you are miguel cervantes de navas y colin, captain in the royal spanish army in sevilla in the year 1842. Outside your barracks window is a stack of cannonballs. on an idle afternoon you decide to calculate the number on cannonballs. what is the number of the cannonballs?

ANSWER

C. Factoring a perfect square trinomial.

EXPLANATION

The first step shown is:

[tex] {x}^{2} + \frac{b}{a}x + ( \frac{b}{2a} )^{2} = - \frac{c}{a} + ( \frac{b}{2a} )^{2}[/tex]

Observe that the left hand side is a perfect square trinomial.

In other words, the left hand side is of the form,

[tex] {m}^{2} + 2mn + {n}^{2} [/tex]

which can be factored as:

[tex] {m}^{2} + 2mn + {n}^{2} = {(m + n)}^{2} [/tex]

When we factor the perfect square trinomial on the left hand side, we obtain:

[tex]( x + \frac{b}{2a} )^{2} = - \frac{c}{a} + ( \frac{b}{2a} )^{2}[/tex]

The correct answer is C

Answer:

FACTORING A PERFECT SQUARE TRINOMIAL!

Step-by-step explanation:

GOT IT CORRECT ON 3.8.3 AP-EX...

it's not sq root because that comes afterwards.

it's not completing the square because that's

x^2+ bx/a +(b/2a)^2=-c/a+(b/2a)^2

Then from there it's

x^2 + bx/a + b^2/4a^2 = -c/a + b^2/4a^2

(x + b/2a)^2 = b^2/4a^2 -c/a

Then that step ends. If you don't believe me look at study 3.3.1 page 13.

This will help!

To find the answer, I used:

Volume = Length • Height • Width

Each book in box 1 has a volume of 132 inches^3 and there are 16 of them, so I multiplied 132 inches^3 by 16 and got a total volume of 2,112 inches^3 in box 1

Each book in box 2 has a volume of 30 inches^3 and there are 30 of them, so I multiplied 30 inches^3 by 30 and got a total volume of 900 inches^3 in box 2

2,112 inches^3 is greater than 900 inches^3 so box 1 should be more than twice as big as box 2

2112 cubic inches.

To determine which of the two boxes is larger, we need to calculate the volume of each box. For the first box, containing books each measuring 3/2 in by 8 in by 11 in, the volume of one book is calculated as:

For the second box, containing books each measuring 3/4 in by 5 in by 8 in, the volume of one book is calculated as:

Comparing the two totals, the second box, with a total volume of 4500 cubic inches, is larger than the first box, which has a total volume of 2112 cubic inches. Hence, we know that the second box is larger because it has a greater total volume.

The liabilities only is 57,379

Answer:

Step-by-step explanation:

It has to be another circle with its center as the same center as the other two.

It must be equadistant from both.

The circle must have a radius of 2 which makes it one away from the 3 cm circle and 1 away from the 1 cm circle.

Answer:

Well I think it is A because domain is the x values.

Step-by-step explanation:

So when you plug this in your calculator (mine is a ti-84 plus ce) you would hit graph. After it graphs it press Zoom, 0 to center it then press 2nd, trace which pulls up parabola menu's. Press 0 and find the left bound, right bound and then press enter which would give you x values of 2.9375 < t< 6

At the same time I don't know if this is right. I never really excelled at parabolas just trying to help.

Check the picture below.

so the domain will be the values that "x" gets, now, the maximum height of the ball is when it reaches the vertex or U-turn up above, well, what is the x-coordinate anyway?

[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+94}t\stackrel{\stackrel{c}{\downarrow }}{+12} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{94}{2(-16),}\qquad \qquad \right)\implies \left( \cfrac{487}{16},\qquad \qquad \right)\implies (2.9375,\qquad \qquad )[/tex]

so then x = 2.9375 at the vertex, now, what is "x" when it hits the ground? recall y = 0 at that instant.

[tex]\bf \stackrel{f(t)}{0}=-16t^2+94t+12\implies 0=-2(8t^2-47t-6) \\\\\\ 0=(8t+1)(t-6)\implies t= \begin{cases} \boxed{6}\\ \begin{matrix} -\frac{1}{8} \\[-0.5em]\cline{1-1}\\[-5pt]\end{matrix} \end{cases}[/tex]

so then, the values for "x" or namely the domain from the vertex till the ball hits the ground is 2.9375 < t < 6.

Answer:

There will be approx 283908 hits.

