The range, standard deviation, and variance of the numbers of medals won by these countries are 28, 8.845, and 78.2353, respectively.
What is a Range?A range is given to a parameter to allow maximum leverage to the parameter. for example, if a vendor wants a rod of diameter 20 cm, then he may give a range of ±1 cm., which means he will accept the rod of 19(20-1) cm to 21(20+1) cm.
The range of the numbers of medals won by these countries is,
Range = Max - Min = 29 - 1 = 28
To find the standard deviation we need to know the following details,
Sum of the number of medals = ∑x = 234Sum of the square of the number of medals = ∑x² = 4372Number of observations = n = 18Now, the standard deviation of medals won by these countries is,
[tex]\sigma = \sqrt{\dfrac{\sum x^2 - \frac1n (\sum x)^2}{n-1}}\\\\\sigma = \sqrt{\dfrac{\4372 - \frac{234^2}{18}}{18-1}}\\\\\sigma = 8.845[/tex]
The variance of the numbers of medals won by these countries is,
v = σ²
v = 78.2353
Hence, the range, standard deviation, and variance of the numbers of medals won by these countries are 28, 8.845, and 78.2353, respectively.
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In the year 2000, a house was valued at $60 000.
In 2010, the same house was valued at $80 000.
Work out the value of the house in 2010 as a percentage of it value in 2000
The percentage by which the cost is increasing will be 75%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A fraction of 100 can be used to express the ratio.
The percentage of the 8th graders who want to go to the water slides is found from;
In the year 2000, a house was valued at $60 000.
In 2010, the same house was valued at $80 000.
The percentage value is found as;
[tex]\% = \frac{60000}{80000} \times 100 \\\\ \% =75 \%[/tex]
Hence the percentage by which the cost is increasing will be 75%.
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Find the perimeter of this
Tringle
8 cm
7 cm
5 cm
answer is
A. 35 cm
B. 40 cm
C. 20 cm
D. 12.5 cm
Answer:
C) 20cm
Step-by-step explanation:
Perimeter is the distance around the edge of the shape.
8 + 7 + 5 = 20
Answer:
20 is answer
Step-by-step explanation:
as perimeter= sum of all side
= 8 +7+5=2ocm
What is the length of CD? In this diagram, AABC~ AEDC.
The length of CD will be option C. 3
From given diagram, triangle ABC and EDC meet at a common vertex C.
So, triangle ABC and EDC both are congruent to each other.
Applying the similarity property of congruence, ratio of the congruent triangles' corresponding sides will be equal.
Therefore,
AB/ED = AC/EC = BC/CD
AC/EC = BC/CD
18/6 = (12 - x)/x
Simplifying the expression,
We get
18x = 6(12 - x)
Multiplicating the terms in right hand side,
18x = 72 - 6x
Solving 6x on both sides,
we get
18x + 6x = 72 - 6x + 6x
24x = 72
Dividing both the sides by 24, we get
24x/24 = 72/24
x = 3
Hence, the length of CD is 3.
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What are the roots of x In-10x2 + 12x-9=0? OA. 61√6 -1 10 31√6 10 OB. O C. 31√24 10131/24 OD. ti√24 OE. 1, 2:√6 51 10 What are the roots of x In - 10x2 + 12x - 9 = 0 ? OA . 61√6 -1 10 31√6 10 OB . O C. 31√24 10131/24 OD . ti√24 OE . 1 , 2 : √6 51 10
Answer:
9=0
Step-by-step explanation:
9=0
The roots of x in the equation -10x² + 12x - 9 = 0 are:
x = (3/5) + (3/5)√(6)i
x = (3/5) - (3/5)√(6)i
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
To find the roots of x in the equation -10x² + 12x - 9 = 0, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation in standard form (ax² + bx + c).
In this case, a = -10, b = 12, and c = -9. Substituting these values into the quadratic formula, we get:
x = (-12 ± √(12² - 4(-10)(-9))) / 2(-10)
x = (-12 ± √(144 - 360)) / (-20)
x = (-12 ± √(-216)) / (-20)
Substituting this into the expression for x, we get:
x = (-12 ± 6√(6)i) / (-20)
Simplifying the expression further, we get:
x = (3/5) ± (3/5)√(6)i
Therefore, the roots of x in the equation -10x² + 12x - 9 = 0 are:
x = (3/5) + (3/5)√(6)i
x = (3/5) - (3/5)√(6)i
These roots are complex conjugates of each other.
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Identify the common ratio and first term and fill in the recursive formula for each of the following geometric sequences.
The first term will be 4 and the common ratio will be 2. And the nth term will be given as [tex]\rm a_n = a_{n -1} \cdot 2[/tex].
The complete question is attached below.
What is the geometric sequences?Let a be the first term and r be the common ratio. Then the geometric sequences will be
[tex]\rm a_n = a_{n -1} \cdot r[/tex]
The geometric sequence is given below.
4, 8, 16, 32, 64,................
Then the first term will be 4 and the common ratio will be 2.
And the nth term will be given as [tex]\rm a_n = a_{n -1} \cdot 2[/tex].
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I need to know the answer
Answer: [tex]f(x)=-(x-5)^{2}(x+2)[/tex]
Step-by-step explanation:
There is a double root at x=5 and a single root at x=-2, so we know f(x) is of the form [tex]f(x)=a(x-5)^{2}(x+2)[/tex] for some constant a.
To find a, we can substitute the coordinates of the y-intercept, (0, -50).
[tex]-50=a(0-5)^{2}(0+2)\\\\-50=50a\\\\a=-1[/tex]
So, [tex]f(x)=-(x-5)^{2}(x+2)[/tex]
Mary is going to roll a six-sided die. What is the probability that the die lands on the number 3? Input your answer in fraction form
Answer:
added in the picture
Step-by-step explanation:
added in the picture
Lila wants to represent the following statement: seven times some number plus thirteen. How can she write this as an expression?
Answer: 7x+13
Step-by-step explanation:
7 is being multiplied by some number (x) and then the answer to that is added to 13.
Suppose you are standing in a parking lot near a building, and the winter air temperature is 0 degrees Celsius. At that temperature, sound travels about 331 meters per second. If you sound a horn and it takes 0.7 seconds to hear the echo, how far away is the building?
The building is 231.7 m far away.Distance can refer to a physical length or an estimate based on other factors in physics or common use.
What is distance?Distance is a numerical representation of the space between two objects or locations. |AB| is a symbol for the distance between two points A and B.
Given data;
Speed of sound = 331 meters per second
Time = 0.7 sec
The distance from the building is;
d=v×t
d=331 m/sec × 0.7 sec
d=231.7 m
Hence the building is 231.7 m far away.
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Which expression is equivalent to...
Answer: the fourth one
Step-by-step explanation:
Answer:
D.) 8x¹²y³
Step-by-step explanation:
When an expression is raised to a power, you have to raise everything in the expression to the power when simplifying. This includes the coefficients and variables. When a variable already raised to a power is raised to another power, the powers are multiplied.
Therefore,
2³ = 8
(x⁴)³ = x⁴*³ = x¹²
(y)³ = y³
Combined, the final answer is 8x¹²y³.
How do I find the domain and range in this graph?
Answer:
Domain: [tex]-4 < x \leq 4[/tex]Range: [tex]0 \leq y \leq 4[/tex]Step-by-step explanation:
The domain is the set of x values, and the range is the set of y values.
10. A Chemical balance needs to weigh 237 grams using weights of 50 grams , 20 grams , 10 grams and 1 gram . How many of each weight is needed ?
Answer:
237 grams
50 * 4
= 200
4 weight of 50 g
1 weight of 20g
1 weight of 10g
7 weight of 1g
Group of 5 people can do a piece of work in 6hrs- Calculate the time a group of 8 people working half the rate of first group could take
The time taken by a group of 8 people working half the rate of the first group is 7.5 hours.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
A Group of 5 people can do a piece of work in 6hrs.
5 people, at a rate of 1, and the time taken is 6 hours
Work done is 30
8 people, at a rate of 1/2, and the time taken is x hours
8(1/2)x = 30
x = 60/8 = 7.5 hours
Thus, the time taken by a group of 8 people working half the rate of the first group is 7.5 hours.
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How to 24-[5408÷48{×41+701]-240}-240÷16
do in oder of pemdas....
answer this 14+20-48
t
if cp=rs 400, loss=10% find sp
Answer:
cp = rs 400
loss = 10%
Then SP = 400 - 10% of 400
= 400 - 40
= 360
Therefore SP = Rs. 360
Question 4(Multiple Choice Worth 4 points)
Which of the following is a rational number?
√1. √2. √3, √5
O√1
O √2
O√3
√√5
Answer:
1
Step-by-step explanation:
The square root of 1 is 1 so it is a rational number while others are irrational
Please help! Solve the equation on the interval [0,2pi)
Answer:
[tex]\frac{5pi}{6}[/tex]
Step-by-step explanation:
Answer:
[tex]x = \dfrac{\pi}{6}, \dfrac{5 \pi}{6}[/tex]
Step-by-step explanation:
[tex]\begin{aligned}3 \sin x & = \sin x + 1\\\implies 3 \sin x - \sin x & = 1\\2 \sin x & = 1\\\sin x & = \dfrac{1}{2}\\\implies x & = \sin^{-1}\left(\dfrac{1}{2}\right)\\x & = \dfrac{\pi}{6} \pm 2 \pi n, \dfrac{5 \pi}{6}\pm 2 \pi n\end{aligned}[/tex]
Therefore, the value of x in the interval [0, 2π) is:
[tex]x = \dfrac{\pi}{6}, \dfrac{\boxed{5} \pi}{\boxed{6}}[/tex]
Triangle P R Q is shown. Angle R P Q is 39 degrees. The length of P R is 6, the length of R Q is p, and the length of P Q is 8.
Law of cosines: a2 = b2 + c2 – 2bccos(A)
Which equation correctly uses the law of cosines to solve for the missing side length of TrianglePQR?
62 = p2 + 82 – 2(p)(8)cos(39°)
p2 = 62 + 82 – 2(6)(8)cos(39°)
82 = 62 + p2 – 2(6)(p)cos(39°)
p2 = 62 + 62 – 2(6)(6)cos(39°)
According to law of cosines the length of RQ can be written as [tex]p^{2} =6^{2} +8^{2} -2*6*8cos(39)[/tex].
Given the length PR is 6 , the length of RQ is p, the length of PQ is 8 and the angle RPQ is 39 degrees.
A length of the triangle can be written as according to law of cosines if sides are given and one angle is [tex]a^{2} =b^{2} +c^{2} -2bccos(A)[/tex]
We have to just put the values in the above equation.
as [tex]p^{2} =6^{2} +8^{2} -2*6*8cos(39)[/tex].
p is the side opposite to angle given , the length of other sides are 6 and 8 and angle is 39 degrees.
Hence the side can be written as according to law of cosines if the angle is 39 degrees is as [tex]p^{2} =6^{2} +8^{2} -2*6*8cos(39)[/tex].
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Answer: OPTION B
Step-by-step explanation:
edge22
Find the area.
O 121.12 ft²
O 53.1 ft²
O 152.3 ft²
O212 ft²
7 ft
8 ft
The area of the geometry will be 53.1 square feet. Then the correct option is B.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The figure is the combination of the triangle and semicircle.
Then the area will be
Area = area of triangle + area of semicircle
Area of triangle = 1/2 x 8 x 7
Area of triangle = 28 square ft
Area of semicircle = (π / 8) x 8²
Area of semicircle = 25.13 square ft
Then the area of the geometry will be
Area = 28 + 25.13
Area = 53.1 square feet
Then the correct option is B.
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Which statement is true of the function f(x) = Negative RootIndex 3 StartRoot x EndRoot? Select three options.
The function is always increasing.
The function has a domain of all real numbers.
The function has a range of {y|–Infinity < y < Infinity}.
The function is a reflection of y = .
The function passes through the point (3, –27).
the correct options are:
The function has a domain of all real numbers.The function has a range of {y|–Infinity < y < Infinity} (this is the same as saying that the range is the set of all real numbers.Which statements are true about the function?
Here we have the function:
[tex]F(x) = -\sqrt[3]{x}[/tex]
First, this is a cubic root, so its domain is the set of all real numbers (same for the range). And we know that the cubic root is an increasing function, so if we put a negative sign before it, we will have a decreasing function.
Then the correct options are:
The function has a domain of all real numbers.The function has a range of {y|–Infinity < y < Infinity} (this is the same as saying that the range is the set of all real numbers.The fourth option is incomplete, so we can't conclude if it is true or not, it would be true if it said:
"The function is a reflection over the x-axis of y = ∛x"
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Answer:
b, c, d
Step-by-step explanation:
calculate the median for: 5, 10, 12, 4, 6, 11, 13, 5r
Step-by-step explanation:
please mark me as brainlest
Answer:
8
Step-by-step explanation:
We need to sort your set into Least-to-Greatest order.
4, 5, 5, 6, 10, 11, 12, 13
That is your set in least to greatest order.
Which 2 numbers are in the middle?
They are 6 and 10.
Now, we find the mean of 6 and 10.
(6+10)/2 = 8
8 is your median
Someone answer this, thank you!
Step-by-step explanation:
1) the equation of the line represented is
y=0.5x+3 (slope-interception form), the slope is 0.5, the intercept is 3.
x-2y+6=0 (common form);
2) x-intersection is at -6, y-intersection is at 3.
3(2x - 3) = 4(2x + 4)
Answer:
Step-by-step explanation:
Open the brackets
3 x 2x = 6x
3x -3 = -9
4 x 2x= 8x
4 x 4= 16
6x - 9 = 8x + 16
Move same to same side
-16 -9 = 8x - 6x
-25 = 2x
x -25/2
x = -12.5
Answer:
x = -25/2 or -12.5Step-by-step explanation:
3*(2x - 3) = 4*(2x + 4)
6x - 9 = 8x + 16
6x - 8x = 16 + 9
-2x = 25
x = -25/2 or -12.5
------------------------
check
3 * (2 * (-12.5) - 3) = 4 * (2 * (-12.5) + 4)
3 * (25 - 3) = 4 * (12.5 + 4)
3 * 22 = 4 * 16.5
66 = 66
the answer is good
David rolls a fair dice 30 times. How many times would David expect to roll a number greater than 3?
Answer:
15
Step-by-step explanation:
so if its a 6 faced dice then there is a 3/6 numbers greater than 3. which simplifies to 1/2. 30(1/2)= 15
Solve the following system of equations. -7x+5y=-11; -4x+3y= -7
Answer:
X = (-2) Y = (-5)- 7x + 5y= (-11) -------(1)
-4x + 3y,= (-7) ----------(2)
Solving by using elimination methodMultiplying eq 1 with 3 and eq 2 with 5
3( -7x + 5y) = 3(-11)
5(- 4x + 3y) = 5(-7)
-21x + 15y = (-33)
-20x + 15y,= (-35)
Subtracting both the eq.
-x = 2
x = (-2)
Putting this value in eq. 1
- 7x + 5y= (-11)
-7(-2)+ 5y= (-11)
14 + 5y = (-11)
5y = (-11) - 14
5y= (-25)
y = (-5)
Tina's application for graduate school was ranked 54 out of 300 applications. Her twin sister's application to a
different graduate school was ranked 23 out of 175 applications.
a. Which sister had the higher percentile ranking?
b. If you had the data on the cumulative GPA of each student in each school in June 2019, which measure of
average would be the most meaningful - mean, median, mode? Explain
A percentage is a way to describe a part of a whole. The percentile ranking of Tina's sister is higher than her.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
A.)
The percentile ranking of Tine is,
Tina's Ranking = [1 - (54/300)] × 100% = 82%
Tina's soster Ranking = [1 - (23/175)] × 100% = 86.85%
Hence, the percentile ranking of Tina's sister is higher than her.
B.) It shows that you can succeed in the graduate examination if you exceed this value.
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Drag each sign and value to the correct location on the image. Each sign and value can be used more than once, but not all signs and values will be used. The vertices of an ellipse are at (-5, -2) and (-5, 14), and the point (0, 6) lies on the ellipse. Drag the missing terms and signs to their correct places in the standard form of the equation of this ellipse.
The complete equation of the ellipse is [tex]\frac{(x + 5)^2}{5^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]
How to complete the vertex equation?The complete question is in the attachment
The given parameters are:
Vertex = (-5,-2) and (-5,14)Point = (-0,6)The vertex is represented as (h, k ± a).
So, we have:
h = -5
k + a = 14
k - a = -2
Add the last two equations
2k = 12
Divide by 2
k = 6
Substitute k = 6 in k + a = 14
6 + a = 14
Solve for a
a = 8
The ellipse equation is represented as:
[tex]\frac{(x - h)^2}{b^2} + \frac{(y - k)^2}{a^2} = 1[/tex]
So, we have:
[tex]\frac{(x + 5)^2}{b^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]
The ellipse passes through the point (0,6).
So, we have:
[tex]\frac{(0 + 5)^2}{b^2} + \frac{(6 - 6)^2}{8^2} = 1[/tex]
This gives
[tex]\frac{5^2}{b^2} + \frac{0}{8^2} = 1[/tex]
Evaluate the quotient
[tex]\frac{5^2}{b^2} = 1[/tex]
Cross multiply
[tex]b^2 = 5^2[/tex]
Take the square root of both sides
b = 5
Substitute b = 5 in [tex]\frac{(x + 5)^2}{b^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]
[tex]\frac{(x + 5)^2}{5^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]
Hence, the complete equation of the ellipse is [tex]\frac{(x + 5)^2}{5^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]
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What is the length of BC¯¯¯¯¯?
Answer:
meight you gotta do better then that
Step-by-step explanation:
a picture is probably necessary
Find the x-intercept of the line whose equation is 8x + 2y = 4.
Answer: Hope this helps you
1/2
Step-by-step explanation:
To find the x-int of any equation, you will need to replace the y with a 0 since when the x-int is when y is 0.
8x+2y = 4 ➨ 8x+2*0 = 4
Now I will do 2*0 which anything times 0 is equal to 0. And we are left with the equation of:
8x = 4
Now I will divide both sides by 8, which isolates our x.
x = 1/2
The x-int is 1/2.
