Salaries for teachers in a particular state have a mean of $ 52000 and a standard deviation of $ 4800. a. If we randomly select 17 teachers from that district, can you determine the sampling distribution of the sample mean? Yes If yes, what is the name of the distribution? normal distribution The mean? 52000 The standard error? b. If we randomly select 51 teachers from that district, can you determine the sampling distribution of the sample mean? ? If yes, what is the name of the distribution? The mean? The standard error? C. For which sample size would I need to know that population distribution of X, teacher salaries, is normal in order to answer? ? v d. Assuming a sample size of 51, what is the probability that the sampling error is within $1000. (In other words, the sample mean is within $1000 of the true mean.) e. Assuming a sample size of 51, what is the 90th percentile for the AVERAGE teacher's salary? f. Assuming that teacher's salaries are normally distributed, what is the 90th percentile for an INDIVIDUAL teacher's salary?

Greek number prefixes are employed in the naming of molecular (covalent) substances.

Greek number prefixes are employed in the naming of molecular (covalent) substances. Prefixes are always combined in order of size (left-to-right in the table below). For instance, "heptadecatetracta" (7 + 10 + 400) would be the prefix for the number 417.

We utilise prefixes (mono-, di-, tri-, etc.) at the beginning of each element in molecular compounds to denote the element's subscript, but we only use the prefix mono- for the compound's second element.

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Answer:

Points are (3, 1) and (6, 2) ....

Step-by-step explanation:

When y is 1

[tex]{ \tt{1 = \frac{1}{3}x }} \\ \\ { \tt{x = 3}}[/tex]

Point: (3, 1)

When y is 2;

[tex]{ \tt{2 = \frac{1}{3}x }} \\ \\ { \tt{x = 6}}[/tex]

Point: (6, 2)

Answer:  The geometric series is convergent and the value is 16.

Step-by-step explanation:

How to illustrate the information?

Recall that the sum of an infinite geometric series, S, given first term, t_1, and common ratio, r, is given by:

S = t_1/(1 - r)

Note that:

3 = (4)(3/4)

9/4 = (3)(3/4

27/16 = (9/4)(3/4)

So this a geometric series with t_1 = 4 and r = 3/4. Therefore:

4 + 3 + 9/4 + 27/16 + ... = 4/(1 - 3/4) = 4/(1/4) = 16

The correct option is 16.

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum 4+3+ 9/4 +27/16 +???

choices are

1. 3/4

2. 12

3. 4

4. divergent

5. 16

Using the t-distribution, the 99% confidence interval for the true average number of alcoholic drinks all UF female students (over 21) have in a one week period is (3.25, 4.85).

First, we find the number of degrees of freedom, which is the sample size subtracted by 1, thus:

df = 170-1 = 169

Using the following formulas the lower and upper limits of the Interval are calculated,

n = 170

x = 4.05

s = 4.66 = 99% = 0.99

Because the population standard deviation is unknown, the Student T-distribution should be used. Yet, because the sample is huge, some books will utilise the normal distribution. I'll provide solutions for both techniques.

Error = z x s/√n

= 1.99 x 4.66/√170

Error margin ≈ 0.8

Lower limit = 4.05 - Error

= 4.05 - 0.8

= 3.25

Upper limit = 4.05 + Error

= 4.05 + 0.8

= 4.85

Therefore, the upper limit and lower limit is 3.25 and 4.85.

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Answer:

x = 3

Step-by-step explanation:

Solving systems of linear equations via substitution:

[tex]2x-6y=-6[/tex]

[tex]y=1.5x-2.5[/tex]

We are already given the value of y, so to find the value of x, we need to plug in the y value in the other equation.

[tex]2x-6(1.5x-2.5)=-6[/tex]

Distribute 6

[tex]2x-9x+15=-6[/tex]

Combine our like terms

[tex]-7x+15=-6[/tex]

Subtract 15 to both sides

[tex]-7x=-21\\[/tex]

Divide by -7

[tex]x=3[/tex]

As per the unitary method, Arun's mother would be 36 years old if Arun is 3 years old.

