Se the first five terms of the trigonometric series to approximate the value of cos 4pi/7 to four decimal places. Then compare the approximation to the actual value. A. –0. 9609, –0. 9659 c. –0. 9649, –0. 9659 b. –0. 2224, –0. 2225 d. –0. 9568, –0. 9659

The length of the third board the builders will add to create a right triangle, according to the Pythagorean Theorem is about 8.72 ft

Pythagorean Theorem is the relationship between the lengths of the three sides of a right triangle. The theorem states that the square of the length of the hypotenuse is equivalent to the sum of the square of the other two sides of the right triangle.

The specified dimensions of the ramp are;

Length of one side of the ramp = 20 ft

Length of the other side of the ramp = 18 ft

The shape of the triangle the builders would like to create = A right triangle

Let x represent the length of the third board, and let the 20 ft board represent the hypotenuse side. Pythagorean Theorem indicates that we get;

20² = 18² + x²

20² - 18² = x²

x² = 20² - 18² = 76

x = √(76) = 2·√(19) ≈ 8.72

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The measure of angle a is 59 degrees and the measure of angle b is 87 degrees. Based on the information given, we know that angles a and b are opposite angles of the quadrilateral abcd,

So they are supplementary (their sum is 180 degrees).

We also know that angles c and d are opposite angles of the quadrilateral abcd, and they are given in the problem. Using the fact that angles on the same side of a chord are equal, we can say that angles a and d are equal, and angles b and c are equal.

Therefore, we can set up the following equation:

a + d = 180 (because they are supplementary)
d = 121
a = d (because they are opposite angles of the quadrilateral)
b = c (because they are opposite angles of the quadrilateral)
c + d = 180 (because they are supplementary)
c = 93

Substituting the known values, we get:

a + 121 = 180
a = 59

b + 93 = 180
b = 87

Therefore, the measure of angle a is 59 degrees and the measure of angle b is 87 degrees.

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The reasonable amount of weight of his cargo Mr. Jackers while transporting a giraffe from one zoo to another is 1 ton and 2 tons. Options C and D are correct.

To arrive at a reasonable estimate, we can consider the average weight of a giraffe, which ranges between 2,600 lbs and 4,250 lbs for adult males and females, respectively.

Therefore, a reasonable amount for the weight of Mr. Jackers' cargo would be between 2,600 lbs and 4,250 lbs, which translates to either 1 ton or 2 tons.

Thus, options c and d are the only reasonable answers, with d (2 tons) being the safer choice.

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To find out how much Peter eats in one week (which is 7 days), we need to multiply this expression by 7.

Peter eats 3 carrot sticks and 1 cup of peanut butter before lacrosse practice every day, so in one day he eats:

3 + p

To find out how much he eats in one week (which is 7 days), we need to multiply this expression by 7:

7(3 + p)

Distributing the 7, we get:

21 + 7p

So the equivalent expressions that represent how much Peter eats before practice in one week are:

3 + 4p + 3p

4(3 + p)

21 + 7p

7(3p + 1)

So the correct answers are:

4(3 + p)

21 + 7p

7(3p + 1)

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Answer:

d

Step-by-step explanation:

so b = 4

and the slope is rise over run = 5/2

Answer:

D) [tex]y=\frac{5}{2}x+4[/tex]

Step-by-step explanation:

The line equation of a line is:

[tex]y=mx+b[/tex] with m being the slope and b being the y-intercept.

We can see from the graph that the y-intercept is 4, as that's where the line intercepts the y-axis, and when x=0.

To find the slope, we first need to pick 2 points: (0,4) and (2,9).

The formula for slope is:

[tex]\frac{rise}{run}[/tex]

The rise is how many units you go up/down from one point to another.  The run is how many units you go left/right from one point to another.
We can see that we go up 5 units and we go right 2 units.  This means our slope is 5/2.

The completed line equation is:

[tex]y=\frac{5}{2}x+4[/tex], which means D is the correct option.

Hope this helps! :)

Answer:

Sure, I can help you with that!

To find the area of a regular pentagon, we can use the formula:

Area = (1/2) x apothem x perimeter

where apothem is the distance from the center of the pentagon to the midpoint of any side, and perimeter is the total length of all the sides.

So, to find the area of your pentagon, we can first calculate the perimeter:

Perimeter = 5 x side

Perimeter = 5 x 10.6

Perimeter = 53

Now, we can plug in the values for apothem and perimeter into the formula:

Area = (1/2) x apothem x perimeter

Area = (1/2) x 7.3 x 53

Area = 193.45

Therefore, the area of your pentagon is approximately 193.45 square units.

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The number of servings did Pablo make is (B) 26.

Unit conversion is the process of converting a value expressed in one unit of measurement to another unit of measurement that represents the same quantity but is expressed in a different unit.

The given quantities are in different units, so we need to convert them to a common unit to determine the number of servings. For this, we need to convert quarts and gallons to fluid ounces.

Here we have

Pablo mixed 2 1/2 quarts of fruit juice with 1 gallon of seltzer.  

Each serving is 8 fluid ounces

Let's first convert the quantities to the same units.

=> 1 gallon = 4 quarts

Total amount of liquid = 2 1/2 + 4 = 6 1/2 quarts

Now, let's find how many 8-ounce servings are in 6 1/2 quarts:

=> 1 quart = 32 fluid ounces

=> 6 1/2 quarts = 6.5 x 32 = 208 fluid ounces

Given that, 1 serving = 8 fluid ounces

Number of servings = 208/8 = 26

Therefore,

The number of servings did Pablo make is (B) 26.

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Complete Question:

Pablo mixed 2 1 /2 quarts of fruit juice with 1 gallon of seltzer. If each serving is 8 fluid ounces, how many servings did Pablo make?

A: 20    B: 26     C: 32    D: 36

Answer:

x = 0.35

Step-by-step explanation:

We Know

x · 10 = 3 1/2

Find the missing number.

3 1/2 = 7/2 = 3.5

x · 10 = 3.5

x = 0.35

So, the answer is 0.35.

Answer:

Step-by-step explanation:

Total of rides from Tyler's house to Cousin's house and Cousin's house to Tyler's house = 1.8km = 1800m

So, the distance from Tyler's house to his cousin's house is

= 1800m ÷ 2 = 900m

The minimum value of the function is -5 and the maximum value of the function is 15.

The minimum and maximum value of the given trigonometric function f(x)=10sin(2/5x)+5 can be determined by analyzing the amplitude and period of the sine function. The amplitude of the sine function is 10, which means that the maximum value of the function is 10+5=15 and the minimum value is -10+5=-5.

The period of the sine function is given by 2π/2/5=5π. This means that the function completes one full cycle every 5π units. To find the minimum and maximum values of the function, we need to evaluate it at the critical points of the function, which occur at intervals of 5π.

At x=0, the function has a value of 5+10sin(0)=15, which is the maximum value of the function. At x=5π/2, the function has a value of 5+10sin(2π/5)=5, which is the minimum value of the function.

At x=[tex]5π[/tex], the function has a value of 5+10sin(4π/5)=-5, which is the maximum value of the function. At x=15π/2, the function has a value of 5+10sin(6π/5) =5, which is the minimum value of the function.

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Point 5 is located on the x-axis (horizontal one)

On a general coordinate axis we have two axes.

The vertical one is called the y-axis, and here we put the outputs.

The horizontal one is called the x-axis, here we put the inputs.

Here we can see that point 5 (P5) is located on the horizontal axis, then the correct option is the first one, x-axis.

