Assume that the weight loss for the first month of a diet program varies between 6 pounds and 14 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost.

1) P(x = 7)

2) Between 8.25 po9unds and 12 pounds.

3) Greater than 10.50 pounds.

Please show work.

Answer:

a = 3

b = -7

c = 13

Step-by-step explanation:

[tex]\sf{given \ equation: 3x^2+bx+c[/tex]

[tex]\sf{sum \ of \ roots :\sf\frac{7}{3}[/tex]

[tex]\sf{product \ of \ the \ roots:\frac{13}{3}[/tex]

[tex]\sf{sum \ of \ roots \ = -\dfrac{coefficient \of \ x}{coefficient \ of \ x^2} }[/tex]

[tex]\sf \frac{-b}{3} = \frac{7}{3}[/tex]

[tex]\sf b = \frac{-7*3}{3}[/tex]

[tex]\sf b =- 7[/tex]

[tex]\sf{product \ of \ roots \ = \dfrac{constant \ term}{coefficient \ of \ x^2} }[/tex]

[tex]\sf{\frac{c}{3} =\frac{13}{3}[/tex]

[tex]\sf c = \frac{13*3}{3}[/tex]

[tex]\sf c = 13[/tex]

Therefore found that a = 3, b = -7, c = 13

Answer:

b = -7

c = 13

Step-by-step explanation:

[tex]3x^2+bx+c[/tex]

[tex]\textsf{sum of roots}=\dfrac{-b}{a}\\\\\textsf{product of roots}=\dfrac{c}{a}[/tex]

[tex]\textsf{Given sum of roots}=\dfrac73:[/tex]

[tex]\implies \dfrac{-b}{a}=\dfrac73[/tex]

[tex]\implies a=3, b=-7[/tex]

[tex]\textsf{Given product of roots}=\dfrac{13}{3}:[/tex]

[tex]\implies \dfrac{c}{a}=\dfrac{13}{3}[/tex]

[tex]\implies a=3, c=13[/tex]

Therefore,

[tex]3x^2-7x+13[/tex]

NB: The actual calculated roots are imaginary numbers as the function [tex]f(x)=3x^2-7x+13[/tex] does not intercept the x-axis

I do not really know what the exact answer you are looking for is but please give me brainiest  in return

Feet: 75

Years: 35

Answer:

[tex]\huge\boxed{\bf\:A = 3W}[/tex]

Step-by-step explanation:

If [tex]\sf\:W = \frac { A } { 3 }[/tex], then A = ?

At first let's shift the the term 'W' to the LHS & A/3 to the RHS to bring the equation in the standard form.

[tex]\sf\:\frac{A}{3}=W[/tex]

Now, we know that, A/3 is the same as ⅓ A. Then,

[tex]\sf\:\frac{1}{3}A=W[/tex]

By multiplting both sides by 3..

[tex]\sf\:\frac{\frac{1}{3}A}{\frac{1}{3}}=\frac{W}{\frac{1}{3}} \\\sf\: A=\frac{W}{\frac{1}{3}}[/tex]

Divide [tex]\sf\:\frac{W}{\frac{1}{3}}[/tex] by its reciprocal.

[tex]\sf\:A=\frac{W}{\frac{1}{3}} \\ \sf\:A = \frac{3W}{1}\\[/tex]

So, the value of A is [tex]\downarrow[/tex]

[tex]\boxed{\bf\:A = 3W}[/tex]

__________

Have a great day ahead!

Answer:

?????

Step-by-step explanation:

is there any questions you need help with ?

Answer:

you jump 32 times in one minute

Step-by-step explanation:

192 ÷ 6 = 32

Answer:

32 times in one minute.

Step-by-step explanation:

192/6 = 32

Answer:

B. 3x = 15

Step-by-step explanation:

To find out which equation is the correct one, we just have to replace x with 5 for each one.

2 + x = 3

2 + 5 = 7

Since 2 + 5 is 7, this one is incorrect.

3 x 5 = 15

3 times 5 is 15, so B is correct. Let's try out the other ones anyway.

5 / 2 = 2.5

Incorrect.

5 - 7 = -2

Incorrect.

The only correct equation was B. 3x = 15

Using the volume of the rectangular prism, it is found that it takes 7 hours to fill the pool.

The volume of a rectangular prism of dimensions l, w and h is given by the multiplication of it's dimensions, that is:

V = lwh.

In this problem, the dimensions in meters are: l = 7, w = 3, h = 0.75. Hence, the volume in cubic meters is:

V = lwh = 7(3)(0.75) = 15.75.

It fill 2.25 cubic meters per hour, hence, for 15.75 cubic meters, the time taken is:

15.75/2.25 = 7 hours.

More can be learned about volume of a rectangular prism at https://brainly.com/question/17223528

There are 12 dimes and 19 nickels

Since Jace has $2.15 in nickels and dimes.

We know that 1 nickel = $ 0.05 and 1 dime = $0.10

Let

We have that

0.05n + 0.10n' = 2.15   (1)

Since he has 7 more nickels than dimes, we have that

n = n' + 7       (2)

Substituting equation (2) into (1), we have

0.05n + 0.10n' = 2.15   (1)

0.05(n' + 7) + 0.10n' = 2.15  

0.05n' + 0.35 + 0.10n' = 2.15  

0.15n' + 0.35 = 2.15  

0.15n' = 2.15 - 0.35

0.15n' = 1.8

n' = 1.8/0.15

n' = 12

Since the number of nickels, n = n' + 7

Substituting n = 12 into the equation, we have

n = n' + 7

n = 12 + 7

n = 19

So, there are 12 dimes and 19 nickels

Learn more about simultaneous equations here:

https://brainly.com/question/21654746

Answer:

0.35

Step-by-step explanation:

Answer: 12/50

Step-by-step explanation: convert all of them to decimals.

Answer:

59.4/ 82.5 = 9/12.5

Step-by-step explanation:

6.6/p = 9/12.15

A fraction equal with another fraction, so we can cross multiply to to have a multiplication equal another multiplication.

6.6 * 12.5  = 9* p

To isolate p (our unknown) we divide both sides by 9

( 6.6 * 12.5) /9   = (9* p)/ 9

( 6.6 * 12.5) /9   = p

82.5 / 9 = p

The proportion is:

6.6/p = 9/12.15, substitute p = 82.5 / 9

6.6/(82.5/9) = 9/12.15, use that: a / (b/c) = (a/1 )*(c/b) = (a*c) / b

(6.6*9)/82.5 = 9/12.5

59.4/ 82.5 = 9 /12.5

Answer:

cos²Θ

Step-by-step explanation:

simplify the expression using the identities

tanΘ = [tex]\frac{sin0}{cos0}[/tex]

cos2Θ = 1 - 2sin²Θ

cos²Θ = 1 - sin²Θ

then

tanΘ × sinΘ × cosΘ + cos2Θ

= [tex]\frac{sin0}{cos0}[/tex] × sinΘ × cosΘ + 1 - 2sin²Θ ( cancel cosΘ on numerator/ denominator )

= sinΘ × sinΘ + 1 - 2sin²Θ

= sin²Θ + 1 - 2sin²Θ

= 1 - sin²Θ

= cos²Θ

Answer:

[tex]\cos^2(\theta)[/tex]

Step-by-step explanation:

Trig identities used:

[tex]\cos(2\theta)=\cos^2(\theta)-\sin^2(\theta)[/tex]

[tex]\tan(\theta)=\dfrac{\sin(\theta)}{\cos(\theta)}[/tex]

Therefore,

[tex]\tan(\theta)\times\sin(\theta)\times\cos(\theta)+\cos(2\theta)[/tex]

[tex]=\dfrac{\sin(\theta)}{\cos(\theta)}\times\sin(\theta)\times\cos(\theta)+\cos(2\theta)[/tex]

[tex]=\sin^2(\theta) +\cos(2\theta)[/tex]

[tex]=\sin^2(\theta) +\cos^2(\theta)-\sin^2(\theta)[/tex]

[tex]=\cos^2(\theta)[/tex]

Answer:

B (6,0) because when graphed it would make a 90° angle

Answer: (B)

Step-by-step explanation:

For the triangle formed to be a right triangle in this case, the next point has to have the same x value as one of the two points in order for it to form a right triangle.

Hope that helps!

Answer:

x=4

Step-by-step explanation:

In a parallelogram opposite sides are congruent. That means BC and AD are congruent if ABCD must be a parallelogram.

[tex]6+3x=x+14\\6+2x=14\\2x=8\\x=4[/tex]

To double check you can substitute x into the equations again and check if they are equal.

[tex]6+3(4)=(4)+14\\6+12=18\\18=18[/tex]

If it's not 6 cubic feet (because by the wording the answer is given).

If one dimension of the amount of soil they remove is 6, then you have to do 6*6*6= 216

If the total amount of soil removed is 6 cubic feet, then the dimensions of the cube would be [tex]\sqrt[3]{6}[/tex]

Alternate exterior angles are formed by a transversal intersecting two parallel lines, therefore, your alternate exterior angles are <1 and <5.

Your alternate interior angles are  <2 and <6/ <3 and <7.

Corresponding angles are formed when two parallel lines are intersected by a transversal. (<1 and <3)

Vertical angles are formed when two lines intersect each other. Therefore, <1 and <7 fall into this category.

Answer:

less than.

Step-by-step explanation:

Any negative number is less than 0

Answer:

The answer is b, which is 3+x+3

Answer: 19

Step-by-step explanation:

We know that [tex].\overline{6}=2/3[/tex], so [tex].0\overline{6}=2/30 = 1/15[/tex]

Meaning we have [tex]3.1+1/15 = \frac{31}{10}+\frac{1}{15}=\frac{31(3)+1(2)}{30}=\frac{95}{30}=\frac{19}{6}[/tex]

Answer:

[tex]4\frac56[/tex]

Step-by-step explanation:

[tex]\frac56=0.8 \dot{3}[/tex]

[tex]\implies 4.8 \dot{3}=4\frac56[/tex]

4 5/6 if you need more answers go to decimal converts fractions and you will have it on your own

have a wonderful day

Hailey lee

Answer:

Step-by-step explanation:

WX = 18sin(57) = 15.1

XZ = 18cos(57) = 9.8

m∠W = 90 - 57 = 33°

Answer:

so, 10 laps in 25 mins we want to make mins=1 so

10/25=2/5 times 5/5=2/5

if you multiply 2/5 by 2/2 then you get 4/10 and 4/10=0.4

the runner can run 0.4 or 2/5 lap in 1 minute

Step-by-step explanation:

it is the answer box I'm a genius

Answer:

y = -5/2x + 27/2

Step-by-step explanation:

line formula is y = mx + b

perpendicular means number next to the x (slope or m) becomes a negative reciprocal

2/5x -> -5/2x

then use point slope formula

y - y1 = m (x - x1)

y - 6 = -5/2 (x - 3)

y - 6 = -5/2x + 15/2

y = -5/2x + 15/2 + 6

y = -5/2x + 15/2 + 12/2

y = -5/2x + 27/2

Answer:

A: Vertical angles are congruent, C is the midpoint of BE, and ∠B ≅ ∠E.

B: C is the midpoint of AD, BC ≅ EC, and Vertical angles are congruent.

C: I assume you cannot use CPCTC so AAS and ASA.

Step-by-step explanation:

A: Since vertical angles are congruent, the interior angles using point C of the triangles are congruent. If C is the midpoint of BE, BC ≅ EC. Draw the congruent parts based on the 3 statements with tick marks and you will see that you have two pairs of congruent angles with an included pair of congruent sides, so ASA applies.

B: If C is the midpoint of AD, AC ≅ DC. Since vertical angles are congruent, the interior angles using point C of the triangles are congruent. Draw the congruent parts based on the 3 statements with tick marks and you will see that you have two pairs of congruent sides with an included pair of congruent angles, so SAS applies.

C: ∠B ≅∠E and ∠A ≅∠D since these are pairs of alternate interior angles. Since vertical angles are congruent, the interior angles using point C of the triangles are congruent and it is given that AB ≅ DE. When making the appropriate marks, you will see that only AAS and ASA can be used without CPCTC.