to determine how probable it is that:
The alternative hypothesis is true.
The null hypothesis is true.
The alternative hypothesis is false.
The null hypothesis is false.
In inferential statistics, the objective is to determine the probability of the alternative hypothesis being true or the null hypothesis being true.
This involves using sample data to make inferences and draw conclusions about a larger population. By analyzing the data and performing statistical tests, we assess the likelihood of the alternative hypothesis or the null hypothesis being accurate.
The alternative hypothesis represents a claim or statement that contradicts the null hypothesis and suggests that there is a significant relationship or difference between variables. To determine its probability, statistical methods such as hypothesis testing and p-values are employed. These methods evaluate the strength of evidence against the null hypothesis and support the alternative hypothesis when the evidence is substantial.
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Round to the nearest hundredth
48.849
Use the information to answer the question.
Karim has 71 beads. Thomas has 7 beads.
How many more beads does Karim have than Thomas? Enter the answer
in the box.
Answer: 54
Step-by-step explanation:
71-7= 54
Uhm... What grade are you in?
Hope this helps!
Hi guys! I really need help with this because im so stressed with my other classes and i need to pass this class in order to graduate. can someone help
Answer:
\(94.6ft^{2}\)
Step-by-step explanation:
\(A=\frac{(bx_{1}+bx_{2} )h }{2}\)
\(A=\frac{(7.7+14.3)(8.6)}{2}\)
\(answer:- 94.6 ft^{2}\)
\(---------\)
hope it helps...
have a great day!!
Answer:
area = 94.6 ft.sq
Step-by-step explanation:
here's your solution
==> area of trapezium = 1/2*(sum of parrel side)*distance between them
==> area of trapezium = 1/2(7.7 + 14.3)*8.6
==> area of trapezium = 1/2*22*8.6
==> area = 11*8.6
==> area = 94.6 ft.sq
hope it helps
a rectangular piece of metal is 10 in longer than it is wide. squares with sides 2 in long are cut from the four corners and the flaps are folded upward to form an open box. if the volume of the box is 671 in, what were the original dimensions of the piece of metal?
The length and width of the piece of metal are 28 and 18 inches respectively.
What is volume?
The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.
Dimension of the rectangle;
Width(w)
Length,L= 10 + w
volume of the box = length * width * height
Dimension of the box;
length of box, (x + 10) - 4 = x + 6
width of box,(x - 4)
height of box = 2
The volume of the box is 672 in³;
⇒V=lwh
⇒V=2 (x -4)( x + 6)
⇒672 in³ = 2x² + 4x - 48
⇒2x² + 4x - 720 = 0
⇒x^2 + 2x - 360 = 0
⇒(x +20)(x - 18) = 0
⇒x = 18
⇒x=-20 (value of the dimension will not be negative.
The width of an original piece of metal is;
Width,w=18 inches
length,l= 28 inches
Hence. the length and width of the piece of metal are 28 and 18 inches respectively.
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Select all the functions that show an inverse variation...
a) y=6x
b) y=3/x
c) y=1/3x
d) y= -.07x
e) y= 2/x+4
f) xy=-3
Function y=3/x, y= 2/x+4, and xy=-3 shows an inverse variation option (b), (e), and (f) are correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
As we know, when x is not equal to zero and k is a nonzero real number constant, the equation of the form xy = k describes the nonlinear function known as inverse variation.
a) y=6x
The above function is a linear function
b) y=3/x
or
xy = 3
The above function shows an inverse variation.
c) y=1/3x
or
y = (1/3)x
The above function is a linear function
d) y= -.07x
The above function is a linear function
e) y= 2/x+4
or
y = (2+4x)/x
xy = 2 + 4x
The above function shows an inverse variation.
f) xy=-3
The above function shows an inverse variation.
Thus, function y=3/x, y= 2/x+4, and xy=-3 shows an inverse variation option (b), (e), and (f) are correct.
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if the chi-squared goodness-of-fit test is used with a significance of 0.05 to test whether random values have been appropriately generated by the device, what is the p-value of the test rounded to two places after the decimal, and what is the appropriate decision?
The random number generation by the device is not appropriate for generating values according to the Binomial distribution with n=5 and p=0.45.
To test whether the generated values follow the expected Binomial distribution, we can use the Chi-squared goodness-of-fit test. The steps to perform this test are as follows
Define the null hypothesis and alternative hypothesis. In this case, the null hypothesis is that the generated values follow the expected Binomial distribution with n=5 and p=0.45. The alternative hypothesis is that the generated values do not follow this distribution.
Choose a significance level. In this case, the significance level is 0.05.
Calculate the expected frequencies for each category of the Binomial distribution with n=5 and p=0.45. We can use the formula for the Binomial distribution to calculate the probabilities, and then multiply them by the total number of observations to get the expected frequencies.
Expected frequency for each category = P(category) x total number of observations
Expected frequency for category 0 = P(0) x 1200 = 0.0176 x 1200 = 21.12
Expected frequency for category 1 = P(1) x 1200 = 0.1284 x 1200 = 154.08
Expected frequency for category 2 = P(2) x 1200 = 0.3574 x 1200 = 428.88
Expected frequency for category 3 = P(3) x 1200 = 0.4162 x 1200 = 499.44
Expected frequency for category 4 = P(4) x 1200 = 0.1949 x 1200 = 233.88
Expected frequency for category 5 = P(5) x 1200 = 0.0055 x 1200 = 6.6
Calculate the Chi-squared test statistic. The formula for the Chi-squared test statistic is:
Chi-squared = Σ ( (observed frequency - expected frequency)^2 / expected frequency )
where Σ is the sum over all categories. Using the expected frequencies and the observed frequencies from the table, we can calculate the Chi-squared test statistic
Chi-squared = ( (28-21.12)^2 / 21.12 ) + ( (168-154.08)^2 / 154.08 ) + ( (423-428.88)^2 / 428.88 ) + ( (459-499.44)^2 / 499.44 ) + ( (105-233.88)^2 / 233.88 ) + ( (17-6.6)^2 / 6.6 ) = 94.67
Calculate the degrees of freedom. The degrees of freedom for the Chi-squared test are equal to the number of categories minus 1. In this case, there are 6 categories, so the degrees of freedom are 5.
Calculate the P-value of the test. We can use a Chi-squared distribution table or a calculator to find the P-value for the Chi-squared test with 5 degrees of freedom and a test statistic of 94.67. The P-value is less than 0.01 (about 0.000000000000000000000000000000000000000001), so we reject the null hypothesis that the generated values follow the expected Binomial distribution with n=5 and p=0.45.
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The given question is incomplete, the complete question is:
A random number generation device is expected to generate random values according to the Binomial distribution with n=5 and p=0.45. To ensure that the device's random number generation is appropriate, 1200 recently generated random values by this device have been organized in the following table. If the Chi-squared goodness-of-fit test is used with a significance of 0.05 to test whether random values have been appropriately generated by the device, what is the P-value of the test rounded to two places after the decimal, and the decision made?
3+5.2x=1−2.8x? what is the solution? im stuck
Answer:
x = -1/4
Step-by-step explanation:
3 + 5.2x = 1 - 2.8x
5.2x + 2.8x = 1 - 3
8x = -2
x = -1/4
what's the name of the ray
I need help with this question. Pls give me an answer /steps and explanations.
\(\bold{30s^{5}t^{9}u^{10}v^{8}}\)
Answer:
Express your answer using positive exponent.
\(\bold{(5st³u^{9}v^{7})(6s⁴t^{6}uv)}\)
adding power of common term and multiply constant term:
\(\bold{5*6*s^{1+4}*t^{3+6}*u^{9+1}*v^{7+1}}\)
\(\bold{30s^{5}*t^{9}*u^{10}*v^{8}}\)
\(\bold{30s^{5}t^{9}u^{10}v^{8}}\)
Answer:
\(30s^5t^9u^{10}v^8\)
Step-by-step explanation:
We'll be using the following exponent property to solve this problem:
\(a^b\cdot a^c=(a)^{b+ c}\)
This will allow us to combine terms with the same variable.
In \((5st^3u^9v^7)(6s^4t^6uv)\), we have four variables, \(s\), \(t\), \(u\), and \(v\).
Let's start with the \(s\) terms, \(5s\) and \(6s^4\). The number in front of each term is called the coefficients, and can be multiplied directly. Remember that if there is no exponent written, it's the same thing as if there was an exponent of 1.
Therefore, combine using the exponent property I mentioned above:
\(5\cdot 6\cdot s^1\cdot s^4=30\cdot s^{1+4}=30s^5\)
Next, we'll move on to the \(t\) terms, \(t^3\) and \(t^2\).
Combine using the exponent property:
\(t^3\cdot t^6=t^{3+6}=t^9\)
Repeat for the \(u\) and \(v\) terms:
\(u^9\cdot u=u^{9+1}=u^{10}\)
\(v^7\cdot v=v^{7+1}=v^8\)
Finally, combine all the terms together:
\(\implies \boxed{30s^5t^9u^{10}v^8}\)