The integral ∫2(3+5)9 = 16(81/2 + C) = 648 + 16C.
To find the definite integral ∫2(3+5)9, you need to evaluate the expression using the formula of integration.
Here's how you can solve the integral:∫2(3+5)9= ∫2(8)9Taking 8 as constant, we can further simplify the equation:∫2(8)9 = 16∫9 Now using the formula of integration,∫and = (x^n+1) / (n+1) + C where C is the constant of integration.
∫9dx = (9^1+1) / (1+1) + C= (9^2) / 2 + C= 81/2 + C
Hence, the answer is 648 + 16C. Note that the integration constant C can be any real number as it has no effect on the integral.
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A university conducted a survey of its recent graduates. The university wanted to
measure the quality of a new Engineering course. A survey was conducted during the
first offering of the course to evaluate its overall quality. The results of the survey
are shown below:
Needs Improvement: 55%
Meets Expectations: 30%
Excellent: 15%
The university made improvements to the course earlier this year. Then it conducted
another survey to evaluate how these improvements worked. A total of 500 students
were surveyed. Their results are shown below:
Needs Improvement: 175 students
Meets Expectations: 225 students
Excellent: 100 students
You want to perform a chi-squared test for goodness of fit, to see if students’ views have changed about the course. Which of the following python scripts prints the P-value and test statistic for the chi-squared test?
Step-by-step explanation:
To perform a chi-squared test for goodness of fit in Python and obtain the P-value and test statistic, you can use the scipy.stats module. Here's an example script that calculates the chi-squared test and prints the P-value and test statistic:
pythonCopy code
from scipy.stats import chi2_contingency # Observed frequencies from the first survey observed_freq_1 = [55, 30, 15] # Expected frequencies based on the proportions in the second survey total_students_2 = 500 expected_freq_2 = [total_students_2 * 0.55, total_students_2 * 0.3, total_students_2 * 0.15] # Perform chi-squared test chi2, p_value = chi2_contingency([observed_freq_1, expected_freq_2]) # Print the results print("Test statistic:", chi2) print("P-value:", p_value)
In this script, we use the chi2_contingency function from scipy.stats to perform the chi-squared test. We provide the observed frequencies from the first survey and the expected frequencies based on the proportions in the second survey. The function returns the test statistic and P-value, which we then print.
Note that this chi-squared test assumes that the observed and expected frequencies are independent. It also assumes that the expected frequencies are not too small (typically, no expected frequency should be less than 5) for the test to be valid.
e manager of a store that specializes in selling tea desides to experiment with a new blend. she will mix some earl gray tea that sells for $4 per pound with some orange pekoe the that sells for $2 per pound to get 200 pounds of the new blend. the selling price is the new blend is to be $2.50 per pound. and there is to be no difference in revenue from selling the new brand versus selling the other types. how many pounds of earl gray tea and pekoe tea are required
The manager needs 50 pounds of Earl Grey Tea and 150 pounds of Orange Pekoe Tea.
Let the amount of Earl Grey Tea (which sells for $4 per pound) be represented by x, then the amount of Orange Pekoe Tea (which sells for $2 per pound) is 200-x. We want to determine how much of each type of tea should be mixed so that the new blend will sell for $2.50 per pound.
Step-by-step explanation:The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey Tea that sells for $4 per pound with some Orange Pekoe Tea that sells for $2 per pound to get 200 pounds of the new blend.
We are to determine how many pounds of Earl Grey Tea and Pekoe Tea are required if the selling price of the new blend is to be $2.50 per pound. Let x be the amount of Earl Grey Tea (which sells for $4 per pound). Then the amount of Orange Pekoe Tea (which sells for $2 per pound) is 200-x.
We want to determine how much of each type of tea should be mixed so that the new blend will sell for $2.50 per pound. We can start the problem by setting up an equation that relates the price of the new blend with the prices of the two types of tea:4x + 2(200-x) = 2.5(200).
Simplify and solve for x:4x + 400 - 2x = 5002x + 400 = 5002x = 100x = 50.
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45 percent of consumers prefer to purchase electronics online. You randomly select 8 consumers. Find the probability that the number of consumers who prefer to purchase electronics online is (a) exactly five, (b) more than five, and (c) at most five.
a) The probability that exactly five consumers prefer to purchase electronics online is: 0.2604.
b) The probability that more than five consumers prefer to purchase electronics online is: 0.3624.
c) The probability that at most five consumers prefer to purchase electronics online is: 0.6376.
How to solve Binomial Probability Distribution Problems?(a) The binomial probability formula is expressed as:
P(X = k) = ([tex].^{n} C_{k}[/tex]) * [tex]p^{k}[/tex] * [tex](1 - p)^{n - k}[/tex]
where:
n = number of trials
k = number of successes
p = probability of success
We are given:
n = 8
k = 5
p = 0.45
Thus,
P(X = 5) = (8C5) * (0.45)⁵ * (1 - 0.45)⁽⁸⁻⁵⁾
P(X = 5) ≈ 0.2604
(b) To find the probability that more than five consumers prefer to purchase electronics online is:
P(X > 5) = P(X = 6) + P(X = 7) + P(X = 8)
P(X > 5) = [(⁸C₆) * (0.45)⁶ * (0.55)²] + [(⁸C₇) * (0.45)⁷ * (0.55)¹] + [(⁸C₈) * (0.45)⁸ * (0.55)⁰]
P(X > 5) ≈ 0.3624
(c) To find the probability that at most five consumers prefer to purchase electronics online is:
P(X ≤ 5) = 1 - P(X > 5)
P(X ≤ 5) ≈ 1 - 0.3624
P(X ≤ 5) ≈ 0.6376
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What is the standard form of the equation of f(x)?
Answer:
Standard form: f(x) = -x^2 + 6x + 16
Step-by-step explanation:
Identifying the function:
The graph is a parabola, which means f(x) is a quadratic function.General equation of a quadratic's standard form:
The general equation for the standard form of a quadratic function is given by:
f(x) = ax^2 + bx + c
Method to find the standard form of the equation of f(x):
We can find either the vertex form or the intercept form, whose general equations are given by:
Vertex form: f(x) = a(x - h)^2 + k, where
a is a constant determining whether the parabola opens upward or downward,and (h, k) are the coordinates of the vertex.Intercept form: f(x) = a(x - p)(x - q), where
a is a constant determining whether the parabola opens upward or downward,and p and q are the x-intercepts (aka roots).Connection between the vertex and intercepts forms and the standard form:
As both these forms show, we're able to expand and expanding and simplifying yields the standard form.Let's convert from vertex form to standard form.Identifying the vertex:
This quadratic opens downward, which means the vertex is the highest point on the graph.The coordinates of the vertex are (3, 25)Finding the vertex form:
We use the opposite sign of the x-coordinate when plugging in the vertex into the vertex formThus, we have part of the vertex form: f(x) = a(x - 3)^2 + 25.
We can find a by plugging in a point that lies on the parabola for (x, f(x)) in the vertex form.We see that the point (-2, 0) iies on the parabola as it is one of the x-intercepts.Thus, we can plug in (-2, 0) for (x, f(x)) in the vertex form to find a:
0 = a(-2 - 3)^2 + 25
0 = a(-5)^2 + 25
0 = a * 25 + 25
(0 = 25a + 25) - 25
(-25 = 25a) / 25
-1 = a
Thus, -1 is a in the vertex form.
Therefore, the full vertex form is given by:
f(x) = -(x - 3)^2 + 25
Convert from vertex form the standard form:
Now we can convert to standard for by expanding:
f(x) = -(x - 3)(x - 3) + 25
f(x) =-(x^2 - 3x - 3x + 9) + 25
f(x) = -x^2 + 3x + 3x - 9 + 25
f(x) = -x^2 + 6x + 16
Thus, the standard form of the equation of f(x) is f(x) = -x^2 + 6x + 16
Please look at the photo. Thank you!
