Simplify -16x^8/-8x^9

Using the weighted mean, the coordinates of the point are given as follows:

B. P(-1.6, -0.2).

The weighted mean is given by the sum of all elements in a data-set multiplied by it's weight, divided by the sum of the weights.

For this problem, the points are given as follows:

The x-coordinate of the mean point is given as follows:

x = (-3 x 4 + 4 x 1)/5 = -1.6.

The y-coordinate of the mean point is given as follows:

y = (4 x -1 + 3 x 1)/5 = -0.2.

The coordinates of the point are given as follows:

B. P(-1.6, -0.2).

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Answer:

63 ft²

Step-by-step explanation:

Given:

Area of rectangle = \( A_1 = 72 ft^2 \)

Area of trinagle = \( A_2 = 9 ft^2 \)

Required:

Square feet of outdoor carpet needed for the hole

Solution:

The square feet of outdoor carpet needed = area of the rectangle - area of the triangle

= \( A_1 - A_2 \)

= \( 72 - 9 = 63 \)

The square feet of outdoor carpet needed is 63 ft²

The equation in terms of x that represents the given relationship is 114 = (1 + 3x) * (Width)

Let's break down the information given:

Height of the rectangular box = 7 ft

Length of the rectangular box = 1 ft longer than thrice the width (x)

Volume of the rectangular box = 798 ft³

To write an equation that represents the given relationship, we need to relate the length, width, and height to the volume.

The volume of a rectangular box is given by the formula: Volume = Length * Width * Height.

Given that the height is 7 ft, we can substitute this value into the equation.

Volume = (Length) * (Width) * (7)

Now, let's focus on the length. It is described as 1 ft longer than thrice the width.

Length = 1 + (3x)

Substituting this value into the equation, we have:

Volume = (1 + (3x)) * (Width) * (7)

Since the volume is given as 798 ft³, we can set up the equation as follows:

798 = (1 + (3x)) * (Width) * 7

Simplifying further, we get:

798 = 7 * (1 + 3x) * (Width)

Dividing both sides of the equation by 7, we have:

114 = (1 + 3x) * (Width)

Therefore, the equation in terms of x that represents the given relationship is:

114 = (1 + 3x) * (Width)

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Based on the RHS rule of congruency of triangles, APC and APB are congruent, therefore, P lies on the bisector of BAC.

To prove that  P lies on the bisector of BAC:

Based on two equal angles (the bisected angle), right angles, and a similar side, the two triangles are said to be congruent (RHS congruence rule). As a result, the perpendiculars are of equal length, and the angle's bisector is equally spaced from its sides.

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For each feeding, the proportion of food eaten by Roxie is:

• Wet dog food = 2/3 of a can

• Dry dog food =1/8 of a bag

• Special meat = 3/5 of a patty

The trainer goes to the store and buys 24 cans of wet dog food, 4 bags of dry dog food, and 3 packages of meat.

Since there are 6 patties in 1 package, the number of patties bought by the trainer = 3 X 6 = 18 Patties

Since the dog is fed twice a day, the dog eats the following per day:

Therefore, the number of days that each food type bought will last will be:

(a)The dog will be fed for 15 days before the trainer needs to buy more food.

(b)The trainer will run out of the special meat first.

Since the dogs will be fed for 15 days, the amount of the other two types of dog food will be left after the first type of dog food runs out will be:

(c)Therefore:

• 4 cans of the wet dog food will remain; and

• 0.25 of a bag of the dry dog food will remain.

Answer:

49.2

Step-by-step explanation:

By using the rules:

\(cos(-x) = cos(x)\\\\sec(x) = \frac{1}{cos(x)}\)

We have proven the identity. Below you can follow the demonstration.

Here you need to remember two things:

\(cos(-x) = cos(x)\\\\sec(x) = \frac{1}{cos(x)}\)

Here we have the expression:

\(\frac{1 - cos(-x)}{sec(-x) - 1}\)

By using the first rule, we can rewrite:

\(\frac{1 - cos(-x)}{sec(-x) - 1} = \frac{1 - cos(x)}{sec(x) - 1}\)

By using the second rule, we can rewrite:

\(\frac{1 - cos(x)}{sec(x) - 1} = \frac{1 - cos(x)}{\frac{1}{cos(x)} - 1}\)

Now if we multiply and divide by cos(x), we get:

\(\frac{1 - cos(x)}{\frac{1}{cos(x)} - 1} = \frac{1 - cos(x)}{\frac{1}{cos(x)} - 1} *\frac{cos(x)}{cos(x) } = \frac{(1- cos(x))*cos(x)}{1 - cos(x)} = cos(x)\)

In this way, the identity was proven.

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The segment lengths are given as follows:

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

Considering the geometric mean theorem, the triangle has bases of 7 and 14 - 7 = 7, hence the altitude BD is given as follows:

BD² = 7 x 7

BD² = 7²

BD = 7.

The segment BC is the hypotenuse of a right triangle of two sides with length 7, hence:

(BC)² = 7² + 7²

\(BC = \sqrt{2 \times 49}\)

\(BC = 7\sqrt{2}\)

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Each letter should be matched to its correct term as follows;

1. A ⇔ Efficiency.

2. B ⇔ Impossible.

3. C ⇔ Inefficiency.

In Economics and Mathematics, a production possibilities curve (PPC) can be defined as a type of graph that is typically used for illustrating the maximum and best combinations of two (2) products that can be produced by a producer (manufacturer) in an economy, if they both depend on the following two (2) factors;

Based on the production possibilities curve shown in the image attached above, we can reasonably infer and logically deduce that each of the letters represent the following terminologies;

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The radius of the pond should be modified to 19.72ft to be able to maintain the original volume of the pond.

The original shape of the pond is the shape of a cylinder and the formula tye can be used to calculate the volume of a cylinder = πr²h

The volume of the original pond is calculated as follows;

π = 3.14

Radius = 18 ft

height = 36ft

Vol = 3.14×18×18×36

= 36,624.96ft³

The radius of the modified pond is calculated as follows; Volume = 36,624.96ft³

height = 30ft

radius = ?

That is;

36,624.96 = 3.14×r²× 30

r² = 36,624.96/94.2

= 388.8

r = √388.8

= 19.72 ft

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Answer: Thats cool.

Step-by-step explanation:

Answer:

To find the fraction of the total audience that were students or teachers, you need to add the fractions of students and teachers and simplify the result.

5/12 + 1/8 = (53) / (123) + (16) / (86) = 15/36 + 6/48 = 15/36 + 3/24 = 18/36 + 3/24 = (18+3) / (36+24) = 21/60

So 21/60 of the total audience were students or teachers.

Answer:

              cvfgrtyukjmn

Step-by-step explanation:

Answer:

Option D - 21x + 16

Step-by-step explanation:

4(6x+4) - 3x

Expand and simplify :

24x+16 - 3x

21x+16

Hope this helped and have a good day

Use the distributive property to multiply 4 by 6x+4.

Collect like terms.

Combine 24x and -3x to get 21x.

The equivalent expression for 4(6x + 4) - 3x is 21x+16.

\(\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}\)

The value of the resistor needed in this scenario is approximately 1.2 ohms.

To find the value of the resistor in the given scenario, we can apply Ohm's Law, which states that the current (I) flowing through a resistor is directly proportional to the voltage (V) across it, and inversely proportional to the resistance (R) of the resistor.

Using Ohm's Law, we have the formula:

V = I * R

Where:

V is the voltage across the resistor (12 volts in this case),

I is the current flowing through the resistor (5 amps for each light, so a total of 10 amps),

R is the resistance of the resistor (which we need to find).

Rearranging the formula, we have:

R = V / I

Plugging in the values:

R = 12 volts / 10 amps

R = 1.2 ohms

Therefore, the value of the resistor needed in this scenario is approximately 1.2 ohms.

It's worth noting that this calculation assumes the lights are connected in parallel, as the current remains the same for each light. If the lights were connected in series, the total resistance would be the sum of the individual resistances, and the calculation would be different.

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Answer:

86.60254

Step-by-step explanation:

30-60-90 triangle, which means that the base is 10. 1/2(10)(10 rt 3). Simplify answer as needed :)

The model predicts a negative population (-843) if the hunting season lasts the entire year.

To find the maximum amount of deer predicted by the quadratic model, we need to determine the vertex of the quadratic function. The vertex of a quadratic function in the form of \(y = ax^2 + bx + c\) can be found using the formula x = -b / (2a). In this case, the quadratic model is \(P = -10h^2 + 30h + 237.\)

Using the formula, we can calculate the value of h at the vertex:

\(h = -30 / (2\times(-10)) = 1.5\)

Substituting this value back into the equation, we can find the maximum population of deer:

\(P = -10(1.5)^2 + 30(1.5) + 237\\P = -22.5 + 45 + 237\\P = 259.5\)

Therefore, the model predicts that the maximum population of deer would be 259.5 at the end of the year if the hunting season duration is optimized based on the quadratic model.

If the government allowed year-round hunting, we can assume the hunting season duration (h) would be 12 months. Substituting this value into the equation, we can find the predicted population of deer:

\(P = -10(12)^2 + 30(12) + 237\\P = -1440 + 360 + 237\\P = -843\)

However, in practical terms, a negative population is not meaningful. It suggests that the quadratic model might not accurately represent the population dynamics in the case of a year-round hunting season. This could be due to various factors, such as migration patterns, breeding habits, or the influence of other ecological factors not considered in the model.

Further research and data analysis would be needed to develop a more accurate model or understand the population dynamics under different hunting scenarios.

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Answer:

Option B

Step-by-step explanation:

704 cubic centimeters

Answer: B. Yellow

Step-by-step explanation: Yellow has the largest number of students out of the entire data set, so it will consume the largest area on a pie chart.

Answer:

A pie chart is a type of graph that shows the relative sizes of different categories of data by dividing a circle into sectors or slices. Each sector represents a fraction of the whole circle, which is equal to 100%. The angle of each sector is proportional to the percentage of the data it represents. To answer a question based on a pie chart, we need to compare the sizes of the sectors and find the one that matches the given condition.

For example, consider the following question:

When asked their favorite color, 20 students said red, 23 students said blue,

25 students said green, and 28 students said yellow. Students with which

favorite color would be represented by the largest wedge in a pie chart?

To answer this question, we need to find the total number of students who participated in the survey. We can do this by adding up the numbers of students who chose each color:

20 + 23 + 25 + 28 = 96

Next, we need to find the percentage of students who chose each color by dividing the number of students by the total and multiplying by 100:

Red: (20 / 96) x 100 = 20.83%

Blue: (23 / 96) x 100 = 23.96%

Green: (25 / 96) x 100 = 26.04%

Yellow: (28 / 96) x 100 = 29.17%

Finally, we need to compare the percentages and find the largest one. In this case, it is yellow with 29.17%. Therefore, students who chose yellow as their favorite color would be represented by the largest wedge in a pie chart.

The answer is B. Yellow.

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Answer:

1 cause its going to be one sometimes

Answer:

x = 9

Step-by-step explanation:

1+1 = x - 7

2 = x - 7

Add 7 to both sides to isolate the x:

2 + 7 = x - 7 + 7

9 = x

Hope this helps!

Answer:

The answer is option C

y = 1/3x - 10 ........ 1

2x + y = 4 .......... 2

Substitute the first equation into the second one

That's

2x + 1/3x - 10 = 4

7/3x = 14

Multiply through by 3

That's

7x = 42

Divide both sides by 7

x = 6

Substitute x = 6 into any of the Equations

y = 1/3x - 10

y = 1/3(6) - 10

y = 2 - 10

y = - 8

Therefore

x = 6 y = - 8

Hope this helps

Answer:

Step-by-step explanation:

Given that :

sample mean = 4.001 inches

sample standard deviation = 0.002 inch

a.

\(C_{pk} = min [\dfrac{(USL- \bar X)}{(3*std \ dev)} \ ; \ \dfrac{ (\bar X- LSL)}{(3*std \ dev)}]\)

specification = \(4 \pm 0.003\)

Upper specification limit USL = 4 + 0.003  = 4.003

Lower specification limit LSL =  4 - 0.003 = 3.997

\(\dfrac{ (\bar X- LSL)}{(3*std \ dev)} = \dfrac{ (4.001-3.997)}{(3*0.002)}\)  \(= 0.667\)

\(\dfrac{(USL- \bar X)}{(3*std \ dev)} =\dfrac{(4.003-4.001)}{(3*0.002)}\)\(= 0.333\)

Thus ;

\(C_{pk} =\)\(min (0.333 , 0.667)\)  = 0.333

\(C_{pk}\)  is a measure of closeness to one's target and the consistency around the average performance.

b) No, C - spec should not use this machine to produce this part because \(C_{pk}\) <  1.33 which typical means that the part is not fully capable of hitting the target specification on a consistent basis .

Answer:

The mean cost of a five pound bag of shrimp is 40 dollars with a standard deviation of 8 dollars.

Step-by-step explanation:

a sample of 49 bags of shrimp is randomly selected, what is the probability that the sample mean would be less than 37.4 dollars? Round your answer to four decimal places.

Answer:

B. What was the highest temperature this month?

Step-by-step explanation:

Rory is recording the highest temperature for the duration of the day for month's worth of data.

B. is the easiest one to answer, as you simply will have to look for the greatest number within the set, and that will be the answer.

A. is too broad, and does not imply that only the "high temperature" is needed, rather just a leveled temperature within day in that month.

C. is the opposite of what Rory had recorded, and without data, he cannot answer it.

D. is answerable as well, but, again, the only temperature recorded is the high temperature. Temperature can fluctuate depending on the time of the day, and can be in the 50s one hour and the 90s in another.

~

Answer: The sheet cake pan should have dimensions 13 inches by 9 inches by 3 inches.

Answer:

129

Step-by-step explanation:

Considering the survey to be representative, you can simply multiply the share of students p preferring “Track & Field” with the whole school population at the same time to estimate the number of such students in the whole school.

First we need to find the relative share p of such answers in the study by dividing it by the sum of answers, assuming that the table is complete for that random sample:

p = 4/(8 + 5 + 4) = 4/17

Then for the whole school we get 550 p ≈ 129.4

Answer:

110

Step-by-step explanation:

4/20 = x/550

550x4 divided by 20 = 110

Answer:

40

Step-by-step explanation:

took the test

The value of the radical √48 is 4√3.

Radical is a symbol (√) that denotes square roots and nth roots. The number inside the symbol is called Radicand and the expression containing the radical or a square root is called a Radical expression.

Here, we are given the radical √48

To find the value of the radical, we will factorize 48

i.e., 48 = 2×2×2×2×3

           = 16×3

Now, the square root of 48, that is, √48

                                                       = \(\sqrt{16\cdot3}\) =\(\sqrt{16} \cdot \sqrt{3}\)

We know 16 is a perfect square of 4, that is, the square root of 16= 4

⇒√16=4

Using this, we have √48= 4√3

The correct answer is 4√3.

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