Problem 1.3 A city has a 5% sales tax. A book costs 32. 55 after tax. How much did it cost before tax?

Answer:

y = 2x - 3

Step-by-step explanation:

A (0,-3)

B (2,1)

slope = (-3-1)/(0-2)

-4/-2

2

y intercept = -3

The total annual salary with a festive bonus is Rs (12r+2000)

In maths, multiply means the repeated addition of groups of equal sizes.

Given that, there is an annual salary at r rupees per month along with a Christmas bonus of, Rs 2000.

Here, a person is getting monthly salary  = Rs r

Therefore, his annual salary = Rs r × 12

= Rs 12r

He is also getting a bonus for Christmas = Rs 2000

So, in total, he will get =  Rs (12r+2000)

Hence, The total annual salary with a festive bonus is Rs (12r+2000)

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Answer:

- 4, - 3, - 2, - 1, 0, 1

Step-by-step explanation:

- 15 < 3n < 6 ( divide each interval by 3 )

- 5 < n < 2

then integer value of n are - 4, - 3, - 2, - 1, 0, 1

Answer:

Step-by-step explanation:

Lacey you can do this one  :D

J = H  ( b/c of red marks)

180= 128 + ∠j

52 = ∠j

t = ∠j

t = 52

180 = s + 2*t

180 = s + 2*52

180 = s + 104

180-104 =s

76 = s

To find the constant of variation in this situation, we need to use the formula for inverse variation, which is:

y = k / x

where y is the number of cigarettes a person smokes, x is the length of time they can hold their breath, and k is the constant of variation.

In this case, we are given that y = 10 cigarettes and x = 50 seconds. We can solve for k by multiplying both sides of the equation by x:

k = y * x

= 10 cigarettes * 50 seconds

= 500

Therefore, the constant of variation in this situation is 500. This means that for every 50 seconds of breath-holding time, a person will smoke approximately 10 cigarettes.

Answer:

Slope: 3

y-intercept: ( 0, −5)

Graph a solid line, then shade the area above the boundary line since

y is greater than 3x −5.

y ≥ 3x −5

To determine the number and type of solutions to the quadratic equation x^2 - x = -1/4, we can use the discriminant, which is the part of the quadratic formula that determines the number of solutions. The quadratic formula is:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

where a, b, and c are the coefficients of the quadratic equation. In this case, the coefficients of the equation are a = 1, b = -1, and c = -1/4. Plugging these values into the formula gives us:

x = (1 +/- sqrt(1^2 - 4(1)(-1/4))) / (2(1))

x = (1 +/- sqrt(1 + 1)) / 2

x = (1 +/- sqrt(2)) / 2

Therefore, the quadratic equation has two solutions: x = (1 + sqrt(2)) / 2 and x = (1 - sqrt(2)) / 2. These solutions are both real numbers.

Answer:

mn/100

Step-by-step explanation:

m% = m/100

m% of n = m% × n = m/100 × n = mn/100

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The domain of a radical is the set of all values of the independent variable for which the radical is defined.

For example, consider the radical expression √x. This expression is defined for all nonnegative values of x, since the square root of a nonnegative number is always real. Therefore, the domain of the radical √x is the set of all nonnegative values of x:

{x | x ≥ 0}

This includes all real numbers that are greater than or equal to zero, such as 0, 1, 2, 3, and so on.

On the other hand, if we consider the radical expression √(x-2), this expression is defined for all values of x such that x-2 is nonnegative. This means that the domain of the radical √(x-2) is the set of all values of x such that x ≥ 2:

{x | x ≥ 2}

This includes all real numbers that are greater than or equal to 2, such as 2, 3, 4, 5, and so on.

In general, the domain of a radical is determined by the values of the independent variable that make the expression under the radical nonnegative. If the expression under the radical is always nonnegative, then the domain of the radical is the set of all real numbers. If the expression under the radical is not always nonnegative, then the domain of the radical is the set of all values of the independent variable that make the expression nonnegative.

Answer:

The domain of a radical is the set of all values that can be plugged into the radical without resulting in an undefined or imaginary value.For example, the domain of the square root function sqrt(x) is all non-negative real numbers, since the square root of a non-negative real number is always a real number. This means that the domain of sqrt(x) is the set of all real numbers x such that x >= 0.On the other hand, the domain of the square root function sqrt(x^2 - 4) is all real numbers except for the values x = 2 and x = -2, since the square root of a negative number is an imaginary number. This means that the domain of sqrt(x^2 - 4) is the set of all real numbers x such that x != 2 and x != -2.In general, the domain of a radical is the set of all values for which the expression inside the radical is greater than or equal to 0. This is because the radical of a negative number is an imaginary number, which is not included in the domain of the radical.

Step-by-step explanation:

Answer: 49/60 mins.

Step-by-step explanation:

First lap time = 5/6 minute

Second lap time = 11/12 minute

Third lap = ?

To find the 3rd lap mins, we need to find 5 x 6, which is 30. Then, we need to find 1 1/12 more than 30. Then, when we get that answer, we need to find 1 1/10 fewer mins to get the 3rd lap time. If you do it all right, you should end up with 49 mins or 49/60 mins as a fraction (The denominator was changed to 60 to make the problem more realistic and easier) I hoped this helped.

The proof principle that you are describing is known as induction. Induction is a method of proof that is used to establish that a property holds for all natural numbers (or, more generally, for all elements of a well-ordered set).

The basic idea behind induction is as follows:

First, you start with a base case, which is a specific natural number (usually 0 or 1) for which you can directly prove that the property holds.

Next, you assume that the property holds for some natural number n. This is known as the induction hypothesis.

Using the induction hypothesis, you then prove that the property also holds for the natural number n+1. This is known as the induction step.

Since you have already established that the property holds for the base case, and you have shown that if it holds for one natural number, it must also hold for the next natural number, it follows that the property holds for all natural numbers.

Induction is a very powerful proof technique and is used extensively in mathematics to prove theorems about the properties of natural numbers and other well-ordered sets.

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I believe the answer is x= 12

Answer:

x² - 3

Step-by-step explanation:

g(f(x))

=> g(x²)

=> x² - 3

The solutions for the given equation is (1, 12), (2, 18), (3, 24), (4, 30) and (5, 36).

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is y=6x+6.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Substitute, x=1, 2, 3, 4, 5,.....

When x=1

y=6x+6

y=12

When x=2

y=6x+6

y=6(2)+6

y=18

When x=3

y=6x+6

y=6(3)+6

y=24

When x=4

y=6x+6

y=6(4)+6

y=30

When x=5

y=6x+6

y=6(5)+6

y=36

Therefore, the solutions for the equation is (1, 12), (2, 18), (3, 24), (4, 30) and (5, 36).

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The equation in the form at point (3m, 2m) is [tex]$\ln y^2+y=2 x-2.62$[/tex], the magnitude of the velocity is 7.81 m/s, the direction of the velocity is 50.19°.

Consider the flow field:

u=2+y & v=2 y

Determine the streamline equation by using the following equation:

[tex]& \frac{d x}{u}=\frac{d y}{v} \\ \frac{d x}{2+y}=\frac{d y}{2 y} \\\\& \int d x=\int\left(\frac{2+y}{2 y}\right) d y \\\\& x=\ln y+\frac{y}{2}+C[/tex]

(A)

Since the stream line passes through (3,2).

[tex]$$\begin{aligned}& x=\ln y+\frac{y}{2}+C \\& 3=\ln 2+\frac{2}{2}+C \\& C=2-\ln 2 \\& C=1.31\end{aligned}$$[/tex]

Substitute the value of C in equation (1).

[tex]& x=\ln y+\frac{y}{2}+C \\\\& x=\ln y+\frac{y}{2}+1.31 \\\\& 2 x-1.31 \times 2=2 \ln y+y \\\\& \ln y^2+y=2 x-2.62[/tex]

Therefore, the equation of streamline equation at point (3m, 2m) is [tex]$\ln y^2+y=2 x-2.62$[/tex].

(B).

Calculate the magnitude of the velocity of a particle located at point (5m , 3m).

[tex]V & =\sqrt{u^2+v^2} \\\\& =\sqrt{(2+y)^2+(2 y)^2} \\\\& =\sqrt{(2+3)^2+(2 \times 3)^2} \\\\& =\sqrt{5^2+6^2} \\\\& =7.81 \mathrm{~m} / \mathrm{s}[/tex]

Therefore, the magnitude of the velocity of a particle located at point (5m , 3m) is 7.81m/s.

(C).

Calculate the direction of the velocity of a particle located at point (5m , 3m) measured counterclockwise from the positive x-axis is

[tex]\tan \theta & =\frac{v}{u} \\\\& =\frac{2 y}{2+y} \\\\& =\frac{6}{5} \\\\& =50.19^{\circ}[/tex]

Therefore, the direction of the velocity of a particle located at point (5m , 3m) is 50.19°.

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A flow field for a fluid is described by u=(2+y) m/s and v=(2y) m/s, where y is in meters.

      A.) Determine the equation of the streamline that passes through point (3m, 2m). Write the equation in the form

 x={x(y)}, where y is in meters.

      B.) Find the magnitude of the velocity of a particle located at point (5m , 3m).

      C.) Find the direction ? of the velocity of a particle located at point (5m , 3m) measured counterclockwise from the positive x axis.

Answer:

Below

Step-by-step explanation:

the difference between 51.2 and a number is  :   51.2 - x

 Now multiply this by 6  :   6 x (51.2-x)    

     and this equals 68.3  :      6 x (51.2-x) = 68.3

Answer:

Step-by-step explanation:

Given angles of elevation of 10° and 50° measured 10 seconds apart from an observation point 1.5 miles away, you want to know the vertical change in distance, and the average speed of the shuttle between the two observations.

The tangent relation tells you ...

  Tan = Opposite/Adjacent

Then the height of the shuttle at the observed angles was ...

  Opposite = Tan · Adjacent

  h1 = tan(10°)·(1.5 mi) ≈ 0.264490 mi

  h2 = tan(50°)·(1.5 mi) ≈ 1.787630 mi

The amount of vertical travel in the 10-second interval was ...

  1.787630 mi -0.264490 mi = 1.523240 mi

The space shuttle traveled about 1.523 miles vertically in the 10-second interval.

In miles per second, the average speed during that time was about ...

  (1.523 mi)/(10 s) = 0.1523 mi/s

In miles per hour, that's about ...

  (0.1523 mi/s)(3600 s/h) ≈ 548 mi/h

If the two expression be 14 - 3a and 7a - 9 then the combined term exists 4a + 5.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: Expression: (Math Operator, Number/Variable, Math Operator).

The addition, subtraction, multiplication, and division mathematical operations are used to create mathematical expressions.

Let the two expression be 14 - 3a and 7a - 9

Expression one - 14 - 3a

Expression two - 7a - 9

Combining both two terms

14 - 3a + (7a - 9)  = 14 - 3a + 7a - 9

simplifying the above equation, we get

= (-3a + 7a) + 114 - 9)

=  4a + 5

If the two expression be 14 - 3a and 7a - 9 then the combined term exists 4a + 5.

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By combination, Three men and three women must be chosen among the six men and seven women that are available. necessary number of methods =  [tex]^6C_3 * ^7C_3 = 20 * 35 = 700.[/tex]

The sequence of the selection is irrelevant since a combination in mathematics is a selection of items from a set having various members. Regardless of the sequence in which the items were chosen, a mathematical approach known as a combination may be used to calculate the number of alternative arrangements within a collection of objects. Any order can be chosen by a combination. Combinations and permutations are two alternative strategies to divide up a collection of items into subsets in mathematics. The subset's elements can be listed in any order in a combination. In a permutation, the components of a subset are listed in a certain order.

Three men and three women must be chosen among the six men and seven women that are available. necessary number of methods =  [tex]^6C_3 * ^7C_3 = 20 * 35 = 700.[/tex]

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43 is equivalent to 64(1/3)

Equivalent is different from equal. Equal means same in all aspects, whereas equivalent means similar but not identical.

For example, 2 is said to be equal to 2 but equivalent to 1 + 1.

Given that, if a=b(1/n) is equivalent to an=b then 43 is equivalent to

If we see the number 43, then converting it according to given pattern

4ⁿ(1/n)

Here, n = 3

So, 43 = 4³(1/3) = 64(1/3)

Hence, 43 is equivalent to 64(1/3)

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The mean is $67,530 from the reported two average household incomes i.e, $49,445 and $67,530.

Averages can only be computed for numeric variables, regardless of whether the variables are discrete or continuous. This is obtained by simply dividing the sum of all values in the dataset by the number of values.

Mathematically, X-bar = Sum of x values/ number of values

We have, the current population survey is conducted by the US Census bureau,

Averages of household income are $49,445 and $67,530. Mean of average incomes is expected to be a right skewed distribution because some individuals belongs to exceptionally high income group which are outliers and which will cause the mean to inflate. Hence, value which is greater will be the mean i.e. $67,530

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A circle of radius 4.6 cm is drawn with its center at the origin. The diameter XY of the circle is also drawn, along with two chords XP and YQ connecting the endpoints of the diameter.

A circle of radius 4.6 cm is drawn with its center at the origin, which is labeled as O. The diameter XY of the circle is also drawn and labeled, with the endpoints X and Y. Two chords XP and YQ are then drawn connecting the endpoints of the diameter. The chord XP starts at X and ends at P, while the chord YQ starts at Y and ends at Q. This diagram demonstrates the idea of a circle and its diameter, as well as how two chords can be drawn from the same two endpoints of a diameter. The circle and its diameter can also be used to calculate the circumference of the circle and the length of the diameter.

Circumference of circle = 2 * π * 4.6 = 28.96 cm

Length of diameter = 2 * 4.6 = 9.2 cm

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The value of the composite function is 2x - 15

A function can be defined as a rule, law ore equation that explicitly shows the relationship between two variables.

These variables are called;

From the information given, we have the functions;

To determine the composite function (fog)(x), we have to substitute the value of g(x) as the variable 'x' in the function, f(x), we have;

(fog)(x) = 2 - (18 -2x) + 1

Now, expand the bracket

(fog)(x) = 2 - 18 + 2x + 1

collect like terms

(fog)(x) = 2x - 15

Hence, the function is 2x - 15

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Simple random sampling is a good way because he will have a more representative sample if he chooses randomly. which is the correct answer would be an option (B).

A sample is randomly chosen from the population in basic random sampling, guaranteeing that each person has an equal chance of being chosen.

Simple random sampling is a good way for a librarian to check a sample of books from the library to get an idea of how many need replacing because it will provide a more representative sample.

In simple random sampling, a sample is selected from the population at random, ensuring that each member of the population has an equal chance of being selected. This means that the sample will accurately represent the characteristics of the population as a whole.

Thus, He will have a more representative sample if he chooses randomly.

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Answer:

11.25

Step-by-step explanation:

If the painter used 2.5 liters of paint every hour, then in 5.5 hours he would have used 2.5 * 5.5 = <<2.5*5.5=13.75>>13.75 liters of paint.

If he had 25 liters of paint to begin with and used 13.75 liters of paint, he would have 25 - 13.75 = <<25-13.75=11.25>>11.25 liters of paint left. Answer: {11.25}.

The painter had 11.25 L paint left.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given here in 1 hour he uses 2.5 L of paint

          then in 5.5 hours he uses 2.5 × 5.5 = 13.5 L

Therefore quantity of paint left is = 25 - 13.5 = 11.5 L

Hence, The painter had left  11.25 L .

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Answer:

-3<c<11/2

Step-by-step explanation:

-7<2c-1

-7+1<2c

-6<2c

-3<c

and

2c-1<10

2c<10+1

2c<11

c<11/2

Final answer (combine both):

-3<c<11/2

Answer:

7

Step-by-step explanation:

4+3=7

7-4=3

7-3=4

Using the fact that all points on a circle are equidistant to its center, we will see that:

a =  -3 ±√21

All the points on a circle are equidistant to its center. Here the center is at (-3, -2), and we know that (0, -6) is on the circle.

The distance between these two is:

d = √( (-3 - 0)^2 + (-2 + 6)^2) = 5

Then the distance between (a, 0) also should be 5 units, so:

5 = √( (-3 - a)^2 + (-2 - 0)^2)

5 = √( (-3 - a)^2 + 4)

5^2 = (-3 - a)^2 + 4

25 - 4 = (-3 - a)^2

21 = (-3 - a)^2

±√21 = -3 - a

a = -3 ±√21

these are the two possible values of a.

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The result of the subtraction of the algebraic expression (5.62n − 2.8) − (4 + 14.3n) is -8.68n - 6.8 Third option is correct.

What is algebraic expression?

An algebraic expression is a mathematical phrase that uses numbers, operations such as addition and multiplication, and variables (letters or symbols that represent unknown values). Algebraic expressions are used to represent real-world problems and situations. Algebraic expressions can be combined and simplified, and they can also be used to solve equations. Algebraic expressions can be used to describe anything from the area of a circle to the cost of a car. Algebraic expressions are an essential part of algebra, and they are used to help students understand mathematics concepts in a more concrete way.

The given algebraic expressions are 5.62n - 2.8 and 4 + 14.3n

Now,

(5.62n − 2.8) − (4 + 14.3n)

5.62n - 2.8 - 4 - 14.3n

-8.68n - 6.8

Third option is correct

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Answer:

the answer is b

Step-by-step explanation:

a) The probability that an apple from the tree has a weight greater than 90 grams is of: 0.2514 = 25.14%.

b) i) The p-value of the test is of: 0.0045.

b) ii) The conclusion of the test is given as follows: There is enough evidence to conclude that the mean weight of apples from tree A is greater than the mean weight of apples from tree B, as the p-value of the test is less than the significance level.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation of the weight of the apples are given as follows:

[tex]\mu = 85, \sigma = 7.5[/tex]

The probability that an apple from the tree has a weight greater than 90 grams is one subtracted by the p-value of Z when X = 90, hence:

Z = (90 - 85)/7.5

Z = 0.67

Z = 0.67 has a p-value of 0.7486.

1 - 0.7486 = 0.2514 = 25.14%.

For each sample, the mean and the standard error are given as follows:

Hence, for the distribution of differences, the mean and the standard error are given as follows:

The test statistic is given by the division of the mean by the standard error of the distribution of differences, hence:

z = 4.2/1.61 = 2.61.

Using the z-table, with z = 2.61, the p-value is of:

0.0045.

As the p-value is less than the significance level, there is enough evidence to conclude that the mean weight of apples from tree A is greater than the mean weight of apples from tree B.

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