amit deposited Rs.5000 in a bank which pays 8% per annum interest deposit . how much interest will he get at the end of 4 years also find the amount​

Step-by-step explanation:

the answer is 10x +100 = 250

The total force on the bottom of the swimming pool is 3.35 × 10⁶ N.

The total force on the bottom of a swimming pool can be calculated by using the formula: F = pA, where F is the force, p is the pressure, and A is the area of the bottom of the pool.

First, we need to calculate the area of the bottom of the pool:
A = 28.5 m × 7.5 m = 213.75 m²

Next, we need to calculate the pressure on the bottom of the pool. The pressure is equal to the weight of the water above the bottom of the pool, which can be calculated by multiplying the density of water (ρ), the acceleration due to gravity (g), and the height of the water (h):
p = ρgh = (1000 kg/m³)(9.8 m/s²)(1.6 m) = 15680 N/m²

Finally, we can calculate the total force on the bottom of the pool by multiplying the pressure and the area:
F = pA = (15680 N/m²)(213.75 m²) = 3.35 × 10⁶ N

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To find the function values, we need to substitute the given values of x into the function:

a) f(2) = 95(0.84)^2 ≈ 66.96

This means that after 2 hours, there are approximately 66.96 milligrams of medicine remaining in the person's bloodstream.

b) f(6) = 95(0.84)^6 ≈ 35.33

This means that after 6 hours, there are approximately 35.33 milligrams of medicine remaining in the person's bloodstream.

To determine an appropriate domain for the function, we need to consider the context of the problem. The function represents the amount of medicine remaining in a person's bloodstream after taking a dose of medication, so the domain should be the set of non-negative real numbers, since the amount of medicine cannot be negative and time cannot be negative. Therefore, an appropriate domain for the function is [0, ∞).

Interpretation: The function f(x) = 95(0.84)^x models the amount of medicine, in milligrams, remaining in a person's bloodstream after x hours of taking the medication. For example, after 2 hours, there are approximately 66.96 milligrams of medicine remaining in the person's bloodstream.

After taking a dose of medication, the amount of medicine remaining in a person's bloodstream, in milligrams, after x hours can be modeled by the function

To find:

Interpret the given function values and determine an appropriate domain for the function.

Solution:

The general form of an exponential function is

Where, a is the initial value, 0<b<1 is decay factor and b>1 is growth factor.

We have,

Here, 110 is the initial value and 0.83 is the decay factor.

It means, the amount of medicine in the person's bloodstream after taking the dose is 110 milligrams and the amount of medicine decreasing in the person's bloodstream with the decay factor 0.83 or decreasing at the rate of (1-0.83)=0.17=17%.

We know that an exponential function is defined for all real values of x but the time cannot be negative. So, x must be non negative.

We know that  for any value of x. So,  for all values of x.

Therefore, domain of the function is  and the range is .

Hope this helps!!!

GTPex-

Answer:  The cost of the 7.5 lbs of walnuts be $2.16 . It costs $3.45 to buy lb of chopped walnuts.

Answer:

$34.50

Step-by-step explanation:

First, find how much 1 lb costs.

To do this divide 3.45 by 3 to get 1/4 lb and then multiply by 4 to get the cost of 1 lb.

3.45/3 = 1.15      1.15 x 4 = 4.60

So 1 lb is $4.60

Multiply the cost of 1 lb by 7.5 to find the cost for 7.5 lbs

$4.60 x 7.5 = $34.50

Hope this helps!

The -value of the test is 1.90. This indicates that the mean processing time is significantly greater than 5.5 hours, supporting the manufacturer's desire to set a standard time required by employees to complete a certain process

The t-value will be equal to 1.39 for the given statistics.

To test if the mean processing time exceeds 5.5 hours, we can use a one-sample t-test.

The null hypothesis is that the mean processing time is less than or equal to 5.5 hours:

H0: µ ≤ 5.5

The alternative hypothesis is that the mean processing time is greater than 5.5 hours:

Ha: µ > 5.5

We will use a significance level of 0.05.