Let Arun's age be m years.

Let Arun's mother's age be n years.

From the problem statement, we know that n = 4m + 6. This means that Arun's mother's age is directly proportional to Arun's age, with a constant ratio of 4 and a constant difference of 6.

To solve for n, we can use the unitary method. We can set up a proportionality between the two ages as follows:

n / m = (4m + 6) / m

To solve for n, we can cross-multiply to get:

n = m x (4m + 6)

Expanding the right-hand side of the equation, we get:

n = 4m² + 6m

Therefore, Arun's mother's age is 4m² + 6m years. We can simplify this expression by factoring out 2m:

n = 2m(2m + 3)

This gives us a simpler form of the equation for Arun's mother's age. To find her age, we simply substitute Arun's age (m) into this expression and simplify.

If Arun is 3 years old (m = 15), then his mother's age would be:

n = 2m(2m + 3) = 2(3)(2(3) + 3) = 2(3)(6) = 36

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The probabilities Z > 0.75 is P(Z > 0.75) = 1 - P(Z < 0.75).

The probability of Z > 0.75 is 1 - 0.77337 = 0.22663

The probability of Z < -1.06 from it. P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968

Suppose Z follows the standard normal distribution. The probabilities using the ALEKS calculator are given below.(a) P(Z < 0.79) = 0.78524. (rounded to 5 decimal places)(b) P(Z > 0.75) = 1 - P(Z < 0.75) = 1 - 0.77337 = 0.22663. (rounded to 5 decimal places)(c) P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968. (rounded to 5 decimal places). In the standard normal distribution, the mean is equal to zero and the standard deviation is equal to 1. The notation for a standard normal random variable is z. Z is a random variable with a standard normal distribution and P(Z) denotes the probability of the random variable Z. Suppose z follows a standard normal distribution then the probability of Z < 0.79 is P(Z < 0.79) = 0.78524. So, the answer is 0.78524(rounded to 5 decimal places).Suppose z follows a standard normal distribution then the probability of Z > 0.75 is P(Z > 0.75) = 1 - P(Z < 0.75). Therefore, the probability of Z > 0.75 is 1 - 0.77337 = 0.22663(rounded to 5 decimal places).Therefore, the probability of -1.06 < Z< 2.17 can be found by finding the probability of Z < 2.17 and then subtracting the probability of Z < -1.06 from it. P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968(rounded to 5 decimal places).

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 The probability of [tex]3X1-1X2 + 3X3[/tex] being greater than 20 is given by[tex]P(3X1-1X2 + 3X3 > 20) = 1- Φ((20-3μ1+μ2-3μ3)/(√3σ11+σ22+3σ33))[/tex].

In this case, [tex]μ1=10, μ2=10, μ3=10, σ11=0.3, σ22=0.3, σ33=0.3,[/tex] so the probability of [tex]3X1-1X2 + 3X3[/tex] being greater than 20 is 1-Φ(-1.0).

1. To answer this question, we can use the formula for a multivariate normal distribution.

The probability of the profit for selling chocolate being greater than 6 million is given by P(X1 > 6) = 1- Φ(6-μ1)/(√σ11). In this case, μ1=10, σ11=0.3, so the probability of the profit being greater than 6 million is 1-Φ(2.667).

2. To answer this question, we need to use the formula for the conditional probability of a multivariate normal distribution.

The probability of the profit for selling chocolate being greater than 6 million, given the sales of marshmallow is 5 million and the sales of graham cracker is 5 million, is given by

[tex]P(X1>6 | X2=5, X3=5) = 1- Φ((6-μ1-Σ12*5-Σ13*5)/(√σ11-Σ12²-Σ13²))[/tex]. In this case,

[tex]μ1=10, σ11=0.3, Σ12=0.3, Σ13=0.3,[/tex]so the probability of the profit being greater than 6 million is 1-Φ(-0.1).

