Answer: The height of the tree is 12.57 ft.
Step-by-step explanation:
The height of a thing is proportional to the its shadow.
Let H = Height and S = length of shadow
Then by equation direct proportion , [tex]\dfrac{H_1}{S_1}=\dfrac{H_2}{S_2}[/tex] (i)
Given : A tree that casts a 22 ft shadow at the same time a 4 ft postpost casts a shadow which is 7-ft long.
Put [tex]S_1=22 ,\ H_2= 4,\ \ S_2=7[/tex] in (i), we get
[tex]\dfrac{H_1}{22}=\dfrac{4}{7}\\\\ H_1=\dfrac{4}{7}\times22\approx12.57[/tex]
Hence, the height of the tree is 12.57 ft.
What the user said above!
A box that has no lid is 13x8x4 in dimensions. What is the maximum number of 3x3x2 bricks able to fit this box without going out of the dimensions or overlapping?
Answer:
Maximum number of 3x3x2 bricks = 23.
Step-by-step explanation:
The volume of the box = 13 x 8 x 4 = 416 cubic unit
The volume of the brick with the dimensions = 18 cubic unit
Now as per the question, we want to fill an empty box with 416 cubic unit with the help of bricks which are 18 cubic unit each.
The maximum number of bricks required to fill the box = Volume of the box ÷ Volume of one brick.
→ The number of bricks required to fill the box = 416 ÷ 18 = 23.11
But, number of bricks can never be in fraction so it means a maximum of 23 bricks can accommodate in the given box. We will not choose 24 or more than 24 bricks because these much bricks will go out of the dimensions.
Note: Volume of a cuboid = length x breadth x height (l x b x h).
To solve the problem, you divide each dimension of the box by the corresponding dimension of the brick, rounding down to the nearest whole number to get the number of bricks that can fit in each direction. You then multiply these together to get the total. In this case, a maximum of 16 bricks can fit.
Explanation:The problem at hand requires spatial reasoning and division. The challenge is to determine how many 'bricks' (which we'll engage as 3x3x2 units) can fit into a larger 'box' (which is 13x8x4 units). This can be determined by individually dividing the dimensions of the box by the dimensions of the brick.
For instance, considering the length, we divide 13 by 3 to get approximately 4.33. Considering that we can't fractionate a brick, we can place only 4 bricks along the length. Using the same approach, we divide 8 by 3 for the width to get approximately 2.67, and we can place 2 bricks here. It's the same for the height; 4 divided by 2 is 2. Therefore, we can place 2 bricks along the height.
To get the total number of bricks that can fit in the box, multiply the numbers together: 4 (length) x 2 (width) x 2 (height), giving a result of 16 bricks. Hence, a maximum of 16 bricks of size 3x3x2 can fit into a box of size 13x8x4 without going out of the box or overlapping.
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1. Type an equation in the equation editor that uses 2 fractions with parentheses around one of them. Example: [tex]\frac{2}{3}[/tex] + (- [tex]\frac{1}{2}[/tex]) = [tex]\frac{4}{6} - \frac{3}{6} = \frac{1}{6}[/tex]
2. Type an expression that has two terms with exponents, and one with a square root. Example: [tex]2^{3}[/tex] + [tex]9^{2}[/tex] + [tex]\sqrt{16}[/tex]
3. Type a compound inequality similar to the one below, but with different numbers. It should be set up the same, with all the symbols in the same places. [tex](\frac{3}{5} )^{2}[/tex] · [tex]^{3} \sqrt{10} \leq x^{3} - 2x + 5 \leq \sqrt{\frac{1}{3}[/tex]
Answer:
i) [tex]\frac{3}{5} + (- \frac{1}{2}) = \frac{6}{10} - \frac{5}{10} = \frac{1}{10}[/tex] [tex]\Rightarrow[/tex] \frac{3}{5} + (- \frac{1}{2}) = \frac{6}{10} - \frac{5}{10} = \frac{1}{10}
ii)[tex]4^{3} + 8^{2} + \sqrt{9}[/tex] [tex]\Rightarrow[/tex] 4^{3} + 8^{2} + \sqrt{9}
iii) [tex](\frac{4}{5})^{2}. \sqrt[3]{8} \leqx^{3} - 3x + 6 \leq \sqrt{\frac{1}{3}} \Rightarrow \hspace{0.2cm}[/tex] (\frac{4}{5})^{2}. \sqrt[3]{8} \leqx^{3} - 3x + 6 \leq \sqrt{\frac{1}{3}}
Step-by-step explanation:
i) [tex]\frac{3}{5} + (- \frac{1}{2}) = \frac{6}{10} - \frac{5}{10} = \frac{1}{10}[/tex] [tex]\Rightarrow[/tex] \frac{3}{5} + (- \frac{1}{2}) = \frac{6}{10} - \frac{5}{10} = \frac{1}{10}
ii)[tex]4^{3} + 8^{2} + \sqrt{9}[/tex] [tex]\Rightarrow[/tex] 4^{3} + 8^{2} + \sqrt{9}
iii) [tex](\frac{4}{5})^{2}. \sqrt[3]{8} \leqx^{3} - 3x + 6 \leq \sqrt{\frac{1}{3}} \Rightarrow \hspace{0.2cm}[/tex] (\frac{4}{5})^{2}. \sqrt[3]{8} \leqx^{3} - 3x + 6 \leq \sqrt{\frac{1}{3}}
Find the area of the sector and round to the nearest tenth.
Answer:
Step-by-step explanation:
The formula for determining the area of a sector is expressed as
Area = θ/360 × πr²
Where
θ represents the central angle formed by the radii.
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
θ = 167 degrees
r = 17.8 yards
Therefore,
Area of sector = 167/360 × 3.14 × 17.8² = 461.5 yards²
A student survey was conducted in a major university, where data were collected from a random sample of 750 undergraduate students. One variable that was recorded for each student was the student's answer to the question: What is your favorite type of movie? Action/Comedy/Drama/Family/Horror/Musical/Science Fiction. These data would be best displayed using which of the following?a. histogramb.IQRc.boxplotd.stemplote.pie chart
Answer:
e. Pie Chart
Step-by-step explanation:
In a student survey, students are asked about their favorite movie and so, the favorite movies can be divided into different categories but can't be meaningfully represented in numerical form. Thus, the favorite movie is a qualitative variable. For the qualitative type of variable pie chart is most suitable chart.
Histogram, IQR, box plot and steam plot are created for quantitative type of data.
Thus, the data would be best displayed by using Pie chart.
David says that the original price of the shorts was $41. Does his answer seem reasonable? Defend your answer by writing and solving an equation that represents the situation
Answer:
The response does not seem reasonable.
Step-by-step explanation:
The current price of shorts is a sum of the original price plus profit. In this case, a simple formula is given:
Profit = Selling price - Buying price
Therefore, the selling price can be anything less than $ 41.
Expressing the information in a linear equation gives x ≤ 41
where x is the buying price of the shorts.
To determine if David's answer that the original price of the shorts was $41 seems reasonable, we can use an equation to represent the situation. By solving the equation, we find that the original price of the shorts is $21.98, not $41.
Explanation:To determine if David's answer that the original price of the shorts was $41 seems reasonable, we can use an equation to represent the situation. Let's assume the original price of the shorts is x dollars.
If the total cost of the T-shirt and shorts, including tax, is $22.45 as given, we can write the equation: x + 1.47 = 22.45.
Simplifying the equation, we subtract 1.47 from both sides: x = 21.98.
Therefore, the original price of the shorts would be $21.98, not $41. Hence, David's answer does not seem reasonable.
Do people who work for non-profit organizations differ from those who work at for-profit companies when it comes to personal job satisfaction? Separate random samples were collected by a polling agency to investigate the difference. Data collected from 422 employees at non-profit organizations revealed that 377 of them were "highly satisfied." From the for-profit companies, 431 out 518 employees reported the same level of satisfaction. Find the standard error of the difference in sample proportions.
Answer:
0.0223
Step-by-step explanation:
Given the following data x(1) = 377, n(1) = 422, x(2) = 431, n(2) = 518
The sample proportion is the number of success divided by the sample.
P(1) = x(1)/n(1) = 377/422 = 0.8934
P(2) = x(2)/n(2) = 431/518 = 0.8320
Formular for the standard error of the difference in sample proportions
S.E = √p(1)q(1)/n(1)+P(2)q(2)/n(2)
S.E = √p1(1-P1)/n1+P2(1-P2)/n2
By substitution we have that,
S.E = √0.8934(1-0.8934)/422+0.8320(1-0.8320)/518
S.E = 0.0223
The perimeter of a rectangular note card is 18 inches. The area is 18 square inches. What are the dimensions of the note card?
Answer:
6 by 3
Step-by-step explanation:
a rectangle as 2 equal sides. so if we know that it is 6 by 3, then 6+6+3+3
=12+6=18
the area of a rectangle is base * height. so 6 * 3 = 18
Answer: the length is 6 inches and the width is 3 inches.
Step-by-step explanation:
Let L represent the length of the rectangular note card.
Let W represent the width of the rectangular note card.
The formula for determining the area of a rectangle is expressed as
Area = L × W
Area of the note card would be
LW = 18 - - - - - - - - - - - - 1
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(L + W)
Perimeter of the note card would be
2(L + W) = 18
(L + W) = 9 - - - - - - - - - - - - 2
Substituting L = 9 - W into equation 1, it becomes
W(9 - W) = 18
9W - W² = 18
W² - 9W + 18 = 0
W² - 6W - 3W + 18 = 0
W(W - 6) - 3(W - 6) = 0
W - 6 = 0 or W - 3 = 0
W = 6 or W = 3
Substituting W = 3 into equation 1, it becomes
3L = 18
L = 18/3 = 6
use multiplier method to increase £88 by 14%. you must show all your working out
Answer:
£100.32
Step-by-step explanation:
£88 + 14% × £88 = £88×(1 +0.14)
= 1.14×£88
= £100.32 . . . . using a calculator
£100.32 is £88 increased by 14%.
Final answer:
£100.32
Explanation:
To increase an amount by a certain percentage using the multiplier method, you can use the following steps:
Convert the percentage increase to a decimal by dividing by 100. In this case, 14% becomes 0.14.Add 1 to the decimal to get the multiplier. Here, 1 + 0.14 = 1.14.Multiply the original amount by the multiplier. So, £88 multiplied by 1.14 gives us the increased amount.Let's do the calculation:
Step 1: Convert the percentage to a decimal. 14% / 100 = 0.14Step 2: Calculate the multiplier. 1 + 0.14 = 1.14Step 3: Multiply £88 by the multiplier. £88 x 1.14 = £100.32What is the domain of the function
Answer:
-∞<x<∞
Step-by-step explanation:
Answer:
First option
Step-by-step explanation:
There's no value of x which makes the function undefined .
So x can take any real value
i.e. -infinity < x < +infinity
the volume of a box is represented by the roduct (x^2+5x+6) times (x+4). Give the polynomial that represents the length of the box.
Answer:
(x+3)
Step-by-step explanation:
Volume = Base area × height
Base area = x²+5x+6
= x²+2x+3x+6
= x(x+2)+3(x+2)
= (x+2)(x+3)
Since the length is the longer side, length = (x+3)
Dimensions of the box are:
(x+2)×(x+3)×(x+4)
construct a line perpendicular to m through P. Then find the distance from P to m.
Line m contains points (1, 1) and (5,1). point P has coordinates of (2, -4)
Line perpendicular to m is y =–4.
Distance from P to m is 5 units.
Solution:
Line m contains points (1, 1) and (5, 1).
Slope passing through two points formula:
[tex]$\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]$=\frac{1-1}{5-1}[/tex]
Slope = 0
Slope of the line perpendicular to the line m:
[tex]$\text{Slope}=\frac{-1}{\text{slope}}=0[/tex]
Equation of a line passing through one point and slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
Here, m = 0 and P(2, –4)
[tex]$\Rightarrow y-(-4)=0(x-2)[/tex]
[tex]$\Rightarrow y+4=0[/tex]
[tex]$\Rightarrow y=-4[/tex]
⇒ y = –4
Equation of a line perpendicular to m and passing through P is y = –4.
Option C is the correct graph. Because it only has slope 0 and P(2, –4).
Point of intersection where line m and P meets is (2, 1).
Let us find the distance between the line m in the point (2, 1) and P(2, –4).
Distance formula:
[tex]\text {Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]=\sqrt{(2-2)^2+(-4-1)^2}[/tex]
[tex]=\sqrt{25}[/tex]
= 5
Distance = 5 units
Hence line perpendicular to m is y =–4.
Distance from P to m is 5 units.
Out of 40 coins, 16 are dimes. Half of the remaining coins are quarters and the rest are pennies and nickels. There are 2 nickels for every penny. How many pennies are there? A. 3 B. 4 C. 9 D. 12
Answer: Option B is the correct answer.
Step-by-step explanation:
Let x represent the number of pennies.
Out of 40 coins, 16 are dimes. This means that the number of coins remaining is
40 - 16 = 24
Half of the remaining coins are quarters. This means that the number of quarters is
1/2 × 24 = 12 quarters
the rest are pennies and nickels. This means that the total number of
pennies and nickels is 12
There are 2 nickels for every penny. This means that the number if nickels is 2x. Therefore,
2x + x = 12
3x = 12
x = 12/3 = 4
there are 4 pennies
Answer:
The answer is B.) 4
Step-by-step explanation:
I took a quiz and according to that its correct
In 2004 the population in Morganton, Georgia, was 43,000. The population in Morganton doubled by 2010. If the growth rate remains the same, what is the expected population in Morganton in 2020?
Answer:
263,606.9
Step-by-step explanation:
In 2004 the population in Morganton, Georgia, was 43,000.
(0, 43000)
The population in Morganton doubled by 2010
In 6 years the population is doubled (86000)
(6,86000)
[tex]A= a(b)^t[/tex]
Use (0,43000) in the above equation
[tex]A= a(b)^t\\43000= a(b)^0\\a=43000[/tex]
Now plug in (6,86000)
[tex]A= a(b)^t\\A= 43000(b)^t\\86000=43000(b)^6\\2=b^6\\b=\sqrt[6]{2} \\b=1.12[/tex]
[tex]A=43000(1.12)^t[/tex]
Now find out A when t=16 (2020)
[tex]A=43000(1.12)^t\\A=43000(1.12)^{16}\\A=263606.9[/tex]
If the growth rate from 2004 to 2010 continues, the expected population in Morganton, Georgia in 2020 would be around 172,000 as the population is doubling every 6 years.
Explanation:The population of Morganton, Georgia in 2004 was 43,000 and it doubled by 2010 to 86,000. This shows a constant growth rate in which the population size doubles every 6 years. If this rate of growth remains consistent, the population of Morganton is expected to double again by 2020. Therefore, by 2020, the population of Morganton, Georgia could be around 172,000 people.
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The number of people estimated to vote in an election was 7,000. The actual number of people who voted was 5,600.
What is the question that is being asked?
Triangle A''B''C'' is formed by a reflection over x=-3 and dilation by a scale factor of 3 from the origin. Which equation shows the correct relationship between ABC and A''B''C'?
Answer: Segments AB / A"B" = √13 / 2 x √13
Step-by-step explanation:
The Triangle's vertices are at points A(-3,3), B(1,-3) and C(-3,-3).
• The reflection over x = 1 shows vertices A, B and C below:
A(-3,3)→A'(5,3);
B(1,-3)→B'(1,3);
C(-3,-3)→C'(5,-3).
• The Dilation by a scale factor of 2 from the origin is expressed as:
(x,y)→(2x,2y)
Therefore,
A'(5,3)→A''(10,6);
B'(1,3)→B''(2,6);
C'(5,-3)→C''(10,-6)
The attachment below completed the calculations and shows the segment in a simple graph.
Technician A recently installed software that required modifications to folder permissions. Users are now having trouble with other software and receiving permissions errors. What can Technician B use to determine what changes were made during installation?
Answer:
With Processor Monitor Tool Technician B should be able to determine what changes were made during installation
Step-by-step explanation:
Technician B, can you a utility software tool called Processor Monitor to check track of system logs.
Process Monitor is an advanced monitoring tool for Windows that shows real-time file system, Registry and process/thread activity. It features include, an extensive list of enhancements including rich and non-destructive filtering, comprehensive event properties such session IDs and user names, reliable process information, full thread stacks with integrated symbol support for each operation, simultaneous logging to a file, and much more.
Its uniquely powerful features will make Process Monitor a core utility in your system troubleshooting and malware hunting toolkit.
With Processor Monitor Tool Technician B should be able to determine what changes were made during installation.
Technician B can use the Event Viewer to determine the changes made to folder permissions during software installation.
Explanation:Technician B can use the Event Viewer to determine the changes made to folder permissions during software installation. Here's how:
Open the Event Viewer by searching for it in the Windows search bar.In the Event Viewer, navigate to Windows Logs and click on Security.In the right-hand pane, look for events with a Task Category of File System. These events will provide information about changes made to folder permissions.Review the details of these events to identify the modifications made during software installation.Using the Event Viewer, Technician B can effectively track the changes that were made and troubleshoot the permissions errors experienced by users.
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Evaluate the expression. 13!/9!
Answer:
17160
Step-by-step explanation:
1×2×3×4×5×6×7×8×9×10×11×12×13 / 1×2×3×4×5×6×7×8×9
10×11×12×13=17160
A recipe for lemonade punch calls for 6 cups of lemonade for every 24 cups of punch. Which equation can be used to find x, the percentage of lemonade in the recipe?
Answer:
The percentage of lemonade in the recipe is 25%.
Step-by-step explanation:
Given:
A recipe for lemonade punch calls for 6 cups of lemonade for every 24 cups of punch.
Now, to find [tex]x[/tex], the percentage of lemonade in the recipe.
In the recipe 6 cups of lemonade for every 24 cups of punch.
The percentage of lemonade = Cups of lemonade / cups of punch.
So, the equation to get the percentage:
[tex]x=\frac{6}{24} \times 100[/tex]
[tex]x=0.25\times 100[/tex]
[tex]x=25\%.[/tex]
Therefore, the percentage of lemonade in the recipe is 25%.
HELP ASAP PLEASE!!!!!!!
Name a segment parallel to segment FC:
Name a segment skew to segment AB:
Answer:
Segment [tex]EB[/tex] is parallel to segment [tex]FC[/tex].
Segment [tex]CD[/tex] is skew to segment [tex]AB[/tex].
Step-by-step explanation:
For this exercise it is necessary to know the following definitions:
1. Coplanar lines are defined as those lines that lie in the same plane.
2. Non-Coplanar lines are defined as those lines that does not lie in the same plane.
3. Parallel lines are defined as Coplanar lines that never intersect each other.
4. Skew lines are defined as Non-Coplanar lines that never intersect each other.
Knowing those definitions, you can solve the exercise.
You need to analize the figure given in the exercise.
Based on the explanation given above, you can conclude that the segment [tex]EB[/tex] is parallel to the segment [tex]FC[/tex], because they are in the same plane and they never intersect each other.
You can also identify in the figure that the segment [tex]AB[/tex] and the segment [tex]CD[/tex] are not in the same plane and they never intersect each other.
Therefore, you can determine that the segment [tex]CD[/tex] is skew to the segment [tex]AB[/tex].
An inelastic collision occurs between a large truck and smaller sedan. Calculate the final velocity of the objects and explain the direction they will be traveling with the following data from before the collision: Small sedan mass = 1300 kg initial velocity = 20 m/s Truck mass = 7100 kg Initial Velocity 15 m/s
The final velocity is 15.8 m/s in the forward direction
Step-by-step explanation:
An inelastic collision occurs when the two object after the collision stick together.
In any case, the total momentum of the system is conserved before and after the collision, in absence of external forces. Therefore, we can write:
[tex]p_i = p_f\\m u + MU = (m+M)v[/tex]
where in this problem:
m = 1300 kg is the mass of the small sedan
u = 20 m/s is the initial velocity of the small sedan
M = 7100 kg is the mass of the truck
U = 15 m/s is the initial velocity of the truck
v is the final combined velocity of the small sedan + truck
Here we have taken both the velocity of the sedan and the truck in the positive (forward) direction
Solving the equation for v, we find the final velocity:
[tex]v=\frac{mu+MU}{m+M}=\frac{(1300)(20)+(7100)(15)}{1300+7100}=15.8 m/s[/tex]
And since the sign is positive, this means that is direction is the same as the initial direction of the sedan and the truck, so forward.
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Melody has hired a new accountant. He has gathered her pay stubs and is trying to determine how many CDs were sold during each month of the previous year. Her pay stub for June indicates that she made $4,889 in that month. Write an equation her accountant could use to determine how many CDs were sold in June
Answer:
The required equation is [tex]4889=4850 +3n[/tex].
Step-by-step explanation:
Consider the provided information.
Melody has a new job recording for the All-Time Favorites record label.
She is paid a monthly base salary of $plus $3 for each CD sold.
Her pay stub for June indicates that she made $4,889 in that month.
Let n represents the number of CDs she sold.
Therefore, the required equation is [tex]4889=4850 +3n[/tex].
i need help asap please dont type random anwsers, that will result in it being deleted. GIVING BRAINLIEST ONLY TO CORRECT, INCORRECT IS DELETED.
Answer:
The area of the rectangle TOUR is 80.00 unit².
Step-by-step explanation:
The area of a rectangle is computed using the formula:
[tex]Area\ of\ a\ Rectangle=length\times width[/tex]
Since the dimensions of the rectangle are not provided we can compute the dimensions using the distance formula for two points.
The distance formula using the two point is:
[tex]distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
Considering the rectangle TOUR the area formula will be:
Area of Rectangle TOUR = TO × OU
The co-ordinates of the four vertices of a triangle are:
T = (-8, 0), O = (4, 4), U = (6, -2) and R = (-6, -6)
Compute the distance between the vertices T and O as:
[tex]TO=\sqrt{(4-(-8))^{2}+(4-0)^{2}}\\=\sqrt{12^{2}+4^{2}} \\=\sqrt{160} \\=4\sqrt{10}[/tex]
Compute the distance between the vertices O and U as:
[tex]OU=\sqrt{(6-4)^{2}+(-2-4)^{2}}\\=\sqrt{2^{2}+6^{2}} \\=\sqrt{40} \\=2\sqrt{10}[/tex]
Compute the area of rectangle TOUR as follows:
[tex]Area\ of\ TOUR=TO\times OU\\=4\sqrt{10}\times 2\sqrt{10}\\=80\\\approx80.00 unit^{2}[/tex]
Thus, the area of the rectangle TOUR is 80.00 unit².
Answer:
This answer is just here so you can give the other guy brainliest, as there can only be brainliest if there are two answers.
Step-by-step explanation:
Give that guy brainliest
How many pieces 3/7 of a foot each can I make out of 7/2 feet of rope?
Answer:
3/2
Step-by-step explanation:
(7/2)/(3/7) = 3/2 or 1.5 pieces
Answer:
The answer to your question is 8 pieces
Step-by-step explanation:
Data
rope = 7/2
length of a piece = 3/7
Process
1.- Divide 7/2 by 3/7
[tex]\frac{7}{2} / \frac{3}{7} = \frac{49}{6}[/tex]
2.- Divide 49 by 6 to get the pieces that can be made out of the rope
49 / 6 = 8 1/6
3.- Conclusion. We can get 8 pieces of the rope and there will be a remainder of 1/6.
Given the arithmetic sequence an=4-4(n-1), what is the domain for n?
The domain for n is [tex]-\infty<n<\infty[/tex]
Explanation:
The arithmetic sequence is
To determine the domain of the sequence, let us consider [tex]a_n[/tex] as [tex]f(n)[/tex]
Thus, the sequence becomes, [tex]f(n)=4-4(n-1)[/tex]
The domain of the function is the set of all x-values for which the function is real and well defined.
Since, the function has no domain constraints or undefined points. Therefore, the domain of the function is
Thus, the domain of the arithmetic sequence [tex]a_n=4-4(n-1)[/tex] is [tex]-\infty<n<\infty[/tex]
For a given geometric sequence, the 4th term, a4, is equal to 19625, and the 9th term, a9, is equal to −95. Find the value of the 13th term? a 13 If applicable, write your answer as a fraction.
Answer:
The value of the [tex]13^{th}[/tex] term is ≈ 1.
Step-by-step explanation:
A geometric sequence is a series of numbers where each term is computed by multiplying the previous term by a constant, r also known as the common ratio.
The formula to compute the [tex]n^{th}[/tex] term of a GP is: [tex]a_{n}=a_{1}\times r^{n-1}[/tex]
Here, a₁ is the first term.
It is provided that a₄ = 19625 and a₉ = 95.
Determine the value of a₁ and r as follows:
[tex]\frac{a_{4}}{a_{9}}=\frac{a_{1}r^{4-1}}{a_{1}r^{9-1}} \\\frac{19625}{95}= \frac{r^{3}}{r^{8}}r^{5}=\frac{95}{19625}\\ r=(\frac{95}{19625})^{1/5}\\=0.344[/tex]
The common ratio is, r = 0.344.
The value of a₁ is:
[tex]a_{4}=19625\\a_{1}\times(0.344)^{3}=19625\\a_{1}=\frac{19625}{0.040707584} \\=482096.898\\\approx482097[/tex]
The first term is, a₁ = 482097.
13th term of this geometric sequence is:
[tex]a_{13}=a_{1}\times r^{13-1}\\=482097\times (0.344)^{12}\\=1.3234\\\approx1[/tex]
Thus, the [tex]13^{th}[/tex] term is approximately equal to 1.
The only types of vehicles sold at a certain dealership last month were sedans, trucks, and vans. If the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively, what was the total number of vehicles sold at the dealership last month?1) The number of vans sold at the dealership last month was between 10 and 20.
2) The number of sedans sold at the dealership last month was less than 10.
Answer:
Therefore, 32 is he total number of vehicles sold at the dealership last month.
Step-by-step explanation:
We know that the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively. We have :
[tex]4:5:7 \implies 4x+5x+7x=16x[/tex]
Therefore, 16x is he total number of vehicles sold at the dealership last month.
We know that:
1) The number of vans sold at the dealership last month was between 10 and 20.
2) The number of sedans sold at the dealership last month was less than 10
We get:
[tex]10\leq 7x \leq 20\\\implies x=2\\\\\\4x\leq 10\\x=1 \, \vee \, x=2[/tex]
We know that x is a positive integer. In order to satisfy both conditions, this is possible only if x = 2.
We get [tex]16x=16\cdot 2=32[/tex]
Therefore, 32 is he total number of vehicles sold at the dealership last month.
Samantha makes hair barrettes from ribbon. She has 3 1/4 ft of ribbon and uses 1/2 ft of ribbon to make each barrette. How many completed barrettes can Samantha make with the ribbon she has.
Answer: she can only make 6 completed barrettes
Step-by-step explanation:
Samantha makes hair barrettes from ribbon. The total length of ribbon that she has is 3 1/4 feet. Converting 3 1/4 feet to improper fraction, it becomes 13/4 feet.
She uses 1/2 feet of ribbon to make each barrette. This means that the number of completed barrettes that Samantha can make with the ribbon she has would be
(13/4)/(1/2) = 13/4 × 2/1
= 6 1/2 barrettes
The complete barrette must be whole number.
Therefore, she can only make 6 completed barrettes
Answer:
6
Step-by-step explanation:
Brenda is building a square fence. She places a fence post at (─3,2). What is the location of the post (in which quadrant) that reflects (─3, 2) across the y-axis?
The location of the reflected post will be in the first quadrant at point (3, 2).
To reflect a point across the y-axis, we simply negate the x-coordinate while keeping the y-coordinate unchanged.
Given the point (-3, 2), when we reflect it across the y-axis, the x-coordinate becomes positive 3, while the y-coordinate remains 2. Therefore, the reflected point is (3, 2).
Since the original point (-3, 2) lies in the second quadrant (negative x, positive y), the reflected point (3, 2) will lie in the first quadrant (positive x, positive y).
How many possible combined page count and color choices are possible? How does this number relate to the number of page size choices and to the number of color choices
ANSWER:
1. How many possible combined page count and color choices are possible?
There are 3 choices for page size and 4 choices for color, and also, there are 3*4=12 possibilities to combine page size and color.
Number possibilities to combine and number of choices for size is: 12:3=4:1
Number of possibilities to combine and number of choices for color is 12:4=3:1
2. How does this number relate to the number of page size choices and to the number of color choices
There are 12 possibilities to combine size and color.
Number of possibilities to combine and number of choices for size is 4:1
Number of possibilities to combine and number of choices for color is 3:1
Answer:
We have 12 possibilities to combine page size and color.
Number of possibilities and number of choices is 12:4 that is 3:1
Step-by-step explanation:
have a nice day.
Determine whether the underlined value is a parameter or a statistic. Mark retired from competitive athletics last year. In his career as a sprinter he had competed in the 100-meters event a total of 328 times. His average time for these 328 races was Modifying 15 seconds with underline.
Answer: Parameter
Step-by-step explanation:
A parameter is defined as :
A value that is evaluated by considering the entire population.For example : Population mean , population standard deviation etc.A statistic is defined as :
A value that is evaluated by considering a sample of the population.For example : sample mean , sample standard deviation etc.Given : Mark had competed in the 100-meters event a total of 328 times.
Here , Population of interest = Number of times Mark competed in the 100-meters event =328
His average time for these 328 races was 15 seconds.
Since this average is calculated from the entire population, therefore , 15 is representing a parameter .
Hence, the correct answer is : "Parameter"