Answer:
15.40 ounces to 16.90 ounces.
Step-by-step explanation:
A flagpole casts a shadow that is 14 feet long. At the same time, a person standing nearby who is 5 feet 6 inches tall casts a shadow
that is 42 inches long. How tall is the flagpole?
Flagpole:
feet
Answer:
22 feet
Step-by-step explanation:
As the given measurements are not all in the same units, convert all measurements to inches using the conversion 1 ft = 12 inches:
14 ft = 14 × 12 = 168 inches5 ft 6 in = 5 × 12 + 6 = 66 inchesTherefore:
Flaghole height = h inFlagpole shadow = 168 inPerson height = 66 inPerson shadow = 42 inDraw a diagram using the given information (see attachment).
From the diagram, we can see that the flagpole and the person are parallel. Therefore, the two triangles are similar.
In similar triangles, corresponding sides are always in the same ratio.
Therefore, set up a ratio of height to shadow length and solve for h:
[tex]\implies \sf Flagpole\;height:Flagpole:shadow=Person\;height:Person\;shadow[/tex]
[tex]\implies \sf h:168=66:42[/tex]
[tex]\implies \sf \dfrac{h}{168}=\dfrac{66}{42}[/tex]
[tex]\implies \sf h=\dfrac{66}{42} \cdot 168[/tex]
[tex]\implies \sf h=\dfrac{11088}{42}[/tex]
[tex]\implies \sf h=264\;inches[/tex]
Convert the height into feet by dividing by 12:
[tex]\implies \sf h=\dfrac{264}{12}=22\;feet[/tex]
Therefore, the height of the flagpole is 22 feet.
Out of a random sample of 300 voters, it was found that 172 voters are in favor of Issue #1.
Out of a total of 75,000 voters, how many do you predict will vote against Issue #1?
It is predicted that ___
voters are against Issue #1.
A- 30,000
B- 32,000
C- 43,000
D- 60,000
Answer:
B)32000
Step-by-step explanation:
Out of 300, 172 are in favor, and 142/300 is simplfieid as 43/75
43/75 is equal to 43,000/75000
Subtract 75000 by 43000
The difference is 32,000.
32,000 voters are against the Issue.
the table below shows the number of hours students spend playing video games at home.which is a valid inference about the data
A valid inference about the data of Video Games Play Time among students is A). 50% of students spend 2- or 3 hours playing video games.
What is an inference?An inference is an evidence-based conclusion.
Inferences are reached when the necessary facts are available, and the researcher has done some calculations and reasoning using the facts.
Video Games Play Time
Hours Played Number of Students
0 2
1 4
2 6
3 8
4 5
5 or more hours 3
Total number of students 28
2 or 3 hours:Number of students = 14 (6 + 8)
14/28 - 50%
50% = 50%
4 or more hours:Number of students = 8 (5 + 3)
8/28 = 28.6%
28.6% > 10%
1 or 2 hours:Number of students = 10 (4 + 6)
10/28 = 35.7%
35.7% > 10%
3 or 4 hours:Number of students = 13 (8 + 5)
13/28 = 46.3%
46.3% ≠ 50%
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Question Completion with Answer Options:Video Games Play Time
Hours Played Number of Students
0 2
1 4
2 6
3 8
4 5
5 or more hours 3
Total number of students 28
A). 50% of students spend 2- or 3 hours playing video games.
B). Less than 10% of the students spend 4 or more hours playing video games.
C). Less than 10% of the students spend 1- or 2 hours playing video games.
D). More than 50% of the students spend 3- or 4 hours playing video games.
help omg….
please help
Answer:
Step-by-step explanation:
Straight line= 180 degrees
|_= 90 degrees
180-90=90
3s-2=52
2s+2=38
52+38=90
s=18
Every day, Austin packs his favorite sandwich in a plastic sandwich box. Austin's sandwich box is 13 centimeters long and 12 centimeters wide, but only 3 centimeters tall. What is the volume of Austin's sandwich box?
The volume of the rectangular sandwich box of Austin is given by the equation V = 468 cm³
What is the Volume of a Rectangle?The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle
Volume of Rectangle = Length x Width x Height
Volume of Rectangle = Area of Rectangle x Height
Given data ,
Let the volume of the rectangular box be represented as V
Now , the equation will be
The length of the sandwich box = 13 cm
The width of the sandwich box = 12 cm
The height of the sandwich box = 3 cm
And , volume of the rectangular box V = Length x Width x Height
Substituting the values in the equation , we get
Volume of the rectangular box V = 13 x 12 x 3
On simplifying the equation , we get
Volume of the rectangular box V = 468 cm³
Hence , the volume of rectangular box is 468 cm³
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It is known that g(x) is the inverse function of f (x). This means that the domain of
f (x) is equal to the [Select]
✓of g (x).
The domain of f(x) is equal to the range of inverse function g(x).
What are inverse functions?
A function from a set X to a set Y in mathematics assigns each element of X the exact same number of elements from Y. A function's inverse function reverses the action of a function or f. If and only if the function is bijective, the inverse of f is true.
Given two functions f(x) and g(x).
It is also said that g(x) is the inverse of f(x).
One of the properties of inverse functions is that only one-to-one functions are inverse. If g is equal to f's inverse, then f is equal to g's inverse.
Both f and g are one-to-one functions if they are the inverses of one another.
f and g are inverses of each other if (fog)(x) = x, x ∈ the domain of g.
The range of g equals the domain of f, and the domain of f equals the range of g.
Therefore the domain of f(x) is equal to the range of inverse function g(x).
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Find all complex zeros of a polynomial function. Give the exact values. List multiple zeros as necessary. f(x)=2x5+11x4+17x3+21x2+45x
The zeros of the polynomial function f(x) are:
x = -1, -3/2, -2 + i/2, -2 - i/2
To find the complex zeros of the given polynomial function f(x), we can use the fact that every polynomial with complex coefficients has at least one complex zero.
First, we can use the Rational Zeros Theorem to find any rational zeros. The possible rational zeros are of the form p/q, where p is a factor of the constant term 45 and q is a factor of the leading coefficient 2. Therefore, the possible rational zeros are ±1, ±3/2, ±5, ±9/2, ±15, and ±45/2. We can test each of these values using synthetic division or long division to see if they are actually zeros of the polynomial.
Using long division, we find that x=−1 and x=−3/2 are zeros of the polynomial. Therefore, we can factor out (x+1) and (x+3/2) from the polynomial to get:
f(x) = (x+1)(x+3/2)(2x^3+8x^2+14x+30)
Next, we can use the quadratic formula to find the zeros of the cubic factor 2x^3+8x^2+14x+30. The quadratic formula gives:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 2, b = 8, and c = 15. Plugging in these values, we get:
x = (-8 ± sqrt(8^2 - 4(2)(15))) / 4
= (-8 ± 2i) / 4
= -2 ± i/2
These are the exact values of the complex zeros of the polynomial function.
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The table of values shows the height of a Ferris wheel car as it travels in a circular motion. Select each true statement.
A:The car makes a complete revolution in 10 seconds
B:The maximum height of the Ferris wheel is 65 feet
C:The radius of the Ferris wheel is 35 feet
D:If the car is loaded at 0 seconds, then the people are loaded at the lowest point of the Ferris wheel.
The following statements are true:
A:The car makes a complete revolution in 10 seconds
B:The maximum height of the Ferris wheel is 65 feet
What is revolution ?A full rotation or turning around a focal point is referred to as a revolution. Revolution is the act of rotating around a fixed point or axis . Examples of this include the rotation of a planet around its star or a wheel around its axle.
A. The car makes a complete revolution in 10 seconds:
This can be deduced from the fact that the height of the Ferris wheel car returns to 35 feet after 10 seconds, which means that it has completed one full revolution.
B. The maximum height of the Ferris wheel is 65 feet:
This can be seen from the table, where the height of the Ferris wheel car reaches 65 feet at 2.5 seconds and 12.5 seconds.
C. If the car is loaded at 0 seconds, then the people are loaded at the lowest point of the Ferris wheel: This can be seen from the table, where the height of the Ferris wheel car is 35 feet at 0 seconds.
It is not possible to determine the radius of the Ferris wheel based on the given information alone.
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Tamon worked 40 hours this week. Assuming he makes $9 an hour, what is his gross pay?
How much was withheld from his check if his total withholding taxes are 20%? What is
his net pay?
Answer:
there will be 1 min added
18. Are girls better at spelling than boys? An SRS of 200 boys and an SRS of 150 girls was administered a
spelling test. The average score for boys was 48.4 with standard deviation 12.96. The girls had an average
score of 48.9 with standard deviation 11.85. Construct and interpret a 95% confidence interval to estimate
the true mean difference in the scores of the spelling test between boys and girls. Does this interval
suggest a difference? Explain.
No, since interval contains 0, thus the difference between boys and girls is not significant.
This can be solved using the concept of standard deviation.
What is standard deviation?Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
Because it makes measures easier to comprehend when the data is spread, standard deviation is significant. The data's standard deviation will increase as the data's distribution becomes more widely scattered.
We have given,
n₁ = 200, n₂ = 150
x₁ = 48.4 x₂ = 48.9
s₁ = 12.96 s₂ = 11.85
95% confidence interval for difference of mean scores of boys and girls
since, n₁ and n₂ are very large therefore we may use standard normal variate , thus 95% CI is given by:
x₁ - x₂ ± 2μ₂ √(s₁²/n₁ + s₂²/n₂)
now, 2μ₂ = 1.96
∴ CI = (48.4 - 48.9) ± 1.96 √(12.96)²/ 200 + (11.85)²/150
or, CI = (-3.119, 2.1119)
no, since interval contains 0, thus the difference between boys and girls is not significant.
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The pto is selling raffle tickets to raise money for classroom supplies. A raffle ticket costs $4. There is 1 winning ticket out of the 200 tickets sold. The winter gets a prize worth $76.
Answer:
Step-by-step explanation:
The profit the PTO makes from selling raffle tickets can be calculated by subtracting the cost of the tickets from the total revenue generated from ticket sales.
Let's first calculate the total revenue:
Number of tickets sold = 200
Price per ticket = $4
Total revenue = 200 * $4 = $800
Next, let's calculate the cost of the tickets:
Number of tickets sold = 200
Price per ticket = $4
Total cost = 200 * $4 = $800
Finally, we can calculate the profit by subtracting the cost of the tickets from the total revenue:
Profit = Total revenue - Total cost
Profit = $800 - $800 = $0
So, the PTO makes no profit from selling the raffle tickets. This is because the cost of the tickets and the prize are equal, and there are no other expenses. In this scenario, the prize money of $76 is given away to the winner, so the PTO does not get to keep the money for classroom supplies.
Find the second and fifth term of 3n(squared)-1
helpThe ratio of the perimeters of two similar quadrilaterals is 2:4. What is the ratio of their areas? PLLLLLLLLLLSSSSSSss
a.1:2
b. 4.8
c. 2:4
d. 4:16
e. 5:3
The correct answer is
d) 4:16
Area and Perimeter of Similar Polygons:
Polygons are said to be similar when their corresponding angles are equal and their corresponding sides are in the same proportion. The perimeters and areas of identical polygons have a unique relationship, just as their corresponding sides do.
Perimeters: The scale factor and the perimeters ratios of perimeters are similar. In reality, the scale factor is identical to any ratio between any two similar forms (diagonals, medians, midsegments, altitudes, etc.).
Areas: If the scale factor of the sides of two similar polygons is [tex]\frac{m}{n}[/tex]
, then the ratio of the areas is [tex](\frac{m}{n} )^{2}[/tex].
(Area of Similar Polygons Theorem). Because area is a two-dimensional quantity, you square the ratio.
It is given that ,
the ratio of perimeters of two similar quadrilateral is 2:4.
now,
to find the ratio of area , we can take two quadrilaterals, say square.
Square ABCD of side 2 units and Square PQRS of side 4 units.
now ratio of areas,
[tex]=\frac{area of square ABCD}{area of square PQRS} \\\\=\frac{2*2}{4*4} \\\\=\frac{4}{16}[/tex]
If the given ratio of perimeters can be further solved as 1:2, then we can see that the ratio of areas can also be further solved as 1:4.
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A box of Almond Oats contains 15 ounces of cereal made of oat flakes and sliced almonds. Oat flakes
cost 15 cents per ounce, and almonds cost 30 cents per ounce. Write and simplify expressions in
terms of a, the number of ounces of almonds in the box.
a. The number of ounces of oat flakes in the box. o =
b. The cost of the almonds (in cents).c
c. The cost of the oat flakes (in cents). c =
=
d. The total cost of a box of Almond Oats (in cents). c =
Answer:
a. The number of ounces of oat flakes in the box is 15 ounces - a ounces, or 15 - a ounces.
b. The cost of the almonds (in cents) is 30 cents * a ounces, or 30a cents.
c. The cost of the oat flakes (in cents) is 15 cents * (15 - a) ounces, or 15 * (15 - a) cents.
d. The total cost of a box of Almond Oats (in cents) is the cost of the almonds plus the cost of the oat flakes, or 30a + 15 * (15 - a) cents.
In 2015, there were about 22 million teenagers (aged 13–17) in the United States. They each sent an average of 800 text messages per month. About how many text messages did all of the teenagers in the United States send each month? Express your answer using scientific notation.
The number of text messages all of the teenagers in the United States send each month is 17600 million.
What are integers?In mathematics, an integer is a grouping comprising both positive and negative numbers. Integers are similar to whole numbers in that they do not include the fractional portion. Integers are thus numbers that can be positive, negative, or zero but not fractions. All mathematical operations, including addition, subtraction, multiplication, and division, can be carried out on integers.
Given that,
Number of teenagers = 22 million
Text sent on average = 800
Total messages sent = (22)(800) = 17600 million
Hence, the number of text messages all of the teenagers in the United States send each month is 17600 million.
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help me with this please i need help because i dont get it <33
Answer:B
Step-by-step explanation:
Answer:
Step-by-step explanation
D
because V = 1/3Hxr
^
pie
so 1/3(5)pie(1.75)
1.75 is from the diameter 1/2 which makes 1.75 the radius
help i need it
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
Answer:
Step-by-step explanation:
heyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
Select the correct answer from each drop-down menu. Stacy rolls a pair of six-sided fair dice. The probability that the sum of the numbers rolled is either a multiple of 3 or an even number is , and the two events are exclusive.
The probability that the sum of the numbers rolled is either a multiple of 3 or an even number is 24/36 = 2/3
The two events are mutually exclusive
"Information available from the question"
Stacy rolls a pair of six-sided fair dice.
Now, According to the question:
Let the probability of getting a multiple of 3 is "A"
Let the probability of getting an even number is "B"
Total number of outcomes=36
Total number of favorable outcomes of either a multiple of 3 or an even number are:-
(1,1) ,(1,2) ,(2,1) ,(1,3) ,(3,1) ,(2,2) ,(1,5) (5,1) ,(3,3) ,(2,4) ,(4,2) ,(2,6) ,(6,2) ,(3,5) ,(5,3) ,(4,4) ,(6,4) ,(4,6) ,(5,5) ,(6,6)
Probability = Number of fav. outcomes/ Total no. of outcomes
The probability that the sum of the numbers rolled is either a multiple of 3 or an even number will be given by counting the numbers that are either even or multiples of 3 and then dividing by the number of possible outcomes, 36.
In our case this will be;
24/36 = 2/3
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If you borrow $1,100 for
9 years at an annual
interest rate of 4%,
what is the total
amount of money you
will pay back?
The amount of interest paid will be $396.6.
What is simple interest?The simple interest is the simple amount paid by the borrower to the bank according to the percentage set by the bank for per year which is a fixed interest rate.
Given that Margo takes out a $600 loan with a 10-month repayment period and a 2% yearly interest rate.
The simple interest will be calculated as:-
SI = ( P x R x T ) / 100
SI = ( 1100 x 9 x 4 ) / 100
SI = 39600 / 100
SI = $396
Therefore, $396 will be paid in interest.
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The hypotenuse of a right triangle measures 7cm and one of its legs measures 2m. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer: 6.7
Step-by-step explanation: 7^2-2^2=45
square 45 =6.7
Trapezoid WXYZ is rotated about its center and then translated down and to the right to produce trapezoid h j KL the side WZ is 7 cm WX is 5 cm y z is 5 cm and XY is 9 cm how long is side LH
The length of side LH is given as follows:
LH = 7 cm.
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
This is relevant because the side lengths remain constant.
The equivalent side to side LH is given as follows:
WZ = 7 cm.
Hence the length of side LH is given as follows:
LH = 7 cm.
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A locker requires a three-digit code to open the lock. The code must contain one letter and two numbers, and no letter or number can be repeated. You can choose from among four letters, A, B, C, and D, and two numbers, 5 and 6.
The size of the sample space is (8, 16, 20, 24)
If a code is chosen at random, the probability that it has a letter that immediately follows an odd number is (1/8, 1/6, 1/3, 2/5, 2/3)
If a code is chosen at random, the probability that D is in the code but is not in the first position is (1/8, 1/6, 1/3, 2/5, 2/3)
The correct answer is that the probability is 2/3. To see why, we can count the number of codes that do not have D in the first position, which is 6 (two options for the first position, and three options for the second position).
The size of the sample space is 4 options for the letter, 2 options for the first number, and 1 option for the second number, giving a total of 4x2x1=8 possible codes. To calculate the probability that a code has a letter that immediately follows an odd number, we first need to count the number of codes that meet this condition. There are two odd numbers to choose from (5 and 6), and two letters that can immediately follow an odd number (B and D). For each odd number, there is only one even number that can come before it, so there are 2x1x2=4 possible codes that meet this condition. Therefore, the probability that a randomly chosen code has a letter that immediately follows an odd number is 4/8, which simplifies to 1/2, or 0.5. To calculate the probability that D is in the code but is not in the first position, we need to count the number of codes that meet this condition. There are two places that D could appear (second or third), and three options for the first position (A, B, or C). Once the first position is chosen, there are two options for the remaining number (5 or 6). Therefore, there are 2x3x2=12 possible codes that meet this condition. The total number of possible codes is 8, so the probability that a randomly chosen code has D but not in the first position is 12/8, which simplifies to 3/2, or 1.5. However, probabilities must always be between 0 and 1, so this answer is not valid.
The correct answer is that the probability is 2/3. To see why, we can count the number of codes that do not have D in the first position, which is 6 (two options for the first position, and three options for the second
position). Of these 6 codes, 4 have D in the second position, and 2 have D in the third position. Therefore, the probability that a randomly chosen code has D but not in the first position is (4+2)/8, which simplifies to 2/3.
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4x=3x+10 transversal
Answer:
x=10.
Step-by-step explanation:
4x = 3x + 10
4x - 3x = 10
x = 10
o TP & E Write the augmented matrix of the system and use it to solve the system. If the system has an infinite number of solutions, express them in terms of the parameter z. X = y = Z= - 3x + - 2x + y 4y 4y + - 2z = -8 7z = 26 8z = 30 Question Help: Video 1 Video 2 M Message instructor
The system of equations can be written as a matrix and then used to solve for the variables x, y, and z.
The augmented matrix of the system is:
-3 -2 1 | -8
0 4 -2 | -8
0 0 7 | 26
We can use row operations to find the row reduced echelon form of the matrix, which will give us the solutions to the system.
Starting with the first row:
1. Multiply row 1 by -3 to get a leading 1 in the first column:
3 6 -3 | 24
0 4 -2 | -8
0 0 7 | 26
2. Add row 1 to row 2:
3 6 -3 | 24
0 4 0 | 16
0 0 7 | 26
3. Add 3 times row 1 to row 3:
3 6 -3 | 24
0 4 0 | 16
0 0 7 | 26
The row reduced echelon form of the matrix is:
1 2 -1 | 8
0 1 0 | 4
0 0 1 | 9
From this, we can see that the solutions to the system are:
x = 8 - 2y
y = 4
z = 9
So the system has a unique solution: x = 8 - 2y = 8 - 2 * 4 = 0, y = 4, z = 9.
Two angles form a linear pair. If one angle is
9 times the measure of the other angle, what are
the measures of each angle?
Answer:
18°, 162°
Step-by-step explanation:
Angles that form a linear pair are supplementary, so their measures add to 180°.
Let the measure of the smaller angle = x.
The larger angle measures 9x.
9x + x = 180
10x = 180
x = 18
9x = 9(18) = 162
Answer: 18°, 162°
Use the data display to answer 11 and 12.
11. Analyze and Persevere What does the mean
describe in the data set?
12. Analyze and Persevere What does the range
describe in the data set?
Answer:
563
Step-by-step explanation:
estimate the percent of 18% of 48
Answer:8.64
Step-by-step explanation:
Answer:
8,64
Step-by-step explanation:
[tex]\frac{18}{100}[/tex]*48=8,64
F(-10)=64 and f(15)=54
What is the slope
Equation and x intercept
The equation of the straight line is 2x+5y=340.
The x-intercept point of that line is (170,0).
What is the equation of a straight line?A straight line has different forms like point-slope form, standard form, slope-intercept form, and others. A specific form is used according to the given data for convenience.
here, we have,
As f(-10)=64 and f(15)=54, two points can be wriiten as (x₁,y₁)=(-10,64) and (x₂,y₂)=(15,54).
Now, use the two-point form of the equation of a line.
(y-y₁)/(x-x₁)=(y₂-y₁)/(x₂-x₁)
(y-64)/(x-(-10))=(54-64)/(15-(-10))
(y-64)/(x-10)=-10/25
25(y-64)=-10(x-10)
5(y-64)=-2(x-10)
5y-320=-2x+20
2x+5y=340
Therefore, the required equation of the line is 2x+5y=340.
To find the x-intercept, substitute y=0 into the equation of the line.
2x+5×0=340
2x=340
x=170
Therefore, the x-intercept point is (170,0).
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In a large group of students who completed STA 2023, 20% earned an A in the course, 12% didn’t bring their phone to class and 85% of those who didn’t bring their phone to class earned an A
It is given that:
20% of the students earned an A in STA 2023.
12% of the students didn't bring their phones to class.
85% of the students who didn't bring their phones to class earned an A.
To answer the following questions, we assume whether all students took STA 2023 and brought their phones to class or not.
a) Let's assume that x% of the students earned an A and brought their phones to class. Then, since the remaining (100% - 12%) = 88% of students brought their phone to class but their grade is not specified, we can set up the following equation:
x% + 85% of 12% = 20%
x% + 0.102 = 0.20
x% = 0.098
Therefore, 9.8% of students earned an A and brought their phones to class.
b) Let's assume that y% of the students didn't earn an A and didn't bring their phones to class. Then, we can set up the following system of equations:
x% + y% = 100% - 12%
0.85*(12%) = y%
Solving for y, we get:
y% = 9.6%
Therefore, 9.6% of students didn't earn an A and didn't bring their phones to class.
What is STA 2023?STA 2023 is a course code used by some colleges and universities to refer to an introductory course in statistics. The course usually covers topics such as descriptive statistics, probability theory, statistical inference, hypothesis testing, and regression analysis. STA 2023 is often a required course for students majoring in fields such as social sciences, business, and health sciences, as well as for students pursuing degrees in mathematics or statistics. The specific content and level of difficulty of STA 2023 may vary depending on the institution and the instructor.
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solve the equations to find where they intersect
y = 6x - 8
y=-3x+10
Answer:
(2,4)
Step-by-step explanation:
