A sample of a radioactive substance decayed 11% over the course of 3 weeks. How many grams were in the sample originally if 30.26 grams of the substance were remaining after the 3 weeks?

Answer:

The equation is [tex]x(t) = -13 cos (8 \pi t )[/tex]

Step-by-step explanation:

From the question we are told that

      The  amplitude is  [tex]A = 13 \ in[/tex]

       The period is  [tex]T = 0.25[/tex]

Generally the displacement function for a simple harmonic motion is mathematically represented as

        [tex]x(t) = A cos (wt )[/tex]

Here  [tex]w[/tex] is the angular frequency which is mathematically represented as

          [tex]w = \frac{2 \pi }{T}[/tex]

substituting values

          [tex]w = \frac{2 \pi }{ 0.25}[/tex]

          [tex]w = 8\pi[/tex]

Given that at t =  0  the displacement is equal to 0 it means that there is no phase shift and also  we are told that it is initially moving downward which implies that its Amplitude is  [tex]A = -13\ in[/tex]

So the equation modeling the displacement d as a function of time t is mathematically represented as

          [tex]x(t) = -13 cos (8 \pi t )[/tex]

Answer:

A. a line segment

Step-by-step explanation:

Answer: 4150

Step-by-step explanation:

You take the 50, becuse the amount earned increases once you surpass 40 you do 40 x 10 and that = 4000 then you take the remaining 10 and times that by 15 (becuse after 40 it is 1.5 of what you where earning before you hit 40 hours and half of ten is 5 so you do 10 plus 5 and times that by 10) then add both numbers together and you have 4150! Hope that helped!

Answer:

Step-by-step explanation:

Formula for area of a triangle:

Height x Base /2

Base (b) = h +4

Height = h

h + 4 x h /2 = 30cm

=> h +4 x h = 60

=> h+4h =60

=> 5h = 60

=> h = 12

Height = 12

Base = 12 +4 = 16

Answer:

[tex]\Large \boxed{\sf 17 \ and \ 18}[/tex]

Step-by-step explanation:

The product means multiplication.

There are two positive consecutive integers.

Let the first positive consecutive integer be x.

Let the second positive consecutive integer be x+1.

[tex](x) \times (x+1) =306[/tex]

Solve for x.

Expand brackets.

[tex]x^2 +x =306[/tex]

Subtract 306 from both sides.

[tex]x^2 +x -306=306-306[/tex]

[tex]x^2 +x -306=0[/tex]

Factor left side of the equation.

[tex](x-17)(x+18)=0[/tex]

Set factors equal to 0.

[tex]x-17=0[/tex]

[tex]x=17[/tex]

[tex]x+18=0[/tex]

[tex]x=-18[/tex]

The value of x cannot be negative.

Substitute x=17 for the second consecutive positive integer.

[tex](17)+1[/tex]

[tex]18[/tex]

The two integers are 17 and 18.

The product of two consecutive positive integers is 306.

We need to find the integers

solution : Let two consecutive numbers are x and (x + 1)

A/C to question,

product of x and (x + 1) = 306

⇒x(x + 1) = 306

⇒x² + x - 306 = 0

⇒ x² + 18x - 17x - 306 = 0

⇒x(x + 18) - 17(x + 18) = 0

⇒(x + 18)(x - 17) = 0⇒ x = 17 and -18

so x = 17 and (x +1) = 18

Therefore the numbers are 17 and 18.

Hope it helped u if yes mark me BRAINLIEST

TYSM!

Answer:

Garden: 36 square feet

Path: 64 square feet

Step-by-step explanation:

Let's first find the total area. The total area will be 100 square feet since the side length is 10. Since the path is 2 feet wide and on all sides, that means that the inside square will have a side length of 6. That means that the vegetable garden is 36 square feet. The path will be 100 - (the garden), and the garden is 36 square feet, which means the outer path will be 64.

Answer:

1+5.3=6.3

Step-by-step explanation:

not sure what your asking for with the 2

explain what your looking for with the 2 and maybe we can help you further

(I have to do it the way I did it because the 2 in the question is confusing)

Answer:

For expression 1 + 5.32: 6.32

For expression 1 + 5.3 × 2: 11.6

Step-by-step explanation:

If the expression is 1 + 5.32:

If the expression is 1 + 5.3 × 2:

Answer:

4, 7, 10, 13

Step-by-step explanation:

Hey there!

Well in the given pattern,

-11, -8, -5, -2, 1

we can conclude that the pattern is +3 every time.

-11 + 3 = -8

-8 + 3 = -5

-5 + 3 = -2

-2 + 3 = 1

And so on

Hope this helps :)

Answer: 2361.53

Step-by-step explanation:

Use long division and round.

(The 3 is repeated)

Answer:

The value of [tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex]  is  [tex]4^{\dfrac{8}{15}}[/tex] .

Step-by-step explanation:

We need to simplify the numeric expression using property. The expression is as follows :

[tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex]

The property to be used is : [tex]x^a{\cdot} x^b=x^{a+b}[/tex]

This property is valid if the base is same. Here, base is x.

In this given problem, x = 4, a = 1/3 and b = 1/5

So,

[tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}}=4^{\dfrac{1}{3}+\dfrac{1}{5}}\\\\=4^{\dfrac{5+3}{15}}\\\\=4^{\dfrac{8}{15}}[/tex]

So, the value of [tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex]  is  [tex]4^{\dfrac{8}{15}}[/tex] .

Answer:

$3,717

Step-by-step explanation:

Hello, in 1 year there are 12 months.

Let's note I the Initial amount.

So, after 1 month we will get the following, because we compute the interest amount for one month only.

I * ( 1 + 6% * (1/12) )

And the next month, we will have interest of the amount available from previous month so it gives

[tex]I * ( 1+6\% * \dfrac{1}{12} ) * ( 1+6\% * \dfrac{1}{12} ) \\\\=I*(1+\dfrac{6}{12*100})^2\\\\=I*(1+\dfrac{1}{200})^2\\\\=I*(1.005)^2[/tex]

... and after n months ...

[tex]I*(1.005)^n[/tex]

8 years is 8*12 = 96 months. so we are looking for I such that

[tex]I*(1.005)^{96}=6000\\\\<=> I =\dfrac{6000}{1.005^{96}}\\\\=\boxed{3717.14345....}[/tex]

Thank you.

Complete Question

In a genetic experiment on peas, one sample of offspring contained 436 green peas and 171 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of 3/4 that was expected? The probability of getting a green pea is approximately: Is the probability reasonably close to 3/4?

Answer:

The  probability is  [tex]P(g) =0.72[/tex]

Yes the result is reasonably close

Step-by-step explanation:

From the question we are told that

   The  number of  of  green peas is  [tex]g = 436[/tex]

     The number of yellow peas is  [tex]y = 171[/tex]

   The sample size is  [tex]n = 171 + 436 = 607[/tex]

The probability of getting an offspring pea that is green is mathematically represented as

       [tex]P(g) = \frac{g}{n}[/tex]

        [tex]P(g) = \frac{436}{607}[/tex]

        [tex]P(g) =0.72[/tex]

Comparing  [tex]P(g) =0.72[/tex]  to   [tex]\frac{3}{4} = 0.75[/tex] we see that the result is reasonably close

Answer:

f(0) = 7

Step-by-step explanation:

f(x) = -3x + 7

Let x =0

f(0) = -3*0 + 7

f(0) = 7

Answer:

Question 1: 40 shirts and 40 magizines

Question 2: $4.4

Question 3: 6 gallons

Answer:

hello

Step-by-step explanation:

Answer:

The probability is 0.31084

Step-by-step explanation:

We can calculate this probability using the z-score route.

Mathematically;

z = (x-mean)/SD/√n

Where the mean = 16, SD = 3 and n = 36

For 15.8, we have;

z = (15.8-16)/3/√36 = -0.2/3/6 = -0.2/0.5 = -0.4

For 16.2, we have

z = (16.2-16)/3/√36 = 0.2/3/6 = 0.2/0.5 = 0.4

So the probability we want to calculate is;

P(-0.4<z<0.4)

We can get this using the standard normal distribution table;

So we have;

P(-0.4 <z<0.4) = P(z<-0.4) - P(z<0.4)

= 0.31084

Answer:

y - 1 = -2(x - 4).

Step-by-step explanation:

First, we need to find the slope. Two sets of coordinates are (-3, 3), and (-2, 1).

(3 - 1) / (-3 - -2) = 2 / (-3 + 2) = 2 / (-1) = -2.

The line will be parallel to the given line, so the slope is the same.

Now that we have a point and the slope, we can construct an equation in point-slope form.

y1 = 1, x1 = 4, and m = -2.

y - 1 = -2(x - 4).

Hope this helps!

The slope of the line passing  parallel to the given line and passes through the point (4, 1) is y = -2x + 9

The equation of a straight line is given by:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

The slope of the line passing through the points (-3,3) and  (-2,1) is:

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{1-3}{-2-(-3)} \\\\m=-2[/tex]

Since both lines are parallel, hence they  have the same slope (-2). The line passes through (4,1). The equation is:

[tex]y-y_1=m(x-x_1)\\\\y-1=-2(x-4)\\\\y=-2x+9[/tex]

Find out more at: https://brainly.com/question/18880408

Answer:$40.00

Step-by-step explanation:first divide 20 by 5 and the answer will be 4. now multiply 10 into 4 and you'll get the answer $40.00

Answer:

[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]

Step-by-step explanation:

Given

[tex]Sections = 10[/tex]

[tex]n(Gray) = 5[/tex]

[tex]n(Blue) = 5[/tex]

Required

Determine P(Gray and Blue)

Using probability formula;

[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]

Calculating P(Gray)

[tex]P(Gray) = \frac{n(Gray)}{Sections}[/tex]

[tex]P(Gray) = \frac{5}{10}[/tex]

[tex]P(Gray) = \frac{1}{2}[/tex]

Calculating P(Gray)

[tex]P(Blue) = \frac{n(Blue)}{Sections}[/tex]

[tex]P(Blue) = \frac{5}{10}[/tex]

[tex]P(Blue) = \frac{1}{2}[/tex]

Substitute these values on the given formula

[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]

[tex]P(Gray\ and\ Blue) = \frac{1}{2} * \frac{1}{2}[/tex]

[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]

Answer:

Attachment 1 : Option C

Attachment 2 : Option A

Step-by-step explanation:

( 1 ) Expressing the product of z1 and z2 would be as follows,

[tex]14\left[\cos \left(\frac{\pi \:}{5}\right)+i\sin \left(\frac{\pi \:\:}{5}\right)\right]\cdot \:2\sqrt{2}\left[\cos \left(\frac{3\pi \:}{2}\right)+i\sin \left(\frac{3\pi \:\:}{2}\right)\right][/tex]

Now to solve such problems, you will need to know what cos(π / 5) is, sin(π / 5) etc. If you don't know their exact value, I would recommend you use a calculator,

cos(π / 5) = [tex]\frac{\sqrt{5}+1}{4}[/tex],

sin(π / 5) = [tex]\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}[/tex]

cos(3π / 2) = 0,

sin(3π / 2) = - 1

Let's substitute those values in our expression,

[tex]14\left[\frac{\sqrt{5}+1}{4}+i\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}\right]\cdot \:2\sqrt{2}\left[0-i\right][/tex]

And now simplify the expression,

[tex]14\sqrt{5-\sqrt{5}}+i\left(-7\sqrt{10}-7\sqrt{2}\right)[/tex]

The exact value of [tex]14\sqrt{5-\sqrt{5}}[/tex] = [tex]23.27510\dots[/tex] and [tex](-7\sqrt{10}-7\sqrt{2}\right))[/tex] = [tex]-32.03543\dots[/tex] Therefore we have the expression [tex]23.27510 - 32.03543i[/tex], which is close to option c. As you can see they approximated the solution.

( 2 ) Here we will apply the following trivial identities,

cos(π / 3) = [tex]\frac{1}{2}[/tex],

sin(π / 3) = [tex]\frac{\sqrt{3}}{2}[/tex],

cos(- π / 6) = [tex]\frac{\sqrt{3}}{2}[/tex],

sin(- π / 6) = [tex]-\frac{1}{2}[/tex]

Substitute into the following expression, representing the quotient of the given values of z1 and z2,

[tex]15\left[cos\left(\frac{\pi \:}{3}\right)+isin\left(\frac{\pi \:\:}{3}\right)\right] \div \:3\sqrt{2}\left[cos\left(\frac{-\pi \:}{6}\right)+isin\left(\frac{-\pi \:\:}{6}\right)\right][/tex] ⇒

[tex]15\left[\frac{1}{2}+\frac{\sqrt{3}}{2}\right]\div \:3\sqrt{2}\left[\frac{\sqrt{3}}{2}+-\frac{1}{2}\right][/tex]

The simplified expression will be the following,

[tex]i\frac{5\sqrt{2}}{2}[/tex] or in other words [tex]\frac{5\sqrt{2}}{2}i[/tex] or [tex]\frac{5i\sqrt{2}}{2}[/tex]

The solution will be option a, as you can see.

Answer:

0

Step-by-step explanation:

Hello, dividing by 0 is not defined. so

[tex]\dfrac{2x^2}{6x}[/tex]

is defined for x different from 0

This being said, we can simplify by 2x

[tex]\dfrac{2x^2}{6x}=\dfrac{2x*x}{3*2x}=\dfrac{1}{3}x[/tex]

and this last expression is defined for any real number x.

Thank you

Answer:

The percentage is  k  =  2.3%

Step-by-step explanation:

From the question we are told that

  The  population mean is  [tex]\mu = 47[/tex]

    The  standard deviation is  [tex]\sigma = 14[/tex]

Given that the sales are normally distributed and that students at a certain school who sell at least 75 magazine subscriptions win a prize then the  percent of the fourth grade students receive a prize is mathematically represented as

     [tex]P(X > 75) = P(\frac{X - \mu }{\sigma } > \frac{75 - \mu }{\sigma })[/tex]

Generally

     [tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]

So

   [tex]P(X > 75) = P(Z > \frac{75 - 47 }{14 })[/tex]

   [tex]P(X > 75) = P(Z > 2)[/tex]

From the standardized normal distribution table  

      [tex]P(Z > 2) =0.023[/tex]

=>   [tex]P(X > 75) = 0.023[/tex]

The  percentage of the fourth grade students receive a prize is  

  k =  0.023 * 100

   k  =  2.3%

Answer:

5

Step-by-step explanation:

a^2 + b^2 = c^2

4^2 + 3^2 = c^2

16 + 9 = c^2

25 = c^2

c = 5

Answer:

Step-by-step explanation:

[tex]Hypotenuse = ?\\Opposite = 4\\Adjacent = 3\\\\Pythagoras \: Theorem ;\\\\Hypotenuse^2 =Opposite^2+Adjacent ^2\\\\Hypotenuse^2 = 4^2 +3^2\\\\Hypotenuse^2 = 16+9\\\\Hypotenuse^2 = 25\\\\\sqrt{Hypotenuse^2}=\sqrt{25} \\Hypotenuse = 5[/tex]

Answer:

x=9; one ticket is $9

Step-by-step explanation:

4x+12=48

4x=48-12

4x=36

x=36/4

x=9

Answer:

Nothing further, the simplest answer is 32 1/2

Step-by-step explanation:

Answer:

b. 1

Step-by-step explanation:

All first coordinates are 1/2.

Answer: b. 1

Answer:

[tex]\huge \boxed{x=3}[/tex]

Step-by-step explanation:

[tex]6(x+2)=30[/tex]

[tex]\sf Divide \ both \ sides \ by \ 6.[/tex]

[tex]x+2=5[/tex]

[tex]\sf Subtract \ 2 \ from \ both \ sides.[/tex]

[tex]x=3[/tex]

Answer:

3

Step-by-step explanation:

30 = 6(x+2)

30/6 = 5

5 = x+2

5-2 = 3

3=x

This is a pretty simple question and I tried to make it as simple as possible when explaining it.

Answer:

x=3

Step-by-step explanation:

● -3 (-4x+4) = 15 + 3x

Multiply -3 by (-4x+4) first

● (-3) × (-4x) + (-3)×(4) = 15 + 3x

● 12 x - 12 = 15 +3x

Add 12 to both sides

● 12x - 12 + 12 = 15 + 3x +12

● 12 x = 27 + 3x

Substract 3x from both sides

● 12x -3x = 27 + 3x - 3x

● 9x = 27

Dividr both sides by 9

● 9x/9 = 27/9

● x = 3

Answer:

D.  2i√3

Step-by-step explanation:

You have the expression √-12.  You can divide the number in the radical sign into the numbers that make up the expression.  After you do this, you will be able to take numbers out of the radical sign

√(-12)

√(-1 × 4 × 3)

√-1 = i

√4 = 2

√3 = √3

2i√3

The answer is D.

Answer:

Perimeter=60.18cm

Area=215.495cm^2

Step-by-step explanation:

Given:

Length of book=18.34cm

Breadth=11.75cm

Solution:

Perimeter=2(l +b)

P=2(18.34+11.75)

P=2 x 30.09

P=60.18cm

Area=l x b

A=18.34 x 11.75

A=215.495 cm^2

Thank you!

Answer:

85.36 far north from the center

10.36 far east from the center

Step-by-step explanation:

The extra direction taken in the north side is x

X/sin(360-315)=50/sin 90

Sin 90= 1

X/sin 45= 50

X= sin45 *50

X= 0.7071*50

X= 35.355 steps

X= 35.36

Then the west direction traveled

West =√(50² - 35.355²)

West = √(2500-1249.6225)

West= √1250.3775

West= 35.36 steps

But this was taken in an opposite west direction

From the center

He is 35.36 +50

= 85.36 far north from the center

And

25-35.36=-10.36

10.36 far east from the center