You are required to choose two topics from a list of six to write about on your science test. How many different pairings are possible?
10
15
20
12
Triangle RST was dilated by a scale factor of 1/2. The image, triangle R'S'T', is an isosceles triangle, with each leg measuring 8 units. What is the length of a leg of the pre-image, triangle RST?
Answer:
16 units
Step-by-step explanation:
RST was dilated by a scale factor of 1/2. This means R'S'T' has sides that are 1/2 the length of the sides of RST.
Since the legs of R'S'T' are 8 units, this gives us the equation
8 = 1/2x
Divide both sides by 1/2:
8÷1/2 = x
8 × 2/1 = x
16 = x
Each leg in RST is 16 units.
Square root of -1 divided by (3+8i)-(2+5i)
Will mark 5 stars
The variable used to show correlation is r, which is also known as the correlation complement.
A.True
B.False
Explain why the graph of quadratic function could not contain both a minimum vertex and a maximum vertex at the same time.
Your explanation should be 3-4 sentences and include at least 6 of the following words/phrase.
-parabola
- u-shaped graph
- vertex
- minimum
- maximum
- y-value of the vertex
- x-value of the vertex
- quadratic function
Use the quadratic formula to solve the equation. if necessary, round to the nearest hundredth. a rocket is launched from atop a 101-foot cliff with an initial velocity of 116 ft/s.
a. substitute the values into the vertical motion formula h = −16t2 + vt +
c. let h = 0.
b. use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. round to the nearest tenth of a second.
If you prove that ∆WXZ is congruent to ∆YZX, which general statement best describes what you have proved?
A.Diagonals of a parallelogram bisect each other.
B. Diagonals of a parallelogram are congruent.
C. Opposite sides of a parallelogram are congruent.
D. The diagonal of a parallelogram connects two non-consecutive vertices.
Proving that ΔWXZ is congruent to ΔYZX does not directly prove any of the provided statements about a parallelogram without additional context. Likely, it could imply that diagonals of a parallelogram bisect each other, but more information is needed.
Explanation:If you prove that ΔWXZ is congruent to ΔYZX, you have demonstrated the congruence of triangles within a geometric figure, likely referencing elements of a parallelogram. However, the specific elements such as sides or diagonals are not indicated in the proof of congruence between the triangles in question.
From the options you have provided and general geometric principles, proving congruent triangles within a figure doesn't necessarily directly prove any of those statements without additional context. If we assume ΔWXZ and ΔYZX are created by a diagonal of a parallelogram, congruent triangles might imply that diagonals of a parallelogram bisect each other (Option A). However, it could also relate to the congruence of opposite sides depending on the specifics of the figure, not the diagonals being congruent (Option B), because congruence of triangles does not guarantee equal length of diagonals, just segments within the triangles.
which polynomial is a quadratic factor of 27x^3+64
The solution is that 27x^3+64 factors into (3x+4)(9x^2-12x+16).
The 2nd factor is the quadratic factor that you wanted.
What are Polynomials?Polynomials are sums of k-xⁿ terms, where k can be any number and n can be any positive integer.
3x+2x-5, for example, is a polynomial.
here, we have,
we know that,
In general, a^3+b^3 = (a+b)(a^2-ab+b^2).
given that,
27x^3+64
now, we have to factorize the given expression.
using the above formula, we get,
27x^3+64
= (3x+4)(9x^2-12x+16)
Hence, The solution is that 27x^3+64 factors into (3x+4)(9x^2-12x+16).
The 2nd factor is the quadratic factor that you wanted.
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A shipping box in the shape of a rectangular prism has a volume of 18x^3+5x^2-2x. what are three expressions that can represent possible dimensions of the shipping box?
Answer:
[tex](x), (9x-2), (2x+1)[/tex]
Step-by-step explanation:
[tex]18x^3+5x^2-2x=x(18x^2+5x-2)=x(9x-2)(2x+1)[/tex]
A circle has a circumference of 324\pi324π324, pi. what is the radius of the circle?
The _____ is a measure of variability that is simply the difference between the highest score and the lowest score. variance standard deviation median range
The answer to this is range! Because when you are figuring out the range, you subtract the lowest score from the highest score. Good luck on your test!
The range is a measure of variability that is simply the difference between the highest score and the lowest score. which is the correct answer would be option (D).
What is the range of the data?The range of the data is defined as the difference between the maximum number of data to the minimum number of data.
The range of given data = maximum number - minimum number
The range is the correct answer to this because you subtract the lowest score from the highest score to determine the range.
Therefore, the range is a measure of variability that is simply the difference between the highest score and the lowest score.
Hence, the correct answer would be an option (D).
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Tom bought 7 books. He has space only for 3 books in his bookshelf. In how many ways can he arrange the 3 books?
The required, Tom can arrange the 3 books in the combination of 35 different ways on his bookshelf.
The number of ways to choose a subset of 3 books from a set of 7 books can be calculated using the combination formula:
C(n, k) = n! / (k!(n-k)!)
Where n is the total number of items and k is the number of items we want to choose.
In this case, Tom wants to arrange 3 books out of a set of 7 books. Using the combination formula, we have:
C(7, 3) = 7! / (3!(7-3)!)
= 7! / (3!4!)
Calculating the factorials:
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040
3! = 3 * 2 * 1 = 6
4! = 4 * 3 * 2 * 1 = 24
Substituting these values into the formula:
C(7, 3) = 5040 / (6 * 24)
= 5040 / 144
= 35
Therefore, Tom can arrange the 3 books in 35 different ways on his bookshelf.
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The cost of printing the football roster for games was 25 for 4.00 what is the cost per copy
Bobby is testing the effectiveness of a new cough medication. There are 100 with a cough in the study. Seventy patients received the cough medication, and 30 other patients did not receive treatment. Thirty-four of the patients who received the medication reported no cough at the end of the study. Twenty of the patients who did not receive medication reported no cough at the end of the study. What is the probability that a patiebt chosen at random from this study took the medication, given that they reported no cough?
A. 63%
B. 53%
C. 38%
D. 43%
Answer:
The answer to this question is 63%
An archway is modeled by the equation y = -2x^2 + 8x. A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0. If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, at what distance from the ground level is point B?
A. 8 units
B. 6 units
C. 5 units
D. 3 units
Answer
The answer is 6
Step-by-step explanation:
Need this geometry answer
For f(x)=3x+1 and g(x)=x²-6, find (f o g)(4)
Suppose a term of a geometric sequence is a4 = 121.5 and the common ratio is 3. write the formula for this sequence in the form an = a1 ⋅ rn−1. explain how you arrived at your answer.
Answer:
First I substituted 121.5 for an, 4 for n, and 3 for r in the general form. Then I solved to find a1 = 4.5. Finally, I substituted 4.5 for a1 and 3 for r in the general form to get an = 4.5 ⋅ 3n−1.
An equation of a function y(t) is shown.
y(t)=−t²+14t−40
Which of the following statements are true about the graph of y(t) for
6≤t≤8 and WHY?
a. The value of y(t) increases over the interval 6≤t≤7
b. The value of y(t) increases over the interval 7≤t≤8
c. The average rate of change over the interval 6≤t≤8 is 0
d. The value of y(t) is constant over the interval 6≤t≤8
e. The average rate of changer over the interval 6≤t≤7 is the same as the average rate of change over the interval 7≤t≤8
The graph of y(t) increases over the interval 6≤t≤7 because the derivative is positive. The average rate of change over the interval 6≤t≤8 is 0 due to symmetry about the vertex of the parabola at t=7. The rate of change over the intervals 6≤t≤7 and 7≤t≤8 are equal in magnitude but opposite in direction.
Given the quadratic function y(t)=-t²+14t-40, we need to analyze its behavior over the interval 6≤t≤8. The first derivative y'(t) of the function, which represents the slope of the tangent line to the graph at any point t, is -2t + 14. To determine the intervals of increase and decrease, we can set the first derivative to zero to find the vertex of the parabola, yielding t=7, which means the function increases on the interval 6≤t≤7 and decreases on 7≤t≤8.
The average rate of change over an interval is calculated by taking the difference in the function values at the endpoints of the interval over the difference in t. For the interval 6≤t≤8, since this is a symmetrical interval around the vertex, the average rate of change is 0. Furthermore, it follows from symmetry that the average rate of change over the intervals 6≤t≤7 and 7≤t≤8 should be equal in magnitude but opposite in sign.
Considering the stated properties and analyzing the equation, we can conclude that:
The value of y(t) increases over the interval 6≤t≤7.The value of y(t) decreases over the interval 7≤t≤8, so statement b is false.The average rate of change over the interval 6≤t≤8 is 0, making statement c true.The value of y(t) is not constant over the interval 6≤t≤8.The average rates of change over both intervals 6≤t≤7 and 7≤t≤8 are not equal in value; they are opposite, making e false.Find the exact value. tan240°
The exact value of tan 240° is found by recognizing that 240° is in the third quadrant with a reference angle of 60°. The sine and cosine values are both negative in this quadrant. Therefore, tan 240° simplifies to √3.
To find the exact value of tan 240°, we need to consider its position on the unit circle. The angle 240° is in the third quadrant, where both sine and cosine are negative.
First, recognize that 240° is 60° beyond 180°, making its reference angle 60°.The sine and cosine of 60° are given by sin 60° = √3/2 and cos 60° = 1/2, but since 240° is in the third quadrant, these values will be negative.Thus, sin 240° = -√3/2 and cos 240° = -1/2.Tangent is the ratio of sine to cosine: tan 240° = (sin 240°) / (cos 240°) = (-√3/2) / (-1/2).Simplifying this, we get tan 240° = √3.Therefore, the exact value of tan 240° is √3.
What are the lengths?
Are the two events “choosing a sophomore” and “choosing someone who replied ‘Yes’” independent events?
Frank owns 250 acres of land. If he divides the land into 1/3 acre plots, how many plots will he have?
Uppose it costs $10 to roll a pair of dice. you get paid the sum of the numbers in dollars that appear on the dice. what is the expected value of this game?
Which expression is equivalent to 18x + 45
Hugo is 6 feet 4 inches tall, weighs 225 pounds, and very muscular. if you think hugo is more likely to be a professional football player rather than a professional ballroom dancer, you are using:
Answer:
I think it is the option "representative heuristic"
Step-by-step explanation:
Heuristics are kind of like "mental shortcuts" that we use to make assumptions quickly. They are based off of our category prototypes and what we believe are typical examples of a certain object or group. The reason why it would be representative heuristic is because when you use this, you are comparing the new situation to an already existing image of the object. In this case, you are comparing Hugo to the "typical" image of a football player.
Hope this helps you :)
The GRE is an entrance exam that many students are required to take in order to apply to graduate school. In 2014, the combined scores for the Verbal and Quantitative sections were approximately normally distributed with a mean of 310 and a standard deviation of 12.
What is the probability that a randomly selected score is greater than 334? Write your answer as a decimal.
The probability that a randomly selected score is greater than 334 is 0.0228
How to get the z scores?If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.
If we have [tex]X \sim N(\mu, \sigma)[/tex]
(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] )
then it can be converted to standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
(Know the fact that in continuous distribution, probability of a single point is 0, so we can write
[tex]P(Z \leq z) = P(Z < z) )[/tex]
Also, know that if we look for Z = z in z tables, the p value we get is
[tex]P(Z \leq z) = \rm p \: value[/tex]
For this case, we're given that:
Combined scores were approximately normally distributed with mean of 310 and a standard deviation of 12.If we take:
X = a randomly selected score obtained in the GRE exam.
Then, by the given data, we have:
[tex]X \sim N(\mu = 310, \sigma = 12)[/tex]
And therefore, we can write:
Probability that a randomly selected score is greater than 334 = P(X > 334)
Converting X to standard normal distribution:
[tex]Z = \dfrac{X - \mu}{\sigma} = \dfrac{X - 310}{12}[/tex]
The probability we need can be calculated as:
[tex]P(X > 334) = 1 - P(X \leq 334)\\P(X > 334) = 1 - P(Z \leq \dfrac{334 - 310}{12})\\\\P(X > 334) = 1 - P(Z \leq 2)[/tex]
From the z-tables, the p-value for Z = 2 is 0.9772
Thus, we get [tex]P(Z \leq 2) = 0.9772[/tex], and therefore,
[tex]P(X > 334) = 1 - P(Z \leq 2) = 1- 0.9772 = 0.0228[/tex]
Thus, the probability that a randomly selected score is greater than 334 is 0.0228
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A drawer of loose socks contains 2 red socks, 2 green socks, and 6 white socks. Which best describes how to determine the probability of pulling out a white sock, not replacing it, and pulling out another white sock?
Answer:
The probability that the first sock is white is 6/10 and that the second sock is white is 5/9, so the probability of choosing a pair of white socks is 30/90 = 1/3! Hope that helps.
Step-by-step explanation:
help me please...
Problem: The standard form of a circle is (x-h)2+(y-k)2=r2 and for the parabola, y-k=a(x-h)2. The (h,k) pair will be the center of the circle and the vertex of the parabola. The radius of the circle is ‘r’ and the focal length of the parabola is f=1/(4a). For the following General Conic Equation: x2+y2-4x-6y-12=0 complete the following problems showing all your work:
Complete the square showing all your work to convert to Standard Form:
If this is a circle, state the coordinates of the center and give the radius. If this is a parabola, state the coordinates of the vertex and give the focal length. Show all your work.
Sketch the Conic. Label the values you found in part B. Be sure to draw or show the radius or focal length.
Given a possible triangle ABC with a=5,b=11,and a=23, find a possible value for