1) suppose the state space (i.e., a set of possible locations for the robot) consists of all possible positions (x, y) in the plane. how many possible states are there? how many paths are there to the goal? provide assumptions for your answer

Answer: 67

Step-by-step explanation:

do the math

The probability that fewer than 60 out of a random sample of 500 adults will work from home is 0.03

In the given probability case we have;

What is the likelihood that, out of a random sample of 500 persons, fewer than 60 will work from home if 15% of adults in a particular country do so?

Let,

P = 15% = 0.15

n = 500

By considering the binomial distribution case the formula is given by

P( X = x ) = ⁿCₓ * Pˣ * (1 - P)ⁿ⁻ˣ

P( X ≤ 60 ) = ⁿCₓ * Pˣ * (1 - P)ⁿ⁻ˣ

                 = ⁶⁰∑ₓ=₀ (⁵⁰⁰Cₓ) (0.15)ˣ (1 - 0.15)⁵⁰⁰⁻ˣ

                 = 0.031

                 ≅ 0.03

Hence, the probability that fewer than 60 out of a random sample of 500 adults will work from home is 0.03

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Slope:

The slope is found with m = (y2 - y1) / (x2 - x1).

You can use any two points, so I'd pick ones with positive x and y values.

Using (1,5) and (3,3):

    m = (3 - 5) / (3 - 1) = (-2)/(2) = -1

The slope is -1.

To find the y-intercept, we can go to the point (-1,7) and use the slope of -1.  A slope of -1 means that if x goes up by 1, then then y goes down by 1.  So if we go from x=-1 to x=0, then the y-value of 7 will go down by 1.

y-intercept (0,6)

The equation in slope-intercept form is y = -x + 6, since we already found the slope and y-intercept.

The volume of the composite solid is 340.4 cubic inches

The composite solid is made up of two parts one has

The volume for the uniform height  

= base area * height

base area = 0.5 base * height = 0.5 * 8 * 6.9 = 27.6

= 27.6 * 10

= 276 cubic inches

The volume for the varying height

= 1/3 base area * height

base area = 27.6 (both share same base)

= 1/3 * 27.6 * 7

= 64.4 cubic inches

The total volume

= 276 + 64.4

= 340.4 cubic inches

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Step-by-step explanation:

the slow of a line is the factor of x in a "y = ..." firm of equation.

the line going through (1, 5) has a slope of 3 (when x increases by +1, then y increases by +3, so the slope y/x = 3).

(B) and (C) are out, because there is no line with slope 3 (only -3).

the line going through (-2, 9) has a slope of -2 (when x increases by 1, y decreases by 2, so the slope y/x = -2/1 = -2).

(A) is out, as there is no line with the slope -2 (only +2).

so, (D) is the correct answer.

The probability that the sum of the dice is 9 is, 4/33.

What is dice?

Dice are little, thrown-away devices with marked sides that can rest in various locations. They are frequently employed in tabletop games including dice games, board games, role-playing games, and games of chance to provide random values.

Let two fair dice are rolled.

So the possible number of outcomes are,

(1, 1)  (1, 2)  (1, 3)  (1, 4)  (1, 5)  (1, 6)

(2, 1)  (2, 2)  (2, 3)  (2, 4)  (2, 5)  (2, 6)

(3, 1)  (3, 2)  (3, 3)  (3, 4)  (3, 5)  (3, 6)

(4, 1)  (4, 2)  (4, 3)  (4, 4)  (4, 5)  (4,6)

(5, 1)  (5, 2)  (5, 3)  (5, 4)  (5, 5)  (5, 6)

(6, 1)  (6, 2)  (6, 3)  (6, 4)  (6, 5)  (6, 6)

There are total 36 outcomes.

There are 33 outcomes with sum greater than 3.

The outcomes with sum greater than 9 are, 4 which are (3, 6), (4, 5), (5, 4) and (6, 3).

Hence, the probability that the sum of the dice is 9 is, 4/33.

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The total number of completions Trevor  be expected to make is 25.

For the given question.

Let the number of completion by Trevor be 'x'.

Trevor completes 5 out of 8 passes.

Total passes are 40

Then, proportions set up is-

5/8 = x/40

x = 25

Thus, the total number of completions Trevor be expected to make is 25.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The function shown in the graph above is a discontinuous function, at x = -2

For values of x less than -2, the left side of the graph is applicable. whose equation is :

[tex]\qquad \sf  \dashrightarrow \: y - 0 = \cfrac{1 - 0}{ - 3 - ( - 2)} (x - ( - 2))[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = \cfrac{1}{ - 3 + 2} (x + 2)[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = - 1(x + 2)[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = - x - 2 \:\: ; \:\:x<-2[/tex]

For values of x greater than -2, the right side of the graph is applicable. whose equation is :

[tex]\qquad \sf  \dashrightarrow \: y - 4= \cfrac{4 - 2 }{0 - (-2)} (x -0)[/tex]

[tex]\qquad \sf  \dashrightarrow \: y - 4 = \cfrac{2}{2} (x)[/tex]

[tex]\qquad \sf  \dashrightarrow \: y - 4 = x[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = x + 4 \: \: ;\: \: x > - 2[/tex]

So, the correct choice will be Option " A "

Answer:

[tex]\textsf{A.} \quad \begin{cases}-x -2 \quad \text{if}\;x < -2\\x + 4 \quad \;\;\;\text{if}\;x \geq -2\end{cases}[/tex]

Step-by-step explanation:

When graphing piece-wise functions:

From inspection of the given graph:

Therefore, the definition of the function is:

[tex]\begin{cases}-x + a \quad \text{if}\;x < -2\\x + 4 \quad \;\;\;\text{if}\;x \geq -2\end{cases}[/tex]

where a is some constant.

The only answer option that matches the given parameters is option A.

Answer:

57

Step-by-step explanation:

Straight line is 180 degrees

x+2x+9=180

3x=171

x=171/3

x=57

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Answer: 27 dogs

Step-by-step explanation: 2 cats + 3 dogs= 5 in total for animals. 2/5x45=18 cats

3/5x45= 27 dogs

27+18=45 animals

There is 27 dogs in the shelter

The equation can be given as X+20 = 60

Wyatt needs to save $40 to buy the new game.

What is an equation?

An equation is an expression which has an equality symbol in it.

We are given that, Wyatt is saving up money for a new game. It costs $60,

including tax.

He has already saved $20. At least how much more money, X, does he need to save

Hence the equation can be given as

X + 20 = 60

On solving the equation X = 40

Hence Wyatt needs to save $40 to buy the new game

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The slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is: [tex]y = \frac{5}{8} x + \frac{1}{8}[/tex]

Calculation

from ( - 3, 2) and (5, 7)

slope(m)  = [tex]\frac{y_{2}- y_{1} }{x_{2}- x_{1} }[/tex]

[tex]=\frac{7 - 2}{5 - (-3)}[/tex]

[tex]= \frac{5}{8}[/tex]

from slope-intercept equation

⇒y = mx+ c

⇒( - 3, 2) , [tex]2 = \frac{5}{8} * (-3) + b[/tex]

⇒[tex]2 = \frac{15}{8} + b[/tex]

⇒[tex]2 - \frac{15}{8} = b[/tex]

⇒[tex]\frac{16+15}{8} = b[/tex]

⇒[tex]\frac{31}{8} = b[/tex]

Therefore, the slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is :

⇒[tex]y = \frac{5}{8} x +\frac{31}{8}[/tex]

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The slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is:

One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line.

When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis).

The equation of a line is the equation that each point on the line fulfills. There are several ways to solve the straight line equation given as,

Slope-intercept form

Point slope form

Two-point form

Intercept form

from ( - 3, 2) and (5, 7)

slope(m)  = y²-[tex]y^{1}[/tex]/x²-[tex]x^{1}[/tex]

=7-(-2)/5-(-3)

=5/8

from slope-intercept equation

⇒y = mx+ c

⇒( - 3, 2) , 2=5/8*(-3)+b

⇒2=15/8+b

⇒2-15/8=b

⇒16+15/8

31/8=b

Therefore, the slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is :

⇒y=5/8x +31/8

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A graph of the given equation (x - y = 6) is shown in the image attached below.

In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.

Next, we would rewrite the given equation in standard form as follows:

x - y = 6

Adding y to both sides of the equation, we have the following:

x - y + y = 6 + y

x = 6 + y

Rearranging the equation, we have the following:

y = x - 6

By critically observing the graph (see attachment), the y-intercept is equal to -6 and the x-intercept is equal to 6.

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The factor of the expression 27 + 33 is 3.

