Out of the given options, none of them are resistant, except for the median. The median is a robust measure of central tendency that can resist the impact of outliers. Therefore, if you have a data set that has outliers, it is better to use the median instead of the mean.
Resistant refers to the property of statistical methods or measures that are not influenced by the presence of outliers or extreme values. Hence, they remain effective even after the introduction of unusual values. The term "outlier" refers to values that do not follow the expected pattern of the rest of the data. These values can have a significant impact on statistical analyses, such as correlation, linear regression, etc. Hence, it is essential to identify methods that can resist such an impact.
Out of the given options, the only term that is resistant is "median" or "median absolute deviation." The median is a measure of central tendency that is not affected by outliers. It is defined as the middle value when the data set is arranged in ascending or descending order. On the other hand, the mean is sensitive to outliers, and it can be influenced by the extreme values. Therefore, if you have a data set that has outliers or extreme values, it is better to use the median instead of the mean.
The least-squares regression line (LSRL) is a statistical method that is used to find the relationship between two variables. It is calculated by minimizing the sum of the squared differences between the predicted values and the actual values. However, it is not resistant to outliers. If an outlier is present in the data, it can significantly affect the slope of the line, which can lead to wrong predictions.
Correlation is another statistical method used to determine the relationship between two variables. It measures the strength and direction of the relationship between two variables. However, like LSRL, it is not resistant to outliers.
The residuals are the differences between the predicted values and the actual values. They are used to assess the goodness of fit of a model. However, they are not resistant to outliers, and they can be influenced by extreme values.
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A special observatory on a mountain in Siberia monitors the number of meteoroids entering the Earth's atmosphere above the North Pole. It is an automated system that detects the flashes of light caused by their friction with the atmospheric gases. If on average the system detects 51 per day, what is the estimated annual total number of meteoroids that enter the atmosphere above the pole? Express your answer using scientific notation and assume a non-leap year.
X^2+y^2-12y-12 ≤0
Find Center/Radius of Circle
To find the center and radius of the circle represented by the inequality [tex]\displaystyle \sf x^{2} +y^{2} -12y-12\leq 0[/tex], we can complete the square for the y terms.
The inequality can be rewritten as:
[tex]\displaystyle \sf x^{2} +( y^{2} -12y) -12\leq 0[/tex]
To complete the square for the y terms, we need to add and subtract [tex]\displaystyle \sf ( 12/2) ^{2} =36[/tex] inside the parentheses:
[tex]\displaystyle \sf x^{2} +( y^{2} -12y+36) -36-12\leq 0[/tex]
Simplifying, we have:
[tex]\displaystyle \sf x^{2} +( y-6)^{2} -48\leq 0[/tex]
Now we can rewrite the inequality in the standard form of a circle equation:
[tex]\displaystyle \sf ( x-h)^{2} +( y-k)^{2} \leq r^{2}[/tex]
Comparing this with the obtained equation, we can identify the center and radius of the circle:
Center: [tex]\displaystyle \sf ( h,k)=( 0,6)[/tex]
Radius: [tex]\displaystyle \sf r=\sqrt{48}[/tex]
Therefore, the center of the circle is at [tex]\displaystyle \sf ( 0,6)[/tex], and its radius is [tex]\displaystyle \sf \sqrt{48}[/tex].
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]
Sketch the graph of the given function. Then state the function’s domain and range. y = 4(4)x
To sketch the graph of the function y = 4(4)^x, we can start by plotting a few points to get an idea of the shape of the graph.
Let's choose some x-values and calculate the corresponding y-values:
For x = -2, y = 4(4)^(-2) = 4(1/16) = 1/4
For x = -1, y = 4(4)^(-1) = 4(1/4) = 1
For x = 0, y = 4(4)^0 = 4(1) = 4
For x = 1, y = 4(4)^1 = 4(4) = 16
For x = 2, y = 4(4)^2 = 4(16) = 64
Now we can plot these points on a coordinate plane and connect them to form the graph of the function.
The graph of y = 4(4)^x will start at the point (0, 4) and increase rapidly as x increases. It is an exponential growth function where the base is 4.
The domain of the function is all real numbers since there are no restrictions on the values of x.
The range of the function is the set of positive real numbers greater than zero. As x increases, y grows without bound, approaching positive infinity but never reaching zero or becoming negative.
Which graph represents the function?
f(x)=x√+1
The graph of the function f(x)=√(x + 1) is in the first option
What is a radical graphA radical graph, also known as a square root graph, represents the graph of a square root function. A square root function is a mathematical function that takes the square root of the input variable.
The general form of a square root function is f(x) = √(ax + b) + c,
where a, b, and c are constants that determine the characteristics of the graph.
In the given function:
a = 1
b = 1
c = 0
The graph is plotted and attached
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4 childen go to a party but there is only 2 spots left how mank cobnasies are there
Out of the four children attending the party, with only two spots left, there are six different ways to select two children to fill those spots.
If there are four children and only two spots left at the party, we need to determine the number of combinations possible for selecting two children out of the four. To calculate this, we can use the concept of combinations from combinatorics.
Combinations refer to the selection of items from a larger set without considering the order. In this case, the order in which the children are selected does not matter; we only need to know which two children are chosen. The formula for combinations is given by:
C(n, r) = n! / (r! * (n - r)!)
where n is the total number of items (in this case, children) and r is the number of items we want to select (in this case, the two available spots at the party).
Using the formula, we can substitute n = 4 and r = 2:
C(4, 2) = 4! / (2! * (4 - 2)!)
Simplifying further:C(4, 2) = 4! / (2! * 2!)
Now, let's calculate the factorial terms:
4! = 4 * 3 * 2 * 1 = 24
2! = 2 * 1 = 2
Substituting the factorial terms:
C(4, 2) = 24 / (2 * 2)
Simplifying the denominator:
C(4, 2) = 24 / 4 = 6
Therefore, there are 6 different combinations possible for selecting two children out of the four to fill the two available spots at the party.
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Note the correct question is
4 childen go to a party but there is only 2 spots left. How many combinations are there?
16 families went on a trip which cost them Rs 2,16,352. How much did each
family pay?
Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522
Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.
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Answer:
Step-by-step explanation
1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.
Now let's check if this result is correct:
1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.
So we have shown that each family paid **Rs 13,522** for the trip
help me with this question please
Answer:
for circle 1 it is -2 for circle 2 it is 13 and for square it is 9
An extremely large sink hole has opened up in a field just outside of the city limits. It is difficult to measure across the sink hole without falling in so you use congruent triangles. You have one piece of rope that is 50 ft. long and another that is 70 ft. long. You pick a point A on one side of the sink hole and B on the other side. You tie a rope to each spot and pull the rope out diagonally back away from the sink hole so that the other ends of the two ropes meet at point C. Then you recreate the same triangle by using the distance from AC and BC and creating new segments CE and CD. The distance DE is 52.2 ft.
a. What type of triangles have you created?
b. How do you know the triangles are congruent?
c. How far across is the sink hole?
d. What is the perimeter of the triangle ABC?
A) The type of triangles are congruent triangles
B) By the use of SAS Congruency Postulate
C) The distance across for the sink hole is: 52.2 ft
D) The perimeter of triangle ABC is: 172.2 feet.
How to solve congruent triangles?A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.
B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.
C) We know that:
AB = ED = 52.2
AB is the distance across the sink hole. Thus, it is 52.2 feet
D) AB = 52.2
BC = 70
AC = 50
Thus:
Perimeter of triangle ABC = AB + BC + AC
Perimeter of triangle ABC = 52.2 + 70 + 50
Perimeter of triangle ABC = 122.2 + 50
Perimeter of triangle ABC = 172.2
The perimeter of triangle ABC is 172.2 feet.
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Answer:
Step-by-step expA) The type of triangles are congruent triangles
B) By the use of SAS Congruency Postulate
C) The distance across for the sink hole is: 52.2 ft
D) The perimeter of triangle ABC is: 172.2 feet.
How to solve congruent triangles?
A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.
B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.
C) We know that:
AB = ED = 52.2
AB is the distance across the sink hole. Thus, it is 52.2 feet
D) AB = 52.2
BC = 70
AC = 50
Thus:
Perimeter of triangle ABC = AB + BC + AC
Perimeter of triangle ABC = 52.2 + 70 + 50
Perimeter of triangle ABC = 122.2 + 50
Perimeter of triangle ABC = 172.2
The perimeter of triangle ABC is 172.2 feet.
lanation:
Enter the number that belongs in the green box 7 4 8
What values of b satisfy 3(2b + 3)² = 36?
Answer:
The values of b that satisfy the equation are:
b = (2√3 - 3) / 2
b = (-2√3 - 3) / 2
In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.
Step-by-step explanation:
To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:
1. Divide both sides of the equation by 3:
(2b + 3)² = 12
2. Take the square root of both sides:
√[(2b + 3)²] = √12
Simplifying further:
2b + 3 = ±√12
3. Subtract 3 from both sides:
2b = ±√12 - 3
4. Divide both sides by 2:
b = (±√12 - 3) / 2
Simplifying further:
b = (±√4 * √3 - 3) / 2
b = (±2√3 - 3) / 2
Therefore, the values of b that satisfy the equation are:
b = (2√3 - 3) / 2
b = (-2√3 - 3) / 2
In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.
URGENT PLEASE
Find the area of the shaded region and round to the nearest tenth.
SHOW WORK AND ANSWER!
ANSWER
61.8 m^[2].
We first examine what we have which is:
A parallelogram with base 14m and height 8m
A circle with DIAMETER 8m
Given our area formulas, we know we have our b and h in our parallelogram formula given. If our circle diameter is 8m, our circle radius must be 4m. Therefore, we have every element of our formulas we need.
parallelogram area = b*h = 14*8 = 112m^[2]
circle area = pi*r^[2] = pi*4m^[2]=16*3.14=50.24m^[2].
now we just subtract our circle area from our parallelogram area, and round our answer to the nearest tenth (the first place to the right of the decimal):
112m^[2]-50.24m^[2]=61.76 m^[2].
Rounded to the nearest tenth, this number becomes 61.8 m^[2].
Twice the difference of a number 9 and 2 is . Use the variable b for the unknown number.
answer: 13/2 or 6 1/2
step-by-step explanation:
hihi so basically your problem is making a solvable equation so w variables and stuff
heres my explanation !
the difference of a number and 2 is b-2
twice the difference of a number and 2 would be 2(b-2)
number 9 = 9 (duh lol)
so
2(b-2) = 9
2b - 4 = 9
2b = 13
improper: b = 13/2
mixed: b = 6 1/2
Simplify the expression. What classification describes the resulting polynomial?
(8x2 + 3x) − (12x2 − 1)
The simplified expression is [tex]-4x^2 + 3x + 1[/tex], which is a quadratic polynomial. Option D.
To simplify the expression [tex](8x^2 + 3x) - (12x^2 - 1)[/tex], we can distribute the negative sign to each term within the parentheses:
[tex]8x^2 + 3x - 12x^2 + 1[/tex]
Next, we can combine like terms by adding or subtracting coefficients of similar powers of x:
[tex](8x^2 - 12x^2) + 3x + 1[/tex]
Simplifying further, we have:
[tex]-4x^2 + 3x + 1[/tex]
The resulting polynomial [tex]-4x^2 + 3x + 1[/tex] is a quadratic polynomial since it has a highest power of x^2 (the exponent of x is 2), which is[tex]-4x^2.[/tex]Quadratic polynomials are polynomials of degree 2 and can be represented by a parabola when graphed.
In summary, the simplified expression [tex](8x^2 + 3x) - (12x^2 - 1)[/tex] simplifies to [tex]-4x^2 + 3x + 1[/tex] , which is a quadratic polynomial. So Option D is correct
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Note the complete question is
Patricia serves the volleyabll to terri with an upward velocity of 19.5 ft/s . The ball is 4.5 feet above the ground when she strikes it. How long does terri have to react before the volleyball hits the ground ? Round your answer to gwo decimal places
Terri have to react 1.42 seconds before the volleyball hits the ground.
What are quadratic equations?Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is:
[tex]\text{ax}^2 + \text{bx} + \text{c} = 0[/tex]
Given data:
Velocity [tex](v_0)[/tex] = 19.5 ft/sHeight [tex](h_0)[/tex] = 4.5 ftThe height can be modeled by a quadratic equation.
[tex]h(t)=-16t^2+v_0t+h_0[/tex]
Where h is the height and t is the time.
[tex]h(t)=-16t^2+19.5t+4.5[/tex]
[tex]-16t^2+19.5t+4.5=0[/tex]
[tex]a = -16, b = 19.5, c = 4.5[/tex]
It looks like a quadratic equation. we can solve it by quadratic formula.
[tex]\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\rightarrow t=\dfrac{-19.5\pm\sqrt{(-19.5)^2-4\times(-16)(4.5)} }{2(-16)}[/tex]
[tex]\rightarrow t=\dfrac{-19.5\pm\sqrt{380.25+288} }{-32}[/tex]
[tex]\rightarrow t=\dfrac{-19.5\pm25.851 }{-32}[/tex]
[tex]\rightarrow t=\dfrac{-19.5-25.851 }{-32}, \ t=\dfrac{-19.5+25.851 }{-32}[/tex]
[tex]\rightarrow t=1.42, \ t=-0.20[/tex]
Time cannot be in negative. So neglect t = –0.235.
Hence, Terri have to react 1.42 seconds before the volleyball hits the ground.
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Using the physics concept of projectile motion and inputting the given values into the appropriate equation, we can determine the time it takes for the volleyball to hit the ground after being served
Explanation:This question is a classic use of physics, more specifically, the concept of projectile motion. Here, the volleyball can be conceived as a projectile. When Patricia serves the ball upward, the ball will first ascend and then descend due to gravity.
Let's use the following equation which is a version of kinematic equations to solve this problem, adjusting for the fact that we're dealing with an initial height of 4.5 ft and an ending height of 0 ft (when the ball hits the ground). The equation y = yo + vot - 0.5gt² , where:
y is the final vertical position (which we'll take to be 0),yo is the initial vertical position (in this case, the 4.5 feet above the ground),vo is the initial vertical velocity, t is the time (which we're trying to find), andg is the acceleration due to gravity, with the value approximately 32.2 feet per second squared.
Setting y=0, yo=4.5 feet, vo=19.5 feet/second, and g=32.2 feet/second², and plug these values into the equation, we'll get a quadratic equation in the form of 0 = 4.5 + 19.5t - 16.1t². Solve that equation for t to find the time it takes for the ball to hit the ground.
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question is in the picture, please explain how you got the answer with steps.
Answer: [tex]\frac{8}{5}[/tex]
Step-by-step explanation:
You can put it into a ratio when the units are the same.
Let's convert 15 ft to yards
3 ft = 1 yd
So divide 15 by 3
15ft = 5 yd
So the ratio you want is:
8 yds to 5 yds
To write that in fraction ratio form:
[tex]\frac{8}{5}[/tex] >Keep as improper fraction for ratios
Find the probability that a randomly selected point within the square falls in the red-shaded triangle. 3 3 4 P = [?] 4
The required probability is 3 √7 / 32.
Given, a square with sides of length 4 units and a red-shaded triangle with sides 3 units, 3 units and 4 units. We need to find the probability that a randomly selected point within the square falls in the red-shaded triangle.To find the probability, we need to divide the area of the red-shaded triangle by the area of the square. So, Area of square = 4 × 4 = 16 square units. Area of triangle = 1/2 × base × height.
Using Pythagorean theorem, the height of the triangle is found as: h = √(4² − 3²) = √7
The area of the triangle is: A = 1/2 × base × height= 1/2 × 3 × √7= 3/2 √7 square units. So, the probability that a randomly selected point within the square falls in the red-shaded triangle is: P = Area of triangle/Area of square= (3/2 √7) / 16= 3 √7 / 32.
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what is the y intercept of y=7
Answer:
7
Step-by-step explanation:
The line represented by the equation y = 7 is a horizontal line that passes through the y-axis at 7, so the y intercept of this line is 7
A rocket is fired vertically upward. Its height h(t) in meters above the ground at t seconds is given
by h = -4.9t² +232t + 185.
How high was the rocket when it was initially launched?
meters
How high is the rocket after 9 seconds?
meters
What is the velocity of the rocket after 9 seconds?
m/s
What is the acceleration of the rocket after 9 seconds?
m/s^2
Submit Question
The rocket is at a height of 1876.1 meters after 9 seconds,the velocity of the rocket after 9 seconds is 143.8 m/s and the acceleration of the rocket after 9 seconds is -9.8 m/s².
To find the height of the rocket when it was initially launched, we can plug in t = 0 into the equation h(t) = -4.9t² + 232t + 185.
h(0) = -4.9(0)² + 232(0) + 185
= 0 + 0 + 185
= 185
Therefore, the rocket was initially launched at a height of 185 meters.
To find the height of the rocket after 9 seconds, we can plug in t = 9 into the equation h(t) = -4.9t² + 232t + 185.
h(9) = -4.9(9)² + 232(9) + 185
= -4.9(81) + 2088 + 185
= -396.9 + 2088 + 185
= 1876.1
Therefore, the rocket is at a height of 1876.1 meters after 9 seconds.
To find the velocity of the rocket after 9 seconds, we can take the derivative of the height function h(t) with respect to time (t) and evaluate it at t = 9.
The velocity function v(t) is the derivative of h(t) with respect to t:
v(t) = dh/dt = d/dt(-4.9t² + 232t + 185)
= -9.8t + 232
v(9) = -9.8(9) + 232
= -88.2 + 232
= 143.8
Therefore, the velocity of the rocket after 9 seconds is 143.8 m/s.
To find the acceleration of the rocket after 9 seconds, we can take the derivative of the velocity function v(t) with respect to time (t) and evaluate it at t = 9.
The acceleration function a(t) is the derivative of v(t) with respect to t:
a(t) = dv/dt = d/dt(-9.8t + 232)
= -9.8
a(9) = -9.8
Therefore, the acceleration of the rocket after 9 seconds is -9.8 m/s².
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What are the coordinates of the focus of the parabola?
y=−18x2−2x−4
A (−8, 6)
B (−8, 2)
C (8, 6)
D (8, 2)
Step-by-step explanation:
To find the coordinates of the focus of a parabola in the general form y = ax^2 + bx + c, you can use the formula (h, k) where h = -b/(2a) and k = (4ac - b^2)/(4a).
In the given equation y = -18x^2 - 2x - 4, we can identify that a = -18, b = -2, and c = -4. Plugging these values into the formulas, we get:
h = -(-2)/(2*(-18)) = 1/18
k = (4*(-18)*(-4) - (-2)^2)/(4*(-18)) = -71/9
Therefore, the focus of the parabola is (1/18, -71/9).
None of the given answer options match the coordinates of the focus calculated, so none of the options (A, B, C, D) are correct.
Like us, mice are warm-blooded creatures. Their bodies must maintain a constant
temperature of 37°C, regardless of the temperature of their environment. Doing so burns
calories. The more severe the temperature difference, the more calories the mouse must
burn to maintain its body temperature. Consulting the research literature, you found the
following model:
C = 0.37219T + 1,560
Where C is the number of calories an idle mouse burns each day and T is the temperature
of its environment in °C. What is the most comfortable temperature for an idle mouse?
(This is the temperature where it burns the least calories per day). How many calories will
it burn each day at that temperature?
At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.
According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.
To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.
To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:
dC/dT = 0.37219 = 0
Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.
Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.
For example, if we take a temperature of 20°C, we can calculate the calorie burn:
C = 0.37219 * 20 + 1,560
C = 7.4438 + 1,560
C ≈ 1,567.4438 calories per day
Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.
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write three fractions that equal to 5%
Answer:
4/10 simplified 2/5
if it does not help I am so sorry
Step-by-step explanation:
What type of equation will best fit the data below
Answer:
Quadratic equation. Linear would be a straight line and exponential would continue to grow; only quadratic equations are shaped like parabolas.
linear
if you add 2 cats to a tree and took one down you would have 0 in the tree so if you add 2+2=4 you can find every answer in the book.
your wellcomed
write an inequality to represent the situation. The temp. stayed above -15 degrees. answer The question correctly or no brainliest
Answer: t > -15
Step-by-step explanation:
Let t be equal to the temperature. If the temperature stayed above -15, this means the temperature was greater than -15 (not equal to or less than). We can write this inequality as:
t > -15
Help pls! Fairly easy
Answer:
1/2 of an hour ( I think )
Step-by-step explanation:
The second longest time that was recorded was 2/3/4 (whole/numerator/denominator) of a hour while the second shortest time was 2/1/4 of a hour. When you subtract 2/1/4 from 2/3/4 you end up with 2/4. Since 2/4 can be simplified to 1/2 you would say there is a 1/2 hour different between the second longest and second shortest time spent reading.
Write and solve an inequality to find the possible values of x.
The inequality tha calculates the possible values of x is x < 2
How to determine the inequality tha calculates xFrom the question, we have the following parameters that can be used in our computation:
The figure
Where, we have
3x + 2 < 10
And, we have
2x + 6 < 10
Evaluate the expressions
So, we have
3x < 8 and 2x < 4
Evaluate
x < 8/3 and x < 2
Hence, the inequality tha calculates x is x < 2
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The water usage at a car wash is modeled by the equation W(x) = 5x3 + 9x2 − 14x + 9, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours. Write a function, C(x), to model the water used by the car wash on a shorter day. C(x) = 5x3 + 7x2 − 14x − 6 C(x) = 4x3 + 7x2 − 14x + 6 C(x) = 4x3 + 7x2 − 14x − 6 C(x) = 5x3 + 7x2 − 14x + 6
URGENT
The area of a kite is 180 cm^2. The length of one diagonal is 16cm. What is the length of the other diagonal?
SHOW WORK AND ANSWER PLEASE
The length of the other diagonal is 11.25 cm.
What is area?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
In this question, we are given the following:
The area of a kite is 180. One of the diagonals is 16.
What is the length of the other diagonal?
The details of the solution are as follows:
We know that,
The area of a kite is the product of the diagonals divided by 2:
[tex]\text{A} = \dfrac{(\text{d}^1 \times \text{d}^2)}{2}[/tex]
You can substitute what we have:
[tex]180= \dfrac{(16 \times \text{d}^2)}{2}[/tex]
And solve.
[tex]180 = 16 \times \text{d}^2[/tex]
[tex]\text{d}^2=\dfrac{180}{16}[/tex]
[tex]\text{d}^2=\bold{11.25 \ cm}[/tex]
Therefore, the length of the other diagonal = 11.25 cm.
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if a coin is flipped 35 times and lands on heads 21 times what is the relative frequency of Landing on heads
Work Shown:
21/35 = (7*3)/(7*5) = 3/5
To find the number in a square, add the numbers in the two circles
connected to it.
Fill in the missing numbers.
The missing values in the quantitative reasoning given are : -2, 13 and 9
Given the rule :
square = circle + circleWe can deduce that :
circle = square - circleFor the left circle :
circle = -6 - (-4) = -6 + 4 = -2
For the right circle :
circle = 11 - (-2) = 11 + 2 = 13
For the left square :
square = 13 + (-4)
square = 13 -4 = 9
Therefore, the missing values are : -2, 13 and 9
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The data reflects the amount of time spent on homework (x), paired with a corresponding test grade (y).
A graph has time spent on homework (hours) on the x-axis and test grade on the y-axis. A line of best fit has equation y = 7.9 x + 72.
How can the y-intercept of the line be interpreted?
The minimum time spent on homework is approximately 72 hours.
The average time spent on homework is approximately 7.9 hours.
If no time is spent on homework, the test grade is approximately 72.
If no time is spent on homework, the test grade is approximately 7.9.
The y-intercept of the line of best fit can be interpreted as the predicted test grade when no time is spent on homework, which in this case is approximately 72. However, it is important to consider the limitations and potential sources of error in any statistical analysis.
In statistics, linear regression is a commonly used statistical method for analyzing the relationship between two variables, such as time spent on homework and test grades. A line of best fit, also known as a regression line, is a line that summarizes the linear relationship between the variables. In this case, the line of best fit has an equation of y = 7.9 x + 72.
The y-intercept of the line is the point where the line intersects with the y-axis. It represents the value of y when x is equal to zero. In other words, it is the predicted test grade when no time is spent on homework. According to the given equation, the y-intercept is 72. This means that if a student spends no time on homework, they can still expect to receive a test grade of 72.
However, it is important to note that this interpretation assumes that the line of best fit is an accurate representation of the relationship between time spent on homework and test grades. Additionally, there may be other variables that influence test grades, such as innate ability, test-taking skills, or external factors like test anxiety or distractions during the exam.
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