Explanation
A unit rate is a rate where the bottom number is 1 (also called a single-unit rate),it can be found using the expression
[tex]\text{unit rate = }\frac{total\text{ amount}}{\text{total el}emets}[/tex]Step 1
Let
total amount = 3 tablespoons
total elements = 1.5 serving, so replacing
[tex]\begin{gathered} \text{unit rate = }\frac{total\text{ amount}}{\text{total el}emets} \\ \text{unit rate =}\frac{3\text{ tablespoons}}{1.5\text{ servings}}=2\text{ tablespoons per serving} \\ \text{unit rate =}2\frac{tablespoon}{\text{serving}} \end{gathered}[/tex]therefore, the answer is
[tex]\text{unit rate =}2\frac{tablespoon}{\text{serving}}[/tex]I hope this helps you
a space agency is tracking the height of a lunar probe as it descends to the surface of the moon, They model its height using the function h(t)=-82t +12520, where t is the number of hours since the probe started its decent and h is the height above the surface in miles. Explain what the two parameters, -82 and 12520, represent in the problem using proper units.
Step-by-step explanation:
12520 is the functional result for t = 0, that is the moment the function or procedure starts.
so, it means
12520 miles above the surface, where the probe started its descent.
-82 means that with every hour of descent the probe loses 82 miles of height above the surface (continuously subtracted from the 12520 miles starting height).
What are the solutions to the equation x? - 8x = 24?1) X= 4+2102) X= 4+2/103) x=4+2124) r=-41212
Simplify the quadratic equation.
[tex]\begin{gathered} x^2-8x=24 \\ x^2-8x-24=0 \end{gathered}[/tex]The value of coefficients are, a = 1, b = -8 and c = -24.
Determine the solutions of equation by using quadratic formula.
[tex]\begin{gathered} x=\frac{-(-8)\pm\sqrt[]{(-8)^2-4\cdot(1)\cdot(-24)}}{2\cdot1} \\ =\frac{8\pm\sqrt[]{64+96}}{2} \\ =\frac{8\pm\sqrt[]{160}}{2} \\ =\frac{8\pm\sqrt[]{4\cdot4\cdot10}}{2} \\ =\frac{2(4\pm2\sqrt[]{10})}{2} \\ =4\pm2\sqrt[]{10} \end{gathered}[/tex]So solutions of the equation are,
[tex]4\pm2\sqrt[]{10}[/tex]convert decimal to fraction and simplify if possible0.24 =
O.24 = to fraction
= 24/100
divide by m,c,d of 24 and 100, its 4
=( 24/4)/(100/4)= 6/25
Then answer is ,fraction = 6/25
What is the standard form of the quadratic function that has a vertex at (34)and goes through the point (4.5)?A y=2p - 12x+22B y=x-5x+ 13O cy=+6x+5O R y=x2- 6x+9
To check what is the correct option we can start evaluating which one passes through point 3,4. This is the vertex of the correct equation, so it has to pass through this point. We can evaluate later whether it is the vertex or not, in case it is required.
To check if any option passes through that point, we just need to replace x = 3 and y = 4:
For option A:
[tex]\begin{gathered} y=2x^2-12x+22 \\ 4=2\cdot(3^2)-12\cdot3+22 \\ 4=2\cdot9-36+22 \\ 4=18-14 \end{gathered}[/tex]The equation in option A is satisfied. This equation passes through point 3,4. Let's check every other option the same way:
Option B
[tex]\begin{gathered} y=x^2-6x+13 \\ 4=9-6\cdot3+13 \\ 4=9-18+13 \\ 4=4 \end{gathered}[/tex]Option B also passes through that point.
Option C:
[tex]\begin{gathered} y=x^2+6x+5 \\ 4=9+6\cdot3+5 \\ 4=9+18+5 \\ 4=32 \end{gathered}[/tex]The equation in option C is not satisfied, does not passes through point 3,4; then we can discard this option.
Option D:
[tex]\begin{gathered} y=x^2-6x+9 \\ 4=9-6\cdot3+9 \\ 4=9-18+9 \\ 4=0 \end{gathered}[/tex]The equation in option D is not satisfied either. We can also discard this option.
The only options passing through point 3,4 are A and B. Now we need to check which one passes also through point 4,5. We can check the same way: replacing 4 where we have x, and 5 where we have y, but this time only for options A and B.
For option A:
[tex]\begin{gathered} y=2x^2-12x+22 \\ 5=2\cdot(4^2)-12\cdot4+22 \\ 5=2\cdot16-48+22 \\ 5=32-26 \\ 5=6 \end{gathered}[/tex]The equation in option A does not pass through point 4,5. The only option left is option B. Let's check it:
[tex]\begin{gathered} y=x^2-6x+13 \\ 5=16-6\cdot4+13 \\ 5=16-24+13 \\ 5=5 \end{gathered}[/tex]The equation in option B passes through point 4,5.
If we had more than one option left, we would need which one has the vertex exactly at 3,4. However, we have proved that the only option that passes through both points (3,4 and 4,5) is option B. Then, that is the correct answer.
The correct answer is option B.
The length of a rectangle is one unit shorter than one-sixth of the width, x.Which expression represents the perimeter of the rectangle? 73x−813x−273x−213x−4
We are given a rectangle that has a width "x" and a length that is one unit shorter than one-sixth of its length. This rectangle can be visualized in the following diagram:
The perimeter of a rectangle is the sum of all of its sides, therefore, the perimeter is given by:
[tex]P=x+x+\frac{x}{6}-1+\frac{x}{6}-1[/tex]Adding like terms:
[tex]P=2x+\frac{2x}{6}-2[/tex]Adding the fractions we get:
[tex]P=\frac{14x}{6}-2[/tex]Simplifying the fraction we get:
[tex]P=\frac{7x}{3}-2[/tex]And thus we get the expression for the perimeter of the given rectangle.
NEED HELP ASAP I have 30 minutes please help tutor I just need the answers
given that angle x is central angle, find the value of x
To determine the measure of the central angle you have to keep the following properties in mind:
- The measure of the intercepted arc of an angle that has its vertex on the circle is twice the measure of the angle.
-The measure of an angle with a vertex on the center of the circle is equal to the measure of the intercepted arc.
The intercepted arc for both angles is the same so that:
So, you can determine the value of x as follows:
[tex]\begin{gathered} xº=2\cdot60º \\ xº=120º \end{gathered}[/tex]The value of x is 120º
Find coordinates of the midpoint of the segment with the given endpoints.A(-4,6) and B(0,5)
We are given the following two endpoints
[tex]A\mleft(-4,6\mright)\text{ and }B\mleft(0,5\mright)[/tex]We are asked to find the coordinates of the midpoint of segment AB
Recall that the midpoint formula is given by
[tex]\mleft(x_m,y_m\mright)=\mleft(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\mright)[/tex][tex]\text{where (}x_1,y_1)=\mleft(-4,6\mright)\text{ and (}x_2,y_2)=\mleft(0,5\mright)\text{ }[/tex]Let us substitute the given values into the midpoint formula
[tex]\begin{gathered} (x_m,y_m)=(\frac{-4_{}+0_{}}{2},\frac{6_{}+5_{}}{2}) \\ (x_m,y_m)=(\frac{-4_{}}{2},\frac{11_{}}{2}) \\ (x_m,y_m)=(-2,\frac{11_{}}{2}) \end{gathered}[/tex]Therefore, the coordinates of the midpoint between segment AB are found to be
[tex](x_m,y_m)=(-2,\frac{11_{}}{2})[/tex]what is the volume of the figure? V= __ cm 3little three^round to nearest tenth as needed
To answer this question we will use the following formula to compute the volume of a cone:
[tex]Volume=\frac{\pi\times radius^2\times height}{3}.[/tex]From the given diagram we get that:
[tex]\begin{gathered} radius=3cm, \\ height=5cm. \end{gathered}[/tex]Therefore the volume of the given cone is:
[tex]Volume=\frac{\pi\times(3cm)^2\times5cm}{3}.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} Volume=\frac{45\pi cm^3}{3}=15\pi cm^3 \\ \approx47.1cm^3. \end{gathered}[/tex]Answer:
[tex]V=47.1cm^3.[/tex]Part Cexplain why the above answers are reasonable. include numbers and talk about wind chill, wind and temperature in your explanation.
Answer:
[tex]\begin{gathered} a)\text{ Wind chill}=-31\text{ degrees Fahrenheit} \\ b)_{}\text{ Wind chill}=33.7\text{ degrees Fahrenheit} \end{gathered}[/tex]Step-by-step explanation:
Given the equation that represents the feeling of the wind on a cold day, substitute the velocity and temperature respectively.
a) substitute T=-6 and V=23 mi/hr
[tex]\begin{gathered} \text{ Wind chill}=35.74+0.6215T-35.75(V^{0.16})+0.4275T(V^{0.16}) \\ \text{ Wind chill}=35.74+0.6215(-6)-35.75((23)^{0.16})+0.4275T((23)^{0.16}) \\ \text{ Wind chill}=-31\text{ degrees Fahrenheit} \end{gathered}[/tex]b) substitute T=4.8 and v=19 km/hr
Since the equation is given in Fahrenheit and miles per hour, so we need to convert the given values:
[tex]\begin{gathered} \mleft(4.8\degree C\times\frac{9}{5}\mright)+32=40.64\degree F \\ T=40.64\text{ }\degree F \\ v=19\text{ }\frac{km}{hr} \\ v=\text{ }11.8\text{ }\frac{km}{hr} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \text{ Wind chill}=35.74+0.6215(40.64)-35.75((11.8)^{0.16})+0.4275(40.64)((11.8)^{0.16}) \\ \text{ Wind chill}=33.7\text{ degrees Fahrenheit} \end{gathered}[/tex]can u help please with this practice
Polynomial Factoring
We are given the polynomial
[tex]P=d^2+12d+36[/tex]To factor the polynomial, we need to recall the identity:
[tex]\mleft(a+b\mright)^2=a^2+2ab+b^2[/tex]The trinomial (right side of the equation) consists in:
* the square of a variable
* twice the product of both variables
* the square of the other variable
The given expression has the corresponding terms:
* d^2 is the perfect square of d
* 36 is a perfect square, the square of 6
* 12d is twice 6d. Note the terms 6 and d are exactly the perfect squares, thus we can write:
[tex]P=d^2+12d+36=(d+6)^2[/tex]The third choice is correct
Find the linear approximation to f(x)=10-3x^2 at a=-2
Solution:
Given the function;
[tex]f(x)=10-3x^2[/tex]The linear approximation formula is;
[tex]y=f(x)=f(a)+f^{\prime}(a)(x-a)[/tex]Where;
[tex]a=-2[/tex]Then, the derivative is;
[tex]f^{\prime}(x)=-6x[/tex][tex]\begin{gathered} f(a)=f(-2)=10-3(-2)^2 \\ f(a)=10-3(4)_{} \\ f(a)=10-12 \\ f(a)=-2 \end{gathered}[/tex]Also,
[tex]\begin{gathered} f^{\prime}(a)=f^{\prime}(-2)=-6(-2) \\ f^{\prime}(a)=12 \end{gathered}[/tex]Thus, the linear approximation is;
[tex]\begin{gathered} y=-2+12(x-(-2)) \\ y=-2+12(x+2) \\ y=-2+12x+24 \\ y=f(x)=12x+22 \end{gathered}[/tex]FINAL ANSWER:
[tex]f(x)=12x+22[/tex]A toy maker produces wooden trains and wooden airplanes. Each train requires 3 ounces of paint and each airplane requires 5 ounces of paint. The toy maker has a gallon can of paint (64 ounces). If he wants to use it to paint 14 toys, how many of each can he paint?
Let be "t" the number of wooden trains that he can paint and "a" the number of wooden airplanes he can paint.
Based on the information given in the exercise, you can set up the following System of equations:
[tex]\begin{cases}t+a=14 \\ 3t+5a=64\end{cases}[/tex]You can solve it using the Substitution method:
1. You can solve for "a" from the first equation:
[tex]a=14-t[/tex]2. Substitute the new equation into the second equation.
3. Solve for "t".
Then:
[tex]\begin{gathered} 3t+5a=64 \\ 3t+5(14-t)=64 \\ 3t+70-5t=64 \\ -2t=64-70 \\ \\ t=\frac{-6}{-2} \\ \\ t=3 \end{gathered}[/tex]4. Substitute the value of "t" into any original equation.
5. Solve for the variable "a".
Then:
[tex]\begin{gathered} t+a=14 \\ 3+a=14 \\ a=14-3 \\ a=11 \end{gathered}[/tex]The answer is: He can paint 3 trains and 11 airplanes.
I need help and the problems are not making sense to me
Take into account that the range of a function is given by all values of the dependent variable. In this case, the dependent variable is the distance represented by the y-axis.
You can notice that the values of the distance (the range in this case) is in between the following interval:
100 ≤ y ≤ 350
.Find the value of x and then find the length of JC.X =JC =
In this problem we have that
Triangle JKL and triangle JCD are similar
that means -----> If two triangles are similar, then the ratio of its corresponding sides is proportional
so
JK/JC=JL/JD
sbstitute the given values
88/(2x+6)=110/40
solve the proportion for x
88(40)=110(2x+6)
2x+6=88(40)/110
2x+6=32
2x=32-6
2x=26
x=13
Find the length of JC
JC=2x+6
substitute the value of x
JC=2(13)+6
JC=32 units
What is the answer to this Dilations of Segments and Angles problem?
Solution:
Remember that the dilation does not change the measure of angles. According to this, the correct answer is:
[tex]46^{\degree}[/tex]how to find the denominator, the associates of x & y
Given the following System of equations:
[tex]\begin{cases}-3x+2y=18 \\ -2x-y=5\end{cases}[/tex]You can identify that it has this form:
[tex]\begin{cases}a_1x+b_1y=c_1_{} \\ a_2x+b_2y=c_2\end{cases}[/tex]Where:
[tex]\begin{gathered} a_1=-3 \\ a_2=-2 \\ b_1=2 \\ b_2=-1 \\ c_1=18_{} \\ c_2=5 \end{gathered}[/tex]The determinant D is, by definition:
[tex]D=\begin{bmatrix}{a_1} & {b_1} & {} \\ {a_2} & {b_2} & {} \\ {} & {} & \end{bmatrix}=a_1b_2-a_2b_1[/tex]Then, in this case this is:
[tex]D=\begin{bmatrix}{-3} & {2_{}} & {} \\ {-2_{}} & {-1_{}} & {} \\ {} & {} & \end{bmatrix}=(-3)(-1)-(-2)(2)=7[/tex]By definition, the determinant associated with "x" is given by:
[tex]D_x=\begin{bmatrix}{c_1} & {b_1} & {} \\ {c_2} & {b_2} & {} \\ {} & {} & \end{bmatrix}=c_1b_2-c_2b_1[/tex]Then, in this case:
[tex]D_x=\begin{bmatrix}{18_{}} & {2_{}} & {} \\ {5_{}} & {-1_{}} & {} \\ {} & {} & \end{bmatrix}=(18)(-1)-(5)(2)=-28[/tex]The determinant associated with "y" is given by:
[tex]D_y=\begin{bmatrix}{a_1} & {c_1} & {} \\ {a_2} & {c_2} & {} \\ {} & {} & \end{bmatrix}=a_1c_2-a_2c_1[/tex]Then, this is:
[tex]D_y=\begin{bmatrix}{-3_{}} & {18_{}} & {} \\ {-2_{}} & {5_{}} & {} \\ {} & {} & \end{bmatrix}=(-3)(5)-(-2)(18)=21[/tex]The solution of the System of equations can be found as following:
1. For the x-coordinate:
[tex]x_{}=\frac{D_x}{D}=\frac{-28}{7}=-4[/tex]2. For the y-coordinate:
[tex]y=\frac{D_y}{D}=\frac{21}{7}=3[/tex]The answers are:
[tex]\begin{gathered} D=7 \\ D_x=-28 \\ D_y=21 \\ \text{Solution}=(-4,3) \end{gathered}[/tex]The population of algae in an experiment has been increasing by 30% each day. If there were 100 algae at the beginning of the experiment, predict the number of algae in 5 days.Pls help
The algae has an increase rate of 30% per day, this is an exponential increase, to calculate ot you have to use the following formula:
[tex]y=a(1-r)^x[/tex]Where
a is the initial value
r is the growth rate
x is the time passed
y is the total growth after x time has passed
For this exercise, the initial number is 100 algae, the rate of growth is 0.3 and the time is 5 days, replace it in the formula:
[tex]\begin{gathered} y=100(1+0.3)^5 \\ y=371.293 \end{gathered}[/tex]After 5 days you'll expect that the number of algae will gro by 371.293
1. Draw a scaled copy of either Figure A or B using a scale factor of 3.2. Draw a scaled copy of either Figure C or D using a scale factor of 1/2
For a Scaled copy multiply each side length by the scale factor
1.
A
Multiply each side by 3 , and then connect the missing side:
C. figure C
Multiply each side length by 1/2
A "factor-rich" integer is defined as one for which the sum of its positive factors, not including itself, is greater than itself. Which of the following is a "factor-rich" integer?A. 6B. 8C.10D.12
We will determine it as follows:
A. The factors of 6 are 1, 2, 3 & 6, thus:
[tex]1+2+3=6[/tex]So, 6 is not a "factor-rich" integer.
B. The factors of 8 are 1, 2, 4, 8, thus:
[tex]1+2+4=7[/tex]So, 8 is not a "factor-rich" integer.
C. The factors of 10 are 1, 2, 5 & 10, thus:
[tex]1+2+5=8[/tex]So, 10 is not a "factor-rich" integer.
D. The factors of 12 are 1, 2, 3, 4, 6 & 12. thus:
[tex]1+2+3+4+6=16[/tex]So, 16 is a "factor-rich" integer.
The Wildcats and the Leopards are evenly matched football teams. Whenthey play, there is a 0.5 probability that the Wildcats will win. If they play 9times, what is the probability that the Wildcats will win 6 of the games?Round your answer to the nearest tenth of a percent.A 24.6%B. 0.2%O C. 7.0%D. 16.4%
To answer this question, we need to use the probability using the Binomial Distribution. Because we are finding an exact probability, we can use the next formula:
[tex]C(9,6)\cdot(\frac{1}{2})^6\cdot(\frac{1}{2})^{(6-3)}=0.1640[/tex]Or the probability is about 16.40%.
C(9, 6) is the combination of 9 out of 6. They are going to play 9 games, but we are finding the probability that the Wildcats win 6. Then:
[tex]C(n,k)=\frac{n!}{(n-k)!\cdot k!}\Rightarrow C(9,6)=\frac{9!}{(9-6)!\cdot6!}=\frac{9\cdot8\cdot7\cdot6!}{3!\cdot6!}=\frac{9\cdot8\cdot7}{3\cdot2\cdot1}=84[/tex]Then, the general formula for the Binomial Distribution is:
[tex]C(n,k)\cdot(p)^k\cdot(q)^{n-k}[/tex]In this case, the probability of p = q = 1/2, k = 6, n = 9. Then, applying the formula, we obtain a probability of 0.1640 or about 16.40%. The correct option is D.
Cedric's monthly net income is $3,788. The following is withheld from him monthly gross income: 6.2% for social security • 1.45% for Medicare 16% for federal income tax 6.15% for state income tax Determine Cedric's monthly gross income. Round your answer to the nearest cent.
EXPLANATION
Let's see the facts:
Income = $3,788
Withheld:
6.2% for social security
1.45% for medicare
16% for federal income tax
6.15% for state income tax
Now, with this given data, we can assevere that the gross income is obtained by multiplying the net income by the sum of percentages as follows:
Sum of contributions: 6.2+1.45+16+6.15 = %29.8
So, we know that we must ad 29.8% more,in decimal form, to the net income in order to get the gross income.
The gross income is:
Gross income= 3,788x 1.298 [Because 1 represents 100% and 0.298 represents %29.8]
Gross income = $4,916.82
Debby filled 10 times as many buckets of water as Marty, and Melissa filled 6 times as many buckets as Marty. All
3 together filled 136 buckets of water to fill a pool. How many buckets did Marty fill?
ANSWER
Marty filled 8 buckets of water
EXPLANATION
Let
• x: number of buckets Marty filled
,• y: number of buckets Debby filled
,• z: number of buckets Melissa filled
We know that Debby filled 10 times as many buckets as Marty:
[tex]y=10x[/tex]And that Melissa filled 6 times as many buckets as Marty:
[tex]z=6x[/tex]All three of them together fulled 136 buckets:
[tex]x+y+z=136[/tex]Replace y and z as functions of x:
[tex]x+10x+6x=136[/tex]And solve for x. First add like terms:
[tex]\begin{gathered} (1+10+6)x=136 \\ 17x=136 \end{gathered}[/tex]And divide both sides by 17:
[tex]\begin{gathered} \frac{17x}{17}=\frac{136}{17} \\ x=8 \end{gathered}[/tex]We found that Marty filled 8 buckets of water.
13 units find area of sector GHJ. In circle H with m/GHJ 36 and GH Round to the nearest hundredth. H G
Explanation
The area of a circular sector is given by:
[tex]\text{Area}_{cir\sec }=\pi r^2\cdot(\frac{\Theta}{360})[/tex]where r is the radius and theta is the angle
then
Let
angle=36
radius=13
now ,replace.
[tex]\begin{gathered} \text{Area}_{cir\sec }=\pi r^2\cdot(\frac{\Theta}{360}) \\ \text{Area}_{cir\sec }=\pi(13)^2\cdot(\frac{36}{360}) \\ \text{Area}_{cir\sec }=\pi\cdot169\cdot(\frac{36}{360}) \\ \text{Area}_{cir\sec }=53.0929 \\ \text{rounded} \\ \text{Area}_{cir\sec }=53.09\text{ square units} \end{gathered}[/tex]I hope this helps you
andre has x dollars. He buys lunch using 1/6 of his money and earns 8$ by doing chores after school
Which expressions represent how much money Andre has left? Select TWO that are correct.
Answer:
Correct Answers: B,C
Step-by-step explanation:
Lets set up the equation. In this problem, they are using "x" as the amount of money Andre has. Andre currently has "x" dollars. Since he uses 1/6 of his money, you subtract 1/6x as he has x money . Since he earns 8 dollars, add 8.
x - 1/6x + 8
The reason why option "b" works is because 1 - 1/6 = 5/6.
find the value of expression with a=1/3, b=9, c=5, d=10; the equation is d^2 /2c - b + 3a)
Equation:
[tex]d^2\colon2c-b+3a[/tex]Replace d with 10, b with 9 , c with 5, and a with 1/3.
[tex]\frac{10^2}{2\cdot5}-9+3\cdot\frac{1}{3}[/tex]Solve:
[tex]\frac{100}{10}-9+1[/tex][tex]10-9+1[/tex][tex]2[/tex]Question 2 of 46 Which of the following is the definition of compound interest?
The compound interest is interest calculated on the initial principal which includes all the accumulated interest from previous periods on a deposit or loan.
Therefore, from the options, the right answer will be that the compound interest is the interest applied to both the principal and to any previously earned interest.
Option A is right.
1. Tyrone has four times as many books as Lei. Together they have 50 books. How many books does each have?
Let x represent the number of books that Tyrone has.
Let y represent the number of books that Lei has.
Given that Tyrone has four times as many books as Lei, it means that
x = 4y
Together they have 50 books. It means that
x + y = 50
Substituting x = 4y into x + y = 50, it becomes
4y + y = 50
5y = 50
y = 50/5
y = 10
x = 4y = 4 * 10
x = 40
Tyrone has 40 books
Lei has 10 books
Write and graph a direct variation equation that passes through the given point. (2,-5)
A variation equation has a general form of:
[tex]y=mx[/tex]Where:
m= constant of variation
You have an especific point (2 , -5)
You can use this point to find the m (constant of variation), as follow:
x = 2
y = - 5
[tex]-5=m(2)[/tex][tex]m=-\frac{5}{2}[/tex]Now you can use the value of m to get the final equation:
[tex]y=-\frac{5}{2}x[/tex]Hello, I would like to know how the last two questions are connected to the first question.
13) Notice that:
[tex]\begin{gathered} 5^{-4}=\frac{1}{5^4}, \\ 5^{-3}=\frac{1}{5^3}, \\ 5^{-2}=\frac{1}{5^2}, \\ 5^{-1}=\frac{1}{5^1}. \end{gathered}[/tex]Therefore we can rewrite the given sequence as follows:
[tex]\frac{1}{5^4},\frac{1}{5^3},\frac{1}{5^2},\frac{1}{5^1},5^0,5^1,5^2,5^3,5^4.[/tex]14) Simplifying the above sequence we get:
[tex]0.0016,0.008,0.04,0.2,1,5,25,125,625.[/tex]15) Notice that:
[tex]\begin{gathered} 5^{-3}=5^{-4}*5, \\ 5^{-2}=5^{-3}*5 \\ 5^{-1}=5^{-2}*5, \\ 5^0=5^{-1}*5, \\ 5^1=5^0*5, \\ 5^2=5^1*5, \\ 5^3=5^2*5, \\ 5^4=5^3*5. \end{gathered}[/tex]Therefore as the numbers increase, we multiply the previous term by 5, also, as the number decrease, we divide the previous term by 5.
Answer:
13)
[tex]\frac{1}{5^4},\frac{1}{5^3},\frac{1}{5^2},\frac{1}{5^1},5^0,5^1,5^2,5^3,5^4.[/tex]14)
[tex]0.0016,0.008,0.04,0.2,1,5,25,125,625.[/tex]15)
As the numbers increase, you multiply the previous term by 5.
As the number decrease, you divide the previous term by 5.