This equation tells us that the cost in dollars c is equal to the unit rate of $0.55 per green pepper.
what is linear equation?
A linear equation is a mathematical equation that represents a straight line when graphed on a coordinate plane. It is an equation of the form:
y = mx + b
where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept (the point where the line intersects the y-axis).
To find the unit rate, we need to divide the total cost of the green peppers by the number of peppers purchased:
Unit Rate = Total Cost ÷ Number of Green Peppers
Unit Rate = $4.40 ÷ 8 = $0.55 per green pepper
Now, to write an equation relating the cost in dollars c to the number of green peppers p, we can use the unit rate we just calculated. We know that for each green pepper, the cost is $0.55, so we can write:
c = $0.55p
This equation tells us that the cost in dollars c is equal to the unit rate of $0.55 per green pepper, multiplied by the number of green peppers p being purchased.
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please help!!!!!!!!!!!
Therefore, the value of tan N rounded to the nearest hundredth is approximately 0.85.
What is triangle?A triangle is a basic geometrical shape that is formed by connecting three non-collinear points in a plane using straight line segments. The three points are called the vertices of the triangle, and the line segments connecting them are called the sides. The angles formed between the sides of a triangle are also an important characteristic of the triangle. Triangles come in many different shapes and sizes, and they have many interesting properties and applications in mathematics, science, engineering, and other fields.
Since the opposite side of angle N is √67 and the adjacent side is √92, we can use the following formula for tangent:
tan(N) = opposite / adjacent
tan(N) = √67 / √92
We can simplify this expression by rationalizing the denominator:
tan(N) = (√67 / √92) * (√92 / √92)
tan(N) = √(67*92) / 92
tan(N) = √6164 / 92
tan(N) = 78.43 / 92
tan(N) ≈ 0.85 (rounded to the nearest hundredth)
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at a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 14 cubic feet per minute. the diameter of the base of the cone is approximately three times the altitude. at what rate (in ft/min) is the height of the pile changing when the pile is 12 feet high? (hint: the formula for the volume of a cone is v
The height of the pile is increasing at a rate of approximately 0.056 feet per minute when the pile is 12 feet high.
We are given that sand is falling off at a rate of 14 cubic feet per minute, and the diameter of the base of the cone is approximately three times the altitude. Let h be the height of the pile at a given time t, then we can write the volume of the cone as V = (1/3)πr^2h, where r is the radius of the base of the cone. Since the diameter is three times the altitude, we have r = 3h/2.
Taking the derivative of the volume with respect to time, we get dV/dt = (1/3)π(9h^2/4)(dh/dt). Plugging in the given values, we get:
14 = (1/3)π(9h^2/4)(dh/dt)
Simplifying, we get:
dh/dt = 56/(3πh^2)
When the height of the pile is 12 feet, the rate of change of the height of the pile is:
dh/dt = 56/(3π(12)^2) ≈ 0.056 ft/min.
Therefore, the height of the pile is changing at a rate of approximately 0.056 ft/min when the pile is 12 feet high.
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Classify each polynomial on the left by degree
The greatest power of "p" in this situation is 4, which is the coefficient of p4. Consequently, the polynomial has a degree of 4.
What is a polynomial?Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates.
This equation is provided:
1) [tex]$2p^{4}+p^{3}$[/tex]
The greatest power of the polynomial's variable "p" must be identified to categorize this polynomial by degree.
Therefore, the polynomial [tex]$2p^{4}+p^{3}$[/tex] is a polynomial of the fourth degree.
2) [tex]$2x^{2}$[/tex]
The greatest power of the polynomial's variable "x" must be identified to categorize this polynomial by degree.
The greatest power of "x" in this situation is 2, which is the coefficient of . Consequently, the polynomial has a degree of 2.
Therefore, the polynomial [tex]2x^2[/tex] is a polynomial of the second degree.
3) [tex]$-5n^{4}+10n-10$[/tex]
The greatest power of the polynomial's variable "n" must be identified to categorize this polynomial by degree.
The greatest power of "n" in this situation is 4, which is the coefficient of . Consequently, the polynomial has a degree of 4.
Therefore, the polynomial [tex]n^4[/tex] is a polynomial of the fourth degree.
4) 6n
The greatest power of the polynomial's variable "n" must be identified to categorize this polynomial by degree.
The greatest power of "n" in this situation is 1, which is the coefficient of [tex]n^1[/tex]. Consequently, the polynomial has a degree of 1.
Therefore, the polynomial [tex]n^1[/tex] is a polynomial of one degree.
5) -6
The greatest power of the polynomial's variable "n" must be identified to categorize this polynomial by degree.
The polynomial in this instance doesn't have a component. It has a value of 6 and is a constant word. A constant word is thought to have a degree of zero.
Therefore, equation 6 is a zero-degree polynomial.
6) [tex]$x^{3}-3$[/tex]
The greatest power of the polynomial's variable "x" must be identified to categorize this polynomial by degree.
The greatest power of "x" in this situation is 3, which is the coefficient of . Consequently, the polynomial has a degree of 3.
Therefore, the polynomial [tex]x^3[/tex] is a polynomial of the third degree.
7) [tex]$2n^{5}$[/tex]
The greatest power of the polynomial's variable "n" must be identified to categorize this polynomial by degree.
The greatest power of "n" in this situation is 5, which is the coefficient of . Consequently, the polynomial has a degree of 5.
Therefore, the polynomial [tex]n^5[/tex] is a polynomial of the fifth degree.
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which of the following statements is false? a the power of a hypothesis test is a measure of the ability of the test to detect a difference between the estimated value and the true value of a parameter. b as the -level increases, the -level of a hypothesis test decreases. c is the measure of the probability of a type ii error. d the power of a hypothesis test increases as increases. e the power of a hypothesis test does not depend on the sample size.
The false statement among the options is E. The power of a hypothesis test does depend on the sample size.
The power of a hypothesis test is indeed a measure of the test's ability to detect a difference between the estimated value and the true value of a parameter (Statement A). It represents the probability of correctly rejecting the null hypothesis when it is actually false.
Statement B is true as well. As the alpha level increases, the beta level of a hypothesis test decreases. Alpha (α) represents the probability of a Type I error (rejecting the null hypothesis when it is true), while beta (β) represents the probability of a Type II error (failing to reject the null hypothesis when it is false). Statement C is accurate, as beta is the measure of the probability of a Type II error, meaning the likelihood of failing to reject a false null hypothesis. Statement D is also true. The power of a hypothesis test increases as alpha increases because increasing the alpha level means that you are more likely to reject the null hypothesis when it is false, which ultimately increases the power of the test.
However, statement E is false. The power of a hypothesis test does depend on the sample size. As the sample size increases, the power of the test increases as well. Larger sample sizes provide more accurate estimates of the population parameters, which helps in better differentiating between the null and alternative hypotheses, leading to a higher power for the hypothesis test. Therefore, the correct option is E.
The question was incomplete, Find the full content below:
which of the following statements is false?
A. the power of a hypothesis test is a measure of the ability of the test to detect a difference between the estimated value and the true value of a parameter.
B. as the alpha level increases, the beta level of a hypothesis test decreases.
C.Beta is the measure of the probability of a type ii error.
D. the power of a hypothesis test increases as alpha increases.
E. the power of a hypothesis test does not depend on the sample size.
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By selling a jeans for ₱10,800, John loses 44%. For how much should John sell it to gain 6%.
Requirements:
Given and Mathematical sentence:
Solution:
Thanks in advance!
John should sell the jeans for ₱20,500 to gain a profit of 6%
what is formula for Loss Percentage?if the cost price of a product is more than the selling price, but a profit may be made if the cost price of the product is lower than the price at which it is being sold. Loss percentage= Loss/CP x 100.
Given:
Selling price of jeans with a loss of 44% = ₱10,800
Profit percentage required = 6%
Let the cost price of the jeans be 'x'
Mathematical sentence:
According to the given information, we can write the following equation:
Selling price with loss of 44% = Cost price (1 - Loss %)
⇒ 10800 = x(1 - 0.44)
⇒ x = 10800 / 0.56
⇒ x = 19371.43
To find the selling price with a profit of 6%, we can use the following formula:
Selling price with profit % = Cost price (1 + Profit %)
Substituting the values, we get:
Selling price with profit of 6% = 19371.43(1 + 0.06)
⇒ Selling price with profit of 6% = 20500
Therefore, John should sell the jeans for 20,500 to gain a profit of 6%.
