on average, the number of days it takes for a caterpillar to become a butterfly is 15 days with a standard deviation of 3.5 days.

If there are 10000 caterpillars at a sanctuary, how many out of the 10000 would you expect to become a butterfly in 17.8 days or more? ​

The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

Let's assign variables to represent the statements:

q: The aquarium is full of fish.

r: There are penguins.

The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

∧ represents the logical operator "and" which connects the statements r and q.

→ represents the logical operator "implies" or "if...then".

o represents the statement "this is an octopus".

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Chay can use 3 bags of mulch per flower bed.

Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?The number of bags of mulch that can be used in each flower bed can be found by dividing the total number of bags of mulch by the number of flower beds, as given by the problem.Let X be the number of bags of mulch used in each flower bed. Then, the following equation can be written:Total number of bags of mulch = X × number of flower beds (20)Or, 55 = 20XDividing both sides of the equation by 20, we get: X = 55/20X = 2.75.Therefore, Chay can use 2.75 bags of mulch in each flower bed. However, since we cannot have a fraction of a bag of mulch, she would have to round up to 3 bags of mulch per flower bed to ensure each flower bed has enough mulch.

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Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

The polar coordinates that represent the same point is

(3, -(π/2)) ⇒  (-3, (5π/2)

(-3, -(π/2)) ⇒   (-3, (3π/2))

(-3, -(7π/4)) ⇒  (3, (5π/4))
(3, -(π/4)) ⇒    (-3, (3π/4))

Polar coordinates are a method that is used to display a point's position in a 2D space or graph by using their x or y value. They have various representation for each the same point.

The distance is known as the radial coordinate, denoted by r, and the angle is known as the angular coordinate, denoted by θ.

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Answer:

The numbers of doors that will have no blemishes will be about 6065 doors

Step-by-step explanation:

Let the number of counts by the  worker of each blemishes on the door be (X)

The distribution of blemishes followed the Poisson distribution with parameter  \(\lambda =0.5\) / door

The probability mass function on of a poisson distribution Is:

\(P(X=x) = \dfrac{e^{- \lambda } \lambda ^x}{x!}\)

\(P(X=x) = \dfrac{e^{- \ 0.5 }( 0.5)^ x}{x!}\)

The probability that no blemishes occur is :

\(P(X=0) = \dfrac{e^{- \ 0.5 }( 0.5)^ 0}{0!}\)

\(P(X=0) = 0.60653\)

P(X=0) = 0.6065

Assume the number of paints on the door by q = 10000

Hence; the number of doors that have no blemishes  is = qp

=10,000(0.6065)

= 6065

If an auto body shop repaired 22 cars and trucks and there were 8 fewer cars than trucks, 15 trucks were repaired.

Let's assume the number of trucks repaired is "x". We know that the total number of cars and trucks repaired is 22. Since there were 8 fewer cars than trucks, the number of cars repaired must be x-8. Therefore, we can set up the following equation:

x + (x-8) = 22

Simplifying, we get:

2x - 8 = 22

Adding 8 to both sides:

2x = 30

Dividing by 2:

x = 15

We can check this by plugging x back into the equation and verifying that the number of cars repaired is 7, which is 8 fewer than 15.

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The number of M&M's that were in the bowl before Amelia arrived is; 12

Let the original amount in the bowl be x. Thus;

If Amelia grabbed 50%, then amount left = (100% - 50%)x = 50%x = 0.5x

Now, we are told that domicick took 50% of what was keft after amelia. Thus; New amount left = 100%x - (0.5x + 0.25x) = 0.25x

Now, we are told that there were finally 3 left after all the deductions. Thus;

0.25x = 3

x = 3/0.25

x = 12

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We have the next data set:

{36.6, 39.8, 33.3, 34.8, 38.5, 39.6, 36.7, 36.9, 37.5, 32.2, 33.1, 33.3}

And we must find the range.

To find the range we need to know that

So, we must take the largest and the smallest value and then subtract them.

To make it easier we can organize the data:

32.2, 33.1, 33.3, 33.3, 34.8, 36.6, 36.7, 36.9, 37.5, 38.5, 39.6, 39.8

Now we can see that:

- the largest value is 39.8

- the smallest value is 32.2

Finally, we must subtract them

So, the range is 7.6

ANSWER:

The range of this data set is 7.6

Answer 7.6

explanation: K12

Let (r,q) represent P's polar coordinates, with r being positive and 0 equaling q being pi/2. If so, r = 3m. And A = 0.20136

All points in a plane that are at a specific distance from a specific point, the center, form a circle.
Formula for the first circle: x²+ y² = 9

Formula for the second circle:

center is (0, 7.5) and the radius is 15/2, so

x² + (y - 7.5)² = (7.5)²

Combining these yields:

9 - y² + (y - 7.5)² = (7.5)²

9 - y² + y² - 15y + (7.5)² = 7.5²

9 - 15y = 0

y = 9/15 = 3/5

∴ y = 0.6

x² + y² = 9 = x² + (3/5)²

x² = 9 - (9/25)

x² = [(225 - 9)/25] = 216/25

∴ x = 2.9394

r = √(x² + y²) =

r = √[( 216/25) + (9/25)]

r = √(225/25) = 15/5
∴ r = 3

The x and y values appear to be accurate because this must be the same as the radius of the circle cantered at the origin.

sin(A) = y/r

sin(A) = (3/5)/3 = 1/5

Sin(A) = 0.2

∴ A = 0.20136

COMPLETE QUESTION:

A circle C has center at the origin and radius 4. Another circle K has a diameter with one end at the origin and the other end at the point (0,14). The circles C and K intersect in two points. Let P be the point of intersection of C and K which lies in the first quadrant. Let (r,q) be the polar coordinates of P, chosen so that r is positive and 0 = q =pi/2. Find r and q.

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Answer:

Expected value = $115.83

The following form has two parallel sides, and, in accordance with the provided assertion, its area is 21 cm².

Area is the entire amount of space occupied by a flattened (2-D) surface or form of an item. The area of a planar figure is the space that its perimeter encloses. The quantity of unit rectangles that completely encircle a closed figure's surface is its area. Square units such as cm² and m² are used to measure area.

The ratio will also be 1/2 * (bases 1 + base 2) * length since it is a trapezium.

So, 1/2 * ( 9+5) * 3

   = 1/2 * 14 * 3

   =  1/2 * 42

   =  21 cm²

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Answer:

Step-by-step explanation:

The vertices of the already rotated triangle are:

D '(4, 4)

E '(1, 3)

F '(2, 1)

Answer:

D '(4, 4)

E '(1, 3)

F '(2, 1)

Step-by-step explanation:

Answer:

1:2

Step-by-step explanation:

The ratio unsimplified of blue marbles to red and yellow is 3:6, but since both numbers in the ratio can be divided by 3, we can simplify the ratio to 1:2.

Answer:

\(\displaystyle \sec(\theta)=\frac{9\sqrt{17}}{17}\)

Step-by-step explanation:

We are given that:

\(\displaystyle \sin(\theta)=\frac{8}{9}\text{ and } \tan(\theta)>0\)

And we want to find sec(θ).

First, note that both sine and tangent are positive. The only quadrant in which this can occur is QI. Hence, all trig ratios will be positive.

Also, recall that sine is the ratio of the opposite side to the hypotenuse. Using this information and the Pythagorean Theorem, we can determine the adjacent side:

\(a=\sqrt{9^2-8^2}=\sqrt{17}\)

So, with respect to θ, the adjacent side is √(17), the opposite side is 8, and the hypotenuse is 9.

Secant is the ratio of the hypotenuse to the adjacent. Hence:

\(\displaystyle \sec(\theta)=\frac{9}{\sqrt{17}}=\frac{9\sqrt{17}}{17}\)

Again, since θ is in QI, all trig ratios are positive.

Answer:

78 stamps

Step-by-step explanation:

50 stamps collected after 3 days

4 stamps added a day

next 7 days added= 7*4= 28 stamps

Total after 10 days= 50+28= 78 stamps

The surface area of a cell phone screen is 117 cm².

What is unit conversion?

Unit conversion is the process of converting a quantity expressed in one unit of measurement to an equivalent quantity expressed in another unit of measurement.

We can convert mm² to cm² by dividing the area in mm² by the square of the conversion factor, which is (10 mm / 1 cm) = 100 mm² / cm². Therefore, we have:

11700 mm² / (100 mm² / cm²) = 117 cm²

Rounding to the nearest whole number, we get 117 cm².

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Answer:I am pretty sure the answer is

C. "They are perpendicular to each other."

Step-by-step explanation:

For a shape to be reflected, it must be reflected across a line.

The true statement about the relationship between segments M, M' and the x-axis is that (c) they are perpendicular to each other

Given that:

When the shape is reflected across the x-axis, we have the following perpendicular and congruent lines

Hence, the relationship between segments M, M' and the x-axis is that (c) they are perpendicular to each other

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The monthly payment, car cost in total, and the interest to be paid, based on the loan amount and the number of years are:

First, find the loan amount:

= Cost of car x ( 1 - down payment percent)

= 14, 800 x ( 1 - 12%)

= $13, 024

Then find the monthly rate and the number of periods:

Monthly rate:

= Yearly rate / 12 months per year

= 4.5% / 12

= 0.375%

Number of periods:

= Number of years x Months per year

= 6 years x 12

= 72 months

Using these, the monthly payment can be found by the formula:

= Loan amount / Present value interest factor of annuity, 72 periods , 0.375%

= 13, 024 / 62.995976235992

= $206.74

Total cost paid on loan for car:

= Monthly payment x Number of months

= 206. 74 x 72

= $14, 885. 52

This means that the total interest paid was:

= Total amount paid on cost of car - Loan amount

= 14, 885.52 - 13, 024

= $1, 861.52

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Answer: It is a reflection of Reflections of You (second location) in the x-axis.

Step-by-step explanation: Based on the given information, the relationship between the new location (The Gridiron) and the previous locations can be determined.

The correct answer is:

   It is a reflection of Reflections of You (second location) in the x-axis.

The coordinates of the first three checkpoints of The Gridiron (A''(0,−5), B''(9,−5), and C''(4,−5)) indicate that they have the same y-coordinate (-5) as the corresponding checkpoints in the second location, Reflections of You. However, there is no indication of a reflection in the y-axis or any transformation related to the first location, Transformation Fitness Studios. Therefore, the correct answer is that The Gridiron is a reflection of Reflections of You in the x-axis.

Answer:

  ∠HGB = 20°

  ∠ECD = 34°

  ∠GBH = 36°

  ∠FGH = 37°

Step-by-step explanation:

There are several useful rules regarding angles:

This last observation is a consequence of the 2nd and 3rd observations.

__

angle ECD

Using the last observation, ∠ECD = 124° -90° = 34°.

angle HGB

Again, using the last observation, ∠HGB = 110° -90° = 20°.

angle GBH

There are at least a couple of ways to find this one. We assume that lines FB and EC are parallel, so angles HBC and ECD are corresponding, hence congruent. Angle GBC is the supplement of of 110°, so is 70°. Then ...

  ∠GBH = 70° -34° = 36°

angle FGH

Again, this angle can be found multiple ways. Here, we'll use the sum of angles in triangle FGB.

  ∠FGB +∠GBF +∠BFG = 180°

  (∠FGH +∠HGB) +∠GBF +∠BFG = 180°

  ∠FGH +20° +36° +87° = 180°

  ∠FGH = 180° -143° = 37°

__

Least to greatest, the angles are ...

  ∠HGB = 20°

  ∠ECD = 34°

  ∠GBH = 36°

  ∠FGH = 37°

Answer:

y= -3x-5

Step-by-step explanation:

Answer:

The answer is

\(y = 3x - 5\)

Step-by-step explanation:

❃Incase you forgot what the linear equation fo

formula is ☟

\(y = mx + b\)

❃Incase you also forgot, The is what the slope formula is ☟

\(m = \frac{y_2 - y_1 }{x_2 - x_1}\)

➊ First: We are going to be solving for the slope.

\(m = \frac{ 4 - ( - 5)}{3 - 0} = \frac{ 9}{3} = 3\)

➋Second: We find the y-intercept.

➌Third: Plug in.

\(y = mx + b \\ - 5 = 3(0) + b \\ - 5 = 0 + b \\ \frac{ - 0 = - 0 \: \: \: \: \: }{ - 5 = b}\)

➌Third: Plug in.

\(y = 3x - 5\)

Answer:

the two numbers that add up to 3 but multiply to 18 are 6 and -3.

Step-by-step explanation:

We can start by using algebra to solve for the two numbers. Let x and y be the two numbers we are looking for. Then we can write two equations:

x + y = 3 (since the numbers add up to 3)

xy = 18 (since the numbers multiply to 18)

We can solve for one of the variables in terms of the other using the first equation. For example, we can solve for y:

y = 3 - x

Then we can substitute this expression for y into the second equation:

x(3 - x) = 18

Expanding the left side and simplifying, we get:

3x - x^2 = 18

Rearranging and factoring, we get:

x^2 - 3x + 18 = 0

(x - 3)(x - 6) = 0

Therefore, either x = 3 or x = 6. If x = 3, then y = 3 - x = 0, which doesn't work since we want two numbers that multiply to 18. So the two numbers are x = 6 and y = 3 - x = -3.

So the two numbers that add up to 3 but multiply to 18 are 6 and -3.

The logarithm expression can be simplified to:

In(6x^9)-In(x^2) =7·ln(6x)

There are some logarithm properties we can use here.

log(a) - log(b) = log(a/b)

log(a^n) = n*log(a)

(these obviously also apply to the natural logarithm)

Now let's look at our expression, it says that:

In(6x^9)-In(x^2)

Using the first rule, we can rewrite this as.

In(6x^9)-In(x^2) = ln(6x^9/x^2)

Now solving the quotient in the argument:

ln(6x^9/x^2) = ln(6x^7) = 7·ln(6x)

That is the expresison simplified.

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To prove that S is a group, we need to show that it satisfies the four group axioms: Closure, Associativity, Identity, Inverse. We are given that the equations ax = b and ya = b has a solution for every a, b, S, and E.

The four group axioms are as follow:

Closure: Let a, b be arbitrary elements of S. By assumption, there exist elements x, y in S such that ax = b and ya = b. Then, we have ab = a (yax) = (ay)ax = bax. Since b and a are in S, and the product of two elements in S is also in S, we conclude that ab is in S.

Associativity: This property holds for any semigroup S, so we can assume it holds for S.

Identity: We need to show that there exists an element e in S such that ae = ea = a for all a in S. Consider the equation ax = x and ya = y. Since S is a semigroup, we know that ax and ya are well-defined elements of S for any a, x, y in S. Therefore, there exists an element e in S such that ae = ea = a for all a in S.

Inverse: Let a be an arbitrary element of S. By assumption, there exists an element x in S such that ax = e. We need to show that there exists an element b in S such that ab = ba = e. Consider the equation ya = e. By the same argument as above, there exists an element b in S such that ab = ba = e.

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The zeros with each multiplicity are given as follows:

The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the linear factors of the function in this problem, the zeros are given as follows:

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Answer:

\(\frac{2}{7}+\frac{3}{7}=\frac{5\\}{7}\)

but if you want only the numerator it is 5

decimal form: 0.714

Answer:

x=3,y=-3

Step-by-step explanation:

Isolate x for 4x +y=9: x=9-y/4

Substitute x = 9-y/4

[5 x 9-y/4+2y =9]

Isolate y for (45+3y/4)=9:

y=-3

For x= 9-y/4

Substitute y = -3

x= 9-(-3)/4

9-(-3)/4=3

X=3

The solutions to the system of equations are:

x=3 y= -3

The inequality of the graph is given as follows:

x - 4 ≥ -2x + 8.

The solution to the inequality is composed by the numbers to the right of the closed interval at x = 4, hence it is given as follows:

x ≥ 4.

Then the equivalent inequality is the one that has the same solution as the inequality graphed, and thus it is given as follows:

x - 4 ≥ -2x + 8

3x ≥ 12

x ≥ 12/3

x ≥ 4.

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