Rectangle A is 10 times as long as rectangle B.



If rectangle A is 80 units long, select all the ways to find the length of rectangle B. *

Answer: D.

Step-by-step explanation:

You can start out with the form AX = B and solve for matrix X that would yield the answer

Then X = (A^-1)(B)

A = [1    -1]

      [1     1]

A^-1 = (1/(1 - (1)(-1)))*[1    1]

                             [-1   1]

which can be written as (1/2) * [1    1]

                                                  [-1   1]

B = [26]

     [6]

(A^-1)(B) = (1/2)*[1    1] [6]

                        [-1   1] [26]

= (1/2)*[32]

          [20]

= [16]

  [10]

Answer:

The length of the arc is 1.6 cm

Step-by-step explanation:

To find the value of the length of the arc, we use the length of arc formula

Mathematically, this is;

theta/360 * 2 * pi * r

where theta is the central angle

In this case pi/4 = 180/4 = 45 degrees

r = 2 cm

So the measure of the length of the arc will be;

L = 45/360 * 2 * 22/7 * 2

= 1/8 * 4 * 22/7

= 22/7 * 1/2 = 11/7 = 1.57 cm which is approximately 1.6 cm

Answer:

π/2

Step-by-step explanation:

Khan

The total number of ways to earn extra credit is n + m + p + q.

There are four options given for earning extra credit: redoing an assignment, redoing a quiz, completing a project, or doing corrections for a quiz. To determine the number of ways you can earn extra credit, we can consider each option individually and count the possibilities.

Redoing an assignment: If there are 'n' assignments available to redo, you have 'n' ways to earn extra credit by choosing one of them.

Redoing a quiz: If there are 'm' quizzes available to redo, you have 'm' ways to earn extra credit by choosing one of them.

Completing a project: If there are 'p' projects available to complete, you have 'p' ways to earn extra credit by choosing one of them.

Doing corrections for a quiz: If there are 'q' quizzes available for corrections, you have 'q' ways to earn extra credit by choosing one of them.

To find the total number of ways to earn extra credit, we can sum up the possibilities for each option:

Total ways = (Number of ways to redo an assignment) + (Number of ways to redo a quiz) + (Number of ways to complete a project) + (Number of ways to do corrections for a quiz)

Total ways = n + m + p + q

Therefore, the total number of ways to earn extra credit is n + m + p + q.

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Answer:  All real numbers.

Step-by-step explanation:

4(a+3) = 12 + 4a

4a + 12 = 12 + 4a

Any value of a will work in this equation, since it is a simple identity.  4a + 12 will always equal 4a + 12, regardless of a.

All real numbers, although I don't know why imaginary numbers wouldn't also work.

Answer:

the answer would be 211

Step-by-step explanation:

you simply add the length and width together to find perimeter. since you have the total perimeter and the length you would instead subtract the two.

292-81= 211

Answer:

68m

Step-by-step explanation:

The perimeter  of a rectangle with length  and width  is given by the following.

P=21+2w

We need to find w when P=292 m  and l+78m .

Using these values in the equation above, we'll solve for w.

P=21+2w

292=2(78)+2w

292=156+2w

136=2w

68=w

Subtracting 156  from both sides

Dividing both sides by  2

So the width of the parking lot is 68m

Thus, Differentiation Part of the Fundamental Theorem of Calculus:

a) sin(t^4)/4

b) sin(sqrt(s^4 + 1))/sqrt(s^4 + 1)

c)  (t + 1)ln(t + 1) - (t + 1)

d)  (1/2)ln|z + 2| + z

e)  (1/ln2)(sqrt(pi)/2)erfi(sqrt(ln2)t)

The Differentiation Part of the Fundamental Theorem of Calculus states that if f(x) is a continuous function on the interval [a,b] and F(x) is an antiderivative of f(x), then:
d/dx integral^b_a f(t) dt = f(x)

Using this theorem, we can find the derivatives of the given integrals as follows:

a) d/dx integral^x_2 cos(t^4) dt
= cos(x^4) [by applying the Differentiation Part of the FTC and noting that the antiderivative of cos(t^4) is sin(t^4)/4]

b) d/dx integral^6_x cos (squareroot s^4 + 1)ds
= -cos(sqrt(x^4 + 1)) [by applying the Differentiation Part of the FTC and noting that the antiderivative of cos(sqrt(s^4 + 1)) is sin(sqrt(s^4 + 1))/sqrt(s^4 + 1)]

c) d/dx integral^2x + 1_2 In(t + 1)dt
= In(x + 1) [by applying the Differentiation Part of the FTC and noting that the antiderivative of ln(t + 1) is (t + 1)ln(t + 1) - (t + 1)]

d) d/dx integral^x_-x z + 1/z + 2 dz
= 0 [by applying the Differentiation Part of the FTC and noting that the antiderivative of z + 1/(z + 2) is (1/2)ln|z + 2| + z]

e) d/dx integral^2_-3x 2^t2 dt
= -6x2^(9x^2) [by applying the Differentiation Part of the FTC and noting that the antiderivative of 2^(t^2) is (1/ln2)(sqrt(pi)/2)erfi(sqrt(ln2)t)]

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The slope for the function f(t) = 3 - 3/5t at point (3/5, 2) is 5/3.

What is slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

The given function is - f(t) = 3 - 3/5t.

The data points are - (3/5, 2)

Rewrite the function -

f(t) = 3 - 3/5 t^-1

Differentiate with respect to t. Use the difference rule.

d/dt (3) - d/dt (3/5 t^-1)

Use the constant rule and the constant multiple rule.

0 - 3/5 d/dt (t^-1)

Use the power rule.

-3/5(-1)t^(-1 - 1)

3/5t^-2

Now plug in 3/5 for t on the derivative in order to find the slope at point (3/5, 2).

3/5(3/5)^-2

3/5(5/3)^2

3/5 × 25/9

5/3

Therefore, the slope value is 5/3.

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Find the slope of the graph of the function at the given point.

Function Point f(t) = 3 - 3/5t (3/5, 2)

The value of x to the nearest tenth is 24.30 units.

The tangent of an angle in trigonometry is the ratio of the lengths of the adjacent side to the opposing side. In order for the value of the cosine function to not be 0, it is the ratio of the sine and cosine functions of an acute angle. One of the six fundamental functions in trigonometry is the tangent function.

Given that the opposite side to angle R = 38 degrees is 19.

Using trigonometric identities we have:

Tan R = 19 / x

Tan (38) = 19/x

x = 19/0.78

x = 24.35

Hence, the value of x to the nearest tenth is 24.30 units.

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The complete question is:

The task requires analyzing a list of departments and performing several tasks related to relationship codes, activity relationship diagrams, reason codes, a worksheet, and a dimensionless block diagram.

We need to consider the number of departments. Since we have 7 departments listed, the number of relationship codes can be calculated using the formula: (n * (n-1)) / 2, where n is the number of departments.

Substituting the value of n = 7, we get:

Relationship Codes = (7 * (7-1)) / 2

= (7 * 6) / 2

= 42 / 2

= 21

Therefore, there will be 21 relationship codes in the chart.

Create an activity relationship diagram:

An activity relationship diagram visually represents the relationships between departments. Here is a basic diagram representing the given departments:

Receiving --+

           +-- Assembly & Shipping -- Offices

Fabrication--+

           +-- Painting -- Stores

Restrooms & Lockers

Populate the diagram with codes for all the relationships:

To populate the diagram with codes, we can assign a unique code to each relationship. Here's an example of assigning codes to the relationships in the diagram:

Receiving (R) --+

               +-- Assembly & Shipping (AS) -- Offices (O)

Fabrication (F)--+

               +-- Painting (P) -- Stores (S)

Restrooms & Lockers (RL)

What is the percentage of codes in each category? Does it follow the standard percentages?

