Three letters are randomly chosen from the word PROBABILITY. What is the probability that one of the letters is P?

Answer:

$24.25

Step-by-step explanation:

$(17.75 + 6.5)

= $24.25

Hope this helped!

Answer:

The answer would be 100/3

Step-by-step explanation:

Answer: 33 1/3% as a fraction is 1/3. It cannot be simplified. Hope this helps!

Answer:

a = 1 ; b = - 8

Step-by-step explanation:

x² + 2x - 7 = (x² + 2x + 1) - 1 - 7 = (x + 1)² - 8

a = 1

b = - 8

Answer:

a = 1 , b = -8

Step-by-step explanation:

(x+1)^2 = x^2+2x+1

x^2+2x+1-8 = x^2+2x-7

Answer:

7x-21

Solution:

7 times x and 7 times negative 3

Answer:

[tex]\huge\boxed{\sf{7x-21}}[/tex]

Step-by-step explanation:

Hello.

The Distributive property states that

a(b+c)=ab+ac

Where

a, b, and c = variables/constants

Now, simplify the expression:

7(x-3)

Multiply x and 3 times 7 and subtract the products:

7x-21

I hope it helps & have an outstanding day.

[tex]\boxed{imperturbability}[/tex]

Answer:

x = 8 is a solution for the equation

Answer:

x^2+5x-14=0

Step-by-step explanation:

(x+7)(x-2)=0

x (x-2)+7 (x-2)=0

x^2-2x+7x-14=0

x^2+5x-14=0

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete as what is required of the question is not stated.

However, since the question is only limited to distance, a likely question could be to calculate the distance from Bayville to Colleyville.

Represent the distance from Atlanta to Colleyville with AC

Represent the distance from Atlanta to Bayville with AB

Represent the distance from Bayville to Colleyville with BC

So, we have that:

[tex]AC = 25.5\ miles[/tex]

[tex]AB = 10\frac{2}{3}\ miles[/tex]

The relationship between AB, AC and BC is:

[tex]AC = AB + BC[/tex]

Make BC the subject of formula:

[tex]BC = AC - AB[/tex]

[tex]BC = 25.5 - 10\frac{2}{3}[/tex]

Convert fraction to decimal

[tex]BC = 25.5 - 10.7[/tex]

[tex]BC = 14.8[/tex]

Hence, the distance from Bayville to Colleyville is 14.8 miles

Answer:

B) Yes

C) C = 3x + 25

Step-by-step explanation:

Given that:

Yearly charge = $25

Charge per visit = $3

The yearly cost will depend on the number of visits for the year :

B.) Cost can be represented by a linear function, as the graph it yields is a straight line graph having intercept and slope.

C.) C = mx + b

Where ;

b = intercept = yearly cost

m = slope or gradient = cost per visit

C = total cost

x = number of visits

Hence,

C = 3x + 25

Answer:

6.25 kilometers

Step-by-step explanation:

2.45km + 3.8km

= 6.25km

Answer: 6.25 Kilometers

Step-by-step explanation:

First, take 2.45 Kilometers from day one

Then take 3.8 Kilometers from day two

Now add them together for the result of

6.25 Kilometers

Answer:

$45,000 at 13% =  B-rated bond

$5,000 at 3% = CD

Step-by-step explanation:

Let us assume the x amount at 13% be 0.13x

And, y amount at 3% be 0.03x

Total interest = $6,000

The equation is

0.13x + 0.03x = $6,000 ................(1)

Now the total amount is $50,000

So

x + y = $50,000

y = $50,000 - x ................(2)

Now put the y value in the equation 1

So,

0.13x + 0.03 ($50,000 - x)  = $6,000

0.13x + $1,500 - 0.03x = $6,000

0.10x = $6,000 - $1,500

0.10x = $4,500

x = $4,500 ÷ 0.10

= $45,000 at 13%

now y value would be

= $50,000 - $45,000

= $5,000 at 3%

The rate of flow of water through a pipe is gallons per day is 3.333%.

Given that, water flows through a pipe at a rate of 4 quarts per month.

We need to express this rate of flow in gallons per day.

4 quarts will make a gallon.

Now, according to the question, 1 gallon of water flows through a pipe per month.

We know that number of days in a month is equal to 30 days.

Per day=1 gallon of water/Number of days in a month

=1/30 gallons of water.

The rate of flow in gallons per day=1/30 × 100

=3.3333%≈3.333%

Therefore, the rate of flow of water through a pipe is gallons per day is 3.333%.

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Answer: 3.971

Step-by-step explanation: first, you need to set up your addition problem. When adding decimals, you need to line up the decimal points. So you get something like this:

3.85

0.004

0.117

+————-

Then you add vertically and you get your answer of 3.971

Your welcome :)

The value of the given expression ( 3.85+0.004+0.117 ) is 3.971.

The process of increment of any number of quantities or the process of integrating small parts to make a big part is called summation.

first, you need to set up your addition problem. When adding decimals, you need to line up the decimal points. So you get something like this:

 3.850

 0.004

 0.117

+————-

3.971.

Then you add vertically and you get your answer of 3.971.

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Answer:

[tex]T_{10} = 0.05078125[/tex]

[tex]S_{18} = 51.9998016358[/tex]

Step-by-step explanation:

Given:

Sequence = 26, 13, 6.5 ....

Solving (a): The 10th term

The sequence is a geometric progression and the nth term will be solved using:

[tex]T_n = ar^{n-1}[/tex]

In this case:

[tex]n = 10[/tex]

[tex]r = \frac{T_2}{T_1}[/tex] --- Common Ratio

[tex]r = \frac{13}{26}[/tex]

[tex]r = 0.5[/tex]

[tex]a = 26[/tex] --- First term

So, [tex]T_n = ar^{n-1}[/tex] becomes

[tex]T_{10} = 26 * 0.5^{10-1}[/tex]

[tex]T_{10} = 26 * 0.5^{9}[/tex]

[tex]T_{10} = 26 * 0.001953125[/tex]

[tex]T_{10} = 0.05078125[/tex]

Solving (b): The sum of first 18 terms

This will be calculated using:

[tex]S_n = \frac{a(1 - r^n)}{1 - r}[/tex]

Substitute values for n, a and r

[tex]S_{18} = \frac{26 * (1 - 0.5^{18})}{1 - 0.5}[/tex]

[tex]S_{18} = \frac{25.9999008179}{0.5}[/tex]

[tex]S_{18} = 51.9998016358[/tex]

Hence, the sum of first 18 terms is 51.9998016358

Answer: No because BC is not perpendicular to AB.

Step-by-step explanation:

Yes, rhombus ABCD is a square as all four angles of the rhombus are right angles.

A square is a special type of rhombus where all four sides have the same length and all four angles are right angles.

In this case, we can see that all four sides of the rhombus have the same length by calculating the distance between each pair of vertices. For example, the distance between A and B is:

distance = [tex]\sqrt{[/tex] [tex]((-8 - (-1))^2[/tex] + [tex](11 - (-13))^2[/tex])

distance = [tex]\sqrt{[/tex] ([tex]7^2[/tex] + [tex]24^2[/tex])

distance = [tex]\sqrt{[/tex] (625) = 25

The distance between each other pair of vertices is also 25, so all four sides of the rhombus have the same length.

We can also see that all four angles of the rhombus are right angles by calculating the angles between each pair of adjacent sides. For example, the angle between sides AB and BC is:

angle = arctan((13 - (-13))/(-8 - (-1)))

angle = arctan(26/7)

angle = 78.6°

The angle between each other pair of adjacent sides is also 78.6°, so all four angles of the rhombus are right angles.

Therefore, rhombus ABCD is a square.

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Answer:

x=(3a+5)/(2a-b)

Step-by-step explanation:

first we distribute the a to the 2x and -3

2ax -3a=bx+5

we move the -3a over by adding 3a

2ax=bx+5+3a

then we move the bx over

2ax-bx=5+3a

we can now group the left side like this

x(2a-b)=5+3a)

to find x all we must do is divide both sides by (2a-b)

x=(3a+5)/(2a-b)

Answer:

The linear function that models the charge for hiring the technician for x hours is y=45*x + 55

Step-by-step explanation:

The linear function is defined by the equation

f(x) = mx + b or y = mx + b

where m is the slope of the line and b is the y-intercept.

In this case you want to represent a linear function that models the charge for hiring the technician for x hours, that is, y represents the charge for hiring the technician and x the number of hours.

Given the coordinates of two points (x1, y1) and (x2, y2), you can determine the equation of the line first knowing the slope m by:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

In this case, the points are:

So:

[tex]m=\frac{370-190}{7-3}[/tex]

Solving:

m=45

To obtain the value of b, once you have replaced the value of m in the equation, you must substitute the values ​​of x and y for the values ​​of the coordinates of one of the points, and solve for b to obtain its value. In this case you replace the value of point 1:

[tex]y=45*x+b[/tex]

[tex]190=45*3+b[/tex]

And you get:

190= 135 + b

190 - 135= b

55= b

So, the linear function that models the charge for hiring the technician for x hours is y=45*x + 55

We want to find a linear equation that models the charge for hiring the technician for x hours.

The correct option is D, the equation is:

y = ($45/h)*x + $55

We know that a general linear equation is written as:

y = a*x + b

where a is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope can be written as:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we have two points, one given by:

(3 hours, $190)

The other given by:

(7 hours, $370)

Then the slope is given by:

[tex]a = \frac{\$ 370 - \$ 190}{7h - 3h} = \$ 45/h[/tex]

This means that he charges $45 per hour.

Replacing that in the general equation we get:

y = ($45/h)*x + b

To find the value of b, we use the fact that he charges $190 for 3 hours, then we can solve:

$190 = ($45/h)*3h + b

$190 = $135 + b

$190 - $135 = b = $55

Then the equation is:

y = ($45/h)*x + $55

So the correct option is D.

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You can first condense the series to make it simpler to study. If n is odd, then n = 2k - 1, and if n is even, then n = 2k for some k ≥ 1. So for each k, you can pair up the k-th terms of the odd- and even-indexed series.

odd:

[tex]\dfrac1{3^{\frac{n+3}2}}=\dfrac1{3^{k+1}}[/tex]

even:

[tex]\dfrac1{3^{\frac n2}}=\dfrac1{3^k}[/tex]

So the series can be re-indexed as

[tex]\displaystyle\sum_{n=1}^\infty a_n=\sum_{k=1}^\infty a_k=\sum_{k=1}^\infty \left(\frac1{3^{k+1}}+\frac1{3^k}\right)=\sum_{k=1}^\infty\frac4{3^{k+1}}[/tex]

By the root test, the series converges, since

[tex]\displaystyle\lim_{k\to\infty}\sqrt[k]{\left|\frac4{3^{k+1}}\right|}=\frac13\lim_{k\to\infty}\left(\frac43\right)^{\frac1k}=\frac13<1[/tex]

Answer:  0.92 feet (choice B)

You're close but not quite there. To get the answer, you divide 29.44 over 32

If you had 32 feet of banner and 32 students, then each student would get 32/32 = 1 foot. Since the length of the banner is smaller than the number of students, this means each student only gets a fraction of a foot. This fraction value is fairly close to 1 because 29.44 is close to 32.

Answer:

B: 0.92

Step-by-step explanation:

Divide the banner length by the amount of students

[tex]\frac{29.44}{32}[/tex]

Answer:

2 gallons an hour

Step-by-step explanation:

This is a fraction equal to

2 gal ÷ 1 hours

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 1

2 gal

÷ 1

1 hours

÷ 1

=

2 gal

1 hour

=

2 gal

hour

= 2 gal per hour

Answer:

3/8

Step-by-step explanation:

1/4 ÷ 2/3 = 3/8

Answer: $9.25 an hour

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find the diagram attached. From the diagram, we can see that;

<USW = <TSR (vertically opposite angles)

Given

<USW = 7x-34

<TSR = 4x+29

Equate

7x-34 = 4x+29

7x-4x = 29+34

3x = 63

x = 63/3

x = 21°

Find <USW

<USW =7x-34

<USW =7(21)-34

<USW = 147-34

<USW = 113°

Hence the measure of <USW is 113°

Answer:

Percentage increase= 37.5%

Step-by-step explanation:

Giving the following information:

Sales on weekdays (Q0)= 240 units

Sales on weekends (Q1)= 330 units

To calculate the percentage increase, we need to use the following formula:

Percentage increase= [(Q1/Q0) - 1]*100

Percentage increase= [(330/240) - 1]*100

Percentage increase= 37.5%

Answer:

I'll try my best in explaining the steps.

Considering both signs are greater than and less than sign, its an open circle.

For the first equation, you would have an open circle, basically one that isn't colored in, on 8 on the number line. The arrow would be pointing to the left because the equation is telling us numbers that are less than 8.

For the second equation, you would have an open circle, basically one that isn't colored in, on -1 on the number line. The arrow would be pointing to the right because the equation is telling us numbers that are greater than -1.

Step-by-step explanation:

Answer:

Length = [tex]5\ \text{ft}[/tex]

Breadth = [tex]5\ \text{ft}[/tex]

Step-by-step explanation:

Let [tex]x[/tex] be the length of the garden

and [tex]y[/tex] be the width of the garden

From the details of the cost in the question we get

[tex]20x+2\times (10y)=200\\\Rightarrow 20x+20y=200\\\Rightarrow x+y=\dfrac{200}{20}\\\Rightarrow x+y=10\\\Rightarrow y=10-x[/tex]

Now area of the garden is

[tex]A=xy\\\Rightarrow A=x(10-x)\\\Rightarrow A=10x-x^2[/tex]

Differentiating with respect to x we get

[tex]\dfrac{dA}{dx}=10-2x[/tex]

Equating with 0

[tex]0=10-2x\\\Rightarrow x=\dfrac{-10}{-2}\\\Rightarrow x=5[/tex]

Double derivative of the area is

[tex]\dfrac{d^2A}{dx^2}=-2<0[/tex]

So, area is maximum at [tex]x=5[/tex]

[tex]y=10-x=10-5\\\Rightarrow y=5[/tex]

So, the length and breadth of the rectangle is [tex]5\ \text{ft}[/tex].

Answer:

[tex] \huge A (n) = 5 ({2})^{n - 1} \\ [/tex]

Step-by-step explanation:

The nth term of a geometric sequence is given by

[tex]A(n) = a _ 1( {r})^{n - 1} [/tex]

a1 is the first term

r is the common ratio

From the question we have the final answer as

[tex]A (n) = 5 ({2})^{n - 1} [/tex]

Hope this helps you

Answer:

a

[tex]P(X = 4 ) = 0.0677 [/tex]

b

[tex]P(X \ge 1  ) =   0.9424 [/tex]

Step-by-step explanation:

From the question we are told that

   The probability of a US household having an internet access in 2001 is  p = 0.51

   The sample size is  n = 4

Generally the distribution of the number of US household with internet access at 2001  follows a binomial distribution  

i.e  

         [tex]X  \~ \ \ \  B(n , p)[/tex]

and the probability distribution function for binomial  distribution is  

      [tex]P(X = x) =  ^{n}C_x *  p^x *  (1- p)^{n-x}[/tex]

Here C stands for combination hence we are going to be making use of the combination function in our calculators  

   Generally  the probability that all four had Internet access in 2001 is mathematically represented as

      [tex]P(X = 4 ) =  ^{4}C_4 *  (0.51)^4  (1- 0.51)^{4-4}[/tex]

=>  [tex]P(X = 4 ) = 0.0677 [/tex]

Generally  the probability that at least one of four randomly selected U.S. households had Internet access in 2001 is mathematically represented as

      [tex]P(X \ge 1  ) =  1 - P(X <  1 ) =  1-  P(X = 0 )[/tex]

=>   [tex]P(X \ge 1  ) =   1-  [^{4}C_0 *  (0.51 )^0 *  (1- 0.51 )^{4-0 } ][/tex]

=>   [tex]P(X \ge 1  ) =   1-  [1 *  1 *  (0.49 )^{4 } ][/tex]

=>   [tex]P(X \ge 1  ) =   0.9424 [/tex]

Answer:

1+5+7+10=23

hope that's what u meant?

Answer:

✔ 2/10 + 7/10

✔ 9/10

Step-by-step explanation: