The vertex form of equation is discussed below,
What is Vertex form?The vertex form of a quadratic function is f(x) = a(x – h)² + k, where a, h, and k are constants. of the parabola is at (h, k).
As, A parabola has a lowest point if it opens upward.
Additionally, a parabola has a highest point if it opens downward.
The vertex of the parabola is located at this lowest or highest point.
Now, the parent function f(x) = x² has its vertex at the origin.
Also, The vertex form of a quadratic function is
f(x) = a(x – h)² + k, where a, h, and k are constants.
For example, The parent function f(x) = x² is vertically stretched by a
factor of 4/3 and then translated 2 units left and 5 units down.
So, the vertex form : g(x) = 4/3 (x+2)² - 5.
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6. jessie and bob are financing $425,500 to purchase a house. they obtained a 30/8 balloon mortgage at 6.55%. what will their balloon payment be? (3 points)
o $379,659.89
0 $637,130.99
o $357,491.39
o $380,040.19
So, on solving the provided question we can say their balloon payment will be $380,040.19.
What is balloon payment ?A balloon loan is a type of loan arrangement where only a portion of the original balance is repaid during the course of the loan's relatively short repayment term. When only a fraction of the initial debt is repaid during the duration of the loan's relatively short repayment term, the loan is referred to as a "balloon loan."
the monthly fixed payment. there is a formula
Pmt = (A * i * (1 + i)ⁿ) / ((1 + i)ⁿ - 1)
Pmt - monthly payment;
A is Loan amount;
i is periodic interest rate; and
n is number of periods.
Mortgage amount: $425,500
[tex]Term in years: 8 years[/tex]
Interest rate: 6.55%
Amortization period is - 30 years.
pmt=(425500*6.55*(1+6.55)^12)/((1+6.55)^12-1)
Balloon payment=[tex]$380,301.82.[/tex]
Total interest paid[tex]$211,630.52.[/tex]
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Aubrey is older than Chase. Their ages are consecutive integers. Find Aubrey's age if the product of their ages is 56.
Divide $3300 into three parts with the ratio of 1:3:7
PLEASE ANSWER QUICKLy!!!!!!
Answer:
Step-by-step explanation:
So you add 1+3+7 which gives you 11
And the you divide 3300 by 11 which gives you 300 and from that you do:
1 x 300= 300
3 x 300= 900
7 x 300= 2100
And there you have it in the ratio of 1:3:7
300:900:2100
And to simplify it you find a number which you can divide them all from in this case is 100 and so:
300÷100=3
900÷100=9
2100÷100=21
3:9:21
Hope that helped.
suppose that it is reported that 75% of workers aged 18 and over drive to work. find the probability that more than 3 of the 10 workers chosen drive to work alone.
On solving the provided question, we can say that Probability 8 drive to work[tex]= C(8,8) 0.77^8 * 0.23^0 = 0.77^8 = 0.123 = > 1 - 0.1236 = 0.8764[/tex]
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
x = number that drive to work alone
Likelihood that exactly eight people drive alone to work is equal to the probability that no more than seven people drive alone.
[tex]P(x < = 7) = 1 - P(x > 7) = 1- P(x = 8)[/tex]
That probability
Probability 8 drive to work
[tex]= C(8,8) 0.77^8 * 0.23^0 = 0.77^8 = 0.123\\=1 - 0.1236 = 0.8764[/tex]
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The line l cuts the y-axis at (0,5).
l also passes through the point (2, 1).
find the equation of the line which is parallel to l and which passes through the point
(3,0).
The equation of the line is y = -5/2x + 5.
1. We know that the equation of a straight line is given by y = mx + c, where m is the slope of the line and c is the y-intercept.
2. We need to find the slope of line l. To find the slope, we can use the formula: m = (y2-y1)/(x2-x1). In this case, we have y2 = 1, y1 = 5, x2 = 2, and x1 = 0. Therefore, m = (1-5)/(2-0) = -4/2 = -2.
3. We now have the slope of line l, so we can find the equation of the line which is parallel to l and which passes through the point (3,0). To do this, we can use the formula y = mx + c, where m is the slope of the line and c is the y-intercept.
4. In this case, m = -2 and c is the y-intercept, which is the point at which the line intersects the y-axis.
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1) coffee is draining from a conical filter into a cylindrical coffeepot at the rate of 10 3 in / min . a) how fast is the level in the pot rising when the coffee in the cone is 5 in. deep? b) how fast is the level in the cone falling then?
The rate at which the level in the pot is rising at the instant when the coffee in the pot is 10 cm, is 16/9π cm/min.
A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface.
For cylindrical pot,
Volume, V = πr²h
dV/dt = π(r²dh/dt+h * 2r dr/dt)
Since r is constant,
Therefore, dr/dt = 0
dV/dt = 100 = πr²dh/dt
100 = π * 225/4 *dh/dt (since r = 15/2 cm)
=> dh/dt = 400/ 225π = 16/9π cm/min.
Thus, The rate at which the level in the pot is rising at the instant when the coffee in the pot is 10 cm, is 16/9π cm/min.
Correct question: Coffee is draining from a conical filter with height and diameter both 15 cm, into a cylindrical coffee pot with diameter 15 cm. The rate at which coffee drains from the filter into the pot is 100 cc/min. The rate in cm/min at which the level in the pot is rising at the instant when the coffee in the pot is 10 cm, is?
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a box contains some green marbles and exactly four red marbles. the probability of selecting a red marble is $x\%$. if the number of green marbles is doubled, the probability of selecting one of the four red marbles from the box is $(x - 15)\%$. how many green marbles are in the box before the number of green marbles is doubled?
The number of green marbles in the box before the number of green marbles is doubled is given by [tex]$\frac{4 - 4x + 60}{2x - 30}$\\[/tex], where x is the probability of selecting a red marble before the number of green marbles is doubled.
Let the number of green marbles be 'g'.
The probability of selecting a red marble before the number of green marbles is doubled is[tex]$\frac{4}{g+4} * 100 = x\%$[/tex]
The probability of selecting one of the four red marbles from the box after the number of green marbles is doubled is [tex]$\frac{4}{2g+4} * 100 = (x - 15)\%$[/tex]
Rearranging the equations and solving for g, we get:
[tex]\frac{4}{g+4} * 100 = x$\frac{4}{2g+4} * 100 = (x - 15)$$2g+4 = \frac{4}{x-15}$$g = \frac{4 - 4x + 60}{2x - 30}$[/tex]
Therefore, the number of green marbles before the number of green marbles is doubled is [tex]$\frac{4 - 4x + 60}{2x - 30}[/tex]
The number of green marbles in the box before the number of green marbles is doubled is given by [tex]$\frac{4 - 4x + 60}{2x - 30}$\\[/tex], where x is the probability of selecting a red marble before the number of green marbles is doubled.
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Since
∠
AOB
is a right angle, it is
90
∘
.
∠
AOB
is supplementary to
∠
BOC
, so
m
∠
AOB
+
m
∠
BOC
=
180
∘
. By the substitution property of equality,
90
∘
+
m
∠
BOC
=
180
∘
. Applying the subtraction property of equality,
m
∠
BOC
=
90
∘
.
What statement is missing from the proof?
A.
∠
AOB
and
∠
BOC
form a linear pair.
B.
∠
AOB
and
∠
DOC
are vertical angles.
C.
∠
COD
and
∠
AOD
form a linear pair.
D.
∠
DOA
and
∠
BOC
are vertical angles.
The missing piece of information in the proof is that m ∠ DOA and m ∠ BOC are vertical opposite angles.
What is meant by subtraction property of equality?According to the equality's subtraction property, equality is unaffected by removing the same amount from both sides of an equation. When the same quantity or value is removed from both sides of an equation, the resultant difference is also identical on both sides.
Both the equality's addition and subtraction properties are related. The same integer added to or subtracted from both sides of an equation maintains equality on both sides.