To determine the percentage of codes in each category, we need to count the number of codes in each category and calculate the percentage relative to the total number of codes (21).

In this case, we have the following categories and their respective codes:

Production: R, F, AS, P (4 codes)

Administration: O, S (2 codes)

Support: RL (1 code)

Percentage of Production codes = (4 / 21) * 100 ≈ 19.05%

Percentage of Administration codes = (2 / 21) * 100 ≈ 9.52%

Percentage of Support codes = (1 / 21) * 100 ≈ 4.76%

These percentages do not necessarily follow any standard percentages. The distribution of codes among categories can vary depending on the specific organization or context.

Provide at least 3 reason codes for the chart:

Reason codes are used to provide explanations or justifications for the relationships depicted in the chart. Here are three example reason codes for the given chart:

R01: Receiving department receives raw materials and supplies from external sources.

AS01: Assembly & Shipping department assembles products and prepares them for shipment.

O01: Offices department provides administrative support and management functions for the organization.

Create a worksheet to assist in the creation of the dimensionless block diagram:

Here's an example of a worksheet that can assist in creating the dimensionless block diagram:

Relationship Code From Department To Department

R Receiving Fabrication

F Fabrication Painting

AS Assembly & Shipping Offices

P Painting Stores

RL Restrooms & Lockers -

O Offices -

S Stores -

This worksheet lists the relationship codes along with the corresponding "From" and "To" departments.

Create a dimensionless block diagram for your data B. Show the flow through the dimensionless block diagram:

A dimensionless block diagram represents the flow of activities or information between different departments. Here's an example of a dimensionless block diagram based on the given data:

Receiving --> Fabrication --> Painting --> Stores

                  |

                  v

        Assembly & Shipping --> Offices

                  |

                  v

       Restrooms & Lockers

The arrows indicate the flow of activities or information from one department to another.

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The value of the function g(x) at g = 4 is 18.

Given is a function g(x) as follows -

g(x) = 3x² - 5(x + 2)

We have the following function as -

g(x) = 3x² - 5(x + 2)

For g(4), we can write -

g(4) = 3 x (4)² - 5(4 + 2)

g(4) = 3 x 16 - 5 x 6

g(4) = 48 - 30

g(4) = 18

Therefore, the value of the function g(x) at g = 4 is 18.

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\(2x {}^{2} = - 8 \\ x {}^{2} = \frac{ - 8}{2} \\ x {}^{2} = - 4 \\ x = ± \sqrt{ - 4} \\ x_{1} = 2i \: \: \: \: \: \: x_{2} = - 2i\)

The number of red balls Luke has at the start is 47.

blue ball per day = 2

red ball per day = -3 ('-' ve sign as he is loosing them)

let the number of red balls be represented by r

let the number of blue balls be represented by b

after 5 days

b+ 10 = r -15 -(i)

After 9 days

b + 18 =2(r-27)-(ii)

subtracting (i) from (ii)

b + 18 - b - 10 = 2r - r - 54 +15

8 = r - 39

r = 39 + 8

r = 47

The number of red balls Luke has at the start is 47

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Young people respond more favorably to literature that reflects their cultural customs, and this is because of the importance of cultural background in children’s reading development. Ethnic and cultural differences play an essential role in the children's reading development.

Children's cultural and ethnic background has a considerable impact on their learning, and thus the type of literature they respond to. Children tend to read more when they find that the stories and books reflect their cultural customs and identity. This enhances their literacy and reading skills, which in turn leads to an increased interest in reading and a better understanding of what they are reading.

Cultural diversity can help children become more empathetic and accepting of differences, and can help them to learn about new cultures. Therefore, it is crucial to provide children with access to a range of culturally diverse literature to help them understand the experiences of others. Children learn more effectively when they can make connections between what they are learning and their own experiences.

In conclusion, children's reading development is influenced by their ethnic and cultural background. Young people respond more favorably to literature that reflects their cultural customs, which can help them to become more empathetic and accepting of differences, as well as develop their literacy and reading skills. Therefore, it is essential to provide children with a range of culturally diverse literature to help them learn about new cultures and understand the experiences of others.

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Answer:

\( \frac{11}{12} \)

Step-by-step explanation:

\(( \sin \theta) ^{2} + ( \cos \theta) ^{2} = 1 \\ \\ \therefore \: { \bigg( \frac{ \sqrt{23} }{12} \bigg)}^{2} + ( \cos \theta) ^{2} = 1 \\ \\ \frac{23}{144} + ( \cos \theta) ^{2} = 1 \\ \\ ( \cos \theta) ^{2} = 1 - \frac{23}{144} \\ \\ ( \cos \theta) ^{2} = \frac{144 - 23}{144} \\ \\ ( \cos \theta) ^{2} = \frac{121}{144} \\ \\ ( \cos \theta) = \sqrt{\frac{121}{144} } \\ \\ \cos \theta = \frac{11}{12} \)

On solving the provided  question, we can say that value for the function g[h(−3)] is 12.

A mathematical function is a rule that determines the value of the dependent variable based on the values of the independent variables. A table, a formula, or a graph are just a few examples of how a function might be expressed.

In mathematics, a function is an expression, rule, or law that establishes the relationship between independent and dependent variables.

For equation h(x)

x = -3

then h(-3) = x²-1

h(-3) = (-3)² -1

h(-3) = 9-1 = 8 now using this value in g(x)

g(x) = x+ 4

g(8) = 8+ 4 = 12

Hence the value for the function is g[h(−3)] = 12

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The earnings per share can be calculated as $0.066 per share (rounded to the nearest cent).

a. The earnings per share for Company XYZ can be calculated by dividing the closing price by the P/E ratio. In this case, the closing price is $100.76 and the P/E ratio is 1525. Therefore, the earnings per share can be calculated as $0.066 per share (rounded to the nearest cent).

b. Based on the historical P/E ratio range of 12-14, the stock price of Company XYZ seems overpriced. The P/E ratio indicates the price investors are willing to pay for each dollar of earnings generated by the company. A higher P/E ratio suggests that investors have higher expectations for future earnings growth. In this case, the P/E ratio of 1525 is significantly higher than the historical range of 12-14, indicating that the stock is being valued at a much higher premium relative to its earnings. This suggests that the stock price may be inflated and not in line with the company's historical valuation metrics, indicating an overpriced condition.

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Answer:

4 x 10^7

Step-by-step explanation:

1 x 10^7 is 10 million, just multiply that 1 by 4 to get your answer

Answer:

4 x 10^7

Step-by-step explanation:

Answer:

(1/2)^2 - ((-3/4)+1)^3

1/4 - 1/64

15/64

Answer:

15/64

Step-by-step explanation:

a^2 - ( b + 1)^3

Let a = 1/2  and b = -3/4

(1/2)^2 - ( -3/4 + 1)^3

Parentheses first

(1/2)^2 - ( 1/4)^3

Exponents

1/4 - 1/64

Get a common denominator and subtract

16/64 -1/64

15/64

To find the common ratio (r), we divide any term of the sequence by its previous term. The common ratio (r) of the geometric sequence is 2/3. The fifth term (a₅) is $4/9. The nth term (aₙ) can be represented as           aₙ = (2/3)^(n-1).

To find the common ratio (r), we divide any term of the sequence by its previous term. In this case, we divide the second term (s₂/9) by the first term (1) to get (s₂/9) / 1 = s₂/9. Similarly, we divide the third term ($4/9) by the second term (s₂/9) to get ($4/9) / (s₂/9) = $4/9 * 9/s₂ = $4/s₂ = 2/3. Therefore, the common ratio (r) is 2/3.

To find the fifth term (a₅), we use the formula aₙ = a₁ * r^(n-1), where a₁ is the first term and n is the position of the term we want to find. In this case, a₁ = 1 and n = 5. Plugging in these values, we have a₅ = 1 * (2/3)^(5-1) = 1 * (2/3)^4 = 1 * 16/81 = $16/81 = $4/9.

Therefore, the fifth term (a₅) is $4/9.

The nth term (aₙ) of a geometric sequence can be represented as aₙ = a₁ * r^(n-1), where a₁ is the first term and r is the common ratio. In this case, a₁ = 1 and r = 2/3.

Thus, the nth term (aₙ) can be expressed as  aₙ = 1 * (2/3)^(n-1).

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\(area = lw\)

\(area = (8)(8)\)

\(area = 64 \: {inches}^{2} \)

//

\(perimeter = 2(l) + 2(w)\)

\(perimeter = 2(8) + 2(8)\)

\(perimeter = 32 \: inches\)

The complete statement is -

"Even though the triangles are all different sizes, the decimal values for each ratio are same."

A triangle is a two - dimensional figure with three sides and three angles.

The sum of the angles of the triangle is equal to 180 degrees.

∠A + ∠B + ∠C = 180°

Given is that -

"Even though the triangles are all different sizes, the decimal values for each ratio are ​_____."

We can write the complete statement as -

"Even though the triangles are all different sizes, the decimal values for each ratio are same."

Therefore, the complete statement is -

"Even though the triangles are all different sizes, the decimal values for each ratio are same."

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Step-by-step explanation:

LCM is lowest common factor and HCF is highest common factor.

Given numbers are 236 and 92.

We can find it using prime factorization method.

Prime factorization of 236 = 2 x 2 x 59

Prime factorization of 92 = 2 x 2 x 23

HCF = 2 x 2 = 4

LCM = 2 x 2 x 59 x 23 = 5428

We know that,

LCM×HCF = product of two numbers

⇒ LCM×HCF = 5428×4 = 21712

⇒ product of two numbers = 236× 92 = 21712

Hence, proved.

Answer:

The value of the tangent is \(-\frac{4}{5}\).

Step-by-step explanation:

Let be \(A(x,y) = (-10, 8)\) on the terminal side of an angle in standard position and let be \(O(x,y)\) the origin of the angle and the origin of the Cartesian plane. By definition of tangent, we make use of the following expression:

\(\tan \theta = \frac{y_{A}-y_{O}}{x_{A}-x_{O}}\) (1)

Where:

\(x_{A}, x_{O}\) - x-Coordinates of point A and point O.

\(y_{A}, y_{O}\) - y-Coordinates of point A and point O.

If we know that \(x_{A} = -10, x_{O} = 0\), \(y_{A} = 8\) and \(y_{O} = 0\), then the value of the tangent is:

\(\tan \theta = \frac{y_{A}-y_{O}}{x_{A}-x_{O}}\)

\(\tan \theta = \frac{8-0}{-10-0}\)

\(\tan \theta = -\frac{4}{5}\)

Answer:

A

Step-by-step explanation:

1/2f

Answer:

A

the first option

Step-by-step explanation:

1) To have 0 bad sectors there are 364 ways.

2) To have 0 good sectors there are 20 ways.

3) To have 1 bad sectors there are 564 ways.

Given there are 20 computer disks.

Defective disks = 6

Non defective disks = 20-6

= 14

1)

Therefore , to have 0 bad sectors, we need to select 3 sectors from the given 14 good sectors, hence no of ways is \(14C_{3}\) ways .

We know that,

\(nC_{r}=\frac{n!}{(n-r)! * r!}= \frac{nP_{r}}{r!}\)

\(14C_{3}= \frac{14P_{3}}{3!}\\\\= \frac{14*13*12}{6} \\\\= 364 ways\)

Therefore it is done in 364 ways.

2)

Therefore , to have 0 good sectors, we need to select 3 sectors from the given 6 bad sectors, hence no of ways is \(6C_3\) ways.

