tom paid $120 for his sons laser tag birthday party. He paid $35 for pizza and $5.00 for each person at the party. How many people were at the birthday party?

Heyo!

So, the best prediction for the height of the rocket after 5.5 seconds, based on the given data above, I believe would be C. 220 ft.

Hope this helps! Pls, LMK if it does! Good Luck!

The best prediction for the height of the rocket after 5.5 sec will be 220 feet.

A quadratic equation is an equation where the highest power of the variable is 2.

Given data for the height of the rocket at different time is modeled by the function  h(t) = -16t² + 128t

The height of the rocket after 5.5 sec will be

= h(5.5) = [- 16(5.5)² + 128 × 5.5] feet = (- 484 + 704) feet = 220 feet.

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Answer:

10 + 3π cm

Step-by-step explanation:

In the given figure,

Here, we are asked to find the perimeter of the shaded figure, i.e, SA + AC + CT + Arc SBT.

The perimeter of arc SBT can be found using the formula 2πr/4 [Given ⟶ arc SBT = quarter (¼) of a circle].

So,

2πr/4

= 2π(6)/4

= 12π/4

= 3π cm

Now, from the figure..

SA + AC + CT

= (SR - AR) + AC + (RT - RC)

By, rearranging the terms...

= SR + AC + RT  - (AR + RC) ---------> (1)

Again, from the figure, we can see that,

So, by substituting these values in (1)

SR + AC + RT  - (AR + RC)

= 6 + 6 + 6 - (8)

= 18 - 8

= 10 cm

And, the perimeter of the shade figure is,

SA + AC + CT + Arc SBT.

\(= \boxed{\tt\:10 + 3\pi \: cm}\)

_________

Hope it helps!

\(\mathfrak{Lucazz}\)

Answer:

Step-by-step explanation:

Take into account that:

Since R is the center and B is on the circle we have:

The arc SBT is the quarter of the length of circle:

Find the sum of SA and CT:

So the perimeter of shaded zone is:

As a result of answering the given question, we may state that As a expressions result, your 200-kilometer trip will cost $245.41 in gasoline.

An expression in mathematics is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, and so on) that expresses a quantity or a value. Expressions might be simple, such as "3 + 4", or complex, such as "(3x2 - 2) / (x + 1)". They can also include functions like "sin(x)" or "log(y)". Expressions can be evaluated by substituting values for the variables and performing the mathematical operations in the order specified. For example, if x = 2, the formula "3x + 5" evaluates to 3(2) + 5 = 11. Expressions are frequently used in mathematics to express real-world situations, create equations, and simplify complex mathematical problems.

To calculate the cost of gasoline for your journey, you must first determine the distance you will go. Assume you'll be travelling 200 kilometres.

To calculate the amount of gasoline you will need, use the following formula:

(Distance Traveled / 100) x Fuel Efficiency = Petrol Used

In place of the values we have:

(200 / 100) x 5.5 = 11 litres of gasoline used

To calculate the cost of gasoline, simply multiply the amount used by the price per litre:

Petrol Cost = Petrol Used x Price per Litre

Fuel cost = 11 x $22.31

Fuel price = $245.41

As a result, your 200-kilometer trip will cost $245.41 in gasoline.

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Answer:

w^2 + 13w + 39

Step-by-step explanation:

Multiplying Polynomials (FOIL- Firsts, Outs, Inners, Lasts)

(w+9) (w+4)          Multiply- Firsts (w*w)   Outs (w*4)   Inners (9*w)   Lasts (9*4)

w*w + w*4 + 9*w + 9*4     Multiply the FOIL

w^2 + 4w + 9w + 36          Combine like terms (same variables, numbers)

w^2 + 13w + 39

Answer:

P=0.0000037

P=0.00037%

Step-by-step explanation:

Probability

A standard deck of 52 playing cards has 4 aces.

The probability of getting one of those aces is

\(\displaystyle \frac{4}{52}=\frac{1}{13}\)

Now we got an ace, there are 3 more aces out of 51 cards.

