c) Mrs. Chamling earns Rs 6,000 in a week. She spends Rs 250 for food Rs 75 for transportation everyday. (i) Write a mathematical expression to show this information. (ii) How much money does she save in a week? Cl LC and she divided the In this way, whole prime and compos of numbers, set of are the subset of 3.2 Prime and Prime numbe​

Answers

Answer 1

(i) The mathematical expression to show Mrs. Chamling's earnings and expenses can be written as:

Weekly earnings = Rs 6,000

Daily food expenses = Rs 250

Daily transportation expenses = Rs 75

Total weekly expenses = (Rs 250 + Rs 75) x 7 = Rs 2,275

Total weekly savings = Weekly earnings - Total weekly expenses

= Rs 6,000 - Rs 2,275

= Rs 3,725

(ii) Mrs. Chamling saves Rs 3,725 in a week.

As for the second part of the question, I am not sure what is being asked. The sentence is incomplete and unclear. Please provide more information or context so I can assist you better.


Related Questions

................................................

Answers

Answer:

4,12,36,108,324.....

Step-by-step explanation:

The sequence represented by the equation [tex]a=4(3)^{n-1}[/tex]is a geometric sequence with first term 5 and common ratio 3. The first 4 terms of the sequence are:

[tex]a_1 = 4(3)^{1-1} =4(3)^0 = 4[/tex]

[tex]a_2 =4(3)^{2-1} = 4(3)^1 = 12[/tex]

[tex]a_3 =4(3)^{3-1} = 4(3)^2 = 36[/tex]

[tex]a_4 = 4(3)^{4-1} =4(3)^3 = 108[/tex]

[tex]a_5=4(3)^{5-1} =4(3)^4=324[/tex]

The sequence can be written as:

[tex]a_n = 4(3)^{n-1}[/tex]

where n is the term number.

Therefore, the sequence is 4,12,36,108,324.....

Answer:

The answer is 4,12,36,108,324

Step-by-step Explanation:

a1=4(3)¹‐¹=4(3)⁰=4

a2=4(3)²‐¹=4×3=12

a3=4(3)³‐¹=4(3)²=4×9=36

a4=4(3)⁴‐¹=4(3)³=4×27=108

a5=4(3)⁵‐¹=4(3)⁴=4×81=324

Darlene purchases $20,000 worth of stock on her brokers advice and pays her broker a 1.5% broker fee

Answers

Darlene's net proceeds from the investment into shares would be $ 8, 279 .

How to find the net proceeds ?

First, find the initial broker fee:

=  Initial investment × Broker fee rate

= 20, 000 x 1. 5 %

= 20, 000 x 0. 15

= $ 300

The total fees incurred to buy and sell are:

= 300 initial broker + 21 later broker

= $ 321

The net proceeds would then be:

= Final value of stock - Initial investment - Total fees

= 28, 600 - 20, 000 - 321

= 8, 600 - 321

= $ 8, 279

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Full question is:

Darlene purchases $20,000 worth of stock on her brokers advice and pays her broker a 1.5% broker fee. She sells her stock when it increases to $ 28,600  two years later, and uses a discount broker who charges $21 per trade. Compute Darlene's net proceeds after the broker fees are taken out.

lim[tex]\frac{n^{2} +4n-5}{3n^{3}+n^{2}+7 }[/tex]

Answers

Step-by-step explanation:

limit for n going to what ?

I think you mean n going to ±infinity.

for very large n (when n goes to infinity) such a fraction is reduced to the ratio of the terms with the highest exponents of n. the terms with lower exponents simply get less and less impact with growing n, and fade away for really, really large n going to infinity.

so, this limit evaluation is reduced to

lim n²/(3n³ + n²) = 1/(3n + 1)

which is again for very large n

lim 1/(3n), which goes to 1/infinity = 0

the same for going to 1/-infinity = 0

if you meant e.g. limit for n going to 0, then for the limit we set n to 0 and see, that all terms are turning 0, except for the constants -5 in the numerator and +7 in the denominator.

so, that limit is then

-5/7 = -0.714285714...

The algebraic expression below is a polynomial. x-1^k, where k is a real number

Answers

Answer: True

Step-by-step explanation:

17 in. 16 in. 14 in.​

Answers

The surface area of the rectangular prism is 1468 square inches

What is the surface area of the rectangular prism?

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

17 in by 16 in by 14 in

The surface area of the rectangular prism is calculated as

Area = 2 * (17 * 16 + 17 * 14 + 16 * 14)

Evaluate

Area = 1468

Hence, the area is 1468 square inches

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Question

What is the surface area of this rectangular prism?

17 in. by 16 in. by 14 in.​

Pls Need this ASAP
When purchasing a home, you need a loan for $80,000. The interest rate of the
loan is 8% and you are required to make monthly payment of $587.

Answers

Answer:

1) 5m

2) 0.25tan

Step-by-step explanation:

During the winter, if the low temperature outside is a °C, the daily cost to heat a
building can be determined using the function f(x) = 5 (1.3) * . Find and
interpret the given function values and determine an appropriate domain for the function.
round all function values to the nearest hundredth.
f:7)= __, meaning when the low temp outside is __ celsius it would cost $__ to heat the building. this interpretation _______________ in the context of your problem.
f(9.5)=___, meaning when the low temp outside is ___ celsius it would cost & __ to heat the building. this interpretation _______________ in the context of the problem.
based on the observations above it is clear that an appropriate domain for the function is —————
PLEASE HELP

Answers

The values of the function are 5 and 1.5 and the domain is,

⇒ - ∞ < x < ∞

Here, The equation of the function is given as

f(x) = 5 (1.3)ˣ

The above function is an exponential function.

An exponential function is represented as

f(x) = abˣ

Where

a represents the initial value, b represents the rate of growth or decay

While x and f(x) are the input and output values

Hence, By comparison, we have

a = 5 and b = 1.3

This means that the function values are 5 and 1.3.

Since, the function is an exponential function.

The domain of an exponential function is the set of all real values

Hence, the domain of f(x) is the set of all real values.

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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

Answers

From the relationship of AC bar ≅ BD bar, we can tell that ABCD is a rectangle.

How is this a rectangle ?

A quadrilateral with two sets of parallel sides is known as a parallelogram.

If ABCD is a parallelogram where AC and BD have equal lengths, then the opposite sides of ABCD are also equal. ABCD has two sets of sides that are parallel and have the same length.

The fact that ABCD possesses two sets of sides that are parallel and of equal length logically leads to the conclusion that it also has four angles that are right. One reason for this is that the angles opposite each other in a parallelogram are of equal measure, while the sum of the angles at each corner of a parallelogram is always 180 degrees.Therefore, ABCD is a rectangle.

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e
B
0
14. The table shows the number of inches of
rain over five months. What would be an
appropriate display of the data? Explain.
(Lesson 2)
Month
Number
of Inches
of Rain
Jan. Feb. Mar.
1.5
2.2
3.6
Apr.
5.3
May
4.8

Answers

The graph of the given function is attached.

Given is a function for the rainfall in 5 months in inches.

We need to display the data,

So, as we can see that the data is not showing any proportion or pattern,

So, it can be displayed as a line chart.

Hence the chart is attached for the function.

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Cameron surveyed her friends about the number of apps they use. The responses were 15, 16, 18, 9, 18, 4, 19, 20, 17, and 36 apps. Use the range and interquartile range to describe how the data vary.

Answers

The middle half of the data values vary by:

Interquartile = [tex]Q_3-Q_1[/tex] =>  19.25 - 13.5 = 5.25

The given data is :

15, 16, 18, 9, 18, 4, 19, 20, 17, and 36 apps.

We have to find:

Use the range and interquartile range to describe how the data vary.

We have to arrange the data from smallest to largest.

4, 9, 15, 16, 17, 18, 18, 19, 20, 36

Range of the data is : Highest no. - lowest no.

Range of the data is: 36 - 4 = 32

The location of the [tex]Q_1[/tex] = (n + 1) × 0.25 (where n is the total no. in the data)

The location of the [tex]Q_1[/tex] = (10 + 1)  × 0.25 = 11  × 0.25 = 2.75

∴[tex]Q_1[/tex] = 15 × 0.75 + 9 × 0.25  = 13.5

The location of the [tex]Q_3[/tex] = (n + 1) × 0.75

The location of the [tex]Q_3[/tex] = 11 × 0.75 = 8.75

∴[tex]Q_3[/tex] = 19 × 0.75 + 20 × 0.25 = 19.25

Hence, The middle half of the data values vary by:

Interquartile = [tex]Q_3-Q_1[/tex] =>  19.25 - 13.5 = 5.25

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Tell whether the given value is a solution to the inequality.

y + 5 > 8l; y = 1

Answers

The solution of the inequality equation is determined as y > 3.

What is the solution of the inequality equation?

A solution for an inequality in y is a number such that when we substitute that number for y we have a true statement.

For the given inequality equation, which is;

y + 5 > 8

The solution of the inequality equation is calculated as follows;

y + 5 > 8

Subtract 5 from both sides of the equation as shown below;

y + 5 - 5 > 8 - 5

y > 3

The solution of the inequality equation is determined as 3, so we can conclude that any value less than  3 is not true and the proposed solution of 1 is not true or correct for the inequality equation.

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What is the value of x?

Answers

Solving a simple equation, we can see that x = 35.

How to find the value of x?

The 3 lines with an arrow that go to the left are parallel lines, thus, the relation between the sets of values in each of the sides must be the same ones.

Then we can take the quotients between the respective values, and these quotients must be equal, so we can write:

30/12 = x/14

And now we can solve that equation for x, we will get:

x = 14*(30/12)

x = 35

That is the value of x.

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A telephone pole is 54 feet tall. A guy wire runs 83 feet, from point A at the top of the telephone pole, to the ground at point B. The base of the telephone pole is at point C. Triangle ABC is a right triangle.

How far from the base of the telephone pole, to the nearest tenth of a foot, is the guy wire secured to the ground at point B?

Answers

Okay, let's break this down step-by-step:

* The telephone pole is 54 feet tall

* The guy wire runs 83 feet from point A (top of pole) to point B (ground)

* So the hypotenuse (AB) of the right triangle is 83 feet

* The opposite side (AC) is 54 feet (height of pole)

To find the adjacent side (BC), we use the Pythagorean theorem:

a^2 + b^2 = c^2

54^2 + BC^2 = 83^2

Solving for BC gives:

BC = sqrt(83^2 - 54^2) = sqrt(1296 - 2916) = sqrt(1620) = 40 feet

So the guy wire is secured 40 feet from the base of the telephone pole.

Rounded to the nearest tenth is 40.0 feet.

Therefore, the final answer is:

40.0

Let me know if you have any other questions!

b) tan 2A cot A-1 = sec 2A

Answers

The trigonometric equation is tan 2A cot A-1 = sec 2A

We have to prove the trigonometric equation

tan 2A cot A-1 = sec 2A

Now let us take LHS

tan 2A cot A-1  

2tanA/1-tan²A - 1 . cotA - 1

2-1+tan²A/1-tan²A

1+tan²A/1-tan²A

sec2A

Hence, the trigonometric equation is tan 2A cot A-1 = sec 2A

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Will give you brainly! :) Thank you for taking time out of your day to answer this!​

Answers

The probability values are P(30 ≤ Amount ≤ 59) = 0.43, P(Amount ≥ 60 or Amount < 30) = 0.57 and P(Amount ≥ 40) = 0.45

Calculating the probability values

At least $30 but not more than $59

This means that we use the money spent from 30 to 59

So, we have

30 to 59 = 76 + 58 + 67

30 to 59 = 201

Total = 85 + 98 + 201 + 84

Total = 468

Next, we have

P(30 ≤ Amount ≤ 59) = 201/468

P(30 ≤ Amount ≤ 59) = 0.43

At least $60 or less than $30

This means that we use the money spent less than 30 and greater than or equal to 60

So, we have

At least $60 or less than $30 = 84 + 85 + 98

At least $60 or less than $30 = 267

Next, we have

P(Amount ≥ 60 or Amount < 30) = 267/468

P(Amount ≥ 60 or Amount < 30) = 0.57

At least $40

This means that we use the money spent greater than or equal to 40

So, we have

At least $40 = 58 + 67 + 84

At least $40 = 209

Next, we have

P(Amount ≥ 40) = 209/468

P(Amount ≥ 40) = 0.45

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5. [0.5/1 Points] DETAILS PREVIOUS ANSWERS SALGTRIG4 7.3.112.
A rectangle is to be inscribed in a semicircle of radius 4 cm as shown in the following figure.
10
4 cm-
(a) Find the function that models the area of the rectangle.
A(0) = 16 sin (20)
Need Help? Read It
MY NOTES
4
ASK YOUR TEACHER
(b) Find the largest possible area for such an inscribed rectangle. [Hint: Use the fact that sin(u) achieves its maximum value at u=/2.]
16
cm²
(c) Find the dimensions of the inscribed rectangle with the largest possible area. (Round your answers to two decimal places.)
smaller dimension 2
x cm
larger dimension 25
x cm
PR.

Answers

The Area function [tex]A(x) = 2x * \sqrt(16 - x^2).[/tex]

How to solve

(a) For a rectangle inscribed in a semicircle of radius 4 cm, let half-length be x and height be y.

Therefore, the Area function [tex]A(x) = 2x * \sqrt(16 - x^2).[/tex]

(b) Maximum area occurs when x = [tex]4 * sin(\pi/4), so A(4 * sin(\pi/4)) = 16 cm^2.[/tex]

(c) Dimensions for the largest inscribed rectangle are smaller dimension (height) ≈ of 2.83 cm, a larger dimension (base) ≈ of 5.66 cm.

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A researcher performed an experiment with two groups. She found the difference of the means for each group. Then
she combined the groups, chose two new groups, and found the difference between the means of those groups. She
repeated this process 200 times. The normal distribution of the difference in the means she found is given below. How
great would the difference in means between the first two groups have to be in order to be considered significant?
At least 8
O At least 10
At least 9
At least 7

Answers

Answer:

Step-by-step explanation:

To determine the significance level for the difference in means between the first two groups, we need to refer to the provided normal distribution. However, you haven't provided the details or parameters of the normal distribution, such as the mean and standard deviation. Without this information, it is not possible to determine the exact significance level required.

In hypothesis testing, the significance level, typically denoted as α (alpha), is chosen by the researcher before conducting the experiment. It represents the threshold at which the researcher considers the results to be statistically significant. Commonly used significance levels are 0.05 (5%) or 0.01 (1%).

Please provide the necessary parameters or more information about the normal distribution to determine the specific significance level for the difference in means between the first two groups.

3.3.4√20+5-43 calculate ​

Answers

Here are the steps to calculate the expression √20 + 5 - 43 :

Step 1: Simplify the square root of 20:

[tex]\sqrt{20}[/tex]

Step 2: Calculate the value of the square root:

[tex]\sqrt{20} = 2\sqrt{5}[/tex]

Step 3: Substitute the value of the square root into the expression:

[tex]2\sqrt{5} + 5 - 43[/tex]

Step 4: Perform addition:

[tex]2\sqrt{5} + 5 = 2\sqrt{5} + \frac{5}{1} = \frac{2\sqrt{5} + 5}{1}[/tex]

Step 5: Perform subtraction:

[tex]\frac{2\sqrt{5} + 5}{1} - 43 = \frac{2\sqrt{5} + 5 - 43}{1}[/tex]

Step 6: Simplify the numerator:

[tex]\frac{2\sqrt{5} - 38}{1}[/tex]

Step 7: Simplify the expression:

[tex]2\sqrt{5} - 38[/tex]

Therefore, the calculation √20 + 5 - 43 simplifies to 2√5 - 38.

Find area of the shape

Answers

Answer:

130.4

Step-by-step explanation:

6 x 14 = 84

8 x 4 = 32

(4 x 7.2)/2 = 14.4

-49 = 7i, what number is the i.

Answers

Answer:

-7

Step-by-step explanation:

divide by 7 on both sides and you get i = -7

A popular brand has introduced a new design of jeans. All major stores have stocked the jeans because the brand usually sells very well. But the cost of these jeans is much higher than those of other brands, so people don't buy them.

Answers

The price of the jeans will decrease because supply is greater than demand hence the stores will sell them at discounted prices.

How do we calculate?

The store owners would be forced to cut pricing if the jeans weren't purchased at all or as frequently as the other brands. Either they choose that choice, return the goods if possible  or just toss the jeans away. It generally takes some trial and error to determine the proper price.

For instance, the owner may lower the price to $75 and test whether the 25% discount works or not if the jeans initially sell for $100 and nobody buys them for a week.

The price might remain there if people continue to buy and if not, the cost might decrease even further.

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HELP ASAP PLEASE

LATE ASSIGNMENT

Answers

The measure of angle ABC is given as follows:

m < ABC = 55º.

How to obtain the measure of angle ABC?

First we look to the exterior angle of angle C in the bottom parallel line, as a ray is formed, hence the missing angle measure is given as follows:

50 + 75 + x = 180

125 + x = 180

x = 55º.

The exterior angle relative to angle B is supplementary with the angle of 55º, as they are consecutive angles, hence it’s measure is obtained as follows:

y + 55º = 180

y = 125º.

By the exterior angle theorem, an interior angle is supplementary with it’s respective exterior angle, hence the measure of angle ABC is given as follows:

m < ABC + 125 = 180

m < ABC = 55º.

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Find the Value of x. Round to the nearest tenth.

hyp = x
28°
11​

Answers

The calculated value of x in the right triangle is 12.5

How to calculate the value of x

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

The right triangle

The value of x can be calculated using the following cosine rule

So, we have

cos(28) = 11/x

make x the subject of the formula

So, we have

x = 11/cos(28)

Evaluate the quotient

This gives

x = 12.5

Hence, the value of x is 12.5

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Please help due 5 min!!!!

Answers

The midsegments of a trapezoid is parallel to each base, and its length is one-half the sum of the lengths of the bases

The weight (in kilograms) of 14 patients were measured as 59, 63, 61, 62, 58, 60, 58, 57, 57, 56, 50, 69, 58 and 50. What is the range weight (in kilograms) of these patients?

Answers

Answer:

57 kilograms. .........................................................................kg

The length and breadth of a rectangular flower bed are 16m and 9 m, respectively. How many plants can be planted in it, if each plant requires a space of 1.2m x 1m?​

Answers

The calculated number of plants the flower bed can contain is 120

Calculating hw many plants can be planted in it

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

Dimensions = 16 m by 9 m

So, the area of the flower bed is

Area = 16 * 9

Evaluate

Area =  144

Also, we have

Each plant requires a space of 1.2m x 1m?

This means that

Plant area = 1.2 * 1

Plant area = 1.2

So, we have

Plants = 144/1.2

Evaluate

Plants = 120

Hence, the number of plants is 120

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Answer:

Step-by-step explanation:

To calculate the number of plants that can be planted in the rectangular flower bed, we need to calculate the area of the flower bed and divide it by the space required for each plant.

The area of the flower bed is calculated by multiplying its length and breadth.

So, the area of the flower bed is 16m x 9m = 144 sq.m.

Each plant requires a space of 1.2m x 1m = 1.2 sq.m.

Therefore, the number of plants that can be planted in the flower bed is:

144 sq.m. ÷ 1.2 sq.m./plant = 120 plants.

So, you can plant 120 plants in the rectangular flower bed.

50 Points! Multiple choice geometry question. Photo attached. Thank you!

Answers

Answer:

5/4 = h/44, so h = 55

The height of the tree is 55 feet.

D is correct.

What are the solutions of the equation 2 log x = log (5x-6)? Select all that apply.
A x=1
B. x=2
C. x= 3
D. x = 5
E. x=6

Answers

Answer:

B, C

Step-by-step explanation:

x^2 = 5x - 6

x = 2 or x = 3

solve for v, PV/T=pv/t

Answers

No matter the values of P, V, T, p, and t, as long as the equation PV/T = pv/t holds true, the solution for v is always equal to V.

To solve for v in the equation PV/T = pv/t, we can manipulate the equation to isolate v on one side.

Starting with the given equation:

PV/T = pv/t

To isolate v, we can cross-multiply:

PVt = pVt

Next, we divide both sides of the equation by pt:

V = v

Therefore, the solution is v = V.

In other words, v is equal to V, which means they represent the same values.

This implies that v and V are interchangeable and can be used interchangeably in the equation.

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Identify the sequence graphed below and the average rate of change from n = 1 to n = 3.

coordinate plane showing the points 2, 10, point 3, 5, point 4, 2.5, and point 5, 1.25

a
an = 20(one half)n − 1; average rate of change is fifteen halves

b
an = 10(one half)n − 1; average rate of change is fifteen halves

c
an = 20(one half)n − 1; average rate of change is negative fifteen halves

d
an = 10(one half)n − 1; average rate of change is negative fifteen halves

Answers

The sequence based on the information would be: B. an = [tex]10 1/2^{-1}[/tex]average rate of change is negative fifteen halves.

How to explain the function

This question is about exponent function/series. You are given 3 points from the function, point A (1,10), point B( 2, 5), and point  C(4,1.25).  

If you insert point A to the function, an will give a result of 10 for n=1.

For n=0, the result would be:

an= 10([tex]1/2^{-1}[/tex])

= 10 * 2

= 20

Then the average rate of change from n=0 to n=2 would be:

Rate of change= (y₂ -y₁)/ (x₂ -x₁)

Rate of change= (5-20)/ (2-0)

= -15/2

= negative fifteen halves

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based on usda regulations. not more than ____ percent of calories should come from saturated fats I. When does the development of a child's nervous system begin? *1 pointa month after fertilizationas soon as fertilizationsecond week after fertilizationthird week after fertilization2. Homeostasis is better understood as the_____. *1 pointbalance of flow in the substances that sustain lifeexchange of substances that sustain lifeoverall functions of life in the wombenergy flow within the embryo3. What does regulation mean? *1 pointTo adjust something so that it works correctly as requiredTo control or direct something by rulesTo allow passage of air, gas, etc. To make something to go faster or slower. 4. Which part of the brain handles the incoming and outgoing messages? *1 pointcerebrumcerebellumhypothalamusthalamus5. Which among the protective measures of the nervous system serves a cushion to minimize damage? *1 pointbonestissuescerebrospinal fluidmeningesTRUE or FALSE1. Neurons travel through synapses in order to pass on information. *1 pointTrueFalse2. When we are out on a jog, it is our somatic nervous system that is controlling our jogging movement. *1 pointTrueFalse3. The nervous system is made up of these three major parts: the brain spinal cord, and nerves. *1 pointTrueFalse4. When the blood sugar level is too high, the body performs negative feedback by producing more glucagon. *1 pointTrueFalse5. The dendrite is the protective layer around the body of a neuron. *1 pointTrueFalse what was important about the election of 1856 a positive pressure gas valve, 1/2 inch in size minimum cv is what? Use the tabulated half-cell potentials to calculate the equilibrium constant (K) for the following balanced redox reaction at 25C. Can you please show each step 3I2 (s) + 2Fe (s) ---> 2Fe3+ (aq) + 6I- (aq) Determine the longitudinal modulus E1 and the longitudinal tensile strength F1t of a unidirectional carbon/epoxy composite with the propertiesVf=0.65E1f=235 GPa (34 Msi)Em=4.14 GPa (0.6 Msi)Fft = 3450 MPa (500 ksi)Fmt = 104 MPa (15 ksi) Using the Taylor rule, calculate the target for the federal funds rate for July 2010 using the following information: Equilibrium real federal funds rate 3% Target inflation rate 2% Current inflation rate 0.9% output gap -8% The target for the federal funds rate for July 2010 is ____%. How did Japanese conquests in East Asia compare to European and American conquests in Asia and Africa? a. Both denied their subjects political equality because of perceived racial inferiority. b. Both paired industrialized militaries with proselytism to conquer new territories. c. The Japanese claimed that conquered territories historically belonged to it, and Europeans and Americans did not. d. Europeans and Americans encountered local resistance to colonialism, and the Japanese did not. A Stone of Mass 5g was lowered into a solution of turpentine of relative density 1. 6. Lf the relative density of a Stone is 2. 0. Calculate the mass in kilograms of the turpentine displaced by a Stone. You walk along the outside of a park starting at point P to point Q. You then take a shortcut back to point P, represented by PQ on the graph. What happened at Little Rock Central High School in response to the decision? There are two wooden sticks of lengths A and B respectively. Each of them can be cut into shorter sticks of integer lengths. Our goal is to construct the largest possible square. In order to do this, we want to cut the sticks in such a way as to achieve four sticks of the same length (note that there can be some leftover pieces). What is the longest side of square that we can achieve? Write a function: class Solution { public int solution(int A, int B ) ; }that, given two integers A,B, returns the side length of the largest square that we can obtain. If it is not possible to create any square, the function should return 0 . Examples: 1. Given A=10,B=21, the function should return 7. We can split the second stick into three sticks of length 7 and shorten the first stick by 3 . 2. Given A=13,B=11, the function should return 5 . We can cut two sticks of length 5 from each of the given sticks. 3. Given A=2,B=1, the function should return 0 . It is not possible to make any square from the given sticks. 4. Given A=1,B=8, the function should return 2 . We can cut stick B into four parts. Write an efficient algorithm for the following assumptions:- A and B are integers within the range [1..1,000,000,000]. Consider the furan-maleic anhydride Diels-Alder adduct. The melting point for the endo-Diels-Alder adduct of furan and maleic anhydride is reported to be 70C. The melting point for the exo-Diels- Alder adduct is reported to be 110C.a. What isomer is obtained in the synthesis?b. Mp of product = _____c. Is the Product ENDO or EXO? (circle one).d. Considering that formation of the endo-adduct is kinetically favored in Diels-Alder reactions, how is the result explained? when a product is in the maturity stage, the company should most likely consider The following are the populations for the top twelve largest cities in the U. S. New York City, NY: 8,336,817 Los angeles CA: 979.576 Chicago, il:2,693,976 Houston, TX: 2,320,268 Phoenix AZ: 1,680,992 Philadelphia PA: 1,584,064 San Antonio TX: 1, 547,253 San Diego CA: 1,423,851 Dallas TX: 1,343,573 San Jose CA: 1,021,795 Austin TX:978,908 Jacksonville FL: 911,507. What is the mean population?, what is the median population?, what is the mode?, what is range?, what is the standard Deviation? A mother sees that her child's contact lens prescription is 1.75 D. > A What is the child's near point, in centimeters? Assume the near point for normal human vision is 25.0 cm. NP= hardy and weinberg derived their famous equation by extending mendel's first law, which is called the law of This method changes the capacity of the underlying storage for the array elements. It does not change values or order of any elements currently stored in the dynamic array. It is intended to be an "internal" method of the Dynamic Array class, called by other class methods such as append(), remove_at_index(), insert_at_index() to manage the capacity of the underlying storage data structure. Method should only accept positive integers for new_capacity. Additionally, new_capacity can not be smaller than the number of elements currently stored in the dynamic array (which is tracked by the self.size variable). If new_capacity is not a positive integer or if new_capacity < self.size, this method should not do any work and just exit.#Starter Codeclass DynamicArrayException(Exception):"""Custom exception class to be used by Dynamic ArrayDO NOT CHANGE THIS METHOD IN ANY WAY"""passclass DynamicArray:def __init__(self, start_array=None):"""Initialize new dynamic arrayDO NOT CHANGE THIS METHOD IN ANY WAY"""self.size = 0self.capacity = 4self.data = [None] * self.capacity# populate dynamic array with initial values (if provided)# before using this feature, implement append() methodif start_array is not None:for value in start_array:self.append(value)def __str__(self) -> str:"""Return content of dynamic array in human-readable formDO NOT CHANGE THIS METHOD IN ANY WAY"""out = "DYN_ARR Size/Cap: "out += str(self.size) + "/"+ str(self.capacity)out += " " + str(self.data[:self.size])return outdef resize(self, new_capacity: int) -> None:"""TODO: Write this implementation"""returndef append(self, value: object) -> None:"""TODO: Write this implementation"""if self.sizeself.data[self.size]=valueself.size+=1else:temp=[None] * self.capacitytsize=self.capacityfor i in range(tsize):temp[i] = self.data[i]self.capacity *= 2self.size = 0self.data = [None] * self.capacityfor i in range(tsize):self.append(temp[i])self.append(value)self.size = 0self.data = [None] * self.capacityfor i in range(tsize):self.append(temp[i])self.append(value)#returnA few examples of how the method might be used:Example #1:da = DynamicArray()print(da.size, da.capacity, da.data)da.resize(10)print(da.size, da.capacity, da.data)da.resize(2)print(da.size, da.capacity, da.data)da.resize(0)print(da.size, da.capacity, da.data)Output:0 4 [None, None, None, None]0 10 [None, None, None, None, None, None, None, None, None, None]0 2 [None, None]0 2 [None, None]NOTE: Example 2 below will not work properly until after append() method is implemented.Example #2:da = DynamicArray([1, 2, 3, 4, 5, 6, 7, 8])print(da)da.resize(20)print(da)da.resize(4)print(da)Output:DYN_ARR Size/Cap: 8/8 [1, 2, 3, 4, 5, 6, 7, 8]DYN_ARR Size/Cap: 8/20 [1, 2, 3, 4, 5, 6, 7, 8]DYN_ARR Size/Cap: 8/20 [1, 2, 3, 4, 5, 6, 7, 8] the equilibrium constant, kc, for this process is 326 at a certain temperature. if the initial concentration of br2 = i2 is 0.619 m, what is the equilibrium concentration of ibr in m? list the four basic types of human societies in order from least to most complex.