find the area of the trapezium

The width of the rectangle is 12 feet and the length is 30 feet.

The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape.

Given that, The perimeter of a rectangle is 84 feet. The ratio of the width to the length is 2:5.

Let the width be 2x and length be 5x,

Perimeter = 2(l+w)

2(2x+5x) = 84

2x+5x = 84/2

2x+5x = 42

7x = 42

x = 42/7

x = 6

Therefore, width = 6x2 = 12

Length = 5x6 = 30

Hence, The width of the rectangle is 12 feet and the length is 30 feet.

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The enclosure can be as large as 606 m2 in total.

Given that,

Let x be length of y be width of enclosure

fencing material cost $ 30 / m

Partition material cost $25/m

Total cost = (x+x+y+y)x 30+(y + y) x 25

c= 60(x+y) + 50y = 60 x + 110 y

4000 = 60 x + 110y

y = ( 400 - 6x / 11)

Now,Area of enclosure = x*y

A = x*(400 - 6x / 11)

A'(x)= 400-12x/11

for maximum area A'(x) = 0

400 - 12x/11 = 0,12x = 400,x = 100/3

A " ( x) = - 12/11 < 0  i.e., maximum

y = 400 - 6( 400/12 ) = 200/11 m

Maximum area = xy = 100/3 * 200/11 = 20000/33

                                                            =606.0606

A max = 606m²

Hence, the maximum area you can achieve for the enclosure is 606m²

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There is no vertex in the graph and the transformations from are

By definition, a graph that has a vertex would have an obvious maximum or minimum point on it

In this case, there is no point that can be regarded as the minimum or the maximum in this graph

This means that the graph has no maximum or minimum; in other words, there is no vertex

The parent function of the above graph is a cubic function

A cubic function passes through the origin

However in this graph, we can see that the graph is 4 units to the left of the origin and 2 units below the origin

This means that the transformation is (x - 4, y - 2)

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From the logistic population differential equation for approximate the growth of the world population , which is given here as [tex]P = L/1+ e^{-k(x-x_{0} )[/tex]

The general form of the logistic population equation is given as [tex]dP/dt = kP(1- P/L)[/tex]. While k is the relative growth rate, L is the carrying capacity.An ordinary differential equation with a logistic function as the solution is known as a logistic differential equation. Standard exponential functions do not account for the limitations that prevent infinite growth, but logistic functions correct this oversight. This is how bounded growth is represented by logistic functions. These contexts include machine learning, chess ratings, medical therapy (e.g., modelling tumour growth), economics, and even language adoption research.

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Answer:

Step-by-step explanation:

1. The vertex is where the parabola is changing from increasing to decreasing

2. From the picture, we can see that the vertex is at (1,2)

3. The formula for vertex form is f(x)=a(x-h)^2+k

4. Vertex is (1,2) or (h,k)

5. You can see that the parabola opens upside down like a "n" so it has been reflected in the x axis

6. So, your equaltion is f(x)=-(x-1)^2+2

7. In this cause you can see that a=-1, but if not given you would choose a random point on the parabola and plug it in :). Example:(0,1): 1 = a(0-1)^2+2

a=-1.

8. Your answer: f(x)=-(x-1)^2+2

The evaluation of the expression (2.4) · (1.3) gives 3.12

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

(2.4) · (1.3)

Express as products

This gives

(2.4) * (1.3)

Remove the brackets

So, we have the following representation

2.4 * 1.3

Evaluate the product

3.12

Hence, the solution is 3.12

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0.0147 is the standard deviation for the number of people .

How to interpret a standard deviation?

standard deviation = sqrt(p*(1-p)/n)

                                = sqrt(0.07 * 0.93/300)  

                               = 0.0147

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Given the slope of the line and the pair of points, the missing y - value can be found to be - 17

The slope formula is:

y = Slope(x) + y - intercept

Using the point (4, 8), the y - intercept can be found by the formula:
8 = 5/2 (4) + y - intercept

y - intercept = 8 - 10

y - intercept = -2

The missing y value is therefore:

y = Slope(x) + y - intercept

= -6 (5/2) - 2

= -15 - 2

= - 17

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The cost of 190 bon-bons is $154.8

According to the question ,

The shape of chocolate bon-bons is Sphere

Radius of sphere = 1.7cm

Density = 1.32g/cm³

[tex]Volume \ of\ sphere = \frac{4}{3}\pi r^{3}\\[/tex]

[tex]Volume of chocolate bon-bons = \frac{4}{3}\pi (1.7)^{3}[/tex]

[tex]= \frac{4}{3}\pi (4.913)\\= 20.5795cm^{3}[/tex]

Weight of bon-bons = volume × density

weight = 20.5795 × 1.32

= 27.1649g

Given , the cost of chocolate = $0.03

then cost of bon-bons = 0.03 × 27.1649

= $0.81494

We have to find cost of 190 bon-bons.

Cost of 190 bon-bons = 190 × 0.81494

= $ 154.8

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Answer:

64/125 > 150/512

Step-by-step explanation:

4/5 *4/5 *4/5 = 64/125 (also equals 0.512)

5/8 * 6/8 * 5/8 = 150/512 (also equals 0.293)

Therefore: 0.512 > 0.293

The 5th letter of the alphabet is E.

An alphabet is a standardized collection of basic written symbols or graphemes that represent the phonemes of different spoken languages.

The letter a begins the English alphabet and ends with the letter z. The alphabet is always written in the same order: a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-q-r-s-t-u-v-w-x-y-z. A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z. This is known as "alphabetical order."

The set of 26 symbols represents sounds used in speech and writing. Each character in a syllabary, for example, represents a syllable, whereas characters in logographic systems represent words, morphemes, or other semantic units. In this case, E is the 5th letter.

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I eat pizza or drink bottled water, for example, is a symbolic representation of the following statement.

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Answer:

146 degrees

Step-by-step explanation:

Sum of all triangle angles equal 180 degrees

We know 2

56 and 90 so we add them

90+56=146

Now we subtract to 180 to find the third angle of the triangle

180-146=34

To find x we gotta subtract 34 from 180 since it’s on a flat plane

180-34=146

angle x=146 degrees

hopes this helps please mark brainliest

The cost per dog treat is 0.55 dollars

How to determine this,

The cost of 8 dog treats is 4.40 dollars

And the number of 1 dog treat is x dollar

x dollar=4.40 dollars×1 dog treat/8 dog treats

x=0.55 dollar per one dog treat

To complete the table,

For 18 dog treats

when 1 dog treat is 0.55 dollar

18 dog treats is x dollar

x=18 dog treats×0.55 dollar/1 dog treat

x=9.9dollars

For 25 dog treats,

when 1 dog treat is 0.55 dollar

for 25 dog treats is x dollar

x=25 dog treats×0.55 dollar/1 dog treat

x=13.75 dollars

For 6.05 dollars,

when 1 dog treat is 0.55 dollar

x dog treat is 6.05 dollars

x=6.05 dollars×1 dog treat/0.55 dollar

x=11 dog treat

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Answer:

Step-by-step explanation: 0.55

Answer:

I think that the answer is going to be 34-21+6=19

Step-by-step explanation:

4a)

that means all 4 events happen in combination as one event.

so, we have to multiply the probabilities of all 4 events.

that means

0.63⁴ = 0.15752961... ≈ 0.16

so, there is a 16% chance that all 4 children get sick.

in other words, the probabilty for that is about 0.16.

b)

the probabilty of at least 1 kids getting sick is the opposite of the probability of no kids is getting sick.

the probability of getting sick is 0.63, so the probability of not getting sick is 1 - 0.63 = 0.37.

the probability of no kids getting sick is similar to a)

0.37⁴ = 0.01874161 ≈ 0.02

the probabilty of at least one kid getting sick is the opposite of that :

1 - 0.01874161... = 0.98125839 ≈ 0.98

5)

A u B is the sample space. so, any possible event is either part of A or B or both.

that means

P(A') = 0.35 = 1 - P(A)

P(A) = 1 - 0.35 = 0.65

P(A and B') = P(of every A that is not B) = 0.25.

because P(A) = 0.65

that means that

P(A and B) = P(every A that is also B) =

= 0.65 - 0.25 = 0.4

P(B) = P(A') + P(A and B) = 0.35 + 0.4 = 0.75

FYI

we could have gotten this directly from

P(A and B') = P(of every A that is not B = everything that is only A) = 0.25.

because

P(A and B')' = P(of everything that is not "only A" = everything that is B) = P(B) = 1 - 0.25 = 0.75

The probability that the squad will have exactly three women members is 0.389

Total number of people in CU Boulder triathlon = 21

Number of Men = 9

Number of Women = 12

We are told that a 5-member squad is selected and now we want to find the probability that the squad will have exactly 3 women members.

Thus;

P(exactly 3 womens) = (12C3 * 9C2)/(21C5)

P(exactly 3 womens) =7920/1716

P(exactly 3 womens) = 0.389

Hence, the probability that the squad will have exactly three women members is 0.389

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The value of the shorter base which is x is 8 feet.

A trapezium is a quadrilateral with exactly one pair of opposite sides parallel to each other. The trapezium is a two-dimensional shape that appears as a table when drawn on a sheet of paper.

It has four sides and four vertices.

The trapezium is made of a rectangle and triangles.

Area of a trapezium = 1/2 (a + b ) h

where a = small base, b = big base and h = height.

from the above, b = 24 feet, h = 6 feet, a = x and area = 96 square feet

substituting the above into the equation

1/2 ( 24 + x) x 6 = 96

6(24 + x) = 96 x 2

6(24 + x ) = 192

multiplying the terms by 6

144 + 6x = 192

6x = 192 - 144

6x = 48

x = 48/6

x = 8 feet

In conclusion, the value of x is 8 feet

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The graph of the linear inequality 4x + 0.5y ≤ 40 is given by the image at the end of the answer.

The first step in graphing the linear inequality is identifying the domain of the situation.

Only numbers in the first quadrant are plotted, hence the first two constrains for the domain are given as follows:

The inequality is a linear inequality, hence the next step is identify the intercepts and then trace a line connecting them.

The x-intercept is the value of when y = 0, hence:

4x = 40

x = 40/4

x = 10.

Hence it is represented by point (10,0).

The y-intercept is the value of y when x = 0, hence:

0.5y = 40

2 x 0.5y = 2 x 40

y = 80.

Hence it is represented by point (0,80).

The values less than the inequality are plotted, hence the graph is composed by the points on the first quadrant and below the line 4x + 0.5y = 40, as shown by the image at the end of the answer.

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Ramundo will get a better deal at Roller worlds.

This is a question of percentages.

Given that:-

Regular price of rollerblades at roller world = $ 94

Discount at rollerworld = 15 %

Price of rollerblades at Outdoor adventures = $ 81.50

Sales tax = 6 %

Price of rollerblades at roller world after discount = 94 - (15/100)*94 = 94 - 14.1 = $79.9

Price of rollerblades at roller world after sales tax = 79.9 + (6/100)*79.9 = 79.9 + 4.794 = $ 84.694

Price of rollerblades at outdoor adventures = $81.50

Price of rollerblades at roller world after sales tax = 81.50 + (6/100)*81.50 = 81.50 + 4.89 = $ 87.39

As,

$ 84.694 <  $ 87.39

Ramundo will get a better deal at Roller worlds.

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The answer to the given quadratic equation is y =  ( x + 4 )²

A(x + m)2 + n is the formula for completing the square, where m is any real number and n is a constant factor.

The following straightforward formula can be used to finish the square instead of the intricate step-by-step procedure. Find the following in order to complete the square in the phrase ax2 + bx + c:

N = c - (b2/4a) and m = b/2a

Enter these numbers where they belong: ax2 + bx + c = a(x + m)2 + n. These equations are geometrically derived.

Given : A quadratic equation y = 7x² + 56x + 117

this can also written as y = x² + 8 x + 17

y = x² + 4² - 4² + 17

y =  ( x + 4 )²

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The probability that fewer than 60 adults will work from home will be 2%.    

we have to use the Normal probability distribution to find the probability

In a normal distribution with mean μ, SD σ, z-score Z of a measure X  is given by

Z = (X-μ)/ σ

here,

15% adults work from home , So  p= 0.15

                                                       n = 500

∴  μ = np = 500(0.15) = 75

σ  = [tex]\sqrt{np(1-p)}[/tex]

σ = 7.98

Now we have  selected adults(60) less than n (500)

So using the continuity correction , the probability is P(X< 60 - 0.5)

                                                                            = P( X< 59.5)

which is the p-value of Z when X = 59.5

∴ Z = (X-μ)/ σ

Z  =  (59.5 - 75)/7.98

Z =   - 1.98

so the p-value is 0.02

0.02 = 2% probability that fewer than 60 adults will work from home.

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Answer: The answer is Fact Family

Step-by-step explanation:

The graph g(x) is graph of f(x) translated down 10 units.

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

In a line graph, the information or data is plotted as a series of markers, or dots, and is then connected to one another by a straight line.

Usually, data that changes over time is represented by a line graph.

Given:

f(x) = x, when g(x) = f(x) - 10

As, from the graph we can see that both function f(x) and g(x) shows a parallel relation.

Also, the function f(x) is subtracted from 10 then the function is translated down by 10 units.

Hence, g(x) is graph of f(x) translated down 10 units.

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Answer:

A. -9, -6, 8, 13

B. -4/5, -1/2, -.2, .25

C. -8/3, -2 1/2, 9/2, 4.75

D. -8, -3, -1, 4

E. -1/2, -1/4, .5, 3/4

F. -3/2, -5/4, -4/5, 1.5

Step-by-step explanation:

The easiest thing to do is to put them all in the same format. Fractions are just division problems, so just divide. 4/5 is 4 divided by 5, which is .8.

Remember, the farther a negative number is from 0 on the number line, the smaller it is. So, -8 is smaller than -5. -5 is smaller than -2, etc.

The probability that the average completion time for a sample of 28 students will be more than 24 minutes is 0.46

The mean of freshman mason basic completion time  is 24.6 minutes

The standard deviation is 5.8 minutes

The probability of completion for a sample of 28 students will be more than 24 minutes and can be found using the normal distribution,

                      P(x > 24)

We need to find the standard form of this random sample using the formula,

              Z = X - μ / σ

where Z is the standard form

           X is the random sample

          μ is the mean

          σ is the standard deviation

Let us substitute the known values in the above equation, we get

                  Z = 24 - 24.6/5.8

                     = -0.6 / 5.8

                     = -0.103

So the standard form is

         P(x > 24) = P(z > -0.103)

By using the z-table, we could find the value of z,

        P(z > -0.103) = 0.46

Therefore, the probability is 0.46

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The probability that a computer will not crash in a period of 4 months is 0.632.There is a 75% chance that the computer will not crash in a period of 4 months.

To solve this problem stepwise, first calculate the probability that the computer will crash in a given month. This can be done by using the Poisson distribution. The probability that the computer will crash in a given month is 0.0333.

Next, calculate the probability that the computer will not crash in a given month. This is simply 1 - 0.0333, or 0.9667.

Now, to calculate the probability that the computer will not crash in a period of 4 months, simply take the probability of not crashing in a given month and raise it to the 4th power. This gives us a probability of 0.632.

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Answer: The answer would be 4 biking outfits o=4

Step-by-step explanation:

First add all the money he spent excluding the outfits. The answer would be 315.72. Then subtract 600 and 315.72 = 284.28. Last multiply 71.07 by 4 which gets you 284.28. The EXACT amount he has left. Answer is he can be 4 new biking outfits within his budget. Hope I could help!

Answer:

negative, as the points are slowly making their way "down" the graph :)