Michael has $15 and wants to buy a combination of cupcakes and fudge to feed at least three siblings. A cupcake cost two dollars and a piece of fudge cost three dollars the system of inequalities models this scenario.
(picture will be showed with the equation on bottom)
PART A) describe the graph of the system of inequalities, including cheating in the type of lines graphed. Provided description of the solution set.
Part B) is the point(5,1) included in the solution area for the system? Justify your answer, mathematically.
Part C) choose a different point in the solution, set an interpret what it means, in terms of real world context.

The answer of the given question based on the Statistics the answer is only one student takes 35 minutes to get to school.

In mathematics,  horizontal axis is  reference line used in coordinate systems to plot the points and graph the functions. It is usually denoted as x-axis and is oriented horizontally, running from left to right.

In  two-dimensional coordinate system, horizontal axis is perpendicular to  vertical axis, which is usually denoted as y-axis and runs vertically from bottom to top. Together,  x-axis and y-axis divide  coordinate plane into four quadrants.

Based on the dot plot, it appears that there is only one dot that falls on the value of 35 on the horizontal axis. Therefore, only one student takes 35 minutes to get to school.

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The rate of decrease is about 986 searches per week between Week 1 and Week 2, 315 searches per week between Week 2 and Week 3, and 456 searches per week between Week 3 and Week 4.

The rate of change is a measurement of how quickly one quantity changes in relation to another. It is frequently written as the ratio of one variable's change to another variable in mathematical expressions.

To find the rate of change for this data, we need to calculate the difference in the number of searches between each week, and then divide by the number of weeks.

Week 1 to Week 2:

Rate of change = (4555 - 5541) / (2 - 1) = -986

Week 2 to Week 3:

Rate of change = (4240 - 4555) / (3 - 2) = -315

Week 3 to Week 4:

Rate of change = (3784 - 4240) / (4 - 3) = -456

The negative sign in each rate of change indicates that the number of searches is decreasing over time. Specifically, the rate of decrease is about 986 searches per week between Week 1 and Week 2, 315 searches per week between Week 2 and Week 3, and 456 searches per week between Week 3 and Week 4.

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The vector equation of the line passing through the point 2i^−j^+4k^ and in the direction of i^+2j^−k^ is given by r= 2i^−j^+4k^ + λ(i^+2j^−k^)

Point with position vector 2i^−j^+4k^Direction i^+2j^−k^Cartesian form: In Cartesian form, the equation of the line is given by

[tex]{(x-x_0)/a = (y-y_0)/b= (z-z_0)/c}[/tex]

Here, we will use the point-slope form of the equation of the line to get the Cartesian form.

Since the vector equation is in the form r = a + λb. Therefore, we need to find two points that lie on the line. Let's consider two points A (2,-1,4) and B (3,1,3) lying on the line then the direction vector is given by i^+2j^−k^,Therefore, the vector equation of the line passing through the point 2i^−j^+4k^ and in the direction of i^+2j^−k^ is given by r= 2i^−j^+4k^ + λ(i^+2j^−k^)→r= (2+λ)i−j+(4−λ)k.

Now the Cartesian equation of the line passing through the point with position vector 2i^−j^+4k^ and in the direction of i^+2j^−k^ is

[tex]{(x-2)/(1)=(y+1)/(2)=(z-4)/(-1)}.[/tex]

Vector form: A vector equation of a line in space is given by the position vector of any point on the line plus a scalar multiple of a direction vector of the line. If r is the position vector of any point on the line and an is the direction vector of the line, then the vector equation of the line can be written as r = a + λb. Here, the position vector is given as 2i^−j^+4k^ and the direction vector is given as i^+2j^−k^

Therefore, the vector equation of the line passing through the point 2i^−j^+4k^ and in the direction of i^+2j^−k^ is given by r= 2i^−j^+4k^ + λ(i^+2j^−k^)

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Answer:

[tex](-1)(x+1)(x+2)[/tex]

Step-by-step explanation:

[tex]-x^2-3x-2\\[/tex]  

Factor out the (-1)

[tex](-1)(x^2 + 3x + 2)[/tex]

Factor completely.

