Jordan works in a science lab where he is studying the behavior of a certain unstable isotope. He has 240 milligrams of the sample, and the amount of the substance remaining in the sample decreases at a rate of 8% each day. After t days, there are less than 115 milligrams of the substance remaining. Which inequality represents this situation, and after how many days will the amount of the sample be less than 115 milligrams?

Answer:

138 pipe cleaners can make 23 kit

Step-by-step explanation:

6 pipe cleaners = 1 kit

1 pipe cleaner = 1/6 kit

138 pipe cleaners = 1/6 x 138

138 pipe cleaners = 23

In this scenario, the combined capacity of the three roads leading to the stadium is 12,000 vehicles per hour. Therefore, to park 10,000 vehicles, it would take approximately 50 minutes.

The question involves an understanding of traffic flow and rates. To find the total capacity of these roads leading to the stadium, we multiply the number of roads by the number of lanes on each road and the capacity of each lane, resulting in 4 lanes per road x 3 roads x 1,000 vehicles per lane per hour, equal to 12,000 vehicles per hour.

With 10,000 vehicles expected for the game, we can then divide the total number of vehicles by the total capacity of the roads per hour to find out how many hours it will take for all vehicles to enter the parking lots. Therefore, it will take approximately 10,000 vehicles / 12,000 vehicles per hour = 0.83 hours, or about 50 minutes.

The increased traffic due to a new manufacturing plant, increased businesses, and route changes in the nearby streets can also affect the traffic flow, however these factors are not quantified in the question. In the real world, proper planning and infrastructure can solve campus parking issues, as the example mentioned about Twelfth and Locust Streets.

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Answer:

a_n=a_(n−1)+1.4 , where a_1=4.4

Step-by-step explanation:

Given a sequence as

4.4, 5.8, 7.2, 8.6, 10, …

We find that first term is 4.4

II term = 5.8 = 4.4+1.4

III term = 7.2 = 5.8+1.4

Iv term = 8.6 = 7.2+1.4

V term = 10.0 = 8.6+1.4

i.e. each term is got by adding 1.4 to the previous term.

In other words, this is an arithmetic sequence with I term =4.4 and d = common difference =1.4

I term = a_1 = 4.4

and a_2 = a_1+1.4 and so on.

Hence correct answer is

a_n=a_(n−1)+1.4 , where a_1=4.4

There is a certain pattern:

As x is increased by 1/4 every time, y is increased by 3 every time. You can make a proper ratio and set up proportions with these numbers.

2x - 5 = x + 25

-x         -x        

x - 5  =       25

   +5          +5

x       =       30

Answer: x = 30

One inch is greater than centimeter

Answer:

If a polygon has not got four right angles then it is not a square.

Step-by-step explanation:

Contrapositive is

if A implies B then not B implies not A.

Answer: Comparison Postulate

This is the idea that exactly one statement shown below is true

a > b

a = b

a < b

So if you compare two numbers, then either the left value is larger, the left is smaller, or the the left is the same as the value on the right.

26 is a multiple of 2 but 39 isn't

39 is a multiple of 3 but 26 isn't

Dividng by the next three prime numbers, neither 26 nor 39 is a multiple of 5, 7, or 11

Moving up to the sixth prime number (13), we see that BOTH 26 and 39 are divisible by 13.  26 = 2 * 13 and 39 = 3 * 13 and 13 is the lowest common multiple of 26 and 39.

Let's rewrite the expression as

[tex] 8x+3ax-5ax = 8-2a \iff 8x - 2ax = 8-2a \iff 2x(4-a) = 2(4-a) [/tex]

So, if [tex] a \neq 4 [/tex], you may divide both sides by [tex] 4-a [/tex], the equation becomes [tex] 2x=2 [/tex], and the only solution is [tex] x=1 [/tex], which means that this is not an identity (an indentity is tautologically true, no matter the value of x).

If instead [tex] a = 4 [/tex], you are multiplying both sides by zero, so the equation becomes

[tex] 2x \cdot 0 = 2 \cdot 0 \iff 0=0 [/tex]

So, it doesn't matter which value for x you choose, because you will always end up with [tex] 0=0 [/tex], which is obviously always true.

Hi there!

To calculate a discount or a mark-up in the price of a retail item, you need to multiply the given price of the item by the percentage, like so:

1.35 × 0.2 = 0.27

Then you add or subtract as necessary. In your case you would subtract since you are trying to find a discount price.

1.35 - 0.27 = 1.08

So the final price of the product after the discount is $1.08

Your friend, ASIAX

Answer:

The value of the equation is [tex]x=\frac{y-a}{b}[/tex].

Step-by-step explanation:

Consider the provided equation.

[tex]y=bx+a[/tex]

We need to solve the provided equation for x.

Subtract a from both side.

[tex]y-a=bx+a-a[/tex]

[tex]y-a=bx[/tex]

Divide both sides by b.

[tex]\frac{y-a}{b}=\frac{bx}{b}[/tex]

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

Hence, the value of the equation is [tex]x=\frac{y-a}{b}[/tex].

The variable 'x' as the subject of the formula of the equation y = bx + a is x = ( y - a )/b.

Given the equation in the question:

y = bx + a

To make the variable 'x' the subject of the formula of the equationy = bx + a, first isolate term with the variable 'x'.

y = bx + a

To isolate the term containing variable 'x', first subtract 'a' from both sides of the equation:

y - a = bx + a - a

y - a = bx

Reaorder:

bx = y - a

Now, divide both sides by 'b':

bx/b = ( y - a )/b

x = ( y - a )/b

Therefore, the variable 'x' equals ( y - a )/b.

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Answer:

Domain = {4,-9,5}

Range = {2,4,17}

Step-by-step explanation:

We are given ordered pairs as

{(4,2), (-9,2), (5,4), (4,17)}

This is a subset of cartesian product AXB where

A = {4,-9,5} and B = {2,4,17}

Note: Repeated values are written only once in the set.

Hence we find that 4 is mapped on to 2 and 17,

-9 to 2 and 5 to 4

Domain = I item in the ordered pair of mapping =  {4,-9,5}

Range = II item in the ordered pair of mapping =  {2,4,17}

Hey there!!

What is a coordinate form?

... Coordinate form is written as ( x , y )

What is domain?

... Domain are also called as the 'x' values.

What is the range?

... Range is the other word for the 'y' values.

Given ordered pairs :-

( 4 , 2 ) ; ( -9 , 2 ) ; ( 5 , 4 ) ; ( 4 , 17 )

Hence, the domain is :-

... { 4 , -9 , 5 )

Hence, the range is :-

...  { 2 , 4 , 17 )

Remember :- The values "can not" be repeated!

Hope my answer helps!!

24 dollars.

1/4 + 1/3 = 3/12 + 4/12 = 7/12

7/12 a + 8 = 22

7/12 a = 14

a = 14 x 12/7

a = 24 dollars

It is a function.  It passes the vertical line test, meaning for each x there's at most one y.

When x=2 we see y=-3 as (2,-3) is a point on the graph

The question's subject is about interpreting and representing data using different types of graphs. Each type of graph is chosen based on what we want to show with our data. For instance, line graphs are useful for displaying change over time.

The question refers to the use of graphs to illustrate data. These graphs represent the position of a moving object plotted against time. In the presented case, Part A of the graph begins with a nonzero y-intercept with a downward slope that levels off at zero, while Part B begins at zero with an upward slope that decreases in magnitude until the curve levels off.

When creating graphs, it's important to label the axes correctly and, if multiple datasets are shown on one graph, various symbols should be used to differentiate between them. In the example given, three types of graphs can be used: a line graph to show change over time, a bar graph to compare different categories, and a pie chart to represent proportions. The choice of graph depends on the type of data and what you want to show.

As mentioned, a graphing utility allows us to compare trajectories, highlighting the differences and similarities. It is crucial to use that visualization and analysis tool to make effective interpretations.

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An even function is when f(x) = f(-x) ... or ... g(x) = g(-x).

f(x) = - (x + 1)(x - 4)

     = -(x² - 3x - 4)

     = -x² + 3x + 4                  f(x) = -x² + 3x + 4

f(-x) = -(-x)² + 3(-x) + 4

      = -x² - 3x + 4                 f(-x) = -x² - 3x + 4

                            f(x) ≠ f(-x) so it is NOT even.

********************************************************

g(x) = [tex]\frac{3}{2}|x|[/tex]

g(-x) = [tex]\frac{3}{2}|-x|[/tex]

       =  [tex]\frac{3}{2}|x|[/tex]  since absolute value becomes positive

g(x) = g(-x) so it IS even

Answer: C

Answer:

You were the 35th caller.

Step-by-step explanation:

For one minute, every 5th caller will win a music player and every 7th caller will win concert tickets.

If you were just the first caller to win both a music player and concert tickets, that means we need to find a least number which is divisible by both 5 and 7.

Actually we will find the LCM(Least common multiple) of 5 and 7.

[tex]5=1*5\\ \\ 7=1*7\\ \\ So, LCM = 1*5*7=35[/tex]

That means, you were the 35th caller.

Answer:

35

Step-by-step explanation:

Every 3 Parrots there will be 5 Birds

3/5

Answer:

Every 3 Parrots there will be 5 Birds

3/5

Step-by-step explanation:

Answer:

The remaining child got a fraction of  [tex]\frac{1}{10}[/tex].

Step-by-step explanation:

Lets take the fraction of the money fourth child got is [tex]x[/tex]

Addition of all these fractions should be equal to 1.

⇒[tex]\frac{1}{3} +\frac{1}{6} +\frac{2}{5} +x=1[/tex]

⇒[tex]\frac{10+5+12+30x}{30} =1[/tex] (Taking a common denominator)

⇒[tex]\frac{27+30x}{30} =1[/tex]

⇒[tex]27+30x=30[/tex]

⇒[tex]30x=3[/tex]

⇒[tex]x=0.1[/tex]

Therefore,

The remaining child got a fraction of  [tex]\frac{1}{10}[/tex].

By calculating the combined fractions of the inheritance received by the first three children, we've determined that 27/30 of the inheritance has been allocated. Subtracting this from the whole leaves us with 3/30, which simplifies to 1/10 of the inheritance for the remaining child.

The student has asked about how much the remaining child will receive from a father's inheritance if the first received 1/3, the second received 1/6, and the third received 2/5 of the inheritance. To answer this, let's first add up the portions of the inheritance that the first three children received:

First child: 1/3

Second child: 1/6

Third child: 2/5

Now, we will find a common denominator to add these fractions. The least common multiple of 3, 6, and 5 is 30. Let's convert each fraction:

First child: 1/3 = 10/30

Second child: 1/6 = 5/30

Third child: 2/5 = 12/30

Now, add these fractions:

10/30 + 5/30 + 12/30 = 27/30

Once we add up these portions, we get 27/30 which represents the total part of the inheritance that has been given out to the first three children. To find out the portion for the remaining child:

30/30 (the whole inheritance) - 27/30 (the part given away) = 3/30

Reducing the fraction 3/30 gives us 1/10. So, the remaining child would receive 1/10 of the inheritance.

Explanation:

Anna gets paid $8.75/hour working as a barista.

She gets paid $9.00/hour for creating weekly advertisement signs.

In total she works 25 hours a week.

Let 'x' represent the number of hours that she works as a barista, then [tex]25-x[/tex] would represent the number of hours she works to create signs.

A. We need to write a function h(x) that represents the amount of money that Anna earns working as a barista.

Since she is earning $8.75 per hour and she works as a barista for 'x' hours a week so the function is:

[tex]h(x)=8.75\times x=8.75x[/tex]

[tex]h(x)=8.75x[/tex]

B. We need to write a function f(x) to represent the hours Anna works creating the signs.

Since, in total she works for 25 hours a week so the function to represent the number of hours she work to create signs can be given by:

[tex]f(x)=(25-x)[/tex]

C. If 's' represents the number of hours that Anna works creating signs, we need to create a function g(s) that represents her earning creating signs.

So the number of hours Anna works creating signs for the coffee break is [tex]s[/tex], she gets paid $9.00 an hour for creating signs, so:

[tex]g(s)=9\times s=9s[/tex]

[tex]g(s)=9s[/tex]

D. We need to finf a composite function [tex]g(f(x))[/tex], to find the desired function we need to plug value of f(x) in the function g(s):

[tex]g(f(x))=9s=9(f(x))=9(25-x)=225-9x[/tex]

[tex]g(f(x))=225-9x[/tex]

The composite function g(f(x)) represents Anna's earnings while working just to create signs for the Coffee break.

E. To represent Anna's total earnings the functions that can be combined are h(x) and g(f(x)) because h(x) represents Anna's earnings while working as a barista and g(f(x)) represents Anna's earnings while she creates signs for the coffee break.

The function to represent Anna's total earnings can be given as:

[tex]T(x)=h(x)+g(f(x))=8.50x+225-9x[/tex]

where we must keep in mind that 'x' represents the number of hours she spent working as a barista in a 'week'.

Answer:

A

Step-by-step explanation:

yes

It would be subtraction because 2-1 would result into 1 multiplied by 4 would make 4 your answer. And then 6-3 would equal to 3, multiply 3 by 2, you would get 6. Then finally when you add both 4 and 6, you would get the final answer of 10.

x - length of side of a square

A perimeter of a square: P = 4x

We know:

20 ≤ P ≤ 32

20 ≤ 4x ≤ 32       |divide by 4

5 ≤ x ≤ 8

Answer: b. 5 ≤ x ≤ 8

Answer:

ans in b

Step-by-step explanation:

Explanation:

First we consider ΔABC and ΔBCD,

∠C=∠C  (common)

∠B=∠D=[tex]90\textdegree[/tex]

So, ΔABC ≈ ΔBCD (By AA similarity rule )

So by taking corresponding sides in ratios we get

[tex]\frac{AB}{BD}=\frac{AC}{BC}=\frac{BC}{CD}[/tex]      

Now

[tex]AC.CD=BC.BC\\BC^{2} =AC.CD[/tex]              -------- Eqn (1)

Similarly,

We consider ΔABD and ΔABC

∠A=∠A (Commom)

∠B=∠D=[tex]90\textdegree[/tex]

So,

ΔABD ≈ ΔABC (By AA similarity rule )

So by taking corresponding sides in ratios we get

[tex]\frac{BC}{BD}=\frac{AC}{AB}=\frac{AB}{AD}[/tex]  

Now,

[tex]AB.AB=AC.AD\\AB^{2} =AC.AD[/tex]              --------Eqn (2)

By Adding both the equation we get

[tex]AB^2+BC^2=AC.CD+AC.AD\\AB^2+BC^2=AC(CD+AD)\\AB^2+BC^2=AC.AC\\AB^2+BC^2=AC^2[/tex]

Hence, we proved the pythagorean theorem by using similarity of triangle.

To translate the given sentence into an equation, use the equation 2m = 32 and then divide both sides by 2 to solve for Mabel's age, which is 16 years old.

The sentence '32 is the product of Mabel's age and 2' can be translated into an equation using the variable m to represent Mabel's age. The product of two numbers means you multiply them together. We are given that when you multiply Mabel's age by 2, you get 32. The equation that represents this relationship is:

2m = 32

To find Mabel's age, we simply divide both sides of the equation by 2 to isolate m, which gives us:

m = 32 / 2

m = 16

Mabel's age is 16 years old.

I'm pretty sure its the 28th day?? If not let me know.

Answer: k = -1 +/- √769

Step-by-step explanation:

48x - ky = 11

-48x           -48x

         -ky = -48x + 11

         [tex]\frac{-ky}{-k} = \frac{-48x}{-k} + \frac{11}{-k}[/tex]    

           [tex]y =\frac{48x}{k} - \frac{11}{k}[/tex]

Slope: [tex]\frac{48}{k}[/tex]

*************************************************************************

 (k + 2)x + 16y = -19

- (k + 2)x             -(k + 2)x

                 16y = -(k + 2)x - 19

                  [tex]\frac{16y}{16} = -\frac{(k + 2)x}{16} - \frac{19}{16}[/tex]

                  [tex]y = -\frac{(k + 2)x}{16} - \frac{19}{16}[/tex]

Slope: [tex]-\frac{(k + 2)}{16}[/tex]

**********************************************************************************

[tex]\frac{48}{k}[/tex] and [tex]-\frac{(k + 2)}{16}[/tex] are perpendicular so they have opposite signs and are reciprocals of each other.  When multiplied by its reciprocal, their product equals -1.

[tex]-\frac{(k + 2)}{16}[/tex] *  [tex]\frac{k}{48}[/tex] = -1

[tex]\frac{(k + 2)k}{16(48)}[/tex] = 1

Cross multiply, then solve for the variable.

(k + 2)(k) = 16(48)

k² + 2k - 768 = 0

Use quadratic formula to solve:

k = -1 +/- √769

Assuming that Richard always reads with the same rate, there is a direct proportion between the time spent reading and the portion of book read:

[tex] \text{portion}_1 : \text{time}_1 = \text{portion}_2 : \text{time}_2 [/tex]

So, we can set up and solve the following proportion:

[tex] \dfrac{1}{4} : \dfrac{4}{5} = x : 1 \iff x = \dfrac{\frac{1}{4}}{\frac{4}{5}} = \dfrac{1}{4}\cdot \dfrac{5}{4} = \dfrac{5}{16} [/tex]

Answer:

'Kilometers' is the most appropriate unit to measure this distance.

Step-by-step explanation:

The distance between the baseball stadium and the airport is  [tex]1.6\times 10^6[/tex] centimeters.

[tex](1.6\times 10^6)cm = (16\times 10^5)cm[/tex]

Now,  10⁵ centimeters is equal to 1 kilometer.

That means,  [tex](16\times 10^5)cm = (16\times 1)km= 16 km[/tex]

So, 'Kilometers' is the most appropriate unit to measure this distance.

 1 inch :  3 meters

x 4          x 4        

4 inch :  12 meters

Answer: 12 meters