Answer:
C. G(x) is a negative number with a small absolute value
Step-by-step explanation:
As x increases, G(x) goes towards 0 from the a negative quadrant.
Find: (4x2y3 2xy2 â€"" 2y) â€"" (â€""7x2y3 6xy2 â€"" 2y) Place the correct coefficients in the difference. X2y3 xy2 y.
The required coefficient is 11,-4 and 0.
Given expression is,
\((4x^2y^3 + 2xy^2- 2y) -(-7x^2y^3 + 6xy^2-2y)\)
we have to find the coefficient of the above expression.
ON solving the above expression,
\((4x^2y^3 + 2xy^2- 2y) -(-7x^2y^3 + 6xy^2-2y)=4x^{2} y^{3} +2xy^2-2y+7x^2y^3-6xy^2+2y\)
\((4x^2y^3 + 2xy^2- 2y) -(-7x^2y^3 + 6xy^2-2y)=11x^2y^3-4xy^2+0y\)
Hence from the above expression, it is clear that the coefficient of \(x^2y^3\) is 11,\(xy^2\) is -4 and \(y\) is 0.
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calculate the mean and median number of hours rashawn listened to music for the 6 days. round your answers to the nearest tenth.
The mean and median number of hours Rashawn spend in listening to music is 5.7 hours and 6 hours, under the condition that there were 6 days in which Rashawn listened to music.
Now to evaluate the mean number of hours Rashawn listened to music for the 6 days, we have to sum up all the hours and divide by the number of days.
Then, total number of hours Rashawn heard music for 6 days is
= 6 + 5 + 5 + 6 + 5 + 7
= 34 hours
Mean = Total number of hours / Number of days
= 34 / 6
= 5.7 hours
Now,
For evaluating the median number of hours Rashawn heard music in the interval of 6 days
We have to set the number in the order of smallest to largest
The numbers in order are 5, 5, 5, 6, 6, 7
The median is the middle value which is 6
The mean and median number of hours Rashawn spend in listening to music is 5.7 hours and 6 hours, under the condition that there were 6 days in which Rashawn listened to music.
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The complete question is
Rashawn kept a record of how many hours he spent listening to music for 6 days during school vacation and displayed his results in the table
Day -
Monday
Number of hours - 6
Tuesday
Number of hours - 5
Wednesday
Number of hours - 5
Thursday
Number of hours - 6
Friday
Number of hours - 5
Saturday
Number of hours - 7
calculate the mean and median number of hours Rashawn listened to music for the 6 days. Round your answers to the nearest tenth.
Need help with my work please
Joe overheard 5 girls talking about how much they love princess movies and reaches the conclusion that all girls love princess movies. this is an example of___________.
The situation described, where Joe overheard 5 girls talking about their love for princess movies and then concluded that all girls love princess movies, is an example of a hasty generalization.
A hasty generalization occurs when a person makes a broad assumption or generalization based on a small or limited sample size. In this case, Joe is assuming that all girls share the same interest in princess movies based on the opinion of only 5 girls.
It is important to recognize that not all girls have the same preferences and interests, and it would be more accurate to gather a larger and more diverse sample before making such a conclusion.Making hasty generalizations can lead to inaccurate or unfair judgments.
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A large western stare consists of 3872 million acres of land. Approximately 82% of this land is federally owned. Find the number of acres that are not federally owned.
Answer:
696.96 million acres of land
Step-by-step explanation:
Acres not federally owned = Percentage of acres not federally owned x total acres of land
Percentage of acres not federally owned = 100% - percentage of acres federally owned
100% - 82% = 18%
0.18 x 3872 = 696.96 million acres of land
If the sampled population distribution is skewed, then in most cases the sampling distribution of the mean can be approximated by the normal distribution if the sample size n is at least 30. T/F
True. The central limit theorem states that if the sample size n is large enough (usually considered to be at least 30), then the sampling distribution of the mean will be approximately normal, regardless of the shape of the population distribution.
The sampling distribution of the mean can be approximated by the normal distribution if the sample size (n) is at least 30. This statement is based on the Central Limit Theorem, which states that the sampling distribution of the mean of a random sample drawn from any population will approach a normal distribution as the sample size increases, regardless of the shape of the population distribution. A sample size of 30 is often considered the threshold for approximating a normal distribution in such cases.
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Order from least to greatest {-6,-8, 3,-1,-4}
Answer:
-8, -6, -4, -1, 3
Step-by-step explanation:
Hope it helps! =D
3. Amanda threw her Algebra book off a 4-story
building at the end of the school year. The
equation h = -16t2 + 24t + 40 gives the height
of the book after t seconds.
0
At what time will her book hit the ground?
Given statement solution is :-Time cannot be negative in this context, we discard the solution t = -1, the book will hit the ground after approximately 2.5 seconds.
To find the time when the book hits the ground, we need to determine when the height (h) becomes zero. We can set up the equation and solve for t.
The equation given is:
h = -\(16t^2 + 24t + 40\)
Setting h = 0, we have:
0 = \(-16t^2 + 24t + 40\)
Now we can solve this quadratic equation. There are a few methods to solve quadratic equations, such as factoring, completing the square, or using the quadratic formula. In this case, we'll use the quadratic formula:
t = \((-b ± √(b^2 - 4ac)) / (2a)\)
For our equation, a = -16, b = 24, and c = 40. Plugging these values into the quadratic formula, we get:
t = \((-24 ± √(24^2 - 4*(-16)40)) / (2(-16))\)
t = \((-24 ± √(576 + 2560)) / (-32)\)
t = (-24 ± √3136) / (-32)
t = (-24 ± 56) / (-32)
Now we have two possible solutions:
t = (-24 + 56) / (-32) = 32 / (-32) = -1
t = (-24 - 56) / (-32) = -80 / (-32) = 2.5
Since time cannot be negative in this context, we discard the solution t = -1. Therefore, the book will hit the ground after approximately 2.5 seconds.
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Beverly's average mark for nine examination papers was 89.5. How many marks did she score altogether?
Answer:
805.5 out of 900
Step-by-step explanation:
A test is out of 100 and because there are 9 tests: 9 x 100 which equals 900.
To get the average we add up each test mark and divide by the number of tests. The same can be applied here but reversed. So because there were 9 tests we can multiply 89.5 by 9 which gives us 805.5. Beverly scored 805.5 marks out of 900 which makes her average 89.5% for 9 tests.
An implicit equation for the plane passing through the point (1,2,5) that is perpendicular to the line L(t)=⟨1+2t,3−4t,t−2⟩ is z−3(x−5)=−4(5−y) 1 point) Find the distance of the point (3,3,−5) from the line r(t)=⟨−1+2t,−1+2t,7−2t⟩. Answer:
The distance of the point (3, 3, -5) from the line r(t) = ⟨-1+2t, -1+2t, 7-2t⟩ is 3√3 units. To find the distance between a point and a line, we can use the formula for the distance between a point and a line in three-dimensional space.
The formula is:
d = |(r - r₀) × v| / |v|
where r₀ is a point on the line, v is the direction vector of the line, and r is the given point.
For the line r(t) = ⟨-1+2t, -1+2t, 7-2t⟩, we can choose any point on the line as r₀. Let's choose the point (1, 1, 7). The direction vector of the line is ⟨2, 2, -2⟩.
Now, we can calculate the distance using the formula:
d = |(⟨3, 3, -5⟩ - ⟨1, 1, 7⟩) × ⟨2, 2, -2⟩| / |⟨2, 2, -2⟩|
Expanding and calculating the cross product and the magnitude, we find:
d = |⟨2, 2, -12⟩| / √12
Simplifying further, we get:
d = 3√3 units
Therefore, the distance of the point (3, 3, -5) from the line r(t) = ⟨-1+2t, -1+2t, 7-2t⟩ is 3√3 units.
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consider the function . for what values of does the intermediate value theorem tell us that there is a in the interval such that ?
The intermediate value theorem is a fundamental concept in calculus that provides information about the existence of a specific value within a given interval for a continuous function.
In order to determine the values of x for which the intermediate value theorem guarantees the existence of a particular y-value, we need to consider the properties of the function and the interval.
To apply the intermediate value theorem, we need to ensure that certain conditions are met:
The function f(x) must be continuous on the interval [a, b]. This means that there are no abrupt jumps, holes, or vertical asymptotes within this interval. A continuous function can be drawn without lifting the pen from the paper.
The interval [a, b] must be closed and bounded. A closed interval includes its endpoints, denoted by square brackets [ ]. A bounded interval means that there are finite values for both a and b.
The y-value must lie between f(a) and f(b). In other words, if y is greater than or equal to min(f(a), f(b)) and less than or equal to max(f(a), f(b)), then there exists at least one x-value c in [a, b] such that f(c) = y.
By satisfying these conditions, we can conclude that there exists at least one x-value c in the interval [a, b] such that f(c) = y.
It is important to note that the intermediate value theorem only guarantees the existence of a solution; it does not provide any information about the uniqueness or multiplicity of the solution. Additionally, the theorem does not provide a method for finding the exact value of c; it only assures us that such a value exists.
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“Solve the following systems of equations using any method” ( elimination, substitution, graphing)
Answer:
(0, 3)===========================
Given systemy = 2x + 3y = - 3x + 3Solve by substitution/elimination2x + 3 = - 3x + 32x + 3x = 3 - 35x = 0x = 0y = 2*0 + 3y = 3Answer:
x = 0y = 3Step-by-step explanation:
Forming the equation,
→ 2x + 3 = -3x + 3
Now the value of x will be,
→ 2x + 3 = -3x + 3
→ 2x + 3x = 3 - 3
→ 5x = 0
→ x = 0/5
→ [ x = 0 ]
Then the value of y will be,
→ y = -3x + 3
→ y = -3(0) + 3
→ y = 0 + 3
→ [ y = 3 ]
Hence, the value of y is 3.
The school physics class has built a trebuchet (catapult) that is big enough to launch a watermelon. the math class has created the function h(t) = -16( t - 5)2 + 455 to model the height, in feet, after t seconds, of a watermelon launched into the air from a hilltop near the school the x - intercepts of this function are (-0.33 , 0) and (10.33 , 0)
the watermelon is hitting the ground at around ____ seconds
The watermelon is hitting the ground at around 10.33 seconds.
To find out when the watermelon hits the ground, we need to look for the time when the height of the watermelon is zero. This is because the watermelon will be on the ground at that point.
The x-intercepts of the function h(t) give us the times when the height is zero. So, we know that the watermelon will hit the ground at t = -0.33 seconds and t = 10.33 seconds.
However, the negative value doesn't make sense in this context, so we can ignore that solution. Therefore, the watermelon is hitting the ground at around 10.33 seconds.
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pleas please help me !!
“A relation contains to points (-5,-10) (-2,-4) (-1,-2) (4,8) and (5,10) is this a function?
please explain how you did the work step by step pls!!!
Answer:
This is a function and there is no value of x for which we will get two or more different values of y.
Step-by-step explanation:
Now, this is a function and there is no value of x for which we will get two or more different values of y
The equation is y = 2x
bye
-7(a - 3) = 11 - 7a
what’s the answer
Answer:
the statement is false there is no solution
Step-by-step explanation:
step 1 -7(a-3)=11-7a
step 2 -7a+21=11-7a
step 3 cancel out the -7a's
step 4 you are left with 21=11 which does not work so it is false
f(x)=-4(x-9)^2+15 in standard form
Answer:47r64765
Step-by-step explanation:no
What is the answer to 2/5 + 1/4 + 1/10?
Answer:
the answer to your question should be 0.75 aka 3/4
Step-by-step explanation:
Rearrange each equation into slope y-intercept form
11c.) 4x - 15y + 36 =0
Answer:
y= 2/5x+3.6
Step-by-step explanation
used the formula
mark brainlist pls
The length of a rectangle is 5.2cm and its breadth is 3.4cm. What is the area of the rectangle?
Answer:
\( \huge{ \boxed{ \sf{17.68 \: {cm}^{2} }}}\)
Step-by-step explanation:
\( \underline{ \text{Given}} : \)
\( \longrightarrow \sf{ \: Length \: of \: a \: rectangle \: = \: 5.2 \: cm}\)
\( \longrightarrow{ \sf{Breadth \: of \: \: rectangle \: = \: 3.4 \: cm}}\)
\( \underline{ \text{To \: find} } : \sf{Area \: of \: a \: rectangle}\)
\( \boxed{ \sf{Area \: of \: a \: rectangle \: = \: Length \: \times \: Breadth}}\)
\( \mapsto{ \sf{Area \: = \: 5.2 \: cm \: \times \: 3.4 \: cm}}\)
\( \mapsto{ \sf{Area \: = \: 17.68 \: {cm}^{2} }}\)
Hope I helped!
Best regards! :D
~\( \text{TheAnimeGirl}\)
Jorge walked 25 steps north. then he walked 75 steps south what is Jorges final position
Answer:
If Jorge goes up 25 (positive) and then goes 75 steps south (negative). Then you have to calculate 25-75. This equals -50. We know negative distance is south so he's final position will be 50 steps south.
Step-by-step explanation:
The area of cross-section of a solid cylinder is 803. 84 ft2, and the height of the solid is 12. 25 ft. Find the volume of the solid
cylinder using the Cavalieri's Principle.
9800. 25 ft
9587. 15 f3
9847. 04 ft3
9807. 50 ft
V = π(√(803.84/π))^2(12.25) = 9587.15 ft^3. Hence, following Cavalieri's theory, the solid cylinder has a volume of around 9587.15 ft3.
According to Cavalieri's principle, if two solids have the same height and every plane section passing through one solid along the height has the same area as the corresponding plane section passing through the other solid, the two solids must also have the same volume.
A circle of radius r has the same cross-section as a solid cylinder. A = r2 calculates the circle's area.
Therefore, πr^2 = 803.84 r^2 = 803.84/π\sr = √(803.84/π)
The solid cylinder is 12.25 feet tall.
We may get the volume of the solid cylinder using the volume of a cylinder formula, V = r2h: V = π(√(803.84/π))^2(12.25) = 9587.15 ft^3
Hence, following Cavalieri's theory, the solid cylinder has a volume of around 9587.15 ft3.
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Someone please answer these questions I need help!! :(
Answer:
4. the answer is 20
5. x=12 y=30
6. MLV = TUV bySSS
7. ABC=HGF by SSS
to show work:
4. 15/12=25/x (cross multiply)
=15x=300 (divide both sides by 15)
= x=20
5. the triangle is equilatieral so all the angles are the same. this means 60=2y.
if you isolate the variable and divide both sides by 2, you get y=30
6. 49/14 = 28/8 ?
if you solve both the division problems, they both equal 3.5, meaning the side lengths are the same so the rule would be SSS or side side side
and you do the same thing with the next triangle too
hope this helps!! also brainliest would be nice but you dont have to
The angle of elevation to a nearby tree from a point on the ground is measured to be 54°. How tall is the tree if the point on the ground is 89 feet from the tree? Round your answer to the nearest hundredth of a foot if necessary. a) 114.57 ft b) 66.91 ft c) 73.67 ft d) 80.33 ft
The height of the tree, rounded to the nearest hundredth of a foot, is approximately 114.57 feet.
To solve this problem, we can use trigonometry and the concept of similar triangles. Let's call the height of the tree "h". We can create a right triangle with one leg being the height of the tree and the other leg being the distance from the point on the ground to the base of the tree (which is 89 feet). The angle between the ground and the line of sight to the top of the tree is the angle of elevation, which we know is 54°.
Using the trigonometric function tangent (opposite/adjacent), we can set up the following equation:
tan(54°) = \(\frac{h}{89}\)
To solve for h, we can cross-multiply and simplify:
h = 89 × tan(54°)
Using a calculator, we get:
h ≈ 114.57 ft
Therefore, the height of the tree is approximately 114.57 feet. Our answer is (a) 114.57 ft, rounded to the nearest hundredth of a foot.
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Erika write the following word expression on the board: The quotient of 24 and k. Write an algebraic expression for the word expressions. THEN evaluate (solve) the expression for k = 3
Answer:
a) x=24/k
b) x=24/3
x=8
Step-by-step explanation:
Quotient meant division and you are trying to find the quotient (x) so you divide 24 by 3 to get 8
David made 4/6 of a quart of fruit juice. Daniel made ⅔ of a quart of juice. Each mug he has holds 1/3 of a quart. How many mugs will they be able to fill together?
Answer:
together, they will fill 4 mugs
Step-by-step explanation:
Given;
a mug holds 1/3 of a quart.
First determine how many mugs to be filled by 4/6 of a quart of fruit juice made by David;
\(= \frac{\frac{4}{6} }{\frac{1}{3} }\\\\ = \frac{4}{6}* \frac{3}{1}\\\\ = 2 \ mugs\)
Lastly, determine how many mugs to be filled by ⅔ of a quart of juice made by Daniel;
\(= \frac{\frac{2}{3} }{\frac{1}{3} }\\\\ = \frac{2}{3} *\frac{3}{1}\\\\ = 2 \ mugs\)
Therefore, together, they will fill 4 mugs
Ray QM is the angle bisector of angle NQR. If angle PQN = 7x + 15 and angle NQM = 4x, what is the value of x?
Answer:
x = 2.7
Step-by-step explanation:
From the question given above, the following data were obtained:
QM = angle bisector of angle PQR
Angle PQN = 7x + 15
Angle NQM = 4x
x =?
Since QM is the angular bisector, it means that it bisect PQR into two equal angle i.e 45° each.
See attachment for diagram.
Thus, we can obtain the value of x as follow:
7x + 15 + 4x + 45= 90° (angle in a right angle triangle)
7x + 4x + 15 + 45= 90
11x + 60 = 90
Collect like terms
11x = 90 – 60
11x = 30
Divide both side by 11
x = 30/11
x = 2.7
Therefore, the value of x is 2.7
1. John is interested in determining if frequency of exercise affects pulse rate. John randomly samples individuals at a local gym to ask if they will participate in his study. 55 individuals agree, and they are divided into three groups of exercisers: 1 = high frequency, 2 = moderate frequency, 3 = low frequency. Next, John measures their pulse after their workout. Do pulse rates differ among individuals who exercise with high frequency versus those who exercise moderately versus those who exercise with low frequency?
John's study aims to determine if exercise frequency has an effect on pulse rate. Statistical analysis can be used to verify the alternate hypothesis.
John wants to determine whether the frequency of exercise affects pulse rate. To investigate this, he randomly selects individuals at a local gym who agree to participate in his research. John divides the 55 individuals who agree into three exercise frequency categories: high, moderate, and low.
Following their exercise, he calculates their pulse rates. Is there a difference in pulse rates among those who exercise frequently, moderately, and infrequently?The null hypothesis for this research question would be that there is no relationship between the frequency of exercise and pulse rate. The alternate hypothesis would be that there is a correlation between frequency of exercise and pulse rate. Statistical tools like ANOVA or T-test can be used to test the hypothesis.
In conclusion, John's study aims to determine if exercise frequency has an effect on pulse rate. Statistical analysis can be used to verify the alternate hypothesis.
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Pump A and Pump B fill the pool in 35 minutes, Pump B and Pump C fill it in 40
minutes, and Pump A and Pump C fill it in 56 minutes. How many minutes will it take
all three pumps, working together, to fill the pool?
It will take all three pumps, Working together, 1.56 minutes to fill the pool.
The given information, we can write three equations as follows:
1) (1/A + 1/B)*35 = C ---(Equation 1)
2) (1/B + 1/C)*40 = C ---(Equation 2)
3) (1/A + 1/C)*56 = C ---(Equation 3)
We want how many minutes it will take all three pumps, working together, to fill the pool, so let's represent the time taken by all three pumps working together as "t".
When all three pumps work together, they can fill the pool in one minute, so their combined rate is 1/C.
Using the rate formula, we can write the following equation:
1/A + 1/B + 1/C = 1/t ---(Equation 4)
We have four unknowns (A, B, C, and t), so we need to solve for one of them to get the answer. Let's solve for "t".
First, we can simplify Equations 1, 2, and 3 as follows:
1) 1/A + 1/B = C/35
2) 1/B + 1/C = C/40
3) 1/A + 1/C = C/56
Next, we can substitute these equations into Equation 4 to get:
(C/35) + (C/40) + (C/56) = 1/t
Now, we can simplify and solve for "t":
LCD = 39200
1120C + 980C + 700C = 39200
2800C = 39200
C = 14
Substituting this value of "C" into any of the simplified equations, we can solve for "A" and "B". Let's use Equation 1:
1/A + 1/B = 14/35
5(A+B) = 98
A+B = 19.6
Now we can use A+B+C = 1/t to solve for "t":
t = 1 / (A+B+C) = 1 / (19.6 + 14) = 0.026 hours = 1.56 minutes
Therefore, it will take all three pumps, working together, 1.56 minutes to fill the pool.
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Which fraction is the largest? 7/9 3/4 1/2 2/3
Rewrite the fractions as decimals by dividing:
7/8 = 0.7777
3/4 = 0.75
1/2 = 0.5
2/3 = 0.666
0.777 is the largest number so 7/9 is the largest fraction.
Answer: 7/9
Answer:
2/3
Step-by-step explanation:
L.C.M:36
7/9:28/36
3/4:27/36
1/2:1836
2/3:36/36
For each triangle check all that apply
Answer:
Triangle A - Scalene
Triangle B - Isosceles
Triangle C - Isosceles
Triangle D - Equilateral
Step-by-step explanation:
Scalene - No equal sides or angles
Isosceles - 2 equal sides or 2 equal angles
Equilateral - all equal sides or all equal angles