The two compositions between the functions are:
g(g(x)) = xh(h(x)) = (x² + 9)² + 9How to find the compositions?To do so, just evaluate one of the functions into the other one.
We start with:
g(x) = 8/x
The composition of g and g will be:
g(g(x)) = 8/(g(x)) = 8/(8/x) = x
And for the case of h(x) = x² + 9 we will get:
h(h(x)) = h(x)² + 9 = (x² + 9)² + 9
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You received a Score Of 3.4 on your annual review. Merit increases are given out starting at 0.5% at a score of 2.6 and it goes up 1% every 0.4 points. So, I will be receiving an increase of what?
Based on your annual review score of 3.4, you would receive a merit increase of 2.5%.
To determine the merit increase based on your annual review score of 3.4, we need to calculate the increase increment based on the given scale.
First, we need to determine the number of 0.4-point increments between your score of 3.4 and the baseline score of 2.6, which is the starting point for merit increases. The difference is 3.4 - 2.6 = 0.8.
Since the merit increases go up by 1% for every 0.4 points, we divide the difference of 0.8 by 0.4 to find the number of 0.4-point increments:
0.8 / 0.4 = 2
So, there are 2 increments of 0.4 points.
Next, we calculate the merit increase percentage. The baseline increase is 0.5%, and it increases by 1% for each 0.4-point increment. Since we have 2 increments, the increase percentage would be:
0.5% + 2 * 1% = 0.5% + 2% = 2.5%
Therefore, based on your annual review score of 3.4, you would receive a merit increase of 2.5%.
It's important to note that this calculation assumes a linear progression of merit increases based on the given criteria. The actual merit increase policy may vary depending on company practices and policies.
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I need answer quick help: Combine the like terms to create an equivalent expression.
9+a-5b-2=9+a−5b−2=9, plus, a, minus, 5, b, minus, 2, equals?
Answer:
Combining the like terms in the expression 9 + a - 5b - 2, we can group the constants together and the variables together:
(9 - 2) + a + (-5b) = 7 + a - 5b
Therefore, the equivalent expression after combining the like terms is 7 + a - 5b.
Step-by-step explanation:
What is the meaning of "[tex] \varphi (x,y)[/tex] be [tex] y\wedge \phi (x)[/tex] "?
The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.
The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:
Define the formula p(x, y) as x = yo(x).
This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.
Define the set F as {(x, x) (x)}.
This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.
Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.
This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.
The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.
Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.
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The diagram shows
A
B
⟷
,
C
D
⟷
, and
G
E
⟶
. Which statement can be proven true from the diagram?
The lines A G B, and E G are perpendicular to each other. Another increasing line C D passes through G.
A.
∠DGB is supplementary to ∠EGA.
B.
∠DGB is supplementary to ∠CGB.
C.
∠CGB is supplementary to ∠AGD.
D.
∠EGA is supplementary to ∠EGC.
E.
∠EGD is supplementary to ∠CGB.
The statement that can be proven true from the diagram include the following: B. ∠DGB is supplementary to ∠CGB.
What is a complementary angle?In Mathematics and Geometry, a complementary angle refers to two (2) angles or arc whose sum is equal to 90 degrees (90°).
In Mathematics and Geometry, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that only the sum of these angles are supplementary angles:
m∠DGB + m∠CGB = 180°
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
6a^2 b - 3b^3 me ajudem pvfrr
Answer:
3b(2[tex]a^{2}[/tex] - [tex]b^{2}[/tex])
Step-by-step explanation:
help asap ty
will possibly mark brainliest.
Answer:
Step-by-step explanation:
Letter B is the correct answer
Initial population is 200, tripled every hour
200 x 3 = 600
First hour 200
Second hour = 600 + 200 = 800
Third hour 800x3 = 2400 + 800 = 3200
and so on.
For the following piecewise-defined function, find (a) f(-2), (b) f(2), (c) f(4), and (d) f(9). 3x ifx < -1 if -1≤x≤8 ifx-8 (a) f(-2)= (Type an integer or a decimal.) (b) f(2)= (Type an integer or a decimal.) (c) f(4)= (Type an integer or a decimal.) (d) f(9) = (Type an integer or a decimal.)
For the following piecewise-defined function the answers are:
(a) f(-2) = -6
(b) f(2) = 4
(c) f(4) = 16
(d) f(9) = 1
To find the values of the piecewise-defined function at different points, we evaluate each case separately.
(a) For f(-2), we need to evaluate the function at x = -2. Since -2 is less than -1, we use the first case: f(x) = 3x. Plugging in x = -2, we have f(-2) = 3(-2) = -6.
(b) For f(2), we again evaluate the function at x = 2. Since 2 falls within the range -1 ≤ x ≤ 8, we use the second case: f(x) = x^2. Plugging in x = 2, we have f(2) = 2^2 = 4.
(c) For f(4), we evaluate the function at x = 4. Again, 4 falls within the range -1 ≤ x ≤ 8, so we use the second case: f(x) = x^2. Plugging in x = 4, we have f(4) = 4^2 = 16.
(d) For f(9), we need to evaluate the function at x = 9. Since 9 is greater than 8, we use the third case: f(x) = x - 8. Plugging in x = 9, we have f(9) = 9 - 8 = 1.
The answers are:
(a) f(-2) = -6
(b) f(2) = 4
(c) f(4) = 16
(d) f(9) = 1
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A rope that is 6 meters long will be cut into 24 pieces that are all of the same length. What will be the length of each piece in centimeters?
The length of each piece of a rope which is 6 m long and that has to be cut into 24 pieces will be equal to 25 cm.
We have given a rope whose length is 6m and that has to be cut into 24 pieces.
Length (L) = 6m
Now, as we need the answer in cm we have to convert m into cm
1m = 100 cm
Multiplying both sides by 6 we get,
1m * 6 = 100cm * 6
6m = 600cm
Given that, we have to cut the rope into 24 pieces, the length of each piece will be:
Length of each piece = Length of rope(in cm)/ Number of cuts
Putting values in the above equation we get,
Length of each piece = 600÷24
Solving the above equation,
Length of each piece of a rope = 25 cm
Therefore, we obtain the length of each piece to be 25 cm
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Fill in the blanks to complete the equation that describes the diagram. − 3 + blank = blank
Step-by-step explanation:
negative three PLUS negative three equals negative six
Quadrilateral EFGH is an isosceles trapezoid with bases EH and FG. The measure of angle HGF is (9y + 3)°, and the measure of angle EFG is (8y + 5)°. What is the measure of angle HGF?
Answer:
21°
Step-by-step explanation:
In an sosceles trapezoid, the lower base and upper base angles are congurent
⇒ ∠HGF = ∠EFG
⇒ 9y + 3 = 8y + 5
⇒ 9y - 8y = 5 - 3
⇒ y = 2
⇒ ∠HGF = 9(2) + 3
= 18 + 3
= 21
The measure of angle HGF in the given isosceles trapezoid EFGH is calculated to be 21 degrees.
Explanation:This problem deals with the properties of an isosceles trapezoid, which is a type of quadrilateral. In an isosceles trapezoid, opposite angles are equal. In this case, angle EFG and angle HGF would be equal to each other given the shape is an isosceles trapezoid. So, their measures should be equal.
Here, the measure of angle HGF is given as (9y + 3)°, and the measure of angle EFG is (8y + 5)°. Setting these equal to each other to find the value of y, we get 9y + 3 = 8y + 5. By simplifying, we get the value of y is 2. Substituting the found value of y in angle HGF we get, 9*2+3 = 21 degrees.
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Find the Cartesian equation for the curve.
r^2 = 5
Answer:
[tex]\displaystyle{x^2+y^2=5}[/tex]
Step-by-step explanation:
Given the polar equation of:
[tex]\displaystyle{r^2 =5}[/tex]
We know that 'r' represents the radius which equals to:
[tex]\displaystyle{r = \sqrt{x^2+y^2}}[/tex]
Therefore, by substitution, we have:
[tex]\displaystyle{\left(\sqrt{x^2+y^2} \right)^2=5}[/tex]
Cancel the square root:
[tex]\displaystyle{x^2+y^2=5}[/tex]
Therefore, the cartesian equation is:
[tex]\displaystyle{x^2+y^2=5}[/tex]
5) Solve and simplify. Record your work in the space provided. There are two trees in Mr. Kline's front yard that he planted several years ago when he moved into the house. One tree is 12 feet 8 inches tall. The other tree is 15 feet 1 inch tall. Calculate the difference in height of the two trees.
The difference in height between the two trees is 29 inches.
To find the difference in height between the two trees, we need to subtract the height of one tree from the height of the other tree.
Let's convert the measurements to a consistent unit, such as inches, for easier calculation.
The first tree is 12 feet 8 inches tall. In inches, this is calculated as:
12 feet [tex]\times[/tex] 12 inches/foot + 8 inches.
= 144 inches + 8 inches
= 152 inches.
The second tree is 15 feet 1 inch tall.
In inches, this is calculated as:
15 feet [tex]\times[/tex] 12 inches/foot + 1 inch = 180 inches + 1 inch = 181 inches.
Now we can find the difference in height by subtracting the height of the first tree from the height of the second tree:
181 inches - 152 inches = 29 inches.
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Which of the following is the smallest value 3.11 0.956 36 4.21 10.1
Answer:
0.956
Step-by-step explanation:
The smallest value among the given numbers is 0.956.
Answer:
0.956
Step-by-step explanation:
To make this problem more clear, I will take every number and find what two numbers it's between.
3.11
Between 3 and 4
0.956
Between 0 and 1
4.21
Between 4 and 5
10.1
Between 10 and 11
Since 0.956 is between the smallest numbers, then it too must be the smallest of the four numbers.
If this answer helped you, please leave a thanks!
Have a GREAT day!!!
A marble is selected from a bag containing eight marbles numbered 1 to 8. The number of the marble selected will be recorded as the outcome. Consider the following events. Event A: The marble selected has an even number.
Event B: The marble selected has a number from 3 to 6.
a) Event "A or B":
b) Event "A and B":
c) The complement of the event A.
A) - Event "A or B" Consists of the Outcomes:
{2, 3, 4, 5, 6, 8}
B) - Event "A or "B" Consists of the Outcomes:
{4, 6}
C) - The "COMPLEMENT of EVENT "A" Consists of the Outcomes:
{1, 3, 5, 7}
Step-by-step explanation:MAKE A PLAN:
List The OUTCOMES for EACH EVENT and their COMBINATIONS:
SOLVE THE PROBLEM:a) - EVENT "A": {2, 4, 6, 8}
EVENT "B": {3, 4, 5, 6}
EVENT "A" or "B": {2, 3, 4, 5, 6, 8}
b) - EVENT "A" or "B": {4, 6}
c) - The COMPLEMENT of the EVENT "A": {1, 3, 5, 7}
Draw the conclusion:A) - Event "A or B" Consists of the Outcomes:
{2, 3, 4, 5, 6, 8}
B) - Event "A or "B" Consists of the Outcomes:
{4, 6}
C) - The "COMPLEMENT of EVENT "A" Consists of the Outcomes:
{1, 3, 5, 7}
I hope this helps!
Every day, there are 4 times more likes on an internet video of a horse that is modeled by the function c(n)=(4)^N-1, where n is the number of days since the video posted. On the first day, there
were 100 likes. What is the function that shows the number of likes each day? (1 point)
c(n)-100(4)-1
c(n)-(4)(100)(n-1)
c(n)-(100)n-1
c(n)-(4) 100-1
The function c(n) = (4)^(n-1) does not represent the number of likes each day based on the given information.
