The given data are
2, 9, 8, 7, 9, 7
To find the standard deviation we will find the mean at first
[tex]Mean=\frac{sum}{no.}[/tex]The sum = 2 + 9 + 8 + 7 + 9 + 7 = 42
The no. = 6, then
[tex]\begin{gathered} Mean=\frac{42}{6} \\ \\ Mean=7 \end{gathered}[/tex]Then we will square the difference between each number and the mean
[tex]\begin{gathered} (2-7)^2=25 \\ (9-7)^2=4 \\ (8-7)^2=1 \\ (7-7)^2=0 \\ (9-7)^2=4 \\ (7-7)^2=0 \end{gathered}[/tex]Add all the answers
[tex]\sum_^(x-M)^2=25+4+1+0+4+0=34[/tex]Divide it by the no. and find the square root
[tex]\begin{gathered} \sigma=\sqrt{\frac{\sum_^(x-M)^2}{N}} \\ \\ \sigma=\sqrt{\frac{34}{6}} \\ \\ \sigma=2.380476143 \end{gathered}[/tex]The standard deviation is about 2.38 to the nearest hundredth
complete the flow proof . complete parts a. through d.
KS is common in both the triangles
so, to complete SSS rule KS = KS will be the answer.
so the answer is b
The table shows values for a linear function, f(x). What is an equation for f(x)?
Given a table that shows values for a linear function, f(x). we are asked to determine the equation of f(x).
Table:
x f(x)
-1 -8
3 -5
7 2
11 1
First, let us consider the lines of the equation as:
f(x) = ax + b
When x = -1 f(x) = -8
f(-1) = a(-1) + b
-8 = -a + b ------------------ eqn I
When x = 3 f(x) = 5
f(3) = a(3) + b
-5 = 3a + b ------------------- eqn II
subtract eqn I from eqn II:
-5 - (-8) = (3a + b) - (-a + b)
-5 + 8 = 3a + b + a - b
3 = 4a (-b and +b cancels out).
divide both sides by 4:
a = 3/4
Let's put the value of a = 3/4 into equation I
-8 = -a + b
-8 = -3/4 + b
make b the subject of formula:
b = -3/4 + 8
b = -32 + 3
4
b = -29/4
Let's now place the values of a an b into the lines equation:
recall the lines equation is :
f(x) = ax + b
f(x) = 3/4 x - 29/4.
Determine the most specific name for quadrilateral JKLM if the coordinates of the vertices are:J(-4,6), K(-1,2), L(1,6), M(4,2)JL ll KM PROOF:J.5JL is parallel to X-axis.bothvertices have y-coordinate at y = 6.KM Parallel to x axis, bothvertices have y-coordinate aty=2.43KM M1Determine Stopes of JK & LM(If slopes ave ithen sides arparallel):4517-42-8-3-10JK: 31-4,6) K(+1,2)x2 Y2xiyo2-6-4
To finish the demonstration that the quadrilateral JKLM is a rhombus we need to prove that side JK is congruent with side LM.
The length of a segment with endpoints (x1, y1) and (x2, y2) is calculated as follows:
[tex]\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substituting with points L(1,6) and M(4,2) we get:
[tex]\begin{gathered} LM=\sqrt[]{(4-1)^2+(2-6)^2} \\ LM=\sqrt[]{3^2+(-4)^2} \\ LM=\sqrt[]{9+16^{}} \\ LM=5 \end{gathered}[/tex]Given that opposite sides are parallel, all sides have the same length, and, from the diagram, the quadrilateral is not a square, we conclude that it is a rhombus.
Cecily's teacher held a raffle. To win the raffle, a student has to pick a paper scroll with an integer written on it. The chart shows the scrolls picked by Cecily and her friends. Name Paper Scroll Cecily 6.7 Marty -37 Jon 7/ 9 Fiona 3 1/3who picked the winning scroll a. Cecily picked the winning scrollb.Marty picked the winning Scrollc.jon picked the winning scrolld. fiona picked the winning scroll
Answer:
Note:
Integers are whole numbers.
They include 0, negative whole numbers, and positive whole numbers
Since the condition to win the rafle is to pick an interger, let us consider the number picked by each of the students and see if it is an integer or not.
Cecily picked 6.7
This is a decimal number, it is not an integer
Marty picked -37
This is an integer, since it is not a decimal and does not have a fraction component
Jon picked 7/9
This is a proper fraction, and it is not an integer
Fiona picked 3 1/3
This is a mixed fraction, it is not an integer.
The only student that picked an integer number is Marty, hence, she is the winner of the raffle.
Students are asked to add one tenth and 0.1. Several different answers were submitted: 1.1, 0.11, 0.2, 0.21, and 10.1. For each response, write a decimal number sentence that would produce that answer.
The wording for the decimal will be:
1.1 = one point one
0.11 = zero point eleven
0.2 = zero point two
0.21 = zero point two one
10.1 = ten point one
How to explain the decimal?It is important to note that a decimal simply means the number that's made of a whole number and a fraction.
From example 10.1 in wordings will be ten point one. In this case, the students are asked to add one tenth and 0.1. The decimals have been given in words above.
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Given a planar trapezoid ABCD whose height is BE. It is known that AB = 8cm A = 60 *, find the height ofthe trapezoid.
Solution:
Given the trapezoid:
To solve for the height of the trapezoid, we use the trigonometric ratio.
From the trigonometric ratios,
[tex]\sin\theta=\frac{opposite}{hypotenuse}[/tex]In this case, in the triangle AEB, θ is ∠A.
Thus,
[tex]\sin A=\frac{BE}{AB}[/tex]By cross-multiplying, we have
[tex]\begin{gathered} BE=AB\times\sin A \\ =8\times\sin60 \\ =8\times\frac{\sqrt{3}}{2} \\ \Rightarrow BE=4\sqrt{3}\text{ cm} \end{gathered}[/tex]Hence, the height of the trapezoid is
[tex]4\sqrt{3\text{ }}\text{ cm}[/tex]the volume of a sphere is 12348 pi in ³ calculate the radius of the sphere
The volume of a sphere is given by the expression:
[tex]V=\frac{4}{3}\pi\cdot r^3[/tex]Where V is the volume and r is the radius of the sphere. Solve this expression for r and replace for the given values to find the radius of the sphere, this way:
[tex]\begin{gathered} V=\frac{4}{3}\pi\cdot r^3 \\ 12348\pi=\frac{4}{3}\pi\cdot r^3 \\ \frac{12348\pi}{\pi}\cdot\frac{3}{4}=r^3 \\ 9261=r^3 \\ r=\sqrt[3]{9261} \\ r=21 \end{gathered}[/tex]The radius of the sphere is 21 inches.
Fill in the table using function rule
Y=6x+2
Using our equation y = 6x + 2, we were able to write out values for our table of function.
Function TableA function table is a table that shows which coordinates should be plotted in the coordinate system, so that you can draw the graph of the function.
Since we have our equation, we can proceed to find what values of y we would have when x is in a certain condition.
Using from -2 to + 5, we can have a good table of function.
When x = -2
y = 6x + 2
y = 6(-2) + 2 = -10
When x = -1
y = 6(-1) + 2 = -4
When x = 0
y = 6(0) + 2 = 2
When x = 1
y = 6(1) + 2 = 8
When x = 2
y = 6(2) + 2 = 14
When x = 3
y = 6(3) + 2 = 20
When x = 4
y = 6(4) + 2 = 26
When x = 5
y = 6(5) + 2 = 32
Using the values above, we have a good function table and can proceed to plot a graph if needed.
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Area of a triangle Find the area of the triangle below. Be sure to include the correct unit in your answer. Explanation Check 9 cml 19 cm 10 cm A 0 cm X cm² cm³ ?
Given
To find:
The area of the triangle.
Explanation:
It is given that,
That implies,
The area of the triangle is,
[tex]\begin{gathered} A=\frac{1}{2}\times b\times h \\ =\frac{1}{2}\times10\times9 \\ =5\times9 \\ =45cm^2 \end{gathered}[/tex]Hence, the area of the triangle is 45cm
²
19.Solve the inequality. Express your answer in the form of a graph and in interval notation. (x-3) / (x+6) ≤ 0
The inequality is given as,
[tex]\frac{x-3}{x+6}\leq0[/tex]Note that the denominator can never be zero otherwise the rational function would become indeterminate. So we have to exclude the value at which the denominator,
[tex]\begin{gathered} x+6=0 \\ x=-6 \end{gathered}[/tex]So the function is not defined at x = - 6.
Consider that the division of the numbers can be non-positive, only if exactly one of the numbers is non-positive.
So we have to obtain the interval in which one of the factors is positive and the other is negative.
CASE-1: When the numerator is positive and the denominator is negative,
Need help with figuring out if this is a system of equations
Given:
The system is:
[tex]\begin{cases}{2x+3y+10z=9} \\ {-x+2y+5z=1} \\ {3x+z=5}\end{cases}[/tex]The solution is (2,3,-1)
Find-:
The (2,3,-1) is the solution of function or not
Explanation-:
The solution is (2,3,-1) which means:
[tex]\begin{gathered} x=2 \\ \\ y=3 \\ \\ z=-1 \end{gathered}[/tex]Check the value for the given expression:
[tex]\begin{gathered} 2x+3y+10z=9 \\ \\ 2(2)+3(3)+10(-1)=9 \\ \\ 4+9-10=9 \\ \\ 3\ne9 \end{gathered}[/tex]So, it is not a solution of system.
85 is ___ tens and 25 ones
Answer:
6
Step-by-step explanation:
Because 25 ones is 25
So 85 - 25 = 60
60 = 6 tens
Which expressions are equivalent to log_4 (1/4 x2)
Answer:
The expression equivalent to the given logarithm is:
[tex]2\log _4(\frac{x}{2})[/tex]Explanation:
We want to know which expressions are equivalent to
[tex]\log _4(\frac{1}{4}x^2)[/tex]We have:
[tex]\begin{gathered} \log _4(\frac{x}{2})^2 \\ \\ =2\log _4(\frac{x}{2}) \end{gathered}[/tex]Function gis represented by the equation.g(x)=9(1/3)^x-4Which statement correctly compares the two functions?
So,
As you can see, the function g:
[tex]g(x)=9(\frac{1}{3})^x-4[/tex]Has the same behavior of the graph above.
That's because the rate (1/3) is less than 1, so the graph will decay.
The y- intercept of the function g is obtained when we make x=0:
[tex]\begin{gathered} g(0)=9(\frac{1}{3})^0-4 \\ g(0)=9-4 \\ g(0)=5 \end{gathered}[/tex]If we compare, both y-intercepts seem to be different.
Therefore,
what is the distance between -1 1/2 +5. Find absolute value
To find the absolute value of -1 1/2 +5 you make the addition:
You can write the mixed number also as -3/2 (because -1 is equal to -2/2 and -2/2 and 1/2 is -3/2).
You add fractions as follow:
[tex]\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d+b\cdot c}{b\cdot d}[/tex]You can write the 5 as 5/1:
[tex]-\frac{3}{2}+\frac{5}{1}=\frac{-3\cdot1+5\cdot2}{2\cdot1}=\frac{-3+10}{2}=\frac{7}{2}[/tex]As the addition of the given numbers is 7/2, the absolute value or the distance is:
[tex]\lvert\pm a\rvert=a[/tex][tex]\lvert-1\frac{1}{2}+5\rvert=\lvert\frac{7}{2}\rvert=\frac{7}{2}[/tex]Then, the distance is 7/2AC, DF, and GI are parallel. Use the figure to complete the proportion.JFFE?DE
Given that AC, DF, and GI are parallel, we can see that line JH bisects angle J. This means that triangles formed with the parallel lines are similar. Considering triangle JDF,
JF corresponds to JD
FE corresponds to DE
Thus, the ratios are
JF/FE = JD/DE
Find the median for the scores: 93,69,72,86,72,95,88,74,72,89,89,95,74,79
A set of data is given and it is required to find the median:
[tex]93,69,72,86,72,95,88,74,72,89,89,95,74,79[/tex]Recall that the Median is the middle element or the mean of two middle elements in a numerical data set with the elements ordered by their value.
Hence, to find the median, rearrange the scores either in ascending or descending order.
[tex]69,72,72,72,74,74,79,86,88,89,89,93,95,95[/tex]Next, highlight the two middle numbers since the frequency of the scores is even (14):
[tex]69,72,72,72,74,74,\boxed{79,86},88,89,89,93,95,95[/tex]Find the mean of the two middle numbers to calculate the median for the scores:
[tex]\frac{79+86}{2}=\frac{165}{2}=82.5[/tex]Hence, the median score is 82.5.
The median score is 82.5.
Simplify. (-3)2 -32 -30
We need to simplify the next given expression:
[tex](-3)^2-3^2-3^0[/tex]Let's solve each term:
[tex](-3)^2=(-3)(-3)=9[/tex][tex]3^2=3\cdot3=9[/tex]Finally, for the last term we need to use the next property:
[tex]a^0=1[/tex]Every whole number with an exponent of 0 will always equal one.
Therefore:
[tex]3^0=1[/tex]Now, we have the next expression:
[tex]9-9-1[/tex][tex]=-1[/tex]Hence, when we simplified the expression the result is -1.
what digit is in the thousands place 506,234
The thousands place is corresponding to the digit that if fourth from the unit.
So the digit in the thousands place of 506,234 is 6.
you roll a six-sided number cube find theprobabilsty of rolling each of the followingP(1 or 6)
When you roll a six-sided number cube you can get the next set of possible results:
[tex]\lbrace1,2,3,4,5,6\rbrace[/tex]You have a total of 6 possible results.
From the set of possible results you get the set of presults that are 1 or 6:
[tex]\lbrace1,6\rbrace[/tex]You have 2 results that are 1 or 6
The probability of rolling (1 or 6) is: The number of results that are 1 or 6 divided in the total number of possible results:
[tex]P(1or6)=\frac{2}{6}=\frac{1}{3}[/tex]Then, the probability of rolling (1 or 6) is 1/3PLEASE HELP ASAP!!! Evaluate!!!
Answer:
-5 I think
Step-by-step explanation:
Answer: -5
Step-by-step explanation:
1. Since f(-1) is -1, substitute it into the x's of the equation. The question would now be 4(-1)^2+5(-1)-4.
2. Solve and it would be -5
1) What is the remainder when 3x3 - 4x2 - 14x + 3 is divided by3x+5?A)A.43B)wiu0WI)D)IM
SOLUTION
The given polynomail is
[tex]3x^3-4x^2-14x+3[/tex]To be divided by
[tex]3x+5[/tex]Since the question requires to find the remainder
Then following remainder theorem
Set 3x+5 to zero and solve for x
[tex]\begin{gathered} 3x+5=0 \\ x=-\frac{5}{3} \end{gathered}[/tex]Substitute x=-5/3 into the given polynomial to get the remainder
[tex]\begin{gathered} 3(-\frac{5}{3})^3-4(-\frac{5}{3})^2-14(-\frac{5}{3})+3 \\ =3(-\frac{125}{27})-4(\frac{25}{9})+14(\frac{5}{3})+3 \\ =-\frac{125}{9}-\frac{100}{9}+\frac{70}{3}+3 \\ =\frac{-125-100+210+27}{9} \\ =\frac{12}{9} \\ =\frac{4}{3} \end{gathered}[/tex]Therefore, the remainder is
[tex]\frac{4}{3}[/tex]it is a graph I will send a picture of it
SOLUTION
The image of f(x) is given in the diagram.
Then the image of the function
[tex]f(x)-1\text{ means the f(x) as b}een\text{ shifted vertically down by one unit }[/tex]Thence the image of f(x)-1 is given below as
Therefore the right option is A
I WILL GIVE BRAINLIEST
Juan bought three and three-fourths pounds of pineapple and three and three-eighths pounds of strawberries for a fruit salad. After eating one and fifteen-sixteenths pounds of the fruit salad, how much was left?
five and three-sixteenths pounds
five and three-eighths pounds
five and nine-sixteenths pounds
seven and twenty-one sixteenths pounds
Salad was left (A) Five and three-sixteenths pounds.
Fraction is the comparison between numbers or mathematical quantities.
Given that, Juan bought pineapple of = (3 + 3/4) pounds = 15/4 pounds
Juan bought strawberries of = (3 + 3/8) pounds = 27/8 pounds
So now the amount total fruit salad = 15/4 + 27/8 = (30+27)/8 = 57/8 pounds
Juan eats = (1+15/16) = 31/16 pounds
Now salad left = 57/8 - 31/16 = (114-31)/16 = 83/16 = (5+3/16) pounds
Hence the correct option is (A).
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Question 60 state wether the triangle is an isosceles triangle,right triangle, neither of these or both.
Given:
The points of the triangle:
[tex]P_1=(7,2);P_2=(-4,0);P_3=(4,6)[/tex]Required:
To find out if the given triangle is an equilateral triangle or an isosceles triangle or both or none of these.
Explanation:
To find if the triangle is an equilateral triangle or an isosceles triangle we will have to first find the length of the sides by distance formula.
Distance formula is given by:
[tex]d=\sqrt{(x_2-x_1)_^2+(y_2-y_1)^2}[/tex]So applying the distance formula on side P₁P₂
Substituting the value of P₁ and P₂ in the distance formula we get
[tex]P₁P₂=\sqrt{(-4-7)^2+(0-2)^2}=\sqrt{(-11)^2+(-2)^2}=\sqrt{121+4}=\sqrt{125}=5\sqrt{5}[/tex]Now lets find the length of P₂P₃
Substituting the value of P₂ and P₃ in the distance formula we get
[tex]P₂P₃=\sqrt{(4-(-4))^2+(6-0)^2}=\sqrt{(4+4)^2+6^2}=\sqrt{8^2+6^2}=\sqrt{64+36}=\sqrt{100}=10[/tex]Now lets find the length of P₁P₃
Substituting the value of P₁ and P₃ in the distance formula we get
[tex]P₁P₃=\sqrt{(4-7)^2+(6-2)^2}=\sqrt{(-3)^2+(4)^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]S now we have the length of all three sides, that is
[tex]\begin{gathered} l(P₁P₂)=5\sqrt{5} \\ \\ l(P_2P_3)=10 \\ \\ l(P₁P_3)=5 \end{gathered}[/tex]If we add any two sides of triangle then it is greater than the third side so it is a triangle.
[tex]\begin{gathered} 5\sqrt{5}+5>10 \\ 5+10>5\sqrt{5} \\ 5\sqrt{5}+10>5 \end{gathered}[/tex]So it is a valid triangle. But the length of all the sides of triangle are different.
In equilateral triangle all the sides are same.
In isosceles triangle any sides are same.
Since here none of the sides are same so it is neither an equilateral triangle nor an isosceles triangle. It is a Scalene triangle with all three sides different.
Final answer:
The answer is none of these.
Mackenzie has a bag that contains 6 red marbles, 4 blue marbles, and 14yellow marbles. If she chooses one marble from the bag, what is theprobability that the marble is not yellow?O A. 7/ 금B.LINdC.soOD.
Probability that the marble is not yellow = 5/12
Explanations:Number of red marbles, N(Red) = 6
Number of blue marbles, N(Blue) = 4
Number of yellow maebles, N(Yellow) = 14
Total number of marbles, N(Total) = N(Red) + N(Blue) + N(Yellow)
N(Total) = 6 + 4 + 14
N(Total) = 24
Probability that the marble chosen is yellow, P(yellow) = N(yellow) / N(Total)
P(yellow) = 14/24
P(yellow) = 7/12
P(yellow) + P(not yellow) = 1
P(not yellow) = 1 - P(yellow)
P(not yellow) = 1 - 7/12
P(not yellow) = 5/12
Probability that the marble is not yellow = 5/12
Convert the angle 225° from degrees to radians. Enter your answer in terms of π.
Remember that:
[tex]\pi\text{ rad}=180^{\circ}[/tex]Dividing both sides by 180° we get:
[tex]\frac{\pi\text{ rad}}{180^{\circ}}=1[/tex]Which we can use as conversion factor to convert degrees to radians.
For an angle of 225°:
[tex]225^{\circ}=\frac{\pi\text{ rad}}{180^{\circ}}=\frac{225}{180}\cdot\pi\text{ rad}=\frac{5}{4}\cdot\pi\text{ rad}[/tex]Therefore, in terms of π:
[tex]225^{\circ}=\frac{5}{4}\pi\text{ rad}[/tex]Brad is going to send some flowers to his wife. Silvergrove Florist charges $3 per rose, plus $20 for the vase. Noah's Flowers, in contrast, charges $1 per rose and $30 for the vase. If Brad orders the bouquet with a certain number of roses, the cost will be the same with either flower shop. What would the total cost be?Write a system of equations, graph them, and type the solution.
To solve this exercise we must first identify our variables
• C, = Total cost
,• r ,= number of roses
,• v ,= number of vases
Now, with these variables we will formulate the equations that model the price of each of the flower shops. We have to take into account that Brad is only going to buy one vase
[tex]v=1[/tex]Silvergroce Florist
[tex]\begin{gathered} C=3r+20v \\ C=3r+20(1) \\ C=3r+20\to(1) \end{gathered}[/tex]Noah's Flowers
[tex]\begin{gathered} C=1r+30v \\ C=r+30(1) \\ C=r+30\to(2) \end{gathered}[/tex]We have two equations (1) and (2), to find the total cost that is the same in both flower shops, we only have to equal them to find the number of roses that Brad should buy
[tex]\begin{gathered} 3r+20=r+30 \\ 3r-r=30-20 \\ 2r=10 \\ r=\frac{10}{2} \\ r=5 \end{gathered}[/tex]Brad must buy 5 roses so that it costs the same at both florists. To know the cost we substitute in any equation (1) or (2) the number of roses
[tex]\begin{gathered} C=r+30 \\ C=5+30 \\ C=35 \end{gathered}[/tex][tex]\begin{gathered} C=3r+20 \\ C=3(5)+20 \\ C=15+20 \\ C=35 \end{gathered}[/tex]The total cost for 5 roses and a vase is $35Answer:
y = 20 + 3x
y = 30+x
( 5,35)
Step-by-step explanation:
Writing and solving a system of equations
Silvergrove Florist: 20 + 3x
Noah's Flowers: 30 + 1x where x is the number of roses
We want to know when they are equal
20+3x = 30+1x
Subtract x from each side
20+3x-x = 30+x-x
20+2x = 30
Subtract 20 from each side
20+2x-20 = 30-20
2x = 10
Divide by 2
2x/2 = 10/2
x = 5
The number of roses is 5
The cost is
30 +x = 30+5 = 35
(5,35)
Find the polynomial that represents the perimeter of the figure. simplify your answer.
The given diagram is a pentagon with different side measurements.
The perimeter is defined as the sum of all external boundaries of the figure.
So the perimeter (P) of the pentagon is equal to the sum of the 5 sides of the figure,
[tex]\begin{gathered} P=(3t^2-9)+(3t^2-9)+(2t^2+5)+(2t^2+5)+(t^3-t^2+8) \\ P=3t^2-9+3t^2-9+2t^2+5+2t^2+5+t^3-t^2+8 \\ P=t^3+(3t^2+3t^2+2t^2+2t^2-t^2)+(-9-9+5+5+8) \\ P=t^3+9t^2+(0) \\ P=t^3+9t^2 \end{gathered}[/tex]Thus, the perimeter of the figure is,
[tex]t^3+9t^2[/tex]Graph the function by first finding the relative extrema. f(x) = x² + 4x2-x-4 7 4 6 2
Graph the function by first finding the relative extrema.
__________________________________
f(x) = x^3 + 4x^2 - x - 4
f'(x) = 3x ^2 + 8x -1
c= 3x ^2 + 8x -1
Using the quadratic equation
[tex]x=\frac{-b\text{ }\pm\text{ }^{}\sqrt[]{b^2\text{ -4ac}}}{2a}\text{ = }\frac{-(8)\text{ }\pm\text{ }^{}\sqrt[]{8^2\text{ -4}\cdot3\cdot\text{ (-1)}}}{2\cdot3}[/tex]___________________
They want you to see the extreme points, but the easiest way is to evaluate 0 and check which graph matches
f(0) = 0^3 + 40^2 - 0 - 4
Point (0, -4)