Step-by-step explanation:

A website had 342,000 hits in 2011.

This is a decline of 2.3% from the previous year.

Decline rate = 2.3% or 0.023

So, increase rate will be [tex]1-.023=0.977[/tex]

Time = [tex]2019-2011=8[/tex]

We can calculate the answer as:

[tex]342000\times(0.977)^{8}[/tex]

= [tex]342000\times0.83014[/tex]

= 283907.88 rounding to 283908.

Therefore, there will be approx 283908 hits.

Let a,b & c be the number of cookies Adrian, Bobby and Calvin baked respectively.

(a+b+c)/3 =138

(a+b)/2 =136

a+b=272

a=272-b

(b+c)/2 =125

b+c=250

c=250-b

Sub a=272-b and c=250-b into (a+b+c)/3 =138,

(a+b+c)/3 =138

[(272-b)+b+(250-b)]/3 = 138

272-b+b+250-b = 414

-b = -108

b=108

From the above,

a=272-b

=272-108

a=164

c=250-b

=250-108

c=142

∵ a=164

b=108

c=142

∴ Adrian baked 164 cookies.

Bobby baked 108 cookies.

Calvin baked 142 cookies.

Answer:

The answer is 450

Step-by-step explanation:

V = l*w*h

V = 15*10*3

V= 450

ANSWER

[tex]450 {cm}^{3} [/tex]

EXPLANATION

The prism shown is a rectangular prism or cuboid.

The volume of a cuboid is given by:

[tex]Volume=l \times b \times h[/tex]

From the diagram, the length is l=15cm ,the breadth is b=10cm and the height is h=3cm.

We substitute the values into the formula to obtain,

[tex]Volume=15 \times 10 \times 3[/tex]

We simplify to get,

[tex]Volume=450 {cm}^{3} [/tex]

Answer:

the answer is 500cm^3 and 250cm^3

Step-by-step explanation:

This is the correct answer to your question. Btw I wasn't able to answer it before so I commented on the answer above but now I can answer it like this, hope it helps! :)

The on second day and third day the amount of the helium gas will be left in the balloon gas will be 500 and 250 cubic cm respectively.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have:

A helium balloon is filled with 1,000 cm3 of helium.

First day of the balloon has 1000 cubic cm helium gas

Each day, the balloon loses half its helium.

After second day the amount of helium gas = 1000/2 = 500 cubic cm

After third day, the amount of helium gas = 500/2 = 250 cubic cm

Thus, the on second day and third day the amount of the helium gas will be left in the balloon gas will be 500 and 250 cubic cm respectively.

Learn more about the sequence here:

brainly.com/question/21961097

#SPJ2

Answer:

[tex]\large\boxed{C.\ domain:\ \{x\ |\ x\ \text{is a real number}\};\ range:\ \{y\ |\ y>2\}}[/tex]

Step-by-step explanation:

[tex]f(x)=\left(\dfrac{1}{6}\right)^x+2\\\\\text{The domain:}\ x\in\mathbb{R}\to\{x\ |\ x\ \text{is a real number\}}\\\\\lim\limits_{x\to\infty}\bigg[\left(\dfrac{1}{6}\right)^x+2\bigg]=\lim\limits_{x\to\infty}\left(\dfrac{1}{6}\right)^x+\lim\limits_{x\to\infty}2=0+2=2\\\\\lim\limits_{x\to-\infty}\bigg[\left(\dfrac{1}{6}\right)^x+2\bigg]=\lim\limits_{x\to-\infty}\left(\dfrac{1}{6}\right)^x+\lim\limits_{x\to\infty}2=\infty+2=\infty\\\\\text{The range:}\ y\in(2,\ \infty)\to\{y\ |\ y>2\}\\\\\bold{Look\ at\ the\ picture}[/tex]

Answer: Option C

domain: {x | x is a real number}; range: {y | y > 2}

Step-by-step explanation:

We have the function [tex]f(x) =(\frac{1}{6})^x + 2[/tex]

Note that f(x) is an exponential function.

By definition the exponential functions of the form [tex]a(b)^x +k[/tex]  have as domain all real numbers and as range {y | y > k}  if [tex]a>0[/tex], [tex]b>0[/tex]

Where a is the main coefficient, b is the base and k is the vertical displacement.

In this case [tex]k = 2[/tex], [tex]b=\frac{1}{6}[/tex], [tex]a=1[/tex]

Therefore the domain of f(x) is all real numbers and the range of f(x) is

{y | y > 2}

Answer:

x = - 2

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

f(x) + g(x) = x² - 2x + 6x + 4 = x² + 4x + 4 ← equating to 0

x² + 4x + 4 = 0 ← in standard form

(x + 2)² = 0 ← in factored form, thus

x + 2 = 0 ⇒ x = - 2

Answer:

1)m<AOB,m<BOC

2)m<EOD,m<AOB

3)m<AOE,m<EOD

Step-by-step explanation:

Complementary Angles-either of two angles whose sum is 90°.

Vertical Angles-each of the pairs of opposite angles made by two intersecting lines.

Supplementary Angles-either of two angles whose sum is 180°.

Answer:2 and 5

Step-by-step explanation:

Answer:

12 I think........?....

Answer:

The answer is 12

Step-by-step explanation:

In this case, we just have to try with all of them:

Then it is not divisible (it is not integer). This proves the statement false.

Let's try with the others as well, just to check:

All the others don't prove false that statement.

Answer:

6

Step-by-step explanation:

In order to solve this we must use order of operations or PEMDAS.

Parentheses:

First perform operations within parentheses. In this case, do 8-2.

Now we have 8 - 6 / 3.

Exponents:

There are no exponents.

Multiplication or Division:

Divide 6 by 3.

Now we have 8 - 2.

Addition or Subtraction:

Subtract 8-2.

The answer is 6

Answer:

[tex]\begin{array}{cccc}&\text{Like fish}&\text{Don't like fish}&\text{Total}\\\text{Like turtle}&6&15&21\\\text{Don't like turtle}&11&12&23\\\text{Total}&17&27&44\end{array}[/tex]

Step-by-step explanation:

From the Venn diagram:

So, in total,

6+11+15+12=44 participants took part in survey.

The two-way table looks like

[tex]\begin{array}{cccc}&\text{Like fish}&\text{Don't like fish}&\text{Total}\\\text{Like turtle}&6&15&21\\\text{Don't like turtle}&11&12&23\\\text{Total}&17&27&44\end{array}[/tex]

[tex]\bf \left( \cfrac{6^5}{7^3} \right)^2\implies \left( \cfrac{6^{5\cdot 2}}{7^{3\cdot 2}} \right)\implies \cfrac{6^{10}}{7^6}\implies \cfrac{60466176}{117649}\implies 513\frac{112239}{117649}[/tex]

Answer:

a) The sold games of Jezebel had the greatest spread.

b) The middle 50% of the games sold by Colin has the least spread.

c) Jezebel sold more games than colin.

Step-by-step explanation:

Range is sued to calculate the spread of the given data.

Range is given by:

[tex]Range=Max\ Value-Min\ Value[/tex]

So,

Part a)

For Collin:

Range=21-3=18

For Jezebel:

Range=26-5=21

Part b)

Middle 50% of the values will be the values between 1st quartile and 3rd quartile

So, to find quartiles:

For Colin:

=3,9,9,14,15,16,17,20,21

The median is 15.

The lower half is 3,9,9,14

Q1 = (9+9)/2= 18/2 = 9

The upper half is 16,17,20,21

Q3 = (17+20)/2= 37/2= 18.5

The middle 50% is first quartile subtracted from third quartile

So, the spread is:

18.5-9=9.5

For Jezebel:

4,5,8,10,11,14,20,20,26

The median is 11.

The lower half is 4,5,8,10

Q1 = (5+8)/2=13/2=6.5

The upper half is 14,20,20,26

Q3 = (20+20)/2=40/2=20

The middle 50% values' spread is:

20-6.5=13.5

Part c) The answer to part a tells us that Jezebels sold games have more spread than Colin's sold games. Similarly the answer of part b tells us that the spread of middle 50% values of Jezebel's sold games was more than the spread of middle 50% values of Colin's sold games ..

Answer:6.5%

Step-by-step explanation:

There are 4, number three cards and 4 diamond cards in a deck of 52 cards. Divide 52 by 8.

Answer:

30.8% or 4/13

Step-by-step explanation:

There are 52 cards in a deck of cards.

There are 4 nines (4/52) and 13 (13/52) diamonds in a deck of cards.

When you add them together, you get 17/52. Then, you have to subtract the card that is both a nine and in a diamond suite, so you subtract -1 because there is only one card that fits both categories. You should have 16/52, which simplifies to 4/13 / 30.8%.

Answer:

The measure of angle LMN is 68° ⇒ the last answer

Step-by-step explanation:

* Lets revise the properties of the rhombus

- The rhombus has 4 equal sides in length

- Every two opposite angles are equal in measure

- Every two adjacent angles are supplementary (their sum = 180°)

- The two diagonals bisect each other

- The two diagonals perpendicular to each other

- The two diagonals bisect the vertices angles

* Lets solve the problem

∵ LMNO is a rhombus

∴ ∠LMN and ∠MNO are adjacent angles

∴ ∠LMN and ∠MNO are supplementary

∴ m∠LMN + ∠MNO = 180°

∵ m∠MNO = 112°

∴ m∠LMN + 112° = 180° ⇒ subtract 112 from both sides

∴ m∠LMN = 68°

* The measure of angle LMN is 68°

Answer:

68

Step-by-step explanation:

Answer:

[tex]y=\frac{1}{60}x^2[/tex]

Step-by-step explanation:

The focus of the parabola is (0,15)

and the directrix is y=-15.

The equation of this parabola is given by:

[tex]x^2=4py[/tex]

The vertex of this parabola is at the origin (0,0)

The value of p is the distance from the vertex to the focus.

p=15-0=15

The equation of the parabola is

[tex]x^2=4(15)y[/tex]

[tex]x^2=60y[/tex]

Or

[tex]y=\frac{1}{60}x^2[/tex]

The solution to the system of equations y=4x+6 and y=2x-4 is (-5, -14) by solving the equations simultaneously.

The solution to the system of equations y = 4x + 6 and y = 2x - 4 is found by setting the two equations equal to each other since they both equal y. This gives us 4x + 6 = 2x - 4. By subtracting 2x from both sides, we get 2x + 6 = -4. Subtracting 6 from both sides gives us 2x = -10. Dividing both sides by 2 gives us x = -5. Substitute x = -5 into either original equation to find y. Let's use the first equation: y = 4(-5) + 6, which simplifies to y = -20 + 6, and finally y = -14. Hence, the solution to the system of equations is (-5, -14).

Answer:

cdc

Step-by-step explanation:

1. The option is (A) mean = –25; median = –26.5; mode = –28; range = 40.

2. The option is (C) 13; 17.6; 20.

The median is the value that splits the mathematical numbers or expressions in the half. The median value is the middle number of data points. to find the median first arrange the data points in ascending order.

To find the mean, median, mode, and range of the data set, we first need to arrange the data in order:

–46, –39, –28, –28, –25, –17, –11, –6

Mean: To find the mean, we add up all the values and divide by the total number of values:

Mean = (-46 + -39 + -28 + -28 + -25 + -17 + -11 + -6) / 8

Mean = -25

Median: To find the median, we need to find the middle value of the data set.

Since there are 8 values, the median is the average of the 4th and 5th values:

Median = (-28 + -25) / 2

Median = -26.5

Mode: The mode is the value that appears most frequently in the data set. In this case, the mode is –28, since it appears twice and no other value appears more than once.

Range: To find the range, we subtract the smallest value from the largest value:

Range = -6 - (-46)

Range = 40

Therefore, the answer is (A) mean = –25; median = –26.5; mode = –28; range = 40.

2.

A. The outlier in the data set is 37, since it is much larger than the other values.

B. To find the mean with the outlier, we add up all the values and divide by the total number of values:

Mean = (21 + 13 + 13 + 37 + 13 + 23 + 25 + 15) / 8

Mean = 17.6

C. To find the mean without the outlier, we need to exclude the value 37 and then calculate the mean using the remaining values:

Mean = (21 + 13 + 13 + 13 + 23 + 25 + 15) / 7

Mean = 17.6

Therefore, the answer is (C) 13; 17.6; 20.

To learn more about the median;

https://brainly.com/question/28060453

#SPJ3

Answer:

Option D. 17%

Step-by-step explanation:

we have

[tex]f(x)=250,000(1.17)^{x}[/tex]

This is a exponential function of the form

[tex]f(x)=a(b)^{x}[/tex]

where

a is the initial value

b is the base

In this problem

a=250,000 people

b=1.17

Remember that

b=1+r

so

1+r=1.17

r=1.17-1=0.17

Convert to percentage

0.17*100=17%

Answer:

3 houses have all pink, blue, and yellow.

Answer:

The answer is 3 houses.

Step-by-step explanation:

This question is based on the Least Common Multiple (LCM) method. We will find the LCM of the numbers 4, 6 and 8.

4 = 2 x 2 = [tex]2^{2}[/tex]

6 = 2 x 3 = 2 x 3

8 = 2 x 2 x 2 = [tex]2^{3}[/tex]

So, LCM is = [tex]2^{3}\times3=24[/tex]

Therefore, at every 24th houses, we will find all three trolls colors.

And 24 is the number of houses we will find all color trolls. Then in a group of 75 houses, it will occur thrice and at every 24th place. Means. 3 houses will have all color trolls.

The broken flagpole forms a right triangle, where the vertical leg is the piece still standing and the hypotenuse is the broken piece.

So, the original length is the sum of the hypotenuse and the vertical leg.

The hypotenuse can be found using the pythagorean theorem:

[tex]h=\sqrt{7^2+24^2}=25[/tex]

So, the flag was originally [tex]7+25=32[/tex] meters long.

Answer:

[tex]Area=1,325\ yd^2\\Perimeter=204\ yd[/tex]

Step-by-step explanation:

You can use the following formula to calculate the area of the triangle:

[tex]A=\frac{bh}{2}[/tex]

Where "b" is the base and "h" is the height.

You can observe in the figure that:

[tex]b=53\ yd\\h=50\ yd[/tex]

Then, the area is:

[tex]A=\frac{(53\ yd)(50\ yd)}{2}=1,325\ yd^2[/tex]

To find the perimeter you must add the lenght of each side of the triangle. Then, this is:

[tex]P=97\ yd+53\ yd+54\ yd\\\\P=204\ yd[/tex]

Answer:

Step-by-step explanation:

23

Answer:

([tex]\frac{27}{2}[/tex], 4 )

Step-by-step explanation:

Use the midpoint formula

midpoint = [[tex]\frac{1}{2}[/tex](x₁ + x₂), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]

with (x₁, y₁ ) = (14, - 6) and (x₂, y₂ ) = (13, 14), hence

[[tex]\frac{1}{2}[/tex](14 + 13), [tex]\frac{1}{2}[/tex](- 6 + 14) ]

= ([tex]\frac{27}{2}[/tex], 4)

Answer:

24 Days

Step-by-step explanation:

The smallest common multiple of 6 and 8 is 24. Therefore, both girls will bring cheese and crackers for lunch on the same day 24 days from today.

This question is about finding the least common multiple (LCM) of the two numbers. Sandra brings cheese and crackers for lunch every 6 days and Lily every 8 days. The first step in solving this problem is to list the first few multiples of each number to find the smallest number that both numbers have in common.

So, for Sandra, the multiples of 6 are 6, 12, 18, 24, 30, 36, etc. And for Lily, the multiples of 8 are 8, 16, 24, 32, 40, etc. The least common multiple of 6 and 8 is 24.

Therefore, it will be 24 days before both Sandra and Lily bring cheese and crackers for lunch on the same day again.

https://brainly.com/question/34291727

#SPJ2

Answer:

The height is [tex]h=8\ in[/tex]

Step-by-step explanation:

we know that

The area of a trapezoid is equal to

[tex]A=\frac{1}{2}[b1+b2]h[/tex]

we have

[tex]b1=11\ in[/tex]

[tex]b2=27\ in[/tex]

[tex]A=152\ in^{2}[/tex]

substitute in the formula and solve for h

[tex]152=\frac{1}{2}[11+27]h[/tex]

[tex]304=[38]h[/tex]

[tex]h=304/38[/tex]

[tex]h=8\ in[/tex]

[tex]\bf \textit{area of a sphere}\\\\ SA=4\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} SA=64\pi \end{cases}\implies 64\pi =4\pi r^2 \\\\\\ \cfrac{64\pi }{4\pi }=r^2\implies 16=r^2\implies \sqrt{16}=r\implies 4=r[/tex]

The radius of the sphere will be 4 meters. Thus, the correct option is D.

Let r be the radius of the sphere. Then the surface area of the sphere will be given as,

SA = 4πr² square units

The surface area of the sphere is 64π square meters. Then the radius of the sphere is calculated as,

64π = 4 x π x r²

r² = 16

r = 4 meters

Thus, the correct option is D.

More about the surface area of the sphere link is given below.

https://brainly.com/question/29251585

#SPJ3