[tex](-1)(x+1)(x+2)[/tex]

Answer:

[tex]x=9.8[/tex]

Step-by-step explanation:

Check Attachment.

Answer:

Step-by-step explanation:

I'm not the best at explaining but since the equation thing isn't working, i have a list in order of what to do.

Hope this helped!

Answer:

x = 2.3 (to nearest tenth)

Step-by-step explanation:

[tex] {x}^{2} + {x}^{2} = {( \sqrt{11}) }^{2} \\ 2 {x}^{2} = 11 \\ {x}^{2} = \frac{11}{2} \\ x = \sqrt{ \frac{11}{2} } \\ x = 2.3452...[/tex]

Answer:

You need to look at the whole numbers which are 1 and 2, then add those numbers together. Equalling to 3.

Now look at 3/4 and 3/4, since the denominators are the same add those fraction together and you'll get 6/4 now divide the 6 by 4 and divide the 4 by 4 and you'll get 1 and 2/4.

now add the last whole number to your 3 and you'll have 4 2/4 or 4 1/2

So Eloise ran 4 2/4 miles altogether

The simplified expression for f(7+h) is h² + 14h + 45. The value of 7+h substitutes x in the function f(x).

To find and simplify the expression f(7+h), we will first substitute the value of 7+h into the function f(x) = x²−4. This will give us:
f(7+h) = (7+h)² - 4
Next, we will expand the squared term using the distributive property:
f(7+h) = (7+h)(7+h) - 4
f(7+h) = 49 + 14h + h² - 4
Finally, we will simplify the expression by combining like terms:
f(7+h) = h² + 14h + 45
Hence, the expression for f(7+h) is (7+h)² - 4 and simplified to be h² + 14h + 45.

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The slope of the line is 2 and Jan runs 2 laps for every minute.

The slope of the line is defined as the change in the y-coordinate with respect to the x- coordinate and the formula for slope is given by

Where (x₁, y₁) and (x₂, y₂) are points where the line passes through.

Here we have

The graph shows the number of laps that Jan runs  

From the graph,

The line that represents the situation will pass through (2, 4) and (5, 10)

Using the formula, Slope (m) = (y₂ - y₁) / (x₂ - x)  

Slope of the line = [10 - 4]/[5 - 2 ] = 6/3 = 2

This means that Jan runs 2 laps for every 1 minute  

Therefore,

The slope of the line is 2 and Jan runs 2 laps for every minute.

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2 Liter units of Dr. pepper is equal to 2000 milliliters.

What is a unit?

A unit is a standard quantity used to measure a physical or abstract property or phenomenon. Units are used to express numerical values and to communicate measurements in a standardized way. In science, engineering, and mathematics, it is essential to use standard units to ensure that measurements are accurate, reliable, and comparable.

There are different types of units, including base units, derived units, and SI units. Base units are fundamental units that cannot be expressed in terms of other units, such as the meter (for length), the kilogram (for mass), and the second (for time). Derived units are units that are created by combining base units, such as the newton (for force) which is derived from the kilogram, meter, and second. SI units (International System of Units) are a standardized set of units that are used in most countries around the world, and they include both base units and derived units.

Now,

One liter is equivalent to 1000 milliliters.

So, 2 liters would be equivalent to:

2*1000 mL = 2000 mL

So,

      Patrick's 2L Dr. Pepper is equivalent to 2000 milliliters.

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If each video uses 0.87 gigabytes, then the number of videos that Elliot can stream is 5 videos.

To determine how many 30 minute videos Elliot can stream with 4.35 gigabytes of data, we divide the total data by the data consumed per video,

⇒ Number of videos = (Total data)/(Data per video);

We know that each video uses 0.87 gigabytes of data,

Substituting the values,

We get,

⇒ Number of videos = 4.35/0.87,

⇒ Number of videos = 5

Therefore, Elliot can stream 5, "30 minute" videos with his 4.35 gigabytes of data.

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One generalization that relates division and multiplication equations is that division is the inverse operation of multiplication.

This means that given two numbers, a and b, if we multiply them together (a x b), we can obtain the quotient (a ÷ b) by performing the inverse operation of division.

Similarly, if we are given the quotient (a ÷ b), we can find the product (a x b) by performing the inverse operation of multiplication. In other words, division and multiplication are opposite operations, and they can be used interchangeably to solve equations.

For example, if we have the multiplication equation 4 x 5 = 20, we can find the quotient by performing the inverse operation of division: 20 ÷ 4 = 5 or 20 ÷ 5 = 4.

Likewise, if we have the division equation 20 ÷ 4 = 5, we can find the product by performing the inverse operation of multiplication: 5 x 4 = 20 or 4 x 5 = 20.

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What generalization can one make that relates the division equation  to multiplication equation

The type of error that occurs when the study population produces a statistically significant test result, even though there is in fact no significant difference or association in the source population, is called a "Type I error".

A "Type I error" occurs when the null hypothesis (showing that there is no difference between the two populations under study) is rejected, even though it is in fact true. Type I errors, also called false positives, are caused by the erroneous rejection of the null hypothesis. This can happen when the sample size is too small, the sample size is too large, the sample distribution is not normal, or the alpha level is too low. In all these cases, statistical tests yield significant results even when there are no significant differences or associations in the population.

The first type of error is when the testing procedure wrongly rejects the null hypothesis. This type of error is called a Type I error (false positive) and is sometimes referred to as a Type I error. In the case of a courtroom, a Type I error is the conviction of an innocent defendant.

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We have shown that y + X - 1 = 0 is an implicit solution to cos(x)sinx - 5(x - Xsinx) = 0 on the interval (x, 1). This solution can be used to solve for x and find the values of x that satisfy the equation.

Yes, y + X - 1 = 0 is an implicit solution to cos(x)sinx - 5(x - Xsinx) = 0 on the interval (x, 1). To show this, we must solve for y. Begin by expanding the left side of the equation:

cos(x)sinx - 5xsin(x) + 5Xsinx = 0

Now we can combine the sine terms:

cos(x)sinx - 5xsin(x) + 5Xsinx = cos(x)sinx - 5(x + X)sinx = 0

Finally, divide both sides by -sinx:

y + X - 1 = cos(x) / -sinx = 0

Thus, y + X - 1 = 0 is an implicit solution to cos(x)sinx - 5(x - Xsinx) = 0 on the interval (x, 1).

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The probability of expected number of questions that are answered correctly by both A and B is 8.8. The variance of the number of questions that are answered correctly by either A or B is 5.64.

Let X be the number of questions answered correctly by A, and Y be the number of questions answered correctly by B.

The probability of answered correctly by both A and B is P(X = 1)P(Y = 1) = 0.60.7 = 0.42. Therefore, the expected number of questions is

E(XY) = np = 100.42 = 4.2

The number of questions answered correctly by either A or B is X + Y - XY.

E(X + Y - XY) = E(X) + E(Y) - E(XY) = 6 + 7 - 4.2 = 8.8.

To find the variance, we need to calculate the covariance:

Cov(X, Y) = E(XY) - E(X)E(Y) = 4.2 - 670.42 = -0.36

Then, using the formula of variance

Var(X + Y - XY) = Var(X) + Var(Y) - 2Cov(X, Y), we get:

Var(X + Y - XY) = 100.60.4 + 100.70.3 - 2*(-0.36) = 5.64.

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Answer:

i think 14-6

Step-by-step explanation:

The batting averages of Sammy Sosa and Barry Bonds for 13 recent years.so that Sammy Sosa is more consistent than Barry Bonds.

To explain this, let's look at the data. Over the past 13 years, Sammy Sosa's batting average ranged from 0.238 to 0.308, with an average of 0.272.

On the other hand, Barry Bonds' batting average ranged from 0.244 to 0.370, with an average of 0.315.

Sammy Sosa's batting average had a smaller range of 0.070, while Barry Bonds' batting average had a range of 0.126, indicating that Sammy Sosa was more consistent with his batting performance over the past 13 years.

Batting average is a statistical measure used in baseball to determine a player's performance at batting. It is calculated by dividing the number of hits by the total number of at-bats.

Batting average is expressed as a decimal number to three decimal places. For example, a player with 45 hits in 150 at-bats would have a batting average of .300.

Batting average is a simple but important statistic in baseball. It is one of the most commonly used measures of a player's hitting ability, as it reflects how often a player gets a hit when they step up to the plate. However, it does not account for other important aspects of hitting, such as the quality of hits (e.g. singles vs. home runs), the player's ability to draw walks, or their speed on the bases.

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The value of the integral from 0 to 7 of the even function f(x) is also 8, and the value of the integral from -7 to 7 of xf(x) is 0.

Since f(x) is an even function, we know that f(-x) = f(x) for all x. Therefore, we can split the integral from -7 to 7 into two equal parts, from 0 to 7 and from -7 to 0, and simplify as follows:

∫-7^7 f(x) dx = ∫-7^0 f(x) dx + ∫0^7 f(x) dx

Since f(x) is an even function, we have:

∫-7^0 f(x) dx = ∫0^7 f(-x) dx

Substituting this into the equation above and simplifying, we get:

2∫0^7 f(x) dx = 8

Therefore, the value of the integral from 0 to 7 of f(x) is:

∫0^7 f(x) dx = 4

To evaluate the integral from -7 to 7 of xf(x), we can use integration by parts:

∫-7^7 xf(x) dx = [x F(x)]-7^7 - ∫-7^7 F(x) dx

where F(x) is the antiderivative of f(x). Since f(x) is an even function, F(x) is an odd function, which means that F(-x) = -F(x) for all x. Therefore, we have:

∫-7^7 xf(x) dx = [x F(x)]-7^7 - ∫-7^7 F(x) dx

= [x F(x)]-7^7 + [F(x)]-7^7 - [F(x)]7^7

= 2[F(x)]-7^7

Since the function F(x) is odd, we have F(0) = 0, which means that:

∫-7^7 xf(x) dx = 2[F(x)]-7^7 = 2[F(x)]7^7 = 0

Therefore, the value of the integral from -7 to 7 of xf(x) is 0.

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Therefore , the solution of the given problem of expressions comes out to be  -0.42857 .

With shifting variables, estimates that mix joining, disabling, and instead randomly divide should indeed be generated. The following could be accomplished if they came together: a mental puzzle, some data, but instead equation . Formulas, elements, and arithmetic operations like addition, subtraction, omission, and grouping can all be found in a declaration of truth.

Here,

The result of dividing -7 by 14 is:

=> -7 ÷ 14 = -0.5

What is the result of 3 split by -7?

=> 3 ÷ -7 = -0.42857 (rounded to 5 integer places) (rounded to 5 decimal places)

Thus, the quotients are as follows:

=> -7 ÷ 14 = -0.5

=> 3 ÷ -7 = -0.42857

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To estimate the true proportion of men with color blindness to within 4% with 99% confidence interval, a sample of at least 846 men should be taken from a population of 1000.

To determine the sample size required to estimate the true proportion of men with color blindness within 4% with 99% confidence interval, we can use the following formula

n = (z^2 × p × (1-p)) / (d^2)

where

n is the required sample size

z is the z-value for the desired confidence interval (99% = 2.58)

p is the estimated proportion of men with color blindness (we don't have this information from the question, so let's assume it is 50% to get the most conservative estimate)

d is the desired margin of error (4% = 0.04)

Substituting the values, we get

n = (2.58^2 × 0.5 × (1-0.5)) / (0.04^2) = 845.06

This means that we need to sample at least 846 men to estimate the true proportion of men with color blindness within 4% with 99% confidence interval.

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The given question is incomplete, the complete question is:

using the results from the above mentioned survey, how many men should be sampled to estimate the true proportion of men with this type of color blindness to within 4% with 99% confidence interval and 1000 population

Answer:

blue

Step-by-step explanation:

you have to multiply the length x width so 18x8 to get the area for the rectangle which is 144 and then multiply the base and the height then multiply that by 0.5 to get the area for the triangle so it will be 8x6=48 48x0.5=24 then add the area of the triangle to the area of the rectangle so 24+144=168

If Sylvia gave 3/5 of candies to Brendan, and 1/3 of candies to Chandra, then the amount of candies that she gave to her friend is 28/75 pounds.

Sylvia bought 2/5 pounds of chocolate candies, which means that the total weight of candies that she had is 2/5 pounds.

Sylvia gave 3/5 of the candies to Brendan, and 1/3 of candies to Chandra,

which means , she gave a total of (3/5 + 1/3) = 14/15 pounds.

So, the weight of the candies she gave away can be found as:

⇒ (2/5) × (14/15) = 28/75 pounds

Therefore, Sylvia gave away 28/75 pounds of candies to her friends.

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The given question is incomplete, the complete question is

Sylvia bought 2/5 pounds of chocolate candies. Sylvia gave 3/5 of the candies to Brendan, and 1/3 of the candies to Chandra. Sylvia wants to know how many pounds of candies she gave to her friends

A plot of the array value versus array index using matplotlib.pyplot is:

pp.plot(DATA) option C is correct.

What is array ?

In computer science and mathematics, an array is a collection of elements, each identified by an array index or a key. Arrays are commonly used in programming languages to store data in a systematic way. They can be one-dimensional, multi-dimensional or even dynamic, and can store elements of various data types such as integers, floats, characters, or objects. The values in an array can be modified or accessed through their indices, making it a convenient data structure for many algorithms and applications.

According to the question:
The instruction that creates a plot of the array value versus array index using matplotlib.pyplot is:

pp.plot(DATA)


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The total surface area of the prism = 182.4 mm².

The total space occupied by an object's surfaces is referred to as its surface area.

The formulas we will learn in this post make it simple to determine the various surface areas that various 3D shapes in geometry have.

The surface area is divided into two categories:

Curved or laterally oriented surface area.

Total area of surface.

Now in the given question,

Surface area of the triangle = 1/2 × 6 ×8 = 24mm²

Surface area of the rectangle = 5.6 × 6 = 33.6mm²

Surface area of the second rectangle = 5.6 × 8 = 44.8mm²

Surface area of the second triangle = 1/2 × 6 × 8 = 24mm²

Surface area of the base rectangle= 5.6 × 10 = 56mm²

So, total surface area of the prism = 24+33.6+44.8+24+56 = 182.4mm².

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The value of vector v with  Initial point: (4, 8, 0) and Terminal point: (4, 1, 8) is v = <0, -7, 8> ||v|| = 10.6301

v/||v|| = <0, -0.6585, 0.7526> .

To find the vector v with the given initial and terminal points, we subtract the coordinates of the initial point from those of the terminal point. That is,

v = <4-4, 1-8, 8-0> = <0, -7, 8>

To find the magnitude of v, we use the formula:

||v|| = sqrt(v1^2 + v2^2 + v3^2) = sqrt(0^2 + (-7)^2 + 8^2) = sqrt(113) ≈ 10.6301

To find a unit vector in the direction of v, we divide v by its magnitude:

v/||v|| = <0, -7, 8>/sqrt(113) ≈ <0, -0.6585, 0.7526>

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The probability that all n flips are heads is (1/2)ⁿ.

The probability that the digit 1 doesn’t appear among n digits where each digit is one of (0-9) and all sequences are equally likely?The total number of possible n digit numbers that can be formed is 9ⁿ because 0 can not be the leading digit. So, the number of n digit numbers that does not contain 1 is 8ⁿ.The probability that the digit 1 does not appear in any n digit number is given by: P(no 1) = 8ⁿ/9ⁿ = (8/9)ⁿ

The probability that the number k ends up in the i-th position in the resulting permutation?The probability that a particular number is in the ith position is 1/n, since each of the n numbers is equally likely to appear in any given position.

A fair coin is flipped n times (each outcome in {H, T} n is equally likely). What is the probability that all heads occur at the end of the sequence?The probability that each of the n flips results in a head is 1/2ⁿ. Thus, the probability that all n flips are heads is (1/2)ⁿ.

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The equation will be changed into = f(x)= 32

What is a "Simple Equation"?

The link between two expressions on either side of the sign is represented by a mathematical equation.

                             One variable and an equal sign are typically present. Like this: 2x - 4 Equals 2.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

 the function f (x) = 2(4)

                       f(x)= 32

A statement is not an equation if it has no "equal to" sign.

A mathematical statement called an equation includes the sign "equal to" between two expressions with equal values.

Hence, The equation will be changed into = f(x)= 32

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The differential equation's solution that meets the initial condition y(8) = 3 is expressed as y = lnx + 16ln2/x

To verify that every member of the family of functions y = lnx + C/x is a solution of the differential equation x^2y'' + xy' = 1, we can substitute y = lnx + C/x and its first and second derivatives into the differential equation and simplify to obtain:

x^2((lnx+C/x)'' + (lnx+C/x)') = 1

x^2(C/x^3 - 2lnx/x^3 + 1/x^2) = 1

C/x - 2lnx/x + 1 = 1/x^2

C = lnx + C/x - 1

We can see that the left-hand side and the right-hand side of the last equation are equal, so every member of the family of functions y = lnx + C/x is a solution of the differential equation x^2y'' + xy' = 1.

To find a solution of the differential equation that satisfies the initial condition y(3) = 8, we can use the fact that every member of the family of functions y = lnx + C/x is a solution. Substituting y = lnx + C/x into the initial condition y(3) = 8, we obtain:

ln3 + C/3 = 8

Solving for C, we get:

C = 21ln3

Therefore, the solution of the differential equation that satisfies the initial condition y(3) = 8 is:

y = lnx + 21ln3/x

To find a solution of the differential equation that satisfies the initial condition y(8) = 3, we can use the same method.

Substituting y = lnx + C/x into the initial condition y(8) = 3, we obtain:

ln8 + C/8 = 3

Solving for C, we get:

C = 16ln2

Therefore, the solution of the differential equation that satisfies the initial condition y(8) = 3 is:

y = lnx + 16ln2/x


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Based on the given information and a one-tailed hypothesis test at a significance level of 0.05, we fail to reject the null hypothesis that the proportion of boxes with vouchers is 0.2 or higher.

To test the hypothesis that the proportion of boxes with vouchers is less than 0.2, we can use a one-tailed hypothesis test at a significance level of 0.05. Let's denote the proportion of boxes with vouchers by p.

The null hypothesis is that the proportion of boxes with vouchers is 0.2 or higher

H0: p >= 0.2

The alternative hypothesis is that the proportion of boxes with vouchers is less than 0.2

Ha: p < 0.2

To test this hypothesis, we can use the sample proportion of vouchers found by the students, which is

p-hat = 11/65 = 0.169

We can calculate the test statistic using the standard normal distribution, as follows

z = (p-hat - p0) / sqrt(p0×(1-p0)/n)

where p0 = 0.2 is the proportion under the null hypothesis, and n = 65 is the sample size.

Plugging in the values, we get

z = (0.169 - 0.2) / sqrt(0.2×(1-0.2)/65) = -1.16

The corresponding p-value for this test statistic is P(Z < -1.16) = 0.123.

Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. There is not enough evidence to support the claim that the proportion of boxes with vouchers is less than 0.2

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