The formula for the t-test statistic is:

t = (X - µ) / (s / √n)

Where:

X = sample mean

µ = hypothesized population mean

s = sample standard deviation

n = sample size

Substituting the given values, we get:

t = (6 - 5.5) / (2 / √21) = 1.386

The degree of freedom for the t-test is n-1 = 20.

Using a t-table or calculator, the p-value associated with a t-value of 1.386 and 20 degrees of freedom is 0.093.

Since the p-value (0.093) is greater than the significance level (0.05), we fail to reject the null hypothesis. Therefore, there is not enough evidence to suggest that the mean processing time exceeds 5.5 hours.

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Answer:

The time of fall is 9 seconds

Step-by-step explanation:

We are asked to find the time between when the penny was dropped and when it landed.

To do this, we have to start with what we are given and see how we can relate it to find what we are looking for.

From the problem, we are given the equation which represents the height which the penny travels as it falls. It is given by

\(h(t) = 16t^2 - 144.\) ----------- equation 1

in addition to that, we are also given that h = 144ft at the end of the fall; that is, where t = t max, and h = hmax

Hence, it is safe to say that at the end of the fall, that the heigh is no more changing. This means that dh/dt = 0

We can now differentiate equation 1 above to get

h max  = 16t - 0 ------------- equation 2

recall that h max = 144

plugging the value of h max into equation 2, we have

144 = 16t

t = 9 seconds

Therefore the time of fall is 9 seconds

Answer:

t= 3 seconds

Step-by-step explanation:

I took the quiz and this is the answer

Answer:

8/10

Step-by-step explanation:

add the numerator but keep the denominators the same

you could also simplify to 4/5

Answer:

2/10 + 6/10

= 8/10

=4/5

Therefore the answer is 4/5

If Debra has 1152 ft of wallpaper, she can cover 8 boxes shaped like rectangular prisms with lengths, widths, and heights of 6, 6, and 3 respectively. This can be found by calculating area of the prism.

To calculate the total area of each box, we need to find the area of each side and add them up. Since there are six sides to a rectangular prism, we have:

2 sides with length 6 and height 3

2 sides with width 6 and height 3

2 sides with length 6 and width 6

The area of each side is the product of its length and width. So the total area of each box is:

2(6 x 3) + 2(6 x 3) + 2(6 x 6)

= 36 + 36 + 72

= 144 sq ft

Therefore, each box requires 144 square feet of wallpaper to cover all its sides.

If Debra has a total of 1152 square feet of wallpaper, she can cover:

1152 / 144 = 8 boxes.

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Answer:

b gang

Step-by-step explanation:

Answer:

37

Step-by-step explanation:

Add all the numbers up and you will get 370. How many numbers are there in total? 10 right so you divide 370 with 10 and get 37.

hope this help

The statements that are true include the following:

B. Both graphs are exponential function.

C. Both graphs have exactly one asymptote.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x) = a(b)^x\)

Where:

In Mathematics and Geometry, a horizontal asymptote is a horizontal line (y = b) where the graph of a function approaches the line as the input values (domain or independent value) approach negative infinity (-∞) to positive infinity (∞).

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Answer:

5

Step-by-step explanation:

slopes of the parallel lines are always same this line has slope five

because equation in y intercept form is y=mx+b

where m is the slope.

so the slope of the new line will be five

The domain of the function is all real numbers, and the range is [0, 1] and [11, 21].

To find the domain and range of the function f(x) = 1 - dx² - x + 2, we can analyze its properties without graphing.

Domain:

The domain of a function consists of all the valid input values, or the values of x for which the function is defined. In this case, the only restriction we need to consider is the square root of a negative number.

In the given function, there are no square roots involved. Therefore, the function is defined for all real numbers. The domain is the set of all real numbers, which can be represented as (-∞, ∞).

Range:

The range of a function consists of all the possible output values, or the values that f(x) can take. To determine the range, we need to consider the behavior of the function as x approaches positive or negative infinity.

As x approaches positive or negative infinity, the dominant term in the function is -dx². If d is positive, as x gets larger, the term -dx² becomes more negative, approaching negative infinity. Similarly, if d is negative, as x gets larger, the term -dx² becomes more positive, approaching positive infinity.

Since the remaining terms in the function (1-x+2) are constants, they do not affect the behavior as x approaches infinity. Therefore, the range of the function depends on the value of d.

If d is positive, the range of the function is (-∞, 1+d). As x approaches negative infinity, the function approaches positive infinity, and as x approaches positive infinity, the function approaches 1+d.

If d is negative, the range of the function is (1+d, ∞). As x approaches negative infinity, the function approaches 1+d, and as x approaches positive infinity, the function approaches negative infinity.

Given that the range is [0, 1] & [11, 21], we can conclude that d is positive, and the range is [0, 1+d]. Since the range also includes [11, 21], we can infer that 1+d = 11, and solving for d gives d = 10.

Therefore, the domain of the function is (-∞, ∞), and the range is [0, 1] & [11, 21].

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Answer:

Step-by-step explanation:

The equation is y=7x

x      y          Calculation

5     35         y=7x, y=7*5, y=35

6     42         y=7x, y=7*6, y=42

7      49       y=7x, y=7*7, y=49

8     56          y=7x, y=7*8, y=56

The data in the table represent a direct variation

The equation is y = 5x

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

x  1 3 4 7

y 5 15 20 35

In the above table of values, we can see that

As the x values, the y values increase

This means that the table of values represent a direct variation

The equation is a direct variation

So, we have

y = kx

The value of k is calculated as

k = 5/1

So, we have

k = 5

This means that

y = 5x

Hence, the equation is y = 5x

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For equation (1), y' = xy + y, we can see that it is a linear differential equation since it is a first-order equation and the terms involving y and its derivatives have a power of 1.

For equation (2), y' = y^2(22+y^2), we can see that it is a Bernoulli differential equation since it is a first-order equation and the terms involving y and its derivatives have a power of 2.

To find the general solution of equation (2), we can use the following steps:

Divide both sides by y^2 to obtain y^(-2)y' = 22+y^2.

Substitute u = y^(-1) to obtain u' = -22u - 1.

Solve for u using separation of variables to obtain u = Ce^(-22x) - (x+D), where C and D are constants.

Substitute back y^(-1) for u to obtain the general solution y = (Cx+D)/(1-22xy), where C and D are constants.

Therefore, the general solution of equation (2) is y = (Cx+D)/(1-22xy), which is a rational function.

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If z is a standard normal variable, find P(z > 0.97). Round to four decimal places is option B: 0.1922.

To arrive at this answer, we first need to understand what a standard normal variable is. A standard normal variable is a random variable that has a normal distribution with a mean of 0 and a standard deviation of 1. This means that the distribution of values that the variable can take follows a bell-shaped curve, with most values being close to 0 and fewer values further away from 0 as we move towards the extremes.

In this case, we are asked to find the probability that the standard normal variable z is greater than 0.97. This means we are looking for the area under the bell-shaped curve to the right of 0.97.

We can use a table of standard normal probabilities, such as the Z-table, to find this probability. The Z-table provides the probability that a standard normal variable is less than or equal to a certain value. To find the probability that z is greater than 0.97, we need to subtract the probability that z is less than or equal to 0.97 from 1.

Looking up 0.97 in the Z-table, we find that the probability that z is less than or equal to 0.97 is 0.8340. Subtracting this value from 1, we get 0.1660. However, we need to round this value to four decimal places as per the instructions, which gives us 0.1660.

Therefore, the correct answer is not A or D, but B: 0.1922.

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\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)

Answer:

They are equal to one another

Step-by-step explanation:

1/2 is equal to .5, so id you have 6.5 on one side and 6.5 on the other, they are equal.

