Answer: hello your table is incomplete here is the complete table
Fertilizer Amount (ounces) Tomato Plant Height (inches)
1.9 20.4
5.0 49.2
4.2 56.1
1.3 24.3
4.9 29.2
5.4 60.8
3.1 24.6
0.0 25.3
2.3 26.2
2.5 25.7
0.9 26.5
1.0 28.6
4.5 62.9
3.8 30.8
5.3 43.2
2.3 33.4
4.0 35.1
1.4 22.1
3.9 40.6
4.0 44.5
3.6 29.7
0.6 21.1
1.6 25.4
2.5 29.6
4.5 27.6
3.6 32.6
2.0 33.5
0.0 22.5
2.5 27.6
3.1 46.4
Answer : a)Height = 18.639 + 5.208 * fertilizer
b) The Y intercept make practical sense because without fertilizer there will still be an increase in plant height ( y intercept )
c) 34.263
Step-by-step explanation:
A) Estimating the model
Height = β0 + β1 FERTILIZER + ∈
β0 = 18.639
β1 = 5.208
hence
Height = 18.639 + 5.208 * fertilizer ( using excel )
B) The y- intercept
The Y intercept make practical sense because without fertilizer there will still be an increase in plant height ( y intercept )
C ) using the estimated model to predict after four months
the model = 18.639 + 5.208 * fertilizer
fertilizer ounce given = 3
therefore height of tomato plant after 4 months that received 3 ounces of fertilizer = 18.639 + 5.208 * 3 = 34.263
What is the sum of the series? ∑j=152j Enter your answer in the box.
Answer:
Hope this is correct
HAVE A GOOD DAY!
Which of the following proves ABC DEF?
A.
SAS
B.
SSS
C.
SSA
D.
ASA
Answer:
SAS
Step-by-step explanation:
SAS
two side 1 angle
if not that try SSA
Answer:
SAS
Step-by-step explanation:
We have two sides are equal and the angle between the two sides are equal so we can use the side angle side
Which of the following situations may be modeled by the equation y = 2x +20
A. Carlos has written 18 pages of his article. He plans to write an
additional 2 pages per day.
B. Don has already sold 22 vehicles. He plans to sell 2 vehicles per
week.
C. Martin has saved $2. He plans to save $20 per month.
D. Eleanor has collected 20 action figures. She plans to collect 2
additional figures per month
Answer:
D.
m = 2 = figures/month
b = 20 = # of action figures
janie and her friends played a question and answer game. their scores at the end of thegame were 14, 15, 8, 15, 3, 0, and 12. find the median score of the game
Answer:
12
Step-by-step explanation:
Well first step to finding median is order the scores from least to greatest,
0, 3, 8, 12, 14, 15, 15
Now we can start crossing the numbers off.
After we've crossed 3 numbers off from each side,
we get 12.
Thus,
12 is the median of the number set,
Hope this helps :)
Answer:
12
Step-by-step explanation:
First we need to put the numbers in order from smallest to largest
14, 15, 8, 15, 3, 0, and 12
becomes
0 , 3 , 8 , 12 , 14, 15, 15
Then the median is the middle number
There are 7 numbers
7/2 = 3.5
The middle is the 4th number ( 3 on the left and 3 on the right)
0 , 3 , 8 , 12 , 14, 15, 15
The median is 12
In the year 2000, the population of Mexico was about 100 million, and it was growing by 1.53% per year. At this growth rate, the function f(x) = 100(1.0153)x gives the population, in millions, x years after 2000. Using this model, in what year would the population reach 111 million? Round your answer to the nearest year.
Answer: The population reach 111 million in 2007.
Step-by-step explanation:
In the year 2000, the population of Mexico was about 100 million, and it was growing by 1.53% per year.
At this growth rate, the function [tex]f(x) = 100(1.0153)^x[/tex] gives the population, in millions, x years after 2000.
Put f(x)=111 million.
Then,
[tex]111=100(1.0153)^x\\\\\Rightarrow\ (1.0153)^x=\dfrac{111}{100}=1.11\\\\\Rightarrow (1.0153)^x=1.11[/tex]
Taking log on both the sides , we get
[tex]x\log1.0153=\log1.11\\\\\Rightarrow\ x=\dfrac{\log1.11}{\log1.0153}=\dfrac{0.045323}{0.0066}=6.86712121212\approx7[/tex]
Hence, the population reach 111 million in 2007 (approx).
Identify the parameter n in the following binomial distribution scenario. A basketball player has a 0.479 probability of
making a free throw and a 0.521 probability of missing. If the player shoots 17 free throws, we want to know the probability
that he makes more than 9 of them. (Consider made free throws as successes in the binomial distribution.)
Answer:
n = 17
Step-by-step explanation:
Assuming
- probability of success (making free throw) does not vary
We have
n = 17 (trials)
p = 0.479
x > 9
The answer is "[tex]\bold{p(x>9)=0.2550319}[/tex]"
[tex]\to X:[/tex] Number of creating free throws in a set [tex]\bold{17\ \ x \sim bin(17,0.479)}[/tex]
Know we calculating the P(makes more than 9 of them)
[tex]=\bold{9(X>9)=1-P(Z<=9)}[/tex]
Using the R-code:
[tex]\to \bold{1-p\ binom(9,17,0.479)}\\\\\to \bold{[1]0.2550319}\\\\\bold{\therefore}\\\\ \to \bold{p(x>9)=0.2550319}[/tex]
Learn more:
binomial distribution: brainly.com/question/9065292
Factor the polynomial completely.
Q(x) = x4 − 1
Q(x)=
Find all its zeros. State the multiplicity of each zero. (Order your answers from smallest to largest real, followed by complex answers ordered smallest to largest real part, then smallest to largest imaginary part.)
x= ?? multiplicty= ??
x= ?? multiplicty= ??
x= ?? multiplicty= ??
x= ?? multiplicty= ??
Answer: (x^2-1)(x^2+1)=(x-1)(x+1)(x^2+1)
Step-by-step explanation:
(x²+1)(x²-1) are factors of polynomial x4-1 and x=1,-1, i are the roots of x⁴ − 1.
What is Polynomial?A polynomial is an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.
The given polynomial is Q(x) = x⁴ − 1.
We can write it as (x²)²-1²
We have a algebraic formula which is
a²-b²=(a+b)(a-b)
Similarly
(x²)²-1²=(x²+1)(x²-1)
Now let us find the roots of factors (x²+1) and (x²-1)
x²+1=x=√-1=i,-i
x²-1=x=1,-1
The multiplicity of the roots is always one.
Hence (x²+1)(x²-1) are factors of polynomial x4-1 and x=1,-1, i are the roots of x⁴ − 1.
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At a firm, ten entry-level employees earn $40,000 a year, 6 junior-level employees earn $60,000 a year, and 3 managers earn $80,000 a year per person respectively. Find the weighted average of the firm.
Answer: answer is: 1000000/19
Step-by-step explanation:
10/19 - 40k -> 10/19*40k= 400000/19
6/19- 60k -> 6/19*60k= 360000/19
3/19 - 80k -> 3/19*80k=240000/19
400000/19+360000/19+240000/19=1000000/19
answer is: 1000000/19
Solve application problems using radical equations. A hang glider dropped his cell phone from a height of 450 feet. How many seconds did it take for the cell phone to reach the ground?
Answer:
[tex]\large \boxed{\text{5.29 s}}[/tex]
Step-by-step explanation:
The appropriate free fall equation is
y = v₀t + ½gt²
Data:
v₀ = 0
g = 32.17 ft·s⁻²
Calculation:
[tex]\begin{array}{rcl}450 &=& v_{0}t + \dfrac{1}{2}gt^{2}\\\\& = & 0 \times t + \dfrac{1}{2}\times 32.17t^{2}\\\\& = & 16.08t^2\\t^{2}& = & \dfrac{450}{16.08}\\\\& = & 27.97\\t & = & \textbf{5.29 s}\\\end{array}\\\text{It took $\large \boxed{\textbf{5.29 s}}$ for the phone to reach the ground.}[/tex]
A sample of size 60 from one population of weights had a sample average of 10.4 lb. and a sample standard deviation of 2.7 lb. An independent sample of size 100 from another population of weights had a sample average of 9.7 lb. with a sample standard deviation of 1.9 lb. Find a 95% confidence interval for the difference between the population means.
Answer:
z= 0.278
Step-by-step explanation:
Given data
n1= 60 ; n2 = 100
mean 1= x1`= 10.4; mean 2= x2`= 9.7
standard deviation 1= s1= 2.7 pounds ; standard deviation 2= s2 = 1.9 lb
We formulate our null and alternate hypothesis as
H0 = x`1- x`2 = 0 and H1 = x`1- x`2 ≠ 0 ( two sided)
We set level of significance α= 0.05
the test statistic to be used under H0 is
z = x1`- x2`/ √ s₁²/n₁ + s₂²/n₂
the critical region is z > ± 1.96
Computations
z= 10.4- 9.7/ √(2.7)²/60+( 1.9)²/ 100
z= 10.4- 9.7/ √ 7.29/60 + 3.61/100
z= 0.7/√ 0.1215+ 0.0361
z=0.7 /√0.1576
z= 0.7 (0.396988)
z= 0.2778= 0.278
Since the calculated value of z does not fall in the critical region so we accept the null hypothesis H0 = x`1- x`2 = 0 at 5 % significance level. In other words we conclude that the difference between mean scores is insignificant or merely due to chance.
there are three oranges in 200g of bag . if the weight of them with bag is 1.4kg. find the weight of an orange.i want full methods
the bag is 200g
total weight with oranges is 1400g
deduct the bags weight from total weight
1400 - 200
1200g
this is the weight of the three oranges
so each orange would be
1200 ÷ 3
400g
A company has five employees on its health insurance plan. Each year, each employee independently has an 80% probability of no hospital admissions. If an employee requires one or more hospital admissions, the number of admissions is modeled by a geometric distribution with a mean of 1.50. The numbers of hospital admissions of different employees are mutually independent. Each hospital admission costs 20,000.
Calculate the probability that the company's total hospital costs in a year are less than 50,000.
Answer:
the probability that the company's total hospital costs in a year are less than 50,000 = 0.7828
Step-by-step explanation:
From the given information:
the probability that the company's total hospital costs in a year are less than 50,000 will be the sum of the probability of the employees admitted.
If anyone is admitted to the hospital, they have [tex]\dfrac{1}{3}[/tex] probability of making at least one more visit, and a [tex]\dfrac{2}{3}[/tex] probability that this is their last visit.
If zero employee was admitted ;
Then:
Probability = (0.80)⁵
Probability = 0.3277
If one employee is admitted once;
Probability = [tex](0.80)^4 \times (0.20)^1 \times (^5_1) \times (\dfrac{2}{3})[/tex]
Probability = [tex](0.80)^4 \times (0.20)^1 \times (\dfrac{5!}{(5-1)!}) \times (\dfrac{2}{3})[/tex]
Probability = 0.2731
If one employee is admitted twice
Probability = [tex](0.80)^3 \times (0.20)^2 \times (^5_2) \times (\dfrac{2}{3})^2[/tex]
Probability = [tex](0.80)^3 \times (0.20)^2 \times (\dfrac{5!}{(5-2)!}) \times (\dfrac{2}{3})^2[/tex]
Probability = 0.1820
If two employees are admitted once
Probability = [tex](0.80)^4\times (0.20)^1 \times (^5_1) \times (\dfrac{1}{3}) \times (\dfrac{2}{3})[/tex]
Probability = [tex](0.80)^4 \times (0.20)^1 \times (\dfrac{5!}{(5-1)!}) \times (\dfrac{1}{3}) \times (\dfrac{2}{3})[/tex]
Probability = 0.0910
∴
the probability that the company's total hospital costs in a year are less than 50,000 = 0.3277 + 0.2731 + 0.1820
the probability that the company's total hospital costs in a year are less than 50,000 = 0.7828
Write 21/7 as a whole number
Answer: 3
Step-by-step explanation:
7x=21 21/7=3
Assume production time per unit is normally distributed with a mean 40 minutes and standard deviation 8 minutes. Using the empirical rule, what percent of the units are produced in MORE than 32 minutes?
Answer:
84%
Step-by-step explanation:
We find the z-score here
z= x-mean/SD = 32-40/8 = -1
So the probability we want to find is;
P(z>-1)
This can be obtained using the standard score table
P(z>-1) = 0.84 = 84%
Write in expanded form
3
(-a)
Answer:
-3a
Step-by-step explanation:
3(-a)
Expand brackets.
3 × -1a
-3a
Y is directly proportional to x. Create an equation using k as the constant of proportionality.
Answer:
[tex]y = kx[/tex]
Step-by-step explanation:
y is directly proportional to x.
[tex]y \propto x[/tex]
[tex]y = kx[/tex]
Where k is as the constant of proportionality.
Answer:
y = kx
Step-by-step explanation:
Y is directly proportional to x which means that
=> y ∝ x
=> y = kx
Where k is the constant of proportionality.
Which expression is equivalent to 486 – 9 + 6 + 33 × 2?
Answer:
549
Step-by-step explanation:
Remember PEMDAS (this is the order of operations).
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
So, lets do multiplication first.
33*2 = 66
So, our new expression is 486 - 9 + 6 + 66.
Remember that addition and subtraction are reversible.
486 - 9 = 477
477 + 6 = 483
483 + 66 = 549
Answer:
404
Step-by-step explanation:
P-parenthesis
E-exponents
M-multiplication
D-division
A-addition
S-subtraction
486-9+6+33*2
486-9+6+66
486-81=404
can someone help me with this question?l
Answer:
1. 32x³ - 25x² + 35x2. 6x - 11y + 14z - 7Step-by-step explanation:
1).(4x³ - 5x² + 3x ) - 4(5x² - 7x³ - 8x)
Remove the brackets and simplify.
We have
4x³ - 5x² + 3x - 20x² + 28x³ + 32x
Group like terms and simplify
That's
4x³ + 28x³ - 5x² - 20x² + 3x + 32x
We have the final answer as
32x³ - 25x² + 35x2).- 3 - ( 4x + 3y - 2z ) - 4 + 2( 5x - 4y + 6z)
Remove the brackets and simplify
That's
- 3 - 4x - 3y + 2z - 4 + 10x - 8y + 12z
Group like terms and simplify
- 4x + 10x - 3y - 8y + 2z + 12z - 3 - 4
We have the final answer as
6x - 11y + 14z - 7Hope this helps you
A ball always bounces to 3/5 of the height from which it is dropped. The ball is dropped from 1.8m and bounces 3 times. How high will it rise from the third bounce?
Answer: 0.388 m
Step-by-step explanation:
Ok, if the ball is dropped from 1.8 meters, then the height after the first bounce will be 3/5 times 1.8 meters:
h1 = (3/5)*1.8m = 1.08m
now we can think that the ball is dropped from a height of 1.08 meters, then the height after the second rebound will be:
h2 = (3/5)*1.08m = 0.648m
Now, using the same method as before, the height after the third bounce will be:
h3 = (3/5)*0.648m = 0.388 m
Notice that we can write this relation as:
h(n) = 1.8m*(3/5)^n
where n is the number of bounces.
if n = 0 we have the initial height, and if n = 3 we are on the third bounce, then:
h(3) = 1.8m*(3/5)^3 = 0.388 m
Suppose that the probability distribution below shows the number of colleges that children of celebrities applied to in 2018. Compute the standard deviation for the number of college applications.
x 0 2 4 6
P(x) 0.4 0.3 0.2 0.1
Complete Question
The complete question is shown on the first uploaded image
Answer:
The standard deviation is [tex]\sigma = 2.45[/tex]
Step-by-step explanation:
From the given data we can compute the expected mean for each random values as follows
[tex]E(X) = \sum [ X * P(X = x )]\\\\ X \ \ \ \ \ \ X* P(X =x )\\ 0 \ \ \ \ \ \ \ \ \ \ 0* 0.4 = 0 \\ 2 \ \ \ \ \ \ \ \ \ \ 2 * 0.3 = 0.6 \\ 4 \ \ \ \ \ \ \ \ \ \ 4 * 0.2 = 0.8\\ 6 \ \ \ \ \ \ \ \ \ \ 6* 0.1 = 0.6[/tex]
So
[tex]E(x) = 0 + 0.6 + 0.8 + 0.6[/tex]
[tex]E(x) = 2[/tex]
The
[tex]E(X^2) = \sum [ X^2 * P(X = x )]\\\\ X \ \ \ \ \ \ \ \ \ \ X^2 * P(X=x ) \\ 0 \ \ \ \ \ \ \ \ \ \ 0^2 * 0.4 = 0 \\ 2 \ \ \ \ \ \ \ \ \ \ 2^2 * 0.3 = 12 \\ 4 \ \ \ \ \ \ \ \ \ \ 4^2 * 0.2 = 3.2 \\ 6 \ \ \ \ \ \ \ \ \ \ 6^2 * 0.1 = 3.6[/tex]
So
[tex]E(X^2) = 0 + 1.2 + 3.2 + 3.6[/tex]
[tex]E(X^2) = 8[/tex]
Now the variance is mathematically evaluated as
[tex]Var (X) = E(X^2 ) -[E(X]^2[/tex]
Substituting value
[tex]Var (X) = 8-4[/tex]
[tex]Var (X) = 6[/tex]
The standard deviation is mathematically evaluated as
[tex]\sigma = \sqrt{Var(x)}[/tex]
[tex]\sigma = \sqrt{4}[/tex]
[tex]\sigma = 2[/tex]
A section of concrete pipe 3.0 m long has an inside diameter of 1.2 m and an outside diameter of 1.8 m. What is the volume of concrete in this section of pipe?
Answer:
4.24m³
Step-by-step explanation:
The inside diameter of 1.2 m of the pipe
Radius of the inside pipe = Diameter/2 = 1.2/2 = 0.6m
The outside diameter of 1.8 m
Radius of the outer of the pipe = 1.8/2 = 0.9m
Height of the pipe = 3.0m
A Pipe looks like the shape of the cylinder. Hence,
Volume of concrete in the pipe = Volume of the outer section of the Pipe - Volume of the inner section of the pipe
Volume of the outer section of the Pipe = πr²h
h = 3.0m
r = 0.9
= π × 0.9² × 3.0
= 7.63m³
Volume of the inner section of the Pipe = πr²h
h = 3.0m
r = 0.6
= π × 0.6² × 3.0
= 3.39m³
Volume of concrete in the pipe = Volume of the outer section of the Pipe - Volume of the inner section of the pipe
= 7.63m³ - 3.39m³
= 4.24m³
Therefore, volume of concrete in the pipe is 4.24m³
The perimeter of the rectangle below is 132 units.
Answer:
The answer is 29 unit.
Step-by-step explanation:
Here,
given that,
DC (l) =4z+1
CD (b)=5z+2
perimeter (p)= 132
now,
perimeter of rectangle (p) is= 2(l+b)
or, 132 = 2×{(4z+1)+(5z+2)}
or, 132= 2×(9z+3)
or, 132= 18z+6
or, 18z=132-6
or, z=126/18
or, z= 7.
therefore, 4z+1=4×7+1=29
5z+2= 5×7+2=37.
As our question is about to find AB,
DC = AB. (as opposite side of rectangle is equal).
so, the valueof AB is 29unit.
Hope it helps...
Find the dimensions of a rectangle with perimeter 68 m whose area is as large as possible. (If both values are the same number, enter it into both blanks.)
Answer:
Length is 17m and Breadth is also 17mStep-by-step explanation:
The perimeter of a rectangle is expressed as 2(L+B) where;
L is the length and B is the breadth of the triangle.
P = 2(L+B)
68 = 2(L+B)
L+B = 68/2
L+B = 34
L = 34 - B ... 1
Area of the rectangle A = LB... 2
Substituting equation 1 into 2 will give;
A = (34-B)B
A = 34B-B²
To maximize the area of the triangle, dA/dB must be equal to zero i.e
dA/dB = 0
dA/dB = 34 - 2B = 0
34-2B = 0
2B = 34
Dividing both sides of the equation by 2 we will have;
B = 34/2
B = 17
Substituting B = 17 into equation 1 to get the length L
L = 34-17
L = 17m
This shows that the rectangle with maximum area is a square since L = B = 17m
The dimension of the rectangle is Length = 17m and Breadth = 17m
The dimensions are 17m and 17m.
The perimeter of a rectangle is given as:
= 2(length + width)
Since in their case, the lengths have same values, this will be:
Perimeter = 2(l + l)
Perimeter = 4l
4l = 68
L = 68/4
L = 17m
Therefore, the dimensions are 17m and 17m.
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The length of a rectangle is 4yd longer than its width. If the perimeter of the rectangle is 36yd, find its area
Answer:
[tex] \boxed{\sf Area \ of \ the \ rectangle = 91 \ yd^{2}} [/tex]
Given:
Length of the rectangle = 4 yd longer than its width
Perimeter of the rectangle = 36 yd
To Find:
Area of the rectangle
Step-by-step explanation:
Let the width of the rectangle be 'w' yd
So,
Length of the rectangle = (w + 4) yd
[tex] \therefore \\ \sf \implies Perimeter \: of \: the \: rectangle = 2(Length + Width) \\ \\ \sf \implies 36 = 2((4 + w) + w) \\ \\ \sf \implies 36 = 2(4 + w + w) \\ \\ \sf \implies 36 = 2(4 + 2w) \\ \\ \sf 36 =2(2w+4) \: is \: equivalent \: to \: 2(2w + 4) = 36: \\ \sf \implies 2(2w + 4) = 36 \\ \\ \sf Divide \: both \: sides \: of \: 2 (2w + 4) = 36 \: by \: 2: \\ \sf \implies 2w + 4 = 18 \\ \\ \sf Subtract \: 4 \: from \: both \: sides: \\ \sf \implies 2w = 14 \\ \\ \sf Divide \: both \: sides \: of \: 2w = 14 \: by \: 2: \\ \sf \implies w = 7[/tex]
So,
Width of the rectangle = 7 yd
Length of the rectangle = (7 + 4) yd
= 13 yd
[tex] \therefore \\ \sf Area \ of \ the \ rectangle = Length \times Width \\ \\ \sf = 7 \times 13 \\ \\ \sf = 91 \: {yd}^{2} [/tex]
HELPNEEDED.Two boys and three girls are auditioning to play the piano for a school production. Two students will be chosen, one as the pianist, the other as the alternate.
What is the probability that the pianist will be a boy and the alternate will be a girl?
30%
40%
50%
60%
Find the midpoint of AC.
B (0, a)
C (a, a)
A(0, 0) D (a,0)
Answer:
[tex]\huge\boxed{\bigg(\dfrac{a}{2};\ \dfrac{a}{2}\bigg)}[/tex]
Step-by-step explanation:
The formula of a midpoint:
[tex]M\bigg(\dfrac{x+1+x+2}{2};\ \dfrac{y_1+y_2}{2}\bigg)[/tex]
We have the points
[tex]A(0;\ 0)\to x_1=0;\ y_1=0\\\\C(a;\ a)\to x_2=a;\ y_2=a[/tex]
Substitute:
[tex]\dfrac{x_1+x_2}{2}=\dfrac{0+a}{2}=\dfrac{a}{2}\\\\\dfrac{y_1+y_2}{2}=\dfrac{0+a}{2}=\dfrac{a}{2}[/tex]
Answer:
The answer is (a/2,a/2)
Step-by-step explanation:
Fill in 2 then a
In conclusion (a/2,a/2)
ASAP PLEASE HELP!!!!!! Find the y-intercept of the rational function. A rational function is graphed in the first quadrant, and in the second, third and fourth quadrants are other pieces of the graph. The graph crosses the x axis at negative 10 and crosses the y axis at negative 2.
Answer:
(0,-2)
Step-by-step explanation:
The y-intercept is simply when the function touches or crosses the y-axis.
We're told that the graph crosses the y-axis at -2. In other words, the y-intercept is at -2.
The ordered pair would be (0,-2)
A company had a market price of $38.50 per share, earnings per share of $1.75, and dividends per share of $0.90. its price-earnings ratio equals:
Answer: Price-earnings ratio= 22.0
Step-by-step explanation:
Given: A company had a market price of $38.50 per share, earnings per share of $1.75, and dividends per share of $0.90
To find: price-earnings ratio
Required formula: [tex]\text{price-earnings ratio }=\dfrac{\text{ Market Price per Share}}{\text{Earnings Per Share}}[/tex]
Then, Price-earnings ratio = [tex]\dfrac{\$38.50}{\$1.75}[/tex]
⇒Price-earnings ratio = [tex]\dfrac{22}{1}[/tex]
Hence, the price-earnings ratio= 22.0
Identify the lower class limits, upper class limits, class width, class midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary.
Age (yr) when award was won: 25-34, 35-44, 45-54, 55-64, 65-74, 75-84, 85-94
Frequency: 29, 34, 16, 3, 5, 1, 2
Step-by-step explanation:
kindly find attached detailed information of the remaining information as requested for your reference
1. The lower class limit is the left number in the age column
i.e in the 25-34 the lower class limit is 25
2. The upper class limit is the right number in the age column
i.e in the 25-34 the lower class limit is 34
3. The class width is the difference between the class boundaries of a single class
class width = 34.5-24.5= 10
4. The number of individuals is= 29+34+16+3+5+1+2= 90
TRIANGLE ABC IS DILATED BY A SCALE FACTOR OF 0.5 WITH THE ORIGIN AS THE CENTER OF DILATION, RESULTING IN THE IMAGE TRIANGLE A'B'C. IF A=(2,2). IF A (2,2), B= (4,3) AND C=(6,3), WHAT IS THE LENGTH OF LINE B'C'?
Answer: The length of the line B'C" is 1 unit.
Step-by-step explanation:
Given: Triangle ABC is dilated by a scale factor of 0.5 with the origin as the center of dilation , resulting in the image Triangle A'B'C'.
If A (2,2), B= (4,3) and C=(6,3).
Distance between (a,b) and (c,d): [tex]D=\sqrt{(d-b)^2+(c-b)^2}[/tex]
Then, BC [tex]=\sqrt{(3-3)^2+(6-4)^2}[/tex]
[tex]\\\\=\sqrt{0+2^2}\\\\=\sqrt{4}\\\\=2\text{ units}[/tex]
Length of image = scale factor x length in original figure
B'C' = 0.5 × BC
= 0.5 × 2
= 1 unit
Hence, the length of the line B'C" is 1 unit.