There are approximately 819 children who weigh between 40 kilograms and 55 kilograms.
What is Standard deviation ?
Standard deviation is a measure of the spread or dispersion of a set of data from its mean. It is calculated as the square root of the variance.
To solve this problem, we can use the properties of a normal distribution, assuming that the weights of the children follow a normal distribution.
We know that the mean weight of 1000 children is 50 kilograms and the standard deviation is 5 kilograms. This means that the weights of the children are distributed around the mean with a spread of 5 kilograms.
We want to find the number of children who weigh between 40 kilograms and 55 kilograms. To do this, we can standardize the values using the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can use the following formula to standardize the values:
z = (x - μ) ÷ σ
where z is the standard score, x is the raw score, μ is the mean, and σ is the standard deviation.
For x = 40 kilograms:
z = (40 - 50) ÷ 5 = -2
For x = 55 kilograms:
z = (55 - 50) ÷ 5 = 1
Now, we can use a standard normal distribution table or calculator to find the area under the curve between z = -2 and z = 1. This area represents the proportion of children who weigh between 40 kilograms and 55 kilograms.
Using a standard normal distribution table or calculator, we find that the area under the curve between z = -2 and z = 1 is approximately 0.8186.
Therefore, the number of children who weigh between 40 kilograms and 55 kilograms is:
0.8186 * 1000 = 818.6 children
Since we can't have a fraction of a child, we round this number to the nearest whole number, which is 819 children.
Therefore, there are approximately 819 children who weigh between 40 kilograms and 55 kilograms.
To learn more about Standard deviation from given link.
https://brainly.com/question/13905583
#SPJ1
Adzo says the graph is of the function y = 2-¹x - √25.
Ben says it is y- 5 = 0.5x. Who is correct? Explain your answer.
Based on the information provided, I think that Ben is correct.
Let's analyze and compare the given expressions:
Adzo says the graph is of the function y = 2-¹x - √25.
In this expression, y is equal to 2 raised to the power of -1 multiplied by x, minus the square root of 25. This can also be written as y = (1/2)x - 5.
Ben says it is y - 5 = 0.5x.
In this expression, y - 5 is equal to 0.5 times x.
How do we compare the expressions?Comparing the two expressions, we can see that Ben's expression, y - 5 = 0.5x, is a linear equation in slope-intercept form, where the slope is 0.5 and the y-intercept is -5, representing a straight line on a graph.
On the other hand, Adzo's expression, y = (1/2)x - 5 or y = 2-¹x - √25, also represents a straight line on a graph with a slope of 1/2, but it is shifted vertically downward by 5 units due to the subtraction of 5 in the expression.
Thus, both expressions represent straight lines on a graph, however Ben's expression is in the standard slope-intercept form.
Learn more about graph at brainly.com/question/9590016.
#SPJ1
Recursive Rules from Word Problems
1) Sally started a new job. After depositing her 1st paycheck into her bank account she had
$225. Every week she was paid the same amount. After her 8th paycheck she had $1275 in her
bank account.
Complete the table
after her 2nd paycheck, Sally had $375 in her bank account, after her 3rd paycheck she had $525, after her 4th paycheck she had $675, after her 5th paycheck she had $825, after her 6th paycheck she had $975, and after her 7th paycheck she had $1125.
How to solve the problem?
Let's call the amount that Sally gets paid every week "x". We know that after her 1st paycheck, she had $225, so we can write:
1st paycheck: $225
2nd paycheck: $225 + x
3rd paycheck: $225 + 2x
4th paycheck: $225 + 3x
5th paycheck: $225 + 4x
6th paycheck: $225 + 5x
7th paycheck: $225 + 6x
8th paycheck: $225 + 7x = $1275
To solve for "x", we can start by subtracting $225 from both sides of the equation for the 8th paycheck:
$225 + 7x = $1275
7x = $1050
x = $150
So Sally gets paid $150 every week.
To find the amount of money she had in her account after each paycheck, we can substitute "x" into the equations above:
1st paycheck: $225
2nd paycheck: $225 + $150 = $375
3rd paycheck: $225 + 2($150) = $525
4th paycheck: $225 + 3($150) = $675
5th paycheck: $225 + 4($150) = $825
6th paycheck: $225 + 5($150) = $975
7th paycheck: $225 + 6($150) = $1125
8th paycheck: $225 + 7($150) = $1275
Therefore, after her 2nd paycheck, Sally had $375 in her bank account, after her 3rd paycheck she had $525, after her 4th paycheck she had $675, after her 5th paycheck she had $825, after her 6th paycheck she had $975, and after her 7th paycheck she had $1125.
To know more about paycheck visit :-
https://brainly.com/question/28905653
#SPJ1
A speaker claimed that if the number of factories in the country increases by 3% per annum, then even if they all immediately reduced the amount of pollution they produce by 80%, the total annual pollution will be back to its present level in about 50 years. (Hint use Logarithms)
Actual time is much longer than the 50-year timeframe suggested by the speaker.
How to verify the statement?
This claim is based on the assumption that the rate of pollution reduction from each factory remains constant at 80%, and the number of factories increases by 3% per annum.
To verify this claim, we can use the following formula to calculate the expected total pollution after n years:
Total pollution after n years = [tex]Present \: pollution \: level x (1 + 0.03)^n \times (1 - 0.8)^n[/tex]
Here, the first factor represents the increase in pollution due to the growth in the number of factories, and the second factor represents the reduction in pollution due to the 80% reduction in pollution from each factory.
We can set the expected total pollution after n years equal to the present pollution level and solve for n:
[tex]Present \: pollution \: level = Present \: pollution \: level \times (1 + 0.03)^n \times (1 - 0.8)^n[/tex]
Simplifying this equation, we get:
[tex]1 = 1.03^n \times 0.2^n[/tex]
Taking the logarithm of both sides of the equation, we get,
[tex]n \times log(1.03) + n \times log(0.2) = 0 \\ n \times (log(1.03) + log(0.2)) = 0 \\ n = \frac{0} { (log(1.03) + log(0.2))} \\ n = 271.56[/tex]
Therefore, according to this calculation, it would take approximately 272 years for the total annual pollution to return to its present level if the number of factories in the country increases by 3% per annum, and they all immediately reduce the amount of pollution they produce by 80%. This is much longer than the 50-year timeframe suggested by the speaker.
It is important to note that this calculation assumes that the pollution reduction from each factory remains constant at 80% and does not take into account any other factors that may affect pollution levels, such as changes in technology or regulations. Therefore, this should be considered as a rough estimate and not as an exact prediction.
Learn more about pollution here,
https://brainly.com/question/24704410
#SPJ1
Correct question is "A speaker claimed that if the number of factories in the country increases by 3% per annum, then even if they all immediately reduced the amount of pollution they produce by 80%, the total annual pollution will be back to its present level in about 50 years. Verify the statement. (use logarithm)"
Prove the following: a finite group with an even number of elements contains an even number of elements [tex]x[/tex] such that [tex]x^{-1}=x[/tex]. State and prove a similar statement for a finite group with an odd number of elements?
a finite group with an even number of elements contains an even number of elements such that. x inverse = x.
a similar statement for a finite group with an odd number of elements
For a finite group with an even number of elements, we can prove that it contains an even number of elements such that their order is 2.
Let G be a finite group of even order.
We can define t(G) as the set { g ∈ G | g ≠ g − 1 }.
if g ∈ t(G), then g − 1 ∈ t(G), and by definition g − 1 ≠ g.
Now let A = { { g, g − 1 } | g ∈ t (G) }.
Thus we have | t (G) | = ∑ α ∈ A | α | = 2 k for some positive integer k;
in particular, t (G) contains an even number of elements 1.
Hence [tex]x^{-1}=x[/tex]
For a finite group with an odd number of elements, we can prove that it contains an odd number of elements such that their order is 2. For any element in G-{e}, there must be an inverse of that element in G-{e}. Take any element in G-{e}, say b, If bb=e, then the proof is done. If the inverse of b is not itself, then there must be one element in G-{e}, say c, such that bc=e. Because there are an odd number of elements, I keep doing this until I have left with one
learn more about the finite group,
https://brainly.com/question/29744084
#SPJ1
|||
9
C
Erica has $120. If sweatshirts cost $28.99, estimate the maximum number of
shirts she can buy by rounding the price to the nearest ten.
Erica can buy a maximum of 4 sweatshirts by rounding the cost to the nearest ten.
How to calculate Rounding off?A number is approximated to a certain degree of accuracy by rounding it off. The purpose of doing this is usually to make the number easier to deal with or to portray it in a clearer, more accessible manner.
You must take the following actions in order to round off a number:
The digit in the number that you want to round off is known as the rounding digit. The rounding digit is the third digit following the decimal point, or 1, in the example above, if you wish to round off 3.1416 to two decimal places.
Look at the digit that is directly above it: You should round up if this digit is 5 or higher. You should round it down if it is less than 5.
Replace the digits to the right of the rounding digit with zeros: If you are rounding to a certain number of decimal places, you will need to add zeros to the right of the rounding digit to maintain the correct level of precision. For example, if you are rounding 3.1416 to two decimal places, you will need to replace the digits to the right of the rounding digit with zeros, giving you 3.14.Adjust the rounding digit if necessary: If you round up, you will need to
To estimate the maximum number of sweatshirts Erica can buy, we need to divide her total amount of money by the cost of each sweatshirt rounded to the nearest ten.
Rounding $28.99 to the nearest ten gives us $30.
Dividing $120 by $30 gives us:
$120 ÷ $30 = 4
Therefore, Erica can buy a maximum of 4 sweatshirts by rounding the cost to the nearest ten.
Learn more about Rounding of a digit here
https://brainly.com/question/28799337
#SPJ1
Text → Graphing Exponential Functions: Mastery Test
2
Select the correct answer.
Which statement correctly compares the graph of function g with the graph of function f?
f(x) = e - 4
g(x) =
- 4
OA.
OB.
O C.
O D.
The graph of function g is a horizontal shift of the graph of function f to the left.
The graph of function g is a vertical stretch of the graph of function f.
The graph of function g is a horizontal shift of the graph of function f to the right.
The graph of function g is a vertical compression of the graph of function f.
Answer:
x=2
Step-by-step explanation:
4 x1,2 =2
The correct statement which compares the graph of function g with the graph of function f is,
⇒ The graph of function g is a vertical compression of the graph of function f.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
Functions are,
f (x) = eˣ - 4
g (x) = 1/2eˣ - 4
Now, We have to find that;
The graph of function g is a vertical compression of the graph of function f.
Hence, The correct statement which compares the graph of function g with the graph of function f is,
⇒ The graph of function g is a vertical compression of the graph of function f.
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ5
Given: circle k(O) with diameter AB and CD ⊥ AB
Prove: AD·CB=AC·CD
For a circle [tex]k(O)[/tex] with diameter AB and CD [tex]\bot[/tex] AB, it is proved that [tex]AD\times CB=AC\times CD[/tex], using similarity of triangles.
Given:
circle [tex]k(O)[/tex] with diameter AB
CD [tex]\bot[/tex] AB
To Prove: [tex]AD\times CB=AC\times CD[/tex]
Proof:
In [tex]\Delta ADC[/tex] and [tex]\Delta CDB[/tex],
[tex]\angle ADC = \angle CDB = 90^\circ[/tex]
[∵Both are right angle triangles]
[tex]CB = CB[/tex] [Common side]
[tex]\implies\dfrac{AC}{CB} =\dfrac{CD}{DB}[/tex]
Thus, [tex]\Delta ACD[/tex] is similar to [tex]\Delta CDB[/tex] by RHS similarity.
Therefore, we can write,
[tex]\dfrac{AD}{CD} =\dfrac{AC}{CB}[/tex] [Since corresponding sides of similar triangles are proportional]
[tex]\implies AD\times CB = AC\times CD[/tex]
Hence proved.
Learn more about similarity here:
brainly.com/question/25882965
You can get 52 to point if you answer every single answer hurry up this a test
Determine the number of units a given figure would be translated using the given notation.
The number of units a given figure would be translated using the given notation are shown below.
What is a translation?In Mathematics, the translation of a graph to the left is a type of transformation that simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph to the right is a type of transformation that simply means adding a digit to the value on the x-coordinate of the pre-image.
Based on each of the transformation rule, the number of units a given figure would be translated using the given notation include the following:
(x, y) → (x + 7, y - 6)
7 units right.
6 units down.
(x, y) → (x - 9, y + 2)
9 units left.
2 units up.
(x, y) → (x - 11, y)
11 units left.
0 units up/down.
(x, y) → (x - 8, y - 5)
8 units left.
5 units down.
(x, y) → (x + 13, y + 3)
7 units right.
3 units up.
(x, y) → (x, y + 9)
0 units right/left.
9 units up.
(x, y) → (x - 14, y + 12)
14 units left.
12 units up.
(x, y) → (x, y - 4)
0 units right/left.
4 units down.
Read more on translation here: brainly.com/question/26869095
#SPJ1
Which equation or inequality shows the relationship between the values?
|7| > |-7|
|7| < |-7|
|7| = |-7|
|7| ≠ |-7|
The cοrrect equatiοn that shοws the relatiοnship between the values is |7| < |-7|
What is inequality?An inequality is a relatiοn that cοmpares twο numbers οr οther mathematical expressiοns in an unequal way.
The absοlute value οf a number represents its distance frοm zerο οn the number line. The absοlute value οf 7 and -7 are bοth 7, sο |7| = |-7|.
The inequality |7| < |-7| means that the absοlute value οf 7 is less than the absοlute value οf -7. This is true because the absοlute value οf -7 is alsο 7, but negative, sο it is farther frοm zerο οn the number line than the absοlute value οf 7.
The cοrrect equatiοn that shοws the relatiοnship between the values is:
|7| < |-7|
To know more about inequality visit,
brainly.com/question/24372553
#SPJ9
1. I ............. she will to the party, I really want to see her.
a) expect
b) hope
c) want
d) believe
Answer:
1. I ............. she will to the party, I really want to see her.
a) expect
b) hopec) want
d) believe
Step-by-step explanation:
You're welcome.
if the volume of a cube can be represented by a polynomial of degree 9, what is the degree of the polynomial that represents each side lenght
Answer:
Each side length of the cube will be a polynomial of degree 3.
you ride a bike to campus a distance of 5 miles and return home on the same route. Going to campus, you ride mostly downhill and average 9 miles per hour faster than on your return trip home. If the round trip one hour and ten minutes that is 7/6 hours; what is your average velocity on your return trip
there are several possible heights at which the higher end of the bridge can be attached to the higher end of the mountain. Fill in the table below to use 5 possible values for y, and calculate the resulting values for r
The resulting values for r will be sqrt(140).
Let's assume that the bridge is a straight line segment that connects the top of the mountain (point A) to a point on the ground (point B).
Let's also assume that the distance from the top of the mountain to point B is a fixed value d.
If we attach the higher end of the bridge to the top of the mountain at a height y, the distance between point A and the attachment point can be calculated using the Pythagorean theorem as:
x = sqrt([tex]d^2[/tex] - [tex]y^2[/tex])
The length of the bridge, which is also the hypotenuse of the right triangle formed by points A, B, and the attachment point, can then be calculated as:
r = sqrt([tex]x^2[/tex] + [tex](d-y)^2[/tex])
To find the values of r for different heights y, we can simply substitute different values of y into these equations and calculate the resulting values of r.
For example, if we use the values d=10 and y=3, we get:
To calculate the values for "r" given 5 possible values for "y," we need to use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the bridge is the hypotenuse, and we know the height of the mountain (x) and the distance from the mountain to the lower end of the bridge (d). So we can write:
r^2 = [tex]x^2[/tex] + [tex](d + y)^2[/tex]
x = sqrt([tex]10^2[/tex] - [tex]3^2[/tex])
x = sqrt(91)
r = sqrt((sqrt([tex]91))^2[/tex] + [tex](10-3)^2[/tex])
r = sqrt(91 + 49)
r = sqrt(140)
For similar question on resulting values :
https://brainly.com/question/18136991
#SPJ11
Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation.
(-8, - 7); y = -8x - 9
Answer:9
Step-by-step explanation:
0
If x/6=x+10/42 what is the value of 6x+10
Answer:
If the entire mass of the Milky Way was due to gas and stars, how would you expect the rotational speed of a star near the edge of the galaxy to compare to the rotational speed of a star near the center?
Step-by-step explanation:
Which is a solution for the following system of inequalities?
which of the following describes a move away from capitalism
The nationalization of major industries in Hugo Chavez's Venezuela describes a move away from capitalism. Thus, option C is correct.
What is capitalism?
Capitalism is an economic system characterized by private ownership of the means of production and the creation of goods or services for profit in a competitive market. In capitalism, individuals and businesses are free to invest and produce goods and services that they can sell for a profit.
A move away from capitalism would entail a shift in economic system from one that is primarily driven by profit and private ownership to one that prioritizes social welfare and collective ownership.
Chavez, a clοse ally οf Cuba’s cοmmunist leaders, has steadily increased the rοle οf the state in Venezuela with a slew οf natiοnalizatiοns and tοugh cοntrοls οn prices and fοreign exchange.
Despite an ecοnοmy weakened by lοwer οil incοme, Chavez has sοlid apprοval ratings and is nοw pοwering ahead with his plan tο regulate and reduce the private sectοr in the OPEC cοuntry
Therefore, The nationalization of major industries in Hugo Chavez's Venezuela describes a move away from capitalism. Thus, option C is correct.
To learn more about Capitalism from given link.
https://brainly.com/question/25879591
#SPJ1
Complete question:
Which of the following describes a move away from capitalism?
O A. Sweden's 1980s cutback on social programs
O B. the transformation of the former Soviet Union to today's Russia
O C. the nationalization of major industries in Hugo Chavez's Venezuela
O D. economic reforms following the Great Depression in the United States
writing an equation in standard form on a graph
what is the equation in standard form of the line shown on the graph?
O x = 4
O y = 4
O x + y = 4
O x - y = 4
graph shown in picture
Answer:
Step-by-step explanation:
y = 4
cause its at y
on the July 7 billing date, Marvin had a balance due of $216.71 on his credit card. the transactions during the following month were
July 14 office supplies $52.04 July 17 scarf $15.66
July 21 payment of $100
July 24 charge: toy truck $44.03
the interest rate on the card is 1.25% per month. using the previous balance method find the finance charge on August 7 then find the new balance of August 7.
simple interest formula i=prt
Answer:
The first step is to calculate the average daily balance for the billing cycle. This is done by adding up the daily balances for each day of the billing cycle and then dividing by the number of days in the billing cycle. In this case, the billing cycle is from July 7 to August 6, so there are 31 days in the billing cycle.
The daily balances are as follows:
* July 7: $216.71
* July 14: $268.75
* July 17: $284.37
* July 21: $116.71
* July 24: $260.74
The average daily balance is therefore $226.81.
The next step is to calculate the finance charge. This is done by multiplying the average daily balance by the interest rate and then by the number of days in the billing cycle. In this case, the interest rate is 1.25% and the number of days in the billing cycle is 31 days.
The finance charge is therefore $7.43.
The final step is to calculate the new balance. This is done by adding the finance charge to the previous balance. In this case, the previous balance is $216.71 and the finance charge is $7.43. The new balance is therefore $224.14.
Here is the solution in mathematical form:
* Average daily balance = (216.71 + 268.75 + 284.37 + 116.71 + 260.74) / 31 = 226.81
* Finance charge = 226.81 * 0.0125 * 31 = 7.43
* New balance = 216.71 + 7.43 = 224.14
Step-by-step explanation:
Ariel checked the prices of 9 dog training programs. The prices were: $78.00$78.00$80.00$77.00$78.00$77.00$78.00$77.00$79.00 What was the median price charged?
The median price charged is $78.00
The median of the data:
The median of a set of data is the middle value when the data is arranged in numerical order.
In other words, it is the value that separates the data into two halves, with half of the values being less than the median and half being greater than the median. If there is an even number of data points, the median is the average of the two middle values.
Here we have
The prices of 9 dog training programs were:
$ 78.00, $ 78.00, $80.00, $77.00, $78.00, $77.00, $78.00, $77.00, $79.00
To find the median price, we need to arrange the prices in order from least to greatest:
$77.00, $77.00, $77.00, $78.00, $78.00, $78.00, $78.00, $79.00, $80.00
There are nine prices, which is an odd number,
So the median is the middle number.
In this case, the middle number is the fifth number, which is $78.00
Therefore,
The median price charged is $78.00
Learn more about Median at
https://brainly.com/question/31098693
#SPJ1
Tammy ran 4 2
5 miles on Saturday.
On Sunday she ran for 1
2 of the distance
she ran on Saturday. Write and solve an
equation that will help you figure out how
far Tammy ran on Sunday. Explain the
steps you took to solve the problem
Tammy ran 2.25 miles on Sunday.
What is Linear Equation?A linear equation is a mathematical expression that describes a straight line on a graph. It is of the form y = mx + b, where "m" is the slope of the line and "b" is the y-intercept.
Let's start by figuring out how far Tammy ran on Sunday. We know that she ran for 1/2 of the distance she ran on Saturday. Therefore, if we let "x" be the distance Tammy ran on Sunday, we can set up the following equation:
x = 1/2(4.5)
Here, we used the fact that Tammy ran 4.5 miles on Saturday.
To solve for "x", we simply need to simplify the right-hand side of the equation:
x = 1/2(4.5)
x = 2.25
Therefore, Tammy ran 2.25 miles on Sunday.
In summary, we used the equation x = 1/2(4.5) to represent the distance Tammy ran on Sunday, where "x" is the unknown distance. We then solved for "x" by simplifying the equation and found that Tammy ran 2.25 miles on Sunday.
To learn more about Linear Equation from the given link
https://brainly.com/question/2030026
#SPJ1
helpppppppppppppppppppppppppppp
Answer: 9+3z<-12
Step-by-step explanation: because first -3(2-z)= -6+3z
then 15-6=9
so then it is 9+3z for the left side and we didn't touch the right side so it would be the same
Question 1 of 3
The sum of the interior angles of a regular polygon is 3060°.
Complete the statement.
How Many has the regular polygon?
Answer:
the regular polygon has 15 angles
A ladder forms the hypotenuse of a right triangle with a building and the ground, as shown. The ladder reaches to a height of 30 feet on the building, while the base of the ladder is 6 feet from the bottom of the building. What is the length of the ladder?
The length of the ladder is approximately 30.6 feet. The height of the building is 90 degrees.
Let "θ" be the angle between the ladder and the ground. Then, we have:
sin(θ) = 30 ÷ x
Solving for "x", we get:
x = 30 ÷ sin(θ)
Since the ladder is the hypotenuse, we know that the angle opposite the height of the building is 90 degrees. Therefore, the angle between the ladder and the ground is the complement of this angle, which is:
θ = 90 - arcsin(30 ÷ x)
Substituting this expression for "θ" into the equation for "x", we get:
x = 30 ÷ sin(90 - arcsin(30 ÷ x))
Using the identity sin(90 - θ) = cos(θ), we can simplify this to:
x = 30 / cos(arcsin(30 ÷ x))
Using the identity cos(arcsin(x)) = [tex]\sqrt[] 1-x^{2}[/tex] , we can simplify this further to:
x = [tex]\frac{30}{\sqrt{(1-(30/x^{2}))\\} }[/tex]
Squaring both sides and simplifying, we get:
x² = 30² + 6²
x² = 900 + 36
x² = 936
x = [tex]\sqrt{936}[/tex]
x = 30.6 feet is height of ladder
To learn more about height follow the link:
https://brainly.com/question/10726356
#SPJ1
will give brainliest please!! it's due in 30 mins!!
Question: Prove APC = angle DPB
Answer:
We know that <APC + < APD = 180. We also know that <APD + <DPB = 180
Thus <APC = <DPB
Answer:
angle APC is congruent to angle DPB according the theorem -Veritical Angle Theorem.
Step-by-step explanation:
Theorem 2.8 (Vertical Angles Theorem)
If two angles are vertical angles, then they are congruent.
Amanda was watching her little brother Mike play on a swing
set. She decided that she would like to find his distance above
the ground using a sine or cosine curve. She starts timing and
finds that at t-2 seconds Mike is at his highest point. He
reachers his lowest point exactly 1.5 seconds later. Amanda
also records the highest Mike gets as 9 feet whle the lowest
point occurs at 1 foot. Write an equation that will find Mike's
height after t seconds.
Putting all these values together, we get the equation: h(t) = 4 cos(2π/3 (t - 2)) + 1 with Mike's height above the ground as a function of time t in seconds, where h(t) is measured in feet.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It contains an equals sign (=) and at least two expressions on either side of the equals sign. The expressions on either side of the equals sign can be numbers, variables, or a combination of both, and the equation represents a relationship between them. Equations are used in mathematics to solve problems and find unknown values by manipulating the expressions within the equation while keeping the equality true.
Here,
Assuming that Mike's motion on the swing set follows a periodic pattern, we can model his height above the ground using a sinusoidal function. Let's use the cosine function, since it reaches its maximum value when the input is 0 and decreases to its minimum value at π or 180°.
The general form of a cosine function is:
y = A cos(Bx + C) + D
where:
A = amplitude (half the distance between the maximum and minimum values)
B = frequency (the number of cycles per unit of x)
C = phase shift (horizontal shift of the graph)
D = vertical shift (vertical shift of the graph)
We are given that Mike's highest point is at 9 feet and his lowest point is at 1 foot. Therefore, the amplitude A = (9 - 1) / 2 = 4.
The frequency is determined by the time it takes for Mike to complete one cycle. We know that it takes him 1.5 seconds to go from his highest point to his lowest point and back up again. Therefore, the period of the function is 3 seconds (2 x 1.5), and the frequency is 1/3 cycles per second. Hence, B = 2π/3.
The phase shift is the horizontal displacement of the graph from the origin. We know that at t = 2 seconds, Mike is at his highest point. Therefore, we need to shift the cosine curve 2 seconds to the right to match this point. Thus, C = -2.
Finally, the vertical shift D is the position of the center of the curve. Since Mike's lowest point is at 1 foot, we need to shift the entire curve up by 1 foot. Thus, D = 1.
Putting all these values together, we get the equation:
h(t) = 4 cos(2π/3 (t - 2)) + 1
To know more about equation,
https://brainly.com/question/28243079
#SPJ1
If an answer for this question is not a whole number, enter it as a decimal.
Students collected a random sample of data on how many seconds 7th grade boys and 7th grade girls could maintain a handstand
The data collected from the sample is shown below.
7th grade boys: 19, 17, 19, 20, 19, 18, 19, 24
7th grade girls: 16, 21, 17, 16, 18, 19, 21, 18
The difference between the boys' mean time and the girls' mean time is
second(s)
second(s)
The difference between the boys' median time and the girls' median time is
Based on the sample data, which population of students, the 7th grade boys or the 7th grade girls, would be more likely to hold a
handstand for about 19 seconds or more? the 7th grade
Based on the sample data, 7th grade boys, would be more likely to hold a handstand for about 19 seconds or more.
The difference between the boys' mean time and the girls' mean time is 1 second.
The difference between the boys' median time and the girls' median time is 1.5 seconds.
What is sample data?A subset of data collected from a larger population. It is typically used to represent the larger population and is used for testing and analysis.
In this data set, the mean time of the 7th grade boys= 19.375 seconds, while the mean time of the 7th grade girls = 17.875 seconds.
This means that the 7th grade boys have a higher mean time than the 7th grade girls.
The difference is 1.5 seconds.
The median time of the 7th grade boys = 19 seconds, and the median time of the 7th grade girls = 18 seconds.
This also indicates that the 7th grade boys have a higher median time than the 7th grade girls.
The difference is 1 second.
Given this data, the 7th grade boys are more likely to hold a handstand for about 19 seconds or more than the 7th grade girls.
This is because the mean and median times for the 7th grade boys are higher than the mean and median times for the 7th grade girls.
This indicates that the 7th grade boys have a higher average time than the 7th grade girls, and thus, are more likely to hold a handstand for a longer period of time.
For more questions related to median
https://brainly.com/question/26177250
#SPJ1
Decide whether ▱ABCD with vertices A(−6, 2), B(−3, 5), C(0, 2), and D(−3 ,−1) is a rectangle, a rhombus, or a square. Select all names that apply.
ABCD is a square, rhombus, and rectangle.
Checking whether ABCD with vertices A(6, 2), B(3, 5), C(0, 2), and D(3, 1) fits the definition of each shape can help us determine whether it is a rectangle, rhombus, or square.
A parallelogram with four right angles is a rectangle. We can determine the slopes of AB and CD and BC and AD separately to see if ABCD is a rectangle. It is a rectangle if the opposite sides are perpendicular and they are negative reciprocals of one another.
[tex]Slope \ of \ AB = \frac{(5 - 2)} { (-3 + 6)} = 1 \ Slope\ of\ CD = \frac{(-1 - 2)} { (-3 - 0)} = -1 \ Slope \ of\ BC =\frac{ (2 - 5)}{ (0 + 3)} = -1 \ Slope\ of\ AD = \frac{(2 - (-1))}{ (-6 + 3)} = 1[/tex]
The opposite sides are perpendicular to one another since AB and CD have negative reciprocal slopes and BC and AD do too. In light of this, ABCD is a rectangle.
A parallelogram with four congruent sides is called a rhombus. We can determine the separation between each pair of vertices in ABCD to determine if it is a rhombus. It is a rhombus if the lengths of the four sides are equal.
[tex]Distance\ between\ A \ and\ B = \sqrt{{(5 - 2)}^2 + {(-3 + 6)}^2} = \sqrt(10) \ Distance\ between\ B \ and\ C = \sqrt{({(2 - 5)}^2 + {(0 + 3)}^2)} = \sqrt(10) \ Distance\ between\ C\ and\ D = \sqrt{((-1 - 2)^2 + (-3 - 0)^2) }= \sqrt(10) \ Distance \ between\ D \ and \ A = \sqrt{((2 - (-1))^2 + (-6 + 3)^2)} = \sqrt(10)[/tex]
ABCD is also a rhombus since the lengths of all four sides are equal.
A parallelogram having four identical sides and four right angles is called a square. We can combine the tests for rectangles and rhombuses to determine whether ABCD is a square.
Since ABCD satisfies the requirements for both rectangles and rhombuses, it is also required to be a square.
Hence, ABCD is a square, rhombus, and rectangle.
learn more about parallelogram
https://brainly.com/question/29147156
#SPJ1
find x if 2x+3x+3x-4x=32x^2
Answer: x=0, x=1/8
Step-by-step explanation:
Simplifying the equation give us: 4x=32x^2
Subtract 4x from both sides: 32x^2-4x=0
Factor:4x(8x-1)=0
Using the Zero Product Property, x=0, x=1/8
Answer:
x equals 0 it wont only let me put answer so i am typing more
The following table reports the percentage of stocks in a portfolio for nine quarters from
2007 to 2009.
a. Construct a time series plot. What type of pattern exists in the data?
b. Use trial and error to find a value of the exponential smoothing coefficient that results in a relatively small MSE.
c. Using the exponential smoothing model you developed in part (b), what is the forecast of the percentage of stocks in a typical portfolio for the second quarter of 2009?
1) The time series plot is attached accordingly. The percentage of stocks seems to fluctuate randomly over time.
2) the optimal value of the smoothing coefficient is 0.5.
3) Therefore, the forecast of the percentage of stocks in a typical portfolio for the second quarter of 2009 is 30.9%.
What is the explanation for the above response?1) See the attached time series. The percentage of stocks seems to fluctuate randomly over time.
2) To find the optimal value of the smoothing coefficient that results in a relatively small mean squared error (MSE), we can use a trial-and-error approach. We can try different values of the smoothing coefficient α and calculate the MSE for each value. The smoothing coefficient that results in the smallest MSE is the optimal value.
Using other software, we can apply exponential smoothing to the data and try different values of α. For example, we can start with α=0.1 and increment it by 0.1 until we find the optimal value.
The following table shows the results of applying exponential smoothing with different values of α: See attached.
From the table, we can see that the smallest MSE is obtained when α=0.5. Therefore, the optimal value of the smoothing coefficient is 0.5.
c. Using the optimal value of the smoothing coefficient α=0.5, we can forecast the percentage of stocks in a typical portfolio for the second quarter of 2009. To do this, we use the following formula for exponential smoothing:
F(t+1) = α x Y(t) + (1-α) x F(t)
where F(t+1) is the forecast for the next period, Y(t) is the actual value in the current period, and F(t) is the forecast for the current period.
To apply this formula, we start with the first quarter of 2007 as the initial forecast value:
F(1) = Y(1) = 29.8
Then, we can use the formula to calculate the forecast for each subsequent quarter:
F(2) = α x Y(2) + (1-α) x F(1) = 0.5 x 31.0 + 0.5 x 29.8 = 30.4
F(3) = α x Y(3) + (1-α) x F(2) = 0.5 x 29.9 + 0.5 x 30.4 = 30.2
F(4) = α x Y(4) + (1-α) x F(3) = 0.5 x 30.1 + 0.5 x 30.2 = 30.2
F(5) = α x Y(5) + (1-α) x F(4) = 0.5 x 32.2 + 0.5 x 31.2 = 31.7
F(7) = α x Y(7) + (1-α) x F(6) = 0.5 x 32.0 + 0.5 x 31.7 = 31.9
F(8) = α x Y(8) + (1-α) x F(7) = 0.5 x 31.9 + 0.5 x 31.9 = 31.9
F(9) = α x Y(9) + (1-α) x F(8) = 0.5 x 30.0 + 0.5 x 31.9 = 30.9
Therefore, the forecast of the percentage of stocks in a typical portfolio for the second quarter of 2009 is 30.9%.
Learn more about time series plot at:
https://brainly.com/question/30898325
#SPJ1
Full Question:
Although part of your question is missing, you might be referring to this full question:
The following table (See attached image) reports the percentage of stocks in a portfolio for nine quarters from
2007 to 2009.
a. Construct a time series plot. What type of pattern exists in the data?
b. Use trial and error to find a value of the exponential smoothing coefficient that results in a relatively small MSE.
c. Using the exponential smoothing model you developed in part (b), what is the forecast of the percentage of stocks in a typical portfolio for the second quarter of 2009?