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Answer:

12

Step-by-step explanation:

6=a/4+2

L.C.M=4

4(6)=a+6(2)

24=a+12

24-12=a

a=12

In this particular question, we are being asked to find the number of normal subgroups of order 7 in a group of order 14. Before we begin, let's try to understand the different types of subgroups.Subgroups can be of two types: Proper Subgroups and Improper SubgroupsProper Subgroups are defined as subgroups which have more than one element and not equal to the entire group. Improper Subgroups are the subgroups which contain every element of the group.To determine the number of normal subgroups of order 7 in a group of order 14,

we need to use the following formula: `n_p = n/H`, where `n` represents the total number of subgroups of the group, `p` is the order of the subgroup we are looking for, and `H` is the normalizer of the subgroup in question.Using this formula, we can find that the order of the group is 14, and since 7 is a prime number, any subgroup of order 7 will be cyclic. Now, let's look at the different subgroups of the group of order 14:As 7 is a prime number and 7 divides 14, there will be one unique subgroup of order 7, and it will be cyclic.Since the group of order 14 is not a cyclic group, there are no other subgroups of order 7 besides the cyclic subgroup. Thus, the number of normal subgroups of order 7 in a group of order 14 is 1.

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There are 59 groups of 3 girls, or 177 girls in total, taking classes at the school.

A ratio is a means to indicate the relative sizes of two or more items for the purpose of comparison. It can be shown with a colon or as a fraction. Mathematicians employ ratios for a variety of purposes, including comparing numbers, scaling up or down, and resolving proportions. Moreover, ratios can be employed in other mathematical processes, simplified, and transformed to percentages or decimals.

Given that for every three girls there are 4 boys in class.

Thus, the proportion can be given as:

4x = 236

x = 59

Now, the proportion of girls are 3x.

3(59) = 177 girls.

Hence, there are 59 groups of 3 girls, or 177 girls in total, taking classes at the school.

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Answer:

NO.2- SSA is not the method to show the congruency of two triangles.

In data analytics, a population refers to all possible data values in a certain dataset.

Data analytics is a set of procedures and processes for examining datasets in order to draw conclusions from the information they contain, often aided by specialized systems and software. Organizations use data analytics to aid decision-making, increase efficiency, and evaluate outcomes.

The population and sample are two concepts in statistics. The population and sample are two concepts in statistics. The population is the entire set of objects or individuals being studied, while the sample is a subset of the population that is chosen for analysis. The sample is a subset of the population, chosen at random or according to some other criteria in order to represent the population as a whole.

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The given data is quantitative, The data is discrete and The highest level of measurement for this data is ratio

The given data is quantitative, as it involves measuring the number of defective circuits per CPU for a sample of 100 CPUs.

The data is discrete, since we are counting the number of defective circuits, which can only take integer values.

The highest level of measurement for this data is ratio, since the data involves measuring the number of defective circuits per CPU, and the ratio of one measurement to another is meaningful (for example, a CPU with 2 defective circuits has twice as many as a CPU with 1 defective circuit).

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Answer: Yes Leah Is Correct.

Step-by-step explanation: Leah is correct because if you have a rectangle divided into 4 parts than if you will be asked how much parts will you need to make this fraction a whole you’ll say 4 since if you say for example six you will be wrong since six is too much so if you shade one part in than it’s 1/4 ths now let’s say you shaded in 3/4th you will see 3 shaded and one more left not shaded in which gives the fraction the name 3/4.

hope this made sense.

Answer: graph is attached

Step-by-step explanation:

your equation is y = -3.5x + 50

your slope is - 3.5, your y intercept is 50

to graph it yourself using a line tool

start your first point at the y intercept of 50

put your first point

next, your slope is - 3.5 this means y/x for slope is -3.5 / 1

rise is -3.5 down and run is over right +1

because we want a straight line and the slope is a fraction, make a table and you can use points that are on exact numbers instead of fractions.

at x = 0, y = 50

at x = 1, y = 46.5 ( 50 - 3.5)

at x = 2, y = 43  (46.5 - 3.5)

at x = 3, y = 39.5 ( 43 - 3.5)

at x = 4, y = 36  ( 39.5 - 3.5)

you can graph the even numbers and draw your line.

see attached graph and table.

The perimeter of the non-shaded region in the figure can be calculated to be 14 inches.

Given a figure.

The middle portion of the figure is not shaded.

It is required to find the perimeter of the non-shaded region.

It is given that:

The whole area of the shaded region = 78 inches²

The area of the small square which is situated at the bottom is:

Area of small square = 2 × 4

                                  = 8 inches²

So, the area of the rest of the shaded area = 78 - 8

                                                                       = 70 inches²

Now, the area of the whole region without the small square is:

Area = 10 × (10 - 2)

        = 80 inches²

So, the area of the non-shaded region = 80 - 70

                                                                = 10 inches²

The width of the non-shaded rectangle is 2 inches.

So, length = 5 inches.

So, the perimeter is:

P = 2(5 + 2)

  = 14 inches

Hence, the perimeter is 14 inches.

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The figure is given below.

The correlation coefficient, r, that indicates a strong, but not perfect, linear relationship between the two variables are r = -0.85 and  R = 0.90.

The correlation coefficient, r, calculates the strength and movement of the linear relationship between the two variables. It ranges from -1 to 1. Here -1 implies a perfect negative linear relationship, 0 implies no linear relationship, and 1 implies a perfect positive linear relationship.

A strong correlation should be close to -1 or 1 but not an equal value. In the given options strong, but not perfect, linear variables are r = -0.85 and 0.90 are closer to the r values.

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If an angle of measurement of 140° then; a circle is centered at the vertex of the angle, then the arc subtended by the angle's rays is 0.0233 cm times as long as 1/360th of the circumference of the circle. Also if a circle is centered at the vertex of the angle, and 1/360th of the circumference is 0.06 cm long then length of the arc subtended by the angle's rays 8.4 cm. Another circle is centered at the vertex of the angle then arc subtended by the angle's rays is 70 cm long,Therefore the circumference of the circle is 180 cm.

a.) To find the fraction of the circle's circumference subtended by the angle's rays, we divide the angle measure by 360 degrees:

fraction of circle's circumference = 140/360

Simplifying this fraction, we get:

fraction of circle's circumference = 7/18

To find the length of the arc subtended by the angle's rays, we multiply the fraction of the circle's circumference by the circumference of the circle. Let's call the circumference of the circle "C":

length of arc = (7/18)*C

We're also told that the length of 1/360th of the circumference is equal to 0.06 cm. So, we can write:

(1/360)*C = 0.06

Multiplying both sides by 360, we get:

C = 360*0.06 = 21.6 cm

Now, we can substitute this value of C into the expression for the length of the arc:

length of arc = (7/18)*C

length of arc = (7/18)*(21.6)

length of arc = 8.4 cm (rounded to one decimal place)

Therefore, the length of the arc subtended by the angle's rays is 8.4 cm.

b.) We're given that 1/360th of the circumference of the circle is 0.06 cm long. To find the length of the arc subtended by the angle's rays, we need to multiply 140/360 by 0.06:

length of arc = (140/360)*0.06

length of arc = 0.0233 cm (rounded to four decimal places)

Therefore, the length of the arc subtended by the angle's rays is approximately 0.0233 cm.

c.) We're told that the length of the arc subtended by the angle's rays is 70 cm. To find the circumference of the circle, we need to find the length of 1/360th of the circumference first. We can do this by dividing 70 by 1/360:

(1/360)*C = 70

Multiplying both sides by 360, we get:

C = 70*360 = 25,200 cm

Therefore, the circumference of the circle is 25,200 cm. We can also verify this by dividing the length of the arc by the fraction of the circumference subtended by the angle's rays:

length of arc = (7/18)*C

C = (18/7)*length of arc

C = (18/7)*70

C = 180 cm (rounded to one decimal place)

This is a different value than we got earlier, so we need to check our calculations. It turns out that the previous calculation was incorrect - we made a mistake when multiplying 7/18 by 21.6. The correct calculation gives us:

length of arc = (7/18)*C

length of arc = (7/18)*(21.6)

length of arc = 8.4 cm (rounded to one decimal place)

Now, we can calculate the circumference of the circle:

length of arc = (7/18)C

C = (18/7) *length of arc

C = (18/7) *70

C = 180 cm (rounded to one decimal place)

Therefore, the circumference of the circle is 180 cm.

Also, If an angle of measurement of 140° then; a circle is centered at the vertex of the angle, then the arc subtended by the angle's rays is 0.0233 cm times as long as 1/360th of the circumference of the circle.

b. A circle is centered at the vertex of the angle, and 1/360th of the circumference is 0.06 cm long.The length of the arc subtended by the angle's rays 8.4 cm

c. Another circle is centered at the vertex of the angle.

The arc subtended by the angle's rays is 70 cm long,Therefore the circumference of the circle is 180 cm.

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Answer:

The square root of 2,100 is approximately 45.8257569495584 when rounded to 15 decimal places.

The last two rows of the table should be completed as follows:

Input   Output

8       22.80

10      28.50

An algebraic expression is a mathematical phrase that contains numbers, variables, and operations. It is used to represent a single quantity or value, and can be written in terms of one or more variables.

The rule given is an algebraic expression, x, which is the input, multiplied by 2.85, which is the output. Using this information, we can determine the cost of 10 muffins.

To find the cost of 10 muffins, we can use the algebraic expression given. First, we will multiply 10, the number of muffins, by 2.85, the cost of one muffin. This gives us a total of 28.50. Therefore, the cost of 10 muffins is 28.50.

Using this same rule and process, we can also determine the cost of any number of muffins. For example, if we want to know the cost of 15 muffins, we can simply multiply 15 by 2.85, giving us a total of 42.75.

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Answer:

Ans = 8

Step-by-step explanation:

because -- is + and  −−√70 is positive

so square root =8.366600265340757

and 8 is bigger as 8.366600265340757 is a decimal number.

You walked a total of 4576 yards to get to the basketball court.

In order to represent amounts in a more practical or acceptable unit of measurement, unit conversions are crucial for addressing mathematical issues. In this task, for instance, we were given distances in miles but had to translate them into yards to get the overall distance travelled. We wouldn't be able to compare or combine values that are stated in various units without unit conversions. When working with formulae or equations that contain physical quantities with multiple units, unit conversions are also crucial.

Given that, the distance walked is 1.5 miles and 1 1/10 miles.

Coverting into yards we have:

1.5 miles is equal to 1.5 x 1760 = 2640 yards

1 1/10 miles is equal to (1 + 1/10) x 1760 = 1936 yards

Total distance is:

2640 + 1936 = 4576 yards

Hence, you walked a total of 4576 yards to get to the basketball court.

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Cindy and tom, working together, can rake the yard in 8 hours. Working alone, Tom takes twice as long as Cindy, it takes Cindy to rake the yard 2 hours

To find the time it takes Cindy to rake the yard alone, let's use the following steps:Let x be the time taken by Cindy to rake the yard alone . Then the time taken by Tom to rake the yard alone will be 2xIt is given that Cindy and Tom can rake the yard in 8 hours when they work together.

Using the formula for working together, we get:[tex]\[\frac{1}{x} + \frac{1}{2x} = \frac{1}{8}\][/tex] Multiplying the equation by the least common multiple of the denominators, we get:[tex]\[16 + 8 = 2x\][/tex] Simplifying, we get:[tex]\[2x = 24\][/tex]Dividing both sides by 2, we get:[tex]\[x = 12\][/tex]Therefore, it takes Cindy 12 hours to rake the yard alone.

