Here is a tree diagram to represent the sample space of Jill tossing a coin three times:
H T
/ \ / \
H T H T
/ \ / \ / \ / \
H T H T H T H T
What is sample space?The concept of the sample space is fundamental to the calculation of probabilities because it defines the set of all possible outcomes that we are interested in measuring the likelihood of. By specifying the sample space, we can define events (subsets of the sample space) and assign probabilities to those events.
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Mario is training for a mile-long swim race. In the first week of training, he swims 3/5 three times, 9/10 two times and 23/25 two times . How many total miles did he swim in the first week of training?
To find out how many total miles Mario swam in the first week of training, we need to add up the distances he swam each time:
3/5 + 3/5 + 3/5 + 9/10 + 9/10 + 23/25 + 23/25
To add these fractions, we need to find a common denominator. The smallest common multiple of 5, 10, and 25 is 50.
3/5 = 30/50
9/10 = 45/50
23/25 = 46/50
Now we can add the fractions:
30/50 + 30/50 + 30/50 + 45/50 + 45/50 + 46/50 + 46/50
= (30 + 30 + 30 + 45 + 45 + 46 + 46)/50
= 272/50
= 5.44
Therefore, Mario swam a total of 5.44 miles in the first week of training.
A biomedical manufacturing process has only 12.5% chance of producing a commercially successful result. The mean number of processes to be performed before a commercially successful one is?
The mean number of processes to be performed before a commercially successful one is 8.
The probability of success in each attempt is 0.125, so the parameter of the geometric distribution is p=0.125.
The mean of a geometric distribution with parameter p is equal to 1/p, so:
Mean = 1/p = 1/0.125 = 8
Therefore, the mean number of processes to be performed before a commercially successful one is 8.
In probability and statistics, the mean (or average) is a measure of the central tendency of a set of numbers. It is calculated by adding up all the numbers in a set and then dividing the sum by the total number of values in the set. The mean is a commonly used measure of the central tendency because it takes into account all the values in the set and provides a single value that represents the "typical" value.
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If the smaller of two numbers is one-half of the larger number and the sum of the two numbers is 63, find the numbers.
Answer:
21 and 42
Step-by-step explanation:
Lets say x and y are our numbers. x is the smaller number, y is the larger.
We can construct the equations:
x = 0.5y
x + y = 63
Substitute 0.5y for x in the second equation.
0.5y + y = 63
1.5y = 63
y = 42.
Plug y into the first equation.
x = 0.5 * 42
x = 21.
Your numbers are 21 and 42.
100 POINTS!
Question:
Answer: the answer is f
Step-by-step explanation:
Answer:
answer is f
Step-by-step explanation:
In circle X, m/VWU = 43°. Solve for x if mVU = (7x + 46)°. If necessary,
round your answer to the nearest tenth.
U
V
W
The measure of angle x of the circle is x = 5.7
Given data ,
Let the center of the circle be represented as x
Now , the value of x is given by
The measure of angle ∠VWU = 43°
And , the measure of arc VU = ( 7x + 46 )°
Now , from the arc theorem of circle , we get
mVU = 2 ∠VWU
On simplifying , we get
2 ( 43 ) = ( 7x + 46 )
7x + 46 = 86
Subtracting 46 on both sides , we get
7x = 40
Divide by 7 on both sides , we get
x = 5.71
Hence , the measure of x of circle is x = 5.7
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40
Selena is training for a race. Last week, she ran 4 miles each day on 3 different
days. Use the symbol X to make an array that represents the total number of miles
Selena ran last week.
Show your work.
The array that represents the total number of miles is X = 12
Given that;
Selena ran 4 miles per day
And she ran for 3 different days
Let the total miles she ran = X
therefore
X = miles of 1st day + miles of 2nd day + miles of 3rd day
⇒ X = 4 + 4 + 4
⇒ X = 12 miles
Thus the symbolic form of miles Selena ran is,
X = 12.
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I need help with this please
The matrix formed by performing R2 -> 4R1 + R2 on M is given as follows:
[tex]\left[\begin{array}{ccc}-4&3&1\\-18&9&8\end{array}\right][/tex]
How to do the row operation?The matrix in the context of this problem is defined as follows:
[tex]\left[\begin{array}{ccc}-4&3&1\\-2&-3&4\end{array}\right][/tex]
The rows are given as follows:
R1: -4, 3 and 1.R2: -2, -3 and 4.Hence the row 2 of the resulting matrix has the elements given as follows:
Column 1: 4 x -4 - 2 = -18.Column 2: 4 x 3 - 3 = 9.Column 3: 4 x 1 + 4 = 8.Thus the resulting matrix is:
[tex]\left[\begin{array}{ccc}-4&3&1\\-18&9&8\end{array}\right][/tex]
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8 is less than or equal to -3x +26
The solution is: x ≥ 6.
What is linear inequalities?
Linear inequality is an equation or expression that do not have a definite solution. Thus it consist of either of greater than, less than, greater than or equal to, less than or equal to etc.
In the given inequality question, we have;
8 is less than or equal to -3x +26
This can be expressed as;
8 ≤ -3x +26
so that collecting like terms,
8 - 26 ≤ -3x
-18 ≤ -3x
-18/ -3 ≤ x
6 ≤ x
Therefore, x ≥ 6.
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please help me quick on this math work, here is the screenshot what answer should I put? please help quick and right answers only!!
The functions that have a range of all real numbers include the following:
Option 1; f(x) = -x + 2
Option 3; [tex]h(x) = 2^x +1[/tex]
What is a range?In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following range for f(x) and h(x):
Range = {-∞, ∞}, y|y ∈ R, or all real numbers.
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The amount of money in a saving account increases bu D. 2% every month
Write a function for the amount of money in the accounts, after t months with an initial deposit of tr $ 100
By what' factor does the amount in the account increases ever meant every year?
The exponential function giving the balance of the account after t months is:
[tex]y = 100(1.02)^t[/tex]
The yearly growth factor is given as follows:
26.82%.
How to define an exponential function?An exponential function has the definition presented as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The parameter values for this problem are given as follows:
a = 100 -> initial deposit.b = 1.02 -> increase of 2% every month -> 1 + 0.02 = 1.02.Hence the function is:
[tex]y = 100(1.02)^t[/tex]
The yearly growth factor can be obtained as follows:
[tex](1.02)^{12} = 1.2682[/tex]
Increase of 26.82% each year, which is composed by 12 months.
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if you divide 781.253 by 100, what will be the place value of 2
Answer:
When you divide 781.253 by 100, you get 7.81253 as the result.
The digit 2 is in the hundredths place in the dividend 781.253. Since we are dividing by 100, which has two decimal places, we move the decimal point two places to the left in the dividend to get the quotient.
Therefore, the digit 2 is in the ten-thousandths place in the quotient 7.81253.
Patrick spent last summer working in construction with his dad, and he put of his earnings into a new high-yield savings account. The money in this savings account will increase by each . Write an exponential equation in the form Patrick's account, , after starting the account. that can model the amount of money in Use whole numbers, decimals, or simplified fractions for the values of and . □ \frac {\square }{\square } (\square ) If Patrick makes no other deposits or withdrawals, after how many will his account have more than ? Submit
a) An exponential equation in the form of y = a(b)ˣ that can model the amount of money (future value) in Patrick's account, y, x years after starting the account is y = 894(1.02)ˣ.
b) If Patrick makes no other deposits or withdrawals, after 5 years or approximately 6 years his account will have more than $1,000 (future value).
What is an exponential equation?An exponential equation is a mathematical function, written in the form of y = a(b)ˣ, where y is the ending value, a is the initial value, b is the growth or decay rate, and x is the exponent or number of years.
Thus, there are two types of exponential functions: exponential growth and exponential decay functions.
y = 894(1.02)^6
1,000 ≤ 894(1.02)ˣ
I/Y (Interest per year) = 2%
Present Value = $894
FV (Future Value) ≥ $-1,000
Results:
x = 5.658
x ≈ 6 years
= $1,006.79
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Complete Question:Patrick spent last summer working in construction with his dad, and he put $894 of his earnings into a new high-yield savings account. The money in this savings account will increase by 2% each year.
a) Write an exponential equation in the form of y = a(b)ˣ that can model the amount of money in Patrick's account, y, x years after starting the account. Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =
b) If Patrick makes no other deposits or withdrawals, after how many years will his account have more than $1,000?
The mean age of students in a Large math class is less than 30. A simple random sample of the students has a mean age of 29.3
Choose the correct answer
Option B is correct. The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim.
How to get the correct optionWe are utilizing the rare event rule and subjective estimation to verify the legitimacy of a claim. The assertion states that, within a considerable math class, the mean age of pupils is below 30. When selecting students at random, we observe that their average age is 29.3 years.
Given that the sample's mean age only subtlety fluctuates from the value expected (i.e., 30), the result obtained is not improbable if the premise holds true (thus validating the claim). Furthermore, it would be non-ambiguous even if the proposition is false due to the minuscule difference between 29.3 and 30 years of age.
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Can sum help me with this
Answer:
36°
Step-by-step explanation:
x+27+27+90=180
x=36°
Can the following list represent a complete probability model? P(2)= 1/12 P(3) = 2/3 P(4) = 1/4
Therefore , the solution of the given problem of probability comes out to be a complete probability model cannot be represented by this list.
What exactly is probability?The main objective of each considerations technique is to calculate the likelihood that a claim is true or that a particular incident will occur. Anything between 0 and 1, were 0 traditionally denotes a percentage and 1 typically denotes the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.
