Laurence earned scores of 87, 80, 75, and 85 on four biology tests. What score must he earn on his next test to have an 85 average?.
To get an 85 average, Laurence needs a score of 25 on his upcoming biology exam.
We can use the formula for the average (or mean) of a series of variables to determine Laurence's next biology test score in order to achieve an average of 85:
Average = (sum of values) / (number of values)
The total of Laurence's marks on the first four biology exams can be calculated using the following formula:
Sum of scores = 87 + 80 + 75 + 85
= 327
We need the total of all five scores to be 85 x 5 = 425 in order to obtain an average of 85 for five tests.
Therefore, We need the total of all five scores to be 85 x 5 = 425 in order to obtain an average of 85 for five tests.
By deducting Laurence's first four scores from the desired total of all five scores, and dividing the result by one (the number of scores left), we can get the score that Laurence has to achieve in his next biology exam:
Next score = (sum of all five scores) - (sum of first four scores)
= (85 x 5) - 327
= 25
Therefore, To get an 85 average, Laurence needs a score of 25 on his upcoming biology exam.
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If you took many random samples of a variable with a BIMODAL distribution, the means of your random samples would follow a (normal, uniform, skewed, or bimodal) distribution?
If you took many random samples of a variable with a VERY SKEWED distribution, the means of your random samples would follow a (normal, uniform, skewed, or bimodal) distribution?
Answer:
Step-by-step explanation:
If you took many random samples of a variable with a BIMODAL distribution, the means of your random samples would follow a normal distribution.
If you took many random samples of a variable with a VERY SKEWED distribution, the means of your random samples would follow a normal distribution. This is due to the Central Limit Theorem, which states that as the sample size increases, the distribution of the sample means approaches a normal distribution, regardless of the shape of the underlying population distribution.
The Central Limit Theorem (CLT) is a fundamental theorem in statistics that states that, as the sample size increases, the distribution of the sample means approaches a normal distribution, regardless of the shape of the underlying population distribution. This means that even if the original population distribution is skewed, bimodal, or any other shape, the distribution of the sample means will tend towards a normal distribution as the sample size increases.
The reason for this is that the sample means are essentially an average of a number of independent random variables, and the normal distribution is the result of the combination of many independent random variables. When the sample size is large, the distribution of the sample means becomes very close to a normal distribution, even if the underlying population is far from normal.
In the case of a bimodal distribution, the sample means will still approach a normal distribution as the sample size increases, but the distribution may have a different mean and standard deviation than the original population.
In the case of a very skewed distribution, the sample means will also approach a normal distribution as the sample size increases, but the distribution may still be skewed, just less so than the original population.
In conclusion, the Central Limit Theorem states that the distribution of the sample means will tend towards a normal distribution as the sample size increases, regardless of the shape of the underlying population distribution.
If my answer has satisfied your requirements, I would appreciate it if you would give me a rating : Brainliest Answer!
pls help me i’ll give you brainlist!
For the linear equation 3x + y = 9 we have:
x-intercept (3, 0)y-intercept (0, 9).How to find the x and y-intercepts?Here we want to find the two intercepts for the linear equation:
3x + y = 9
First, the x-intercept is the point that we get when we evaluate on y = 0.
3x + 0 = 9
3x = 9
x = 9/3
x = 3
Then we get: x-intercept (3, 0)
And for the y-intercept we need to evaluate in x = 0.
3*0 + y = 9
y = 9
Then the y-intercept is (0, 9).
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When we are given the value of the ______ variable, we can use the least-squares regression line to predict the value of the ______ variable.
When we are given the value of the explanatory variable, we can use the least-squares regression line to predict the value of the outcome variable.
The least square method is the process of finding the best-fitting curve or line of best fit for a set of data points by reducing the sum of the squares of the offsets (residual part) of the points from the curve. During the process of finding the relation between two variables, the trend of outcomes is estimated quantitatively. This process is termed as regression analysis. The method of curve fitting is an approach to regression analysis. This method of fitting equations that approximates the curves to give raw data is the least squares.
It is quite obvious that the fitting of curves for a particular data set is not always unique. Thus, it is required to find a curve having a minimal deviation from all the measured data points. This is known as the best-fitting curve and is found by using the least-squares method.
When we are given the value of the explanatory variable, we can use the least-squares regression line to predict the value of the outcome variable.
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please help me, be quick!
The simplified value of the expression is [a² + b² - 2ab]/[2a²b² - ab³ - a³b]
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
1/(b² - ab) - 1/(ab - a²)
Take the LCM of the expression
So, we have the following representation
[ab - a² - b² + ab]/[(b² - ab)(ab - a²)]
Evaluate the like terms
So, we have the following representation
[2ab - a² - b²]/[(b² - ab)(ab - a²)]
Open the bracket
[a² + b² - 2ab]/[2a²b² - ab³ - a³b]
Hence, the solution is [a² + b² - 2ab]/[2a²b² - ab³ - a³b]
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What is the slope of the line that passes through the points ( 6 , 7 ) (6,7) and ( 16 , 22 ) (16,22)? write your answer in simplest form.
Answer:
Step-by-step explanation:
The slope of a line is the change in y (the vertical axis) divided by the change in x (the horizontal axis).
Given the two points (6,7) and (16,22), we can calculate the slope as follows:
Change in y = 22 - 7 = 15
Change in x = 16 - 6 = 10
Therefore, the slope of the line passing through the two points is:
slope = change in y / change in x = 15 / 10 = 3/2
So the slope of the line is in its simplest form, 3/2.
Regenerate response
NEED HELP FAST for 25pts
The coordinates of point C in the given right triangle ABC is (2, 2√3-2)
What is a triangle?A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
Given that, triangle ABC is a 30°-60°-90° triangle, where two vertices are A(-4, -2) and B(4, -2).
Now, AB=4-(-4)=8
AC=AB×sin60°= 8×√3/4√3
In right triangle ACD
AD=AC×cos30°
= 4√3×√3/2
= 6
Xc=6-4=2
Yc=AC×sin30°-2
= 4×3×1/2-2
= 2√3-2
The coordinates of point C(2, 2√3-2)
Therefore, coordinates of C(2, 2√3-2).
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x + 17 = -50 + x + 34 + 33
HELP!
The figure on the right is a scaled copy of the figure on the left, though it might have
also been rotated.
U
W
Η,
Which side in the figure on the right corresponds to segment UW?
What is the scale factor?
Answer:
HI
The scale fact from the smaller to the larger is 3. The scale factor from the larger to the smaller is 1/3
Step-by-step explanation:
Help with these questions pls?
Answer:
76
Step-by-step explanation:
(16x3)+28
Its 16x3 because there's 3 half hours in 1.5hrs
Designer builds and sells small chairs and large chairs. The cost of material is $10 for each small chair and $15 for each large chair. The selling price is $22 for a small chair and $51 for a large chair. The designer spends $305 on material to make chairs. The designer makes eight more small chairs than large chairs. Write a system of equations that can be used to determine s, the number of small chairs and T, the numbers large chairs, the designer makes. How many small chairs did the designer make?
After solving the system of equations, we found that the number of small chairs is 53 and the number of large chairs is 45.
What is meant by the system of equations?
A set of equations with a finite number of solutions is referred to as a system of equations. A system of equations in algebra consists of two or more equations and looks for common answers to the equations. A group of equations that are all satisfied by the same set of variables are referred to as a system of linear equations.
Given,
Cost of material for small chair = $10
Cost of material for large chair = $15
The selling price for a small chair = $22
The selling price for a large chair = $51
The total money spent on materials = $305
Designer makes 8 more small chairs than large chairs.
If the number of large chairs = t and the number of small chairs = s
Using the given equations, we can write the following system of equations.
10s + 15t = 305
s - t = 8
Now we make the coefficient of s in both equations the same.
Multiply 10 in the second equation.
10s + 15t = 305
10s - 10t = 80
Subtracting,
5t = 225
t = 45
s = 8 + t = 45 + 8 = 53
Therefore after solving the system of equations, we found that the number of small chairs is 53 and the number of large chairs is 45.
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Find the inverse of each of the given functions.
f(x)=4x-12
DONE
+
h(x)
O
O
H
2x - 4
3
h¯¹(x) = 3x - 12
2
h¯¹(x) =
h"¹(x) =
DONE
3
(2x - 4)
3x + 4
2
Answer:B
Step-by-step explanation:
$10000 is deposited in an account earning 8% interest compounded continuously. Use the continuous interest formula below to determine how long it takes for the amount in the account to double. Round answer to 2 decimal places.
A=Pe^rt
____Years?
By using the continuous interest formula, we get 8.54 years that the amount will take to double itself.
What is continuous interest formula?The continuous interest formula is used to calculate the future value of a compound interest investment. It is written as follows:
Future Value = Principal × [tex](1 + r)^{n}[/tex]
where Principal is the original investment, r denotes the yearly interest rate, and n denotes the number of compounding periods.
The continuous interest formula is used to compute the future worth of an investment given its current value, yearly interest rate, number of times the interest is compounded each year, and number of years held.
In the given question,
A = A_0[tex]e^{rt}[/tex]
2A_0 = A_0[tex]e^{rt}[/tex]
2 = [tex]e^{rt}[/tex]
ln(2) = rt
t = [tex]\frac{2}{r}[/tex]
t = [tex]\frac{2}{0.08}[/tex]
t = 8.54 years
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HELP ME i need help please
A transformation rule, if applied to a polygon on a coordinate grid, which does not preserve congruence include the following: C. (x, y) → (3x, 3y).
What is dilation?In Geometry, dilation simply refers to a type of transformation which changes the size of a geometric figure and the location of its points based on the scale factor, but not its shape.
Generally speaking, a dilation is not a rigid transformation because it can preserve angle measure, orientation, perpendicular lines, betweenness of points, parallel lines, and collinearity in any geometric figure.
In conclusion, we can reasonably infer and logically deduce that dilations does not preserve congruence.
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What is the correct answer answer asap for brainlist
Based on the information provided, the passage that explains the citation is "The outcome...is situational irony..." (option A).
What does explaining a citation mean?When you cite information from other sources or authors, there are three elements that should be included:
Introduction: Introduce your citation, for example by saying "Twain claimed that..."Citation: Here you add the words of the author or you paraphrase them.Explanation: This step requires connecting the citation to your text by explaining its meaning.Learn more about citation in https://brainly.com/question/30066031
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Solve the quadratic equation by the square root method and write the solutions in radical form. Simplify the solutions.
(3x+20)2=125
Answer:
Step-by-step explanation:
To solve the equation (3x + 20)^2 = 125 using the square root method, we start by taking the square root of both sides:
√[(3x + 20)^2] = √125
3x + 20 = ± 5
Next, we subtract 20 from both sides:
3x = -20 ± 5
Finally, we divide both sides by 3:
x = -8 or x = 3/3
So, the two solutions to the equation (3x + 20)^2 = 125 are x = -8 and x = 1. These solutions are in radical form and are already simplified.
Write the numeral in its expanded form.
34
x 10
) + (4 x 10
)
Answer:
380
Step-by-step explanation:
(34 * 10) + (4 x 10) =
= 10 * (34 + 4) =
= 10 * 38 =
= 380
A tailor charges a basic fee of $20 plus $4 per letter to sew an athlete's name on the back of a jacket. Write a linear equation that will find the cost c to have a name containing x letters
The equation will be;
c = 20 + 4x
What are Linear Equations?Linear equations are equations of the first order. When a linear equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable. A linear equation can also have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on. An equation is a mathematical statement, which has an equal sign (=) between the algebraic expression. Linear equations are the equations of degree 1. It is the equation for the straight line.
A linear equation that will find the cost c to have a name containing x letters will be;
c = $20 + 4x
where c = cost
$20 = basic fee
x = number of letters
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A city bowling league is holding a tournament in which the top 8 bowlers with the highest three-game totals are awarded cash prizes. First place will win $1250, second place $1132, third place $1014, and so on.
(a) Write a sequence a, that represents the cash prize awarded in terms of the place n in which the bowler finished
(b) Find the total amount of prize money awarded at the tournament.
The sequence will be aₙ=$1250-118ⁿ⁻¹ where n= place at which a bowler finished.
What exactly is a sequence?
A sequence is a collection of numbers that follows pattern. Olivia, for example, has been offered a position with a beginning monthly pay of $1000 and a yearly raise of $500. To figure out her monthly pay for the first three years? The prices will be $1000, $1500, and $2000. Note that Olivia's income over a number of years creates a sequence as they follow a pattern where the numbers increase by $500 each time.
Now,
given award money for 1, 2, 3 places is given as $1250, $1132 and $1014
that means for the sequence, first term is 1250 and difference between the next terms will be 118 (less)
So, the sequence will be aₙ=$1250-118ⁿ⁻¹
where
n=place at which a bowler is placed.
Hence,
The sequence will be aₙ=$1250-118ⁿ⁻¹.
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Slope int form or general form PLS HELP
Answer:
y = 4x + 32
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 4x ← is in slope- intercept form
with slope m = 4 and y- intercept = 0
• Parallel lines have equal slopes , then
y = 4x + c ← is the partial equation
to find c substitute (- 8, 2 ) into the partial equation
2 = 4(- 8) + c = - 32 + c ( add 32 to both sides )
34 = c
y = 4x + 32 ← in slope- intercept form
Please help!!!!! Due tomorrow need to understand how to properly do this question :(
Answer:
f(x)=3x^2+2
Step-by-step explanation:
use pm
The longer leg of a right triangle is nine less than three times the shorter leg. The
hypotenuse is two more than the longer leg. What is the length of the hypotenuse if the
perimeter is 24?
Answer: 71/7
Step-by-step explanation:
I like this problem a lot!
Let the shorter leg length be x:
then the longer leg length is 3x - 9
the hypotenuse length is (3x - 9) + 2 = 3x - 7
Perimeter of Triangle = Sum of all 3 sides of a triangle
24 = x + (3x - 9) + (3x - 7)
24 = 7x - 16
40 = 7x
.: x = 40/7
.: hypotenuse = 3x - 7 = (120/7) - 7 = 71/7
Done!
A bicycle wheel has a radius of 225 mm and has 25 equally spaced spokes. What is the approximate arc length, rounded to the nearest hundredth, between each spoke? Use 3.14 for π. Show your work.
The approximate arc length is 56.52mm.
What is an arc length?
The distance between two places along a segment of a curve is known as the arc length. Curve rectification is the process of measuring the length of an irregular arc section by simulating it with connected line segments. There are a finite number of segments in the rectification of a rectifiable curve.
Here, we have
Given: A bicycle wheel has a radius of 225 mm and has 25 equally spaced spokes.
To solve this question, we have to use the formula of the length of an arc which is given as
L = θ/360 * 2πr
To find the angle between each spoke, let's divide 360 by 25
θ = 360/25
θ = 14.4
Now that we have the value of the angle, let's substitute it and solve for the length of the arc.
L = 14.4/360 * 2(22/7)(225)
L = 56.52mm
Hence, the approximate arc length is 56.52mm.
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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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At a college, the ratio of faculty/staff to students is 3 to 13. If there are 4000
people at the college, how many students are there?
Answer:
Let's call the number of students at the college "x". Then, the number of faculty/staff is 3 times that number, or 3x. The total number of people at the college is the sum of the students and faculty/staff, which is x + 3x = 4x.
According to the problem, the ratio of faculty/staff to students is 3 to 13, so we can write an equation:
3x / x = 3 / 13
To find the number of students, we can solve for x:
4x = 4000
x = 1000
So, there are 1000 students at the college.
Shaun White, the Flying Tomato, is rolling down a 30° ramp on his skateboard (because he's not just a snowboarding gold medalist, the bro can skate too). The total mass of Shaun and his skateboard is 75 kg. The rolling friction between the skateboard wheels and the concrete is 9N acting backward against the skateboard. The drag force due to air resistance is 11 N acting backwards against Shaun. What is Shaun's acceleration? 30° 4.64 m/s2 down the slope
Previous question
If the drag force due to air resistance is 11 N acting backwards against Shaun. Shaun's acceleration is 4.64 m/s^2 down the slope.
To find Shaun's acceleration, we need to calculate the net force acting on him and his skateboard. The net force is the vector sum of all the forces acting on the object. We can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and its acceleration:
Net force = mass × acceleration
Let's break down the forces acting on Shaun and his skateboard:
The force of gravity, which acts vertically downwards with a magnitude of mg, where m is the total mass of Shaun and his skateboard and g is the acceleration due to gravity (9.8 m/s^2).
F₁ = m * g * sin(30°) = 75 kg * 9.8 m/s^2 * sin(30°) = 367.5 N
The force due to rolling friction between the skateboard wheels and the concrete, which acts backward against the skateboard.
F₂ = 9 N (given)
The drag force due to air resistance, which acts backward against Shaun.
F₃ = 11 N (given)
Now, let's add up the forces to get the net force:
Net force = F₁ - F₂ - F₃
= 367.5 N - 9 N - 11 N
= 347.5 N
Using Newton's second law of motion, we can now calculate Shaun's acceleration:
acceleration = Net force / mass
= 347.5 N / 75 kg
= 4.64 m/s^2 (down the slope)
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Sets A and B are subsets of the universal set U.
These sets are defined as follows.
U= {f, k, m, q, x,y}
A={f, k, m, y}
B = {f, m,q}
Find the following sets.
Write your answer in roster form or as Ø.
(a) AUB' =
(b) A' B' =
(a) The union set is AUB'={f, k, m, x, y}.
(b) The union set is A'UB'={q,k, x, y}.
What is the union of two sets?The union of two sets is also a set. This set contains all the elements of both two sets.
The universal set is U= {f, k, m, q, x,y} and two subsets are A={f, k, m, y} and B = {f, m,q}.
(a)
B' is the complementary set of B. So, find the elements of B'=U-B.
B'= {f, k, m, q, x,y}-{f, m,q}
={k, x,y}
Now, find the union set AUB'.
AUB' ={f, k, m, y}U{k, x,y}
={f, k, m, x, y}
Therefore, the required answer is AUB'={f, k, m, x, y}.
(b)
Also, A' is the complementary set of A. So, find the elements of A'=A-B.
A'= {f, k, m, q, x,y}-{f, k,m, y}
={q,x}
Now, find the union set A'UB'.
A'UB' ={q,x}U{k, x,y}
={q,k, x, y}
Therefore, the required answer is A'UB'={q,k, x, y}.
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Rewrite in simplest terms:-2(-10v+1)-6v
Answer:
14v-2
Step-by-step explanation:
1. distribute
2. combine like terms
see photo for more information
Find the slope of the line that passes through (-8,-1) and (12,4). Write the answer as a fraction in simplest form
slope:
Now write the equation of the line in slope intercept form:
The slope of the line that passes through (-8,-1) and (12,4) is 1/4.
The equation of the line in slope intercept form is y = x/4 - 31/4.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, we have the following;
Slope, m = (4 + 1)/(12 + 8)
Slope, m = 5/20
Slope, m = 1/4.
At point (-8, -1), a linear equation of this line can be calculated in slope-intercept form as follows:
y - y₁ = m(x - x₁)
y - (-8) = 1/4(x - (-1))
y + 8 = x/4 + 1/4
y = x/4 - 31/4.
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what is the volume of the prism?
The volume of the prism with a trapezoidal base is 312 m³
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
The volume of the prism is the product of the base area and the height. It is given by:
Volume = area of base * height
The prism shown in the diagram is a trapezoid prism, hence:
Area of base = (1/2)(5 + 8)(4) = 26 m²
Volume = area of base * height
Volume of prism = 26 m² * 12 m = 312 m³
The volume of the prism is 312 m³
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