The following data represent trunk circumferences (in mm) for a random sample of 60 four-year-old apple trees at East Malling Agriculture Research Station in England. â⬠108 99 106 102 115 120 120 117 122 142 106 111 119 109 125 108 116 105 117 123 103 114 101 99 112 120 108 91 115 109 114 105 99 122 106 113 114 75 96 124 91 102 108 110 83 90 69 117 84 142 122 113 105 112 117 122 129 100 138 117 (a) Make a stem-and-leaf display of the age distribution. (Use the tens digit as the stem and the ones digit as the leaf. Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values. )

Answer:

9 yds

Step-by-step explanation:

Because one yard is equal to 3 feet we can divide the number of feet by 3. Which is 27÷3= 9.

So the answer would be that the width of the backyard is 9 yards.

Hope that helps and have a great day!

Answer:

9 yd.

Step-by-step explanation:

The backyard is 27 feet wide. How many yards wide is the backyard:

27 feet = 1 yd

3 feet = ?

27 ÷ 3 = 9 yd

If a merchant bought an item for $50.00 and sold it for 30% more (markup), the item's selling price was $65.00.

The markup is the percentage or amount by which an item is sold.

The markup is based on the cost price.  After adding the markup amount, the selling price is determined to generate some profits for the seller.

The purchase price of an item = $50.00

The markup = 30%

Markup factor = 1.3 (1 + 0.3)

The selling price of the item = $65.00 ($50.00 x 1.3)

Thus, for adding 30% more (markup) on the cost of the item, the selling price is determined as $65.00.

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9514 1404 393

Answer:

Step-by-step explanation:

Let t represent the third-place prize value. Then the first place prize has a value of 2t+500, and the second-place prize is 2t+100. The total value of the three prizes is ...

  t +(2t+500) +(2t+100) = 1850

  5t +600 = 1850

  5t = 1250

  t = 250 . . . . . . . . . . . third place prize

  2t +500 = 1000 . . . . first place prize

  1000 -400 = 600 . . .second place prize

The prizes for 1st, 2nd, and 3rd places are $1000, $600, and $250, respectively.

√x + 6 = x

Well the solution to the equation would be B because x=9.

Therefore your answer is 9.

Answer:

B

Step-by-step explanation:

√x + 6 = x

x - √x - 6 = 0

(√x - 3)(√x + 2) = 0

so

√x = -2 (impossible)

or

√x = 3 => x = 9

Answer:

Picture A: statement c is incorrect. It should be: The scale factor used was 0.4.

Picture B: statement B is incorrect. It should be: Line KL corresponds with line FG.

Second pic:

Amos was correct

Tash was correct

Both were correct

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

Answer:

x=y+1,y=y

Step-by-step explanation:

If you have access to a linear programming solver or software like Excel Solver or MATLAB's Optimization Toolbox, you can enter the dual problem and use the solver to obtain the optimal solution.

To solve the dual of the given problem using the dual simplex algorithm, we first need to rewrite the primal problem in standard form. The primal problem is as follows:

Maximize: z = 11x + x + 6w

Subject to:

6x + 15x - 3w ≥ 60

3x + 2x + w ≤ 21

2x + 3x - w = 34

x ≥ 0, y ≥ 0, w ≥ 0

The dual problem will have the following form:

Minimize: w = 60y + 21z + 34u

Subject to:

6y + 3u + 2v ≥ 11

15y + 2u + 3v + u + v ≥ 1

-3y + v = 6

y ≥ 0, u ≥ 0, v unrestricted

Now, we can apply the dual simplex algorithm to solve the dual problem. The steps involved in the dual simplex algorithm include:

Start with an initial feasible solution.

Check for optimality.

If not optimal, select a pivot column and pivot row.

Perform row operations to make the pivot element 1 and all other elements in the pivot column 0.

Repeat steps 2-4 until the optimal solution is reached.

The detailed calculations and iterations involved in the dual simplex algorithm can be quite lengthy and involve complex matrix operations. It would be best to use a specialized software or linear programming solver to perform these calculations accurately and efficiently.

If you have access to a linear programming solver or software like Excel Solver or MATLAB's Optimization Toolbox, you can enter the dual problem and use the solver to obtain the optimal solution.

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The image is plotted and attached

The rectangle started with ABCD. Then following the reflection along line AC. point B and point D swapped so we have B' replacing D and D' replacing B.

180 degrees rotation through C, resulted to B'' D'' and A'. Point C maintains it's position since the rotation is about point C.

Enlargement by a factor of 2 results to C' B''' D''' A'' and this is the final image.

While the reflection and rotation preserves the geometry, the enlargement affects the geometry, producing a rectangle with a bigger size twice the initial size

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If you paid $16 in sales tax on a new phone. The phone costs $320. the percent of sales tax is 5%.

To find the percent of sales tax, we need to divide the amount of sales tax by the cost of the phone, and then multiply by 100 to convert to a percentage:

Percent of sales tax = (Sales tax / Cost of phone) x 100%

Percent of sales tax = (16 / 320) x 100%

Simplifying the expression inside the parentheses:

Percent of sales tax = 0.05 x 100%

Multiplying:

Percent of sales tax = 5%

Therefore, the percent of sales tax is 5%.

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Therefore , the solution of the given problem of function comes out to be  f(N) = 360/N the cost per individual for any number of contributors to the gift is provided by this function.

The math lesson includes a wide range of topics, such as mathematics, integers, as well as one's divisions, architecture, and both actual mostly and fictitious geographic locations. The relationships between various components that all cooperate to create the same outcome are covered by a work. A utility is composed of numerous unique elements that work together to produce unique outcomes for each input.

Here,

To figure out how much each individual would spend, we need to divide the cost of the gift by the number of people contributing. Here are the estimates for various populations:

Each person would spend $180 ($360 / 2) if there were two people splitting the expense.

The expense would be divided among three people, who would each pay

=>  $120 = ($360 / 3).

If the cost were divided among five individuals, each person would pay =>  $72 = ($360 / 5).

Ten people would split the expense equally, each spending

=>  $36 =  ($360 / 10).

Each person would spend

=>  $3.60 = ($360 / 100)

if there were 100 people splitting the expense.

II. The algorithm is as follows:

Cost per individual equals total expense / number of individuals

=> f(N) = C/N

where f(N) is the price per individual.

The function for the cost per individual, for instance, is:

=>  f(N) = 360/N

The cost per individual for any number of contributors to the gift is provided by this function.

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Given:

The sequence is:

\(6, -24, 96, -384,...\)

To find:

The explicit formula for the given sequence and then find the 16th term.

Solution:

We have,

\(6, -24, 96, -384,...\)

The ratio between two consecutive terms are:

\(\dfrac{-24}{6}=-4\)

\(\dfrac{96}{-24}=-4\)

\(\dfrac{-384}{96}=-4\)

The given sequence has a common ratio. So, the given sequence is a geometric sequence with first term 6 and common ratio \(-4\).

The explicit formula of a geometric sequence is:

\(a_n=ar^{n-1}\)

Where, a is the first term and r is the common ratio.

Putting \(a=6, r=-4\) in the above formula, we get

\(a_n=6(-4)^{n-1}\)

We need to find the 16th term. So, put \(n=16\) in the above formula.

\(a_n=6(-4)^{16-1}\)

\(a_n=6(-4)^{15}\)

\(a_n=6(-1073741824)\)

\(a_n=-6442450944\)

Therefore, the explicit formula for the given sequence is  \(a_n=6(-4)^{n-1}\) and 16th term of the given sequence is \(-6.442450944\).

SSS - Side - Side - Side

SAS - Side - Angle - Side

ASA - Angle - Side - Angle

AAS - Angle - Angle - Side

The above theorems can be used to compare two triangles.

SSS, which stands for "side, side, side," represents two triangles having identical angles on each of their three sides. Two triangles are said to be congruent if their third sides coincide with those of another triangle.

That is what the SAS regulation says. The triangles are congruent if the two sides and included angle of one triangle match the two sides and included angle of the other triangle. Any angle that may be made by two particular sides is regarded as an included angle.

A triangle is comparable to another if its two matching angles are congruent, according to the AAA postulate of Euclidean geometry. The AAA postulate is derived from the observation that the total internal angle of a triangle is always equal to 180°.

While in case of ASA the angle - side and another angle of first triangle is equal to the corresponding angle - side - angle of other triangle.

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SSS, SAS, ASA, and AAS are four types of triangle congruence.

SSS (Side-Side-Side) is the congruence of three sides of a triangle. This means that all three sides of the triangle have the same length. To prove SSS congruence, you need to show that the corresponding sides of the two triangles have the same length. This can be done by calculating the length of each side and comparing them.

SAS (Side-Angle-Side) is the congruence of two sides and the included angle of a triangle. This means that the two sides of the triangles must have the same length, and the angles between those two sides must also be the same. To prove SAS congruence, you need to show that the corresponding sides of the two triangles have the same length, and that the angles between those two sides are also the same.

ASA (Angle-Side-Angle) is the congruence of two angles and the included side of a triangle. This means that the two angles of the triangles must have the same measure, and the side between those two angles must also be the same length. To prove ASA congruence, you need to show that the corresponding angles of the two triangles have the same measure and that the side between those two angles is also the same length.

AAS (Angle-Angle-Side) is the congruence of two angles and a non-included side of a triangle. This means that two angles of the triangles must have the same measure, and the side not included between those two angles must also be the same length. To prove AAS congruence, you need to show that the corresponding angles of the two triangles have the same measure, and that the side not included between those two angles is also the same length.

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The probability that both will be married before the age of 18 is 0.0036. The probability that both will be married by the age of 25 is 0.25. Finally, the probability that both will be married by the age of 30 is 0.5476.

According to the brief report by NCHS, approximately 6% of women in the United States married for the first time before their 18th birthday, and 50% of women married by their 25th birthday. 74% of women married by their 30th birthday.The probability of a family with two daughters marrying at different ages is asked in the question. The probability that both daughters will be married by the ages of 18, 25, and 30 will be determined

The question requires finding the probability that both daughters of a family will be married by the ages of 18, 25, and 30 respectively. Since each daughter's wedding is a separate event, the individual probability of a daughter marrying at a given age will be determined separately and then multiplied together to get the probability of both daughters being married at the given age. So, let's find the probabilities of each daughter marrying at a given age:

Probability of one daughter getting married by 18 years:

As per the brief report, 6% of women in the United States married before the age of 18.

Therefore, the probability of one daughter getting married before the age of 18 is 0.06

Probability of one daughter getting married by 25 years:

As per the brief report, 50% of women in the United States get married by the age of 25. Therefore, the probability of one daughter getting married by 25 years is 0.5.

Probability of one daughter getting married by 30 years:

As per the brief report, 74% of women in the United States get married by the age of 30. Therefore, the probability of one daughter getting married by 30 years is 0.74.

The probability of both daughters getting married at the same age is the product of each daughter's probability of getting married at that age.

The probability that both daughters will get married before the age of 18 is:

P(both daughters married at 18 years) = P(daughter1 married at 18) × P(daughter2 married at 18)= 0.06 × 0.06= 0.0036

The probability that both daughters will get married by the age of 25 is:

P(both daughters married at 25 years) = P(daughter1 married at 25) × P(daughter2 married at 25)= 0.5 × 0.5= 0.25

The probability that both daughters will get married by the age of 30 is:

P(both daughters married at 30 years) = P(daughter1 married at 30) × P(daughter2 married at 30)= 0.74 × 0.74= 0.5476

The probability that in a family with two daughters, both will be married before the age of 18 is 0.0036. The probability that both daughters will be married by the age of 25 is 0.25. Finally, the probability that both daughters will be married by the age of 30 is 0.5476.

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Answer:5/6

Step-by-step explanation:

simplify

Decimal point in product is the sum of the decimal points in the numbers which we are multiplying.

For ex :

2.6 × 6.7 = 17.42

1    +    1  =  2

For, 1.7 × 2.5  the sum of decimal in each number is 1 and 1 .

So, decimal in product is at 2 i.e 4.25 .

For, 3.62 × 1.7 the sum of decimal in each number is 2 and 1.

Decimal in product is at 2 + 1 = 3 i.e 6.154 .

Therefore, solution is 1.7 × 2.5 = 4.25 and 3.62 × 1.7 = 6.154 .

Hence, this is the required solution.

Answer:

The first one is ¨4¨. The second one is ¨6¨.

Step-by-step explanation:

i got it right on edg. when i guessed the first time

Answer:

x= 33

y= 106

Step-by-step explanation:

4x-58=74

+58 +58

4x=132

4x/4=132/4

x=33

If two parallel lines intersect another two parallel lines then all corresponding angles will be the same thus the value of y is 106° and x is 33°.

Two lines in the same plane that are equally spaced apart and never cross each other are said two lines in the same plane that are equally spaced apart and never cross each other to be parallel lines.

It is known that the If two parallel lines intersect another two parallel lines then all corresponding angles will be the same.

Therefore, 74 = 4x - 58

4x = 132

x = 33.

Since 74° and the adjacent angle of y° are made by two parallel lines on the same line thus both will also same.

The adjacent angle of y = 74°

Since,  adjacent angle + y = 180°

y = 180 - 74 = 106°.

Hence "If two parallel lines intersect another two parallel lines then all corresponding angles will be the same thus the value of y is 106° and x is 33°".

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The total number of integral solutions of x + y + z = 12, where −3 ≤ x ≤ 4, 2 ≤ y ≤ 11, and z ≥ 3 is; 59 integer solutions

We are given the condition that;

−3 ≤ x ≤ 4

Thus, we will use x values of -3, -2, -1, 0, 1, 2, 3, 4

When;

x = -3 and y = 2, in x + y + z = 12, solving for z gives z = 13

x = -3 and y = 3,  in x + y + z = 12, solving for z gives z = 12

x = -3 and y = 4,  in x + y + z = 12, solving for z gives z =11

x = -3 and y = 5,  in x + y + z = 12, solving for z gives z = 10

x = -3 and y = 6,  in x + y + z = 12, solving for z gives z = 9

x = -3 and y = 7,  in x + y + z = 12, solving for z gives z = 8

x = -3 and y = 8,  in x + y + z = 12, solving for z gives z = 7

x = -3 and y = 9,  in x + y + z = 12, solving for z gives z = 6

x = -3 and y = 10,  in x + y + z = 12, solving for z gives z = 5

x = -3 and y = 11,  in x + y + z = 12, solving for z gives z = 4

Thus, there are 10 solutions with x =-3

Repeating the above with x = -2, we will have 10 solutions

Similarly, with x = -1, we will have 9 more solutions

Similarly, with x = 0, we will have 8 more solutions.

Similarly, with x = 1, we will have 7 more solutions.

Similarly with x = 2, we will have 6 more solutions.

Similarly with x = 3, we will have 5 more solutions.

Similarly with x = 4, we will have 4 more solutions.

Thus,

Total number of solutions = 4 + 5 + 6 + 7 + 8 + 9 + 10 + 10

= 59 integer solutions

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The probability that a randomly chosen member of the society has a grade point average between 3 and 3.2 is 0.2 or 20%.

The probability distribution function (pdf), f(x), for the grade point averages of the gourmet society can be represented by a uniform distribution between 2.5 and 3.5. In a uniform distribution, the probability density is constant within the range and zero outside the range. The formula for the pdf is:

f(x) = 1 / (b - a)

where a is the lower bound (2.5 in this case) and b is the upper bound (3.5 in this case). Therefore, for this scenario:

f(x) = 1 / (3.5 - 2.5) = 1

To find the probability that a randomly chosen member of the society has a grade point average between 3 and 3.2, we need to calculate the area under the probability distribution curve within that range. Since the probability density is constant within the range, the probability is equal to the width of the range divided by the total width of the distribution.

The width of the range is 3.2 - 3 = 0.2, and the total width of the distribution is 3.5 - 2.5 = 1. Therefore, the probability is:

Probability = (width of range) / (total width)

= 0.2 / 1

= 0.2

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Using mathematical induction, we can prove that for all n ∈ N (natural numbers), the expression 7n - 5n is even.

To prove that 7n - 5n is even for all n ∈ N, we will use mathematical induction.

Base case:

First, we check if the statement holds for the smallest value of n. When n = 1, we have 7(1) - 5(1) = 7 - 5 = 2, which is indeed an even number.

Inductive step:

Assuming that the statement holds for some arbitrary value k (i.e., 7k - 5k is even), we need to prove that it also holds for k + 1. So, we assume 7k - 5k is even.

Now, we consider the expression for k + 1:

7(k + 1) - 5(k + 1) = 7k + 7 - 5k - 5 = (7k - 5k) + (7 - 5) = 2k + 2.

Since 7k - 5k is even (by the assumption) and 2 is even, the sum 2k + 2 is also even.

Therefore, by mathematical induction, we have shown that for all n ∈ N, the expression 7n - 5n is even.

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The area, in square inches, of the larger triangle is 12.

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The dashed blue curve represents the normal distribution with the greater standard deviation.

The z-score of a measure X of a normally distributed variable that has mean represented by \(\mu\) and standard deviation represented by \(\sigma\) is obtained by the equation presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

Considering the format of the normal curve, we have that a flatter curve, with lower peak, will have a higher standard deviation, hence the dashed blue curve represents the normal distribution with the greater standard deviation.

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The value of f(r(t)) is \(3t + 20t^2\), and the value of ds is 5√2 dt.

To calculate f(r(t)), we substitute the parameterization r(t) = (3t, 5t, 4t) into the function f(x, y, z) = x + yz:

\(f(r(t)) = x + yz \\= 3t + (5t)(4t) \\= 3t + 20t^2.\)

Therefore,\(f(r(t)) = 3t + 20t^2.\)

To calculate ds, we need to find the derivative of r(t) with respect to t:

r'(t) = (d/dt)(3t, 5t, 4t)

= (3, 5, 4).

Then, we find the magnitude of r'(t):

||r'(t)|| = √\((3^2 + 5^2 + 4^2)\)

= √(9 + 25 + 16)

= √50

= 5√2.

Finally, we multiply ||r'(t)|| by dt to obtain ds:

ds = ||r'(t)|| dt

= 5√2 dt.

Therefore, \(f(r(t)) = 3t + 20t^2\) and ds = 5√2 dt.

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Y (b).

The function is given as,

It is asked to determine the output corresponding to the following inputs,

Substitute 902 for 'x' to obtain the corresponding output as,

Thus, the first output will be 160.

Now, substitute 202 for 'x' to obtain the corresponding output,

Thus, the second output will be 20.

Kennedy made her initial error in Step 4 of the completion of the square process. In this step, she incorrectly computed 3 - 6 as 133 instead of the correct value of -3.

Completing the square is a method used to solve quadratic equations by manipulating the equation to form a perfect square trinomial. In Kennedy's case, she was attempting to solve the equation 63 + 3 = 0. However, her error in Step 4 caused the subsequent steps to be based on an incorrect value. As a result, the final answer she obtained was incorrect.

This mistake propagated throughout the subsequent steps, leading to an incorrect final answer. By miscalculating this term, Kennedy introduced an error that affected the outcome of the equation.

It is crucial to be meticulous and accurate when applying mathematical procedures such as completing the square. A small mistake in one step can lead to significant errors down the line. By double-checking calculations and carefully following the steps, Kennedy could identify and rectify her error, ultimately arriving at the correct solution.

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Zack is expected to be at (-12,-10.5) by finding the midpoint of line segment WT and reflecting T over it.

What is coordinate ?

A coordinate is a set of numerical values that are used to identify the position of a point in a specific space, such as a two-dimensional plane or a three-dimensional space. In two-dimensional space, coordinates are commonly represented by an ordered pair (x, y) or (x, y, z) in three-dimensional space.

The problem states that the balloon lands at point W(42,-15) and Tahir ends up at point T(-18,36). We know that Tahir and Zack are flying off in opposite directions from point W at equal distances. To find the point where Zack is expected to land, we can use the midpoint formula which states that the midpoint of a line segment is the average of the x-coordinates and the average of the y-coordinates.

We can find the midpoint of line segment WT by taking the average of the x-coordinates and y-coordinates:

x_midpoint = (x1 + x2) / 2 = (42 + -18) / 2 = 12

y_midpoint = (y1 + y2) / 2 = (-15 + 36) / 2 = 10.5

So the midpoint of line segment WT is (12,10.5). Since Zack is flying off in the opposite direction from Tahir at the same distance, we can expect Zack to end up at the point which is the reflection of point T over the midpoint of line segment WT.

This point would be (-12,-10.5)

Therefore , Zack is expected to be at (-12,-10.5) by finding the midpoint of line segment WT and reflecting T over it.

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Answer:

A) 51 \(m^2\)

Step-by-step explanation:

Answer:

x = 20

y = 7.2

Step-by-step explanation:

12/x = 9/15

9x = 180

x = 20

12/x= y/12

12/20 = y/12

144 = 20y

y = 7.2

y = 20

Answer: 10

Step-by-step explanation:

6-5 = 1

-2 x 1 = -2

-2 x -5 = 10