Here,
The probabilities assigned to the outcomes do not add up to 1, hence the following list cannot be a complete probability model.
=> P(2) + P(3) + P(4)
=> 1/12 + 2/3 + 1/4
=> (1 + 8 + 3) / 12
=> 12 / 12 = 1
In a complete probability model, the total of the probabilities should always be equal to 1, indicating that there is a probability of 1 that one of the events will occur.
In this instance, there is a missing probability since the sum of the probabilities assigned to the possible possibilities is less than 1.
Therefore, a complete probability model cannot be represented by this list.
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Need an answer step by step for this ASAP
Answer:
Step-by-step explanation:
There are 2 parts for your function. (see image)
y=4x, which is a line with a slope of 4 but x≠0, so there is a hole there
y=1 only at x=0 so the point is above the line
(a) Domain: All real numbers. There is a value for all x's
(b) There is no x-intercept because the graph never touches x
y-intercept (1,0) That's where the graph touch y
(c) see image
(d) range: (-∞, 0) U (0, +∞) there is a stop at 0 for y values
can also be written -∞<x<1 and 1<x<+∞
(e) yes it's continuous for domain but not range. because even though there is a jump at that point, i still have an x value. The jump causes me to not have a y value at y=0, that's why range is discontinuous
Rotate 180 degrees about the origin
The rotation transformation of the quadrilateral IJKL, to obtain the quadrilateral I'J'K'L', are; I'(-2, 3), J'(0, -2), K'(-2, -3), L'(-3, 1)
What is a rotation transformation?A rotation transformation is one in which the coordinates of a geometric figure are rotated about a point.
The coordinates of the vertex points on the figure are;
J(0, 2), K(2, 3), L(3, -1), and I(2, -3)
The coordinates of the point (x, y) following a rotation of 180° about the origin are (-x, -y)
Therefore, the coordinates of the image of the figure J(0, 2), K(2, 3), L(3, -1), and I(2, -3), following a rotation about the origin are;
J(0, 2) ⇒ J'(0, -2)
K(2, 3) ⇒ K'(-2, -3)
L(3, -1) ⇒ L'(-3, 1)
I(2, -3) ⇒ I'(-2, 3)
Therefore, we get;
The coordinates of the image are; I'(-2, 3), J'(0, -2), K'(-2, -3), L'(-3, 1)
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James is performing statistical analysis to determine whether the effects of the treatment in his experiment might actually have reflected a chance occurrence; Kendra is performing an analysis to combine the results of a number of experiments to yield an overall conclusion. James is performing a _____, Kendra, a _____.
Hello !
James is performing statistical analysis to determine whether the effects of the treatment in his experiment might actually have reflected a chance occurrence; Kendra is performing an analysis to combine the results of a number of experiments to yield an overall conclusion. James is performing a significance test, Kendra, a meta-analysis.
Find the LCD of the given rational equation
The LCD of the rational equation above is 4(x + 7)(x - 7).
What is the explanation for the above response?To find the LCD (Least Common Denominator) of the given rational equation, we need to factor the denominators of each fraction and then take the product of the highest powers of each factor.
The first denominator, x^2 - 49, can be factored using the difference of squares formula:
x^2 - 49 = (x + 7)(x - 7)
The second denominator, 4x + 28, can be factored by factoring out the greatest common factor:
4x + 28 = 4(x + 7)
Therefore, the LCD is the product of the highest powers of each factor, which is:
LCD = 4(x + 7)(x - 7)
So we need to multiply each term in the equation by an appropriate form of 1 so that the denominators of all the fractions become the LCD, 4(x + 7)(x - 7).
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Please help me with this question
Answer:
A
Step-by-step explanation:
based on summation, this is an integral from 1 to 6
answer choice A makes sense since plugging in K value gives appropriate riemann sum
write the equation of a circle with the dynameter is 14 and whose Center is (-4,6)
Answer:
The equation of the circle with a diameter of 14 and whose center is (-4,6) is [tex]x^{2}+y^2+8x-12y+3=0[/tex]
Step-by-step explanation:
Given that diameter is 14. So, the radius is 14/2 which is equal to 7.
Also, the center is (-4,6).
We know that the equation of a circle with center (h,k) and radius r units is
[tex](x - h)^2+(y-k)^2=r^2 .[/tex]
Here, h=-4, k=6 and r=7.
Putting these values in the above equation,
[tex](x - (-4))^2+(y-6)^2=7^2 .[/tex]
[tex](x +4)^2+(y-6)^2=49 .[/tex]
On solving, the equation of the circle is
[tex]x^2+y^2+8x+-12y+3=0[/tex].
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Students in a math class recorded the number of text messages they received the previous day. How many students received at least 10 messages? Number of text messages line plot from 0 to 25 by fives. 5 has 2 marks, 10 has 3 marks, 15 has 2 marks, 20 has 4 marks, and 25 has 5 marks. 14 students 11 students 3 students 2 students
Answer:
Step-by-step explanation:
same goes 4 him i though he loved me but 10 =5x2
Describe the graph proportional relationship represented by the equation y=5.5x
Suppose a normal distribution has a mean of 34 and a standard deviation of
2. What is the probability that a data value is between 30 and 36? Round your
answer to the nearest tenth of a percent.
Answer:
it’s 86.6%
Step-by-step explanation:
could be wrong
what is 9v+–3v+–4v–2+1 simplified
Answer:
2v-1
Step-by-step explanation:
9v+-3v+-4v-2+1
=9v-3v-4v-1
=6v-4v-1
=2v-1
Find the coefficient of determination. Round to three decimal place
The coefficient of determination, given the total variation and the explained variation would be 0.898.
How to find the coefficient of determination ?R-squared, or the coefficient of determination, represents the proportion of variation within a response variable that can be explained by the regression model. This calculation is achieved through dividing the explained variation by the total variation.
We are given the explained variation as 18. 592. We are also given the total variation as 20. 711.
The coefficient of determination is:
= explained variation / total variation
= 18. 592 / 20.711
= 0. 898
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Full question is:
A regression equation is obtained for a collection of paired data. It is found that the total variation is 20.711, the explained variation is 18.592, and the unexplained variation is 2.119.
Find the coefficient of determination. Round to three decimal place
PLEASE HURRY
Write the vector v in terms of i and j whose magnitude and direction angle are given ||v|| = 2/3, theta = 116 deg
The vector v can be expressed as v = -0.161 i + 0.618 j, where i and j are the unit vectors
To express a vector v in terms of i and j, we need to find its x and y components. The magnitude ||v|| of a vector is given by:
||v|| = √(v₁² + v₂²)
where v₁ and v₂ are the x and y components of v, respectively.
The direction angle θ of a vector with respect to the positive x-axis is given by:
θ = atan(v₂/v₁)
where atan denotes the arctangent function.
In this problem, we are given that the magnitude ||v|| of the vector v is 2/3, and its direction angle θ with respect to the positive x-axis is 116 degrees. Therefore, we can write:
||v|| = √(v₁² + v₂²) = 2/3
θ = atan(v₂/v₁) = 116°
Solving for the x and y components, we get:
v₁ = ||v|| cos(θ) = (2/3) cos(116°) ≈ -0.161
v₂ = ||v|| sin(θ) = (2/3) sin(116°) ≈ 0.618
Therefore, the vector v can be expressed as:
v = -0.161 i + 0.618 j
where i and j are the unit vectors in the x and y directions, respectively.
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A recursive rule for a geometric sequence is a1=
4
9
;an=3an−1.
What is the explicit rule for this sequence?
ANSWER:
4
9
(3n−1) just took the test
The explicit rule for the geometric sequence with a recursive rule of a1=4/9 and an=3an-1 is: an = (4/9) * (3)^(n-1)
What is the explicit rule for this sequence?To find the explicit rule for a geometric sequence, we use the formula:
an = a1 * r^(n-1)
where a1 is the first term, r is the common ratio, and n is the term number.
Given the recursive rule for this geometric sequence as a1=4/9 and an=3an-1, we can find the common ratio:
an = 3an-1
an/an-1 = 3/1
r = 3
Now we can use the formula to find the explicit rule:
an = a1 * r^(n-1)
an = (4/9) * (3)^(n-1)
Therefore, the explicit rule is: an = (4/9) * (3)^(n-1)
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Enter your answer in the box.
Answer:
- 63
Step-by-step explanation:
When x = 0, x - 1 = -1
f(x - 1) = f(-1) = 21 from the table
-3f(x-1) = -3 (21)
= -63
Consider the line y = -8x + 7.
Find the equation of the line that is perpendicular to this line and passes through the point (-5, 3).
Find the equation of the line that is parallel to this line and passes through the point (-5, 3).
The equation of the line that is parallel to the line that passes through the point (7, 6) is y = 8x - 50.
What is a line?A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature.
Since lines can exist embedded in two, three, or higher dimensions environments, they are one-dimensional objects.
The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.
So, the lines with the same slope but a different y-intercept are said to be parallel.
Therefore, we must use the same slope to plug in the point (7, 6) and solve for the y-intercept.
We thus have:
y = 8x + b
6 = 8(7) + b
6 = 56 + b
b + 56 = 6
b + 56 - 56 = 6 - 56
b = -50
The equation is: y = 8x - 50
Therefore, the equation of the line that is parallel to the line that passes through the point (7, 6) is y = 8x - 50.
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Correct question:
Consider the line y = 8x - 4. Find the equation of the line that is parallel to this line and passes through the point (7, 6).