Express as simply as possible with a rational denominator
1
√
10

If the sequence is 36 , 32 , 28, then the explicit formula for term aₙ , the nth term is 40 - 4n.

The given sequence is 36, 32, 28, which is a decreasing arithmetic sequence with a common difference of -4.

To find the nth term of an arithmetic sequence, we can use the formula:

aₙ = a₁ + (n - 1)d

where a₁ is the first term, d is the common difference, and n is the term we want to find.

In this case, a₁  = 36, d = -4, and we want to find the nth term.

So, the formula for the nth term of the sequence is:

aₙ = 36 + (n - 1)(-4)

Simplifying this expression:

aₙ = 36 - 4n + 4

aₙ = 40 - 4n

Therefore, the explicit formula for the nth term of the given sequence is aₙ = 40 - 4n.

This formula can be used to find any term of the sequence by substituting the desired value of n. For example, to find the 6th term, we would plug in n = 6:

a₆ = 40 - 4(6) = 16

To learn more about sequence click on,

https://brainly.com/question/26092125

#SPJ4

The point οn the graph of [tex]f(x) = 5-x^2[/tex] that is clοsest to the point (1, 0) is (0.492, 4.592).

What is a graph ?

Graph can be defined as visual representation of data using given οrdered pairs.

To find the pοint on the graph οf [tex]f(x) = 5-x^2[/tex] that is closest to the point (1, 0), we need to minimize the distance between the two points. The distance between two points (x1, y1) and (x2, y2) is given by the formula:

d = sqrt((x2 - x1)² + (y2 - y1)²)

Sο, in this case, we want tο minimize the distance between (1, 0) and a pοint οn the graph οf f(x) = 5 − x², which can be written as (x, f(x)).

The distance between these twο pοints is:

d = sqrt((x - 1)² + (f(x) - 0)²)

We want tο minimize this distance, sο we need tο find the value οf x that minimizes this expressiοn. Tο dο this, we can use Newtοn's Methοd.

Let's define a functiοn g(x) as:

g(x) = (x - 1)² + (f(x) - 0)²

We want tο find the value οf x that minimizes g(x). Tο dο this, we need tο find the derivative οf g(x):

g'(x) = 2(x - 1) - 2f(x)f'(x)

We can substitute f(x) = 5 - x² and f'(x) = -2x intο this equatiοn:

g'(x) = 2(x - 1) + 4x(5 - x²)

Simplifying this expressiοn, we get:

g'(x) = 12x² - 8x - 8

Nοw we can use Newtοn's Methοd with the initial guess x0 = 0:

x1 = x0 - g(x0)/g'(x0)

x1 = 0 - g(0)/g'(0)

x1 = -0.6667

Using x1 as οur new guess, we repeat the prοcess:

x2 = x1 - g(x1)/g'(x1)

x2 = -0.6667 - g(-0.6667)/g'(-0.6667)

x2 = 0.4293

We cοntinue this prοcess until we reach a desired level οf accuracy. Let's say we want tο rοund οur final answer tο three decimal places. Then we can stοp οnce we find an xn such that |xn - xn-1| < 0.001.

Using a spreadsheet οr calculatοr, we can cοntinue this prοcess and find that:

x3 = 0.4873

x4 = 0.4915

x5 = 0.4916

Since |x5 - x4| < 0.001, we can rοund οur final answer tο three decimal places:

(x, y) = (0.492, 4.592)

Therefοre, the pοint οn the graph οf f(x) = 5 − x² that is clοsest tο the pοint (1, 0) is (0.492, 4.592).

To learn more about Graph from given link.

https://brainly.com/question/17267403

#SPJ1

Answer:

R 270

Step-by-step explanation:

Amount paid for one hour =  [tex]\frac{360}{12}[/tex]

Amount paid for one hour = Rs 30

Amount paid for 9 hours = 9 × 30

Amount paid for 9 hours = Rs 270

The painter will be paid Rs 270 for 9 hours of work.

a) The probability that it will not rain on the homecoming parade in Amina's first year is 0.84. b) The probability that it will not rain on any of the homecoming parades during Amina's four years at the school is 0.49. c) The probability that it will rain on Amina's parade at least once during her four years of attendance is 0.51.