The given function c(n) = (4)^(n-1) represents the number of likes on the video on each day, where n is the number of days since the video was posted.
We are told that on the first day, there were 100 likes. Therefore, we can substitute n = 1 into the function and solve for the constant factor:
c(1) = (4)^(1-1) = 4^0 = 1
Since c(1) represents the number of likes on the first day and it is given as 100, we can equate it with the value obtained from the function:
1 = 100
However, this equation is not true. Therefore, the function c(n) = (4)^(n-1) does not represent the number of likes each day based on the given information.
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Write an
expression for the nth term of the geometric sequence. Then find the indicated term
a₁ = 6, r = — 1/5, n = 12
The expression for the nth term is [tex]f(n) = 6 * (-1/5)^{n-1[/tex] and the 12th term is -6/48828125
The expression for the nth term of the geometric sequenceFrom the question, we have the following parameters that can be used in our computation:
a = 6
r = -1/5
The nth term of the geometric sequence is represented as
[tex]f(n) = ar^{n-1[/tex]
using the above as a guide, we have the following:
[tex]f(n) = 6 * (-1/5)^{n-1[/tex]
For the 12th term, we have
[tex]f(12) = 6 * (-1/5)^{11[/tex]
Evaluate
f(12) = -6/48828125
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In a certain video game, there is a mini-game where the main character can choose from a selection of twenty
presents. The presents are wrapped, so the character does not know what is in them. If 7 presents contain money, 3
presents contain gems, 6 presents contain ore, and 4 presents contain fish, what is the probability that the main
character chooses a present that contains a gem?
Your answer should be an exact decimal value.
The probability of randomly selecting a present that contains a gem is
Answer:
There are 20 presents in total, and 3 of them contain gems.
The probability of randomly selecting a present that contains a gem is 3/20 = 0.15 or 15%.
Convert 10 pounds and 12 ounces to ounces.
Answer: 172 ounces
Step-by-step explanation:
We are given 10 pounds and 12 ounces to convert to ounces.
There are 16 ounces in 1 pound.
We can create a proportion to find out how much ounces 10 pounds is.
10 pounds / x ounces = 1 pound / 16 ounces
We need to solve for x by isolating the variable x.
10/x = 1/16
10 = x/16
10 * 16 = x
160 ounces = x
so 10 pounds is equivalent to 160 ounces. But we are not done yet.
We were asked to convert 10 pounds and 12 ounces.
So add together the ounces to find the total ounces:
160 ounces + 12 ounces = 172 ounces.
Compete the slope intercept form of this line.
y= -4x+
Step-by-step explanation:
.... + b b is the y value where the graph crosses the y axis....you didn't include the graph, so YOU will have to complete this
The lines on the graph below represent the cost of apples at four different stores.
Cost of Apples
10-
9
Total Cost in Dollars
C
2 3 4 5 6 7 8 9 1
Pounds of Apples
At which store is the cost of apples the least?
O A
The store at which the apple will cost the cheapest is: Store A
How to find the slope of the line graph?The formula for the slope between two coordinates is:
Slope = (y₂ - y₁)/(x₂ - x₁)
Now, all the lines in the attached graph pass the origin and so they will all have the coordinate (0, 0)
The slope for each line will give us the cost for each apple in the store.
Thus:
Slope for store A = (3 - 0)/(4 - 0)
Cost for store A apple = $0.75
Slope for Store B = (5 - 0)/(5 - 0)
Cost for store B apple = $1
Slope for Store C = (5 - 0)/(4 - 0)
Cost for store C apple = $1.25
Slope for Store D = (6 - 0)/(3 - 0)
Cost for store C apple = $2
Thus, store A has the cheapest Apple
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I have 38 coins in my hand. Some coins are worth one dollar some coins are worth two dollars. The total worth of the coins is 54 dollars. How many coins of each denomination do I have?
