Use a graphing tool to solve the equation below for x.

-3(-x) − 6 = -3x + 10

A. x ≈ -2.50
B. x ≈ 2.50
C. x ≈ -6.00
D. x ≈ -0.50

Answer:

54 is the width

Step-by-step explanation:

65+65=130

238-130=108

108÷2=54

Answer:

The width of the rectangular is 54yards

Step-by-step explanation:

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9514 1404 393

Answer:

  13, 22

Step-by-step explanation:

Let s represent the smaller. The sum of the numbers is ...

  s + (s+9) = 35

  2s = 26 . . . . . . subtract 9

  s = 13

  s+9 = 22

The two numbers are 13 and 22.

_____

Additional comment

As you can see, the smaller number is half the difference of the sum and difference: s = (35-9)/2. This is the generic solution to a "sum and difference" problem.

If you came for a short answer

A=1.50

B=1

a) Each jigsaw puzzle costs $1.5.

b) Each paddle ball paddle costs $1.

Given that Do-Nothing #1 paid $8 for 2 paddle ball paddles and 4 jigsaw puzzles.

Do-Nothing #2 paid $18 for 3 paddle ball paddles and 10 jigsaw puzzles.

We need to find how much each cost.

Let's solve the problem step by step.

Let's assume the cost of each jigsaw puzzle is 'x' dollars, and the cost of each paddle ball paddle is 'y' dollars.

According to the given information:

The first person paid $8 for 2 paddle ball paddles and 4 jigsaw puzzles. So, we can write the equation as:

2y + 4x = 8............. eq(i)

The second person paid $18 for 3 paddle ball paddles and 10 jigsaw puzzles. So, we can write the equation as:

3y + 10x = 18............. eq(ii)

Now, we can solve these two equations to find the values of 'x' and 'y'.

To do so, we can multiply Equation 1 by 3 and Equation 2 by 2 to eliminate the 'y' term:

6y + 12x = 24............. eq(iii)

6y + 20x = 36............. eq(iv)

Subtracting Equation 3 from Equation 4, we get:

6y + 20x - (6y + 12x) = 36 - 24

6y + 20x - 6y - 12x = 12

8x = 12

x = 12/8

x = 1.5

Now, substitute the value of 'x' back into Equation 1 to find 'y':

2y + 4(1.5) = 8

2y + 6 = 8

2y = 8 - 6

2y = 2

y = 2/2

y = 1

So, the cost of each jigsaw puzzle is $1.5, and the cost of each paddle ball paddle is $1.

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Step-by-step explanation:

perimeter = 2×(7+5) = 2×12= 24 units

area = 7×5 = 35 sq. units

Answer:

(x-6)^3x-5 =6

Step-by-step explanation:

logb a=c ------>  b^c =a

Answer:

Hello! In this picture I marked the new dot for that point and reflected it across the x axis!

The original coordinates are: 5, -3

and the new coordinates are: 5, 3

Hope that helps!

Answer:

B

Step-by-step explanation:

Use quadratic formula

Answer:

P(0) = 0.055

P(1) = 0.16

P(2) = 0.231

P(3) = 0.224

P(4) = 0.162

P(5 or more) = 0.168

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Here λ = 2.90 is the average number of bacteria colonies per field.

This means that [tex]\mu = 2.90[/tex]

Compute P(r) for r = 0, 1, 2, 3, 4, and 5 or more.

[tex]P(0) = \frac{e^{-2.9}*(2.9)^{0}}{(0)!} = 0.055[/tex]

[tex]P(1) = \frac{e^{-2.9}*(2.9)^{1}}{(1)!} = 0.16[/tex]

[tex]P(2) = \frac{e^{-2.9}*(2.9)^{2}}{(2)!} = 0.231[/tex]

[tex]P(3) = \frac{e^{-2.9}*(2.9)^{3}}{(3)!} = 0.224[/tex]

[tex]P(4) = \frac{e^{-2.9}*(2.9)^{4}}{(4)!} = 0.162[/tex]

5 or more:

This is

[tex]P(X \geq 5) - 1 - P(X < 5)[/tex]

In which:

[tex]P(X < 5)  = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.055 + 0.16 + 0.231 + 0.224 + 0.162 = 0.832[/tex]

[tex]P(X \geq 5) - 1 - P(X < 5) = 1 - 0.832 = 0.168[/tex]

So

P(5 or more) = 0.168

9514 1404 393

Answer:

  16 miles

Step-by-step explanation:

The problem can be modeled by a right triangle with one angle of 7° and the side opposite being 10,000 ft. The distance needed is the hypotenuse of the triangle, so the relevant trig relation is ...

  Sin = Opposite/Hypotenuse

  Hypotenuse = Opposite/Sin

  air distance = (10,000 ft)/sin(7°) ≈ 82,055 ft

At 5,280 ft per mile, that is ...

  (82,055 ft)/(5,280 ft/mi) ≈ 15.54 mi

The plane's air distance to the airport is about 16 miles.

Answer:

b

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

Determining the limit from a graph edge

Answer:

-2

Step-by-step explanation:

Answer:

3) (I) Numeric , and (II) Numeric

Step-by-step explanation:

Numeric variable:

The variable assume number values.

Categorical values:

The variable assumes labels. Examples are yes/no, good/bad.

(I) Fuel economy (miles per gallon) of used car

(II) Number of auto insurance claims in a month

Both of these variables are numbers, none have labels, so they are both numeric. The correct answer is given by option 3).

Answer:

100degrees

Step-by-step explanation:

From the given diagram;

<2 = <6 (corresponding angle)

Since <6 + 80 = 180

<6 = 180 - 80

<6 = 100 degrees

Since <2 = <6, hence <2 = 100degrees

Answer:

5 years

Step-by-step explanation:

3000x.06=180 interest per year.

900/180 =5 years to earn 900 interest.

Answer:

sum of exterior angles of a polygon=360

Step-by-step explanation:

4x+2x+x+4+x+4x+2=360

12x+6=360

2x+1=60

x=59/2

29.5

Answer:

A =16.25 cm^2

Step-by-step explanation:

The area of a triangle is given by 1/2 bh where b is the base and h is the height

A = 1/2 (5) * 6.5

A =16.25 cm^2

Answer:

The tank must remain intact for 1183 years.

Step-by-step explanation:

Exponential equation for decay:

The amount of a substance after t years is given by:

[tex]A(t) = A(0)e^{rt}[/tex]

In which A(0) is the initial amount and r is the decay rate.

A storage tank contains a liquid radioactive element with a half-life of 96 years.

This means that [tex]A(96) = 0.5A(0)[/tex], and we use this to find r.

[tex]A(t) = A(0)e^{rt}[/tex]

[tex]0.5A(0) = A(0)e^{96r}[/tex]

[tex]e^{96r} = 0.5[/tex]

[tex]\ln{e^{96r}} = \ln{0.5}[/tex]

[tex]96r = \ln{0.5}[/tex]

[tex]r = \frac{\ln{0.5}}{96}[/tex]

[tex]r = -0.0072[/tex]

So

[tex]A(t) = A(0)e^{-0.0072t}[/tex]

It will be relatively safe for the contents to leak from the tank when 0.02% of the radioactive element remains. How long must the tank remain intact for this storage procedure to be safe?

This is t for which [tex]A(t) = 0.0002A(0)[/tex]. So

[tex]A(t) = A(0)e^{-0.0072t}[/tex]

[tex]0.0002A(0) = A(0)e^{-0.0072t}[/tex]

[tex]e^{-0.0072t} = 0.0002[/tex]

[tex]\ln{e^{-0.0072t}} = \ln{0.0002}[/tex]

[tex]-0.0072t = \ln{0.0002}[/tex]

[tex]t = -\frac{\ln{0.0002}}{0.0072}[/tex]

[tex]t = 1183[/tex]

The tank must remain intact for 1183 years.

Well formatted version of question:

Find the expected value of a random variable x having the following probability distribution.

x (-5,-1,0,1,5,8)

Probability (.12, .16, .28, .22, .12, .1)

Answer:

0.86

Step-by-step explanation:

The expected value E(X) is calculated as :

E(X) = Σ(x * p(x))

(-5)(0.12) + (-1)(0.16) + (0)(0.28) + 1(0.22) + 5(0.12) + 8(0.10)

-0.6 + -0.16 + 0 + 0.22 + 0.6 + 0.8

= 0.86

Answer:

$15, 300 a loan

Step-by-step explanation:

14, 400/2 = 7200

25000- 7200 = 17,800

17, 800- 2500 for a scholarship = 15,300

Answer:

1. 50000

2.

i 274625000cm

ii 274.625m

Step-by-step explanation:

1. Area of a rectangle: length*width

250*200=50000cm

2. Volume of a cube: length^3

i 650^3=274625000cm

ii 650 cm=6.5m; 6.5^3=274.625m

Answer:

12.56m²

Step-by-step explanation:

So the formula for the circumference of a circle is π x diameter, so we just have to plug into our equation (we're using 3.14 as π):

3.14 x 4 = 12.56

So the circumference of your circle is 12.56 meters²

hope this helps:)

Answer:

1/3P

Step-by-step explanation:

P/3 is equal to 1/3P

Answer:

a) The linear function that models the volume of hydrogen in the balloon at any time [tex]t[/tex] is [tex]V(t) = 2 + 0.5\cdot t[/tex].

b) 26 seconds are needed to completely fill the balloon.

Step-by-step explanation:

The statement has a mistake, the correct form is described below:

Weather balloons are filled with hydrogen and released at various sites to measure and transmit data about conditions such as air pressure and temperature. A weather balloon is filled with hydrogen at the rate of [tex]0.5\,\frac{ft^{3}}{s}[/tex]. Initially, the balloon has [tex]2\,ft^{3}[/tex] of hydrogen.

a) The volume of weather balloons is increasing linearly in time ([tex]t[/tex]), in seconds, since the rate of change of volume ([tex]\dot V[/tex]), in cubic feet per second, is stable. The linear function of the volume of the weather balloon in terms of time is:

[tex]V(t) = V_{o} + \dot V\cdot t[/tex] (1)

Where:

[tex]V(t)[/tex] - Current volume, in cubic feet.

[tex]V_{o}[/tex] - Initial volume, in cubic feet.

If we know that [tex]V_{o} = 2\,ft^{3}[/tex] and [tex]\dot V = 0.5\,\frac{ft^{3}}{s}[/tex], then the volume as a function of time is:

[tex]V(t) = 2 + 0.5\cdot t[/tex]

b) If we know that [tex]V(t) = 2 + 0.5\cdot t[/tex] and [tex]V(t) = 15\,ft^{3}[/tex], then the time taken to fill the balloon is:

[tex]V(t) = 2 + 0.5\cdot t[/tex]

[tex]V(t) - 2 = 0.5\cdot t[/tex]

[tex]t = \frac{V(t) - 2}{0.5}[/tex]

[tex]t = \frac{15-2}{0.5}[/tex]

[tex]t = 26\,s[/tex]

26 seconds are needed to completely fill the balloon.

Answer:

D.f(x)=2x-9and g(x)=X+9/2

Number of ways to choose two colors of three colors when order of choice is relevant and relevant are 6 and 3 respectively.

Permutation refers to placing all members of a set in a particular order or choice of order. Combination is a way of selecting items from a collection, so the order of selection (unlike permutation) does not matter.  

Given,

Three colors, red, blue and green

a) Number of ways of choosing 2 colors out of three colors when order matter

= ³p₂

= 3!/(3-2)!

= (3×2×1)

= 6

b) a) Number of ways of choosing 2 colors out of three colors when order does not matter

= ³C₂

= 3!/(3-2)!2!

= (3×2×1)/(2×1)

= 3

Hence, when 6 and 3 are the number of ways to choose 2 colors from three colors when order matter and dose not matter respectively.

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Answer:

0.433

Step-by-step explanation:

From the given information;

Let represent Urn 1 to be Q₁ ;

Urn 2 to be Q₂

and the event that a blue token is taken should be R

SO,

Given that:

Urn 1 comprises of 4 blue token and 9 red tokens,

Then, the probability of having a blue token | urn 1 picked is:

 [tex]P(R|Q_1) = \dfrac{4}{4+9}[/tex]

[tex]= \dfrac{4}{13}[/tex]

Urn 2 comprises of 12 blue token and 5 red tokens;

Thus [tex]P(R| Q_2) = \dfrac{12}{12+5}[/tex]

[tex]=\dfrac{12}{17}[/tex]

SO, if two coins are flipped, the probability of having two heads = [tex]\dfrac{1}{4}[/tex]

(since (H,H) is the only way)

Also, the probability of having at least one single tail = [tex]\dfrac{3}{4}[/tex]

(since (H,T), (T,H), (T,T) are the only possible outcome)

Thus: so far we knew:

[tex]P(Q_2) = \dfrac{1}{4} \\ \\ P(Q_2) = \dfrac{3}{4}[/tex]

We can now apply Naive-Bayes Theorem;

So, the probability P(of the token from Urn 2| the token is blue) = [tex]P(Q_2|R)[/tex]

[tex]P(Q_2|R) = \dfrac{P(R \cap Q_2)}{P(R)} \\ \\ = \dfrac{P(R|Q_2) * P(Q_2)}{P(R|Q_2) \ P(R_2) + P(R|Q_1) \ P(Q_1)} \\ \\ \\ \\ = \dfrac{\dfrac{12}{17} \times \dfrac{1}{4} }{\dfrac{12}{17} \times \dfrac{1}{4} + \dfrac{4}{13} \times \dfrac{3}{4}} \\ \\ \\ = \dfrac{13}{30}[/tex]

= 0.433

12x = (10)(11)

12x=110

x=110÷12

x=55/6