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Using an exponential function, it is found that:

a) The base is of 0.877.

b) The half-life of cobalt-60 is of 5.3 years.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

Item a:

Each year the amount present is reduced by 12.3%, hence [tex]r = 0.123[/tex], and the base is:

[tex]1 - r = 1 - 0.123 = 0.877[/tex]

Item b:

This is t for which A(t) = 0.5A(0), hence:

[tex]A(t) = A(0)(0.877)^t[/tex]

[tex]0.5A(0) = A(0)(0.877)^t[/tex]

[tex](0.877)^t = 0.5[/tex]

[tex]\log{(0.877)^t} = \log{0.5}[/tex]

[tex]t\log{0.877} = \log{0.5}[/tex]

[tex]t = \frac{\log{0.5}}{\log{0.877}}[/tex]

[tex]t = 5.3[/tex]

The half-life of cobalt-60 is of 5.3 years.

You can learn more about exponential functions at https://brainly.com/question/25537936

Answer:

B

Step-by-step explanation:

The graph hits the x axis at 5, -2, and -3/

Answer:

y = -3x + 14.

it's my answer

Answer:

Step-by-step explanation:

Convert the given equation into slope - intercept form:

The matching choice is B

Answer:

5/5=8

Step-by-step explanation:

The identity property means any factor multiplied by 1 (in this case 5/5=1) is itself.

Answer:

D. [tex]\frac{5}{5} * 8[/tex]

Step-by-step explanation:

In identity property of multiplication, any number multiplied by 1 stays the same. Here we need 1 multiply to a number which is 8. Here we can get 1 from only ( 5/5 ) multiplied with 8 and gives as well 8. So the answer is D.

Answer:Option B.Step-by-step explanation:The given inequalities are The related equations of given inequalities areThe tables of values areFor line 1                    For line 2x      y                           x      y0     -1                          0     -33     0                           9     0Plot these ordered pairs on a coordinate plane and connect them by straight lines.The sign of both inequalities is "<" it means both lines are dotted and everything below the lines is shaded.From the below graph it is clear that all values that satisfy  are solutions. Therefore, the correct option is B.

Answer:

  add the opposite of the constant

Step-by-step explanation:

The opposite of the constant must be added to the expression:

  (x +14.1) +(-14.1) = x +(14.1 -14.1) = x +0 = x

Answer:

AC is b

[tex]tan55 = \frac{15}{b} [/tex]

15/tan55 = b

tan 55 = 1.428

15/1.428 = 10.5 cm = AC

Answer:

THIS IS THE ANSWER

Step-by-step explanation:

The graph is an illustration of a linear function

The term that can be used to describe Dan's earning is that he earns $10.25 per hour

From the graph, we have the following ordered pairs

(x,y) = {(4,41) (7,71.75)}

The slope (m) is then calculated as:

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

So, we have:

[tex]m = \frac{71.75 - 41}{7 -4}[/tex]

Simplify

[tex]m = \frac{30.75}{3}[/tex]

Evaluate the quotient

[tex]m = 10.25[/tex]

Hence, Dan's hourly earning is $10.25 per hour

Read more about linear functions at:

https://brainly.com/question/15602982

Answer:

7.85 m (3 significant figures)

Step-by-step explanation:

Formula:   arc length = [tex]2\pi r(\frac{\theta}{360} )[/tex]

The radius of a circle is half the diameter, so r = 10 ÷ 2 = 5

Therefore, arc length = 2 x [tex]\pi[/tex] x 5 x [tex](\frac{90}{360} )[/tex]

                                    = [tex]\frac{5}{2}\pi[/tex]

                                    = 7.853981634...

                                    = 7.85 m (3 significant figures)

Answer:

Step-by-step explanation:

Step-by-step explanation:

the first thing we notice : the quadrilateral has 2 pairs of equally long sides with 2 angles being openly 90°.

so, we are dealing with a rectangle here.

we know that one pair of the sides (NK = LM) are 24 cm long.

and we know that KL:LM = 3:4.

that means that the pair KL = MN are the shorter sides of the rectangle. and their length is according to the ratio 3/4 of NK=LM.

3/4 × 24 = 18 cm

the area of that rectangle is therefore

18 × 24 = 432 cm²

Answer:

14.56

Step-by-step explanation:

Answer:

Your answer would be 14.56.

Step-by-step explanation:

The liter of oil tin contained

The liter of oil used and leak

The liter of oil left in the tin

~nightmare 5474~

Answer:

2.2 l of oil was left.

Step-by-step explanation:

[tex]Total=10\frac{3}{5} =10.6l\\Used=7\frac{1}{10} =7.1l\\Leaked=1\frac{2}{7} =1.28l\\[/tex]

Total used=7.1l+1.28l=8.38l

[tex]Left=10.6l-8.38l=2.22l[/tex]

Answer:

x = -2

y = 2

Step-by-step explanation:

In addition to my explanation, I will include a graph.

Since both equations are in slope-intercept form [tex]y=mx+b[/tex], where m is the slope of the line and b is the y-intercept, we can easily plot both lines.

First you plot the first points, which are (0,-4) and (0,4).

Next, we can use rise over run to determine where our next points will go.

Rise over run is just taking the slope as a fraction and using that to move points. For example, a slope with 3/4 would mean I move my points 4 spots to the right on the x-axis and 3 up on the y-axis. Every whole number is that number with #/1, so for the first equation we go right 1 spot and down 3 spots. For the next equation we go up 1 and right one. Keep doing this until you have a line formed and find where the lines intersect, or share a point.

Answer:-9

Step-by-step explanation:

Answer:

-9

Step-by-step explanation:

It is -9 because, using order of operations, you need to do the parentheses first. 25 + 15 is 40. Then, you do subtraction. 31-40=-9.

Hope this helps :)

Answer:

42

Step-by-step explanation:

Answer:

how to get a mean of the data in the morning and after some time

Answer:

slope

[tex] = \frac{y2 - y1}{x2 - x } \\ [/tex]

[tex] \frac{5 - j}{ - 9 - 4} = - 1 \\ \frac{5 - j}{- 13} = - 1 \\ 5 - j = 13 \\ - j = 13 - 5 \\ - j = 8 \\ j = - 8[/tex]

Answer:

Catherine's GPA is 2.48

Step-by-step explanation:

A z-score of 2.010 means that Catherine's GPA is 2.01 standard deviations above the mean. Therefore, Catherine's GPA is [tex]\bar{x}+2.01\sigma=1.963+2.01(0.257)\approx2.48[/tex]

Answer:

The answer is A

Step-by-step explanation:

Answer:

pls mark me as brainliest

Step-by-step explanation:

Using the normal distribution, it is found that x = 3.5 has a z-score of -2, which means that it is 2 standard deviations below the mean.

--------------------------------

In a normal distribution with mean  and standard deviation , the z-score of a measure X is given by:

The z-score measures how many standard deviations the measure X is from the mean, above or below.  

X∼N(6.5,1.5), which means that .

The measure is

The z-score is:

The measure x = 3.5 has a z-score of -2, which means that it is 2 standard deviations below the mean.

Answer: A≈2827.43cm²

Step-by-step explanation:

A= πr² =π·30²≈2827.43339cm²

substitution
y = 7x-26 (1)

y = 4x-11 (2)

1⇒2

7x-26=4x-11

3x=15

x=5

y = 7(5)-26

y = 9

point (5,9)

Answer:

x-intercept: [tex]\bigg(\frac{5}{2}, \:0\bigg)[/tex]

y-intercept: [tex](0,\:5)[/tex]

Step-by-step explanation:

To find the x-intercept, substitute in [tex]0[/tex] for [tex]y[/tex] and solve for [tex]x[/tex].

[tex]-4x + 7 = 2y - 3[/tex]

[tex]-4x+7=2\left(\bold{0}\right)-3[/tex]

Simplify 2(0):                                          [tex]-4x+7=2\cdot \:0-3[/tex]

Subtract 0 - 3 = -3:                         [tex]-4x+7=-3[/tex]

Subtract 7 from both sides:          [tex]-4x+7-7=-3-7[/tex]

Simplify:                                         [tex]-4x=-10[/tex]

Divide both sides by -4                [tex]\frac{-4x}{-4}=\frac{-10}{-4}[/tex]

[tex]\bold{x=\frac{5}{2}}[/tex]

To find the y-intercept, substitute in [tex]0[/tex] for [tex]x[/tex] and solve for [tex]y[/tex].

[tex]-4x + 7 = 2y - 3[/tex]

[tex]-4(\bold{0})+7=2y-3[/tex]

Switch sides:                               [tex]y-3=-4\left(0\right)+7[/tex]

Simplify -4(0):                              [tex]2y-3=-0+7[/tex]

Add 3 to both sides:                  [tex]2y-3+3=7+3[/tex]

Simplify:                                      [tex]2y=10[/tex]

Divide both sides by 2:             [tex]\frac{2y}{2}=\frac{10}{2}[/tex]

[tex]\bold{y=5}[/tex]

Answer:

  B.  30x

  D.  x(45-15)

Step-by-step explanation:

The distributive property lets you factor out the common factor of x. The sum of coefficients can be simplified to a single coefficient.

  45x -15x = x(45 -15) = 30x