Answer: 60 in.
Chain of Thought Reasoning:
Step 1: P = 2L + 2W
Step 2: 18 = 2L + 2(4)
Step 3: 18 = 8 + 2L
Step 4: 10 = 2L
Step 5: 5 = L
Step 6: Convert feet to inches: 1 foot = 12 inches
Step 7: 5 feet = 5 * 12 inches
Step 8: 5 feet = 60 inches
Therefore, the length of the rectangular yard is 60 inches.
Question 7 of 10
Which expressions are equivalent to the one below? Check all that apply.
27
A. 3*
B. 9x
□ C. 9
□ D. (27) ²
9.3
DE 9
OF. (27-9)*
Answer:B,C
hope it helps
2. The amount of a radioactive element at time t is given by the formula A(t)= A0ekt, (1) where A(0)= A0 is the initial amount of the element and k < 0 is the constant of proportionality which satisfies the equation (instantaneous rate of change of A(t) at time t) = kA(t). Iodine–131 is a commonly used radioactive isotope used to help detect how well the thyroid is functioning. Suppose the decay of Iodine–131 follows the model given in Equation (1), and that the half–life of Iodine–131 is approximately 10 days. If 5 grams of Iodine– 131 is present initially, find a function which gives the amount of Iodine–131, A, in grams, t days later, and then after 20 days.
The function that gives the amount of Iodine-131, A, in grams, t days later is A(t) = 5(1/2)^(t/10), and the amount after 20 days is 5/4 grams.
To find the function that gives the amount of Iodine-131, A, in grams, t days later, we can use the given formula A(t) = A0e^(kt).
Given that the half-life of Iodine-131 is approximately 10 days, we know that after each 10-day period, the amount of Iodine-131 will be reduced by half. This information allows us to determine the value of k.
Let's substitute the initial values into the equation:
A(0) = A0 = 5 grams.
We know that after 10 days, the amount is reduced by half. Therefore:
A(10) = 5/2 grams.
Using these two points, we can solve for k:
5/2 = 5e^(10k).
Dividing both sides by 5, we get:
1/2 = e^(10k).
Take the natural logarithm (ln) of both sides:
ln(1/2) = 10k.
Now, solve for k:
k = ln(1/2) / 10.
Now that we have the value of k, we can use it to find the function for the amount of Iodine-131, A, in grams, t days later.
The function is:
A(t) = A0e^(kt).
Substituting the known values:
A(t) = 5e^((ln(1/2)/10)t).
Simplifying:
A(t) = 5(1/2)^(t/10).
To find the amount of Iodine-131 after 20 days, we substitute t = 20 into the equation:
A(20) = 5(1/2)^(20/10).
A(20) = 5(1/2)^2.
A(20) = 5(1/4).
A(20) = 5/4 grams.
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The hexagonal prism below has a base area of 36 units and a height of 5.9 units. Find its volume.
The volume of the given hexagonal prism is 212.4 cubic units.
Given that, the hexagonal prism below has a base area of 36 square units and a height of 5.9 units.
Formula to find the volume of the object is Volume = Area of a base × Height.
Here, volume = 36×5.9
= 212.4 cubic units
Therefore, the volume of the given hexagonal prism is 212.4 cubic units.
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Mass of the earth greater than mass of hydrogen atom
Yes, the mass of the Earth is much larger than the mass of an atom of hydrogen.
A hydrogen atom weighs around 1.67 x 10⁻²⁷ kilograms (kg) in mass. The mass of a hydrogen atom is approximately 1051 times smaller than that of the Earth, which has a mass of about 5.97 x 10²⁴ kg.
The majority of the mass of the Earth is made up of the following elements: iron, oxygen, silicon, magnesium, Sulphur, nickel, calcium, and aluminium. Despite its minor presence, hydrogen does not significantly contribute to the mass of the Earth.
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In triangle DEF, EF = 4cm, DF = 7cm, Find angle D
And E is the right angle
Hello !
1. The triangleD
I\
I \
I \
I \ 7cm
I \
I \
I \
E 4cm F
2. Find the ratio of the angle DThe ratio = hypotenuse ; opposite
⇒ calculate sin(D)
3. Calculate the angle Dsin(D) = opposite/hypotenuse = 4/7
arcsin(4/7) ≈ 34,84.. ≈ 35°
4. ConclusionThe angle D measures 35°.
3
f(x)=3(2¹)-1
g(x)=3(2-)-1
Which statement is TRUE?
A. The y-values of both functions decrease by a
factor of 2 for each unit increase in x.
C. The functions both have the same x-intercept.
B. The y-values of both functions increase by a factor
of 2 for each unit increase in x.
D. The functions both have the same y-intercept.
The correct statement regarding the exponential functions in this problem is given as follows:
D. The functions both have the same y-intercept.
How to define an exponential function?An exponential function has the definition presented according to the equation as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The functions in this problem are given as follows:
[tex]f(x) = 3(2^x) - 1[/tex][tex]g(x) = 3(2^{-x}) - 1[/tex]Hence the y-intercept for each function is given as follows:
[tex]f(0) = 3(2^0) - 1 = 3 - 1 = 2[/tex][tex]g(x) = 3(2^{0}) - 1 = 3 - 1 = 2[/tex]More can be learned about exponential functions at brainly.com/question/2456547
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Find a polynomial function with real coefficients that has the given zeros:
2, 5 + i
By the complex conjugate root theorem, there must also be another zero - [tex]5-i[/tex].
Therefore
[tex]f(x)=(x-2)(x-(5+i))(x-(5-i))\\f(x)=(x-2)(x-5-i)(x-5+i)\\f(x)=(x-2)((x-5)^2+1)\\f(x)=(x-2)(x^2-10x+25+1)\\f(x)=(x-2)(x^2-10x+26)\\f(x)=x^3-10x^2+26x-2x^2+20x-52\\f(x)=x^3-12x^2+46x-52[/tex]
A relationship is represented by the equation y = x - 12 which of the following tables best represent the equation
A table that best represent the equation include the following: H. table H.
How to determine the table that best represent the equation?In order to determine the table that best represent the equation, we would have to substitute each of the values of x (x-values) into the linear function and then evaluate as follows;
When the value of x = 1 in table F, the linear function is given by;
y = x - 12
y = 1 - 12
y = -11 (False).
When the value of x = 0 in table G, the linear function is given by;
y = x - 12
y = 0 - 12
y = -12 (True).
When the value of x = 2 in table G, the linear function is given by;
y = x - 12
y = 2 - 12
y = -10 (False).
When the value of x = 0 in table H, the linear function is given by;
y = x - 12
y = 2 - 12
y = -10 (True).
When the value of x = 4 in table H, the linear function is given by;
y = x - 12
y = 4 - 12
y = -8 (True).
When the value of x = 6 in table H, the linear function is given by;
y = x - 12
y = 6 - 12
y = -6 (True).
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
5. Match the steps for constructing a congruent line segment to their pictures.
▼
▼
1. Step 2: Draw a second line
segment that is longer than the
first.
2. Step 4: That intersection is the
final endpoint of the copied
segment.
3. Step 1: Put the point of the
compass on one endpoint of the
segment to be copied. Change the
compass setting so that the
pencil end is just touching the
other endpoint, make a small arc
to see this.
4. Step 3: Without changing the
compass setting, put the
compass point on the new
endpoint on a new line. Make a
small arc that intersects the line.
We can see here that matching the steps for constructing a congruent line segment to their pictures, we have:
Step 1 - Picture a
Step 2 - Picture b
Step 3 - Picture c
Step 4 - Picture c.
What is a line segment?Any portion of a line with two ends and a set length is referred to as a line segment. It differs from a line that has neither a beginning nor an end and can be stretched in both directions.
The endpoints of a line segment can be used to define it. The portion of the line that begins at point A and finishes at point B, for instance, is known as the line segment AB.
A ruler or measuring tape can be used to determine the length of a line segment. The distance between two line segments' endpoints is the segment's length.
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Answer:
Step-by-step explanation:
Question 8 of 10
If f(x) = x² is horizontally compressed to g(x), which could be the equation of
g(x)?
O A. g(x) - (x)
O B. g(x) - (x-6)²
OC. g(x)=x² +6
O D. g(x) - (6x)²
SUBMIT
The horizontally compressed function is [tex]\(\text{g(x)} = x^2 + 6\)[/tex]. The correct option is OC. [tex]\(\text{g(x)} = x^2 + 6\)[/tex].
To horizontally compress the function [tex]f(x) = x^2[/tex], we can modify the equation by introducing a horizontal compression factor. Let's call the compressed function [tex]g(x)[/tex].
The general equation for a horizontally compressed function can be expressed as [tex]g(x) = f(ax)[/tex], where a is the compression factor.
In this case, we want to compress [tex]f(x) = x^2[/tex]. Let's choose a compression factor of [tex]\frac{1}{2}[/tex].
Therefore, the equation for [tex]g(x)[/tex] would be:
[tex]\[ g(x) = f\left(\frac{x}{2}\right) = \left(\frac{x}{2}\right)^2 \][/tex]
Simplifying this equation, we have:
[tex]\[ g(x) = \frac{x^2}{4} \][/tex]
Hence, the equation of [tex]g(x)[/tex] is:
[tex]\[ \text{g(x)} = \frac{x^2}{4} \][/tex]
So, the correct option is OC. [tex]\(\text{g(x)} = x^2 + 6\)[/tex].
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Find the value of x.
The calculated value of x in the circle is 7
How to find the value of x.From the question, we have the following parameters that can be used in our computation:
The circle
From the circle, we have
Center = H
Also, we have
LIne GH bisects the chord FD
Using the above as a guide, we have the following:
DG = FG
So, we have
5x + 2 = 7x - 12
This gives
2x = 14
So, we have
x = 7
Hence, the value of x is 7
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Can I have help finding the area
Answer: For Area A, 60
For Area B, 16
For Area C, 16
For the entire shape, 92
Step-by-step explanation:
If you look at the top of the entire shape, it says the width is 10 cm, that means 10 cm's for the entire width and not just shape A.
If you look at shape B, it says the width is 4 cm, that means 4 out of those 10 cm's are for B and not A but we dont need the width of shape B, so we subtract that 4 bc it isnt necessary since its not in shape A
if you look at the left of shape A, it says 10 cm for the height, when finding area for a rectangle, always do width x height. We have both the width and the height so now we just multiply them, 10 x 6 = 60
Answer:
A = 60cm^2
Step-by-step explanation:
Given:
Length of figure: A = 10cm
Width of figure: B = 10 - 4 = 6cm
Figure A is rectangular in nature.
So, the Area of the figure: A = 1 x b = 10 x 6 = 60cm^2
Find the y-intercept and the slope of the line.
-8x -4y =5
Answer:
[tex]\sf m = -2\\\\y-intercept =\dfrac{-5}{4}[/tex]
Step-by-step explanation:
Slope and y-intercept of the line:
Write the equation in slope y-intercept form: y =mx +c
Here, m is the slope and c is the y-intercpet.
To isolate y, add 8x to both side,
-8x - 4y = 5
-4y = 8x + 5
Now, divide the entire equation by (-4),
[tex]\sf \dfrac{-4y}{-4}=\dfrac{8x}{-4} + \dfrac{5}{-4}\\\\\\y = -2x -\dfrac{5}{4}[/tex]
Now, compare with y = mx +c
[tex]\boxed{\sf m= -2}\\\\\\\boxed{\sf y-intercept=\dfrac{-5}{4}}[/tex]
Answer:
y-intercept = -5/4
slope = -2
Step-by-step explanation:
To quickly find the slope and y-intercept of a given linear equation, we can express it in the following form, called the slope-intercept form:
[tex]\boxed{y = mx + c}[/tex],
where:
m ⇒ slope
c ⇒ y-intercept
In order to take the given equation into the slope-intercept form, we have to make y the subject of the equation:
[tex]-8x - 4y = 5[/tex]
⇒ [tex]-4y = 8x + 5[/tex] [Adding 8x to both sides of the equation]
⇒ [tex]y = -\frac{1}{4}(8x + 5)[/tex] [Dividing both sides of the equation by -4]
⇒ [tex]y = -2 x - \frac{5}{4}[/tex]
Comparing the above equation with the slope-intercept form, we can see that m = -2 and c = -5/4.
Therefore, y-intercept = -5/4, and slope = -2.
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Add the vectors: 10 - 3 + 7
The result of adding these numbers is 14.
To add the vectors 10, -3, and 7, we simply sum their corresponding components.
In mathematics, vectors typically represent quantities that have both magnitude and direction. They are usually denoted by an arrow or boldface letters. However, in your question, the numbers provided (10, -3, and 7) are not explicitly described as vectors. They are just numerical values.
To add these numbers together, you can simply perform the arithmetic operation of addition:
10 - 3 + 7 = 14
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Colin walks two times around at one and 1 7/8 mile trail there are park benches everywhere 1/4 mile long trail but there are no benches at the store or another trail how many park benches are there in the trail
Answer:
15
Step-by-step explanation:
2 x 1 and 7/8 = 3 and 6/8 miles
= 3.75 miles
Since there are park benches every 1/4 mile on the trail, we can find the number of benches by dividing the total length of the trail by the distance between the benches:
Number of benches = (3.75 miles) / (1/4 mile per bench)
Number of benches = 15
Which equation represents a horizontal line? A.y=x+1 b. X=2 c.x=y+2 d. Y=2
Answer: d. Y=2
Step-by-step explanation:
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
tan pi/6 is tan 30
Step-by-step explanation:
tan 30 is a special degree in trigonometric ratios which makes it easy to solve
tan 30=1√3 .this is the same as √3/3(B)
The diagram shows two squares constructed on the sides of a rectangle. What is the area of square A?
The area of the square A is 19.98 square feet
Calculating the area of square A?From the question, we have the following parameters that can be used in our computation:
Two squares constructed on the sides of a rectangle.
Let the side lengths of square C be x
Let the side lengths of rectangle B be x and y
So, we have
x² = 5
xy = 10
Solving for x and y, we have
x = 2.24 and y = 4.47
The area of square A is
Area = y²
So, we have
Area = 4.47²
Evaluate
Area = 19.98
Hence, the area of the square A is 19.98 square feet
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Need help with this problem
The length of side j, considering the trigonometric ratios, is given as follows:
j = 7.88.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.For the angle of 21º, we have that:
j is the opposite side.22 is the hypotenuse.Hence the length j is obtained as follows:
sin(21º) = j/22
j = 22 x sine of 21 degrees
j = 7.88.
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100 Points! Algebra question. Photo attached. Will give Brainliest! Please show as much work as possible. Thank you!
Answer:
6.6, 22/73,
Step-by-step explanation:
Alright, here we go.
A: The mean is all of the values divided by the number of values, which is equal to 1,927.5 or:
0.5 * 5 + 1 * 16 + 2 * 28 + 3 * 22 + 4 * 17 + 5 * 98 + 8 * 13 + 10 * 73 + 12 * 5 + 15 * 2 + 20 * 4 + 25 * 9.
There are 292 or 5 + 16 + 28 + 22 + 17 + 98 + 13 + 73 + 5 + 2 + 4 + 9 packages. 1,927.5 / 292 = 6.6
B: The packages that weigh less than five pounds are 5 + 16 + 28 + 22 + 17 or 88 / 292 = 22 / 73
C and D: Manager original mean result not given.
31]
PLS HELP I NEED THIS TO GRADUATE
hi
what's the title of the question?
The family then travelled 38km from Camp Carol and reached Phoenix in 27minutes. Determine the average speed they travelling at?
The family traveled from Camp Carol to Phoenix at an average speed of approximately 84.44 kilometers per hour.
How to calculate average speed?Speed is simply referred to as distance traveled per unit time.
It is expressed mathematically as:
Speed = Distance / time
Given that the family traveled 38 km from Camp Carol to Phoenix in 27 minutes:
Distance traveled = 38 kilometers
Time taken = 27 minutes
First, convert the time from minutes to hours:
Time taken = ( 27 / 60 ) hours
Time taken = 0.45 hour
We can now calculate the average speed using the above formula as follows:
Average speed = Distance / time
Average speed = 38 km / 0.45 h
Average speed = 84.44 km/h
Therefore, the average speed is approximately 84.44 km/h.
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In a town, 60% of the police officers have ride-alongs with teenagers who want to join the police force. 258 police officers have ride-alongs. How many police officers are there altogether?
Hello !
1. Calculate the rest100% - 60% = 40%
=> 40% of police officers have ride-alongs
2. Make a tabletotal
number of policier 258 ? ??
frequency in % 60% 40% 100%
3. Calculate the total3.1 Calculate the number of of the police officers have ride-alongs with teenagers who want to join the police force
? = 258 x 40 ÷ 60 = 172
3.2 Calculate the total
?? = 258 + 172 = 430
4. ConclusionIn total there are 430 police officers.
Have a good day !
Please help questions 5-10 this is easy…. NO SCAMS I WILL BE REPORTING ALL SCAMMERS U WILL NOT GET THE POINTS
The value of the missing probability for the given probabilities and condition of independent events is equal to 0.45.
Here,
Probability of the events A and B are,
P(A) = 7/10
P(A or B) = 167/200
Apply the formula for the probability of the union of two events,
P(A or B) = P(A) + P(B) - P(A and B)
Since events A and B are independent, we know that,
P(A and B) = P(A) x P(B)
This implies,
P(A or B) = P(A) + P(B) - P(A) x P(B)
Substitute the values we have,
⇒ 167/200 = 7/10 + P(B) - (7/10) x P(B)
⇒ 167/200 = [ 7 + 10P(B) - 7P(B) ] /10
⇒167/20 = 7 + 3P(B)
⇒3P(B) = 167/20 - 7
⇒ 3P(B) = (167 - 140)/20
⇒3P(B) = 27 /20
⇒P(B) = 9/20
⇒P(B) = 0.45
Therefore, the value of the probability P(B) is equal to 0.45.
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complete question:
Events [A] and [B] are independent. Find the missing probability.
P(B) = ?
P(A) =
7/10
P(A or B)
167/200
Find the area of each figure. Round to the nearest tenth, if necessary
Answer:
Solution is in the attached photo.
Step-by-step explanation:
This question tests on the concept of shapes, this shape can be separated into 2 basic shapes, triangle and rectangle.
As a salesperson at Scrapbooks and
Treasures, Alysse receives a monthly
base pay plus commission on all that she
sells. If she sells $500 worth of
merchandise in one month, she is paid
$515. If she sells $900 of merchandise in
one month, she is paid $607.
Find Alysse's total salary function, s(x), when
she sells x dollars of merchandise.
s(x)=
Answer:
s(x) = 0.23x + 400
Step-by-step explanation:
Let x = cost of merchandise sold
We start by finding the slope which is the percent of commission Alysse receives.
Let's start with doing 607 - 515. This is because we are subtracting the commissions, which also can be y2 - y1. Then, we do 900-500=400 (x2-x1). This is how to find the slope of the function. [tex]\frac{y2-y1}{x2-x1}=\frac{92}{400} =0.23[/tex], 0.23 being the slope.
s(x) = b+0.23x, now substitute values making the money received as s(x).
515 = b+0.23(500)
515=b+115
-115 -115
400 = b
607 = 400+0.23(900)
607 = 400 + 207
607 = 607
So, s(x) = 0.23x + 400
Burning Brownie has five varieties of cakes as Chocolate fudge cake (Cake 1), Nutella-filled Cake
(Cake 2), Marble Cake (Cake 3), Cheese cake (Cake 4) and Fruit Cake (Cake 5) at their store. The
selling prices of each of the cakes are $9, $12, $4, $5, $8 respectively.
a. Formulate the Revenue function
The revenue function for the cakes can be shown as: R(x1, x2, x3, x4, x5) = $9x1 + $12x2 + $4x3 + $5x4 + $8x5
What is revenue function?The revenue function is described as the total amount of money earned from selling a certain quantity of cakes.
We make the following
Cake 1 sold = x1
Cake 2 = x2
Cake 3 = x3,
Cake 4 = x4,
Cake 5= x5.
The revenue generated from selling each cake is:
Revenue1 = $9 * x1
Revenue2 = $12 * x2
Revenue3 = $4 * x3
Revenue4 = $5 * x4
Revenue5 = $8 * x5
Total revenue = Revenue1 + Revenue2 + Revenue3 + Revenue4 + Revenue5
Total revenue = $9 * x1 + $12 * x2 + $4 * x3 + $5 * x4 + $8 * x5
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What measurement is equal to 1 2/3 yards
1 2/3 yards is equal to 5 1/3 feet.
How to find the measurement is equal to 1 2/3 yardsTo convert from yards to feet, we know that 1 yard is equal to 3 feet. Therefore, we can calculate:
1 2/3 yards = (1 + 2/3) yards = (3/3 + 2/3) yards = 5/3 yards
Now, to convert yards to feet, we multiply by 3:
5/3 yards * 3 feet/1 yard = 15/3 feet = 5 feet
Therefore, 1 2/3 yards is equal to 5 1/3 feet.
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We sample bags of candy under the assumption that the average weight is 16oz. with a population standard deviation of 1.25oz. Let x represent the average weight of our sample of bags of candy. What is the probability the average weight of our sample is greater than 15.8oz if our sample size is 40 bags of candy?
The Probability that the average weight of our sample is greater than 15.8 oz, given a sample size of 40 bags of candy, is approximately 0.8438 or 84.38%.
The probability that the average weight of our sample is greater than 15.8 oz, we need to use the concept of the sampling distribution of the sample mean and the Central Limit Theorem.
Given:
Population mean (μ) = 16 oz.
Population standard deviation (σ) = 1.25 oz.
Sample size (n) = 40 bags of candy.
The Central Limit Theorem states that for a large enough sample size (typically considered n > 30), the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution.
In this case, we can assume that the sampling distribution of the sample mean is approximately normally distributed.
To calculate the probability, we need to standardize the sample mean using the z-score formula:
z = (x - μ) / (σ / sqrt(n))
where x is the given value (15.8 oz), μ is the population mean, σ is the population standard deviation, and n is the sample size.
Substituting the values:
z = (15.8 - 16) / (1.25 / sqrt(40))
z = -0.2 / (1.25 / 6.3246)
z = -0.2 / 0.1988
z ≈ -1.006
Now, we need to find the probability that the standardized sample mean is greater than -1.006. Since we want the probability of the sample mean being greater than 15.8 oz, we need to find the area under the normal curve to the right of z = -1.006.
Using a standard normal distribution table or a calculator, we can find that the corresponding probability is approximately 0.8438.
Therefore, the probability that the average weight of our sample is greater than 15.8 oz, given a sample size of 40 bags of candy, is approximately 0.8438 or 84.38%.
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The following table gives the number of women age 16 years and older (in
millions) in a country's civilian workforce for selected years from 1950 and
projected to 2050.
Complete parts (a) and (b) below.
a. Use x as the number of years past January 1st, 1950 to create a cubic model, y, using these data.
y=0x³+x²+x+O
To create a cubic model, we need to find a cubic equation in the form of [tex]y = ax^3 + bx^2 + cx + d[/tex] that fits the given data. Let's use the data provided in the table and the equation [tex]y = 0x^3 + x^2 + x + 0[/tex].
Since the coefficient of [tex]x^3[/tex] is 0, the cubic term does not contribute to the equation. Therefore, the cubic model simplifies to [tex]y = x^2 + x[/tex].
The equation [tex]y = x^2 + x[/tex]represents a quadratic function rather than a cubic function.
Thus, if we assume that the cubic term is indeed meant to be 0, we can use the simplified equation [tex]y = x^2 + x[/tex] as the cubic model based on the given data.
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