A population has a proportion of 0. 62 and a standard deviation of sample proportions of 0. 8. A sample of size 40 was taken from this population. Determine the following probabilities. Illustrate each on the normal curve shown below each part.


a. ) The probability the sample has a proportion between 0. 5 and 0. 7



b. ) The probability the sample has a proportion within 5% of the population proportion



c. ) The probability that the sample has a proportion less than 0. 50



d. ) The probability that the sample has a proportion greater than 0. 80

The value of "n" is 6.

"n" is related to a circle with intersecting chords labeled 5, n+4, 7, and n+8 [1]. To find the value of "n", we can use the property that states that if two chords intersect inside a circle, the products of their segments are equal. Using this property, we can set up the following equation:

7(n+4) = 5(n+8)

Expanding the brackets, we get:

7n + 28 = 5n + 40

Simplifying, we get:

2n = 12

n=6

A circle is a two-dimensional geometric shape that is defined as a set of all points in a plane that are at a fixed distance (called the radius) from a given point (called the center). It is a closed shape, meaning that it has no beginning or end, and its boundary is a continuous curve.

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The point of intersection of the hypotenuse is where the perpendicular bisectors of a right triangle intersect.

A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other terms, a perpendicular bisector separates a line segment into two equal halves by intersecting it at a 90° angle. A line that is perpendicular to the side and passes through the middle of one of the triangle's sides is called the perpendicular bisector. The circumcenter is the location where the three perpendicular bisectors of a triangle's sides meet.

Given

Triangle LMN is isosceles, construct the perpendicular bisector of LM, MN, and LN. For LM, label the point of intersection W. For MN, label the point of intersection X. For LN, label the point of intersection Y.

A triangle's three perpendicular bisectors come together at a single point. The circumcenter is the location where the perpendicular bisectors coincide.

The point of intersection for the three perpendicular bisectors Z.

The point of intersection of the hypotenuse is where the perpendicular bisectors of a right triangle intersect.

Ways to find perpendicular bisector:

Place the compasses' point on one of the line's endpoints.

2 Draw a second arc that intersects the first arc using compasses.

3 the two locations where the arcs converge.

The new line bisects the old line segment y perpendicularly.

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Answer:

111 / 190

Step-by-step explanation:

Let us first compute the probability of picking 2 of each sweet. Take liquorice as the first example. There are 12 / 20 liquorice now, but after picking 1 there will be 11 / 19 left. Thus the probability of getting two liquorice is demonstrated below;

\(12 / 20 * 11 / 19 = \frac{33}{95},\\Probability of Drawing 2 Liquorice = \frac{33}{95}\)

Apply this same concept to each of the other sweets;

\(5 / 20 * 4 / 19 = \frac{1}{19},\\Probability of Drawing 2 Mint Sweets = 1 / 19\\\\3 / 20 * 2 / 19 = \frac{3}{190},\\Probability of Drawing 2 Humbugs = 3 / 190\)

Now add these probabilities together to work out the probability of drawing 2 of the same sweets, and subtract this from 1 to get the probability of not drawing 2 of the same sweets;

\(33 / 95 + 1 / 19 + 3 / 190 = \frac{79}{190},\\1 - \frac{79}{190} = \frac{111}{190}\\\\\)

The probability that the two sweets will not be the same type of sweet =

111 / 190

Answer:

2

Step-by-step explanation:

Prime Factorization of 14

Prime factors of 14 are 2, 7. Prime factorization of 14 in exponential form is:

14 = 21 × 71

Step-2: Prime Factorization of 32

Prime factors of 32 are 2. Prime factorization of 32 in exponential form is:

32 = 25

Step-3: Factors of 14

List of positive integer factors of 14 that divides 14 without a remainder.

1, 2, 7

Step-4: Factors of 32

List of positive integer factors of 32 that divides 14 without a remainder.

1, 2, 4, 8, 16

Final Step: Greatest Common Factor Number

We found the factors and prime factorization of 14 and 32. The biggest common factor number is the GCF number.

