During the Middle Ages, Henry Ill of England made an Assize of Arms in 1252. It obligated all freemen between the ages
of 15 and 60 In England to swear an oath to bear arms in the service of the king. Citizens were ordered to practice archery on
Sundays and holidays. One of the weapons that were used was the longbow. A skilled longbowman could release 10-12 arrows
per minute with a range of about 200 yards. Young boys were used to run additional arrows to the archers. Longbows were a
very beneficial weapon because since they were made of wood they could be easily crafted during times of war. Longbowman
were used to both defend their castles and on the battlefield.


Question 1. The path of the arrow is modeled by the equation h(t) =-16t^2 + 80t + 4 where t is the time in seconds and h(t) is the height of the arrow at time t. What type of vertex (minimum or maximum), would this quadratic function create? Explain, using any method, how you found your answer

Question 2. Find the coordinates of the vertex algebraically

Question 3. Construct an appropriate table of values to model this function. Choose an appropriate domain

T. h(t)

Answer:

3 and 0

Step-by-step explanation:

34.08

The digits from left to right are

3 (tens) , 4 (units) , 0 (tenths), 8 (hundredths )

So 3 is in the tens place and 0 is in the tenths place

Answer:

3 is in the tens place

0 is in the tenths place

Step-by-step explanation:

Hope it helps! :)

Answer:

8 / 29 = .276

Step-by-step explanation:

29 is the total number of jelly beans

When we have replacement, we do not reduce the number of total jelly beans, so the probably of drawing blue stays the same.

Answer:

.276

Step-by-step explanation:

The quadratic equation with zeros at -6 and 2 is y² + 4y - 12 = 0. This is in standard form, which is ax² + bx + c = 0, with a = 1, b = 4, and c = -12.

To find the quadratic equation with zeros at -6 and 2, we can start by using the fact that if a quadratic equation has roots x₁ and x₂, then it can be written in the form

(y - x₁)(y - x₂) = 0

where y is the variable in the quadratic equation.

Substituting the given values of the zeros, we get

(y - (-6))(y - 2) = 0

Simplifying this expression, we get

(y + 6)(y - 2) = 0

Expanding this expression, we get

y² - 2y + 6y - 12 = 0

Simplifying this expression further, we get

y² + 4y - 12 = 0

So the quadratic equation with zeros at -6 and 2 is

y² + 4y - 12 = 0

This is the standard form of a quadratic equation, which is

ax² + bx + c = 0

where a, b, and c are constants. In this case, a = 1, b = 4, and c = -12.

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Answer:

Just use m a t h w a y for the answer

Step-by-step explanation:

Thank me later,or dont thank me at all

a) The length of the third side of the triangle is 5√3.

b) The area of the triangle is (25/4) * √3.

Let us now analyze in a detailed way:
a) The length of the third side of the triangle can be found using the law of cosines. Let's denote the length of the third side as c. According to the law of cosines, we have the equation:

c^2 = a^2 + b^2 - 2ab*cos(C),

where a and b are the lengths of the other two sides, and C is the angle between them. Substituting the given values into the equation:

c^2 = 5^2 + 10^2 - 2*5*10*cos(π/3).

Simplifying further:

c^2 = 25 + 100 - 100*cos(π/3).

Using the value of cosine of π/3 (which is 1/2):

c^2 = 25 + 100 - 100*(1/2).

c^2 = 25 + 100 - 50.

c^2 = 75.

Taking the square root of both sides:

c = √75.

Simplifying the square root:

c = √(25*3).

c = 5√3.

Therefore, the length of the third side of the triangle is 5√3.

b) The area of the triangle can be calculated using the formula for the area of a triangle:

Area = (1/2) * base * height.

In this case, we can take the side of length 5 as the base of the triangle. The height can be found by drawing an altitude from one vertex to the base, creating a right triangle. The angle opposite the side of length 5 is π/3, and the adjacent side of this angle is 5/2 (since the base is divided into two segments of length 5/2 each).

Using trigonometry, we can find the height:

height = (5/2) * tan(π/3).

The tangent of π/3 is √3, so:

height = (5/2) * √3.

Substituting the values into the formula for the area:

Area = (1/2) * 5 * (5/2) * √3.

Simplifying:

Area = (5/4) * 5 * √3.

Area = 25/4 * √3.

Therefore, the area of the triangle is (25/4) * √3.

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Step-by-step explanation:

1:4 bcos u need to divide both sides by 4

The standard deviation is a measure of the spread of data in a histogram, calculated as the square root of the variance, and it indicates how much the data deviates from the mean.

The standard deviation is a measure of the spread of data around the mean in a histogram. It tells us how much the data deviates from the average value. A low standard deviation indicates that the data is closely clustered around the mean, while a high standard deviation indicates that the data is more spread out.

In other words, a low standard deviation means that the data points are similar to each other, while a high standard deviation means that the data points are more diverse. The standard deviation is a useful tool for comparing the variability of data across different groups or regions and for identifying any outliers or unusual data points.

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--The complete question is, What is the standard deviation and how is it used to measure the spread of data in a histogram?--

Answer:

\(y=x-1\)

Step-by-step explanation:

The line of symmetry of an isosceles triangle is perpendicular to its base.

Given vertices of the isosceles triangle:

By sketching the triangle with the given points, we can see that AB is its base.  (See attached graph).

To find the equation for the line of symmetry, first find the slope of the line AB.  To do this, use the coordinates of points A and B and the slope formula.

Define the points:

\(\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{6-2}{3-7}=-1\)

As the line of symmetry is perpendicular to line AB, its slope is the negative reciprocal of the slope of line AB.

Therefore, the slope of the line of symmetry = 1.

The line of symmetry will pass through point C (4, 3).

Therefore, substitute the found slope and the coordinates of point C into the point-slope formula:

\(\implies y-y_1=m(x-x_1)\)

\(\implies y-3=1(x-4)\)

\(\implies y-3=x-4\)

\(\implies y=x-1\)

Therefore, the equation of the given isosceles triangle's axis of symmetry is:

\(y = x - 1\)

If we graph the points

then we will get AC=CB

That means C is the point from where the axis of symmetry passes

Foot of perpendicular is midpoint of AB

Midpoint of AB

Find equation of C and foot of perpendicular

Slope

Equation

Answer:

10

Step-by-step explanation:

\(\sqrt{36 + 64}\)

\(\sqrt{100}\)

10

Step-by-step explanation:

the exact answer of this question is 34.6

Answer:

slope = \(\frac{9}{4}\)

Step-by-step explanation:

Equation to find slope: \(\frac{y1-y2}{x1-x2}\)            (-3, 4) (-7, -5)

\(\frac{4+5}{-3+7}\) = \(\frac{9}{4}\)

Answer:

The answer is B!

Step-by-step explanation:

Using the vertical line test, two points meet while up and down. It'd be B.

Answer: 1.5 hours

Step-by-step explanation:

14 times in 21 hours

1 time would be 21 ÷ 14

21 ÷ 14 = 1.5

It took 1.5 hours to orbit the earth 1 time

Hope I helped!

Answer: G) 50.24

Step-by-step explanation: you have to find the circumference of the circle. Since you already have the diameter which is 16 all you have to do is multiply that by 3.14. If you only had the radius then you will have to multiple the radius times 2 times 3.14. The formulas for circumference are: pi(3.14) x diameter or pi(3.14) x radius x 2

Answer:

The fraction of the factor of 17.5 which is due to differences in capital per person is approximately 4.375, and the fraction due to differences in TFP is approximately 13.125.

Step-by-step explanation:

Based on the given information, we know that one-fourth (1/4) of the differences in per capita GDP across countries are due to differences in capital per person, and three-fourths (3/4) are due to differences in TFP.

Now, let's calculate the fractions for the United States and Kenya, given that the United States is 17.5 times richer than Kenya.

Let's represent the fraction due to differences in capital per person as "f_capital" and the fraction due to differences in TFP as "f_TFP".

Given:

f_capital = 1/4

f_TFP = 3/4

The factor of difference in wealth = 17.5

We need to determine the fractions of this factor of 17.5 that are due to each component.

The fraction due to differences in capital per person (f_capital) can be calculated as:

f_capital = (1/4) / (1/4 + 3/4)

f_capital = (1/4) / (4/4)

f_capital = 1/4

The fraction due to differences in TFP (f_TFP) can be calculated as:

f_TFP = (3/4) / (1/4 + 3/4)

f_TFP = (3/4) / (4/4)

f_TFP = 3/4

Now, to determine the fraction of the factor of 17.5 that is due to each component, we multiply each fraction by the factor:

Fraction due to differences in capital per person = f_capital * factor

= (1/4) * 17.5

= 4.375

Fraction due to differences in TFP = f_TFP * factor

= (3/4) * 17.5

= 13.125

Therefore, the fraction of the factor of 17.5 that is due to differences in capital per person is approximately 4.375, and the fraction due to differences in TFP is approximately 13.125.

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Correct Question:

That about one-fourth of the differences in per capita GDP across countries were due to differences in capital per person and about three-fourths were due to differences in TFP. Carry out this, calculation for Kenya. The United States is 17.5 times richer than Kenya; what fraction of this factor of 175 is due to differences in capital per person and what fraction is due to differences in TFP?

Answer:

x=49

Step-by-step explanation:

los 3 angulos del triangulo deben de sumar 180

76+55=131

180-131=49

76+55+49=180

There are 6 pairs of strings that have at least 6 beads.We have to evaluate 35*17 - 15*7

Given expression: 35*17-15*7= 595-105= 490Thus, the required value is 490.There are 16 pairs of two strings of beads that can be formed if you want each string to have at least 6 beads. We have 18 beads, so when the necklace is divided into two, the minimum number of beads on each string is six.To count the number of ways we can do this, we should first count the total number of ways the necklace can be split into two parts. We know that the order in which the strings are arranged does not matter, so we can divide by 2 to account for this.We can divide the necklace at any point, resulting in 18 possible locations.

This gives us a total of 18/2=9 ways to split the necklace.Next, we'll figure out how many of these possibilities result in at least one string with fewer than 6 beads. This can only happen if we cut the necklace at one of the three positions closest to either end (positions 1, 2, or 3, or positions 16, 17, or 18). The other six cuts (positions 4 through 9) result in each string having at least 6 beads.Instead of counting the number of ways we can get at least one short string, we'll count the number of ways we can avoid getting one. This means we'll count the number of ways both strings can have 6 or more beads. There are 6 possible positions for each string, for a total of 6x6=36 ways to pick two strings with at least 6 beads. Out of the total 9 possible cuts, 3 of them result in at least one string with fewer than 6 beads. So, the number of possible pairs of strings with at least 6 beads is:9 - 3 = 6Therefore, there are 6 pairs of strings that have at least 6 beads.

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If 40% of a number is 120 and 55% of the same number is 165 then 15% of that number is 45.

According to the question,

We have the following information:

40% of a number = 120

55% of the same number = 165

Now, let's take the number to be x.

So, we have the following expression:

40x/100 = 120

Using the cross multiplication method:

40x = 120*100

x = 120*100/40

x = 300

Now, we will find 15% of 300 by following the given steps:

15*300/100

15*3

45

Hence, if 40% of a number is 120 and 55% of the same number is 165 then 15% of that number is 45.

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Answer: The volume of the circular swimming pool to the nearest cubic meter is 151 \(m^{3}\).

Step-by-step explanation: According to the question the swimming pool is in the shape of a cylinder, and the top is circular having a radius and depth.
To calculate the volume of a cylinder(pool) we will use the formula for the volume of a cylinder:
The radius of the cylinder = 4 m
height h=3
The volume of the cylinder (V) = \(\pi r^{2} h\)
=\(\pi (4)^{2} *3\)
Plugging π =3.142
= 3.14*16*3
=150.72 \(m^{3}\)
rounding off to the nearest cubic meter
=151 \(m^{3}\)
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Answer:

Step-by-step explanation:

-10 and 9

-10×9=-90

-10+9=-1

The density of a liquid does indeed have an impact on the total dynamic head and the hydraulic power curves in a pumping system. The total dynamic head refers to the total energy required to move the liquid through the system, including overcoming friction losses, elevation changes, and any other resistance encountered.

When the density of the liquid increases, the total dynamic head also increases. This is because denser liquids have more mass per unit volume, which means more energy is needed to move them through the system. On the other hand, if the density decreases, the total dynamic head will decrease as well.

Similarly, the hydraulic power curves of a pump are affected by the density of the liquid being pumped. Hydraulic power is the rate at which a pump can transfer energy to the fluid, and it is directly proportional to the product of the flow rate and the total dynamic head.

When the density of the liquid increases, the hydraulic power curve of the pump will shift upwards. This means that for a given flow rate, more power is required to achieve the desired total dynamic head. Conversely, if the density decreases, the hydraulic power curve will shift downwards, indicating that less power is needed to achieve the same total dynamic head.

Regarding the impact of liquid viscosity on pump performance curves, yes, it does have an effect. Viscosity refers to the internal friction or resistance to flow within a liquid. Higher viscosity liquids have more resistance, which can result in increased losses and reduced pump performance.

When the viscosity of the liquid increases, the pump's performance curves tend to shift downwards. This means that for a given flow rate, the total dynamic head and hydraulic power requirements may increase. Conversely, if the viscosity decreases, the performance curves will shift upwards, indicating that less power is needed to achieve the desired flow rate and total dynamic head.

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Therefore, the standard deviation of the data set is approximately 4.14.

The standard deviation is calculated by taking the square root of the variance, which is the sum of the squared deviations divided by the sample size minus 1.

So, first we need to calculate the variance:

variance = sum of squared deviations / (sample size - 1)

variance = 103 / (7 - 1)

variance = 17.17

Now we can find the standard deviation:

standard deviation = √(variance)

standard deviation = √(17.17)

standard deviation = 4.14 (rounded to two decimal places)

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Answer:

im gonna assume you mean y=2x-6, if so the answer is -2 (multiply 2*2 then subtract 6)

if you really did mean y=2-6, then you would just subtract 6 from 2 and your answer would be -4

Answer: 81,000

Step-by-step explanation:

We can solve this by using the formula given.

If f(1)=1000x3^1, then 1,000x3=3,000

If f(2)=1000x3^2, then 3^2=9 and 1000x9=9000,

and so on,

Now, f(4) will equal 1000x3^4, and 3^4 is 3x3x3x3, which is 9x9 or 9^2, which would be equal to 81, and 81x1000=81,000

To complete the table of values for the exponential function f(x) = 1000*3^x, we can evaluate the function for x = 0, 1, 2, 3, and 4, since we are interested in the number of bacteria on the phone after 4 hours.

x f(x)

0 1000

1 3000

2 9000

3 27,000

4 81,000

Therefore, after 4 hours, there will be 81,000 bacteria on the surface of the phone, assuming the number of bacteria triples every hour and can be described by the exponential function f(x) = 1000*3^x.

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Answer: 126

Step-by-step explanation:

A=2(wl+hl+hw)

According to the Question, The interest earned in 4 years is $1,954.83.

What is compounded quarterly?

A quarterly compounded rate indicates that the principal amount is compounded four times over one year. According to the compounding process, if the compounding time is longer than a year, the investors would receive larger future values for their investment.

The principal is $10,000.

The annual interest rate is 4.5%, which is compounded quarterly.

Since there are four quarters in a year, the quarterly interest rate can be calculated by dividing the annual interest rate by four.

The formula for calculating the future value of a deposit with quarterly compounding is:

\(P = (1 + \frac{r}{n})^{nt}\)

Where P is the principal

The annual interest rate is the number of times the interest is compounded in a year (4 in this case)

t is the number of years

The interest earned equals the future value less the principle.

Therefore, the interest earned can be calculated as follows: I = FV - P

where I = the interest earned and FV is the future value.

Substituting the given values,

\(P = $10,000r = 4.5/4 = 1.125n = 4t = 4 years\)

The future value is:

\(FV = $10,000(1 + 1.125/100)^{4 *4} = $11,954.83\)

Therefore, the interest earned is:

\(I = $11,954.83 - $10,000= $1,954.83\)

Thus, the interest earned in 4 years is $1,954.83.

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