Using BIDMAS order of operations, we have: 1. 3 + 7 x (3 – 2) = 10; 2. (3 + 7) x 10 – 5 = 95; 3. 5 + (5 + 2) x (6 – 4) = 19.
What is BIDMAS?BIDMAS is a mnemonic acronym that stands for the order of operations in arithmetic expressions:
B: Brackets (or Parentheses)
I: Indices (or Powers)
D: Division
M: Multiplication
A: Addition
S: Subtraction
It is a rule to determine the order in which to perform mathematical operations in an expression that contains more than one arithmetic operation.
1. 3 + 7 x (3 – 2)
= 3 + 7 x 1 (subtracting inside the parentheses first)
= 3 + 7
= 10
Therefore, 3 + 7 x (3 – 2) = 10.
2. (3 + 7) x 10 – 5
= 10 x 10 - 5 (adding inside the parentheses first)
= 100 - 5
= 95
Therefore, (3 + 7) x 10 – 5 = 95.
3. 5 + (5 + 2) x (6 – 4)
= 5 + 7 x 2 (subtracting inside the parentheses first)
= 5 + 14
= 19
Therefore, 5 + (5 + 2) x (6 – 4) = 19.
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find the slope of the line that that passes through each pair of points (8,-2) (4,-3)
Answer:
slope = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (8, - 2 ) and (x₂, y₂ ) = (4, - 3 )
m = [tex]\frac{-3-(-2)}{4-8}[/tex] = [tex]\frac{-3+2}{-4}[/tex] = [tex]\frac{-1}{-4}[/tex] = [tex]\frac{1}{4}[/tex]
Find all critical points for the function
4x + 6
x² + x + 1
on (-∞, ∞) and then list them (separated by commas) in the box below.
List of critical points:
f(x) =
The critical points for the function are [tex]x=-\frac{3+\sqrt{7}}{2},\:x=-\frac{3-\sqrt{7}}{2}[/tex]
How to detemine the critical points for the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = (4x + 6)/(x² + x + 1)
The critical points are the points where the derivative of f(x) equals 0 or undefined when the function is defined
When f(x) is differentiated, we have
f'(x) = 4/(x² + x + 1) - [(2x + 1)(4x + 6)/[(x² + x + 1)²]
Set to 0 and evaluate
4/(x² + x + 1) - [(2x + 1)(4x + 6)/[(x² + x + 1)²] = 0
So, we have
[(2x + 1)(4x + 6)/[(x² + x + 1)²] = 4/(x² + x + 1)
This gives
[(2x + 1)(4x + 6)/[(x² + x + 1)] = 4
Cross multiply
(2x + 1)(4x + 6) = 4x² + 4x + 4
12x² + 12x + 4x + 6 = 4x² + 4x + 4
12x² + 12x + 6 = 4x² + 4
Evaluate
8x² + 12x + 2 = 0
So, we have
4x² + 6x + 1 = 0
Using a graphing tool, we have
[tex]x=-\frac{3+\sqrt{7}}{2},\:x=-\frac{3-\sqrt{7}}{2}[/tex]
Hence, the critical points are [tex]x=-\frac{3+\sqrt{7}}{2},\:x=-\frac{3-\sqrt{7}}{2}[/tex]
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Suppose you borrow $15,000 for three years from your rich uncle and agree to pay simple interest of 8.5% annually. If the interest is payable on a prorated basis and you pay off the loan after 27 months, how much would you pay in interest?
A $3,165.75
B $2,868.75
C $2,486.50
D $3,338.25
After addressing the issue at hand, we can state that This is an odd result interest because it implies that point A is on line segment BC, and thus triangle ABC is a straight line.
what is interest ?Marketing uses the formula return = principal + interest + hours. Interest can be assessed most easily with this method. Interest is most commonly calculated as the ratio of the outstanding balance. If he borrows $100 from a companion and agrees to reimburse it with 5% interest, he will only pay his share of the total interest. $100 (0.05) = $5. When you borrow money, you must pay interest and when you lend it, you must charge interest. Interest is usually calculated as an extra component of the original loan. This portion is known as the loan's interest.
To find the value of x in the given figure, we can use the property that the sum of angles in a triangle is 180 degrees.
We can begin by using the given information to calculate the value of angle ABC:
angle ABC = 180 - angle ABD - ACD = 180 - 35 - 58 = 87 degrees
angle ABE = angle ACD = 58 degree angle CDE = angle CBE = 35 degrees
angle BAC = 180 - angle ABC - angle ABE - angle CBE = 180 - 87 - 58 - 35 = 0 degrees
This is an odd result because it implies that point A is on line segment BC, and thus triangle ABC is a straight line.
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I need help with both of these!
What is the part in the equation “45 is 15% of what number”?
Answer:
Step-by-step explanation:
help with both of these!
What is the part in the equation “45 is 15% of what number”?
The total cost of producing a type of boat is given by C(x)=22000−40x+0.02x2
, where x is the number of boats produced. How many boats should be produced to incur minimum cost?
Answer:
To find the number of boats that should be produced to incur minimum cost, we need to find the value of x that minimizes the cost function C(x).
We can do this by taking the derivative of the cost function with respect to x, setting it equal to zero, and solving for x.
C(x) = 22000 - 40x + 0.02x^2
C'(x) = -40 + 0.04x
Setting C'(x) = 0, we get:
-40 + 0.04x = 0
0.04x = 40
x = 1000
Therefore, the number of boats that should be produced to incur minimum cost is 1000.
Step-by-step explanation:
Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the following step function.
They have different y-intercepts but the same end behavior. Thus, option A is correct.
What is Step functiοn?A step functiοn is mathematical functiοn that takes οn finite number οf cοnstant values οver intervals οf its dοmain. It is alsο knοwn as staircase functiοn οr piecewise cοnstant functiοn. The cοnstant values that functiοn takes οn are οften referred tο as "steps" οf the functiοn.
Tο graph the step functiοn, yοu wοuld start by drawing a cοοrdinate plane with the hοrizοntal axis ranging frοm -5 tο 5 and the vertical axis ranging frοm -2 tο 2. Then, yοu wοuld plοt the pοints (-5,-1), (-4,-1), (-3,0), (-2,1), (-1,1), (0,0), (1,1), (2,-1), (3,-1), (4,0), and (5,1) οn the graph.
They have different y-intercepts but the same end behavior.
They have different y-intercepts because function f(x) is 4, while the y-intercept on graph is 6
But they have the same end behavior at 2.
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Complete question:
Function g is represented by the equation.
[tex]\rm g(x) = 4 (\frac14)^x + 2[/tex]
Which statement correctly compares the two functions?
A. they have different Y-intercepts but the same end behavior
B. they have the same Y-intercept and the same end behavior
C. they have the same Y-intercept but different end behavior
D. they have different Y-intercepts and different end behavior
please!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
There are two features of a function, domain and range. Domain corresponds to the set of x-values, while range corresponds to the set of y-values. The set of y-values corresponding to this function would be
-7 [tex]<[/tex] y [tex]\leq \\ \\[/tex] 2. It can also be written in interval notation as (-7,2] where the parentheses is inclusive of -7 and the square bracket is inclusive of 2.
know that domain means x-axis values and range means y-axis values. So for your question, we need to determine all the y values of the function which is from 3 to (-7), but to express this algebraically, we need to express it in the manner, 'x<y<z'. For your condition it would be, '-7 < y < 3' (no symbols intended with the '<' and the '3'). Be careful that I arranged '-7' and '3' so that 'y' is less than '3', but is greater '-7'. So for example, 3<y<-7 would be incorrect since you are saying that 'y' is less than '-7' and greater than '-3' which is a whole other parabola. I also chose y to represent the y-axis and range since if we used x, it would refer and confuse to/with the x-axis and domain.
Please help will mark Brainly
The point is where the parabola's vertex is (2, -5).
Hence, the axis of symmetry is x = 2, and the vertex is (2, -5).
We change the original function's value of x to 2 and evaluate the equivalent value of y to determine the vertex:
[tex]f(2) = 0.5(2)^2 - 2(2) - 2[/tex]
= 1 - 4 - 2
= -5
what is symmetry?
A balanced and proportionate likeness between an object's two halves is referred to as symmetry in geometry. It implies that one half is the other's mirror image. The term "line of symmetry" refers to the fictitious axis or line that can be used to fold a figure into symmetrical halves.
A symmetrical object is one that is equal on both sides. Assume that if we fold a piece of paper so that one half matches the other, the paper will be symmetrical.
from the question:
The fact that the axis of symmetry goes through the vertex of a parabola can be used to determine the axis of symmetry and vertex of the function [tex]f(2) = 0.5(2)^2 - 2(2) - 2[/tex]
The vertical line known as the axis of symmetry separates the parabola into two symmetrical parts. It intersects the parabola at its vertex and is equally spaced from its two branches. The following is the equation for the axis of symmetry:
x = -b/2a
where a and b are the coefficients of the quadratic equation in standard form, [tex]ax^2 + bx + c = 0.[/tex]
In this case, a = 0.5 and b = -2, so the equation of the axis of symmetry is:
x = -(-2)/(2*0.5) = 2
Hence, a vertical line going through x = 2 serves as the axis of symmetry.
We change the original function's value of x to 2 and evaluate the equivalent value of y to determine the vertex:
[tex]f(2) = 0.5(2)^2 - 2(2) - 2[/tex]
= 1 - 4 - 2
= -5
Thus, the point is where the parabola's vertex is located (2, -5).
the axis of symmetry is x = 2
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Please help, tomorrow is Math examination!
We know that the circumference (C) of a circle can be calculated using the formula:
C = 2πr, where r is the radius of the circle.
We are given that the circumference of the circle is 2.20 cm, so we can use this to solve for the radius (r):
C = 2πr
2.20 = 2πr
r = 2.20 / (2π)
r ≈ 0.350 cm
Therefore, the radius of the circle is approximately 0.350 cm.
To find the area (A) of the circle, we can use the formula:
A = πr^2
Substituting the value we found for r:
A = π(0.350)^2
A ≈ 0.385 cm^2
Therefore, the area of the circle is approximately 0.385 cm^2.
Please mark this answer as brainliest if possible.
Answer:
a) Radius of circle is 35 cm.b) Area of the Circle is 3850 cm²Step-by-step explanation:
Question :-
The circumference of the circle is 220 cm.
Find :
a) Radius
b) Area of the Circle
Solution :
a)
Circumference of circle = 2πr
[tex] \longrightarrow \: \: 220 = 2 \pi r \\ \\ \longrightarrow \: \: \frac{220}{2} = \pi r \\ \\ \longrightarrow \: \: 110 = \frac{22}{7} × r \\ \\ \longrightarrow \: \: r = 110 \times \frac{7}{22} \\ \\\longrightarrow \: \: r = \frac{770}{22} \\ \\ \longrightarrow \: \: r = 35 \: cm \\ [/tex]
b)
Area of circle = πr²
[tex]\longrightarrow \: \: \frac{22}{7} \times 35 \times 35 \\ \\ \longrightarrow \: \:22 \times 5 \times 35 \\ \\ \longrightarrow \: \:3850 \: {cm}^{2} \\ [/tex]
Hence,
a) Radius of circle is 35 cm.
b) Area of the Circle is 3850 cm²
please help fast!! Given m∥n, find the value of x.
(4x+3) (8x-3)
Identify the parts of the expression and write a word expression for the numerical or algebraic expression:
8 + (10 - 7)
Answer:
8 is a constant
10 and 7 are constants
(10 - 7) is a numerical expression in parentheses that represents the difference between 10 and 7
8 + (10 - 7) is an algebraic expression that represents the sum of 8 and the difference between 10 and 7.
Word expression: Eight added to the difference between ten and seven.
Step-by-step explanation:
summation from n equals 2 to 6 of quantity 4 times n plus 5 end quantity period a 85 b 105 c 114 d 147
The value of the sum from n = 2 to n = 6 of 4n + 5 is given as follows:
b. 105.
How to obtain the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression.
The expression of this problem is given as follows:
4n + 5.
The sum is the sum of the numeric values from n = 2 to n = 6, hence:
n = 2: 4(2) + 5 = 13.n = 3 -> 17.n = 4 -> 21.n = 5 -> 25.n = 6 -> 29.Hence the sum has the result given as follows:
13 + 17 + 21 + 25 + 29 = 105.
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This shape is made up of one half-circle attached to an equilateral triangle with side lengths 24 inches. You can use 3.14 as an approximation for π.
The perimeter οf Shape is 286.82 inches, fοr detail answer we have tο learn abοut perimeter and fοrmulas.
What is Perimeter?Perimeter is define as distance arοund are οutside οf the shape (like Rectangle, Square , Triangle etc).
Perimeter οf Equilateral Triangle = [tex]\frac{\sqrt{3} }{4}[/tex] side²
Here Side = 24 inch
Sο, Perimeter οf Equilateral Triangle = [tex]\frac{\sqrt{3} }{4}[/tex] × 24²
= [tex]\frac{\sqrt{3} }{4}[/tex] × 24 × 24
= √3 × 24 × 6
= 249.41 inches
Perimeter οr Circumference οf Semi-Circle = πr + 2r
But here Perimeter = πr ( Since the base οf Semi Circle is Cοunted in Perimeter οf Equilateral Triangle)
3.14 × 12
= 37.68 inches
Sο, the perimeter οf Shape
= 249.41 + 37.68
= 286.82 inches
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60,000 is 10 times as much as
Answer:
6,000
that is the answer to your question. hope this helps!
Look at the set of ordered pairs.
{(4, 6), (−7,−15), (13, 15), (−21, 8), (?, ?)}
Which of the following could replace the missing ordered pair to make the set not a function?
(−2, 4)
(21, 9)
(−7, 15)
(6, 8)
(13,−15)
The ordered pair that could replace the missing ordered pair to make the set not a function is given as follows:
(−7, 15).
When does a set of ordered pairs represent a function?A set of ordered pairs represents a function if every input (first component of the ordered pair) is associated with exactly one output (second component of the ordered pair). In other words, if no two ordered pairs in the set have the same first component but different second components.
Hence the ordered pair (-7,15) would make the relation not a function, as the set already has the ordered pair (-7,-15), in which the input 7 is already mapped to an output of -15, hence it cannot be mapped to an output of 15.
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An automobile company is running a new television commercial in five cities with approximately the same population. The following table shows the number of times the commercial is run on TV in each city and the number of car sales (in hundreds). Find the Pearson correlation coefficient r for the data given in the table. Round any intermediate calculations to no less than six decimal places, and round your final answer to three decimal places. r=
Pearson correlation coefficient r for the data is approximately 0.915. Since the value is positive and close to 1, we can say that there is a strong positive correlation between the number of times the commercial is run on TV and the number of car sales.
What is expression ?
In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, ×, ÷) that represents a value or a quantity. It can be a single number or variable, or a combination of them, and can also include functions, parentheses, and other mathematical symbols. For example, 3x + 7 is an expression, where 3 and 7 are constants, x is a variable, and + is an operator. Expressions can be simplified, evaluated, or used as part of a larger mathematical statement or equation.
We can use the formula for Pearson correlation coefficient r to calculate it for the given data:
r = (nΣXY - ΣXΣY) / sqrt[(nΣX² - (ΣX)²)(nΣY² - (ΣY)²)]
where n is the number of observations, Σ represents the sum of the indicated values, and X and Y represent the two variables being correlated. Using the data from the table, we can calculate the following:
n = 5
ΣX = 25, ΣY = 25.8
ΣX² = 275, ΣY² = 288.68
ΣXY = 139.2
Substituting these values into the formula, we get:
[tex]$r = (5 * 139.2 - 25 * 25.8) \sqrt{[(5 * 275 - 25^2)(5 * 288.68 - 25.8^2)]} $[/tex]
r ≈ 0.915
Therefore, the Pearson correlation coefficient r for the data is approximately 0.915. Since the value is positive and close to 1, we can say that there is a strong positive correlation between the number of times the commercial is run on TV and the number of car sales.
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One wall of a room measures 14 feet long and 8 feet
high. It contains a window 5 feet wide and 3.5 feet
high. The wall has an effective total R-value of 15.5.
Find the rate of heat flow through the wall when
the inside air temperature is 68 °F and the outside
temperature is 5 °F.
Answer: the rate of heat flow through the wall when the inside air temperature is 68 °F and the outside temperature is 5 °F is 257.42 BTU per hour.
Step-by-step explanation: The rate of heat flow through the wall can be found using the formula:
Rate of heat flow = (Temperature difference) / (Effective R-value)
The temperature difference is the difference between the inside and outside temperatures, which is:
Temperature difference = (68°F) - (5°F) = 63°F
The effective R-value of the wall is given as 15.5.
To calculate the total area of the wall, we first need to find the area of the window, which is:
Area of window = (width) x (height) = (5 ft) x (3.5 ft) = 17.5 square feet
The area of the wall without the window is:
Area of wall = (length) x (height) - Area of window
Area of wall = (14 ft) x (8 ft) - 17.5 square feet
Area of wall = 105.5 square feet
So, the rate of heat flow through the wall is:
Rate of heat flow = (Temperature difference) / (Effective R-value) x (Total area of the wall)
Rate of heat flow = (63°F) / (15.5) x (105.5 square feet)
Rate of heat flow = 257.42 BTU per hour
A 6000-seat theater has tickets for sale at $26 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $195.200?
The probability that a person in the United States has type At blood is 31 %. Three unrelatedata person eUnited sleds are selected at random.
The required Probabilities of type of blood are A) 0.029791, B) 0.328509, C) 0.671491.
How to find Probability?A: event that a person has type A positive blood
A': event that a person does not have type A positive blood
We know that P(A) = 0.31, which means P(A') = 0.69.
A) To find the probability that all three people have type A positive blood, we use the multiplication rule for independent events:
P(A and A and A) = P(A) x P(A) x P(A) = 0.31 x 0.31 x 0.31 = 0.029791.
B) To find the probability that none of the three people have type A positive blood, we use the multiplication rule for independent events again:
P(A' and A' and A') = P(A') x P(A') x P(A') = 0.69 x 0.69 x 0.69 = 0.328509.
C) To find the probability that at least one of the three people have type A positive blood, we can use the complement rule:
P(at least one A) = 1 - P(none have A) = 1 - 0.328509 = 0.671491.
Alternatively, we could find this probability directly by considering the three possible cases where at least one person has type A positive blood:
one person has A and two do not: P(A and A' and A') x 3 = 0.31 x 0.69 x 0.69 x 3
two people have A and one does not: P(A and A and A') x 3 = 0.31 x 0.31 x 0.69 x 3
all three have A: P(A and A and A) = 0.029791
Then, we add up these probabilities:
P(at least one A) = (0.31 x 0.69 x 0.69 x 3) + (0.31 x 0.31 x 0.69 x 3) + 0.029791 = 0.671491.
D) The event of all three people having type A positive blood (0.029791) can be considered unusual because it has a low probability. If we define "unusual" as an event with probability less than or equal to 0.05, then this event meets that criterion. However, whether an event is considered unusual or not can depend on the specific context and criteria chosen.
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Complete question:
Simplify the equation (show work)
Answer:
use the l.c.m and use formula of two square.cut + and+ or - and -
Answer:
Step-by-step explanation:
[tex]\frac{3x+4}{x+2}+ \frac{x^{2}+2x}{2x+4}\\\frac{2(3x+4)+x(x+2)}{2(x+2)}==\frac{x^{2}+8x+8}{2(x+2)}[/tex]
The price of an item has been reduced by 60%. The original price was $90. What is the price of the item now?
Answer:
$36
Step-by-step explanation:
$90/100%=.9
100%-60%=40%
$.9 x 40%=36
Solve for w.
(w+5)² =2w² +3w+37
Answer:
w = 3; w = 4
Step-by-step explanation:
We can start by expanding the equation on the left hand side:
[tex](w+5)^2=2w^2+3w+37\\(w+5)(w+5)=2w^2+3w+37\\w^2+5w+5w+25=2w^2+3w+37\\w^2+10w+25=2w^2+3w+37[/tex]
We can first simplify the equation subtracting all the terms on the right hand side and having the equation equal 0:
[tex]w^2+10w+25=2w^2+3w+37\\(w^2-2w^2)+(10w-3w)+(25-37)=0\\-w^2+7w-12=0[/tex]
Now, we have one equation in standard form (ax^2 + bx + c = 0).
We can solve this equation using the quadratic equation which is
[tex]x = \frac{-b+\sqrt{b^2-4ac} }{2a} \\\\x=\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]
Since -1 is our a value, 7 is our b, and -12 is c, we simply plug in our values and solve for x:
First x:
[tex]x=\frac{-7+\sqrt{7^2-4(-1)(-12)} }{2(-1)}\\ \\x=\frac{-7+\sqrt{1} }{-2}\\ \\x=\frac{-7+1}{-2}\\ \\x=\frac{-6}{-2}\\ \\x=3[/tex]
Second x:
[tex]x=\frac{-7-\sqrt{7^2-4(-1)(-12)} }{2(-1)}\\ \\x=\frac{-7-\sqrt{1} }{-2}\\ \\x=\frac{-7-1}{-2}\\ \\x=\frac{-8}{-2}\\ \\x=4[/tex]
Finally, we must check for extraneous solutions, which (if present) will make the equations not true. We simply plug in 3 for w and 4 for w to check for such solutions:
Checking 3:
[tex](3+5)^2=2(3)^2+3(3)+37\\8^2=2(9)+9+37\\64=18+9+37\\64=64[/tex]
Checking 4:
[tex](4+5)^2=2(4)^2+3(4)+37\\9^2=2(16)+12+37\\81=32+12+37\\81=81[/tex]
Since the equations are true for both 3 and 4, both values work for w.
Someone help me with 4 and 5 please!!!
4) The value of 5-30+180-1,080+... when n=11 is 302,330,880.
5) Required number of terms are 10 ( approximately)
What is the formula for a finite geometric series?
[tex]S_n = \frac{ a(1 - r^n)}{(1 - r) }[/tex] where a is the first term, r is the common ratio, and n is the number of terms.
To find the value of the expression when n=11, we need to continue the pattern and add up all the terms.
5-30+180-1,080+... can be written as:
5 - 30 + 180 - 1080 + 6480 - 38880 + 233280 - 1,399,680 + 8,398,080 - 50,388,480 + 302,330,880
In this case, a = 5, r = -6, and n = 11. Plugging these values into the formula, we get:[tex]S_11 = \frac{5(1 - (-6)^11)}{(1 - (-6))} = 302,330,880[/tex]
So the answer is A) 302,330,880.
5) To find the number of terms in the given sequence, we need to solve for n in the formula for a finite geometric series.
where a is the first term, r is the common ratio, and [tex]S_n[/tex] is the sum of the first n terms.
In this case, a = 100,000 and r = 1/2, since each term is half the previous one. Also, we know that S_n = 199,609.375 - (6 + 7 + 8 + 9) = 199,588.375. Plugging these values into the formula, we get:
[tex]199,588.375 = 100,000 \times \frac{(1 - (1/2)^n)}{(1 - 1/2)} \\ 199,588.375 = 200,000 \times (1 - (1/2)^n) \\ 0.997942 = (1/2)^n \\ n = \frac{log(0.997942)}{log(1/2)} \\ = 9.9916[/tex]
So the number of terms is approximately 10. Answer: none of the above (not provided in the answer choices).
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please help me...........................
the οther simplest fοrm οf the given expressiοn is =-8x+5y+7z-9.
What is pοlynοmials?Pοlynοmials are expressiοns that use variables and cοefficients in algebra. Sοmetimes when describing variables, the term "indeterminates" is used. The wοrds "pοlynοmial" and "nοminal" cοllectively denοte "many" and "terms," and they are used tο fοrm this wοrd.
A pοlynοmial is the end prοduct οf the additiοn, subtractiοn, multiplicatiοn, and divisiοn οf expοnents, cοnstants, and variables (Nο divisiοn οperatiοn by a variable). Accοrding οn hοw many terms the expressiοn cοntains, it is classified as a mοnοmial, binοmial, οr trinοmial.
The expressiοn is 8x-5y-7z+9
Sο if yοu want tο change that multiple by -ve
-8x+5y+7z-9.
Hence the οther simplest fοrm οf the given expressiοn is =-8x+5y+7z-9.
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An analogue sensor has a bandwidth which extends from very low frequencies up to 8.75 kHz. Using the Sampling Theorem (Section 3.3.1), what is the minimum sampling rate (number of samples per second) required to convert the sensor output signal into a digital representation without incurring any aliasing?
If each sample is now quantised into 512 levels, what will be the resulting sensor output bitrate in kbps?
Give your answer in scientific notation to one decimal place.
Hint: you need to determine the number of bits per sample that allows for 512 quantisation levels (see Sections 2.4 (Block 1) and 3.3.2 (Block 3)).
Answer:
Step-by-step explanation:
According to the Sampling Theorem, the minimum sampling rate required is at least twice the highest frequency component in the signal. In this case, the highest frequency component is 8.75 kHz, so the minimum sampling rate required is:
2 x 8.75 kHz = 17.5 kHz
Therefore, the minimum sampling rate required to avoid aliasing is 17.5 kHz.
To determine the resulting sensor output bitrate in kbps, we need to calculate the number of bits per sample. Since the signal is quantised into 512 levels, we need at least 9 bits per sample to represent all possible levels (2^9 = 512).
The sensor output bitrate is the product of the sampling rate and the number of bits per sample. Using the minimum sampling rate of 17.5 kHz and 9 bits per sample, we get:
bitrate = 17.5 kHz x 9 bits/sample = 157.5 kbps
Expressing the result in scientific notation to one decimal place, we get:
bitrate = 1.6 x 10^5 kbps
what is the value of x in the following figure
Answer: 38 degrees
Step-by-step explanation: 90+52+x=180
180-142=38
x=38
Work out the following sheet below
Answer:
a) 6
b) 38p
Step-by-step explanation:
p = pence
= penny
£ = Sterling pound
Step I:
Make sure the unit of the currency is consistent throughout the question.
Either convert p to £ OR £ to p
Conversion rate applied:
1 £ = 100 p
∴Unit multipliers: [tex]\frac{100p}{1 Sterling Pound}[/tex] OR [tex]\frac{1 Sterling Pound}{100p}[/tex]
In the calculation steps below, the above unit multipliers will be used and arranged in such a way that it cancels out the current unit and assigns the answer with the desired unit:
Let’s convert p to £:
77p = [tex](77p)[/tex] × ( [tex]\frac{1SterlingPound}{100p}[/tex])
= £0.77
Step II:
1 mango = £0.77
x mangoes = £5.00
Cross-multiplication is applied:
(£5.00)(1 mango) = (£0.77)(x mangoes)
x needs to be isolated and made the subject of the equation:
∴ x mangoes = [tex]\frac{(5.00)(1)}{0.77}[/tex]
x = 6.493
a) ∴The greatest number of mangoes you can buy is 6
b) Change you should receive = £5.00 - [(£0.77)(6)]
= £5.00 - £4.62
= (£0.38) × ([tex]\frac{100p}{1 Sterling Pound}[/tex])
= 38p
Assume that 58% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below, rounded to four decimal places:
a. There are some lefties ( ≥ 1) among the 5 people.
b. There are exactly 3 lefties in the group.
c. There are at least 4 lefties in the group.
d. There are no more than 2 lefties in the group.
e. How many lefties do you expect?
f. With what standard deviation?
Answer:
a. To find the probability that there are some lefties among the 5 people, we need to find the probability of the complement event, which is that there are no lefties among the 5 people. The probability of an individual being right-handed is 1 - 0.58 = 0.42. Therefore, the probability of none of the 5 people being left-handed is:
P(no lefties) = 0.42^5 = 0.0070 (rounded to four decimal places)
The probability of there being some lefties (≥ 1) is the complement of this:
P(some lefties) = 1 - P(no lefties) = 1 - 0.0070 = 0.9930 (rounded to four decimal places)
Therefore, the probability of there being some lefties among the 5 people is 0.9930.
b. To find the probability of there being exactly 3 lefties in the group, we can use the binomial probability formula:
P(exactly 3 lefties) = (5 choose 3) * (0.58)^3 * (0.42)^2
where (5 choose 3) = 10 is the number of ways to choose 3 people out of 5. Plugging in the values, we get:
P(exactly 3 lefties) = 10 * 0.58^3 * 0.42^2 = 0.3383 (rounded to four decimal places)
Therefore, the probability of there being exactly 3 lefties among the 5 people is 0.3383.
c. To find the probability of there being at least 4 lefties in the group, we can use the binomial probability formula again:
P(at least 4 lefties) = P(4 lefties) + P(5 lefties)
P(4 lefties) = (5 choose 4) * (0.58)^4 * (0.42)^1 = 0.2684
P(5 lefties) = (5 choose 5) * (0.58)^5 * (0.42)^0 = 0.1037
Adding these probabilities, we get:
P(at least 4 lefties) = 0.2684 + 0.1037 = 0.3721 (rounded to four decimal places)
Therefore, the probability of there being at least 4 lefties among the 5 people is 0.3721.
d. To find the probability of there being no more than 2 lefties in the group, we can use the binomial probability formula again:
P(no more than 2 lefties) = P(0 lefties) + P(1 lefty) + P(2 lefties)
P(0 lefties) = (5 choose 0) * (0.58)^0 * (0.42)^5 = 0.0022
P(1 lefty) = (5 choose 1) * (0.58)^1 * (0.42)^4 = 0.0344
P(2 lefties) = (5 choose 2) * (0.58)^2 * (0.42)^3 = 0.1866
Adding these probabilities, we get:
P(no more than 2 lefties) = 0.0022 + 0.0344 + 0.1866 = 0.2232 (rounded to four decimal places)
Therefore, the probability of there being no more than 2 lefties among the 5 people is 0.2232.
Step-by-step explanation:
Find a value of the standard normal random variable z, call it Zo, such that the following
probabilities are satisfied.
a. P(z≤zo) = 0.0981
b. P(-Zo sz≤zo) = 0.99
c. P(-Z₁ ≤z≤zo) = 0.95
d. P(-Z₁ ≤z≤z) = 0.8994
e. P(-Zo ≤z≤0)=0.3106
f. P(-3
g. P(Z
h. P(z ≤ z)= 0.0014
Answer:
a. Using a standard normal table or calculator, we find that z = -1.28 satisfies P(z≤zo) = 0.0981.
b. Since the standard normal distribution is symmetric, P(-Zo≤z≤zo) = 0.99 is equivalent to P(z≤-zo) = 0.005. Using a standard normal table or calculator, we find that z = -2.33 satisfies this probability.
c. Since the standard normal distribution is symmetric, P(-Z₁ ≤z≤zo) = 0.95 is equivalent to P(0 ≤z≤Zo) = 0.475. Using a standard normal table or calculator, we find that z = 1.96 satisfies this probability.
d. Since the standard normal distribution is symmetric, P(-Z₁≤z≤z) = 0.8994 is equivalent to P(0≤z≤Z₁) = 0.4497. Using a standard normal table or calculator, we find that z = 2.66 satisfies this probability.
e. Since the standard normal distribution is symmetric, P(-Zo≤z≤0) = 0.5 - P(0≤z≤Zo) = 0.5 - 0.3106 = 0.1894. Using a standard normal table or calculator, we find that z = -0.84 satisfies this probability.
f. Since the standard normal distribution is symmetric, P(-3≤z≤3) = 0.998. Therefore, P(z>3 or z<-3) = 0.002.
g. P(Z<z) = 0.0014 is equivalent to P(z>-z₁) = 0.0014, where z₁ is the z-value such that P(z≤z₁) = 0.0014. Using a standard normal table or calculator, we find that z₁ = -2.96. Therefore, z > 2.96 satisfies P(Z<z) = 0.0014.
h. P(z≤z) = 0.5 + 0.0014/2 = 0.5007. Using a standard normal table or calculator, we find that z = 2.59 satisfies this probability.
Step-by-step explanation:
Helena sketches a circular backyard skating pond that fits into a square
section of her yard. In her sketch, what is the area of the shaded region?
Factor out the GCF. Explain.
The area of the shaded region equals 21.43 sq. units.
Why do we use area?When calculating how much material is needed to cover a wooden table, how many tiles are needed to tile the floor, how much space is needed for a parking lot, how much paint is needed for the walls, etc., we employ the notion of area.
Given, A circle is circumscribed in the square,
Area of shaded region = area of square - area of circle
Area of square = Side²
= 10 × 10 = 100 sq. units,
Area of circle = Πr²
Radius = Diameter / 2
radius = 10 / 2 = 5 units
Area of circle = 22/7 × 5 × 5
= 78.57 sq. units
Area of shaded region = 100 - 78.57,
Area of shaded region = 21.43 sq. units
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