The equation which relates the number of triangles in figure (n) to the perimeter of the figure (P) is P = 6n + 18. Option A is correct.
We are given:
The perimeter of the 1 triangle = 24
The perimeter of the 2 triangle = 30
The perimeter of the 3 triangle = 36
As we can see in the given figures two sides with lengths of 9 are fixed and the side with a length of 6 is varying.
So, we can write this as,
P = 6n + 18, where n = number of triangles.
Now, check the equation formed by substituting the values;
Substitute n = 1, and we get;
P = 6(1) + 18
P = 6 +18
P = 24 True.
Substitute n = 2, and we get;
P = 6(2) + 18
P = 12 +18
P = 30 True.
Substitute n = 3, and we get;
P = 6(3) + 18
P = 18 + 18
P = 36, true.
So, it is true for all the figures.
Thus, the equation which relates the number of triangles in figure (n) to the perimeter of the figure (P) is P = 6n + 18. Option A is correct.
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the number of cars sold annually by used car salespeople is normally distributed with a standard deviation of 15. a random sample of 430 salespeople was taken and the mean number of cars sold annually was found to be 79. find the 97% confidence interval estimate of the population mean.
At the 97% confidence interval estimate of the population mean is
(80.55, 77.45).
Following are the calculation to the confidence interval :
Given that,
σ = 15
n = 430
X = 79
Here C = 97% = 0.97
⇒ α = 1 -C = 1 - 0.97 = 0.03
∴ Zₙ = Zₙ/2 = Z₀.₀₁₅ = 2.17
Now,
97% confidence interval,
C.I = X ± σ/√n
= 79 ± 2.17 × (15/√430)
= 79 + 2.17 × (15/ 21) [taking round figure of √430=2.0736441]
= 80.55
Now taking the negative sign,
= 79 - 2.17 × (15/√430)
= 79 - 2.17 × (15/ 21)
= 77.45
The final answer is (80.55, 77.45).
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Can someone please help me!!
Please help me with my math homework
Given system has no solution.
The correct answer is an option (D)
In this question, we have been given the graph of system of equations.
The solution of given system is the point of intersection of all lines.
We can observe that the graph of any two lines intersected at points (2, -1), (-2, 3) and (0, 3)
But there is no common point of intersection for given system.
This means, the system has no solution.
Therefore, the given system has no solution.
The correct answer is an option (D)
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a 4-sided die is a pyramid whose four faces are labeled with the numbers 1, 2, 3, and 4 (see image). imagine rolling two fair, 4-sided dice and recording the number along the base of each pyramid. (a) what is the sample space for this chance process? (1,1), (1,2), (1,3), (1,4), (2,2), (2,3), (2,4), (3,3), (3,4), (4,4) (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4). (1,1), (2,2), (3,3), (4,4) (1,1), (1,2), (1,3), (1,4) because the dice are fair, each of the outcomes in the sample space are equally likely. what is the probability of each outcome in the sample space? enter a fraction. (b) define event a as getting a sum of 5. p(a)
The probability of each outcome in the sample space = 1/16
The probability of getting a sum of 5 = 1/4
Step-by-step explanation:
We have been given a four-sided die is a pyramid whose four faces are labeled with the numbers 1, 2, 3 and 4
sample space = {(1,1), (1,2), (1,3), (1,4), (2,1),(2,2), (2,3), (2,4),(3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4)}
Two fair 4-sided dices are rolled and all sixteen possible outcomes are equally likely.
The possible outcomes can be deduced by making combinations of different faces with a particular face.
given that each of the outcomes in the sample space is equally likely. So the probability of each outcome in the sample space is the same.
now we find the probability of each of the outcomes in the sample space
(a) when two dices are rolled, we have n(s) = 4*4=16
the chances of getting the outcome as (1,1) n(a) = 1
the probability of getting the outcome as (1,1) p(a)= n(a)/n(b)
p(a) = 1/16
so the probability of each outcome in the sample space = 1/16
(b) P(A) is the probability of getting 5 as a sum
P(A) = Total outcomes with 5 as a sum/Total outcomes
Total outcomes with 5 as sum= 4
Total outcomes= 16
P(A)=4/16=1/4
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Factor each sum or difference of cubes
a) 8-1/8a^3
b) 1/64m^3+1000
c) 125a^3-64b^3
d) 1/27x^3+1/125y^3
Write each polynomial as the square of a binomial as an expression opposite to the square of a binomial
e) 0.25x^2-0.6xy+0.36y^2
f) -a^2+0.6a-0.09
g) 9/16a^4+a^3+4/9a^2
The following are the answers:
a) 7 / (2a)³
b) 1/(4m)³ + 10³
c) (5a)³ - (4b)³
d) 1/(3x)³ + 1/(5y)³
e) (0.5x - 0.6y)²
f) (-a - 0.3)²
g) ((3/4)²a² + (2/3)²a)²
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
a)
(8 - 1) / 8a^3
= 7 / (2a)³
b)
1/64m^3 + 1000
= 1/(4m)³ + 10³
c)
125a^3 - 64b^3
= (5a)³ - (4b)³
d)
1/27x^3 + 1/125y^3
= 1/(3x)³ + 1/(5y)³
Now,
Polynomial is an expression of writing with more than one term.
We will write it in the form of:
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
e)
0.25x^2 - 0.6xy + 0.36y^2
= (0.5x)² - 2 x 0.5 x 0.6 + (0.6y)²
= (0.5x - 0.6y)²
f)
-a^2 + 0.6a - 0.09
-a² - 2 x (-a) x 0.3 - (0.3)²
= (-a - 0.3)²
g)
9/16a^4 + a^3 + 4/9a^2
((3/4)²a²)² + 2 x (3/4)²a² x (2/3)²a + ((2/3)²a)²
= ((3/4)²a² + (2/3)²a)²
Thus,
The following are the answers:
a) 7 / (2a)³
b) 1/(4m)³ + 10³
c) (5a)³ - (4b)³
d) 1/(3x)³ + 1/(5y)³
e) (0.5x - 0.6y)²
f) (-a - 0.3)²
g) ((3/4)²a² + (2/3)²a)²
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What’s the value of a?
Answer these two related questions please thank you
Answer:
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the question is already answerd by Yna9141
here is his text:
The average of the certain set of data can be calculated by dividing the sum of the given numbers/data by their count.
(a) In this item, we are given with: -0.05, 0.09, -0.04, -0.08
Their sum is as follows:
S = (-0.0.5) + (0.09) + (-0.04) + (-0.08)
S = -0.08
Then, divide the sum by 4.
M = -0.08 / 4 = -0.02
b. The answer to this question can be calculated through the equation below,
M₂ = (S + F) / 5
Substituting the known values,
-0.01 = (-0.08 + F) / 5
the value of F is equal to 0.03.
Answer:
15a: -0.02 15b: 0.03
Step-by-step explanation:
15a.
To find the mean, you need to add the values together and divide by the number of values.
(-0.05+0.09+-0.04+-0.08)/4
Simplify:
(-0.05+0.09-0.04-0.08)/4
(-0.05+0.09-0.12)/4
(0.09-0.05-0.12)/4
(0.04-0.12)/4
-0.08/4
-0.02
15b.
let's say the change for Friday is "x"
insert the numbers and add in -0.08 from earlier:
(-0.08+x)/5=-0.01
rearrange (-0.08+x):
(x-0.08)/5=-0.01
multiply both sides by 5:
x-0.08=-0.05
add 0.08 to both sides:
x=0.03
help please i really need this done
Solving an equation we will see that x = 13, then the measure of interior angle G is 63°.
How to find the measure of angle G?
Here we have the 3 interior angles of a triangle defined with a variable x.
m∠E = (5x + 6)°
m∠F = (4x - 6)°
m∠G = (5x - 2)°
Now, remember that the sum of the interior angles of a triangle is always equal to 180°.
Then we can write:
(5x + 6)° + (4x - 6)° + (5x - 2)° = 180°
We can solve this for x.
14x - 2 = 180
14x = 180 + 2
x = 182/14 = 13
Now that we know the value of x, we can find the value of angle G.
m∠G = (5x - 2)° = (5*13 - 2)° = (15 - 2)° = 63°
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pls, hurry!!!!!!!
I will give brainliest to the one who finishes the table!
Answer: 1 is 77 3 is 231 5 is 308 and 7 is 385
Step-by-step explanation:
Determine the value of x and the indicated angle measure.
I understand the concept of solving for x usually and solving the missing angle but I could use some help with this one. I'm stuck!
Please and thanks! ^_^
The value of x for the given triangle is 4.5
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of all three angles of a triangle is always 180°
In the given triangle ABC,
∠A=(9x+16)°, ∠B=(6x+15)°
And the extrior angle ∠C=(19x+3)°
Use the external angle property,
The sum of two interior angles is equal to an exterior angle.
Therefor,
∠C=∠A+∠B
(19x+3)°=(9x+16)°+(6x+5)°
19x+3=15x+21
4x=18
x=4.5
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The diagonal of a square is x units. What is the area of the square in terms of x?
The area of the square is (x²/2) square units.
We are given a square. The length of the diagonal of the square is x units. We have to find the area of the square in terms of "x".
Let the side of the square be denoted by the variable "s". We will use the Pythagorean theorem to find the length of the side of the square.
s² + s² = x²
2s² = x²
s² = x²/2
s = √(x²/2)
s = (x/√2)
The area of the square is given by the square of the side length. Let the area of the square be denoted by the variable "A".
A = s²
A = (x/√2)²
A = x²/2
Hence, the area of the square is (x²/2) square units.
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Richard’s cumulative gpa for 3 semesters was 2. 0 for 42 credits. His fourth semester gpa was 4. 0 for 14 course units. What is richard’s cumulative gpa for all 4 semesters?.
Richard earned a cumulative GPA of 2.5 in all four semesters.
Here, we know that the cumulative GPA for the first 3 semesters is 2.0
He had earned 42 credits in total in all three semesters.
Cumulative GPA = Total points earned/credits rewarded
Hence,
Total points earned in 3 semestes= 2 X 42
= 84 points
In the fourth semester,
he had earned 14 credits with a GPA of 4.0
Hence total points earned = 4 X 14
= 56 points
Therefore, total points earned in all four semesters = 84 + 56 points
140 points
Total credits = 14 + 42
= 56
Hence, the cumulative GPA of all 4 semesters
= 140/56
= 2.5 points.
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Find the measure of each missing angle. a || b
Answer:
though the answers are scattered but I worked them all , just patiently study it.
A square with perimeter p has sides of length
p
4
. The playground at DeVille Elementary School is square-shaped, and has a perimeter of 600 feet.
What is the length of each side of the playground?
The length of each side of the playground is 150 feet.
Calculating the length of a square-shaped playgroundFrom the question, we are to determine the length of each side of the playground.
From the given information,
The perimeter of a square is given by the formula,
P = 4l
Where P is the perimeter of the square
and l is the length of a side of the square
"The playground at DeVille Elementary School is square-shaped, and has a perimeter of 600 feet."
That is,
P = 600 feet
Now, we will determine the value of l
Substitute the value of P into the equation
P = 4l
600 = 4l
Divide both sides by 4
600/4 = 4l/4
150 = l
Therefore,
l = 150 feet
Hence, the length is 150 feet
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Which one is the function here and why
Answer:B
Step-by-step explanation:no points on be colide with each other on either axis
Serenity invested $16,000 in an account paying an interest rate of 4. 5% compounded annually. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 9 years?.
The amount of money that would be in the account after 9 years, giving the interest rate and the amount invested is $23, 777.52
How to find the amount in future?The amount in the account after 9 years is called the future value of the amount that Serenity invested.
To find this future value, you use the future value formula which is:
= Amount invested x ( 1 + interest rate) ^ number of years
The amount in the account after 9 years would therefore be:
= 16, 000 x ( 1 + 4.5%) ⁹
= $23777.52224662808994653125
= $23, 777.52
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math homework similar shapes pls help
Answer: Both p and q are 8cm long.
Step-by-step explanation:
BE created a similar triangle that is exactly half of the larger triangle.
So if BE is 4 and AE is 8 then we know that CD is 8 and AD is 16.
However we only need segment q which is half of AD so the answer is:
p=8 and q=8
;)
If the line passes through the point (0,4) and has a slope of -1, find the solution to the system.
Answer:
y = - x + 4
Step-by-step explanation:
Use point-slope form: y-k = m(x-h) for point (h,k) with slope m
now just plug and chug:
y-4 = -1(x-0)
y-4 = -x
y= -x+4
not sure about what you meant by "solution." Just gonna assume that you were looking for the equation.
6. Jung purchased several video games priced at $29.95 each and paid $5.95 for express shipping. His total purchase was $185.65. How many video games did he purchase?
Answer:
6 video games
Step-by-step explanation:
We can solve this question with an algebraic equation.
29.95x + 5.95 = 185.65
29.95x + 5.95 - 5.95 = 185.65 - 5.95
29.95x ÷ 29.95 = 179.7 ÷ 29.95
x = 6
mia identified a point located at (-5,-8) her directions told her to flip it across the y axis and then across the x axis. mia wrote that the point would now be at (8,5) what was mia's error in her thinking? where would the point be actually located
Mia's error in her thinking was that she interchanged the coordinate of both the x- and y-axis. Also, the point would actually be located at (5, 8).
What is a reflection across the x-axis?In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate would change from positive to negative. Therefore, a reflection across the x-axis is given by this transformation rule:
(x, y) → (x, -y)
In Geometry, a reflection across the y-axis of a graph is given by this transformation rule (x, y) → (-x, y).
(x, y) → (-x, y)
(-5, -8) → (5, -8)
Next, we would apply another reflection across the x-axis of a graph as follows:
(x, y) → (x, -y)
(5, -8) → (5, 8)
In conclusion, we can logically deduce that Mia was wrong in her calculations.
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What is 1/2 of 17 by estimating each product
Which expreion are equivalent to
−
90
−
60
w
−90−60wminu, 90, minu, 60, w?
Chooe 3 anwer:
Chooe 3 anwer:
(Choice A, Checked)
A
−
30
(
3
2
w
)
−30(32w)minu, 30, left parenthei, 3, plu, 2, w, right parenthei
(Choice B)
B
(
−
9
−
6
w
)
⋅
10
(−9−6w)⋅10left parenthei, minu, 9, minu, 6, w, right parenthei, dot, 10
(Choice C)
C
−
3
(
30
−
20
w
)
−3(30−20w)minu, 3, left parenthei, 30, minu, 20, w, right parenthei
(Choice D)
D
(
6
4
w
)
×
15
(64w)×15left parenthei, 6, plu, 4, w, right parenthei, time, 15
(Choice E)
E
−
20
(
4. 5
3
w
)
−20(4. 53w)minu, 20, left parenthei, 4, point, 5, plu, 3, w, right parenthei
The expression equivalent to the expression -90 - 60w is -30(3 + 2w), (-9 - 6w)10 and -20(4.5 + 3w)
We need to find the expressions that are equivalent to given expression
We solve the expression and check,
A) -30(3 + 2w)
-90 - 60w
Yes it is equivalent.
B) (-9 - 6w)10
-90 - 60w
Yes it is equivalent.
C) -3(30 - 20w)
-90 + 60w
No it is not equivalent.
D)(6 + 4w)15
90 + 60w
No it is not equivalent.
E) -20(4.5 + 3w)
-90 - 60w
Yes it is equivalent.
Therefore, The expression equivalent to the expression -90 - 60w is -30(3 + 2w), (-9 - 6w)10 and -20(4.5 + 3w)
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If R and S are parallel lines and <1= 4x-3 and <7= 3x+4, find the measure of <2
If R and S are parallel lines and ∠1= 4x-3 and ∠7= 3x+4, The measure of ∠2 will be 179.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called an "Angle."
It is given that, R and S are parallel lines and <1= 4x-3 and <7= 3x+4,
From the given figure it is obtained that R and S are parallel lines,
∠1=∠7
4x-3=3x+4
4x-3x=4+3
7x=7
x=1
If the ∠1 and ∠2 are supplementary,
∠1+∠2=180
4x-3+∠2=180
∠2=180-4x+3
Substitute the value of x,
∠2=180-4(1)+3
∠2=179
Thus, if R and S are parallel lines and ∠1= 4x-3 and ∠7= 3x+4, The measure of ∠2 will be 179.
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(3x-8)(2x+1) in simplest form
3x(2x+1)-8(2x+1)
6x²+3x-16x+16
6x²+13+16
Evaluate 9/g + 2h + 5
Evaluated expression of the given mathematical expression is (9+2gh+5g)/g.
Given the mathematical expression is 9/g + 2h + 5.
So, now the LCM (g,1,1) = g
So evaluating the given expression we get,
9/g + 2h + 5 = (9+2gh+5g)/g
Hence the evaluated expression is (9+2gh+5g)/g .
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J(13,-5), K(2, 6), L(-1,-5), M(-4,-2)
J10
L(-3,2
Answer:
is there a graph for this
Step-by-step explanation:
i need a grapg or to know what they wanted to know
NEED ANSWER WITHIN 5 MINS! THE BEST ANSWER GETS BRAINLIEST!!!
Use the drawing tools to form the correct answer on the provided graph.
Graph the line that represents the equation y = -2/3x + 1.
The required graph of the given line y = -(2/3)x + 1 is shown in the attached figure.
The equation of the line is given in the question as:
y = -(2/3)x + 1
First, we have to find the intercepts of the equation y = -(2/3)x + 1
The y-intercept is the value of y when the value of x is appropriately zero.
For x = 0
y = -2/3(0)+1
y = 1
The y-intercept is the point where (0.1)
Determine the x-intercept.
The x-intercept is the value of x when the value of y equals zero.
For y = 0
0 = (-2/3)x + 1
-1 = (-2/3)x
x = 3/2 or 1.5
The y-intercept is the point (1.5,0).
To graph, the line, draw the intercepts and connect the dots as indicated in the image.
As a result, the graph for the line y = -(2/3)x + 1 is provided below.
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Actual Unemployment Rate = 12%
Cyclical Unemployment Rate = 7%
What is the Natural Unemployment Rate?
The Natural Unemployment Rate based on the information is 5%.
What is natural rate of unemployment?The natural rate of unemployment is the lowest unemployment rate when inflation is stable, or the unemployment rate when inflation is not accelerating. The natural rate of unemployment (NAIRU) is the rate of unemployment caused by all factors other than changes in aggregate demand. Potential GDP estimates are based on the long-term natural rate.
The unemployment rate is the proportion of the total labor force that is unemployed but actively looking for work and willing to work. Cyclical unemployment is associated with an industry's business cycle. It is a direct result of a drop in consumer demand, which has resulted in a drop in labor demand. If cyclical unemployment rises, it indicates that the economy is slowing, which is not good.
Cyclical unemployment occurs when labor forces are reduced as a result of business cycles or economic fluctuations. If you are cyclically unemployed, it means that your employer has laid you off to save money during a period of slow business.
In this case, the unemployment will be:
= Actual unemployment rate - Cyclical unemployment rate
= 12% - 7%
= 5%
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Write the point-slope form of the equation of the line through the given points:
1) through: (5, 4) and (-2, 5)
2) through: (4, -5) and (0, 2)
3) through: (0, 4) and (2, 1)
The equation of the line in point slope form is as follows:
y - 4 = - 1 / 7(x - 5)y + 5 = - 7 / 4(x - 4)y - 4 = - 3 / 2(x - 0)How to represent linear equation in slope intercept form?Linear equation can be represented in different form such as point slope form, slope intercept form, standard form and general form.
Therefore, equation in point slope form can be represented as follows:
y - y₁ = m(x - x₁)
where
m = slopeTherefore, let's find the point slope form of the lines.
1) through: (5, 4) and (-2, 5)
m = 5 - 4 / -2 - 5
m = 1 /- 7 = - 1 / 7
Therefore,
y - 4 = - 1 / 7(x - 5)
2) through: (4, -5) and (0, 2)
m = 2 + 5 / 0 - 4
m = 7 / -4 = - 7 / 4
Therefore,
y + 5 = - 7 / 4(x - 4)
3) through: (0, 4) and (2, 1)
m = 1 - 4 / 2 - 0
m = - 3/ 2
Therefore,
y - 4 = - 3 / 2(x - 0)
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A new bank customer with $3,000 wants to open a money market account. The bank is offering a simple interest rate of 1.4% What will the account balance be after 10 years
The account balance after 10 years is $7200.
How to calculate the interest?It should be noted that simple interest is calculated as:
= (Principal × Rate × Time) / 100
= ($3000 × 1.4 × 10) / 100
= $4200
The total amount that will be in the account will be:
= Principal + Interest
= $3000 + $4200
= $7200
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