A hockey coach was taking her team out to a picnic lunch to celebrate their first win. She made 15 sandwiches, 6 of which were turkey.
If ants randomly chose to nibble on 6 of the sandwiches, what is the probability that exactly 3 of the chosen sandwiches are turkey?

If the patio is as wide as the fire pit, and 5 feet long then area of backyard can be expressed as [tex]2x^{2}+16x+30[/tex].

Given that the patio is as wide as the fire pit, and 5 feet long.

We are required to form an equation which can describe the area of the backyard.

Equation is relationship between two or more variables that are expressed in equal to form. Equations of two variables look like ax+by=c. It may be linear equation, quadratic equation, cubic equation or many more depending on the powers of the variable.

If we see the figure carefully then we can find that the length of the backyard is 2x+6 and the breadth of the backyard is 5+x and backyard is in shape of rectangle.

Area of rectangle =Length *breadth

=(2x+6)*(5+x)

=30+10x+6x+2[tex]x^{2}[/tex].

Hence if the patio is as wide as the fire pit, and 5 feet long then area of backyard can be expressed as [tex]2x^{2}+16x+30[/tex].

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Answer:

Step-by-step explanation:

(1400x14.5x5%) + 1400 =2415

Answer: 14.5 months

Compute the first two derivative.

[tex]f(x) = x \sqrt{16 - x^2} = x (16 - x^2)^{1/2}[/tex]

[tex]f'(x) = x \dfrac{d}{dx} (16 - x^2)^{1/2} + (16 - x^2)^{1/2} \dfrac{d}{dx} x \\\\ ~~~~ = \dfrac x2 (16 - x^2)^{-1/2} \dfrac{d}{dx} (16-x^2) + (16 - x^2)^{1/2} \\\\ ~~~~ = \dfrac x2 (16 - x^2)^{-1/2} (-2x) + (16 - x^2)^{1/2} \\\\ ~~~~ = (16-x^2)^{-1/2} \left(-x^2 + (16 - x^2)\right) \\\\ ~~~~ = \dfrac{16 - 2x^2}{(16 - x^2)^{1/2}}[/tex]

[tex]f''(x) = \dfrac{(16-x^2)^{1/2} \frac d{dx} (16-2x^2) - (16-2x^2) \frac{d}{dx} (16-x^2)^{1/2}}{\left((16-x^2)^{1/2}\right)^2} \\\\ ~~~~ = \dfrac{(16-x^2)^{1/2} (-4x) - (8-x^2) (16 - x^2)^{-1/2} \frac{d}{dx} (16-x^2)}{16 - x^2} \\\\ ~~~~ = \dfrac{-4x (16-x^2) - (8-x^2) (-2x)}{(16 - x^2)^{3/2}} \\\\ ~~~~ = \dfrac{2x^3-48x}{(16 - x^2)^{3/2}}[/tex]

Take note of the domain of [tex]f(x)[/tex]. We must have [tex]16-x^2\ge0[/tex] for the square root to be defined, so

[tex]16 - x^2 \ge 0 \implies x^2 \le 16 \implies |x| \le 4[/tex]

and [tex]f(x)[/tex] exists only for [tex]-4 \le x \le 4[/tex].

Intercepts

Set [tex]x=0[/tex] to find the [tex]y[/tex]-intercepts. The only one is (0, 0), since

[tex]f(0) = 0 \sqrt{16-0^2} = 0[/tex]

The first intercept you listed is not a valid intercept. One or both coordinates must be 0.

Set [tex]f(x)=0[/tex] and solve for [tex]x[/tex] to find [tex]x[/tex]-intercepts. We already found (0, 0); there are two others at (-4, 0) and (4, 0).

[tex]f(x) = x \sqrt{16 - x^2} = 0 \\\\ x = 0 \text{ or } \sqrt{16 - x^2} = 0 \\\\ x = 0 \text{ or } 16 - x^2 = 0 \\\\ x = 0 \text{ or } x^2 = 16 \\\\ x = 0 \text{ or } x = \pm4[/tex]

The instructions say to list these in order from smallest to largest by [tex]x[/tex]-coordinate first, then by [tex]y[/tex]-coordinate. So the proper order of the intercepts would be (-4, 0), (0, 0), and (4, 0).

Relative minima/maxima

Find the critical points. We have [tex]f'(x) = 0[/tex] when

[tex]f'(x) = \dfrac{16 - 2x^2}{(16 - x^2)^{1/2}} = 0 \\\\ 16 - 2x^2 = 0 \\\\ x^2 = 8 \\\\ x = \pm2\sqrt2 \approx \pm 2.83[/tex]

and [tex]f'(x)[/tex] is undefined when

[tex](16 - x^2)^{1/2} = 0 \\\\ 16 - x^2 = 0 \\\\ x^2 = 16 \\\\ x = \pm4[/tex]

Check the sign of the second derivative at the first two critical points.

[tex]f''(-2\sqrt2) = 4 > 0 \implies \text{rel. min. at }  f(-2\sqrt2) = -8[/tex]

[tex]f''(2\sqrt2) = -4 < 0 \implies \text{rel. max. at } f(2\sqrt2) = 8[/tex]

For posterity, we should also check the value of [tex]f(x)[/tex] at the endpoints of the domain.

[tex]f(-4) = f(4) = 0[/tex]

So [tex]f(x)[/tex] has a relative minimum at (-2.83, -8) and a relative maximum at (2.83, 8).

Inflection points

We have [tex]f''(x) = 0[/tex] for

[tex]f''(x) = \dfrac{2x^3-48x}{(16 - x^2)^{3/2}} = 0 \\\\ 2x^3 - 48x = 0 \\\\ 2x (x^2 - 24) = 0 \\\\ 2x = 0 \text{ or } x^2 - 24 = 0 \\\\ x = 0 \text{ or } x = \pm2\sqrt6\approx\pm4.90[/tex]

The two non-zero solutions fall outside the domain, so the only inflection point is (0, 0).

Answer:x2−7x−8=0

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Step-by-step explanation:

El volumen que queda entre la esfera y el cubo es:  30.49cm^3

El volumen sobrante será simplemente la diferencia entre el volumen del cubo y el volumen de la esfera.

Para el cubo que tiene una arista de 4cm, el volumen es:

V = (4cm)^3 = 64 cm^3

Para la esfera con un diametro de 4cm, el radio es:

R = 4cm/2 = 2cm

Y el volumen será:

V' = (4/3)*3.141592654*(2cm)^3 = 33.51 cm^3

El volumen que queda entre la esfera y el cubo es:

V - V' = 64 cm^3 - 33.51 cm^3 = 30.49cm^3

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The series of fractions is 1, 2/3, 8/9, 16/27, 64/81, 128/243, 512/729, 2048/2187, 4096/6516, 16384/19683, 32768/59049, 131072/177147.

The string lengths are fractions whose numerators are powers of 2 and denominators are powers of 3, and the fractions are larger than 1/2 but smaller than 1.

Some powers of 2 are:

2⁰ = 1, 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, 2⁵ = 32, 2⁶ = 64, 2⁷ = 128, 2⁸ = 256, 2⁹ = 512, 2¹⁰ = 1024, 2¹¹ = 2048, 2¹² = 4096, 2¹³ = 8192, 2¹⁴ = 16384,  2¹⁵ = 32768, 2¹⁶ = 65536, and 2¹⁷ = 131072.

Some powers of 3 are:

3⁰ = 1, 3¹ = 3, 3² = 9, 3³ = 27, 3⁴ = 81, 3⁵ = 243, 3⁶ = 729, 3⁷ = 2187, 2⁸ = 6561, 3⁹ = 19683, 3¹⁰ = 59049, and 3¹¹ = 177147.

The fractions, for which the numerator is a power of 2, the denominator is a power of 3, and the value is between 1/2 and 1 are:

2/3, 8/9, 16/27, 64/81, 128/243, 512/729, 2048/2187, 4096/6516, 16384/19683, 32768/59049, 131072/177147.

Thus, the series of fractions is 1, 2/3, 8/9, 16/27, 64/81, 128/243, 512/729, 2048/2187, 4096/6516, 16384/19683, 32768/59049, 131072/177147.

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The identity of  sin²Ф + cos²Ф  = 1 is verified below

Trigonometry ratio can be evaluated by following the laid down rules with the the use of table and calculator

Given that tan Ф =  1/√5

Where Tan Ф = Opposite / adjacent

We can calculate the hypotenuse by using Pythagoras theorem

Hyp² = 1² + (√5)²

Hyp² = 1 + 5

Hyp = √6

sin Ф = opp / hyp

sin Ф = 1/√6

sin²Ф = 1/6

cos Ф = adj / hyp

cosФ = √5 / √6

cos²Ф = 5/6

sin²Ф + cos²Ф =  1/6 + 5/6

sin²Ф + cos²Ф  = 6/6

sin²Ф + cos²Ф  = 1

Therefore, the identity of  sin²Ф + cos²Ф  = 1 is verified.

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The probability that the person is a man or heavy smoker is 621 / 1124.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability that the respondent is a man or heavy smoker can be determined by adding the probability that the respondent is a man and the probability that the respondent is a heavy smoker together.

The probability that the person is a man or heavy smoker = (number of men / total number of respondents) + (number of heavy smokers / total number of respondents)

(531 / 1124) + (90 / 1124) = 621 / 1124

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Since L₂ is twice as long as L₁, the length of L₁ should be 12' and 6 3/4".

First of all, we would convert the value of the overall length in feet to inches as follows:

1 feet = 12 inches

37 × 8 1/4 feet = X inches

Cross-multiplying, we have:

X = 1809/4 inches.

Since L₂ is twice as long as L₁, we have:

L₂ = 2L₁

Also, the overall length is given by:

T = 2L₁ + 2L₂

T = L₂ + 2L₂

T = 3L₂

1809/4 = 3L₂

L₂ = 1809/4 × 1/3

L₂ = 1809/12

L₂ = 150.75''

L₂ = 12' and 6 3/4".

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The subsets of the set of novels is given as follows:

{Ø, {Light}, {Zami}, {Money}, {Light, Zami}, {Light, Money}, {Zami, Money}, {Light, Zami, Money}}.

Suppose we have a set with cardinality n, that is, with n elements. This set will have 2^n subsets, which are all the possible combinations with the elements of the set, including the empty set.

In this problem, the novels are given as follows:

Light, Zami, and Money.

Hence the possible subsets are given as follows:

{Ø, {Light}, {Zami}, {Money}, {Light, Zami}, {Light, Money}, {Zami, Money}, {Light, Zami, Money}}.

With is the list that is asked for this problem, which are the subsets of the set of novels.

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Answer:

[tex](17x)^{\frac{2}{4}}[/tex]

Step-by-step explanation:

There's not much work to show for this problem, but I'll explain it for you

Use the exponent rule for roots to combine the 4 and the 2 like a fraction

2 on the top and 4 on the bottom

[tex](17x)^{\frac{2}{4} }[/tex]

That's it!  Pretty easy

Good Luck!

pls mark brainliest

The quartic equation behind the graph is y = - 2 · x⁴ + 4 · x³ + 6 · x² - 8 · x - 8.

Quartic functions are fourth grade polynomials and according to the fundamental theorem of algebra, such kind of expressions have at least two real roots and at most four real roots. The graph of the picture shows a polynomial with two roots of multiplicity 2: x₁ = - 1, x₂ = 2.

y = a · (x + 1)² · (x - 2)²      (1)

Where a is the leading coefficient.

If we know that (x, y) = (0, 4), then the leading coefficient of the polynomial is:

4 = a · (0 + 1) · (0 - 2)

4 = - 2 · a

a = - 2

Then, the quartic equation is equal to:

y = - 2 · (x + 1)² · (x - 2)²

y = - 2 · (x² + 2 · x + 1) · (x² - 4 · x + 4)

y = - 2 · [(x² + 2 · x + 1) · x² + (x² + 2 · x + 1) · (- 4 · x) + (x² + 2 · x + 1) · 4]

y = - 2 · (x⁴ + 2 · x³ + x² - 4 · x³ - 8 · x² - 4 · x + 4 · x² + 8 · x + 4)

y = - 2 · (x⁴ - 2 · x³ - 3 · x² + 4 · x + 4)

y = - 2 · x⁴ + 4 · x³ + 6 · x² - 8 · x - 8

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Using proportions, the billed amount for the month of June is:

D. $42.50

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The discount will be applied only for the second half of the month, from June 16 to June 30, hence instead of a discount of 30%, it will count as a discount of 15%, meaning that 85% of the bill will be paid, hence the amount paid will be of:

A = 0.85 x $50 = $42.50.

Hence option D is correct.

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Answer: 4/7

Step-by-step explanation:

Slope = Rise/Run = (7-3)/(9-2) = 4/7

Answer:

4/7

Step-by-step explanation:

The formula to find the slope is: (change in y)/(change in x)

Or also: Rise/Run

The change in y is: 3 --> 7 which is +4

The change in x is: 2 --> 9 which is +7

So the (change in y)/(change in x) will be 4/7.

Since 4/7 cannot be simplified further, that is our final answer.

Answer:

1.

2. Additive Identity

3. Associative Property

4. Multiplication Inverse Property

5. Multiplication Property of 0

6. Commutative Property

7.

8.

Step-by-step explanation:

A: The coordinates of the point R' are (- 6, 21).

B: The coordinates of the point T' are (1, 3).

In this question we must make use of rigid transformations to find the location of new points, rigid transformations are transformations used in geometric loci such that Euclidean distance is conserved. In this case, we need to use a kind of rigid transformation known as dilation, which is defined below:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]      (1)

Where:

Part A - If we know that O(x, y) = (0, 0), R(x, y) = (- 2, 7) and k = 3, then the coordinates of point R' are:

R'(x, y) = (0, 0) + 3 · [(- 2, 7) - (0, 0)]

R'(x, y) = (- 6, 21)

Part B - If we know that O(x, y) = (- 2, 7), T(x, y) = (4, - 1) and k = 1/2, then the coordinates of point T' are:

T'(x, y) = (- 2, 7) + (1 / 2) · [(4, - 1) - (- 2, 7)]

T'(x, y) = (- 2, 7) + (1 / 2) · (6, - 8)

T'(x, y) = (- 2, 7) + (3, - 4)

T'(x, y) = (1, 3)

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It can be said that the total amount of fuel that was used by Michael when he was away to his friends was 12 gallons.

The question said that the tank was full before he left to his friends. This was after he checked the gauge of the gas tank.

The question says that the required quantity needed to fill up this tank is 24 gallon. Hence if it is full, then the total gallon it had before he made this trip was 24 gallon.

Then we are told that he went ahead to check the gauge when he finished and was at home. The quantity of fuel he had at this time was 1/2 of what was there.

This would be 1/2 * 24

12

Hence he made use of 12 gallons when he was away.

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Split up [0, 16] into 4 equally-spaced subintervals of length [tex]\frac{16-0}4=4[/tex],

[0, 16] = [0, 4] U [4, 8] U [8, 12] U [12, 16]

with midpoints 2, 6, 10, and 14, respectively.

Then with the midpoint rule, we approximate the integral to be about

[tex]\displaystyle \int_0^{16} \sin(\sqrt x) \, dx \approx 4 \left(\sin(\sqrt2) + \sin(\sqrt6) + \sin(\sqrt{10}) + \sin(\sqrt{14})\right) \approx \boxed{4.1622}[/tex]

The quartiles of the data are: 60.5,64,66

Option(b) is correct.

The quartile divides the distribution into four groups and calculates the range of values above and below the mean.

A quartile separates the dataset into four categories by dividing the data into three points: the lowest, median, and upper quartiles.

Similar to how the median divides the data in half, with 50% of the measurements falling below it and 50% falling above it, the quartile divides the data into fourths, with 25% of the measurements falling below the lower quartile, 50% falling below the median, and 75% falling below the upper quartile.

The interquartile range, a measurement of variation around the median, is calculated using quartiles.

For the given data set: 58,60,60,61,62,64,64,64,66,70,72

Median = 64

Lower quartile = Median of the lower half = 60.5

Upper quartile = Median of the upper half = 66

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Answer:

[tex]\frac{15}{49}[/tex]

Step-by-step explanation:

[tex]\frac{3}{14} /\frac{7}{10} =\frac{3}{14} *\frac{10}{7} = \frac{3}{7} *\frac{5}{7} =\frac{15}{49}[/tex]

Step-by-step explanation:

the total sale price for the magazines were

2×4.95 = $9.90

so,

100% = 9.9

1% = 100%/100 = 9.9/100 = 0.099

6.75% = 6.75×1% = 6.75×0.099 = 0.66825 ≈ $0.67

so, he paid in total

$9.90 + $0.67 = $10.57

The graph of the parabola can be seen in the image below.

We need to find some points on the parabola, and then draw a curve that connects them.

On the graph you already have the x-intercepts, so you already have two points.

Now let's get another point which is the vertex.

For our parabola:

[tex]y = -x^2 + 10x - 24[/tex]

The vertex is at:

[tex]x = -10/(2*-1) = 5[/tex]

Evaluating in x = 5 we get:

[tex]y = -5^2 + 10*5 - 24 = 1[/tex]

So we also have the point (5, 1), now we can just connect the points and get the parabola:

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The equation in term of p that models the above experience is:
2p + 10 = 0.8p + 20.

Any statement that models or captures the factors of a problem where in an equal sign is present to equate two of the factors or expressions therein is called an equation.

Total cost of baking p pizzas with brick oven = A =  p(cost of one pizza) + cost of baking = p(2) + 10 (in dollars).

Total cost of  baking p pizzas with electric oven = B =  p(cost of one pizza) + cost of baking = p(0.8) + 20 (in dollars).

B = A - 1 (as using electric oven saves $1 per day, as given)

Thus, we get:

2p + 10 = 0.8p + 20

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Answer:

20

Step-by-step explanation:

u add 13+7 and that gives you 20, so if you subtract 20 and 7 that gives you 13

Answer:

Step-by-step explanation:

You worked 16 hours and 45 minutes

5 1/2 = 5 hours and 30 minutes

6 3/4 = 6 hours and 45 minutes

4 1/2 = 4 hours and 30 minutes

Add the hour and minutes.

5 hours 30 min + 4 hours 30 min = 10 hours

10 hours + 6 hours 45 min = 16 hours and 45 minutes

The initial membership fee for Club A is; $2.5.

The initial membership fee for Club B is; $3.

Hence, Club A has a lower initial membership fee.

It follows from the concepts of linear graphs that the interpretation of the initial membership fee is the y-intercept of the graphs given.

This is so because, it corresponds to the total cost at a point when the number of movies watched is; 0. That is, before any movie is watched.

Consequently, the graph calibrations (including the missing Club A graph) allow the determination of the initial membership fee (y-intercept) as declared above.

Ultimately, Club A has a lower initial membership fee.

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Answer:

3:26 to be on time!

Step-by-step explanation:

If you leave your house at 3:26 am and then walk 34 minutes it will be 4 am

once you get to work.

a = amount invested at 5%

b = amount invested at 2%

now, we know the total invested by Mr Wilson was 20000, so whatever "a" and "b" might be, we know that a + b = 20000.

[tex]a + b = 20000\implies b = 20000-a \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{5\% of a}}{\left( \cfrac{5}{100} \right)a}\implies 0.05a~\hfill \stackrel{\textit{2\% of b}}{\left( \cfrac{2}{100} \right)a}\implies \begin{array}{llll} 0.02b\\\\ \stackrel{substituting}{0.02(20000-a)} \end{array}[/tex]

now, we know the total of earned interest is 550 bucks, so then

[tex]0.05a~~ + ~~0.02(20000-a)~~ = ~~550\implies 0.05a+400-0.02a=550 \\\\\\ 0.03a+400=550\implies 0.03a=150\implies a=\cfrac{150}{0.03}\implies a=5000 \\\\\\ ~\hspace{24em}\stackrel{20000~~ - ~~5000}{b=15000}[/tex]

We conclude that 375 portions can be sold.

We know that 500 portions have been ordered, but only 5/6 of that was delivered, so the number of delivered portions is:

p = (5/6)*500 = 416.6

Which we can round to the next whole number, 417.

Now we know that 10% of these are given to the players and staff, then the number of portions that can be sold is the 90% of 417, which is:

N = 417*(90%/100%) = 417*0.9 = 375

We conclude that 375 portions can be sold.

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