Opposite of an integer on the number line is the same integer with opposite sign
what is number line ?
The visual representation of numbers on a straight line is called a number line. On an endless line that extends on both sides, either horizontally or vertically, this line is used to compare numbers that are spaced at equal intervals. The numbers on a horizontal number line grow as we approach towards the right side and drop as we move towards the left.
The number line's opposite of the integer "a" is "-a"; hence, the opposite of the integer "-a" is "a" on the number line, but on the other side of 0.
For example,
The number line's opposite of the integer "4" is "-4"
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Assume that you want to test the claim that the paired sample data come from population for which the mean difference is Kd = 0. Compute the value of the test statistic. Round intermediate calculations to four decimal places as needed and final answers to three decimal places as needed. Subject Before 168 180 157 132 202 124 190 210 171 After 162 178 145 125 171 126 180 195 163 0 A 0.351 .052 3.156 9.468
The test statistic value for the given sample data with population mean difference is equal to optic C. 3.156.
As given in the question,
Given population mean difference μd = 0
sample size 'n' = 9
Sample data is:
x y [tex]d_{i}[/tex] ( x - y) [tex]( d_{i} - \bar{d} )^{2}[/tex]
168 162 6 15.21
180 178 2 62.41
157 145 12 4.41
132 125 7 8.41
202 171 31 445.21
124 126 -2 141.61
190 180 10 0.01
210 195 15 26.01
171 163 8 3.61
∑[tex]d_{i}[/tex] = 89 ∑ [tex]( d_{i} - \bar{d} )^{2}[/tex] = 706.89
[tex]\bar{d}[/tex] = ( 1/ n ) ∑[tex]d_{i}[/tex]
= (1/9) (89)
= 9.889
= 9.9
Standard deviation of the mean difference '[tex]S_{d}[/tex]'
= √[1 / (n - 1)]( ∑ [tex]( d_{i} - \bar{d} )^{2}[/tex] )
= √706.89/ 8
=√88.361
= 9.4
test statistic
t = ( [tex]\bar{d}[/tex] - μd)/ ( [tex]s_{d} /\sqrt{n}[/tex] )
= ( 9.9 - 0) / ( 9.4 / √9)
= 9.9/ 3.133
= 3.156
Therefore, the test statistic value for the given sample data is equal to option C. 3.156
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Question 61 A recipe calls for 1 cup of milk for every 2 ...
To make the similar cake for 8 persons , the number of cups of both flour and milk will be needed is [tex]4\frac{2}{3}[/tex] cups .
In the question ,
it is given that ,
number of cups of milk needed to make the cake is = 1 cup
number of cups of flour needed to make the cake is = [tex]2\frac{1}{2}[/tex] = 5/2 cups .
So , the total is = cups of milk + flour
= 1 + 5/2 = 7/2
So , for 6 persons , 7/2 cups of milk and flour is needed .
for 1 person 7/12 cups of milk and flour is needed .
and for 8 persons = 8×7/12 cups of milk and flour is needed .
= 14/3
= [tex]4\frac{2}{3}[/tex] cups .
Therefore , the number of cups of milk and flour needed is [tex]4\frac{2}{3}[/tex] cups .
The given question is incomplete , the complete question is
A recipe calls for 1 cup of milk for every [tex]2\frac{1}{2}[/tex] cups of flour to make a cake that would feed 6 persons. How many cups of both flour and milk will be needed to make a similar cake for 8 persons ?
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Solve 1w^2-54=0 by using the square root method.
Step 1: Isolate w^2:
w^2 = 54
Step 2: Apply the sq. rt. property:
w = ± sqrt(54)
Step 3: Simplify the sqrt:
w = ± sqrt(9 · 6)
w = ± sqrt(9) · sqrt(6)
w = ± 3 sqrt(6)
Step 4: Approximate:
w ≈ ± 7.3
Help me on this plsss
Answer:
First blank: 90° Second blank: 12
Step-by-step explanation:
The two shapes have a ratio of 4:1, and have the same angles.
This means that if m∠B = 90°, then m∠D = 90°.
Because the shape ratio is 4:1 (16:4 simplified) we can use this to find out 48:? 48/4 = 12
Please tell me ALL the partial products of 3.4 times 1.2
Answer:
34
× 12
---------
8
60
40
+ 300
----------
= 408
If the vertex angle of an isosceles triangle is 90 degree then find the base angle
The base angle is calculated to be 45 degrees if the vertex angle of the isosceles triangle is 90 degrees
An isosceles triangle in mathematics is used to describe a triangle with two equal sides and two equal angles.
As the vertex angle is given to be 90 degrees, therefore the other two angles of the triangle will be equal. Considering x to be the base angle;
x + x + 90° = 180°
2x + 90° = 180°
Rearranging;
2x = 180° - 90°
2x = 90°
Solving for x;
x = 90° ÷ 2
x = 45°
Therefore, 45° is calculated to be the base angle of the isosceles triangle.
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What is the next term in the geometric sequence 8 24 72?; What is the rule of this number pattern 8/24 72 216?; What is the common ratio R of 8/24 72?; What is the common ratio between the terms of the geometric progression 72?
Using basic geometric sequence rule with common ratio of 3, The answer is 216.
What do you mean by sequence?A sequence is a list of objects that is in order in mathematics (or events). Similar to a set, it has members (also called elements, or terms). The length of the sequence is the number of ordered elements (potentially infinite).
What do you mean by Geometric Sequence and What is the formula for common ratio?Each phrase in a geometric sequence is obtained by multiplying the one before it by a constant.
Formula for common ratio is:
[tex]r= \frac {x^{n+1}}{x^{n}}[/tex]
r= 24/8
=3
Next term in sequence = 72 * 3
=216
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the discriminant of a quadratic equation is given below. find the value of that guarantees the equation has exactly one real root. c
The value of that guarantees the equation has exactly one real root is Zero
A quadratic equation has exactly one real number solution, then the value of its discriminant is always zero.
Quadratic
The word Quadratic is derived from the word Quad which means square. In other words, a quadratic polynomial is a polynomial function of degree 2.There are many scenarios where quadratic polynomials are used. When a rocket is launched, its path is described by the zero of a quadratic polynomial.
Polynomial
A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable).
A quadratic equation in variable x is of the form ax2 + bx + c = 0, where a ≠ 0.
In the case of one real solution, the value of discriminant b2 - 4ac is zero.
For example, x2 + 2x + 1 = 0 has only one solution x = -1.
Discriminant = b2 - 4ac = 22 - 4 (1) (1) = 0
Thus, a quadratic equation has exactly one real number solution, then the value of the discriminant is always zero.
The value of that guarantees the equation has exactly one real root is Zero.
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Suppose that 14 inches of wire costs 84 cents. At the same rate, how many inches of wire can be bought for 42 cents
Edmund is designing his garden. For every yellow tulip, he plans to plant two whites lilies. Using only these two types of flower, he plans to plant 12 flowers in his garden. How many of each type of flower will Edmund plant in his garden? Edmund will plant _______ tulips and _______ lilies.
Answer:
4 yellow tulips and 8 white lilies.
Step-by-step explanation:
Ratio is 1:2:3 for yellow tulips, white lilies and the total.
Set up a proportion
[tex]\frac{yellow}{total}[/tex] = [tex]\frac{yellow}{total}[/tex] Three of these numbers you know, Solve for the unknown
[tex]\frac{1}{3}[/tex] = [tex]\frac{x}{12}[/tex] Cross multiply and solve for x
3x = 12 Divide both sides by 3
x = 4 This is the number of yellow tulips
Set up another proportion:
[tex]\frac{white lilies}{total}[/tex] = [tex]\frac{white lilies}{todal}[/tex]
[tex]\frac{2}{3}[/tex] = [tex]\frac{x}{12}[/tex] I can see that 3 x 4 = 12 so I will multiply the top number to 2 by 4 to get 8.
What qualities does a regular polygon have select all that apply?
Answer: Two dimensions.
Straight sides.
Congruent (equal-length) sides.
An interior and exterior.
Equal interior angles.
Equal exterior angles.
Step-by-step explanation:
compete the equation -5 + 13
Answer: the answer is 8
Answer:8 or 18
Step-by-step explanation: 5+13 is 18 and -5+13 is 8
a bakery sold 26 vanilla cupcakes in a day which was 13 percent of the total number of cupcakes sold that day. How many total cupcakes did the bakery sell that day
Answer:
200 cupcakes
Step-by-step explanation:
Let "x" be the total number of cupcakes sold at the bakery.
We know that 26 cupcakes represents 13% of the total number of cupcakes sold, so:
26 cupcakes = 13/100 * x
Solving for x, we get:
x = 26 / (13/100)
Simplifying the fraction, we get:
x = 2600 / 13
Dividing 2600 by 13 gives us 200, so:
x = 200
Therefore, the bakery sold a total of 200 cupcakes on that day.
15. Two leaky containers are filling with water. Water enters container A at a rate of 2 cup per 1 • minute and leaks out at 3 2 , 1 3 a rate of 4 cup per a minute. Water enters container B at a rate of 3 cup per 1 5 minute and leaks out at a rate of 1 2 cup per 3 _ minute. Which container needs to be filled faster in order for both containers to gain the same amount of water per minute? By how much more water per minute? Explain.
Container B needs to be filled faster in order for both containers to gain the same amount of water per minute , and by 1/6 water per minute .
What is the rate at which water is filled?Since water enters container A at a rate of 2/3 cup per 1/2 minute, then we can say that;
Rate of Filling container A = (2/3)/(1/2) = 4/3 cups per minute
We are also told that in container A, water leaks out at a rate of 1/4 cup per 3/4 minute. Thus;
Rate of leaking container A = (1/4)/(3/4) = 1/3 cups per minute
Amount of water in Container A in one minute = (4/3) - (1/3)
= 1
Similarly;
Since water enters container B at a rate of 3/4 cup per 1/2 minute, then we can say that;
Rate of Filling container B = (3/4)/(1/2) = 3/2 cups per minute
We are also told that in container B, water leaks out at a rate of 1/2 cup per 3/4 minute. Thus;
Rate of leaking container B = (1/2)/(3/4) = 2/3 cups per minute
Amount of water in Container B in one minute = (3/2) - (2/3) = 5/6
Since amount of water per minute in container A is 1 and the amount of water per minute in container B is 5/6 , then it means that container A fills faster by container B by; 1 - 5/6 = 1/6
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Complete question is;
two leaky containers are filling with water. water enters container a at a rate of 2/3 cup per 1/2 minute and leaks out at a rate of 1/4 cup per 3/4 minute. water enters container b at a rate of 3/4 cup per 1/2 minute and leaks out at a rate of 1/2 cup per 3/4 minute. which container needs to be filled faster in order for both containers to gain the same amount of water per minute? by how much more water per minute? explain
based on the graph below, which of the following statements is true? select one:
a. has a derivative that is zero at two values of x, one is a local maximum on the interval while the other is neither a local maximum nor a minimum. b. has a derivative that is zero at two values of x, both being local maxima. c. has a derivative that is zero at one value of x where it is a local minimum. d. has a derivative that is zero at two values of x, one is a local minimum on the interval while the other is neither a local maximum nor a minimum. e. has a derivative that is zero at two values of x, one is a local maximum while the other is a local minimum.
A local minimum or a local maximum are both examples of local extremums.
Find the function's local maximum and minimum points ?A point (x,y) on the function's graph at which the y coordinate is larger than all other y coordinates at positions "near to" it is known as a local maximum point (x,y).More specifically, if there is an interval (a,b) with axb and f(x)f(z) for every z in both (a,b) and the domain of f, then (x,f(x)) is a local maximum.Similar to this, if (x,y) has the smallest y coordinate locally, it is a local minimum point. If there is an interval (a,b) with axb and f(x)f(z) for every z in both (a,b) and the domain of f, then (x,f(x)) is a local minimum.A local minimum or a local maximum are both examples of local extremums.This is 0 at x=3-/3 and is defined everywhere.When we first consider x=3-/3, we can see that f(3-/3)=23-/9.Since 3-3, 3-/31, and we can use x=0 and x=1, we can test two points on either side of x=3-/3, making sure that neither is further away than the closest critical value.Given that f(0)=0>23-/9 and f(1)=0>23-/9, a local minimum at x=3-/3 is required. We observe that f(x=3-3/3)=23-/9 for x=3-/3.This time, we have the option of using x=0 and x=1, and we discover that f(x)=f(0)=023-/9, indicating that a local maximum exists at x=x-3/3.To learn more about Maxima and Minima refer to:
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The inclusion of seasonal dummy variables to a multiple regression model may help eliminate autocorrelation if the data are characterized by seasonal fluctuations. A. perfect multicollinearity. B. bias in OLS slope estimates caused by autocorrelation. C. near multicollinearity. D. All of the options are correct.
The correct option among the given is option B , bias in OLS slope estimates caused by autocorrelation.
In the presence of autocorrelation, as in the case of heteroscedasticity, the OLS estimators are still linearly unbiased, consistent, and asymptotically normally distributed, but they are no longer efficient (i.e., minimum variance).
A dummy variable is a binary variable with a value of either 0 or 1. Such variables are added to a regression model to represent binary factors, which are either observed or not observed.
A dummy variable can be used to indicate whether a data point possesses a specific property. A dummy variable, for example, can be used to indicate whether a car engine is 'Standard' or 'Turbo.' Or whether a participant in a drug trial is in the placebo or treatment groups.
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Solomon has taken two tests each out of ten. his average score is 18. if the product of his scores is 56. what did he score in each test ?
The scores of both test Solomon took are 14 for the first test and 4 for the second test.
How to calculate the score of bother test?let a represent the first score and b represent the second score.
since the average score is 18, you get (a + b) / 2 = 18
multiply both sides of this equation by 2 to get a + b = 36
the product of her scores is 56 means that a × b = 56.
you have 2 equations that need to be solved simultaneously.
they are a + b = 36 and a × b = 56
solve for a in the second equation to get a = 56 / b.
replace a with 56/ b in the first equation to get 56/ b + b = 18
multiply both sides of this equation by b to get 56 + b^2 = 18b
subtract 14b from both sides of this equation and arrange the terms in descending order of degree to get b^2 - 18b + 56 = 0
Factorise the quadratic equation to get the following:
(b-4 ) ( b - 14) = 0
Solve for b to get b = 4 and b = 14
Therefore, the product of the of the two scores:
= 14×4 = 56. This means that he scored 14 in first test and 4 in the second test.
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0.800 divided by 10
Please help meeee
Answer:
.0800
Step-by-step explanation:
Dividing by ten will just move the decimal point one position further to the left
10x-8y=4
20x-16y=8
Please help me solve this
How much money should be deposited today in an account that earns 4% compounded monthly so that it will accumulate to 12000 dollars in three years?
$9483.774 money should be deposited in the account.
Let the amount to be invested be P=$x so that the amount accumulated is A = $12000. We have t=3 years. The rate of interest is r=0.04 per year. n = 2 as interest will be compounded twice a year.
What is interest?
Interest, in its most simple form, is calculated as a percent of the principal.
Interest is the amount of money a lender or financial institution receives for lending out money. Interest can also refer to the amount of ownership a stockholder has in a company, usually expressed as a percentage.
Now,
[tex]x (1 + \frac{0.04}{2} )^{2 * 3}[/tex] [tex]= 12000[/tex]
[tex]x(1.04)^{6}[/tex] [tex]= 12000[/tex]
[tex]x = \frac{12000}{(1.04)^{6} }[/tex]
≈ 9483.774
∴ Amount invested ≈ $9483.774.
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The propagation of fatigue cracks in various aircraft parts has been the subject of extensive study in recent years. The accompanying data consists of propagation lives (flight hours/104) to reach a given crack size in fastener holes intended for use in military aircraft. 0.737 0.843 0.871 0.911 0.920 0.932 0.961 1.010 1.039 1.050 1.102 1.120 1.138 1.161 1.241 1.352 (a) Compute and compare the values of the sample mean x and median . (Round your answers to four decimal places.) x = flight hours/104 = flight hours/104 (b) By how much could the largest sample observation be decreased without affecting the value of the median? (Enter your answer to three decimal places.) flight hours/104
On solving the provided question we got to know that, the median value won't change if the greatest sample Observation is decreased to 1.3735.
What is median?One of three ways to gauge central tendency is the median. The center position of a record is specified when describing it. A measure of central tendency is what this is. The mean, median, and mode are the three most frequently used indicators of central tendency.
The sum of all the values is divided by the total number of values, giving the mean value.
[tex]0.736 + 0.863 + 0.865 + 0.913 + 0.915 + 0.937 + 0.983 + 1.001 + 1.011 + 1.064 + 1.109 + 1.132 + 1.140 + 1.153 + 1.253 + 1.397 = 16.472\\16.472 /16 = 1.0295\\1.0295 is the mean value[/tex]
The number near the middle of the point is the median value. At the halfway point, there are two values.
[tex](1.001 + 1.011) / 2 = 1.006\\ 1.006 is the median value.[/tex]
As a result, the median value, which depicts the middle value of the numbers in the result, is less than the mean value, which depicts the real middle value of the numbers if they were equally distributed.
Their difference is that 1.0295 - 1.006 = 0.0235
1.397 observations make up the biggest sample. It may be made smaller by taking the number and removing the difference between the mean and median.
Consequently, there is a 0.0235-point difference between the mean and median.
Therefore;
[tex]1.397 - 0.0235 = 1.3735[/tex]
The median value won't change if the greatest sample Observation is decreased to 1.3735.
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best buy was having a sale on a bluetooth speakers they offered a 40% discount on a JBI speaker that was originally priced at $4.50. after the new sale , the discounted price of the speaker was increased by 40%, what is the new price of the speaker after this increase?
Answer:
$3.78
Step-by-step explanation:
To find the new price of the speaker after the sale, you can use the following formula:
New price = (1 + discount percentage) * (original price - discount amount)
In this case, the discount percentage is 40%, or 0.4, and the discount amount is 40% of the original price, or 0.4 * $4.50 = $1.80. Plugging these values into the formula, we get:
New price = (1 + 0.4) * ($4.50 - $1.80)
= 1.4 * $2.70
= $3.78
So the new price of the speaker after the sale and the subsequent price increase is $3.78.
If you want to invest $20,000 in a no-load mutual fund with a 6.5% yield, how much will you earn each year?
If you want to invest $20,000 in a no-load mutual fund with a 6.5% yield then 1300 we earn each year.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
The amount to invest is $20,000
Twenty thousand is the investment
and 6.5% is the yield.
We need to find how much we earn in each year.
Convert 6.5% to decimal
6.5/100=0.065
Multiply 0.065 with the 20000
0.65×20000
1300
Hence, we earn 1300 each year as an interest.
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:) anything helps. I dont understand
The values of x in the triangles are (a) 15 and (b) 4
How to determine the values of x in the figures?From the question, we have the following parameters that can be used in our computation:
Triangle 1 and Triangle 2
Solving triangle 1
In this triangle, we can see that the side lengths of the triangles are congruent
This means that the triangles is an equilateral triangle
The individual angles in an equilateral triangle are 60 degrees
So, we have the following representation
4x = 60
Divide both sides of the equation by 4
x = 15
So, the value of x is 15
Solving triangle 2
In this triangle, we can see that the length KM of the triangle divides the length JL into congruent parts
This means that the JM and LM are congruent
So, we have the following representation
x + 1 = 5
Subtract from both sides of the equation by 1
x = 4
So, the value of x is 4
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The side effects of a new drug are being tested against a placebo. A simple random sample of 565 patients yields (he results below. At a significance level of & = 0.10,(S there enough evidence to conclude that the treatment is independent of the side effect of nausea?
At a significance level of 0.10, there is enough evidence to conclude that the treatment is dependent to the side effect of Nausea
How to solve chi square statistics?The observed values are given as;
Result Drug Placebo Total
Nausea 36 13 49
No Nausea 254 262 516
Total 290 275 565
The expected values are as follows;
EXPECTED
DRUG PLACEBO
NAUSEA (290 * 49/565) = 25.150442 (275*49/565) = 23.849558
NO NAUSEA (290*516/565) = 264.849558 (275*516/565) = 251.150442
Test statistic = ∑((observed - (expected)²)/expected = ∑(O - E²)/E
This gives the test statistic as;
DRUG PLACEBO
NAUSEA 4.680351 4.935643
NO NAUSEA 0.444452 0.468695
∑(O - E²)/E = 10.52914
From a chi square calculator, our critical Value = 2.71
The conditions are;
If (calculated value > crit Value), then we reject Null hypothesis and accept the Alternative hypothesis
If (calculated value < critical value) we accept Null hypothesis and reject Alternative hypothesis
We are given;
Null Hypothesis; The two variables are independent
Alternative Hypothesis; The two variables are dependent
Since (10.52914 > 2.71) we reject Null Hypothesis and Accept Alt Hypothesis
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the point (-4,-6,10) lies on the surface of a sphere with centre (2,3,-1). hence find the volume of the sphere
The radius of the sphere with the given point and the center is √238.
Here we have to find the radius of the sphere.
Given data:
The point on the surface of a sphere is (-4, -6, 10) and the point on the center is (2, 3, -1).
The formula for the radius:
r² = (x2 - x1)² + (y2 - y1)² + (z2 - z1)²
where (x1, y1, z1) = point on the center
(x2, y2, z2) = point on the sphere
Now putting the values we have
r² = (-4-2)² + ( -6-3)² + ( 10 +1)²
=( -6)² +(- 9)² + (11)²
= 36 + 81 + 121
= 238
r = √238.
Therefore the radius is √ 238.
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given the system of inequalities below, determine the shape of the feasible region and find the vertices of the feasible region. report your vertices starting with the one which has the smallest x-value. if more than one vertex has the same, smallest x-value, start with the one that has the smallest y-value. proceed clockwise from the first vertex. leave any unnecessary answer spaces blank. x+y<5 8x + y >7 x >0 y>0 The feasible region is Unbounded The first vertex is The second vertex is The third vertex is The fourth vertex is
The area on the graph that is not shaded is the region of feasibility. The shape is a triangle and the vertices of the feasible region are: (5,1.5), (.75,.75), (1.5,.5)
The system of inequalities below, We need to determine the shape of the feasible region and find the vertices of the feasible region
x+y<=2
3x+y>=3
x+3y>=3
x>=0
y>=0
Now, we would graph with the following inequalities
x+y>=2
3x+y<=3
x+3y<=3
x<=0
y<=0
Therefore, the area on the graph that is not shaded is the region of feasibility and the shape is a triangle, the vertices of the feasible region are: (5,1.5) (0.75, 0.75), (1.5,.5).
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A bag has four balls labeled A, B, C, and D. One ball will be randomly picked, and its letter will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of choosing the letter A. If there is more than one element in the set, separate them with commas.
Answer:
B
hope you like it
Please help I’m really confused about this please help asap I’ll give brainliest if correct
Answer:
p=31
Step-by-step explanation:
sum of all three angles of any triangle equal 180 degrees
2p+(p+46)+(p+10)=180
4p+56=180
-56. -56
4p=124
/4. /4
p=31
hopes this helps please mark brainliest
Suppose a bag of colored marbles contains 33 marbles numbered 1 to 33. If you draw one marble at a time from the bag, without replacement, how many different ways can you draw all of the marbles from the bag? Remember that "without replacement" means that the marbles are not returned to the bag after they are chosen. Write your answer in factorial notation.
The ways you can draw all of the marbles from the bag is 33! ways
How to determine the ways you can draw all of the marbles from the bag?From the question, we have the following parameters that can be used in our computation:
Total number of marbles, n = 33
Total numbers of marbles picked at a time, r = 1
From the question, the marbles are selected without replacement
This means that the number of ways the marbles can be drawn from the bag is calculated using the following factorial formula
Total = n!
Where
n = 33
Substitute the known values in the above equation
Total = 33!
Apply the factorial formula
n! = n * (n - 1) * (n - 2) * .... * 1
So, we have
Total = 33 * 32 * 31 * 30 * .... * 1
Evaluate
Total = 8.6833176e+36
Hence, the number of ways is 33!
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