What is the probability that a randomly chosen contestant tried raking the ground or charmed 5 - 10 worms

To find the day when daily ticket sales will peak and the number of tickets sold on that day, we can analyze the given quadratic equation \(\displaystyle\sf N = -0.5x^{2} + 15x + 11\).

The equation is in the form of \(\displaystyle\sf y = ax^{2} + bx + c\), where \(\displaystyle\sf a = -0.5\), \(\displaystyle\sf b = 15\), and \(\displaystyle\sf c = 11\).

The peak of the quadratic function occurs at the vertex, which can be found using the formula \(\displaystyle\sf x = -\frac{b}{2a}\).

Substituting the given values:

\(\displaystyle\sf x = -\frac{15}{2(-0.5)} = -\frac{15}{-1} = 15\)

The peak day is 15 days since the concert was first announced.

To find the number of tickets sold on that day, we substitute \(\displaystyle\sf x = 15\) into the equation:

\(\displaystyle\sf N = -0.5(15)^{2} + 15(15) + 11\)

Simplifying the equation:

\(\displaystyle\sf N = -0.5(225) + 225 + 11\)

\(\displaystyle\sf N = -112.5 + 225 + 11\)

\(\displaystyle\sf N = 123.5\)

Therefore, the daily ticket sales will peak on the 15th day, and 123.5 tickets (rounded to the nearest whole number) will be sold on that day.

Answer:

The daily ticket sales will peak on day 15.

The number of tickets sold that day will be 123.

Step-by-step explanation:

To find the day when the daily ticket sales peak and the number of tickets sold on that day, we need to determine the vertex of the quadratic function representing the ticket sales.

The quadratic function given for the number of tickets sold each day is:

\(N(x) = -0.5x^2 + 15x + 11\)

The x-coordinate of the vertex of a quadratic function in the form of f(x) = ax² + bx + c can be found using the formula:

\(x = \dfrac{-b}{2a}\)

For the given equation, a = -0.5 and b = 15.

Substitute these values into the formula:

\(x = \dfrac{-15}{2(-0.5)}\)

\(x = \dfrac{-15}{-1}\)

\(x=15\)

Therefore, the x-coordinate of the vertex is x = 15.

As x is the the number of days since the concert was first announced, this means that the daily ticket sales peak is day 15.

To determine the number of tickets sold on that day, substitute the found value of x into the equation:

\(N = -0.5(15)^2 + 15(15) + 11\)

\(N = -0.5(225) + 225 + 11\)

\(N = -112.5 + 225 + 11\)

\(N = 123.5\)

Therefore, on the 15th day since the concert was first announced, the daily ticket sales will peak, and approximately 123.5 tickets will be sold on that day.

Since the number of tickets sold has to be a whole number, we can round this down to 123 tickets.

Answer:

See below

Step-by-step explanation:

\(14. \: vertex \: ( - 4, \: - 3) \\ require \: quadratic \: equation \\ {x}^{2} - ( - 4 - 3)x + ( - 4)( - 3) = 0 \\ {x}^{2} + 7x + 12 = 0 \\ \\ 15. \: vertex \: ( - 2, \: 1) \\ require \: quadratic \: equation \\ {x}^{2} - ( - 2 + 1)x + ( - 2)( 1) = 0 \\ {x}^{2} + x - 2 = 0\\ \\ 16. \: vertex \: ( 3, \: 8) \\ require \: quadratic \: equation \\ {x}^{2} - ( 3 + 8)x + (3)( 8) = 0 \\ {x}^{2} + 11x - 24 = 0\)

The element of A n B is { 7, 8}

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind.

For example, if the element of P is even numbers from 1 to 20 and element of Q is factor of 6 from 1 to 20 then we can say that set Q is a subset of set P.

The sign 'n' means intersection and this means what is common to two or more set.

If set A = { 1,2,5,7,8}

set B = { 6,7,8,9}

then we can see that 7 and 8 are common to both sides, then

A n B = { 7,8}

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The correct statements are;

The x-intercept of f(x) and the y-intercept of f–1(x) are reciprocals of each other.

The point of intersection of the two functions indicates that the functions are inverses.

Option C and D

To accurately compare a function and its inverse based on the graphs, we have to know the following;

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The amount of water that the tank will contain at 6:10 PM that day is 4174 L.

The conversion rate of a physical quantity is the method by which a unit of measurement is changed from one process to another by following a standard conversion rate and dimensional analysis.

From the information given:

The difference in the water in the tank within these two periods is:

= 22917 L - 8077 L

= 14840 L

In one minute, the amount of Liter is:

= 14840/160

= 92.75 Liter/minute

Similarly, between 6:10 pm and 5:25 pm, there are 45 minutes difference.

Therefore, the amount of water that the tank will contain at 6:10 PM that

day is;
= 45 minutes × 92.75 Liter/minute

= 4174 Liters

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Answer:

I think one of them may be C and B but I'm not sure

The difference in height of the two checkpoints is 3487 feet.

The term above mean sea level (AMSL) refers to the elevation (on the ground) or altitude (in the air) of any object, relative to the average sea level datum.

Given here: The table containing the altitude of different checkpoints in a race.

Height above mean sea level is a measure of the vertical distance (height, elevation or altitude) of a location in reference to a historic mean sea level taken as a vertical datum.

The altitude of checkpoint 1 is -164 and Checkpoint 2 as 3487

Thus Difference in the height of the two checkpoints is

3487-(-164)

3651 feet lower.

If the top of a hill rises 291 feet above checkpoint 1 we get

-164+291=127 feet

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Answer:

\(\frac{8x^{18} }{y^{2} }\)

Step-by-step explanation:

Answer:

The answer is 36

Step-by-step explanation:

First:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

92÷18

Applying the fractions formula for division,

=9×82×1

=722

Simplifying 72/2, the answer is

=36

Answer:

x = 4 is a straight, vertical line at 4 on the x axis.

The scale factor used to create the image is given as follows:

k = 1/4.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The equivalent segment lengths for the original figure and the image are given as follows:

Hence the scale factor used to create the image is given as follows:

k = 2/8

k = 1/4.

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The number of students who will be going on the trip is B. 40 students.

A mathematical expression is a rule-based set of numbers, variables, and mathematical operations performed to compute the output value.

The mathematical operations used to solve mathematical expressions include additions, subtractions, divisions, and multiplications.

The total of the weekend trip = $4,030

The cost of cleaning for the bus = $30

The cost of food and lodging per student = $60

The bus charge per student = $40

Total cost per student = $100 ($60 + $40)

The total cost, y = 4,030 - 30 - 100x

The number of students = x

x= (4,030 - 30)/100

= (4,000/100)

= 40.

Thus, the number of students who will be going on the trip is B. 40 students.

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Answer:

answer = 12

Step-by-step explanation:

Let the smallest number be x

So

X+(x+2)+(x+4)+(x+6)=60

4x+12=60

4x=48

X=12

This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.

Elimination of the parameter means to rewrite the equations in terms of only x and y. To do this, substitute t from one equation into the other equation. Here, the two equations are:x = t1/3 and y = t – 4Substitute t from the first equation into the second equation:y = (x^3) – 4Now the equation is in terms of x and y only.

This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.The rectangular equation, y = (x^3) – 4 can be plotted on a graph. It is a cubic equation. The graph will look like a curve that passes through the point (0, -4) and continues to move towards infinity. The graph will be symmetric to the origin because the equation involves an odd power of x.

If the equation involved an even power of x, the graph would be symmetric to the y-axis. The graph will never touch the x-axis or y-axis, it will only approach them.In conclusion, the rectangular equation y = (x^3) – 4 is derived from the two parameter equations, x = t1/3 and y = t – 4. The graph of this equation is a cubic curve that is symmetric to the origin. The curve passes through (0, -4) and approaches the x and y-axes but never touches them.

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Answer

Measure the shape yourself and follow the explanation.

Step-by-step explanation:

Measure each side of the Triangles with your ruler. Record it.

For example,

I measured and got 3cm, 3.5cm, 3.5cm.

Multiply by scale factor r 2.

for example, 3cm × 2 = 6cm

3.5cm × 2 = 7.0cm

3.5cm × 2 = 7.0cm

Use your pencil to draw your new numbers to form the new Triangle.

As for the second shape, measure each four sides using ruler

for example, I measured and had 4cm, 6cm, 4cm, 6m.

Multiply by scale factor r 2.

for example, 4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

Use your ruler to measure 1cm, 1.5cm, 1cm and 1.5cm, then to draw your new shape

Applying the two-tangent theorem, the length of AN is: 21 units.

The two-tangent theorem is a geometric theorem that states that if two tangents are drawn to a circle from a point outside the circle, then the lengths of the tangent segments are equal. This theorem is often used in geometry to find the length of tangent segments and to prove the existence of tangents to circles.

More formally, the two-tangent theorem states that if P is a point outside a circle with center O, and if PA and PB are tangents to the circle from point P, then PA = PB. In other words, the lengths of the two tangent segments are equal.

From the image above, AM and AN are two tangents from the same circle. Also, AN is also tangent with 29 - 2y.

This implies that the three tangents are congruent. Therefore:

6y - 3 = 29 - 2y

6y + 2y = 29 + 3

8y = 32

y = 32/8

y = 4

AN = 6y - 3

Plug in the value of y

AN = 6(4) - 3

AN = 21 units.

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The answer is D: conjecture

The key words in the description are "look for a pattern and then form an educated guess." This suggests making a hypothesis or assumption based on the observed pattern, which is the definition of a conjecture.

The other answer choices are defined as follows:

A. conjugation - the act of changing a verb to agree with its subject

B. conjunction - a connecting word

C. congruence - the state of agreeing, matching, or coinciding

D. conjecture - an opinion or conclusion formed on the basis of incomplete information

So option D, conjecture, is the best match for forming an educated guess based on an observed pattern in induction.

Step-by-step explanation:

I assume you meant :

the restaurant has 20 1/2 pounds of bananas.

one smoothie uses 1/8 pound of bananas.

how many smoothies can be made with the amount of available bananas ?

the answer is as many as the times 1/8 fit into 20 1/2.

so, we actually calculate

(20 1/2) / (1/8)

first we will convert the mixed number into a true fraction :

20 1/2 = 40/2 + 1/2 = 41/2

so we have

41/2 / 1/8

and then, when dividing fractions we have 2 choices (they do both the same, of course, but start looking differently) :

a/b / c/d = a×d / b×c

a/b / c/d = a/b × d/c = a×d / b×c

so,

41/2 / 1/8 = 41×8 / 2×1 = 41×4 = 164

they can make 164 smoothies.

Answer:

  x = 3

Step-by-step explanation:

Maybe you want the value of x such that ...

  4(6^x) = 864

Dividing by 4 gives ...

  6^x = 216

You may know that 216 = 6^3. Using that, we can equate exponents:

  6^x = 6^3

  x = 3

Alternatively, we can use logarithms to find x. Taking logs gives ...

  x·log(6) = log(216)

  x = log(216)/log(6) = 3

The translations that map to the four tiles are 1 to 2: (x,y) → (x + 2, y), 1 to 4: (x,y) → (x, y + 2), 1 to 6: (x,y) → (x + 4, y + 2) and 1 to 8: (x,y) → (x + 2, y + 4)

From the question, we have the following parameters that can be used in our computation:

The graph

From 1 to 2, we can see that the figure is shifted to the right by 2 units

This is represented as

1 to 2: (x,y) → (x + 2, y)

From 1 to 4, we can see that the figure is shifted up by 2 units

This is represented as

1 to 4: (x,y) → (x, y + 2)

From 1 to 6, we can see that the figure is shifted up by 2 units and shifted right by 4

This is represented as

1 to 6: (x,y) → (x + 4, y + 2)

From 1 to 8, we can see that the figure is shifted up by 4 units and shifted right by 2

This is represented as

1 to 8: (x,y) → (x + 2, y + 4)

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Answer:

\( (240-210) -1.984 \sqrt{\frac{8.6^2}{100}+\frac{5.7^2}{100}}=27.953\)

\( (240-210) +1.984 \sqrt{\frac{8.6^2}{100}+\frac{5.7^2}{100}}=32.047\)

And the confidence interval for the difference is between:

\( 27.953 \leq \mu_1 -\mu_2 \leq 32.047\)

Step-by-step explanation:

We have the following info given:

\( \bar X_1 = 240\) sample mean for medium Pizzas from Prim's

\( \bar X_2 = 210\) sample mean for medium Pizzas from Pizza Place

\( s_1 =8.6\) sample deviation for Prim's

\( s_2 =5.7\) sample deviation for Pizza Palca

\( n_1 =n_2 = 100\)  sample size selected for each case

The confidence interval for the difference of means is given by:

\( (\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}\)

And for the 95% confidence we need a significance level of \(\alpha=1-0.95=0.05\) and \(\alpha/2 =0.025\), the degrees of freedom are given by:

\( df= n_1 +n_2 -2= 100+100-2 =98\)

And the critical value would be

\( t_{\alpha/2}= 1.984\)

And replacing we got:

\( (240-210) -1.984 \sqrt{\frac{8.6^2}{100}+\frac{5.7^2}{100}}=27.953\)

\( (240-210) +1.984 \sqrt{\frac{8.6^2}{100}+\frac{5.7^2}{100}}=32.047\)

And the confidence interval for the difference is between:

\( 27.953 \leq \mu_1 -\mu_2 \leq 32.047\)

Answer:

E

Step-by-step explanation:

30 plus or minus 1.98 sqrt 8.6^2/100 + 5.7^2/100

Answer:

The equation of the line, in slope-intercept form, that passes through (3,-1) and has a slope = -2/3 is:

\(\mathbf{y=-\frac{2}{3}x+1}\)

Step-by-step explanation:

We need to write equation of the line, in slope-intercept form, that passes through (3,-1) and has a slope = -2/3.

The equation for slope-intercept form is: \(y=mx+b\)

where m is slope and b is y-intercept.

We are given slope m = -2/3 and we need to find y-intercept i.e b to write equation of line.

Using point (3,-1) and slope m=-2/3 we can find y-intercept i.e b

\(y=mx+b\\-1=-\frac{2}{3}(3)+b\\-1=-2+b\\b=-1+2\\b=1\)

So, y-intercept b = 1

The equation of the line, in slope-intercept form, that passes through (3,-1) and has a slope = -2/3 is:

\(y=mx+b\\\mathbf{y=-\frac{2}{3}x+1}\)

Answer:

Step-by-step explanation:

Whenever you add two number x and -x and it becomes 0 . IT is the identity property.

Ex:

-1/3 + 1/3 = 0

-1 + 1 = 0

-58 + 58 = 0

The question provides that:

Therefore, we have that:

To check if we can use the normal distribution as an approximation, we will check the values of np and nq:

Since,

then we can use the normal distribution as an approximation.

To evaluate P (at least 10), we are evaluating:

The standard deviation of the distribution is gotten to be:

The mean is 6.5.

Therefore, the Z-score is gotten to be:

Hence, it is calculated to be:

The probability is therefore given to be:

Using the Probability Distribution Table, we have:

Therefore, the answer is:

The angles are -4π/3, -2π/3, 4π/3 and 8π/3 which are  coterminal with an angle measure of 2π/3.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Angles that are coterminal with an angle measure of 2π/3 are those that can be obtained by adding or subtracting integer multiples of 2π to 2π/3.

Thus, the angles that are coterminal with 2π/3 are:

-4π/3 (subtracting 2π)

-2π/3 (subtracting π)

4π/3 (adding π)

8π/3 (adding 2π)

Hence,  the angles are -4π/3, -2π/3, 4π/3 and 8π/3 which are  coterminal with an angle measure of 2π/3.

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Answer:

mixed number: 3 9/100

improper fraction: 309/100

word form: three and nine hundredths

expanded: 3 + 0.09

Scientific or sometimes called standard in british curricula: 3.09 x 10 power 1

Answer:

(4,0)

Step-by-step explanation:

You basically are plotting a point on the positive number 4 on the x line. Since they're only asking for an X and not a Y, you'd leave it as (4,0). Hope this helps!

The value of x is 9 cm, and angle O is 0 degrees.

To solve the triangle LMN and find the values of x and angle O, we can use the Law of Cosines and the Law of Sines. Let's go step by step:

(i) To find the value of x, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we want to find side NM (x), which is opposite to angle N. The given sides and angles are:

LN = 12 cm

NK = 6 cm

KM = 8 cm

Let's denote angle N as angle C, side LN as side a, side NK as side b, and side KM as side c.

Using the Law of Cosines, we can write the equation for side NM (x):

x^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(N)

We don't know the value of angle N yet, so we need to find it using the Law of Sines.

(ii) To find angle O, we can use the Law of Sines. According to the Law of Sines, in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:

sin(A) / a = sin(B) / b = sin(C) / c

In our case, we know angle N and side NK, and we want to find angle O. Let's denote angle O as angle A and side KM as side b.

We can write the equation for angle O:

sin(O) / 8 = sin(N) / 6

Now, let's solve these equations step by step to find the values of x and angle O.

To find angle N, we can use the Law of Sines:

sin(N) / 12 = sin(180 - N - O) / x

Since we know that the angles in a triangle add up to 180 degrees, we can rewrite the equation:

sin(N) / 12 = sin(O) / x

Now, we can substitute the equation for sin(O) from the Law of Sines into the equation for sin(N):

sin(N) / 12 = (6 / 8) * sin(N) / x

Now, we can solve this equation for x:

x = (12 * 6) / 8 = 9 cm

So, the value of x is 9 cm.

To find angle O, we can substitute the value of x into the equation for sin(O) from the Law of Sines:

sin(O) / 8 = sin(N) / 6

sin(O) / 8 = sin(O) / 9

9 * sin(O) = 8 * sin(O)

sin(O) = 0

This implies that angle O is 0 degrees.

Therefore, the value of x is 9 cm, and angle O is 0 degrees.

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The figure for the given question is provided here :