Answer: =

6 \(\frac{1}{2}\) = 50/100

=6.5

so 6.5 = 6 \(\frac{1}{2}\)

Answer: 165

Step-by-step explanation:

55 x 3 = 165

Answer:

2, 4

Step-by-step explanation:

m = multiple choice, s = short response

23m + 10s = 86, 28m + 5s = 76

Multiply the 2nd equation x 2 to make a variable the same amount

28m + 5s = 76, so 56m + 10s = 152

Now subtract the first equation

56m + 10s = 152

23m + 10s = 86

33m = 66

m = 2

If m = 2, and 23m + 10s = 86

23(2) + 10s = 86

46 + 10s = 86

10s = 40

s = 4

(1) The area of the trapezoid is 192 square meters.

(2) The area of the circle is A = 144π square cm or A ≈ 452 square cm.

(3) The circumference of the circle is C = 24π cm or C ≈ 75 cm.

(4) The perimeter of the figure is ≈ 110 cm.

(5) The area of the figure is 321 square meters.

The measurement that indicates the size of a region on a plane or curved surface is called the area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

(1)

The height of the trapezoid is 12m and the lengths of the parallel sides are 11m and 21 m.

The area of the trapezoid is:

A = (1/2)(11 + 21)(12)

A = 192 square meters.

(2)

The area of the circle with a radius of 12 cm is:

A = π(12)²

A = 144π

A ≈ 452 square cm.

(3)

The circumference of the circle with a radius of 12 cm is:

C = 2π(12)

C = 24π

C ≈ 75 cm

(4)

To find the perimeter of the figure, first, find the circumference of the semicircle,

The diameter of the semicircle is 30 - 12 = 18.

Therefore, the radius is 18/2 = 9 cm.

Hence, the perimeter of the figure is:

12 + 20 + 30 + 20 + π(9)

≈ 110 cm

(5)

To find the area of the figure, first, find the area of the large horizontal rectangle, then the upper triangular part, and then the lower rectangular part, and add them together.

The area of the large horizontal rectangle is:
(24 + 5) × 8

= 232

The area of the triangular portion is:

(1/2)×(24 + 5 -10 -10)×12

= 54

The area of the small rectangular part is:
5×7

=35

Now, add all the areas together to find the total area of the figure:

232 + 54 + 35

= 321

Hence, the area of the fifth figure is 321 square meters.

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Answer:

7 busses

Step-by-step explanation:

Answer:

Here ya go!

Step-by-step explanation:

(look at picture below

Main Answer:The points on the given curve where the tangent line is horizontal are (8, 0), (-8, π), (8, 2π), (-8, 3π), and so on and the Vertical tangent  are (0, π/2), (0, 3π/2), (0, 5π/2),so on.

Supporting Question and Answer:

How do we find points on a curve where the tangent line is horizontal or vertical?

To find points on a curve where the tangent line is horizontal or vertical, we need to determine the values of θ (or any parameter) that correspond to those points. This can be done by analyzing the derivatives of the curve equation and identifying the conditions under which the derivative is zero or undefined. Horizontal tangent lines occur when the derivative with respect to θ is zero, while vertical tangent lines occur when the derivative with respect to r is undefined or infinite.

Body of the Solution:To find the points on the curve r = 8 cos θ where the tangent line is horizontal or vertical, we need to determine the values of θ that correspond to those points.

  Differentiating r = 8 cos θ with respect to θ, we get:

dr/dθ = -8 sin θ

Setting dr/dθ = 0, we have:

-8 sin θ = 0

Since sin θ = 0 when θ is an integer multiple of π, the values of θ that give a horizontal tangent line are: θ = 0, π, 2π, 3π, ...

For each value of θ, we can find the corresponding value of r by substituting it back into the equation r = 8 cos θ.

   Differentiating r = 8 cos θ with respect to r, we get:

dθ/dr = -1 / (8 sin θ)

For a vertical tangent line, sin θ must be equal to zero, which occurs when θ is an integer multiple of π.

Therefore, the values of θ that give a vertical tangent line are: θ = π/2, 3π/2, 5π/2, ...

Again, for each value of θ, we can find the corresponding value of r by substituting it into the equation r = 8 cos θ.

Combining the values of θ and their corresponding values of r, we have: Horizontal tangent: (8, 0), (-8, π), (8, 2π), (-8, 3π), ... Vertical tangent: (0, π/2), (0, 3π/2), (0, 5π/2), ...

Final Answer:Thus, the points on the given curve where the tangent line is horizontal are (8, 0), (-8, π), (8, 2π), (-8, 3π), and so on, while the points where the tangent line is vertical are (0, π/2), (0, 3π/2), (0, 5π/2), and so on.

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The points on the given curve where the tangent line is horizontal are (8, 0), (-8, π), (8, 2π), (-8, 3π), and so on and the Vertical tangent  are (0, π/2), (0, 3π/2), (0, 5π/2),so on.

To find points on a curve where the tangent line is horizontal or vertical, we need to determine the values of θ (or any parameter) that correspond to those points. This can be done by analyzing the derivatives of the curve equation and identifying the conditions under which the derivative is zero or undefined. Horizontal tangent lines occur when the derivative with respect to θ is zero, while vertical tangent lines occur when the derivative with respect to r is undefined or infinite.

To find the points on the curve r = 8 cos θ where the tangent line is horizontal or vertical, we need to determine the values of θ that correspond to those points.

Horizontal tangent line: A horizontal tangent line occurs when the derivative of r with respect to θ is equal to zero.

 Differentiating r = 8 cos θ with respect to θ, we get:

dr/dθ = -8 sin θ

Setting dr/dθ = 0, we have:

-8 sin θ = 0

Since sin θ = 0 when θ is an integer multiple of π, the values of θ that give a horizontal tangent line are: θ = 0, π, 2π, 3π, ...

For each value of θ, we can find the corresponding value of r by substituting it back into the equation r = 8 cos θ.

Vertical tangent line: A vertical tangent line occurs when the derivative of θ with respect to r is undefined or infinite.

  Differentiating r = 8 cos θ with respect to r, we get:

dθ/dr = -1 / (8 sin θ)

For a vertical tangent line, sin θ must be equal to zero, which occurs when θ is an integer multiple of π.

Therefore, the values of θ that give a vertical tangent line are: θ = π/2, 3π/2, 5π/2, ...

Again, for each value of θ, we can find the corresponding value of r by substituting it into the equation r = 8 cos θ.

Combining the values of θ and their corresponding values of r, we have: Horizontal tangent: (8, 0), (-8, π), (8, 2π), (-8, 3π), ... Vertical tangent: (0, π/2), (0, 3π/2), (0, 5π/2), ...

Thus, the points on the given curve where the tangent line is horizontal are (8, 0), (-8, π), (8, 2π), (-8, 3π), and so on, while the points where the tangent line is vertical are (0, π/2), (0, 3π/2), (0, 5π/2), and so on.

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The value of the algebraic expression 11.5x + 10.9y  at x = 6 and y = 7 is 145.3

What is an algebraic expression?

Algebraic expression consists of variables and numbers connected with addition, subtraction, multiplication and division

The given algebraic expression is 11.5x + 10.9y

We have to find the value of the algebraic expression at x = 6 and y = 7

Putting x = 6 and y = 7 in the algebraic expression,

\(11.5 \times 6 + 10.9 \times 7\)

69 + 76.3

145.3

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(a) The Nash equilibrium for the $20 ultimatum game is a 50-50 split: the proposer offers $10 and the responder accepts. (b) Experimental findings show deviations from the Nash equilibrium due to fairness considerations, strategic behavior, and social preferences. (c) Proposers deviate from Nash equilibrium due to fairness concerns and strategic considerations. (d) To test the explanation, conduct experiments manipulating fairness norms and incentives to observe proposers' behavior.

(a) The Nash equilibrium for the $20 ultimatum game, where offers are made to the nearest $0.50, is a 50-50 split, where the proposer offers $10 and the responder accepts.

(b) The experimental literature has found deviations from the Nash equilibrium in both proposers and responders. These deviations can be attributed to various factors such as fairness considerations, strategic behavior, and social preferences.

(c) The behavior of the proposer deviates from the Nash equilibrium due to factors like fairness concerns and strategic considerations. Proposers may make more generous offers to avoid rejection or to signal fairness and maintain a positive reputation.

(d) To test the explanation that proposers deviate from the Nash equilibrium due to fairness concerns, one could design an experiment where fairness is manipulated. Participants could be exposed to different fairness treatments, and their offers could be observed and compared to those in a control group. Statistical analysis can then be used to determine if there is a significant difference in offers between the fairness treatments and the control group.

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Total apples.

Total oranges

Total peaches

Total fruits

Answer:

130

Step-by-step explanation:

We have given in the question 'she put 10 apples into each of 4 baskets.

we have to Multiply 10 with 4

=> 10 × 4

=> 40 Apples

Similarly, in the case of oranges we have to Multiply 10 with 3

=> 10 × 3

=> 30 Oranges

Same method will be followed to find the number of peaches that she picked .

=> 12 × 5

=> 60 Peaches

Total fruits Amber picked = Number of apples + Number of oranges + Number of peaches

=> Total fruits = 40 + 30 + 60

=> Total Fruits = 130 .

Answer:

For the first one, I believe you would need to use a rotation matrix; to rotate 90º counterclockwise, the matrices would look like ; you would then multiply those out. A reflection across the x-axis would be changing the sign of f(x) (from negative to positive or positive to negative), a reflection across the y-axis would be changing the sign of x, translation a units to the right would be subtracting a from x, translation b units up would be adding b to x. Rotation of 180º about the origin would be the same format as the first matrix, except it would be cos180 and cos0 on the top and sin180 sin0 on the bottom. Reflection across the y-axis would be changing the sign of x again.

OR

1. We know that, 'Translation shifts the figure in any direction'.

As, the function f(x) is translated 'a' units to the right, the new form of function is f(x-a).

Again, the function is translated 'b' units up, the final form of the function is f(x-a)+b.

2 and 3. We know that, ' Reflection flips the image over a line'.

As the function g(x) is reflected over y-axis, the new form of the function is g(-x).

As the function h(x) is reflected over x-axis, the new form of the function is -h(x).

4 , 5 and 6. We know that, 'Rotation turns the image around a point to a certain degree'.

Let us assume the function to be a point (x,y).

As the function is rotated by 90° counterclockwise about the origin, the new function becomes ( y,-x ) i.e. R_{90}R

90

(x,y) = ( -y,x ).

As the function is rotated by 180° counterclockwise about the origin, the new function becomes ( y,-x ) i.e. R_{180}R

180

(x,y) = ( -x,-y ).

As the function is rotated by 2700° counterclockwise about the origin, the new function becomes ( y,-x ) i.e. R_{270}R

270

(x,

Step-by-step explanation:hopes this helps lol?

Therefore, the solar flux density for mercury after the calculation is 9.12 x 10⁻³ W/m².

The solar flux density also referred to as the solar constant is the total amount of energy derived from the sun per unit area per given unit of time. It is considered to be equal to solar luminosity divided by the surface area of a given sphere that has a radius equivalent to the distance between the respective planet from the sun.

using the formula for finding the solar flux density,

solar flux density =  solar luminosity /(4 x π x distance between mercury and the sun)

solar flux density =  3.865 x \(10^{26}\) /(4 x π x ( 5.791 x \(10^{10}\)))

solar flux density = 9.12 x 10⁻³ W/m²

Therefore, the solar flux density for mercury after the calculation is 9.12 x 10⁻³ W/m².

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