To prove that m ∠ BOC = 90°.
Given that m ∠ AOB exists a right angle triangle.
Therefore; m ∠ BOC must also be equivalent to 90°.
Since m ∠ BOC and m ∠ AOB are right angles, it follows that m ∠ DOA and m ∠ BOC are also vertical opposing angles and, as such, are equal.
So, the fact that m ∠ DOA and m ∠ BOC are vertical opposing angles is the crucial piece of information missing from the proof.
The complete question is:
Given: AOB is a right angle
Prove: m BOC = 90°
Since AOB is a right angle, it is 90°. AOB is supplementary to BOC,
so m AOB + m BOC = 180°. By the substitution property of equality,
90 + m BOC = 180°. Applying the subtraction property of equality,
m BOC = 90%. What statement is missing from the proof?
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can someone help me with this please
The value of x is 16 cm.
What is the equilateral triangle?
An equilateral triangle is a type of triangle that has three sides of equal length and three equal angles of 60 degrees each. All equilateral triangles are also equiangular and isosceles triangles. The sides of an equilateral triangle are congruent, and it is symmetrical in all ways, meaning that it has rotational and line symmetry.
We have given,
Lengths of sides:
16 cm, 16cm, and x cm,
we have to find the value of x.
The given triangle is an equilateral triangle,
so, The length of all three sides of an equilateral triangle is equal.
16 cm = 16cm = x cm,
x = 16 cm
Hence, The value of x is 16 cm.
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Evaluate 4-0.25g+0.5h when g=10=5
Answer:
4
Step-by-step explanation:
First, substitute in g and h:
4-(0.25x10)+(0.5x5)
4-2.5+2.5
Then -2.5 and +2.5 cancel out, so you are left with:
4
[tex]25 \div 2 [/tex]
How to solve this?
Answer:
25÷2=12.5
Step-by-step explanation:
you put the 25 inn the division box and the 2 on the outside and 12.5 is your answer
Answer: 12.5
How do you solve the given equation?[tex]\frac{25}{2} =12.5[/tex]
[tex]\frac{5^{2}}{2} = 12 \frac{1}{2} = 12.5[/tex]
3. In the figure, DE and DF are midsegments of AABC. Find BC. (Example 3) 1 point
B
D
122°
E
8
А.
F
с
15
O A 8
B. 15
C. 16
O D. 30
The midsegments of AABC, hypotenuse BC is B. 15.
In a triangle, a midsegment is a line segment that connects the midpoints of two non-adjacent sides of the triangle. In this figure, DE and DF are the midsegments of AABC, which means that they connect the midpoints of the sides AB and AC, respectively. Since DE and DF are parallel, we know the triangle isosceles (both legs are congruent).
Since the angle at A is 122°, we know that the angle at B and C are 78° (180-122=58). Therefore, if we draw the altitude from B to AC, we have a 30-78-72 triangle. We have been given the length of the altitude, 8, and the angle of the base, 72. We can use the Sine Ratio to calculate the hypotenuse, BC.
sin(72) = opposite / hypotenuse = 8/BC
Solving for BC, we get 15
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what is the answer for this-order of operation?
Answer:
Step-by-step explanation:
always follow BODMAS or BIDMAS-
Do the multiplication, which is 15/3 and when simplifiyed becomes 5.
Then work out 6 divided by 3/2. In division for fractions, you always find the reciprocal of the 2nd number and multiply instead of divide, so its 6 x 2/3 which is 12/3, simplifiyed to be 4. 5+4=9. 9+10 is 19, and 19-4=15
calculate the double integral. 3xy2 x2 + 1 da, r = {(x, y) | 0 ≤ x ≤ 3, −2 ≤ y ≤ 2} r
The double integral for [tex]3xy^2/x^2+1[/tex] is 8㏑(2).
[tex]3\int\limits^1_0 \int\limits^2_2 \frac{xy^2}{x^2 + 1} \, dy dx[/tex]
3* 1/2 (㏑(2) - ㏑(1) ) * 1/3 (8+8)
8㏑(2)
A multiple integral in mathematics is a definite integral of a function with multiple real variables, such as f(x, y), or f(x, y) (x, y, z). In the real-number plane, integrals of functions of two variables over an area are referred to as double integrals, and integrals of functions of three variables over a region in real-number three-dimensional space are referred to as triple integrals.
The Cauchy formula for repeated integration can be used to calculate multiple integrals of a single-variable function.
The double integral of a positive function of two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where z = f(x, y)) and the plane that contains its domain, just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis.
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a) we roll 50 dice to find the distribution of the number of spots on the faces. b) howlikelyisitthatinagroupof120themajority may have type a blood, given that type a is found in 43% of the population? c) we deal 7 cards from a deck and get all hearts. how likely is that? d) we wish to predict the outcome of a vote on the school budget, and poll 500 of the 3000 likely voters to see how many favor the proposed budget. e) a company realizes that about 10% of its packages are not being sealed properly. in a case of 24, is it likely that more than 3 are unsealed?
We can use probability to find the answers to the questions - the final answers are given below.
The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence.
We will answer each part in detail.
Part (a)
No, there are more than 2 outcomes in this particular scenario.
Part (b)
Yes, there are two outcomes (Type A or not).
Part (c)
No, probability changes as the cards are dealt.
Part (d)
No, the trials are not independent.
Part (e)
Yes, two outcomes (more than 3 or not)
These are the final answers:
(a): No
(b): Yes
(c): Yes
(d): No
(e): Yes
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A car travels the 200 miles along the M1 from London to Leeds. The car leaves London at 8am and travels at a constant speed of 60mph for the first 60 miles. The driver takes a break of 30mins at a motorway services before continuing the journey at a constant speed of 70mph a) Draw a distance-time graph of the journey
Answer:
The distance-time graph of the journey would be as follows:
From 8am to 8:01am, the car travels 0 miles (at 8am, it leaves London)
From 8:01am to 9:01am, the car travels 60 miles (at a constant speed of 60mph)
From 9:01am to 9:31am, the car travels 0 miles (the driver takes a break of 30mins)
From 9:31am to 12:51pm, the car travels 140 miles (at a constant speed of 70mph)
The graph would be a line with a slope of 60 for the first hour, a flat line for the 30 minutes break, and then a line with a slope of 70 for 2 hours and 20 minutes.
Note: Since we don't have a time-scale and time unit, this graph is just a representation of the pattern of the journey, and the actual values are not accurate.
A hip H leave a port P and ail 30km due outh then it ail 60km due wet. What i the bearing of H to P
The bearing of H from P is 243°26′
In mathematics, an angle is a measure of the amount of rotation between two lines or planes. It is measured in units of degrees or radians. An angle is formed by two rays that have a common endpoint called the vertex. The rays are the sides of the angle and the vertex is the point where the rays meet.
An angle is defined by its measure, which is the amount of rotation between the two rays. The most common way to measure angles is in degrees, where a full rotation is equal to 360 degrees. Another way to measure angles is in radians, where a full rotation is equal to 2*pi radians.
Let the bearing of H from P be represented by x°.
tanθ=3060=0.5
θ=tan−1(0.5)=26.565°
x=180°+(90−26.565)
x=180+63.435=243.435°
= 243°26′
Hence, the bearing of H from P is 243°26′
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Calcula el área de las bases y el área lateral, de un cilindro de 10cm de radio y 20cm de altura.
El area de las bases es 628 cm^2 (ambas bases) y el area lateral es 1,256 cm^2
¿Como calcular el area de las caras del cilindro?Tenemos un cilindro con un radio de 10 centimetros y 20 centimetros de altura.
El cilindro tiene dos tapas que son circulares, el area de estas se calcula como el area de un circulo cualquiera, esta sera:
A = 2*( pi*R^2)
Donde R es el radio y pi = 3.14, entonces tendremos:
A = 2*(3.14*(10cm)^2)
A = 628 cm^2
El area lateral será igual que el producto entre la altura y la circunferencia:
A' = 2*pi*R*H
Donde H es la altura.
Remplazando los valores que conocemos obtendremos:
A' = 2*3.14*(10cm)*20cm
A' = 1,256 cm^2
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decrease the number 35 by 0.6 of it
Answer:
14
Step-by-step explanation:
1) "the number 35" means 35
2) "decrease 35 by 0.6 of it" means -(0.6)*(35)
Put them together:
35 - (0.6)*(35)
35 - 21
= 14
how long would it take them to get to the point on the ferris wheel closest to the polar coordinate
It would depend on the rate of the ferris wheel, so it is impossible to answer this question without knowing the wheel's speed.
1. The question is asking for an estimate of the time it would take for a person to get from the start of the ferris wheel to the point closest to the polar coordinate (6, 0).
2. To answer this question, we need to know the speed of the ferris wheel. Without this information, it is impossible to answer the question.
It would depend on the rate of the ferris wheel, so it is impossible to answer this question without knowing the wheel's speed.
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What is no solution called?
An inconsistent system is a set of equations that have no solution.
Consider the following as the lines' equation:[tex]p_1x+q_1y+a_1=0 , p_2x+q_2y+a_2=0[/tex]
We can start analyzing the equations of lines and evaluating their various properties now that we understand how to display points on a coordinate plane and graph linear equations. The common forms for writing linear equations and the characteristics of lines that can be inferred from their equations are covered in this section.
If both lines are parallel to one another, there is no answer because the lines never cross.
In such a circumstance, the pair of linear equations in two variables is considered to be inconsistent because algebraically, [tex]\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}[/tex].
For example, line of equations are
[tex]2x-y=4\\\\4x-2y=8[/tex]
[tex]\frac{a_1}{a_2}=\frac{2}{4}=\frac{1}{2}\\\frac{b_1}{b_2}=\frac{1}{2}\\\frac{c_1}{c_2}=\frac{4}{8}=\frac{1}{2}[/tex]
Here, both equation has no solution so equation are called inconsistent equation.
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10 1/2 cup of flour are needed to make three lova of bread how many cup are needed
The offered statement states that 42 cups of grain are required to produce three loaves of bread.
Where did the loaves and fishes tradition start?As a completely volunteer hot meal service in 1983, Breads & Fishes quickly evolved into a pre-packaged shopping bag contribution program for locals. This nonprofit's first year's budget was $6,500, at which time the pantry supplied food to about 50 homes.
We know we need four times 10 1/2 cups of flour since 12 was 4 times higher than three (3 * 4 = 12).
We only have to calculate 10.5 * 4 = x but then just solve for x.
42 cups - grain (10.5 * 4)
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The complete question is-
10 1/2 cups of flour are needed to make 3 loaves of bread. How many cups are needed for 12?
How do you do this please help me
Step-by-step explanation:
you know how equations are transformed ?
by applying the same operation on both sides of the equation (so that the equality remains).
x + 38 = 79
to get "x = ...", we need to eliminate the "+ 38" in the x side.
clearly we need to subtract 38.
again, whatever e do, we have to do on both sides, otherwise the equality relation is destroyed.
so,
x + 38 - 38 = 79 - 38
x = 41
that is the height of the avocado tree : 41 in.
it is 38 in shorter than 79 in (the fig tree).
that's all that is to this. it is a really simple method.
the same applies to any operation you want to do (+, -, ×, ÷, ...).
Which formula describes the range?
On solving the provided question, we can say that a function's range includes all conceivable values for y. Y = f(x) is the formula to determine a function's range (x).
What is range?The variable's range is obtained by finding its largest observed value (maximum) and subtracting its smallest observed value (minimum). Variational bounds or possible range: various steel prices; various styles; The extent or magnitude of a procedure or action: insight. the maximum or expected range of a weapon's projectile. The range of a list or set is the number between the minimum and maximum. Prior to identifying the region, align all the numbers. Remove (remove) the lowest number from the highest number next. The list's range is provided in the solution. The solution provides the list's range.
A function's range includes all conceivable values for y. Y = f(x) is the formula to determine a function's range (x).
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consider an urn that initially contains 3 red balls and 5 blue balls. you remove a ball from the urn, and then (regardless of the color of the ball that you removed) you add two red balls to the urn. then you remove another ball from the urn. (a) what is the conditional probability that the second ball you remove is red given that the first ball you remove is red? (b) what is the probability that both balls that you remove are red? (c) what is the probability that the second ball that you remove is red?
The probability that both balls removed are red is 10.7%, while the probability that the second ball removed is red is 19.0%.
(a) The conditional probability that the second ball you remove is red given that the first ball you remove is red is 2/7 or 28.6%.
P(second ball is red | first ball is red) = P(second ball is red and first ball is red) / P(first ball is red)
= (2/7) / (3/8)
= 2/7
(b) The probability that both balls that you remove are red is (3/8)*(2/7) = 6/56 or 10.7%.
P(both balls are red) = P(first ball is red) * P(second ball is red | first ball is red)
= (3/8) * (2/7)
= 6/56
(c) The probability that the second ball that you remove is red is (2/7)*(5/9) + (3/8)*(2/7) = 4/21 or 19.0%.
P(second ball is red) = P(second ball is red and first ball is red) + P(second ball is red and first ball is blue)
= (2/7)*(5/9) + (3/8)*(2/7)
= 4/21
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Using -1, -2, -1.68 as examples, describe where negative numbers are located on a number line, based on the locations of 0 and 1.
The location on negative integers will be on left side of zero.
What is Number system?A number system is defined as a system of writing to express numbers.
A number line is a picture of a graduated straight line that serves as visual representation of the real numbers.
On a number line the integers were represented.
Integers are collect of positive numbers, negative numbers and zero.
On the right side of zero the number are positive 1,2,3..
To the left side of zero there are negative integers -1,-2,-3...
Fom left to right the value of numbers be increases.
Hence, the location on negative integers will be on left side of zero.
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Please help. Hate geometry tbh
Answer: The lines are only parallel if these pairs of angles are of equal size:
Angle 1 ≡ Angle 5
Angle 2 ≡ Angle 6
Angle 3 ≡ Angle 7
Angle 5 ≡ Angle 8
Step-by-step explanation:
All these angles follow a rule called corresponding angles. The rule goes that corresponding angles on parallel lines are equal. If the pairs of angles are equal, this must mean that the lines are parallel and vice versa.
60% of ms. howard's class ordered a hot lunch from the cafeteria. if 15 students ordered a hot lunch, how many students are in ms. howard's class?
Based on the number of 60% students, the total number of students in Ms. Howard's class are 25.
Let the total number of students be x. Based on the mentioned information, we can say that 60% of total number of students ordering a hot lunch are 15. Rewriting the mentioned information as equation -
60% × x = 15
60/100 × x = 15
x = 15 × 100/60
Performing multiplication on Right Hand Side of the equation
x = 1500/60
Cancelling zero and performing division on Right Hand Side of the equation
x = 25
Therefore, there are 25 students in the class.
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What is the formula for finding absolute value?
Answer:
|x| = x if x >= 0, -x if x < 0
Step-by-step explanation:
for breakfast bob has three options: cereal, eggs or fruit. he hasto choose exactly two items out of the three available.(a) describe the sample space of this experiment
According to the concept of probability, the sample space for the experiment is explained below.
The term probability in math is called as the occurrence of a random event and the sample space is defined as a collection or a set of possible outcomes of a random experiment.
Here we have know that the same space of this experiment is the possible outcomes of selecting two out of the three breakfast.
Here let us consider that the sample space is B
And the the sample space is written as.
=> {(cereal and egg), (cereal and fruit), (fruit and egg), (fruit and cereal), (egg and fruit), (egg and cereal)}
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