Based on available research and studies, the answer is B: A higher percentage of millennials have at least $100,000 saved for retirement when comparing to Gen X.
How to explain the informationAccording to a report from Fidelity Investments, 30% of millennials have saved at least $100,000 for retirement. In contrast, a 2019 study from the Transamerica Center for Retirement Studies found that 31% of Gen Xers have no retirement savings at all.
This suggests that the fraction of millennials with at least $100,000 saved for retirement is higher than the portion of Gen X people who have no retirement savings.
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If f(x)=x+2 and g(x + 1) = x + 1 then find g. f(4).
Answer:
[tex]x + 2[/tex]
see the below process of the equation:
Step-by-Step Explaination:
Given, f(x)=x+1 and g(x)=x+1
∴g(g(x))=g(x+1)
=(x+1)+1
=x+2
-Thank You By MrIshaan
The net of a triangular prism and its approximate dimensions are shown in the diagram.
4in. 12 in. 12in. 12 in. 12 in. 10.4 in. Which measurement is closest to the total surface area of the triangular prism in square inches?
The measurement closest to the total surface area of the triangular prism is J) 393.6 [tex]in^{2}[/tex] .
To find the surface area of a triangular prism, we need to find the area of all its faces and add them up.
Looking at the net of the triangular prism, we can see that it has two congruent triangles and three rectangular faces.
The area of each triangular face can be found using the formula for the area of a triangle:
Area of a triangle = (1/2) x base x height
In this case, the base of each triangle is 12 inches and the height is 4 inches. So, the area of one triangular face is:
(1/2) x 12 x 4 = 24 [tex]in^{2}[/tex]
The area of each rectangular face can be found using the formula:
Area of a rectangle = length x width
In this case, the length and width of the rectangular faces are:
12 in. x 10.4 in.
12 in. x 12 in.
4 in. x 10.4 in.
So, the area of each rectangular face is:
12 x 10.4 = 124.8 [tex]in^{2}[/tex]
12 x 12 = 144 [tex]in^{2}[/tex]
4 x 10.4 = 41.6 [tex]in^{2}[/tex]
Therefore, the total surface area of the triangular prism is:
2 x 24 + 124.8 + 144 + 41.6 = 393.6 [tex]in^{2}[/tex]
So, the measurement closest to the total surface area of the triangular prism in square inches is J) 393.6 [tex]in^{2}[/tex] .
Correct Question :
The net of a triangular prism and its approximate dimensions are shown in the diagram, 4 in, 12 in, 10.4 in, 12 in, 12 in, 12 in. Which measurement is closest to the total surface area of the triangular prism in square inches?
F) 268.8 [tex]in^{2}[/tex]
G) 432 [tex]in^{2}[/tex]
H) 288 [tex]in^{2}[/tex]
J) 393.6 [tex]in^{2}[/tex]
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The triangle above has the following measures.
m
a=7.5 y
Use the 45-45-90 Triangle Theorem to find the length of the hypotenuse. Include correct units.
Show all your work.
The length of the hypotenuse is 10.61 yd.
We have,
The sum of the angles in a triangle = 180
Now,
Two angles are 45.
This means,
The side opposite to angle 45 are equal.
So,
a = c
And,
a = 7.5 yd
Now,
Applying the Pythagorean theorem.
b² = a² + c²
b² = 7.5² + 7.5²
b² = 112.5
b = √112.5
b = 10.61
Thus,
The length of the hypotenuse is 10.61 yd.
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Which cone has a volume of 24 лcm³? 3,5 cml 1 2 B = 25 cm 6,5 cml L 3 cm 4.5 cm₁ L 8 cm 7/5 cml B = 4
The cone that has the volume of 24л cm³ is the third cone which has a diameter of 8 cm and a height of 4.5 cm.
What is the Volume of a Cone?The formula for determining the volume of a cone is expressed as the following:
Volume of a cone (V) = 1/3 * πr²h
We are given the following information about the third cone in the image given:
Diameter of the cone = 8 cm
Radius of the cone (r) = 8/2 = 4 cm
Height of the cone (h) = 4.5 cm
Plug in the values:
Volume of a cone (V) = 1/3 * π * 4² * 4.5
Volume of the third cone (V) = 24л cm³
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Please help!! Worth 100PTS
The regular polygon has the following measures.
a= 7√3 cm
s=14cm
Segment a is drawn from the center of the polygon perpendicular to one of its sides.
What is the vocabulary term for segment a?
What is the area of the polygon?
Round to the nearest tenth and include correct units.
Show all your work.
The vocabulary term for segment a is called the apothem.
The area of the polygon is 319.8 cm²
How did we get the value?To find the area of the polygon, we can use the formula:
Area = (1/2) × Perimeter × Apothem
The perimeter of the polygon can be found by multiplying the number of sides by the length of each side, so:
Perimeter = number of sides × length of each side
Perimeter = 6 × 14 cm (since it's a regular hexagon)
Perimeter = 84 cm
Finding the apothem, use the fact that it forms a right triangle with half of one side length and the apothem as the legs, and the apothem as the hypotenuse. Thus,
a² = s² - (s/2)²
a² = 196 - 49
a² = 147
a = √(147) = 7.65 cm
Now, we can plug in our values into the formula for the area:
Area = (1/2) × Perimeter × Apothem
Area = (1/2) × 84 cm × 7.65 cm
Area = 319.8 cm²
Rounding to the nearest tenth and including the correct units, we get:
Area ≈ 319.8 cm²
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Use slopes and y-intercepts to determine if the lines y=−x+3 and −3x−3y=1 are parallel.
Answer:
YES PARALLEL
Step-by-step explanation:
The slopes of
y=−x+3 and −3x−3y=1 are both −1.
Parallel
x<-5
How do you graph this equation?
To graph the inequality X < -5 on a number line, we start by drawing a number line and marking a point at -5.
We have,
To graph the inequality X < -5 on a number line, we start by drawing a number line and marking a point at -5.
Since the inequality is strict (X is less than -5), we will draw an open circle at -5 to indicate that -5 is not included in the solution set.
Next, we shade the portion of the number line to the left of -5, since any value of X less than -5 satisfies the inequality.
Note that the open circle at -5 indicates that X cannot be equal to -5, since the inequality is strict.
Any value to the left of -5 on the number line would satisfy the inequality.
Thus,
To graph the inequality X < -5 on a number line, we start by drawing a number line and marking a point at -5.
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The price (in S) of a cookbook is determined by the number of cookbooks x demanded by consumers and supplied by the publisher.
Supply: p=0.003.x
Demand: p = -0.007x+300
(a) Solve the system of equations defined by the supply and demand models.
(b) What is the equilibrium price?
(c) What is the equilibrium quantity?
a) The solution of the system of equations is, x = 30,000
b) the equilibrium price is, p = 90
c) the equilibrium quantity is, p = 90
Given that;
The price (in S) of a cookbook is determined by the number of cookbooks x demanded by consumers and supplied by the publisher.
Supply: p=0.003.x
Demand: p = -0.007x+300
Hence, We can simplify as;
⇒ 0.003x = - 0.007x + 300
Solve for x;
⇒ 0.003x + 0.007x = 300
⇒ 0.01x = 300
⇒ x = 300/0.01
⇒ x = 30,000
Hence, the equilibrium price is,
p=0.003.x
p=0.003 × 30,000
p= 90
And, the equilibrium quantity is,
p = -0.007x+300
p = -0.007 × 30,000+300
p = - 210 + 300
p = 90
Thus, a) The solution of the system of equations is, x = 30,000
b) the equilibrium price is, p = 90
c) the equilibrium quantity is, p = 90
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A 3 1/2 inch by 5 inch photo is to be enlarged to a similar rectangle. If the width is 6 inches what should the length be?
Answer:
4.2, or 4 1/4
Step-by-step explanation:
Usually, "3 1/2 inch by 5 inch" is in the format of "length by width."
Therefore, the original length is 3.5 and width is 5.
If the new width is 6, the scale factor is determined by the following:
n/o, where 'n' is new, and 'o' is old: 6/5 = 1.2. Check the work: 5 * 1.2 = 6.
Therefore, the scale factor is 1.2. Now, multiply the old length by the scale factor to determine the new length:
3.5 * 1.2 = 4.2, or 4 1/4 inches, as there are 8 sections in an inch, and 2/8 = 0.25, which is a quarter, or 1/4.
If I helped, please make this answer brainliest! ;)
Fill in the table using this function rule.
y=-6x-3
Substitute each x-coordinate into equation y = - 6x - 3 to find the corresponding y-coordinate:
For x = - 1:y = - 6(-1) - 3 = 6 - 3 = 3For x = 0:y = - 6(0) - 3 = 0 - 3 = - 3For x = 1:y = - 6(1) - 3 = - 6 - 3 = - 9For x = 5:y = - 6(5) - 3 = - 30 - 3 = - 33Select the correct answer. What are the solutions to this equation? 7x2 − 28 = 0 A. B. C. D.
Select the correct answer.
What is the domain of y = cos(z)?
O A. [0, 00)
О в. 27
O C. (-00,00)
OD. [-1, 1]
Reset
Next
The domain of the function y = cos(z) is (-00,00)
Calculating the domain of the functionFrom the question, we have the following parameters that can be used in our computation:
y = cos(z)
The above equation means that
the variable y is a function of z
Also, we can see that the above function is a cosine function
In a cosine function. the input value can take any real value
This means that y can take any real value
And as such, the domain is the set of all real numbers
This is represented as (-00,00)
Hence, the domain of the function is (-00,00)
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would like help asap
Answer:
A
Step-by-step explanation:
You need to take a ruler and join the points for A and B. I can't do it here.. C and D are not right because they're incorrectly plotted. If A/B join as a straight line for all the points then it's linear. If they don't (and you find it a little curvy) it's a a quadratic. You can cross check as well but imo it's A.
C and D are out of question. Your only options are A and B. And I find the points joining a straight line so my answer would be A
Determine the value of (3³)².
A: 711
B: 645
C: 729
D:12
Answer:
729
Step-by-step explanation:
3^3=27
and 27^2=729
So the final answer is 729!
Answer:
the answer is C: 729
Step-by-step explanation:
3×3×3=27
27×27=729
Help please When writing a proof, how do you construct the first statement?
A) By writing the justification for the first statement in the right column.
B) By copying the “prove” statement(s) from the original problem.
C) By writing the next logical statement from the current one.
D) By copying the “given” statement(s) from the original problem.
When writing a proof, we construct the first statement by copying the “given” statement(s) from the original problem. Hence, option D is correct.
When writing a proof, the first statement is typically either the "given" statement(s) or a previously proven result. Therefore, option D ("By copying the 'given' statement(s) from the original problem") is often the correct choice for constructing the first statement.
In some cases, option C ("By writing the next logical statement from the current one") may be a more appropriate choice. Regardless of which option is chosen, it is important to clearly justify each statement in the right column of the proof.
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Which statement is true regarding the parallel and perpendicular lines in the diagram? k Parallel to n and w Perpendicular to m k Parallel to n and n Perpendicular to m w Parallel to n and n Perpendicular to m w Parallel to n and wPerpendicular to m
Answer:
Based on the diagram, we can see that there are four lines: k, n, w, and m. The relationship between these lines is important in understanding their geometric properties.
We can see that line k and line n are both straight lines and never intersect, which means they are parallel to each other. This is indicated by the two small arrows on line k and line n that are pointing in the same direction.
On the other hand, line w intersects line m at a right angle (90 degrees). This means that line w is perpendicular to line m. This is indicated by the small square in the corner where line w and line m meet.
Understanding parallel and perpendicular lines is important in many areas of mathematics and science, such as geometry, trigonometry, physics, and engineering.
Step-by-step explanation:
Answer:
The correct statement is: w is parallel to n and w is perpendicular to m.
Step-by-step explanation:
4.1.3 Bathu Sneakers have been looking into different shoebox sizes: a large box for male shoes and small box for female shoes. The cost of the cardboard to make the boxes is 0,502 cents/cm². Calculate the percentage savings Bathu Sneakers will make if the smaller box is used compared to the normal larger box. Larger Box Total Surface Area = 4 093 cm² 19 cm 26 cm 34,5 cm Smaller Box Total Surface Area = 3 034 cm² 25 cm 17 cm 26 cm (6)
Answer:
Step-by-step explanation:To calculate the savings percentage, we first need to find out the cost of the cardboard required for each box.
For the larger box:
Total Surface Area = 2 * (1926 + 1934.5 + 26*34.5) = 2 * (494 + 655.5 + 897) = 4093 cm²
Cost of cardboard for larger box = 0.502 * 4093 = 2055.986 cents = 20.55986 dollars (rounded to 5 decimal places)
For the smaller box:
Total Surface Area = 2 * (2517 + 2526 + 1726) + 6 * (25-21)* (17-2*1) = 3034 cm²
Note that the additional term in the equation is the surface area of the six sides of the lid and base of the box.
Cost of cardboard for smaller box = 0.502 * 3034 = 1522.268 cents = 15.22268 dollars (rounded to 5 decimal places)
The difference in cost between the larger and smaller boxes is:
20.55986 - 15.22268 = 5.33718 dollars (rounded to 5 decimal places)
The percentage savings can be calculated as follows:
Percentage savings = (difference in cost / cost of larger box) * 100%
= (5.33718 / 20.55986) * 100%
= 25.98%
Therefore, using the smaller box will result in a savings of approximately 26% on cardboard costs for Bathu Sneakers compared to using the normal larger box.
Please help and show work
Answer:
B. (1,7)
Step-by-step explanation:
The net below shows a square pyramid. What is the lateral surface area? 8in
7in
The lateral surface area of the square pyramid is 176 in².
The first thing we need to do is find the slant height of the pyramid, which is the height of each of the triangular faces. We can use the Pythagorean theorem to do this:
slant height² = height² + (1/2base)²
slant height² = 7² + (1/28)²
slant height² = 49 + 16
slant height² = 65
slant height = √(65)
Now that we have the slant height, we can find the lateral surface area by multiplying the perimeter of the base by half the slant height. The perimeter of the base is simply 4 times the length of one of the sides, which is 8 inches.
lateral surface area = (perimeter of base * slant height) / 2
lateral surface area = (4 * 8 * √(65)) / 2 lateral surface area = 16 * √(65)
To simplify the radical, we can factor out any perfect squares that are factors of 65:
lateral surface area = 16 * √(65)
lateral surface area = 16 * √(513)
lateral surface area = 16 * √(5) * √(13)
lateral surface area = 16 * √(5) * √(43.25)
lateral surface area = 16 * √(5) * (2 * √(3.25))
lateral surface area = 64 * √(5) = 176.42 square inches.
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A bank loaned out 20,500, part of it at the rate of 9% annual interest, and the rest at 11% annual interest the total interest earned for both loans was 2,225.00 how much was loaned at each rate
The money loaned at 9% annual interest was 1500 and the money loaned at 11% annual interest was 19000.
Let the amount of money loaned at 9% be x
the amount of money loaned at 11% be y
According to the question,
Total money loaned = 20,500
Thus the equation formed is,
x + y = 20,500 ------ (i)
Simple interest is calculated by
I = P * r * t
where I is the simple interest
r is the rate of interest
t is the time
Thus, the interest on x = 0.09x
the interest on y = 0.11y
Total interest gained = 2,225
Thus the equation formed is,
0.09x + 0.11y = 2225 -------(ii)
Multiply (i) by 0.09
0.09x + 0.09y = 1845
Subtract the above from (ii)
0.02y = 380
y = 19000
x = 1500
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2. The population of a town was 7,250 in 2014
and 7,375 in 2015. What was the percent
increase from 2014 to 2015 to the nearest
tenth of a percent?
A) 1.5%
B) 1.6%
C) 1.7%
D) 1.8%
E) 2.0%
E
The percentage change of the population is P = 1.7 %
Given data ,
To calculate the percent increase from 2014 to 2015, we need to find the difference between the two population values, divide it by the initial value, and then multiply by 100 to get the percentage.
Population increase = 7,375 - 7,250 = 125
Percent increase = (Population increase / Initial population) * 100
Percent increase = (125 / 7,250) * 100 ≈ 1.7241
Rounding to the nearest tenth of a percent, the percent increase is approximately 1.7%.
Hence , the percentage change is P = 1.7 %
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ABCD is a rhombus. What is the value of x?
B
(3x+10)°
A
8
20
10
12
D
C
(2x+20)°
Answer:
3x+10+2x+20=180(oppite <s of parallogram)
30+3x=180
3x=180-30
3x=150
x=50
Step-by-step explanation:
The opposite angle of rhombus are equal
so,
here,
or,3x+10=2x+20
or,3x-2x=20-10
Therefore x=10
What is the mean absolute deviation of 8,4,8,8,10,2,4,4
Mean absolute deviation is 2.5.
The mean absolute deviation (MAD) measures how spread out a set of data is by calculating the average distance between each data point and the mean of the data set.
To find the MAD of the given data set {8,4,8,8,10,2,4,4}, we first need to find the mean of the data set.
Mean = (8+4+8+8+10+2+4+4)/8 = 6
Next, we need to find the absolute deviation of each data point from the mean:
|8-6| = 2
|4-6| = 2
|8-6| = 2
|8-6| = 2
|10-6| = 4
|2-6| = 4
|4-6| = 2
|4-6| = 2
To find the MAD, we need to take the mean of the absolute deviations:
MAD = (2+2+2+2+4+4+2+2)/8 = 2.5
Therefore, the mean absolute deviation of the data set {8,4,8,8,10,2,4,4} is 2.5. This means that, on average, the data points in the set are about 2.5 units away from the mean of the set.
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PLEASE HELP !!!
Which equation represents the graph?
y=-1/3x-3
y=3x-3
y=-1/3x+1/3
y=-3x-1/3
Answer:
Step-by-step explanation:
Y=-3x-1/3
The answer should be y=-3x-3. The slope is -3, and the y intercept is -3. I don't see this as an option!
O
X
y
X
y
X
y
X
y
0
2
0
0
-1
0
1
0
5
2
113
1
2
2
8
4
WIN
3
3
4
11
2.5 -2.5-7.5 -12.5
6
W/W
5
6
Select all table’s that represent proportional relationship between x and y
All tables that represent proportional relationship between x and y are:
B. table B.
E. table E.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the x-variable.x represents the y-variable.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = (20 - 15)/(10 - 5) = (5 - 4)/(1 - 0)
Constant of proportionality, k = 1.
Therefore, the required linear equation is given by;
y = kx
y = x
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
f(x)=x2+1 g(x)=5-x (f+g)(x)=
Answer:
x²-x+6
Step-by-step explanation:
Use (f+g)(x) = f(x)+g(x), substitute and simplify
What is the volume of this triangular pyramid
Answer:
The right triangular pyramid volume is given by the formula V = 1 3 × B × h , where B is the area of the triangular base and h is the height (the distance from the apex to the base).
Step-by-step explanation:
Answer:
192 cubic feet
Step-by-step explanation:
The volume V of a triangular pyramid is given by the formula:
V = (1/3) * base area * height
where base area is the area of the triangular base.
In this case, the triangular base has a length of 8 ft and a width of 8 ft, so it is a square with area:
base area = length * width = 8 ft * 8 ft = 64 sq ft
Substituting the given values into the formula, we get:
V = (1/3) * 64 sq ft * 9 ft
V = 192 cubic feet.
Therefore, the volume of the triangular pyramid is 192 cubic feet.
A bag contains 8 red pens, 7 blue pens, and 14 black pens. Denato wants to pull a blue pen from the bag.
What is the sample space for this experiment?
[red, black]
[blue]
[red, blue, black]
[blue, red]
Answer:
Step-by-step explanation:
The sample space represents the set or collection of all possible outcomes. It's often written as S = [outcome1, outcome2, outcome3].
For this problem, there are 3 possible outcomes: red pen, blue pen or black pen. (The fact that Denato wants to pull a blue pen is irrelevant when defining the sample space bc we are just listing the possible outcomes.)
So the answer is [red, blue, black].
Please help !!!!!! 20 points
The value of x in the polygon will be 13.25 degrees.
The value of x is 10.
We can find the value of x by plugging in the number of sides of the regular polygon into the formula x = (n-2)*15° - 1.
How to calculate the valueThe sum of the interior angles of a regular polygon with n sides is (n-2) x 180 degrees.
Sum of angles = (24-2) x 180 = 22 x 180 = 3960 degrees
Since all the angles in a regular polygon are congruent, we can divide the sum of the angles by the number of angles to find the measure of one angle:
Measure of one angle = 3960/24 = 165 degrees
165 = 12x + 6
159 = 12x
x = 13.25
Therefore, the value of x is 13.25 degrees.
Each of the triangles in our decomposition has one angle equal to (17x+2)°, so the sum of all the angles in the triangles is 43 × (17x+2)° = 731x+86°.
Therefore, we have:
731x+86° = 7380°
Solving for x, we get:
731x = 7294°
x = 10
Therefore, the value of x is 10.
The equation that can be used to find the value of x is:
(9x+48)° + (15x-24)° = (n-2)*180°
24x + 24 = (n-2)*180°
Dividing both sides by 24, we get:
x + 1 = (n-2)*15°
Subtracting 1 from both sides, we get:
x = (n-2)*15° - 1
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12. ABC-A'B'C' is a reflection. Use this to answer the questions below.
(A) Which figure is the preimage?
(B) Which figure is the images
(C) What are the coordinates of the output?
Input. Output
A(0,9). A
B(-4,4) B
C(0,4). C
(A) The figure before the reflection is called the preimage. In this case, the preimage is ABC. (B) The figure after the reflection is called the image. In this case, the image is A'B'C'. (C) The outputs for the given inputs are:
Input: A(0,9) Output: A(0,9)
Input: B(-4,4) Output: B'(-8,0)
Input: C(0,4) Output: C(0,4)
(C) The coordinates of the output for each input point can be found by reflecting the input point across the line of reflection. In this case, the line of reflection is the perpendicular bisector of the line segment connecting A and C. For point A, the reflection is itself, so the output is (0,9).
For point B, we can find its reflection as follows: draw the line perpendicular to the line of reflection that passes through B, and find the point where it intersects the line of reflection. This point is the midpoint of the line segment connecting B and its image. The reflection of B is (-8,0), and the output is B'. For point C, the reflection is itself, so the output is (0,4).
Reflection is a type of transformation in geometry where an object is flipped across a line. In this case, ABC was reflected across the line of reflection to form A'B'C'. The line of reflection is the perpendicular bisector of the line segment connecting A and C.
The reflection of a point is the point on the other side of the line of reflection that is equidistant from the line. By applying the reflection rule, we can find the coordinates of the output for each input point.
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