The event the number is even and less than 12 covers the entire sample space of this experiment.
What is sample space?
In probability theory, the set of all feasible outcomes or outcomes of an experiment or random trial is referred to as the sample space. The sample points, or potential ordered outcomes, are listed as elements in the set used to represent the sample space.
Given:
A number is selected at random from the set {2, 4, 6, 8, 10}.
Let's examine each instance:
A. There are more than two.
When we get number 2, this does not apply to the situation. 2 is equal to 2 and not greater, therefore.
B. The number is not divisible by 5, whereas 10 and 5 are. As a result, the sample space is not completely covered.
C. It's an even number or less than 12.
Let's note that every number from "2, 4, 6, 8, 10" is less than 12, indicating that the event's even portion has no bearing. This encompasses the whole sample area.
D. Neither the number is prime nor is it a composite.
There cannot be a number that is neither prime nor composite because they are mutually exclusive terms in mathematics. No number of the set is covered by this event.
E. The number's square root is less than 3.
This excludes the number 10, whose square root is approximately 3,16, which is greater than 3.
Hence, the event the number is even and less than 12 covers the entire sample space of this experiment.
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75 POINTS!!
Write a system of equations to model Monica's savings and Shanna's savings. Let x represent the number of weeks and y represent savings.
Type your response in the box
The system of equations to model Monica's and Shanna's savings is y = 10x + 50 for Monica and y = 15x + 100 for Shanna.
To model Monica's savings and Shanna's savings using a system of equations, we can use the variables x and y, where x represents the number of weeks and y represents the savings.
Let's start by defining the equation for Monica's savings. We'll use the equation y = mx + b, where m represents the savings per week and b represents the initial savings.
Next, let's define the equation for Shanna's savings. We'll use the same equation, y = mx + b, but with different values for m and b.
For example, let's say Monica saves $10 per week and initially has $50 in savings. The equation for Monica's savings would be y = 10x + 50.
Now, let's say Shanna saves $15 per week and initially has $100 in savings. The equation for Shanna's savings would be y = 15x + 100.
So, the system of equations to model Monica's and Shanna's savings would be:
Monica: y = 10x + 50
Shanna: y = 15x + 100
By using this system of equations, we can determine Monica's and Shanna's savings at any given number of weeks, x. Simply substitute the value of x into the equations and solve for y.
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Natsumi paints walls for a living. She paints at a constant speed, and then she takes a constant amount of time to clean up. The table compares the total area natsumi paints (in square meters) and the time it takes natsumi to finish painting and cleaning up (in hours). Area (square meters) time (hours) 303030 222 454545 2. 752. 752, point, 75 606060 3. 53. 53, point, 5 how long does it take natsumi to paint 111 square meter?.
To paint 111 square meters of walls, it takes 6.05 hours. The result is obtained by using the speed of Natsumi to paint per hour.
How to calculate the time to paint the wall?With a constant speed to paint the wall, Natsumi has done painting as the shown data in the table.
Area (square meters) - Time (hours)
30 square meters - 2 hours45 square meters - 2.75 hours60 square meters - 3.5 hoursThis is a problem with comparison. Let's take two samples of the data!
45 - 30 = 15 square meters3.5 - 2.75 = 0.75 hoursFrom the data, we know that for every additional 15 square meters, the time needed increases by 0.75 hours.
Then, we can continue the table.
75 square meters - 4.25 hours90 square meters - 5 hours105 square meters - 5.75 hours111 square meters - x hoursThe speed of Natsumi to paint per hour is
15/0.75 = 20 square meters/hour
The remain area
111 - 105 = 6 square meters
Time needed for the remain area is
6/20 = 0.3 hours
To paint 111 square meters of walls, it takes
x = 5.75 hours + 0.3 hours
x = 6.05 hours
Hence, time needed to finish painting and cleaning up 111 square meters of walls is 6.05 hours.
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What is the sum of 2/8+3/9?????
Answer:42/72 simplify =7/ 12
Step-by-step explanation:
given that about 25% of the mammalian genome is associated with genes, including introns and regulatory sequence, what would be the approximate average length of dna per gene if the genome contained 20,000 genes?
According to the question,
Given data in the question.
If the genome contained 20,000 genes, the average length of DNA per gene will be 40,000 base pairs.
What is the average length of DNA per gene?
Only 2.5% of the human genome is protein-coding. Introns make up the remaining 97.5%. The male nuclear diploid genome is 6.27 Giga base pairs (G b p), 205.00 cm (cm) long, and 6.41 picograms in weight (p g). Female measurements are 6.37 G b p, 208.23 cm, and 6.51 p g
For a 25% mammalian genome with 20,000 genes, the total number of base pairs, which is the length of DNA per gene, will be approximately double the payment of genes contained in the genome, in this case 40,000.
The average length of DNA per gene, assuming 20,000 genes in the genome, is 40,000 base pairs.
How long does DNA typically be per gene?
Only 2.5% of the human genome codes for proteins. The remaining 97.5% is made up of introns. The size and weight of the male nuclear diploid genome are 6.27 Giga base pairs (G bp), 205.00 centimetres (cm), and 6.41 picograms (p g). 6.37 G bp, 208.23 cm, and 6.51 p g are the female measurements.
The total number of base pairs, which is 20,000 for a 25% mammalian genome with 20,000 genes,
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The average length of DNA per gene would be 40,000 base pairs if the genome had 20,000 genes.
What is the average length of DNA per gene?The human genome only codes for proteins in 2.5% of it. The remaining 97.5% are introns. The male nuclear diploid genome measures 205.00 centimeters (cm), is 6.27 Gigabase pairs (Gbp), and weighs 6.41 picograms (pg). 208.23 cm, 6.51 pg, and 6.37 Gbp are the female measurements.
Is genetics a lot of math?Although there may be some hereditary component to math aptitude, this probably only accounts for a small portion of it. Even in the current study, genetics alone could only account for 20% of math prowess. According to Libertus, "this leaves more than 80% of the variety in children's math aptitude unexplained."
The overall number of base pairs, which is the length of DNA per gene, will be roughly twice the number of genes present in the genome, in this example 40,000, for a 25% mammalian genome with 20,000 genes.
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which is more 2,005 pounds or 1 ton
Answer: 2005 pounds
Step-by-step explanation:
1 ton is 2000 pounds
Answer:
2,005 pounds
Step-by-step explanation:
Hope it helps!
Consider the function y = 3 | x - 1 | +3 under the restricted domain 0 ≤ x ≤ 3. The range is a ≤ y ≤b.
The range of the given function y = 3 | x - 1 | +3 for the domain 0 ≤ x ≤ 3 will be [3,9].
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
The given function has been drawn below.
The minimum value of the function in interval 0 ≤ x ≤ 3 is 3 while the maximum value is 9.
The range will be [3,9].
Hence "For the domain 0 x 3, the provided function, y = 3 | x - 1 | +3, will have a range of [3,9].".
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What is the rule about splitting infinitives How would you rewrite the quote above?
The rule about splitting infinitives is avoid using a word between TO and the verb if at all possible. The correct quote is "To go boldly where no one has gone before."
In the given question, we have to explain the rule about splitting infinitives and how we rewrite the quote based on this rule
The given quote is
"To boldly go where no one has gone before."
Splitting infinitives is prohibited according to grammar rules. Avoid using a word between TO and the verb if at all possible. Split infinitives are improper grammatically, therefore avoid using them.
So, in order to change this quote, you should:
"To go boldly where no one has gone before."
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The right question is:
What is the rule about splitting infinitives? How would you rewrite the quote above based on this rule?
read this quote that comes from a popular television and movie franchise:
"To boldly go where no one has gone before."
let nn be the least positive integer that is both 2222 percent less than one integer and 1616 percent greater than another integer. find the remainder when nn is divided by 10001000.
The smallest integers k and m that satisfy this are k=1450 and m=975, so N = 1131.
How to solve word problems?
It's actually fairly easy to solve word problems using a tried-and-true step-by-step approach.
Aloud to yourself, read the issue.Make a Drawing.Ask yourself, "What am I looking for?"List the items that have been provided.Locate the key phrases.Solve.Verify your work.If N is 22 percent less than one integer k, then
N = 78/100 k
= 38k/100
In N is 16 percent greater than another integer m, So
N = 116m / 100
= 29m/25.
Therefore, k is divisible by 50 and m is divisible by 25.
Setting these two equal, we have 38k/100 = 29m/25.Multiplying by $50$ on both sides, we get 39k = 58m
Hence, The smallest integers k and m that satisfy this are k=1450 and m=975, so N = 1131.
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Annie was given two pieces of information and must write the equation of a line. She knows the line crosses the y-axis at the point(0,6)and has a slope of7. What is the equation of the line?
A.y=7x+6
B.y=7x−6
C.y=6x+7
D.y=−6x+7
half of the quantity of 6 less than a number f is 4. how do u put in the algebraic form
Wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww
Solve the system
x+y=6
5x-y=3
by graphing and by substitution. Compare the
methods. Which method is more accurate? Explain
We can solve the given linear equations using graphing and substitution method. Substitution is more accurate, since it provides an exact answer.(x,y)=(1.5,4.5) is the answer for the given linear equation.
What is Substitution and Graphing method ?As Math Planet correctly notes, to solve a system of linear equations by graphing, we simply graph both equations in the same coordinate plane and locate the intersection of the two lines. Substitution-Based Graphing of Linear Equations. By substituting values for x, we may obtain the appropriate y values and display the points on a line with the equation y = ax + b. (x, y). Two points must be produced by replacement in order to create a line between them.
Calculation:x + y = 6 → y = 6 − x
5x − y = 3
⇒5x − (6 − x) = 3
⇒5x + x − 6 = 3
⇒6x = 9
⇒x = 1.5
⇒1.5 + y = 6
⇒y = 4.5
(x,y)=(1.5,4.5)
We can solve the given linear equations using graphing and substitution method. Substitution is more accurate, since it provides an exact answer.(x,y)=(1.5,4.5) is the answer for the given linear equation.
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formula for area and perimeter of a circle
Answer:a=pi*r^2
Step-by-step explanation:
area=pi*radius squared
three people A, B, C, are to share 44,000usd among themselves in the ration a:b:c: respectively .if a = ½b c=⅓b how much will B receive more than C
There are B receives an amount of $35,733.33 more than C.
What is Ratio?A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
Let "b" be the amount that B receives.
A receives 1/2 × b, and C receives 1/3 × b.
The total amount that A and C receive is 1/2 × b + 1/3 × b = 5/6 × b.
Since A, B, and C are to share $44,000 in the ratio a:b:c, the total amount that A and C receive is 5/6 × b = $44,000.
Solving this equation for b, we get:
b = $44,000 / (5/6)
b = $44,000 x (6/5)
Apply the multiplication operation, and we get
b = $53,600
Therefore, B receives $53,600, and C receives 1/3 x $53,600 = $17,866.67.
B receives $53,600 - $17,866.67 = $35,733.33 more than C.
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if you subtract 12 from my number and multiply the difference by -3, the result is -27. what is my number
Answer:
21
Step-by-step explanation:
27/3 + 12
w(t)-2t +3; Find w(0)
Answer:
3
Step-by-step explanation:
w(0) = 2(0) + 3
w(0) = 0 + 3
w(0) = 3
the mean of a distribution of data is 3.56 . if the distribution is symmetric , what is the median ?
Since, the mean of distribution of data is 3.56 then the median is also 3.56 because the distribution is symmetric.
Symmetric Distribution:
A symmetric distribution is when the values of a variable occur with regular frequency, often the mean, median, and mode all occurring at the same point. A line in the middle of the chart indicates that the two planes are mirror images of each other.
In graphical form, a symmetric distribution is displayed as a normal distribution (that is, a bell curve). Symmetric distribution is a central concept in technical trading as it assumes that the price movements of an asset over time follow a symmetric distribution curve. A symmetric distribution can be contrasted with an asymmetric distribution.
Relation between Median and Mean
A distribution always has a median and a mode, but not always a mean. Consider the Cauchy distribution. No average exists. Modes are always present, but may not be unique. This means that you can get a distribution that is not unimodal (that is, multimodal).
So, if we have a symmetric distribution with a mean and the distribution is unimodal, we can say:
Mean = Median = Mode
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Solve the equation
5+16w=6-45
Answer:
w = 6 / 21.
Step-by-step explanation:
To solve this equation, we first need to get all of the terms with the variable w on one side of the equation and all of the constants on the other side. To do this, we can use the distributive property to combine like terms on each side of the equation.
We can use the distributive property to combine the two terms on the left side of the equation to get 5 + 16w = 21w. This gives us the equation 21w = 6 - 45.
Next, we can add 45 to both sides of the equation to get 21w + 45 = 6 + 45. This simplifies to 21w + 45 = 51.
Finally, we can divide both sides of the equation by 21 to get the value of w. This gives us the equation w = (51 - 45) / 21 = 6 / 21.
Therefore, the solution to the equation is w = 6 / 21.
-0.47x+0.27x = 5.8 Solve for X
Answer:
-29
Step-by-step explanation:
you add both decimals together you get -.2x=5.8 you divide both sides by -.2x and you get x=-29
Monica would like to save up $10,000. She is going to make monthly deposits for 5 years into an account that will get 2.05% compounded monthly. How much does she need to deposit in the account to reach her goal?
The amount of money that Monica needs to deposit each month in order to save up $10,000 in 5 years is; $91017.17865
How to solve compound interest problems?The formula for compound interest is;
A = P (1 + r/n)^(nt)
where;
A is the total amount of money in the account after the interest has been compounded.
P is the initial deposit.
r is the interest rate.
n is the number of times the interest is compounded in a year
t is the number of years the money is deposited.
We are told that Monica would like to save up $10,000. Thus;
The initial deposit = $10,000.
The interest rate = 2.05%.
The number of times the interest is compounded per year; n = 12 (because the interest is compounded monthly),
The number of years the money is deposited; t = 5.
Plugging these values into the compound interest formula, we get:
A = 10000 (1 + (0.0205 / 12))^(12 * 5)
A = 10000 (1.001708333)^60
A = 10000 (1.101717865)
A = $101017.17865
Thus, the total amount of money in the account after 5 years will be $101017.17865.
Since Monica wants to save up $10,000, we can subtract this amount from the total amount in the account to find out how much she needs to deposit each month in order to reach her goal:
101017.17865 - 10000 = 91017.17865
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i need help asap pls help im on a time limit so pls help me
Answer:
What is even the question?
Step-by-step explanation:
A rectangular storage container without a lid is to have a volume of 10 m3. The length of its base is twice the width. Material for the base costs $5 per square meter. Material for the sides costs $3 per square meter. Let w denote the width of the base. Find a function in the variable w giving the cost C (in dollars) of constructing the box.
A function in the variable w giving the cost C is 81.77 dollars.
What is meant by volume?Volume is a unit of measurement for the area occupied in three dimensions. It is widely quantified and measured using SI-derived units, alternative imperial units, or US standard units (such as the gallon, quart, cubic inch). Volume and length (cubed) have a similar meaning.
First, volume was calculated using naturally occurring vessels with a similar shape, and then using standardized containers.
Surface area of an open lid container is:
A=2×sides+Base
So,
A=2(lh+wh)+lw
Cost of the base is $5 per square meter and the cost of the sides is $3 per square meter.
Now, the cost function is:
C=3×2(lh+wh)+5×lw
C=6(lh+wh)+51w
Here, the length is twice the width then,
l=2w
C=6(2wh+wh)+5×2w²
C=6(3wh)+10w²
C=18wh+10w²
And we know that the volume is,
V= lwh
2w²h=10
h=5/w²
C=18wh+10w²
C=18w×(5/w²)+10w²
C=(90/w)+w²
C'=(-90/w²)+20w
0=(-90/w)+20w
20w=(90/w²)
20w³=90
w³=45
w=1.65
C=(90/1.65)+10×1.65²
C=81.77
Therefore, a function in the variable w giving the cost C is 81.77 dollars.
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PLEASE HELPPPPP Determine the type of correlation represented in the scatter plot below.
The graph shows:
A. A perfect positive correlation
B A strong positive correlation
C. A weak postitive correlation
D. No correlation
E. A weak negative correlation
F. A strong negative correlation
G. A perfect negative correlation
The answer is weak negative correlation.
What is meant by correlation?Positive correlation: An increase or decrease in one variable causes an increase or decrease in the other when the values of the two variables move in the same direction.A drop or increase in one variable causes a decrease or increase in the other when the values of the two variables move in the opposite direction.No linear dependency or correlation exists.An illustration of how these connections appear in a graph is shown below:As a result, we can see from the provided image that there is a negative correlation between x and y, i.e., as x increases, y lowers. Additionally, the dispersion of the dots indicates a poor association.The degree to which two variables are linearly connected is expressed by the statistical concept of correlation (meaning they change together at a constant rate). It is a typical technique for outlining straightforward connections without stating cause and consequence.A statistical term known as correlation indicates the strength and direction of a relationship between two or more variables. It is expressed as a number. However, just because two variables are correlated does not necessarily imply that the change in one of the variables is what changed the values of the other.To learn more about correlation refer to:
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Need done asap !!
Point A :
Point B :
And what is the rate of change of y with respect to x for this line?
Rate of change :
10x+5=3x-23 how do u solve for x
Step 1: Subtract 5 from Both Sides
10x + 5 = 3x - 23
10x = 3x - 28
Step 2: Subtract 3x from Both Sides
10x = 3x - 28
7x = -28
Step 3: Divide Both Sides By 7
7x = -28
x = -4
Answer: x = -4
Hope this helps!
Answer:
-4
Step-by-step explanation:
Given,
10x+5=3x-23
10x-3x=(-23)-5
7x=-28
x=-28/7
x=-4
6.652 rounded to the nearest tenth
Answer: 6.7
Step-by-step explanation:
What are the vertex and range of y = |x − 5| 4? (5, 4); −[infinity] < y < [infinity] (5, 4); 4 ≤ y < [infinity] (−5, 4); −[infinity] < y < [infinity] (−5, 4); 4 ≤ y < [infinity]
The range and the vertex is 4 ≤ y < [infinity] and (5, 4).
To find the vertex, we can take the derivative of the function and set it equal to 0:
y' = |x − 5|' = 0
=> x − 5 = 0
=> x = 5
Then, we can plug x = 5 into the original equation to find the y-value at the vertex:
y = |x − 5| = |5 − 5| = |0| = 0
So, the vertex of y = |x − 5| is (5, 4).
To find the range, we need to consider the range of the absolute value function. The range of the absolute value function is:
−[infinity] < y < [infinity]. So, the range of y = |x − 5| is also −[infinity] < y < [infinity] (or 4 ≤ y < [infinity]).
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Find the measure of angle 1
Answer:
∠1 = 47°
Step-by-step explanation:
angles in a triangle add up to 180°
∠1 + 63 + 70 = 180
∠1 + 133 = 180
∠1 = 180 - 133
∠1 = 47°
The rules of a game allow a team to score either 2 points or 5 points, depending on the nature of the scoring play. If the final score between two teams was 34 to 29, and there were 18 scoring plays altogether, how many 5-point plays were there?
(Use only the digits 0 – 9 to enter a number.)
Answer:
9
Step-by-step explanation:
for this we make systems of equations
x= 2 points plays
y= 5 points play
2x+5y=34+29
2x+5y=63
x+y=18
-y. -y
x=18-y
2(18-y)+5y=63
36-2y+5y=63
16+3y=63
-36. -36
3y=27
/3. /3
y=9
hopes this helps
In the diagram, /\ABC \cong≅ /\DEF, write an equation and find the value of y, then write another question to find the value of x.
The values of x and y of the corresponding sides of the congruent triangles are;
y = 3.8
x = 4.6
How to solve congruent triangles?There are 5 main congruence postulates pertaining to congruent triangles and they are;
SSS - Side Side Side congruence postulate
SAS - Side Angle Side congruence postulate
ASA - Angle Side Angle congruence postulate
AAS - Angle Angle Side congruence postulate
HL - Hypotenuse Leg Congruence Postulate
Now, we are given the three sides of both triangles that are said to be congruent and this means that the three corresponding sides are congruent. Thus;
AB = DE;
10 = 3x - y ------(1)
Similarly;
BC = EF
18.8 = 6y - 4 -----(2)
Add 4 to both sides in equation 2 to get;
22.8 = 6y
y = 22.8/6
y = 3.8
Thus;
10 = 3x - 3.8
3x = 13.8
x = 13.8/3
x = 4.6
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what needs to be known to determine the critical values for an independent-samples t test?
Total degree of freedom should be known to determine the critical values for an independent sample t test.
The largest number of logically independent values—that is, values with the freedom to change—in the data sample is referred to as the degree of freedom. When calculating degrees of freedom, one is subtracted from the number of items in the data sample.
An independent t-test must be performed, and the following is required: a single categorical variable with two levels and groups that is independent. a single ongoing dependent variable.
For instance, the number of degrees of freedom to be employed in computations would be n - 1 if the sample size on a chi-square test was 'n'. to figure out the degrees of freedom for an N=9 sample size. 9 less 1 equals 8 (df=9-1=8).
Hence we get the required answer.
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