Please explain how to solve the linear equation to get 20 simply, please. Thank you!

Answer:

Her brothers pulse rate is 76.

Step-by-step explanation:

95% of 80 is 76. That only means that her brother's pulse rate must be 76 beats per minute.

The time period of the animals life cycles are,

⇒ Beluga whole = 35 years

⇒ Bengal tiger = 10 years

⇒ Elephant = 20 years

⇒ Giraffe = 25 years

⇒ Orangutan = 40 years

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

There are some animals and there ages.

Now,

Since, There are some animals and there ages are given.

Hence, The correct ages of the animals are,

⇒ Beluga whole = 35 years

⇒ Bengal tiger = 10 years

⇒ Elephant = 20 years

⇒ Giraffe = 25 years

⇒ Orangutan = 40 years

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9514 1404 393

Answer:

  x = 3.6

Step-by-step explanation:

The angle bisector divides the segments proportionally. This means they satisfy ...

  bottom segment / side segment = x/6 = (6-x)/4

Multiplying by 12 gives ...

  2x = 3(6 -x)

  2x = 18 -3x . . . . . eliminate parentheses

  5x = 18 . . . . . . . . add 3x

  x = 3.6 . . . . . . . . . divide by 5

_____

Alternate solution

I like to try to work these mentally. The total of side lengths is 10, so the total base length (6) is 6/10 = 0.6 times that. Then x will be 0.6 times the left side length: 0.6·6 = 3.6 = x.

Given matrices are from here

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=====================================================

Problem 3

a)

B - C = DNE

We cannot subtract matrices of different sizes. Matrix B is 2x2 while C is 3x2. Both matrices must have the same number of rows, and they must also have the same number of columns. The matrices don't have to be square.

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

b)

\(A+B = \begin{bmatrix}-5 & 6\\7 & 4\end{bmatrix}\)

You add the corresponding elements. For instance, in the top left corner we have -1+(-4) = -5. The other entries are treated in a similar manner.

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

c)

\(-2E = \begin{bmatrix}6 & -4 & 8\\-12 & 14 & -16\\-10 & -18 & 20\end{bmatrix}\)

You get this from multiplying each entry in matrix E by -2. Eg: top left corner has -2*(-3) = 6

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

d)

\(CD = \begin{bmatrix}4 & 7 & 8\\ 1 & 3 & 4\\14 & 17 & 16\end{bmatrix}\)

Matrix C has 3 rows and D has 3 columns. The final answer will be size 3x3

To generate each value in the answer matrix, you'll highlight rows of C to pair with columns of D. Then you'll multiply out the corresponding values, after which you add those products. This is done for every entry in the answer shown above.

For example, the first row of C is highlighted and the second column of D is highlighted. Those values pair up and multiply getting -1*(-1) + 2*3 = 1+6 = 7, which goes in the first row and second column of the answer matrix. The other entries are handled in a similar fashion.

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

e)

\(\det(B) = -46\)

The 2x2 matrix determinant formula is \(\begin{vmatrix}a & b\\c & d\end{vmatrix} = a*d - b*c\)

In this case, a = -4, b = 6, c = 5, d = 4.

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

f)

\(B^{-1} = \begin{bmatrix}-2/23 & 3/23\\ 5/46 & 2/23\end{bmatrix}\)

Swap the top left and bottom right corners of matrix B. Change the sign of the other two corner values. Then multiply each entry by 1/d where d is the determinant found back in part (e) above. Be sure to reduce any fraction as much as possible.

=====================================================

Problem 4

Answers: x = 2  and y = -10

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

Work Shown:

\(\begin{bmatrix}2x & 4\\-5 & -2\end{bmatrix}+\begin{bmatrix}3 & -7\\11 & y-1\end{bmatrix} = \begin{bmatrix}7 & -3\\6 & -13\end{bmatrix}\\\\\\\begin{bmatrix}2x+3 & 4+(-7)\\-5+11 & -2+(y-1)\end{bmatrix} = \begin{bmatrix}7 & -3\\6 & -13\end{bmatrix}\\\\\\\begin{bmatrix}2x+3 & -3\\6 & y-3\end{bmatrix} = \begin{bmatrix}7 & -3\\6 & -13\end{bmatrix}\\\\\\\)

In the top left corners of each matrix, in line 3, we have 2x+3 = 7 which solves to...

2x+3 = 7

2x = 7-3

2x = 4

x = 4/2

x = 2

In the bottom right corners, we have y-3 = -13 which solves to....

y-3 = -13

y = -13+3

y = -10

Answer:

The two figures are not congruent because non rigid motions are used to map figure 1 onto figure 2(This is dilation)

Point corresponding to point J: R

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

2

4x² + 64 ← factor out the common factor of 4 from each term

= 4(x² + 16)

3

(a - 10)² = 121 ( take square root of both sides )

a - 10 = ± \(\sqrt{121}\) = ± 11 ( add 10 to both sides )

a = 10 ± 11

then

a = 10 - 11 = - 1

a = 10 + 11 = 21

Answer:

D. -7

Step-by-step explanation:

Since positive 7 represents a gain of seven yards, a loss would be represented by a negative number.

So, a loss of seven yards will be represented by -7.

So, the correct answer is D. -7

The integral\int(1/x^4 + 9x^2) dx converges by comparison to a convergent integral, and its value is 1/3

To determine whether the integral converges or diverges, we can use the limit comparison test with the integral:

Since for all x > 0, we have:

Thus, by the limit comparison test:

converges if and only if converges.

We can evaluate  using the power rule of integration:

where C is the constant of integration. Evaluating this integral from 1 to infinity, we get:

∫(1/x^4) dx from 1 to infinity = lim as b → infinity

=>

=> 0 - (-1/3)

=> 1/3

Since the integral  dx converges by comparison to a convergent integral, and its value is 1/3.

To learn more about  Convergent integral :

Note: The full question is

Determine whether the integral converges or diverges; if it converges, evaluate. (If the quantity diverges, enter DIVERGES. Do not use the [infinity] symbol in your answer.) [infinity] dx x4 + 9x2 1

Sarah's fuel efficiency is approximately 32.91 miles per gallon.

From the question, we are to calculate Sarah's fuel efficiency.

To find Sarah's fuel efficiency in miles per gallon, we need to convert the distance she drove to miles and the amount of gasoline she used to gallons.

From the given information,

1 km = 0.6214 mi

1 gal = 3.8 L

First, let's convert the distance from kilometers to miles:

691.4 km × 0.6214 mi/km = 430.10196 mi

So, Sarah drove a distance of 430.1 miles.

Also,

Convert the amount of gasoline from liters to gallons:

49.7 L ÷ 3.8 L/gal = 13.0789 gal

So, Sarah used 13.0789 gallons of gasoline.

Calculate her fuel efficiency in miles per gallon:

Fuel efficiency = distance ÷ gasoline used

Fuel efficiency = 430.1 mi ÷ 13.0789 gal

Fuel efficiency = 32.9065 mi/gal

Hence, Sarah's fuel efficiency is 32.91 mi/gal

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For the number line given the compound inequality is  -∞ ≤ x ≤ 1 and 5 ≥ x ≥ ∞.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The number line is given.

The inequality contains black dots that means that the inequality will be inclusive of the starting points.

The first inequality will be starting form 1 and moving towards negative infinity.

So, the inequality is -

-∞ ≤ x ≤ 1

The second inequality will be starting form 5 and moving towards positive infinity.

So, the inequality is -

5 ≥ x ≥ ∞

Therefore, the compound inequality is -∞ ≤ x ≤ 1 and 5 ≥ x ≥ ∞.

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Answer:

A, C, E

Step-by-step explanation:

By analyzing the graph, we can see that the roots are \(-2\) and \(-4\).

We now want to find all equations of the form \((x-(-2))(x-(-4))=(x+2)(x+4)=0\).

This immediately gives C as 1 answer.

We can expand our equation to find other possible solutions!

By the FOIL method: \((x+2)(x+4)=(x)(x)+(2)(x)+(4)(x)+(2)(4)=x^2+6x+8=0\)

We can then divide both sides of the equation to find that \(-x^2-6x-8=0\), so A is another answer.

We can complete the square on \(x^2+6x+8\) to find the last possible solution.

\(x^2+6x+8=x^2+6x+9-9+8=x^2+6x+9-1=(x+3)^2-1=0\).

We can then multiply both sides of the equation by \(4\) to find that \(4(x+3)^2-4=0\), so E is the last answer.

The proof that the other answers don't work is left as an exercise.

So, the answers are A, C, and E, and we're done!

Answer:

its going to be letter b  because  2 and  4 well the x intercepts those  

Step-by-step explanation:

1. Based on the producer theory, an increase in the demand for labor (L) would be caused by An increase in the productivity of labor, A decrease in the wage rate and A decrease in the rental rate of capital.

2. Missing variables in this simple producer theory would include The technology used to produce output, The preferences of consumers and Quality of labor and capital.

In the standard producer theory, a producer minimizes costs for a given level of output.

This involves choosing the optimal mix of inputs, such as labor (L) and capital (K), to produce the desired output (y).

The cost function is represented by C = wL + rK, where w is the wage rate (cost of labor) and r is the rental rate (cost of capital).

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The average rate of change of the function over the interval is 4

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

y = 4x + 1

The interval is given as

[-1, 1)

The function is a linear function

This means that it has a constant average rate of change

From y = 4x + 1, we have

Rate = 4

Hence, the rate is 4

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Answer:

The right triangular pyramid volume is given by the formula V = 1 3 × B × h , where B is the area of the triangular base and h is the height (the distance from the apex to the base).

Step-by-step explanation:

Answer:

192 cubic feet

Step-by-step explanation:

The volume V of a triangular pyramid is given by the formula:

V = (1/3) * base area * height

where base area is the area of the triangular base.

In this case, the triangular base has a length of 8 ft and a width of 8 ft, so it is a square with area:

base area = length * width = 8 ft * 8 ft = 64 sq ft

Substituting the given values into the formula, we get:

V = (1/3) * 64 sq ft * 9 ft

V = 192 cubic feet.

Therefore, the volume of the triangular pyramid is 192 cubic feet.

Large Tractors Sold at Break Even Point= 26 units

Small Tractors Sold at Break Even Point= 39 units

Break-even point is where sales are equivalent to the sum of all costs incurred by the company. It is a significant concept in accounting as it gives the managers vital information on how many units must be sold to make business operations profitable.

From the question, it was stated that Wagner Enterprises sells for every three small tractors, two large tractors. Therefore, the sales mix will be:

The contribution margin per unit will be computed first, after which we multiply the sales mix by the computed margin per unit to get the Weighted Average Contribution Margin (WACM). This is shown below:

For Large Tractor:

Selling Price per Unit = $62,000

Variable Cost per Unit = $28,520

Contribution Margin per Unit = ($62,000 - $28,520) = #33,480

Multiply by sales-mix of 2/5 = 2/5 times $33,480 = 13,392 (WACM)

For Small Tractor:

Selling Price per Unit = $34,000

Variable Cost per Unit = $16,320

Contribution Margin per Unit = ($34,000 - $16,320) = #17,680

Multiply by sales-mix of 3/5 = 3/5 times $17,680 = 10,608 (WACM)

The Total Weighted Average Contribution Margin per unit is therefore:

$13,392 + $10608, equaling $24,000.

Now we can find the Break-even Point in Unit.

Formula for Break-even Point in Unit = Total Fixed Cost (TFC) divided by Weighted Average Contribution Margin in unit

Total Fixed Costs = $1,560,000

WACM in unit = $24,000

Break-Even Point = \(\frac{1,560,000}{24,000}\) = 65 units

From the calculations, the total units that must be sold to break-even are equivalent to 65 units. Given the above sales mix, the 65 units will be shared thus:

Therefore, 26 units of Large Tractors and 39 units of Small Tractors were sold at Wagner's Enterprise break-even point.

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Answer:

hello some parts of your question is missing attached below is the missing part

"Class A" Class B Class C

  111  120  107

 75   96    93

 109  112  89

 101   89    117

 102  103  82

  81   112   64

  103  98  107

  87   101  101

  88  82   114

answer :  a) Test statistic  = 0.46

                b) p-value = 0.64

Step-by-step explanation:

A) To calculate the Test statistic ; use excel software

steps involved :

i) import Data, ii) choose Anova; single factor

iii) choose input range and column in groups iv) choose output range

attached below is the table

b ) calculate the P -value

P-value = 0.64

Answer:

6d - 24e

Step-by-step explanation:

Answer:

-43

Step-by-step explanation:

-4(-3)² + 2(-3) - 1

=-4×9+2(-3)-1

=-36+2(-3)-1

=-36-6-1

=-43

Using conditional probability, it is found that there is a 0.3266 = 32.66% probability that the person first went on tour T2.

Conditional Probability

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

In this problem:

The percentages associated with a return are:

Hence:

\(P(A) = 0.75(0.5) + 0.667(0.3333) + 0.5(0.1667) = 0.6806611\)

The probability of both returning and first going on T2 is:

\(P(A \cap B) = 0.667(0.3333)\)

Hence, the conditional probability is:

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.667(0.3333)}{0.6806611} = 0.3266\)

0.3266 = 32.66% probability that the person first went on tour T2.

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Answer:

96 boxes of muffins

Step-by-step explanation:

so how you would get to this answer would be 1152÷12

12 is equal to a dozen and so that is why you divide it by 12

the answer would be 96

Answer:

1/6?

Let's do it...

( (3^(3/4))/(3^(3/8)) )^4/9

According to indices rules here the denominator and numerator has the same base and they are dividing so the powers will subtract..... Its just a formulae not rocket science so don't freak out.

So ( 3^(3/4 - 3/8)) ^4/9

= ( 3^(3/8)) ^4/9

Again with indices rule the powers will multiply

Which will return us 3^1/6 which corresponds 3^x..... Hence x =1/6

Thank you

\( \boxed{ \boxed{x = \frac{1}{6} }}\)

\( \hookrightarrow \: {\bigg( \dfrac{3 {}^{ \frac{3}{4} } }{ {3}^{ \frac{3}{8} } } \bigg) }^{ \frac{4}{9} } \)

\( \hookrightarrow \: {(3 {}^{ \frac{3}{4} } \div 3 {}^{ \frac{3}{8} } ) } ^{ \frac{4}{9} } \)

\( \hookrightarrow \: {(3 {}^{ \frac{3}{4} - \frac{3}{8} } ) }^{ \frac{4}{9} } \)

\( \hookrightarrow \:{ (3 {}^{ \frac{3}{8} } ) }^{ \frac{4}{9} } \)

\( \hookrightarrow \: 3 {}^{ \frac{3}{8} \times \frac{4}{9} } \)

\( \hookrightarrow \: {3}^{ \frac{1}{6} } \)

therefore,

the required value of x is 1/6

Answer: area = 30 square units

The diagram is below. Ignore point G and the red dashed line when drawing the final hexagon needed.

======================================================

Explanation:

On the grid your teacher has given you, plot the 6 points. Then connect them to form hexagon ABCDE. All of this is shown in blue in the diagram below.

Let's add point G as shown in red. I'll connect G to point C with a red dashed line. These will be temporary and erased later. Though if your teacher doesn't mind you leaving it in (so you can show your steps), then its probably not a bad idea to keep it. It's best to ask your teacher.

Anyways, the red segment GC splits the original hexagon into a trapezoid up top and a rectangle down below.

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

The trapezoid has the parallel bases of b1 = GC = 4 and b2 = AB = 2. The height is h = GA = 3

This leads to,

area = h*(b1+b2)/2

area = 3*(4+2)/2

area = 3(6)/2

area = 18/2

area = 9

Trapezoid ABCG has area of 9 square units.

-----------

The rectangle has length EF = 7 and width ED = 3

area = length*width

area = 7*3

area = 21

Rectangle DEFG has area of 21 square units.

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

Add up those two area results to get the area of the overall hexagon.

trapezoid + rectangle = 9 + 21 = 30 square units.

It is given that Dodi has two cups of liquid starch

2 cups =16 fluid ounces

1 container  can hold 6 fluid ounces

We are required to find that how many containers are required

1 container contains 6 ounces

Hence 16 ounces will be contained in 3 containers

Hence Dodi will required 3 containers.

Disclaimer:

The question is incomplete and jumbled

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Answer:

(a) 1.8 eggs

(b) 0.52 eggs

Step-by-step explanation:

According to the problem, computation of the given data are as follows:

The mean number of broken eggs in a dozen E(X) = 0.6

Standard deviation SD(X) = 0.3

(a). For 3 dozen eggs, number of broken eggs can be calculated by using following formula,

E(X) for 3 dozen = 3 × 0.6

= 1.8 eggs

(b). Standard deviation for 3 dozen can be calculated as follows,

SD (X) = ×\(\sqrt{3* (0.3)^{2}\)

= \(\sqrt{27}\)\(\sqrt{27}\)

= 0.52 eggs

The graph of the function is added as an attachment

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

f(x) = 4x

The above expression is a linear equation that implies that:

Slope = 4

y-intercept = 0

Next, we plot the graph using a graphing tool

One of the points on the line is (1, 4)

See attachment for the graph of the equation

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The unknown angles in the cyclic quadrilateral is as follows:

∠BGX = 74° (sum of angles in a triangle)

∠BGF = 180° (opposite angles of cyclic quadrilateral are supplementary)

∠BCF = 100°(sum of angles in a triangle)

∠BCG  = 26°

∠BFG = 22°

A cyclic quadrilateral has all its angles equal to 360 degrees. The sum of angles in a cyclic quadrilateral is equals to 360 degrees.

Let's find the missing angles as follows:

∠BGX = 180 - 48 - 58 = 74° (sum of angles in a triangle)

∠BGF = 180 - 100 = 80° (opposite angles of cyclic quadrilateral are supplementary)

∠BCF = 180 - 22 - 58 = 100°(sum of angles in a triangle)

∠BCG = 100 - 74 = 26°

∠BFG ≅ CBF = 22°(alternate angles)

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root*324=18

441=21

529=23

hope it helps

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