The probability of getting one of those aces is

\(\displaystyle \frac{3}{51}=\frac{1}{17}\)

Now we have 2 aces out of 50 cards.

The probability of getting one of those aces is

\(\displaystyle \frac{2}{50}=\frac{1}{25}\)

Finally, the probability of getting the remaining ace out of the 49 cards is:

\(\displaystyle \frac{1}{49}\)

The probability of getting the four consecutive aces is the product of the above-calculated probabilities:

\(\displaystyle P= \frac{1}{13}\cdot\frac{1}{17}\cdot\frac{1}{27}\cdot\frac{1}{49}\)

\(\displaystyle P= \frac{1}{270,725}\)

P=0.0000037

P=0.00037%

Answer:

2 x 3 + 7 x 2 + 14 x + 12÷ 2x+ 3 = x² +2x+ 4  

Step-by-step explanation:

We multiply the first term 2x of the divisor with a term ( quotient) to get the first term of the dividend. Then we multiply the same term with each term of the divisor  and subtract it from the dividend. The process continues unless we get the zero or a much smaller number than the dividend as the remainder

               x² +2x+ 4                        

2x+3    ║2 x 3 + 7 x 2 + 14 x + 12

               2x³ + 3x²

                 -      -      

                         4x² +14x+12

                          4x²+ 6x

                        -        -      

                                   8x+12

                                     8x+12      

                                   -        -  

                                     0        

Answer:

Step-by-step explanation:Use the long division method to find the result when 2 x 3 + 7 x 2 + 14 x + 12 2x 3 +7x 2 +14x+12 is divided by 2 x + 3 2x+3

The length of midsegment of the trapizoid with bases 35 and 71 is 53.

A trapezoid, commonly referred to as a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel opposing sides and a set of non-parallel sides. The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.

A trapezoid is a closed, four-sided, two-dimensional shape that has both a perimeter and an area. The bases of the trapezoid are the two sides of the form that are parallel to one another. The legs or lateral sides of a trapezoid are the non-parallel sides. The altitude is the smallest distance between two parallel sides. Calculating a trapezoid's area is easy since its opposite sides are parallel to one another.

A trapezoid differs from other quadrilaterals in that it has the following characteristics:

The length of midsegment is sum of bases divided by 2

therefore midsegment = (35 + 71)/2 = 53.

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\(\\ \rm\longmapsto (x-5)^2+3(x-5)-4\)

\(\\ \rm\longmapsto x^2-10x+5^2+3x-15-4\)

\(\\ \rm\longmapsto x^2-7x+25-19\)

\(\\ \rm\longmapsto x^2-7x+6\)

Answer: The unit value of a cubic centimeter (cm^3) is the same as the metric measurement of a milliliter (mL).

This is because 1 milliliter is equal to 1 cubic centimeter. In other words, if you have a cube that measures 1 centimeter on each side, its volume would be 1 cubic centimeter, which would also be equivalent to 1 milliliter of volume.

This relationship between cm^3 and mL is commonly used in scientific and medical measurements involving liquids and gases.

The unit value of a cubic centimeter (cc) is equivalent to one milliliter (mL) in the metric system. Both cubic centimeters and milliliters are used to measure volume, and their conversion is straightforward: 1 cc = 1 mL.

The metric system uses base units such as meters, liters, and grams, and applies prefixes like kilo-, centi-, and milli- to indicate larger or smaller units of measurement.
Cubic centimeters are often used to measure the volume of solid objects or the capacity of containers, while milliliters are more commonly used to measure the volume of liquids. However, both units represent the same volume and can be used interchangeably.
It is important to understand the difference between volume measurements and other metric measurements, such as length or mass. For instance, meters are used to measure length or distance, and grams are used to measure mass or weight. These units cannot be directly converted to cubic centimeters or milliliters, as they represent different physical properties.
In summary, a cubic centimeter (cc) is a unit of volume in the metric system that is equivalent to one milliliter (mL). Both units can be used to measure volume, and they have a simple conversion of 1 cc = 1 mL. Understanding the relationship between these units and other metric measurements is essential for accurately quantifying and comparing different physical properties.

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Answer:

A=P+Prt

A-P=Prt

(A-P)/Pt=r

r=(A-P)/Pt

Answer:

3rd option

Step-by-step explanation:

- 10 ≥ 6x - 4 ( add 4 to both sides )

- 6 ≥ 6x , then

6x ≤ - 6 ( divide both sides by 6 )

x ≤ - 1

Thus x = - 1 is a solution to the inequality

Answer:

Its the fourth option

Step-by-step explanation:

Question 37:  The following is a solution to the differential equation y = t - 1. d.

Question 38:  The tea temperature be after a very long time is dT/dt = k(S - T); T ≈ 20 degrees after a very long time. a.

To determine the solution to the given differential equation: t²(d²y/dt²) - 6t(dy/dt) + 12 = 0, we can solve the equation by assuming a solution in the form of y = tⁿ, where n is a constant.

By differentiating y with respect to t, we can substitute the derivatives into the differential equation to determine the value of n.

Let's differentiate y = tⁿ with respect to t:

dy/dt = n × tⁿ⁻¹

d²y/dt² = n(n-1) × tⁿ⁻²

Substituting these derivatives into the differential equation:

t²(n(n-1)tⁿ⁻²) - 6t(ntⁿ⁻¹) + 12 = 0

Simplifying the equation:

n(n-1)tⁿ - 6ntⁿ + 12 = 0

n(n-1)tⁿ - 6ntⁿ = -12

Since this equation must hold for all values of t, the coefficients of the tⁿ terms on both sides of the equation must be equal.

We can equate the coefficients:

n(n-1) = 0

n = 0 or n = 1

The general solution to the differential equation is y = c₁ + c₂ × t, where c₁ and c₂ are constants.

According to Newton's law of cooling, the rate of change of the temperature T of an object is proportional to the temperature difference between the object's temperature T and the surroundings' temperature S.

We can write the differential equation as follows:

dT/dt = k(S - T)

dT/dt represents the rate of change of temperature, k is the proportionality constant, and (S - T) represents the temperature difference between the object and the surroundings.

The cup of tea starts at 100 degrees and cools to 50 degrees in 3 minutes, with the room temperature at 20 degrees.

We can assume that the temperature of the tea will tend toward the room temperature as time goes to infinity.

This option correctly represents that as time goes to infinity, the temperature T of the tea will approach the temperature S of the surroundings, which is approximately 20 degrees.

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Answer:

Algebra Examples

Popular Problems Algebra Find the Axis of Symmetry f(x)=x^2-5 f(x)=x2−5 Set the polynomial equal to y to find the properties of the parabola. y=x2−5

Rewrite the equation in vertex form.

y=(x+0)2−5 Use the vertex form,  y=a(x−h)2+k, to determine the values of a, h, and k.a=1h=0k=−5

Since the value of a is positive, the parabola opens up.

Opens Up

Find the vertex

(h,k).(0,−5)

Find p, the distance from the vertex to the focus.

14 Find the focus.

(0,−194)

Find the axis of symmetry by finding the line that passes through the vertex and the focus.

x=0

According to the solving  function f could describe the bacteria population d days after the scientists first measured it, assuming it grows exponentially F(d) = 10000 - a\(^\frac{d}{5}\).

A mathematical expression, rule, or law known as a function defines the relationship between two independent variables and a dependent variable (the dependent variable). In mathematics, functions are often utilised, and they are essential for creating physical connections in the sciences.

Substituting d = 5 and f(d)

Solution: fid) = 10000⋅ ad

{substitute d=5 and fid)=20000 into fid=10000. ady

10000- a⁵ =20000

a⁵ =2\(^\frac{1}{5}\)

a = 2

F(d) = 10000 - a\(^\frac{d}{5}\)

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The coordinates of Q between points R and S are (0, 5)

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

R(-2, 6) and S(4, 3)

We have the partition to be

m : n = 1 : 2

The coordinate is then calculated as

Q = 1/(m + n) * (m₂ + nx₁, my₂ + ny₁)

Substitute the known values in the above equation, so, we have the following representation

Q = 1/3 * (1 * 4 + 2 * -2, 1 * 3 + 2 * 6)

Evaluate

Q = (0, 5)

Hence, the coordinate of point Q is (0, 5)

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Question

Given the point R(-2, 6) and S(4, 3), the point Q on directed line segment RS that partitions RS into the ratio 1 to 2.

Write down the coordinates of Q​

As per the given confidence interval, the value of P is lees than significant.

Confidence interval:

In statistics, a range around a measurement that conveys how precise the measurement is referred as confidence interval.

Given,

A precision instrument is guaranteed to read accurately to within 2 units. a sample of four instrument readings on the same object yielded the measurements 353, 351, 351, and 355. find a 90% confidence interval for the population variance.

Here we need to find the assumptions of the given situation,

From the given question we have identified the following,

Reading of instruments = 353, 351, 351, and 355.

Confidence interval = 90% = 0.09

Number of units = 2.

Based on these details, the standard deviation of this temple is 0.7.

So, the Z score is the same as the sample mean minus the population mean divided by the standard error, which is 2.857.

Therefore, P value was less than significant.

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It should be noted that when Kara lines up all the 3/4 inch buttons, the total length will be 2 1/4 inches.

From the information, it should be noted that Kara is sorting buttons by length for a craft project.

It should be noted that based on the information, the total length of the 3/4 inch button will be calculated thus:

= 3 × 3/4

It should be noted that there are three buttons having 3/4 inch

= 3 × 3/4.

= 9 / 4

= 2 1/4 inches

Therefore, when Kara lines up all the 3/4 inch buttons, the total length will be 2 1/4 inches.

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Answer:Y< 5x2 - 5 because it will be squared making it an exponential function

Step-by-step explanation:

EXPLANATION:

We are given the absolute value functions below;

Note that for this function, we have a v-shaped graph, since the values of the output is always positive (absolute value) and the vertex is at (0, 0). Also, if the value of a in the function;

is positive, the graph opens upwards, and if the value of a is negative;

then it opens downwards.

Therefore,

ANSWER;

Answer:

105

Step-by-step explanation:

0 (104) is equal to 0, so let's cross that out. 103 times 102 is definitely not equal to 105. The third one is 105. The fourth one is not 105. The last one is not 105 either.

The eccentricity of an infinitely long ellipse will be less than 1.

The ratio of the focus's distance from the ellipse's center and the ellipse's distance from one of its ends.

It is easy to comprehend how circular an ellipse is in relation to a circle when we consider its eccentricity. It also measures the ovalness of the ellipse and eccentricity close to one refers to the high degree of ovalness.

The eccentricity of an ellipse is always less than 1 i.e e < 1. The formula for the eccentricity of an ellipse is given by

Which can be written as

Where

e = Eccentricity of the ellipse

c = Distance of the focus from the center of the ellipse

a = Distance of the end of the ellipse from the center

As we know the eccentricity of an ellipse is always less than 1, So we can conclude that the eccentricity of an infinitely long ellipse is less than 1.

Therefore,

The eccentricity of an infinitely long ellipse will be less than 1.

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Answer:

12

Step-by-step explanation:

[1+(2×3)]-[1-(2×3)]

[1+6]-[1-6]

12

To determine when the ball strikes the ground, we need to find the value of t when the height h(t) is 0.

The equation for the ball's height h at time t seconds after launch is:

h(t) = -4.9t^2 + 9.31t + 239.12

Setting h(t) to 0, we get:

0 = -4.9t^2 + 9.31t + 239.12

We can solve this quadratic equation using the quadratic formula:

t = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = -4.9, b = 9.31, and c = 239.12.

Answer: 6.12 seconds

Step-by-step explanation:

To find when the object strikes the ground, we need to find the time t when the height h(t) is equal to 0 (since the ground is at height 0). We have the equation:

h(t) = -4.9t² + 9.31t + 239.12

To find the time when the object strikes the ground, we need to find the value of t when h(t) = 0:

0 = -4.9t² + 9.31t + 239.12

This is a quadratic equation of the form at² + bt + c = 0, where a = -4.9, b = 9.31, and c = 239.12. We can solve this equation for t using the quadratic formula:

t = (-b ± √(b² - 4ac)) / 2a

Plugging the values of a, b, and c into the formula, we get:

t = (-(9.31) ± √((9.31)² - 4(-4.9)(239.12))) / (2(-4.9))

t = (-9.31 ± √(86.6161 + 4694.336)) / (-9.8)

t = (-9.31 ± √(4780.9521)) / (-9.8)

t ≈ (-9.31 ± 69.14) / (-9.8)

We will have two possible values for t:

t₁ ≈ (-9.31 + 69.14) / (-9.8) ≈ 6.12 (rounded to two decimal places)

t₂ ≈ (-9.31 - 69.14) / (-9.8) ≈ 8.00 (rounded to two decimal places)

Since the height function describes the motion of the ball from a platform, we can discard the negative solution as it represents an invalid time before the ball is launched. Thus, the object strikes the ground at approximately t ≈ 6.12 seconds.

Answer:

\(\dfrac{1}{729}\)

Step-by-step explanation:

\(\left(\dfrac{}{}(-3)^2\dfrac{}{}\right)^{-3}\)

First, we should evaluate inside the large parentheses:

\((-3)^2 = (-3)\cdot (-3) = 9\)

We know that a number to a positive exponent is equal to the base number multiplied by itself as many times as the exponent. For example,

\(4^3 = 4 \, \cdot\, 4\, \cdot \,4\)

       ↑1 ↑2 ↑3 times because the exponent is 3

Next, we can put the value 9 into where \((-3)^2\) was originally:

\((9)^{-3}\)

We know that a number to a negative power is equal to 1 divided by that number to the absolute value of that negative power. For example,

\(3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{3\cdot 3} = \dfrac{1}{9}\)

Finally, we can apply this principle to the \(9^{-3}\):

\(9^{-3} = \dfrac{1}{9^3} = \boxed{\dfrac{1}{729}}\)

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Using proportions, it is found that 8 more seventh graders are involved in the yearbook.

What is a proportion?

A proportion is a fraction of a total amount.

Researching the problem on the internet, it is found that 10% of the 6th graders and 18% of the 7th graders are on the yearbook, hence:

0.1 x 280 = 28 6th graders.

0.18 x 200 = 36 7th graders.

36 - 28 = 8

8 more seventh graders are involved in the yearbook.

Answer:

2 : 3

Step-by-step explanation:

Given the square has a side of 6 in , then

perimeter = 4 × 6 = 24 in

area = 6² = 36 in²

Then ratio of perimeter : area

= 24 : 36 ( divide both parts by 12 )

= 2 : 3

Answer:

Is, 6x+18+x=7x+2+1

7x+18=7x+2+1

P(A'∩B) is equal to 0.08. To compute P(A'∩B), we need to first find P(A') and then calculate the intersection of A' and B.

P(A) = 0.2

P(B) = 0.4

P(A|B) = 0.1

To find P(A'), we can use the complement rule:

P(A') = 1 - P(A)

P(A') = 1 - 0.2

P(A') = 0.8

Now, we can calculate P(A'∩B) using the intersection rule:

P(A'∩B) = P(A') * P(B|A')

P(A'∩B) = 0.8 * P(B|A')

To find P(B|A'), we can use the conditional probability formula:

P(B|A') = P(B ∩ A') / P(A')

P(B|A') = P(A'∩B) / P(A')

Since P(A'∩B) is what we're trying to find, we rearrange the formula:

P(A'∩B) = P(B|A') * P(A')

Substituting the values:

P(A'∩B) = 0.1 * 0.8

P(A'∩B) = 0.08

Therefore, P(A'∩B) is equal to 0.08.

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Answer:

circ : 37.7

vol: 144

Step-by-step explanation:

circ: c=2\(\pi\)r

circ= 2\(\pi\)6 = 37.7 (have to use calc)

vol: base area x (pyramid height/3)

vol: 48 x (9/3)

vol: 48 x 3

vol: 144