ACTIVITY 1: Solve the following rational equation.

The rocket will hit the ground after 19.09 seconds.

a) The height of the rocket can be describe as:

h(t) = -16t² + 210t + 75

where

t = time in seconds

h(t) = height of the rocket in feet

b) To find the time at which the rocket reaches its maximum height, we need to find the vertex of the parabolic function. The vertex is given by the formula:

t = -b/(2a)

where

a = -16

b = 210

Substituting these values, we get:

t = -210/(2(-16)) = 6.5625 seconds

To find the maximum height, we substitute this value of t back into the equation for h(t):

h(6.5625) = -16(6.5625)² + 210(6.5625) + 75 = 690.625 feet

This means that the rocket reaches its maximum height of 690.625 feet after 6.5625 seconds.

c) We need to find the time interval during which the height of the rocket is greater than 721 feet. We set the height function h(t) greater than 721 and solve for t:

-16t² + 210t + 75 > 721

-16t² + 210t - 646 > 0

Solving for t using the quadratic formula, we get:

t < 2.975 or t > 14.038

Therefore, the rocket will be more than 721 feet above ground level between 0 and 2.975 seconds, and between 14.038 and infinity seconds.

d) To find the time at which the rocket hits the ground, we set h(t) equal to 0 and solve for t:

-16t² + 210t + 75 = 0

Solving for t using the quadratic formula, we get:

t = [tex]\frac{-b \± \sqrt{b^{2} - 4ac } }{2a}[/tex]

a = -16, b = 210, c = 75

t = [tex]\frac{-210 \± \sqrt{210^{2} - 4(16)(75) } }{2(-16)}[/tex]

t = [tex]\frac{-210 \± \sqrt{22225} }{-32}[/tex]

t = [tex]\frac{-210 \± 149}{-32}[/tex]

t = 2.53125 or t = 13.53125

Since the rocket was launched from the top of a 75-foot building, it will hit the ground after an additional time of:

t + 2.53125 = 5.09375 seconds or t + 13.53125 = 19.09375 seconds

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An example of where past performance does predict future performance would be Mt. Kīlauea's eruption in 2018.

An example of where past performance does not predict future performance would be the eruption of Hualālai last happening in 1801.

Using past data, there was a prediction that Mt. Kīlauea would erupt in the year 2018 and it did happen ( even though it was not very serious ) at the Lower East rift zone of the volcano. Past performance therefore predicted the future.

However, the same prediction said that Hualālai would erupt in 1854 and yet the volcano has not erupted since 1801 which shows that the prediction was wrong.

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The circumference of the small pizza is approximately 47.1 cm, the circumference of the medium pizza is approximately 69.1 cm, and the circumference of the large pizza is approximately 94.2 cm.

The diameter is the distance across the widest part of a circle. To find the circumference of a circle, we use the formula C = πd, where C is the circumference, π is a mathematical constant (approximated as 3.14), and d is the diameter of the circle. Therefore, to find the circumference of each pizza size, we can simply plug in the given diameter into this formula.

For the small pizza with a diameter of 15 cm, the circumference can be calculated as follows:

C = πd

C = 3.14 x 15

C ≈ 47.1 cm

For the medium pizza with a diameter of 22 cm, the circumference can be calculated as follows:

C = πd

C = 3.14 x 22

C ≈ 69.1 cm

For the large pizza with a diameter of 30 cm, the circumference can be calculated as follows:

C = πd

C = 3.14 x 30

C ≈ 94.2 cm

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The value of correct Set-builder form is,

⇒ { x | x ∈ IR ; 4 ≤ x ≤ 8 }

We have to given that;

The set is,

⇒ {4, 5, 6, 7, 8}

Thus, We can write correct Set-builder form as,

⇒ {4, 5, 6, 7, 8}

⇒ { x | x ∈ IR ; 4 ≤ x ≤ 8 }

So, The value of correct Set-builder form is,

⇒ { x | x ∈ IR ; 4 ≤ x ≤ 8 }

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Answer:

2π(10^2) + 2π(10)(16)

= 2π(100) + 2π(160)

= 200π + 320π

= 520π ft^2

Answer:

the 2 angles are 169.1° and 10.9°

Step-by-step explanation:

Supplementary angles add to 180

x = first angle

y = second angle = x - 158.2

x + y = 180

x + (x - 158.2) = 180

2x = 180 + 158.2

2x = 338.2

x = 338.2/2 = 169.1

y = 169.1 - 158.2 = 10.9

x + y = 169.1 + 10.9 = 180

There are 960 bikes in the repair department and  1.98% of the bikes need two repairs.

The number of bikes with flat tires only is 0.25x, where x is the total number of bikes

The number of bikes with bent handlebars only is 0.05x

The number of bikes with ripped seats only is 0.1x

The number of bikes that need two repairs is 0.01Tx, where T is the percentage of bikes that need two repairs (expressed as a decimal)

The number of bikes that need all three repairs is 0.0833...x

So we have the equation:

0.25x + 0.05x + 0.1x + 0.01Tx + 0.0833...x = 101

Simplifying and solving for x, we get:

x = 960

So there are 960 bikes in the repair department.

To find the number of bikes that need two repairs, we can use the equation:

0.25x + 0.05x + 0.1x + 0.01Tx = 101 - 0.0833...x

Substituting x = 960, we get:

0.25(960) + 0.05(960) + 0.1(960) + 0.01T(960) = 101 - 0.0833...(960)

240 + 48 + 96 + 9.6T = 101 - 80

9.6T = 19

T = 1.98

About 1.98% of the bikes need two repairs.

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Answer:

a) 5

Step-by-step explanation:

the question say how many zero-dimensional objects are labeled on the object. so, you would count how many blue dots you see on the object, as you can see their are four dots on the the bottom, and one dot at the top.

so, 4 dots + 1 dot = ?

5 blue dots

so your answer is 5.

hopefully this helps, let me know if it doesn't.

Josh is incorrect because 100 is perfect square not a perfect cube.

We have the number 100.

Now, factorising the number 100 as

100 = 2 x 2 x 5 x 5

100= (2 x 5)  x ( 2x 5)

100 = 10 x 10

As, 100 can be factorised as 10 x 10 which shows 100 is prefect square of 10.

But 100 is not a perfect cube because for the cube we need pair of three number.

Thus, Josh is incorrect.

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Answer:

B’ = (-11, 1)

Step-by-step explanation:

Because the triangle is reflected across the line x = -2, it is being reflected across a vertical line.

Therefore only the x-coordinate will change.

As B is 9 units right of the line x = 2, the coordinates of B’ will be (-2 - 9, 1)

Which will be (-11, 1)

695 divided by 70=9.92 hours

[tex]\sf V_{3 Cylinders} =2.8274(in^{3} ).[/tex]

From the provided information about the ice cubes (height and diameter), it's safe to assume that they are cylinder shaped ice cubes. They could be circular cone ice cubes, but the safest assumption is cylinders. Now, to find the volume of a cylinder we use the following formula:

[tex]\sf V_{Cylinder} =\pi r^{2} h[/tex] or [tex]\dfrac{\pi d^{2} h}{4}[/tex].

For the fist equation, "r" stands for radius, and "h" for height.

On the alternate equation, "d" stands for diameter.

Since we're given the diameter and height, let's use the alternate equation:

[tex]\sf V_{Cylinder} =\dfrac{\pi (1(in))^{2} 1.2(in)}{4}=\dfrac{3}{10} \pi (in^{3} )=0.9425(in^{3} ).[/tex]

This can be done by just multiplying the volume of a single cube ([tex]\dfrac{3}{10} \pi (in^{2} )[/tex]) by 3.

[tex]\sf V_{3 Cylinders} =(3)\dfrac{3}{10} \pi (in^{3} )=\dfrac{9}{10} \pi (in^{3} )=\boxed{\sf 2.8274(in^{3} )}.[/tex]

Assuming the ice cubes have the shape of a circular cone, this is the process for calculating the volume of all 3 cubes:

[tex]\sf V_{Cone} =\dfrac{1}{3} \pi r^{2} h\\ \\\\ \\ V_{3Cones} =3*\dfrac{1}{3} \pi r^{2} h\\ \\ \\= \pi r^{2} h\\ \\ \\=\pi (\dfrac{1(in)}{2} )^{2} (1.2(in))\\ \\\\ =\dfrac{3}{10} \pi (in^{3} )=\boxed{\sf 0.9425(in^{3} )}[/tex]

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Answer:

78°F

Step-by-step explanation:

If the temperature was 75.5°F, and it rose by 6°F on Sunday, then the temperature on Sunday was:

75.5°F + 6°F = 81.5°F

If the temperature on Sunday was 81.5°F, and it dropped by 3.5°F on Monday, then the temperature on Monday was:

81.5°F - 3.5°F = 78°F

Therefore, the temperature on Monday was 78°F.

Based the provided information, the t-value is approximately 1.824.

We shall work out the t-value by calculating the difference between the sample mean and the population mean, divided by the standard error of the mean.

We shall use the t-test formula to calculate the t-value:

t = (sample mean - population mean) / (sample standard deviation / [tex]\sqrt(sample size)[/tex])

where:

sample mean = 86.3

population mean = 83.5

sample standard deviation = 7.2

sample size = 22

Plugging in these values, we have:

t = (86.3 - 83.5) / (7.2 / √22)

t = 2.8 / (7.2 / 4.69)

t = 2.8 / 1.535

t ≈ 1.824

Therefore, the t-value is approximately 1.824.

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Answer:

5 (100y -601.39)

3028

Step-by-step explanation:

The probability that a red shirt and black slacks are on the floor is 1/10.

Probability is the odds that a random event would happen. The odds that the event would happen has a probability value that lies between 0 and 1.

Probability that a red shirt and black slacks are on the floor = (number of red shirts / total number of shirts) x (number of black slacks / total number of slacks)

Total number of shirts = 2 + 2 + 1 = 5

Total number of slacks = 1 + 1 = 2

(1/5) x (1/2) = 1 /1 0

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Answer:

Step-by-step explanation:

You are looking for the tangent ratio, which is opposite side over adjacent side.  Using the tangent ratio of an angle of 37°.

tan37° = x/89

.75355405 = x/89

.75355405 · 89 = x/89 · 89/1

67.06 = x

rounded to 67.1

Answer:

67.1? that's what I got lol

The coordinates for the centroid of the triangle is (0, 2.67)

The centroid of a triangle is the place where the three medians of the triangle meet or intersect.

To find the centroid of the triangle, we use the formula

(x₁ + x₂ + x₃)/3 , (y₁ + y₂ + y₃)/3

We add all the x coordinates together and divide by 3, we also do the same for the y coordinates.

It becomes x = (-4 + 0 + 4)/3  

y = (8 + 2 + (-2))/3

Therefore, the centroid is (0, 2.67)

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When a cylinder is cut parallel to its base, the plane section that results is a circle. This circle will have the same radius as the cylinder's base. The center of the circle will be located at the center of the cylinder's base. This type of cut will create a circular cross-section that is parallel to the base of the cylinder.

Answer:

i dont know if this helps, im not sure if you are telling me to do all of these things or B, c, d are answer

Step-by-step explanation:

To find the total amount of money that the photography club will raise to meet their goal, we can multiply the average amount of money each member must raise by the number of members in the club:

Average amount of money each member must raise = m

Number of members in the club = 20

Total amount of money to be raised = Average amount of money each member must raise x Number of members in the club

Total amount of money to be raised = m x 20

We know that the club is trying to raise at least $1,400, and they have already raised $540. Therefore, the amount of money they still need to raise is:

Amount of money still needed to reach goal = $1,400 - $540

Amount of money still needed to reach goal = $860

We can set up an equation to represent the total amount of money the club will raise to meet their goal:

Total amount of money to be raised = Amount of money still needed to reach goal

m x 20 = $860

We can solve for "m" by dividing both sides of the equation by 20:

m = $860 / 20

m = $43

Therefore, the total amount of money the club will raise to meet their goal is:

Total amount of money to be raised = Average amount of money each member must raise x Number of members in the club

Total amount of money to be raised = $43 x 20

Total amount of money to be raised = $860

B))) We can set up an equation to represent the total amount of money the club will raise to meet their goal:

Total amount of money to be raised = Amount of money already raised + Amount of money still needed to reach goal

We know that the club has already raised $540 and they need to raise $860 more to reach their goal of $1,400. Therefore, we can substitute these values in the equation:

Total amount of money to be raised = $540 + $860

Total amount of money to be raised = $1,400

So the equation that represents the club raising all the money is:

$1,400 = $540 + $860

C)))) To solve the equation:

$1,400 = $540 + $860

We can simplify the right-hand side of the equation by adding $540 and $860:

$1,400 = $1,400

This equation is true, which means that it is a consistent equation. The solution to this equation is that the club will be able to raise all the money they need to buy the new photography equipment.

In the context of the scenario, the solution means that the club will be able to meet their goal of raising at least $1,400 for new photography equipment. They have already raised $540, and they need to raise $860 more to reach their goal. The equation shows that the total amount of money they will raise is exactly $1,400, which is the amount they need to meet their goal.

D))))) To represent the amount of money each member must raise, on average, to meet or exceed their goal, we can use the following inequality:

Average amount of money each member must raise ≥ Total amount of money still needed to reach goal / Number of members in the club

We know that the total amount of money still needed to reach the goal is $860, and there are 20 members in the club. Therefore, we can substitute these values in the inequality:

Average amount of money each member must raise ≥ $860 / 20

To simplify the right-hand side of the inequality, we can divide $860 by 20:

Average amount of money each member must raise ≥ $43

This inequality shows that each member must raise at least $43, on average, to meet or exceed their goal of raising $1,400.

To show the possible average amount of money each club member needs to raise, we can use the following inequality:

0 < Average amount of money each member must raise ≤ Total amount of money still needed to reach goal / Number of members in the club

This inequality shows that the average amount of money each member must raise is greater than 0 (since each member must contribute something), but it is less than or equal to $43 (which is the minimum amount each member must raise to meet or exceed their goal).

Answer:

Step-by-step explanation:

Observation of the real life and way of life of the peoples of Oceania are intertwined in them with local myths.

Answer:

0.00007003 is the standard form of 7.003x10^-5. In scientific notation, the number is expressed as 7.003 multiplied by 10 raised to the power of negative five. To convert it to standard form, the decimal point has to move to the left by five places since the exponent is negative. The resulting number is a decimal with four zeros before the first nonzero digit. Standard form is a way of representing numbers that does not use exponents and is useful in comparing and performing operations on numbers.

If a, b, c are in Harmonic Progression, b+ca+ca+b ac' ab bc are in Arithmetic Progression.

Given a, b, c are in H.P.:

1/a + 1/b = 2/c

Multiplying both sides by abc:

bc + ac = 2ab

Adding c to both sides:

bc + ac + c = 2ab + c

Rearranging the terms:

c + ab = ac + bc

Adding the terms b + ca and ca + b to both sides:

b + ca + ca + b + ac' + ab + bc = ac + bc + b + ca + ca + b

Simplifying:

b + ca + ca + b + ac' + ab + bc = 2ac + 2b

Dividing both sides by 2:

(b + ca + ca + b + ac' + ab + bc)/2 = ac + b

Hence, b+ca+ca+b ac' ab bc are in A.P.

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The equation that represents the consecutive odd numbers whose product is 63 is; (x + 9) (x + 7) = 0

Odd numbers have special properties and relationships to other numbers, which make them important in mathematics. For instance, the sum of two odd numbers and the difference between two odd numbers both always equal one.

We can see that we can solve the double brackets by equation them to zero so we have that;

(x + 9) (x + 7) = 0

x = -9

x = -7

Thus;

(-9) (-7) = 63

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The likelihood that the first question will be true is equally likely and unlikely.

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

The teacher gave a true and false quiz where P(true) = 0.5 for each question.

This means that

P(true) = 0.5

As a percentage,, we have

P(true) = 50%

When the probability of an event is 50%, then the event is equally likely and unlikely.

Hence, the liikelihood is (c) qually likely and unlikely.

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Answer:
A and B

Step-by-step explanation:

-10/3= -3.33333333333

(- (-10))/(-3)= -10/3, (negative sign being erased)

=-3.33333333333

hope it helped:)

The quotient of the two fractions is (x - 5) / (x - 4).

Option D is the correct answer.

We have,

To divide two fractions, we can multiply the first fraction by the reciprocal of the second fraction.

In this case, that means we need to multiply:

(x² - 2x - 15) / (x + 2) x (x + 2) / (x² - x - 12)

Notice that the (x + 2) terms in the numerator and denominator of the first fraction cancel out with the denominator of the second fraction, so we can simplify before multiplying:

(x² - 2x - 15) / 1 x 1 / (x² - x - 12)

Now we can multiply the numerators and the denominators separately:

(x² - 2x - 15) / (x² - x - 12)

To simplify further, we can factor both the numerator and the denominator:

(x - 5)(x + 3) / (x - 4)(x + 3)

Notice that the (x + 3) terms in the numerator and denominator cancel out, leaving:

(x - 5) / (x - 4)

Therefore,

The quotient of the two fractions is (x - 5) / (x - 4).

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The equivalent expression for the given expression 132/11 is 12.

1) Given that, 132/11

Here, the equivalent expression is 132/11 =12

2) 126/7 = 18

3) 7)98(14

      7

_______

     28

     28

________

      0

4) Sixty-four divided by four

That is, 64/4 = 16

5) 28÷2

= 28/2

= 14

6) 28/2 = 14

7) 48/3 = 16

8) 36÷2

= 36/2

= 18

9) 36÷3

= 36/3

= 12

Therefore, the equivalent expression for the given expression 132/11 is 12.

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