PLEASE HELP ME ASAP!!!!!!!!!

The relationship between the height of the pole and the shadow cast by the pole is a proportional relationship, from which the height of the pole can be calculated

The height of the pole is 11.\(\overline 6\) feet

A proportional relationship is one in which the ratio between the elements of an ordered pair is a constant.

The example values for the lengths of the shadows and Sam's height are as follows;

Let the length of the shadow cast by the pole = 3.5 feet

Let the shadow cast by Sam = 1.5 feet

Let Sam's height = 5 feet

Sam's height and the height of the pole and their shadows have proportional relationship.

The constant of proportionality is therefore;

\(K = \dfrac{1.5}{5} =\dfrac{3.5 }{Height \, of \, the \, pole}\)

Therefore;

Height of the pole = 5 × 3.5 ÷ 1.5 = 11.\(\overline 6\)

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The probability that the obstetrician has delivered no child with polydactyly is 0.8187.

To find the probability that the obstetrician has delivered no child with polydactyly, we can use the formula:

P(no polydactyly) = \((1 - P(polydactyly))^{number of births}\)

First, we need to find the probability of a child having polydactyly. This is given as 1 in every 500, which can be expressed as a decimal: 1/500 = 0.002.

Next, we find the probability of a child not having polydactyly: 1 - 0.002 = 0.998.

Now, we can find the probability of the obstetrician delivering no child with polydactyly in 100 unrelated and independent births by raising the probability of no polydactyly to the power of the number of births (100):

P(no polydactyly in 100 births) = (0.998)¹⁰⁰ ≈ 0.8187

So, the probability that the obstetrician has delivered no child with polydactyly is approximately 0.8187.

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Answer:

Step-by-step explanation:

The expressions that are equivalent when m = 1 and m = 4 is;

Option B: 3m + 4 and m + 4 + 2m

We are given m = 1 and m =4;

A) 5m - 3 and 2m + 5 + m

B) 3m + 4 and m + 4 + 2m

C) 2m + 7 and 3m - 3 + m

D) 5m + 3 and 4m + 2 + 2m

For option B; 3m + 4 and m + 4 + 2m

Let's put m = 1

3(1) + 4 = 7

Also, 1 + 4 + 2(1) = 7

Similarly, let us put 4 for m to get;

3(4) + 4 = 16

Also, 4 + 4 + 2(4) = 16

In both cases, the expressions are equivalent and as such option B is the right one.

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The width of the box is 4 inches wide

From the question, we have the following parameters that can be used in our computation:

Area = 20 square inches

Height = 5 inches

The width of the box can be calculated using the following equation

Width = Area/Height

substitute the known values in the above equation, so, we have the following representation

Width = 20/5

Evaluate the quotient

Width = 4

Hence, the width is 4 inches

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Complete question

The side of a box has an area of 20 square inches and a height of 5 inches. How many inches is the width of the box?

Check the picture below.

Answer: B.146 feet

Step-by-step explanation:

The sum of 4 Σ(5k - 4) = k=1 would be equal to 10n² - 14n.

The given expression is `4 Σ(5k - 4) = k=1`.

We need to find the sum of this expression.

Step 1:

The given expression is 4 Σ(5k - 4) = k=1. Using the distributive property, we can expand it to 4 Σ(5k) - 4 Σ(4).

Step 2:

Now, we need to evaluate each part of the expression separately. Using the formula for the sum of the first n positive integers, we can find the value of

Σ(5k) and Σ(4).Σ(5k) = 5Σ(k) = 5(1 + 2 + 3 + ... + n) = 5n(n + 1)/2Σ(4) = 4Σ(1) = 4(1 + 1 + 1 + ... + 1) = 4n

Therefore, the given expression can be written as 4(5n(n + 1)/2 - 4n).

Step 3:

Simplifying this expression, we get: 4(5n(n + 1)/2 - 4n) = 10n² + 2n - 16n = 10n² - 14n.

Step 4:

Therefore, the sum of 4 Σ(5k - 4) = k=1 is equal to 10n² - 14n.

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The value of the sample variance and the sample standard deviation for the given data is equal to 47.4 and 6.9 respectively.

Data values are,

23, 12, 5, 9,8

Number of observations 'n' = 5

Mean = ( sum of all the observations ) / ( number of observations)

         = (23 + 12 + 5 + 9 + 8) / 5

         = 57 /5

         = 11.4

Deviations of each data point from the mean,

(23 - 11.4) = 11.6

(12 - 11.4) = 0.6

(5 - 11.4) = -6.4

(9 - 11.4) = -2.4

(8 - 11.4) = -3.4

Square each deviation is equal to,

11.6² = 134.56

0.6² = 0.36

(-6.4)² = 40.96

(-2.4)² = 5.76

(-3.4)² = 11.56

Sample Variance = ( Sum of squared deviation )/ ( n - 1)

⇒Sample Variance = (134.56 + 0.36 + 40.96 + 5.76 + 11.56) / (5-1)

⇒Sample Variance = 47.35

⇒Sample Variance = 47.4(rounded to one decimal place)

Now,

Standard deviation = √variance

Substitute the value we get,

⇒ Standard Deviation = √(47.35)

⇒ Standard Deviation = 6.9 (rounded to one decimal place)

Therefore, the sample variance is 47.4 and the sample standard deviation is 6.9.

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The above question is incomplete, the complete question is:

Calculate the sample variance and the sample standard deviation for the given data. Provide your sample standard deviation answer precise to one decimal place.

23, 12, 5, 9,8

Answer:

She take 20 cookies to her students.

Step-by-step explanation:

Because 120÷6 is 20

and 20×6 is 120

Answer:

20

Step-by-step explanation:

She baked 120 cookies.

To solve this, use the equation: 120/1/6

In this equation, the 1 is useless. The real equation is 120/6 or 120 divided by 6.

12/6=2

After evaluating 12 divided by 6, add a zero to the end of the answer since you're trying to find 120 divided by 6.

The answer should be 20

Answer:

To determine the speed, we can use the formula:

speed = distance / time

where distance is measured in feet and time is measured in minutes.

In this case, the distance is 264 feet and the time is 3 minutes. Plugging these values into the formula, we get:

speed = 264 feet / 3 minutes

simplifying, we get:

speed = 88 feet/minute

Therefore, the equipment is traveling at a speed of 88 feet per minute.

The lower bound of the 95% confidence interval is given as follows:

7.981 mm.

The level of confidence of the statement is of 95%.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 100 - 1 = 99 df, is t = 1.9842.

The parameters for this problem are given as follows:

\(\overline{x} = 8.1, s = 0.6, n = 100\)

Hence the lower bound of the interval is given as follows:

8.1 - 1.9842 x 0.6/10 = 7.981 mm.

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The graph showing the plotted points are attached accordingly.

In discrete mathematics, and more   particularly in graph theory, a graph is a structure consisting of a set of objects, some of which are "related" in some way.

The items  correspond to mathematical  abstractions known as vertices, and each pair of connected vertices  is known as an edge  

To plot and label the lines y = 1,   y = - 3, x = 2, and x = -4, we can create a simple coordinate system and mark the corresponding points.

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Answer:

First question :

a = 2

Second question :

a = 5

b = \(\frac{-a+5}{0}\)

Anaiah currently spending  $150 on these goods

*He is not spending his entire income  

*His marginal utility per dollar spent is not the same for both goods

What is unit rate?

A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

consumption of eggplant

= 20 price of eggplant

= 3

consumption of kiwi is

= 30 price of eggplant

= 3

Formula:

Spending

= price of eggplant*consumption of eggplant + price of kiwi*consumption of kiwi

= 3*20+3*30

= 150

Utility per one dollar spent on the 20th eggplant

=  160

Marginal utility per dollar spent on the 30th kiwi

= 190 utils.

Note that y 160<190

Currently spending= 150

& budget = 180

150<180

According theory of choice consumer need the maximize the utility so answer is

Answer -:

*He is not spending his entire income

*His marginal utility per dollar spent is not the same for both goods

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Answer:

C) 36 ft squared

Step-by-step explanation:

The area of a kite can be found using the following formula:

\(\boxed{\mathrm{Area = \frac{1}{2} \times d_1 \times d_2}}\),

where \(\mathrm{d_1}\) and \(\mathrm{d_2}\) are lengths of the of the diagonals of the kite.

In this question, the lengths of the diagonals are:

• \(\mathrm{d_1}\) = 6 ft + 12 ft = 18 ft

• \(\mathrm{d_2}\) = 2 ft + 2 ft = 4ft

Substituting these values into the formula:

\(\mathrm{Area = \frac{1}{2} \times 18 \space\ ft \times 4 \space\ ft }\)

         \(\mathrm{= \bf 36 \space\ ft^2}\)

The value of a/b is  \(\sqrt{6}\) / 2

The area of mathematics known as mensuration is concerned with measuring geometric shapes and their various characteristics, such as length, volume, shape, surface area, lateral surface area, etc. In fundamental mathematics, learn about mensuration.

Measurement of agricultural fields, floor areas required for purchase/selling transactions. Measurement of volumes required for packaging milk, liquids, solid edible food items. Measurements of surface areas required for estimation of painting houses, buildings, etc.

According to the question:-

Side of an equilateral triangle equals a/3.

Therefore, the equilateral triangle's area is equal to (1/2)(a/3)2 sqrt (3) / 2 = a2 [sqrt (3)/ 36].

Hexagonal side equals b / 6.

The area is thus 6 (1/2) (b/6)^2 sqrt (3) / 2 

= b^2 [ 3 sqrt (3) / 72] = b^2 [sqrt (3) / 24]

So

sqrt (3) / 36 a2 = sqrt (3) / 24 b2

So

A2 / B2 = [Sqrt(3)/24] / [Sqrt(3)/36]

a^2 / b^2 = [ 36 / 24 ]

a^2/ b^2 = 3/2

A/ B = Sqrt(3) / Sqrt(2)

=Sqrt(6) / 2

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Answer: length = 116, width = 60. Or 116x60 yards

Step-by-step explanation:

The length of the field is 4 yards less than double the width. First, let's put this in mathematical terms.

Suppose L = length and W = width, we know that "The length of the field is 4 yards less than double the width". This can be expressed as L = 2W-4.

Now we know perimeter is length + length + width + width. In terms of L and W, this would be 2L + 2W. We can simplify this to 2(L+W).

Since we know L = 2W-4, we can plug it into the equation of 2(L+W) to get 2(2w-4+w) = 352.

We can then use some basic algebra to solve.

2(3w-4) = 352

3w-4 = 176

3w = 180, w = 60.

Now since L = 2W-4, we know that L = 60 x 2 - 4 = 116.

We can check our work by adding 116 + 116 + 60 + 60 to see if it equals 352. It does.

So length = 116, width = 60

Answer:

Jane has a constant rate of pay because her earnings go up by 12 every unit of time.

13 is the inequality so that it represents the whole-number values.

What is Triangle Inequality Theorem?

Triangle inequality, in Euclidean figure, theorem that the sum of any two sides of a triangle is lesser than or equal to the third side; in symbols, a b ≥ c. In substance, the theorem states that the shortest distance between two points is a straight line.

the Triangle Inequality Theorem, which states that

the sum of the lengths of two sides of a triangle must always be greater than the length of the third side

      a = c + b

         = 7 + 6

         = 13

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The transformation T: R^3 → R^2 defined by T(x1, x2, x3) = (|x1|, 0) is not linear transformation as it violates the additivity and homogeneity properties of linearity.

To show that the transformation T: R^3 → R^2 defined by T(x1, x2, x3) = (|x1|, 0) is not linear, we need to demonstrate that it violates at least one of the two properties of linearity, namely, additivity and homogeneity.

Additivity: T(u + v) = T(u) + T(v) for all vectors u and v in R^3.

Let u = (1, 2, 3) and v = (4, 5, 6) be two vectors in R^3. Then,

T(u) = T(1, 2, 3) = (|1|, 0) = (1, 0)

T(v) = T(4, 5, 6) = (|4|, 0) = (4, 0)

T(u + v) = T(1+4, 2+5, 3+6) = T(5, 7, 9) = (|5|, 0) = (5, 0)

However,

T(u) + T(v) = (1, 0) + (4, 0) = (5, 0)

Since T(u + v) ≠ T(u) + T(v), the transformation T is not additive and hence not linear transformation.

Homogeneity: T(cu) = cT(u) for all vectors u in R^3 and all scalars c.

Let u = (1, 2, 3) be a vector in R^3, and let c = 2 be a scalar. Then,

T(u) = T(1, 2, 3) = (|1|, 0) = (1, 0)

T(cu) = T(2, 4, 6) = (|2|, 0) = (2, 0)

However,

cT(u) = 2(1, 0) = (2, 0)

Since T(cu) ≠ cT(u), the transformation T is not homogeneous and hence not linear.

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IT IS REQUIRED OF YOU TO SOLVE FOR X

\(x - 3x = 17 + 3 \\ - 2x = 20 \\ \frac{ - 2x}{ - 2} = \frac{20}{ - 2} \\ x = - 10\)

Answer:

x = -10

Step-by-step explanation:

x-3 = 3x + 17

-2x -3 = 17

-2x = 20

x = -10

Check:

Does x-3 = 3x + 17 when x = -10?

x-3 = -13

3x+17 = -30+17 = -13  YES

The formula to determine the number of shaded blocks in the nth figure is: n^2 + (n-1)^2

To determine the number of shaded blocks in the nth figure, we need to identify the pattern of how the shading changes from one figure to the next.