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X = 0 and Y = 6 are the answers to the equation system. The system's two equations are satisfied at the location (0, 6). Choice D

To solve the system of equations:

2x + 3y = 18

3x + y = 6

We can employ the substitution or elimination strategy. Let's solve this system via the process of elimination:

To make the coefficients of x in both equations equal, multiply the second equation by two:

2(3x + y) = 2(6)

6x + 2y = 12

Now we have the system of equations:

2x + 3y = 18

6x + 2y = 12

Next, by deducting the first equation from the second equation, we can remove the y term:

(6x + 2y) - (2x + 3y) = 12 - 18

6x + 2y - 2x - 3y = -6

4x - y = -6

4x - y = -6

y = 4x + 6

At this point, we can add this expression for y to one of the initial equations. Let's employ the first equation:

2x + 3(4x + 6) = 18

2x + 12x + 18 = 18

14x + 18 = 18

14x = 0

x = 0

Replacing x = 0 in the equation y = 4x + 6 now:

y = 4(0) + 6

y = 6

Thus, x = 0 and y = 6 are the answers to the system of equations. The system's two equations are satisfied at the location (0, 6). Basketball or baseball in option D is 5/6, or approximately 0.8333.

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Answer:

Option D, (0,6)

Step-by-step explanation:

took the test xx

The sample mean difference from these 24 pairs of siblings is 1.79 inches.

To find the sample mean difference from these 24 pairs of siblings, you can use the given 95% confidence interval for the mean difference in heights, which is (-0.76, 4.34).

The sample mean difference is the midpoint of the confidence interval. To calculate this, add the lower bound (-0.76) and the upper bound (4.34) of the confidence interval, and then divide by 2:

(-0.76 + 4.34) / 2 = 3.58 / 2 = 1.79 inches

So, the sample mean difference from these 24 pairs of siblings is 1.79 inches.

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a) If the supplement of an angle is 30 degrees more than the measure of the angle, the measure of the angle is 75 degrees.

b) If the supplement of an angle is 12 degrees less than twice the measure of the angle, the measure of the angle is 64 degrees.

a) Let x be the measure of the angle. The supplement of the angle is 180-x. According to the problem, the supplement of the angle is 30 degrees more than the measure of the angle. This can be written as:

180 - x = x + 30

Solving for x, we get:

2x = 150

x = 75

b) Let x be the measure of the angle. The supplement of the angle is 180-x. According to the problem, the supplement of the angle is 12 degrees less than twice the measure of the angle. This can be written as:

180 - x = 2x - 12

Solving for x, we get:

3x = 192

x = 64

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The E is enclosed by the planes z = 0 and z = x + y + 5

Why will E is enclosed by the planes z = 0?

The evaluate the triple integral ∫∫∫_E eˣ dV, where E is enclosed by the planes z = 0 and z = x + y + 5, and by the cylinders x² + y² = 4 and x² + y² = 9,

Follow these steps:

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Y-component of the vector as shown in the diagram is 67.84 m in the direction of the negative y-axis.

Vector is a quantity that has both magnitude and direction.

Examples a vectors are

To find the Y-component of the vector, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the y component is 67.84 m.

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Declan's statement is technically correct, it is not a very helpful way to write an equivalent fraction for 5.

Declan's statement is mathematically correct, but it is not a useful way to write an equivalent fraction for 5 in most contexts.

In general, to write an equivalent fraction, we need to multiply or divide both the numerator and the denominator by the same nonzero number. This preserves the value of the fraction, but changes its form.

For example, to write an equivalent fraction for 5, we can multiply both the numerator and denominator by any nonzero number. Let's say we multiply both by 2:

5/1 = (5x2)/(1x2) = 10/2

So 10/2 is an equivalent fraction for 5.

However, if we follow Declan's approach and write 5 as the denominator and 1 as the numerator, we get:

5/1 = 1/5

This is indeed an equivalent fraction for 5, but it is not a particularly useful or common way to write an equivalent fraction. In general, we prefer to write equivalent fractions with a denominator that has some mathematical or practical significance, such as a power of 10 or a factor of the original denominator.

So while Declan's statement is technically correct, it is not a very helpful way to write an equivalent fraction for 5.

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In the circle, the measure of p is 34 (option 3).

First, we know that angle MBC is an exterior angle to triangle PBC. Therefore, the measure of angle PBC is equal to the sum of angles MBC and MCB, which is 100 + (1/2)(angle MCP) = 100 + (1/2)(angle MQP).

Similarly, angle MCD is an exterior angle to triangle PCD. Therefore, the measure of angle PDC is equal to the sum of angles MCD and MDC, which is 62 + (1/2)(angle MPQ) = 62 + (1/2)(angle MQP).

Since angle PBC and angle PDC are both subtended by the same arc BC, they are equal. Therefore, we can set the expressions for these angles equal to each other and solve for angle MQP:

100 + (1/2)(angle MQP) = 62 + (1/2)(angle MQP)

38 = (1/2)(angle MQP)

angle MQP = 76 degrees

Finally, we can use the fact that angles MPQ and MQP form a linear pair, so they add up to 180 degrees. Therefore, angle MPQ is 180 - 76 = 104 degrees.

Since angle MPQ is an exterior angle to triangle PAB, we can use the exterior angle theorem to find the measure of angle P, as follows:

angle P = angle MPQ + angle PAB = 104 + 100 = 204 degrees

However, angles in a circle cannot be greater than 180 degrees, so we need to subtract 180 from angle P to get the actual measure of angle P:

angle P = 214 - 180 = 34 degrees

Therefore, the answer is option (3).

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Each game of skee ball requires 2 tokens and each game of pinball requires 2 tokens.

Let the number of tokens required for each game of skee ball be x and for each game of pinball be y.

From the given information, we can form two equations:

10x + 8y = 44    ... (1)

3x + 8y = 30      ... (2)

Multiplying equation (2) by 3, we get:

9x + 24y = 90     ... (3)

Subtracting equation (1) from equation (3), we get:

- x + 16y = 46

Solving for x, we get:

x = 16y - 46

Substituting this value of x in equation (2), we get:

3(16y - 46) + 8y = 30

Simplifying and solving for y, we get:

y = 2

Substituting this value of y in equation (1), we get:

10x + 8(2) = 44

Solving for x, we get:

x = 2

Therefore, each game of skee ball requires 2 tokens and each game of pinball requires 2 tokens.

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If the S&P stock index fell by an average of 8% each day, we can model the

data using exponential decay. Let P represent the initial value of the S&P

stock index and t represent the number of days. Then, the equation for the

S&P stock index after t days is:

[tex]P(t) = P * (0.92)^t[/tex]

Here, 0.92 represents the daily decay factor, which is derived from

subtracting 8% from 100% (100% - 8% = 92%). As each day passes, the

value of P(t) decreases exponentially by a factor of 0.92.

It's important to note that this equation assumes that the S&P stock index

falls by exactly 8% each day, which may not be a realistic scenario in real

life. Additionally, this equation only models the decay of the S&P stock

index value and does not take into account any external factors that may

affect its value.

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Nora would have to pay a total of $5 + $0.75s in a month when she downloaded "s" songs.

The cost for downloading 30 songs would be:

$0.75 per song × 30 songs = $22.50

Therefore, Nora would have to pay a total of $5 + $22.50 = $27.50 in a month when she downloaded 30 songs.

If she downloaded "s" songs, the cost would be:

$0.75 per song × s songs = $0.75s

Therefore, Nora would have to pay a total of $5 + $0.75s in a month when she downloaded "s" songs.

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In circle P, if m(QR) = 80 , and m(QRT) = 39 , m(QPR) = 39 and m(PT) = 78

Based on the information given, we know that:

- m(QR) = 80 (this is the measure of arc QR)
- m(QRT) = 39 (this is the measure of angle QRT)

To find the other measures, we can use the following formulas:

- The measure of a central angle is equal to the measure of its intercepted arc
- The measure of an inscribed angle is half the measure of its intercepted arc

Using these formulas, we can find the measure of angle QPR and the measure of arc PT as follows:

- m(QPR) = m(QRT) = 39 (since angle QRT and angle QPR intercept the same arc QR)
- m(PT) = 2 * m(QRT) = 78 (since angle QRT and angle PQT intercept the same arc PT, and the measure of an inscribed angle is half the measure of its intercepted arc)

So the final answers are:

- m(QR) = 80
- m(QRT) = 39
- m(QPR) = 39
- m(PT) = 78

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The fish has located a horizontal distance of 7 meters away from the cliff.

How to find the distance between the bird and the fish?

To find the distance between the bird and the fish, we need to find the horizontal distance traveled by the bird during the dive. We can do this by finding the x-coordinate of the vertex of the parabolic curve, which represents the highest point of the dive.

The vertex of the parabolic curve of the given function f(x) = (x-7)^2 - 1 is at the point (7, -1). This means that the highest point of the bird's dive is reached at 7 seconds, and the bird is at a height of -1 meters at this point.

To find the distance traveled by the bird during the dive, we need to find the horizontal distance between the bird's starting point (the cliff) and the highest point of the dive (the vertex). The distance is given by the horizontal coordinate of the vertex, which is 7 seconds.

Therefore, the fish has located a horizontal distance of 7 meters away from the cliff, assuming that the bird started the dive from the edge of the cliff.

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It will take the population 10.5 years to reach 25,000

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

Inital population, a = 15000

Rate of increase, r = 5%

Using the above as a guide, we have the following:

The function of the situation is

f(x) = a * (1 + r)ˣ

So, we have

f(x) = 15000 * (1 + 5%)ˣ

When it reaches 25000, we have

15000 * (1 + 5%)ˣ = 25000

Divide both sides by 15000

(1 + 5%)ˣ = 1.67

Take the logarithm of both sides

x = log(1.67)/log(1 + 5%)

Evaluate

x = 10.5

Hence, the number of years is 10.5

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Answer:

2x + 3x = 475

= 5x = 475

= x = 475/5

= x = 95

Answer:

285 boys

Step-by-step explanation:

2 + 3 = 5

475/5=95

Girls: 2 x 95= 190

Boys: 3 x 95 = 285

Check

285 + 190= 475

The ordered pairs of the system of inequalities are (1, 0) and (0, -5)

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

6x - y > -3

4x + 3y < 4

The above expression is a system of linear inequality

That implies that we graph the inequalites in the system on the same plane and write out ordered pairs from the region that represent the solution of the system

Next, we plot the graph

See attachment for the graph of the inequality

The ordered pairs are (1, 0), (0, -5) and other pairs

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The area of the facade measuring 30' across and 20' in height is 300 square feet.

The front facade of an A-frame house is a triangular shape, with a base of 30 feet and a height of 20 feet. To calculate the area of the facade, we need to use the formula for the area of a triangle, which is 1/2 times the base times the height = 1/2 * b * h, where b is the base and h is the height.

In this case, the base is 30 feet and the height is 20 feet, so we can plug those values into the formula:

Area = 1/2 x 30 x 20

Simplifying the multiplication, we get:

Area = 300 square feet

Therefore, the area of the front facade of the A-frame house is 300 square feet.

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The correct answer is (D) 2,205.

To calculate the number of different combinations of tag codes, we need to consider the possible options for each position in the code.

For the first and third positions (consonants), we have 21 options for each position since there are 21 consonants in the English language.

For the middle position (vowel), we have 5 options since there are 5 vowels in the English language.

Therefore, the total number of different combinations is calculated by multiplying the number of options for each position:

21 (consonant options) * 5 (vowel options) * 21 (consonant options) = 2,205

Therefore, the correct answer is (D) 2,205.

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