Sinx+1 =cos x

Hint: square both sides

Step-by-step explanation:

just look at the graphic : what value do we have on the cost side, when we have 1 pounds on the amount side ?

all the answer options specify a price per pound. that is why we only need to focus on the price for one pound.

we see in the graphic, that for 1 pound the price is $4.

just to make sure, we can also work with the directly specified point (0.5, 2), which means that 0.5 pounds cost $2.

and the function is clearly a straight line.

so, every point on the function has the same y/x ratio (slope).

therefore,

2/0.5 = 4

now, what point with x=1 has the same ratio ?

y/1 = 4

y = $4

perfect, the results are identical. so, $4 per pound is the correct answer.

Answer:

the number of shirts sold

Step-by-step explanation:

that's what the question is asking

Answer: 360

Step-by-step explanation:

done

The bounds for a 95% confidence interval could be option (B) 72 and 79

We know that the 98% confidence interval has bounds of 73 and 80. This means that if we were to repeat the same experiment many times, we would expect that 98% of the time, the true population mean would fall within this range.

To find the bounds for a 95% confidence interval, we can use the fact that a higher confidence level corresponds to a wider interval, and a lower confidence level corresponds to a narrower interval.

Since we want a narrower interval for a 95% confidence level, we can expect the bounds to be closer to the sample mean. We can calculate the sample mean as the midpoint of the 98% confidence interval

(sample mean) = (lower bound + upper bound) / 2 = (73 + 80) / 2 = 76.5

Next, we can use the formula for a confidence interval:

(sample mean) ± (z-score) × (standard error)

where the z-score depends on the desired confidence level, and the standard error depends on the sample size and sample standard deviation. Since we don't have this information, we can assume that the sample size is large enough (i.e., greater than 30) for the central limit theorem to apply, and we can use the formula

standard error = (width of 98% CI) / (2 × z-score)

For a 98% confidence interval, the z-score is 2.33 (found using a standard normal distribution table or calculator). Plugging in the values, we get

standard error = (80 - 73) / (2 × 2.33) = 1.70

Now, we can use this standard error to calculate the bounds for a 95% confidence interval

(sample mean) ± (z-score) × (standard error) = 76.5 ± 1.96 × 1.70

Simplifying, we get

(lower bound) = 76.5 - 3.33 = 73.17

(upper bound) = 76.5 + 3.33 = 79.83

Therefore, the correct option is (B) 72 and 79

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Using a system of equations:

a)

The system is:

\(x + y = 58\)

\(y = 2x + 4\)

b)

Robin is 18 years old and Batman is 40 years old.

-------------------------

Item a:

Batman's age is 4 more than twice of robins age.

Thus, \(y = 2x + 4\)

Sum of the ages is 58, thus:

\(x + y = 58\)

Then, the system is:

\(x + y = 58\)

\(y = 2x + 4\)

Item b:

Applying the second equation into the first:

\(x + y = 58\)

\(x + 2x + 4 = 58\)

\(3x = 54\)

\(x = \frac{54}{3}\)

\(x = 18\)

Then, for y:

\(y = 2x + 4 = 2(18) + 4 = 36 + 4 = 40\)

Robin is 18 years old and Batman is 40 years old.

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Answer:

The y-intercept of this line is (0, 4)

Step-by-step explanation:

Given that the slope of this line is -3, we know the general form of its equation is y = -3x + b.  Arbitrarily choosing the first point, (-2, 10), and substituting -2 for x and 10 for y, we find the y-intercept as follows:

10 = -3(-2) + b, or

10 = 6 + b, or

b = 4  (Answer C)

The y-intercept of this line is (0, 4)

Answer:

Step-by-step explanation:

4

Answer:

Step-by-step explanation:

To find the perimeter of a rectangle, add the lengths of the rectangle's four sides. If you have only the width and the height, then you can easily find all four sides (two sides are each equal to the height and the other two sides are equal to the width). Multiply both the height and width by two and add the results.

Answer:

The answer and explanations are in the pictures.

Step-by-step explanation:

Answer:

here's your answer step by step explanation

Step-by-step explanation:

page 6 is missing comment me i will send you page 6

The cubic centimeter (cm³ or cc) is a unit of volume that is equivalent to a cube with sides measuring one centimeter each. It is commonly used to measure the volume of small objects or substances.

The term "cc" is often used in medical and automotive contexts to denote engine displacement or medication dosages. The cubic centimeter is a convenient unit for expressing small volumes due to its relation to the metric system and its ease of conversion. The cubic centimeter, denoted as cm³ or cc, is a unit of volume in the metric system. It represents the volume of a cube with sides measuring one centimeter each. This unit is widely used to measure the volume of small objects or substances, especially in scientific, medical, and engineering fields. In the medical field, the term "cc" is often used interchangeably with ml (milliliter) to express medication dosages. For example, a doctor may prescribe a certain medication to be administered in 5 cc or 5 ml doses. In the automotive industry, cc is used to denote engine displacement, which represents the total volume swept by all the pistons in an internal combustion engine. It is commonly used to categorize and compare the sizes and capacities of different engines. The cubic centimeter is a convenient unit for measuring small volumes due to its relation to the metric system. It is easily convertible to other metric units of volume, such as liters or milliliters, by using the appropriate conversion factors. For example, 1 cm³ is equivalent to 0.001 liters or 1 milliliter. Overall, the cubic centimeter serves as a practical unit for quantifying small volumes in various fields, providing a common measurement standard and facilitating easy conversions within the metric system.

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Given:

The equation of polynomial is

\(2x^3-5x^2+1=0\)

To find:

All rational roots of the polynomial.

Solution:

According to the rational root theorem, all the possible rational roots of a polynomial are defined as

\(x=\dfrac{p}{q}\)

where, p is a factor of constant term and q is factor of leading coefficient.

We have,

\(2x^3-5x^2+1=0\)

Here, leading coefficient is 2 and constant term is 1.

Factors of 1 are ±1.

Factors of 2 are ±1, ±2.

Using rational root theorem, we get

\(x=\pm \dfrac{1}{1},\pm \dfrac{1}{2}\)

\(x=\pm 1,\pm \dfrac{1}{2}\)

Therefore, all possible rational roots of the given polynomial are \(\pm 1,\pm \dfrac{1}{2}\).

Answer:

\( \sqrt[3]{x} \)

Step-by-step explanation:

\( \sqrt[4]{ \frac{ {x}^{2} }{x ^{ \frac{2}{3} } } } = \frac{ \sqrt[4]{ {x}^{2} } }{ \sqrt[4]{ \sqrt[3]{ {x}^{2} } } } = \frac{x ^{ \frac{2}{4} } }{(x ^{ \frac{2}{3} } ) ^{ \frac{1}{4} } } \\ \\ = \frac{ {x}^{ \frac{1}{2} } }{ {x}^{ \frac{2}{12} } } = \frac{ {x}^{ \frac{1}{2} } }{ {x}^{ \frac{1}{6} } } = {x}^{ \frac{1}{2} - \frac{1}{6} } = {x}^{ \frac{1}{3} } = \sqrt[3]{x} \)

I hope I helped you^_^

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.

In the given question,

The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius of the base, h is the height, and π is approximately 3.14.

Substituting the given values, we get:

V = (1/3) × 3.14 × 3² × 3.8

V ≈ 35.63

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

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The vertex of the graph of f(x) = |x - 5| - 6 is (5, -6). It lies in the fourth quadrant.

Therefore the answer is (5, -6).

The graph f(x) = |x - 5| - 6 is symmetrical about the axis  x = 5.

A vertex of a graph is a node of a graph. For a graph of the form f(x) = a|x - h| + k, the vertex is (h, k). So in this case where f(x) = |x - 5| - 6, a = 1, h = 5 and k = -6. Therefore the vertex of the given graph f(x) is

(5, -6)

We can observe that was added 5 units to the x, that is, a negative translation through the horizontal axis. So, our function is located at x = -5, because a horizontal translation to the left is when we add to the x certain units.

Then, we observe that the function subtracted 6 units to the vertical variable, that is, the function is translated 6 units downside.

Therefore, our functions is locate in (-5;-6), it starts there, which is the vertex.

--The question is incomplete, answering to the question --

"What is the vertex of the graph of f(x) = |x - 5| - 6?"

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Answer:

A is 30 inches

b is Yes

c

Step-by-step explanation:

The polynomial that represents the product of 2X-4 and X² +6X -2 is 2X³ + 8X³ - 24X + 8.

To find the product of the two polynomials, we can use the distributive property of multiplication over addition, which states that:

(a + b)c = ac + bc

Using this property, we can distribute the terms of the first polynomial, 2X-4, to each term of the second polynomial, X² +6X -2, and then simplify the resulting expression:

(2X - 4) × (X² + 6X - 2)

= 2X × X² + 2X × 6X + 2X × (-2) - 4 × X² - 4 × 6X + 4 × 2

= 2X³ + 12X² - 4X² - 24X + 8

= 2X³ + 8X² - 24X + 8

Therefore, the polynomial that represents the product of 2X-4 and X² +6X -2 is 2X³ + 8X³ - 24X + 8.

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Answer:

D

Step-by-step explanation:

bc it starts with -square root of 20 and then - square root of 6 and the 3.14 and then square root of 8 and then square root of 18

==============================================

Explanation:

If there are n apples in a straight line, then there are n-1 gaps between the adjacent apples.

Having 8 apples will have 8-1 = 7 gaps between the apples.

Similarly, having 7 apples will have 7-1 = 6 gaps between those apples.

The 8 by 7 rectangle in the bottom level will have a 7 by 6 rectangle on the second level. The third level will have a 6 by 5 rectangle, and so on.

Here's a table to keep track of everything

\(\begin{array}{|c|c|c|} \cline{1-3}\text{Level} & \text{Dimensions} & \text{Number of apples}\\ \cline{1-3}\text{1} & \text{8 by 7} & \text{56}\\ \cline{1-3}\text{2} & \text{7 by 6} & \text{42}\\ \cline{1-3}\text{3} & \text{6 by 5} & \text{30}\\ \cline{1-3}\text{4} & \text{5 by 4} & \text{20}\\ \cline{1-3}\text{5} & \text{4 by 3} & \text{12}\\ \cline{1-3}\text{6} & \text{3 by 2} & \text{6}\\ \cline{1-3}\text{7} & \text{2 by 1} & \text{2}\\ \cline{1-3}\end{array}\)

The last step is to add up everything in the third column

56 + 42 + 30 + 20 + 12 + 6 + 2 = 168 apples total

Answer:

True

Step-by-step explanation:

This is true if you look at the hundredths value. 7 is greater than 5, therefore 19.67 is greater than 19.657. To simplify it, you can look at it as 19.67 > 19.65 (say we omit the 7).

Given:

The mathematical sentences in the given options.

To find:

Which of the Mathematical sentences below is/are equations?

Solution:

Equation: An equation is a mathematical sentence which contains two expressions and an equals sign "=".

Inequality: An inequality is a mathematical sentence which contains two expressions and an inequality sign ">, <, ≤, ≥".

From the given options it is clear that the options (i) and (ii) contains equals sign "=". So, (i) and (ii) are equations.

The options (iii) and (iv) contains inequality sign ">" and "<" respectively. So, (iii) and (iv) are inequalities.

Therefore, the correct options are (i) and (ii).

Answer:

serían 52^g

Step-by-step explanation:

la g estaría al lado de 52 en la parte superior

The distance traveled by the particle is 4 units (approximately).

The distance traveled by a particle with position (x, y) as t varies in the given time interval is 4 units (approximately).Given,x = 2 sin^2(t),y = 2 cos^2(t),0 ≤ t ≤ 3To find the distance, we can use the formula for distance between two points in a plane which is as follows: Distance = √(x₂ − x₁)² + (y₂ − y₁)²where (x₁, y₁) and (x₂, y₂) are the initial and final points respectively. Substituting the given values, we get;x₁ = 2 sin²(t₁),y₁ = 2 cos²(t₁),x₂ = 2 sin²(t₂),y₂ = 2 cos²(t₂)∴ Distance = √(2 sin²(t₂) − 2 sin²(t₁))² + (2 cos²(t₂) − 2 cos²(t₁))²= 2 √sin⁴(t₂) − sin⁴(t₁) + cos⁴(t₂) − cos⁴(t₁)Now, we can simplify this equation by using trigonometric identities.Sin²x + cos²x = 1⇒ sin⁴x + cos⁴x + 2(sin²x cos²x) = 1-2 sin²x cos²x⇒ sin⁴x + cos⁴x = 1- 2(sin²x cos²x)Substituting these values in the above equation, we get;Distance = 2√(1-2 sin²(t₁) cos²(t₁)) - 2(sin²(t₂) cos²(t₂))= 2√(cos⁴(t₁) - sin²(t₁) cos²(t₁)) - (cos⁴(t₂) - sin²(t₂) cos²(t₂)))= 2√(cos²(t₁)(1 - sin²(t₁))) - cos²(t₂)(1 - sin²(t₂)))= 2 cos(t₁) sin(t₁) - cos(t₂) sin(t₂)≈ 4 units (approximately).

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We have the following equations to compute the distance traveled by a particle with position (x, y) as t varies in the given time interval:

The content describes the position of a particle as it moves over a specific time interval. The particle's position is defined by two equations: x = 2 sin^2(t) and y = 2 cos^2(t), where t represents time. The given time interval is 0 ≤ t ≤ 3.

To find the distance traveled by the particle in this time interval, we can use the concept of arc length. The arc length formula for a parametric curve is given by:

s = ∫√((dx/dt)^2 + (dy/dt)^2) dt,

where dx/dt and dy/dt represent the derivatives of x and y with respect to t, respectively.

In this case, let's calculate the derivatives:

dx/dt = d(2 sin^2(t))/dt = 4 sin(t) cos(t),

dy/dt = d(2 cos^2(t))/dt = -4 sin(t) cos(t).

Now, substitute these derivatives into the arc length formula and integrate it over the given time interval (0 ≤ t ≤ 3) to find the distance traveled by the particle.

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Based on the number of members and the ratio in which they chose the types of film, the number who chose Action in the second week more than the first week is 6 people.

Assuming that the number of members is 99 members, the number who chose Action on the second week were:

= (7 / (5 + 7 + 6)) x 99

= 39 people

The number who chose Action in the first week:

= (5 / (2 + 5 + 8)) x 99

= 33

The difference is:

= 39 - 33

= 6 people

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The rate of change of this simple index over 1 week as calculated from the data given in the question is found out to be as -  -8.81 %.

  Day one simple index value ,

= (8000 x $4.25) + (5000 x $2.90) + (2000 x $6.40)

= $61,300

Value at day 8 = (8000 x $3.90) + (5000 x $2.50)+(2000*6.10)  

= 55900

therefore, the rate of change of this simple index over 1 week

= (55900-61300)/ 61300 x 100 %

= -8.81 %

Simple index numbers are the numbers which gives equal importance to all items no matter what share it has. We can say that , it takes into consideration each item to be equal with respect to the given variable. Consequently, it is a simple average and is less accurate when compared to the other class of index numbers.

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Each line above the numbers multiply it by 1000. So this number is being multiplied by 1000000.

Each "C" is equal to 100, since there are "CCC" the number is 300.

"XL" is equal to 40, because "X" is equal to 10 and "L" is equal to 50, but since he X is on the left of the L we subtract them.

The number CCCXL is then 340, but there are the two lines. So we have:

Answer:

I think option c is correct

:::::::::::::::::::::::::::::::::::::::::::::::::

Alex has $15.78 and Rick has $12.15 money.

According to the question,

We have the following information:

Alex had $3.63 more than Rick. Together they had $27.93.

Let's take the money Rick has to be $x.

Now, we have the following expression for the money Alex has:

3.63+x

Now, we have:

x+3.63+x = 27.93

2x+3.63 = 27.93

Subtracting 3.63 from both the sides:

2x = 27.93-3.63

2x = 24.3

Dividing by 2 on both the sides:

x = 24.3/2

x = $12.15

So, Rick has $12.15.

Now, the money Alex has:

3.63+12.15

$15.78

Hence, Alex has $15.78 and Rick has $12.15 money.

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Based on the data, it can be inferred that Harrisburg, PA is 158 miles from Trento, NJ.

To calculate the distance between Harrisburg and Trento we must carry out the following procedure. First we look at the entire table to see the different distance values between the cities. As we can see, the values for Trento, NJ are not there, so we will have to look elsewhere for additional information.

In this case, we must take as a reference the closest city to Trento that is on the list, this would be Filadeldia. Now, we must find the distance between Philadelphia and Trento and add this value to the distance between Philadelphia and Harrisburg.

According to the above, Philadelphia is 114 miles from Harrisburg and 44 miles from Trneto.

Based on the above, the total distance between Trento and Harrisburg is 158 miles.

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