Answer:
22 one-dollar coins and 16 two-dollar coins----------------------
Let the number of one-dollar coins be x and two-dollar coins be y.
Number of coins is 38:
x + y = 38Total worth of the coins is 54 dollars:
x + 2y = 54We have a system of equations. Solve it by elimination, subtract the equations side-by-side:
x + 2y - x - y = 54 - 38y = 16Find the value of x by substituting 16 for y:
x + 16 = 38x = 22The answer is
Number of one dollar coins = 22.Number of two dollar coins = 16.Explanation:
Total number of coins = 38
let number of one dollar coins be a
number of two dollar coins be b
Then,
a + b = 38
a = 38 - b .......(equation 1)
Also The total worth of the coins is 54 dollars.
a + 2b = 54 ......(equation 2)
Put equation 1 in equation 2 ,
a + 2b = 54
38 - b + 2b = 54
Move all terms containing b to the Left hand side of the equation.
-b + 2b = 54 - 38
b = 16
Now put value of b in equation 1.
a = 38 - b
a = 38 - 16
a = 22
Hence,
Number of one dollar coins is 22.Number of two dollar coins is 16.find the sample variance and standard deviation.
22,11,4,9,10
The sample variance is approximately 44.79 and the sample standard deviation is approximately 6.692.
To find the sample variance and standard deviation, follow these steps:
1. Calculate the mean of the data set:
Mean (μ) = (22 + 11 + 4 + 9 + 10) / 5 = 56 / 5 = 11.2
2. Calculate the difference between each data point and the mean, and square each difference:
[tex](22 - 11.2)^2 = 121.00 \\(11 - 11.2)^2 = 0.04 \\(4 - 11.2)^2 = 51.84 \\(9 - 11.2)^2 = 4.84 \\(10 - 11.2)^2 = 1.44[/tex]
3. Calculate the sum of all the squared differences:
121.00 + 0.04 + 51.84 + 4.84 + 1.44 = 179.16
4. Calculate the sample variance:
Variance [tex](s^2)[/tex] = sum of squared differences / (n - 1)
= 179.16 / (5 - 1)
= 179.16 / 4
= 44.79
5. Calculate the sample standard deviation:
Standard Deviation (s) = square root of the variance
= √44.79
≈ 6.692
Therefore, the sample standard deviation is about 6.692, while the sample variance is about 44.79.
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Owen has a credit card with an APR of 12.5% and a balance of $1,892.32. The interest is compounded monthly. What is the monthly periodic rate?
The new balance is$1,912.40 (rounded to two decimal places).To calculate the new balance after one month, we can multiply the current balance by (1 + Periodic Rate):
To find the monthly periodic rate, we can use the formula:Periodic Rate = (1 + Annual Percentage Rate)^(1/Number of Periods) - 1.
In this case, the Annual Percentage Rate (APR) is 12.5%, and since the interest is compounded monthly, the Number of Periods is 12.
Substituting the values into the formula, we have:
Periodic Rate = (1 + 0.125)^(1/12) - 1.
Calculating this expression, we find:
Periodic Rate ≈ 0.0103.
Therefore, the monthly periodic rate is approximately 0.0103, or 1.03%.
This means that every month, the balance on Owen's credit card will increase by 1.03% due to the compounded interest.
New Balance = $1,892.32 * (1 + 0.0103).
New Balance ≈ $1,912.40 (rounded to two decimal places).
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Determine the equation
Answer:
y=12.5x+25
Step-by-step explanation:
y intercept where x =0 is 25
gradient between two points: (0,25) , (8,125)
(y2-y1)/(x2-x1) = 100/8 = 12.5
When should the inequality symbol be reversed when solving a two step inequality
Answer:
You should reverse the inequality sign when you multiply or divide both sides of an inequality by a negative number. Addition and subtraction never change the direction of the inequality sign. Multiplication and division do change the direction of the inequality, but only if the number you’re multiplying or dividing by is a negative number.
Step-by-step explanation:
