On a television game show, a contestant is given five tries to guess the winning prize behind three curtains. The prize changes after every guess. Find the expected number of correct guesses a contestant will have. Show all work to find your answerand round to three decimal places.

Answer:

Point-slope form:

\(y-4=\displaystyle\frac{1}{3}(x+4)\)

\(y-8=m(x-8)\)

Slope-intercept form:

\(y=\displaystyle\frac{1}{3}x+\displaystyle\frac{16}{3}\)

Standard form:

\(-x+3y=16\)

Step-by-step explanation:

Hi there!

1) Point-slope form

Point-slope form: \(y-y_1=m(x-x_1)\) where \((x_1,y_1)\) is a point on the line and m is the slope

First, determine the slope:

\(m=\displaystyle\frac{y_2-y_1}{x_2-x_1}\) where two points on the line are \((x_1,y_1)\) and \((x_2,y_2)\)

Plug in the points (-4,4) and (8,8):

\(m=\displaystyle\frac{8-4}{8-(-4)}\\\\m=\displaystyle\frac{8-4}{8+4}\\\\m=\displaystyle\frac{4}{12}\\\\m=\displaystyle\frac{1}{3}\)

Therefore, the slope of the line is \(\displaystyle\frac{1}{3}\). Plug this into  \(y-y_1=m(x-x_1)\):

\(y-y_1=\displaystyle\frac{1}{3}(x-x_1)\)

Now, for \((x_1,y_1)\), we can either plug in (-4,4) or (8,8):

\(y-4=\displaystyle\frac{1}{3}(x-(-4))\\\\y-4=\displaystyle\frac{1}{3}(x+4)\)

or

\(y-8=m(x-8)\)

2) Slope-intercept form

Slope-intercept form: \(y=mx+b\) where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

\(y=mx+b\)

Plug in the slope

\(y=\displaystyle\frac{1}{3}x+b\)

Now, to determine the y-intercept, plug in one of the points (-4,4) or (8,8) and solve for b:

\(8=\displaystyle\frac{1}{3}(8)+b\\\\8=\displaystyle\frac{8}{3}+b\\\\8-\displaystyle\frac{8}{3}=b\\\\b=\frac{16}{3}\)

Therefore, the y-intercept is \(\displaystyle\frac{16}{3}\). Plug this back into \(y=\displaystyle\frac{1}{3}x+b\):

\(y=\displaystyle\frac{1}{3}x+\displaystyle\frac{16}{3}\)

3) Standard form

Standard form:

\(Ax+By=C\) where A, B, and C are numbers which are typically integers

\(y=\displaystyle\frac{1}{3}x+\displaystyle\frac{16}{3}\)

Organize this into standard form:

\(-\displaystyle\frac{1}{3}x+y=\displaystyle\frac{16}{3}\)

Multiply both sides by 3 so A, B, and C are integers:

\(-x+3y=16\)

I hope this helps!

Answer:

Step-by-step explanation:

\(1\)

By calculating, If 10% of 170 is 17, then 90% of 170 is 153 is true.

What is Algebraic expression ?

Algebraic expressions are mathematical phrases that combine numbers, variables, and operations (like addition, subtraction, multiplication and division). They provide a way to represent and analyze mathematical relationships. Examples of algebraic expressions include "3x + 5" and "6y - 3x".

Given expression,

10% of 170

10/100 * 170

= 17

which is equals to RHS

Then,

90% of 170

= 90/ 100 * 170

= 9*17

= 153

which is also equals to RHS .

And the yes the given expressions are true.

Hence, If 10% of 170 is 17, then 90% of 170 is 153 is true.

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Answer:

hhjbvft

Step-by-step explanation:

jojo giving kbjvuvuvvuvugubibbibiogg

endpoint: (14, 28) coordinates of the other endpoint c.

The x-value at the midpoint lies halfway between the values at the two positions. The y-value midway between the two positions is known as the midpoint.

I start by placing the endpoint coordinate at the top and the halfway coordinate at the bottom.

(2, 10)

(6, 9)

I then calculate the difference between endpoint 1 and the midpoint.

+8 and+19

Applying that to the second coordinate's midpoint

(6 ,9)

 8 +19

endpoint: (14, 28)

you can check using the midpoint formula ( x + x / 2, y + y / 2)

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The expression for the difference of two linear functions is (f - g)(x) = 4x - 6.

A linear function is a type of function in mathematics that has the form f(x) = mx + b, where x is the independent variable, f(x) is the dependent variable, m is the slope of the line, and b is the y-intercept.

To find the expression for the difference of two linear functions, f(x) and g(x), denoted by (f - g)(x).

The expression for (f - g)(x) can be found by subtracting g(x) from f(x):

(f - g)(x) = f(x) - g(x)

Substituting the given functions f(x) = x - 2 and g(x) = -3x + 4, we get:

(f - g)(x) = f(x) - g(x)

= (x - 2) - (-3x + 4) [Substitute the given values of f(x) and g(x)]

= x - 2 + 3x - 4 [Distribute the negative sign in front of (-3x + 4)]

= 4x - 6 [Combine like terms]

Therefore, (f - g)(x) = 4x - 6.

Option D (-3x² - 2x - 8) is incorrect as it involves squaring a linear expression, which would result in a quadratic expression. Option A (which has no operation between 3 and 22) is not a valid expression. Option B (-3x - 8) and C (3x3x22 or 198) do not take into account the fact that each sundae can be made using one of 3 syrups and one of 3 candy toppings.

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Answer: the scale factor would be 2

Step-by-step explanation:

If you add all lengths for triangle ABC you can see that triangle ADE x 2 will give you the lengths for ABC

Answer: -4

Step-by-step explanation: well when it’s absolute value the -5 turns to positive 5 and the value of -9 turns to positive 9. So that leaves 5-9=-4

Answer:

hi

Step-by-step explanation:

Answer:

\(x = 9\)

Step-by-step explanation:

\(7x + 49 = 2x + 94 \\ 7x - 2x = 94 - 49 \\ 5x = 45 \\ \\ x = \frac{45}{5} \\ \\ x = 9\)

I hope I helped you^_^

The population growth of Farmville was approximately 100-141%

For the population growth of Farmville, we need to calculate the percentage increase from 1950 to 2000.

First, We find the absolute increase in population:

25,370 - 10,520 = 14,850

Next, the percentage increase:

(14,850 / 10,520) x 100 = 141%

So, the population of Farmville grew by approximately 141% from 1950 to 2000.

Alternatively, we can also use the rule of 70 to estimate the population growth.

The rule of 70 states that if a quantity grows at a constant rate, it will double in size approximately every 70 divided by the growth rate.

In this case, the population growth rate can be calculated as:

ln(25,370/10,520)/50 = 0.025

So the population of Farmville grew at a rate of approximately 2.5% per year. Using the rule of 70, we can estimate the number of years it took for the population to double:

70 / 2.5 = 28

So the population of Farmville doubled approximately every 28 years. This means that the population would have doubled once between 1950 and 2000, resulting in a growth rate of around 100%.

Therefore, both methods suggest that the population growth of Farmville was , 100-141%

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Answer:

The future value of P at interest rate r compounded n times per year for t years is ...

 FV = P(1  +r/n)^(nt)

 4000 = P(1 +.08/4)^(4·10)

 P = 4000·1.02^-40 ≈ 1811.56

$1811.56 must be deposited now in order to have $4000 in 10 years.

Step-by-step explanation:

Answer:

Each month is Y and the # of books sold is x

Step-by-step explanation:

Answer:

Step-by-step explanation:

im going with x is month and y is numbers of books sold

Answer:

A) x+5

B) 121

Step-by-step explanation:

A) If Tim is 5 pounds heavier than Amy, an equation for this situation can be modeled by x+5, where Amy is x pounds.

B) If Tim is 126 pounds, then Amy's weight is 126-5=121 pounds.

Not a function because 4 has two outputs, 3 and 4.

1) Examining that diagram we can see that

The entry 4 in the Domain has two corresponding values.

And because of that, this cannot be taken as a function, since each entry in the Domain (diagram to the left) must correspond to one and only output on the right.

2) So, examining the options the best one is

"Not a function because 4 has two outputs, 3 and 4."

The values of the trigonometric identities are;

1. tan X = 10/17

2.  tan X = 29/25

3. sin A = 24/25

4. tan C = 15/17

5. sin A = 8/17

6. cos A = 9/41

7. cos Z = 3/4

Note that fractions are the part of a whole number.

Also,

sin θ = opposite/hypotenuse

cosθ = adjacent /hypotenuse

tan θ = opposite/adjacent

1. tan X = opposite/ adjacent

tan X = 30/21 = 10/7

2. tan X = 29/25

3. sin A = opposite/hypotenuse

sin A = 24/25

4. tan C = opposite/adjacent

tan C = 30/34

tan C = 15/17

5. sin A = 16/34

sin A = 8/17

6. cos A = adjacent/hypotenuse

cos A = 9/41

7. sin A = 21/35

8. cos Z = 21/28

cos Z = 3/4

Hence, the fractions takes the function of the trigonometric identities.

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Given:

The data values are 21, 18, 37, 42, 47, 75, 66.

To find:

The range of the given data set.

Solution:

The data values are

21, 18, 37, 42, 47, 75, 66

Arrange these values in ascending order.

18, 21, 37, 42, 47, 66, 75

Now,

Range = Maximum value - Minimum value

           = 75 - 18

           = 57

Therefore, the range of given data set is 57.

Answer:

21

Step-by-step explanation:

The theorem is shown in a pythagoras theorem is c² = a² + b²

The theorem shown in the Pythagorean theorem is "a² + b² = c²". This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with discovering it.

The Pythagorean theorem applies to right-angled triangles and states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Mathematically, we can express this as:

c² = a² + b²

Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides (called the legs) of the right-angled triangle.

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It depends on the length of the festival, the length of each band's performance, and other factors. There could be any number of ways to schedule their appearances.

The number of ways to schedule the bands' appearances at the weekend festival depends on a variety of factors such as the length of the festival, the length of each individual band's performance, and the number and type of stages available.

For example, if the festival runs for two days and each band's performance is one hour, there could be a total of 22 hours of music, so eleven bands could each perform twice, once on each day.

Alternatively, if the festival has three stages and two of the stages are dedicated to different genres of music, then the bands could be scheduled to perform on those stages, with each stage hosting five bands each day.

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Answer:

0.04 is the answer

Step-by-step explanation:

that is the answer

The question seems to be written incorrectly, because m(3) = 4 and that is not an option.

If instead we wanted to find m(2) (where the function has the jump) we can see that m(2) = 2, and in this case the third option is the correct one.

Here we have the graph of a piecewise function m(x), we can see that this function has a jump at x = 2 (where you can see the jump from the line with negative slope to a line with positive slope).

We want to use this graph to find the value m(3)

Notice that x = 3 belongs in the second line, just find x = 3 in the horizontal axis and then go up until you meet the graph.

At that point move to the left until you meet the y-axis at the correspondent value of m(3).

Doing that, we can see that:

m(3) = 4

That is not an option, and I think that your teacher actually should have asked to find the value of m(2), where we have the jump.

To identify the value just need to locate which of the segments has the closed circle, that is the correct option.

With that in mind we can se that m(2) = 2, so in this case the third option is the correct.

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The domain of the function that models Salvatore's price scale is;  {x 0 < x < 8}.

The domain of a graph is defined as the set of possible input values of a function.

Now, we are told that he charges $100  for all work that is completed in less than 2 hours and also that he charges $400 for work that takes between 5 and 8 hours.

This means that the number of hours will be less than 2 but cannot be zero but it is less than or equal to 8

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The value of α for which the system has a center as its critical point is α = -3.

The given system of equations is:

x₁' = αx₁ + 2x₂

x₂' = -3x₁ + 2x₂

To find the critical points, we set the derivatives equal to zero:

αx₁ + 2x₂ = 0

-3x₁ + 2x₂ = 0

From the first equation, we can solve for x1 in terms of x₂:

x₁ = (-2x₂) / α

Substituting this expression into the second equation:

-3((-2x₂) / α) + 2x₂ = 0

(6x₂ / α) + 2x₂ = 0

Multiplying through by α:

6x₂ + 2αx₂ = 0

Factoring out x₂:

6 + 2α) x₂ = 0

For x₂ to be nonzero, the term (6 + 2α) must be zero:

6 + 2α = 0

Solving for α:

2α = -6

α = -3

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The exact value of surface area of the solid is 24 square units.Given, The intersection of the cylinders x² + z² = 4 and y² + z² = 4 in the first octant. We need to find the exact value of surface area of the solid.

As we know that x² + z² = 4 represents the circular cylinder with center at (0, 0, 0) and radius of 2 units and y² + z² = 4 represents the circular cylinder with center at (0, 0, 0) and radius of 2 units.Similarly, as it is given that solid is in first octant so x, y, and z will be positive.So, both cylinders intersect in the first octant at (0, 2, 0) and (2, 0, 0).The solid that is formed by the intersection of the two cylinders is a rectangle. Length and breadth of rectangle, both are equal to 2 units because radius of both cylinders is 2 units.

The height of the solid will be equal to the length of the axis of the cylinder. So, height of the solid is 2 units.Surface area of the solid is given as,

2 (length x height + breadth x height + length x breadth)Putting length = breadth = 2 and height = 2

Surface area of the solid is,

= 2 (2 x 2 + 2 x 2 + 2 x 2)= 2 (4 + 4 + 4)= 2 (12)= 24 sq units

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AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

What is congruent ?

Congruent refers to having the same shape and size. In mathematics, two objects are said to be congruent if they are identical in shape and size, and can be superimposed onto one another. The symbol used to represent congruence is ≅. Congruence applies to various geometric objects, such as triangles, rectangles, circles, and more. When two objects are congruent, they have all corresponding angles equal and all corresponding sides equal in length.

Step 1: Statement: \($\angle DBE = \angle EBC$\)

Reason: Given that overline BE bisects \($\angle DBC$\)

Step 2: Statement: \($\angle DBC + \angle EBC = 180^\circ$\)

Reason: Angle sum property of a straight line.

Step 3: Statement: \($\angle ABC + \angle EBC = 180^\circ$\)

Reason: Angles on a straight line sum to \(180^\circ$, and $\overline{BE} || \overline{AC}$\) implies that \(\angle ABC$ and $\angle EBC$\) are co-interior angles.

Step 4: Statement: \($\angle ABC = \angle DBC$\)

Reason: From step 2 and step 3, \($\angle ABC + \angle EBC = \angle DBC + \angle EBC = 180^\circ$\). Thus, \($\angle ABC = \angle DBC$\).

Step 5: Statement: \($\triangle ABE \cong \triangle CBE$\)

Reason: By the angle-angle-side congruence criterion, since \($\angle DBE = \angle EBC$\) (from step 1) and \($\angle ABC = \angle DBC$\) (from step 4), and \($\overline{BE}$\) is common to both triangles.

Step 6: Statement: \($AB = BC$\)

Reason: By step 5, \($\triangle ABE \cong \triangle CBE$\), so corresponding sides are congruent, including \($\overline{AB} \cong \overline{BC}$\).

Therefore, AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

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Answer:

leader of the group...

Step-by-step explanation:

lmk if there are choices I can elaborate

Answer:

(8/5) Centimeyers

Step-by-step explanation:

From 1 PM to 6 PM there is a 5 Hour difference.

Mean (total/hours) = 8/5

Answer:

1.6 cm/hour.

Step-by-step explanation:

Yes it is the unit rate.

So mean horly snowfall = total snowfall / time

= 8 / (6 - 1)

= 8/5

= 1.6 cm/hour.