So the greatest common factor 14 and 32

According to the venn diagram, the circle surrounds four pizzas. Ham is present in Meat Feast, Scorcher, Hawaiian, and Capricciosa.

The Venn diagram, a frequent style of diagram showing logical connections between sets, was made popular by John Venn in the 1880s. Diagrams are used to teach fundamental set theory and to show simple set relationships in probability, logic, statistics, linguistics, and computer science. The relationships between two or more groups of elements are shown in a Venn diagram by overlapping circles and other shapes. When arranging information graphically, it is frequently advantageous to emphasize the similarities and differences between components. The intersection of two large circles forms the central empty area of a Venn diagram.

given

From the image,

ham is an ingredient in Meat feast, Scorcher, Hawaiian, and Capricciosa.

According to the venn diagram, the circle surrounds four pizzas. Ham is present in Meat Feast, Scorcher, Hawaiian, and Capricciosa.

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Answer:

100.8

Step-by-step explanation: I tried solving this

Answer:

100.8

Step-by-step explanation:

Polly Petunia, the Chief Horticulturalist for the Southwest region, is using a method called stratified random sampling to survey amateur gardeners in her region.

Stratified random sampling involves dividing the population into distinct groups or strata based on certain characteristics that are relevant to the research objective.

In this case, Polly is dividing the population of amateur gardeners in the Southwest region into three strata based on the states: Arizona, New Mexico, and Texas.

Once the population is divided into strata, Polly selects a random sample from each stratum. She sends her survey to 150 randomly selected gardeners from each state, resulting in a total sample size of 450 gardeners (150 from each state).

By using stratified random sampling, Polly ensures that her sample is representative of the population in terms of the geographic distribution across the three states.

This method allows her to obtain insights specific to each state while still maintaining a random selection within each stratum.

Using stratified random sampling helps increase the precision and accuracy of the survey results.

It allows Polly to make more accurate inferences and draw conclusions about the water conservation practices of amateur gardeners in each state, as well as the overall Southwest region.

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Answer:

a. The length of the box = (40 - 2·x) cm

The height of the box = x cm

The width of the box = (25 - 2·x) cm

b. The formula for the volume of the box as a function of x is 4·x³ - 130·x² + 1000·x

c. The value of x that would maximize the volume of the box is x = 5 cm

d. The largest volume of the box is 2250 cm³

Step-by-step explanation:

a. The given parameters are;

The length of the cardboard = 40 cm

The width of the cardboard = 25 cm

The length of the box = (40 - 2·x) cm

The height of the box = x cm

The width of the box = (25 - 2·x) cm

b. The formula for the volume of the box = The area of the base of the box × Height of the box

The area of the base of the box =  (40 - 2·x) × (25 - 2·x) = 1000 - 80·x - 50·x + 4·x²

∴ The area of the base of the box = 4·x² - 130·x + 1000

The height of the box = x

The volume of the box = (4·x² - 130·x + 1000) × x = 4·x³ - 130·x² + 1000·x

The volume of the box in terms of x, V = 4·x³ - 130·x² + 1000·x

c. At the extremum point, dV/dx = 12·x² - 260·x + 1000 = 0

x = (260 ± √((-260)² - 4 × 12 × 1000))/(2 × 12)

x = (260 ± 140)/(24)

x = 5 or x = 16.\(\bar 6\)

At x = 5, the volume of the box is V = 4×5³ - 130×5² + 1000×5 = 2250

The volume of the box is V = 2250 cm³

At x = 16.67, the volume is 4×16.67³ - 130×16.67² + 1000×16.67 = -925.\(\overline {925}\)cm³

Therefore, the value of x that would maximize the volume of the box is x = 5 cm

d. The largest volume of the box is 4×(5 cm)³ - 130×(5 cm)² + 1000×(5 cm) = 2250 cm³.

Answer:

The correct option is;

The graph of h(x) passes the horizontal line test

Step-by-step explanation:

In order to determine if a function has an inverse, and also if the inverse of the function is also a function, the function can be tested by drawing an horizontal line the graph of the function and viewing to find the following conditions;

A graph of a function that is intersected at only one point in all places (vertically) by an horizontal line indicates that the function has an inverse that is also a function, while a graph of a function that is intersected at more than one point in some places (vertically) by an horizontal line indicates that the function does not have an inverse that is also a function.

Answer:

D

Step-by-step explanation:

EDGE 2020

If vector V has an initial point at (7, -1) and a terminal point at (7,−2), then the exact value of V is (0, -1).

In mathematics, a vector is a mathematical object that has both magnitude and direction. It is represented by a directed line segment, where the length of the segment represents the magnitude and the direction of the segment represents the direction of the vector.

In the given problem, we are given the initial point and terminal point of the vector V, and we need to find its exact value. To do this, we subtract the coordinates of the initial point from the coordinates of the terminal point to get the coordinates of the vector. This gives us a vector with magnitude 1 (since the difference in the y-coordinates is 1) and direction pointing downwards in the y-axis.

The vector V can be found by subtracting the initial point from the terminal point:

V = (7, -2) - (7, -1) = (7 - 7, -2 - (-1)) = (0, -1)

So the exact value of V is (0, -1).

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Answer:

19 throws.

Step-by-step explanation:

For her success rate to be 80% in 37 throws she must make  0.8 * 37

= 29.6 throw - that is 30 to nearest throw.

So for the next 20 throws she must make  30 - 11 = 19 throws.

a) the calculated t-value (2.344) is greater than the critical t-value (1.984), we reject the null hypothesis. b) The p-value associated with a t-value of 2.344 is approximately 0.010 (two-tailed test).

(a) To determine if the differences in average yearly reading growth between Program A and Program B are significant at a 5% level, we can conduct a two-sample t-test.

Let's define our null hypothesis (H0) as "there is no significant difference in average yearly reading growth between Program A and Program B" and the alternative hypothesis (H1) as "Program A leads to higher average yearly reading growth than Program B."

We have the following information:

For Program A:

Sample size (na) = 64

Sample mean (xA) = 1.2

Sample standard deviation (sA) = 0.26

For Program B:

Sample size (nb) = 100

Sample mean (xB) = 1.0

Sample standard deviation (sB) = 0.28

To calculate the test statistic, we use the formula:

t = (xA - xB) / sqrt((sA^2 / na) + (sB^2 / nb))

Substituting the values, we have:

t = (1.2 - 1.0) / sqrt((0.26^2 / 64) + (0.28^2 / 100))

t ≈ 2.344

Next, we determine the critical t-value corresponding to a 5% significance level and degrees of freedom (df) equal to the smaller sample size minus 1 (df = min(na-1, nb-1)). Using a t-table or statistical software, we find the critical t-value for a two-tailed test to be approximately ±1.984.

(b) To calculate the p-value, we compare the calculated t-value to the t-distribution. The p-value is the probability of observing a t-value as extreme as the one calculated, assuming the null hypothesis is true.

From the t-distribution with df = min(na-1, nb-1), we find the probability corresponding to a t-value of 2.344. This probability corresponds to the p-value.

(c) Based on the results of the hypothesis test, where we rejected the null hypothesis, we can conclude that there is evidence to suggest that Program A leads to higher average yearly reading growth compared to Program B.

(d) To calculate the probability of a Type II error (β), we need additional information such as the significance level (α) and the effect size. The effect size is defined as the difference in means divided by the standard deviation. In this case, the effect size is (xA - xB) / sqrt((sA^2 + sB^2) / 2).

Let's assume α = 0.05 and the effect size (xA - xB) / sqrt((sA^2 + sB^2) / 2) = 0.1. Using statistical software or a power calculator, we can calculate the probability of a Type II error (β) given these values.

Without the specific values of α and the effect size, we cannot provide an exact calculation for the probability of a Type II error. However, by increasing the sample size, we can generally reduce the probability of a Type II error.

In summary, the differences in average yearly reading growth between Program A and Program B are significant at a 5% level, suggesting that Program A leads to higher average yearly reading growth. The p-value of the test results is approximately 0.010. Based on these findings, it may be recommended to adopt Program A over Program B. The probability of a Type II error (β) cannot be calculated without specific values of α and the effect size.

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Interval data are numerical measurements, while ratio data are numerical measurements with a true zero value.

The most appropriate level of measurement for doctors who measure the weights of preterm babies is quantitative data. Quantitative data is a type of numerical data that can be measured. The weights of preterm babies are numerical, and they can be measured using a scale in pounds, which makes them quantitative.

Levels of measurement, often known as scales of measurement, are a method of defining and categorizing the different types of data that are collected in research. This is because the levels of measurement have a direct relationship to how the data may be utilized for various statistical analyses.

Levels of measurement are divided into four categories, including nominal, ordinal, interval, and ratio levels, and quantitative data falls into the last two categories. Interval data are numerical measurements, while ratio data are numerical measurements with a true zero value.

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Answer:

9 ..... .................

The coordinates which are the best estimate of the solution to the system of equations is: D. (1, 4), begin ordered pair 1 comma 4 end ordered pair.

In order to graphically determine the solution for this system of linear equations on a coordinate plane, we would make use of an online graphing calculator to plot the given system of linear equations while taking note of the point of intersection;

2x + 3y = 12            ......equation 1.

4x + 2y = 10      ......equation 2.

Based on the graph shown (see attachment), we can logically deduce that the solution for this system of linear equations is the point of intersection of each lines on the graph that represents them, which is represented by this ordered pair [0.8, 3.6] ≈ [1, 4].

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We can use Lagrange multipliers to find the distance from the plane x + y + z = 0 to the center of the sphere S, which is given by the point (5,7,9).

Let f(x,y,z) be the distance between the point (x,y,z) and (5,7,9), which is given by the formula:

f(x,y,z) = √[(x-5)² + (y-7)² + (z-9)²]

Let g(x,y,z) be the equation of the plane x + y + z = 0, which can be rewritten as:

g(x,y,z) = x + y + z

We want to minimize f(x,y,z) subject to the constraint g(x,y,z) = 0, which means we need to solve the system of equations:

∇f = λ∇g

g(x,y,z) = 0

where ∇f and ∇g are the gradient vectors of f and g, respectively, and λ is a Lagrange multiplier.

Taking the partial derivatives of f and g, we have:

∂f/∂x = (x-5)/√[(x-5)² + (y-7)² + (z-9)²]

∂f/∂y = (y-7)/√[(x-5)² + (y-7)² + (z-9)²]

∂f/∂z = (z-9)/√[(x-5)² + (y-7)² + (z-9)²]

∂g/∂x = 1

∂g/∂y = 1

∂g/∂z = 1

Setting ∇f = λ∇g, we get the following system of equations:

(x-5)/√[(x-5)² + (y-7)² + (z-9)²] = λ

(y-7)/√[(x-5)² + (y-7)² + (z-9)²] = λ

(z-9)/√[(x-5)² + (y-7)² + (z-9)²] = λ

x + y + z = 0

Squaring the first three equations and adding them up, we get:

(x-5)² + (y-7)² + (z-9)² = λ²[(x-5)² + (y-7)² + (z-9)²]

Simplifying, we get:

(1-λ²)x² + (1-λ²)y² + (1-λ²)z² - 10x - 14y - 18z + 135 = 0

This is a quadratic form in x, y, and z, which can be diagonalized using a rotation of coordinates. The diagonalization yields:

(1-λ²)(x'-5)² + (1-λ²)(y'-7)² + (1-λ²)(z'-9)² = 135 - 25λ²

where (x',y',z') are the new coordinates obtained by the rotation. The minimum value of λ is achieved when the right-hand side of the above equation is minimized, which occurs when λ = ±1. Therefore, the distance between the plane x+y+z=0 and the center of the sphere S is given by:

d = √[(x'-5)² + (y'-7)² + (z'-9)²]

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The line integral of f(x,y,z) = xy + z over the helix r(t) = (cos(t), sin(t), t) for 0 ≤ t ≤ 2π is (2π√2) obtained using the parameterization of the curve and integration.

To compute the line integral of f(x,y,z) = xy + z over the helix r(t) = (cos(t), sin(t), t) for 0 ≤ t ≤ 2π, we first need to parameterize the curve and express f in terms of the parameter.

The parameterization of the curve r(t) is given by:

x = cos(t)

y = sin(t)

z = t

The function f(x,y,z) can be expressed in terms of the parameter as:

f(x,y,z) = xy + z = cos(t)sin(t) + t

Now, we can evaluate the line integral using the parameterization of the curve and the expression for f as follows:

∫[0,2π] f(r(t)) * ||r'(t)|| dt

where ||r'(t)|| is the magnitude of the derivative of r(t), which can be computed as:

||r'(t)|| = √(cos^2(t) + sin^2(t) + 1) = √2

Substituting the expressions for r(t), f(r(t)), and ||r'(t)||, we get:

∫[0,2π] (cos(t)sin(t) + t) * √2 dt

Using integration by parts, we can evaluate the integral as follows:

∫[0,2π] (cos(t)sin(t) + t) * √2 dt = [√2/2 * (sin^2(t) - cos^2(t)) + t√2] |[0,2π]

= (2π√2)

Therefore, the line integral of f(x,y,z) = xy + z over the helix r(t) = (cos(t), sin(t), t) for 0 ≤ t ≤ 2π is (2π√2).

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Answer:

yo

Step-by-step explanation:

Answer:

71.55

Step-by-step explanation:

a2 + b2 = c2

c=square route (a2+b2)

Answer:15.6

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The cost of painting the wall is Rs.48.75 .

The square shape wall whose length is 10m has a door of length 2m and breadth 1m.   It also has a window of length 1m and breadth 0.5m.

Therefore, the cost of painting the wall can be calculated as follows:

cost of painting per meters = Rs0.5 per metre square

Therefore, the area of the wall to be painted will exclude the window and the door.

Hence,

area of wall of the wall to be painted = area of the wall - area of the window - area of the door

Therefore,

area of wall of the wall to be painted = 10² - (1 ×  0.5) - (2 × 1)

area of wall of the wall to be painted = 100 - 0.5 - 2

area of wall of the wall to be painted = 97.5 metres²

Therefore,

1 metres square = Rs0.5

97.5 metres squared = ?

cross multiply

cost to paint the wall = 0.5 × 97.5

cost to paint the wall = Rs.48.75

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Step-by-step explanation:

this just means

q = k×p

and we need to find k.

the sum of both q values when p = 6 and p = 11 is then

k×6 + k×11 = 51

17k = 51

k = 51/17 = 3

so, our equation is

q = 3p

and when q = 72

72 = 3p

p = 72/3 = 24

Answer:

6m

Step-by-step explanation:

the side of first square = 3 m

area of first square = 3^2= 9 m^2

let the side of second square = x m

since diagonal of first square = x m as per the question

in a square each angle is 90 degree

therefore by applying pythagorus theorem ,

diagonal ^2 = side^2 + side ^2

diagonal^2 = 3^2+3^2=9+9

DIAGONAL= square root of 18

diagonal= 3\(\sqrt{2}\) m = side of second square

therefore in second square ,

one angle is 90  degree , therefore by applying pythagorue theorem

diaqonal^2 = side ^2 + side ^2 = (3\(\sqrt{2}\))^2 + ( 3\(\sqrt{2}\))^2

diagonal ^2 = 18 + 18

diagonal = square root of 36

therefore diagonal of second square is 6m

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Answer:

6m explained it all hope it helps

Thus, the test for homogeneity follows the same procedures as the test for independence because the assumptions for performing the chi-square test for independence and chi-square test for homogeneity are the same.