What is meaning of factor?

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

Factors can be found using either division or multiplication. Rules of divisibility can also be applied.

What meaning of expression?

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

Given expression is 27 + 33

The factors of 27 are 1, 3, 9, 27.

The factors of 33 are 1, 3, 11, 33.

The common factor of 27 and 33 is 3.

Taking common 3 from the given expression:

27 + 33 = 3 (9 + 11)

The factor of the given expression is 3.

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Last year, Maria earned $54,000

In this question, we have been given  Maria earns a $50,000 salary plus a 10% commission on any sales over $20,000.

Last year Maria made $40,000 in sales.

This means, she got 10% commission

We find the 10 percent of 40000.

40000 * (10/100) = 4000

Her total earning would be,

$50,000 + $4000(commission) = $54,000

Therefore, Maria earned $54,000

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The p-value is higher than 0.05, so we are unable to rule out the null hypothesis. There is little proof to back up the director's claim.

Hypothesis:

H₀ : μ = 3000

H₁ : μ > 3000

The t-test should be employed when the population mean and standard deviation are unknown. Since the sample size is high, we can infer that the sample mean's sampling distribution is normal.

The following information is provided:

s = 450

x = 3200

n = 14

Therefore, test statistics will be:

t = (x - μ) / (s / √n) = (3200 - 3000) / (250 / √14) = 1.66

The test in this instance is right-tailed, and its degree of freedom is df=n-1=14-1=13.

0.0601 is the p-value.

We are unable to reject the null hypothesis since the p-value is higher than 0.05. The director's allegation is not supported by a lot of evidence.

Since p =.0601, the director's assertion cannot be supported by the available data.

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Using the concept of application of derivative it is concluded that the rate of change in the area of square tile is 94.25 cm²/hour.

The area of the square is defined as the square of its sides.

Let the side of the square is a then its area will be a².

Area of square figure = Side².

Let the side of the square is x= 29cm.

It is given that the side 29 cm tile is growing by 1.625 cm per hour on heating.

And the rate of change in side of square dx/dt = 1.625 cm/hour

We have to calculate the rate of change in an area of the square (A).

hen, area A = x²

On differentiating A with respect to time(t) we get a rate of change in area

dA/dt = d(x²)/dt

= 2x dx/dt

= 2×29×1.625

= 94.25 cm²/hour

Hence, the rate of change in the area of the square tile is 94.25 cm²/hour.

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Answer:

Step-by-step explanation:

Find x:-

[tex]\sf 11x-9+72+6x-2=180[/tex]

[tex]\sf 17x+61=180[/tex]

[tex]\sf 17x=119[/tex]

[tex]\sf x=7[/tex]

Find y:-

[tex]\sf 30+11(7)-9+5y-8=180[/tex]

[tex]\sf 5y+90=180[/tex]

[tex]\sf 5y=90[/tex]

[tex]\sf y=18[/tex]

So, therefore, x = 7° & y = 18°!!

____________________

Hope this helps!

Have a great day! :)

The locations of the destinations given by the angles formed between parallel lines and their common transversal in the question are;

1) US Capitol

2) CIA Building

3) US Capitol

4) US Treasury

5) Walmart

The relationship between the angles formed are;

1) The location that is at a corresponding angle to the White House is the Supreme Court

The location at the vertical angle to the Supreme Court is the Smithsonian Institute

The location that is at the angle right adjacent to the Smithsonian Institute is the US Capitol

2) The location that is vertical angles to the FBI Building is the National Zoo

The same side interior angle to the National Zoo is the National Coffee shop

The location at the alternate interior angle to the National Coffee Shop is the CIA Building

3) The location at the alternate exterior angles to Lincoln Memorial is Walmart

The adjacent location that is a right angle to Walmart is the White House Gardens

The location that is at the corresponding angle to the White House Gardens is the US Capitol

4) The location that is at the corresponding angle location to the Smithsonian Institute is the National Zoo Gift Shop

The location that is at the same side interior angle to the national gift shop is the US Capitol

The location that is at the vertical angle location to the US Capitol is the US Treasury

5) The location that is at alternate interior angle location to the Ford's theater is the US Capitol.

The location that is supplementary with the Vietnam War Memorial and the National Zoo is the National Coffee Shop

The location at the angle that is vertical from the National Coffee Shop is the Lincoln  Memorial

The location that is at alternate exterior angle with the Lincoln Memorial is Walmart

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Answer:

357 national parks

Step-by-step explanation:

420x85/100

420x17/20

21x17=

357

ANSWER: 137

Step-by-step explanation:

This can be rewritten as:

18 × 7 - (-1)² -(-9)

Using BODMAS

firstly open the brackets using the negative sign, we have;

18 × 7 +1² + 9

Now you can apply your BODMAS.

126 + 1 + 9

ANS = 137

The value of x in 3² × [tex]3^{x}[/tex] = 3² is 0.

According to the question,

We have the following information:

3² × [tex]3^{x}[/tex] = 3²

We know that when two numbers with the same base are in multiplication then the powers of the numbers are added. So, in this case, 2 will be added to x. And this expression of addition will be equal to the powers of the number on the right hand side.

Now, we have the following expression:

2+x = 2

x = 2-2

x = 0

Hence, the value of x in 3² × [tex]3^{x}[/tex] = 3² is 0.

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The height of the poster is 20 inches.

The original width of the poster was 6 inches. The original height of the poster was 4 inches. The size of the poster is scaled up. This is a transformation of the size of the poster. The width of the scaled-up poster is 30 inches. We need to find out the height of the scaled-up poster.

The scaling transformation preserves the shape of the object. This means the sides must still be in the same proportion. Let the constant of proportionality be represented by the variable "k".

30 = k*6

k = 30/6

k = 5

Hence, the poster is scaled up by a factor of five.

H = k*4

H = 5*4

H = 20

Hence, the height of the scaled-up poster is 20 inches.

The complete question is given below.

Amir wants to scale up a photo to create a poster for his room. The original picture is 6 inches in width and 4 inches in height. What will be the height of the poster if its width is 30 inches?

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A) The matrix equation that represents the given information is;

[tex]\left[\begin{array}{ccc}5&14\\8&9\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right] = \left[\begin{array}{ccc}1.30&\\1.41\\\end{array}\right][/tex]

B) The cost of a banana is; $0.05

The cost of an orange is; $0.12

A matrix equation is defined as an equation where a variable stands for a matrix .

Let x represent cost of oranges

Let y represent cost of bananas

5 oranges and 14 bananas cost me $1.30 and 8 oranges and 9 bananas

cost me $1.41. Thus, the equations are;

5x + 14y = 1.30  ----(1)

8x + 9y = 1.41   -----(2)

A) Now, the matrix form of the simultaneous equation above will be;

[tex]\left[\begin{array}{ccc}5&14\\8&9\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right] = \left[\begin{array}{ccc}1.30&\\1.41\\\end{array}\right][/tex]

B) Multiply the first equation by 8 and the second one by 5 to get;

40x + 112y = 10.4

40x +   45y = 7.05   Subtract to get;

            67y = 3.35

Divide both sides by 67 to get;

y = $0.05 per banana

Plug in 0.05 for y into eq 1 to get;

5x + 14(0.05) = 1.30

5x + 0.7 = 1.3

5x = 1.3 - 0.7

5x = 0.6

x = 0.6/5

x = $0.12

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The angle which corresponds with angle 2 given that; lines m and n are parallel and are intersected by transversal p is; angle 6.

Corresponding angles by definition are any pair of angles each of which happens to be on the same side of one of two lines cut by a transversal and also on the same side of the transversal.

Therefore, it follows from the definition above that the angle which is corresponding to Angle 2 as required in the task content is; angle 6.

This follows from the fact that angles 2 and 6; each happens to be on the same side of one of two lines cut by a transversal and also on the same side of the transversal.

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Answer:

The coefficient is 7 and the term that has it.

The speed at which raina can swim if there is no current is 3 km/hor 3 kilometers per hour.

Given that,

In the same length of time it took raina to swim kilometers with the river, she was able to swim 8 kilometers against it. The current flowed at a kilometer per hour rate.

Distance 1 * (Raina's velocity - current velocity) = Distance2 * (Raina's velocity + current velocity)

16 * (Raina's velocity - 1) = 8 * (Ivan's velocity + 1)

(16 * Raina's velocity) - 16 = (8 * Ivan's velocity) +8

8 * Raina's velocity = 24

Raina's velocity = 3 kilometers per hour

As a result, Raina can swim at a speed of 3 km/hr in the absence of a current.

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