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Which one is greater 45% or 40%
45% is greater than 40%
Please help me with this I am no good thank you so much
Answer:
its b
Step-by-step exiplanation:
Is Y=8.35x proportional or non proportional
The equation Y=8.35x represents a proportional relationship between Y and x.
What is proportion?
In mathematics, two quantities are said to be proportional if they vary in a way that can be expressed as a ratio or fraction. Specifically, if two quantities x and y are proportional, this means that as x increases or decreases, y also increases or decreases by the same factor.
The equation Y=8.35x represents a proportional relationship between Y and x.
In a proportional relationship, when one variable (x) increases or decreases, the other variable (Y) changes by a constant factor. This constant factor is known as the constant of proportionality.
In the given equation, Y and x are directly proportional to each other, with a constant of proportionality of 8.35. This means that if x is multiplied by any factor, Y will also be multiplied by the same factor. For example, if x is doubled, Y will also be doubled (since 2 times 8.35 is 16.7).
Therefore, the equation Y=8.35x represents a proportional relationship between Y and x.
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Which shows all the like terms in the expression? 4 x minus 3 + 7 x + 1 –3 and 1; 4x and –3 –3 and 1; 4x and 7x 4x and 1; 7x and –3 4x and –3; 1 and 7x. and Quick because it's a test
Work out 9 sin 60°- 5/√3 Give you answer in the form a/b√3 where a and b are integers b
Answer:
17/6√3
Step-by-step explanation:
You want the simplified form of 9·sin(60°) -5/√3.
Simplify[tex]9\sin(60^\circ)-\dfrac{5}{\sqrt{3}}=9\cdot\dfrac{\sqrt{3}}{2}-\dfrac{5\sqrt{3}}{\sqrt{3}\cdot\sqrt{3}}= \dfrac{3\cdot9\sqrt{3}}{3\cdot2}-\dfrac{2\cdot5\sqrt{3}}{2\cdot3}\\\\=\dfrac{(27-10)\sqrt{3}}{6}=\boxed{\dfrac{17}{6}\sqrt{3}}[/tex]
Hilary has 45 inches of lace to decorate the circular bottom of a lampshade. What is the approximate diameter of the largest lampshade she can put lace around?
The largest lampshade Hillary can wrap laces around has an estimated diameter of [tex]14.32[/tex] inches.
What are radius and diameter?The better measure across the edge of the circle is its diameter. The radius of a circle is the farthest from to any place on the edge. The diameter and radius are inversely proportional, or 2r=d2 r=d.
What is an illustration of diameter?For instance, if a circle has a circumference of 25 cm, its diameter is 25 cm/, or 7.96 cm. For instance, calculate the square root of 12cm2 if that is the circle's area. Hence, the circle's diameter becomes 1.95 x 2 Equals 3.90 cm.
[tex]C = 2pir[/tex]
where [tex]C[/tex] is the circumference, π (pi) is a mathematical constant approximately equal to [tex]3.14[/tex], and r is the radius of the circle.
We can do this by rearranging the formula for the circumference:
[tex]C = 2pir[/tex]
[tex]r = C / (2pi)[/tex]
We are given that Hilary has [tex]45[/tex] inches of lace, which is the circumference of the circle.
[tex]r = 45 / (2pi) =7.16 inches[/tex]
Finally, we can find the diameter of the circle by doubling the radius:
[tex]d = 2r = 14.32 inches[/tex]
Therefore, the approximate diameter of the largest lampshade Hilary can put lace around is [tex]14.32[/tex] inches.
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The table shows the balance of a money market account over time. Write a function that represents the balance y
(in dollars) after t years.
Year, t Balance
0 $200
1 $230
2 $264.50
3 $304.18
4 $349.80
5 $402.27
The value of a boat is $23,400. It loses 8% of its value every year. Write a function that represents the value y
(in dollars) of the boat after t years.
Answer:
y = 200·1.15^t The required function is y=1.047t + 199.12
Step-by-step explanation:
The ratio from one year to the next is 1.15, so the balance is a geometric sequence. Since t starts at zero, we can write the balance (y) after t years as ...
y = initial value · (common ratio)^t
y = 200·1.15^tThe given table shows the balance of a money market account over time.
Time (t) Balance(y)
0 200
1 210
2 220.5
3 231.53
4 243.1
5 255.26
The function that represents the balance y(in dollars) after t years is linear regression line, because the value of y increased linearly.
The linear regression function is defined as
Where,
Put the values from the below table in the above formulas.
The value of b is 11.047 and the value of a is 199.12. Here, the variable is t.
Therefore the required function is the anser up top
develop an estimated regression equation to estimate weekly gross revenue with the amount of television advertising as the independent variable. what is the interpretation of this relationship?
The estimated relationship may not hold for all levels of TV advertising, and there may be non-linearities or interactions with other variables that should be taken into account in a more sophisticated model.
What is the interpretation of this relationship?
To develop an estimated regression equation to estimate weekly gross revenue with the amount of television advertising as the independent variable, we would need a dataset that includes information on both variables. Assuming we have such a dataset, we could use linear regression to estimate the relationship between the two variables.
The estimated regression equation would take the form:
Weekly Gross Revenue = [tex]b_0 + b_1[/tex]×Amount of TV Advertising + error
where [tex]b_0[/tex] is the intercept (the value of weekly gross revenue when the amount of TV advertising is zero), [tex]b_1[/tex] is the slope (the estimated increase in weekly gross revenue associated with a one unit increase in TV advertising), and error represents the random variation in the relationship between the two variables that is not explained by the model.
The interpretation of the relationship between weekly gross revenue and amount of TV advertising would depend on the sign and magnitude of the slope coefficient
[tex](b_1)[/tex]. If [tex]b_1[/tex] is positive, it would suggest that an increase in TV advertising is associated with an increase in weekly gross revenue. The magnitude of [tex]b_1[/tex] would indicate the strength of this relationship - a larger positive value of[tex]b_1[/tex] would indicate a stronger relationship between TV advertising and weekly gross revenue.
If [tex]b_1[/tex] is negative, it would suggest that an increase in TV advertising is associated with a decrease in weekly gross revenue. This could occur if the advertising is perceived as irritating or offensive to viewers, leading them to avoid the advertised product or service.
It is important to note that correlation does not imply causation, and there may be other factors that affect weekly gross revenue that are not captured in the model.
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Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
Step-by-step explanation:
To find the price of one tire patch, you could use the equation:
4x = 22.2 + 1.9
which simplifies to:
4x = 24.1
Then divide both sides by 4 to isolate x:
x = 6.025
So the equation that applies here is:
4x = 22.2 + 1.9
SOMEONE PLEASEEEE HELP MEEEEEEE ASAPPPP
Find the perimeter of a polygon. Assume that lines which appear to be tangent are tangent
A. 32.1
B. 39
C. 45.2
D. 59.7
Answer:
(C). 45.2
Step-by-step explanation:
the predicted temperature for the next 10 days in fahrenheit is the following: 71, 75, 74, 80, 83, 86, 90, 85, 81, 80 what is the mean temperature in fahrenheit? do not round your answer.
mean temperature=sum of all the temperatures to the total number of temperatures:
Mean temperature = (71 + 75 + 74 + 80 + 83 + 86 + 90 + 85 + 81 + 80) / 10
Mean temperature = 805 / 10
Mean temperature = 80.5°F
Therefore, the mean temperature for the next 10 days is 80.5 degrees Fahrenheit.
The mean temperature in Fahrenheit for the next 10 days is 79.5.
The mean temperature in Fahrenheit for the next 10 days can be calculated as follows;
Add all the given temperatures together:
71 + 75 + 74 + 80 + 83 + 86 + 90 + 85 + 81 + 80 = 795
Divide the sum obtained by the total number of temperatures, which is 10: 795 ÷ 10 = 79.5.
Therefore, the mean temperature in Fahrenheit for the next 10 days is 79.5.
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The graph shows a function. Is the function linear or nonlinear?
Part A
Does this curved line represent a function? If not, at what points does it fail the vertical line test?
Calvin wants to know the proportion of students at his school who plan to
attend college. he interviews a random sample of students at his school.
he finds that 70% of the students in the sample plan to attend college.
what conclusion can he draw from the sample?
Answer:
30% of students do not plan to attend college.
Given that 5 sin x + 4 cos x = 0, find the value of tan x
We can start by rearranging the equation 5 sin x + 4 cos x = 0 by dividing both sides by cos(x):
5
sin
�
cos
�
+
4
=
0
5
cosx
sinx
+4=0
Recall that $\frac{\sin x}{\cos x} = \tan x$. So we can substitute this in:
5
tan
�
+
4
=
0
5tanx+4=0
Now we can solve for $\tan x$:
\begin{align*}
5 \tan x + 4 &= 0 \
5 \tan x &= -4 \
\tan x &= \frac{-4}{5}
\end{align*}
Therefore, the value of $\tan x$ is $\boxed{\frac{-4}{5}}$.
Hakeem gave out a survey to some students in his school about their favorite color. 325 of those surveyed said their favorite color was red. If 65% of the students surveyed said their favorite color was red, how many students were surveyed in total?
Answer: Let's say the total number of students surveyed is "x".
We know that 65% of the students surveyed said their favorite color was red, which means that 325 students said their favorite color was red.
We can set up a proportion to solve for "x":
65/100 = 325/x
To solve for "x", we can cross-multiply:
65x = 32500
Dividing both sides by 65, we get:
x = 500
Therefore, Hakeem surveyed 500 students in total.
Step-by-step explanation:
a random sample of 100 people was taken. eighty-five of the people in the sample favored candidate a. we are interested in determining whether or not the proportion of the population in favor of candidate a is significantly more than 80%. the p-value is group of answer choices 0.2112 0.05 0.1056 0.025
a) The null and alternative hypothesis are defined as
[tex]H_0 : p = 0.80 [/tex]
[tex]H_a : p > 0.80[/tex]
So, right choice is option (iii) here.
b) The test statistic value is equals to the 1.25.
c) The p-value of distribution is equals to the 0.1056. So, option(b) is right one here.
d) Conclusion: a fail to reject the null hypothesis, that is p = 0.80. So, there is no evidence to support the claim.
The claim about the population proportion that the proportion is more than 80% is tested under the null and the alternative hypothesis at the 5% level of significance. To calculate the P-value and the test statistic value, we will use Z-test. . We have a random sample of 100 people. So, sample size, n = 100
Number of people who favored candidate from the sample = 85
level of significance, [tex] \alpha[/tex]
= 0.05
Population proportion, [tex] \hat p[/tex]
= 85% = 0.85
a) The null hypothesis is,
[tex]H_0 : p = 0.80[/tex]
The alternative hypothesis is,
[tex]H_a : p>0.80[/tex]
(Right-Tailed)
Therefore, Option (iii) is correct.
b)Now, we determine the z statistic value : z-test statistic is defiend as:
[tex]z= \frac{\hat p−p}{\sqrt{\frac{p(1−p)}{n}}}[/tex]
=> [tex]z = \frac{0.85 - 0.80}{\sqrt{\frac{0.80(1 - 0.80)}{100}}}[/tex]
=> z = 0.05/0.04 = 1.25
so, Z-statistic value is 1.25.
c) Using the Z-distribution table, the value of P( z = 1.25 ) is 0.1056.
d) As we see, p-value (0.1056) > 0.05, so we fail to reject the null hypothesis. There is no evidence to reject null hypothesis.
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Complete question:
a random sample of 100 people was taken. eighty-five of the people in the sample favored candidate a. we are interested in determining whether or not the proportion of the population in favor of candidate a is significantly more than 80%.
a) The correct set of hypothesis for this problem is I)H0:p=0.85 and
HA:p>0.85
ii. H0:p>0.80 and
HA:p=0.80
iii.) H0:p=0.80 and
HA:p>0.80
iv.) H0:p=0.80 and HA:p≥0.80
b) find out the Z-statistic value?
c)the p-value is ? group of answer choices 0.2112 0.05 0.1056 0.025
d) What is your conclusion?
please help me with my math on my profile it's due in 2hrs
With only two hours left, it's important to stay focused and work efficiently. Take breaks as needed to avoid burnout, but don't procrastinate or get distracted by other tasks.
Hi there! I'd be happy to help you with your math on your profile. Could you please provide me with more specific information about the assignment? What topics does it cover and what kind of problems do you need help with? It's difficult to provide a comprehensive answer without more information.
In the meantime, I can offer some general tips for tackling math problems. First, read the problem carefully and make sure you understand what it's asking. Look for key words or phrases that indicate what type of problem it is. Next, identify the relevant formulas or concepts that you'll need to solve the problem. If you're unsure, check your textbook or notes for guidance.
As you work through the problem, be sure to show your work and label each step clearly. This will help you avoid mistakes and make it easier to check your work later. If you get stuck, don't be afraid to ask for help from a teacher or tutor.
Good luck, and let me know if you have any more specific questions or concerns!
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The perimeter of a rectangular jewelry store is 186 feet. The store is 60 feet long. How wide is it?
Answer:
The width of the jewelry store is 33 feet.
Step-by-step explanation:
To solve the problem, we can use the formula for the perimeter of a rectangle, which is P = 2L + 2W where P is the perimeter, L is the length, and W is the width. Substituting the given values, we get 186 = 2(60) + 2W. Simplifying the right side, we get 186 = 120 + 2W. Subtracting 120 from both sides, we get 66 = 2W. Dividing both sides by 2, we get W = 33.
Therefore, the width of the jewelry store is 33 feet.
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
Polynomial expressions of [tex]2^{nd}[/tex] degree with one unknown (only [tex]x[/tex]) have [tex]2[/tex] roots. We use the formula below to determine these roots;
[tex]x_{1}=\frac{-b+\sqrt{b^2-4(ac)} }{2a}[/tex][tex]x_{2}=\frac{-b-\sqrt{b^2-4(ac)} }{2a}[/tex]This formula is valid for equations of the form [tex]ax^2+bx+c[/tex]. We can convert the equation given in the question into this format to get the result;
[tex]ax^2+bx+c = 8x^2+16x+3=0[/tex]Hence, the value of [tex]a[/tex]: [tex]8[/tex],
the value of [tex]b[/tex]: [tex]16[/tex],
the value of [tex]c[/tex]: [tex]3[/tex].
Now, we can find the roots of this equation by using this formula;
[tex]x_{1}=\frac{-16+\sqrt{160} }{16} = \frac{-4+\sqrt{10}}{4}[/tex][tex]x_{2}=\frac{-16-\sqrt{160} }{16}=\frac{-4-\sqrt{10}}{4}[/tex]5 1/3 yards long and 2 1/6 yards wide. What’s the area
The area of the rectangle has a width of 5 1/3 yards long and 2 1/6 yards wide is 104/9 square yards or 11.56 square yards.
What is the equation to determine the rectangle's area?When calculating a rectangle's area, we multiply the length by the breadth of the rectangle.
What is a mixed fraction?A mixed fraction is one that is expressed by its quotient and remainder.
Area = length * breadth
Given: Length = [tex]5 \frac{1}{3}[/tex] yards
breadth = [tex]2 \frac{1}{6}[/tex] yards
First, we need to convert a mixed number into the improper fraction
[tex]5 \frac{1}{3}[/tex] = [tex]\frac{(5*3) + 1}{3}[/tex] = [tex]\frac{16}{3}[/tex]
[tex]2 \frac{1}{6} = \frac{(2*6) +1}{6} =\frac{13}{6}[/tex]
Therefore the area of the rectangle = Length * width
= [tex]\frac{16}{3} * \frac{13}{6}[/tex]
=[tex]\frac{104}{9}[/tex]
=[tex]\frac{104}{9} yards^{2}[/tex]
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Complete question:
The rectangle has [tex]5\frac{1}{3}[/tex] yards long and [tex]2 \frac{1}{6} \\[/tex] yards wide. What’s the area
4. Mrs. Selcer transforms f(x) = x² to create
g(x) = 6x². John claims the graph of g(x) will
be narrower than f(x). Jane claims the graph
will be a vertical stretch. Which student is
correct? Explain your reasoning.
