The average human heart beats 1.15x10^5 times per day. There are 3.65x10^2 days in one year. How many times does the heart beat in one year? Write your answer in scientific notation, and round to one decimal place.

Answer:

The answer is C

Step-by-step explanation:

It can express as tan (θ) =  -√(sec² (θ) - 1).

A quadrant is defined as an area contained by the x and y axes, which there are four quadrants in a graph.

We have to express tan(θ) in terms of sec(θ) for θ in Quadrant II.

As per the trigonometry identity, we know that

sec² (θ) - tan² (θ) = 1

tan² (θ) = sec² (θ) - 1

Apply the square root property to both sides, and we get

tan (θ) = ± √(sec² (θ) - 1)

Since θ in Quadrant II, so we take a negative value

tan (θ) =  -√(sec² (θ) - 1)

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The possible arrangements would be:

Combination refers to the various ways that certain objects or numbers can be arranged. If the set already has an order, rearranging its elements, or placing its members in a linear or sequential order.

Given that solar panels use the sun's energy to generate power. A town wants to install 28 solar panels in an array.

The possible arrangements would be:-

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Answer:

see explanation

Step-by-step explanation:

using the identity

sin²Θ = 1 - cos²Θ

consider the left side

1 - [tex]\frac{sin^20}{1+cos0}[/tex]

= 1 - [tex]\frac{1-cos^20}{1+cos0}[/tex]

1 - cos²Θ is a difference of squares and factors as (1 - cosΘ)(1 + cosΘ)

= 1 - [tex]\frac{(1-cos0)(1+cos0)}{1+cos0}[/tex] ← cancel (1 + cosΘ) on numerator/ denominator

= 1 - (1 - cosΘ) ← distribute parenthesis by - 1

= 1 - 1 + cosΘ

= cosΘ

= right side

She can generate one of 30 results by tossing a coin, rolling a fair die with six sides labeled 1 through 6, and spinning a spinner with multiple equal-sized sections marked Walk, Run, and Stop.

We only apply the basic concept of counting. According to this rule, the number of options for both occurrences is equal to p x q if there are p possibilities once per event as well as q possibilities for just a second event. This formula can be expanded to include more events.

Let's say there are p possible outcomes when a coin is flipped based on the information provided. Therefore, p=2 because there are two alternative results, heads or tails.

Let q represent the result of a fair die that is shaped like a six-sided cube.

Labeled 1 to 6. So, q = 6.

and let r represent the results of spinning a wheel with three equally sized sections marked Walk, Run, and Stop. then, r = 3.

∴ Total possible outcomes  

= 2×6×3

= 36 outcomes

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The net yardage the Bobcats football coach logged over four plays of game is  19.8x - 11.1y

The net yardage is calculated using the addition and subtraction operation as follows

For the gains the calculation is as follows

= Gain 25x yards + Gain 0.9y yards.

= 25x + 0.9y

For the lose the calculation is as follows

= Lose 12y yards + Lose 5.2x yards.

= 5.2x + 12y

the net yardage is solved as follows

net yardage = gains - loses

net yardage = (25x + 0.9y) - (5.2x + 12y)

removing the parenthesis and rearranging

net yardage = 25x + 0.9y - 5.2x - 12y

net yardage = 25x - 5.2x + 0.9y - 12y

net yardage = 19.8x - 11.1y

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option C again correct if I'm wrong

An arithmetic sequence has a constant difference between each consecutive pair of terms. This is similar to the linear functions that have the form y=mx+b. A geometric sequence has a constant ratio between each pair of consecutive terms. This would create the effect of a constant multiplier.

Answer:

y=6

Step-by-step explanation:

right!!

The four statemen that describes the relationship of the model

A model refers to images, objects variables meant to depict a relation

In the model provided the relationship existing between the models is that the mass are equal hence there will be an equality sign to balance the relationship in the left and right hand side

examining the model shows that

3 cylinders = 1 cylinder + 1 cube

3 cylinders - 1 cylinder = 1 cube

2 cylinders = 1 cube

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The given model is exponential.

The formula for an exponential function is f (x) = ax, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

When b > 0 and b 1, an exponential function has the form f(x) = bx. The base is b, and the exponent is x, just like in any exponential expression. The development of bacteria is an illustration of an exponential function. Some germs multiply by two per hour.

As it is clear from the figure, 1 block has 2 boxes, then 4, 8.

So, it is in the form 2ⁿ.

∴ It is Exponential model.

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Complete question -

Answer:

16 gallons of gas are needed to travel 300 miles

Step-by-step explanation:

75x4=300

4x4=16

Answer: (-b + a, b + a).

Step-by-step explanation:

To find the radius of convergence of the series, we use the formula:

R = 1/limsup|bn|^(1/n)

To find the interval of convergence, we can use the following:

If R > 0, the series converges for all |x-a| < R and diverges for |x-a| > R.

If R = 0, the series converges only at x = a and diverges for all other values of x.

If R = ∞, the series converges for all values of x.

Therefore, the interval of convergence of the series is (-R + a, R + a).

In this case, the radius of convergence R is given as b, and the interval of convergence is (-b + a, b + a).

The domain is the area enclosed by the circle, which is all the points inside the unit circle.

The domain of a function is the set of all possible input values (x, y) for which the function is defined and produces a valid output.

For f(x, y) = ln(25 − x2 − 25y2), the function is defined as long as 25 − x2 − 25y2 > 0. This is because the natural logarithm (ln) is only defined for positive numbers. To find the domain, we can set 25 − x2 − 25y2 > 0 and solve for x and y.

25 − x2 − 25y2 > 0

x2 + 25y2 < 25

x2 / 25 + y2 < 1

This is the equation of a unit circle centered at (0,0) with a radius of 1.

So the domain is the area enclosed by the circle, which is all the points inside the unit circle.

You can graph this on the x-y plane.

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The value of the mathematical statement is (d) 0.9m  - 4.9n - 1

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

A mathematical statement

The mathematical statement is give as

1.4m + 3.7n +1 subtracted from 2.3m−1.2n

When this is represented as an expression

We have the following representation

2.3m−1.2n - (1.4m + 3.7n +1)

Express properly

2.3m − 1.2n - (1.4m + 3.7n + 1)

Open the brackets

So, we have the following representation

2.3m − 1.2n - (1.4m + 3.7n + 1) = 2.3m − 1.2n - 1.4m - 3.7n - 1

Collect the like terms

So, we have the following representation

2.3m − 1.2n - (1.4m + 3.7n + 1) = 2.3m - 1.4m  − 1.2n - 3.7n - 1

Evaluate the like terms

So, we have the following representation

2.3m − 1.2n - (1.4m + 3.7n + 1) = 0.9m  - 4.9n - 1

Hence, the expression is (d) 0.9m  - 4.9n - 1

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Step-by-step explanation:

With bodmas rule

first should be solve divide

so 2^6/2^3=2^3

6^3*2^3=1728

Everybody votes in a direct democracy to select a place for  the yearbook signing party.

Rules, institutions, and procedures known as "direct democracy" allow members of the public to vote directly on proposed constitutional amendments, laws, treaties, or policy decisions. Referendum and initiatives are the two most significant examples of direct democracy that are addressed in this primer.

Given:

It's the end of the school year, and your class of 250 students must decide the best place for the yearbook signing party.

To select the place:

They vote in direct democracy.

Because they have only 250 people.

And 250 people can have direct say.

Number of people is less.

So, selecting representatives would be not fair.

Therefore, everybody votes in a direct democracy.

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The acute angle of a triangle is an angle that measures less than 90°. Hence, in the triangle ABC, an acute angle is any angle that is smaller than 90°.

An angle is the figure created by two rays whose termini coincide. The measure of an angle is the amount of rotation required to bring one ray onto the other. A degree or angle that is less than 90° is said to be acute. This means that the two rays forming the angle can be brought together without making a full rotation.

A right angle is an angle having a measurement of precisely 90°. A right angle is formed when the two rays are perpendicular to each other, meaning they form a 90-degree angle. A right angle is often symbolized with a small square at the angle's vertex.

If an angle measures more than 90°, it is called an obtuse angle. An obtuse angle is formed when the two rays forming the angle can be brought together by making more than one full rotation. Obtuse angles are larger than right angles, but smaller than straight angles (which measure 180°).

It's important to note that the terms "acute," "right," and "obtuse" are not just limited to angles. They can also be used to describe other geometric shapes, such as triangles and circles. In these cases, the definitions may vary slightly, but the basic concept remains the same.

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A sequence is a function whose domain is the set of natural numbers or a subset of the natural numbers.

The domain basically can be defined a set of all possible inputs for the function.

The range  is basically the difference between the highest and the lowest numbers of a sequence.

To find the range, first put all the numbers in order. Then subtract the lowest number from the highest. The difference gives you the range of the list.

The domain of a sequence consists of the natural (counting) numbers 1, 2, 3, 4, ...Whereas the range of a sequence consists of the terms of the sequence.

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Answer; Five-halves

Step-by-step explanation:

Put triangles on graph

To find the answer you divide the A' to B' by the A to B distance.

So you divide 5/2

The driver is safer in the inside lane. The equation for fc=mv^2 states that the force of centripetal acceleration increases with velocity, so the faster the driver goes, the greater the force of centripetal acceleration.

This means that in an icy roundabout, it is safer to drive in the inside lane since the inside lane has a lower speed limit and thus a lower force of centripetal acceleration.

The driver is safer in the inside lane of a roundabout when it is icy, as the equation for fc=mv^2 states that the force of centripetal acceleration increases with velocity, so the lower speed inside lane will have a lower force of centripetal acceleration.

The driver is safer in the inside lane. The equation for fc=mv^2 states that the force of centripetal acceleration increases with velocity, so the faster the driver goes, the greater the force of centripetal acceleration.

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The equation with the same solutions are; 2.3·p - 10.1 = 6.5·p - 4 - 0.01·p

The properties of equality can be used to rewrite the equations in

simplified form.

Two equations that have the same solution as the given equation are;

2.3p-10.1=6.49.p-4

230.p-1010=650.p-400-p

Reasons:

The given equation is; 2.3·p - 10.1 = 6.5·p - 4 - 0.01·p

Simplifying the above equation by collecting like terms gives;

2.3·p - 10.1 = 6.5·p - 0.01·p - 4 = 6.49·p - 4

2.3·p - 10.1 = 6.49·p - 4

Multiplication property of equality:

Both sides of an equation will remain equal, when both sides are

multiplied by the same amount.

Multiplying both sides of the original equation by 100 gives the same

solution as follows;

100 × (2.3·p - 10.1) = 100 × (6.5·p - 4 - 0.01·p)

230·p - 1010 = 650·p - 400 - p

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Answer:

B-2.3p – 10.1 = 6.49p – 4 and C- 230p – 1010 = 650p – 400 – p

Step-by-step explanation:

The y-intercept represents the number of snapper fish in the area in 2004, which is the year that t = 0.

An area can be represented by the given formula:

[tex]F = 1500(1.02)^t[/tex]

where t represents the number of years since 2004.

The y-intercept of this equation is the point where the graph of the equation crosses the y-axis. In other words, it is the value of F when t is equal to 0.

Plugging in t = 0 into the equation above gives us:

F = 1500(1.02)⁰

= 1500(1)

= 1500

So the y-intercept of this equation is 1500.

Thus, the y-intercept reflects the amount of snapper fish caught in the area in 2004, the year t = 0.

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The Quadratic form is (x² - 1)(x² - 9) = 0 and the value of x is {1, -1, 3, -3}.

What is Quadratic form ?

In mathematics, a polynomial with all terms of degree two is called a quadratic form.

Given, x^4-10x^2+9=0

here, a + b = -10

and, ab = 9

So, a = -1 and b = -9

So, It can be written in Quadratic form as :

(x² - 1)(x² - 9) = 0

Now, we can solve as follows:

       x² - 1 = 0                         and,    x² - 9 = 0

      (x+1)(x-1) = 0                              (x+3)(x-3)=0

         x = ±1                           and, x = ±3

∴ Value of x = {1, -1, 3, -3}

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Answer:

y = 2/5x + 10 (1st box)

y = -1/2x + 1/2 (2nd box)

y = 3/2x - 11/2 (3rd box)

y = 4/3 x - 7/3 (4th box)

y = 3/4x - 10 (5th box)

Step-by-step explanation:

Answer:

x = 33

Step-by-step explanation:

67 = 2x + 1

66 = 2x

x = 33

2(33) + 1 = 67

As they are symmetric around the graph's origin, cosine and secant are even functions.

This indicates that the resulting graph will be identical to the original graph if you reflect it around the x-axis. This is due to the fact that sec(x) = sec(-x) and cos(x) = cos(-x).

Because their values are the same for both positive and negative angles, the cosine and secant functions are even. This indicates that the cosine and secant of any given angle will be identical to one another for any given angle, as will the cosine of that angle and the secant of that angle. They are useful for a wide range of tasks because of this property, such as resolving differential equations and working with periodic functions.

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Answer:

x = 4

y = 12

Step-by-step explanation:

Replace all occurrences of y with 3x in each equation.

7x = 28

y = 3x

Divide each term in 7x = 28 by 7 and simplify.

x = 4

y = 3x

Replace all occurrences of x with 4 in each equation.

y = 12

x = 4

The solution to the system is the complete set of ordered pairs that are valid solutions.

(4,12)

The result can be shown in multiple forms.

Point Form:

(4,12)

Equation Form:

x = 4,y = 12

Hope I helped <3

The derivative of the function h(x) = 1 - x^2 sin^-1(x) -x^2-x is h'(x) = - x^2/(sqrt(1-x^2)) - 2x - 1.

What is derivative ?

The derivative of a function is a measure of how much the output of the function changes with respect to the change in its input. It is represented by the symbol "d/dx" or "∂/∂x" and it is a fundamental concept in calculus.

First, we will apply the chain rule to the term -x^2 sin^-1(x)

Let u = sin^-1(x)

du/dx = 1/(sqrt(1-x^2))

so, -x^2sin^-1(x) = -x^2u

then dh/du = -x^2

then dh/dx = -x^2 * (du/dx) = -x^2/(sqrt(1-x^2))

Next, we will differentiate the rest of the function ,

h(x) = 1 - x^2sin^-1(x) - x^2 - x

h'(x) = - x^2/(sqrt(1-x^2)) - 2x - 1

So, the derivative of the function h(x) = 1 - x^2 sin^-1(x) -x^2-x is h'(x) = - x^2/(sqrt(1-x^2)) - 2x - 1.

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Answer:

See Below

Step-by-step explanation:

Answer:

Line: Solid

Shade: Above

m = -4/5

b = 2

(0,2) - True -Yes

(3,4) - True - Yes

(-2,-2) - False - No

Step-by-step explanation:

Given:

4x + 5y ≥ 10

Questions:

Line: Solid or Dashed?

Shade: Above or Below?

m= [?]

b= [?]

Are these points solution:

Solve:

Inequalities that use '< or >' symbols are plotted with a dashed line. Due to that dashed line means the solution doesn't include the line itself.

< = Less than

> = Greater than

Inequalities that use '≤ or ≥' symbols are plotted with a solid line. Due to that solid line means the solution does includes the line itself

≤ = Less than or equal to

≥ = Greater than or equal to

Therefore, based on the given, the line is solid. Which also means the solution does includes the line itself.

We also know that the given info with the inequalities of "≥".

"≥" Means greater than or equal to which means shade above. If it was "≤ " which means less than or equal to you have to shade below.

To find the m and b we first have to know that;

y = mx + b

m = Slope

b = y-intercept

To find the Slope(m) and b(y-intercept) we first have to put 4x + 5y ≥ 10 in  slope-intercept form.

4x + 5y ≥ 10

4x-4x + 5y ≥ 10-4x {Subtract 4x from both sides}

5y ≥ -4x + 10

5y ≥ -4x + 10 {Divided all by 5}

5y/5  ≥ -4x/5 + 10/5

y =-4/5x+2

Hence, now we know that;

m = -4/5

b = 2

To see if the following points {(0,2) (3,4) (-2,-2)} are solutions for 4x + 5y ≥ 10

All we have to do is to substitute it in.

Starting with (0,2)

x = 0

y = 2

4(0) + 5(2) ≥ 10

0 + 10 ≥ 10

10≥ 10

True. 10 isn't greater than 10 but- It's equal to 10. ≥ Means greater than or equal to Hence, (0,2) is a solution.

Next we have (3,4)

x = 3

y = 4

4(3) + 5(4)  ≥ 10

12 + 20  ≥ 10

32  ≥ 10

True. 32 is greater than 10 - Hence, (3,4) is a solution.

Finally we have (-2,-2)

x = -2

y = -2

4(-2) + 5(-2)  ≥ 10

-8 + -10  ≥ 10

-18  ≥ 10

False. Although you may probably think 18 is greater than 10 it is not correct. -18 isn't greater than 10 due to that it is negative.

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