We know that\(nC_{r}=\frac{n!}{(n-r)! * r!}= \frac{nP_{r}}{r!}\)

\(6C_{3}= \frac{6P_{3}}{3!}\\\\= \frac{6*5*4}{6} \\\\= 20 ways\)

Therefore it is done in 20 ways .

3)

Therefore , to have 1 bad sectors, we need to select 1 sectors from the given 6 bad sectors, hence no of ways is \(6C_{1}\) ways and 2 sectors from 14 good sectors can be done in \(14C_{2}\) ways.

We know that \(nC_{r}=\frac{n!}{(n-r)! * r!}= \frac{nP_{r}}{r!}\)

\(14C_{2}= \frac{14P_{2}}{2!}\\\\= \frac{14*13}{2} \\\\= 91 ways\\\\6C_{1}= \frac{6P_{1}}{1!}\\\\= \frac{6}{1} \\\\= 6 ways\)

So total ways \(= 14C_2 * 6C_1\)

= 91*6

= 546 ways

Therefore it is done in 546 ways.

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Answer:

Option (B)

Step-by-step explanation:

Let the amount of apricots purchased = a pounds

and the amount of bananas purchased = b pounds

Since, Andre purchased total amount of apricots and bananas = 5 pounds

Equation for the total amount will be,

a + b = 5

If the cost of bananas = $4 per pounds and the cost of apricots = $6 per pound

Total amount spent = $24.50

Therefore, equation for the expense will be,

6a + 4b = 24.50

Therefore, Option (B) will be the answer.

Answer:

:)

Step-by-step explanation:

B is correct

( I got it right in class thank you other person who answered)

Answer

\(168in^{2}\)

Step-by-step explanation:

SA=2(wl+hl+hw)

2·(6·2+9·2+9·6)

=168

The statement is true: If x and y are linearly independent, and if z is in Span {x, y}, then {x, y, z} is linearly dependent.

The statement is true.
Let's first understand the terms used:
Linearly independent:

A set of vectors is linearly independent if none of them can be expressed as a linear combination of the other vectors. In other words, no vector in the set can be written as a sum of scalar multiples of the other vectors.
Span:

The span of a set of vectors is the set of all linear combinations of those vectors.

In this case, Span\({x, y}\) is the set of all vectors that can be formed by adding scalar multiples of x and y.
Now, let's consider the given statement:
If x and y are linearly independent, it means that neither x nor y can be expressed as a linear combination of the other. However, it is given that z is in the Span\({x, y}.\)

This means that z can be expressed as a linear combination of x and y:
\(z = ax + by\), where a and b are scalar constants.
Let's analyze the set\({x, y, z}\). We know that z can be expressed as a linear combination of x and y, as shown above. This implies that the set \({x, y, z}\)is linearly dependent, because one vector (z) can be expressed as a linear combination of the others \((x and y)\).

Thus, the statement is true: If x and y are linearly independent, and if z is in Span\({x, y}\), then\({x, y, z}\) is linearly dependent.

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The correct answer is 4 km per hour Lashonda would swim if there were no current.

Here, we'll suppose that Lashonda is moving at x km/hr. in the absence of any current.

Speed of the current is 2 km/hr.

Distance swim against current is 5km

Time taken to swim against current is  5 ÷ (x - 2)

Distance swim with current is 15km

Time is taken to swim with current is 15 ÷ (x + 2)

Now,

Given that  if the time taken in both instances are the same, So, the equation will be 5 ÷ (x - 2) = 15 ÷ (x + 2)

After solving for x we will be solving;

⇒ 5 ÷ (x + 2) = 15 ÷ (x - 2)

⇒ 5x + 10 = 15x - 30

⇒ 10 + 30 = 15x - 5x

⇒ 40 = 10x

⇒ x= 40 ÷ 10 = 4 km per hour

Hence, 4 km per hour Lashonda would swim if there were no current.

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