The table below represents the amount, in grams, of a substance remaining after t years.

Answers

Answer 1

Answer:

Step-by-step explanation:

The equation we'd use for this problem is y=a(1-b)^x (exponential decrease)

a is the initial amount, the number in the parentheses is the amount it decreases by, and x is time.

The initial amount is 8,500 since that is what we start with after 0 years. By looking at the chart we can see that the number decreases over time by a constant rate of .5, so that is the number in the parentheses. You then end the equation with ^t since t would be time in years

Related Questions

f(9)=-4(9)^2-4(9)+18=

Answers

The answer is -342

Step - by - step

f(9)=-4(9)^2-4(9)+18

= -4*81-36+18

= -324-36+18

= -360+18

= -342

A 2-cup bottle of glass cleaner costs $6.56. What is the price per fluid ounce?

Answers

Answer:

82 cents per ounce

Step-by-step explanation:

There are 8 oz in a cup so two cups = 16 ounces

$6 .56 / 8 oz = $ .82 / oz

The endpoints of AB are A(-8,-6) and B(-3,-1). Point C lies on Ab and is 3/5 of the way from A to B. What are the coordinates of point C?

Answers

Answer: C(-6.125,-4.125)

Step-by-step explanation:

[tex]\displaystyle\\A(-8,-6)\ \ \ \ B(-3,-1)\\Let\ \frac{3}{5}=\lambda \\Hence,\\\boxed {x_C=\frac{x_1+x_2\lambda}{1+\lambda} }\ \ \ \ \ \ \boxed {y_C=\frac{y_1+y_2\lambda}{1+\lambda} }\\\\x_1=-8\ \ \ \ x_2=-3\\\lambda=\frac{3}{5} \\\\\lambda=\frac{0.6*5}{5}\\\\\lambda=0.6\\\\x_C=\frac{-8+(-3)*0.6}{1+0.6} \\\\x_C=\frac{-8-1.8}{1.6} \\\\x_C=\frac{-9.8}{1.6} \\\\x_C=-\frac{9.8*10}{1.6*10} \\\\x_C=-\frac{98}{16} \\\\x_C=-6.125\\\\\\[/tex]

[tex]\displaystyle\\y_1=-6\ \ \ \ y_2=-1\ \ \ \ \lambda=0.6\\\\y_C=\frac{-6+(-1)*0.6}{1+0.6} \\\\y_C=\frac{-6-0.6}{1.6}\\\\y_C=\frac{-6.6}{1.6} \\\\y_C=-\frac{6.6*10}{1.6*10} \\\\y_C=-\frac{66}{16} \\\\y_C=-4.125[/tex]

[tex]Thus,\ C(-6.125,-4.125)[/tex]

At a school, the average of the number of boys, girls, male teachers, and female teachers is 117. The average of the number of boys, girls, and male teachers is 151At a school, the average of the number of boys, girls, male teachers, and female teachers is 117. The average of the number of boys, girls, and male teachers is 151. There are 6 fewer male teachers than there are female teachers. The number of female teachers is 1/16 the number of girls. How many boys are there at the school? boys

Answers

Using a system of equations, it is found that there are 204 boys at the school.

What is a system of equations?

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.

For this problem, the variables are given as follows, considering the situation described:

Variable x: number of boys in the school.Variable y: number of girls in the school.Variable z: number of male teachers in the school.Variable w: number of female teachers in the school.

The average of the number of boys, girls, male teachers, and female teachers is 117, hence:

(x + y + z + w)/4 = 117

x + y + z + w = 468.

The average of the number of boys, girls, and male teachers is 151, hence:

(x + y + z)/3 = 151

x + y + z = 453.

Then:

x + y + z + w = 468.

453 + w = 468

w = 15.

There are 6 fewer male teachers than there are female teachers, hence:

z = w - 6 = 15 - 6 = 9.

So:

x + y + z = 453.

x + y = 444.

The number of female teachers is 1/16 the number of girls, hence:

y = 16w = 16 x 15 = 240.x = 444 - y = 444 - 240 = 204.

There are 204 boys at the school.

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Which of the following is an equivalent expression of 15x2 +12x + 8?

Answers

Answer:

15 (x + 2\/5)^2 + 28\/5

Step-by-step explanation:

Solve the simultaneous equations
3y + 11 = 4x
10x + 2y + 1 = 0

Answers

In linear equation the solution set of the equations x = 1/2, y = -3.

What in mathematics is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Multiply both sides of the equation by a

coefficient - 2(4x - 3y ) = 11 × 2

3 ( 10x + 2y ) = ( - 1 ) × 3

apply multiplicative distribution law

8x - 6y = 11 × 2

3( 10x + 2y ) = (-1) × 3

calculate the first terms

8x - 6y = 22

3( 10x + 2y ) = ( -1) × 3

remove the parentheses

8x - 6y = 22

30x + 6y = -3

add up the two equation

8x - 6y + ( 30x + 6y ) = 22 + ( -3)

remove parentheses - 8x - 6y + 30x + 6y = 22 -3

cancel the unknown variables - 8x + 30x = 22 -3

combine like terms - 38x = 22 - 3

calculate the sum or difference - 38x = 19

reduce the greatest common factor on both

sides of equation - 2x = 1

divide both sides of the equation by the coefficient of variable - x = 1/2

substitute one unknown quantity into the elimination 8 * 1/2 - 6y = 22

reduce the expression to the lowest term 4-6y = 22

reduce the greatest common factor on both sides of the equation

2 - 3y = 11

Rearrange unknown terms to the left side of the equation - 2 - 3y = 11

calculate the sum or difference -3y = 9

reduce the greatest common factor on both sides of the equation -y = 3

divide both sides of the equation by the coefficient of variable y = -3

the solution set of the equations

x = 1/2

y = -3

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The maximum speed, in miles per
hour, of a cheetah is 18 more than 3 times
If the maximum speed of a cheetah is
the maximum speed of a hippopotamus.
75 miles per hour, which equation could be
used to find the maximum speed of a
hippopotamus h? (Lesson 1-2)
A. h= 3(75) + 18
B. 75=3h
C. 75 = 3h + 18
D. 18 + 75 = 3h

Answers

The equation could be used to find the maximum speed of a hippopotamus h is C. 75 = 3h + 18

The question has to do with linear equation

What is a linear equation?

A linear equation is a mathematical expression in which the highest power of the unknown is 1.

How to find the equation for the maximum speed of the hippopotamus

Let

x = speed of cheetah and h = speed of hippopotamus

Given that the maximum speed, in miles per hour, of a cheetah is 18 more than 3 times the maximum speed of the hippopotamus

Now, since the maximum speed of the hippopotamus is h, 3 times the maximum speed of the hippopotamus is 3h.

Since the cheetah is 18 more than 3 times the maximum speed of the hippopotamus, we have that

x = 3h + 18

Substituting x = 75 into the equation, we have

75 = 3h + 18

So, the equation could be used to find the maximum speed of a hippopotamus h is C. 75 = 3h + 18

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The sum of 4 consecutive odd integers is -24. What are they?

Answers

Step-by-step explanation:

4 consecutive odd integers means we start with x, then have x+2, x+4 and then x+6.

and then we have

-24 = x + x+2 + x+4 + x+6 = 4x + 12

4x = -36

x = -9

x+2 = -7

x+4 = -5

x+6 = -3

so, in sequence from small to large these 4 numbers are

-9, -7, -5, -3

Given (2x + 3) (3x − 2) = 0
What are the values of x in 10th decimal places?
X=
X=
please answer fast

Answers

x1 = -3/2 or -1.5
x2 = 2/3 or .666667

The first term of arithmetic sequence is 2 and 10th term is 39 find the 30th term

Answers

To be honest I have no clue but I know you got this bro

what is the perimeter of the vertices (1,4),(-1,-2),(2,0),(4,0) to the nearest hundredth

Answers

The Perimeter of the quadrilateral = 16.93 units

How to Find the Perimeter of a Quadrilateral?

The perimeter of the quadrilateral with the given vertices is the sum of the distance between every vertices.

Calculate the distance between the vertices using the distance formula, d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

Name the vertices as shown below:

A(1,4)

B(-1,-2)

C(2,0)

D(4,0)

Distance between A and B:

AB = √[(−1−1)² + (−2−4)²]

AB = √(4 +36)

AB = 6.32 units

Distance between B and C:

BC = √[(−1−2)² + (−2−0)²]

BC = 3.61 units

Distance between C and D:

CD = √[(4−2)² + (0−0)²]

CD = 2 units

Distance between A and D:

AD = √[(4−1)² + (0−4)²]

AD = 5 units.

Perimeter of the quadrilateral = AB + BC + CD + AD = 6.32 + 3.61 + 2 + 5

Perimeter of the quadrilateral = 16.93 units

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Three angles are shown, ZHRM, ZHRD, and ZDRM.
D
M
H
If m/HRM = 54°, m/HRD =
m/DRM =
(²7*+11) ².
4
R
(1/22 +22), ar
x
and
what is the value of x?

Answers

Answer:

Step-by-step explanation:

By the angle addition postulate,

[tex]54=\frac{1}{2}x+22+\frac{1}{4}x+11 \\ \\ 54=\frac{3}{4}x+33 \\ \\ 21=\frac{3}{4}x \\ \\ x=28[/tex]

What type of variable is the number of customers in line at the bank in a 24 hour period? qualitative continuous attribute discrete

Answers

The number of customers waiting in line at the bank over a 24-hour period is a discrete variable type.

By discrete variable, what do you mean?

A variable whose value is determined by counting is referred to as a discrete variable. examples: the number of pupils in attendance. how many red marbles are in the container. when triple coins are turned, the count of heads. The number of pupils, kids, the shoe size, and so forth are some typical examples of discrete data. A statistical variable is referred to as a discrete variable if it presupposes a finite collection of data and a countable number of values. Contrarily, a continuous variable is a quantitative variable that accepts an endless quantity of data and an uncountable number of values.

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49^((1)/(2))- 25^((3)/(2))

Answers

Answer: -118

Step-by-step explanation:

49^((1)/(2))- 25^((3)/(2))=

49^(1/2) -25^(3/2)=

7-25^((2+1)/2)=

7-25^((2/2)+(1/2))=

7-25^(1+1/2)=

7-25^(1) *25^(1/2)=

7-(25*5)=

7-125=-118

Write the equation of the line through (3,-5) and perpendicular to -3x + 2y = 12 in slope-intercept form.

Answers

The equation of the line through (3,-5) and perpendicular to -3x + 2y = 12 in slope-intercept form is y = -2/3x + 1

Equation of a line

The equation of a line is expressed as;

y = mx + b

m is the slope

b is the y-intercept

Given the equation -3x + 2y = 12

2y = 3x + 12

y = 3/2x + 6

From the equation, the slope that is perpendicular to the slope is -2/3

Determine the equation

y-(-5) = -2/3(x-3)

y+5 = -2/3x + 6

y = -2/3x + 6 - 5

y = -2/3x + 1

Hence the equation of the line through (3,-5) and perpendicular to -3x + 2y = 12 in slope-intercept form is y = -2/3x + 1

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Stella buys 5 pineapples for $4.50. How much would she pay if she bought 7 pineapples? (hint: find the unit rate first then multiply)
*

Answers

Answer:

Step-by-step explanation:

4.50 divides by 5 than times the answer by 7

4.50 divided by 5 is .90 so .90 times 7 is 6.3

find the area of the shaded region.
round to the nearest tenth.

Answers

The area of the shaded region is 294.4 square meters

How to find the area of the shaded region?

The given parameters are represented on the figure

By this;

The area of the shaded region is the sum of the area of the major sector and the area of the triangle

The area of the major sector is

A1= ∅/360 * πr²

The area of the triangle is

A2 = 0.5r²sin(x)

So, the total area is

Total = ∅/360 * πr² + 0.5r²sin(x)

This gives

Total = (360 - 130)/360 * 3.14 * 11.1^2 + 0.5 * 11.1^2 * sin(130 deg)

Evaluate

Total = 294.4

Hence, the area of the shaded region is 294.4 square meters

Answers

Answer:

Step-by-step explanation:

Which number rounds to 3,000 if you round it to the nearest thousand, AND to 2,500 if you round it to the nearest hundred?

Answers

Answer:

2,739 and 2,489

Step-by-step explanation:

There are many solutions to both problems:

(Rules)
If the number is 5 or higher round (up)
If the number is 4 or lower round (down)

2,739⇒3,000
↑↑↑
Higher than 500 so round up to get 3,000

2,489⇒2,500
↑↑
Higher than 50 so round up to get 2500

2,739 and 2500 are both possible solutions.

Use the data and create a formula for the function that approximates the ground roll for a fully loaded cessna 172 at an elevation of:_____

Answers

The formula for the function that approximates the ground roll for a fully Cessna 172 at an elevation of x is y = 585(1.00009)x .

What is angle of elevation ?

The angle from the horizontal upward to an item is referred to as the angle of elevation. The line of sight of an observer would be above the horizontal. The angle from the horizontal downward to an item is referred to as the "angle of depression." The line of sight of an observer would be below the horizontal.

Let the formula for the exponential function that approximates the ground roll for a fully loaded Cessna 172 at an elevation of x be

y =A(B)x ....(1)

Here,

A = ground roll at x =0,

B = growth factor.

Since at x =0, , Ground roll is = A = 585 ft ....(2)

On putting A = 585 in equation (1), we get

y = 585(B)x ....(3)

Now, at elivation of x = 1000 ft ,

Ground roll y = 640 ft.

So, putting these values in equation (3), to get

640 = 585(B)1000

Reversing the sides to get

585(B)1000 = 640

Or B1000 = 640/585

Or B1000 = 1.09017094

Or B = (1.09017094)1/1000

Or B = 1.00009 .....(4)

On putting the value of B in equation (3), we get

y = 585(1.00009)x

Hence, the formula for the function that approximates the ground roll for a fully Cessna 172 at an elevation of x is y = 585(1.00009)x .

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If you roll a standard 6 sided die and you get paid $1 for every spot it lands on (so if you roll a 5 that would mean $5), what's the average payout for one roll?

Answers

Answer:

Step-by-step explanation:

I need help with this ASAP please

Answers

Answer:

c between 30 and 40 mins

Step-by-step explanation:

if you look at the graph that's the only line going down.

Please Help me ASAP 100 points for correct answer

Answers

Answer:

Step-by-step explanation:

pls help with this question ASAP

What equations do u insert in between these numbers to get the answer

a.5 8 3 9 =50

b.12 6 2 10=14

c.4 5 6 10=24

d.7 4 6 9 7= 16

e.4 9 6 2 =52

f.45 5 9 3 7=102

Answers

hduodoydiyd9ydiydoyeykdoyx95eeykyei6djj

Step-by-step explanation:

a) 5

Which of the following options are examples of how you can name the angle? Select all that apply.

Answers

Answer:thr lerrkmaf

Step-by-step explanation:

and we are so cool DEA

The water level in Colorado river is 2.55 m below average. a large rainfall caused The water level to rise 0.8 m. what is the water level after the rainfall?

Answers

The water level after the rainfall is 3.05m

How to calculate the measurement of the water level after the rainfall ?

The water level in colorado river is 2.55m below average

A larger rainfall happened and the water level rose by 0.8m

Therefore the water level after the rainfall can be calculated by adding the previous water level which is 2.55 by the new increase which is 0.8

= 2.55 + 0.8

= 3.05

Hence the water level after the rainfall is 3.05 m

Answers

The value of the expression (12 - 3/5√25)^2 + (2 - 4)^2 is 85

How to evaluate the expression?

The expression is given as

(12 - 3/5√25)^2 + (2 - 4)^2

Evaluate the square root of 25

So, we have

(12 - 3/5√25)^2 + (2 - 4)^2 = (12 - 3/5 * 5)^2 + (2 - 4)^2

Evaluate the product

So, we have

(12 - 3/5√25)^2 + (2 - 4)^2 = (12 - 3)^2 + (2 - 4)^2

Evaluate the difference

So, we have

(12 - 3/5√25)^2 + (2 - 4)^2 = 9^2 + (2 - 4)^2

Evaluate the exponent and the sum

So, we have

(12 - 3/5√25)^2 + (2 - 4)^2 = 85

Hence, the value of the expression (12 - 3/5√25)^2 + (2 - 4)^2 is 85

Answers

The number of medals won by team A is 15 medals while the number of medals won by Team B is 9 medals.

How to solve Algebra Word Problems?

Team A won 3 more medals than two times the medals won by Team B.

If the number of medals won by team B is x, than;

Number of medals won by team A = 3 + 2x

Number of medals won by team B = x

Also, we are told that Team A won 9 more medals than Team B.

Thus;

(3 + 2x) = x + 9

2x - x = 9 - 3

x = 6

3 + 2x = 3 + 2(6) = 15 medals

Thus, we conclude that the number of medals won by team A is 15 medals while the number of medals won by Team B is 9 medals.

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Solve 2x+18=6y for x.

Answers

Answer:

x=3y−9

Step-by-step explanation:

2x+18=6y

2x=6y−18

(2x)/2=(6y−18)/2

x=3y−9

Answer:

x = 3y−9

Step-by-step explanation:

Add -18 to both sides:

2x + 18+− 18=6y + −18

2x = 6y − 18

Divide both sides by 2:

2x / 2= 6y −18 / 2

x = 3y −9

first person 2 answer will give u brainliest need to submit by 2 nite :)

Two angles are Complementary, if the measure of one of the angles is 66.7 degrees what is the measure of the other angle? Answer to the first decimal place, IE 79.5.

Answers

Answer:

probly 79.5

Step-by-step explanation:

i d k

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