Answer:
Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.23
If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Likely
Compare the probabilities and interpret the likelihood. Which statement is true?
Player 1 is more likely to hit the ball than Player 3 because P(Player 1) > P(Player 3)
Joseph has a bag filled with 3 red, 3 green, 15 yellow, and 9 purple marbles. Determine P(not red) when choosing one marble from the bag.
90%
A student randomly draws a card from a standard deck of 52 cards. He records the type of card drawn and places it back in the deck. This is repeated 20 times. The table below shows the frequency of each outcome.
Outcome Frequency
Heart 7
Spade 3
Club 6
Diamond 4
Determine the experimental probability of drawing a spade.
0.15
A spinner with repeated colors numbered from 1 to 8 is shown.
Sections 1 and 8 are purple.
Sections 2 and 3 are yellow.
Sections 4, 5, and 6 are blue.
Section 7 is red.
Determine the theoretical probability of the spinner not landing on blue, P(not blue).
0.375
A spinner with repeated colors numbered from 1 to 8 is shown.
Sections 1 and 8 are purple.
Sections 2 and 3 are yellow.
Sections 4, 5, and 6 are blue.
Section 7 is orange.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
List the sample space for rolling a fair eight-sided die.
S = {1, 2, 3, 4, 5, 6, 7, 8}
There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials.
Outcome Frequency
Brown 13
Black 9
Green 7
Gold 11
Likely
Equally likely and unlikely
Which event will have a sample space of S = {h, t}?
Flipping a fair, two-sided coin
Julia had a bag filled with gumballs. There were 1 lemon-lime, 2 watermelon, and 3 grape gumballs. What is the correct sample space for the gumballs in her bag?
Sample space = lemon-lime, watermelon, watermelon, grape, grape, grape
A roller coaster car rapidly picks up speed as it rolls down a slope. As it starts
down the slope, its speed is 4 m/s. 3 seconds later, at the bottom of the slope,
its speed is 22 m/s. What is the cars acceleration?
A cylinder has a volume of 243 pi
and a diameter of 18. What is its height?
Answer:
0.955
Step-by-step explanation:
Height= volume x pi x radius squared (h = V x pi x r^2)
Volume (V) = 243
Height (h) = ?
Pi = 3.14
Radius (r) = 9
Diameter to radius = 18/2 = 9
h = 243 x 3.14 x 9^2
=0.955
The probability that a passenger is chosen for customs inspection is 10 %. Emma and Michael go through customs. What is the probability that neither of them is chosen for inspection? The probability of one passenger being chosen is independent of that of other passengers.
a) 81 %
b) 90 %
c) 99 %
d) other
The probability that neither of them is chosen for inspection is given as follows:
a) 81 %
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The parameter values for this problem are given as follows:
n = 2, p = 0.1.
The probability of neither is P(X = 0), hence:
P(X = 0) = (1 - 0.1)² = 0.81.
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What is the surface area of the polyhedron
Answer: equal to the sum of the area of all of its faces
Step-by-step explanation:
calculate the length of AC to 1 decvimL POINT
Answer:The length of AC to one decimal place in the trapezium is 18.1 cm
Step-by-step explanation: Using Pythagoras theorem, we can find the length AC
Pythagoras theorem
c² = a² + b²
Therefore, draw a line from the point B to the line AD and call it line BX.
BX ║ CD
Therefore,
16² - 7² = BX²
256 - 49 = BX²
BX² = 207
BX = √207
BX = 14.3874945699
BX = 14.4 cm
Therefore,
11² + 14.4² = AC²
121 + 207.36 = AC²
AC = √328.36
AC = 18.120706388
AC = 18.1 cm
What is the sum of the measures of the exterior angles of the polygon shown below? If necessary, round to the nearest tenth.
5 stars and like
The sum of the measures of the exterior angles of the polygon is, 360°
What is an angle ?An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.
Interior angles:- The inner angle made by the intersection of two polygonal sides.
Exterior angles:- The outer angle made by the intersection of two polygonal sides.
Given that,
A polygon,
Having 9 equal sides,
The sum of the measures of the exterior angles of the polygon = ?
The sum of each interior & exterior angles are 180°
Suppose, interior angles are respectively
a, b, c, d, e, f, g, h, i,
Now, exterior angles are respectively
180°-a, 180°-b, 180°-c, 180°-d, 180°-e, 180°-f, 180°-g, 180°-h, 180°-i,
The sum of the measures of the exterior angles of the polygon =
180°-a + 180°-b +180°-c +180°-d + 180°-e + 180°-f + 180°-g +180°-h + 180°-i,
1620 - (a + b + c + d + e + f + g + h + i)
Sum of all the interior angles = (9-2)x180°
= 1260°
The sum of the exterior angles of the polygon = 1620 - 1260°
= 360°
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Write the phrase as an expression. a number x divided by 2
Answer: x/2
Step-by-step explanation: Good morning. I am not sure what you mean by "A number x", so I suppose that is a typo.
Answer: x/2 IS CORRECT
Step-by-step explanation:
I TRIED IT :)
What is the sum of 3 of the interior angles of a regular pentagon?
5 stars and like
Answer: 540°.
Step-by-step explanation:
by
Celine purchased a ball of red yarn costing $2.33. She gave the cashier $7.19. How much change did the cashier give back to Celine?
Answer:
$ 4.86
Step-by-step explanation:
Subtract 7.19 and 2.33
7.19-2.33=4.86
Assume the following
actual machine hours during the period of 54000 hours
estimates machine hours to be worked during the coming period of 55000 hours manufacturing overhead applied to production during the period of 432000 estimated variable manufacturing overhead per machine hour of 2.7
which is the fixed MOH cost
Based on the manufacturing overhead applied to production during the period of $432,000, the fixed manufacturing overhead cost is $286,200.
What is the manufacturing overhead applied?The manufacturing overhead applied is determined as the product of the predetermined overhead rate and the actual machine hours consumed during the period.
Estimated machine hours to be worked = 55,000 hours
Actual machine hours during the period = 54,000 hours
Total manufacturing overhead applied to production = $432,000
Estimated variable manufacturing overhead per machine hour = $2.70
Total variable manufacturing overhead = $145,800 ($2.70 x 54,000)
Fixed manufacturing overhead (MOH) cost = $286,200 ($432,000 - $145,800)
Thus, the fixed manufacturing overhead cost is the difference ($286,200) between the total overhead cost applied and the variable manufacturing overhead cost.
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(x+2)^2=4(x+5)+y standard form
The standard form of the equation (x + 2)² = 4 (x + 5) + y is:
x² + y - 16 = 0
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The standard form of an equation is Ax + By = c.
Now,
(x + 2)² = 4 (x + 5) + y
x² + 4x + 4 = 4x + 20 + y
x² + 4 = 20 + y
x² + y = 20 - 4
x² + y = 16
x² + y - 16 = 0
Thus,
x² + y - 16 = 0 is the standard form of an equation.
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ria is buying plates and cubs for a party. she wants the same numbers of each.Plates are sold in packs of 8. cups are sold in packs of 12. what is the least number of plates and cups that ria can buy
The least number of plates and cups she can buy is 24. She will buy 3 packs of plates and 2 packs of cup
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, ria is buying plates and cubs for a party. she wants the same numbers of each. Plates are sold in packs of 8. cups are sold in packs of 12.
Plates = 8 per pack
Cups = 12 per pack
the Lowest common multiple of 8 and 12
8 = 16, 24, 32, 40, 48, 56, 64, 72, 80
12 = 24, 36, 48, 60, 72
The Lowest common multiple of 8 and 12 is 24
The least number of plates and cups she can buy is 24
Packs of plates = 24 plates / 8 per pack
= 3 packs
She will buy 3 packs of plates
Packs of cups = 24 / 12 per pack
= 2 packs
She will buy 2 packs of cup
Therefore, The least number of plates and cups she can buy is 24. She will buy 3 packs of plates and 2 packs of cup
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evaluate without a calculator: sec 30°
Answer:
sec 30° = 1/cos 30° = 2.
Step-by-step explanation:
The secant function (sec) is the reciprocal of the cosine function. So, sec(x) = 1/cos(x). The value of cosine at 30 degrees is sqrt(3)/2, and its reciprocal is 2/sqrt(3), which can be simplified to 2. Hence, sec(30°) = 2.
URGENT!!!
Sharon invested $5,000 in a bond for 2 years. The total interest earned on the investment was $600. What was the interest rate on the investment?
The interest rate required to pay a simple interest of $600 from an investment of $5000 in 2 years is 6%.
What is the interest rate on the investment?Simple interest is expressed as;
I = P × r × t
Where I is interest, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $5,000Interest I = $600Elapsed time t = 2 yearsInterest rate r = ?Plug the given values into the above formula and solve for r.
I = P × r × t
r = I / Pt
r = 600 / ( 5,000 × 2 )
r = 600 / ( 10,000 )
r = 0.06
Interest rate = r × 100%
Interest rate = 0.06 × 100%
Interest rate = 6%
Therefore, the interest rate is 6%.
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Describe how the graph of the function is a transformation of the original function f.
y=f(x+16)
The graph of the function y = f(x + 16) is a transformation of the original function f. This transformation has shifted the graph of f to the right by 16 units on the x-axis. This means that the value of x in the original function has been increased by 16, which has an effect on the corresponding value of y in the transformed function.
For example, if the point (a, b) is on the graph of f, then the point (a + 16, b) will be on the graph of y = f(x + 16). The x-coordinate of the point has been increased by 16, and since the transformation is a horizontal shift, the y-coordinate remains unchanged.
In summary, the graph of y = f(x + 16) is a reflection of the graph of f about the vertical axis. The transformation has the effect of shifting the graph to the right, but preserving the shape and overall form of the original function.
2. What is the difference in rainfall from the wettest and driest months?
The difference in rainfall between the wettest and driest months is 3.97 inches.
What is a bar graph?A bar graph is a graphical depiction of information, amounts, or numbers using bars or strips. They are utilized to contrast and compare various data types, frequencies, or other measurements of several categories of data.
On the graph, there are two axes. The numerical data is displayed against the category data on one axis, which is used to depict the numerical values.
Given the graph which shows the rainfall of the wettest and driest months,
here red blocks are for the driest months and blue blocks show the wettest months,
From the graph, we can see that the wettest month has a rainfall height of 2.3 inches
The driest month has a rainfall of -1.67 inches
So the difference between the two will be;
2.3 - (-1.67)
= 2.3 + 1.67 = 3.97 inches
Hence the difference is 3.97 inches.
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The complete question is,
The bar graph shows the differences in a city’s rainfall from the historical average. What is the difference in rainfall between the wettest and the driest months? Write your answer as a decimal.
The difference in rainfall between the wettest and the driest months is inches.
Which equation represents the graph? a graph of a line that passes through the points 0 comma negative 3 and 4 comma negative 1 y equals negative one half times x plus 6 y equals one half times x minus 3 y = 2x − 3 y = −2x + 6
the equation of line passes through points (0, -3) and (4, -1) is 4y = 3x -12.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given, an equation of a line in the graph.
Since the graph shows that the line passes through points (0, -3) and (4, -1).
The slope-intercept form of the equation of a line
y=mx+b,
where m is the slope
b is the y-intercept (value of y at x =0)
since
slope = (y - y')/(x -x')
In our case,
slope (m) = (-1 - (-3))/(4 -0)
m = 3/4
b = -3
Thus, the equation of the line:
y = 3/4x - 3
or, 4y = 3x -12
therefore, the equation of the line will be 4y = 3x -12.
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HELP
_______________
The correct statements regarding the translation from function f(x) to function g(x) are given as follows:
Function f is translated down 2 units.Function f is translated to left 3 units.What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.The translations for this problem are defined as follows:
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in 2010 an earthquake below the ocean floor initiated a devastating tsunami in Samatra. scientists can approximate the velocity V in feet per second of a tsunami in water of depth d feet with the formula [tex]\sqrt{16} \\[/tex] [tex]\sqrt{d}[/tex]. Determine the velocity of a tsunami in 300 feet of water. Write your answer in simplified radical form.
Its velocity is 69.28 feet/sec of a tsunami in 300 feet of water.
What is speed?Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
here, we have,
Since the depth of the water 'd' (in feet) and the velocity of the wave 'v' (in feet per second) are related by the equation
v = √(16d)
a wave forms in water with a depth of 300 feet,
therefore d = 300 ft
so, we get,
velocity = √(16*300)
= 4√300
=4*17.32
=69.28
Hence, Its velocity is 69.28 feet/sec of a tsunami in 300 feet of water.
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A museum charges $7 per person for a guided tour with a group of 1 to 14 people or a fixed $105 fee for a group of 15 or more people. Write a function relating the number of people, n, to the cost, C.
The value of function relating the number of people, n, to the cost, C is,
⇒ C (n) = 7n ; if 0 < n < 15
= 105n ; if n ≥ 15
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;
A museum charges $7 per person for a guided tour with a group of 1 to 14 people or a fixed $105 fee for a group of 15 or more people.
Hence, he value of function relating the number of people, n, to the cost, C is,
⇒ C (n) = 7n ; if 0 < n < 15
= 105n ; if n ≥ 15
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I need this for math homework anyone on tonight to help? 5/8 = x/12 x=
x = 15/2
do u need an explanation?
How much is invested at 5% and 7%, with annual interest is $490, with a total of $8000
The amount invensted at 5% and 7% are 3500 and 4500 respectively.
What is a system of equations?A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given that, an amount $8000, is invested at 5% and 7%, with annual interest is $490,
For this we will establish the a system of equations,
x + y = 8000......(i)
0.05x + 0.07y = 490
Multiplying by 100,
5x + 7y = 49000.....(ii)
Multiplying eq(i) by 5,
5x + 5y = 40000
Subtract eq(i) from eq(ii)
2y = 9000
y = 4500
Put y = 4500 in eq(i)
x = 8000 - 4500
x = 3500
Hence, the amount invensted at 5% and 7% are 3500 and 4500 respectively.
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Hey guys please help me with my quiz its about finding the values of letters in angles!!
The value of x is given as follows:
x = 24.
The measure of angle DFE is given as follows:
<DFE = 62º.
How to obtain the measures?To obtain the measures, we consider that the sum of the measures of the internal angles of a triangle is of 180º.
The internal angle measures for this problem are given as follows:
180 - (5x - 14) -> each angle is supplementary with it's external.44º.3x - 10.Hence the value of x is obtained as follows:
180 - 5x + 14 + 44 + 3x - 10 = 180
228 - 2x = 180
2x = 48
x = 24.
The measure of angle DFE is obtained as follows:
<DFE = 3(24) - 10
<DFE = 72 - 10
<DFE = 62º.
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13, 11, 9, 7 In the number pattern above, each term is 2 less than the previous term. Which of the following is also true about the pattern?
A. All the numbers are multiples of 3.
B. All the numbers are even.
C. All of the numbers are prime.
D. All the numbers are odd.
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The truth about the pattern that we have here is that all of the numbers are: odd.
What are odd numbers?In the number pattern given, each term is 2 less than the previous term. Starting from 13, we have 11 (13 - 2), 9 (11 - 2), and 7 (9 - 2). All of these numbers are odd, making answer D the correct choice.
A. All the numbers are multiples of 3: This is not true, as 9 is the only number that is a multiple of 3.
B. All the numbers are even: This is not true, as all of the numbers are odd.
C. All of the numbers are prime: This is not true, as 9 is not a prime number.
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I need help ASAP!!!!!
Answer:
Nope
Step-by-step explanation:
No, because if you add the angles of B and C (since they're asking for line BC), they must equal the angles of A and D (Since the other line was AD)
The sum of B and C is 90+45 which = 135
The sum of A and D is 90+135 which = 225
135 =/= 225
Find the surface area of the sphere. Use 3.14 for pi.
A. 1519.8 yd2
B. 276.3 yd2
C. 6079.0 yd2
D. 552.6 yd2
Answer:
A
Step-by-step explanation:
please memorize this formula for area of sphere
A=4π r²
so d = 22, which means r=11
so A = 4* π*11² = 4*121*π =484π = 1519.76
Please use the law of sines to show me how to solve the triangle please. Thank you .
Answer:
[tex]\angle A= 27.2 \textdegree\\\angle B=37.3 \textdegree\\\angle C=115.5 \textdegree\\[/tex]
[tex]a=38.5[/tex] ft
[tex]b=51[/tex] ft
[tex]c=76[/tex] ft
Step-by-step explanation:
Here is the formula for the Law of Sines.
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]`
In this example we are given
[tex]\angle A =27.2 \textdegree\\\angle C=115.5 \textdegree\\c=76.0[/tex]
Angle B
The sum of the interior angles in a triangle add up to 180º. Given 2 angles, we can evaluate the 3rd.
[tex]180\textdegree-115.5\textdegree-27.2\textdegree=37.3 \textdegree[/tex]
[tex]\angle B=37.3 \textdegree[/tex]
Side a
We can use the Law of Sines formula [tex]\frac{a}{\sin A}=\frac{c}{\sin C}[/tex] to evaluate side a.
Inserting our values into the equation gives us
[tex]\frac{a}{\sin 27.2}=\frac{76}{\sin 115.5}[/tex]
Cross multiply to evaluate side a.
[tex]76*\sin 27.2=a*\sin 115.5[/tex]
Divide both sides by [tex]\sin 115.5[/tex].
[tex]\frac{76*\sin 27.2}{\sin 115.5} =a[/tex]
[tex]38.49=a[/tex]
Side b
We can use the Law of Sines formula [tex]\frac{b}{\sin B}=\frac{c}{\sin C}[/tex] to evaluate side b.
Inserting our values into the equation gives us
[tex]\frac{b}{\sin 37.3}=\frac{76}{\sin 115.5}[/tex]
Cross multiply to evaluate side b.
[tex]76*\sin 37.3=b*\sin 115.5[/tex]
Divide both sides by [tex]\sin 115.5[/tex].
[tex]\frac{76*\sin 37.3}{\sin 115.5} =b[/tex]
[tex]51.03=b[/tex]
[tex]\angle A= 27.2 \textdegree\\\angle B=37.3 \textdegree\\\angle C=115.5 \textdegree\\a=38.5\\b=51\\c=76[/tex]
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sin(A) / a = sin(B) / b = sin(C) / c
where A, B, and C are the angles of the triangle, and a, b, and c are the lengths of the sides opposite those angles.
A solution contains furosemide (frusemide) 10 mg/mL. How many milligrams of frusemide are in 3 mL of solution?
Answer:
30mg
Step-by-step explanation:
10 mg/mL x 3 mL
solve the given initial-value problem. Dy dx + y = f(x), y(0) = 1, where f(x) = 1, 0 ≤ x ≤ 1; -1 , x ≥ 1
The general solution of the ODE is:
y(x) = e^-x * (1 - (e^x - 1) / 1) + (e^x - 1) / 1 * (e^x + 1) / 1, 0 ≤ x ≤ 1
y(x) = e^-x * (1 + (e^x - 1) / 1) - (e^x - 1) / 1 * (e^x + 1) / 1, x ≥ 1
How did we get the values?This is a first-order linear ordinary differential equation (ODE) with constant coefficients. It can be solved using the method of integrating factors.
Let's multiply both sides by the integrating factor e^(∫p(x)dx), where p(x) = 1.
e^(∫p(x)dx) * Dy/dx + e^(∫p(x)dx) * y = e^(∫p(x)dx) * f(x)
D/dx (e^(∫p(x)dx) * y) = e^(∫p(x)dx) * f(x)
Integrating both sides, we get:
e^(∫p(x)dx) * y = ∫ e^(∫p(x)dx) * f(x) dx + C
where C is an arbitrary constant of integration.
Using the initial condition y(0) = 1, we can find the value of the constant C.
y(0) = 1 = e^(∫p(x)dx) * y(0) = e^(∫p(x)dx) * 1 = ∫ e^(∫p(x)dx) * f(x) dx + C
So, C = 1 - ∫ e^(∫p(x)dx) * f(x) dx
For 0 ≤ x ≤ 1, we have f(x) = 1 and:
∫ e^(∫p(x)dx) * f(x) dx = ∫ e^x dx = (e^x - 1) / 1
For x ≥ 1, we have f(x) = -1 and:
∫ e^(∫p(x)dx) * f(x) dx = ∫ -e^x dx = -(e^x - 1) / 1
Therefore, the general solution of the ODE is:
y(x) = e^-x * (1 - (e^x - 1) / 1) + (e^x - 1) / 1 * (e^x + 1) / 1, 0 ≤ x ≤ 1
y(x) = e^-x * (1 + (e^x - 1) / 1) - (e^x - 1) / 1 * (e^x + 1) / 1, x ≥ 1
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Write an expression to represent:
3
33 minus the product of
2
22 and
�
xx.
The expression to represent the given statement is:33 - (2 * 22 * ½x)
The expression "33 - (2 * 22 * ½x)" represents a mathematical calculation. Breaking it down, we start with the product of 2 multiplied by 22, which equals 44. Then, we multiply the result by ½x, where ½ represents one-half and x is a variable. This gives us the term 44 * ½x. Finally, we subtract this term from 33. In simpler terms, we have 33 minus half of 44 times x. The expression allows us to compute the value of the expression based on the input for the variable x, providing a way to evaluate the equation numerically.Let's dive deeper into the explanation.
The given expression is "33 - (2 * 22 * ½x)".
To simplify it, let's break it down step by step:
The term "2 * 22" is a multiplication operation that calculates the product of 2 and 22, resulting in 44.
Next, we have "½x". Here, ½ represents one-half, or 0.5. Multiplying 0.5 by x gives us 0.5x.
Putting it together, we have the term "44 * ½x". This means multiplying 44 by 0.5x, resulting in 22x.
Finally, we subtract the term "22x" from 33, giving us the expression "33 - 22x".
In summary, the expression represents the number 33 minus the product of 22 and the value of x, denoted as 22x. This expression allows us to calculate the result by substituting a specific value for x. It provides a way to compute the numerical outcome based on the given mathematical relationship.
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