The function f(x) = x² + 12x - 3 has two distinct real roots and no rational or complex roots. The possible rational roots are ±1 and ±3, but they are not actual roots of the equation.
To find the number of complex zeros and possible rational zeros of the function f(x) = x² + 12x - 3 = 0, we can use the same methods as in the previous question.
According to the rational root theorem, any rational root of the polynomial must be of the form p/q, where p is a factor of the constant term (-3) and q is a factor of the leading coefficient (1). The possible rational roots are therefore ±1, ±3.
To determine if there are any complex roots, we can use the quadratic formula. The solutions to the equation f(x) = 0 are given by
x = (-b ± √(b² - 4ac)) / 2a
Plugging in the coefficients of the polynomial, we get
x = (-12 ± √(12² - 4(1)(-3))) / 2(1)
x = (-12 ± √(156)) / 2
x = -6 ± 3√(13)
Since the discriminant (b² - 4ac) is positive, the square root is real, and the roots are two distinct real numbers. Therefore, there are no complex roots.
The possible rational roots we found earlier, ±1 and ±3, are not actual roots of the equation, since plugging them into the equation does not give us zero. Therefore, there are no rational roots either.
In conclusion, the equation f(x) = x² + 12x - 3 = 0 has two distinct real roots and no complex or rational roots.
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--The given question is incomplete, the complete question is given
" State the number of complex zeros and the possible rational zeros for the function f(x) = x² + 12x -3 = 0
show your work"--
Which ordered pair could be the y intercept of a function?
Answer:
C) (0,1)
Step-by-step explanation:
What is a y-intercept?
A y-intercept is a value when x=0, so up and down the y-axis of a graph.
Given this, we can see that x must be equal to 0 to have a y-intercept number.
The first option, (1,1), is located in the first quadrant, making this incorrect.
The second option, (1,0) is when y=0, so the point would be on the x-axis, making this also incorrect.
The third option, (0,1), is when x=0, meaning that the point would be on the y-axis, making this the correct option.
Hope this helps! :)
In the figure shown, what are ∠ and ∠? Triangle S T U has right angle U and is labeled as follows: S T, 10; T U, 4; and the long leg, unlabeled
The measures of angle T and S in a right angles triangle STU with side Lengths ST = 10 units and UT = 4 units are equals to
We have a triangle STU has a right angle at U so, we can call it a right angled triangle STU. Length of side ST = 10 units
Length of side TU = 4 units
We have to determine the measure of angle T and measure of angle S.
As we know that sum of inner angles of a triangle = 180°
So, m∠S + m∠T + m∠U = 180°
=> m∠S + m∠T = 180° - 90°
= 90°
Using the trigonometry formula, in right angles triangle STU,
tan (m∠T ) = US/UT
=> m∠T = √86/4
=>
Hence, required value are
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Complete question:
The above figure completes the question.
In the figure shown, what are ∠ and ∠? Triangle S T U has right angle U and is labeled as follows: S T, 10; T U, 4; and the long leg, unlabeled
Here is an inequality: -2x > 10.
1. List some values for x that would make this inequality true.
2. How are the solutions to the inequality -2x [tex]\geq[/tex] 10 different fomt the solutions to -2x > 10? Explain your reasoning.
Therefore , the solution of the given problem of inequality comes out to be the solutions x = -6 or x = -10 would be acceptable.
What exactly is an inequality?Algebra, which lacking a symbol for this difference, can represent it using a pair or group of numbers. Equity usually comes after equilibrium. Inequality is bred by the persistent gap of standards. Equality and disparity are not the same thing. As was my least preferred symbol, notwithstanding knowing that the pieces are often not connected or close to one another. (). No matter how small the variations, they all affect value.
Here,
Finding values of x that cause the left side of the inequality to be bigger than the right side is necessary to make the inequality -2x > 10 true. Divide both sides by -2 and invert the inequality sign to achieve this:
=> -2x > 10
=> x < -5
The inequality is therefore true for any value of x that is less than -5. For instance, the solutions x = -6 or x = -10 would be acceptable.
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what is the length of the hypotenuse of the triangle when x=2? round your answer to the nearest tenth
Answer:
17.1
Step-by-step explanation:
A shipping container is in the shape of a right rectangular prism with a length of 7 feet, a width of 14 feet, and a height of 13. 5 feet. The container is completely filled with contents that weigh, on average, 0. 66 pound per cubic foot. What is the weight of the contents in the container, to the nearest pound?
The weight of the contents in the container is approximately 873 pounds.
A shipping container is in the shape of a right rectangular prism with a length of 7 feet, a width of 14 feet, and a height of 13.5 feet.
To find the volume of the container, we multiply the dimensions: 7 ft × 14 ft × 13.5 ft = 1,323 cubic feet. The container is completely filled with contents that weigh, on average, 0.66 pound per cubic foot.
To find the weight of the contents in the container, we multiply the volume by the average weight: 1,323 ft³ × 0.66 lb/ft³ ≈ 873.18 pounds.
Rounded to the nearest pound, the weight of the contents in the container is approximately 873 pounds.
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the correct answer is supposedly 3
Answer: I agree the answer is 3
Step-by-step explanation:
Brainliest pls:)
the number of tickets purchased by an individual for beckham college's holiday music festival is a uniformally distributed random variable ranging from 3 to 8. find the mean and standard deviation of this random variable
The value of mean is 5.5 and the value of standard deviation is 1.44.
Now, we need to find the mean and standard deviation of this random variable. The mean of a uniformly distributed random variable can be found by taking the average of the lower and upper bounds of the distribution. In this case, the lower bound is 3 and the upper bound is 8, so the mean would be:
Mean = (3+8)/2 = 5.5
So, the expected number of tickets purchased by an individual is 5.5.
Next, we need to find the standard deviation. The standard deviation is a measure of the deviation or spread of the data from the mean. For a uniform distribution, the formula for standard deviation is:
Standard Deviation = (Upper Bound - Lower Bound) / √12
Plugging in the values, we get:
Standard Deviation = (8-3) / √(12) = 1.44
This means that on average, the number of tickets purchased by an individual is expected to deviate from the mean by about 1.44 tickets.
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Find the area of the polygon
ASAP PLEASE HELP!!!!
20PTS
Hello!
This shape is a "Strange" shape, but if you look closer at it, you can see that it can be divided into "normal shapes" like rectangles and squares
On the bottom on the "polygon" we can dived it into 2 squares
One square would have the dimensions of 6 and 6
The other one would have 4 and 6
The formula of area is: Base*Height
So the first square would have an area of 36
The second square would have an area of 24
Now we solve for the big rectangle
On first thought, it may seem like the dimensions are 16 and 25, but it is actually 10 and 25. Because 16 is the whole height of the polygon.
So we subtract it by 6
So the big rectangle is 250
=================
Now we add the areas together to get a total result of 310
If you have questions, feel free to ask
A) Eight percent (8%) of all college graduates hired by companies stay with the same company for more than five years. (i) What is the probability, rounded to four decimal places, that in a random sample of 15 such college graduates hired recently by companies, exactly 2 would stay with the same company for more than five years?(4 marks)
(ii) What is the probability, rounded to four decimal places, that in a random sample of 15 such college graduates hired recently by companies, more than 3 would stay with the same company for more than five years? (5 marks)
(iii) If 24 college graduates were hired by companies, how many are expected to stay with the same company for more than five years. (2 marks)
(iv) Describe the shape of this distribution. Justify your answer using the relevant statistics
The probability that exactly 2 out of 15 college graduates stay with the same company 0.0246, the probability that more than 3 out of 15 college graduates stay with the same company is 0.0567, 2 college graduates would stay in the company and the shape of the binomial distribution is approximately normal
(i) To find the probability that exactly 2 out of 15 college graduates stay with the same company for more than five years, we use the binomial probability formula:
P(X = 2) = (15 choose 2) * (0.08)^2 * (0.92)^13
= 105 * 0.0064 * 0.3369
≈ 0.0246
So the probability, rounded to four decimal places, is 0.0246.
(ii) To find the probability that more than 3 out of 15 college graduates stay with the same company for more than five years, we can use the complement rule and find the probability of 3 or fewer staying with the same company, and then subtract that from 1:
P(X > 3) = 1 - P(X ≤ 3)
= 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)]
= 1 - [(15 choose 0) * (0.08)^0 * (0.92)^15 + (15 choose 1) * (0.08)^1 * (0.92)^14 + (15 choose 2) * (0.08)^2 * (0.92)^13 + (15 choose 3) * (0.08)^3 * (0.92)^12]
≈ 0.0567
So the probability, rounded to four decimal places, is 0.0567.
(iii) If 8% of all college graduates hired by companies stay with the same company for more than five years, then we would expect 0.08 * 24 = 1.92 college graduates to stay with the same company for more than five years. Since we cannot have a fractional number of college graduates, we would expect 2 college graduates to stay with the same company for more than five years.
(iv) The distribution of the number of college graduates staying with the same company for more than five years follows a binomial distribution. This is because each college graduate either stays with the same company for more than five years or they do not, and the probability of success (staying with the same company for more than five years) is constant for all college graduates.
The shape of the binomial distribution is approximately normal, provided that both np and n(1-p) are greater than or equal to 10, where n is the sample size and p is the probability of success. In this case, np = 15 * 0.08 = 1.2 and n(1-p) = 15 * 0.92 = 13.8, which are both greater than or equal to 10, so we can assume that the distribution is approximately normal.
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If m< a=3x and m< d=4x+6 what is the value of x?
Based on the given information that angles a and d are equal, the value of x is determined to be -6.
To find the value of x in the given scenario, we can equate the measures of the angles using the given information:
m< a = 3x
m< d = 4x + 6
Since angles a and d are stated to be equal, we can set up the equation:
3x = 4x + 6
To solve for x, we subtract 3x from both sides:
0 = x + 6
Next, we subtract 6 from both sides:
-6 = x
Therefore, the value of x is -6.
In conclusion, based on the given information that angles a and d are equal, the value of x is determined to be -6.
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Perry wants to replace the net on his basketball hoop. The hoop is 10 feet high. Perry places his ladder 4 feet from the base of the hoop. How long must the ladder be to reach the hoop?
According to the information the length of the ladder to reach the hoop will be approximately 10.77 feet.
How to calculate the length of the ladder?
Analyzing the problem, we can see that the ladder, the height and the distance from the base of the basket will form a right triangle. We can then use the Pythagorean theorem to calculate the length of the ladder, which will be the hypotenuse of the triangle. The formula used will be:
Ladder²=Height²+Distance²Substituting the information in the formula we have:
Ladder²=10²+4²Ladder²=100+16Ladder²=116So let's use the square root of 116 to find how long the ladder must be to reach the hoop, which in this case will be:
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Are the events "having a dog" and "having a cat" independent from each other?
a) Cannot tell with the given information
b) Yes, because P(cat) = P(cat | dog) and P(dog) = P(dog | cat)
c) The events are disjoint
d) No, because P(cat) is not equal to P(cat | dog) and P(dog) is not equal to P(dog | cat)
Option A) Cannot tell with the given information as the question doesn't provide any information about the relationship between having a dog and having a cat.
Without additional information, we cannot determine if these events are independent, dependent, disjoint, or have any other relationship. Independent events are events in which the occurrence or non-occurrence of one event does not affect the occurrence or non-occurrence of the other event.
In other words, the probability of one event happening does not depend on whether or not the other event happens.
Formally, events A and B are independent if and only if:
P(A ∩ B) = P(A) * P(B)
Where P(A) is the probability of event A occurring, P(B) is the probability of event B occurring, and P(A ∩ B) is the probability of both events A and B occurring simultaneously.
If the above equation holds true, then we can say that events A and B are independent. If not, then events A and B are dependent.
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We want to find the mass of a solid 8 enclosed within a sphere of radius 1 centred at 2 the origin whose density is given by 8(x, y, z) 1 + (x2 + y2 + 22)3/2 Recall that the mass of B is given by the triple integral [S]_568, , z) AV. Since the region of integration is spherical, we will use spherical coordinates to carry out our work. (a) What is the density 8 as a function of spherical coordinates, that is, as a function of p. 0, and ? (Use the Vars tab that appears when you click in the answerbox, or you may type in rho, theta, or phi, respectively.) Answer: 8(0,0,0) (b) In spherical coordinates the bounds of integration for p. 0, and 6 are given by SP SOS sºs (C) What is the mass of the solid ? (If you enter your answer using a decimal approximation, then round your answer to three decimal places.)
A. 8(p, phi, theta) = 8p sin(phi) cos(theta) / (1 + p^2 + 2p cos(phi))^(3/2)
B. ∫0^(2π) ∫0^π ∫0^1 8p sin(phi) cos(theta) / (1 + p^2 + 2p cos(phi))^(3/2) p^2 sin(phi) dp d(phi) d(theta)
C. the mass of the solid 8 enclosed within the sphere is approximately 8.378.
(a) Using the conversion formulas for spherical coordinates, we have:
x = p sin(phi) cos(theta)
y = p sin(phi) sin(theta)
z = p cos(phi)
Substituting these expressions into the given density function, we get:
8(x, y, z) = 8(p sin(phi) cos(theta), p sin(phi) sin(theta), p cos(phi))
= 8p sin(phi) cos(theta) / (1 + p^2 + 2p cos(phi))^(3/2)
Therefore, the density 8 as a function of spherical coordinates is:
8(p, phi, theta) = 8p sin(phi) cos(theta) / (1 + p^2 + 2p cos(phi))^(3/2)
(b) Since the solid 8 is enclosed within a sphere of radius 1 centred at 2 the origin, we have:
0 ≤ p ≤ 1
0 ≤ theta ≤ 2π
0 ≤ phi ≤ π
Therefore, the bounds of integration in spherical coordinates are:
∫0^(2π) ∫0^π ∫0^1 8p sin(phi) cos(theta) / (1 + p^2 + 2p cos(phi))^(3/2) p^2 sin(phi) dp d(phi) d(theta)
(c) Evaluating the triple integral using a computer algebra system or numerical integration, we get:
M = 8π/3
Therefore, the mass of the solid 8 enclosed within the sphere is approximately 8.378.
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Appreciate if somebody answered this question
Thank you
A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
A probability can be classified as experimental or theoretical, as follows:
Experimental -> calculated after previous trials.Theoretical -> calculate before any trial.Over a small number of trials, these two probabilities can be different, but over a large number of trials, their values get closer.
The dice has eight sides, hence the theoretical probability of rolling a six is given as follows:
1/8 = 0.125 = 12.5%.
(each of the eight sides is equally as likely, and a six is one of these sides).
The experimental probabilities are obtained considering the trials, hence:
100 trials: 20/100 = 0.2 = 20%.400 trials: 44/400 = 0.11 = 11%.(given in the problem).
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Choose the definition for the function acellus
Acellus is a powerful tool for students looking to achieve academic success and gain the skills they need to succeed in today's competitive world.
Acellus is an online learning management system designed to provide students with personalized, self-paced education. The system offers a wide range of courses in subjects such as mathematics, science, language arts, and social studies. The courses are designed to be interactive, engaging, and challenging, providing students with a comprehensive education in each subject area.
Acellus utilizes advanced technology to provide students with an adaptive learning experience. The system uses data analytics to track student progress and adapt the coursework to meet the needs of each individual student. This allows students to learn at their own pace, and to receive personalized instruction that is tailored to their specific needs.
In addition to providing high-quality educational content, Acellus also offers a number of other features and tools to support student learning. These include assessments, quizzes, and interactive games, as well as a student dashboard that allows students to track their progress and stay on top of their coursework.
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A large chocolate bar has a base area of 61.04 square feet and its length is 0.3
foot shorter than twice its width. Find the length and the width of the bar.
The length and width of the chocolate bar is 14.5 feet and 7.6 feet.
What is length?
Length is a measure of the size of an object or distance between two points. It refers to the extent of something along its longest dimension, or the distance between two endpoints.
What is width?
Width refers to the measure of the distance from one side of an object to the other side, perpendicular to the length. In geometry, width is usually measured in units such as meters, feet, or inches.
According to the given information:
Let's start by assigning variables to represent the length and width of the chocolate bar. Let x be the width of the chocolate bar in feet. Then, according to the problem:
The length of the chocolate bar is 0.3 feet shorter than twice its width, which means the length is (2x - 0.3) feet.
The base area of the chocolate bar is given as 61.04 square feet. We can use this information to set up an equation:
x(2x - 0.3) = 61.04
Expanding the left side of the equation:
2x^2 - 0.3x = 61.04
Moving all the terms to one side of the equation:
2x^2 - 0.3x - 61.04 = 0
Now we can solve for x using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 2, b = -0.3, and c = -61.04. Substituting these values and simplifying:
x = (0.3 ± sqrt(0.3^2 + 4(2)(61.04))) / (2(2))
x ≈ 7.6 or x ≈ -4.0
Since the width of the chocolate bar cannot be negative, we can discard the negative solution. Therefore, the width of the chocolate bar is approximately 7.6 feet.
To find the length, we can use the equation we set up earlier:
length = 2x - 0.3
Substituting x = 7.6:
length = 2(7.6) - 0.3
length ≈ 14.5
Therefore, the length of the chocolate bar is approximately 14.5 feet and the width is approximately 7.6 feet.
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The highest BASE drop zone in the world is the Kjerag in Norway, where BASE jumpers make an almost straight down plunge at a height of 3,228 feet. The function
represents the time t (in seconds) that it takes a BASE jumper to fall d feet. How far will a BASE jumper fall in 4. 5 seconds?
feet
A BASE jumper will fall 324 feet in 4.5 seconds.
What are velocity ?
velocity is a unit of measurement for the Distance an object travels in a
the predetermined period of time. Here is a word equation that illustrates the connection between space, speed, and time: velocity is calculated by dividing the total Distance traveled by the journey time.
We can use the given function to find out how far a BASE jumper will fall in 4.5 seconds:
d = 16t²
where d is the distance (in feet) and t is the time (in seconds).
Substitute t = 4.5 into the formula:
d = 16(4.5)²
d = 324
Therefore, a BASE jumper will fall 324 feet in 4.5 seconds.
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how to find vertex form when you have the parabola
Answer:
Step-by-step explanation: The vertex is the point at the bottom if the parabola opens up and at the top if it opens at the bottom.
Darren made a display board in the shape of a trapezoid.
Part A
The height of the trapezoid is half the length of the shorter base, and the longer base is twice the length
of the shorter base.
4 yd
2 yd
2 yd
b
What are the lengths of the height and the longer base? Enter your answers in the boxes.
h =
yd
b=
yd
Part B
Use the measurements from Part A to find the area of Darren's display board.
o 8 yd?
12 yd?
O 16 yd
24 yd2
Part A:
The height (h) of the trapezoid is half the length of the shorter base (b), so h = (1/2)b.
The longer base is twice the length of the shorter base, so the longer base is 2b.
Given: 4 yd + 2 yd + 2 yd + b = 8 yd (since the sum of all sides of the trapezoid is equal to the perimeter of the display board)
Solving for b, we get:
b = 2 yd
Substituting this value in the equation for h, we get:
h = (1/2)(2 yd) = 1 yd
Therefore, the length of the height is 1 yd and the length of the longer base is 4 yd.
Part B:
The formula for the area of a trapezoid is A = (1/2)(h)(b1 + b2), where h is the height and b1 and b2 are the lengths of the two bases.
Using the values from Part A, we have:
A = (1/2)(1 yd)(2 yd + 4 yd)
A = (1/2)(1 yd)(6 yd)
A = 3 yd^2
Therefore, the area of Darren's display board is 3 yd^2.
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Does anyone know the answer?
Answer:
B. ∠FBG
Step-by-step explanation:
When an angle is in the three letter form, the first letter is the first line that forms the angle, the second letter is where the angle is located, and third letter is the line that forms the angle with the first line.
Thus, we can see that line E combines with line F, and the actual angle is located at point B.
The two angles adjacent to ∠EBF are ∠DBE and ∠FBG. Only ∠FBG is one of the answer choices so this is our final answer.
If you multiply each value in the data set below by 3, what are the mean, median, mode, and range of the resulting data set?
2 3 9 0 5 8 3
Answer: range=9 mode=3 mean=9
Step-by-step explanation:
Let C = {factors of 12}
Work out n(C)
The value or n(C) based on the information will be 6.
How to explain the FactorIn mathematics, a factor is a number or algebraic expression that divides another number or expression without leaving a remainder. More formally, if a is a factor of b, then b can be expressed as a product of a and some other number or expression.
For example, in the expression 12 = 2 x 2 x 3, the numbers 2 and 3 are factors of 12. Similarly, in the expression x² - 4, (x - 2) and (x + 2) are factors because if we multiply them together we get x² - 4.
The factors of 12 are 1, 2, 3, 4, 6, and 12. Therefore, the set C contains six elements. Hence, n(C) = 6.
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The Average Rate Of Change In The Interval (0, 2) Of The Function F F(X) = X^2 – 3x Is
To find the average rate of change of a function in a given interval, we need to calculate the difference in the function values at the endpoints of the interval and divide it by the length of the interval.
In this case, the interval is (0,2) and the function is f(x) = x^2 - 3x.
At the left endpoint, x=0, we have f(0) = 0^2 - 3(0) = 0.
At the right endpoint, x=2, we have f(2) = 2^2 - 3(2) = -2.
Therefore, the difference in the function values is f(2) - f(0) = -2 - 0 = -2.
The length of the interval is 2 - 0 = 2.
So the average rate of change of f(x) over the interval (0,2) is:
(-2)/2 = -1
Therefore, the average rate of change of f(x) over the interval (0,2) is -1.
Hi! To find the average rate of change in the interval (0, 2) for the function f(x) = x^2 - 3x, you can use the following formula:
Average Rate of Change = (f(b) - f(a)) / (b - a)
In this case, a = 0 and b = 2. First, calculate the function values at these points:
f(0) = (0)^2 - 3(0) = 0
f(2) = (2)^2 - 3(2) = 4 - 6 = -2
Now, apply the formula:
Average Rate of Change = (f(2) - f(0)) / (2 - 0) = (-2 - 0) / (2) = -2 / 2 = -1
So, the average rate of change in the interval (0, 2) for the function f(x) = x^2 - 3x is -1.
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3.72÷ 10 4 which of these shows and explains the correct location of the decimal point when the expression is evaluated?
a 0.0000372 because 4 zeros are placed in front of the number when you divide by 104 b 0.000372 because the decimal point moves 4 places to the left when you divide by 104 c 37,200 because the decimal point moves 4 places to the right when you divide by 104 d 3,720,000 because 4 zeros are placed after the number when you divide by 104
The correct location of the decimal point when the expression 3.72 divided by 10⁴ is evaluated is: 0.000372 because the decimal point moves 4 places to the left when you divide by 10 to the fourth power. The correct option is B.
To evaluate this expression, we need to move the decimal point 4 places to the left, since the exponent is positive.
Option A is incorrect because placing 4 zeros in front of the number would give us a much smaller value than the original number. Option B is correct because moving the decimal point 4 places to the left would give us 0.000372, which is equivalent to 3.72 divided by 10⁴.
Option C is incorrect because moving the decimal point 4 places to the right would give us a much larger value than the original number. Option D is also incorrect because placing 4 zeros after the number would give us a value that is 10,000 times larger than the original number.
Therefore, the correct answer is B, which shows and explains the correct location of the decimal point when the expression 3.72 divided by 10⁴ is evaluated. The correct option is B.
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Complete question:
3.72 divided by 10⁴ which of these shows and explains the correct location of the decimal point when the expression is evaluated?
A 0.0000372 because 4 zeros are placed in font of the number when you divide by 10 to the fourth power
B 0.000372 because the decimal point moves 4 places to the left when you divide by 10 to the fourth power
C 37,200 because the decimal point moves for places to the right when you divide by 10 to the fourth power
D 3,720,00 because 4 zeros are placed after the number when you divide by 10 to the fourth power
A square name tag has an area of 64 square centimeters. How long is each side?
Answer:
I think it's 8...
Step-by-step explanation:
8x8 = 64
since each side is the same.
sorry if I'm wrong though-
Answer: 16 cm long
Step-by-step explanation:
Since we already have given the Area of the Square i.e. 64cm²
So, putting values into the Formulae, we get-
Area of the Square = side X side
64 = 8 x 8
since the sides have to be equal because the square has 4 equal sides, we multiply it by 4, it has to be 4 x 4 = 16
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The table shows the number of beads used to make a necklace.
Ginger wants to make a smaller necklace using the same ratio of pink to white beads.
How many different necklaces could Ginger make?
How do you know?
explain detailed
Considering the ratio, Ginger can make four different smaller necklaces.
How to obtain the ratio between two amounts?The ratio between two amounts a and b is given as follows:
a to b.
Which is also the division of the two amounts.
The ratio for this problem is given as follows:
Pink/White = 30/35
Pink/White = 6/7 -> as 30/6 = 5 and 35/7 = 5.
5 - 1 = 4, hence, considering the ratio, Ginger can make four different smaller necklaces.
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Question 10 Multiple Choice Worth 4 points)
(Diversifying Portfolios MC)
Name of Stock Symbol High Low Close
Stock A
105.19 103.25 103.38
Stock B
145.18 143.28 144.05
A
B
Last year, an investor purchased 115 shares of stock A at $90 per share and 30 shares of stock B at $145 per share. What is the difference in overall loss or gain between selling
at the current day's high price or low price?
The difference in overall gain is $208.10.
The difference in overall loss is $208.10.
The difference in overall gain is $280.10.
P
The difference in overall loss is $280.10.
The difference in overall gain is $280.10. OPtion C
How to solveWe have to first find the gains for Stock A and Stock B at high and low prices:
Stock A:
High price gain: 115 * ($105.19 - $90) = $1,747.85
Low price gain: 115 * ($103.25 - $90) = $1,523.75
Stock B:
High price gain: 30 * ($145.18 - $145) = $5.40
Low price gain: 30 * ($143.28 - $145) = -$51.60
Calculate total gains:
High price total gain: $1,747.85 + $5.40 = $1,753.25
Low price total gain: $1,523.75 + (-$51.60) = $1,472.15
Difference in overall gain: $1,753.25 - $1,472.15 = $280.10
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Mayumi was asked to determine whether quadrilateral rstu is a trapezoid given the vertices r(-2, 3), s(1, 4), t(1, -4) and u(-2, 1). she noticed that the slopes of ru and st are undefined, so she concluded that the quadrilateral could not be a trapezoid. do you agree? explain.
No, I do not agree with Mayumi's conclusion that the quadrilateral RSTU cannot be a trapezoid just because the slopes of RU and ST are undefined.
RSTU is a trapezoid with RU and ST are parallel and have the same x-coordinates.
A trapezoid is defined as a quadrilateral with at least one pair of parallel sides.
The fact that the slopes of RU and ST are undefined does not necessarily mean that they are not parallel.
As vertical lines have undefined slopes and are parallel to each other.
To determine if RSTU is a trapezoid,
Mayumi should check if any pair of opposite sides are parallel.
The slopes of the two pairs of opposite sides RS and TU, and RU and ST and check if they are equal.
Slope of RS = (4 - 3)/(1 - (-2))
= 1/3
Slope of TU = (1 - (-4))/(-2 - 1)
= -5/3
Slope of RU is undefined (vertical line)
Slope of ST is undefined (vertical line)
Since the slopes of RS and TU are not equal, they are not parallel.
The slopes of RU and ST are undefined does not give us any information about their parallelism.
Check at other properties of the quadrilateral to determine if they are parallel.
One property is the coordinates of the points.
If we draw the quadrilateral, RS and TU are not parallel, but RU and ST are parallel and have the same x-coordinates.
Therefore, quadrilateral RSTU is a trapezoid with bases RS and TU, and legs RU and ST.
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Find the coordinates of the parallel translation P if it moves the point A(3; −2) to the point B(–1; 4).
The coordinates of the parallel translation P are (-1, 4).
What is meant by coordinates?
Coordinates are a series of numbers or values that denote the position or location of a point in a particular system, such as a geographic or Cartesian coordinate system. They are used to represent locations or objects in space.
What is meant by parallel?
Parallel refers to lines or planes that are always the same distance apart and never intersect, even if they extend infinitely in both directions.
According to the given information
To find the coordinates of the parallel translation P that moves point A(3, -2) to point B(-1, 4), we need to find the vector that connects A to B, and then translate A by that same vector.
The vector that connects A to B is:
B - A = (-1 - 3, 4 - (-2)) = (-4, 6)
To move point A by this vector, we add the vector to the coordinates of A:
P = A + (-4, 6) = (3, -2) + (-4, 6) = (-1, 4)
Therefore, the coordinates of the parallel translation P are (-1, 4).
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54/g - h when g=6 and h=3
Answer:
18
Step-by-step explanation:
54/g - h g = 6 and h = 3
54/6 - 3
= 54/3
= 18
So, the answer is 18.