In this case, we can observe that the nth figure has n rows and n columns of squares, and the shading occurs in a diagonal pattern from the top left to the bottom right corner of the figure.

To count the number of shaded squares, we can use the formula for the sum of the squares of the first n natural numbers, which is n(n+1)(2n+1)/6. However, this formula counts all the squares in the nth figure, including the unshaded ones.

Since only half of the squares are shaded in the diagonal pattern, we need to divide the result by 2 to get the number of shaded squares.

Therefore, the formula for the number of shaded blocks in the nth figure is n^2 + (n-1)^2, which simplifies to 2n^2 - 2n + 1. This formula works for any value of n and can be used to quickly determine the number of shaded blocks without having to count them manually.

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IfIf the amount of sugar you need depends on the amount of lemonade mix you use. Yes, the amount of sugar you need proportional to the amount of lemonade mix you use.

To determine if the amount of sugar is proportional to the amount of lemonade mix, we need to compare the ratios of sugar to lemonade mix for each combination:

   When 1 packet of lemonade mix is used, the amount of sugar needed is 1/3 cup.

   When 3 packets of lemonade mix are used, the amount of sugar needed is 1 cup.

   When 9 packets of lemonade mix are used, the amount of sugar needed is 3 cups.

Now we can compare the ratios of sugar to lemonade mix for each combination:

   When 1 packet of lemonade mix is used, the ratio of sugar to lemonade mix is 1/3.

   When 3 packets of lemonade mix are used, the ratio of sugar to lemonade mix is 1/3.

   When 9 packets of lemonade mix are used, the ratio of sugar to lemonade mix is 1/3.

Since the ratios are all the same, we can conclude that the amount of sugar needed is proportional to the amount of lemonade mix used.

Therefore, the answer is A) Yes.

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Answer:

New point (x+6, y-4)

Step-by-step explanation:

Given:

Points = (x , y)

Mapping

6 units to the right

4 units down

Find:

New point

Computation:

On line X, numbers are add on move right side

So,

x+6

On line Y, numbers are subtract on move down

So,

y-4

New point (x+6, y-4)

Answer:

1/18

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

The ratio of nuts to fruits is 5 : 1 and for every 5 cups of nuts, there is 1 cup of dried fruit cup.

Given is that a granola recipe calls for 3 cups of oats, 1 cup of almonds. 1 cup of pecans, and 1 cup of dried fruit

The ratio of nuts to fruits is -

r = (3 oat cups + 1 almond cup + 1 pecan cup)/(1 dried fruit cup)

r = 5/1

5 : 1

For every 5 cups of nuts, there is 1 cup of dried fruit cup.

Therefore, the ratio of nuts to fruits is 5 : 1 and for every 5 cups of nuts, there is 1 cup of dried fruit cup.

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Answer:

I think it is C

Step-by-step explanation:

Answer:

The minimum unit cost is $12,197.

Explanation:

The cost function is given below:

To find the minimum unit cost, first, find the derivative of C(x).

Next, set the derivative equal to 0 and solve for x.

Finally, substitute x=260 into C(x) to find the minimum cost.

The minimum unit cost is $12,197.

The height of the cylinder can be described in terms of inches by using the formula for the lateral area of a cylinder and solving for the height. Given a lateral area of 3,620 square inches and a radius of 9 inches, the height of the cylinder is approximately 16 inches.

To find the height of the cylinder, we use the formula for the lateral area of a cylinder, which is A = 2πrh, where A represents the lateral area, π is a mathematical constant (approximately 3.14159), r is the radius of the cylinder's base, and h is the height of the cylinder.
In this case, we are given that the lateral area is 3,620 square inches and the radius is 9 inches. Substituting these values into the formula, we have:
3,620 = 2π(9)h
To solve for h, we isolate it on one side of the equation. Dividing both sides of the equation by 2π(9), we get:
h = 3,620 / (2π(9))
Simplifying the expression, we calculate:
h ≈ 3,620 / (2 * 3.14159 * 9)
h ≈ 16.0525
Therefore, the height of the cylinder, in terms of inches, is approximately 16 inches.

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Answer: The answer will be 3 if not I'm wrong sorry.

Step-by-step explanation: