[tex]\displaystyle\\Answer:\ x=\frac{\pi }{4} \ \ \ \ \ x=\frac{7\pi }{4}[/tex]
Step-by-step explanation:
[tex]\displaystyle\\secx=\sqrt{2} \ \ \ \ 0\leq x\leq 2\pi \\\\\frac{1}{cosx} =\sqrt{2} \\\\cosx=\frac{1}{\sqrt{2} } \\\\cosx=\frac{(1)(\sqrt{2)} }{(\sqrt{2})(\sqrt{2)} } \\\\cosx=\frac{\sqrt{2} }{2} \\\\x=\frac{\pi }{4} \\\\x=\frac{7\pi }{4}[/tex]
What is another name for AÉ?
Answer:almost everywhere.
Step-by-step explanation:
What would be your preferred measure of central tendency if you had the following data: 57 males and 23 females?
The preferred measure of central tendency for the following data is Mode.
Given,
Number of males = 57
Number of females = 23
The preferred measure of central tendency for the given data is Mode.
Mode
The mode is the number in a set of numbers that appears the most often. The mean of a set of numbers is the sum of all the numbers divided by the number of values in the set.
To find the mode manually, arrange the numbers in ascending or descending order, then count how often each number appears. The number that appears most often is the mode. It's now easy to see which numbers appear most often
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Use f(x) = |x|
f(x) is shifted left 5 and shifted up 2 to create g(x). Write the equation g(x).
g(x)=
....i dk if you need this or not but if you do it is here: g(x) = |x + 2| + 1
Answer:
[tex]g(x) = f(x + 5) + 2[/tex], or [tex]g(x) = | x + 5| + 2[/tex]
Step-by-step explanation:
To shift f(x) left 5, we should add 5 to x.
That way, each value of the new function takes the value of 5 tiles right in the original function.
So far, we have [tex]g(x) = f(x + 5)[/tex].
We also need to shift it up 2, therefore, we should add 2 to every y value.
Therefore, we have [tex]g(x) = f(x + 5) + 2[/tex].
PLEASEEE HELPP
If a₁ = 10 and an
10 and an = -4an-1 then find the value of a4.
Given the recursive relation:
[tex]a_{n}=-4a_{n-1}[/tex]
[tex]a_{2}=-4a_{2-1} = -4a_{1} = - 4(10) = -40 \\ a_{3}=-4a_{3-1} = -4a_{2} = - 4( -4 0) = 160 \\ a_{4}=-4a_{4-1} = -4a_{3} = - 4(160) = -640[/tex]
Write an equation for the translation of y=2/x that has the given asymptotes. x=-2 and y=3
Translation of y=2/x that has the given asymptotes. x=-2 and y=3 will be y = 2 / (x+2) + 3
What is meant by an asymptote of a graph?
An asymptote is a line that a graph of a curve continuously approaches but never crosses. Discover the meaning of asymptotes, read a detailed explanation, and learn about the three different asymptotes: vertical, horizontal, and oblique.
The asymptote(s) of a curve may often be found by looking at the limit of a value when the function is not defined. These points include and the point where the numerator of a rational function equals zero, as well as others.
As, x=-2, the vertical asymptote will be (x+2)
y=3, the horizontal asymptote will be 3.
The equation will be -
y = 2 / (x+2) + 3
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In an independent random sample of 10 juniors and 10 seniors, the number of minutes spent on social media per day are given by the back-to-back stem-and-leaf plots.
Time Spent on Social Media
Juniors
Seniors
2 11
51
542 13
8 14
12 3
6
15
16 6
17 25
18 36
5 19 147
0 20 1
Key: 1215-125
Part A: Describe the shape of each data set. (4 points)
Part B: Wyatt analyzed the data and stated that the better measure of center for the seniors is the mean. Is Wyatt correct? Explain your reasoning. (5 points)
Part C: Wyatt decided there are no outliers in the juniors' data set. Is he correct? Justify your answer mathematically. (5 points)
From the stem-and-leaf plot, and statistical concepts such as mean, median and IQR, we have that:
a) The distribution of Juniors is right skewed, while the distribution of Seniors is left skewed.
b) Since the distribution is skewed, Wyatt is not correct, as the better measure of center is the median.
c) Wyatt is correct that there are no outliers in the juniors' data-set, as there are no measures that are more than 1.5 IQR below Q1 or above Q3.
What is a stem-and-leaf plot?The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:
4|5 = 45.
From the graphed plot at the end of the answer, the Junior's measures are given as follows:
112, 121, 125, 132, 134, 135, 146, 156, 195, 200.
The Seniors' measures are given as follows:
123, 166, 172, 175, 183, 186, 191, 194, 197, 201.
How to classify the shape of a distribution?To classify the shape of a distribution, we have to find the mean and the median, which are defined as follows:
The mean of a data-set is given by the sum of all observations divided by the number of observations.The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile, also called the middle value of the distribution.Then the classifications are given as follows:
Right skewed: Mean > Median.Left skewed: Median > Mean.For Juniors, we have that:
The median is of (134 + 135)/2 = 134.5.The mean is of (112 + 121 + 125 + 132 + 134 + 135 + 146 + 156 + 195 + 200)/10 = 145.6.Hence the distribution is right skewed, as mean > median.
For Seniors, we have that:
The median is of (183 + 186)/2 = 184.5.The mean is of (123 + 166 + 172 + 175 + 183 + 186 + 191 + 194 + 197 + 201)/10 = 178.8..Hence the distribution is left skewed, as median > mean.
For item b, we have that:
Since the distribution is skewed, Wyatt is not correct, as the better measure of center is the median.
What are the quartiles of a distribution, and how they are related to outliers?The first quartile Q1 is the median of the first half of the data-set.The third quartile Q3 is the median of the second half of the data-set.The interquartile range(IQR) is the difference between Q3 and Q1.A measure is considered to be an outlier if it is more than 1.5 IQR below Q1 or more than 1.5 IQR above Q3.For juniors' data-set, we have that:
The first half is 112, 121, 125, 132, hence Q1 = (121 + 125)/2 = 123.The second half is 146, 156, 195, 200, hence Q3 = (156 + 195)/2 = 175.5.Hence the IQR is: 175.5 - 123 = 52.5.The bounds for outliers are given as follows:
123 - 1.5 x 52.5 = 44.25.123 + 1.5 x 52.5 = 201.75.Hence, for item c:
Wyatt is correct that there are no outliers in the juniors' data-set, as there are no measures that are more than 1.5 IQR below Q1 or above Q3.
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a call center receives 25 callers per minute on average. on average, a caller spends1 minute on hold and 3.5 minutes talking to a service representative. on average, howmany callers are "in" the call center (meaning that they are either on hold or talking to aservice representative)?question 2 options:a) 87.5 callersb) 25 peoplec) 112.5 callersd) 1500 callers
The average number of callers in the call centre is 112.5.
Number of callers received by the call centre per minute = 25
Average time each person spends on hold = 1 minute
Average time each caller spends talking = 3.5 minutes
The total amount of time of spending by each caller in the call centre is,
= Time spend on hold + Time spend on talking
= 1 + 3.5
= 4.5 minutes
The total amount of time spent by each caller in the call centre is 4.5 minutes.
The average number of callers in the call centre is,
= Total time spent in the call centre × Number of callers per minute
= 4.5 × 25
= 112.5
Therefore, the average number of callers in the call centre is 112.5.
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Evaluate each logarithm.
log₆₄ 4
Evaluation of logarithm is [tex]log_{64}4 = \frac{1}{3}[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_aN = x[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms :
[tex]log a + log b = log a.b[/tex][tex]log a - log b = log \frac{a}{b}[/tex][tex]log a^x = x loga[/tex][tex]log_aa=1[/tex][tex]log_a1=0[/tex]According to statement,
[tex]log_{64}4\\[/tex]
this equation can be written as
[tex]log_{2^6} 4 \\= > \frac{1}{6}log_24 \\\\ = > \frac{1}{6}log_2{2^2}\\\\= > \frac{1}{6}2log_2{2}\\\\= > \frac{1}{6}. 2 = \frac{1}{3}[/tex]
Thus solution for this equation is [tex]log_{64}4 = \frac{1}{3}[/tex]
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Suppose you pick a marble from a box containing five red and seven blue marbles. You record the color and put the marble back in the box. What is the probability of getting a red marble both times if you do this twice?.
Pls give answer asap!
The numeric value at x = 12 for the given piecewise function is:
g(12) = 10.
What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
How to find the numeric value of a function/expression?To find the numeric value of a function, we replace each instance of the variable in the function by the desired value. For example, to find f(12), we replace each instance of x by 12.
From the piecewise function given in the problem, the definition for x = 12 is given by the following rule:
g(t) = 5t/6.
Hence the numeric value is:
g(12) = 5 x 12/6 = 5 x 2 = 10.
The numeric value at x = 12 for the given piecewise function is:
g(12) = 10.
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Jonathan spent 20.5 hours at the beach this summer. how many minutes did he spend at the beach?
Answer:
1230 minutes
Step-by-step explanation:
All you have to do is multiply 20.5 times 60. Since 60 minutes are in an hour and there is 20.5 hours.
*Please mark brainliest answer
slope 3, passes through (0,-2) in slope intercept form
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{ 3}(x-\stackrel{x_1}{0}) \implies y +2= 3 (x -0) \\\\\\ y+2=3x\implies y=3x-2[/tex]
All students in peters class have $1.05, consisting of nickels and or dimes and or quarters. each student has a different combination of coins. what is the probability peter is unable to give his friend jenny change for $1.00
Answer:
2 is to 4
Step-by-step explanation:
when u comnbkdkd the osapkbdbd
Answer:
Step-by-step explanation:
Answer: 2/31
Explanation: When doing this question, it is best to make a chart with all the possibilities. From there, look and see which possibilities cannot get a change of a dollar to get the answer.
E.
DATE
Topic
PERI
mountain road is 5 miles long and gains elevation at a constant rate.
fter 2 miles, the elevation is 5,500 feet above sea level.
Fter 4 miles, the elevation is 6,200 feet above sea level. (Lesson 3-6)
Find the elevation of the road at the point where the road begins.
Step-by-step explanation:
this is about the overall slope of the mountain road.
remember, the slope is (y change / x change). in this case it is elevation change / distance change.
getting from 2 to 4 miles the changes are
distance changes by +2
elevation changes by + 700 (from 5500 to 6200).
the slope is +700/+2 = 350/1 = 350.
the road begins at distance = 0.
the elevation of the begin of the road = x.
so going from 2 miles down again to 0 the changes are
distance changes by -2 (from 2 to 0)
elevation changes by x - 5500 (from 5500 to x).
the slope there must be the same as the slope further up (as it is said it has a constant rate) :
(x - 5500)/-2 = 700/2
(5500 - x)/2 = 700/2
5500 - x = 700
x = 5500 - 700 = 4,800 ft
the road started at an elevation of 4,800 ft above sea level.
Use each graph to make a table and to write an equation.
Answer:
[tex]y = 3x -2[/tex]
Step-by-step explanation:
Step 1) Find two points from the graph to work with
I would personally use the points (0, -2) and (1, 1) as they are the most comfortable to work with from the given graph.
Step 2) Find the slope
A function's slope is given by the formula: [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
We can now substitute the coordinates of the points we found in Step 1 in the formula to find the function's slope.
[tex]m = \frac{1 - (-2)}{1 - 0} = \frac 31 = 3[/tex]
Step 3) Find the line's equation
Finally, we can substitute the slope we found in Step 2, as well as one of the points we found in Step 1, into the formula [tex]y - y_1 = m(x - x_1)[/tex] to find the line's equation.
[tex]y - 1 = 3(x - 1)\\\to y - 1 = 3x - 3 \text{ / Add 1}\\\to y = 3x -2[/tex]
The velocity of the water that flows from an opening at the base of a tank depends on the height of water above the opening. The function v(x)=√2gx models the velocity v in feet per second where g , the acceleration due to gravity, is about 32ft/s² and x is the height in feet of the water. What is the depth of water when the flow is 40ft/s, and when the flow is 20ft/s ?How can you use the inverse function to help you find the answer?What restrictions are on the domain of v(x) ? of v⁻¹(x) ?
The depth is 0.884 feet when the water flows at 40 ft. / s and the depth is 0.442 feet when the water flows at 20 ft. / s.
We are given the function:
v(x) = √2 g x
where v = velocity
g = gravity's acceleration
x = height / depth of water
Also, we are given that g = 32 ft. / s²
Now, we have v = 40 ft. / s
So, we get that:
40 = √ 2 (32) x
40 / 32 = √ 2 x
5 / 4 = √2 x
x = 5 / 4√2
x = 0.884 feet.
Now, we have v = 20 ft. / s
So, we get that:
20 = √ 2 (32) x
20 / 32 = √ 2 x
5 / 8 = √2 x
x = 5 / 8√2
x = 0.442 feet.
Therefore, we get that, the depth is 0.884 feet when the water flows at 40 ft. / s and the depth is 0.442 feet when the water flows at 20 ft. / s.
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Solve the math problem
Answer: 4.9 years old
Step-by-step explanation: it’s the ages added up divided by the total (to find the average)
Answer:
hiya not sure of this is right but I would add all the dots up so with 3 add 3+3+3+3+3. because there is 5 dots do this with all of them and then divided by the amount of dots hope this helps
answer 4.9
Prior to an election, 6,504 people vote in the advance polls for a riding. On election day, thepolling stations for that riding record an average of 407 voters per hour. How long were thepolls open on election day, if a total of 10,167 people voted in that riding?
**USE LET STATEMENTS, AND THEREFORE STATEMENTS**
Answer:
The polls were open for 9 hours on election day.
Step-by-step explanation:
10167 - 6504 = 3663
3663 / 407 = 9
Will the probability of winning plus the probability of losing always equal 1?
Answer:
[tex] \sf \huge \fbox{{No}}[/tex]
Step-by-step explanation:
Consider an event or an competition is going on. two competetors (let A & B) are racing with each other to win something. Let's see what are the possible events that can occur,
Event 1- Competetor A wins the race against B
Event 2- Competetor B wins the race against B
Event 3- Match draw, either both of them are winner or none of them are winner.
So there are three possible events that can occur & we know that total probability always equals one, let's calculate the probability for each event individually.
The probability of occuring each event is equal, hence,
[tex] \sf Probability \: of \: winning \: p(w)= \frac{1}{3} [/tex]
[tex] \sf Probability \: of \: losing \: p(l)= \frac{1}{3}[/tex]
[tex] \sf Probability \: of \: match \: draw \: p(d)= \frac{1}{3}[/tex]
Now,
the sum of probability of winning & probability of losing,
[tex]p(w) +p(l) = \frac{1}{3} + \frac{1}{3} = \frac{2}{3} ≠1[/tex]
Hence, the result is contradiction to the statement the probability of winning plus the probability of losing always equal 1.
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The variables x and y are related proportionally. When x=8 and y=12. Find y when x=80
Y= 120
Given :
Function :
trigonometric function, in mathematics, one of six functions (sine [sin], cosine [cos], tangent [tan], cotangent [cot], secant [sec], and cosecant [csc]) that represent ratios of sides of right triangles. These six trigonometric functions in relation to a right triangle are displayed in the figure.
They are also known as circular functions since their values can be defined as ratios of the x and y coordinates (see coordinate system) of points on a circle of radius 1 that correspond to angles in standard positions. Trigonometry can be easily applied to surveying, engineering, and navigation problems in which one of a right triangle’s acute angles and the length of a side are known and the lengths of the other sides are to be found.
The fundamental trigonometric identity is sin2θ + cos2θ = 1, in which θ is an angle.
X = 8
Y = 12
f (x) = x*3/2
f(8) = 8*3/2 = 12
y = 12
hence proof f(x)=x*3/2
x = 80
f(x) =x*3/2
f(80) = 80*3/ 2
y = 40 *3
y = 120
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Lisa gathered and shelled 12 lbs of pecans from her backyard.
She is going to make
3/4 lb bags of pecans for gifts.
How many
3/4 lb bags of pecans can Lisa make?
A .15
B. 16
C.11 1/4
D.9
Lisa can make 16 '3/4 lb' bags of pecans.
Given,
Amount of lbs of pecans Lisa gathered from her backyard = 12 lbs
Amount of lb bags of pecans Lisa going to make for gifts = 3/4 lb
We have to find the number of 3/4 lb bags of pecans Lisa can make:
That is,
Total number of 3/4 lb bags = (Amount gathered from backyard) ÷ (Amount of lb bags going to make for gifts)
= 12 ÷ 3/4
= 12 × 4/3
= 4 × 4
= 16
Therefore, Lisa can make 16 3/4 lb bags of pecans.
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Can someone help I really need it
Answer:
A) -1 B) -3 C) -7
Step-by-step explanation:
A) -2(-1)-3=2-3=-1
B) -2×0-3=0-3=-3
C) -2×2-3=-4-3=-7
PLEASE HELP ASAP 100 PTS WILL MARK BRAINLIEST FOR THE PERSON WHO ANSWERS ALL CORRECT FIRST
1. State whether the Law of Detachment or the Law of Syllogism was used to draw the conclusion from the given statements. If it's an invalid conclusion, select invalid.
Given: If the Patriots win their next game, then they will win their division.
Given: If the Patriots win their next game, then they willl go to the playoffs.
Conclusion: If the Patriots win their division, theny they will go to the playoffs.
2. State whether the Law of Detachment or the Law of Syllogism was used to draw the conclusion from the given statements. If it's an invalid conclusion, select invalid.
Given: If two lines are parallel, then they never intersect.
Given: If two lines never intersect, then they have the same slope.
Conclusion: If two lines are parallel, then they have the same slope.
3. State whether the Law of Detachment or the Law of Syllogism was used to draw the conclusion from the given statements. If it's an invalid conclusion, select invalid.
Given: If you sell $1000 worth of popcorn, then your Boy Scout dues are free.
Given: If Ethan sold $1000 worth of popcorn.
Conclusion: Ethan's Boy Scout dues are free.
4.
State whether the Law of Detachment or the Law of Syllogism was used to draw the conclusion from the given statements. If it's an invalid conclusion, select invalid.
Given: If you are at least 18 years old, then you can apply for a credit card.
Given: Kelly applied for a credit card.
Conclusion: Kelly is at least 18 years old.
Using the Laws of Detachment and Syllogism, the conclusions can be described as follows:
1. Invalid.
2. Law of Syllogism.
3. Law of Detachment.
4. Invalid.
What are the Law of Detachment and the Law of Syllogism?The Law of Detachment makes it possible to conclude the hypothesis from the conclusion, that is, if both p and p -> q are true, then q is also true.The Law of Syllogism states that if p -> q and q -> r are true, the p -> r is also true, basically applying the transitive property.For item 1, the events are given as follows:
p: Patriots win their next game.q: Patriots win their division.r: Patriots go to the playoffs.Neither of the laws are reached in the conclusion, hence we have an invalid conclusion.
For item 2, the transitive property was applied correctly, hence the Law of Syllogism was used.
For item 3, p and p -> q are true, then we concluded that q is true, hence the Law of Detachment was used.
For item 4, we have an invalid conclusion, as we have p -> q and q, but no conclusion can be reached regarding p.
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Which of the following are TRUE of line graphs?
(MORE THAN ONE ANSWER)
They often will have the independent variable in the x-axis and the dependent variable in the y-axis.
They can be used for density curves.
They are often used to indicate continuity in the data. (i.e. no gaps)
They are always straight lines.
All of the statements are true.
- They often will have the independent variable on the x-axis and the dependent variable on the y-axis.
- They can be used for density curves.
- They are often used to indicate continuity in the data. (i.e. no gaps)
- They are always straight lines.
What is a line graph?A line graph is a type of chart used to show information that changes over time.
We have,
- They often will have the independent variable on the x-axis and the dependent variable on the y-axis.
This statement is true because the independent variable belongs on the x-axis (horizontal line) of the graph and the dependent variable belongs on the y-axis (vertical line).
- They can be used for density curves.
A density curve is a graph that shows probability.
This statement is true.
- They are often used to indicate continuity in the data. (i.e. no gaps)
Line graphs can be used for continuous data on the y-axis since continuous data are measured on a scale with many possible values.
This statement is true.
- They are always straight lines.
We plot line graphs using several points connected by straight lines.
This statement is true.
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15. Chip earns
a base salary of $500 per month
as a salesman. In addition to the
salary, he earns $90 per product that he sells. If his goal is to earn $5000 per
month, how many products does he need to sell?
According to the linear equation, he has to sold 50 products to collect a amount of 5000 rs.
According to the statement
We have to find that the value of the products he sold.
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
Chip earns a base salary of $500 per month as a salesman. In addition to the salary, he earns $90 per product that he sells. If his goal is to earn $5000 per month.
Then
The equation become
90x + 500 = 5000
Here x is the product he sold
Then
90x + 500 = 5000
90x = 5000 - 500
90x = 4500
x = 4500/90
x = 50.
So, According to the linear equation, he has to sold 50 products to collect a amount of 5000 rs.
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PLEASE HELP ME WILL GIVE THE FIRST PERSON 15 POINTS Solve x – 7 = 10. x = 0.7 x = 70 x = 17 x = 3
Answer:
x = 17
Step-by-step explanation:
x - 7 = 10
17 - 7 = 10
Pls help I’m really confused
Answer:
Negative.
Step-by-step explanation:
Adding B to A brings the total below zero. making it negative.
Suppose the diameter of a similarly shaped crater is 1 km . What is the volume of the crater? Use the formula given in Problem 3 .
The volume of crater is 0.0375 km³.
We are given the diameter of crater which is 1 kilometer. Now, the formula to be used for calculation of volume is -
d = 2∛(V÷0.3)
Keep the value of diameter in the formula to find the volume of crater -
1 = 2∛(V÷0.3)
Dividing both sides of the equation by the number 2
1/2 = (2∛(V÷0.3))/2
Solving the equation we get -
0.5 = ∛(V÷0.3)
Taking cube on both sides of the equation
0.5³ = (∛(V÷0.3))³
On solving we get
0.125 = V÷0.3
Shifting 0.3 to numerator on Left Hand Side of the equation
V = 0.125×3
Performing multiplication on Right Hand Side on the equation
V = 0.0375 km³
Hence, the volume of crater is 0.0375 km³.
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Can someone please help me on this
5z+3y-15x+9
The factorized expression of 5z + 3y - 15x + 9 is 5(z - 3x) + 3(y + 3)
How to evaluate the expression?The expression is given as
5z+3y-15x+9
Rewrite the above expression properly
So, we have
5z + 3y - 15x + 9
Regroup the expression, as follows
So, we have:
5z + 3y - 15x + 9 = 5z - 15x + 3y + 9
Factorize the expression, as follows
So, we have:
5z + 3y - 15x + 9 = 5(z - 3x) + 3(y + 3)
Hence, the factorized expression of 5z + 3y - 15x + 9 is 5(z - 3x) + 3(y + 3)
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Find the least integer greater than each number. Do not use a calculator.
log₁.₅2.5
The answer to this question is log₁.₅ 2.5 = 3
A logarithm is the degree to which a number must be raised in order to produce another number. For instance, the logarithm of 100 in base ten is 2, since ten multiplied by two equals 100: log 100 = 2, since 10² = 100.
Let y = log₁.₅ 2.5
We know, logₐ x = y, only if a^y= x
Therefore, 1.5^y= 2.5
So, we must find an integer y such that 1.5 > 2.5
1.5^y > 2.5
1.5^3 > 2.5
(As, 1.5² = 2.25; 1.5³ = 3.375)
(Since, 1.5² < 2.5, the answer will be 1.5³, as 1.5³ > 2.5)In this case, y = 3 will be the least integer to satisfy this inequality.
Therefore, the the value of the equation log₁.₅ 2.5 is 3
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