round 4.9 to the nearest whole number
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Hello!

We have the expression below:

Let's remember how we can use the sum identity formula:

Knowing it, let's use this property:

Let's solve the sum:

We can simplify it by two:

cos(4pi/5)

∠8 is the corresponds with ∠3.

Hence, option B is the correct answer.

Congruent angles are those that correspond. Corresponding pairs are all angles that are positioned in relation to the parallel and transversal lines in the same way. When two parallel lines are intersected by another line, comparable angles are the angles that are created in matching corners or corresponding corners with the transversal (i.e. the transversal).

we know that

m∠3=m∠8 --------> by corresponding angles

m∠7=m∠8 -------> by vertical angles

so

m∠3=m∠7 -------> by alternate interior angles

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NOTE: The given question is incomplete on the portal. Here is the complete question.

QUESTION: Which angle corresponds to ∠3?

A) ∠6

B) ∠8

C) ∠1

D) ∠7

The 0.0035 hr⁻¹ first-order degradation rate constant in the 40 °C, 1.0 mg/ml solution, where R = 1.987 cal/mol/degree and 2,000 cal/mol activation energy indicates;

a. The rate constant for first-order degradation of N₂O₂ at room temperature is approximately 4.12595 × 10⁻² hr⁻¹

A first order reaction is one that has a rate that varies linearly with the concentration of one reactant

The given parameters are;

Temperature of the solution = 40°C

T₁ = 40 °C + 273.15 = 313.15 K

The rate constant, K₁ = 0.00351 hr⁻¹

Concentration of the solution = 1.0 mg/ml

Activation energy, Eₐ = 2000 Cal/mol

R = 1.987 cal/mol/degree

The formula by which the rate constant can be found is presented as follows;

\(log\dfrac{k_2}{k_1} =\dfrac{E_a}{2.303\times R} \times \dfrac{T_2-T_1}{T_1\cdot T_2}\)

a. Room temperature = 25 °C

T₂ = 25 °C + 273.15 = 298.15 K

Therefore;

\(log\dfrac{k_2}{0.00351} =\dfrac{2000}{2.303\times 1.987} \times \dfrac{313.15-298.15}{313.15 \times 298.15}\)

\(k_2=0.00351 \times 10^{\left(\dfrac{2000}{2.303\times 1.987} \times \dfrac{313.15-298.15}{313.15 \times 298.15}\right)} \approx 4.12595\times 10^{-2}\)

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Part A: We can complete the model representing Sage's minutes by putting n and 7 in the box.

Part B: We can complete the model representing Tom's minutes by putting n and 7 in the box

Part C: An algebraic expression to represent the number of minutes Sage has left is S = n - 7, where S equals the remaining talk minutes for Sage and n is the initial number of talk minutes.

Part D. An algebraic expression to represent the number of minutes Tom has left is T = n - 7, where T equals the remaining talk minutes for Tom and n is the initial number of talk minutes.

Part E: Sage and Tom have the same number of talk minutes left on their cell phone plans because they started with the same amount and consumed the same amount at the end of the month.

An algebraic expression is a mathematical expression that consists of variables and constants, along with algebraic operations and equality or inequality symbols.

The basic algebraic operations include addition, subtraction, division, and multiplication.

Thus, algebraic expressions can be used to mathematically model or represent the number of minutes that Sage and Tom have left.

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The exact value of x is √1156 and it follows the Pythagorean triple

From the question, we have the following parameters that can be used in our computation:

Legs of the right triangle = 16 and 30

Using the pythagoras theorem, we have

Hypotenuse^2 = the sum of the squares of the other lengths

So, we have

x^2 = 16^2 + 30^2

When evaluated, we have

x^2 = 1156

This gives

x = √1156

Hence, the exact value is √1156

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Answer:

1) x=-1

Step-by-step explanation:

The red one is 3x+4

The green one is x+2

Answer:

The function y=x^2 +1 is even.

The  expressions are factors of the polynomial 3x4 - 14x³ 3x²+54x -40 are

Generally, To factor a polynomial using synthetic division, we need to find a factor of the polynomial that can be divided into the leading coefficient and the constant term of the polynomial.