We can solve this problem as:
a) This can be calculated by subtracting the probability of rain during the parade (0.16) from 1.

So, the probability is,

1 - 0.16 = 0.84.

b) This can be calculated by taking the probability of no rain (0.84) and multiplying it by itself four times.

So, the probability is,

0.84^4 = 0.49.

c) This can be calculated by subtracting the probability of no rain (0.49) from 1.

So, the probability is,

1 - 0.49 = 0.51.

In conclusion, the probability that it will not rain on the homecoming parade in Amina's first year is 0.84, the probability that it will not rain on any of the homecoming parades during Amina's four years at the school is 0.49, and the probability that it will rain on Amina's parade at least once during her four years of attendance is 0.51.

Know more about probability here:

https://brainly.com/question/13604758

#SPJ11

The cup will hold more ice cream than cone since volume of cup is 169.6 cubic inches which is greater than volume of 25.1 cubic inches.

The volume of a cone is given by the formula:

V= 1/3.π[tex]r^{2}[/tex]h

where r is the radius of the circular base and h is the height.

The volume of a cylinder is given by the formula:

V= π[tex]r^{2}[/tex]h

where r is the radius of the circular base and h is the height.

Assuming that the height of both the cone and the cup is the same, we can compare their volumes by comparing their radii.

For the cone, the radius r is equal to half the diameter of the circular base, which is equal to w/2 = 2 in.

The height of the cone is equal to y, which is 6 in.

V= 1/3.π[tex]r^{2}[/tex]h= 1/3.π[tex]2^{2}[/tex]6

For the cup, the radius r is equal to x/2 = 3

The height of the cup is equal to y, which is also 6 in.

Using these values, we can calculate the volume of the cup as:

[tex]V_cup[/tex]= π[tex]r^{2}[/tex]h=π[tex]3^{2}[/tex]6

Therefore, the cup will hold more ice cream than the cone.

learn more about Volume of cylinder here:

https://brainly.com/question/6204273

#SPJ4

Answer:

Step-by-step explanation:u better not be him cause im him

Answer:

y > -5

Step-by-step explanation:

This modification will reduce the amount he needs to borrow from the lender and thus lower his monthly mortgage payments.

The down payment is the amount of money that the buyer pays upfront towards the purchase price of the property. The more significant the down payment, the less money the buyer has to borrow from the lender, and this can have a significant impact on the monthly mortgage payments.

In the case of Nick, he has saved up 35,000 for a down payment, which is approximately 18% of the purchase price of the house. If he decides to go with the 20% down payment option, he will need to pay 38,400 upfront, which is 20% of 192,000. The remaining 153,600 will be the amount he borrows from the lender.

Now, let's assume that Nick has taken a 30-year fixed-rate mortgage at 6.25% interest. If he decides to pay 20% down payment, his monthly mortgage payments would be approximately 940. However, Nick wants to spend no more than 30% of his income on his mortgage payment, which is 997.50 per month (30% of 3,325). Therefore, the modification that can be made to this loan to make it a viable option is to reduce the loan amount.

If Nick reduces the loan amount to 153,000, his monthly mortgage payment will be approximately 910, which is within his budget. To achieve this, he will need to increase his down payment to 39,000, which is 20.3% of the purchase price. This modification will reduce the amount he needs to borrow from the lender and thus lower his monthly mortgage payments.

In summary, a larger down payment reduces the amount borrowed from the lender and, consequently, lowers the monthly mortgage payments. To make the loan option viable, Nick needs to increase his down payment to reduce the loan amount and meet his budget.

for such more question on income

https://brainly.com/question/15530787

#SPJ4

Answer:

  80°

Step-by-step explanation:

You want the larger of two acute angles in a right triangle if their relationship is cos(8x°) = sin(2x-10°).

The cosine of an acute angle is equal to the sine of its complement. The given relation between the angles means ...

  (8x) +(2x -10) = 90 . . . . . the angles are complementary

  10x = 100 . . . . . . . . . . . add 10

  x = 10 . . . . . . . . . . . . . divide by 10

The two angles are 8·10° = 80° and (2·10 -10)° = 10°.

The larger of the two acute angles is 80°.

The expression that was not found for the pair of students is given as follows:

5x + 3.

To add or subtract polynomials, we must combine the like terms on the polynomials.

The polynomials for this problem are given as follows:

Hence the addition of these polynomials is given as follows:

3x + 4 - 2x - 1 = x + 3.

(addition keeps the signal of each term in the second polynomial).

The subtraction is given as follows:

3x + 4 + 2x + 1 = 5x + 5.

(subtraction changes the signal of each term in the second polynomial).

For the product, we multiply all terms then combine the like terms, hence:

(3x + 4)(-2x - 1) = -6x² - 3x - 8x - 4 = -6x² - 11x - 4.

5x + 3 is not a solution of any of the operations, hence it is the answer.

More can be learned about the addition of polynomials at https://brainly.com/question/20404672

#SPJ1

The point which is a solution to the equation 2x - 7y = 7 as required to be determined is; (0, -1).

As evident from the task content; the point which is a solution to the given equation is to be determined.

For a given equation; the y-intercept represents a solution to the equation.

On this note, if x = 0; therefore, we have that;

2 (0) - 7y = 7

y = 7 / -7

y = -1.

Ultimately, the point which is a solution to the equation is; (0, -1).

Read more on y-intercept;

https://brainly.com/question/10700419

#SPJ1

Answer: Bonato

Step-by-step explanation:

Answer:

Point A represents -1 1/3.

Point A is correct.

An effective indicator for assessing retail store efficiency, spotting market trends, and making strategic business decisions is annual earnings per employee for profits.

The retail sales industry's annual profits per employee are shown in the data. The data's mean or median is most likely about $4,000,000, according to the assumption. You may compare the productivity of several retail stores by looking at the annual profits per employee. Businesses that generate more annual earnings per employee are typically more productive than those that do not.

The information can also be utilized to spot patterns in the retail sector, such as which businesses are operating better than others. For instance, if a business has been steadily increasing its annual profit per employee, it can be a sign that it is growing or streamlining its operations. In contrast, a business with declining annual profits per employee might be having trouble or seeing a drop in the demand for its goods.

Learn more about profits here:

https://brainly.com/question/15190155

#SPJ1

Monica is not correct. Monica will earn $13.50 in 1 year while Paul will earn $13.20 in 1 year.

Simple interest is a linear function of the amount deposited, the interest rate and the number of years.

Simple interest = amount deposited x interest rate x time

Interest earned by Monica = $400 x 0.033 x 1 = $13.20

Interest earned by Paul = $500 x 0.027 x 1 = $13.50

Difference in the interest = $13.50 - $13.20 = $0.30

To learn more about simple interest, please check: https://brainly.com/question/27328409

#SPJ1

This function has zeros at x = -2, x = -5, and x = 7, since when any of these values are plugged into the function, the corresponding factor becomes zero, making the entire expression zero.

An expression is a combination of numbers, variables, and operators that represents a mathematical quantity or relationship. It can consist of a single number or variable, or it can be a more complex combination of terms.Expressions can be used to represent a wide range of mathematical ideas, such as functions, equations, inequalities, and identities.

In the given question,

A possible function that has zeros at -2, -5, and 7 is:

f(x) = a(x+2)(x+5)(x-7)

where a is a constant that determines the scale of the function.

Expanding the expression, we get:

f(x) = a(x³ + 5x² - 14x - 70)

This function has zeros at x = -2, x = -5, and x = 7, since when any of these values are plugged into the function, the corresponding factor becomes zero, making the entire expression zero.

Note that there are other possible functions that could have the same zeros, but this is one example.

To know more about expressions, visit:

https://brainly.com/question/14083225

#SPJ1

Simple Interest = (Principal x Rate x Time)

where:

Principal = R500 (the amount invested)

Rate = 12% per annum = 0.12 (expressed as a decimal)

Time = 4 years

So, the simple interest earned by John over 4 years is:

Simple Interest = (500 x 0.12 x 4) = R240

To find the total amount of money John will have at the end of 4 years, we need to add the simple interest to the principal:

Total amount = Principal + Simple Interest = 500 + 240 = R740

Therefore, John will have R740 at the end of 4 years.

Answer:

The total amount he has at the end is ₹740.

Step-by-step explanation:

Simple Interest = [tex]\frac{PRT}{100}[/tex]

                          =  [tex]\frac{500 * 12 * 4}{100}[/tex] = ₹240

Total amount he has at the end of 4 years = Principal + Interest
                                                                       = ₹500 + ₹240

                                                                       = ₹740

If a painter mixed 56 ounces of blue and yellow paint. The ratio is 3 to 11, 12 ounces of blue paint were utilized by the painter.

To solve the problem, we can use the ratio of blue to the total amount of paint to determine how many ounces of blue paint were used. The ratio of blue to the total paint is 3 to 11. This means that for every 3 parts of blue paint, there are 11 parts of total paint. We can use this information to set up a proportion:

3/14 = x/56

Where x represents the number of ounces of blue paint used. To solve for x, we can cross-multiply and simplify:

356 = 14x

168 = 14 × x

x = 12

Therefore, the painter used 12 ounces of blue paint.

To learn more about ratio click here

brainly.com/question/13419413

#SPJ4

The ratio of the number of squares to the number of triangles in simplest form is 5:2. The number of triangles that need to be added to make the ratio of the number of squares to the number of triangles 1 : 1 is 3.

What is the ratio?

A fraction that demonstrates how several times one quantity is of the other is the ratio of two quantities of the same kind and in the same units. Ratio is represented by the symbol ":". The expression a/b, which originally stood for the ratio of two measurements a and b (b≠ 0), is used.

Given that the number of squares are 5 and the number of triangles are 2.

The ratio of the number of squares to the number of triangles in simplest form is 5 : 2.

Assume that x number of triangles that needs to be added to make the ratio of the number of squares to the number of triangles 1 : 1.

The equation is:

5:(2+x) = 1:1

5/(2+x) = 1/1

Cross multiply both sides:

5 = 2 + x

x = 5 - 2

x = 3

3 triangles need to be added to make the ratio of the number of squares to the number of triangles 1 : 1

To learn more about the simplest form of ratio, click on the below link:

https://brainly.com/question/8705569

#SPJ1

In triangle ABC, AB + BC > AC is the correct option.

Three straight sides and three angles make up the two-dimensional geometric shape known as a triangle. they can be of many types .

I think that the question is related to the triangle,

Choose the correct option for ∆ABC,

a. AB + BC > AC

b. AB + BC < AC

c. AB + AC < BC

d. AC + BC < AB

Given, ABC is a triangle.

We are aware that the length of a triangle's third side is always greater than the sum of its other two sides.

Let the two sides of ∆ABC is AB and BC and the third side is AC.

So, AB + BC > AC

Therefore, option a is true.

To know more about triangle visit:

brainly.com/question/1058720

#SPJ1

What are the possible orderings of the sides of triangle ABC, given the three sides are AB, BC, and AC?

a: BC, AB, AC

b: AB ,BC, AC

c: AC ,AB, BC

d: AB ,AC, BC

Answer: We can solve this problem using trigonometry and basic geometry. Let's first draw a diagram:

               A (top of house)

              /|

             / | h

            /  |

           /   |

          /θ1  |

         /     |

        /      |

       /       |

      /        |

     /         |

    /          |

   /           |

  /            |

 /             |

B (top of column)  

 | d          

 |            

 |

 |

C (bottom of column)

We are given that angle theta 1 (θ1) is 45 degrees, angle theta 2 (θ2) is 60 degrees, and the height of the column BC is 95.62 meters. We want to find the height of the house AB, which we'll call "h".

First, we can use trigonometry to find the length of segment CD. Since we know angle θ2 and the length of BC, we can use the tangent function:

tan(θ2) = opposite / adjacent

tan(60°) = d / 95.62

d = 95.62 * tan(60°)

d ≈ 165.30 meters

Now we can use the fact that angles ABD and CBD are complementary to find the length of segment AD:

tan(θ1) = opposite / adjacent

tan(45°) = h / (d + 165.30)

h = (d + 165.30) * tan(45°)

h ≈ 165.30 meters

Therefore, the height of the house is approximately 165.30 meters.

Step-by-step explanation:

Answer:

Step-by-step explanation:The width would be 2 the same for the height

[tex]\tan^2(\theta )+3\tan(\theta )=0\implies \tan(\theta )[\tan(\theta )+3]=0 \\\\[-0.35em] ~\dotfill\\\\ \tan(\theta )=0\implies \theta =\tan^{-1}(0)\implies \theta = \begin{cases} 90^o\\ 270^o \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \tan(\theta )+3\implies \tan(\theta )=-3\implies \theta =\tan^{-1}(-3)\implies \theta \approx \begin{cases} \stackrel{ II~Quadrant }{108.43^o}\\ \stackrel{ IV~Quadrant }{288.43^o} \end{cases}[/tex]

Answer: Its 12 the answer.

Step-by-step explanation:

(5+4) divided bye 3  is not equals 9 divided by 4

Division is a basic arithmetic operation used to find how many times one quantity is contained within another quantity. It involves splitting a number or quantity into equal parts or groups. The result of a division is called the quotient.

In division, the number being divided is called the dividend, the number by which it is divided is called the divisor, and the result is the quotient. For example, in the division problem 10 ÷ 2 = 5, 10 is the dividend, 2 is the divisor, and 5 is the quotient.

Given 5+4=9

To prove;  (5+4) divided bye 3 = 9 divided by 4

Taking LHS,

(5+4) divided bye 3

=9/3

=3

Taking RHS,

9 divided by 4

=9/4

=2.25

LHS is not equal to RHS

Hence, given statement is false.

To know more about quotient, visit:

https://brainly.com/question/16134410

#SPJ1

The t-test, contributed to the development of Monte Carlo methods by using it to study the normal distribution in small sample sizes.

Monte Carlo methods can be used to test the effect of violating statistical tests' assumptions. This technique is primarily used in creating new statistical methods, including the t test for independent means.The t-test is a statistical hypothesis test used to determine whether there is a significant difference between the means of two groups, which may be related in certain characteristics. The t-test is one of the most frequently used tests in statistics for testing hypotheses about the mean of a population based on a sample mean.

Assumptions are essential for a t-test because they help researchers make logical, trustworthy assumptions based on their statistical data. These assumptions may include the normality assumption, homogeneity of variance, and independent random sampling.

It is important to meet these assumptions to get the correct statistical results. Violating these assumptions can affect the accuracy of the results.Monte Carlo methods are used to simulate the probability of different outcomes in a process that cannot be easily predicted because of random variables. They are used to study systems with many variables that are not easily solved. Egon Pearson and Karl Pearson invented these methods to study Brownian motion. "Student" (Gosset), who is known for creating the t-test, contributed to the development of Monte Carlo methods by using it to study the normal distribution in small sample sizes.

Learn more about T-test

brainly.com/question/15870238

#SPJ4

Answer:

Step-by-step explanation: It would help if you added the picture but its all good.

each person would have 2 feet and two inches of tape