part a.
The equation that has the variable in the correct place to match the given situation is: Sunday's mile
part b
the Mansour family drove 210 miles on Sunday.
What is an equation?An equation is described as a formula that expresses the equality of two expressions, by connecting them with the equals sign =..
We have that the equation that has the variable in the correct place to match the given situation is: Sunday's mile
Sunday's miles = Total miles - Friday's miles - Saturday's miles
Sunday's miles = 687 - 313 - 164
Sunday's miles = 210
In conclusion, the Mansour family drove 210 miles on Sunday.
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at football practice, gustavo does push ups for 2 minutes for every 6 minutes playing if he plays for 42 minutes how many of push ups will he do
Answer:
14 mins
Step-by-step explanation:
2/6 = x/42
6x=84
x=14
Please answer this please you will not understand how much this means 25 points
The solutions to f(x) = 0 on the interval [0, 2pi) are x = 0 and x = pi.
Understanding Trigonometric Function(a) For f(x) = 0
We set the function equal to zero and solve for x:
f(0) = sec²x - 1 = 0
sec² x = 1
Taking the square root of both sides, we get:
sec x = ±1
Recall that sec x = 1/cos x = cos⁻¹ x
Therefore
x = cos⁻¹ (1) = 0 (using calculator or table)
x = cos⁻¹(-1) = pi
Therefore, the solutions to f(x) = 0 on the interval [0, 2pi) are x = 0 and x = pi.
(b) For f(x) > 0
To get the positive values of x, we can start by factoring f(x):
f(x) = sec²x - 1 = (sec x + 1)(sec x - 1)
Since the square of the secant function is always positive, we have:
f(x) > 0 if and only if (sec x + 1)(sec x - 1) > 0
There are two cases to consider:
sec x + 1 > 0 and sec x - 1 > 0
sec x + 1 < 0 and sec x - 1 < 0
For case 1, we have:
sec x > -1 and sec x > 1
Since secant is always positive, we have sec x > 1.
For case 2, we have:
sec x < -1 and sec x < 1 (This is not possible)
(c) For f(x) < 0
By using the factored form of f(x) from part (b), we can find the values of x where f(x) is negative.
f(x) < 0 if and only if (sec x + 1)(sec x - 1) < 0
There are two cases to consider:
sec x + 1 > 0 and sec x - 1 < 0
sec x + 1 < 0 and sec x - 1 > 0
For case 1, we have:
sec x > 1 and sec x < -1 (not possible)
For case 2, we have:
sec x < -1 and sec x > 1
Since secant is always positive, this case is not possible either.
Therefore, there are no solutions to f(x) < 0 over the interval [0, 2pi).
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A dot plot titled seventh grade test score. There are 0 dots above 5, 6, 7, 8 and 9, 1 dot above 10, 1 dot above 11, 2 dots above 12, 1 dot above 13, 1 dot above 14, 2 dots above 15, 3 dots above 16, 3 dots above 17, 2 dots above 18, 2 dots above 19, 3 dots above 20. A dot plot titled 5th grade test score. There are 0 dots above 5, 6, and 7, 1 dot above 8, 2 dots above 9, 10, 11, 12, and 13, 1 dot above 14, 3 dots above 15, 2 dots above 16, 1 dot above 17, 2 dots above 18, 1 dot above 19, and 1 dot above 20.
Students in 7th grade took a standardized math test that they also had taken in 5th grade. The results are shown on the dot plot, with the most recent data shown first.
Find and compare the means to the nearest tenth.
7th-grade mean:
5th-grade mean:
What is the relationship between the means?
Note that 7th grade mean = 277.86
the 5th grade mean = 254.77
So th relationship between the mean is that the 7 th grade mean is higher than the 5 th grade mean .
How is this so ?To compute the means here is what we did
7 th grade mean = (1 × 10) + (1 × 11) + (2 × 12) + (1 × 13) + (1 × 14) + (2 × 15) + (3 × 16) + (3 × 17) + (2 × 18) + (2 × 19) + (3 × 20) / 21
= 277.857142857
≈ 277.86
For the 5th grade mean
5th grade mean = (1 × 8) + (2 × 9) + (2 × 10) + (2 × 11) + (2 × 12) + (1 × 13) + (3 × 15) + (2 ×16) + (1 × 17) + (2 × 18) + (1 × 19) + (1 × 20) / 26 = 12.5
= 254.769230769
≈ 254.77
This means that trully, the relationship between the mean is that the 7 th grade mean is higher than the 5 th grade mean.
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Need the answer ASAP
A function whose graph is the graph of y = √x, but is shifted to the left 9 units is [tex]y=\sqrt{x+9}[/tex].
What is a translation?In Mathematics and Geometry, the translation of a geometric figure or graph to the left means subtracting a digit from the value on the x-coordinate of the pre-image;
g(x) = f(x + N)
Conversely, the translation a geometric figure upward means adding a digit to the value on the positive y-coordinate (y-axis) of the pre-image; g(x) = f(x) + N.
Based on the information provided, the transformed function should be written as follows:
y = √x
g(x) = (√x + 9)
[tex]y=\sqrt{x+9}[/tex]
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What is k? k - 9 < - 6
Answer:
Step-by-step explanation:
2
2-9=-7
In negative numbers, the greater number that is negative is less than the smaller negative number. For example, -9<-8. Even though 9 is a bigger number when positive, it's the opposite for negative numbers. While there can be many numbers for k like 0,1, or 2, 1 will probably be the best answer.
Answer:
[tex]\mathrm{k < 3}[/tex]Step-by-step explanation:
[tex]\mathrm{ k - 9 < - 6}[/tex]
Add both sides by 9 :-
[tex]\mathrm{ k - 9+6 < - 6+6}[/tex]Simplify :-
[tex]\mathrm{k < -6+9}[/tex][tex]\mathrm{k < 3}[/tex]___________________
Hope this helps!
Review the proof.
Step
1
2
3
5
6
7
8
Statement
cos(2x)= 1-2sin²(x)
Let 2x = 0.
Then x =
cos() = 1-2sin²()
-1 + cos() = -2sin²)
1 + cos(e) = 2sin²)
1-cos(0) = sin²)
sin() = ±
1-cos(0)
2
Which step contains an error?
O step 2
O step 4
step 6
O step 8
The error is in step 2 based on the given statement.
How to solveThe given statement is[tex]cos(2x) = 1-2sin^2(x),[/tex] and it is not appropriate to simply let 2x = 0.
By doing this, you are only considering a specific case where x = 0, rather than proving the statement for all values of x.
To properly prove the given statement, you should consider using trigonometric identities or double-angle formulas to establish the equivalence between cos(2x) and 1-2sin²(x) for all x.
Thus, the error is in Step 2
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A right rectangular prism and its net are shown below.
Answer:
A = 5
B = 4
C = 8
D = 3
Step-by-step explanation:
This is more of a visual calculation so I can't really explain much about it other than that you match up the side in the prism with the side in the net
Answer: 108
Step-by-step explanation:
If you turn the shape, where the pointy side of the ramp is facing you and you flipped it open and laid out the sides, that's the "net" image on right
A = 5 the long side of that triangle is also the short side of that rectangle
B = 3 it's the short side of the triangle
C = 8 long part of the rectangle
D = 4 long side of triangle
To find surface area. Find the area of each of the shapes and add it all up
Top Rectangle:
A=Lw=C*A = 5*8 = 40
Middle Rectangle:
A=Lw = B*C = 3*8 = 24
Bottom Rectangle:
A=LW = 4*C = 4*8=32
Triangles are same
A=1/2 bh = 1/2 D*B = 1/2 * 4* 3 =6
But there are 2 of them so A=12
Now add all the shapes together
A(total)=40+24+32+12=108
Graph the equation y = − x² + 8 x − 12 on the accompanying set of axes. You must plot 5 points including the roots and the vertex. Using the graph, determine the roots of the equation − x² + 8 x − 12 = 0
A graph that represent the quadratic equation y = -x² + 8x - 12 is shown in the image attached below.
The roots of the equation are (2, 0) and (6, 0).
What is the graph of a quadratic function?In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the given quadratic function, we can logically deduce that the graph would be a downward parabola because the coefficient of x² is negative and the value of "a" is less than zero (0).
Since the leading coefficient (value of a) in the given quadratic function y = -x² + 8x - 12 is negative 1, we can logically deduce that the parabola would open downward and the x-intercept (roots) is given by the ordered pair (2, 0) and (6, 0).
In conclusion, the turning point and vertex is given by the ordered pair (4, 4).
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A New York City hotel surveyed its visitors to determine which type of transportation they used to get around the city. The hotel created a table of the data it gathered.
Type of Transportation Number of Visitors
Walk 120
Bicycle 24
Car Service 45
Bus 30
Subway 81
Which of the following circle graphs correctly represents the data in the table?
circle graph titled New York City visitor's transportation, with five sections labeled walk 80 percent, bus 16 percent, car service 30 percent, bicycle 20 percent, and subway 54 percent
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 40 percent, bus 8 percent, car service 15 percent, bicycle 10 percent, and walk 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 80 percent, bicycle 20 percent, car service 30 percent, bus 16 percent, and walk 54 percent
Answer:
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent.
Step-by-step explanation:
To find the correct percentages, we need to calculate the percentage of visitors who used each mode of transportation out of the total number of visitors, which is the sum of all the numbers in the table:
Total number of visitors = 120 + 24 + 45 + 30 + 81 = 300
Percentage of visitors who walked = (120 / 300) x 100% = 40%
Percentage of visitors who used a bicycle = (24 / 300) x 100% = 8%
Percentage of visitors who used a car service = (45 / 300) x 100% = 15%
Percentage of visitors who used a bus = (30 / 300) x 100% = 10%
Percentage of visitors who used the subway = (81 / 300) x 100% = 27%
Therefore, the circle graph that correctly represents the data in the table is:
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent.
CAN SOMEONE HELP WITH THIS QUESTION?
The total cost for the first 25 units is given as follows:
$140.
How to obtain the total cost?The marginal cost function is defined as follows:
[tex]c(x) = \frac{14}{\sqrt{x}} = 14x^{-\frac{1}{2}}[/tex]
The total cost function is the integral of the marginal cost function, hence it is given as follows:
[tex]t(x) = \int c(x) dx[/tex]
[tex]t(x) = 28\sqrt{x}[/tex]
Applying the Fundamental Theorem of Calculus, the total cost from x = 0 to x = 25 is given as follows:
t(25) - t(0).
Thus:
t(25) = 28 x 5 = 140.t(0) = 28 x 0 = 0.Hence:
140 - 0 = $140.
(Applying the Fundamental Theorem of Calculus, we subtract the numeric values at each endpoint of the integral).
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Which of the following explains why this inequality is true?
7 3/8 × 4/5 < 7 3/8
Answer:
Step-by-step explanation:
To compare these two values, we first need to convert the mixed number 7 3/8 to an improper fraction. To do so, we multiply the whole number (7) by the denominator of the fraction (8), then add the numerator (3), and put the result over the denominator:
7 3/8 = (7 x 8 + 3) / 8 = 59/8
Now we can rewrite the inequality as:
(59/8) × (4/5) < 59/8
To simplify the left-hand side of the inequality, we multiply the numerators and denominators:
(59/8) × (4/5) = (59 × 4) / (8 × 5) = 236/40 = 59/10
So the inequality becomes:
59/10 < 59/8
To compare these fractions, we need to find a common denominator. The least common multiple of 8 and 10 is 40, so we can convert both fractions to have a denominator of 40:
59/10 = (59 x 4) / (10 x 4) = 236/40
59/8 = (59 x 5) / (8 x 5) = 295/40
Now we can see that 236/40 < 295/40, which means that:
59/10 < 59/8
Therefore, the inequality 7 3/8 × 4/5 < 7 3/8 is true.
Look at this pictograph:
Library books checked out
December
January
February
March
April
Each = 5 books
How many more books were checked out in March than in April?
books
There were no more books checked out in March than in April.
What is the pictograph about?The pictograph provided shows the number of books checked out from the library during the months of December, January, February, March, and April. Each picture represents 5 books.
The pictograph tells us that for each of these months, 5 books were checked out. So, in March, 5 books were checked out, and in April, 5 books were also checked out.
To find the difference between the number of books checked out in March and April, we subtract the number of books checked out in April from the number of books checked out in March:
5 books (March) - 5 books (April) = 0 books
Therefore, The result shows that there were no more books checked out in March than in April. Both months had the same number of books checked out, which is 5.
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Can sum help me with this
Answer:
36°
Step-by-step explanation:
x+27+27+90=180
x=36°
Julian is using a biking app that compares his position to a simulated biker traveling Julian's target speed. When Julian is behind the simulated biker, he has a negative position.
Julian sets the simulated biker to a speed of
20
km
h
20
h
km
20, start fraction, start text, k, m, end text, divided by, start text, h, end text, end fraction. After he rides his bike for
15
1515 minutes, Julian's app reports a position of
−
2
1
4
km
−2
4
1
km minus, 2, start fraction, 1, divided by, 4, end fraction, start text, k, m, end text.
What has Julian's average speed been so far?
To solve the problem, we need to find Julian's average speed, given that he started biking from a position behind the simulated biker at a speed of 20 km/h, and after 15 minutes, his position was reported as -214 km.
We can use the formula for average speed:
Average speed = total distance / total time
To find the total distance, we need to calculate the displacement of Julian from the initial position of -d (where d is the distance between Julian and the simulated biker when he started biking) to the position of -214 km after 15 minutes.
Displacement = final position - initial position
Displacement = (-214 km) - (-d) = d - 214 km
The total distance covered by Julian is equal to the absolute value of the displacement, since the direction of the motion does not matter when computing distance.
Total distance = |d - 214 km|
To find the total time, we need to convert 15 minutes to hours:
Total time = 15 minutes / 60 minutes/hour = 0.25 hours
Now we can substitute the values into the formula for average speed:
Average speed = total distance / total time
Average speed = |d - 214 km| / 0.25 hours
Since Julian was traveling at a constant speed of 20 km/h, we can also express the distance in terms of time:
Average speed = (20 km/h) x t / 0.25 hours
where t is the time Julian biked in hours.
Setting the two expressions for average speed equal to each other, we can solve for t:
|d - 214 km| / 0.25 hours = (20 km/h) x t / 0.25 hours
|d - 214 km| = 20 km/h x t
Solving for t:
t = |d - 214 km| / 20 km/h
Now we can substitute this expression for t into either expression for average speed:
Average speed = (20 km/h) x t / 0.25 hours
Average speed = |d - 214 km| / 0.25 hours
Substituting the expression for t:
Average speed = |d - 214 km| x 4 / |d - 214 km|
Simplifying:
Average speed = 80 km/h
Therefore, Julian's average speed so far has been 80 km/h.
Find the perimeter of each figure
The hexagon with sides of length 5 inches, 4 inches, 4 inches, 5 inches, 3 inches, and 3 inches has a perimeter of 24 inches.
What is a hexagon?A hexagon is a regular polygon, meaning all sides and angles are equal in size. It is a symmetrical shape, which means it can be divided into two equal halves.
To calculate the perimeter of this hexagon, we must first identify the length of each side.
All sides of the hexagon have a length of either 5 inches, 4 inches, or 3 inches, as there are two sides of each length.
The perimeter of the hexagon is the sum of the length of all its sides. Adding the length of all the sides, we get
5 + 4 + 4 + 5 + 3 + 3 = 24.
Thus, the perimeter of the hexagon is 24 inches.
Hence, the sum of the length of the sides of a hexagon is always greater than the length of any one of its sides.
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which value of x is in the solution set of -4/3x+5<17
A. -8
B. -9
C. -12
D. -16
Please help!
Answer:
-9
Step-by-step explanation: Definitely correct
Use the Law of Cosines. Find x to the nearest tenth.
2
B
15
ro
30
16
C
The value of x for the triangle is,
x = 58.67 degree
We have to given that;
By Use the Law of Cosines. Find x to the nearest tenth.
And, A triangle ABC is shown in figure.
Hence, We can formulate;
c = √a² + b² - 2ab cos x
16 = √15² + 30² - 2 × 15 × 30 cos x
16 = √225 + 900 - 900 cos x
256 = 725 - 900 cos x
900 cos x = 725 - 256
900 cos x = 469
cos x = 469 / 900
cos x = 0.52
x = 58.67 degree
Thus, The value of x for the triangle is,
x = 58.67 degree
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3.6 is 5% of I need help with all
Answer: 3.6 is 5% of 72
Step-by-step explanation: If 3.6 is 5% then just multiply 3.6 by 95 to get 68.4 and add to get 72, Yw.
A savings account starts with $312.50. After 9 years of continuous compounding at an interest rate, r, the account has $1250.
What is the interest rate percentage?
Round the answer to the nearest hundredth.
The interest rate of the savings account would be = 33.3%
How to calculate the interest rate of the savings account?To calculate the interest rate of the savings account, the formula for simple interest should be used. That is;
Simple interest = Principal × time × Rate/100
simple interest = 1250-312.50 = 937.5
Principal amount = $312.50
Time = 9 years
rate = ?
That is;
937.5 = 312.50 × 9 × R/100
make R the subject of formula:
R = 937.5× 100/312.50 × 9
= 93750/2812.5
= 33.3%
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Amelia has a music box that is shaped like a right rectangular
prism. She wants to pack the music box into a container,
with 1 in. of packing material between each face of the
music box and the container. A bag contains 200 in.3 of
packing material. How many bags of packing material will
Amelia need? Show your work.
The number of packing materials the Amelia will need = 2.4
How to calculate the quantity of packing materials Amelia will need?From the diagram given above, the formula for the volume of a right rectangular prism = Length×width ×height.
Where;
Length = 10in
Width = 6 in
Height = 8 in
The volume = 10×6×8 = 480 in³
But one bag = 200in³
The amount of bag that the music box can contain = 480/200 = 2.4
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‼️‼️‼️WILL MARK BRAINLIEST IF HELPFUL‼️‼️‼️
Answer:
S = 2π(10^2) + 2π(10)(3)
= (200 + 60)π = 260π cm^2
So 250 cm^2 is not a reasonable answer for the surface area of this cylinder.
I need to know this for math the clay they shown is shaped like a rectangular prism with a hole inside that is shaped like a smaller rectangle prism I need this right now please help me I will give you a lot of points and extra if you answered
The volume of the clay used to make the vase is 36 in³
How to determine the volumeTo determine the volume of clay that was used for the vase, we need to consider that;
The formula for the volume of a rectangular prism is expressed as;
Volume = lwh
Such that;
V is the volume of the prism.l is the length of the rectangular prism.w is the width of the rectangular prism.h is the height of the rectangular prism.For the bigger prism, we have;
Volume = 3 × 3 × 5
Multiply the values
Volume = 45 in³
For the hole, we have;
Volume = 4 × 3/2 × 3/2
Multiply the values
Volume = 9 in³
Then, the volume of clay used for the vase = 45 - 9 = 36 in³
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write a situation that matches this inequality 8x+14<100
Suppose you are a small business owner who sells handmade crafts. You have a budget of $100 to purchase materials for your next batch of products. You know that each craft requires some amount of materials, which costs $8 per unit. Additionally, you will need to pay a fixed cost of $14 for other expenses related to production and shipping.
How the situation matches inequality 8x+14<100 ?To make a profit, you must ensure that the cost of materials and fixed expenses does not exceed the $100 budget. Therefore, you can write an inequality to represent this situation:
8x + 14 < 100
Here, x represents the number of units of materials needed for each craft. The inequality states that the total cost of materials (8x) plus fixed expenses ($14) must be less than $100.
To solve this inequality, you can subtract 14 from both sides:
8x < 86
Finally, you can divide both sides by 8:
x < 10.75
This means that for each craft, you can use no more than 10.75 units of materials in order to stay within budget and make a profit.
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Please can someone assist me on this question I have no idea
Answer:
x2+10x+25
Step-by-step explanation:
It goes like this:
X2+2*1x*5+5*5
Which ordered pair is a solution of y = x + 12?
A.( 24, 12)
B. (–12, –24)
C.( 9, 21)
D. (0, –12)
(9,21) is a solution of y=x+12
Step-by-step explanation:When is an ordered pair a solution?
To find if an ordered pair (x,y) is a solution to an equation, substitute the x-value and y-value from the ordered pair into the equation, evaluate both sides of the equation individually, and see if the equation is true.
If the two sides are equal, the ordered pair is a solution.If the two sides are not equal, the ordered pair is not a solution.Warning: A common mistake is to use the first coordinate (the x-coordinate, on the left of the ordered pair) as the value on the left side of the equation, and the second coordinate (the y-coordinate, on the right of the ordered pair), as the value for the right side of the equation. Make sure to substitute the x-value for the "x" in the equation, and the y-value for the "y" in the equation.
Going through the choices:
Point A (24,12)
y = x+12
(12) ?? (24) + 12
12 ≠ 36
not equal -- not a solution
Point B (-12,-24)
y = x+12
(-24) ?? (-12) + 12
-24 ≠ 0
not equal -- not a solution
Point C (9,21)
y = x+12
(21) ?? (9) + 12
21 = 21
equal -- (9,21) is a solution
Point D (0,-12)
y = x+12
(-12) ?? (0) + 12
-12 ≠ 12
not equal -- not a solution
Michael purchased stereo equipment for $2500. His wife claims that was not a smart investment because stereo equipment decreases in value at a rate of 9% per year. How much will his stereo equipment be be worth after 8 years?
Based on an exponential decay factor, Michael's stereo equipment will be worth $2,116 after 8 years, given the decreasing rate of 9% per year.
What is an exponential decay factor?The decay factor is represented by (1 - r), where r is the constant periodic decreasing rate.
The decay factor is used in exponential decay functions to determine the depreciated value of an asset.
Current price of stereo equipment = $2,500
Annual decreasing rate = 9%
Decrease factor = 0.91 (100% - 9%)
The number of years = 8 years
Value of the equipment after 8 years = ($2,500 x 0.91^8)
= $2,116.125 ($2,500 x 0.47025)
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Ina Crespo rowed 16 miles down the Habashabee River in 2 hours, but the return trip took her 4 hours. Find the rate Ina rows in still water and the rate of the current. Let x represent the rate Ina can row in still water and let y represent the rate of the current.
Ina rows at a rate of 6 mph in still water, and the current flows at a rate of 2 mph.
What is distance?Distance is the overall length of a journey that a person, item, or vehicle takes to get from one place to another. Due to its scalar nature, it has simply magnitude and no direction. Typically, distance is expressed in terms of metres, kilometres, miles, or feet. It is distinct from displacement, which describes the shift in an object's location from its starting point to its ending point while also taking the movement's direction into consideration.
According to given information:We can start by using the formula:
distance = rate × time
Let's first consider the trip downstream. In this case, Ina's speed relative to the river current adds up to the distance traveled per unit of time. So we have:
16 = (x + y) × 2
Simplifying and solving for x + y, we get:
x + y = 8
Now let's consider the trip upstream. In this case, Ina's speed relative to the river current subtracts from the distance traveled per unit of time. So we have:
16 = (x - y) × 4
Simplifying and solving for x - y, we get:
x - y = 4
We now have two equations with two variables, so we can solve for x and y using either substitution or elimination. Let's use elimination:
(x + y) + (x - y) = 8 + 4
2x = 12
x = 6
Now we can substitute x = 6 into either of the original equations to solve for y. Let's use the first equation:
x + y = 8
6 + y = 8
y = 2
Therefore, Ina rows at a rate of 6 mph in still water, and the current flows at a rate of 2 mph.
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Marla, Jamie, and Sarah have each led their book club’s monthly meeting. Jamie has led 2/6 of the meetings, and Sarah has led 1/6 of the meetings. What fraction of the meetings has Marla led?
Step-by-step explanation:
1-2/6-1/6= 3/6
= 1/2
Marla has led 1/2 of the meetings
The table below shows primary school enrollment for a certain country. Here, x represents the number of years after 1820, and y represents the enrollment percentage. Use Excel to find the best fit linear regression equation. Round the slope and intercept to two decimal places.
x y
0 0.1
5 0.1
10 0.1
15 0.2
20 0.2
25 0.3
30 0.4
35 0.5
40 0.6
45 1.1
50 1.5
55 3.0
60 4.5
65 5.5
70 6.1
75 6.8
80 7.0
85 8.0
90 9.3
95 10.7
100 12.4
105 14.1
110 16.6
115 17.5
120 19.7
125 19.4
130 32.7
135 40.9
140 47.6
145 57.8
150 57.0
155 61.7
160 63.2
165 75.0
170 76.5
175 96.0
180 92.0
185 100.0
190 100.0
The best-fit linear regression equation gives us the equation y = 0.0804x + 1.1794, where the slope is 0.0804 and the y-intercept is 1.1794.
The trendline equation will give us the equation for the linear regression line, which can be written in the form of y = mx + b, where m is the slope and b is the y-intercept.
Once we have the trendline equation, we can use it to make predictions about future enrollment percentages based on the number of years after 1820.
The slope of the line tells us the rate at which the enrollment percentage is increasing or decreasing over time, and the y-intercept tells us the enrollment percentage when x is equal to zero (i.e., in 1820).
Here we have find that the best-fit linear regression equation gives us the equation
=> y = 0.0804x + 1.1794,
where the slope is 0.0804 and the y-intercept is 1.1794.
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Brent starts with 16 identical white socks in his sock drawer. Imagine he receives 2 identical black socks as a gift and mixes them in with his 16 white socks. If he draws one sock without looking to put on his left foot, then draws a second sock without looking to put on his right foot, what is the probability that he draws mismatched socks?
The probability that Brent draws mismatched socks is approximately 31/153.
After adding 2 identical black socks, Brent has a total of 18 socks in his drawer. The probability of drawing a white sock on the first draw is 16/18 (since there are 16 white socks out of 18 total socks).
After drawing a white sock on the first draw, there are 15 white socks and 2 black socks left in the drawer. The probability of drawing a black sock on the second draw is 2/17 (since there are 2 black socks out of 17 total socks left). So the probability of drawing a white sock followed by a black sock is;
(16/18) × (2/17) = 32/306
Similarly, the probability of drawing a black sock followed by a white sock is;
(2/18) × (15/17) = 30/306
However, the probability of drawing mismatched socks is;
32/306 + 30/306 = 62/306
= 31/153
Therefore, the probability will be 31/153.
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