In this case, the leading coefficient is 3 and the constant term is -40. One factor of 3 and -40 is (-4)(10).

The complete factorization of the polynomial is 3x⁴ - 14x³ + 3x² + 54x - 40  gives The remainder is 0, so the other factor is (x - 4)(x + 2)(x - 1)(x + 1).

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Answer:

Between 50 and 60

Step-by-step explanation:

4,346/82 is 53 which is between 50 and 60.

Hope this helps!

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Answer:

she ate my. s aa a awwosewrtfgfdswertyu

Step-by-step explanation:

wwwwojwojwowj

Answer:

$3,221.02

Step-by-step explanation:

Month 1: $2000 x 1.10 = $2,200

Month 2 = $2,200 x 1.10 = $2,420

Month 3 = $2,420 x 1.10 = $2,662

Month 4 = $2,662 x 1.10 = $2,928.2

Month 5 = $2,928.2 x 1.10 = $3,221.02

Answer:

last one

Step-by-step explanation:

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If Athlete J continues at that speed, it will take 12 minutes to run 1 mile

It will take Athlete J 60 minutes to run 5miles

Since the speed of Athlete H is greater than that of J, hence Athlete H runs faster.

The formula for calculating the speed of the athlete is expressed as:

Speed = Distance/Time

1) If Athlete J runs 2/3 of a mile in 8 minutes, this can be expressed as:

2/3 miles = 8 minutes

If the athlete runs for 1 mile, then;

1 mile = x

Divide both expressions

2/3 = 8/x

2x = 24

x = 12 minutes

Hence If Athlete J continues at that speed, it will take 12 minutes to run 1 mile

2) if athlete J run 5 miles, the time taken will be expressed as;

2/3(5) = 8/x

2/15 = 8/x

2x = 120

x = 60minutes

Hence it will take Athlete J 60 minutes to run 5miles

3) If Athlete H runs 2 3/4 miles in 1/2 hour, then the speed of athlete H will be expressed as:

Speed = (2 3/4)/0.5

Speed = 2.75/0.5

Speed = 5.5miles/hr

For Athlete J;

Speed = 5/1

Speed = 5 miles/hr

Since the speed of Athlete H is greater than that of J, hence Athlete H runs faster.

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Answer:

I would say that answer is proportional

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

Given statement solution is :- It  would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

To find the cost of installing tile in the dining room and carpet in the bedroom, we need to calculate the areas of both rooms first.

Given:

Every 2 centimeters on the floor plan represents 1 meter of the house.

Dining Room:

On the floor plan, the dining room is 8 cm by 10 cm.

Converting this to meters, the dimensions of the dining room are 8 cm / 2 = 4 meters by 10 cm / 2 = 5 meters.

The area of the dining room is 4 meters * 5 meters = 20 square meters.

Bedroom:

On the floor plan, the bedroom is 6 cm by 10 cm.

Converting this to meters, the dimensions of the bedroom are 6 cm / 2 = 3 meters by 10 cm / 2 = 5 meters.

The area of the bedroom is 3 meters * 5 meters = 15 square meters.

Now, let's calculate the costs.

Cost of Tile:

The cost of installing tile is $34 per square meter.

The area of the dining room is 20 square meters.

Therefore, the cost of installing tile in the dining room is 20 square meters * $34/square meter = $680.

Cost of Carpet:

The cost of installing carpet is $21 per square meter.

The area of the bedroom is 15 square meters.

Therefore, the cost of installing carpet in the bedroom is 15 square meters * $21/square meter = $315.

Therefore, it would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

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Answer:

Step-by-step explanation:

Exchange rates are the rates at which one currency can be exchanged for another currency. They represent the value of one currency relative to another currency.

Answer: The answer is 35.43 feet rounded to the nearest hundredth.

Step-by-step explanation:  

Answer:

The answer is 35.43 feet rounded to the nearest hundredth.

Step-by-step explanation:

If it is a square and the area is 1,255, the width and height of the square is the same. Find the square root of 1,255 and it will give you the length of the height and width (they are both the same being a square).

