A caterpillar eats 18 leaves every day How many leaves will it eat after 12 days?

It is given that m∠AOB = 42° and m∠EOF = 66°. By the congruent rule m∠EOF ≅ m∠BOC. Therefore, m∠BOC = 66°. By the sum of m∠AOB and m∠BOC, m∠AOC = 108°, and by the supplementary rule m∠AOC + m∠COD = 180°. After application of the supplementary rule, m∠COD = 72°

Congruent angles are angles that have the same measure, in degrees and are often represented by the symbol "≅"

m∠EOF and m∠BOC are vertical angles and so they are equal and satisfy the congruent rule.

The angles m∠AOB and m∠BOC form the larger angle m∠AOC so;

m∠AOC = 42° + 66° = 108°

The supplementary rule states that if two angles add up to 180°, they are considered supplementary angles, thus m∠AOC + m∠COD = 180° is correct as m∠AOC and m∠COD both lie on a straight line AD.

Therefore, application of the supplementary rule will give the size of the angle m∠COD = 72° as follows:

108° + m∠COD = 180°

m∠COD = 180 - 108°

m∠COD = 72°.

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The compound inequality that represents the range of the actual weight of the object is 125.4 ≤ w ≤ 126.2.

Part A: The absolute value inequality that describes the range of the actual weight of the object is:

|w - 125.8| ≤ 0.4

Part B: To solve the absolute value inequality, we can break it down into two separate inequalities:

w - 125.8 ≤ 0.4 and - (w - 125.8) ≤ 0.4

Solving the first inequality:

w - 125.8 ≤ 0.4

Add 125.8 to both sides:

w ≤ 126.2

Solving the second inequality:

-(w - 125.8) ≤ 0.4

Multiply by -1 and distribute the negative sign:

-w + 125.8 ≤ 0.4

Subtract 125.8 from both sides:

-w ≤ -125.4

Divide by -1 (note that the inequality direction flips):

w ≥ 125.4

Combining the solutions, we have:

125.4 ≤ w ≤ 126.2

The object is 125.4 ≤ w ≤ 126.2.

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Answer:

h. x=11

i. x=4 1/6 (1/6 is a fraction)

k. x=-8

l. x= 3 1/2 (1/2 is a fractio)

Step-by-step explanation:

Answer: He does have enough crates to ship out the avocados.

Step-by-step explanation: 205 avocados fit inside a shipping container. At a big grove, 7000 avocados were picked. 36 cargo containers belong to the owner. As a result, he can fit a total of = avocados. And since he has 7000 avocados, he does indeed have enough crates to carry the fruit.

Answer:

No

Step-by-step explanation:

In order to solve this, we plug in the values for x and y. Remember that x = -1 and y = -9

-9 = 7 - 2(-1)

-9 = 7 + 2

-9 ≠ 9

a = 7

Answer:

b= 7 * (1 + 8)

Step-by-step explanation:

hope it helps

The probability that it is raining and the flight is delayed is 0.011, or approximately 0.011 rounded to the nearest thousandth.

Let's use the formula for calculating the probability of the intersection of two events: P(A and B) = P(A) × P(B|A), where P(B|A) is the probability of event B occurring given that event A has occurred.

Let A be the event that it is raining, and B be the event that the flight is delayed. We are looking for P(A and B).

We know that:

P(A) = 0.1 (the probability that it will rain)

P(B) = 0.11 (the probability that the flight will be delayed)

P(not A and not B) = 0.88 (the probability that it will not rain and the flight will leave on time)

We can use the complement rule to find P(A or B):

P(A or B) = 1 - P(not A and not B)

P(A or B) = 1 - 0.88

P(A or B) = 0.12

Now we can use the formula for the intersection of two events:

P(A and B) = P(A) × P(B|A)

We know that P(A) = 0.1, and we need to find P(B|A), the probability of the flight being delayed given that it is raining.

We can use Bayes' theorem to find P(B|A):

P(B|A) = P(A and B) / P(A)

P(B|A) = (P(A) × P(B|A)) / P(A)

P(B|A) = P(B and A) / P(A)

We can rearrange this to get:

P(A and B) = P(B|A) × P(A)

Substituting the values we know:

P(B|A) = P(A and B) / P(A)

0.11 = P(A and B) / 0.1

P(A and B) = 0.11 × 0.1

P(A and B) = 0.011

Therefore, the probability that it is raining and the flight is delayed is 0.011, or approximately 0.011 rounded to the nearest thousandth.

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Answer:

The right triangular pyramid volume is given by the formula V = 1 3 × B × h , where B is the area of the triangular base and h is the height (the distance from the apex to the base).

Step-by-step explanation:

Answer:

192 cubic feet

Step-by-step explanation:

The volume V of a triangular pyramid is given by the formula:

V = (1/3) * base area * height

where base area is the area of the triangular base.

In this case, the triangular base has a length of 8 ft and a width of 8 ft, so it is a square with area:

base area = length * width = 8 ft * 8 ft = 64 sq ft

Substituting the given values into the formula, we get:

V = (1/3) * 64 sq ft * 9 ft

V = 192 cubic feet.

Therefore, the volume of the triangular pyramid is 192 cubic feet.

Answer:

The solution to the system of equations is:

\(x=0,\:y=0\)

Step-by-step explanation:

Given the system of equations

2x = -6y

12x + 12y = 0

solving the system of equations by elimination method

\(\begin{bmatrix}2x=-6y\\ 12x+12y=0\end{bmatrix}\)

Arrange equation variables for elimination

\(\begin{bmatrix}2x+6y=0\\ 12x+12y=0\end{bmatrix}\)

Multiply 2x+6y = 0 by 6:   12x+36y=0

\(\begin{bmatrix}12x+36y=0\\ 12x+12y=0\end{bmatrix}\)

subtracting the equations

\(12x+12y=0\)

\(-\)

\(\underline{12x+36y=0}\)

\(-24y=0\)

solve -24y=0 for y

\(-24y=0\)

divide both sides by -24

\(\frac{-24y}{-24}=\frac{0}{-24}\)

Simplify

\(y=0\)

For 12x+36y=0 plug in y = 0

\(12x+36y=0\)

\(12x+36\cdot \:0=0\)

\(12x+0=0\)

\(12x=0\)

Divide both sides by 12

\(\frac{12x}{12}=\frac{0}{12}\)

Simplify

\(x=0\)

Therefore, the solution to the system of equations is:

\(x=0,\:y=0\)

The expansion of the function \((3x - 4)^4\) simplifies to \(81x^4 - 432x^3 + 864x^2 - 768x + 256.\)

To expand the function \(f(x) = (3x - 4)^4\), we can use the binomial theorem. According to the binomial theorem, for any real numbers a and b and a positive integer n, the expansion of \((a + b)^n\) can be written as:

\((a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^{(n-1)} b^1 + C(n, 2)a^{(n-2)} b^2 + ... + C(n, n-1)a^1 b^{(n-1)} + C(n, n)a^0 b^n\)

where C(n, k) represents the binomial coefficient, which is given by C(n, k) = n! / (k!(n-k)!).

Applying this formula to our function \(f(x) = (3x - 4)^4\), we have:

\(f(x) = C(4, 0)(3x)^4 (-4)^0 + C(4, 1)(3x)^3 (-4)^1 + C(4, 2)(3x)^2 (-4)^2 + C(4, 3)(3x)^1 (-4)^3 + C(4, 4)(3x)^0 (-4)^4\)

Simplifying each term, we get:

\(f(x) = 81x^4 + (-432x^3) + 864x^2 + (-768x) + 256\)

Therefore, the expanded form of the function \(f(x) = (3x - 4)^4\) is \(81x^4 - 432x^3 + 864x^2 - 768x + 256\).

Note that the coefficient of \(x^3\) is -432, the coefficient of \(x^2\) is 864, the coefficient of x is -768, and the constant term is 256.

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Note the complete question is

Answer:

16x+8y

Step-by-step explanation:

Let's simplify step-by-step.

3x+8y+13x

Combine Like Terms:

=3x+8y+13x

=(3x+13x)+(8y)

=16x+8y

Answer:

The 95% confidence interval for the mean consumption of meat among people over age 29 is between 2.8 pounds and 3 pounds.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1-0.95}{2} = 0.025\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1-\alpha\).

So it is z with a pvalue of \(1-0.025 = 0.975\), so \(z = 1.96\)

Now, find the margin of error M as such

\(M = z*\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

\(M = 1.96*\frac{1.4}{\sqrt{2092}} = 0.1\)

The lower end of the interval is the sample mean subtracted by M. So it is 2.9 - 0.1 = 2.8 pounds

The upper end of the interval is the sample mean added to M. So it is 2.9 + 0.1 = 3 pounds.

The 95% confidence interval for the mean consumption of meat among people over age 29 is between 2.8 pounds and 3 pounds.

Answer:

\(2.9-1.96\frac{1.4}{\sqrt{2092}}=2.84\)    

\(2.9+1.96\frac{1.4}{\sqrt{2092}}=2.96\)    

The confidence interval is given by \(2.84 \leq \mu \leq 2.96\)

Step-by-step explanation:

Information given

\(\bar X=2.9\) represent the sample mean

\(\mu\) population mean

\(\sigma =1.4\) represent the population standard deviation

n=2092 represent the sample size  

Confidence interval

The confidence interval is given by:

\(\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\)   (1)

Since the Confidence interval is 0.95 or 95%, the significance is \(\alpha=0.05\) and \(\alpha/2 =0.025\), and the critical value would be \(z_{\alpha/2}=1.96\)

Replacing the info we got:

\(2.9-1.96\frac{1.4}{\sqrt{2092}}=2.84\)    

\(2.9+1.96\frac{1.4}{\sqrt{2092}}=2.96\)    

The confidence interval is given by \(2.84 \leq \mu \leq 2.96\)

5x+7x=660;

12x=660;

x=660:12;

x=55 (kg).

Then 5x=5×55=275 kg and 7x=7×55= 385 kg.

The required ratio is therefore

660= 275:385.

Answer:

25, 25, 22.5, 22

Step-by-step explanation:

It gives you a hint; K = y/x. They give you what x and y are so use that to solve for the last row.

We are given all of these values:

x -> 2, 3, 4, 5

y -> 50, 75, 90, 110

Use the formula given and solve for K.

50/2 = 25

75/3 = 25

90/4 = 22.5

110/5 = 22

Best of Luck!

Answer:

5n + 12p + 12m

Step-by-step explanation:

Perimeter means you are adding up all three sides.

4m + 3n + 8m + 10p + 2p + 2n

= 2n+3n + 10p+2p + 4m+8m

Combine like terms.

= 5n + 12p + 12m

Answer:

A. P(EC) = 0.4  

B. P(E∪E) = 0.75

C. P(EC ∩ FC) = 0.25

Step-by-step explanation:

Let us calculate -:

we are given with - P(E) = 60 and P(F) =.15,

Thus , (a) \(P(E^C)=1-P(E)\)

                   \(=1-0.6\)

                   \(=0.4\)

(b) P(E∪F) = P(E) + P(F)

   = 0.60 + 0.15

   = 0.75

(c) \(P(E^C\)∩\(F^C)\) \(=1-P(E\)∪ \(F)\)

   \(=1-0.75\)

   = \(0.25\)

Hence , the answers are -A. P(EC) = 0.4  , B. P(E∪E) = 0.75  , C. P(EC ∩ FC) = 0.25.

Answer:

The answer is in my screen shot:


Explanation:

It's a geometric sequence with common ratio 3. You can calculate the common ratio by dividing the 240 by 80 or likewise 720 by 240.

Answer:

My sister is

18

years old.

Step-by-step explanation:

s = m + 8        Eq. 1

s + m = 28      Eq. 2

s = my sister age

m = my age

Replacing Eq. 1 in Eq. 2:

(m+8) + m = 28

2m + 8 = 28

2m = 28 - 8

2m = 20

m = 20/2

m = 10

From Eq. 1:

s = m + 8

s = 10 + 8

s = 18

Check:

from Eq. 2:

s + m = 28

18 + 10 = 28

Answer:

7 cookies are left out, If Amanda packs 11 boxes of cookies.

Step-by-step explanation:

Amanda has to pack cookies in boxes. The function describes how many cookies she puts in a certain number of boxes:

\(c=-6b+ 73\)

here variable c represents number of cookies and variable b represents the number of boxes packed.

We need to find If she packs 11 boxes, how many cookies are left out.

We are given:

b = 11

We need to find c

Putting value of b and finding value of c in the equation.

\(c=-6b+ 73\\c=-6(11)+73\\c=-66+73\\c=7\)

So, we get the value of c: c=7

Therefore,  7 cookies are left out, If Amanda packs 11 boxes of cookies.

Answer:The reciprocal of 2/3 is 3/2. The product of 2/3 and its reciprocal 3/2 is 1.

Step-by-step explanation:

Answer:

Option D - Line P

Step-by-step explanation:

Look at the coordinates in the (x, y) column of Max's table and see which line has the same points.

Answer:

\(\frac{1}{2} x+5\)

Step-by-step explanation:

h(x)=2x-10

    y =2(x-5)

   interchanging the value of x and y,

x=2(y-5)

\(\frac{x}{2} =y-5\)

\(\frac{1}{2} x+5\)=y

so,h(x)=\(\frac{1}{2}x+5\)

Answer:

Step-by-step explanation:

Given function

Its inverse is

Correct option is D.

Answer:

21.6 magazines

Step-by-step explanation:

260/12=21.6

Based on the changes that occurred in Ariel's bank account, the missing values are -$223.75, -$1.40, and -$4.40.

The missing values from the given table of the changes that occurred in Ariel's bank account balance is determined as follows:

Week 4 change:

Change = -$41.40 - $182.35

Change =  -$223.75

Week 5 balance: this is obtained from the sum of the change and the balance of the previous week:

Balance = -$41.4 + $40

Balance = -$1.40

Week 6 change:

Change = -$5.80 - (-$1.4)

Change  = -$4.40

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Geometry encompasses various topics such as angles, lines, triangles, circles, polygons, and more.

Whether you need help with a specific theorem, a geometric proof, or solving a particular problem, feel free to describe the problem or provide any relevant information.

You can also ask general questions about geometry concepts or seek clarification on any topic you find challenging. Remember to provide all the necessary details, such as given information, diagrams, or specific requirements of the problem, to help me understand and assist you better.

Geometry often involves visual representation, so if you can provide any diagrams or illustrations related to your question, it would be helpful. However, if you can only describe the problem or concept in words, that's perfectly fine too.

Rest assured that I'll do my best to provide clear explanations, step-by-step solutions, and any additional information or insights to help you understand and solve your geometry problem.

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Answer:

I do not understand the question I am so sorry :(

Step-by-step explanation:

The given function presents a local minimum in the coordinates (0,-1).

In math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization.  One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.

For solving this question, the given equation should be rewritten  from the factoring.

\(x^5-x^3+x^2-1=\left(x+1\right)^2\left(x-1\right)\left(x^2-x+1\right)=0\). Then, you have 3 equations.

From the Zero Factor Principle, you can write

Equation 1

(x+1)²=0

x+1=0

x= -1

Equation 2

x-1=0

x=1

Equation 3

x²-x+1=0

\(x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \:1}}{2\cdot \:1}\\ \\ x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{3}i}{2\cdot \:1}\)

From these points it is possible to plot a graph and you can see that the local minimum presents the coordinates (0,-1).

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