Find the area of the shaded triangle, if the side of each square is 1 unit long.

Answer:

Aquarium dimensions:

x = 3,106 m

h = 6,22 m

C(min) = 1277,62 $

Step-by-step explanation: (INCOMPLETE QUESTION)

We have to assume:

The shape of the aquarium  (square base)

Let´s call "x" the side of the base, then h ( the heigh)

V(a) = x²*h          h = V(a)/x²      

Cost of Aquarium   C(a) = cost of the base (in stones) + 4* cost of one side (in glass)

C(a) = Area of the base *120 + 4*Area of one side*30

Area of the base is x²

Area of one side  is   x*h   or  x*V(a)/x²  

Area of one side is V(a)/x

C(x) = 120*x² + 4*30*60/x

C(x) = 120*x² +  7200/x

Taking derivatives on both sides of the equation we get

C´(x) = 2*120*x  - 7200/x²

C´(x) = 0 means    240 *x  - 7200/x² = 0

240*x³ - 7200 = 0

x³ = 7200/240

x = 3,106 m   and  h = 60 /x²     h =   6,22 m

and C (min) = 120*(3,106)³ - 7200 / 3,106

C(min) =  3595,72 - 2318,1

C(min) = 1277,62

Answer:

Step-by-step explanation:

cool

*see the attachment below for the missing figure

Answer:

[tex] sin B = \frac{24}{25} [/tex]

Step-by-step explanation:

Given a right angled triangle, ∆ABC

AB = 25

BC = 7

AC = 24

<ACB = 90°

Required:

Value of Sin B

Solution:

Using trigonometric ratio formula,

[tex] sin B = \frac{opposite}{hypotenuse} [/tex]

Opposite = AC = 24 (the side opposite to <B)

Hypotenuse = AB = 25 (the longest side facing the right angle)

[tex] sin B = \frac{24}{25} [/tex]

Answer:

[tex]B(a)=\frac{a}{5} -7[/tex]

Step-by-step explanation:

The input it taken as the unknown base value, while the output here is the area of the trapezoid. b is therefore the base value, and A( b ) is the area of the trapezoid. Let's formulate the equation for the area of the trapezoid, and isolate the area of the trapezoid. To find the inverse of this function, switch y ( this is A( b ) ) and b, solving for y once more, y ➡ y ⁻ ¹.

y = height [tex]*[/tex] ( ( unknown base value ( b ) + 7 ) / 2 ),

y = 10 [tex]*[/tex] ( ( b + 7 ) / 2 )

Now switch the positions of y and b -

b = 10 [tex]*[/tex] ( ( y + 7 ) / 2 ) or [tex]b=\frac{\left(y+7\right)\cdot \:10}{2}[/tex] - now that we are going to take the inverse ( y ⁻ ¹ ) or B( a ), b will now be changed to a,

[tex]y+7=\frac{a}{5}[/tex],

[tex]y^{-1}=\frac{a}{5}-7 = B(a)[/tex]

Therefore the equation that represents the inverse function will be the following : B(a) = a / 5 - 7

Answer:

13=x

Step-by-step explanation:

Since BE is a bisector

ABE = EBC

2x+20 = 4x-6

Subtract 2x from each side

2x+20-2x =4x-6-2x

20 = 2x-6

Add 6 from each side

20+6 = 2x-6+6

26 = 2x

Divide each side by 2

26/2 = 2x/2

13=x

Answer:

x = 13

Step-by-step explanation:

The angle bisector theorem means that m<ABE = m<EBC. Now that we know they are equal, we can set the equations to each other and solve for x.

2x + 20 = 4x - 6

26 = 2x

13 = x

So the value of x is 13.

Cheers.

Answer:

D.

m = 2 = figures/month

b = 20 = # of action figures

Answer and Step-by-step explanation:

1. Data provided

[tex]\frac{d^2y}{dx^2} + 4y = x - x^2 + 20\\\\ \frac{d^2y}{dx^2} + 4y = - x^2 + x + 20[/tex]

Now as a non homogeneous part which is

[tex]- x^2 + x + 20[/tex] let us assume the computation is

[tex]y_p(x) = Ax^2 + Bx + C[/tex]

2. Data provided

[tex]\frac{ d^2y}{dx^2} + \frac{6dy}{dx} + 8y = e^{2x}[/tex]

As a non homogeneous part is [tex]e^2x[/tex] , let us assume the computation is

[tex]y_p(x) = Ae^{2x}[/tex]

3. Data provided

[tex]y'' + 4y' + 20y = -3sin2x[/tex]

As a non homogeneous part −3sin(2x), let us assume the computation is

[tex]y_p(x) = Acos(2x) + Bsin(2x)[/tex]

4. Data provided

[tex]y'' - 2y' - 15y = 3xcos(2x)[/tex]

As a non homogeneous part  3xcos(2x), let us assume the computation is

[tex]y_p(x) = (Ax+B)cos2x+(Cx+D)sin2x[/tex]

Answer:

1.union = {20 21 22 23 25 27 29}

2. intersection = {5 14 22}

3.1/3

Step-by-step explanation:

1. union U of sets a nd b ={20 21 22 23 25 27 29}

2. intersection n of sets a nd b = {5 14 22}

3. probability = one item / total

= 1/3

1.

A. {22, 25, 27, 29}

B. {20, 21, 22, 23}

Answer: A∪B = {22, 25, 27, 29, 20, 21, 23}

2.

A. {1, 5, 10, 14, 22}

B. {5, 14, 20, 22, 27}

Answer: A∩B = {5, 14, 22}

3.

A. {1, 5, 10, 14, 22}

B. {5, 14, 20, 22, 27}

Answer: The three items that are intersecting each have a 1/3 chance of being chosen.

C. y= -28/x

y=k/x

cross multiply

k= y×x

k = -2×14

k = -28

y = -28/x [ equation connecting x and y]

The equation that connects x and y si y = –28∕x.

The correct option is (C)

The constant of proportionality is the ratio of two proportional values at a constant value. Two variable values have a proportional relationship when either their ratio or their product gives a constant. The proportionality constant's value is determined by the proportion between the two specified quantities.

For example,  The number of apples in a crop, for example, is proportional to the number of trees in the orchard, the ratio of proportionality being the average number of apples per tree.

We have given that

y ∝ 1∕x

To remove proportional sign we use proportionality constant

y=k/x

Now, cross multiply

k= y×x

k = -2×14

k = -28

y = -28/x

Hence, the equation is y = -28/x .

Learn more about proportionality here:

https://brainly.com/question/8598338

#SPJ2

Answer: V = 193.25π

Step-by-step explanation: The method to calculate volume of a solid of revolution is given by an integral of the form:

V =  [tex]\pi\int\limits^a_b {[f(x)]^{2}} \, dx[/tex]

f(x) is the area is the function that rotated forms the solid.

For f(x)=y= [tex]\frac{5}{36}-x^{2}[/tex] and solid delimited by x = 2 and x = 4:

V = [tex]\pi\int\limits^4_2 {(\frac{5}{36}-x^{2} )^{2}} \, dx[/tex]

V = [tex]\pi\int\limits^4_2 {(\frac{25}{1296}-\frac{10x^{2}}{36}+x^{4}) } \, dx[/tex]

V = [tex]\pi(\frac{25.4}{1296}-\frac{10.4^{3}}{108}+\frac{4^{5}}{5}-\frac{25.2}{1296}+\frac{10.2^{3}}{108}-\frac{2^{5}}{5} )[/tex]

V = [tex]\pi(\frac{50}{1296}-\frac{560}{1296}+\frac{992}{1296} )[/tex]

V = 193.25π

The volume of a solid formed by y = [tex]\frac{5}{36} - x^{2}[/tex] and delimited by x = 2 and x = 4

is 193.25π cubic units.

━━━━━━━☆☆━━━━━━━

▹ Answer

19%

▹ Step-by-Step Explanation

0.19 → hundreth's place.

19/100 (since the denominator is 100, that represents 100% while 19 represents 19%)

Final Answer - 19%

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

This represent 19% of his salary.

Given, Joe's salary goes for tax is 0.19.

We have to represent the value in percent.

Here 0.19 can be written in fraction form as,

[tex]\dfrac{19}{100}[/tex]

It means 19 part from 100 part goes for taxes, means 19% of the Joe's salary goes for taxes.

Hence this represent 19% of his salary.

For more details follow the link:

https://brainly.com/question/8011401

Answer:

Step-by-step explanation:

To find the length of BC we use tan

tan ∅ = opposite / adjacent

From the question

AC is the opposite

BC is the adjacent

So we have

tan 61 = AC / BC

tan 61 = 47/BC

BC = 47/tan 61

Hope this helps you

Answer:

18

Step-by-step explanation:

23^0 - 15^1 + 18^0 + (43 - 12) =

= 1 - 15 + 1 + 31

= -14 + 1 + 31

= -13 + 31

= 18

The area of the rectangle is [tex]25q^2-9[/tex].

The area of the rectangle is the product of length and width.

The length of the sides of the square is 5q.

3 is added and 3 is subtracted to the length and the width of the square so, the dimensions of the new quadrilateral is (5q+3) and (5q-3).

So, the area of the rectangle is-

[tex]A=(5q+3)\times (5q-3)\\=25q^2-9[/tex]

Thus, the area of the rectangle is [tex]25q^2-9[/tex].

Learn more about the area of the rectangle here- https://brainly.com/question/20693059

#SPJ2

Answer:25q^2-9

Step-by-step explanation:

your welcomeeeeeeee

Answer:

The percent of households with rates from $100 to $115. is      [tex]P(100 < x < 115) =[/tex]94.1%

Step-by-step explanation:

From  the question we are told that  

   The  mean rate is [tex]\mu =[/tex]$ 106.50  per month

    The standard deviation is  [tex]\sigma =[/tex]$3.85

Let the lower rate be  [tex]a =[/tex]$100

Let the higher rate  be  [tex]b =[/tex]$ 115

Assumed from the question  that the data set is normally

The  estimate of the percent of households with rates from $100 to $115. is mathematically represented as

         [tex]P(a < x < b) = P[ \frac{a -\mu}{\sigma } } < \frac{x- \mu}{\sigma} < \frac{b - \mu }{\sigma } ][/tex]

here x is a random value rate  which lies between the higher rate and the lower rate so

     [tex]P(100 < x < 115) = P[ \frac{100 -106.50}{3.85} } < \frac{x- \mu}{\sigma} < \frac{115 - 106.50 }{3.85 } ][/tex]

      [tex]P(100 < x < 115) = P[ -1.688< \frac{x- \mu}{\sigma} < 2.208 ][/tex]

Where  

      [tex]z = \frac{x- \mu}{\sigma}[/tex]

Where z is the standardized value of  x

So

     [tex]P(100 < x < 115) = P[ -1.688< z < 2.208 ][/tex]

     [tex]P(100 < x < 115) = P(z< 2.208 ) - P(z< -1.69 )[/tex]

Now  from the z table we obtain that

      [tex]P(100 < x < 115) = 0.9864 - 0.0455[/tex]

     [tex]P(100 < x < 115) = 0.941[/tex]

    [tex]P(100 < x < 115) =[/tex]94.1%

Maricopa's Success scholarship fund receives a gift of $ 170000. The money is invested in stocks, bonds, and CDs. CDs pay 3.25 % interest, bonds pay 4.4 % interest, and stocks pay 11.4 % interest. Maricopa Success invests $ 25000 more in bonds than in CDs. If the annual income from the investments is $ 10055 , how much was invested in each account?

--------------------------

Equations:

s + b + C = 170000

11.4s + 4.4b + 3.25C = 1005500

b = C + 25000

-----------------------

Rearrange::

s + b + C = 170000

1140s + 440b + 325C = 100550000

0 + b - C = 25000

--------------------------

Use any method you know to solve the system to get:

stocks = 45000

bonds = 75000

CD's = 50000

----------------

Cheers,

Stan H.

--------------

Maricopa Success invested $

in stocks.

Maricopa Success invested $

in bonds.

Maricopa Success invested $

--------------

Hope this helps!

Brainliest would be great!

--------------

With all care,

07x12!

Answer:

We should reject H0

At the 5% significance level, there is sufficient evidence to conclude that the die is not fair.

Step-by-step explanation:

Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. The critical value is 15.091 and  test statistic is 11.070. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value Test statistics is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. In the given case p-value is less than critical value then we should reject the null hypothesis.

Answer:

1

Cans              4cans                  8 cans                   12 cans

Cost                $2.25                   $4.5                      $6.75

2

Ice Cream   180 q       360 q      540 q       720q        900q           1080 q

Hours       2 hours     4 hours    6 hours    8 hours   10 hours      12 hours

***q = quarts

3

Distance        650 miles           1300 miles           1950 miles

Hours              3 hours                 6 hours                9 hours

Answer:

Question 1 - 8 cans = $4.50, 12 cans = $10.13

Question 2 - 4 hours = 360 quarts, 6 hours = 540 quarts, 8 hours = 720 quarts, 12 hours = 1,170

Question 3 - 1,950 miles in 9 hours

Hope this helps :)

Answer:

The height of the elephant is [tex]\dfrac{15}{\sqrt3}\ ft[/tex].      

Step-by-step explanation:

It is given that,

Distance between a person and an elephant is 15 ft

The angle of elevation of the elephant is 30 degrees.

We need to find the height of the elephant. For this let us consider that height is h. So,

[tex]\tan\theta=\dfrac{P}{B}\\\\\tan(30)=\dfrac{h}{15}\\\\h=15\times \tan(30)\\\\h=\dfrac{15}{\sqrt3}\ ft[/tex]

So, the height of the elephant is [tex]\dfrac{15}{\sqrt3}\ ft[/tex].      

Answer:

I always factor out the -1 so my leading coefficient is 1

Step-by-step explanation:

-x^2 + 10x -24

I always factor out the -1 so my leading coefficient is 1

-1 ( x^2 -10x +24)

Then what 2 terms multiply to 24 and add to -10

-6*-4 = 24

-6+-4 = -10

-1( x-6)(x-4)

Answer:

The answer is "20".

Step-by-step explanation:

It is also known as the group of the study, that targets the population, which helps to find the survey, which is the sampled population. It is measured by an ideal world, which will be the same, and they're always unique.  

Answer:

B. 3.19b + 4.59m = 137.24

3.49b + 4.39m = $140.04

Step-by-step explanation:

A B

Bread $3.19 $3.49

Milk $4.59 $4.39

Sue paid $137.24 in supermarket A

Sue paid $140.04 in supermarket B

Let

Price of bread A=$3.19

Price of bread B=$3.49

Price of milk A=$4.59

Price of milk B=$4.39

Quantity of Bread=b

Quantity of Milk=m

Pb=price of bread

Pm=price of milk

Qb=Quantity of bread

Qm=Quantity of milk

For each supermarket

Supermarket A Equation

PbQb + PmQm =$137.24

3.19b+ 4.59m = 137.24

Supermarket B Equation

PbQb + PmQm=$140.04

3.49b + 4.39m = $140.04

Combining both equations

3.19b + 4.59m = 137.24

3.49b + 4.39m = $140.04

Answer:

retype that im not understanding .

Step-by-step explanation:

Answer:

Surface area of the reflective glass is 543234.4 square feet.

Step-by-step explanation:

Given that: height = 311 feet, sides of square base = 619 feet.

To determine the slant height, we have;

[tex]l^{2}[/tex] = [tex]311^{2}[/tex] + [tex]309.5^{2}[/tex]

   = 96721 + 95790.25

   = 192511.25

⇒ l = [tex]\sqrt{192511.25}[/tex]

      = 438.761

The slant height, l is 438.8 feet.

Considering one reflecting surface of the pyramid, its area = [tex]\frac{1}{2}[/tex] × base × height

  area =  [tex]\frac{1}{2}[/tex] × 619 × 438.8

          = 135808.6

          = 135808.6 square feet

Since the pyramid has four reflective surfaces,

surface area of the reflective glass = 4 × 135808.6

                                                          = 543234.4 square feet

Answer: hello your table is incomplete here is the complete table

Fertilizer Amount (ounces) Tomato Plant Height (inches)

1.9 20.4

5.0 49.2

4.2 56.1

1.3 24.3

4.9 29.2

5.4 60.8

3.1 24.6

0.0 25.3

2.3 26.2

2.5 25.7

0.9 26.5

1.0 28.6

4.5 62.9

3.8 30.8

5.3 43.2

2.3 33.4

4.0 35.1

1.4 22.1

3.9 40.6

4.0 44.5

3.6 29.7

0.6 21.1

1.6 25.4

2.5 29.6

4.5 27.6

3.6 32.6

2.0 33.5

0.0 22.5

2.5 27.6

3.1 46.4

Answer : a)Height = 18.639 + 5.208  * fertilizer

b) The Y intercept make practical sense because without fertilizer there will still be an  increase in plant height ( y intercept )  

c) 34.263

Step-by-step explanation:

A) Estimating  the model

Height = β0 + β1 FERTILIZER + ∈

β0 = 18.639

β1 = 5.208

hence

Height = 18.639 + 5.208  * fertilizer  ( using excel )

B) The y- intercept

The Y intercept make practical sense because without fertilizer there will still be an  increase in plant height ( y intercept )  

C ) using the estimated model to predict  after four months

the model = 18.639 + 5.208 * fertilizer

fertilizer ounce given = 3

therefore height of tomato plant after 4 months that received 3 ounces of fertilizer = 18.639 + 5.208 * 3 = 34.263

Answer:

it took 7 hours for the bread to drop at a constent rate

Step-by-step explanation:

Answer:

The temperature droped from 17 5/8° C to - 8 1/2° C = 26 1/8° C, simply add the 2 mixed fractions together and you'll get the temperture change.

Step-by-step explanation:

Convert to a mixed number:

209/8

Divide 209 by 8:

8 | 2 | 0 | 9

8 goes into 20 at most 2 times:

| | 2 | |  

8 | 2 | 0 | 9 |  

- | 1 | 6 | |  

| | 4 | 9 |  

8 goes into 49 at most 6 times:

| | 2 | 6 |  

8 | 2 | 0 | 9 |  

- | 1 | 6 | |  

| | 4 | 9 |  

| - | 4 | 8 |  

| | | 1 |  

Read off the results. The quotient is the number at the top and the remainder is the number at the bottom:

| | 2 | 6 | (quotient)

8 | 2 | 0 | 9 |  

- | 1 | 6 | |  

| | 4 | 9 |  

| - | 4 | 8 |  

| | | 1 | (remainder)

The quotient of 209/8 is 26 with remainder 1, so:

Answer: 26 1/8° C

Answer:

a. x = 36°, y = 36°, z = 34°

Step-by-step explanation:

X = 36° because x and 144° are supplementary angles and the sum of supplementary angles = 180°

The sum of interior angles in a triangle is equal to 180° since one of the angle is given as 110° the sum of z and y must be equal to 70° the option that fits these qualities is a. x = 36°, y = 36°, z = 34°

Answer: d) Not in Col in Nul A

Step-by-step explanation: The definition of Column Space of an m x n matrix A is the set of all possible combinations of the columns of A. It is denoted by col A. To determine if a vector is a column space, solve the matrix equation:

A.x = b or, in this case, [tex]A.x=u[/tex].

To solve, first write the augmented matrix of the system:

[tex]\left[\begin{array}{cccc}1&0&3&-4\\-2&-1&-4&-5\\3&-3&0&3\\-1&3&6&1\end{array}\right][/tex]

Now, find the row-echelon form of matrix A:

1) Multiply 1st row by 2 and add 2nd row;

2) Multiply 1st row by -3 and add 3rd row;

3) MUltiply 1st row by 1 and add 4th row;

4) MUltiply 2nd row by -1;

5) Multiply 2nd row by 3 and add 3rd row;

6) Multiply 2nd row by -3 and add 4th row;

7) Divide 3rd row by -15;

8) Multiply 3rd row by -15 and add 4th row;

The echelon form matrix will be:

[tex]\left[\begin{array}{cccc}1&0&3&-4\\0&1&-2&13\\0&0&1&-\frac{51}{15}\\0&0&0&-13 \end{array}\right][/tex]

Which gives a system with impossible solutions.

But if [tex]A.x=0[/tex], there would be a solution.

Null Space of an m x n matrix is a set of all solutions to [tex]A.x=0[/tex], so vector u is a null space of A, denoted by null (A)

Answer:

The hypothesis test is right-tailed.

Step-by-step explanation:

We are given that we want to test the claim that the majority of adults are in favor of raising the voting age to 21.

Let p = proportion of adults who are in favor of raising the voting age to 21

So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 50%

Alternate Hypothesis, [tex]H_A[/tex] : p > 50%

As we know that the majority is there when we have more 50% chance of happening of that event.

Here, the null hypothesis states that the proportion of adults who are in favor of raising the voting age to 21 is less or equal to 50%.

On the other hand, the alternate hypothesis states that the proportion of adults who are in favor of raising the voting age to 21 is more than 50%.

This shows that our hypothesis test is right-tailed because in the alternate hypothesis, the greater than sign is included.