(A) The required down payment is $48,000.

(B) The amount of the mortgage is $192,000.

(C) Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

(a) To find the required down payment, we need to calculate 20% of the house price.

Down payment = 20% of $240,000

Down payment = 0.2 * $240,000

Down payment = $48,000

The required down payment is $48,000.

(b) The amount of the mortgage is equal to the total cost of the house minus the down payment.

Mortgage amount = Total cost of the house - Down payment

Mortgage amount = $240,000 - $48,000

Mortgage amount = $192,000

The amount of the mortgage is $192,000.

(c) To find the monthly payment for the mortgage, we can use the formula for the monthly payment on a fixed-rate mortgage:

Monthly payment = P * r * (1 + r)^n / ((1 + r)^n - 1)

Where:

P = Principal amount (mortgage amount)

r = Monthly interest rate (8.5% annual interest divided by 12 months and converted to a decimal)

n = Total number of monthly payments (30 years multiplied by 12 months)

Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

Using this formula and performing the calculation will give you the monthly payment amount.

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Answer:

(4,0)

Step-by-step explanation:

You basically are plotting a point on the positive number 4 on the x line. Since they're only asking for an X and not a Y, you'd leave it as (4,0). Hope this helps!

Regression equation correctly models the data is: y = -43.98x + 1,279.93

To determine the regression equation that correctly models the data, we can use the method of linear regression. The regression equation for a straight line is generally expressed as y = mx + b, where m is the slope and b is the y-intercept.

Using the given table, we can calculate the necessary values to determine the regression equation. Let's denote the sigma notation as Σ.

The slope (m) can be calculated using the formula:

\(m = (Σxy - (Σx)(Σy) / n(Σx^2) - (Σx)^2)\)

Plugging in the values from the table:

m =\((776,600 - (299)(12,400) / 6(18,109) - (299)^2)\)

m = (776,600 - 3,708,800 / 6(18,109) - 89,401)

m = (-2,932,200 / 66,654)

m ≈ -43.98

The y-intercept (b) can be calculated using the formula:

b = (Σy - m(Σx)) / n

Plugging in the values from the table:

b = (12,400 - (-43.98)(299)) / 6

b ≈ 1,279.93

The correct regression equation that models the data is:

y = -43.98x + 1,279.93

Out of the given options, the correct regression equation is:

y = -43.98x + 1,279.93

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Answer:

The probability the he or she will answer correctly is 1.5%

Step-by-step explanation:

Answer:

9 hours, 20 minutes

Step-by-step explanation:

When two ferries work together, they transport a day's cargo in 7 hours

The speed proportion or ratio of larger ferry to smaller ferry is given as 3 : 1

The sum of the ratio = 4 (3 + 1)

This means that it will take the smaller ferry = 7 x 4 hours to work alone = 28 hours, since the larger ferry is faster by 3.

Therefore, when larger ferry works alone, it will take it (7 x 4)/3 = 9.33 hours.

9.33 hours = 9 hours, 20 minutes.

The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is, 3 / 5

We have to given that;

the terminal side of theta in standard position contains the point (6,-8)

Hence, For given condition we get;

The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is,

Here, x = 6, y = - 8

Hence, We get;

r = √x² + y²

r  = √6² + 8²

r = √36 + 64

r = √100

r = 10

So, The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is,

cos θ = x / r

cos θ = 6 / 10

cos θ =  3 / 5

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The Vales of x in the equations are : 1) 3 (2) 1  (3) 5  (4) 14  (5) 10 respectively

A linear equation in one variable is that in which the highest power of its variable is 1

The given equations and their solutions are

2x +1 = 7

By collecting like terms we have

2x = 3

x = 3

2) The given equation is 4x +7 = 11

By collecting like terms we have

4x = 4

Making x the subject we have

x = 1

3) 2x -3 = 7

By collecting like terms we have

2x = 10

Making x the subject we have

x = 5

4) 1/2 x - 3 = 7

By collecting like terms we have

1/2x = 7

x= 14

5) The given equation is 3x - 11 = 19

By collecting like terms we have

3x= 30

Therefore x= 10

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