Write the expression as the sine, cosine, or tangent of an angle.

(tan (pi/5) + tan (pi/2))/(1-tan (pi/5) tan (pi/2))

The person will gain Rs. 5,500 after 3 years by lending the whole amount to a shopkeeper at the same rate of compound Interest for the same time.

Given, Principal amount (P) = Rs. 16,000

Rate of Interest (R) = 12.5%

Time (T) = 3 years(a)

The amount to be paid to the bank as simple interest can be calculated as follows:

Simple Interest (SI) = (P × R × T) / 100= (16000 × 12.5 × 3) / 100= Rs. 6,000Therefore, the amount to be paid to the bank as simple interest is Rs. 6,000.

(b) The amount to be received by the person from the shopkeeper as compound interest can be calculated as follows: Compound Interest (CI) = P × [1 + (R/100)]T – P= 16000 × [1 + (12.5/100)]3 – 16000= Rs. 21,500

Therefore, the amount to be received by the person from the shopkeeper as compound interest is Rs. 21,500.(c) Gain = CI - P= 21500 - 16000= Rs. 5,500

Therefore, the person will gain Rs. 5,500 after 3 years by lending the whole amount to a shopkeeper at the same rate of compound interest for the same time.

For more questions on Interest .

https://brainly.com/question/25720319

#SPJ8

Answer:2 9/50

Step-by-step explanation:

2 18/100

Simplifies to 2 9/50

Answer:

109/50

Step-by-step explanation:

First, let's split this number up.

2.18 = 2.00 + 0.18

Remember that 0.18 means 18 hundredths, which can be represented as 18/100. Simplified, this equals 9/50.

Now, we have the mixed number 2 9/50.

Remember how to turn a mixed number into a fraction? Multiply 2 by 50, then add 9! That's the numerator. The denominator will be 50, the denominator of the fraction in the mixed number.

2 9/50 in fraction form is 109/50.

This is the simplest form!

Hope this helps! Feel free to reach out to me if you have any more questions :)

Answer:

4w + 12

Step-by-step explanation:

Perimeter of a rectangle = 2(length + width)

Let

Width of the rectangle = w feet

Length of the rectangle = (w + 6) feet

Perimeter of a rectangle = 2(length + width)

= 2{(w+6) + w}

= 2(w + 6 + w)

= 2(2w + 6)

= 4w + 12

Perimeter of a rectangle = (4w + 12) feet

Answer:

12/23

Step-by-step explanation:

Area = length x width

Width = area ÷ length

12 ÷ 23 = 0.5217

Or in fraction form: 12/23

Answer:

The area for a rectangle is calculated by multiplying its length and width. You are given the area and one side, so you can set up an equation and solve for the other side.

Step-by-step explanation:

A = 12 sq. mi.

L = 23 mi.

W = ?

A = L x W, so 12 = 23 x W

Solve for W by dividing both sides by 23.

W = 12/23 mi.

You can't reduce that fraction any further.

Just as a side note, the answer tells us that the park is long and narrow. It is 23 miles long, but just over half a mile wide.

Answer:

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

The experimental probability is the ratio of actual outcomes and total outcomes:

By the analysis of histogram , 40% percent of the cars was less than 20 years old or more than 40 years old.

The histogram may be seen here. Each column lists the age range at the bottom and the number of automobiles in that age group on the left.

The number of vehicles in the first two columns from the left (age 0-9 and 10-19) and the last two columns (age > 40) must be added together to determine the percentage of vehicles with less than 20 years or more than 40 years of age (age 40-49 and 50-59).

The total number of requested vehicles is equal to 8 that is (3 + 2 + 0 + 3).

The total number of automobiles must now be determined (by adding the cars in each column): 3 + 2 + 8 + 4 + 0 + 3 = 20

The ratio of the number of automobiles of the specified age to the total number of cars must then be calculated and converted into a percentage.

\(\frac{8}{20}\)\(= 0.40 = 40%\)

40% percent of the cars was less than 20 years old or more than 40 years old.

Learn more about histogram

brainly.com/question/30354484

#SPJ4

Answer:

Yes because its a pattern of sixes???

Answer:

No

Step-by-step explanation:

There is no common ratio between these numbers

12/6 = 2

18/12 = 1.5

24/18 1.333 etc

However, this is an arithmetic progression as it has a common difference of 6

The volume of the solid is (11π/3) cubic units.

We have,

To find the volume of the solid obtained by rotating the region bounded by y = x and y = x^2 about the line x = -3, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is given by:

V = 2π ∫ [a, b] x h(x) dx,

where [a, b] is the interval of integration, x represents the variable of integration, and h(x) represents the height of the shell at each value of x.

In this case, we want to rotate the region bounded by y = x and y = x² about the line x = -3.

Since we are rotating about a vertical line, the height of the shell at each value of x will be given by the difference between the x-coordinate of the curve and the line of rotation:

h(x) = (x - (-3)) = x + 3.

To find the interval of integration, we need to determine the x-values where the two curves intersect.

Setting x = x², we have:

x = x²,

x² - x = 0,

x (x - 1) = 0.

This gives us two intersection points: x = 0 and x = 1.

Therefore, the interval of integration is [0, 1].

Now we can set up the integral to find the volume:

V = 2π ∫ [0, 1] x (x + 3) dx.

Evaluating this integral, we have:

V = 2π ∫ [0, 1] (x² + 3x) dx

= 2π [x³/3 + (3/2)x²] evaluated from 0 to 1

= 2π [(1/3 + 3/2) - (0/3 + 0/2)]

= 2π [(2/6 + 9/6) - 0]

= 2π (11/6)

= (22π/6)

= (11π/3).

Therefore,

The volume of the solid is (11π/3) cubic units.

Learn more about the volume of solids here:

https://brainly.com/question/31259146

#SPJ1

Answer:

1

0.5

0.8

Step-by-step explanation:

i just did it and was right

The required values of the r that shows the positive slope are 1, 0.5, and 0.8.

Given that,
To select the values  for r that indicate a positive slope for the line

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

y -y₁ =(y₂ - y₁) /  (x₂ - x₁) (x - x₁)

Here,
The positive slope is defined as the positive value of the r, not also zero because zero represents the contant nature of the function while the positive slope shows the increasing nature of the function or curve.

Thus, the required values of the r that shows the positive slope are 1, 0.5, and 0.8.

Learn more about slopes here:
https://brainly.com/question/3605446

#SPJ2

In the event  of alteration in the rate at which the water level of the funnel is changing when the water is 15 inches high is 0.42 cubic inches per second.
The volume of a cone is given by the formula V = (1/3)πr²h here r is the radius of the base and h is the height of the cone.

Now we have differentiate this formula concerning t to get
dV/dt = (1/3)πr²dh/dt + (2/3)πrh²dr/dt.

It is given to us  that water is coming out a giant cone shaped funnel at a rate of 15 cubic inches per second, then we  can say that
dV/dt = -15 cubic inches per second

Therefore the funnel has a maximum radius of 40 inches and a height of 75 inches. We need to evaluate  dh/dt
If h = 15 inches.

In order to find dh/dt,
we need to evaluate  dr/dt and place it in  equation for dV/dt.

Therefore, to find dr/dh = r/h.
Given
when h = 75 inches,
r = 40 inches.
Therefore, dr/dh
= 40/75.

Staging this into the equation for dV/dt,

-15 = (1/3)π(40²)(dh/dt) + (2/3)π(40)(15)²(40/75)

Here simplification takes place


dh/dt = -0.4π/3
≈ -0.42 cubic inches per second
In the event  of alteration in the rate at which the water level of the funnel is changing when the water is 15 inches high is 0.42 cubic inches per second.


To learn more about volume,
https://brainly.com/question/14197390
#SPJ4                                                                                                                          

Hello there!

2/15 is impossible to simplify because 15 isn't divisible by 2. Hope it helps!

#HaveAnAmazingDay

\(GraceRosalia\)

Answer: -19r + 31.7s i think

Step-by-step explanation:

Answer:

64 pi

Step-by-step explanation:

Answer:100-K

Step-by-step explanation:

"100 decreased by a number K" can be written algebraically as:

100 - K

This expression represents the result of subtracting the value of K from 100.

Answer: 12x

Step-by-step explanation: -(2x-y)=-2x+y

14x+y-y=14x

14x-2x= 12x

name me brainliest, plz

The population multiple regression model includes a response variable, a constant term, multiple explanatory variables, and an error term.

In multiple regression analysis, the population multiple regression model is a statistical model that represents the relationship between a response variable and multiple explanatory variables. The model assumes that the relationship between the response variable and the explanatory variables can be expressed as a linear combination of the variables, including a constant term. The constant term represents the intercept of the regression line and accounts for the average value of the response variable when all the explanatory variables are zero.

Additionally, the model includes an error term, also known as the residual term or the disturbance term. The error term captures the variability in the response variable that is not explained by the explanatory variables. It represents the random and unobservable factors that affect the response variable and are not accounted for in the model. The presence of the error term acknowledges that the relationship between the variables is not deterministic but contains some degree of uncertainty.

To learn more about regression click here:

brainly.com/question/17731558

#SPJ11

The molar mass of compound X is approximately 150 g/mol.

To determine the molar mass of compound X, we can use the concept of freezing point depression. Freezing point depression is a colligative property, which means it depends on the number of solute particles present in a solution, rather than the specific identity of the solute.

The freezing point depression (ΔTf) can be calculated using the equation:

ΔTf = Kf * m

where Kf is the cryoscopic constant of the solvent (formamide in this case) and m is the molality of the solution.

We are given the freezing point depression (ΔTf) as 1.9 °C and the mass of formamide (m) as 80.0 g. The molality (m) of the solution can be calculated using the formula:

m = moles of solute / mass of solvent (in kg)

We know the moles of formamide (NH2COH) from its given mass, which is 80.0 g. By dividing the mass by its molar mass (46 g/mol), we find that the moles of formamide are approximately 1.739 moles.

Now, to calculate the moles of compound X, we need to use the relationship between moles of solute and the freezing point depression. Since compound X is the solute, the moles of compound X can be calculated using the formula:

moles of X = ΔTf / (Kf * m)

Substituting the given values, we have:

moles of X = 1.9 °C / (Kf * 1.739 moles)

At this point, we need the cryoscopic constant (Kf) for formamide, which can be found in the ALEKS Data resource. Let's assume the value of Kf for formamide is 4.6 °C·kg/mol.

Now, substituting the known values into the equation:

moles of X = 1.9 °C / (4.6 °C·kg/mol * 1.739 moles)

Simplifying the equation, we find:

moles of X ≈ 0.237 mol

Finally, to determine the molar mass of compound X, we can use the equation:

molar mass = mass of X / moles of X

Given that the mass of compound X is 3.99 g, we have:

molar mass = 3.99 g / 0.237 mol

Calculating this value, we find that the molar mass of compound X is approximately 16.8 g/mol.

Learn more about Molar mass

brainly.com/question/31545539

#SPJ11

The probability that a student who has an A is a male is 60%.

To find the probability that a student who has an A is a male, we need to calculate the ratio of the number of male students with an A to the total number of students with an A.

Given that there are 19 students in total, and 6 of them are female, we can determine that there are 19 - 6 = 13 male students. Out of these male students, 7 do not have an A. Therefore, the number of male students with an A is 13 - 7 = 6.

Now, we know that there are 10 students in total who have an A. Therefore, the probability that a student with an A is a male can be calculated as the ratio of the number of male students with an A to the total number of students with an A:

Probability = Number of male students with an A / Total number of students with an A

Probability = 6 / 10

Probability = 0.6 or 60%

For more such questions on probability

https://brainly.com/question/30390037

#SPJ8

The approximate value of f(1) using Euler's method with two steps of equal size is 6.636. The range of f for t > 0 is 0 < f(t) < 6.

a. The limiting factor in this logistic differential equation is the carrying capacity, which is 6 in this case. As y approaches 6, the growth rate of y slows down, until it eventually levels off at the carrying capacity.

b. To use Euler's method, we first need to calculate the slope of the solution at t=0. Using the given differential equation, we can find that the slope at t=0 is y(0)/8(6-y(0)) = 8/8(6-8) = -1/6.

Using Euler's method with two steps of equal size, we can approximate f(1) as follows:

f(0.5) = f(0) + (1/2)dy/dx|t=0

= 8 - (1/2)(1/6)*8

= 7.333...

f(1) = f(0.5) + (1/2)dy/dx|t=0.5

= 7.333... - (1/2)(7.333.../8)*(6-7.333...)

= 6.636...

Therefore, the approximate value of f(1) using Euler's method with two steps of equal size is 6.636.

c. The range of f for t > 0 is 0 < f(t) < 6, since the carrying capacity of the logistic equation is 6. As t approaches infinity, f(t) will approach 6, but never exceed it. Additionally, f(t) will never be negative, since it represents a population size. Therefore, the range of f for t > 0 is 0 < f(t) < 6.

Learn more about Euler's method here

https://brainly.com/question/21245378

#SPJ11

1. Sensitivity =  0.85,  Specificity = 0.54, Precision = 0.74. 2.  are the answers

Sensitivity, specificity, and precision are performance measures for binary classification problems. In binary classification, there are two possible outcomes, positive and negative, and the task is to assign a new instance to one of the two categories.

The four possible outcomes are True Positive (TP), False Positive (FP), True Negative (TN), and False Negative (FN).

Sensitivity: The sensitivity, also known as Recall, is the ability of the classifier to identify all positive instances correctly. It is computed as the ratio of true positives to the sum of true positives and false negatives.

Sensitivity = TP / (TP + FN) = 17 / (17 + 3) = 0.85

Specificity: Specificity is the ability of the classifier to identify all negative instances correctly. It is calculated as the ratio of true negatives to the sum of true negatives and false positives.

Specificity = TN / (TN + FP) = 7 / (7 + 6) = 0.54

Precision: The precision is the fraction of instances that the classifier labeled positive that are truly positive.

Precision = TP / (TP + FP) = 17 / (17 + 6) = 0.74

The formula to calculate sensitivity, specificity, and precision are as follows:

Sensitivity = TP / (TP + FN)

Specificity = TN / (TN + FP)

Precision = TP / (TP + FP)

The difference between Maximization of likelihood function and OLS method for linear regression are as follows:

Maximization of likelihood function:

It is a statistical technique that determines the parameters of a model that best describe the relationship between the dependent and independent variables. Maximum Likelihood Estimation (MLE) is a technique used to estimate the parameters of a statistical model based on the likelihood function.

Optimization of the likelihood function of the observed data is the primary objective of MLE. The best values of the parameters that maximize the probability of the observed data are determined by MLE. MLE is widely used in linear regression, logistic regression, and other statistical models.

OLS Method for Linear Regression:

The Ordinary Least Squares (OLS) method is a statistical technique for linear regression analysis that minimizes the sum of the squares of the differences between the observed and predicted values. OLS is the most common method used for estimating the parameters of a linear regression model. The sum of the squared errors (SSE) is the objective function that is minimized in OLS.

Optimizing SSE in OLS involves minimizing the difference between the observed and predicted values of the dependent variable. OLS is used to estimate the regression coefficients in a linear regression model.

Example: Suppose you want to predict the number of hours a student needs to study to achieve a particular grade. The dependent variable is the number of hours studied, and the independent variable is the grade.

The data consist of 10 observations. The OLS method estimates the regression coefficients, beta-0 and beta-1, in the following linear regression model:

Y = beta-0 + beta-1*X + e,

where Y is the dependent variable, X is the independent variable, and e is the error term.

to know more about Ordinary Least Squares method visit:

https://brainly.com/question/30548812

#SPJ11

Answer:

x=2

Step-by-step explanation

Answer:

2x + 3y = -21

Step-by-step explanation:

Parallel lines have same slope.

2x + 3y = -21

      3y = - 2x - 21

y = \(y = \dfrac{-2}{3}x-\dfrac{21}{3}\\\\y=\dfrac{-2}{3}x-7\)

I will plug in the POINTS including k in the equation each point in its place either x or y.

\(( - 2)^{2} +( {k})^{2} = 20 \\ 4 + {k}^{2} = 20 \\ k^{2} + 4 - 20 = 0 \\ {k}^{2} - 16 = 0 \\ (k + 4)(k - 4) = 0 \\ \\ k + 4 = 0 \\ \\ or \\ \\ k - 4 = 0 \\ \\ k = 4 \\ or \\ k = - 4\)

ATTACHED IS THE SOLUTION

The height of the triangle is given as follows:

\(h = 2\sqrt{3}\) cm.

The area of the triangle is given as follows:

\(A = 4\sqrt{3}\) cm².

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

Considering an equilateral triangle, in which all the side lengths are of 4, we have a right triangle in which:

Hence the height is obtained as follows:

h² + 2² = 4²

h² = 12

\(h = \sqrt{3 \times 4}\)

\(h = 2\sqrt{3}\) cm

The area of a triangle is given as half the multiplication of the base and of the height, hence:

\(A = 0.5 \times 4 \times 2 \sqrt{3}\)

\(A = 4\sqrt{3}\) cm².

More can be learned about the Pythagorean Theorem at brainly.com/question/30203256

#SPJ1

The equation of the parabola with focus at f(0 -4) and directrix x = 4 is

y² = 16x.

A parabola is a quadratic function graph. A parabola, according to Pascal, is a circle's projection. Galileo demonstrated that projectiles falling under the influence of uniform gravity have a path known as a parabolic path. Many bodily motions follow a curvilinear route that is shaped like a parabola. In mathematics, a parabola is any mirror-symmetrical planar curve that has an approximate U shape. The goal of this section is to comprehend the derivation of a parabola's standard formula, the several standard forms of a parabola, and the properties of a parabola.

Given

Focus at f(0, -4)

Directrix x = 4

As we know, the equation of a parabola with focus (a, 0) and directrix x = a

y² = 4ax.

y² = 4(4)x

y² = 16x

The equation of the parabola with focus at f(0 -4) and directrix x = 4 is

y² = 16x.

To learn more about parabola, visit:

https://brainly.com/question/4074088

#SPJ4

Given:

90 + 27

Let's apply the distributive property to factor out the greatest common factor.

First find greatest common factor of 90 and 27

Greatest common Factor of 90 and 27 = 9

Thus, we have:

Applying distribuive property, we could rewrite as: 9(10 + 3)

ANSWER:

9(10 + 3)

\(\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ SA=196\pi \end{cases}\implies \begin{array}{llll} 196\pi =4\pi r^2\implies \cfrac{196\pi }{4\pi }=r^2 \implies 49=r^2 \\\\\\ \sqrt{49}=r\implies 7=r~\hfill \underset{diameter}{\stackrel{2(7)}{14}} \end{array}\)

Answer: The perimeter is 34 cm

Step-by-step explanation:

14cm + 14cm = 28cm

3cm + 3cm = 6cm

28cm + 6cm = 34 cm

Answer:

34

Step-by-step explanation:

Perimeter is equal to :

Length + length + width + width

So theres two ways we can do this:

2(14) + 2(3)

OR

14 + 14 + 3 + 3

either way, solving will give us an answer of 34