The probability that a continuous random variable takes a value less than zero is any number between zero and one.
The standard deviation of a normal distribution cannot be negative.
For any continuous random variable, the probability that it takes a value less than zero is given by the cumulative distribution function (CDF) at zero. Since the CDF is a monotonically increasing function that ranges from 0 to 1, the probability that the random variable takes a value less than zero is any number between 0 and 1, inclusive.
The standard deviation of a normal distribution is always a positive number since it is the square root of the variance, which is defined as the average of the squared deviations from the mean.
Since the deviations are squared, they are always non-negative, and their average (the variance) cannot be negative. Therefore, the standard deviation of a normal distribution cannot be negative.
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Consider the right triangle.
What is the value of x?
Responses
3
3
5
5
7
7
9
The value of x in the right triangle with acute angles 8x and 4x + 6 is 7
Calculating what is the value of x?From the question, we have the following parameters that can be used in our computation:
The right triangle with acute angles 8x and 4x + 6
The sum of acute angles in a right triangle is 90
Using the above as a guide, we have the following:
8x + 4x + 6 = 90
So, we have
12x = 84
Divide by 12
x = 7
Hence, the value of x is 7
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a box with a square base and open top must have a volume of 62,500 cm3. find the dimensions of the box that minimize the amount of material used. sides of base 107.72 incorrect: your answer is incorrect. cm height incorrect: your answer is incorrect. cm
The dimensions of the box that minimize the amount of material used are a base side length of 25 cm and a height of 25 cm.
Let x be the side length of the square base and h be the height of the box. Since the box has a square base, the volume of the box is V = x²h. We want to minimize the amount of material used, which is given by the surface area of the box, A = x² + 4xh.
Using the volume constraint, we can solve for h in terms of x: h = V / x² = 62,500 / x². Substituting this into the expression for A, we get A = x² + 4x(62,500 / x²) = x² + 250,000 / x.
To minimize A, we take its derivative with respect to x and set it equal to zero: dA/dx = 2x - 250,000 / x² = 0. Solving for x, we get x = 25 cm. Substituting this back into the expression for h, we get h = 25 cm.
Therefore, base side length is 25 cm and height is 25 cm.
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Let a, b, c be any integers. For each of the following
statements, if it is true prove it or if it is false provide a
counterexample.
If b = 0(mod a) and c = 0(mod b), then c = 0(mod a)
We have shown that if b = 0(mod a) and c = 0(mod b), then c = 0(mod a).
The statement "If b = 0(mod a) and c = 0(mod b), then c = 0(mod a)" is true.
To prove this, we need to show that if b is a multiple of a and c is a multiple of b, then c is a multiple of a.
Suppose that b = ak and c = bk' for some integers k and k'. Then, we have:
c = bk' = (ak)k' = a(kk')
Since k and k' are both integers, their product kk' is also an integer. Therefore, we can write c = a(kk'), which shows that c is a multiple of a.
Hence, we have shown that if b = 0(mod a) and c = 0(mod b), then c = 0(mod a).
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Given field F = x ax + y ay. Evaluate the left side of Green's Theorem where C -> rectangular path around the region: x = 2.8 to 8, y = 2.1 to 7.5, z = 0
The left side of Green's theorem for this vector field and rectangular path is 32.28 ay.
To evaluate the left side of Green's theorem, we need to compute the line integral of the vector field F along the boundary of the region enclosed by the rectangular path C.
First, let's parameterize the rectangular path C as follows:
r(t) = (x(t), y(t)), where 2.8 ≤ x ≤ 8 and 2.1 ≤ y ≤ 7.5.
The boundary of the rectangular path C is composed of four line segments:
From (2.8, 2.1) to (8, 2.1): r(t) = (t, 2.1), where 2.8 ≤ t ≤ 8.
From (8, 2.1) to (8, 7.5): r(t) = (8, t), where 2.1 ≤ t ≤ 7.5.
From (8, 7.5) to (2.8, 7.5): r(t) = (t, 7.5), where 8 ≤ t ≤ 2.8 (note the reverse order).
From (2.8, 7.5) to (2.8, 2.1): r(t) = (2.8, t), where 7.5 ≥ t ≥ 2.1 (note the reverse order).
We can now evaluate the line integral of F along each of these line segments using the parameterization r(t) and the definition of the line integral:
∫_C F · dr = ∫_(C1) F · dr + ∫_(C2) F · dr + ∫_(C3) F · dr + ∫_(C4) F · dr,
where the dot product F · dr is given by:
F · dr = (x dx + y dy) · (dx ax + dy ay) = x dx^2 + y dy^2.
Let's evaluate each of the line integrals separately:
∫_(C1) F · dr = ∫_(2.8)^8 (t ax + 2.1 ay) · dt = (8 - 2.8) ax + 2.1 (0) ay = 5.2 ax
∫_(C2) F · dr = ∫_(2.1)^7.5 (8 ax + t ay) · dt = 8 (7.5 - 2.1) ay + 8 (0) ax = 46 ay
∫_(C3) F · dr = ∫_(8)^2.8 (t ax + 7.5 ay) · (-dt) = (8 - 2.8) ax + 7.5 (0) ay = -5.2 ax
∫_(C4) F · dr = ∫_(7.5)^2.1 (2.8 ax + t ay) · (-dt) = 2.8 (2.1 - 7.5) ay + 2.8 (0) ax = -13.72 ay
Therefore, the line integral of F along the boundary of the rectangular path C is:
∫_C F · dr = ∫_(C1) F · dr + ∫_(C2) F · dr + ∫_(C3) F · dr + ∫_(C4) F · dr = 5.2 ax + 46 ay - 5.2 ax - 13.72 ay = 32.28 ay.
So the left side of Green's theorem for this vector field and rectangular path is 32.28 ay.
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Find mZQPR. 5 P 48° R Q
The measure of the missing angle which is named ∠PQR = 84°
Why is this so?The first step to solving the problem is to identify the nature of the triangle.
Note that the information states that:
Side PQ and QR are equal,
This means that it is an isosceles triangle because only isosceles triangles have two equal sides.
Another property of isosceles triangles that will help determine the m∠PQR is that the angles at the base of those equal sides are always equal.
Since that is true, then,
∠PQR = 180 - (QPR x 2 )
We know ∠QPR is 48°, so
∠PQR = 180 - (48x 2 )
∠PQR = 180 - 96
Thus,
∠PQR = 84°
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See attached image.
Mona pays $1. 00 for the first call of the day on her mobile phone plus $0. 15 per minute of the call. She paid $2. 95 for her first call today. Write an expression that you could use to calculate the length in minutes of the phone call
The expression to calculate the length in minutes of the phone call is:
(length of call in minutes) = (total cost - fixed cost) / (cost per minute)
Where the fixed cost is $1.00 and the cost per minute is $0.15.
Mona's mobile phone plan charges a fixed cost of $1.00 for the first call of the day and an additional $0.15 per minute for the length of the call. To calculate the length of the call in minutes, we need to subtract the fixed cost of $1.00 from the total cost of the call and then divide the result by the cost per minute of $0.15. This gives us the equation:
(length of call in minutes) = (total cost - fixed cost) / (cost per minute)
Substituting the values given in the problem, we get:
(length of call in minutes) = ($2.95 - $1.00) / ($0.15)Simplifying this expression, we have:
(length of call in minutes) = $1.95 / $0.15Dividing $1.95 by $0.15 gives us the answer:
(length of call in minutes) = 13Therefore, Mona's phone call lasted 13 minutes.
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PLEASE HELP ME. WORTH 13 POINTS!!
Test scores for the 19 members of the geometry class are represented in the histogram below. How many students scored from 110 to 119 points?
A. 12
B. 4
C. 3
D. 2
Answer:
The answer is D.2
Step-by-step explanation:
Can Ihave brainliest bc you said it was worth 13 but it's worth 7 :l
This means that there are 3 students who scored within that range. Therefore, the correct answer is C. 3.
The histogram displays the test scores for the 19 students in the geometry class. To determine how many students scored from 110 to 119 points, we need to look at the height of the bars in that range.
A histogram is a graphical representation of data that displays the frequency or distribution of a set of continuous or discrete variables. It consists of a series of bars, where each bar represents a specific category or range of values, and the height of the bar corresponds to the frequency or count of observations falling within that category or range.
Based on the histogram, we can see that the bar representing the range from 110 to 119 points has a height of 3. This means that there are 3 students who scored within that range. Therefore, the correct answer is C. 3.
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What's the answer? Geometry
The area of the trapezoid in this problem is given as follows:
C. [tex]A = 96\sqrt{3}[/tex] mm².
How to obtain the height of the trapezoid?The area of a trapezoid is given by half the multiplication of the height by the sum of the bases, hence:
A = 0.5 x h x (b1 + b2).
The bases in this problem are given as follows:
11 mm and 15 + 6 = 21 mm.
The height of the trapezoid is obtained considering the angle of 60º, for which:
The adjacent side is of 6 mm.The opposite side is the height.We have that the tangent of 60º is given as follows:
[tex]tan{60^\circ} = \sqrt{3}[/tex]
The tangent is the division of the opposite side by the adjacent side, hence the height is obtained as follows:
[tex]\sqrt{3} = \frac{h}{6}[/tex]
[tex]h = 6\sqrt{3}[/tex]
Thus the area of the trapezoid is obtained as follows:
[tex]A = 0.5 \times 6\sqrt{3} \times (11 + 21)[/tex]
[tex]A = 96\sqrt{3}[/tex] mm².
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Find the exact values of x and y.
The values of x and y are given as follows:
x = y = 5.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The diagonal length of the rectangle is the hypotenuse of a right triangle of sides 6 and 8, hence:
d² = 6² + 8²
d² = 100
d = 10.
The segments x and y are each half the length of the diagonal, and the two diagonals have the same length for a rectangle, hence:
x = y = 5.
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Use the theoretical method to determine the probability of the given outcome or event. Assume that the die is fair Rolling a single six-sided die and getting a 2, 3, 4, or 5. The probability rolling a single six-sided die and getting a 2, 3, 4, or 5 is ___ (Type an integer a simplified fraction.)
The probability of rolling a single six-sided die and getting a 2, 3, 4, or 5 is:
4/6 or 2/3
To determine the probability of the given outcome or event using the theoretical method, follow these steps:
1. Identify the total number of possible outcomes when rolling a single six-sided die. In this case, there are 6 possible outcomes (1, 2, 3, 4, 5, or 6).
2. Identify the number of successful outcomes, which are the outcomes that meet the criteria of the event. In this case, the successful outcomes are rolling a 2, 3, 4, or 5. There are 4 successful outcomes.
3. Calculate the probability by dividing the number of successful outcomes by the total number of possible outcomes. In this case, the probability is:
Probability = (Number of successful outcomes) / (Total number of possible outcomes)
Probability = 4/6
4. Simplify the fraction if possible. In this case, you can simplify 4/6 to 2/3.
The probability of rolling a single six-sided die and getting a 2, 3, 4, or 5 is 2/3.
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Joseph has a bag filled with 2 red, 6 green, 15 yellow, and 7 purple marbles. Determine P(not green) when choosing one marble from the bag.
90%
80%
60%
20%
Answer:
Step-by-step explanation:
80%
Point A is translated 5 units right and 2 down. Find A'.
Answer:
(3,1)
Step-by-step explanation:
what do I need to do,help Please?!
The slope of the graph is 50, and it represents the rate of change of the total cost of the gym membership per month.
To write an equation for C, the total cost of the gym membership, we can use the slope-intercept form of a linear equation, which is y = mx + b. In this case, y represents the total cost, m represents the slope, x represents the number of months, and b represents the y-intercept (the initial cost of joining the gym).
From the graph, we can see that the initial cost of joining the gym is $700 (the y-intercept), and the monthly fee is $50 (the slope of the line connecting the dots). So, the equation for C is:
C = 50t + 700
where t is the number of months.
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Which of these is a correct expansion of (3x – 2)(2x2 + 5)?
A. 3x • 2x2 + 3x • 5 + (–2) • 2x2 + (–2) • 5
B. 3x • 2x2 + 3x • 5 + 2 • 2x2 + 2 • 5
C. 3x • 2x2 + (–2) • 2x2 + 2x2 • 5 + (–2) • 5
The correct expansion of (3x – 2)(2[tex]x^2[/tex] + 5) is 3x * 2[tex]x^2[/tex] + 3x * 5 + (–2) * 2[tex]x^2[/tex] + (–2) * 5. Thus option A is the most appropriate option as the answer the above question
The expansion of the given algebraic expression follows the distributive rule of multiplication that is (a + b)(c + d) = ac + ad + bc + bd.
Thus the first term of the first expression which is 3x is multiplied by the the second expression and we get 3x • 2[tex]x^2[/tex] + 3x • 5 + (–2)
Then the second term that is -2 is multiplied by the second expression and we get 5 + (–2) • 2[tex]x^2[/tex] + (–2) • 5
Then we add both expressions and get the answer 3x * 2[tex]x^2[/tex] + 3x * 5 –2 * 2[tex]x^2[/tex] –2 * 5.
After further simplification of the above expression we get, 6[tex]x^3[/tex] + 15x - [tex]4x^2[/tex] - 10.
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GEOMETRY PLEASE HELP!! for 30 points!
Looking up, Joe sees two hot air balloons in the sky as shown. He determines that the hot air balloon is 700 meters away, at an angle of 38 degrees from the vertical. The higher hot air balloon is 1,050 meters away, at an angle of 26 degrees from the vertical. How much higher is the balloon on the right than the balloon on the left?
Do not round any intermediate computations. Round your answer to the nearest tenth.
Note that the figure below is not drawn to scale.
Answer:
Sure, I can help you with that. Here are the steps on how to solve the problem:
1. Let x be the height of the balloon on the left and y be the height of the balloon on the right.
2. Using the tangent function, we can write the following equations:
```
tan(38) = x/700
tan(26) = y/1050
```
3. Solve the first equation for x:
```
x = 700tan(38)
```
4. Substitute this value of x into the second equation:
```
y/1050 = tan(26)
y = 1050tan(26)
```
5. Subtract the two equations to find the difference between the heights of the two balloons:
```
y - x = 1050tan(26) - 700tan(38)
```
6. Evaluate this expression using a calculator and round your answer to the nearest tenth:
```
y - x = 266.51 meters
```
Therefore, the balloon on the right is 266.51 meters higher than the balloon on the left.
Step-by-step explanation:
Which function has the greatest x-intercept?f(x) = 3x – 9g(x) = |x 3|h(x) = 2x – 16j(x) = –5(x – 2)2
The function that has the greatest x-intercept is the function h(x)
h(x) = 2·x - 16What is the x-intercept of a function?The x-intercept of a function is the x-value of the function when the y-value is 0, which is the set of points at which the graph of the function intersects the x-axis.
The x-intercept of each function are found as follows;
f(x) = 3·x - 9 = 0
x = 9/3 = 3
g(x) = |x + 3| = 0
(x + 3) > 0 and |x + 3| = x + 3 = 0
x = 0 - 3 = -3
|x + 3| < 0 and |x + 3| = -(x + 3) = 0
x = -3
h(x) = 2·x - 16 = 0
x = 16/2 = 8
x = 8
j(x) = -5·(x - 2)² = 0
The x-intercept is x = 2
The function that has the greatest x-intercept is therefore the function h(x) = 2·x - 16
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on the first of each month, $100 is deposited into a savings account that pays 6% interest, compoundedmonthly. assuming that no withdraws are made, give a recurrence relation for the total amount of money inthe account at the end of n months.
The recurrence relation for the total amount of money in the savings account at the end of n months can be expressed using a recursive formula that takes into account the monthly deposits and the compounded interest. Let A_n be the total amount of money in the account at the end of the nth month. Then, we have:
A_n = A_{n-1} + 100 + (0.06/12)*A_{n-1}
Here, A_{n-1} represents the total amount of money in the account at the end of the (n-1)th month, which includes the deposits made in the previous months and the accumulated interest. The term 100 represents the deposit made at the beginning of the nth month.
The term (0.06/12)*A_{n-1} represents the interest earned on the balance in the account at the end of the (n-1)th month, assuming a monthly interest rate of 0.06/12.
Using this recursive formula, we can calculate the total amount of money in the account at the end of each month, starting from the initial balance of $0. For example, we can calculate A_1 = 100 + (0.06/12)*0 = $100, which represents the balance at the end of the first month.
Similarly, we can calculate A_2 = A_1 + 100 + (0.06/12)*A_1 = $206, which represents the balance at the end of the second month. We can continue this process to calculate the balances at the end of each month up to the nth month.
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A particular fruit's weights are normally distributed, with a mean of 438 grams and a standard deviation of 17 grams. If you pick one fruit at random, what is the probability that it will weigh between 443 grams and 492 grams
_____
The probability that a fruit picked at random weighs between 443 grams and 492 grams is approximately 0.3695 or 36.95%.
To find the probability that a fruit picked at random weighs between 443 grams and 492 grams, we need to standardize these values using the formula:
z = (x - μ) / σ
where x is the weight of the fruit, μ is the mean weight (438 grams), σ is the standard deviation (17 grams), and z is the standardized score.
For the lower end of the range (443 grams), we have:
z = [tex]\frac{(443 - 438)}{17} = 0.29[/tex]
For the upper end of the range (492 grams), we have:
z = [tex]\frac{(492 - 438)}{17} = 3.18[/tex]
Using a standard normal distribution table or calculator, we can find the probability that a standardized score falls between these values.
The probability of a z-score between 0.29 and 3.18 is approximately 0.3695.
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What two numbers add to make -17 and times to get 30
Answer:
-15 and -2
Step-by-step explanation:
Two negatives multiply to be a positive. We know -15 • -2 = +30
Combine (add) them and you get -17.
determine the partial fraction expansion for the rational function below.
To determine the partial fraction expansion for a rational function, we need to express it as a sum of simpler fractions. However, the general process for finding the partial fraction expansion of a rational function is as follows:
1. Factor the denominator of the rational function into linear and/or quadratic factors.
2. Write the rational function as a sum of fractions, one for each factor of the denominator. For each linear factor, use a constant numerator. For each quadratic factor, use a linear numerator.
3. Solve for the constants using algebraic manipulation and equating the numerators of the partial fractions with the original numerator of the rational function.
4. Write the partial fraction expansion as the sum of the fractions found in step 2 with the constants found in step 3.
For example, if the rational function is (3x^2 + 5x + 2)/(x^2 + 4x + 3), we would first factor the denominator as (x + 3)(x + 1). Then we would write the partial fraction expansion as:
(3x^2 + 5x + 2)/(x^2 + 4x + 3) = A/(x + 3) + B/(x + 1)
To solve for A and B, we would equate the numerators:
3x^2 + 5x + 2 = A(x + 1) + B(x + 3)
Expanding and equating coefficients, we get:
3 = B + A
5 = 3B + A
Solving for A and B, we get:
A = 1
B = 2
Therefore, the partial fraction expansion of (3x^2 + 5x + 2)/(x^2 + 4x + 3) is:
(3x^2 + 5x + 2)/(x^2 + 4x + 3) = 1/(x + 3) + 2/(x + 1)
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god filled his gas tanker with 19/5/9 tank of gas if he uses 1 5/6 gallons of gas each day after how many days will he need to refill his tank
It will take God approximately 32 days to use up all the gas in his tanker and need a refill.
If God filled his gas tanker with 19/5/9 tank of gas and uses 1 5/6 gallons of gas each day, we can calculate how many days it will take for him to need a refill.
First, we need to convert the mixed number 19/5/9 to an improper fraction:
19/5/9 = (19 * 9 + 5) / 9 = 176/9
So God has 176/9 tanks of gas in his tanker.
Next, we can calculate how much gas God uses each day:
1 5/6 = (6 * 1 + 5) / 6 = 11/6
So God uses 11/6 gallons of gas each day.
To find out how many days it will take for God to need a refill, we can divide the amount of gas in his tanker by the amount of gas he uses each day:
(176/9) / (11/6) = (176/9) * (6/11) = 32
Therefore, it will take God approximately 32 days to use up all the gas in his tanker and need a refill.
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Please help with part (b) and (c) of the question ((: Thank youuuu
B) Note that in the prompt above, you can use translation to map the line y= 2x -4 onto the line y = 2x + 4.
While you can use axial symmetry in the y - axis to map the line y = x onto the line y = -x.
What is the meaning of Translation and Axial Symmetry?Axial symmetry is symmetry around an axis; an item is axially symmetric if it retains its appearance when rotated around an axis.
A baseball bat with no brand or other design, or a plain white tea saucer, for example, looks the same when rotated by any angle around the line traveling longitudinally through its center, indicating that it is axially symmetric.
A transformation in which the coordinate system's origin is shifted but the orientation of each axis remains constant
So for B) you can use a translation to map the line y = 2x -4 onto the line y = 2x + 4 by shifting the first line 4 units upwards along the y - axis....
mathematically, that would be:
y = 2x - 4 + 4
y = 2x
For C) you can use axial symmetry on the y - axis to achhieve the mapping of y = x onto y = -x by reflection.
The polar opoppsite of y = x is y = -x.
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Father is 20 years older than his son. 5 years ago Father was 3 times as old as his son. Find their present ages?
The present age of the Father is 35 and the age of the Son is 15 years after solving the given problem.
By examining the given problem we can solve it in the following way:
Present age:
Let x = Son's present age
x + 20 = Father's present age
5 years ago:
x - 5 = Son's age 5 years ago
x + 20 -5 = father's age 5 years ago
Father's age 5 years ago = 3( Son's age 5 years ago )
x + 20 - 5 = 3 (x - 5)
x + 15 = 3x - 15
2x = 30
x = 15
x = 15, Son's present age
x + 20 = 35 = father's present age.
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The approximate areas of Colorado and
Hawaii are listed below:
Colorado: 2.7 x 105 square
×
kilometers
Hawaii: 2.83 × 104 square
kilometers
How much larger is Colorado? Express
your answer using scientific notation.
If the approximate areas of Colorado and Hawaii are listed as Colorado: 2.7 x 105 square kilometers. The amount larger is Colorado is: 2.417 x 10^5.
The first step is to divide the area of Hawaii by the area of Colorado and before we do that we must ensure that both of these figures have the same exponent.
So,
2.7 x 10^5 square km - 2.83 x 10^4 square km
2.83 x 10^4 = 0.283 x 10^5
Hence,
2.7 x 10^5 - 0.283 x 10^5
= 2.417 x 10^5
Therefore Colorado is 2.417 x 10^5 square kilometers larger than Hawaii.
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Lena says that 4xy³ and -5x³yare like terms. Is she correct? Why or not ?
No, 4xy³ and -5x³y are not like terms because they cannot be added or subtracted
What are algebraic expressions?Algebraic expressions are defined as expressions that are composed of terms, their coefficients, their variables, constants and factors.
These algebraic expressions are also identified with the presence of arithmetic operations, such as;
BracketParenthesesAdditionSubtractionMultiplicationDivisionIt is important to note that like terms are terms an algebraic expression have like variables but not always coefficients. These terms also can be added or subtracted.
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If A and B are mutually exclusive, then _____.
a. P(A) + P(B) = 0
b. P(A ∩ B) = 1
c. P(A ∩ B) = 0
d. P(A) + P(B) = 1
If A and B are mutually exclusive, then the correct answer is c. P(A ∩ B) = 0. This is because mutually exclusive events cannot occur at the same time, meaning the intersection of the events is empty. Therefore, the probability of A and B occurring together is zero.
To explain further, if A represents the event of flipping heads on a coin and B represents the event of flipping tails on the same coin, then these events are mutually exclusive because both cannot occur at the same time. The probability of flipping heads or tails on a coin is 1, but the probability of flipping heads and tails simultaneously is 0. Therefore, P(A ∩ B) = 0.
It is important to note that if A and B are mutually exclusive, then P(A) + P(B) = 1, which is answer choice d. This is because one of the events must occur, but not both. Therefore, the total probability of either A or B occurring is 1. However, this does not directly answer the question about the probability of the intersection of A and B.
Overall, when working with mutually exclusive events, it is important to recognize that they cannot occur at the same time and therefore have no intersection, which makes the probability of A and B occurring together equal to 0.
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If A and B are mutually exclusive events, this signifies that they cannot both happen simultaneously. Therefore, the probability of both events occurring, expressed as P(A ∩ B), is equal to 0.
Explanation:If A and B are mutually exclusive, it means that events A and B cannot occur at the same time. In terms of probability, we express this statement as: the probability that both A and B occur, denoted by P(A ∩ B), is equal to 0. Hence the correct answer is: c. P(A ∩ B) = 0.
This is fundamental in the study of probability and is crucial for understanding more complex concepts such as conditional probability and independence of events.
It's important to note that answers a, b and d are incorrect. Answer a, P(A) + P(B) = 0, implies that neither event can happen which contradicts the definition of mutually exclusive events. Answer b, P(A ∩ B) = 1, implies that A and B must always occur together, which is the exact opposite of what mutual exclusivity means. Answer d, P(A) + P(B) = 1, would be correct if A and B were exhaustive events, which means that either event A or event B is certain to occur.
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A wooden beam is (6y^2+3y+1) meters long. If a piece of length (y^2-11) meters is cut off, express the length of the remaining piece of beam as a polynomial in y.
(QUESTION)
The length of the remaining piece of beam is _
(Type an expression using y as the variable.)
Answer: 5y^2 +3y+12
Step-by-step explanation:
6y^2+3y+1
y^2-11
equals
5y^2+3y+12
The length of the remaining piece of wooden beam after the cut out in terms of polynomial y is 5y² + 3y + 12
What is the length of the remaining piece of beam?Length of the wooden beam = 6y² + 3y + 1
Length cut out from the wooden beam= y² - 11
Length of the remaining piece of beam = Length of the wooden beam - Length cut out from the wooden beam
= (6y² + 3y + 1) - (y² - 11)
= 6y² + 3y + 1 - y² + 11
= 5y² + 3y + 12
Hence, 5y² + 3y + 12 is the remaining length of the wooden beam.
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Review Worksheet:
Can you use the IVT to say that there is a zero of the function f(x)=x²-4x on the interval [-1, 5]?
Since f(-1) is positive and f(5) is negative, by the IVT, there must exist at least one value c in the interval [-1, 5] where f(c) = 0. This means that the function f(x) = x² - 4x has a zero on the interval [-1, 5].
Yes, we can use the Intermediate Value Theorem (IVT) to say that there is a zero of the function f(x) = x² - 4x on the interval [-1, 5].
The IVT states that if f(x) is a continuous function on the closed interval [a, b] and if k is any number between f(a) and f(b), then there exists at least one value c in the interval [a, b] such that f(c) = k.
In this case, we can evaluate f(-1) and f(5) to determine the sign of f(x) at the endpoints of the interval:
f(-1) = (-1)² - 4(-1) = 5
f(5) = 5² - 4(5) = -5
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Based on a random sample of 25 units of product X, the average weight is 102 lb and the sample standard deviation is 10 lb. We would like to decide whether there is enough evidence to establish that the average weight for the population of product X is greater than 100 lb. Assume the population is normally distributed. Using the critical value rule, at α =. 01, we can reject the null hypothesis
We cannot rule out the null hypothesis that the population means the weight is equal to 100 lb based on the critical value rule at = 0.01.
A one-sample t-test can be used to evaluate whether we can rule out the null hypothesis that the population's average weight is 100 lb.
First, we need to calculate the test statistic t:
[tex]$t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$[/tex]
[tex]$t = \frac{(102 - 100)}{\frac{10}{\sqrt{25}}} = 2$[/tex]
The critical value for the t-distribution with 24 degrees of freedom and a significance level of 0.01 must then be determined. To determine this value, we can utilize a t-table or statistical software.
We establish the critical value to be 2.492 using a t-table. We are unable to reject the null hypothesis because our calculated t-value (2) is smaller than the crucial value (2.492).
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convert the following numbers:(a) 248 to decimal.(b) 2416 to decimal.(c) 2c16 to decimal.(d) 00110011101000112 to hexadecimal.
(a) 248 to decimal
Since it's already in decimal form, there's no need for conversion.
Answer: 248
(b) 2416 to decimal (assuming it's a hexadecimal number)
Step 1: Identify the place values of the hexadecimal number (from right to left): 1, 16, 256
Step 2: Multiply the digits by their place values and sum them up: (2 * 256) + (4 * 16) + (1 * 1) = 512 + 64 + 1 = 577
Answer: 577
(c) 2c16 to decimal (assuming it's a hexadecimal number)
Step 1: Identify the place values of the hexadecimal number (from right to left): 1, 16, 256
Step 2: Convert the letter "c" to its decimal equivalent: C = 12
Step 3: Multiply the digits by their place values and sum them up: (2 * 256) + (12 * 16) + (1 * 1) = 512 + 192 + 1 = 705
Answer: 705
(d) 00110011101000112 to hexadecimal
Step 1: Group the binary digits into sets of four from right to left: 0011 0011 1010 0011
Step 2: Convert each group of four binary digits into their corresponding hexadecimal values:
0011 = 3
0011 = 3
1010 = A
0011 = 3
Step 3: Combine the hexadecimal values: 33A3
Answer: 33A3
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