The weighted average of the points A, B, and C with weights 1, 4, and 1 respectively is (A + 4B + C) / 6.
To find the weighted average of the points A, B, and C with weights 1, 4, and 1 respectively, we first need to multiply each point by its corresponding weight and then add them together.
Finally, we divide the sum by the total weight.
The weighted sum of the points is:
(1 × A) + (4 × B) + (1 × C) = A + 4B + C
The total weight is:
1 + 4 + 1 = 6
Therefore, the weighted average of the points A, B, and C with weights 1, 4, and 1 respectively is:
(A + 4B + C) / 6
Note that the weight of B is four times that of A and C.
Therefore, the weighted average will be closer to B than A or C, reflecting the fact that B has a larger weight.
For example, if A = 3, B = 5, and C = 4, then the weighted average is:
(A + 4B + C) / 6 = (3 + 4 × 5 + 4) / 6 = 26 / 6 = 4.33.
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I ne table below represents the function r, and the tonowing grapn represents the function g.
0 1
-6 -5 -4 -3 -2 -1
-10 -8
-2
22
X
f(x) 8-2-8
Complete the following statements.
The functions / and g have
The y-intercept of fis
the y-intercept of g.
Over the interval [-6, -3), the average rate of change of fis
9
-4 -2
6
4
the average rate of change of g.
Since the average rates of change of f and g cannot be determined from the given information provided.
We can find the average rate of change of function f over the interval [-6, -3) as:
The average rate of change of f;
= (f (6) - f (3)) / (6 - 3)
= (71 - 59) / 2 = 6
We have the two given points to set up equations:
-53 = a(3)^b - 41
-53 = a(5)^b - 41
0 = a(3^b - 5^b)
Since 3^b ≠ 5^b, we must have a = 0, that means g is not a valid exponential function passing through the given points.
Therefore,
We can conclude, that the average rates of change of f and g cannot be determined.
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La señora Luisa pide un presupuesto para reparar ocho joyas. El encargado de la joyería le dice que cobrará $6 por la primera joya, y por cada pieza sucesiva lo triple que la anterior. ¿Cuánto le cobrará el joyero a la señora Luisa?
The amount that the jeweler would charge Mrs. Luisa, given the prices of the successive jewelry would be $ 19, 680
How to find the total cost ?The charge for repairing the jewelry pieces is calculated in a geometric progression:
= 6, 63, 63 ², 63 ³, ..., 63 ⁷
The sum of the first n terms in such a progression is:
S = a x (r ⁿ - 1) / ( r - 1 )
Seeing as there are 8 pieces of jewelry, the total cost to Mrs. Luisa would be:
S = 6 x ( 3 ⁸ - 1) / ( 3 - 1 )
S = 6 x ( 6561 - 1 ) / 2
S = 6 x 6560 / 2
S = 3 x 6560
S = $ 19, 680
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On an overnight camping trip, the Adventure Scouts could choose to sleep in a cabin, in a tent, or outside under the stars. A total of 115 scouts went on the trip. Twice as many scouts slept in a cabin as slept in a tent. The same number of scouts slept outside as slept in a cabin.
How many Adventure Scouts slept outside?
There are 58 Adventure Scouts slept outside on the camping trip.
Let's denote the number of scouts who slept in a cabin, tent, and outside as c, t, and o, respectively. We know that the total number of scouts is 115, so:
c + t + o = 115
We also know that twice as many scouts slept in a cabin as slept in a tent, so:
c = 2t
And we know that the same number of scouts slept outside as slept in a cabin, so:
o = c
We can use these equations to solve for the number of scouts who slept outside:
c + t + o = 115
2t + t + t = 115 (substituting c = 2t and o = c)
4t = 115
t ≈ 28.75
Since we can't have a fractional number of scouts, we need to round this up or down. However, we also know that the number of scouts who slept outside is the same as the number who slept in a cabin, which means that either c or o must be even (since c is twice t). Therefore, we'll round t up to 29 and use that to solve for c and o:
c = 2t ≈ 58
o = c ≈ 58
So, we can conclude that 58 Adventure Scouts slept outside on the camping trip.
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Answer:
46
Step-by-step explanation:
You need to find how many Adventure Scouts slept outside. Start with the information in the problem.
A total of 115 scouts went camping.
Twice as many slept in a cabin as slept in a tent.
The same number slept outside as slept in a cabin.
You can use a diagram to model the problem. Fewer scouts slept in a tent than the other choices. So, start with the scouts who slept in a tent.
Twice as many scouts slept in a cabin as slept in a tent. So, draw 1 box to represent the number who slept in a tent and 2 boxes to represent the number who slept in a cabin.
tent
cabin
outside
The same number of scouts slept outside as slept in a cabin. There are 2 boxes for scouts who slept in a cabin. So, draw 2 boxes to represent the number who slept outside.
tent
cabin
outside
There are 5 boxes in the diagram in all. There were 115 scouts on the trip altogether. So, each box represents 115÷5 scouts. Divide.
2 3
5
1 1 5
– 1 0
1 5
– 1 5
0
Each box represents 23 scouts. There are 2 boxes for the scouts who slept outside. Multiply to find the number of scouts who slept outside.
2 3
× 2
4 6
46 Adventure Scouts slept outside.
An amount of $21,000 is borrowed for 13 years at 8.75% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?
Answer: To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the initial principal (the amount borrowed)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the time period in years
In this case, we have:
P = $21,000
r = 8.75% = 0.0875
n = 1 (interest is compounded annually)
t = 13 years
So, plugging these values into the formula, we get:
A = 21,000(1 + 0.0875/1)^(1*13)
A = 21,000(1.0875)^13
A = $58,150.51
Therefore, if the loan is paid in full at the end of the 13-year period, $58,150.51 must be paid back, which includes the original principal plus the interest accrued over the 13-year period.
Step-by-step explanation:
Solve these using quadratic formula
Write out your work!
I need the vertex
Axis of symmetry
Intercepts -also include the function to find the intercepts-
The vertex is at (1, 4).
The vertex is at (-1, -4).
The axis of symmetry is x = 1.
The axis of symmetry is x = -1.
The x-intercepts are (3, 0) and (-1, 0).
The x-intercepts are approximately (-2.3, 0) and (0.3, 0).
The y-intercept is (0, 3).
The y-intercept is (0, -6).
We have,
To solve the equations using the quadratic formula, we need to rewrite them in the standard form ax² + bx + c = 0.
-x² + 2x + 3 = 0 can be rewritten as -1x² + 2x + 3 = 0
Here, a = -1, b = 2, and c = 3
Using the quadratic formula, we have:
x = (-b ± √(b² - 4ac)) / 2a
x = (-2 ± √(2² - 4(-1)(3))) / 2(-1)
x = (-2 ± √(16)) / -2
x = 1 ± 2
So, x = 3 or x = -1
2x² + 4x - 6 = 0 is already in the standard form with a = 2, b = 4, and c = -6
Using the quadratic formula, we have:
x = (-4 ± √(4² - 4(2)(-6))) / 2(2)
x = (-4 ± √(52)) / 4
x = (-2 ± √(13)) / 2
To find the vertex of each parabola, we can use the formula x = -b / 2a and then substitute the value of x into the equation to find y.
For -x² + 2x + 3 = 0
We have a = -1 and b = 2, so the vertex is at
x = -b / 2a = -2 / (2(-1)) = 1.
Substitute x = 1 into the equation to find y:
y = -1(1)² + 2(1) + 3 = 4.
So the vertex is at (1, 4).
For 2x² + 4x - 6 = 0,
We have a = 2 and b = 4, so the vertex is at x = -b / 2a = -4 / (2(2)) = -1. Substitute x = -1 into the equation to find y: y = 2(-1)² + 4(-1) - 6 = -4.
So the vertex is at (-1, -4).
The axis of symmetry is a vertical line that passes through the vertex.
For -x² + 2x + 3 = 0, the axis of symmetry is x = 1.
For 2x² + 4x - 6 = 0, the axis of symmetry is x = -1.
To find the x-intercepts, we can set y = 0 in each equation and solve for x using the quadratic formula.
For -x² + 2x + 3 = 0, we have:
x = (-2 ± √(2² - 4(-1)(3))) / 2(-1)
x = (-2 ± √(16)) / -2
x = 1 ± 2
So the x-intercepts are (3, 0) and (-1, 0).
For 2x² + 4x - 6 = 0, we have:
x = (-4 ± √(4² - 4(2)(-6))) / 2(2)
x = (-4 ± √(52)) / 4
x = (-2 ± √(13)) / 2
So the x-intercepts are approximately (-2.3, 0) and (0.3, 0).
To find the y-intercept, we need to set x = 0 and solve for y.
Setting x = 0 in -x² + 2x + 3 = 0.
-0 + 0 + 3 = 3
Therefore, the y-intercept is (0, 3).
Setting x=0 in 2x² + 4x - 6.
2(0)² + 4(0) - 6 = -6
Therefore, the y-intercept is (0, -6).
Thus,
The vertex is at (1, 4).
The vertex is at (-1, -4).
The axis of symmetry is x = 1.
The axis of symmetry is x = -1.
The x-intercepts are (3, 0) and (-1, 0).
The x-intercepts are approximately (-2.3, 0) and (0.3, 0).
The y-intercept is (0, 3).
The y-intercept is (0, -6).
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Describe in words each of the transformations
represented by the rules below:
a. (x,y) → (x-5, y + 6)
b. (x,y) → (y, -x)
c. (x, y) (1.2x, 1.2y)
d. (x,y) → (x, y)
Write "forty-two thousand, fifteen" as a whole number using digits.
The whole number for "forty-two thousand, fifteen" is 42,015.
We have, "forty-two thousand, fifteen".
To write a sentence as a whole number using digits, you would typically replace the words with their numerical representations. Here's an example:
Sentence: "I have three apples and four bananas."
Whole number: "I have 3 apples and 4 bananas."
Here the numeric terms are forty- thousand and fifteen then the numerical digit will be
= 42, 015.
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Pls help asap RSM QUESTION!!!
Find the derivative of the function
thank you guys sm
The derivative of the function is f' ( x ) = 9 / ( 4 + 3x ) ( ln 2 )
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = log₂ ( 3x + 4 )³
On simplifying , we get
On taking the derivative of the function , we get
f' ( x ) = d/dx ( log₂ ( 3x + 4 )³ )
d/dx ( log₂ ( 3x + 4 )³ ) = 1/ ln ( 2 ) [ d/dx( 3x + 4 )³ ]
On applying chain rule , we get
f' ( x ) = 1/ ln ( 2 ) 1/( 3x + 4 )³ ( 9 ( 3x + 4 )² )
So , cancelling out the similar terms , we get
f' ( x ) = 9 / ( 4 + 3x ) ( ln 2 )
Hence , the derivative is f' ( x ) = 9 / ( 4 + 3x ) ( ln 2 )
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What is the solution to |x-2| + 3 > 17?
Ox<-12 or x > 16
Ox<-14 or x>7
O-12
O-14
Answer:
x<-12 or x>16
Step-by-step explanation:
Answer:
|x - 2| + 3 > 17
|x - 2| > 14
x - 2 < -14 or x - 2 > 14
x < -12 or x > 16
Help please I will give brainlist!!
The angles in the circle are as follows:
mBC = 107°m∠BAC = 53.5° mBC = 92°How to find arc angles?The central angle of an arc is the central angle subtended by the arc.
The measure of an arc is the measure of its central angle.Therefore,mBC = 107 degrees
The angle subtended by an arc at the center is twice the angle subtended at the circumference.
Therefore, m∠BAC = 107 / 2 = 53.5 degrees
The inscribed angle is half the intercepted arc angle.
Therefore, to find mBC, we solve:
46 = 1 / 2
Next, we cross multiply mBC = 46 × 2
Therefore, mBC = 92 degrees
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4 2/3 divided by 7 write the quotient in simplified fraction
Answer: The correct answer is 42
Step-by-step explanation:
Answer:
8/21
Step-by-step explanation:
4 2/3=8/3, times 1/7 (or divide by 7) equals 8/21.
Sarah spends 30 minutes reading,20 minutes writing,and 20 minutes doing her math. How many minutes does she spends on school work in all
Answer:
She spends 70 minutes in total or 1h 10min
PLEASE MARK IT THE BRAINLIEST!!!!!
Stuck on question number 3
Answer:90
Step-by-step explanation:
Dos ángulos de un cuadrilátero miden 60° y 80°. Los otros dos ángulos están en una
proporción de 2:9. ¿Cuáles son las medidas de esos dos ángulos?
Answer:
La suma de los cuatro ángulos de un cuadrilátero es igual a 360 grados. Entonces, si dos ángulos miden 60° y 80°, la suma de esos ángulos es de 140 grados.
Los otros dos ángulos están en una proporción de 2:9, lo que significa que la suma de sus medidas es de 11 partes. Si representamos las medidas de estos ángulos como 2x y 9x, respectivamente, entonces podemos escribir la ecuación:
2x + 9x = 11 partes
11x = 11 partes
x = 1 parte
Por lo tanto, el ángulo más pequeño mide 2x = 2 partes o 2 × 1 = 2 grados, y el ángulo más grande mide 9x = 9 partes o 9 × 1 = 9 grados.
En resumen, los dos ángulos faltantes miden 2° y 9°.
Step-by-step explanation:
Which statements describe finding the limit shown?
Check all that apply.
O Multiply by √x+2+3
√x+2+3
Getx-1 in the numerator.
Get (x-7)(√x+2-3) in the denominator.
O Divide out a common factor of x-7.
Calculate the limit as 1.
The correct statement is:
"Divide out a common factor of x - 7." The limit of the given expression is 1/6.
Multiply by (√(x + 2) + 3)/(√(x + 2) + 3):
This statement is not correct.
We generally multiply by the conjugate of the expression to eliminate square roots, but in this case, multiplying by (√(x + 2) + 3)/(√(x + 2) + 3) does not help simplify the expression.
Get x - 1 in the numerator:
This statement is not correct. The expression does not involve x - 1 in the numerator.
Get (x - 7)(√(x + 2) - 3) in the denominator:
This statement is not correct. We want to simplify the expression, not introduce a more complex denominator.
Divide out a common factor of x - 7:
This statement is correct. By factoring out (x - 7) from both the numerator and denominator, we can cancel out the common factor.
Calculate the limit as 1/6:
This statement is not correct. We need to perform further simplification to determine the limit.
After canceling out the common factor of x - 7, the simplified expression becomes:
lim x -> 7 (√(x + 2) - 3)/(x - 7) = lim x -> 7 1/(√(x + 2) + 3)
To find the limit, we substitute the value x = 7 into the simplified expression:
lim x -> 7 1/(√(7 + 2) + 3) = 1/(√(9) + 3) = 1/(3 + 3) = 1/6
Therefore, the correct statement is: "Divide out a common factor of x - 7." The limit of the given expression is 1/6.
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write equivalent fraction for 1 1/5 and 1 1/3
Answer:
1 1/5 = 6/5
1 1/3 = 4/3
Step-by-step explanation:
hope this helps, if you’re looking for 1 1/5 + 1 1/3 please tell me and I will solve that for you
If it rains tomorrow, the probability is 0.7 that John will practice his cello. If it does not rain tomorrow, there is only a 0.6 chance that John will practice.
Suppose the chance of rain tomorrow is 60%.
What is the probability that John will practice his cello?
P(John will practice) =
(Type an integer or a decimal.)
Answer:
0.66
Step-by-step explanation:
please read attachments
Help Screenshot need help
The probability that the student was female and got grade C is P ( A ) = 0.12833
Given data ,
Let the table represent the group of students with their gender and the grades in school
Now , the probability that the student was female = total number of females / total number of students
So , probability that the student was female = 22/60
Now , the probability that the student got grade C = 21/60
So , the compound probability P ( A ) = probability that the student was female and got grade C
On simplifying , we get
P ( A ) = ( 22/60 ) ( 21/60 )
P ( A ) = 462/3600
P ( A ) = 0.12833
Hence , the probability is P ( A ) = 0.12833
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what is greater 54300ml or 54L?
Answer:
54300 ml is greater than 54 L. This is because 54300 ml is equivalent to 54.3 L, which is larger than 54 L.
A small rectangular prism has a length of 5 inches, a width of 4 inches, and a volume of 100 cubic inches. A large rectangular prism also has a length of 5 inches and a width of 4 inches, but its volume is 200 cubic inches.
How much taller is the large prism than the small prism?
Write your answer as a whole number or decimal. Do not round.
the volume of a prism is
length × width × height
so, for the small prism we have
5 × 4 × height = 100 in
height = 100/20 = 5 i
for the large prism we have
5 × 4 × height = 200 in³
height = 200/20 = 10 in
the larger prism is 10/5=2 times taller than the small prism.
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Find the area of a rectangle with a base of 9 feet and a height of 7 feet
Answer:
63
Step-by-step explanation:
b x h = A
9 x 7 = 63
i need help graphing y=-4/3+2
If f(x) = (3+x)/(x-3) , what is f(a+2)
Answer:
Step-by-step explanation:
f(x) = [tex]\frac{3+x}{x-3}[/tex]
f(a+2) = [tex]\frac{3+a+2}{a+2-3}[/tex]
f(a+2) = [tex]\frac{5+a}{a-1}[/tex]
A path is made of white tiles and grey tiles.
There is a total of 56 tiles.
Work out the number of grey tiles.
The number of tiles that would be grey tiles out of the total tiles given would be = 28 tiles.
How to calculate the number of grey tiles?To calculate the number of grey tiles, the total number of tiles given should be divided into two since the path is made up of only white and grey tiles.
The total number of tiles = 56 tiles.
Therefore the grey and the white tiles have the same number of tiles = 56/2 = 28 grey tiles
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The table below shows the demand for a new bath soap in a shop for each of the last 7 months.
Month 1 2 3 4 5 6 7 8
Demand 23 29 33 40 41 43 49 52
Calculate a 3-month moving average for months two to nine.
Indicate which of the following variables are continuous.
1. Length of a frog's jump.
2. Monthly TV cable bills.
3. Lottery revenues of states.
4. Number of wheels of a car.
5. Monthly spendings of a family.
O 1, 2, 3 and 5
O 1, 4 and 5
O 1, 2, 3 and 4
O 1 and 2
The correct variables which are continuous are,
1. Length of a frog's jump.
2. Monthly TV cable bills.
3. Lottery revenues of states.
4. Number of wheels of a car.
We have to given that;
To find correct variables which are continuous.
Since, The number of wheels of a car is a discrete variable, because it can only take certain integer values (2, 3, 4, etc.), while the other variables can take any real value within a certain range.
Hence, The correct variables which are continuous are,
1. Length of a frog's jump.
2. Monthly TV cable bills.
3. Lottery revenues of states.
4. Number of wheels of a car.
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Which of the following is the result of expanding
8.5
15.5
32
60
Based on the information, the required result of the expansion for the expression is 8.
How to calculate the value of the expressionIn mathematics, an expression is a combination of numbers, variables, operators, and/or functions that can be evaluated to obtain a numerical or symbolic result. Expressions can take many forms, but typically involve some combination of mathematical symbols such as +, -, ×, ÷, =, and parentheses.
The given expression is 2x-3 .
when x =1, we will get 2(1)-3 = 2-3 =-1
When x=2, we will get, 2(2) -3 = 4-3 =1
When x=3, we will get 2(3)-3 = 6-3=3
When x=4, we will get 2(4)-3 = 8-3=5
The required result of the expansion is -1+1+3+5=8
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Given △RST≅△LMN, m∠R=65°, and m∠M=70°, what is the measure of ∠T?
Enter your answer in the box.
m∠T=
Answer: ∠T=45°
Step-by-step explanation:
If triangle RST is congruent to triangle LMN, then the angles R=L, S=M, and T=N. Knowing that the sum of angles in a triangle= 180 degrees, then:
∠R+∠S+∠T=180°
∠R=65°
∠M=∠S=70°
180°-∠R-∠S=∠T
180°-65°-70°=
∠T=45°
Determine if it’s a 1 proportion z interval, 1 proportion z test, 1 sample T interval or 1 sample T test
The type of test used in this problem is given as follows:
1 proportion z test.
How to test the hypothesis?At the null hypothesis, we consider if there is not enough evidence to conclude that the mean is different of 0.55, hence:
[tex]H_0: p = 0.55[/tex]
At the alternative hypothesis, we test if there is enough evidence to conclude that the mean is different of 0.55, hence:
[tex]H_a: p \neq 0.55[/tex]
We are testing a proportion, hence the z-distribution is used, thus the correct option is given as follows:
1 proportion z test.
(in the case of a proportion, a z test is used, for sample means that we can use either z test or t test depending on the problem).
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