4. The transformation by Mrs. Selcer of the function f(x) = x² to create g(x) = 6·x², is a vertical stretch of the function f(x), therefore;
Jane is correctWhat is the transformation of a function?The transformation of a function is a function that results in a variation in the graph of the parent function.
The rules for the transformation of a function indicates that a transformation of a function f(x) to a·f(x), transform the coordinates of the points of f(x) as follows;
(x, y) → (x, a·y)
Therefore;
The transformation is a vertical stretch when a > 1
The transformation is a horizontal compression when a < 1
Since f(x) = x², and g(x) = 6·x², we get;
g(x) = 6·f(x)
Therefore, comparing, we get; a = 6 > 1, which indicates that the function is vertically stretched.
Therefore, Jane is correct.
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as people exit the polling booth, researchers ask those between the ages of 20 and 40 how they voted on the various propositions on the ballot in order to predict election outcomes. this sampling method is called sampling.
The sampling method described in the question is called "quota sampling."
Quota sampling is a non-probability sampling technique in which researchers select participants based on pre-determined quotas or characteristics, such as age or gender. In this case, the researchers are selecting participants between the ages of 20 and 40.
However, this method may not be representative of the entire population as it does not guarantee that all subgroups within the population have an equal chance of being selected. Therefore, the results may be biased and not accurately reflect the opinions of the entire population.
Therefore, it is important to consider the limitations of quota sampling when interpreting the results
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a fair coin is tossed until either a head comes up or four tails are obtained. what is the expected number of tosses?
The expected number of tosses until either a head comes up or four tails are obtained is 7/4
Let X be the random variable representing the number of tosses until either a head comes up or four tails are obtained.
Let's consider the first toss. There are two possible outcomes: heads or tails. If a head comes up on the first toss, then we stop and X = 1. If a tail comes up, we need to continue tossing until we get four tails in a row or a head.
Let Y be the random variable representing the number of additional tosses needed if the first toss is a tail. There are two possible outcomes for the second toss: heads or tails. If a head comes up, we stop and X = 2. If a tail comes up, we need to continue tossing until we get three tails in a row or a head.
Similarly, we can define Z as the random variable representing the number of additional tosses needed if the first two tosses are tails. There are two possible outcomes for the third toss: heads or tails. If a head comes up, we stop and X = 3. If a tail comes up, we need to continue tossing until we get two tails in a row or a head.
Finally, let W be the random variable representing the number of additional tosses needed if the first three tosses are tails. There are two possible outcomes for the fourth toss: heads or tails. If a head comes up, we stop and X = 4. If a tail comes up, we need to continue tossing until we get four tails in a row.
We can write X in terms of Y, Z, and W as follows
X = 1 + Y if the first toss is heads
X = 1 + 1 + Z if the first two tosses are tails and the third toss is heads
X = 1 + 1 + 1 + W if the first three tosses are tails and the fourth toss is heads
X = 1 + 1 + 1 + 1 if the first four tosses are tails
Now, we need to compute the expected values of Y, Z, and W.
If the first toss is a tail, the probability of getting another tail on the second toss is 1/2, and the probability of getting a head is also 1/2. Therefore,
E[Y] = 1/2(1) + 1/2(1 + Z)
If the first two tosses are tails, the probability of getting another tail on the third toss is 1/2, and the probability of getting a head is also 1/2. Therefore,
E[Z] = 1/2(1) + 1/2(1 + W)
If the first three tosses are tails, the probability of getting another tail on the fourth toss is 1/2, and the probability of getting a head is also 1/2. Therefore,
E[W] = 1/2(1) + 1/2(4)
Note that the expected value of W is 2, not 3, because if we get three tails in a row, we stop and X = 4.
Putting it all together, we have:
E[X] = 1/2(1) + 1/2(1 + E[Z])
= 1/2(1) + 1/2(1 + 1/2(1) + 1/2(1 + E[W]))
= 1/2(1) + 1/2(1 + 1/2(1) + 1/2(1 + 2))
= 7/4
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