The deceptive amount claim is b). P (A n B) = P (A) + P (B) -P ( A U B). This assertion is false since it omits the point where A and B intersect, which is P. (A n B).
The deceptive claim is b). P (A n B) = P (A) + P (B) -P ( A U B). This claim is false because it disregards the fact that P is where A and B overlap (A n B). The stated statement does not take into consideration the intersection of two events, which is the likelihood that both occurrences will occur.
One must factor in the likelihood that the two occurrences will intersect when calculating the likelihood that two events will occur simultaneously. The given statement deducts the probability of the union of two occurrences from the sum of the probabilities of the two separate events because the probability of the union of two events is the chance that at least one of the events occurs. As it ignores the intersection, this method is inaccurate for estimating the likelihood of both occurrences occurring simultaneously. The probability of the intersection must be considered in order to calculate the likelihood of two occurrences occurring simultaneously.
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Wyatt bought a pair of sunglasses online for $56. He used a coupon code to get a 10% discount. The website also applied a 10% processing fee to the price after the discount. How much did Wyatt pay, in the end? Round to the nearest cent.
Answer:
$55.44 is the price of the sunglasses
Step-by-step explanation:
Price Of Sunglasses = $56
10% Discount = $5.6
So, $56-$5.6 = $50.4 <------ Applying Discount
10% of $50.4 = $5.04 <------ Price of Processing Fee for Discounted Price
$50.4+$5.04 = $55.44 <------ Total Price
The discounted price is $50.4 and we take 10% of that [discounted price] and we add it to the discounted price. 10% of that is $5.04. = $55.44
Answer:
$55.44
Step-by-step explanation:
56 - 56(0.10) = 50.40 price with 10% off
50.40 + 50.40(0.10) = 55.44 10% processing fee added to discounted price
The shaded part of the diagram below shows the top surface of an engine part.
5
Diagram not drawn to scale
The measurements taken by a motor engineer are:
• reflex angle BÔC = 240°,
• AO=OD= 6 cm,
• BO=OC=3 cm.
The top surface of the engine part is to be painted.
The paint costs 15p per cm².
75
Using = 3, calculate how much it costs to paint the top surface of 20 engine parts.
Give your answer in pounds.
(1 mark)
Answer:
To calculate the cost of painting the top surface of 20 engine parts, we need to find the surface area of one engine part and then multiply it by 20.
To find the surface area, we need to find the length of the curved surface. We can do this by using the Pythagorean theorem to find AB and then use that to find the circumference of the curved surface.
AB^2 = BO^2 + AO^2 = 9 + 36 = 45
AB = sqrt(45) = 3 sqrt(5)
Circumference = 2 * pi * AB = 2 * pi * 3 sqrt(5) = 6 pi sqrt(5)
Using the fact that the reflex angle BÔC is 240 degrees, we can find the length of the curved surface:
240° / 360° = 2/3 of the circumference
Curved surface length = 2/3 * 6 pi sqrt(5) = 4 pi sqrt(5)
Finally, we can find the surface area of one engine part:
Surface area = (2 * 6 * 3) + (4 pi sqrt(5) * 6) = 36 + (24 pi sqrt(5))
To paint 20 engine parts, the cost would be:
20 * surface area * 15p = 20 * 36 + 20 * 24 pi sqrt(5) * 15p = 720 + (24 * 20 * 15 * pi * sqrt(5)) p = 720 + 720 pi sqrt(5) p
Since 1 pound is equal to 100 pence, the cost in pounds would be:
720 + 720 * pi * sqrt(5) / 100 = 720 + 720 * 0.177 / 100 = 720 + 1.264
So, the cost to paint the top surface of 20 engine parts would be 721.264 pounds.
The table shows the number of goals made by two hockey players.
Player A Player B
2, 3, 1, 3, 2, 2, 1, 3, 6 1, 4, 5, 1, 2, 4, 5, 5, 11
Find the best measure of variability for the data and determine which player was more consistent.
Player B is the most consistent, with an IQR of 3.5.
Player B is the most consistent, with a range of 10.
Player A is the most consistent, with an IQR of 1.5.
Player A is the most consistent, with a range of 5.
The best measure of variability is the standard deviation.
Player A is the most consistent, with an IQR of 1.5.
The correct option is C.
What is a standard deviation?The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.
Given:
The table shows the number of goals made by two hockey players.
Player A:
2, 3, 1, 3, 2, 2, 1, 3, 6
Mean = 2.56
S.D. = 1.51
Player B:
1, 4, 5, 1, 2, 4, 5, 5, 11
S.D. = 3.03
The best measure of variability is the standard deviation.
Player A is the most consistent, with an IQR of 1.5.
Therefore, the best measure of variability is the standard deviation.
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Answer:1.5
Step-by-step explanation:
Use the Distributive Proper
10
9. 2(-3x + 5)
The distributive property is often used to simplify algebraic expressions.
What is algebra?Algebra refers to the involving of unknown quantities into the block relationship between variables.
In this example, the expression 2(-3x + 5) can be simplified using the distributive property. The distributive property states that for any two numbers a and b, and a third number c, a(b + c) = ab + ac. Applying this property to our expression, 2(-3x + 5) = 2(-3x) + 2(5).
By expanding the expression, we see that 2(-3x + 5) = -6x + 10. This simplified expression is much easier to work with than the original expression. The distributive property can be applied to any expression in order to simplify it, making it easier to solve.
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Hey, I need help what is 12+3s+9s+2=?
Answer:
Below
Step-by-step explanation:
12 + 3s + 9s + 2 =
(3s+9s) + (12+2) =
12s + 14 ( or 2 (6s+7) )
6x + y = 9 3x -4y = -18
Answer:
x = 2/3
y = 5
Step-by-step explanation:
6x + y = 9
3x -4y = -18
Times the second equation by -2
6x + y = 9
-6x + 8y = 36
9y = 45
y = 5
Now put 5 in for y and solve for x
6x + 5 = 9
6x = 4
x = 2/3
Let's check
6(2/3) + 5 = 9
4 + 5 = 9
9 = 9
So, x = 2/3 and y = 5 is the correct answer.
What is geometry in mathematics ?
Answer:
Geometry in Mathematics is the study of shape and figures.
Answer:
Geometry refers to a branch of mathematics which is focused on the measurement and relationship of lines, angles, surfaces, solids and points. For instance, the calculation of a triangle's angles is an example of geometry.
3. for questions 3-5, complete the missing values in each table below using the graph
The missing values are derived from the graph as follows:
3 ) 7, 14, 21, 28, 35
4) 3, 7, 10, 14, 17
5) 1, 21, 10, 49, 19
What is a graph?In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.
In order to solve for the above values, the best way is to spot the function that exists in the graph which is given as:
F(y) = 3.5x
In the first table, where x = 2
y= 3.5 *2
= 7
This iteration goes on and on and is consistent for all the values.
In the second table,
Where F(y) is known, for example 10.5, then x is derived as:
10.5 = 3.5x (divide both sides by 3.5)
x = 3
This iteration goes on and on and is consistent for all the values.
In the third table, we simply swap the values back and forth using the function F(y) = 3.5x to derive all values.
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Why is subtracting an expression similar to distribuing a -1 ?
Answer:
Subtracting an expression is similar to distributing a -1 because it cancels out the numbers in the expression.
Step-by-step explanation:
Determine if 0. 54227406110177. Is rational or irrational and give a reason for
your answer.
ASAP pls help
The number 0.54227406110177, is non- repeating and non- terminating, so, that is an irrational number.
We have to determine that the number 0.54227406110177, is rational or irrational.
There is infinite numbers of rationals or irrationals between two real numbers. Rational number is of form p/q where q≠0 and p and q are integers. For example 1/2 , 1/4 are rationals. To identify if a number is rational or not, check the following conditions :
It is expressed in the form of p/q, where q≠0.After simplification, the ratio p/q is represented in decimal form. the decimal expansion of an rational number is repeating and terminating.The numbers which are not rational numbers are called irrationals. Here, see the number 0.54227406110177, no repetition of numbers in decimal form and non- terminating. So, it not a rational number. Hence, it is an irrational.
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the graph of a quadric function moves through the point (0,-2) and (4,0) what is the zero of the function
The zeroes of the quadratic function 2x² - 7x - 4 is 1 and 4,
known as roots.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
itsA quadratic equation has two roots as it's degree is two.
We know, The general form of a quadratic equation is x² + bx + c.
Let, y = x² + bx + c.
At, (0, - 2).
- 2 = 0 + 0 + c.
c = - 2.
At, (4, 0).
0 = 4² + 4b - 2.
0 = 14 + 4b.
b = - 7/2.
So, It is x² - (7/2)x - 2 = 0.
2x² - 7x - 4 = 0.
2x² - 8x + x - 4 = 0.
2x(x - 4) - 1(x - 4) = 0.
(x - 4)(x - 1) = 0.
So, the zeroes of the function are 4 and 1.
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the radius of a circle is increasing at a rate of 7 centimeters per minute. find the rate of change of the area when the radius is 4 centimeters.
By applying rate of change concept it can be concluded that the area will change at a rate of 176 cm² / minute.
Rate of change is the change in values of a dependent variable concerning the independent variables.
The rate of change of a function shows how the function is changing from one x value to another. Whilst, differentiation is when you have an instantaneous rate of change at a single point.
We have the following information:
The rate of change of a circle = 7 cm/minute = dr/dt
We have to find the rate of change of the circle when r = 4 cm
To do so, we will use the derivative of the circle area:
A = πr²
dA/dr = 2πr
dA/dt = dA/dr × dr/dt
= 2πr × 7
= 14πr
Now we input r = 4 cm into this equation:
rate of change of the area = 14*22/7*4
= 176 cm² / minute
Thus, when r = 4 cm, the area will change at a rate of 176 cm² / minute.
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What are the polygon
Step-by-step explanation:
in geometry it is a plane figure with at least three straight sides and angles, and typically five or more.
are the column vectors of this matrix linearly independent or linearly dependent? showall explanations or computations.
The column vectors of the given matrix is linearly dependent as determinant is equal to zero.
To find the column vectors of the matrix is linearly independent or linearly dependent.
Value of the determinant is equal to zero it implies linearly dependent.
And if determinant is not zero it is linearly independent.
Let 'A' be the given matrix is:
A = [tex]\left[\begin{array}{ccc}1&0&5\\-2&1&-6\\0&2&8\end{array}\right][/tex]
Determinant of A
= 1 ( 8 - (-12)) - 0( -16 -0 ) + 5 (-4 -0 )
= 1 (20 ) - 0 -20
= 20 -20
= 0
Here det(A) = 0
Therefore, the column vectors of the matrix is linearly dependent as det(A) = 0.
The above question is incomplete, the complete question is:
Are the column vectors of this matrix linearly independent or linearly dependent? show all explanations or computations.
[tex]\left[\begin{array}{ccc}1&0&5\\-2&1&-6\\0&2&8\end{array}\right][/tex]
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A local Best Buy sells 8 times as many iPads as target. The difference between their sales is 490 iPads how many did each sell?
Answer:
Step-by-step explanation:
Let's assume the number of iPads sold by Target as "x".
Then, the number of iPads sold by Best Buy would be 8 times this value, which is 8x.
We are given that the difference in their sales is 490 iPads. So we can set up an equation:
8x - x = 490
Simplifying and solving for x:
7x = 490
x = 70
Therefore, Target sold 70 iPads, and Best Buy sold 8 times as many, or 560 iPads.
The illustration below shows the graph of yyy as a function of xxx.
Answer:
quadratic or parabola functionStep-by-step explanation:
PLEASE HELP ITS URGENT !!
Answer:
Step-by-step explanation:
[tex]x_{1}[/tex] = - 5 , f( [tex]x_{1}[/tex] ) = 0 ;
[tex]x_{2}[/tex] = - 2 , f( [tex]x_{2}[/tex] ) = 0 ;
[tex]x_{3}[/tex] = 4 , f( [tex]x_{3}[/tex] ) = 0 ;
Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. -5, -1, 2
The polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. -5, -1, 2 is,
⇒ f (x) = x³ + 4x² - 7x - 10
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
For a polynomial,
A leading coefficient = 1,
And, the given zeros = -5, -1, 2
Now, We know that;
The standard polynomial is given by:
⇒ f (x) = a (x - p) (x - q) ...
Where, 'a' is leading coefficient and p, q, .. are zeroes.
Here, A leading coefficient = 1,
And, the given zeros = -5, -1, 2
Hence, The polynomial is,
⇒ f (x) = 1 (x - (-5)) (x - (- 1)) (x - 2)
⇒ f (x) = (x + 5) (x + 1) (x - 2)
⇒ f (x) = (x + 5) (x² - 2x + x - 2)
⇒ f (x) = (x + 5) (x² - x - 2)
⇒ f (x) = x³ - x² - 2x + 5x² - 5x - 10
⇒ f (x) = x³ + 4x² - 7x - 10
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Write an indirect proof for the following statement:
A triangle can have at most 1 obtuse angle.
We can prove that the statement is false by contradiction, as if a triangle had two obtuse angles, the sum of the measures of the internal angles of the triangle would be greater than 180º.
What is proof by contradiction?To prove an statement by contradiction, we must simply take an statement that either accepts the statement (true) or rejects (false).
An angle is classified as obtuse if it has a measure that is greater than 90º.
The sum of the measures of the internal angles of a triangle is of 180º, hence if the triangle had two obtuse angles, then the sum of the measures of the internal angles of the triangle would be greater than 180º.
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When 32 is subtracted from the square of a number, the result is 4 times the number. Find the negative solution.
The two solutions of the quadratic equations are 8,-4 and the negative solution -4
What are quadratic equations?A quadratic equation can be written in the standard form as ax2 + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.
Given here: when 32 subtracted from the square of a number and the result is 4 times the number.
Let x be the number then we have
x²-32=4x
x²-4x-32=0
x²-8x+4x-32=0
x(x-8)+4(x-8)=0
(x-8) (x+4) =0
Thus the two solutions of the quadratic equations are 8,-4
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need help with this question
The zeros of the equation x² - 4x + 4 = 0 is 2.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given:
A quadratic equation,
x² - 4x + 4 = 0.
To find the zeros:
Solving further,
x² - 4x + 4 = 0.
x² - 2x -2x + 4 = 0.
x(x - 2) -2(x - 2) = 0.
(x - 2)² = 0.
x = 2.
Hence, 2 is zeros.
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The complete question:
Solve the quadratic equation and find the zeros.
The equation,
x² - 4x + 4 = 0.
PLEASE HELP‼️‼️
Solve the problem.
As part of her retirement savings plan, Patricia deposited $200 in a bank account during her first year in the workforce. During each
subsequent year, she deposited $50 more than the previous year. Find how much she deposited during her twentieth year in the workforce.
Find the total amount deposited in the twenty years.
The amount deposited in the Patricia retirement savings plan are:
Amount deposited in the twentieth year is $1150.
Total amount deposited in time span of twenty years is $13,500.
Amount deposited by Patricia in the first year ' a₁ ' = $200
Difference between the amount deposited in the subsequent year is
'd' = $50
Amount deposited during 20th year
Let 'n' be the 20th year
The above situation represents it is arithmetic progression problem
nth term of A.P. is :
aₙ = a₁ + ( n - 1 ) d
Substitute the value we get,
a₂₀ = 200 + ( 20 - 1 ) 50
⇒ a₂₀ = 200 + 19 × 50
⇒ a₂₀ = 200 + 950
⇒ a₂₀ = $1150
Total amount deposited in twenty years
S₂₀ = (n/2) [ 2 a₁+ ( n - 1 )d ]
Substitute the value we get,
⇒S₂₀ = ( 20 /2 ) [ 2(200 ) + 19 × 50 ]
⇒ S₂₀ = 10 [ 400 + 950 ]
⇒S₂₀ = $13,500
Therefore, the amount deposited in the twentieth year is $1150 and total amount deposited in twenty years is $13,500.
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You manage a call center. You are reviewing wages for 25 phone operators and 5 supervisors. Phone operators
earn $22.85 per hour, and supervisors earn $27.25 per hour.
What, approximately, is the mean hourly wage for the 30 employees?
$23.02
$23.58
$25.05
$26.52
$27.21
Answer: To find the mean hourly wage, you need to sum up the total wages of all employees and then divide by the number of employees. The total hourly wage for 25 phone operators is 25 * $22.85 = $571.25. The total hourly wage for 5 supervisors is 5 * $27.25 = $136.25. The combined total is $571.25 + $136.25 = $707.50. The mean hourly wage for the 30 employees is $707.50 / 30 = $23.58. So, the answer is approximately $23.58.
Step-by-step explanation:
evaluate
2-6/-2-4-12/6x-3
the / is division
please show step by step
The simplified expression 2-6/-2-4-12/6x-3 is given as follows:
-2 - 2x.
How to simplify the expression?The expression for this problem is defined as follows:
[tex]2 - \frac{6}{-2} - 4 - \frac{12x}{6} - 3[/tex]
The division operation has a higher precedence over the subtraction operations, hence:
6/-2 = -3.12x/6 = 2x.Hence the expression can be written as follows:
2 - (-3) - 4 - 2x - 3 = 2 + 3 - 4 - 2x - 3.
Then combining the like terms, which are the constant, the simplified expression is given as follows:
-2 - 2x.
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1.5 x ? = 0.6. What value of ? makes this number sentence correct? Please show working out.
Answer:
x = 0.4
Step-by-step explanation:
1.5 * x = 0.6
x = 0.6 / 1.5
x = 0.4
Answer:
0.4
Step-by-step explanation:
To solve the equation 1.5 * ? = 0.6 for the value of ?, we need to isolate the variable ? on one side of the equation.
First, we can divide both sides of the equation by 1.5 to isolate the variable:
1.5 * ? / 1.5 = 0.6 / 1.5
Simplifying, we get:
? = 0.4
Therefore, the value of ? that makes the equation 1.5 * ? = 0.6 true is 0.4.
Solve algebraically, show all steps, and round 3 decimal places
Answer:
x = 1.523
Step-by-step explanation:
Given
[tex]\quad\quad e^{x-1} = 3^{2-x}[/tex]
we are asked to solve for x
Take natural logs on both sides:
[tex]\ln \left(e^{x-1}\right)=\ln \left(3^{2-x}\right)\\\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)}\\\\\ln \left(e^{x-1}\right)=\left(x-1\right)\ln \left(e\right)\\\\\rightarrow \left(x-1\right)\ln \left(e\right)=\ln \left(3^{2-x}\right)[/tex]substitute on left side of original eqn
[tex]\ln \left(3^{2-x}\right)=\left(2-x\right)\ln \left(3\right)\\\\[/tex]
Therefore we get
[tex]\left(x-1\right)\ln \left(e\right)=\left(2-x\right)\ln \left(3\right)[/tex]
But ln(e) = 1
So we get
[tex]x - 1 = (2-x)\;\ln(3)\\\\[/tex]
So the expression becomes
[tex]x - 1 = (2- x) \ln(3)\\\\x - 1 = 2\ln(3) - x \ln(3)[/tex]
Add [tex]x\ln(3)[/tex] on both sides:
x + x ln(3) - 1 = 2ln(3)
Add 1 to bot sides:
x + x ln(3) = 2ln(3) + 1
x(1 + ln(3)) = 2 ln3 + 1
ln(1 + \ln(3)) = 2.09861
2ln(3) + 1 =3.1972
So we get
x(2.0986) = 3.1972
x = 3.1972/2.0986 = 1.52349
Rounded to 3 decimal places, the answer is 1.523
can u help me out i could get 100%
Step-by-step explanation:
x+4y=0
2x−y=18
To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
x+4y=0,2x−y=18
Choose one of the equations and solve it for x by isolating x on the left-hand side of the equal sign.
x+4y=0
Subtract 4y from both sides of the equation.
x=−4y
Substitute −4y for x in the other equation, 2x−y=18.
2(−4)y−y=18
Multiply 2 times −4y.
−8y−y=18
Add −8y to −y.
−9y=18
Divide both sides by −9.
y=−2
Substitute −2 for y in x=−4y. Because the resulting equation contains only one variable, you can solve for x directly.
x=−4(−2)
Multiply −4 times −2.
x=8
The system is now solved.
x=8,y=−2
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Your Best,EdwinPut the following linear equation in slope intercept form:
−7x+3y=21
You should have 2 or more steps shown.
The slope-intercept form of the linear equation is:
y = 7 + (7/3)*x
How to write the linear equation in the slope intercept form?A linear equation in the slope-intercept form is:
y = a*x + b
So, to write the given line in that form, we just need to isolate the variable x.
We have the equation:
-7x + 3y = 21
3y = 21 + 7x
y = (21 + 7x)/3
y = 7 + (7/3)*x
That is the equation in the slope-intercept form.
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A quadratic function has the equation, y=a(x+3)(x−5) = ( x+3)( x−5), and passes through the point (6,45). What is the value of a ?
Answer:
Step-by-step explanation:
To find the value of "a" in the equation y = a(x + 3)(x - 5), we can use the fact that the function passes through the point (6, 45).
Step 1: Substitute the x and y values of the point into the equation:
45 = a(6 + 3)(6 - 5)
45 = a(9)(1)
Step 2: Solve for "a":
45 = 9a
a = 45/9
a = 5
The value of "a" in the equation y = a(x + 3)(x - 5) is 5.
5.8 + (-8.45) Please answer!!!!
5.8 + (-8.45)
Remove the plus sign and parentheses:
5.8 - 8.45
-2.65
That's your answer. Hope this helped!
Answer:
-2.65
Step-by-step explanation:
Hope this will help