The interest rate being earned on the college education fund set aside by your parents 14 years ago is 8.51 percent. This rate of interest has resulted in the value of the fund increasing from $7,500 to $26,180 over the period.
The calculation of the interest rate is based on the concept of compound interest, where the interest earned is added to the initial principal amount, and subsequent interest is calculated on the new balance. Using the formula for compound interest, the rate can be determined as follows:
$26,180 = $7,500(1 + r/100)^14
Solving for the interest rate, r, gives a value of 8.51 percent. This means that the fund has been growing at a rate of 8.51 percent per year for the past 14 years. It is worth noting that the actual rate of return may vary due to factors such as fees, taxes, and market fluctuations, but the calculated rate provides a good estimate of the average growth rate of the fund.
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Christine went to mall at 11:30 am they shopped for 5 hours 35 minutes. What time did they finish shopping?
Answer:
5:05 PM
Step-by-step explanation:
Use a time calculator.
Answer:5:05pm
Step-by-step explanation:
It might be easier to split up the 5 hours and 35 min in minutes and hours
11:30 + 5 hours = 4:30pm
There is still 35 minutes left.
4:30 + 35 min = 5:05pm
∴, Christine finished shopping at 5:05pm
Answer ASAP (for pre-algebra notes)
Triangle XYZ is similar to triangle JKL.
Determine the length of side LJ.
The length of side LJ is equal to 11.48 units.
What are the properties of similar triangles?In Mathematics and Geometry, two (2) triangles are only similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Based on the diagram, we can logically deduce the following proportion based on the congruent sides:
XY/JK = YZ/KL = ZX/LJ
8.7/12.18 = 8.2/LJ = 7.8/KL
By cross-multiplying and solving for the length of side LJ, we have the following:
LJ = (12.18 × 8.2)/8.7
LJ = 11.48 units.
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a) Complete
the table of values for y=x²-2x-3
b) i) Which of the three curves drawn
matches y = x² - 2x - 3?
ii) Estimate the value of y
when x = 2.5
iii) Find the values of x
when y = 1
b)i) The curve that matches y = x² - 2x - 3 is the middle one, which is a parabola opening upward. b)ii) we can estimate that y(2.5) ≈ y(2) + 3/2 = -3 + 3/2 = -1.5. b)iii) the only value of x when y = 1 is x = 2.
Answers to the aforementioned questionsa)
| x | y
| -3 | 12
| -2 | 1
| -1 | -4
| 0 | -3
| 1 | -2
| 2 | -3
| 3 | 0
b) i) The curve that matches y = x² - 2x - 3 is the middle one, which is a parabola opening upward.
ii) To estimate the value of y when x = 2.5, we can use the values of y when x = 2 and x = 3 to find the average rate of change, and then add or subtract that from the value of y when x = 2 or x = 3, respectively.
Using x = 2 and x = 3, we have:
Average rate of change = (y(3) - y(2)) / (3 - 2) = 3
So we can estimate that y(2.5) ≈ y(2) + 3/2 = -3 + 3/2 = -1.5.
iii) To find the values of x when y = 1, we can set y = 1 in the equation y = x² - 2x - 3 and solve for x:
x² - 2x - 3 = 1
x² - 2x - 4 = 0
(x - 2)² = 0
x - 2 = 0
x = 2
So the only value of x when y = 1 is x = 2.
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A triangle has two side lengths of 6.5 inches and 2.75 inches. Which of the following side lengths could be the third side?
A.) 2.5 inches
B.) 3.75 inches
C.) 5.5 inches
D.) 9.25 inches
Answer:
9.25 inches
Step-by-step explanation:
9.25 inches
Given that x is a midsegment in the
triangle below, find its length.
6480
X
16
18
X = [?]
Answer:
x=9
Step-by-step explanation:
Since x is a midsegment this means that it bisects the side with a length of 16. Now using ratio and proportion between the large triangle and the small triangle to find the length of x you have to do
18/16=x/(16/2)
16x=18(8)
x= 144/16
x=9
100 points PLEASEEEEEEE HEEELLLLPPPPPPP
true or false: the general fertility rate refers to the number of live births reported in an area during a given time interval divided by the number of women age 15 to 44 years in the area. group of answer choices true false
The general fertility rate refers to the number of live births reported in an area during a given time interval divided by the number of women age 15 to 44 years in the area is false
The general fertility rate refers to the number of live births reported in an area during a given time interval per 1,000 women of reproductive age (usually defined as 15 to 44 years old) in the same area.
Therefore, it is a rate or a ratio that expresses the number of births in relation to the number of women of reproductive age in a population.
Hence, the statement is False that the general fertility rate refers to the number of live births reported in an area during a given time interval divided by the number of women age 15 to 44 years in the area is false
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To indirectly measure the distance across a lake, Moussa makes use of a couple landmarks at points
�
P and
�
Q. He measures
�
�
OS,
�
�
SQ, and
�
�
RS as marked. Find the distance across the lake
(
�
�
)
(PQ), rounding your answer to the nearest hundredth of a meter.
The distance across the lake PQ will be 496.8 meters.
Given that:
Sides, OS = 210 m, SQ = 70 m, and RS = 124.2 m
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The distance across the lake PQ is calculated as,
PQ / RS = OQ / SQ
PQ / 124.2 = (210 + 70) / 70
PQ / 124.2 = 280 / 70
PQ = 496.8 m
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Part A: Cassie hiked 4 tenths of a 4.7-mile trail. How many miles did Cassle have left to hike?
Part B: Dana was 1.6 miles ahead of Cassie. How many miles did Dana hike already?
The distance left to hike by Cassius is equal to 1.44 miles . Dana hiked 3.5986 miles
We are given that Cassie hiked 4 tenths of a 4.7-mile trail and Dana was 1.6 miles ahead of Cassie.
Since Cassius walked 6/10th of the trail of 3.6 miles.
Part of the trail remaining = 1 - 6/10 = 4/10 = 2/5
Distance remaining will be 2/5 of 3.6 miles
= 1.44 miles.
Hence distance left to hike by Cassius = 1.44 miles
b. Total distance by which Dana was ahead of Cassius = 1.6miles.
Distance left to hike by Dana= 1.44 miles - 1.6 miles = 0.0014 miles.
so, the distance hiked by Dana= 3.6 miles - 0.0014 miles = 3.5986 miles.
Dana hiked 3.5986 miles.
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Step 1
Start with a circle with a center O and a point on the circle P.
Step 2
Using a straight edge draw a line that starts at O and goes through P.
Step 3
Put your compass on P and draw two points, Q and R, on the line OP. These points should be the same distance from P.
Step 4
Measure out the distance from Q to R.
Step 5
Draw the point S by creating two
arcs from points Q and R. Use the distance measured in Step 4.
Step 6
Draw the tangent line PS.
In a circle with radius 4.5, an angle measuring 1 radians intercepts an arc. Find the length of the arc to the nearest 10th.
The length of the arc is approximately 4.5 to the nearest 10th.
How to solve for the length of the arcTo find the length of the arc intercepted by an angle in a circle, we can use the formula:
Arc length = radius × angle (in radians)
In this case, the radius is 4.5, and the angle is 1 radian. So, we can calculate the arc length as follows:
Arc length = 4.5 × 1 ≈ 4.5
Therefore, the length of the arc is approximately 4.5 to the nearest 10th.
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consider a biased coin such that observing tails is three times as likely as observing heads. let x denote the number of tails observed after 3 tosses. the probability distribution of x is:
Therefore, the probability distribution of x is:
x P(X=x)
0 1/64
1 3/64
2 9/64
3 27/64
Let's use a probability tree to determine the probability distribution of x, the number of tails observed after 3 tosses of a biased coin where tails is three times as likely as heads.
On the first toss, the probability of observing tails is 3/4, and the probability of observing heads is 1/4. Let's label the branches T and H, respectively.
For each of the T and H branches, we repeat the same probabilities for the second and third tosses, resulting in the following probability tree:
/ T \
/ T / \ H \
/ / \ \
T H T H
/ \ / \ / \ / \
T T T H T H T H
Now, we can determine the probability of each possible outcome for x, the number of tails observed after 3 tosses:
x = 0: This can only occur if all three tosses are heads (H, H, H). The probability of this is (1/4) * (1/4) * (1/4) = 1/64.
x = 1: This can occur in three ways: (T, H, H), (H, T, H), and (H, H, T). The probability of each is (3/4) * (1/4) * (1/4) = 3/64.
x = 2: This can occur in three ways: (T, T, H), (T, H, T), and (H, T, T). The probability of each is (3/4) * (3/4) * (1/4) = 9/64.
x = 3: This can only occur if all three tosses are tails (T, T, T). The probability of this is (3/4) * (3/4) * (3/4) = 27/64.
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How long would you need to save $3400 in the account with .12% interest rate compounded continuously to end up with $5000 
Answer: To determine the time it would take to save $3400 in an account with a 0.12% interest rate compounded continuously to end up with $5000, we can use the continuous compound interest formula:
A = Pe^(rt)
Where:
A = the final amount in the account ($5000 in this case)
P = the initial amount in the account ($3400 in this case)
e = the mathematical constant e (approximately equal to 2.71828)
r = the annual interest rate (0.12% = 0.0012 as a decimal)
t = the time in years
We can rearrange this formula to solve for t:
t = ln(A/P) / r
Substituting the values given, we get:
t = ln(5000/3400) / 0.0012
t = 28.58 years (rounded to two decimal places)
Therefore, it would take approximately 28.58 years to save $3400 in an account with a 0.12% interest rate compounded continuously to end up with $5000.
Step-by-step explanation:
a globe of the world if it's snuggling inside a transparent display Cube the length of an edge of the cube is 5.4 in is the Globes volume greater than less than or equal to 5.4 cubed cubic inches?
The volume of the cube is greater than 5.4 cubic inches.
How to obtain the volume of a cube?The volume of a cube of side length a is given by the cube of the side length, as follows:
V = a³.
The side length in the context of this problem is given as follows:
a = 5.4 in.
Hence the volume of the cube is given as follows:
V = 5.4³
V = 157.5 cubic inches.
(to obtain the volume of the cube, we apply the formula obtaining the cube of the side length).
157.5 > 5.4, hence the volume of the cube is greater than 5.4 cubic inches.
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Conclusión sobre el mínimo común múltiplo y máximo común divisor plis la ocupo ahorita
According to the information, The Least Common Multiple (LCM) and the greatest common divisor (GCD) allow us to simplify fractions and solve proportion problems.
What is the least common multiple and the greatest common factor?The Least Common Multiple (LCM) and greatest common divisor (GCD) are two ways to calculate the smallest number that is a multiple of all given numbers (LCM) and is the largest number that is a common divisor of all the given numbers (GCD)
The usefulness of the LCM and GCD lies in the fact that they allow us to simplify fractions and solve proportion problems. In addition, they are useful in factoring polynomials and solving linear equations.
Note: This question is in Spanish. The answer is in English
Question:
What is th least common multiple and the greatest common divisor?
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29. The ratio of the surface areas of two spheres is 1:9.
a. What is the ratio of the lengths of their radii? What is the
ratio of their volumes?
b. If the volume of the smaller sphere is 64 cubic inches, what
is the volume of the larger sphere?
Answer:
a) 1 : 3 and 1 : 27. b) 1728 inches³
Step-by-step explanation:
a) if ratio of areas is 1:9, then the ratio of lengths is √1 : √9 = 1:3
ratio of volumes is 1³ : 3³ = 1 : 27
b) volume of smaller = 64.
ratio of volumes = 1 : 27
volume of larger sphere = 27 X 64 = 1728 (inches³)
1) A savings account balance is compounded
annually. If the interest rate is 2.1% per
year and the current balance is $1,777.00,
what will the balance be 10 years from
now?
The total balance in the savings account after 10 years will be $2,187.48.
What is the accrued amount after 10 years?The formula accrued amount in a compounded interest is expressed as;
[tex]A = P(1 + \frac{r}{n} )^{(n*t)}[/tex]
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given that:
Principal P = $1,777Compounded annually n = 1Time t = 10 yearsInterest rate r = 12.1%Accrued amount A = ?First, convert R as a percent to r as a decimal
r = R/100
r = 2.1/100
r = 0.021
Now, plug the values into the above formula and simplify.
[tex]A = P(1 + \frac{r}{n} )^{(n*t)}\\\\A = 1,777(1 + \frac{0.021}{1} )^{(1*10)}\\\\A = 1,777(1 +0.021 )^{(10)}\\\\A = 1,777(1.021 )^{(10)}\\\\A = 2,187.48[/tex]
Therefore, the accrued amount is $2,187.48.
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3. Is it possible to solve x (t ) for t, substitute it into y(t) to eliminate the parameter, t, and write it as a rectangular equation with x and y instead? x(t)=0. 5507t^2-1. 5393t-86. 1
Yes, it is possible to solve x(t) for t and substitute it into y(t) to eliminate the parameter t and write it as a rectangular equation with x and y instead.
Starting with the given equation:
x(t) = 0.5507t^2 - 1.5393t - 86.1
To solve for t, we can use the quadratic formula:
t = [-(-1.5393) ± sqrt((-1.5393)^2 - 4(0.5507)(-86.1))]/(2(0.5507))
Simplifying the equation:
t = [1.5393 ± sqrt(1.5393^2 + 190.2122)]/1.1014
t = [1.5393 ± 13.9769]/1.1014
t = -11.098 or 25.682
Since we're interested in the positive value of t, t = 25.682.
Now, substituting t = 25.682 into y(t):
y(t) = 0.5054t - 78.9
y(25.682) = 0.5054(25.682) - 78.9
y(25.682) = 1.504
Therefore, the rectangular equation for the given parametric equations is:
x = 0.5507t^2 - 1.5393t - 86.1
y = 0.5054t - 78.9
Substituting t = 25.682:
x = 358.6
y = 1.504
So the rectangular equation is:
(x, y) = (358.6, 1.504)
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the national health and nutrition examination survey (nhanes) reported that in a recent year, the mean serum cholesterol level for u.s. adults was 202, with a standard deviation of 41 (the units are milligrams per deciliter). a random sample of 100 adults is chosen. what is the probability that the sample mean cholesterol level is less than 190?
Therefore, the probability that the sample mean cholesterol level is less than 190 is approximately 0.23%.
We can use the central limit theorem to approximate the distribution of the sample mean cholesterol level as normal with a mean of 202 and a standard deviation of 41/sqrt(100) = 4.1.
To find the probability that the sample mean cholesterol level is less than 190, we can standardize the sample mean using the formula:
z = (x - mu) / (sigma / sqrt(n))
where x is the sample mean, mu is the population mean, sigma is the population standard deviation, and n is the sample size.
Plugging in the values, we get:
z = (190 - 202) / (4.1) = -2.93
Now we can use a standard normal distribution table or calculator to find the probability that a standard normal random variable is less than -2.93. The probability is approximately 0.0023 or 0.23%.
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if the coefficient of correlation between two variables is -0.6, the coefficient of determination will be
The coefficient of determination will be 0.36.
the coefficient of correlation measures the strength and direction of the linear relationship between two variables, while the coefficient of determination measures the proportion of the total variation in one variable that is explained by the other variable.
The coefficient of determination is equal to the square of the coefficient of correlation, so if the coefficient of correlation is -0.6, we can square it to get 0.36. Therefore, the coefficient of determination will be 0.36.
knowing the coefficient of correlation between two variables can help us determine the coefficient of determination, which represents the proportion of the variation in one variable that is explained by the other variable.
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Solve the equation. Enter your answer as an equation that shows the value of
the variable (like s = 2/3, or 4= w).
-3x+x-5= 25
-15 is the value of the variable x in the given equation -3x+x-5= 25
The given equation is -3x+x-5= 25
Minus three times of x plus x minus five equal to twenty five
x is the variable in the equation
Minus and plus are the operators
Combine the like terms in the equation
-2x-5=25
Add 5 on both sides
-2x=30
x=-15
Hence, the value of x in the equation is -15
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URGENT!! Will give brainliest :)
A line of best fit was drawn for 6 data points. What is the maximum number of these data points that may not actually be on the line?
• A. 6
О B. 3
O c. 5
O D. 4
The maximum number of points that may not be on the line is given as follows:
A. 6.
How to find the equation of linear regression?To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in a linear regression calculator.
When we insert the points on a calculator, we get a linear function that is obtained using the mean and sum of squares of the points. This means that the line has on average the least distance to the points, but it can happen that none of the points is exactly on the line.
Hence option A is the correct option in the context of this problem.
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Two observers A and B, 500 m apart, observed a kite in the same vertical plane and from the same side of the kite the angles of elevation of the kite are 30 and 20 respectively Find the height of the kite, disregarding the height of the observer.
The trigonometric ratios for tangent indicates that the height of the kite, where the distance between the observers is 500 m, and the angle of elevation are 30° and 20° is h ≈ 492.4 meters
What are trigonometric ratios?Trigonometric ratios are mathematical functions that express the relationships between an interior angle of a right triangle and two of the sides of the triangle.
The distance between the two observers = 500 m
The angle of observation of the kite by each of the two observers = 30° and 20°
Let h represent the height of the kite, and let x represent the horizontal distance from the kite to the closer observer (The observer observing with an angle of elevation of 30°), we get;
The horizontal distance from the kite to the other observer = x + 500
Therefore, according to the trigonometric ratios for tangent;
tan(20°) = h/(x + 500)
tan(30°) = h/x
h = x × tan(30°)
Therefore;
tan(20°) = (x × tan(30°))/(x + 500)
(x + 500) × tan(20°) = x × tan(30°)
(x + 500) × 0.36397 = x × (1/(√3))
0.36397·x + 500 × 0.36397 = x/√3
x/√3 - 0.36397·x = 500 × 0.36397 = 181.985
x·(1/√3 - 0.36397) = 181.985
x = 181.985/((1/√3 - 0.36397))
h = 181.985/((1/√3 - 0.36397)) × tan(30°)
h = 181.985/((1/√3 - 0.36397)) × (1/√3) ≈ 492.4
The height of the kite, h ≈ 492.4 meters
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The sum of the squares of two consecutive positive integers is 340. find the integers. 
a highschool class has 12 girls, 19 boys. if one is chosen at random what is the probability that person is a girl (please help now)
Answer:
p(girl) = 12/31
Step-by-step explanation:
p(event) = (number desired outcomes)/(total number of possible outcomes)
Here, we have 12 girls and 19 boys. The total is 12 + 19 = 31. When we pick one out of all of them, we are picking one out of 31, so the total number of possible outcomes is 31, every single one of the girls and boys.
The desired outcome is picking one girl. How many ways can you pick a girl? The answer is 12 since there are 12 different girls. The number of desired outcomes is 12.
p(girl) = (number of desired outcomes)/(total number of possible outcomes)
p(girl) = 12/31
PLEASE HELP ME ITS DUE RIGHT NOW :(
An image of a rhombus is shown.
a rhombus with a base of 18 centimeters and a height of 15.5 centimeters
What is the area of the rhombus?
16.75 cm2
33.5 cm2
139.5 cm2
279 cm2
Answer:279 cm2
Step-by-step explanation:
The area of a rhombus is calculated by multiplying the length of the base by the height.
The base of the rhombus is 18 cm and the height is 15.5 cm.
Therefore, the area of the rhombus is:
18 cm × 15.5 cm = 279 cm²
So the answer is 279 cm².
27) Find the point that is one-fourth of the way
from (2, 4) to (10, 8).
so hmmm let's call them P(2, 4) and Q(10, 8)
[tex]\textit{internal division of a segment using a fraction}\\\\ P(\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad Q(\stackrel{x_2}{10}~,~\stackrel{y_2}{8})~\hspace{8em} \frac{1}{4}\textit{ of the way from P to Q} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_2}{10}-\stackrel{x_1}{2}~~,~~ \stackrel{y_2}{8}-\stackrel{y_1}{4})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment PQ}}}{\left( 8 ~~,~~ 4 \right)} \\\\[-0.35em] ~\dotfill\\\\ \left( \stackrel{x_1}{2}~~+~~\frac{1}{4}(8)~~,~~\stackrel{y_1}{4}~~+~~\frac{1}{4}(4) \right) \implies \boxed{(4~~,~~5)}[/tex]
1.1-8. during a visit to a primary care physician's office, the probability of having neither lab work nor referral to a specialist is 0.21. of those coming to that office, the prob- ability of having lab work is 0.41 and the probability of having a referral is 0.53. what is the probability of having both lab work and a referral?
The probability of having both lab work and a referral during a visit to a primary care physician's office is 0.16 or 16%.
To find the probability of having both lab work and a referral, we can use the formula P(A and B) = P(A) + P(B) - P(A or B), where A and B are events and P is the probability of those events occurring.
Let A be the event of having lab work and B be the event of having a referral.
We know that P(A) = 0.41, P(B) = 0.53, and P(neither A nor B) = 0.21.
To find P(A or B), we can use the formula P(A or B) = P(A) + P(B) - P(A and B). We don't know P(A and B), but we can find it by using the fact that P(neither A nor B) = 0.21:
P(A or B) = P(A) + P(B) - P(A and B)
1 - P(neither A nor B) = P(A) + P(B) - P(A and B)
1 - 0.21 = 0.41 + 0.53 - P(A and B)
0.78 = 0.94 - P(A and B)
P(A and B) = 0.16
Therefore, the probability of having both lab work and a referral is 0.16.
The probability of having both lab work and a referral during a visit to a primary care physician's office can be found using the formula P(A and B) = P(A) + P(B) - P(A or B). Given that the probability of having lab work is 0.41, the probability of having a referral is 0.53, and the probability of having neither is 0.21, we can solve for P(A and B) and get a probability of 0.16. This means that there is a 16% chance of a patient having both lab work and a referral during their visit.
In conclusion, the probability of having both lab work and a referral during a visit to a primary care physician's office is 0.16 or 16%. This calculation was done using the formula P(A and B) = P(A) + P(B) - P(A or B), with the probabilities of having lab work, a referral, and neither being given.
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Janet's Athletic Company makes basketballs and is shipping them to a company that has round containers with a volume of 208,592. How many basketballs can they ship if each basketball has a volume of 13906
Janet's Athletic Company can ship 15 basketballs in the round containers with a volume of 208,592.
To figure out how many basketballs Janet's Athletic Company can ship, we need to divide the volume of the round containers by the volume of each basketball. So we can set up the following equation:
Number of basketballs = Volume of round containers / Volume of each basketball
Plugging in the given values, we get:
Number of basketballs = 208,592 / 13906
Simplifying the division, we get:
Number of basketballs = 15
Therefore, Janet's Athletic Company can ship 15 basketballs in the round containers with a volume of 208,592.
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Help me please! Will give brainliest if the option is available
answer
(1.2, 1) if its asking what i think it is
Step-by-step explanation:
