There was a sample of 450 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 9.4% each year.
Let t be the number of years since the start of the study. Let y be the mass of the sample in milligrams.
Write an exponential function showing the relationship between y and t.

Answer:

The 3rd one

Step-by-step explanation:

My mom is a teacher lol

The expression which reflects the difference between the student's guess and the actual number of marbles is m-1206.

Given that there are 1206 marbles in the jar and student makes a guess of m marbles.

We are required to find the expression that represents the difference between the student's guess and the actual number of marbles.

Expression is the combination of numbers, symbols, fraction, coefficients and are found to be without the equal to sign.

Total number of marbles in the jar=1206

Number of marbles that student guesses=m

The expression that shows the difference between the student's guess and the actual number of marbles is m-1206.

Hence the expression which reflects the difference between the student's guess and the actual number of marbles is m-1206.

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Answer:D

Step-by-step explanation::

Answer:

a) The fact that corresponding angles are equal

b) The fact that alternate angles are equal

Step-by-step explanation:

I hope this helps

a) Measure of corresponding angles are equal.

b) Pair of alternate interior angles are of equal measure.

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

From the given figure the fact used to fund the measure of the angle r is

corresponding angles.

The fact that is used to find the angle t is in a parallelogram measure of opposite angles are equal.

Also, r and t are pairs of alternate interior angles so they measure the same.

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Answer:

[tex]2.5[/tex] pounds,

OR

[tex]2 \frac{1}{2} [/tex] pounds

Therefore, option C is the answer

Answer:

Option C is the correct answer.

Hector can have a total of 14950 number of combinations of 4 movies, from his shortlist of 11 documentaries and 15 foreign films, that he can rent.

As per the question statement, Hector has shortlisted 11 documentaries and 15 foreign films, from which he wants to rent any 4 movies.

We are required to calculate the total of number of combinations of 4 movies from his above mentioned shortlist.

Total number of movies Hector has shortlisted = (11 + 15) = 26.

That is, we will have to calculate the total of number of combinations of 4 movies, Hector can rent from a lot of 26 movies.

Now, we need to know the formula of combination which goes as [tex][nCr=\frac{n!}{r!(n-r)!} ][/tex],

When "r" objects are to be selected from a set of "n" objects, such that order of selection does not matter.

Here, (n = 26) and (r = 4), and using these values in the above mentioned equation of nCr, we get

[tex]26C4=\frac{26!}{4!(26-4)!} =\frac{26!}{4!*22!}=\frac{22!*23*24*25*26}{24*22!}=(23*25*26)=14950[/tex]

That is, Hector can have a total of 14950 number of combinations of 4 movies, from his shortlist of 11 documentaries and 15 foreign films, that he can rent.

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Answer:

Step-by-step explanation:

False, because the inequality is not less than or equal to 14 it should a bracket instead of paratheses. [3, 14]

Answer:

Every element in B is in B.

Step-by-step explanation:

Mediante la ley del seno, la longitud del faro es aproximadamente igual a 8.295 metros.

En esta pregunta nos encontramos con una sistema geométrico con dos ángulos y un lado conocidos, la configuración permite determinar la altura del faro mediante la ley del seno, cuya expresión sería la siguiente:

AC / sin B = AB / sin C = BC / sin A      

Donde BC es la longitud del faro, medida en metros, y AC es la distancia horizontal hasta la base del faro, medida en metros. Si sabemos que AC = 9.9 m, B = 53° and A = 42°, entonces la longitud del faro es:

(9.9 m) / sin 53° = BC / sin 42°

BC = 9.9 m × (sin 42° / sin 53°)

BC ≈ 8.295 m

La longitud del faro es aproximadamente igual a 8.295 metros.

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Answer:

x > 1

Step-by-step explanation:

to make everything under the same denominator

multiply everything by 2

7x + 1 > 8

now subtract 1 to both sides

7x > 7

divide everything by 7

x > 1

that is your asnwer

Answer:

  A)  6.86×10⁴

Step-by-step explanation:

You want to write 68600 in scientific notation.

The number 68600 can be written in expanded form with exponents as ...

  68600 = 6×10⁴ +8×10³ +6×10² +0×10¹ +0×10⁰

The left-most term of this sum tells you the exponent in scientific notation:

  68600 = 6.86×10⁴

Transformation of Reflect image over the y axis for this equation (x ,y)->(x +6,y -3)  is  (3, -1)

Reflecting point (-6,1) on y = x

gives (1, -6)

Translating, (1, -6) by 2,5 is

(1 + 2, - 6 + 5) = (3, - 1)

Therefore, reflect image over the y axis translate by rule (x ,y)->(x +6,y -3) is (3, - 1)

transformation :A function, f,  itself is called the transformation, i.e., f: X → X. After the transformation the pre-image X becomes the image X. This transformation can be any part or the mixture of operations such as translation, reflection, rotation and dilation. The translation is working a function in a particular direction, rotation is rotate the function to a point, reflection is the mirror image of the function, and dilation is the ascend of a function.

Translation, rotation, reflection, and dilation are the four most prevalent types of transformations. From the transformation, we have a rotation about any point, reflection over any line, and translation along any angle. The picture is congruent to its pre-image in these stiff transformations.. They are also called as isometric transformations. Dilation is performed at about any point of angle and it is non-isometric.

Rules for Transformations

Consider a function f(x). On a coordinate grid, we use the x-axis and y-axis to check the movement. Here are the rules for transformations of function that could be applied to the all graphs of functions. Transformations can be shown algebraically and graphically. Transformations are commonly found in algebraic functions. We can use the formula of transformations in graphical functions to obtain the graph just by transforming the fundamental or the parent function, and thereby move the graph around, rather than tabulating the coordinate values. We can visualize and learn algebraic equations with the aid of transformations.

Formula of Transformations

Let us consider the graph f(x) = [tex]x^{2}[/tex]

Suppose we have need to graph f(x) = [tex]x^{2}[/tex] -3, we shift the vertex 3 units down.

Suppose we have need to graph f(x) = 3 [tex]x^{2}[/tex]+ 2, we shift the vertex two units above and extend vertically by 3  factor

Suppose we have need to graph f(x) = 2(x-1)^2, we shift the vertex one unit to the right and extend vertically by 2  factor

Thus, we know the formula of transformations as

f(x) =a(bx-h) n + k

where k is the vertical shift,

h is the horizontal shift,

a is the vertical stretch and

b is the horizontal stretch

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Answer: bacteria 100 in a petri dish

Step-by-step explanation: every 30 min the bacteria doubles

The circumference of the circle with radius 7 and value of pie 3, using the formula C= 2pie r is 42 unit.

Circumference of this circle using 3 for TT and 7 as radius.

The circumference of a circle is the distance around the outside of the circle. It is like the perimeter of other shapes like squares. You can think of it as the line that defines the shape. For shapes made of straight edges this line is called the perimeter but for circles this defining line is called the circumference. There are two other important distances on a circle, the radius (r) and the diameter (d). The radius, the diameter, and the circumference are the three defining aspects of every circle. Given the radius or diameter and pi you can calculate the circumference.

Circumference of circle = π x Diameter of circle.

You can also work out the circumference of a circle if you know its radius. Remember that the diameter is double the length of the radius. We already know that C = πd. If r is the radius of the circle, then d = 2r. So, C = 2πr.

Here, π = 3, r = 7,

So C = 2*7*3 = 42 units.

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Answer:

what do you mean like answer to what

Answer:

there's literally no way to answer that

[tex]p(a \: \cup \: b) = p(a) + p(b) - p(a \: \cap \: b) \\ p(a \: \cup \: b) = 0.2 + 0.4 - p(a \: \cap \: b) \\ p(a \: \cup \: b) = 0.6 - p(a \: \cap \: b) \\[/tex]

[tex]but \: \: p(a \: \cap \: b) = p(a /b) \times p(b) \\ p(a \: \cap \: b) = 0.25 \times 0.4 = 0.1[/tex]

[tex]p(a \: \cup \: b) = 0.6 - p(a \: \cap \: b) \\ p(a \: \cup \: b) = 0.6 - 0.1 \\p(a \: \cup \: b) = 0.5[/tex]

The measure of the supplementary angles are 34.3 and 145.7 degrees.

Supplementary angles are those angles that sum up to 180 degrees.

In other words, two angles are Supplementary when they add up to 180 degrees.

Therefore, the angles measures 111.4° more than the measure of it's supplementary angle.

Hence,

let

x = measure of the other angle

x + x + 111.4 = 180

2x + 111.4 = 180

subtract 111.4 from both sides

2x + 111.4 - 111.4 = 180 - 111.4

2x = 68.6

divide both sides by 2

x = 68.6 / 2

x = 34.3

Other angle  = 34.3 + 111.4 = 145.7°

Therefore, the measure of the supplementary angles are 34.3 and 145.7 degrees.

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For the graphed function, the information is given as follows:

The domain of a function is the set that contains all possible input values for the function. In a graph, it is the set that contains all the values of x of the function.

Hence, the domain is [-4,4] for the given function.

The zeros of a function are the values of x for which f(x) = 0, on the graph they are the values of x when the function crosses the x-axis.

For this problem, the function does not cross the x-axis, hence it has no zeros.

Looking at the graph of the function, we have that:

Hence, for the function in this problem:

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1) Earth is 403,400,000 miles farther from Saturn than it is from Jupiter.

2) The total distance from Saturn to Jupiter and from Jupiter to Mars is 745,400,000 miles.

3) Saturn is 390,000,000 miles closer to Jupiter than is is to Earth.

4) Total distance from Mercury to Earth is 56,700,000 miles.

5) Venus is 22,300,000 miles closer to Earth than Mars.

6) Earth is 745,000,000 miles farther from Mars than Saturn.

Given,

1) Distance from Earth to Saturn = 793,000,000 miles

  Distance from Earth to Jupiter = 390,400,000 miles

793,000,000 - 390,400,000 = 403,400,000

That is, Earth is 403,400,000 miles farther from Saturn than it is from Jupiter.

2) Distance from Saturn to Jupiter = 403,400,000 miles

   Distance from Jupiter to Mars = 342,000,000 miles

403,400,000 + 342,000,000 = 745,400,000

Therefore, the total distance from Saturn to Jupiter and from Jupiter to Mars is 745,400,000 miles.

3) Distance from Saturn to Jupiter = 403,400,000 miles

   Distance from Saturn to Earth = 793,800,000 miles

793,800,000 - 403,400,000 = 390,400,000

So, Saturn is 390,000,000 miles closer to Jupiter than is is to Earth.

4) Distance from Mercury to Venus = 30,700,000 miles

   Distance from Venus to Earth = 26,000,000 miles

30,700,000 + 26,000,000 = 56,700,000

That is, the total distance from Mercury to Earth is 56,700,000 miles.

5) Distance from Earth to Venus = 26,000,000 miles

   Distance from Earth to Mars = 48,300,000 miles

48,300,000 - 26,000,000 = 22,300,000

That is, Venus is 22,300,000 miles closer to Earth than Mars.

6) Distance from Earth to Saturn = 793,800,000 miles

   Distance from Earth to Mars = 48,300,000 miles

793,800,000 - 48,300,000 = 745,500,000

That is, Earth is 745,000,000 miles farther from Mars than Saturn.

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The upper and the lower limits of the class that we have here would be A. 24-29

We have to find the range of the temperature

This is given as maximum - minimum

= 77 - 24

= 53

width = range / n

width = 53 / 10

= 5.3

The approximate width can be given as 5.

The upper class would be the lower class + width

= upper class = 24 + 5 = 29

Hence the limit of the classes would be given as

A. 24-29

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Answer:

(18")T=56.52

Step-by-step explanation:

t=3.14

Answer:

because he is human and human like to dance and eat

The amount of the total rent is 120 dollars.

Four students plan to rent a minivan for the weekend and equally share the rental cost.

By adding one more people, they can each save $6.

Therefore, the 4 students equally share the rent.

Hence,

average for 4 student = total amount shared / number of student

average for 4 student = x / 4

When you add one more person,

average for 5 student = x / 5

Therefore, the difference, will give you the total amount of the rent.

x / 4 - x / 5 = 6

5x - 4x/ 20 = 6

x / 20 = 6

cross multiply

x = 20 × 6

x = 120

Therefore, the amount of the total rent is 120 dollars.

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The equivalent expression of the given expression is 5n/4 -3/8

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

Here, the given expression is :

(-2 ¹/₂n + ¹/₄) + (3 ³/₄n - 5/8)

simplifying the above expression by taking like considering like terms :

= -2 ¹/₂n + 3 ³/₄n +  ¹/₄- 5/8

= (15/4)n - (5/2)n + (2-5)/8

= (15-10)n/4 -3/8

= 5n/4 -3/8

Therefore, the equivalent expression of the given expression is 5n/4 -3/8.

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Answer:

660 ÷ 0.16 = 4,125

Hope this helps :)

Answer:

[tex]r > 2[/tex]

Step-by-step explanation:

1) Rearrange the terms

-6 > 10 - 8r

2) Calculate

8r > 10 + 6

3) Divide both sides

8r > 16

4) Simplify (Cross out the common factor)

[tex]r >[/tex] [tex]\frac{16}{8}[/tex]  

5) r > 2

Answer: 24

Step-by-step explanation: HI = 2 times KL

-8x + 120 = 2(-8x + 96)

-8x + 120 = -16x + 192

8x = 72

x = 9

KL = -8x + 96

KL = -8(9) + 96

KL = 24