Given the expression:
[tex]5^{-2}\ast5^5[/tex]To find the equivalent expression, let's simplify the expression using power rule.
[tex]a^m\ast a^n=a^{m+n}[/tex]Since they have the same base, we are to add the exponents.
We have:
[tex]5^{-2}\text{ }\ast5^5=5^{-2+5}=5^3[/tex]Therefore, the eqivalent expression is 5³
ANSWER:
[tex]5^3[/tex]We a
21. A seamstress made 3 different skirts out of the same material. Each skirt required a dif- ferent amount of material. The chart below shows the number of yards y required for each skirt and the total cost C of the ma- terial. What is the equation for finding the cost per skirt made from the same material? Skirt А B C у 2.5 3.5 4 C С $15.60 $21.84 $24.96
Could you please share the chart the problem refers to?
We are asked to find an equation that gives the cost (C) of the skirt as a function of the number of yards (y) of material used.
The information given is:
y = 2.5 then C = $15.60
y = 3.5 then C = $21.84
y = 4 then C = $24.96
when the cost is $15.60, the amount of material in yards is 2.5 yards
so let's find the cost per yard as the quotient cost in $ divided by yard of material
Cost/yards = $21.84/3.5 = 6.24 $ per yard
The quotient gives the same value for all the three cases:
$15.60 / 2.5 = $6.24 per yard
$24.96 / 4 = $6.24 per yard
then the cost is going to be given by the equation:
C = 6.24 * y
This is the equation they asked you to find (naming "C" the cost, and "y" the number of yards of material used.
The equation contains ""unknowns"
Recall that the question is:
What is the equation for finding the cost per skirt made from the same material?
So they want a mathematical formula/equation that allows everyone to estimate the cost (C) given the number of yards of mwterial used (y)
So if you give the following equation (called equation because it must contain an "equal" sign):
C = 6.24 * y
A second problem gives you the amount paid for number of pounds of blueberries
The data says:
3 pounds cost $5.4
7 pounds cost $12.6
We proceed as before, and get that the amount per pound is obtained via the quatient: Price (C) divided by number of pounds (p)
C / p = $5.4 / 3 = $1.8 per pound
that gives us the equation:
C = $1.8 * p
Find the marked price and the rate of discount for a camcorder whose price has been reduced by 95$ and whose sale price is 255$.
Problem
Find the marked price and the rate of discount for a camcorder whose price has been reduced by 95$ and whose sale price is 255$.
Solution
For this case we can find the real price with this operation:
95+265= 360
And the rate of discount can be founded as:
(95/265)*100= 35.85%
Rounded to the nearest percent would be 36%
Please help ASAP thank you
Answer:
Shade 6 strips out of the 9.
Step-by-step explanation:
Let us find 2/3 of 9
We can write 2/3 of 9 as 2/3 × 9
To multiply fractions through the following steps:
Now, 2/3 × 9 = (2 × 9) / 3 = 18/3 = 6
translating words into algebraic symbols its not -70 or -7
translating words into algebraic symbols
a number x = x
decreased by seventy = -7
y= x-70
___________________
Answer
x-70
If L = 4 inches and KL = 7 inches, what is the length of the diameter JK? Round your answer to at least the nearest hundredth of an inch (2 decimal places).
We have a right triangle and two sides we will use the Pythagorean theorem in order to find the missing side
[tex]c^2=a^2+b^2[/tex]a=7 in
b= 4 in
c=JK
we substitute the values
[tex]JK=\sqrt[]{7^2+4^2}[/tex][tex]JK=8.06[/tex]114. If plane X averages 800 mph and plane Y averages 400 mph, how manyhours will plane X travel before it overtakes plane Y if plane Y has a 2 hourand 30 minute head start?a.1b. 2c. 5d. 72
To determine the time taken for the plane X to travel:
If plane X averages 800 mph and plane Y averages 400 mph
Distance column is found by multiplying the rate
by time.
The time taken for plane Y to travel = 2hr 30 minutes = 2.5hrs head start
Be sure to distribute the 400(t +2.5)for Plane Y,
and Plane X to distribute 800t
As they cover the same distance
[tex]\begin{gathered} Dis\tan ce\text{ is equal ,} \\ 800t=400(t+2.5) \\ 800t=400t+1000 \\ 800t-400t=1000 \\ 400t=1000 \\ t=\frac{1000}{400} \\ t=2\frac{1}{2}hr \end{gathered}[/tex]Therefore the plane X will travel for 2 1/2 hours
Hence the correct answer is Option B
The House of Pizza say that their pizzas are 14 inches wide, but when you measured it, the pizza was 12 inches. What is your percent error? Make sure to include your percent sign! (Round to 2 decimals)
The percent error of the house of the pizza would be 2.
How to calculate the percent error?Suppose the actual value and the estimated values after the measurement are obtained. Then we have:
Error = Actual value - Estimated value
To determine the percent error, we will measure how much percent of the actual value, the error is, in the estimated value.
We have been given that House of Pizza says that their pizzas are 14 inches wide, but when measured, the pizza was 12 inches.
WE know that Error = Actual value - Estimated value
Then Error = 14 - 12 = 2
Therefore, the percent error would be 2.
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Calculate the five-number summary of the given data. Use the approximation method.19, 2, 23, 25, 20, 2, 4, 8, 16, 11, 10, 12, 8, 2, 18
Answer:
Explanation:
Given the data:
19, 2, 23, 25, 20, 2, 4, 8, 16, 11, 10, 12, 8, 2, 18
Step 1: Write in an order (we are writing in an ascending order here)
2, 2, 2, 4, 8, 8, 10, 11, 16, 18, 19, 20, 23, 25,
what is the slope of the line that passes through the points of (5,3) (5.-9)
Answer:
undefined
Step-by-step explanation:
slope = (y_2 - y_1)/(x_2 - x_1)
slope = (-9 - 3)/(5 - 5)
slope = -12/0
Since the slope calculation involves division by zero, this line has undefined slope. The two points have the same x-coordinate, so the line is vertical. The slope of a vertical line is undefined.
A dog walker charges a flat rate of $6 per walk plus an hourly rate of $30. How much does the dog walkercharge for a 45 minute walk? Write an equation in function notation for the situation, and then use it tosolve the problem. Determine if the given statement is True or False.
hello
from the question given, the dog walker charges a flat rate of $6 and an extra $30 per hour.
we can write out an equation in function notation
let the number of hours be represented by x
[tex]f(x)=6+30x[/tex]now we can proceed to solve the cost of the walk for 45 minutes
[tex]\begin{gathered} 1hr=60\min s \\ \text{xhr}=45\min s \\ x=\frac{45}{60} \\ x=\frac{3}{4} \\ \text{therefore 45mins = 3/4 hours} \end{gathered}[/tex]now we can input the value into the equation and know the cost for 45 minutes walk
[tex]\begin{gathered} f(x)=6+30x \\ x=\frac{3}{4} \\ f(x)=6+30(\frac{3}{4}) \\ f(x)=6+22.5 \\ f(x)=28.5 \end{gathered}[/tex]from the calculation above, the cost of 45 minutes walk will cost $28.5
The table shows the outcome of car accidents in a certain state for a recent year by whether or not the driver wore a seat belt. Find the probability of wearing a seat belt, given that the driver did not survive a car accident. Part 1: The probability as a decimal is _ (Round to 3 decimal places as needed.) Part 2: The probability as a fraction is _
Conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.
The table shows the outcome of car accidents by whether or not the driver wearing a seat belt.
Let's call:
A = The event of the driver wearing a seat belt in a car accident.
B = The event of the driver dying in a car accident
The conditional probability is calculated as follows:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]The conditional probability stated in the formula is that for the driver wearing a seat belt knowing he did not survive the car accident.
The numerator of the formula is the probability of both events occurring, i.e., the driver wore a seat belt and died. The denominator is the simple probability that the driver died in a car accident.
From the table, we can intersect the first column and the second row to find the number of outcomes where both events occurred. The probability of A ∩ B is:
[tex]P(A\cap B)=\frac{511}{583,470}[/tex]The probability of B is:
[tex]P(B)=\frac{2217}{583,470}[/tex]The required probability is:
[tex]P(A|B)=\frac{\frac{511}{583,470}}{\frac{2217}{583,470}}[/tex]Simplifying the common denominators:
[tex]P(A|B)=\frac{511}{2217}=0.230[/tex]Benjamin & Associates, a real estate developer, recently built 185 condominiums in McCall,Idaho. The condos were either three-bedroom units or four-bedroom units. If the total numberof bedrooms in the entire complex is 657, how many three-bedroom units are there? How manyfour-bedroom units are there?
we have the following:
x = number of three bedroom
y = number of four bedroom
therefore,
[tex]\begin{gathered} x+y=185 \\ 3x+4y=657 \end{gathered}[/tex]the 9th term of arithmetic sequence. Use the formula for 'an' to find 'a20', the 20th term of the sequence 7,3,-1,-5
We will find the value of the 20th term of the sequence 7, 3, -1, and -5.
We have the following sequence:
[tex]7,3,-1,-5[/tex]Finding the common differenceIf we have an arithmetic sequence here, we need to find the common difference for this sequence, and we can do that by finding the difference between the second term and the first term, the difference between the third term and the second term, and so on. If we obtain the same value for the common difference, we have an arithmetic sequence here.
Then we have:
[tex]\begin{gathered} d=3-7=-4 \\ \\ d=-1-3=-4 \\ \\ d=-5-(-1)=-5+1=-4 \end{gathered}[/tex]Then the common difference in this arithmetic sequence is d = -4.
Finding the formula for the arithmetic sequenceWe know that the explicit formula for an arithmetic sequence is:
[tex]a_n=a_1+(n-1)d[/tex]For this case, we have that d = -4, and that the first term, a1 = 7. Then we have the formula for the arithmetic sequence:
[tex]a_n=7+(n-1)(-4)[/tex]Notice that we can expand this expression as follows:
[tex]\begin{gathered} a_n=7+(-4)(n)+(-4)(-1) \\ \\ a_n=7-4n+4 \\ \\ a_n=11-4n \\ \end{gathered}[/tex]Finding the 20th termThen to find the 20th term of the sequence, we have:
[tex]\begin{gathered} a_{20}=7+(20-1)(-4) \\ \\ a_{20}=7+(19)(-4) \\ \\ a_{20}=7-76=-69 \\ \\ a_{20}=-69 \end{gathered}[/tex]Therefore, in summary, we have that the value for the 20th term of the sequence 7, 3, -1, and -5 is -69.
,
Determine the function that represents the following tables. Time (seconds) 1, 4, 7, 10, 13, the Distance (miles) 5 20 35 50 65.
the function is d= f(t)
when t1= 1 , d1= 5
when t2= 4, d2= 20
[tex]\text{rate od change = }\frac{d_2-d_1}{t_2-t_1}[/tex][tex]\text{rate of change = }\frac{20-5}{4-1}=\text{ }\frac{15}{3}=\text{ 5}[/tex][tex]\begin{gathered} ifd_{2\text{ }}=20,d_{3\text{ }}=35,t_{2\text{ }}=4,t_{3\text{ }}=7 \\ \text{rate of change = }\frac{d_3-d_2}{t_3-t_2}\text{ = }\frac{35-20}{7-4}=\text{ }\frac{15}{3}=\text{ 5} \end{gathered}[/tex]Thus if d is a function of t
and the rate of change is constant
then d = 5t is the function
Which of the following could be the product of two consecutive prime numbers? A. 2 B. 10 C. 14 D. 15
15 because it is the product of 3 and 5 which are consecutive prime numbers.
3A research company produced a study to find out what percentage of people in the state of Mississippi would purchase a new product being developed.Out of the 24 participants polled, 12 stated that they would buy the new product. The research company concluded that about 50% of the residents ofMississippl would purchase the new product. Identify a problem with the study.The conclusion is based on a small sample.
The main problem of the research conducted is the number of participants who polled for the new product. If we want to conduct a study that represents a state, the number of participants must be close as possible to the total population of the state. Of course, 24 participants is very small sample size when we compare it to the population of the state, which means we cannot easily conclude that 50% of the residents would like to purchase the new product based on just 24 participants.
Answer: a. The conclusion is based on a small sample
I need help with this question please help me asap?
Answer
Explanation
• Range (R): the amount between the upper and lower limit.
HELP ASPAPP The general form of an equation is x2+y2−25x+3y+1=0.
What is the equation of the circle in standard form?
Answer:
the first (top) answer option. ... = 129/100
Step-by-step explanation:
the for me qualifying or disqualifying term is the constant term as the product and sum of all the constant parts.
the general form has the constant parts
... + 1 = 0
so, all the constant terms from the squares on the left side minus the constant term on the right side must be 1.
let's start from the bottom : the 4th answer option.
the constant parts are
... + (-1/5)² + ... + (3/2)² = 121/100
... + 1/25 + ... + 9/4 = 121/100
... + 0.04 + ... + 2.25 = 1.21
... + 2.29 - 1.21 = ... + 1.08
and NOT 1. so, this is wrong.
the 3rd answer option.
... + (-1/3)² + ... + (-3/2)² = 221/100
... + 1/9 + ... + 9/4 = 221/100
... + 0.111111... + ... + 2.25 = 2.21
... + 0.111111... + ... + 2.25 - 2.21 = 0
... + 0.111111... + ... + 0.04 = 0
... + 0.111111 + 0.04 = 0.15111111...
and NOT 1. so, this is wrong.
the 2nd answer option.
... + (-1/5)² + ... + (3/2)² = 229/100
... + 1/25 + ... + 9/4 = 229/100
... + 0.04 + ... + 2.25 = 2.29
... + 2.29 - 2.28 = ... + 0
and NOT 1. so, this is wrong.
the first answer option.
... + (-1/5)² + ... + (3/2)² = 129/100
... + 1/25 + ... + 9/4 = 129/100
... + 0.04 + ... + 2.25 = 1.29
... + 2.29 - 1.29 = ... + 1
this IS 1. so, this is correct.
this corresponds now to the original
... + 1 = 0
Answer: Choice A (May vary from test to test)
Step-by-step explanation:
(x-1/5)^2 + (y+3/2)^2 = 129/100
Just an FYI:
I can't stress this enough... Add equation symbols when applicable, for example: √,^,/, etc. You can't expect to have someone give the correct answer when you literally typed the equation out incorrectly.27. If figure A and figure B are similar with a ratio of similarity of 2, and the perimeter of figure A is 28 units,what is the perimeter of figure B?
SOLUTION
Since the two shapes are similar, that is A and B similar with a ratio of 2, then we have that
[tex]\begin{gathered} \frac{length\text{ A}}{lemgth\text{ B}}=\frac{2}{1}=\frac{perimeter\text{ A}}{perimeter\text{ B}} \\ \frac{2}{1}=\frac{perimeter\text{ A}}{perimeter\text{ B}} \\ \frac{2}{1}=\frac{28}{perimeter\text{ B}} \end{gathered}[/tex]Cross multiplying we have
[tex]\begin{gathered} 2Perimeter\text{ B = 28} \\ Perimeter\text{ B = }\frac{28}{2} \\ =14\text{ units } \end{gathered}[/tex]hence the answer is 14 units
Write an equivalent fraction with the given denominator. (Only input numerator in final answer.) 2/3 = /24
Write an equivalent fraction with the given denominator. (Only input numerator in final answer.) 2/3 = /24
we have 2/3
Multiply by 8/8
(2/3)(8/8)=16/24
therefore
the answer is 16given ABCD is congruent EFGH. solve for x. Round the answers to the nearest hundredth
As ABCD is congruent withEFGH, it means that both figures have the same mesarurements, even if their orientation is different.
Then, you have that the angle in A is congruente with the angle in E, the angle B is congruent with the angle F, the angle C is congruent with the angle G, the angle D is congruent with the angle H.
[tex]\begin{gathered} \angle A=\angle E \\ \angle B=\angle F \\ \angle C=\angle G \\ \angle D=\angle H \end{gathered}[/tex]Then:
[tex]3x^2-4x+10=16[/tex]You solve the x from the equation above:
1. Equal the equation to 0
[tex]\begin{gathered} 3x^2-4x+10-16=0 \\ 3x^2-4x-6=0 \end{gathered}[/tex]2. Use the quadratic equation:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex][tex]\begin{gathered} x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(3)(-6)}}{2(3)} \\ x=\frac{4\pm\sqrt[]{16+72}}{6} \\ x=\frac{4\pm\sqrt[]{88}}{6} \\ x_1=\frac{4-\sqrt[]{88}}{6},x_2=\frac{4+\sqrt[]{88}}{6} \\ x_1=-0.896,x_2=2.230 \end{gathered}[/tex]3. As you get two solutions for x. You need to prove which is the right solution:
with x1:
[tex]\begin{gathered} 3x^2-4x+10=16 \\ 3(-0.896^2)-4(-0.869)+10=16 \\ 11.17\ne16 \end{gathered}[/tex]with x2:
[tex]\begin{gathered} 3x^2-4x+10=16 \\ 3(2.23^2)-4(2.23)+10=16 \\ 15.99\approx16 \end{gathered}[/tex]As you can see the right solution is x2, because if you subtitute the x in the equation of the angle A that must be equal to 16, just the x2 gives an approximate value to 16.
Then, the solution for the x is x=2.23Write the slope-intercept form of the equation of each line.4) -3+y=2/5x
where
[tex]\begin{gathered} \text{slope}=\frac{2}{5} \\ y-\text{intercept}=3 \end{gathered}[/tex]Explanation
the equation of a line in slope-intercept form is given by:
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex]Step 1
then, isolate y
[tex]-3+y=\frac{2}{5}x[/tex]i) add 3 in both sides
[tex]\begin{gathered} -3+y=\frac{2}{5}x \\ -3+y+3=\frac{2}{5}x+3 \\ y=\frac{2}{5}x+3 \end{gathered}[/tex]Hence, the answer is
[tex]y=\frac{2}{5}x+3[/tex]where
slope=2/5
y-intercept=3
I hope this helps you
what is the length of the dominant line in the time graph below? l leave your answer in simplest radical form.
Let's first calculate the lenght of the side of the rectangle.
[tex]l=\sqrt[]{8^2+5^2}=\sqrt[]{64+25}=\sqrt[]{89}[/tex]so we get that the dotted line is:
[tex]d=\sqrt[]{2^2+89}=\sqrt[]{93}[/tex]so the answer is square root of 93
A can of diced tomatoes has a height of 11.5 cm and a diameter of 10 cm. What is the volume of the can? Use 3.14 for pie.DO NOT round your answer.
Answer:
902.75 cubic cm.
Explanation:
Given a can with:
• Height, h = 11.5 cm
,• Diameter = 10 cm
A can is in the shape of a cylinder; and the volume of a cylinder is calculated using the formula:
[tex]V=\pi r^2h[/tex]First, find the radius by dividing the diameter by 2.
[tex]r=\frac{10}{2}=5\;cm[/tex]Next, substitute r=5, h=11.5 and π=3.14 into the formula given above:
[tex]\begin{gathered} V=3.14\times5^2\times11.5 \\ =902.75\text{ cubic cm} \end{gathered}[/tex]The volume of the can is 902.75 cubic cm.
Find a polynomial function with real coefficients that has the given zeros
1 -√3i, 2
Answer:
[tex]x^3-4x^2+8x-8[/tex]
Step-by-step explanation:
[tex]\displaystyle\\(x-(1-\sqrt{3} i)(x-(1+\sqrt{3} i)(x-2)=\\\\(x^2-(1-\sqrt{3} i)x-(1+\sqrt{3} i)x+(1-\sqrt{3} i)(1+\sqrt{3} i))(x-2)=\\\\(x^2-x+\sqrt{3} i-x-\sqrt{3} i+1-(\sqrt{3} i)^2)(x-2)=\\\\(x^2-2x-3\cdot(-1))(x-2)=\\\\(x^2-2x+4)(x-2)=\\\\x^3-2x^2+4x-2x^2+4x-8=\\\\x^3-4x^2+8x-8[/tex]
shron spent 1 1/4 hours reading her book report and 2 2/5 hours doing her other homework. how much longer did sharon spent doing her homework than reading her book report
sharon spent 23/20 hour doing her homework than reading.
What is fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
Sharon spent reading the book = [tex]1 \frac{1}{4}[/tex] = 5/4 hours
= 25/20 hours
Sharon spend doing homework = [tex]2 \frac{2}{5}[/tex] = 12/5 hours
= 48/20 hours
So, the difference between both activities
= 48/20- 25/20
= 23/20
Hence, sharon spent 23/20 hour doing her homework than reading.
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If an account is compounded annually at 9%, how much interest will a principal of $12,300 earn in 16 months? Round your answer tothe nearest cent. Note: Assume 365 days in a year and 30 days in a month.
From the question, we have the given information.
[tex]\begin{gathered} \text{Principal =\$12300} \\ \text{rate}=9\text{\%} \\ \text{number of times compounded =1} \\ \text{Time =16 months =}\frac{4}{3}years \end{gathered}[/tex]We will use the formula below to solve the question
[tex]\text{Amount =P(}1+\frac{r}{n})^{nt}[/tex]Therefore;
[tex]\begin{gathered} \text{Amount}=12300(1+\frac{9}{100})^{\frac{4}{3}} \\ =12300(\frac{109}{100})^{\frac{4}{3}} \\ =13797.71 \end{gathered}[/tex]Since the Amount = 13797.71, we can get the interest by using the formula below.
[tex]\begin{gathered} \text{Interest= Amount- Principal} \\ =13797.71-12300 \\ =1497.71 \end{gathered}[/tex]Answer: Interest =$1497.71
What are the coordinates of A B C after a Dilation with a scale factor of 1/2 followed by a reflection over the x-axis
In general, a dilation is the outcome of applying the following transformation on a point,
[tex]D(x,y)\to(kx,ky)[/tex]Where k is the scale factor, this kind of dilation is about the origin, and we will use it since the problem does not specify otherwise.
In our case, the transformation is
[tex]D(x,y)\to(\frac{x}{2},\frac{y}{2})[/tex]Then,
[tex]\begin{gathered} D(A)=D(-6,5)\to(-3,\frac{5}{2}) \\ D(B)=D(3,2)\to(\frac{3}{2},1)_{} \\ D(C)=D(0,-1)\to(0,-\frac{1}{2}) \end{gathered}[/tex]On the other hand, a reflection over the x-axis is given by the following transformation.
[tex](x,y)\to R_x(x,y)=(x,-y)[/tex]Then, in our case,
[tex]\begin{gathered} A^{\prime}=R_x(-3,\frac{5}{2})=(-3,-\frac{5}{2}) \\ B´=R_x(\frac{3}{2},1)=(\frac{3}{2},-1) \\ C^{\prime}=R_x(0,-\frac{1}{2})=(0,\frac{1}{2}) \end{gathered}[/tex]Thus, the answers are
A'=(-3,-5/2)
B'=(3/2,-1)
C'=(0,1/2)
Hi, could I have some help answering this question in the picture attached?simplify the question
Expand and collect like terms:
[tex]\begin{gathered} =\text{ }7s^{\frac{7}{4}}\times t^{\frac{-5}{3}}\times-6s^{\frac{-11}{4}}\times t^{\frac{7}{3}} \\ =\text{ }7\times s^{\frac{7}{4}}\times-6\times s^{\frac{-11}{4}}\times t^{\frac{-5}{3}}\times t^{\frac{7}{3}} \\ =\text{ 7 }\times-6\text{ }\times\text{ }s^{\frac{7}{4}}\times s^{\frac{-11}{4}}\times t^{\frac{-5}{3}}\times t^{\frac{7}{3}} \\ =\text{ -42}\times\text{ }s^{\frac{7}{4}}\times s^{\frac{-11}{4}}\times t^{\frac{-5}{3}}\times t^{\frac{7}{3}} \end{gathered}[/tex]Bring the exponents having same base together:
[tex]\begin{gathered} \text{The multiplication betwe}en\text{ same base becomes addition } \\ \text{when the exponents are brought together} \\ =-42\text{ }\times\text{ }s^{\frac{7}{4}-\frac{11}{4}}\times t^{\frac{-5}{3}+\frac{7}{3}} \\ =\text{ -42 }\times s^{\frac{7-11}{4}}\times t^{\frac{-5+7}{3}} \\ =\text{ -42 }\times s^{\frac{-4}{4}}\times t^{\frac{2}{3}} \end{gathered}[/tex][tex]\begin{gathered} =\text{ -42 }\times s^{\frac{-4}{4}}\times t^{\frac{2}{3}} \\ =\text{ -42 }\times s^{-1}\times t^{\frac{2}{3}} \\ =\text{ -42}s^{-1}t^{\frac{2}{3}} \end{gathered}[/tex]Which is the best interpretation of the averagerate of change of this function?
We can calculate the rate of change as the slope between two points, like (1,2) and (2,4).
The slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-2}{2-1}=\frac{2}{1}=2[/tex]If this is a linear function, this slope m has to be constant.
We will calculate the slope between other points, like (3,8) and (4,16):
[tex]m=\frac{y_4-y_3}{x_4-x_3}=\frac{16-8}{4-3}=\frac{8}{1}=8[/tex]The slope is not constant, so this function is not a linear function.
If we look at how f(x) increases, we can prove that f(x) is:
[tex]f(x)=2^x[/tex]and this function is an exponential function.
Answer: Option B (exponential function).