The intensity (1) of a light source is inversely proportional to the square of the distance (d) from the source. If the intensity is 16 lumens at a distance of 16 feet, what is the intensity at a distance of 14 feet? Round to the nearest hundredth.​

Answer:

y = - 7x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

7x + y = 7 ( subtract 7x from both sides )

y = - 7x + 7 ← in slope- intercept form

The probability of picking a ticket that is green or has a number greater than four is 3/5

The given parameters are:

Yellow = 1 - 5

Green = 1 - 5

Total = 10

There are 2 cards whose numbers are greater than 4 i.e. Yellow 5 and Green 5

So, we have:

P(Number greater than 4) = 2/10

There are 5 green cards.

So, we have:

P(Green) = 5/10

Also, 1 green card is numbered greater than 4

So, we have:

P(Green greater than 4) = 1/10

The required probability is:

P = P(Green) + P(Number greater than 4) - P(Green greater than 4)

This gives

P = 5/10 + 2/10 - 1/10

Evaluate

P = 6/10

Simplify

P =3/5

Hence, the probability of picking a ticket that is green or has a number greater than four is 3/5

Read more about probability at:

https://brainly.com/question/11234923

#SPJ1

Answer:

A

Step-by-step explanation:

It is the quadratic parent function

The simple annual interest rate for the $ 525 loan is equal to 46.35 %.

In this situation we assume that the loan does not accumulate interests continuously in time. Hence, the interest rate for paying the loan back 75 days later is:

575 = 525 · (1 + r/100)

50 = 525 · r /100

5000 = 525 · r

r = 9.524

The loan has an interest rate of 9.524 % for 75 days. Simple annual interest rate is determine by rule of three:

r' = 9.524 × 365/75

r' = 46.350

The simple annual interest rate for the $ 525 loan is equal to 46.35 %.

To learn more on interests: https://brainly.com/question/26457073

#SPJ1

Answer:

10

9

0

Step-by-step explanation:

you subtract the number of all your answers

The rise is the difference in y-coordinates:

The run is the difference in x-coordinates:

The slope is the quotient of rise over run:

========================

If two points on a line are A(10, −3) and B(12, 9), the rise is 12, and the run is 2, so the slope of the line is 6.

Answer: A = JIH

B = GJH

C = GH

D = 300

E = 60

Step-by-step explanation:

A) <JIH is a inscribed angle

B) GJH is a major arc

C) GH is a minor arc

D) m GH = m<GFh = 60

The lateral area of the cone is calculated as: B. 47 in.².

Lateral area = πrl

Given the following:

Slant height (l) = 5 inches

Radius (r) = 3 inches.

π = 3.14

Plug in the values

Lateral area = (3.14)(3)(5)

Lateral area ≈ 47 in.²

Learn more about the lateral area of a cone on:

https://brainly.com/question/23442533

#SPJ1

The value of g(3) is g(3) = 4

The function value is given as:

g(x)

The notation g(3) implies that:

We determine the value of g(x) when x = 3

From the graph, the function has a point at (3,4)

This means that:

When x = 3, g(x) = 4

i.e. g(3) = 4

Hence, the value of g(3) is g(3) = 4

Read more about functions at:

https://brainly.com/question/20896994

#SPJ1

Answer:

x=8   y=2

Step-by-step explanation:

solve for x

1. 4x+4y=40

2. subtract 4y from both sides

3. 4x=40-4y

4. divide both sides by 40

5. [tex]\frac{4x}{4} = \frac{40-4y}{4}[/tex]

6. dividing by four undoes the multiplication by four

7.    [tex]x=\frac{40-4y}{4}[/tex]

8. divide 40 - 4y by 4

9. x=10-y

10. use the last equation to solve the rest

Four CDs must be bought to receive a gift card from an online store.

The total costs are equal to the sum of the shipping cost and the total related to the number of acquired CDs (n). The number of gift cards (m) is equal to the total costs divided by minimum spent money, that is, $ 50. We need to solve the following inequation to find the minimum quantity of CDs:

(12 · n + 5)/50 > 1

12 · n + 5 > 50

12 · n > 45

n > 45/12

n > 3.75

Four CDs must be bought to receive a gift card from an online store.

To learn more on inequalities: https://brainly.com/question/20383699

#SPJ1

Using the z-distribution, the p-value would be of:

b) 0.0086.

At the null hypothesis we test if the means are equal, equivalent to a subtraction of 0, hence:

[tex]H_0: \mu_D - \mu_C = 0[/tex]

At the alternative hypothesis, we test if they are different, hence:

[tex]H_1: \mu_D - \mu_C \neq 0[/tex]

For each sample, they are given as follows:

For the distribution of differences, it is given by:

The test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.

Hence:

[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

z = -2/0.76

z = -2.63.

Using a z-distribution calculator, for a two-tailed test, with z = -2.63, the p-value is of 0.0086.

More can be learned about the z-distribution at https://brainly.com/question/16313918

#SPJ1

Answer:

4

Step-by-step explanation:

Since,

The width of the Longer gear is 7, and the smaller gear has a width of 3..

7-3 = 4

Hope it helps...

Marking me as Brainliest would help me... :(

The choice which is equivalent is  [tex]6x^2\sqrt{3}[/tex] option B

We have that;

[tex]\sqrt{6x^2} * \sqrt{18x^2}[/tex] where [tex]x\geq 0[/tex]

First, we factorize the square root

= [tex]\sqrt{2 * 3 * x^2 } . \sqrt{3 * 3 * 2 * x^2}[/tex]

Find the common factors

= [tex]2 * 3 x^2\sqrt{3}[/tex]

= [tex]6x^2\sqrt{3}[/tex]

Thus, the choice which is equivalent is  [tex]6x^2\sqrt{3}[/tex] option B

The complete question is;

Which choice is equivalent to the product below for acceptable values of X? sqrt 6x² * sqrt 18x²

a. [tex]6\sqrt{3x}[/tex]

b. [tex]6x^2\sqrt{3}[/tex]

c. [tex]6\sqrt{18x}[/tex]

d. [tex]\sqrt{108x^2}[/tex]

Learn more about algebraic expressions here:

https://brainly.com/question/723406

#SPJ1

the expression simplified is:

[tex]12x^3 - 25x^2 + 9[/tex]

Here we have the expression:

[tex](4x - 3)*(3x^2 - 4x - 3)[/tex]

We just need to distribute the product, we will get:

[tex](4x - 3)*(3x^2 - 4x - 3)\\\\(4x)*(3x^2 - 4x - 3) - 3*(3x^2 - 4x - 3)\\\\12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9[/tex]

Now we just need to group terms with the same exponent of x:

[tex]12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9\\\\12x^3 + (-16 - 9)x^2 + (-12 + 12)x + 9\\\\12x^3 - 25x^2 + 9[/tex]

That is the expression simplified

If you want to learn more about simplification:

https://brainly.com/question/723406

#SPJ1

Answer:

India score 290 more than pakistan

Step-by-step explanation:

India score 20 more

The slope of restaurant B is twice that of restaurant A

The tables of values are given as

           X(Bill)     Y(Tip)                          X(Bill)        Y(Tip)

Rest A     10           1                  Rest B      25            5    

Rest A     20          2                 Rest B      50            10

Rest A     30          3                 Rest B      75             15

The slopes are calculated using

Slope = (y2 - y1)/(x2 - x1)

Using the table of values, we have:

Rest A = (2 - 1)/(20 - 10)

Rest A = 0.1

Rest B = (10 - 5)/(50 - 25)

Rest B = 0.2

By comparing the slopes, we have:

Rest B = 2 * Rest A

This implies that the slope of restaurant B is twice that of restaurant A

Read more about slopes at:

https://brainly.com/question/3493733

#SPJ1

Answer:

Step-by-step explanation:

area=length×width

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

Area=6x²-10x+9x-15

=6x²-x-15

73 division 84, 649 would give 8. 64 × 10^-4

In order to determine the value of the division, we have

= [tex]\frac{73}{84649}[/tex]

Using the calculator, put the values in

We would have

= 8. 64 × 10^-4

Thus, 73 division 84, 649 would give 8. 64 × 10^-4

Learn more about BODMAS here:

https://brainly.com/question/16788360

#SPJ1

Answer: answer is B

Step-by-step explanation:

use Pythagorean theorem to find other side. And sine is opposite side over hypotenuse.

The domain of the rational function is:

{x ∈ ℝ| x ≠ –2, 2}

Here we have the rational function:

[tex]f(x) = \frac{x^2 - x - 12}{x^3 - 4x^2 - 4x + 16}[/tex]

We want to get the domain of that function. First, we can rewrite the numerator and denominator as:

[tex]x^2 -x - 12 = (x + 3)*(x - 4)[/tex]

[tex]x^3 - 4x^2 - 4x + 16 = (x - 4)*(x + 2)*(x - 2)[/tex]

Then we can rewrite the rational function as:

[tex]f(x) = \frac{(x + 3)*(x - 4)}{(x - 4)*(x + 2)*(x - 2)}[/tex]

This can be simplified to:

[tex]f(x) = \frac{(x + 3)}{(x + 2)*(x - 2)}[/tex]

Now, the domain will be the set of all real numbers, minus the values of x that generate problems.

In this case, the values:

x = -2 and x = 2 make the denominator to be zero, and we can't divide by zero, so  we conclue that the domain is:

{x ∈ ℝ| x ≠ –2, 2}

If you want to learn more about rational functions:

https://brainly.com/question/1851758

#SPJ1

please send a picture of it

the equation seems a lil bit complicated

The two characteristics that makes the median a better choice are: A. The data are skewed and there are outliers.

In a data distribution, the median is a better choice to use to describe the data over the mean when an outlier exist and the data is skewed.

IN the dot plot given below, the data has an outlier of 10 while the data distribution is also screwed, this makes the median a better choice.

Therefore, the answer is: A. The data are skewed and there are outliers.

Learn more about the median on:

https://brainly.com/question/16800683

#SPJ1

Answer:

the product is 1.32057606543E32

The function which compares the growth of both functions is; The function y = 3x is growing slower than y = 3^x.

The graphs in the task content are given as y=3x which is a linear graph, and y=3^x which is the exponential graph.

Hence, it follows that although both graphs are growing, the graph of function y = 3x is growing slower than y = 3^x.

Read more on growing functions;

https://brainly.com/question/12940982

#SPJ1

This is a simple harmonic motion exercise. The proof that the resultant force on the particle, at time t, is -225 Newtons is indicated below.

Note that we have been given the following:

Mass = 9kg,

Y = 45 N

ζ = 0.4 m

Then, Y/ζ  = 45N/0.4m

= 112.5 N/m

Hence, the spring constant =

K = 112. 5N/m

From this point we can resolve the Amplitude (A):
Amplitude is given as:

A = CB - PB

= 0.6 - 0.5

A = 0.1m

I) So because one spring is elongated by x and the other is compressed by x, Hence, the spring force is:

F[tex]_{net}[/tex] = - Kₓ - Kₓ

= - 2Kₓ
= -2 x 112.5 x* X

F[tex]_{net}[/tex] = -225x Newton ..........Lets call this expression 1

From equation 1 above, we know that

Ma = -225x

a = (-225/m) x

⇒ a ∝ - x,

Hence, the motion is is simple harmonic in nature.

The time period, T = 2 π√m/K[tex]_{eq}[/tex]

Where, K[tex]_{eq}[/tex] = 2K

= 2π√(9/225)

= 2π * 3/15

= 2(22/7) * (3/15)

= 1.25714285714; thus

T ≈ 1.26 secs...............lets call this expression 2

Note that Angular Frequency is = 2π/T

= 2π/1.26

= 4.9866550057

ω = 4.99 rad/s

Since the velocity at any point x from the mean position is given by

V = ω √ (A² - x²); hence

V = 4.99 √[(0.1)² - (0.05)²

V = 4.99 x 0.0866
V = 0.432134

V ≈ 0.432..........Lets call this expression 3

Along the x-axis, A simple harmonic motion can be depicted as:

x = A sin (ωt + Ф) ..........lets call this expression 4

where, Ф = Phase constant

At t = 0; x = A

A = A sinФ

⇒ SinФ = 1

⇒ Ф = π/2

Expression 4 becomes:

x = A sin (ωt + π/2)

Inserting the values of ω and A, we have

x = 0.1 sin (4.99t + π/2).........Lets call this expression 5a

or  x  = 0.1 cos (4.99t).......Lets call this expression 5b

Hence,

Sin(π/2  + Ф) = CosФ

Learn more about simple harmonic motion at;
https://brainly.com/question/17315536
#SPJ1

Answer:

The three planes of motion are the sagittal, coronal (or frontal) and transverse planes.

Sagittal Plane: Cuts the body into left and right halves. Forward and backward movements.

Coronal (or Frontal Plane): Cuts the body into front and back halves. ...

Transverse Plane: Cuts the body into top and bottom halves.

Answer:

the real answer is 2 I hope that

The interest rate needed to double the investment in 18 years is  6%.

Interest earned is a function of the amount invested, interest rate and time. The future value of the investment is to be $6000 (3000 x 2). Interest earned would be $3000 (6000 - 3000)

Interest rate = interest earned / (amount invested x time )

$3000 / ($3000 x 18) = 6%

To learn more about simple interest, please check: https://brainly.com/question/27328409

#SPJ1

The expression that would be simplified to be a multiplicative identity is 2^0

The complete question is added as an attachment

Multiplicative identities are represented as:

a * 1 = a

This means that the definition of multiplicative identities is the product of a number and 1

From the list of options, we have

2^0

When the exponent of a non-zero number is 0, the result is 1.

This means that

2^0 = 1

Hence, the expression that would be simplified to be a multiplicative identity is 2^0

Read more about multiplicative identity at

https://brainly.com/question/2197860

#SPJ1