Write the function for the graph.

          Value of constant 'k' = -0.041097

          Equation modeling the exponential decay → [tex]\text{ln}\frac{N}{N_0}=-0.41097t[/tex]

         [tex]\text{ln}\frac{N}{N_0}=-kt[/tex]

         Here, N = Amount remaining after 't' years

                   N₀ = Initial amount of the radioactive element

                    k = Constant

                    t = Period of decay

Given in the question,

Substitute these values in the expression for the value of 'k',

[tex]\text{ln}\frac{75}{100}=-7k[/tex]

[tex]k=\frac{1}{7}[(\text{ln}(75)-\text{ln}(100)][/tex]

[tex]k=\frac{1}{7}[4.317488-4.605170][/tex]

k = -0.041097

Equation modeling the exponential decay → [tex]\text{ln}\frac{N}{N_0}=-0.41097t[/tex]

  Therefore, value of constant 'k' = -0.041097

               Equation modeling the exponential decay → [tex]\text{ln}\frac{N}{N_0}=-0.41097t[/tex]

Learn more about the radioactive decay here,

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Answer:

$ 1.90 for 1 Gallon

Step-by-step explanation:

11.40/6 = 1.90

another way you can show the answer is: $1.90/1 Gal.

Answer:

6.28 x 3.14 = 19.7192

Step-by-step explanation:

Answer:

£104

Step-by-step explanation:

5:3 = 65:X

65÷5=13

X=13×3

x=39

total=65+39

total=104

129 million I took the application already

Answer: 45

Step-by-step explanation:

From the question, we are informed that Mai is making personal pizzas for a party and that she uses 10 ounces of cheese to make four pizzas. The number of ounce per pizza will be:

= 10/4 = 2.50 ounces per pizza

Therefore, the number of ounces of cheese that will be needed to make 18 pizzas will be:

= 2.50 × 18

= 45 ounces of cheese

Answer:

28

Step-by-step explanation:

The 5 part of the ratio represents 35 girls , then

35 ÷ 5 = 7 ← value of 1 part of the ratio, then

4 parts = 4 × 7 = 28 ← number of boys

Answer:

28 boys

Step-by-step explanation:

4*35=140

140/5=28

so 28 boys

Answer:

The answer is option 2.

Step-by-step explanation:

You have to substitute the expressions into x :

h(x) = x + 4

h(x - 3) = (x - 3) + 4

h(x - 3) = x - 3 + 4

h(x - 3) = x + 1

Answer:

A

Step-by-step explanation:

it should be A because if

x-axis represents the time, at the beginning of the day x = 0 and

y-axis the $, at the beginning of the day should be y= 0

Answer:

a linear graph would best represent the relationship

Step-by-step explanation:

just did the khan academy thing

Answer:

Yes! Total received was $84.525

Step-by-step explanation:

Note that 5% is another way of writing

5

100

Charge:

→

$

70

+

(

5

100

×

70

)

=

$

73.5

15% tip

→

15

100

×

Charge  

→

15

100

×

$

73.5

=

$

11.025

Total income:

→

$

73.5

+

$

11.025

84.525

=

$Did they receive more than $82

→

Yes

Answer:

Total received was $84.52

Answer:

A

Step-by-step explanation:

Vertical Line test will determine if a graph is a function or not

Answer:

6/15

Step-by-step explanation:

3/5*2/3=6/15

Answer:

D

Step-by-step explanation:

D is the right answer for the question

Answer:

52.5

Step-by-step explanation:

Arrange the data in an ascending order and the median is the middle value. If the number of values is an even number, the median will be the average of the two middle numbers.

Answer:

The mean is 47.875 and the median is 51

Explanation:

To find the mean you have to add up all of the numbers together, and then divide that number (383) by how many numbers there are (8) so then you would get 47.875. Now you have to find the median. To find the median you have to place the numbers from the lowest to the greatest which would be 42, 51, 51, 51, 55, 64, 69. Then you basically just pick the number in the middle which is 51, so 51 is the median.

Answer:

m∠3 = 105°

Step-by-step explanation:

Line 'l' is parallel to line 'm' and a transversal is intersecting these parallel lines at two distinct points.

m∠3 + m∠6 = 180° [Consecutive interior angles]

Since, ∠6 = 75° [Given]

m∠3 + 75° = 180°

m∠3 = 180 - 75

        = 105°

Therefore, measure of ∠3 is 105°.

In the given diagram, the measure of ∠3 is 105°

From the question,

We are to determine the measure of ∠3

In the diagram, ∠3 and ∠6 are consecutive interior angles

NOTE:

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary

That is,

∠3 + ∠6 = 180°

From the given information,

∠6 = 75°

Then, we can write that

∠3 + 75° = 180°

∠3 = 180° - 75°

∠3 = 105°

Hence, the measure of ∠3 is 105°

Learn more on finding the measures of angles here: https://brainly.com/question/2883630

Answer:

Step-by-step explanation:

The blue line is the translate in the direction of the red line by , and therefore has equation y = 3 ( x − 4 ) + 5 or y = 3 x − 7 .

The linear equation is y = -x - 1 for the graph of the linear equation where -1 is the slope of the linear equation and -1 is the y-intercept.

It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.

If in the linear equation one variable is present then the equation is known as the linear equation in one variable.

As we can see from the graph of the linear equation:

The x-intercept a = -1

And the y-intercept b = -1

We know the linear equation in terms of a and b can be modeled:

[tex]\rm \frac{x}{a} +\frac{y}{b} =1\\\\\rm \frac{x}{-1} +\frac{y}{-1} =1\\\\[/tex]

x + y = -1

y = - x - 1

Thus, the linear equation is y = -x - 1 for the graph of the linear equation where -1 is the slope of the linear equation and -1 is the y-intercept.

Learn more about the linear equation here:

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Answer:

64p^12 / 27

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

m = 2, b = 4.6

Step-by-step explanation:

The slope intercept formula is y = mx + b, So you can substitute for the values given.

Answer:

Each girl scores 8 points while each boy scores 4 points

Step-by-step explanation:

Let the number of point scored by the 7 girls and 2 boys be x and y respectively.

Thus, since 7 girls and 2 boys scored a total of 64 points, then;

7x + 2y = 64 - - - (1)

Also, difference between the number of points scored by the 7 girls and the number of points scored by the 2 boys is 48. Thus;

7x - 2y = 48 - - - (2)

Add eq(1) to (eq 2) to get;

14x = 64 + 48

14x = 112

x = 112/14

x = 8

Put 8 for x in eq(1) to get;

7(8) + 2y = 64

56 + 2y = 64

2y = 64 - 56

2y = 8

y = 8/2

y = 4

Thus,each girl scores 8 points while each boy scores 4 points

Step-by-step explanation:

[tex]8 + 12 = 20 \\ probability \: = expected \: outcome \div possible \: outcome \\ \\ \\ \frac{12}{20 } = \frac{3}{4} [/tex]

Answer:

each side 5

Step-by-step explanation:

with 2 equal internal base angles, we know this is an isosceles triangle

this being isosceles also tells us that the 2 opposite sides are also equal

Therefore: x + 2 = 3x - 4

solving for x

x - 3x = -4 -2

-2x = -6

x = -6 ÷ -2

× = 3

substituting x:

x +2 = 3 + 2 = 5

3x-4 = 9 - 4 = 5

Answer:

a force is described by its strength and by the direction in which it acts. -The strength of a force is measured in the SI unit called the Newton (N).

Step-by-step explanation:

Answer:

a(7) = 21

Step-by-step explanation:

Using the recursive formula and a(1) = 0, a(2) = 1 , then

a(3) = a(2) + 2a(1) = 1 + 2(0) = 1 + 0 = 1

a(4) = a(3) + 2a(2) = 1 + 2(1) = 1 + 2 = 3

a(5) = a(4) + 2a(3) = 3 + 2(1) = 3 + 2 = 5

a(6) = a(5) + 2a(4) = 5 + 2(3) = 5 + 6 = 11

a(7) = a(6) + 2a(5) = 11 + 2(5) = 11 + 10 = 21

Answer:

21√7

Step-by-step explanation: