The number of students that took all the three classes is 40
The number of students are in Group 2 is 51 students
How to find the number of students that tool all the three classes(i) To find the number of students who have taken all three classes, we need to subtract the number of students who have taken only two classes from the number of students who have taken at least one class.
Let's call the number of students who have taken all three classes "x".
The number of students who have taken Calculus and Sociology is 15 + x.
The number of students who have taken Calculus and Spanish is 20 + x.
The number of students who have taken Sociology and Spanish is 13 + x.
Adding these three equations, we have:
15 + 78 + 72 = 15 + x + 78 + x + 72 + x
solving for x
165 = 45 + 3x
120 = 3x
isolating x
So, x = 40.
hence, 40 students have taken all three classes.
(ii) To find the number of students in Group 2, we need to add the number of students who have taken at least one class to the number of students who have taken none of the classes.
Let's call the number of students in Group 2 "y".
The number of students who have taken at least one class is
32 + 22 + 16 - 10 - 8 - 11 + 5 = 36.
Therefore, y = 36 + 15 = 51.
So, there are 51 students in Group 2.
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T/F the condition probability of a given b must be smaller than the intersection of the same two events a and b
The condition probability of a given b must be smaller than the intersection of the same two events a and b:
This statement is False.
The condition probability of event "b" given event "a" (P(b|a)) must be less than or equal to the probability of event "b" (P(b)). This is because the occurrence of event "a" restricts the sample space to only those outcomes that belong to event "a", and thus the probability of event "b" given event "a" cannot be greater than the unconditional probability of event "b".
The concept of conditional probability is used to describe the probability of an event given that another event has already occurred.
The formula for conditional probability is
P(b|a) = P(a and b) / P(a),where P(b|a) represents the probability of event "b" given that event "a" has already occurred.
In order for this to be meaningful, it is required that P(b|a) <= P(b). This means that the probability of event "b" given that event "a" has already occurred cannot be greater than the unconditional probability of event "b".
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In this activity, a and b are constants and x and t are variables. Identify each notation as always representing a function of x, a function of t, or a number. X d (a) f(t) dt dx a function of x a function oft a number (b) f(x) dx dt a function of x a function oft a number a d (c) f(t) dt dx a function of x a function of t a number
The notations (a) f(t) dt dx, (b) f(x) dx dt, and (c) f(t) dt dx represent functions of x and t, and a number, respectively.
The notation (a) f(t) dt dx can be interpreted as the integral of a function f(t) with respect to t from a to b multiplied by the differential of x with respect to t. By applying the Fundamental Theorem of Calculus, we can calculate this expression by evaluating the antiderivative of f(t) from a to b, which is given by F(b) - F(a), and multiplying it by the derivative of x with respect to t, which is denoted by dx/dt.
Therefore, the expression (a) f(t) dt dx can be written as F(b) - F(a) * dx/dt.
The notation (b) f(x) dx dt can also be interpreted as the integral of a function f(x) with respect to x from a to b multiplied by the differential of t with respect to x. Again, we can calculate this expression by evaluating the antiderivative of f(x) from a to b, which is given by F(b) - F(a), and multiplying it by the derivative of t with respect to x, which is denoted by dt/dx.
Therefore, the expression (b) f(x) dx dt can be written as F(b) - F(a) * dt/dx.
Finally, the notation (c) f(t) dt dx can be interpreted as the integral of a function f(t) with respect to t from a to b multiplied by the differential of x with respect to t. Therefore, this expression can be written as F(b) - F(a) * dx/dt.
It is important to note that this expression is the same as (a) f(t) dt dx, and so it can be seen that it is a number, since F(b) - F(a) * dx/dt is a constant.
The notations (a) f(t) dt dx, (b) f(x) dx dt, and (c) f(t) dt dx represent functions of x and t, and a number, respectively.
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If y varies directly as x^2 and y=4 when x=-1 find y when x=3
The value of y when x = 3 is 36.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 8 is an equation.
We have,
y varies directly as x².
This means,
y = kx²
Now,
When x = -1, y = 4
So,
4 = k(-1)²
k = 4/1
k = 4
Now,
y = 4x²
For x = 3,
y = 4 x 3²
y = 4 x 9
y = 36
Thus,
The value of y is 36.
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1
Write the reason for each step of the proof. Be sure to number each step.
2.
Convert the two column proof that you just wrote into a paragraph proof. Remember to use proper spelling, grammar and punctuation.
The required triangle WYV and XYU are congruent triangles with the SAS postulate.
What is congruent geometry?In congruent geometry, the shapes that are so identical. can be superimposed to themselves.
Here,
Consider triangle WYV and XYU
XY = WY [Given ]
VY = UY [Given ]
∠WYV = ∠UYX [Alternate interior angles for two intersecting lines are always equal]
ΔWYV ≅ ΔXYU by SAS congruency postulate.
As triangles, WYV and XYU are congruent triangles then,
VW = UX [sides of a congruent triangle are always equal]
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find the exact value of each of the remaining trigonometric functions of 0. rationalize denominators when applicable.
sin 0 = v3/6 given that cos 0 = 0
Given that cos (0) = 0, we can use the Pythagorean identity sin^2(x) + cos^2(x) = 1 to find the value of sin (0).
sin^2(0) + cos^2(0) = 1
sin^2(0) = 1 - cos^2(0)
sin^2(0) = 1 - 0^2
sin^2(0) = 1
So, sin (0) = sqrt(sin^2(0)) = sqrt (1) = 1.
However, the given value is sin (0) = v3/6. This means that sin (0) = sqrt (3)/2, which is the value of sin (60). Therefore, the correct value of sin (0) is sqrt (3)/2, not 1.
trigonometry, the branch of mathematics deal with specific functions of angles and their application to calculations. There is total six functions of an angle commonly used in trigonometry.
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choose the best estimate for the division problem below.
38/6
A.8
B.3
C.4
D.6
The best estimate for 38/6 is option C that is equals to 4.
What is division ?
Division is a mathematical operation that involves splitting a number or quantity into equal parts or groups. It is the opposite of multiplication, where we find how many groups of a certain size can fit into a larger number or quantity.
When we divide one number by another, we are finding out how many times one number can be evenly divided by another number. For example, when we divide 12 by 3, we are asking "how many groups of 3 are in 12?" The answer is 4, because we can divide 12 into 4 equal groups of 3.
The best estimate for 38/6 is option C, 4.
We can see that 6 goes into 38 about 6 times (6 x 6 = 36), and there is a remainder of 2. Therefore, the answer is between 6 and 7. Since the options are all whole numbers, the best estimate is 4.
Therefore, The best estimate for 38/6 is option C that is 4.
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which of the following comes from the conservation of mass? bernoulli's equation. neither the continuity equation or bernoulli's equation. both the continuity equation and bernoulli's equation. the continuity equation.
The continuity equation comes from the conservation of mass.
It can be a mathematical statement of the principle of conservation of mass.
According to this, mass inflow in control volume should be equal to the mass outflow from that region at a particular time and the mass can neither be created nor be destroyed.
A continuity equation is an equation that shows the behavior of a quantity as it moves or is transported from one point or state to another
The general form of the continuity equation:
Where p=density of the fluid,
u,v,w=components of velocity in x,v, and z directions respectively.
The above equation is applicable for steady as well as unsteady, uniform s well as non-uniform, compressible as well as incompressible flow.
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The first month Tan had his new phone, he downloaded 5 apps. Six months later, he has 22 apps on his phone. What is the percent increase in the number of apps Tan has on his phone from when he initially had his phone to six months later?
The percent increase in the number of apps Tan has on his phone is 340%
What is the percent increase in the number of apps?Number of apps downloaded in months 1 = 5 apps
Number of apps downloaded in months 7 = 22 apps
Percentage increase in the number of apps = changes in the number of apps downloaded/ Number of apps downloaded in months × 100
= (22 - 5) / 5 × 100
= 17/5 × 100
= 3.4 × 100
= 340%
In conclusion, Tan downloaded 340% more apps on his phone after 6 months.
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please help !!!!!!!!!!
To obtain the other factor is to take the idea x² - 6x - 7 /x+ 1. Option A
What are algebraic expressions?Algebraic expressions are described as expressions comprising of terms, variables, factors, coefficients, and constants.
They are also made up of arithmetic operations, such as;
DivisionAdditionMulitiplicationFloor divisionSubtraction, etcGiven the expression;
x² - 6x - 7
Factorize the terms
x² - 7x + x - 7
Then, we get
(x+1) (x - 7)
The factors are (x + 1) (x -7)
Hence, the step x² - 6x - 7 divided by x - 1
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determine which of the above equations are eigenfunctions of the momentum operator, px, and identify the corresponding eignevalue
The eigenfunctions of the momentum operator px are wave functions which, when acted upon by px, result in a scalar multiple of the wave function itself, with the scalar being the eigenvalue.
To determine which wave functions are eigenfunctions of the momentum operator px, one can start by solving the eigenvalue equation, px ψ = ħkψ, where ψ is the wave function and ħk is the eigenvalue. In this equation, ħ is Planck's constant divided by 2π and k is the wave number.
To find the eigenvalue, one can multiply both sides of the equation by the complex conjugate of the wave function and integrate over all space. The result is ħk times the normalization constant, which can be used to find the eigenvalue.
The wave functions that satisfy this equation are the eigenfunctions of the momentum operator px, and their corresponding eigenvalues are proportional to their wave numbers.
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The function g(x)=5x+3−−−−√3−5 is a transformation of the cube root parent function.
How can these transformations be described?
Drag words to the boxes to correctly complete the statement.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
The function g(x) is translated 3 units ___ Response area, 5 units___ Response area , and undergoes a vertical ___ Response area compared to its cube root parent function.
left
right
up
down
stretch
compression
The complete statement is,
The function g(x) is 3 units stretch Response area , and undergoes a vertical translated 5 unit right Response area compared to its cube root parent function.
What is Refection?Reflection is a type of transformation that flip a shape in mirror line, so that each point is the same distance from the mirror line as its reflected point.
We have to given that;
The function is,
⇒ f (x) = ∛(5x+ 3) - 5
This is a transformation of the cube root parent function.
Now, The parent function is,
⇒ f (x) = ∛x
After 5 units stretch Response area, we get;
⇒ g (x) = ∛5x
And, After translated 3 units right Response area,
⇒ g (x) = ∛ (5x + 3)
And, After translated 5 unit down, we get;
⇒ f (x) = ∛(5x+ 3) - 5
Thus, The complete statement is,
The function g(x) is 3 units stretch Response area , and undergoes a vertical translated 5 unit down Response area compared to its cube root parent function.
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the sum of two number is twenty-six using x to represent the smaller of the two numbers, translate "the difference between five more then the larger number and twice the smaller number' into a variable expression. then simplify
"the difference between five more than the larger number and twice the smaller number' can be written as the expression 31 -3x.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given, the sum of two numbers is twenty-six the difference between five is more than the larger number and twice the smaller number' into a variable expression.
Since x represents the smaller of the two numbers,
Thus the larger number will be 26 - x
The expression asked above will be:
=> 5 + larger number - 2 * smaller number
=> 5 + 26 - x - 2 * x
=> 31 -3x
therefore, "the difference between five more than the larger number and twice the smaller number' can be written as the expression 31 -3x.
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bonsoir pouvez vous m'aidez
Answer:
Treatment for HIV/AIDS involves taking highly effective medicines called antiretroviral therapy (ART) that work to control the virus [1][2]. ART involves taking a combination of HIV medicines (called an HIV regimen) to suppress the virus and stop the progression of the disease [1]. The goal of treatment is to reduce the amount of HIV in the body and keep it at a low, undetectable level to help prevent further damage to the immune system and reduce the risk of transmitting HIV to others.
A bucket is 1/2 full of water. When 12 litres of water is added, it is 3/4 full. How many litres will the tank hold?
Answer:
48 liters.
Step-by-step explanation:
Going from 3/4ths full to 1/2 full has a difference of 1/4; that makes 12 liters 1/4 of the tank.
12 times 4 is 48.
Answer:
48
Step-by-step explanation:
assume holds x litres
1/2 x + 12 = 3/4 x
so 1/4 x =12
x =48
OWX is a sector of a circle with a radius of 35 cm.
OYZ is a sector of a circle with a radius of 24 cm.
The central angle of both sectors is 75°.
Work out the area of the shaded shape WXZY.
Give your answer in cm² to 1 d.p.
2
The area of the shaded shape WXZY is approximately 29.05 cm² to 1 decimal place.
What is area of sector?The sector's area in a circle is the whole area that is included inside the sector's boundary. The middle of the circle is where a sector always begins. The sector of a circle is the region of a circle that is contained between its two radii and the arc next to them. A semicircle is the area of a circle that most frequently represents half of a circle.
Finding the area of the shaded shape WXZY:The area of the sector OWX can be calculated as:
[tex]A = (75/360) \times \pi \times 35^{2} = 63.62 cm^2[/tex]
And the area of the sector OYZ can be calculated as:
[tex]A = (75/360) \times \pi \times 24^{2} = 34.57 cm^2[/tex]
The shaded area WXZY is the difference between the area of the two sectors, which is:
A = 63.62 - 34.57 = 29.05 cm²
Therefore, the area of the shaded shape WXZY is approximately 29.05 cm² to 1 decimal place.
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Complete question -
given that y squared equals x y plus 6. when y equals 3, x apostrophe (t )equals negative 1. determine y apostrophe (t )
The value of y = 3 and x' = -1, y' = -3/7.
Derivative of y with tGiven the equation y² = xy + 6 and knowing that y = 3 and x' = -1, we can use implicit differentiation to find the derivative of y with respect to t, y'.
First, differentiate both sides of the equation with respect to t:d/dt (y²) = d/dt (xy + 6)
2y * y' = x' * y + x * y' + 0
Next, substitute in the known values of y and x':2 * 3 * y' = -1 * 3 + x * y'
6 * y' = -3 + x * y'
Finally, isolate y' by subtracting x * y' from both sides:6 * y' - x * y' = -3
(6 - x) * y' = -3
Divide both sides by (6 - x) to find y':y' = -3 / (6 - x)
Substitute x' = -1 to find y':y' = -3 / (6 - -1)
y' = -3 / 7
So, when y = 3 and x' = -1, y' = -3/7.
The specific case we were discussing is finding the derivative of y with respect to t, given the equation y² = xy + 6, and the values of y and x' at a certain time t. This is a problem in calculus, which is a branch of mathematics that deals with the rate of change and slopes of curves. By differentiating both sides of the equation and substituting in known values, we were able to find the value of y' at a specific time t. This method of finding derivatives is called implicit differentiation and it is used to find the derivative of an implicit equation, where one variable is expressed in terms of another.
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The relationship between the Fahrenheit (F) and Celsius (C) temperature scales is given by the linear function F = 9/5 C + 32.
given function F = 9/5 C + 32
if slope = 9/5 then The slope means that F increases ___ degrees for each increase of 1°C.
The slope of the linear equation F = 9/5 C + 32 is 9/5. This means that for every increase of 1 degree Celsius, the Fahrenheit temperature increases by 9/5 degrees.
Therefore, the slope can be interpreted as "F increases 9/5 degrees for each increase of 1°C."
The conversion formulae we employ are the same ones found in most textbooks. Subtract 32 from the temperature in degrees Fahrenheit and multiply by.5556 (or 5/9). To convert Celsius temperatures to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.
The greater the number assigned to the temperature in fahrenheit, the hotter it is, and the lower, the colder it is.
As the originator of the thermometer as we know it, Fahrenheit had to put something on them to distinguish between different temperatures. The scale he chose became known as the Fahrenheit scale. Fahrenheit set zero to the lowest temperature he could get using a water and salt combination.
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2. What is the most precise name for quadrilateral ABCD with vertices A(-2, 4), B(5, 6), C(12,4), and D(5, 2)?
Oparallelogram
Orhombus
Oquadrilateral
Orectangle
Quadrilateral ABCD with vertices A(-2, 4), B(5, 6), C(12,4), and D(5, 2) is a parallelogram.
What is Quadrilateral?a quadrilateral is a four-sided polygon, having four edges and four corners.
The given vertices of a quadrilateral ABCD are A(-2, 4), B(5, 6), C(12,4), and D(5, 2).
We need to find the name of the quadrilateral.
The distance =√(x₂-x₁)²+(y₂-y₁)²
AB=√(5+2)²+(6-4)²
=√49+4==√53
CD=√(5-12)²+(2-4)²
=√49+4==√53
AB=CD
A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length
Hence, the most precise name for quadrilateral ABCD with vertices A(-2, 4), B(5, 6), C(12,4), and D(5, 2) is a parallelogram.
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find all real solutions of the equation by completing the square. (enter your answers as a comma-separated list. if there is no real solution, enter no real solution.)
The real solutions of the equation of X² + 12X - 64 = 0 are 4 and (-16)
To find the real solutions for a quadratic equation, we need to understand this concept:
(x - a).(x - b) = x² - (a+b)x +ab
We can also use the ABC formula where:
ax² + bx + c = 0
Then:
x = -b ±√(b² - 4ac)
2a
Using the given equation, we know that:
a = 1
b = 12
c = -64
Then, we will use the ABC formula to find the real solutions for the equation:
x = -(12) ± √(12² - 4(1)(-64))
2(1)
x = -(12) ± √(144 - 256)
2
x = -12 ± √400
2
x = -12 ± 20
2
x1 = (-12 + 20) / 2
x1 = 8/2 = 4
x2 = (-12 - 20)/2
x2 = (-32)/2 = -16
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Complete Question:
find all real solutions of the equation by completing the square. (enter your answers as a comma-separated list. if there is no real solution, enter no real solution.) X² + 12X - 64 = 0
drag each expression to the correct location on the table. determine which expressions represent purely real numbers and which expressions represent non-real complex numbers.
The expression 9/4 is a real number, whereas the expression 9i is a non-real complex number.
Real Numbers:
9/4
The expression 9/4 is a real number. This can be seen by dividing the numerator (9) by the denominator (4) to get the answer 2.25. This is a real number as it can be written with a decimal.
Non-Real Complex Numbers:
9i
The expression 9i is a non-real complex number. This can be seen by taking the coefficient (9) and multiplying it by the imaginary number i. The result is 9i, which is a non-real complex number because it cannot be written with a decimal. The imaginary number i is defined as the square root of -1, which is not a real number.
The expression 9/4 is a real number, whereas the expression 9i is a non-real complex number.
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given a collection of images with 50% dog images and 50% cat images, sample 2 images with replacement. what is the probabilities of (round to two decimal places e.g. 0.12):
The probability of getting both a dog and a cat image is 0.25.
The probability of getting two dog images with replacement is 0.25. This is because when selecting with replacement, each draw is independent of the previous draw. Thus, the probability of getting one dog image is 0.50 and the probability of getting a second dog image is 0.50. Thus, the probability of getting two dog images is 0.50 x 0.50 = 0.25. Similarly, the probability of getting two cat images with replacement is 0.25.
The probability of getting one dog image and one cat image with replacement is 0.50 x 0.50 = 0.25. Thus the probability of getting both a dog and a cat image is 0.25.
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consider the system of linear equations where a and b are unspecified constants for which values of a and b will the system have a unique solution
A system of linear equations has a unique solution if and only if the determinant of the matrix of coefficients is non-zero and the rank of the coefficient matrix is equal to the rank of the augmented matrix.
For the system to have a unique solution, the number of equations and the number of variables must be equal. If the determinant of the matrix of coefficients is non-zero, the system will have a unique solution if and only if the number of linearly independent rows in the coefficient matrix is equal to the number of variables. If the rank of the coefficient matrix is less than the number of variables, then the system will have either no solution or infinitely many solutions.
In conclusion, for a system of linear equations to have a unique solution, the number of equations must equal the number of unknowns and the determinant of the coefficient matrix must be non-zero. The values of a and b do not affect the existence of a unique solution.
The system of linear equations,
ax + by = c
dx + ey = f
will have a unique solution if and only if the determinant of the matrix of coefficients is non-zero, i.e., ae - bd ≠ 0. The values of a and b that satisfy this condition will result in a unique solution for the system.
If ae - bd = 0, then the system will have either no solution or infinitely many solutions, depending on the values of c and f.
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Consider the system of linear equations where a and b are unspecified constants for which values of a and b will the system have a unique solution?
Find the value of x and/ory in each diagram below.
Answer:
3.) x=49 4.) x=29
Step-by-step explanation:
3.)
2x+82=180
2x=98
x=49
4.)
3x+3(91)=360
3x+273=360
3x=87
x=29
Solve the equation using the steps:
2(x + 8)= 2x + 8
After solving the Algebraic Expression 2(x + 8)= 2x + 8, we will get x∈∅. Variable x is dissolved in itself, making it impossible to find its value.
How to solve the given equation: 2(x + 8)= 2x + 8?Before moving to solve the equation , let's learn how to solve any algebraic expression:
Step 1: Determine whether the Distributive is necessary.
Property. If so, spread the word!
Step #2: Group similar terms together on either side of the equals symbol.
(meaning: combine all of the similar factors AND
Add up each and every integer (number).
Step #3: Align the variables so that they are all to one side of the equals symbol.
utilizing the inverse process. REMEMBER: No matter what you do
You MUST do to the other side of the equals sign what you did to the one side.
equals (symbol).
Fourth Step: When all of your variables are situated on the same side of the
You must transfer each number to the opposite sign of the equals by applying the inverse procedure on the equals sign. REMEMBER:
fourth Step: When all of your variables are situated on the same side of the
You must transfer each number to the opposite sign of the equals by applying the inverse procedure on the equals sign. REMEMBER:
You MUST do anything you do to one side of the equals sign.
the reverse of the equals symbol).
Step #5: Using the variable's ALONE state, isolate it
the opposite process. DO NOT FORGET: No matter what you do to one
You MUST change the other side of the equals symbol to the equals symbol
Given:
2(x + 8)= 2x + 8
2 × x + 2 × 8= 2x + 8
2x+16= 2x+ 8
16= 8
So, x∈∅.
In this equation , the value of x could not be find because variable x is dissolved in itself.
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Milton says he has written a system of two linear equations that has an infinite number of solutions. One of the equations of the system is y = 3x – 1. Which could be the other equation? y = 3x + 2 3x – y = 2 3x – y = 1 3x + y = 1
The other equation could be [tex]3x + y = 1[/tex] when . One of the equations of the system is [tex]y = 3x - 1[/tex] .
When two lines are written in slope-intercept form [tex](y = mx + b)[/tex], they have an infinite number of solutions if and only if the lines are parallel, which means that they have the same slope (m).
In this case, the first equation,
[tex]y = 3x - 1[/tex] , has a slope of 3,
and the fourth equation,
[tex]3x + y = 1[/tex] , also has a slope of 3
Since the slopes are equal, the lines are parallel and will intersect at an infinite number of points, meaning that the system has an infinite number of solutions.
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3. What is the value of the expression 6(10a + 2b)
Write an expression that shows the sum of exactly two terms
that is equivalent to 6(10a + 2b).
Answer:
60b + 12b
Step-by-step explanation:
Find the minimum, maximum, and range for the given set of data. {30, 24, 8, 21, 35, 23, 23, 19, 13, 17} A. minimum = 8, maximum = 35, range = 43 B. minimum = 17, maximum = 30, range = 47 C. minimum = 8, maximum = 35, range = 27 D. minimum = 17, maximum = 30, range = 23 Please select the best answer from the choices provided A B C D
Answer:
Step-by-step explanation:
D
A map has a scale of 1cm: 4 kilometres.
The actual distance between two cities is 52 kilometres.
What is the distance between the cities on the map?
Answer:
Step-by-step explanation:
You can use conversion to solve for cm
52 km x 1 cm / 4 km = 13 cm
where km cancels out leaving your answer in cm.
the actual distance on the map would be 13 cm
which of the following is the graph of y=(1/2)*?
The graph of function y = (1/2)ˣ is shown in figure.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The function is,
⇒ y = (1/2)ˣ
Now, We can draw the graph of exponential function y = (1/2)ˣ.
Hence, The graph of function y = (1/2)ˣ is shown in figure
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Mills wants to save for a new home theatre that costs $2150. He earns $20/h as a landscaper and works 40 hours a week and 50 weeks a year. His taxes and deductions average 10% of his gross annual income.
His monthly expenses are as follows:
Rent - $1200
Groceries - $400
Insurance - $250
Utilities - $350
Subway - $100
Charitable donations - $50
How many months will it take Mills to save the required amount?
It will take Mills approximately 1 month and 5 days to save the required amount.
Here's how you can calculate the number of months it will take Mills to save the required amount:
Calculate Mills' gross annual income:
Gross income = $20/h × 40 hours/week × 50 weeks/year = $40000/year
Subtract taxes and deductions:
Net income = Gross income - (Gross income × 10%) = $40000 - ($40000 × 10%) = $36000/year
Subtract monthly expenses:
Total monthly expenses = $1200 + $400 + $250 + $350 + $100 + $50 = $2,150/month
Monthly savings = Net income/year ÷ 12 months/year - Total monthly expenses = $36000/year ÷ 12 months/year - $2,150/month = $1,850/month
Divide the cost of the home theater by the monthly savings to find the number of months it will take Mills to save the required amount:
Months = $2150 ÷ $1,850/month = approximately 1.1667 months (or approximately 1 month and 5 days)
Therefore, Mills will need around 1 month and 5 days to save the requisite cash.
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