The annual income of a sole proprietor of a grocery shop is Rs 10,00,000. If the tax is exempted up to Rs 4,50.000, what is his/her taxable income?​

The proportion of the students will have sufficient time to complete the test is of 0.9938 = 99.38%, using the normal distribution.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is given by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation of the time needed to complete the test are given as follows:

\(\mu = 50, \sigma = 12\)

The proportion is the p-value of Z when X = 80, hence:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (80 - 50)/12

Z = 2.5

Z = 2.5 has a p-value of 0.9938.

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Answer:

-3/1 and -2/1

Step-by-step explanation:

Answer: 23

Step-by-step explanation:

2x + 14 = 60

2x = 46

x = 23

Using L'Hôpital's Rule the limit of the given expression as x approaches 0 is 42.

To evaluate the given limit, we can apply L'Hôpital's Rule, which states that the limit of a quotient of two functions can be evaluated by taking the derivative of both the numerator and denominator until a non-indeterminate form is obtained.

So, taking the derivative of the numerator and denominator separately, we get:

lim (7x)sin(6x) = lim [(7sin(6x) + 42xcos(6x))/1]

= lim [42cos(6x) + 42xsin(6x)]

Now, substituting x=0 in the above expression, we get:

lim (7x)sin(6x) = 42(1) + 0(0) = 42

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The appropriate test to examine the relationship between the number of steps taken and HR in a group of 1000 athletes depends on the type of data and the research question.

If the number of steps and HR are both measured on a continuous scale and the research question is to examine the strength and direction of the relationship between the two variables, then the appropriate test would be Pearson's correlation coefficient.

If either the number of steps or HR is measured on a continuous scale and the other variable is measured on an ordinal scale, then the appropriate test would be Spearman's correlation coefficient.

However, if the research question is to predict HR based on the number of steps taken, and there are other variables that may influence the relationship, then multiple regression analysis would be the appropriate test.

Chi-Square test is used to examine the association between two categorical variables. It is not appropriate for examining the relationship between a continuous and categorical variable.

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Explanation:

1 hat = 45 dollars

6 hats = 6*45 = 270 dollars

1 phone = 40 dollars

4 phones = 4*40 = 160 dollars

total = $270 + $160 = $430

Felicia spent a total of $430. Since this amount of money leaves her account, this means we write a negative sign out front to end up with the final answer of -430

In other words, her account balance went down by $430 which is why we use a negative. If someone gave her $430, then the answer would be positive.

Answer:

D

Step-by-step explanation:

It must first translate 1 unit to the left because quadrilateral F'G'H'I is one unit away from to y axis. It can then translate across the y-axis.

The series of transformations that moved Quadrilateral FGHI to Quadrilateral F'G'H'I' is Translation and Reflection. The correct option is D.

Transformation in Geometry is changing the object from its original position on the map to a different position by translating, reflecting, rotating, or dilating.

The image shows two objects which are congruent but have different coordinates.

The series of transformations that changed the quadrilateral from its original position to the transformed one is the Translation of 2 units to the right and then Reflection along y-axis.

Therefore, the correct option is D.

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Answer:

Step-by-step explanation:

1 = 1/3(10x - 3)

3 = 10x - 3

6 = 10x

x = 6/10

x = 3/5

Given:

The equation is

\(2(x+14)=40\)

To find:

The solution of the given equation.

Solution:

We have,

\(2(x+14)=40\)

Using distributive property, we get

\(2(x)+2(14)=40\)

\(2x+28=40\)

Subtracting 28 from both sides.

\(2x=40-28\)

\(2x=12\)

On dividing both sides by 2, we get

\(x=6\)

Therefore, the solution of the given equation is x = 6.

To write a division expression from a fraction, identify the numerator, which is the dividend, while the denominator is the divisor.

A division expression is an algebraic expression using the division operand (÷).

Algebraic expressions involve the combination of numbers, constants, values, and variables with mathematical operands.

The result of a division operation, which is one of the four basic mathematical operations, is known as the quotient.

Thus, we can conclude that the dividend is related to the numerator of the fraction just as the divisor is related to the denominator of the fraction.

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Answer:

488000

(real number)

= 4.88 × 105

(scientific notation)

= 4.88e5

(scientific e notation)

number of significant figures: 3

Answer:

I need the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

The sample is the part of the population that somebody wants to study. therefore, the sample is the 100 male students interviewed

At a 1% significance level, we can infer that σ^2 is less than 100 if the test statistic falls in the rejection region. To determine this, we need to perform a chi-square test.

The test statistic for the chi-square test is calculated as (n - 1)  s^2 / σ^2, where n is the sample size, s^2 is the sample variance, and σ^2 is the hypothesized population variance.

In this case, the test statistic is (50 - 1) * 80 / 100 = 39.2.

To determine the critical value for a chi-square test at a 1% significance level with 49 degrees of freedom, we need to consult the chi-square distribution table or use statistical software. The critical value for this test is approximately 69.2.

Since the test statistic (39.2) is less than the critical value (69.2), we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to infer at the 1% significance level that σ^2 is less than 100.

The chi-square test is used to test whether the population variance (σ^2) is significantly different from a hypothesized value. By comparing the test statistic with the critical value, we determine whether to reject or fail to reject the null hypothesis. In this case, as the test statistic is less than the critical value, we fail to reject the null hypothesis and conclude that there is insufficient evidence to infer that σ^2 is less than 100 at the 1% significance level.

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Answer:

When x = -3.

4(-3)-5y=12.

-12-5y=12.

-5y=12+12.

-5y=24.

y= -4.8

We cannot determine the center or radius of the circle based on the given information.

To find the radius of the circle passing through the point (7, 6), we need to determine the center of the circle.

Let's assume that the center of the circle is (a, b). Since the circle passes through point (7, 6), we can set up an equation using the distance formula between the center (a, b) and point (7, 6) as follows:

√((7 - a)² + (6 - b)²) = r

where r is the radius of the circle.

We can see that this equation represents the distance between the center of the circle and the point (7, 6) is equal to the radius of the circle.

We also know that the distance between the center of the circle and any point on the circle is equal to the radius. Therefore, if we can find the distance between (a, b) and another point on the circle, we can solve for the radius.

However, we do not have any other information about the circle, such as another point or the equation of the circle. Therefore, we cannot determine the center or radius of the circle based on the given information.

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Answer:

your answer will be C.63

Answer:

64.5 pieces

Step-by-step explanation:

Since we know how long our sausage is already, we can solve this problem by simply dividing 43 by our fraction which is 2/3 (or 0.6).

43 / 0.6 = 64.5

The term for the value that occurs most often in a series of numbers is called the mode.

The mode is one of the three main measures of central tendency, along with the mean and the median. It is a useful descriptive statistic that can provide insights into the characteristics of a dataset.

To find the mode of a set of data, you first need to arrange the data in order, either in increasing or decreasing order. Then, you simply identify the most frequent data point, which is the mode. In some cases, there may be more than one mode if multiple data points occur with the same maximum frequency.

The mode is particularly useful when dealing with categorical or nominal data, where there are distinct categories or values that cannot be ordered in a meaningful way. For example, the mode can help identify the most popular color among a group of people or the most common type of car on a given street. It can also be used for continuous data, although it may be less useful in this case than the mean or median.

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The correct answer is option c) infinitely many solutions..

To solve the system of equations using the substitution method, we'll substitute the value of y from the second equation into the first equation and solve for x.

Given:

-6x + 2y = 8 ---(1)

y = 3x + 4 ---(2)

Substitute equation (2) into equation (1):

-6x + 2(3x + 4) = 8

Simplify:

-6x + 6x + 8 = 8

8 = 8

We obtained a true statement (8 = 8), which means the two equations are equivalent. This solution shows that the system has infinitely many solutions.

Therefore, the correct answer is option c) infinitely many solutions..

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Answer:

149.49° (nearest hundredth)

Step-by-step explanation:

To calculate the direction of the plane's resultant vector, we can draw a vector diagram (see attachment).

Since the two vectors form a right angle, we can use the tangent trigonometric ratio.

\(\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$ \tan x=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $x$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}\)

The resultant vector is in quadrant II, since the plane is travelling north (positive y-direction) and then west (negative x-direction).

As the direction of a resultant vector is measured in an anticlockwise direction from the positive x-axis, we need to add 90° to the angle found using the tan ratio.

The angle between the y-axis and the resultant vector can be found using tan x = 767 / 452. Therefore, the expression for the direction of the resultant vector θ is:

\(\theta=90^{\circ}+\arctan \left(\dfrac{767}{452}\right)\)

\(\theta=90^{\circ}+59.4887724...^{\circ}\)

\(\theta=149.49^{\circ}\; \sf (nearest\;hundredth)\)

Therefore, the direction of the plane's resultant vector is approximately 149.49° (measured anticlockwise from the positive x-axis).

This can also be expressed as N 59.49° W.

Answer:

810

Step-by-step explanation:

0.4x=0.6

x=1.5

540*1.5=810

The answer is 810.

Answer:

isosceles right triangle

Answer:

The answer is B - 1/2.

Step-by-step explanation:

Rise over run tells you the slope. You take two points (in this it's (0,-3) and (6,0)) and you see how many units it takes to be on the same y line as the other point. Then you do the same for the x line. You divide the rise (y line) by the run (x line) and that's your slope.

Answer:

Step-by-step explanation:

dad

Answer:

Step-by-step explanation:

Let the speed of the car is x, then the speed of motorcycle is x + 20

The distance = 120 km

Time:

Speed of the car is 40 km/h

Speed of the motorcycle is 60 km/h

Answer:

Speed of the car is 40 km/h

Speed of the motorcycle is 60 km/h

Answer:

52°

Step-by-step explanation:

it should always add up to 180°

This assigns the value 3.14159 to the variable x. Similarly, for a value like 6.02e23, the variable declaration would look like:

x = 6.02e23.This assigns the value 6.02 x \(10^23\)to the variable x, using scientific notation.

In most programming languages, a variable suitable for storing values like 3.14159 and 6.02e23 would typically be declared as a floating-point or double data type. These data types are capable of representing decimal values and scientific notation. The specific syntax for declaring a variable may vary depending on the programming language used. However, an example of declaring such a variable in Python would be:

x = 3.14159

This assigns the value 3.14159 to the variable x. Similarly, for a value like 6.02e23, the variable declaration would look like:

x = 6.02e23

This assigns the value 6.02 x \(10^23\)to the variable x, using scientific notation.

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