Strontium 90 is a radioactive material that decays according to the function Upper A (t )equals Upper A 0 e Superscript negative 0.0244 t Baseline commaA(t)=A0e−0.0244t, where Upper A 0A0 is the initial amount present and A is the amount present at time t​ (in years). Assume that a scientist has a sample of 500500 grams of strontium 90. ​(a) What is the decay rate of strontium​ 90?

Answer:

4

Step-by-step explanation:

g(x) = x² − 2x + 5

g'(x) = 2x − 2

g'(3) = 4

Answer:

+30

Step-by-step explanation:

1255- 1075 = 180

180 /6 = 30

Answer:

SOHCAHTOA

Step-by-step explanation:

Usually, in American schools, the term "SOHCAHTOA" is used to remember them. "SOH" is sine opposite hypotenuse, "CAH" is cosine adjacent hypotenuse, and "TOA" is tangent opposite adjacent. There is also Csc which is hypotenuse/opposite, Sec which is hypotenuse/adjacent, and Cot is adjacent/opposite.

Answer: SOHCAHTOA

Step-by-step explanation:

The pneumonic I learned is SOH-CAH-TOA.  it says that Sin = opposite/hypotenuse.  Cos = adjacent/hypotenuse.  Tan = opposite/adjacent.

Hope it helps <3

Answer:

a) 17.6 + 5.4i

b) 37.6

Step-by-step explanation:

a) (9 + 9.4i) + (8.6 - 4i)

Collect like terms:

9 + 8.6 + 9.4i - 4i

= 17.6 + 5.4i

b) (9.4i)(-4i)

Expand the brackets:

9.4 * -4 * i *  i

[tex]i = \sqrt{-1}[/tex]

Therefore, i * i = -1

=> (9.4i)(-4i) = -37.6 * -1

= 37.6

Answer: 4.3 mi

Step-by-step explanation:

From Oxford, getting to Kingswood takes 7.5mi, and getting to Norwood takes 11.8mi.  Thus, simply do 11.8-7.5 to get 4.3mi.

Hope it helps <3

Hey there! I'm happy to help!

We see that it takes 45 minutes for a person to drive 50 miles. We can write this as a fraction that is 45/50, which simplifies to 9/10, meaning it would take this person 9 minutes to travel 10 miles.

So, how long would it take to travel 120? Well, we know that if we take 10 miles and multiply it by 12 we will have 120 miles. If we take the time it takes to drive those ten miles (9 minutes) and multiply it by 12, we will figure out how long it takes to drive 120 miles!

9×12=108

However, we want this to be written in hours. We know that there are 60 minutes in an hour, and if we subtract 60 from 108 we have 48. This gives us 1 hour and 48 minutes.

Therefore, it will take 1 hour and 48 minutes for this person to travel 120 miles at the same rate.

Have a wonderful day! :D

Answer:

Step-by-step explanation:

In algebra, we always need to follow a set of steps that involve undoing the operations that led to the equation to reveal the value of x.

e < -12

(Since we divided by a negative number, we must reverse the inequality sign.)

(-1/6)(-12) > 2

2 > 2 ✅

Now we check a number less than -12, such as -14.

(-1/6)(-14) > 2

2 1/3 > 2 ✅

Answer:

0.31 ft/s

Step-by-step explanation:

The volume of a cone is given by the formula:

V = πr²h/3

From the question, we are given the diameter and the height to be equal, thus;

r = h/2

Putting h/2 for r into the volume equation, we have;

V = (π(h/2)²h)/3

V = πh³/12

Using implicit derivatives,we have;

dV/dt = (πh²/4)(dh/dt)

From the question, we want to find out how fast is the height of the pile increasing. This is dh/dt.

We have;

dV/dt = 35 ft³/min and h = 12ft

Plugging in the relevant values, we have;

35 = (π×12²/4)(dh/dt)

dh/dt = (35 × 4)/(144 × π)

dh/dt = 0.3095 ft/s ≈ 0.31 ft/s

Answer:

300

Step-by-step explanation:

A(dd): 4+5= 9

D(ivide): 540/9 = 60

T(imes): 4 x 60= 240 beads

             5 x 60= 300 beads

I hope this helped :)

Number of larger share of beads is 300 seeds

Given that;

Number of total beads = 540

Beads ratio = 4:5

Find:

Number of larger share of beads

Computation:

Number of larger share of beads = 5[540 / (4+5)]

Number of larger share of beads = 5[540 / 9]

Number of larger share of beads = 5[60]

Number of larger share of beads = 300 seeds

Learn more:

https://brainly.com/question/13419413?referrer=searchResults

Answer:

(a) (1,5)

(b) Every subset of a cartesian product is a relation, therefore this is a relation.

(c) The relation IS NOT a function.

Step-by-step explanation:

(a)

(1,5)

Notice that  3(1) +1 = 4  < 5 therefore (1,5) is an order pair that satisfies the equation.

(b)

Every subset of a cartesian product is a relation, therefore this is a relation.

(b)

A relation is a function of  the following condition holds

if    (a,b) and (c,b) belong to the relation then (a=c)

In this case, (1,5), (0,5) belong to the relation but  0 is different than 5, therefore the relation IS NOT a function.

Answer:

x=10/3

Step-by-step explanation:

isolate the variable

Answer:

1. x = 4

2. x = 10/3

Step-by-step explanation:

1. 3x - 5 = 3 + x

3x - x = 3 + 5

2x = 8

x = 4

2. x/2 + 5/9 = 2x/3

(x/2 + 5/9) * 18 = (2x/3) * 18

9x + 10 = 12x

10 = 12x - 9x

10 = 3x

x = 10/3

Answer:

Beryllium, 2 times

Step-by-step explanation:

1.12×10⁻¹⁰ has a higher exponent than 5.6×10⁻¹¹.

-10 > -11

The ratio between them is:

(1.12×10⁻¹⁰) / (5.6×10⁻¹¹)

(1.12 / 5.6) (10⁻¹⁰ / 10⁻¹¹)

0.2 × 10¹

2

Answer:

Triangle D is your answer.

Answer:

Hey there!

Triangle C is unique, as one side and two angles determine a unique triangle.

Hope this helps :)

Answer: 6 with milk, 9 without

Step-by-step explanation:

2/5 of the cookies he eats are dunked.  Thus, simply do 2/5, or .4*15 to get that 6 cookies are dunked, and 15-6 to get that 9 cookies are not dunked.

Hope it helps <3

Answer:

D

Step-by-step explanation:

It is a trinomial with a degree of 3.

This is the correct answer on the exam.

Correct question:

A motorcycle stunt rider jumped across the Snake River. The path of his motorcycle was given

approximately by the function H(t) = - 0.0004.x2 + 2.582 + 700, where H is measured in

feet above the river and is the horizontal distance from his launch ramp.

How high above the river was the launch ramp?

What was the rider's maximum height above the river, and how far was the ramp when he reached maximum height?

Answer:

A) 700 feet ; 4866.7025 feet above the river

3227.5 Feets from the ramp

Step-by-step explanation:

Given the Height function:

H(t) = 0.0004x^2 + 2.582x + 700

H = height in feet above the river

x = horizontal distance from launch ramp.

How high above the river was the launch ramp?

H(t) = - 0.0004x^2 + 2.582x + 700

To find height of launch ramp above the river, we set the horizontal distance to 0, because at this point, the motorcycle stunt rider is on the launch ramp and thus the value of H when x = 0 should give the height of the launch ramp above the river.

At x = 0

Height (H) =

- 0.0004(0)^2 + 2.582(0)+ 700

0 + 0 + 700 = 700 Feets

B) Maximum height abive the river and how far the rider is from the ramp when maximum height is reached :

Taking the derivative of H with respect to x

dH'/dx = 2*-(0.0004)x^(2-1) + 2.582x^(1-1) + 0

dH'/dx = 2*-(0.0004)x^(1) + 2.582x^(0) + 0

dH'/dx = - 0.0008x + 2.582

Set dH'/dx = 0 and find x:

0 = - 0.0008x + 2.582

-2.582 = - 0.0008x

x = 2.582 / 0.0008

x = 3227.5 feets

To get vertical position at x = 0

Height (H) =

- 0.0004(3227.5)^2 + 2.582(3227.5)+ 700

- 4166.7025 + 8333.405 + 700

= 4866.7025 feet

4866.7025 feet above the river

3227.5 Feets from the ramp

Using quadratic function concepts, it is found that:

The height after x seconds is given by the following equation:

[tex]H(x) = -0.0004x^2 + 2.582x + 700[/tex]

Which is a quadratic equation with coefficients [tex]a = -0.0004, b = 2.582, c = 700[/tex]

The height of the ramp is the initial height, which is:

[tex]H(0) = -0.0004(0)^2 + 2.582(0) + 700 = 700[/tex]

Thus, the launch ramp was 700 feet above the river.

The maximum height is the h-value of the vertex, given by:

[tex]h_{MAX} = -\frac{\Delta}{4a} = -\frac{b^2 - 4ac}{4a}[/tex]

Then, substituting the coefficients:

[tex]h_{MAX} = -\frac{(2.582)^2 - 4(-0.0004)(700)}{4(-0.0004)} = 4866.7[/tex]

The maximum height is of 4866.7 feet.

The horizontal distance is the x-value of the vertex, given by:

[tex]x_V = -\frac{b}{2a} = -\frac{2.582}{2(-0.0004)} = 3227.5[/tex]

The ramp was 3227.5 feet along when he reached maximum height.

A similar problem is given at https://brainly.com/question/24705734

Answer:

Step-by-step explanation:

Length the length and breadth of the rectangle be x and y.

Area of the rectangle A = Length * breadth

Perimeter P = 2(Length + Breadth)

A = xy and P = 2(x+y)

If the area of the rectangle is 512m², then 512 = xy

x = 512/y

Substituting x = 512/y into the formula for calculating the perimeter;

P = 2(512/y + y)

P = 1024/y + 2y

To get the value of y, we will set dP/dy to zero and solve.

dP/dy = -1024y⁻² + 2

-1024y⁻² + 2 = 0

-1024y⁻² = -2

512y⁻² = 1

y⁻² = 1/512

1/y² = 1/512

y²  = 512

y = √512 m

On testing for minimum, we must know that the perimeter is at the minimum when y = √512

From xy = 512

x(√512) = 512

x = 512/√512

On rationalizing, x = 512/√512 * √512 /√512

x = 512√512 /512

x = √512 m

Hence, the dimensions of a rectangle is √512 m  by √512 m

Answer:

[tex]F = \frac{3}{5} x - 8\cdot \ln |x| + C[/tex]

Step-by-step explanation:

Let be [tex]f(x) = \frac{3}{5}-\frac{8}{x}[/tex] and [tex]F[/tex] is the antiderivative of [tex]f(x)[/tex] such that:

1) [tex]F = \int {\left(\frac{3}{5}-\frac{8}{x} \right)} \, dx[/tex] Given.

2) [tex]F = \frac{3}{5} \int \, dx -8\int {\frac{dx}{x} }[/tex] ([tex]\int {[f(x)+g(x)]} \, dx = \int {f(x)} \, dx + \int {g(x)} \, dx[/tex])

3) [tex]F = \frac{3}{5} x - 8\cdot \ln |x| + C[/tex], where [tex]C[/tex] is the integration constant. ([tex]\int {k} \, dx = k\cdot x[/tex]; [tex]\int {\frac{dx}{x} } = \ln|x|[/tex], [tex]\int {k\cdot f(x)} \, dx = k\int {f(x)} \, dx[/tex]) Result.

Answer:

The answer is

Step-by-step explanation:

a + b + c

a = 5 b = - 1 c = - 8

Substitute the values of a , b , c into the above expression

That's

5 + ( - 1) + ( - 8)

5 - 1 - 8

Subtract the numbers

4 - 8

We have the final answer as

Hope this helps you

Answer:

-4

Step-by-step explanation:

5 + - 1 - 8= -4

Answer:

There will be $4450 left at the end of the year.

Step-by-step explanation:

We first take 11% and multiply it by $5,000. We get 550. This means that the account will lose $550. Next, we take our original amount, $5,000, and subtract $550 from it. We will get $4450.

Answer:

candles = $400

matches = $20

Step-by-step explanation:

Let cost of candles = $c

Let cost of matches = $m

c = 20 m (20 times m)

c + m = 420

20m + m = 420

21 m = 420

m = 20

c = 20 (20) = 400

Answer:

49.923 mph

Step-by-step explanation:

we know that the car traveled 133 miles in h hours at an average speed of x mph.

That is, xh = 133.

We can also write this in terms of hours driven: h = 133/x.

If x was 30 mph faster, then h would be one hour less.

That is, (x + 30)(h - 1) = 133, or h - 1 = 133/(x + 30).

We can rewrite the latter equation as h = 133/(x + 30) + 1

We can then make a system of equations using the formulas in terms of h to find x:

h = 133/x = 133/(x + 30) + 1

133/x = 133/(x + 30) + (x + 30)/(x + 30)

133/x = (133 + x + 30)/(x + 30)

133 = x*(133 + x + 30)/(x + 30)

133*(x + 30) =  x*(133 + x + 30)

133x + 3990 = 133x + x^2 + 30x

3990 = x^2 + 30x

x^2 + 30x - 3990 = 0

Using the quadratic formula:

x = [-b ± √(b^2 - 4ac)]/2a  

= [-30 ± √(30^2 - 4*1*(-3990))]/2(1)  

= [-30 ± √(900 + 15,960)]/2

= [-30 ± √(16,860)]/2

= [-30 ± 129.846]/2

= 99.846/2  -----------  x is miles per hour, and a negative value of x is neglected, so we'll use the positive value only)

= 49.923

Check if the answer is correct:

h = 133/49.923 = 2.664, so the car took 2.664 hours to drive 133 miles at an average speed of 49.923 mph.

If the car went 30 mph faster on average, then h = 133/(49.923 + 30) = 133/79.923 = 1.664, and 2.664 - 1 = 1.664.

Thus, we have confirmed that a car driving 133 miles at about 49.923 mph would have arrive precisely one hour earlier by going 30 mph faster

Answer:

The 98% confidence interval for the difference of the mean amount of June precipitation in Michigan cities and Ohio cities is (-1.77, 0.29).

Step-by-step explanation:

The (1 - α)% confidence interval for the difference between two population mean is:

[tex]CI=(\bar x_{1}-\bar x_{2})\pm t_{\alpha/2, (n-1)}\cdot\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}[/tex]

Compute the value of sample means and sample standard deviations from the provided data.

[tex]\bar x_{1}=3.142\\\\\bar x_{2}=3.882\\\\s_{1}=0.4396\\\\s_{2}=0.4283\\n_{1}=n_{2}=5[/tex]

The critical value of t for 98% confidence level and (n - 1) = 4 degrees of freedom is:

[tex]t_{\alpha/2, (n-1)}=t_{0.02/2, 4}=3.747[/tex]

Compute the 98% confidence interval for the difference of the mean amount of June precipitation in Michigan cities and Ohio cities as follows:

[tex]CI=(\bar x_{1}-\bar x_{2})\pm t_{\alpha/2, (n-1)}\cdot\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}[/tex]

     [tex]=(3.142-3.882)\pm3.747\cdot\sqrt{\frac{0.4396^{2}}{5}+\frac{0.4283^{2}}{5}}\\\\=-0.74\pm 1.0285\\\\=(-1.7685, 0.2885)\\\\\approx (-1.77, 0.29)[/tex]

Thus, the 98% confidence interval for the difference of the mean amount of June precipitation in Michigan cities and Ohio cities is (-1.77, 0.29).

Answer: The average rate of change for this function for the interval from x=3 to x=5 is 12.

Step-by-step explanation:

Complete question is provided in the attachment below.

Formula: The average rate of change for this function y=f(x) for the interval from  x= a to x= b :

[tex]Rate =\dfrac{f(b)-f(a)}{b-a}[/tex]

Let y= f(x) for the given table:

At x= 3 , f(3)=8 and f(5)=32

Then, the average rate of change for this function for the interval from x=3 to x=5:

[tex]Rate=\dfrac{f(5)-f(3)}{5-3}\\\\=\dfrac{32-8}{2}\\\\=\dfrac{24}{2}=12[/tex]

Hence, the average rate of change for this function for the interval from x=3 to x=5  is 12.  (Option A is correct.)

Answer:

C.

Step-by-step explanation:

So, here's what you need to remember:

If we have a function f(x) and a factor k:

k(f(x)) will be a vertical stretch if k is greater than 1, and a vertical compression if k is greater than zero but less than 1.

f(kx) will be a horizontal compression if k is greater than 1, and a horizontal stretch if k is greater than zero but less than 1.

We are multiplying 0.5 to the function. In other words: 0.5f(x).

This is outside the function, so it's vertical.

0.5 is less than 1, so this would be a vertical compression

Answer:

slope of the line through (3, 7) and (-1, 4) is

[tex]m = \frac{4 - 7}{ - 1 - 3} \\ \\ = \frac{ - 3}{ - 4} \\ \\ = \frac{3}{4} [/tex]

Hope this helps you

Answer:

3/4

Step-by-step explanation:

Using the slope formula

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

   = (4-7)/(-1-3)

   = -3/-4

   = 3/4

Answer:

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points

[tex](3;\ 9)\to x_1=3;\ y_1=9\\(1;\ 1)\to x_2=1;\ y_2=1[/tex]

Substitute:

[tex]m=\dfrac{1-9}{1-3}=\dfrac{-8}{-2}=4[/tex]

Answer:

m=4

Step-by-step explanation:

Slope can be found using the following formula:

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are points on the line.

We are given the points (3,9) and (1,1). Therefore,

[tex]x_{1}=3\\y_{1}=9 \\x_{2}=1\\y_{2}=1[/tex]

Substitute each value into the formula.

[tex]m=\frac{1-9}{1-3}[/tex]

Subtract in the numerator first.

[tex]m=\frac{-8}{1-3}[/tex]

Subtract in the denominator.

[tex]m=\frac{-8}{-2}[/tex]

Divide.

[tex]m=4[/tex]

The slope of the line is 4.

Answer:

The answer is option C

Step-by-step explanation:

To find the length of AB we use sine

sin∅ = opposite / hypotenuse

From the question

The hypotenuse is AB

The opposite is AC

So we have

sin 54 = AC/AB

sin 54 = 16 / AB

AB = 16/sin 54

AB = 19.777

Hope this helps you

Answer:

AB = 19.78

Step-by-step explanation:

From the diagram (Right-angle triangle):

AC = 16

AB = ?

Angle = 54°

Applying trig ratio:

Tan 54° = 16/BC

1.376381920 = 16/BC

Therefore;

BC = 16/1.376381920

BC = 11.62

To solve the length AB:

Cos 54° = BC/AB

0.587785252 = 11.62/AB

Solving AB gives:

AB = 11.62/0.587785252

AB = 19.78

Answer:

62

Step-by-step explanation:

Turn 4 and 1/2 into a decimal.

4.5

Divide 279 by 4.5

279/4.5=62

You can cut 62 4 and 1/2 inch pieces.