Use an identity to solve the equation on the interval [0,
2pi)
sin^2 - 5 cos x + 5 = 0

Answer:

$ 144

Step-by-step explanation:

Cost Price = CP = $ 120

Profit % = 20%

\(Selling\ price = \dfrac{100+Profit}{100}*CP\\\\\\\)

                     \(=\dfrac{120}{100}*120\)

                     = 12 * 12

                     = $ 144

The equation for a parabola is x = 4y²p ÷ 5 in its vertex form, and its standard form x = (5 ÷ 4p) × y².

The parabola's standard form may be stated on a form in geometry,

x = Ay² + By + C

and could be changed to represent it in its vertex form,

x = (1 ÷ 4p)(y - k)² + h

where:

H is the vertex's x-coordinate.

The vertex's y-coordinate is given by k.

The latus rectum measures at 4p.

h = 0

k = 0

4p = 5 (positive because it opens to the right)

The equation of the parabola in standard form, x = Ay² + By + C

x = (5 ÷ 4p)(y - 0)² + 0

x = (5 ÷ 4p) × y²

The equation is then converted to standard form and simplified.

x = 4y²p ÷ 5

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Answer:

  4

Step-by-step explanation:

You want to know the leaf unit corresponding to data value 0.014 when values are rounded to thousandths.

The leaf unit for data values in a stem-and-leaf plot is the least-significant digit of the data value, when all data values are expressed to the same precision.

The least significant digit of 0.014 is 4. The leaf unit is 4.

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Answer:

40%

Step-by-step explanation:

\( \frac{48}{120} \times 100 = 40\)

Answer:

40%

Step-by-step explanation:

To find out what percentage of 2 hours is 48 minutes, we need to first convert both values to the same unit of time, such as minutes.

2 hours is equal to 120 minutes (2 x 60).

So, the fraction of 2 hours that is represented by 48 minutes is:

48/120

Simplifying this fraction by dividing both the numerator and denominator by 12, we get:

4/10

Multiplying the numerator and denominator by 10 to convert this fraction into a percentage, we get:

40%

Therefore, 48 minutes is 40% of 2 hours.

The point- slope form of the line is y-5 = -0.25(x+6).

What is line?

A line is an one-dimensional figure. It has length but no width. A line can be made of a set of points which is extended in opposite directions to infinity. There are straight line, horizontal, vertical lines or may be parallel lines perpendicular lines etc.

A line with a slope of –1/4 passes through the point (–6,5)

Any line in point - slope form can be written as

y - y₁= m(x -x₁) -------(1)

where,

y= y coordinate of second point

y₁ = y coordinate of first point

m= slope of the line

x= x coordinate of second point

x₁ = x coordinate of first point

In the given problem (x₁ , y₁) = (-6,5) and m= -1/4

Putting all these values in equation (1) we get,

y-5= (-1/4) (x- (-6))

⇒ y-5 = -0.25(x+6)

Hence, the point- slope form of the line is y-5 = -0.25(x+6).

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Answer:

8x^3/2

Step-by-step explanation:

(4x)^3/2 = ( 4^3/2 ) ( x^3/2 ) =8x^3/2

Answer:

1. no

2. yes

Step-by-step explanation:

The correct option is the third one, the recursive formula is:

aₙ = -4*aₙ₋₁

a₁ = 7

We know that the explicit formula for the sequence is:

aₙ = 7*(-4)ⁿ⁻¹

So we can see that we have a geometric sequence, where to get the next term, we need to multiply the previous one by -4, then the recursive formula is:

aₙ = -4*aₙ₋₁

We also need to define the first term, which is:

a₁ = 7*(-4)⁰ = 7

Then the correct option is the third one.

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62.5% or 62.5 out of every 100 students exceeded the minimum standards.

The teacher found that 62 1/2% of the students exceeded the minimum standards. To find the part of the students who exceeded the standards, we need to convert the percentage to a decimal.
To do this, divide 62.5 by 100: 62.5 ÷ 100 = 0.625.
This means that 0.625 represents the decimal form of 62 1/2%.
To find the part of the students who exceeded the standards, multiply 0.625 by the total number of students.
For example, if there are 100 students in total, multiply 0.625 by 100: 0.625 x 100 = 62.5.
Therefore, 62.5 represents the part of the students who exceeded the minimum standards.

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Among the options given in the question, the following are the properties of the linear correlation coefficient:

The linear correlation coefficient is always between−1 and 1. That​ is,−1≤r≤1.

A linear correlation of −0.742 suggests a stronger negative association between two variables than a linear correlation of −0.472.

If r=−​1, then a perfect negative linear relation exists between the two variables.

Properties of linear correlation coefficient:

Linear correlation coefficient is a value calculated from given data and used to measure the strength of linear relationship between two variables, for instant between x and y variables.

The sign of this coefficient (r) indicates the direction linear relationship will take between x and y. Below are some properties of the linear correlation coefficient:

Now, the properties of the linear correlation coefficient among the given ones in the question are:

b. The linear correlation coefficient is always between−1 and 1. That​ is,−1≤r≤1.

d. A linear correlation of −0.742 suggests a stronger negative association between two variables than a linear correlation of −0.472.

f. If r=−​1, then a perfect negative linear relation exists between the two variables.

Hence, options b, d and f are correct.

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The margin error for the given poll having 95% confidence level with sample size of 410 is equal to 3.15%.

Sample size n = 410

Confidence level = 95%

Margin of error for this poll, use the formula,

ME = Z× (√(p₁(1-p₁) / n))

where Z is the z-score corresponding to the desired level of confidence.

p₁ is the sample proportion = 0.12

Using attached z-score table,

For a 95% confidence level, the corresponding z-score is 1.96.

Substituting the given values, we get,

ME = 1.96 × (√(0.12× (1-0.12) / 410))

Simplifying the expression inside the parentheses, we get,

⇒ME = 1.96 ×  0.0160

⇒ME = 0.0315

Margin of error for this poll at the 95% confidence level is approximately 0.0315.

Therefore,  95% confidence level represents that the true proportion of people who like dogs is within 3.15% of the observed proportion of 12%.

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Answer:

The constant of a polynomial function is the coefficient of the term with the highest degree (the term with the highest power of x), which in this case is 0. Therefore, the constant of the polynomial function f(x)=-(x+3(x+7)²(x-1)⁵(x+1)⁷(x-4) is 0.

Answer: The coordinates of the image of a figure after a rotation of 0.25 degrees about the x-axis can be found using the following formulas:

x' = x

y' = y * cos(θ) - z * sin(θ)

z' = y * sin(θ) + z * cos(θ)

where (x, y, z) are the original coordinates and (x', y', z') are the new coordinates. In this case, we only need to find the y' coordinate because the rotation is about the x-axis and the x coordinate will not change.

For each point, we can use the formula to find the y' coordinate:

A (2, 6) -> y' = 6 * cos(0.25) - 0 * sin(0.25) = 5.99911... ~ 6

B (0, 0) -> y' = 0 * cos(0.25) - 0 * sin(0.25) = 0

C (-5, 8) -> y' = 8 * cos(0.25) - 0 * sin(0.25) = 7.99823... ~ 8

D (-2, 10) -> y' = 10 * cos(0.25) - 0 * sin(0.25) = 9.99649... ~ 10

So, the new coordinates after rotating 0.25 degrees about the x-axis are:

A (2, 6) -> (2, 6)

B (0, 0) -> (0, 0)

C (-5, 8) -> (-5, 8)

D (-2, 10) -> (-2, 10)

The coordinates of the points have not changed after the rotation because the rotation angle is very small.

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

the Andrew's going to be 12 because you have to

know all the sides of cube

Answer:

1 → e

2 → f

3 → b

4 → d

5 → a

Step-by-step explanation:

Look for the corresponding sides by paying attention to the angle pairs since the angles do not change when the polygon is scaled.

Answer:

Angad the eldest=32+9=41year

Step-by-step explanation:

Let peter is x years old. Then Angad is x + 9 years old and Krutika is

x - 12 years old. Then

x+(x+9)+(x−12)=75⟹3x−21=75⟹x−7=25

⟹x=32years

Angad the eldest=32+9=41year

7 14/18

4 2/5

5 7/12

5 5/6​

The number that has not been reduced to simplest form is 7 14/18 (7 7/9)

Answer:

A. 400

Step-by-step explanation:

answer^

432 people rode the roller coaster in the third hour.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

We have,

182 people rode the roller coaster.

307 people rode the roller coaster.

A total of 921 people had ridden the roller coaster.

So, Number of people rode the roller coaster

= 921 - 182 - 307

= 432

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Probability distribution is an assignment of probabilities to each distinct value of a discrete random variable or to each interval of values of a continuous random variable.

What is Probability ?

What is the probability of each value of a discrete random variable?

The probability P(x) that a discrete random variable X will take the value x in one trial of the experiment is connected to each possible value x of the variable.

Which is a discrete random variable?

What is the other name of mean of discrete random variable?

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To write our number as a fraction, the order of the steps is:

First, we define our number:

x = 0.1717...

So we start with the step 3.

Now notice that there are two repeating decimals, so we need to multiply both sides by 100 (as many zeros as repeating decimals)

100*x = 10*0.1717... = 17.1717...

This is step 5.

Now we can subtract the original number in both sides so we remove the repeating decimals:

100*x - 0.1717... = 17.1717... - 0.1717...

99*x = 17

These are steps 4 and 2.

Finally, we divide both sides by 99 to get:

x = 17/99

Which is step 1.

And that is our number written as a fraction.

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The set of all complex numbers with a given modulus (such as 5) always has the shape of a circle

The Euclidean distance between the origin and a complex number is represented by the absolute value within the complex plane framework. The locus of complex numbers with a specific modulus, represented by |z|, creates a circle centered at the origin, with the size of the circle determined by the magnitude of |z|.

A valid example of this assertion is when the magnitude of z is five. In this situation, the group of intricate quantities that possess a magnitude of five creates a circular shape that is centered at the starting point and has a span of five units.

The previously mentioned occurrence can be explained by how the modulus is calculated, which involves finding the square root of the total sum of the squares of both the real and imaginary parts in the complex number mentioned earlier.

The shape of the circle stays the same regardless of the orientation of the complex number.

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i think its 9.9 but if its not that its 8.7

The revenue of US theme parks in 2012 is 14.5 in dollars.

Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.

From the given table, (1990, 5.7), (1992, 6.5), (1994, 7.0), (1996, 7.9), (1998, 8.7), (2000, 9.6), (2002, 9.9), (2004, 10.8), (2006, 11.5).

Using the coordinates (1990, 5.7) and (1992, 6.5), we get

Slope m=(6.5-5.7)/(1992-1990)

= 0.8/2

= 0.4

Substitute m=0.4 and (x, y)=(1990, 5.7) in y=mx+c, we get

5.7=0.4×1990+c

c=5.7-796

c=790.3

Substitute m=0.4 and c=-790.3 in y=mx+c, we get

y=0.4x-790.3

Substitute x=2012, we get

y=0.4×2012-790.3

y=804.8-790.3

y=14.5

Therefore, the revenue of US theme parks in 2012 is 14.5 in dollars.

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Solving for D & C

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

(3c + d) + (-d) = 60 + (-d)

3c + d - d = 60 - d

3c= -d + 60

3c/3 =-d+60/3

c= -d+60/3

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

(3c+d)+(-3c)=60+(-3c)

d = -3c + 60

Option C. Between 1982 and 2012, there were fewer House members who fell between the most liberal Republican and the most conservative Democrat. represents a trend supported by the data in the bar graph

What is bar graph?

A bar graph, also known as a bar chart, is a graphical representation of categorical data using rectangular bars. It is used to compare and display the values of different categories or groups.

In a bar graph, each category or group is represented by a separate bar. The length or height of each bar corresponds to the value or frequency of the category it represents. The bars are typically drawn vertically or horizontally, with the length or height proportional to the data being represented.

The horizontal axis of a bar graph represents the categories or groups, while the vertical axis represents the values or frequencies. Labels or values are often placed along the axes to provide additional information.

Bar graphs are commonly used to visualize and compare data in various fields, including statistics, economics, market research, and social sciences. They provide a clear visual representation of data, making it easy to interpret and understand comparisons between different categories or groups.

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Answer:

  B.  y -6 = 2(x -2)

Step-by-step explanation:

You want the point-slope equation of the line with slope 2 through point (2, 6).

The point-slope equation for a line with slope m through point (h, k) is ...

  y -k = m(x -h)

Then the equation for the line with slope 2 through point (2, 6) is ...

  y -6 = 2(x -2) . . . . . choice B

__

Additional comment

If any function goes through the point (0, 0), it can be translated so that it goes through the point (h, k) by the replacements ...

A line with slope 2 through the origin is y = 2x. When that is translated so it goes through (2, 6), the equation becomes ...

  y -6 = 2(x -2)

<95141404393>

The expected value of X is 100/663.

Let's consider the sequence of 3 number cards as an individual block, then we can see that there are 10 such blocks in the deck (2-3-4, 3-4-5, ..., 9-10-J, 10-J-Q), and there are 39 non-number cards in the deck.

Now, we can consider flipping the cards one by one and keep track of the number of times we see the beginning of a new block of 3 number cards. There are 50 positions in the deck where a block of 3 number cards could begin (the first 2 cards cannot start a block and the last 2 cards cannot end a block). For each position, the probability of seeing the beginning of a new block is given by:

P(new block) = P(first card is a number) x P(second card is the next number) x P(third card is the next number) = 10/52 x 4/51 x 4/50 = 2/663

Therefore, the expected value of X is:

E(X) = P(new block at position 1) + P(new block at position 2) + ... + P(new block at position 50) = 50 x P(new block) = 50 x 2/663 = 100/663

So, the expected value of X is 100/663.

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Answer:

C

Step-by-step explanation:

use y=mx+c

follow the flow

Answer:

the equation should be y=1/2x+5

Step-by-step explanation:

The correct option d. the event can take no more than a maximum amount of time, described the  an event has a timebox.

A timebox is a set amount of time during which a work must be completed in agile software development.

Thus, when an event has a timebox, it signifies that the event can only last a certain length of time.

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The tool that ensures greater accuracy by aligning the numbers scale with the edges or points to be measured is a Vernier caliper.

A Vernier caliper is a tool used to accurately measure small lengths, widths, and diameters with precision. It has two parts: an outer frame and a sliding vernier scale. The frame is used to place the object to be measured, while the vernier scale is moved along the frame to measure the object's length.

The graduations on the vernier scale are smaller than the main scale graduations, allowing for more precise measurements to be made. This makes the Vernier caliper a more accurate measuring tool than a standard ruler or tape measure.

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