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Markov's inequality says that for a positive random variable X and any positive real number a, the probability that X is greater than or equal to a is less than or equal to the expected value of X divided by a.

(i) Let X be the number of automobiles sold next week. We have E(X) = 16, and we want to find an upper bound to P(X > 18).

Using Markov's inequality, we have:

P(X > 18) <= E(X)/18 = 16/18 = 8/9

Therefore, an upper bound to the probability that next week's sales exceed 18 is 8/9.

(ii) Let X be the number of automobiles sold next week. We have E(X) = 16 and Var(X) = 9.

By Chebyshev's inequality, we have:

P(|X-E(X)| < k*sqrt(Var(X))) >= 1 - 1/k^2

We want to find a lower bound to P(10 ≤ X ≤ 22).

First, we standardize X by subtracting the mean and dividing by the standard deviation:

Z = (X - E(X))/sqrt(Var(X)) = (X - 16)/3

We want to find P(10 ≤ X ≤ 22), which is equivalent to finding P(-2 ≤ Z ≤ 2). Using Chebyshev's inequality with k=2, we have:

P(-2 ≤ Z ≤ 2) >= 1 - 1/2^2 = 3/4

Substituting back for X, we get:

P(10 ≤ X ≤ 22) = P(-2 ≤ (X - 16)/3 ≤ 2) >= 3/4

Therefore, a lower bound to the probability that next week's sales are between 10 and 22, inclusively, is 3/4.

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Answer:

you need to show the numbers

Step-by-step explanation:

(a) the tare οf the rice is 800 grams. and (b) the tare percentage οf the rice is 3.10%.

A rate, number, οr amοunt in each hundred

a. The tare οf the rice is the weight οf the packaging οr cοntainer used tο hοld the rice. It can be calculated by subtracting the net weight οf the rice frοm the grοss weight οf the bag:

Tare weight = Grοss weight - Net weight

Tare weight = 25.8 Kg - 25 Kg

Tare weight = 0.8 Kg

Tο cοnvert this tο grams, we can multiply by 1000:

Tare weight = 0.8 Kg × 1000

Tare weight = 800 grams

Therefοre, the tare οf the rice is 800 grams.

b. The tare percentage οf the rice is the percentage οf the grοss weight that is accοunted fοr by the tare weight. It can be calculated using the fοrmula:

Tare percentage = (Tare weight / Grοss weight) × 100%

Substituting the values we fοund earlier, we get:

Tare percentage = (800 g / 25.8 Kg) × 100%

Tare percentage = 3.10%

Therefοre, the tare percentage οf the rice is 3.10%.

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The PQRS and TSUV are congruent parallelograms, they have the same shape and size. angle PQR is congruent to angle TSU, since they are opposite angles in parallelograms PQRS and TSUV, respectively. so angle TSU in parallelogram TSUV is congruent to angle PQR.

The following are a parallelogram's characteristics:

The two opposing sides are level and parallel.

The opposing angles line up evenly.

The following or adjacent angles are extra.

Every angle will be at a right angle if even one of the other angles is.

PQRS and TSUV are congruent parallelograms, which denotes that their dimensions are the same. The parallelograms' corresponding angles are therefore equal.

Angle PQR is an interior angle in the parallelogram PQRS that is opposite to the adjacent angle PQS, whereas angle UTS is an internal angle in the parallelogram TSUV that is opposite to the adjacent angle TSV.

We can infer that angle PQR and angle UTS are related angles and are hence congruent because PQRS and TSUV are congruent.

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Answer:

A

Step-by-step explanation:

Answer: Differential Equation Initial Condition y' + y tan x = sec X + 9 cos x y(0) ... linear differential equation for x > 0 that satisfies the initial condition.

Step-by-step explanation:

Answer:

436g

Step-by-step explanation:

1kg=1000g

3kg=3000g

3000+52=3052

3052÷7=436