Average Points= 20
No. of games = 6
Total points= 20×6=120
So, Sum of Score of five games= 23+18+16+24+27= 108
Therefore, Score in 6th game= 120-108= 12
Hope this helps[tex]\sf\large \green{\underbrace{\red{Answer⋆}}}:[/tex]
To find :-
The sixth score of the game
Given :-
All five scores = 23, 18, 16, 24, and 27
The average of all six score = 20
Solution :-
We will use the average formula to find the sixth score.
[tex]average = \frac{total \: of \: all \: scores}{number \: of \: scores} [/tex]
And let the sixth score be x.
[tex]20 = \frac{23 + 18 + 16 + 24 + 27 + x}{6} [/tex]
Now we will cross multiply, the 6 which on L.H.S will come to R.H.S and multiply with 20.
[tex]20 \times 6 = 23 + 18 + 16 + 24 + 27 + x \\ 120 = 108 + x \\ 120 - 108 = x \\ 12 = x[/tex]
Result :-
The sixth score by the baseball player is 12.
7<2x+3<=13 write solution in interval notation
Answer:
2<x<_5
Step-by-step explanation:
You spin a spinner numbered from 1 to 6 and spin another spinner with the colors violet and yellow. Both spinners are divided into sections with the same area. How many possible outcomes are in the sample space?
Answer all 6 pictures/questions !!
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
First, identify the three vectors in component form (remember to have the direction angle for each vector account for the quadrants they are in!):
[tex]u=\langle90\cos220^\circ,90\sin220^\circ\rangle\\v=\langle 60\cos110^\circ,60\sin110^\circ\rangle\\w=\langle 40\cos30^\circ,40\sin30^\circ\rangle[/tex]
Secondly, we add them:
[tex]u+v+w=\langle90\cos220^\circ+60\cos110^\circ+40\cos30^\circ,90\sin220^\circ+60\sin110^\circ+40\sin30^\circ\rangle\approx\langle-54.824,18.531\rangle[/tex]
Thirdly, find the magnitude of the new vector:
[tex]||u+v+w||=\sqrt{(-54.824)^2+(18.531)^2}\\||u+v+w||\approx57.871[/tex]
And finally, find the direction of the new vector:
[tex]\theta=tan^{-1}(\frac{18.531}{-54.824})\\\theta\approx-18.675^\circ\approx-19^\circ[/tex]
Because our new vector is in Quadrant II, our found direction angle is a reference angle, telling us that the actual direction of our vector is 19° clockwise from the negative x-axis, which would be 180°-19°=161°
Thus, B is the best answer
Problem 2
To find the component form of a vector, we simply subtract the initial point from the terminal point. In this case, our initial point is at (7,-1) and our terminal point is at (1,6). We subtract the horizontal and vertical components separately:
[tex]\langle1-7,6-(-1)\rangle=\langle-6,7\rangle[/tex]
Thus, A is the correct answer
Problem 3
Again, subtract the initial point from the terminal point to find the vector, and then apply scalar multiplication:
[tex]-\frac{1}{2}v=-\frac{1}{2} \langle-8-8,10-4\rangle=-\frac{1}{2}\langle-16,6\rangle=\langle8,-3\rangle[/tex]
Thus, C is the correct answer
Problem 4 (top one in 4th image)
Remember that scalar multiplication only affects the magnitude of the vector and not the direction. Thus, [tex]-3u=-3\bigr[20\langle\cos30^\circ,\sin30^\circ\rangle\bigr]=-60\langle\cos30^\circ,\sin30^\circ\rangle[/tex], which means our magnitude is -60 and our direction remains 30°.
Thus, B is the correct answer
Problem 5 (fake #6, bottom one in 4th image)
Basically, whatever is in front of the i represents the horizontal component, and whatever is in front of the j represents the vertical component, so:
[tex]u=-3i+8j=\langle-3,8\rangle[/tex]
Thus, B is the correct answer
Problem 6 (real one, 5th image)
Recall:
Two vectors are said to be orthogonal if their dot product is 0 and are perpendicular to each other (form a 90° angle)Two vectors are said to be parallel if the angle between the vectors is 0° or 180° i.e. cosθ=-1Knowing these facts, let us compute the dot product:
[tex]u\cdot v=(-4*28)+(7*-49)=(-112)+(-343)=-455[/tex]
Since the dot product of the two vectors is not 0, then the vectors are not orthogonal, so we can eliminate choices A and B
To check if the vectors are parallel, find the angle between them:
[tex]\displaystyle\theta=cos^{-1}\biggr(\frac{u\cdot v}{||u||\:||v||}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{(-4)^2+(7)^2}\sqrt{(28)^2+(-49)^2}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{16+49}\sqrt{784+2401}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{65}\sqrt{3185}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{207025}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{455}\biggr)\\\\\theta=cos^{-1}(-1)\\\\\theta=180^\circ[/tex]
So, since the angle between the two vectors is 180°, this implies that cosθ=-1, and the two vectors must be parallel.
Thus, D is the correct answer
Cual es la formula para calcular la masa de los atomos de carbono y nitrogeno?
POR FAVOR Y DOY CORONA Y CORAZON
Answer:
La masa atómica del carbono (C) es 12 g/mol; para el oxígeno (O) es de 16 g/mol. Esto significa que 6.022 x 1023 átomos de carbono pesan 12 gramos. Según esto, el peso molecular del CO2 es: 12 g/mol [C] + 2 x 16 g/mol [O2] = 44 g/mol.
1 molécula de Nitrógeno por su masa atómica de 14.01 más 3 moléculas de Hidrógeno por su masa atómica de 1.008 = (1 * 14.01) + (3 * 1.008) = 14.01 + 3.024 = 43.038 u = 17.03 masa molecular = 17.03 g/mol de masa molar en el amoníaco.
The graph of y = StartAbsoluteValue x EndAbsoluteValue is transformed as shown in the graph below. Which equation represents the transformed function? On a coordinate plane, an absolute value function is shown. The vertex of the function is at (negative 3, negative 2). It crosses the x-axis at (negative 5, 0) and (negative 1, 0) and it crosses the y-axis at (0, 1). y = StartAbsoluteValue x minus 3 EndAbsoluteValue + 2 y = StartAbsoluteValue x + 3 EndAbsoluteValue minus 2 y = StartAbsoluteValue x minus 2 EndAbsoluteValue + 3 y = StartAbsoluteValue x + 2 EndAbsoluteValue minus 3
Using translation concepts, it is found that the equation of the transformed function is:
y = |x + 3| - 2.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The absolute value function is given by y = |x|, and has vertex at (0,0). After the transformations, the function has vertex (-3, -2), which means that:
It was shifted 3 units to the left, hence x -> x + 3.It was shifted 2 units down, hence y -> y - 2.Thus, the equation of the function is now given by:
y = |x + 3| - 2.
More can be learned about translation concepts at https://brainly.com/question/4521517
Answer:y = |x + 3| - 2.
Step-by-step explanation: B on edge
Please help me with this question
Answer:
x = 110y = 62Step-by-step explanation:
xThe angle where chords cross is the average of the measures of the intercepted arcs. The angle that is the supplement of x° will be the average of interecepted arcs 60° and 80°.
180° -x° = (60° +80°)/2
180 -70 = x . . . . . . . . . . . divide by °, add x-70
x = 110
__
yThe external angle where secants meet is half the difference of the intercepted arcs.
59° = (180° -y°)/2
118 = 180 -y . . . . . . . multiply by 2, divide by °
y = 180 -118 . . . . . add y-118
y = 62
Find the measure of ∠b.
A. 110∘
B. 102∘
C. 111∘
D. 121∘
Answer:
110 :)
Step-by-step explanation:
Triangle total angle measurement: 180
Now lets solve!
28 + 42 + ? = 180
70 + ? = 180
Now we have to subtract!!
180 - 70 = 110
Have an amazing day!!
Please rate and mark brainliest!!
5. You get a car loan for $13,000 to buy a used car. The car dealer who gives you the loan charges
8.4% interest, compounded monthly, for 4 years.
(a) What's the total amount you will have to pay back for this loan?
(b) What is your monthly payment for this loan?
Answer:
Total = $15,351.10
Monthly = $319.81
Who was one of the earliest non-king leaders of the Benin people?
A. Sakura
B. Oranyan
C. Ekewa
D. Sundiata
Answer:
the answer is d , sundiata!
Step-by-step explanation:
the
Solve 5+ 4.7 (21 + 3x) = 41
A shop charges `\$1.95` for a small `3`-ounce soft serve.
What is the cost per ounce of soft serve?
Will give brainliest pls answer!!
Find the volume of the rectangular
prism.
A)29 cm³
B) 87 cm³
C)288 cm³
D)576 cm³
Answer:
D) 576 cubic cm
Step-by-step explanation:
[tex]16 \times 9 \times 4 = 576[/tex]
Answer:
the answer is D
Step-by-step explanation:
volume =height × length × width
so 9×4×16= 576
How can we use the distributive property to find an expression equivalent to
10(5 – 2x)? Place the steps in order.
Answer: multiply 10 to both terms and subrtact products
Step-by-step explanation:
10(5 - 2x)
multipy 10 to both terms
50 20x
subtract products
50 - 20x
Answer:
1. subtract 2×from get 3.×= 682+ 4672
pls like and follow me you byeFind the axis of symmetry and the vertex of the graph of y = 3x2 −18x + 17.
x = 3; (3, −10)
x = −3; (−3, −17)
x = 6; (3, −18)
x = −6; (3, −10)
Answer:
Vertex of y = − 3 x 2 + 18 x − 13 Ans: Vertex (3, 14)
Step-by-step explanation:
Explanation: x-coordinate of vertex: x = ( − b 2 a ) = − 18 − 6 = 3 y-coordinate of vertex: y = f(3) = -27 + 54 - 13 = 14 x-coordinate of the axis of symmetry is the same as the x-coordinate of the vertex: x = 3
No spammers pls and also giving brainliest to correct answer
Answer:
C. (5 , 6)
Step-by-step explanation:
a dilation of center O(0,0) and 3 as a scale factor :
Transform point (x , y) to point (3x , 3y)
Then it transforms R(1 , 2) to R’(3 , 6)
Now ,we translate R’(3 , 6) by the translation (x , y) ——-> (x+2 , y)
So , R’(3 , 6) ————> R’’(3+2 , 6)
What is If a = 3, then 2ª=
Answer:
2^3 = 2 * 2 * 2 which equals 8
Step-by-step explanation:
HELP PLS
WORTH 1 POINT
GIVING 10
WHAT DID I DO WRONG?
supplementary angles form a straight line (together 180°) and the ones that you indicated didn't.
18. What is the value of the 5 in 256
A. 5/10
SO
B. 10/5
C. 5/100
D. 100/5
Answer:
A. 5/10
Step-by-step explanation:
Because the 5 in 256 is ine in tength's place. And 5/10 is 0.5 or 50
The graph of f(x) = -x2 - 2x + 8 is shown. Which of the following describes all solutions for f(x)?
O(x -x2 - 2x + 8) for all real numbers
O(-4,0), (-1,9), (0, 8), (2.0)
O(-4.0), (2,0)
O(x, y) for all real numbers
Answer:
[tex]f(x) = -x^2 - 2x + 8[/tex]
y-intercept is when x = 0:
[tex]\implies f(0) = -(0)^2 - 2(0) + 8=8[/tex]
So the y-intercept is (0, 8)
x-intercepts are when f(x) = 0:
[tex]\implies f(x)=0[/tex]
[tex]\implies -x^2 - 2x + 8=0[/tex]
[tex]\implies x^2 + 2x - 8=0[/tex]
[tex]\implies x^2 - 2x + 4x - 8=0[/tex]
[tex]\implies x(x - 2) + 4(x-2)=0[/tex]
[tex]\implies (x+4)(x - 2)=0[/tex]
Therefore:
[tex]\implies (x+4)=0 \implies x=-4[/tex]
[tex]\implies (x-2)=0 \implies x=2[/tex]
So the x-intercepts are (-4, 0) and (2, 0)
The vertex is the turning point of the parabola. The x-value of the vertex is the x-value between the 2 zeros (x-intercepts).
Therefore, the x-value of the vertex is [tex]\sf \dfrac{x_1+x_2}{2}=\dfrac{-4+2}{2}=-1[/tex]
Substituting x = -1 into the function:
[tex]\implies f(-1) = -(-1)^2 - 2(-1) + 8=9[/tex]
So the vertex is (-1, 9)
The domain is the input values, so x = all real numbers.
The range is the output values, so the range is [tex]f(x)\leq 9[/tex]
Therefore, (-4, 0), (-1, 9), (0, 8) and (2, 0) are solutions of the function, HOWEVER they are not ALL the solutions.
All solutions of the function are:
[tex](x, -x^2 - 2x + 8)[/tex] for all real numbers of x
PLEASE HELP ILL GIVE FIVE STARS AND GIVE BRAINLIEST AND GIVE THANKS PLEASE HELP
Ray is x years old. His brother Ron is y years older than Ray.
What will the sum of their ages be in 5 years?
Answer: X+Y+5
Step-by-step explanation:
There is no single answer you have to write an equation.
Roberto has by saltine crackers at the store. The label on the shelf for brand A says that it’s unit cost is $3.75/lb. Brand B says that its unit cost is $0.18/oz. Which is the better by?
Answer:
Brand A
Step-by-step explanation:
IN the end buying it for $3.75/lb would end up being cheaper then buying it for $0.18/oz. Hopethis helps!
Age of car = 4 years. Original cost = $13,850. The current market value is $
Using an exponential function, supposing that the value decays 10% a year, it is found that the current market value is $9,087.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem, supposing a decay of 10% a year, and the original value of $13,850, the parameters are A(0) = 13850, r = 0.1.
Hence, the value of the car in 4 years is given by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(4) = 13850(0.9)^4[/tex]
A(4) = 9087.
More can be learned about exponential functions at https://brainly.com/question/25537936
Which of the following sets of numbers could represent the three sides of a triangle?
{6,18,24}
{5,16,22}
{11, 17, 27}
{ 8, 15, 24}
{11, 17, 27}
============================================================
Explanation:
Let's go through the answer choices.
A) This won't work because 6+18 = 24 which is not larger than the third side 24. The sum of any two sides must be larger than the other side. Refer to the triangle inequality theorem.B) 5+16 = 21 is not larger than 22, so we rule this out as well.C) We'll come back to this laterD) We rule this out because 8+15 = 23 is not larger than 24.Now return back to choice C. Notice how adding any two sides leads to a sum larger than the third side
11+17 = 28 is larger than 2711+27 = 38 is larger than 1717+27 = 44 is larger than 11The three conditions of the triangle inequality theorem are met, so a triangle is possible for choice C.
can someone help with this?
Answer:
4) r = 10 yd
d = 20 yd
5) r = 7 in
d = 14 in
6) r = 15 ft
d = 30 ft
7) r = 23 in
d = 46 in
8) r = 16 yd
d = 8 yd
9) r = 21 ft
d = 42 ft
Step-by-step explanation:
Diameter = 2 x radius
*diameter (d)*
*radius (r)*
Assuming that you have 50 subjects that you want to randomly assign to two different groups of 25, explain how you would use a random number table to do it. (10 points; 7 for your answer, 3 for response to others' comments.)
A random number table can be used by first assigning a number to each subject and then randomly selecting the subjects for each group.
What is a random number table?This is table that contains random numbers and it is used to select random samples.
How to use it in this case?Assign a number to each participant from 1 to 50.Grab the random number table and without looking point at a number in the table.If the last two digits of the number are between 01 and 50, assign the participant to the first group. If not select another number.Assign 25 participants to the first group using this metho and then automatically assign the remaining 25 participants to the second group.Learn more about numbers in: https://brainly.com/question/17429689
sets of linear systems wherein there is one Consistent & Dependent, Consistent & Independent, and one Inconsistent.
Answer:
What is the difference between entering a formula and entering data ??
HELP ME!!!! please....
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
UW = 97 cm
Step-by-step explanation:
UW is congruent to VX and VX is 97 cm so UW would be 97 cm
Answer:
97
Step-by-step explanation:
As you can see, the marks on that trapezoid show that those 2 sides are equal in length, so both of those sides are equal.
Hope This Helps! :) Please Mark as Brainliest!
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Which equation represents a line which is perpendicular to the line y = – 4/5+ 2
5x + 4y = 28
4x - 5y =-25
4y – 5x = -12
4x + 5y = -30
