Penguin or Duck?
A teacher asked a group of students,
"Which would you rather be, a penguin
or a duck?"
3 students chose penguin.
6 more students chose duck than chose penguin.
How many students would rather be a duck?

Answer:

9

Step-by-step explanation:

it is equilateral, so all angles of triangle are equal to 60. so you set the equation 7x- 3=60. You add three to both sides to get 7x=63. Then you divide both sides to get x=9. Your final answer is 9.

Answer:

solution given:

7x-3=60°[each angle of equilateral triangle is 60°]

7x=60+3

x=63/7

x=9 is a required answer.

Answer:

2(x+2)(3x-2)

Step-by-step explanation:

Hope I helped you

To divide a mixed number by a fraction, we need to convert the mixed number into an improper fraction and then multiply it by the reciprocal of the fraction.

Step 1: Convert the mixed number to an improper fraction:

7 5/6 = (6 * 7 + 5) / 6 = 47/6

Step 2: Multiply the improper fraction by the reciprocal of the fraction:

47/6 ÷ 2/3 = 47/6 * 3/2

Step 3: Simplify the fraction if possible:

47/6 * 3/2 = (47 * 3) / (6 * 2) = 141/12

Step 4: Simplify the fraction further, if necessary:

141/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:

141/12 = (141 ÷ 3) / (12 ÷ 3) = 47/4

Therefore, 7 5/6 ÷ 2/3 is equal to 47/4 or 11 3/4.

The value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the sine of angle 41°

sin 41° = 2.5/x {opposite/hypotenuse}

x = 2.5/sin 41° {cross multiplication}

x = 3.8106

Therefore, the value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.

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The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Let \(f(x) = x^2+4x+1\). If \(f^{-1}(x)\) is the inverse of \(f(x)\), then

\(f\left(f^{-1}(x)\right) = x\)

We're told that \(f(x)\) has a domain of x ≥ -2, so the above can only be valid for \(f^{-1}(x)\ge-2\).

Evaluate the left side in this equation and solve for the inverse :

\(f^{-1}(x)^2 + 4f^{-1}(x) + 1 = x \\\\ f^{-1}(x)^2 + 4f^{-1}(x) + 4 = x + 3 \\\\ \left(f^{-1}(x) + 2\right)^2 = x + 3 \\\\\sqrt{\left(f^{-1}(x)+2\right)^2} = \sqrt{x+3} \\\\ \left|f^{-1}(x) + 2\right| = \sqrt{x+3}\)

Since \(f^{-1}(x)\ge-2\), or \(f^{-1}(x)+2\ge0\), by definition of absolute value we have

\(\left|f^{-1}(x)+2\right| = f^{-1}(x)+2\)

Then it follows that

\(f^{-1}(x) + 2 = \sqrt{x+3} \implies \boxed{f^{-1}(x) = \sqrt{x+3}-2}\)

The approximate x-values for the local maximum and the local minimum are given as follows:

D) max ≈ -0.3 , min ≈ 2.3.

Hence the critical points of the graphed function are given as follows:

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Using the highest common factor, the greatest number of identical binders that the teacher can make is 18.

The highest common factor or multiple of the given numbers is the highest number that can divide them without a remainder.

We know that 2, 9, and 18 can divide 54, 36, and 72 without leaving a remainder.

We can see that the highest common factor is 18.

When we divide 54 by 18, the quotient is 3. If you divide 36 by 18, the quotient is 2.  When you divide 72 by 18, the result is 4.

The number of lined paper = 54 pieces

The number of grid paper = 36 pieces

The number of dividers = 72 dividers

The common factors of 54, 36, and 72 are 2, 9, and 18.

The highest common factor of 54, 36, and 72 is 18.

Thus, 18 binders containing 3 pieces of lined paper, 2 pieces of grid paper, and 4 dividers can be made from the collection, using their HCF.

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Answer:

1. -9/20

2.  1  7/12

3.  -4  1/3

Step-by-step explanation:

When adding and subtracting fractions with unlike denominators, you must first make them like denominators. To do this we must:

1. Find the Least Common Multiple of the denominators (which is called the Least Common Denominator).

2. Change each fraction (using equivalent fractions) to make their denominators the same as the least common denominator.

3. Then add (or subtract) the fractions, as we wish!

The easiest way to this is by multiplying the denominators. Remember that whatever you do to the bottom, you also do to the top

1. -5/4 +4/5

if we multiply 4 and 5, we get 20. Our denominator will be 20 before we simplify.

our new equation is going to be -25/20 + 16/20. Now we can add these together to get an answer of -9/20. Which is in the simplist form.

One more thing: to make a mixed number an improper fraction, you multiply the whole number by the denominator, and add the numerator.

1X4=4

4+1=5

The improper fraction is 5/4.

To make a Whole number a fraction, multiply the number by the denominator

-5x3=15

The improper is -15/3.

To go from an improper to a mixed, divide the numerator by the denominator. The remainders are going to be the fraction attached.

Answer:

C. 7°F

Step-by-step explanation:

Answer:

35.8 miles

Step-by-step explanation:

5.2+9.3+5.2+16.1=35.8

According to the population function, the population of mosquitoes in the area at any time is 400000 = 200000e⁷ⁿ

Population function:

The term population function refers the effective population served over the course of a time

Given,

The population of mosquitoes in a certain area increases at a rate proportional to the current population, and in the absence of other factors, the population doubles each week. There are 200000 mosquitoes in the area initially , and predators (birds, bats, and so forth) eat 20000 mosquitoes/day.

Now, we need to determine the population of mosquitoes in the area at any time.

Here we have given that we have two time frames in the information given; weeks and days.

Now, we need the population after predation lets choose time in days.

And we also know that the population doubles every seven days (ignoring predation) so if P(a) is the population function we have IVP

For one week, the population function of the given situation is written as

=> dP/dt = rP

Then the value of P is P(0) = 200000

And through the given question we know that,

=> P(7) = 2P(0)

While we solving the function then we get

P = Ceⁿᵃ

When we apply the values of P(0) = 200,000 then we get the value of C = 200,000

Then, the function is rewritten as

P = 200000eⁿᵃ

Now, we have to apply the value of P(7) = 2P(0), then we get,

400000 = 200000e⁷ⁿ

When we simplify it then we get,

e⁷ⁿ = 1/2

When we apply the number of days on these function, then we can get the number of mosquitoes in the city.

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Originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

Originality refers to the quality of being unique, new, and innovative. It involves creating something that has not been seen or experienced before. The best description of originality is that it is having a low probability and being unique.

An original idea, product, or work of art is something that has not been copied or imitated from others. It represents a new perspective or approach that can offer a fresh insight into a problem or challenge. Originality requires a high level of creativity, imagination, and inspiration, as well as a willingness to take risks and explore new possibilities.

Nonobviousness is also an important factor in originality. It means that the idea or invention is not something that would be obvious to someone skilled in the same field or industry. In other words, an original idea should not be something that could be easily predicted or anticipated.

Special or interesting are also characteristics of originality, but they are not sufficient to define it. An idea or product can be special or interesting without being truly original. For example, a new flavor of ice cream may be interesting, but it may not be original if it has already been created by someone else.

Convergent thinking, on the other hand, involves finding a single solution to a problem. It is the opposite of divergent thinking, which involves generating multiple ideas and possibilities. Convergent thinking is important for finding effective solutions to problems, but it is not the same as originality.

In conclusion, originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

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Answer:

Should be >A.86 cm2

Step-by-step explanation:

Good luck on your test, Have a great day!

Answer:

The answer is A) 86 cm2, hope this helps!

Answer:

S = {(3,p), (3,0), (4,q), (1,4)} is a set of ordered pairs, where the first element of each ordered pair is an integer and the second element is a variable. The set consists of four ordered pairs:

(3,p): The first element is 3 and the second element is p.

(3,0): The first element is 3 and the second element is 0.

(4,q): The first element is 4 and the second element is q.

(1,4): The first element is 1 and the second element is 4.

The requried, percentage of students who study less than 2.50 hours a day is approximately 25.14 percent.

A Z-score is stated as the fractional model of data point to the mean using standard deviations.

We need to convert 2.50 hours to a standard score (z-score) using the formula,

z = (x - μ) / σ

where x is the value we want to convert, μ is the mean, and σ is the standard deviation.

z = (2.50 - 3.00) / 0.75

z = -0.67

This means that 2.50 hours is 0.67 standard deviations below the mean.

We can use a standard normal distribution table or a calculator to find the percentage of the distribution that falls below this standard score. For example, using a standard normal distribution table, we can look up the area to the left of z = -0.67 and get:

P(z < -0.67) = 0.2514

So the correct answer is (a) 25.14 percent.

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Answer:

Step-by-step explanation: [-2.19] = -3

[3.67] = 3

[-0.83] = -1

The domain of this function is a group of real numbers that are divided into intervals such as [-5, 3), [-4, 2), [-3, 1), [-2, 0) and so on. This explains the domain and range relations of a step function.

This can be generalized as given below:

[x] = -2, -2 ≤ x < -1

[x] = -1, -1 ≤ x < 0

[x] = 0, 0 ≤ x < 1

[x] = 1, 1 ≤ x < 2

Answer:

y = - \(\frac{3}{2}\) x

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, 0) ← 2 points on the line

m = \(\frac{0-3}{0-(-2)}\) = \(\frac{-3}{0+2}\) = - \(\frac{3}{2}\) , then

y = - \(\frac{3}{2}\) x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (0, 0 )

0 = - \(\frac{3}{2}\) (0) + c = 0 + c , so

c = 0

y = - \(\frac{3}{2}\) x + 0 , that is

y = - \(\frac{3}{2}\) x

Answer:

0 = 0 means that there are infinite solutions.

Step-by-step explanation:

Equation is -5(-4+2n)=-10(n-2)

1. Distribute the -5 and -10

20 -10n = -10n + 20

2. Subtract 20 from one side to the other to get only 1 variable on 1 side.

-10n = -10n

3. divide -10 to separate the variable from the constant.

n = n

This means there are infinite solutions.

If two buildings in a sports complex are shaped and positioned like a portion of the branches of the hyperbola.

a. The distance between the two buildings at their closest point is 11.66 meters.

b. The distance d is 22.20 meters.

a. First, we need to rewrite the equation of the hyperbola in standard form:

625x² - 400y² = 250,000

x²/16 - y²/25 = 1

This gives us the center of the hyperbola at (0,0), and the vertices at (-4,0) and (4,0). The distance between the two buildings is twice the distance between the center and one of the foci.

Using the formula c = sqrt(a² + b²) where a=4 and b=5 (since 25-16 = 9, so a = sqrt(9) = 3 and b = sqrt(25) = 5), we get:

c = sqrt(3² + 5²) = sqrt(34)

Therefore, the distance between the two buildings at their closest point is 2c, or 2*sqrt(34), which is approximately 11.66 meters.

(b) To find the distance, we need to find the length of the line segment connecting the two points where the hyperbola intersects the vertical line x = -3.

Plugging x=-3 into the equation of the hyperbola, we get:

625(-3)² - 400y² = 250,000

y² = 425

Taking the positive square root and using the distance formula, we get:

d = sqrt((-3 - (-4))² + sqrt(425)²) = sqrt(2² + 5sqrt(17)²) = sqrt(29*17) = sqrt(493)

Therefore, the distance d  is sqrt(493), which is approximately 22.20 meters.

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Answer:  89 yards

Step-by-step explanation: The perimeter is all the sides added up together. Since the width of the field is 52, the two sides are 52 yards which in total is 104 yards. 282- 104 = 178 yards. The length is 178/2 yards which is 89 yards.

Answer:

75

Step-by-step explanation:

math

Answer:

\(49\pi \approx 153.94\text{ m}^2\)

Step-by-step explanation:

The area of a circle is pi multiplied by the radius squared: \(A=\pi r^2\).

The figure shows a diamater equal to 14 m, so the radius is half of that, 7 m.

\(A=\pi(7)^2=49\pi\)

A calculator gives a decimal approximation of 153.94 meters squared. (\(\pi\approx3.1415927\)

The equations are y = 30x + 13 and y = 28x + 15. And the charge less for cleaning 4 mattresses is $127 given by company B. Then the amount of money saved to clean 7 mattresses is $22.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Let 'x' be the number of mattresses and 'y' be the total cost. Then the equations are given as,

Company A: y = 30x + 13

Company B: y = 28x + 15

The amount for x = 4 is given as,

Company A: y = 30 (4) + 13 = $133

Company B: y = 28 (4) + 15 = $127

The amount for x = 4 is given as,

Company A: y = 30 (7) + 13 = $223

Company B: y = 28 (7) + 15 = $211

Then the amount of money saved is given as,

⇒ $233 - $211

⇒ $22

The amount of money saved to clean 7 mattresses is $22.

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Answer:

Below

Step-by-step explanation:

32/2 x 100% = 1600 %

Answer:

3/7 + 3/7 = 6/7

Step-by-step explanation:

The first rule of adding fractions is that never add the denominators, only the numerators. But this is only in the case that the denominators are the same(in this case, 7).

We only add the numerators:

3     3     6

-- +  --  = --

7      7     7

Notice that all the denominators are the same. The answer that is simplifies would be 6/7.

Happy learning1

--Applepi101

Answer:

\(\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}\)

This can be easily calculated by substituting the value of radius in the formula of area ~

\(Area \: = \pi \: r {}^{2} \\ \\ \implies \: \frac{22}{7} \times 8 \times 8 \\ \\ \implies \: \frac{1408}{7} \\ \\ \implies \: 201.14 \: miles {}^{2} \)

hope helpful ~

\(\huge\color{pink}\boxed{\colorbox{Black}{♔︎Answer♔︎}}\)

200.96 miles²

Step-by-step explanation:

\( \textsf{\underline{\large{To find :-}}}\)

The area of circle

\( \textsf{\underline{\large{Given :-}}}\)

radius of circle (r) = 8 miles

\( \textsf{\underline{\underline{\huge{Solution :-}}}}\)

\( \sf \blue {Area \: of \: circle = \pi {r}^{2} }\)

now we will substitute the value of r

\( \sf \implies Area = \pi {8}^{2} \\ \\ \sf \implies Area = \pi \times 8 \times 8\)

\( \sf \pi = \frac{22}{7} \: or \: 3.14 \\ \sf here \: we \: will \: use \: \pi = 3.14\)

\( \sf \implies Area = 3.14 \times 8 \times 8 \\ \\ \sf \implies { \green{ Area = 200.96 \: {miles}^{2} }}\)

The volume of the cylinder is 769.3 cubic feet and Volume of rectangular pyramid is 432 cubic meter

The cylinder has a height of 5 ft and radius of 7 ft

We have to find the volume of the cylinder

Volume of cylinder =πr²h

Plug in the value of r and h in the formula

Volume of cylinder =3.14×7²×5

=3.14×49×5

=769.3 cubic feet

Volume of rectangular pyramid is 1/3(length ×width×height)

Volume =1/3(12×12×9)

=1296/3

=432 cubic meter

Hence, the volume of the cylinder is 769.3 cubic feet and Volume of rectangular pyramid is 432 cubic meter

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