Boats from all along the Atlantic coast were moored at a busy marina one summer day. Of the 16 boats at the marina, 6 were from Virginia.What is the probability that a randomly selected boat will be from Virginia?

Answer:

what's that

Step-by-step explanation:

Answer:

H = 1/30

H = 0.0333

0.033

Step-by-step explanation:

The time spent waiting at a traffic light can be considered a random variable with values from 0 seconds,

it’s green when you approach and can go on through, to 30 seconds with the following distribution shape

The entire area under the distribution curve must be 1.

Let assume the Shape is rectangle

Given

Time taken from 0s to 30s = 30s - 0s = 30s

To find height of the distribution?

Let H = the height of the distribution

Based on the above assumption;.

H * 30 = 1 --- make H the subject of formula

H = 1/30

H = 0.0333

To three decimal places is 0.033

Answer:

--------------------------------------

Vertex form of a quadratic function:

Given (h, k) = (-2, -13) and a point (0, - 5).

Substitute all into equation and solve for a:

The parabola is:

Convert it to the standard form:

Answer:

\(f(x)=2x^2+8x-5\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}\)

Given:

Substitute the given vertex and point into the Vertex formula and solve for a:

\(\implies -5=a(0-(-2))^2+(-13)\)

\(\implies -5=a(0+2)^2-13\)

\(\implies -5=4a-13\)

\(\implies 4a=8\)

\(\implies a=2\)

Substitute the given vertex and found value of a into the Vertex formula:

\(y=2(x+2)^2-13\)

The standard form of a quadratic function is  f(x) = ax² + bx + c

Expand the function in vertex form to standard form:

\(\implies y=2(x^2+4x+4)-13\)

\(\implies y=2x^2+8x+8-13\)

\(\implies y=2x^2+8x-5\)

Answer:

1.03 %

Step-by-step explanation:

The whole numbers are in millions. We can adjust it when we are done.

58 * x/100 = 60                      Multiply by 100

58*x = 60 * 100

58*x = 6000                           Divide by 58

x = 6000/58

x = 103

Now what exactly do we have. Did it increase by 103 %? Surely it couldn't.

Remember in the equation The % is divided by 100

103/100 = 1.03% And that's the answer.

Answer:

$374

Step-by-step explanation:

First you need to find how much money does the back pay per year

$200*7.25

=1450

1450/100

=14.5

Secondly you need to find how much does Catherine have in 12 years

14.5*12 years

=$174

Lastly add the money she already had 12 years ago to how much the bank payed in that 12 years

$200+$174

=$374

Using the inequality rule we know that 11 is greater than -11, (11 > -11).

Mathematical expressions with inequalities are those in which the two sides are not equal.

Contrary to equations, we compare two values in inequality.

Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Two expressions in inequality aren't always equal, which is denoted by the symbols >, <, ≤, or ≥.

So, let's say the inequality equation looks like this: A

Right now, A is valued at

Let p be used to representing the initial number.

P equals 11, so

Let q be used to representing the second number.

Q has a value of -11.

-11 and 11 are both numbers that are greater than zero.

Then, 11 > -11 ... (1)

A has a value of 11 > -11.

Therefore, using the inequality rule we know that 11 is greater than -11, (11 > -11).

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Correct question:
Is 11 greater than, equal to, or less than -11?

Answer:

y

=

m

x

+

b

.

y

=

10

x

+

23

Step-by-step explanation:

The value of x is; x = 3.14

Here, we have,

from the given diagram, we get,

there is a right angle triangle.

we have to find the value of x.

we know that,

Let the angle be θ , such that

cos θ = base / hypotenuse

here, we get,

cos 17 = 3/x

so, we have,

0.956 = 3/x

so, x = 3.14

Hence, The value of x is;x = 3.14

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Answer:

Step 1: Define your variables. You should begin with a specific research question. ...

Step 2: Write your hypothesis. ...

Step 3: Design your experimental treatments. ...

Step 4: Assign your subjects to treatment groups. ...

Step 5: Measure your dependent variable.

Step-by-step explanation:

Generally, the experimental unit is the person, animal, or object that is the subject of the experiment. Experimental units receive different treatments from one another in an experiment.

I assume the equation is

\(\dfrac6{x^2+2x-15}+\dfrac7{x+5}=\dfrac2{x-3}\)

Notice that

\(x^2+2x-15=(x+5)(x-3)\)

so to get each fraction to have a common denominator, we need to rewrite

\(\dfrac7{x+5}=\dfrac{7(x-3)}{(x+5)(x-3)}=\dfrac{7x-21}{x^2+2x-15}\)

and

\(\dfrac2{x-3}=\dfrac{2(x+5)}{(x+5)(x-3)}=\dfrac{2x+10}{x^2+2x-15}\)

So we have

\(\dfrac6{x^2+2x-15}+\dfrac{7x-21}{x^2+2x-15}=\dfrac{2x+10}{x^2+2x-15}\)

Combine the fractions and put them on one side:

\(\dfrac{6+(7x-21)-(2x+10)}{x^2+2x-15}=0\)

If x ≠ -5 and x ≠ 3, we can ignore the denominator, leaving us with

\(6+(7x-21)-(2x+10)=0\)

\((6-21-10)+(7x-2x)=0\)

\(-25+5x=0\)

\(5x=25\)

\(x=\dfrac{25}5=\boxed{5}\)

Answer:

a = 3x - 6/x

................

Answer:

its A 656 ft

Step-by-step explanation:

the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

Given: The hypotenuse of the right triangle,

c = 159 ft; angle A = 34°

We know that, in a right-angled triangle:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$\)

We know the value of the hypotenuse and angle A. Using trigonometric ratios, we can find the length of sides in the right triangle.We will use the following formulas:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$$$\tan\theta=\frac{\text{opposite}}\)

\({\text{adjacent}}$$\) Length of side a is:

\($$\begin{aligned} \sin A &=\frac{a}{c}\\ a &=c \sin A\\ &= 159\sin 34°\\ &= 91.4 \text{ ft} \end{aligned}$$Length of side b is:$$\begin{aligned} \cos A &=\frac{b}{c}\\ b &=c \cos A\\ &= 159\cos 34°\\ &= 131.5 \text{ ft} \end{aligned}$$\)

Now, we have the values of all sides of the right triangle. We can calculate the area of the triangle by using the formula for the area of a right triangle:

\($$\text{Area} = \frac{1}{2}ab$$\)

Putting the values of a and b:

\($$\begin{aligned} \text{Area} &=\frac{1}{2}ab\\ &=\frac{1}{2}(91.4)(131.5)\\ &= 6006.55 \approx 6007 \text{ sq ft}\end{aligned}$$\)

Therefore, the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

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Answer:

Answer is 29/120 I think i worked it out so if it inst right truly im sorry but i belive this is the answer.

Answer:

=  13

   24

Step-by-step explanation:

3 + 5 / 5

8    6

do the division first as per the law of operation of math requires.

5 / 5  =  5 x 1  =  1

6            6    5     6

3 +  1  =   9 + 4     =  13

8     6         24           24

Answer: x—7

Step-by-step explanation:

Answer:

√52

Step-by-step explanation:

6^2 = 36

4^2 = 16

   a.       b

√36 + √16 = c

c = √52

Step-by-step explanation:

2

\(2 \sqrt{13 } \)

The midpoint is 26.

Midpoint in this scenario = mean

(23+29)/2 = 26

Answer:

-6

Step-by-step explanation:

The perimeter of the rectangular garden is 36 feet

The length of the garden is 6 feet less than twice the width.

Let x represent the width of the garden:

w=x

Then we can multiply it by 2 and subtract 6 to determine the length:

l=2x-6

Lets sketch the garden:

The perimeter of a rectangle is the summ of all its sides, that is twice the width plus twice the length:

Replace the formula with the given value of P and the expressions for w and l:

And solve for x, first is to apply the distributive propperty of multiplications to solve the term in parentheses:

The width of the garden is 8 feet

Now calculate the length of the garden:

The length of the garden is 10 feet

Check the picture below.

\(\tan(26^o )=\cfrac{\stackrel{opposite}{x}}{\underset{adjacent}{5.7}}\implies 5.7\tan(26^o)=x\implies 2.78\approx x\)

Make sure your calculator is in Degree mode.

solution

answer: 85

Answer:

Step-by-step explanation:

p'=(1-0.39)=0.61

Answer:

-5+2

Step-by-step explanation:

Answer:

I would say 6 cm too, also can anyone help me on my math? its powers and exponents

For the given figure,   x = 23°  and      y = 129°

Parallel lines:

                        Parallel lines are lines that always stay the same distance apart and never meet.

Transversal line :

                             A transversal is a line that crosses two or more other lines.

given,

     ∠TLN = (3x - 18)°

    ∠MZQ = (5x + 14)°

    ∠NLM = y°

Now,

         ∠MZP + ∠MZQ = 180°  (Linear Pair)

        ∠MZP  = 180° - ∠MZQ  ...........(I)

again,

          ∠NLM + ∠TLN  =180°  ...........(II)      (Linear Pair)

  As,         ∠TLN = ∠MZP  (Corresponding Angle)

             (3x - 18)° =  180° - ∠MZQ  

           (3x - 18)° = 180° - (5x + 14)°

         3x + 5x  = 180° - 14° + 18°

           8x = 184°

           x = 184 / 8

          x = 23°

      From (II),

      ∠NLM + ∠TLN  =180°

    y° + 3x - 18° = 180°

 y = 180 - 3x + 18

     = 180 - 3* 23 + 18

      = 180 - 69 +18

     y = 129°

For the given figure,

                                     x = 23°  and      y = 129°

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Answer:

1.14285714286 ounces per person

Step-by-step explaination:

To find the unit rate, divide the numerator and denominator of the given rate by the denominator of the given rate

following this rule, 8 divided by 7 is 1.14285714286

Your assignment will probably ask you to simplify

Answer:

C : x=2

Step-by-step explanation:

Edge 2022

Answer:

E) 0.99

Step-by-step explanation:

100 recruits x 0.4 chance of retiring as police officer = 40 officers

probability of being married at time of retirement = (1 - 0.25) x 40 = 30 officers

each new recruit will result in either 0, 1 or 2 new pensions

mean = µ = E(Xi) = (0 x 0.6) + (1 x 0.1) + (2 x 0.3) = 0.7

σ²  = (0² x 0.6) + (1² x 0.1) + (2² x 0.3) - µ² = 0 + 0.1 + 1.2 - 0.49 = 0.81

in order for the total number of pensions (X) that the city has to provide:

the normal distribution of the pension funds = 100 new recruits x 0.7 = 70 pension funds

the standard deviation = σ = √100 x √σ² = √100 x √0.81 = 10 x 0.9 = 9

P(X ≤ 90) = P [(X - 70)/9] ≤ [(90 - 70)/9] =  P [(X - 70)/9] ≤ 2.22

z value for 2.22 = 0.9868 ≈ 0.99

9514 1404 393

Answer:

  2.5 cm

Step-by-step explanation:

The diameter of the circle is shown as 5 cm. The reminder tells you that the radius is half the diameter:

  radius = diameter/2

  radius = (5 cm)/2

  radius = 2.5 cm

1. Number of athletes did not own any of the three items = 259 - 228

= 31.

2. Number of athletes own a convertible and a TV but not a store = 44 - 9

= 35.

3. Number of athletes own a convertible or a TV = 110 + 91 - 44

= 157.

4. Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

5. Number of athletes owned at least one type of item = 259 - 31

= 228

6. Number of athletes own a TV or a store, but not a convertible = 13 + 34 +71

= 118.

The number of athletes did not own any of the three items need to subtract the number of athletes who own at least one item from the total number of athletes surveyed.

Total number of athletes surveyed = 259

Number of athletes own at least one item = 110 + 91 + 120 - 15 - 43 - 44 + 9 = 228

Number of athletes who did not own any of the three items = 259 - 228 = 31.

The number of athletes who owned a convertible and a TV but not a store need to subtract the number of athletes who own all three items from the number of athletes who own a convertible and a TV.

Number of athletes who own a convertible and a TV = 44

Number of athletes who own all three items = 9

Number of athletes who own a convertible and a TV but not a store = 44 - 9 = 35

The number of athletes who owned a convertible, or a TV need to add the number of athletes who own a convertible to the number of athletes who own a TV and then subtract the number of athletes own both a convertible and a TV.

Number of athletes who own a convertible or a TV = 110 + 91 - 44

= 157.

The number of athletes owned exactly one type of item need to add up the number of athletes who own a convertible only the number of athletes own a TV only and the number of athletes who own a store only.

Number of athletes own a convertible only = 110 - 15 - 9 = 86

Number of athletes own a TV only = 91 - 44 - 9 = 38

Number of athletes own a store only = 120 - 15 - 43 - 9 = 53

Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

The number of athletes who owned at least one type of item can use the result from part (1).

Number of athletes who owned at least one type of item = 259 - 31

= 228

The number of athletes who owned a TV or a store but not a convertible need to subtract the number of athletes who own all three items, and the number of athletes own a convertible and a TV from the number of athletes own a TV or a store.

Number of athletes own a TV or a store = 91 + 120 - 43 - 9 = 159

Number of athletes own a TV or a store not a convertible = 13 + 34 +71

= 118.

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