alice passes through four traffic lights on her way to work, and each light is equally likely to be green or red. independent of the others. (a) what is the pmf, the mean, and the variance of the number of red lights that alice encounters?

Answer:

slope=5/4 y intercept=-3/4

Step-by-step explanation:

put it into slope intercept form y=5/4x-3/4

pull out 5/4 as slope and -3/4 as y intercept

Answer:

B is correct: also if u add C and D together there both different and if u added B and A correctly u would have got B as your answer.

Step-by-step explanation:

There is no vertex in the graph and the transformations from the parent function are

The graph represents the given parameter

As a general rule, the maximum or the minimum of a graph is the vertex

In this case, there is no maximum or minimum in the graph

This means that that there is no vertex in the graph

Here, we have:

We can see that:

The graph is 4 units to the left of the origin and 2 units below the origin

This means that the function has been shifted down and shifted to the left

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Answer

12

Step-by-step explanation:

click on square root

click on 144

then your answer will pop out below your equation

The rectangle has its dimensions to be 8.8 units by 12.4 units

From the question, the equation is given as

2x(x + 8) = 110

This equation represents the area of the rectangle

So, we have

2x(x + 8) = 110

Divide by 2

x(x + 8) = 55

Open the brackets

This gives

x² + 8x = 55

Rewrite as

x² + 8x - 55 = 0

Using a graphing calculator, we have the solutions to be

x = -12.4 and x = 4.4

The variable x cannot be negative

So, we have

x = 4.4

In 2x(x + 8) = 110, we have

Length = 2x

Width = x + 8

So, we have

Length = 2 x 4.4

Width = 4.4 + 8

Evaluate

Length = 8.8

Width = 12.4

Hence, the dimensions of the rectangle are 8.8 units by 12.4 units

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Phil lives in a state where his tax rate does not change when his income changes. This is an example of a proportional or flat tax.

Tax is defined as the official way individuals contribute to their state revenue through the compulsory deduction of some amount of money from their monthly income.

There are two types of tax which include the following:

Proportional or flat tax: This is defined as the type of tax that is being paid by individuals from different class in the society whereby all are expected to pay tax with the same rate irrespective of the income.

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Using system of linear equation, the complementary angles (x, y) are 27 and 63 degrees respectively.

When the sum of two angles is equal to 90 degrees, they are called complementary angles. For example, 30 degrees and 60 degrees are complementary angles. However, when the sum of the two angles is equal to 180 degrees, the angles are supplementary angles

In this case, we have two angles x, y which are complimentary to one another.

We can represent this with system of equations;

solving equation (i) and (ii)

The value of x and y are 27 and 63

The complementary angles are 27 and 63

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Answer:

Total Cost = $186

Step-by-step explanation:

All but 8 means that All of them participated except for 8 of them

Since there is 39 Students in the Club

Then the Number of Students participated = 39 - 8 = 31 Students

Total Cost = (Cost per Student ) * ( Number of Students )

                 =$6 * 31 = $186

Glad to Help

Answer:

y=-3/32

Step-by-step explanation:

2-18y=11+78y

-18y-78y=11-2

-96y=9

y=-3/32

Answer:

82 rooms

Step-by-step explanation:

1459/18=81.05

so 82 rooms

Please mark as brainliest

Answer:

82

Step-by-step explanation:

1459/18

[tex]1459 \div 18[/tex]

for each cabin there 18 And there are 1459

81.05 \times 48=159

since you can't have a half a cabinet the answer is 82

The probability that the area covered by a can of spray paint is 0.251

The variable of interest is:

X: are objects that can be painted with a single can of spray paint.

This variable has a normal distribution, with a mean of 25 feet square and a standard deviation of 3 feet square.

Symbolically:

P(X≥27)

To calculate the probability, use the standard normal distribution, so first standardize the value of X using:

Z= (X-μ)/σ

P(X≥27)= P(Z≥(27-25)/3)= P(Z≥0.67)

Now, because the Z-table contains cumulative probability information:

P(Zα≤Z₀)=1-α

you must perform the following conversion to calculate the requested probability:

1 - P(Z<0.67)= 1 - 0.749= 0.251

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The plane which is parallel to the line WXT is UVZW

two segments parallel to VU is ST and WX

two segments skew to XY is UT

two segments skew to VZ is YU and TX

Lines that are always the same distance apart in a plane are said to be parallel. Lines that are parallel never cross. Lines that cross at a straight angle (90 degrees) are said to be perpendicular.

Given : The quadrilateral prism

Parallel lines means lines which does not interact and run parallel meaning they have equal distance between them.

The plane which is parallel to the line WXT is UVZW

two segments parallel to VU is ST and WX

two segments skew to XY is UT

two segments skew to VZ is YU and TX

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Answer:

0,3

Step-by-step explanation:

it between the 2 and it is negative and positive cases in the -2

By solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3

An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign =. In French, an equation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions coupled with an equals sign.

An equation is composed of two expressions joined by an equals sign (=). The expressions on the two sides of the equals sign are referred to as the equation's left-hand side and right-hand side. The right side of an equation is frequently considered to be zero.

Given,

2x+y=4

x-y=1

By solving above two equations we get,

2x+y=4

x-y=1

3x=5

x=5/3

y=-1+x

y=(5/3)-1

y=2/3

Therefore, by solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3

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The statements that are true are:

It should be noted that the two figures can be regrdedas as one that are similar in the case whereby their corresponding angles are congruent ,also their ratios of the lengths with respect to their corresponding sides would also be equal.

In conclusion, when two figures are similar then it can be concluded that their  corresponding angles are congruent .

Hence, the second and third options are correct.

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Answer:

Corresponding angles of congruent figures are the same.

The corresponding sides of congruent figures are the same.

Step-by-step explanation:

The number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.

What is permutation and combination?
A permutation is an orderly arrangement of things or numbers.
Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
The amount of two-letter words that can be created using the letters in a word, like GREAT, is an illustration of permutations: ⁵P₂ = 5!/(5-2)!
How many different ways we may write the words utilizing the vowels in the word GREAT is an example of a combination: ⁵C₂ = 5!/[2! × (5-2)!]

Given, 6 people are to be selected from a group of 10, where the bride must be in the picture.
Following the statements in question, the bride since always there assists for filling five empty spaces using 9 people.
Since five positions are to be filled by nine people, the total number of ways possible = 9 × 8 × 7 × 6 × 5 = 15120
Thus, the number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.

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The confidence interval estimate for the mean of the population at 95% is [$282.70, $317.30].

Confidence interval is defined as the range of values where a parameter might fall at a given confidence level. It can be calculated using the formula below.

CI = μ ± z x (SD / √n)

where CI = confidence interval

μ = sample mean

z = found by using a z-score table

SD = sample standard deviation

n = sample size

At 95% confidence level, the area in each tail of the standard normal curve is 2.5, and the cumulative area up to the second tail is 97.5.

(100 - 95) / 2 = 2.5

100 - 2.5 = 97.5

Find 0.975 in the z-table to get the value of z.

At p = 0.95, z = 1.96

Plug in the values and solve for the confidence interval.

CI = μ ± z x (SD / √n)

CI = 300 ± 1.96 x (45 / √26)

CI = 300 ± 17.30

CI = [$282.70, $317.30]

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Answer:

As a product of prime numbers:

420 = 2 × 2 × 3 × 5 × 7

The length of the diagonal for the given rectangular book using Pythagoras' theorem will be 5.8.

A rectangle is a geometrical figure in which opposite sides are equal.

Area of rectangle = length × width.

The angle between any two consecutive sides will be 90 degrees.

As per the given rectangle with dimensions 3 × 5.

The rectangle has been attached below,

The length of the diagonal using Pythagoras' theorem is,

x = √(3² + 5²)

x = √34 = 5.8

Hence "The length of the diagonal for the given rectangular book using Pythagoras' theorem will be 5.8".

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3Justin's estimated Vo2 max is 25.8(mL*kg*min)

What is Vo2 max ?

 The amount (volume) of oxygen used by your body while exercising as hard as you can is referred to as VO2 max. It's a common tool for determining your level of fitness. Knowing your VO2 max can assist you in training for sports, tracking fitness progress, and improving your heart health.

Here using vo2 max fomula 1.5 miles ,

=> VO2 max = 3.5+483/Time

Here Time= 11 min 25 sec = 25/60 = 0.41 min

Then time=11.42 mins. Now,

=> VO2 max = 3.5+ 483/11.41

=> VO2 max = 3.5+42.3

=>VO2 max = 25.8(mL*kg*min)

Hence His estimated Vo2 max is 25.8(mL*kg*min)

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The solutions to the equation [tex]2x^{2} +3x=-8\\[/tex] are [tex]x=\frac{-3+i\sqrt{55} }{4}[/tex] and [tex]x=\frac{-3-i\sqrt{55} }{4}[/tex] respectively.

What is a quadratic equation?

A second-degree algebraic equation is a quadratic equation in x.

[tex]ax^{2} +bx+c=0[/tex] is the quadratic equation in standard form, where a and b are the coefficients, x is the variable, and c is the constant term.

To find the root value of x, [tex]x= \frac{-b}{2a}[/tex] ± [tex]\frac{\sqrt{b^{2} -4ac} }{2a}[/tex]

Given, [tex]2x^{2} +3x=-8\\[/tex]

or, [tex]2x^{2} +3x+8=0[/tex]

Comparing the equation [tex]2x^{2} +3x+8=0[/tex] with the equation  [tex]ax^{2} +bx+c=0[/tex] , we get

[tex]a=2, b=3, c=8[/tex]

Then, [tex]x= \frac{-3}{2*2}[/tex] ± [tex]\frac{\sqrt{3^{2} -4*2*8} }{2*2}[/tex]

or,  [tex]x= \frac{-3}{4}[/tex] ± [tex]\frac{i\sqrt{55} }{4}[/tex]

Taking '+' sign, we get [tex]x=\frac{-3+i\sqrt{55} }{4}[/tex]  and [tex]x=\frac{-3-i\sqrt{55} }{4}[/tex]

Therefore, the solutions of the given equation are [tex]x=\frac{-3+i\sqrt{55} }{4}[/tex] and [tex]x=\frac{-3-i\sqrt{55} }{4}[/tex].

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The vertex of the graph is (-2, 2), the axis of symmetry of parabola is -2 and the parabola opens downwards.

In the given question we have to find the vertex, axis of symmetry and whether the parabola opens upwards and downwards.

Firstly we find ing the vertex of the graph.

As we know that vertex is the highest and lowest point of the graph.

From the graph the highest point is (-2, 2).

So the vertex of the graph is (-2, 2).

As we know that the axis of symmetry always passes through the vertex of parabola. The x coordinate of the vertex of parabola is the axis of symmetry of parabola.

So the axis of symmetry of parabola is -2.

As we can see that the parabola opens downwards.

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Answer:

See below

Step-by-step explanation:

.105    is    105   THOUSANDTHS    or   105/1000

  Divide top and bottom by '5'

    to get   21/100

He rented the pressure washer for 4 hours, given that the total bill was $86.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.

Let x = total number of hours he rented the pressure washer

The total bill, which was $86, includes the flat fee of $50 plus $9 per hour of use.

Hence, the equation will be 50 + 9x = 86.

Solve for x.

50 + 9x = 86

9x = 86 - 50

9x = 36

x = 4

total number of hours he rented the pressure washer = 4

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Answer:2/5=4/10 and 1/4=2/8

Step-by-step explanation: you can simplify 4/10 to get 2/5 and same with 2/8. You would divide the fraction by two.

Work Shown:

45 beats = 15 seconds

45/15 beats = 15/15 seconds

3 beats = 1 second

To convert to beats per minute (bpm), multiply by 60.

Using the concept of average speed we conclude that the space-mean speed of the vehicles is 0.69 km/min.

The average speed of a vehicle traveling a given segment of a highway in a specific time period is called space-mean speed, i.e.

Average mean speed = total distance traveled / average time travel

Given for vehicles are traversing a 1 km segment of highway. Hence total distance is 4km.

Average time = (1.2 + 1.5 + 1.7 + 1.4)/4

= 5.8/4

= 1.45 min

Now Average mean speed = 1/1.45

=0.689

=0.69 km/min

Hence the space-mean speed of the vehicles is 0.69 km/min

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The null hypothesis is a statement which describe the claim of 'no difference'.

Let μ be the population mean.

Given claim : The mean age of bus drivers in Chicago is 50.2 years.

i.e. μ = 50.2

Since "no difference with mean" or statements with an equal sign are used as the null hypothesis.

Then, the null hypothesis for the given situation is

Ηο : μ = 50.2

If the test fails to reject the null hypothesis, it means there is evidence to support the claim that the the mean age of bus drivers in Chicago is 50.2 years.

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided data. Using sample data, hypothesis testing is performed to evaluate a theory' veracity. It is often referred to as just "the null," and its symbol is Hο.

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The output value of g( -3 ) in the function g( a ) = 3a + 2 is -7.

A function is simply a relationship that maps one input to one output. For relation to qualify as a function,  each x-value can only have one y-value.

Given the data in the question;

To determine the output value of g( -3 ), replace all the occurrence of 'a' with -3 in the function and simplify.

g( a ) = 3a + 2

g( -3 ) = 3( -3 ) + 2

Multiply 3 and -3

g( -3 ) = -9 + 2

Add -9 and 2

g( -3 ) = -7

Therefore, the output value is -7, this forms an ordered pair of (-3,-7).

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