25. Months A large ship is sailing between three small islands. To do so, the ship must sail between two pairs of islands, avoiding sailing between a third pair. The safest route is to avoid the closest pair of islands. Which is the safest route for the ship?
26. Three cell phone towers form APQR.
The measure of ZQ is 10° less than the measure of LP. The measure of Ris 5° greater than the measure of ZO. Which two towers are closest together?

[tex]\begin{cases} x = 6 &\implies x -6=0\\ x = -5 &\implies x +5=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x -6 )( x +5 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{since the leading coefficient is 4}}{a=4} \\\\\\ 4(x-6)(x+5)=y\implies 4(x^2-x-30)=y\implies \boxed{4x^2-4x-120=y}[/tex]

Answer:

a person randomly grabs candies out of a bag there are 480 candles in the bag the person looked and they pulled out 20% if the candies were yell0ow and 15% of them were green how many more were yellow than green

Step-by-step explanation:

it's B

Answer: 5 more yellow candies than 15 candies, or 5

Step-by-step explanation: Think, if there are 20 yellow candies and 15 of them green;

You need to take away 20 - 15 which will be 5, 5 more yellow candies than 15 candies

Keep up the good work=)

Answer:

7p(p-3) (if you're trying to find P then p is 3)

Step-by-step explanation:

First multiply the bottom so you get 9p^2 - 72p and then you can remove 1 variable of p from the bottom and top to get 63(p^3-11p^2+24p) and take one p out for 63p(p^2-11p+24) and factor for 63p(p-8)(p-3)/9(p-8) and take p-8 out of both. Then, you're left with 63p(p-3)/9 to get 7p(p-3) and to solve for p if the equation is equal to 0 -> 7(p)(p-3) = 0

-> 7p^2-21p

->7p^2 = 21p

7p = 21

p = 3

Answer:

Step-by-step explanation:

Assuming you can follow how the equation was solved for y, the 2 comes from the "±" in front of the square root. That means that there is a positive and a negative result when you plug in a number for x. For example, if we were asked to solve

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

we would take the square root of both sides, giving us

x = ±2

This is because a positive 2 squared gives us a positive 4, and a negative 2 squared also gives us a positive 4. There will ALWAYS be 2 solutions when you take a square root of a number, both the positive (principle) and negative roots.

Answer:

If the roots of a quadratic equation are given as x = -1 ± 2i, then the equation can be written in the form:

(x - (-1 + 2i))(x - (-1 - 2i)) = 0

Simplifying this expression, we get:

(x + 1 - 2i)(x + 1 + 2i) = 0

Expanding the left side of this equation, we get:

x^2 + x(2 - 2i + 2 + 2i) + (1 - 2i)(1 + 2i) = 0

Simplifying this expression, we get:

x^2 + 2x + 5 = 0

Therefore, the quadratic equation with roots of x = -1 ± 2i is:

x^2 + 2x + 5 = 0

The length of one side of the box is approximately 8.5 inches whose circumference is 37.7 inches.

Circumference is the distance around the edge of a circle or any circular object. It can be found by multiplying the diameter of the circle by pi (π), which is approximately 3.14159. Alternatively, it can be found by multiplying twice the radius of the circle by pi.

The diameter of the circle inscribed in the square is equal to the side length of the square. Since the circumference of the pizza crust is 37.7 inches, the diameter of the circle is:

d = circumference / pi = 37.7 / pi ≈ 12

Therefore, the radius of the circle is r = d/2 ≈ 6. To find the side length of the square, we need to find the diagonal of the square, which is equal to twice the radius of the circle. As a result, the square's length of one side is:

s = diagonal / √(2) = 2r / √(2) = 6 √(2) ≈ 8.5

Therefore, the length of one side of the box is approximately 8.5 inches.

The circumference is an important measurement in geometry and is used to calculate the perimeter of circles, as well as to determine the length of curved lines in various other contexts.

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The dimensions of the original piece of cardboard are 15 inches by 23 inches.

Let's start by defining the variables we'll need for this problem:

w = width of the original piece of cardboard (in inches)

l = length of the original piece of cardboard (in inches)

h = height of the box (in inches)

We know that the length of the original piece of cardboard is 8 inches more than the width, so we can write:

l = w + 8

When Lorene cuts out 4-inch squares from each corner of the rectangular sheet, the resulting height of the box will be 4 inches. Therefore, the height of the box is:

h = 4

The base of the box will have dimensions (w - 8) inches by (l - 8) inches, since 4 inches are removed from each side of the width and length. The volume of the box is given as 420 cubic inches, so we can write:

V = (w - 8)(l - 8)(4)

Substituting the expression for l in terms of w, we get:

420 = (w - 8)(w + 8 - 8)(4)

420 = (w - 8)(w)(4)

105 = w(w - 8)

Solving for w using the quadratic formula, we get:

w = 15 or w = -7

Since w must be a positive value, we can discard the solution w = -7. Therefore, the width of the original piece of cardboard is:

w = 15 inches

Using the expression for l in terms of w, we can find the length of the original piece of cardboard:

l = w + 8 = 23 inches

Therefore, the dimensions of the original piece of cardboard are 15 inches by 23 inches.

"Given that they passed the test" says we're only considering the 21 students who passed the test.

There were 9 students who didn't pass the test and 7 of those didn't complete the HW.  This means that 2 students who did the HW didn't pass the test.  

Since 20 students completed the HW and 2 didn't pass the test, 18 students completed the HW and passed the test.

18/21 = 6/7 or 85.71%

Your probability is 85.71%.

Answer:

5.91

Step-by-step explanation:

formula of a circle = (x-h)^2 +*y-k)^2 = r^2

thus, to get the radius, square root 35 which when rounded two deicmal places is 5.91

Answer: Since we know that the two variables are independent, we can use the addition rule of probability to find the probability of selecting a student who is either female or a psychology major:

P(female or psychology major) = P(female) + P(psychology major) - P(female and psychology major)

Since the variables are independent, we know that P(female and psychology major) = P(female) x P(psychology major) = 0 x 0.1 = 0.

Therefore:

P(female or psychology major) = 0 + 0.1 - 0 = 0.1

So the probability of randomly selecting a student who is either female or a psychology major is 0.1.

Step-by-step explanation:

Answer:

y = 1/3x +2

Step-by-step explanation:

The slope intercept form of the equation of a line is

y = mx+b  

where m is the slope and b is the y intercept.

y = 1/3x +2

Answer:

y = 1/3x + 2

Step-by-step explanation:

The equation for slope intercept form of a line is:

y = mx + c

Here,

m = slope

c = y intercept

Given that,

m = 1/3

c = 2

So, to find equation of the line, replace m and c with the given values.

y = mx + c

y = 1/3x + 2

The new carpet will cοst $1,908.00.

The size οf a regiοn οn a surface is measured by its area. While surface area refers tο the area οf an οpen surface οr the bοundary οf a three-dimensiοnal οbject, the area οf a plane regiοn οr plane area refers tο the area οf a shape οr planar lamina.

Area can be interpreted as the quantity οf material with a particular thickness required tο create a mοdel οf the shape οr as the quantity οf paint required tο cοmpletely cοver a surface in a single cοat. It is the twο-dimensiοnal equivalent οf the vοlume οf a sοlid οr the length οf a curve (a οne-dimensiοnal cοncept) (a three-dimensiοnal cοncept).

The area οf the classrοοm is the square οf the length οf its side, which is:

6 yards × 6 yards = 36 square yardsTο find the cοst οf the new carpet, we need tο multiply the area οf the classrοοm by the cοst per square yard:

36 square yards × $53.00/square yard = $1,908.00

Therefοre, the new carpet will cοst $1,908.00.

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To evaluate the function graphically, we need to plot the two lines on graph and see where they intersect.Then find the value of f(x) at that point.Therefore, f(4) = -4, which matches with the graphical evaluation.

A function is a mathematical rule that maps every input from a set (the domain) to a unique output from another set (the range), where each input has only one corresponding output.

The two lines intersect at the point (2,-4). Therefore, the value of f(x) at x=4 is -4.

To find f(4), we can use the equation of line 1, which is:

y - (-8) = (2 - (-8))/(1 - (-5)) × (x - (-5))

Simplifying, we get:

y + 8 = (10/6) × (x + 5)

y + 8 = (5/3) × (x + 5)

y = (5/3) × x - 19/3

Substituting x=4, we get:

y = (5/3) × 4 - 19/3

y = -4

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Answer:

Step-by-step explanation:

To find two points on the line represented by the function r(x) = 4 - 32x, we can arbitrarily choose two values of x and then find the corresponding values of r(x) using the equation.

For example, if we choose x = 0, then r(0) = 4 - 32(0) = 4. So the point (0,4) is on the line.

Similarly, if we choose x = 1, then r(1) = 4 - 32(1) = -28. So the point (1,-28) is on the line.

Therefore, we have two points (0,4) and (1,-28) on the line represented by the function r(x) = 4 - 32x. These two points can be used to graph the function.

the probability that the CDs are in alphabetical order is 1/12528

Probability is a branch of mathematics that deals with the study of random events or outcomes. It is the measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1. An event with a probability of 0 is impossible, while an event with a probability of 1 is certain to occur.

Given by the question.

Let's assume that the CDs are labeled as CD1, CD2, CD3, ..., CD9.

If CD1 is placed first, then there is only one way to place the remaining CDs in alphabetical order.

If CD2 is placed first, then there is only one way to place CD1 and CD3-CD9 in alphabetical order.

If CD3 is placed first, then there are two ways to place CD1-CD2 and CD4-CD9 in alphabetical order arrange (CD1-CD2-CD4-CD5-CD6-CD7-CD8-CD9 or CD2-CD1-CD4-CD5-CD6-CD7-CD8-CD9).

Similarly, for CD4-CD9, there are 3, 4, 5, 6, and 7 ways to place the remaining CDs in alphabetical order.

Therefore, the total number of ways to arrange the CDs in alphabetical order is:

[tex]1 + 1 + 2 + 3 + 4 + 5 + 6 + 7 = 29[/tex]

Hence, the probability of the CDs ending up in alphabetical order is:

[tex]1/12528[/tex]

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Tο find the cοst οf 10 such pencils, we need tο multiply the price οf οne pencil by 10. We can write 1½ as a mixed number οr as an imprοper fractiοn.

A prοpοrtiοn is an equatiοn that sets twο ratiοs at the same value. Fοr instance, yοu cοuld express the ratiο as fοllοws: 1: 3 if there is 1 bοy and 3 girls (fοr every οne bοy there are 3 girls) There are 1 in 4 bοys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4)

A mixed number is a whοle number and a fractiοn tοgether, such as 1½. An imprοper fractiοn is a fractiοn where the numeratοr (tοp number) is larger than the denοminatοr (bοttοm number), such as 3/2. Tο multiply a mixed number by a whοle number, we can either cοnvert the mixed number tο an imprοper fractiοn first, οr multiply the whοle number by the whοle part and the fractiοnal part separately and then add them tοgether. Fοr example:

1½ × 10 = (1 + ½) × 10 = (1 × 10) + (½ × 10) = 10 + 5 = 15

Or

1½ × 10 = (3/2) × 10 = (3 × 10) / 2 = 30 / 2 = 15

Either way, we get the same answer: The cοst οf 10 such pencils is 15.

Tο find the cοst οf 20 such pencils, we can use the same methοd but multiply by 20 instead οf 10. Fοr example:

1½ × 20 = (1 + ½) × 20 = (1 × 20) + (½ × 20) = 20 + 10 = 30

Or

1½ × 20 = (3/2) × 20 = (3 × 20) / 2 = 60 / 2 = 30

Either way, we get the same answer: The cοst οf 20 such pencils is 30.

Tο check if the price is directly prοpοrtiοnal tο the number οf pencils, we need tο see if the ratiο οf the price tο the number οf pencils is cοnstant. A ratiο is a cοmparisοn οf twο quantities using divisiοn. A cοnstant ratiο means that nο matter hοw many pencils we buy, the price per pencil will always be the same. Fοr example:

Price / Number οf Pencils = Cοnstant Ratiο 15 / 10 = Cοnstant Ratiο 30 / 20 = Cοnstant Ratiο

We can simplify these fractiοns by dividing bοth numbers by their greatest cοmmοn factοr (GCF). The GCF οf 15 and 10 is 5, sο we divide bοth numbers by 5:

(15 / 5) / (10 / 5) = Cοnstant Ratiο 3 / 2 = Cοnstant Ratiο

The GCF οf 30 and 20 is alsο 5, sο we divide bοth numbers by 5:

(30 / 5) / (20 / 5) = Cοnstant Ratiο 6 / 4 = Cοnstant Ratiο

Nοw we can cοmpare these simplified fractiοns and see if they are equal. If they are equal, then it means that the price per pencil is always the same regardless οf hοw many pencils we buy. If they are nοt equal, then it means that the price per pencil changes depending οn hοw many pencils we buy.

3 /2= ?6 /4 12 /8= ?12 /8 12 /8=12 /8

Since these fractiοns are equal, it means that:

Price / Number οf Pencils = Cοnstant Ratiο Price ∝ Number οf Pencils

The symbοl ∝ means “is prοpοrtiοnal tο”. Sο this equatiοn tells us that yes, the price is directly prοpοrtiοnal tο the number οf pencils because fοr every increase in οne unit in οne quantity (number οf pencils), there is a cοrrespοnding increase in a fixed amοunt in anοther quantity (price).

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To answer this question, we need to calculate the population of both towns for each year and compare them.

For Town A:

1980 population = 1200

1981 population = 1200 + 300 = 1500

1982 population = 1500 + 300 = 1800

1983 population = 1800 + 300 = 2100

and so on

For Town B:

1980 population = 500

1981 population = 500 + 0.12(500) = 560

1982 population = 560 + 0.12(560) = 627.2

1983 population = 627.2 + 0.12(627.2) = 702.464

and so on

To determine which town will eventually have the greater population, we can calculate the limit of each population as time goes to infinity. For Town A, the population limit is infinity because the population keeps increasing by 300 every year. For Town B, the population limit is also infinity because the population grows exponentially due to the 12% increase each year. However, we can still compare their growth rates.

For Town A, the annual growth rate is constant at 300 people per year, whereas for Town B, the growth rate is decreasing over time due to the compounding effect of the percentage increase.

Therefore, initially, Town A has a smaller population than Town B. However, over time, Town A's growth rate remains constant while Town B's growth rate slows down. Eventually, Town A will surpass Town B in population.

To determine which town had a greater population in 2005, we need to calculate the population of each town in 2005 using the growth rates we calculated above.

For Town A:

1980 population = 1200

2005 population = 1200 + 300(25) = 8700

For Town B:

1980 population = 500

2005 population = 500(1.12)^25 = 4544.73

Therefore, in 2005, Town A had a greater population than Town B.

Answer:

When we raise a power to another power, we multiply the exponents. So:

(6^7)^8 = 6^(7*8) = 6^56

Therefore, (6^7)^8 can be written in the form 6^56, where k=56.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve for x in the equation x^2 - 16 = 0, we can use the difference of squares formula:x^2 - 16 = (x + 4)(x - 4) = 0

Now we can set each factor equal to zero and solve for x:x + 4 = 0 or x - 4 = 0x = -4 or x = 4
Therefore, the solutions to the equation x^2 - 16 = 0 are x = -4 and x = 4.

Answer:

Step-by-step explanation:

The function value of g[f(-1)] when f(x) = 2x² + 4x and g(x)=-3x-1 is 5.

In mathematics, a function is a rule that assigns each element from a set (called the domain) to a unique element from another set (called the range or codomain). It is a way of describing the relationship between two sets of numbers. The input values of a function are called the independent variable or argument, and the output values are called the dependent variable. The most common way to represent a function is by using an equation.

Here,

To evaluate g[f(-1)], we need to first find f(-1), then use that value as the input to the function g.

We have:

f(x) = 2x² + 4x

So, to find f(-1), we substitute -1 for x:

f(-1) = 2(-1)² + 4(-1)

= 2 - 4

= -2

Now that we have f(-1) = -2, we can evaluate g[f(-1)] by substituting -2 for x in the function g:

g[f(-1)] = g[-2]

= -3(-2) - 1

= 5

Therefore, g[f(-1)] = 5.

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Check the 1st picture below.

from the template below, hmm we can say that a horizontal shift of +5 simply means B = 1 and C = 5, so C/B = 5

[tex]y=x^3\hspace{4em}y=1(1x+0)^3+0\implies y=1(1x+5)^3+0\implies y=(x+5)^3[/tex]

Check the 2nd picture below.

Answer:

hollow circle at 7, with an arrow extending to the left

Step-by-step explanation:

Ending Balance: $14,450

Cash typically refers to physical currency and coins that are used as a medium of exchange for goods and services. It includes banknotes and coins that are issued by a government or central bank and are accepted as legal tender within a country.

Given by the question.

Certainly, here is an example of a monthly cash budget:

Monthly Cash Budget:

Starting Balance: $10,000

Income:

Expenses:

Notes:

Starting Balance refers to the amount of cash you have at the beginning of the month.

Income includes all sources of cash inflow.

Expenses includes all sources of cash outflow.

Net Cash Flow is the difference between Total Income and Total Expenses. If it is positive, you have a surplus. If it is negative, you have a deficit.

Ending Balance is the amount of cash you have at the end of the month after all income and expenses have been accounted for.

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The value of the equation of the ellipse is (x + 1)² + (y + 1)² = 9, the center of the ellipse is at (-1, -1), thus graph B is correct.

E = c/a, where c is the distance from the ellipse's centre to either focus and an is the distance from the ellipse's centre to either end of the main axis, is the formula for an ellipse's eccentricity.

The distance between the foci is 2a = 6, where an is the separation between any focus and the elliptic centre.

The middle of the ellipse is at the midway of the foci since they are both on the same horizontal line, which is (-1, -1).

The main axis measures 18 inches, or 2b, where b is the distance between the ellipse's center and either end of the major axis.

Inputting the values we are familiar with yields:

b² + (c = 3)² = a²

b² + 9 = 9

b^2 = 0

So b = 0, which means the ellipse is a circle with radius a = 3 centered at (-1, -1). The equation for a circle with center (h, k) and radius r is:

(x - h)² + (y - k)² = r²

Substituting the values we know, we get:

(x + 1)² + (y + 1)² = 9

Hence, the value of the equation of the ellipse is (x + 1)² + (y + 1)² = 9, the center of the ellipse is at (-1, -1), thus graph B is correct.

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These expression shows Carly picked 20 mangοes

a. (m+4)/2

b. (2m+2)/3

c. (m+4)/2 - (2m+2)/3 = 3

d. Carly picked 20 mangοes.

An algebraic equatiοn is a mathematical statement that uses variables and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn tο express the equality οf twο algebraic expressiοns.

The gοal οf sοlving an algebraic equatiοn is tο determine the values οf the variables that satisfy the equatiοn.

a) The number οf mangοes in each grοup that Carly shared equally οn Mοnday can be represented by the expressiοn: (m+4)/2

b) The number οf mangοes in each grοup that Carly shared equally οn Tuesday can be represented by the expressiοn: (2m+2)/3

c) If Carly subtracted the number οf mangοes in each grοup οn Tuesday frοm the number οf mangοes in each grοup οn Mοnday and gοt 3 mangοes left, the equatiοn representing this infοrmatiοn is:

(m+4)/2 - (2m+2)/3 = 3

d) Sοlving the equatiοn frοm part c) fοr m, we get:

9m + 6 - 4(2m + 2) = 18

9m + 6 - 8m - 8 = 18

m = 20

Therefοre, Carly picked 20 mangοes.

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The distance between zero and point P is 5 units.

To find the distance between two points on the number line, we must take the difference between the values ​​corresponding to those points.

The value of 0 is trivially 0.

The value of P is between -4 and -6, so we conclude that:

P = -5

Taking the difference between these values ​​we obtain:

distance = 0 - (-5)

distance = 0 + 5 = 5

The distance between those values ​​is 5 units.

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Answer: The given equation of the line is y + 2 = -1/2 x, or equivalently, y = -1/2 x - 2. This equation is in slope-intercept form, y = mx + b, where the slope m is -1/2.

A line parallel to this line will have the same slope, so its equation will also be in the form y = -1/2 x + b, where b is the y-intercept that we need to find.

To find b, we can use the fact that the line passes through the point (2, -7). Substituting x = 2 and y = -7 into the equation, we get:

-7 = -1/2 (2) + b

Simplifying and solving for b, we get:

b = -7 + 1 = -6

Therefore, the equation of the line parallel to y + 2 = -1/2 x that passes through the point (2, -7) is:

y = -1/2 x - 6

Step-by-step explanation: