find the length of the loop of the given curve. x = 12t − 4t3, y = 12t2

The statement which is true include the following: B. The y-coordinates of the solutions to the system and the zeroes of the equation are not equal.

In Mathematics and Geometry, a polynomial graph simply refers to a type of graph that touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

Generally speaking, the zero of a polynomial function simply refers to a point where it crosses or cuts the x-axis of a graph.

By critically observing the graph of the polynomial function shown in the image attached below, we can logically deduce that the y-coordinates of the solutions to the system of equations and the zeros of the equation are not equal;

3x³ + x = 2x + 1

P(x) = 3x³ + x - 2x - 1

3x³ + x - 2x - 1 = 0

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Answer:

360 in

Step-by-step explanation:

To figure out how many inches the dressmaker has in 10, 3 ft rolls, we can multiply by the conversion ratio:

[tex]\dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies (10 \cdot 3 \text{ ft}) \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30 \text{ ft} \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30\cdot 12 \text{ in} \\ \\ \text{} \ \ \implies \boxed{360 \text{ in}}[/tex]

So, the dressmaker has 360 in of ribbon.

The probability that the archer gets exactly 4 bull's-eyes out of 8 shots is approximately 0.191

This is an example of a binomial distribution problem, where the archer has a probability of hitting the bull's-eye of 0.49 for each arrow and we want to know the probability of getting exactly 4 bull's-eyes out of 8 shots.

The probability of getting exactly 4 bull's-eyes out of 8 shots can be calculated using the binomial probability formula

P(X = k) = (n choose k) × p^k × (1-p)^(n-k)

where

X is the number of successes (bull's-eyes)

k is the specific number of successes we want (4 in this case)

n is the total number of trials (8 in this case)

p is the probability of success on a single trial (0.49 in this case)

(n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items (also written as "nCk")

Plugging in the numbers, we get

P(X = 4) = (8 choose 4) × 0.49⁴ × (1-0.49)⁴

= (8! / (4! × 4!)) × 0.49⁴ × 0.51⁴

≈ 0.191

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The value of x is 12

Similar triangles are triangles that have the same shape, but their sizes may vary. For two triangles to be similar, the corresponding angles of the triangles must be equal.

Also the ratio of the corresponding sides of the similar triangles are equal.

Therefore ;

x/4 = 36/x

x² = 36×4

x² = 144

x = √144

x = 12

therefore the value of x using similar triangles is 12.

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The area of this figure based on the information will be 10mm²

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

From the information, the shape gas sides 5mm and 2mm. The area of this figure will be:

= Length × Width

= 5mm × 2mm

= 10mm²

In conclusion, the area of this figure based on the information will be 10mm²

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A shape gas sides 5mm and 2mm. What is the area of this figure 9mm 7mm 2mm 3mm 10mm

Answer: No profit

Step-by-step explanation: because break even point are when produce costs and selling costs are the same therefore no profit

If this helped brainliest would help! :)

The probability of pulling two skittles of the same colour in a row is 4/13.

Finding the likelihood that the first skittle will be any colour and then the likelihood that the second skittle will be the same colour as the first will allow you to calculate the likelihood of pulling two Skittles of the same colour in a row.

There are a total of 27 Skittles in the bag because there are 9 of each colour there. As a result, there is a one-in-one chance that the first skittle will be of any hue.

There will be a total of 26 skittles left in the bag when the first skittle is pulled, along with 8 skittles of the same colour. The likelihood that the second skittle will be the same colour as the first is thus

Probability = 8/26 or 4/13.

By adding these probabilities, we obtain:

1 x 4/13 = 4/13

Therefore, the probability of pulling two Skittles of the same colour in a row is 4/13.

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The volume of the hemisphere whose radius is 6.8 ft. is 658.2 ft³ rounded to the nearest tenth

The radius of each hemisphere = 6.8 ft.

Volume of sphere = 4/3 πr³

A hemisphere is a 3D geometric object that is made up of half of a sphere, with one side being flat and the other being a bowl-like shape

So by dividing the equation in half we get

Volume of hemisphere = (4/3 πr³ )/2

Volume of hemisphere = 2/3 πr³

Putting the value of r in the equation

Volume of hemisphere = 2/3 × 3.14 × (6.8)³

Volume of hemisphere = 658.2 ft³

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Answer:

  (a)  4.2

Step-by-step explanation:

You want an estimate of √18 to one decimal place.

The squares on either side of 18 are 4² = 16 and 5² = 25. The value 18 is about (18 -16)/(25 -16) = 2/9 of the way between these numbers. So, an estimate of the square root is ...

  4 + 2/9 ≈ 4.2

__

Additional comment

A fast way to improve the estimate is to take the average of this value and the quotient of 18 and this value:

  (4.2 +18/4.2)/2 ≈ 4.2429

Compare this to the actual root of 4.2426.

Using that same method again gives a value that matches the root when rounded to 8 decimal places.

The number of dummy variables to be entered into a regression model is always equal to the number of groups (k) minus 1 because of a statistical concept known as "dummy variable trap" or "multicollinearity".

In the regression analysis we use the variable of dummy to represent a whole group and sort them into group that could be used further in the analyses. A dummy variable takes the value of 0 or 1, depending on whether the observation, belongs to a particular group or not in a data.

Let us assume that we have k groups, so we will need k-1 dummy variable to present the entire group where we create a situation when the sum of all the dummy variable is equal to 1. This creates a perfect multicollinearity, which makes the regression model impossible to estimate.

So, to avoid this problem, we eliminate one group from the model and use k-1 dummy variables to represent the remaining groups for the purpose of easiness in the analysis of the data that we are using for research.

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Completely factored expressions are:

1. x² - 7x - 18 can be factored as:

(x - 9)(x + 2)

Expand the expression using FOIL:

(x - 9)(x + 2) = x² + 2x - 9x - 18 = x² - 7x - 18

2. p² - 5p - 14 can be factored as:

(p - 7)(p + 2)

Expand the expression using FOIL:

(p - 7)(p + 2) = p² + 2p - 7p - 14 = p² - 5p - 14

3. m² - 9m + 8 can be factored as:

(m - 1)(m - 8)

Expand the expression using FOIL:

(m - 1)(m - 8) = m² - 8m - m + 8 = m² - 9m + 8

Therefore, the completely factored expressions are:

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Using Chebyshev's theorem, we can conclude that at least 56% of the gym members' ages fall between 26 and 70.

Chebyshev's theorem states that for any given dataset, regardless of its distribution, at least 1 - 1/k² of the data will fall within k standard deviations from the mean.

We can use Chebyshev's theorem to determine the percentage of gym members aged between 26 and 70. We need to determine how many standard deviations away from the mean these ages are.

To do this, we calculate the z-scores for both ages using the formula z = [tex](x - μ) / σ[/tex], where x is the value (in this case, either 26 or 70), [tex]μ[/tex] is the mean (48), and σ is the standard deviation (10). For x = 26: z = (26 - 48) / 10 = -2.2 For x = 70: z = (70 - 48) / 10 = 2.2

Both ages are 2.2 standard deviations away from the mean. Using Chebyshev's theorem, we know that at least 1 - 1/2.2² = 56% of the gym members' ages fall within this range.This is a lower bound - the actual percentage of gym members aged between 26 and 70 could be higher than 56%, as the distribution of ages may not be perfectly symmetrical or may have outliers.

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Answer:

67 miles per hour

Step-by-step explanation:

We can set up a proportion to find how many miles per hour this person travels:

268/4

=67

So, the rate is 67 miles per hour.

Hope this helps :)

— driving 268 miles in 4 hours is a total rate of 67 miles per hour

why???

268/4 = 67

The value of x as given in the above triangle is x = 12

A hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle, in geometry.

The Pythagorean theorem, states that the square of the length of the hypotenuse is the same as the sum of the squares of the lengths of the other two sides, may be utilized in the calculation the length of the hypotenuse.

Since we have a 45-45-90 triangle, so the sides opposite of the 45-degree angle are the same, while the hypotenuse is √2

6√2(√2) = 6(2) = 12

x = 12

Recall that two of the same roots will become one whole number, for example

√2(√2) = 2

√3(√3) = 3

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The percent increase in temperature when an oven changes from 350 to 362 is approximately 3.4%.

To calculate the percent increase in temperature, we need to find the difference between the initial temperature and the final temperature, divide that difference by the initial temperature, and then multiply the result by 100 to convert it to a percentage.

The difference between the initial temperature of 350 and the final temperature of 362 is

362 - 350 = 12

To find the percent increase, we divide the difference by the initial temperature

12 / 350 = 0.0342857...

Multiplying by 100, we get

0.0342857... * 100 = 3.42857...

Rounding to the nearest tenth of a percent, we get

3.4%

Therefore, the percent increase in temperature is approximately 3.4%.

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The probability of selecting two different counters that are of two different colors is 0.193

In the given question, we have a total of 20 counters, 8 are yellow and 12 are green.

The probability of choosing a 2 different colors will be;

P = 7/20 * 11/20

P = 77 / 400

P = 0.193

This is because the first probability of choosing a green is 11/20 and the second probability of choosing a yellow is 7/20. This is an example of probability without replacement

When we multiply both together to determine the probability of choosing different colors, we would have 0.193

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The statements that are true about the plant are:

The plant did grow 4. 77 cm in two weeks as shown below :

= 2. 8 cm in first week + 1. 97 cm in second week

= 2. 8 + 1. 97

= 4. 77 cm

The plant grew faster in the first week than the second as the plant grew 2.8 cm in the first week and 1.97 cm in the second week, indicating a slower growth rate in the second week compared to the first week.

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Options for this question include:

The plant has grown a total of 4.77 cm in two weeks

The plant grew at a faster rate in the first week than the second week

The plant will be 100 cm tall after 50 weeks

The plant will require at least 5 cm of water per week to continue growing

The plant will die if it doesn't receive enough sunlight each day

The percentage of students that type less than 30 words per minute are given as follows:

30.61%.

An histogram is a graph that shows the number of times each element of x was observed, or the number of observations in each range of a data-set.

For the histogram in this problem, we have that:

The total number of students is given as follows:

5 + 10 + 14 + 20 = 49.

15 students type less than 30 words per minute, hence the percentage is given as follows:

P = 15/49 x 100%

P = 30.61%.

The histogram is given by the image presented at the end of the answer.

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In the above case, the  law of joint proportionality is the one I am going to use to write the equation that stands for the above  situation:

V = k x h  x g²

Note that from the equation written:

V =  the volume of wood produced by the tree

h  = the height of the tree

g =  the circumference of the tree

k = a constant of proportionality.

For one to know the  value of k, we have to make use the data given in the problem.

Since h = 40 m

g = 1.5 m

V = 288 m³

Hence the volume of wood produced is:

288 = k   x  40 x (1.5)²

Simplifying this equation, we have:

288 = k    x  90

When we Divide both sides by 90, we have :

k = 3.2

So one can say  the equation that stands the situation is:

V = 3.2 x   h x  g²

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The domain of f^(-1)(x) is [1, infinity), and the range of f^(-1)(x) is all real numbers.

We are given that;

Function f(z) = Y² + 1.

Now,

Step 1: Replace f(z) with y

y = z^2 + 1

Step 2: Swap x and y

z = y^2 + 1

Step 3: Solve for y

y^2 = z - 1

y = sqrt(z - 1)

Step 4: Replace y with f^(-1)(x)

f^(-1)(x) = sqrt(x - 1)

This is the inverse function of f(z).

Therefore, by domain and range answer will be all real numbers, and the range of f(z) is [1, infinity).

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The surface area of the triangular pyramid is approximately 435.66 square millimeters.

The surface area of the triangular pyramid can be calculated by finding the area of the equilateral triangle base and the area of the three triangular faces, and then adding them together.

To find the area of the equilateral triangle base, we use the formula A = (√(3)/4) * a², where a is the length of one of the legs.

A = (√(3)/4) * 11.7² = 72.9444 mm²

To find the area of each triangular face, we use the formula

A = (1/2) * base * height

where the base is the side length of the equilateral triangle and the height is the slant height of the pyramid.

A = (1/2) * 11.7 * 12.3 = 71.9425 mm²

So, the surface area of the triangular pyramid is:

SA = 3A(Base) + 3A(face)

SA = 3(72.9444) + 3(71.9425)

SA = 435.6621 mm²

Therefore, the surface area of the triangular pyramid is approximately 435.66 square millimeters.

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Concave hexagon with two pairs of congruent sides is:

   /\

   /  \

  /    \

 /      \

/        \

/_____\

\        /

\      /

 \    /

  \  /

   \/

A hexagon is a six-sided polygon. A concave hexagon is a hexagon with at least one interior angle greater than 180 degrees.

We can start with a regular hexagon, which has six congruent sides and six interior angles of 120 degrees each.

We can then extend two opposite sides of the regular hexagon outwards to create two pairs of congruent sides. The extended sides should not be parallel to each other, but rather at an angle, so that the resulting hexagon is concave.

Here is an example of a concave hexagon with two pairs of congruent sides:

   /\

   /  \

  /    \

 /      \

/        \

/_____\

\        /

\      /

 \    /

  \  /

   \/

In this hexagon, sides AB and CD are congruent, and sides EF and GH are also congruent. However, the angles at vertices A and H are greater than 180 degrees, making this a concave hexagon.

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Answer:

GCF, Greatest Common Factor

Step-by-step explanation:

Hope this helped

Answer:

∠ E = 70° , ∠ F = 40° , ∠ G = 70°

Step-by-step explanation:

given EF = FG then Δ EFG is isosceles with base angles congruent, that is

∠ G = ∠ E = 5n

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

4n - 16 + 5n + 5n

14n - 16 = 180 ( add 16 to both sides )

14n = 196 ( divide both sides by 14 )

n = 14

Then

∠ E = 5n = 5(14) = 70°

∠ F = 4n - 16 = 4(14) - 16 = 56 - 16 = 40°

∠ G = 5n = 5(14) = 70°

The surface area of the given shape above would be = 47.2

To determine the surface area of the solid shape above,the surface area of a cone and a cylinder is first determined and then added together.

The formula for the surface area (SA) of cone = πrs + πr²

where;

r = 1

s = 6

S.A = 3.14×1×6 + 3.14×1×1²

= 18.84+3.14

= 21.98

Formula for Surface area of cylinder = 2πr(r+h)

where;

r = 1

h = 3

SA = 2×3.14×1 (1+3)

= 25.12

Therefore, the surface area of the solid shape = 21.98+25.22 = 47.2

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Answer:

y=41/3 and x = -14

Step-by-step explanation:

system of the linear equation :

-3y-4x=15       eq[i]

9y+7x=25      eq[ii]

multiplying eq[i] by -7 and eq[ii] by 4,we get

21y+28x= -105    eq[iii]

36y+28x= 100     eq[iv]

subtracting eq[iii] from eq[iv],we get

15y=205

y=205/15=41/3

and x= -14

Answer:

37.5 liters of water

Step-by-step explanation:

We Know

Mrs.Lim bought 25 bottles of water.

Each bottle contained 1[tex]\frac{1}{2}[/tex] liter of water.

How many liters of water did she buy altogether?

We Take

1.5 · 25 = 37.5 liters of water

So, she bought 37.5 liters of water.

The difference between the volumes of the solids is given as follows:

A. 72π.

The volume of a sphere of radius r is given by the equation presented as follows:

V = 4πr³/3.

The radius is of 6 inches, hence the volume is given as follows:

V = 4π x 6³/3

V = 288π cubic inches.

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

Both the radius and the height are of 6 inches, hence the volume is given as follows:

V = π x 6³

V = 216π cubic inches.

Then the difference of the volumes is given as follows:

π(288 - 216) = 72π.

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