The cost of 6 1/2 kg of apples is Rs. 520. What is the rate of one kg of apples

Answer:

Here is the answer

Step-by-step explanation:

4^4/(6^6)

To find the slope we need two points and the formula

where (x2,y2) is a right point from (x1,y1) so x2>x1

now replacing

the slope is 3/2

Answer:

See below for answers

Step-by-step explanation:

y = -x+1 if x<3

y= x-5 if x>=3

Answer:

51,51 and 78

Step-by-step explanation:

3x+9=4x-5

3x=4x-14

-x=-14

x=14

The function in variable w giving the cost C (in dollars) of constructing the box is C(w) = 30w² + 270/w. The result is obtained by using the formula of volume and area of the box.

We have a rectangular storage container without a lid.

The formula of volume of the box is

V = l × w × h

Where

So, the height is

10 = 2w × w × h

10 = 2w² × h

h = 10/2w²

h = 5/w²

To find the total cost, calculate the area of base and sides of the box!

See the picture in the attachment!

The base area is

A₁ = 2w × w = 2w² m²

The sides area is

A₂ = 2(2wh + wh)

A₂ = 2(3wh)

A₂ = 6wh

A₂ = 6w(5/w²)

A₂ = 30/w m²

The total cost is

C = $15(2w²) + $9(30/w)

C = $30w² + $270/w

The function of the total cost is

C(w) = 30w² + 270/w

Hence, the function of constructing the box is C(w) = 30w² + 270/w.

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Therefore the polynomial (x – 2)(x^2 + 1) – x(x – 3) can be written in the form: ax^3 + bx^2 + cx + d = x^3 - 2x^2 + 4x - 6 where a = 1, b = -2, c = 4, and d = -2

The polynomial (x – 2)(x^2 + 1) – x(x – 3) can be written as:

ax^3 + bx^2 + cx + d = (x - 2)(x^2 + 1) - x(x - 3)

To find the values of a, b, c, and d, we need to multiply out the binomials and combine like terms. Using the distributive property, we get:

ax^3 + bx^2 + cx + d = x^3 - 2x^2 + x^2 + x - x^2 + 3x - 2

Now we can combine like terms:

ax^3 + bx^2 + cx + d = x^3 - 2x^2 + 4x - 2

So we can see that:

a = 1, b = -2, c = 4, and d = -2

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The value of the double integral is approximately equal to 16.38.

We want to evaluate the double integral of ∫∫ D 7y^2 dA, where D is the triangular region with vertices (0,1), (1,2), and (4,1).We want to find the double integral of the function given over the triangular region D. We can write the double integral in terms of x and y coordinates using the limits of integration for x and y.

First, let's sketch the triangular region D. We can find the equations of the lines passing through the vertices of the triangle:

Line passing through (0,1) and (1,2): y = x + 1

Line passing through (1,2) and (4,1): y = (-1/3)x + (7/3)

Line passing through (4,1) and (0,1): y = 1

Now we need to find the limits of integration for x and y. We can integrate with respect to y first and then with respect to x. The limits of integration for y are y = 1 to y = (-1/3)x + (7/3). The limits of integration for x are x = 0 to x = 4. Thus, we have:

∫∫ D 7y^2 dA = ∫0^4 ∫1^(-1/3)x+7/3 7y^2 dy dx

We can evaluate the integral using these limits of integration:

∫∫ D 7y^2 dA = ∫0^4 [(7/3)y^3]1^(-1/3)x+7/3 dx∫∫ D 7y^2 dA = ∫0^4 [(7/3)((-1/3)x + (7/3))^3 - (7/3)(1)^3] dx∫∫ D 7y^2 dA = ∫0^4 [(7/27)x^3 - (14/9)x^2 + (98/27)x - (49/27)] dx∫∫ D 7y^2 dA = [(7/108)x^4 - (14/27)x^3 + (49/54)x^2 - (49/27)x]0^4∫∫ D 7y^2 dA = [(7/108)(4)^4 - (14/27)(4)^3 + (49/54)(4)^2 - (49/27)(4)] - [(7/108)(0)^4 - (14/27)(0)^3 + (49/54)(0)^2 - (49/27)(0)]∫∫ D 7y^2 dA ≈ 16.38

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Answer:

331 the biggest possible number

The probability that all adjacent points differ in colour is \(\frac{1}{5}\).

What is probability ?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Have given ,

We have first three colour Green that is g1 , g2 and g3

And We have next three colour red that is r1 , r2 and r3

The probability that all adjacent points differ in colour = 3! * \(^{4}C_{3}\) 3! / 6!

=> \(\frac{ 3! * 4! *3!}{6!}\)

=> \(\frac{1}{5}\)

The probability that all adjacent points differ in colour is \(\frac{1}{5}\).

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We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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Answer:

one solution

infinite number of solutions  

no solutions

Step-by-step explanation:

i hope this helps :)

Answer:

2072

Step-by-step explanation:

Multiply 14 x 37

518 x 4

2072

Answer: $2,072 a month

Step-by-step explanation:

multiply 14 by 37 to see her weekly rate which is $518 a week. then multiply  518 by 4 (because there are about 4 weeks in a month). then you get the answer of $2,072

If lim (x→2) f(x) = 5, then we can say that f(2) is defined and equal to 5.

Let,  f(x)={ x−2
(2x+1)(x−2)
k
if x

=2
if x=2Now, to make the function f(x) continuous at x=2

we need to find the value of k which satisfies the following condition: lim (x→2) f(x) = f(2)For x < 2, f(x) = 1/(2x+1).

Therefore, lim (x→2-) f(x) = 1/5For x > 2, f(x) = 1/(x-2).

Therefore, lim (x→2+) f(x) = -1/2

Hence, the value of k such that the given function is continuous at x=2 is 2. So, option (B) is correct.

For the next question, The line y=5 is a horizontal asymptote to the graph of the function f(x)= 1-x/5x,

because, lim (x→∞) f(x) = lim (x→∞) [1- (x/5x)] = lim (x→∞) [1 - 1/5] = 4/5

Therefore, option (D) is correct.  

For the next question,If the horizontal line y=2 is an asymptote for the graph of a function f, then lim (x→∞) f(x) = lim (x→-∞) f(x) = 2

Therefore, the correct option is (B).

For the final question, If lim (x→2) f(x) = 5, then we can say that f(2) is defined and equal to 5.

However, it does not ensure that f(x) is continuous at x=2. Hence, option (D) is correct.

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Answer:

Step-by-step explanation:

Since the journey initially costs $2 (this will be our y-intercept), and the variable (x) is $1 for every additional kilometer. This can be modelled as...

y=1x+2

(i) if we want to know the cost of what 3.5 km would cost, we simply plug it into our equation...

y=1(3.5)+2

Answer: $5.5

(ii) For this question you can set the y value equal to 6 and plug in a random number for x until you get 6 on both sides. In this case...

6=1x+2

6=1(4)+2

The distance traveled if the fare was $6 is 4km

I hope this helps you! When I was younger I used to use this site for help and now I'm paying it forward!

x^2 + 6x + 9

x^2 + 3x + 3x + 9

x ( x + 3 ) + 3 ( x + 3 )

( x + 3 ) ( x + 3 )

( x + 3 ) ^2

Answer:

31 DVDs

Step-by-step explanation:

156 / 5 = 31.2

Answer

You can buy 31 DVDS with 156 dollars.

Step-by-step explanation:

If you divid 156 by 5 you get 31.2 but simlfied.

The expression that is used to represent "the product of 3/4 and c" is 3/4c.

The term expression ins math is defined as a sentence with a minimum of two numbers or variables and at least one math operation.

Here we have given the statement "the product of 3/4 and c".

Now, we need to find the suitable expression for this one.

While we looking into the given statement we have identified that the following are presented

3/4 refers number also known as constant

c refers the variable

The term product refers the mathematical operation that has been done between number and variable.

So, as per the standard form of expression is can be written as.

=> 3/4 x c

=> 3/4 c

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Answer:

The domain is

\( - 6 \leqslant x \leqslant 6\)

Answer:

$5

Step-by-step explanation:

Start by finding how much money Jacob has after buying a game for himself:

$50-$15=$35

Now, we have to divide $35 by 7 since he has 7 friends...

$35/7=$5

He can spend $5 on each friend

Answer:

500000000

Step-by-step explanation:

Because you have to do those and then after you divided it took those zeros and made them longer since they are already positive.

Answer:

Its the second one

Step-by-step explanation:

Answer is rational numbers

Based on the definition of Same-side exterior angles, the angle measures are determined as: m<3 = 66°; m<6 = 114°.

Same-side exterior angles are a pair of angles formed by parallel lines and a transversal line on the same side. According to the theorem, these angles have a combined measure of 180 degrees, making them supplementary.

Angles 2 and 7 are Same-side exterior angles, therefore:

m<2 + m<7 = 180

Substitute:

3x + 20 + 2x - 10 = 180

Add like terms:

5x + 10 = 180

5x = 180 + 10

5x = 190

x = 38

m<3 = m<7 [corresponding angles]

m<3 = 2x - 10 = 2(38) - 10

m<3 = 66°

m<6 = 180 - m<3

m<6 = 180 - 66

m<6 = 114°

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Answer:

All of them are right

Step-by-step explanation:

Are you sure the question was that?

Collinear means that it lies on the same line

Now, from every 2 points passes a unique line

So(0,0) and (3,2) are in a line

(0,0) and (1,0) are in an other line and so on

following:

The book "How to Solve It" by George Polya is a classic work in the field of mathematics education. It lays out a four-step method for solving mathematical problems, which includes understanding the problem, devising a plan, carrying out the plan, and reflecting on the solution obtained.

The purpose of the book is to help students and problem solvers develop a systematic and effective approach to solving problems in mathematics and other areas of life. The book is widely used and respected in mathematics education, and its ideas have been applied to many other fields, such as engineering, computer science, and business.

The four steps outlined in the book provide a structure for approaching any problem in a systematic and organized manner, which can be applied to a wide variety of problems in different fields. This structure helps to ensure that all relevant information is considered and that the problem is solved in the most efficient and effective way possible.

Additionally, the step of reflecting on the solution obtained helps to promote a deeper understanding of the problem and the solution, which is important for developing problem-solving skills over time. As a result of its simplicity, clarity, and effectiveness, "How to Solve It" continues to be a popular and highly-regarded book in the field of mathematics education and beyond.

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The independent variable is the brand of algaecide. The dependent variable is the treatment of pool water with algae.

What is the independent and dependent variable?

In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, their values are investigated under the presumption or requirement that they are dependent on the values of other variables due to some law or rule.

Here, we have

Given

A pool store owner wants to determine the effect of algaecide brands on the treatment of pool water with algae. He contacts customers who have purchased the brands of algaecide and asks their opinion of the algaecide.

We have to determine the independent variable and the dependent variable.

We concluded that the independent variable is the brand of algaecide and the dependent variable is the treatment of pool water with algae.

Hence, the independent variable is the brand of algaecide and the dependent variable is the treatment of pool water with algae.

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From the given diagram, we can identify two right-angled triangles. The triangles are shown below:

Using trigonometric ratios, we can find x as follows

We can equate the expressions for DF as follows:

Solving for x:

Answer:

x = 5

Step-by-step explanation:

Strictly increasing functions:

Let a function f(a) for x = a, then,

f(a + h), for x = a + h,

If f(a + h) > f(a), we say this a strictly increasing function, as with increase in x, f(x) also increases.

In the given graph, there are straight lines so you can say increasing interval would have +ve slope.

For x = -4 to 0, it increases = [-4, 0]

For x = 2 to 5, it increases = [2, 5]

Answer: [-4, 0], [2, 5]

It is important to consider the scale of measurement and the specific characteristics of the variables when selecting an appropriate statistical test.The tests can be classified as follows:

1. A researcher measures the proportion of schizophrenic patients born in each season.

This test is nonparametric. The scale of measurement is categorical, as the seasons (spring, summer, fall, winter) represent distinct categories rather than continuous numerical values. Therefore, parametric assumptions, such as normality and equal variances, do not apply to this measurement.

2. A researcher measures the average age that schizophrenia is diagnosed among male and female patients.

This test is parametric. The scale of measurement is continuous and numerical (age in years). Parametric tests, such as t-tests or ANOVA, can be applied when working with continuous data, assuming the data meet the required assumptions (e.g., normality, independence, and equal variances).

3. A researcher tests whether frequency of Internet use and social interaction are independent.

This test can be both parametric or nonparametric, depending on the measurement scale and the specific statistical test used. If the variables are measured on a nominal or ordinal scale, nonparametric tests, such as the chi-square test, would be appropriate. If the variables are measured on a continuous scale, parametric tests, such as logistic regression, could be employed.

4. A researcher measures the amount of time (in seconds) that a group of teenagers uses the Internet for school-related and non-school-related purposes.

This test is parametric. The scale of measurement is continuous (time in seconds), and parametric tests, such as t-tests or ANOVA, can be utilized to compare means or variances, assuming the required assumptions are met.

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