The procedures for the chi-square test of homogeneity are the same as for the chi-square test of independence. The data is different for both tests. Tests of independence are used to determine whether there is a significant relationship between two categorical variables from the same population. One population is segmented based on the value of two variables. So there will be a column variable and a row variable.

The chi-square test of homogeneity of proportions can be used to compare population proportions from two or more independent samples, determining whether the frequency counts are distributed identically among different populations.

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Answer: so the answer is 7.5 for the first one but for the 2nd one i don’t know

Step-by-step explanation:

Answer:

guhakhsadkjgaghafgherqiughnvxcnbdbfkjeqkgefvbxcvzcm zvnbdbeqgheqkghqfkghfdvkbfvkbvkdfbfkghhsdfhsdlkFlfhLHRUHRGFNVSCVAHRGHUEGHBHBJHDFHAFGKFOUJHRIEFDJSKRTGHBFVDSAERTYHJDSAWEDRTYUJNBVCDSWERTYUJHNFDSERTYUJKMNBVCDSXAHJKMNBDSADFGHJKGFDSFGOIKJHNBVCXDFFUFRURFUIFUFUHDFYGDFYHHFUHREUHDHURTHUTGHHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGGHGHGHGHGHGHGHGGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHG

Step-by-step explanation:

To duplicate angle ABC, draw a line segment, position the compass on point A, and then draw an arc that intersects the line segment. Next, position the compass on point B, and then draw a second arc that intersects the first arc at a point on the line segment. Finally, position the compass on the point where the two arcs intersect, but without changing the width, and draw a third arc that intersects the line segment.

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

Common instruments used to measure angles are:

1. Protractor

2.Compass

3.Digital Angle finder

4.Angle finder

5.Clinometer

6. Inclinometer

You can take the following actions to copy angle ABC:

Create a line segment that will serve as the foundation for the new angle you're going to create.

Draw an arc that crosses the line segment you produced in step 1 by positioning the compass on point A.

Draw a second arc that crosses the previous arc at a point on the line segment by setting the compass on point B.

Place the compass on the intersection of the two arcs without adjusting the compass's width, then create another arc that crosses the line segment.

Point D is where the second arc crosses the line segment. To finish the new angle, join points D and C.

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In the given statement is:

You conduct a survey of your small town about having a town wide gargae sale. of those surveyed, 56% are in favor and 44% are opposed. the actual percent could be 5% more or 5% less than the acquired results.

Using the absolute value function, we have that:

A. The least percentage is of 39% and the greatest is of 49%.

B. Since the greatest percentage is below 50%, the statement conflicts with the survey data.

What is the absolute value function?

The absolute function is defined by:

It measures the distance of a point x to the origin.

For this problem, the difference between the percentage of opposed and 44% can be of at most 5%, hence the absolute value equation is:

|x - 44| = 5.

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The product of z and w is 24(cos(107∘)+sin(107∘)). To calculate the product of complex numbers z and w, where =6(cos82∘)+sin(82∘) z=6(cos(82∘ )+isin(82 ).

4(cos25∘)+sin(25∘), w=4(cos(25∘ )+isin(25∘ )), we use the properties of complex numbers. By multiplying their magnitudes and adding their arguments, we find that 24(cos(107∘)+sin(107∘), z⋅w=24(cos(107∘)+isin(107∘)).

In step 1, we determine the magnitudes of z and w by taking the absolute values of the coefficients. The magnitude of z is found to be 6, and the magnitude of w is 4. Moving to step 2, we multiply the magnitudes of z and w together, resulting in 6⋅ 4=24, 6⋅4=24. In step 3, we add the arguments of z and w to obtain the combined argument. Adding 82∘ and 25∘ , we get 107 .

Finally, in step 4, we convert the result back to trigonometric form, expressing z⋅w as 24(cos(107∘)+sin(107∘)), 24(cos(107∘)+isin(107∘)).Therefore, the product of z and w is 24(cos(107∘)+sin(107∘)).

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Answer:

4

Step-by-step explanation: