Suppose a/b c/d and e/f represent three rational numbers. If a/b is less than c/d and c/d is less then e/f compare a/b and e/f explain

[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\dotfill &11\\ P=\textit{initial amount}\dotfill &160\\ t=\textit{elapsed time}\\ h=\textit{half-life}\dotfill &14 \end{cases} \\\\\\ 11=160\left( \frac{1}{2} \right)^{\frac{t}{14}}\implies \cfrac{11}{160}=\left( \cfrac{1}{2} \right)^{\frac{t}{14}}\implies \log\left( \cfrac{11}{160} \right)=\log\left[ \left( \cfrac{1}{2} \right)^{\frac{t}{14}} \right][/tex]

[tex]\log\left( \cfrac{11}{160} \right)=\cfrac{t}{14}\log\left[ \left( \cfrac{1}{2} \right)\right]\implies \cfrac{\log\left( \frac{11}{160} \right)}{\log \left( \frac{1}{2} \right)}=\cfrac{t}{14} \\\\\\ 14\left( \cfrac{\log\left( \frac{11}{160} \right)}{\log \left( \frac{1}{2} \right)} \right)=t\implies {\LARGE \begin{array}{llll} \stackrel{mins}{54.1}\approx t \end{array}}[/tex]

Based on the calculations, the length, in cm, of an adjacent side of this rectangle is equal to 6.0 centimeters.

Given the following data:

Perimeter of rectangle = 40.0 centimeters.

Length of rectangle = 14.0 centimeters.

Mathematically, the perimeter of a rectangle can be calculated by using this formula;

P = 2(L + W)

Where:

Note: The length of an adjacent side refers to the the width of this rectangle.

Substituting the parameters into the formula, we have;

40.0 = 2(14.0 + W)

40.0 = 28.0 + 2W

2W = 40.0 - 28.0

2W = 12.0

W = 12.0/2

Width, W = 6.0 centimeters.

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There are a couple ways to go about this.

By definition of inverse function, if [tex]j^{-1}[/tex] exists, then

[tex]j\left(j^{-1}(x)\right) = x[/tex]

All this means is that if you provide some input [tex]x[/tex], plug it into [tex]j^{-1}(x)[/tex], then plug that into [tex]j(x)[/tex], you end up recovering the original input [tex]x[/tex] that you started with.

We can also do this in the opposite direction, so

[tex]j^{-1}(j(x)) = x[/tex]

So now if [tex]j(x)[/tex] is invertible, then

[tex]j(x) = -\dfrac23 x - 9 \implies j\left(j^{-1}(x)\right) = -\dfrac23 j^{-1}(x) - 9 = x[/tex]

Solve for [tex]j^{-1}[/tex].

[tex]-\dfrac23 j^{-1}(x) - 9 = x[/tex]

[tex]\dfrac23 j^{-1}(x) = -x - 9[/tex]

[tex]j^{-1}(x) = -\dfrac32 (x+9)[/tex]

[tex]\boxed{j^{-1}(x) = -\dfrac32 x - \dfrac{27}2}[/tex]

Another way to do it is by algebraically substituting [tex]x[/tex] within the definition of [tex]j(x)[/tex]

Starting with the given definition

[tex]j(x) = -\dfrac23 x - 9[/tex]

we replace [tex]x[/tex] with some new expression in a new variable [tex]y[/tex] that makes the right side reduce to just [tex]y[/tex]. To demonstrate, if we multiply [tex]-\frac23 x[/tex] by [tex]-\frac32[/tex], we end up with a coefficient of 1. So let [tex]x=-\frac32 y[/tex]. Then

[tex]j\left(-\dfrac32 y\right) = -\dfrac23 \left(-\dfrac32 y\right) - 9 = y - 9[/tex]

As you can see, this doesn't completely reduce to [tex]y[/tex], so we're not done. To adjust for this, we just add 9 to [tex]y[/tex], so our ultimate substitution is [tex]x=-\frac32(y+9)[/tex]. Then

[tex]j\left(-\dfrac32 (y+9)\right) = -\dfrac23 \left(-\dfrac32 (y+9)\right) - 9 = (y+9) - 9 = y[/tex]

Now applying [tex]j^{-1}[/tex] to both sides,

[tex]j^{-1}\left(j\left(-\dfrac32 (y+9)\right)\right) = j^{-1}(y)[/tex]

[tex]\implies \boxed{j^{-1}(y) = -\dfrac32 y - \dfrac{27}2}[/tex]

(we can freely swap out [tex]y[/tex] for [tex]x[/tex] at this point)

Yet another way, since the function here is quite simple, we can just think about the action of [tex]j[/tex] on a given number [tex]x[/tex] - multiply it by -2/3, and subtract 9.

[tex]x \mapsto -\dfrac23 x \mapsto -\dfrac23x - 9 = j(x)[/tex]

The inverse operation undoes this, so given some number [tex]j(x)[/tex], we recover [tex]x[/tex] by adding the additive inverse of -9, or 9, then multiplying the whole result by the multiplicative inverse of -2/3, or -3/2.

[tex]j(x) \mapsto j(x) + 9 \mapsto -\dfrac32(j(x) + 9) \mapsto -\dfrac32 j(x) - \dfrac{27}2 = x[/tex]

You seem to be using some version of this method. You made the mistake of thinking the "multiply by -3/2" step applies only to [tex]j(x)[/tex], and not [tex]j(x) + 9[/tex].

Answer:-1/2

Step-by-step explanation:rise 1 run back 2

The number of groups of three that the college can select is 56.

Total number of students = 8

Number of assistantships available = 3

Groups of three can be selected by the college means that out of the eight students three need to be selected at random and this can be done in ⁸[tex]C_{3}[/tex] ways.

In this case, we use combination and not permutation because the order of selection of the students does not matter.

Now, we know

ⁿ[tex]C_{r}[/tex] = ( n! )/( r! (n-r )!)

Here, n = 8 and r = 3

⁸[tex]C_{3}[/tex]  = ( 8! )/( 3! (8-3)! )

⁸[tex]C_{3}[/tex]  =  ( 8 × 7 × 6 × 5! )/ ( 3 × 2 × 1 × ( 5! ) )

⁸[tex]C_{3}[/tex]  = ( 8 × 7 × 6 )/ ( 3 × 2 )

⁸[tex]C_{3}[/tex]  = 56

The number of groups of three that the college can select is 56.

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Answer: RS=5

QS=18

TS=10

TV=15

Step-by-step explanation:

QV = 23. QT =8. TR = RS = SV.

QV=QT+TR+RS+SV

23=8+RS+RS+RS

23=8+3*RS

3*RS=15

RS=5 ==> TR=5 and SV=5

QS=QT+TR+RS

QS=8+5+5

QS=18

TS=TR+RS
TS=5+5

TS=10

TV=TS+SV

TV=10+5

TV=15

Answer:

RS=5

QS=18

TS=10

TV=15

Step-by-step explanation:

The whole thing is 23. A part of it (QT) is 8 parts of that line as a whole. And if you subtract 8 from 23, that’s what’s left over for the rest of the parts to split amongst themselves. And if you read the question carefully, you’ll realize those last three parts are equal to eachother. Take that information, and after doing 23-8, you should get 15. Take that number and divide by the number of parts left over of the whole line. (Three leftover parts) divide 15 by 3 and that’s the length of each of those parts. From there we just label those parts and add what goes together to get our answers.

For RS: the length of R to S we already know since we just did the math for that. It’s 5.

For QS: from Q to S we have a few parts, but since they should be labeled, this should be easy because it’s just adding! (8+5+5=18)

For TS: since both parts are worth 5, no complicated math needed, just add 5+5 to get the answer, 10!

For TV: we know all parts are worth 5, so again, easy adding and you get! 15!

The total number of bags Sharon have is 7 and the total number of apples Sharon have is 45.

Let total number of bags = x

Let total number of apples Sharon has = y

If she packs 6 apples in each bag, she will have 3 apples left. So, mathematically we can write

6x + 3 = y                                                       equation 1

If she packs 7 apples in a bag, she will be four apples short. So, mathematically we can write

7x - 4 = y                                                         equation 2                

On subtracting equation 1 from equation 2 , we get

x - 7 = 0

⇒ x = 7

Substitute x = 7 in equation 1 , we get

6 ( 7 ) + 3 = y

⇒ y = 45

The total number of bags Sharon have is 7 and the total number of apples Sharon have is 45.

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Missy rode her bicycle 16 miles in 1 1 4 hours. Her average speed in miles per hour is 12.8 mph

Calculating average speed involves dividing the whole distance traveled by the total time it takes to cover that distance.

Speed is the rate of movement of anything at a specific time. Average speed refers to the average speed during the course of a journey. Typically, average speed refers to the speed of moving objects like cars, trains, and aircraft. It is frequently expressed in kilometers per hour (kph) or miles per hour (mph) (kph).

In many different disciplines, such as physics, astronomy, and transportation, average speed is employed.

As we know,

average speed is distance traveled divided by time taken

⇒ average speed = 16 miles × 5/4

⇒ average speed = 12.8 miles/hour

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Answer:

-21 degrees

Step-by-step explanation:

-14 - 7 = 21

According to the given data The value of p is[tex]0.0351<0.1[/tex](alpha) so reject H₀

A left-tailed test is used when the alternative hypothesis claims that the true value of the parameter suggested by the null hypothesis is lower than the null hypothesis implies. If the sample being tested is within the one-sided critical zone, the alternative hypothesis will be accepted rather than the null hypothesis.

Financial analysts employ the one-tailed test to confirm an investment or portfolio hypothesis.

If our statistical analysis finds that the significance level is smaller than the set cut-off value, we reject the null hypothesis and accept the alternative hypothesis (for example, either 0.05 or 0.01).

z = -1.81alpha

= 0.1p [tex]( z < -1.81 )p ( z < -1.81 )[/tex]

= 0.0351 ( from z table )P &lt;

alpha, reject H₀

When the p-value is less than or equal to alpha, hypothesis H0 is rejected;

however,

if the p-value is greater than alpha, hypothesis H0 is not rejected.

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Answer: The m<A = 55

Step-by-step explanation:

1. We know that m<A is likely congruent to m<B (know that m< means measure of angle) {Also noting congruent means same}

2. With that, we can tell that the given info is telling us that 124 is the total degree for m<D.

3. So, this tells us that 2x + x + 41.5 = 124 is the formula we will use.
       3a. 3x + 41.5 = 124 (Simplify)
               3b. 3x = 82.5 (Combine like Terms)
                         3c. x = 27.5 (Divide)

4. Now we know what x is, so finding m<A is easy, 2(27.5) equals to 55, meaning m<A is 55. For m<B, 27.5 + 41.5 equals to 69. To make sure 55 + 69 equals to 124

5. So:
m<A = 55
m<B = 69
m<D = 124

The domain and range of the given function are: domain: {-7,-3,-2,2,4,6} range: {-3,0,1,2,3,6}. (Option A).

Now,

In the given function {(-3,4),(0,6),(2,-2),(1,-3),(6,-7),(3,2)},

Thus, According to the definition of domain and range,

Hence, Option A is correct, i.e., the domain and range of the given function are: domain: {-7,-3,-2,2,4,6} range: {-3,0,1,2,3,6}.

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three digits hope this helped

Answer:

Question: Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead Sea, the lowest elevation, is 1,312 feet below sea level.

Answer:

Equation is 0.5 gal × (0.1) + x gal × (0.35) = (0.5 + x) × (0.15)

0.125 gallons of the 35% acid solution Eli should add.

Step-by-step explanation:

Given: Eli wants to combine 0.5 gallon of a 10% acid solution with some 35% acid solution to make a 15% acid solution.

To find: Equation can you use to determine how many gallons of the 35% acid solution Eli should add?

Solution:

Let x be the gallons of the 35% acid solution.

According to question,

For 0.5 gallon of a 10% acid solution = 0.5×0.1

For x gallon of a 35% acid solution = x×0.35

For (0.5+x) gallon of a 15% acid solution = 0.5 + x × 0.15

The equation form is

0.5 gal × (0.1) + x gal × (0.35) = (0.5+x) × (0.15)

Solving the above equation,

0.05 + 0.35x = 0.075 + 0.15x

0.2x = 0.025

x = 0.025/0.2

x= 0.125

Therefore, 0.125 gallons of the 35% acid solution Eli should add.

Therefore, 0.125 gallons of the 35% acid solution Eli should add.The equation is 0.5 gal × (0.1) + x gal × (0.35) = (0.5 + x) × (0.15)

16 times larger is the new area when compared to the original.

Given that, the length of each side of the square is quadrupled.

We need to find how many times larger is the new area when compared to the original.

A square is a closed two-dimensional shape with four equal sides and four equal angles. The four sides of the square form the four angles at the vertices. The sum of the total length of the sides of a square is its perimeter, and the total space occupied by the shape is the area of the square. The formula to calculate the area of a square is a².

Let the length of each side of the square be x.

Then the length of each side of the new square will be 4x.

Now, the area of the original square = x²

The area of the new square = (4x)² = 16x²

So, the new square = 16 × the original square

Therefore, 16 times larger is the new area when compared to the original.

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Answer:The answer would be the second one since he question is saying square meters.

Step-by-step explanation:Please give brainliest if right.

The number of overtime hours done by electrician, as found by unitary method, is 4.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Now,

Given:

To find: Number of Overtime hours

FInding:

Let the number of overtime hours be 'x'.

By unitary method, Charge of 1 regular hour = $24

Charge of 8 regular hours = $24(8) = $192

Again, by unitary method, Charge of 1 overtime hour = $36

Charge of x overtime hours = $36(x)

Cost of Materials = $202

Now, total bill = sum of all the expenses

=> 538 = 192 + 36x + 202

=> 538 - 294 = 36x

=> 144 = 36x

=> 4 = x

Hence, the number of overtime hours as found by unitary method is 4.

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The diameters of a strand of black hair and a strand of red hair is found to be 1.4×10⁻³.

Scientific notation is a method of expressing extremely large or extremely small numbers.

For the given question;

Convert the decimal value 0.001 in scientific notations;

= 0.001 inch

= 1×10⁻³ inch

Now, calculate the difference;

Difference in diameter = Black hair diameter - Red hair diameter

Difference in diameter =  2.4×10⁻³ - 1×10⁻³

Difference in diameter = 1.4×10⁻³

Therefore, the value of the difference in the diameter of red and black hair is found as 1.4×10⁻³.

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The total amount that Mikaela spent on the paddleboard is $514.16

The given parameters are:

Original cost = $799

Discount = 40%

State tax = 7.25%

The total amount that Mikaela spent on the paddleboard is calculated as

Amount = Original cost * (1 - Discount) * (1 + State tax)

This gives

Amount = 799 * (1 - 40%) * (1 + 7.25%)

Evaluate

Amount = 514.16

Hence, the total amount that Mikaela spent on the paddleboard is $514.16

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Answer:

(B)  $514.16

Step-by-step explanation:

Correct on my quiz.

Square root of Two is an irrational number. because we are unable to express it in the form a/b, where a and b are whole numbers and b is not zero.

Any real number that cannot be written as the quotient of two integers—that is, as p/q, where p and q are both integers—is an irrational number. For instance, the square root of 2 cannot be represented by an integer or a fraction.

Because these numbers may be represented on a number line, they are real numbers rather than complex numbers.

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Step-by-step explanation:

Solve for what?.......

The interest on this installment agreement that Rob pays is $660.00

In short, the loan is an amount that the bank or financial institution makes available to you for a certain period. Basically, every time you apply for credit, whether it's a loan or even a credit card, you're taking out a type of loan.

The amount borrowed to purchase the drum set is the cost price of $5000 minus the down payment of $800

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Answer: 2,8865 million acres of cropland in florida

Step-by-step explanation: To solve this problem we can multiply Alabama's cropland of 2.51 million acres by 1.15 giving: 2.51 million ×1.15=2.8865 million acres of cropland in Florida.

I Hope this helps :)

Answer: Florida has 2.8865 million acres of cropland.

Step-by-step explanation:

We can first do the multiplication, 2.51 x 1.15, and then add 1,255 + 2,510 + 25,100 then we get the answer: 2.8865

Answer:

Hope this helps :)

21) 31 + 14

22) 16 - 9

23) 7 + 4 + 18

24) 3 × 40

25)

26) 81 ÷ 3 OR 81/3 (the fraction bar also means divide)

27) 3 × 2 = 6

28) 7 x 6 = 42 (7 days in a week times by 6 weeks equal 42 days)

Answer:

147 cents

Step-by-step explanation:

If 24 inches of wire cost 72 cents then each inch cost 3 cents. 49*3=147

Answer:

Step-by-step explanation:

To find y = f(g(x)) replace the x in f(x) by g(x):-

y = 4^(x - 3)

---> y = 4^x  * 4^-3

---> y = (4)^x / 64

Answer:

Step-by-step explanation:

Answer:

P=6

Because 6/3=2

And 2+9=11

Step-by-step explanation: