Use the​ power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1. 18sin^2(x)cos^2(x)

Answer:

We can use the Central Limit Theorem to solve this problem since we are dealing with a sample size greater than 30. The distribution of sample means will be approximately normal with a mean of 74 beats per minute and a standard deviation of 12.5 / sqrt(4) = 6.25 beats per minute.

To find the probability that the mean pulse rate of 4 adult females is between 70 and 78 beats per minute, we need to calculate the z-scores for both values and then use a z-table or calculator to find the area under the normal curve between those two z-scores.

The z-score for 70 beats per minute is:

z = (70 - 74) / 6.25 = -0.64

The z-score for 78 beats per minute is:

z = (78 - 74) / 6.25 = 0.64

Using a standard normal distribution table or calculator, the area between these two z-scores is approximately 0.4115.

Therefore, the probability that 4 adult females have pulse rates with a mean between 70 and 78 beats per minute is approximately 0.4115 or 41.15%.

The original numbers multiplied by 10² are:

968

0.002

3.33

When a number is multiplied by 10², the position of the decimal point will move to the right by 2 steps. If the number does not have decimal point, two zeros is added to the back of the number .

6 * 10³  = 6,000

968 * 10² = 96,800

0.002 * 10² = 0.2

70,000 ÷ 10² = 700

3.33 * 10² = 333

Thus, the original numbers multiplied by 10² are 968, 0.002 and 3.33

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A scatter plot would be an appropriate data display to show the relationship between the speed of the vehicle and the number of accidents.

A scatter plot is a graphical representation of two continuous variables, where data points are plotted on a Cartesian coordinate system. The horizontal axis can represent the speed of the vehicle, while the vertical axis can represent the number of accidents. Each data point on the scatter plot would represent a specific observation of speed and the corresponding number of accidents.

By using a scatter plot, the EMT can visually display how changes in vehicle speed are related to the number of accidents. Scatter plots are effective for identifying trends, patterns, and outliers in data, making them suitable for illustrating the relationship between two continuous variables.

Answered question "An EMT wants to use a data display to show students the relationship between the speed of the vehicle and the number of accidents. Choose an appropriate data display for the situation. Explain your reasoning"

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From the circle graph of the survey, 52 more people prefer pigs than chickens.

A sort of data visualisation tool used to depict data as a circular chart is a circle graph, commonly referred to as a pie chart. Each slice of the circle graph, also known as a sector, represents a certain category or chunk of the entire. Each slice's size is proportional to how much data or what percentage it represents, and the sum of all slices is 100%.

Circle graphs are frequently used to depict percentages or categorical data, and they are especially helpful for comparing and illustrating relative proportions among several categories within a data collection.

From the circle graph we see that the percentage of people who prefer chickens are 29%.

Thus, 29/100 (400) = 116 people

Also, 16% people prefer pig:

Thus, 16/100 (400) = 64 people

Thus, the difference is:

116 - 64 = 52

Hence, from the circle graph of the survey, 52 more people prefer pigs than chickens.

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The complete question is:

The surface area of the triangular prism is 162 square inches.

In geometry, a prism is a three-dimensional solid shape that has two identical, parallel faces (called bases) and rectangular or parallelogram-shaped sides. The sides connect the bases, and their shape determines the type of prism.

To find the surface area of the triangular prism, we need to find the areas of all five faces and add them together.

The area of each triangular base is:

A = (1/2)bh

where b is the length of the base (which is equal to 4 in) and h is the height (which is equal to 3 in).

A = (1/2)(4 in)(3 in) = 6 in²

So the total area of both triangular bases is:

2A = 2(6 in²) = 12 in²

The area of each rectangular side is:

A = lw

where l is the length (which is equal to 10 in) and w is the width (which is equal to 5 in).

A = (10 in)(5 in) = 50 in²

So the total area of all three rectangular sides is:

3A = 3(50 in²) = 150 in²

Therefore, the total surface area of the triangular prism is:

12 in² + 150 in² = 162 in²

Thus, the surface area of the triangular prism is 162 square inches.

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The angle that is vertical to angle DEB is A.

A vertical angle is an angle formed by two intersecting lines or planes that are perpendicular to each other. Specifically, it is the angle between two straight lines or planes that intersect each other and are perpendicular to the horizontal plane.

The measure of a vertical angle is always the same as the measure of the other vertical angle formed by the same two intersecting lines or planes. This is because vertical angles are always congruent, meaning they have the same size and shape. Vertical angles are commonly used in geometry and trigonometry to solve problems involving angles, lines, and plane.

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When 3 is divided by 2/5 , the answer is 7.5

Let's compare our whole number and fraction so that we can see the issue we are attempting to tackle.

3 divided by 2/5

In this case, creating a new numerator just requires multiplying the numerator by the full number. After that, the original numerator becomes the new denominator.

3*5/2 = 15/2

Most people prefer to express results in decimals, and all you have to do to do so is divide the numerator by the denominator:

15/2 = 7.5

The portion written above the horizontal line is referred to as the numerator. Example: 2/5 ,here 2 is numerator.

A decimal number consists of both a whole number and a fractional number. The numerical value of complete and partially whole amounts is expressed using decimal numbers, which are in between integers.

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The complete question is

what happens when 3 divide by 2/5ths in a facrtion?

Answer:

The answer to (m+3)(m-3) is m^2-9.

Step-by-step explanation:

We will use distributive law to solve this question.

m(m-3)+3(m-3)

= m^2-3m+3m-9

= m^2-9 (since, 3m-3m=0)

As an alternative method, we can use the direct rule learned in algebra: (a+b)(a-b)=a^2-b^2.

so, here a=m and b=3.

(m+3)(m-3)

=m^2-3^2

=m^2-9

The expression Negative 3 6/7 times negative 3 1/3 has a value of -12 6/7

We have the following statement as the given parameter

Negative 3 6/7 times negative 3 1/3

Next, we rewrite the above statement using numbers and operators

-3 6/7 * 3 1/3

The above statement is a product expression that multiplies the values of -3 6/7 and 3 1/3

Also, there is no need to check if there are like terms in the expression or not

This is  because we are multiplying the factors

So, we have

-3 6/7 * 3 1/3 = -27/7 * 10/3

Evaluate

-3 6/7 * 3 1/3 = -9/7 * 10

Rewrite as

-3 6/7 * 3 1/3 = -90/7

Simplify

-3 6/7 * 3 1/3 = -12 6/7

This means that the value of the expression is -12 6/7

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Answer:

4. b/c

Step-by-step explanation:

In a right-angled triangle with sides of lengths a, b, and c, where c is the hypotenuse (the side opposite the right angle), the sine of the angle opposite side b (angle B) is given by:

Sin theta : Opposite/hypotenuse

sin(B) = b/c

Therefore, the answer is 4. b/c

The distance from the top of the flagpole to the end of its shadow is approximately 10.02 feet.

Explain the term distance

Distance refers to the measurement of the space between two objects or points. It is typically measured in units such as meters, kilometres, miles, or feet. The distance can be calculated using various methods, including using maps, GPS technology, or mathematical formulas.

According to the given information

We can set up the following proportion:

h / 12 = d / 11

We can cross-multiply to get:

h x 11 = 12 x d

Simplifying further:

d = (h x 11) / 12

We need to solve for d, so we need to find the value of h. Using the Pythagorean theorem, we can set up the following equation:

h² + d² = 12²

Substituting d = (h x 11) / 12, we get:

h² + ((h x 11) / 12)² = 12²

Simplifying:

h² + (121h²) / 144 = 144

Multiplying both sides by 144/265:

265h² / 144 = 144

Solving for h:

h² = (144 x 144) / 265

h = √(20736 / 265)

h = √(78.113)

Now we can substitute this value into our earlier equation to find d:

d = (√(78.113) x 11) / 12

d ≈ 10.02 feet

Therefore, the distance from the top of the flagpole to the end of its shadow is approximately 10.02 feet.

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Answer: bellshaped

Step-by-step explanation:

Answer: i think its 366

Step-by-step explanation:

i just did 61X6

If the base diameter of the sawdust pile is 35 feet when the height is 30 feet, then when it is 40 feet high, the diameter will be 46.7 feet, while the volume will be 68,545.37 feet³.

The volume refers to the capacity of a three-dimensional object.

The formula for volume with diameter and height is V = πd²h/4.

Base diameter of the sawdust pile = 35 feet

Height = 30 feet

Base diameter of the sawdust pile when the height is 40 feet = 46.7 feet

(35/30 x 40)

Given height = 40 feet

Computed base diameter = 46.7 feet

Volume = πd²h/4

= 22/7 x 46.7² x 40/4

= 3.143 x 2,180.89 x 10

= 68,545.37 feet³

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The possible values of the random variable P are 0, 1, or 2.

A triangle is a polygon with three straight sides and three angles. It is one of the most fundamental shapes in geometry and is used extensively in mathematics, science, engineering, and art. The sum of the interior angles of a triangle is always 180 degrees, and the length of the sides and the size of the angles determine the shape of the triangle.

Triangles can be classified according to the length of their sides and the size of their angles. A scalene triangle has three unequal sides and three unequal angles. An isosceles triangle has two equal sides and two equal angles. A equilateral triangle has three equal sides and three equal angles, each measuring 60 degrees. Triangles can also be classified based on the size of their angles: an acute triangle has three acute angles (less than 90 degrees), a right triangle has one right angle (90 degrees), and an obtuse triangle has one obtuse angle (greater than 90 degrees).

Triangles have many important properties and applications in geometry. For example, the Pythagorean theorem is a fundamental relationship between the sides of a right triangle, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The area of a triangle can be calculated using the formula 1/2 x base x height, and this formula can be used to solve many practical problems involving triangles.

The random variable P can take on four possible values, depending on how many heads are obtained:

P = 0 if both coins show tails.

P = 1 if exactly one of the coins shows heads.

P = 2 if both coins show heads.

Therefore, the possible values of the random variable P are 0, 1, or 2.

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The equation is given as y = -x + 8

The purpose of an equation is to find the value of the variable that makes the equation true. Equations are used in various fields of mathematics and science to represent relationships between different quantities and to solve problems.

To create an equation that represents the relationship between x and y in the table, we need to first determine the pattern or trend in the data.

From the given data, we can see that as x increases by 2, y decreases by 2. This suggests that there is a linear relationship between x and y.

Using the two points (-2,10) and (0,8), we can find the slope:

m = (y2 - y1) / (x2 - x1) = (8 - 10) / (0 - (-2)) = -1

Now that we have the slope, we can use any point on the line to find the y-intercept. Let's use the point (0,8):

8 = (-1)(0) + b

b = 8

Therefore, the equation that represents the relationship between x and y in the table is:

y = -x + 8

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Answer:

  C  ∫[-a,0] = -∫[0, a]

Step-by-step explanation:

You want an alternate representation of the given integral ...

  ∫(2x⁵ -5x³)dx

on the interval [-a, a].

The function f(x) = 2x⁵ -5x³ being integrated is an odd function. This means ...

  f(-x) = -f(x)   and   f(0) = 0

An even function is characterized by ...

  f(-x) = f(x)

The integral F(x) of this odd function f(x) is an even function, so the parts either side of x=0 have the integrals ...

  [tex]\displaystyle \int_{-a}^0{(2x^5-5x^3)}\,dx=F(0)-F(-a)=F(0) -F(a)[/tex]

  [tex]\displaystyle \int_0^a{(2x^5-5x^3)}\,dx=F(a)-F(0)[/tex]

As we can see, these integrals are the opposites of each other, matching answer choice C.

__

Additional comment

The second attachment shows a numerical value for a=2.

The statement "These lines are perpendicular" is true.

To determine if the two lines are perpendicular, we need to check if the product of their slopes is -1. That is, if:

m1 × m2 = -1

where m1 is the slope of the first line and m2 is the slope of the second line.

The slopes of the two lines are:

m1 = -2/5

m2 = 5/2

So, m1 × m2 = (-2/5) × (5/2) = -1

Since the product of the slopes is -1, the two lines are perpendicular. Therefore, the statement "These lines are perpendicular" is true.

The correct answer is A. true.

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In the first triangle, the angle x = 45°

In the second triangle, the angle y = 75°

In the second triangle, the angle x = 45°

To find the angles in the triangles, we proceed as folows.

a. In the first triangle, let the base angle to the left be p. We know that we have a parallelogram there.

Now, in the parallelogram,

102° + p = 180°sum of (interior angles of a parallelogram)

So, p = 180° - 102°

= 78°

Now, in the larger triangle,

x + p + 57° = 180° (sum of angles in a triangle)

Since p = 78°, we have that

x + 78° + 57° = 180°

x + 135° = 180°

x = 180° - 135°

= 45°

So, x = 45°

b. In figure 2, we have two isoceles triangles.

i. In the first triangle, both base angles are y.

So, y + y + 30° = 180° (sum of angles in atriangle)

2y + 30° = 180°

2y = 180° - 30°

2y = 150°

y = 150°/2

y = 75°

So, y = 75°

ii. In the second triangle also, both base angles are x and the other angle is a right angle which is 90°.

So, x + x + 90° = 180° (sum of angles in a triangle)

2x + 90° = 180°

2x = 180° - 90°

2x = 90°

x = 90°/2

x = 45°

So, x = 45°

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Answer:

22.88

Step-by-step explanation:

O/360 * π r squared

90/360 * 8 squared

1/4 * π (64)

4 π

Next:

b*h/2

8*12/2 = 48

8π - 48

8π = 25.12

48-25.12 = 22.88

The area of circle is represented by quadratic expression A = π · x², for a radius x = 5 units, the area of circle equals 25π square units.

In this question we need to derive the area formula for a circle as a function of radius and compute the value of the figure for a given radius. According to geometry, the area of a circle (A), in square units, is described by following quadratic equation:

A = π · x²

Where x is the radius of the circle, in units.

If we know that x = 5, then the area of the circle is now computed:

A = π · 5²

A = 25π

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Answer:

Step-by-step explanation:

It is -12.

The opposite of a positive number would be its negative.

The equivalent expression of log4 ( 1/4x²) is log4(1/4) + log4(x²) ( option D)

The logarithm is the inverse function to exponentiation. For example log2 (8) = 3 and 2³ = 8

The following are math logarithm rules:

loga (MN) = loga M + loga N.

loga (M/N) = loga M - loga N.

IogaMn = n Ioga M.

For example Log5 (5²) = Log5 (5) + Log5 (5)

= 1+1 = 2

this means Log5 ( 5²) = log5 ( 25) = 2

Therefore if loga (MN) = loga M + loga N.,

we can say that,

log4( 1/4x²) can also be written as ;

log4 (1/4) + log4 (x²) .

therefore the equivalent expressions for

log4 ( 1/4x²) is log4 (1/4) + log4 (x²) .

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Using the inequality rule we know that 11 is greater than -11, (11 > -11).

Mathematical expressions with inequalities are those in which the two sides are not equal.

Contrary to equations, we compare two values in inequality.

Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Two expressions in inequality aren't always equal, which is denoted by the symbols >, <, ≤, or ≥.

So, let's say the inequality equation looks like this: A

Right now, A is valued at

Let p be used to representing the initial number.

P equals 11, so

Let q be used to representing the second number.

Q has a value of -11.

-11 and 11 are both numbers that are greater than zero.

Then, 11 > -11 ... (1)

A has a value of 11 > -11.

Therefore, using the inequality rule we know that 11 is greater than -11, (11 > -11).

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Correct question:
Is 11 greater than, equal to, or less than -11?

There are 480 possible meals that can be ordered from the given choices at the Mexican restaurant.

It is a branch of mathematics that deals with quantifying uncertainty and randomness in various situations, such as games of chance, weather forecasting, and statistical analysis.

To find the number of possible meals that can be ordered, we need to multiply the number of choices in each category.

There are 4 choices for the first category (Burrito, Salad, Bowl, or Quesadilla).

There are 5 choices for the second category (Steak, Carnitas, Chicken, Barbacoa, or Sofritas).

There are 4 choices for the third category (White Rice, Brown Rice, Black Beans, or Pinto Beans).

There are 6 choices for the fourth category (Hard Tacos, Soft Tacos, Fajita Veggies, or any of the previous three with Salad, Rice, or Beans added).

Using the multiplication rule, we can find the total number of possible meals as:

4 x 5 x 4 x 6 = 480

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The expression that can be used to find out the amount of time it would take Sal to finish the remaining homework is C. 4 / 9 x 3 / 5 .

To find the expression that would show the time it would take for Sal to finish his homework, the formula would be:

= Proportion of questions remaining x Time taken to finish one question

Proportion of questions remaining:

= 1 - 5 / 9

= 4 / 9

Time taken to finish one question:

= 3 / 5 minutes

The expression is therefore:

4 / 9 x 3 / 5

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Alpa must take out at least 19 T-shirts from the bag to be absolutely sure of having at least two T-shirts among them that differ only by size or only by color.

What is the Pigeonhole Principle?

The Pigeonhole Principle is a fundamental concept in combinatorics, which is a branch of mathematics that deals with counting and analyzing the properties of sets of objects. The principle states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon.

We can solve this problem using the Pigeonhole Principle, which states that if n+1 objects are distributed among n boxes, then there is at least one box that contains two or more objects.

In this case, we want to be sure that we have at least two T-shirts that differ only by size or only by color.

So we need to find the minimum number of T-shirts that we must take out of the bag to guarantee this.

Let's consider the worst-case scenario, where we take out all the T-shirts that are of one size or one color.

If we take out all 18 small red T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color (since we could still get a small black T-shirt).

Similarly, if we take out all 19 small black T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color.

If we take out all 13 large black T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color.

If we take out all 15 large red T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color.

So we need to take out at least 19 T-shirts to be sure that we have at least two T-shirts that differ only by size or only by color. (We add one to the largest number of T-shirts of one color or size.)

Therefore, Alpa must take out at least 19 T-shirts from the bag to be absolutely sure of having at least two T-shirts among them that differ only by size or only by color.

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Answer:

8x + 2 + 10x - 4 + 38 = 180

18x + 36 = 180

18x = 144, so x = 8

Angle A measures 8(8) + 2 = 64 + 2 = 66°.

Answer:

(C) {-3, 2} is the correct answer.