On solving the provided question we can say that - s and t be function subsets of a. show that x ∈ f(S) V f(T) ∈ f(y) as f(y) = x => x∈f(S)∨x∈f(T)
What is function?
One kind of rule is a function, which gives an output in exchange for an input. Alex Federspiel is the photo's source. In this instance, y=x2. I receive the output from something I placed in x in y. We may say that y is a function of x since x serves as the input value. A relation between a collection of inputs, each with an output, is referred to as a function. A function is a connection between inputs that each have precisely one output, to put it simply.
let S contains all elements that are the image of an element in f(s)
and let T contains all elements that are the image of an element inf(T)
f(y) ∈ f(s) V f(y)
x ∈ f(S) V f(T) ∈ f(y)
as f(y) = x
x ∈ f(S) ∨ x ∈ f(T)
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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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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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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
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
Find the slope of a line parallel to the line whose equation is 3x+2y=8. fully simplify your answer.
Answer:
-3/2
Step-by-step explanation:
Parallel lines have the same slope, but different y-intercepts. We can find the slope by converting to slope-intercept form:
[tex]\displaystyle 3x+2y=8\\\\2y=8-3x\\\\y=4-\frac{3}{2}x\\\\y=-\frac{3}{2}x+4[/tex]
Hence, the slope of the parallel line will also be -3/2
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:
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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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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a + (-7) = 3 a =
1.9 + b = -3.2 b =
-1/6 +7/6 = c c=
The value of the equations are a = 10 , b = -5.1 and c = 1
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
a + ( -7 ) = 3 be equation (1)
On simplifying the equation , we get
a - 7 = 3
Adding 7 on both sides of the equation , we get
a = 3 + 7
a = 10
Substituting the values in the equation , we get
1.9 + b = -3.2 be equation (2)
Subtracting 1.9 on both sides of the equation , we get
b = -3.2 - 1.9
b = -5.1
Substituting the values in the equation , we get
-1/6 + ( 7/6 ) = c be equation (3)
c = ( 7 - 1 ) / 6
c = 6/6
c = 1
Hence , the equations are solved
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Zachariah and Khai collect stamps. Zachariah has 9 American stamps out of 15 stamps. Khai has 13 American stamps out of 20 stamps. Which statement is correct?
Zachariah has a higher ratio of American stamps than Khai because 9 over 15 is greater than 13 over 20.
Khai has a higher ratio of American stamps than Zachariah because 9 over 15 is greater than 13 over 20.
Khai has a higher ratio of American stamps than Zachariah because 9 over 15 is less than 13 over 20.
Zachariah and Khai have the same ratio of American stamps.
Khai has a higher ratio of American stamps than Zachariah because 9 over 15 is less than 13 over 20.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Zachariah has 9 American stamps out of 15 stamps
Zachariah's ratio is 9 / 15 = 3 / 5=0.6
Khai has 13 American stamps out of 20 stamps.
Khai's ratio is 13 / 20 = 0.65.
0.65>0.6
Khai has a higher ratio of American stamps than Zachariah because 9 over 15 is less than 13 over 20.
Hence, Khai has a higher ratio of American stamps than Zachariah because 9 over 15 is less than 13 over 20.
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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
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
consider the following hypothesis test: : : a sample of is used. identify the -value and state your conclusion for each of the following sample results. use . a. with and , the -value is - select your answer - can it be concluded that the population mean is less than ?
The -value of -2.576 is less than the critical value of 0.05, we can reject the null hypothesis and conclude that the population mean is not less than .
The -value is the probability of observing a test statistic result as extreme or more extreme than the observed result given that the null hypothesis is true. In this hypothesis test, the null hypothesis is that the population mean is less than , and the alternative hypothesis is that the population mean is not less than . With and , the -value can be calculated using the t-distribution as follows:
The t-distribution has degrees of freedom (df) equal to the sample size minus 1. Therefore, the df for this hypothesis test is .
Using the t-distribution with df = , the -value can be calculated as:
-value = P(t≤-2.576)
The -value is the probability of observing a test statistic result as extreme or more extreme than the observed result given that the null hypothesis is true.
Since the -value of -2.576 is less than the critical value of 0.05, we can reject the null hypothesis and conclude that the population mean is not less than .
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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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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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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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april borrows $23000 at an interest rate of 6% to purchase a new automobile. at what rate (in dollars per year) must she pay back the loan, if the loan must be paid off in 5 years? (use decimal notation. give your answer to two decimal places.) withdrawal rate: $ 5980 per year
Answer:
6155.84
Step-by-step explanation:
23000
6% annual
5 years
23000*(1+6%)^5= 30799.19
so 6155.84 per year
April must pay back her auto loan at a rate of $5980 per year. This is calculated by first determining the total repayment sum (principal + interest), and then dividing this total by the number of repayment years.
Explanation:In this problem about loan repayment, we are asked to find the rate at which April must pay back her loan of $23000 with an interest rate of 6%, which is to be paid off in 5 years. First, we need to determine the total amount to be paid back which is the principal plus the interest. The interest April will pay is given by the formula: Interest = Principal x Rate x Time. So, Interest = $23000 x 0.06 x 5 = $6900. Thus, the total amount to be repaid is $23000 (the principal) + $6900 (the interest) = $29900.
To find out how much she must pay per year, we divide the total payment by the number of years. Therefore, Annual Payment = $29900 / 5 = $5980 per year. So, April must pay back the loan at a rate of $5980 per year.
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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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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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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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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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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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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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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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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
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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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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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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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 -
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?