A radioactive compound with mass 100 grams decays at a rate of 5.8% per hour. Which equation represents how many grams of the compound will remain after 2 hours?

The transformation rule used to transform Triangle PQR to P'Q'R' is; (x, y) → (⁵/₂x, ⁵/₂y)

We are given from the question that the triangle P'Q'R' was transformed from the triangle PQR.

We see from the image that the coordinates of the original triangle PQR are;

P(-1, 1)

Q(2, 0)

R(-1, -2)

We also see that the coordinates of the transformed triangle P'Q'R' are;

P(-5/2, 5/2)

Q(5, 0)

R(-5/2, -5)

Thus, we can conclude that the transformation rule used here is;

(x, y) → (⁵/₂x, ⁵/₂y)

Read more about Mathematical Transformations at; https://brainly.com/question/4289712

#SPJ1

Answer:

Step-by-step explanation:

Ok:

1. This is a percent problem!

45/100*15=

675/100=

6.75

2. Subtract:

15-6.75=

8.25$

Answer: 8.25$

The option that shows the equation for the line in the graph is

A graph is a pictorial representation of data. The graph shows a linear function which will be written in the slope intercept form  form as

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

calculation of slope

The points used for the slope is gotten from the graph as B(-5. 5)  (-2, -4)

m = (y₂ - y₁) / (x₂ - x₁)

substituting the values

= ( -4 - 5 ) / ( -2 - -5 )

= -9 / -2 + 5

= -9 / 3

= -3

y intercept, c

this is a point where the graph cuts the y axis

c = -10

hence the equation is written using y = mx + c and substituting the values

y = -3x - 10

Learn more about writing equation from graphs:

brainly.com/question/29244324

#SPJ1

Lower Limit = 24.52

Upper Limit = 36.28

Error Bound = 5.88

Lower Limit: - The Lower Limit for every class is the smallest value in that class. For example: 5 is a lower lower limit for the set S= { 5,8,42,34}

Upper Limit: - A value that is greater than or equal to every element of a set of data. For example: - { 3,5,11,20,22} is a upper bound of 22.

Given that,

Population Mean,μ = 33.2

sample Mean, χ (x bar) = 30.4

sample Size, n = 25

α (Alpha) = 0.05

Population standard deviation,σ = 15

95% confidence interval:

μ ± z critical σ / √n

Putting the values, we get,

z critical at α0.05 = ± 1.96

30.4 ±1.96( 15/√25) = 30.4 ± 5.88 = (24.52,36.28)

a) Lower Limit = 24.52

b) Upper Limit = 36.28

c) Error Bound =

Margin of Error = z critical × σ /√n

                         =  1.96 × 15/√25

                          = 1.96  × 15/5

                          = 5.88

Learn more about Lower Limit:

https://brainly.com/question/1999705

#SPJ4

980g of sulphuric acid (H₂SO₄) is needed to prepare 5.0L of a 2M solution.

So, the grams of H₂SO₄ needed will be:

Therefore, 980g of sulphuric acid (H₂SO₄) is needed to prepare 5.0L of a 2M solution.

Know more about Sulfuric acid here:

https://brainly.com/question/10220770

#SPJ1

Answer:

1) 1.96

2) 6

3) 4/3

Step-by-step explanation:

think of exponents as repeated multiplication. the exponent is how many times you're going to multiply the number itself by.

1) [tex]1.4^{2}[/tex] is really just 1.4 * 1.4, which you can solve by long multiplication or a calculator to get 1.96

2) for this one, you can rewrite the expression as a fraction. you'll also want to use PEMDAS, starting with the parentheses

[tex]\frac{300}{ 2(0.5+4.5)^{2}}\\\\\frac{300}{2*(5)^2}\\\\\frac{300}{2*25} \\\\\frac{300}{50} = 6[/tex]

3) [tex](\frac{1}{2})^{3} = \frac{1}{2} *\frac{1}{2} *\frac{1}{2} = \frac{1}{8} \\[/tex]

you can rewrite the division as a fraction again, only this time. you can change the subtraction to the reciprocal of the denominator

[tex]\frac{1}{3} / (2*\frac{1}{8} )= \frac{1}{3} / \frac{1}{4} = \frac{1}{3} * 4 = \frac{4}{3}[/tex]

hope this helped!

Answer:

2.5x

Step-by-step explanation:

Given information for width:

Model: 10 in.

Real: 25 in.

Solve: How much times wider is real than model?

To find this, lets divide 25in. by 10in to find the scale factor.

25/10 = 2.5

2.5

We can verify this by multiplying 10 by 2.5

10 x 2.5 = 25

Answer:

=========================

The smaller figure is added, considering the coordinates of the image follow the rule:

Smaller stage is in blue. See attached

Since each side is half the original, the perimeter of the image is half the larger one:

neverminding the jumbled wording

how much is 20% of 40?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 40}}{\left( \cfrac{20}{100} \right)40}\implies 8[/tex]

The possible numbers of additional miles that Lamar can run are all the solutions of the inequality:

0 ≤ x ≤ 15

We know that Lamar will run at most 37 miles this week, and he already did run 22 miles, then the (maximum) distance left this week is:

D = 37mi - 22mi = 15mi

So he can run at most 15 miles, this means that he can run any distance between 0 miles and 15 miles by the end of the week.

So, if we define x as the distance that he will run on the week (in miles), then we can write the inequality:

0 ≤ x ≤ 15

so the possible numbers of additional miles he will run on this week are all the values of x that are a solution for the above inequality.

Learn more about inequalities:

https://brainly.com/question/24372553

#SPJ1

El precio final, esto es, el precio con descuento, del bolso es igual a $ 36.000.

En este problema debemos determinar el precio final de un bolso (C') adquirido por un cliente con descuento, igual al precio original (C) menos el descuento, descrito en la siguiente fórmula:

C' = C · (1 + r / 100)

Donde r es la tasa de descuento. Nótese que existe descuento para 0 < r < 100.

Si sabemos que C = 40.000 y r = - 10, entonces el precio final del bolso es:

C' = 40.000 · (1 - 10 / 100)

C' = 36.000

El precio final del bolso es igual a $ 36.000.

Para aprender más sobre descuentos: https://brainly.com/question/24130820

#SPJ1

2/5 fraction as a decimal is 0.4.

Any number that is expressed as a fraction has two components, the numerator and the denominator. Typically, we divide the numerator by the denominator to convert a fractional number to decimal form. The formula p/q, where q=0, is used to denote fractions. While the decimal numbers, such as 7.575, are created by joining the entire number and fractional parts with a decimal point. 

There are two methods to convert fraction to decimal which are given below:

For 2/5

We will divide them as mentioned above,

2/5 = 0.4

Hence, 2/5 is equal to 0.4 in decimal form.

To learn more about fraction here:

https://brainly.com/question/10354322

#SPJ1

Answer:

y=4/3x +7

Step-by-step explanation:

4x - 3y = -21

Move 4x to the other side

-3y = -21 -4x

Next divide the other side by -3

y= 7 +4/3x

Move numbers around

y = 4/3x + 7

The compound interest earned by Evelyn in one year is $9.

Evelyn has a bank account. She deposited $90 in her account. She earns 10% interest on her deposited money. The interest earned is compounded annually. We need to calculate the interest earned by her in one year, to the nearest cent.

We need to calculate the compound interest. The formula is given below.

B = p(1 + r)^t

The variables 'B', 'p', 't', and 'r' represent the final amount, the initial amount, the time duration, and the rate of interest, respectively.

B = $90(1 + 0.1)^1

B = $90*1.1

B = $99

The final amount in her bank account after one year is $99. The interest earned is the difference between the final and the initial amount. Let the variable 'I' represent the interest earned.

I = B - p

I = $99 - $90

I = $9

To learn more about compound interest, visit :

https://brainly.com/question/13155407

#SPJ1

Answer:

6(2x - 1)

Step-by-step explanation:

Just look up the answer on the calculator

The percent of increase in Zach's finishing time is 5%.

From the information, at a race a few months ago, he finished in 280 minutes and yesterday, he completed another triathlon and finished in 294 minutes.

The increase in time will be:

= New time - Old time

= 294 - 280

= 14 minutes

The percentage increase will be:

= Increase in time / Original time × 100

= 14 / 280 × 100

= 1/20 × 100

= 5%

Learn more about percentages on:

brainly.com/question/24304697

#SPJ1

Answer:

When we reflect over the x-axis the answer will be (6, -2)

Then when we go 4 units right it will turn into (10,-2)

And lastly, when we go 3 units down, it will be (10,-5)

The Answer is (10,-2)

(Brainiest is optional)

Answer:

answers found in pdf

Step-by-step explanation:

mathaway will help check your answers that what I did.

Systematic errors are consistently in the same direction

In contrast , random errors produce different values in random directions

Random error causes a slight difference of one measurement to from the next. It is quite unpredictable in it's variation during an experiment.

Systematic error always affects measurements by the same proportion, provided that a reading is taken the same way each time. It is predictable

An example that illustrates this difference are

Systematic errors are consistently in the same direction

for example they are always 50g , 1% or 99 mm too large or too small

In contrast , random errors produce different values in random directions

learn more about of systematic error here

https://brainly.com/question/14149934

#SPJ4

Answer:

y = x - 12

Step-by-step explanation:

slope = (-9 - (-5))/(3 - 7) = -4/(-4) = 1

y = mx + b

y = x + b

-5 = 7 + b

b = -12

y = x - 12

Caroline would have $36 more money in her account than Jaxon.

From the question, we have

Caroline amount,

A = P* e^rt

= 900*e^(71*8)/800

= 900*e^(71/100)

=$1830.59

Jaxon amount,

A = P* e^rt

= 900*e^(69*8)/800

= 900*e^(69/100)

=$1794.34

Difference = $1830.59 - $1794.34

= $36.25

= $36 ( to the nearest dollar)

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.

The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

To learn more about subtraction visit: https://brainly.com/question/2346316

#SPJ1

Answer:

x=246 or x=-266

Step-by-step explanation:

First you bring 12x to the other side and simplify to give

x²+20x+116=0

Then solve by completing the square:

(x+10)²-100+116=0

(x+10)²+16=0

(x+10)²=-16

x+10=±256

x=±256-10

x=246 or x=-266

Hope this helps

The total cost of the cosmetics including 2% processing fee rounded up to the nearest cent is $26.27

The cost of the cosmetics is $25.75

The 2% processing fee is calculated as follows:

2/100 × $25.75 = $ 0.515

The total cost including processing fee is $25.75 + $ 0.515 = $26.265 rounded up to $26.27

To learn more about percentage visit: https://brainly.com/question/24877689

#SPJ1

The price range of the Chevrolet HHR retro will be $14,500.

The range of the data is defined as the difference between the maximum value of data and the minimum value of the data.

The given data as:

$8,500, $8,500, $8,500, $9,900, $10,800, 10,800, 11,000, 12,500, $12,500, $13,000, 13,000, $14,500, and $23,000

According to the given information, the required solution would be as:

The maximum value of data = $23,000

The minimum value of data = $8,500

The range of the data = The maximum value of data - The minimum value of data

Substitute the values in the above formula,

The range of the data = 23,000 - 8,500

Apply the subtraction operation to get the answer

The range of the data = 14,500

Therefore, the price range of the Chevrolet HHR retro will be $14,500.

To learn more about the range of the data click here:

https://brainly.com/question/20607770

#SPJ1

The question seems to be incomplete the correct question would be:

Mitzi looked up prices of thirteen used Chevrolet HHR retro" tracks in the classified ads and found these prices: 8,500, 8,500, 8,500, 9,900, $10,800, 10,800, 11,000, 12,500, $12,500, $13,000, 13,000, $14,500, and $23,000. Find the range of the data.

Answer:

145 degrees

Step-by-step explanation:

The side through L is at a 35 degree angle, and the side through N is at a 180 degree angle. Taking the difference, we get 145 degrees.

Answer: -3

Step-by-step explanation: Used calculator

The slope of origin (0, 0) with (1, 31); (5, 155), and (9, 279) is 31

The slope of a line will indicate the direction and steepness. It is also defined as the change in the y-coordinate for a corresponding change in the x-coordinate.  

Slope of a line with given points (x₁, y₁) and (x₂, y₂) is  

Here we have

Points (1, 31) (5, 155) and (9, 279)

We need to find slopes between two points

As we know the formula for slope with given points is

Slope, m = (y₂ -y₁) /(x₂-x₁)

Here coordinates of the origin are (0, 0)

The slope between (0, 0) and (1, 31)

=> m =  (31 - 0) /(1 - 0)  = 31/1 = 31

The slope between (0, 0) and (5, 155)

=> m =  (155 - 0) /(5- 0)  = 155/5 = 31

The slope between (0, 0) and (9, 279)

=> m =  (279 - 0) /(9 - 0)  = 279/9 = 31        

Therefore,

The slope of origin (0, 0) with (1, 31); (5, 155), and (9, 279) is 31

Learn more about the Slope of a line at

https://brainly.com/question/28289355

#SPJ1