Answer:
Step-by-step explanation:
x+x+(x+12)=180
3x=180-12=168
x=56
third angle=56+12=68
so angles are 56°,56°,68°
The larger angle is x + 12 i.e. 56 + 12 = 68⁰.
What is Triangle?A triangle is a closed shape with 3 angles, 3 sides, and 3 vertices.
Let the first angle be x.
then second angle is equal to first i.e. x
and third angle = x + 12
we know that,
Sum of all angles of a triangle is 180⁰.
Now,
x + x + x + 12 = 180
3x = 180 -12
3x = 168
x = 168/3
x = 56
Thus, the larger angle is x + 12 i.e. 56 + 12 = 68⁰.
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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
Jenna is a swimmer and trains every day. The schedule shown outlines the number of hours she trains each day. If she misses the Wednesday practice, what is the total number of hours that she trains?
A) 11 hours
B) 11 3/4 hours
C) 12 hours
D) 12 1/4 hours
Answer:
c
Step-by-step explanation:
in the question there is a confusion about " schedule shown" , either it is missing or by schedule shown it mean looking to the choices given
so if it is missing then sorry, but if it mean choices then the only possible answer is option C i.e. 12 hours because she works daily and missing only one day thus possible answer is 12 i.e. 6*2=12
hope it may help you
Answer:D
Step-by-step explanation:
Hope this helps
What is x given triangleABC ~triangleDBE?
x = 37.5 (or) [tex]\frac{75}{2}[/tex]
Solution:
Given [tex]\triangle A B C \sim \triangle D B E[/tex].
Let us take BE = x and BC = 25 + x.
To determine the value of x:
If two triangles are similar then the corresponding angles are congruent and the corresponding sides are in proportion.
[tex]$\frac{AC}{DE}=\frac{B C}{B E}[/tex]
[tex]$\frac{50}{30} =\frac{25+x}{x}[/tex]
Do cross multiplication, we get
[tex]50x=30(25+x)[/tex]
[tex]50x=750+30x[/tex]
Subtract 30x from both sides of the equation.
[tex]20 x=750[/tex]
Divide by 20 on both sides of the equation, we get
x = 37.5 (or) [tex]\frac{75}{2}[/tex]
Hence the value of x is 37.5 or [tex]\frac{75}{2}[/tex].
PLZ HELP, GIVING BRAINLIEST, LOOK AT THE GRAPH!!
Which of the following is the equation of the circle seen in the graph below?
A. (x + 1)^2 + (y - 4)^2 = 9
B. (x - 1)^2 + (y + 4)^2 = 9
C. (x - 1)^2 + (y + 4)^2 = 9
D. (x + 1)^2 + (y - 4)^2 = 9
Answer:
The answer to your question is letter B or C they have the same response.
Step-by-step explanation:
From the graph we get the center and the radius
- The center is the point shown in the graph and its coordinates are (1, -4).
- The length of the radius is 3 units, from the center we count horizontally the number of squares (3)
Substitution
(x - 1)² + (y + 4)² = 3²
or (x - 1)² + (y + 4)² = 9
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].
Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains liters of a dye solution with a concentration of g/liter. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of liters/min, the well-stirred solution flowing out at the same rate.Find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value.
Answer:
t = 460.52 min
Step-by-step explanation:
Here is the complete question
Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 liters of a dye solution with a concentration of 1 g/liter. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 liters/min, the well-stirred solution flowing out at the same rate.Find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value.
Solution
Let Q(t) represent the amount of dye at any time t. Q' represent the net rate of change of amount of dye in the tank. Q' = inflow - outflow.
inflow = 0 (since the incoming water contains no dye)
outflow = concentration × rate of water inflow
Concentration = Quantity/volume = Q/200
outflow = concentration × rate of water inflow = Q/200 g/liter × 2 liters/min = Q/100 g/min.
So, Q' = inflow - outflow = 0 - Q/100
Q' = -Q/100 This is our differential equation. We solve it as follows
Q'/Q = -1/100
∫Q'/Q = ∫-1/100
㏑Q = -t/100 + c
[tex]Q(t) = e^{(-t/100 + c)} = e^{(-t/100)}e^{c} = Ae^{(-t/100)}\\Q(t) = Ae^{(-t/100)}[/tex]
when t = 0, Q = 200 L × 1 g/L = 200 g
[tex]Q(0) = 200 = Ae^{(-0/100)} = Ae^{(0)} = A\\A = 200.\\So, Q(t) = 200e^{(-t/100)}[/tex]
We are to find t when Q = 1% of its original value. 1% of 200 g = 0.01 × 200 = 2
[tex]2 = 200e^{(-t/100)}\\\frac{2}{200} = e^{(-t/100)}[/tex]
㏑0.01 = -t/100
t = -100㏑0.01
t = 460.52 min
A salesperson earns $99 per day, plus a 9% sales commission. Find a function that expresses her earnings as a function of sales, and use it to compute her earnings if the total sales were $999. The salesperson would take home $____ for the day?
Answer: The salesperson would take home $1088.01 for the day
Step-by-step explanation:
Let x represent the salesperson's total sales per day.
A salesperson earns $99 per day, plus a 9% sales commission. This means that in a day in which the salesperson makes a total sales of x dollars, the total amount that he would earn is
99 + 0.09x
Therefore, the function that expresses her earnings as a function of sales is
99 + 0.09x
if the total sales were $999, then the amount that the salesperson would take home for the day is
99 + 0.99 × 999
= $1088.01
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.
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:
Divide using synthetic division
(3x³ - 17x² + 15x - 25)/(x - 5) =
= (3x³ - 15x² - 2x² + 0x + 5x - 25)/(x - 5)
= [3x²(x - 5) - 2x(x - 5) + 5(x - 5)]/(x - 5)
= (3x² - 2x + 5)(x - 5)/(x - 5)
= 3x² - 2x + 5
(5x³ + 18x² + 7x - 6)/(x + 3) =
= (5x³ + 5x² + 13x² + 13x - 6x - 6³)/(x + 3)
= [5x²(x + 1) + 13x(x + 1) - 6(x + 1)]/(x + 3)
= (x + 1)(5x² + 13x - 6)/(x + 3)
= (x + 1)(5x² + 15x - 2x - 6)/(x + 3)
= (x + 1)[5x(x + 3) - 2(x + 3)]/(x + 3)
= (x + 1)(5x - 2)(x + 3)/(x + 3)
= (x + 1)(5x - 2)
(4x³ + 8x² - 9x - 18)/(x + 2) =
= [4x²(x + 2) - 9(x + 2)]/(x + 2)
= (4x² - 9)(x + 2)/(x + 2)
= (4x² - 9)
= (2x - 3)(2x + 3)
(9x³ - 16x - 18x² + 32)/(x - 2) =
= [x(9x² - 16) - 2(9x² - 16)]/(x - 2)
= (9x² - 16)(x - 2)/(x - 2)
= 9x² - 16
= (3x - 4)(3x + 4)
(- x³ + 75x - 250)/(x + 10) =
= ( - x³ + 5x² - 5x² + 25x + 50x - 250)/(x + 10)
= [ - x²(x -5) - 5x(x - 5) + 50(x - 5)]/(x + 10)
= - (x - 5)(x² + 10x - 5x - 50)/(x + 10)
= - (x - 5)[x(x + 10) - 5(x + 10)]/(x + 10)
= - (x - 5)(x - 5)(x + 10)/(x + 10)
= - (x - 5)²
(3x³ - 16x² - 72)/(x - 6) =
= (3x³ - 18x² + 2x² - 72)/(x - 6)
= [3x²(x - 6) + 2(x² - 36)]/(x - 6)
= [3x²(x - 6) + 2(x - 6)(x + 6)]/(x - 6)
= [3x² + 2(x + 6)](x - 6)/(x - 6)
= 3x² + 2x + 12
Naledi climbed up a mountain. Her initial altitude was 40 meters above sea level, and it increased by 10 meters each hour.Let )g(n)be Naledi's altitude at the beginning of the nth hour of her climb.G is a sequence. What kind of sequence is it? Answer
Answer:
ARITHMETIC SENTENCE
Step-by-step explanation:
Final answer:
Naledi's altitude sequence is an arithmetic sequence because it increases by a constant amount each hour.
Explanation:
Naledi's altitude at the beginning of the nth hour of her climb can be described by the function g(n), where g(n) is the altitude at that hour. Since she starts at 40 meters above sea level and increases her altitude by 10 meters every hour, the sequence representing her altitude over time is an arithmetic sequence. This is because each term in the sequence increases by a constant value, which is the definition of an arithmetic sequence.
The general formula for the nth term of an arithmetic sequence is aₙ = a₁ + (n - 1)d, where a₁ is the first term and d is the common difference between terms. In Naledi's case, a₁ is 40 meters (her initial altitude), and d is 10 meters (the constant increase each hour).
Please help
Julie takes her kids to a playground that has the shape shown.
A. While her kids are playing, Julie wants to get some exercise. If she does 2 laps around the playground, how much distance has she covered?
B. The park service is creating a flyer for the playground and wants to list the area that the playground covers. How much area does the playground cover?
Answer:
a=128 feet b=256 feet
Step-by-step explanation:
hope i got it
Answer:
A.) 128FT
B.) A=256
Step-by-step explanation:
A.)
16 x 4 = 64FT
62 x 2 = 128FT
So, 2 Laps Would Equal Up To 128FT.
B.)
Find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.
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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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"
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.
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠U.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠U = °
Yo sup??
This question can be solved by applying trigonometric ratios
let angle U be x, then
tanx=4/7
x=29.7
Hope this helps
What 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
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%.
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.
Kojo and Duku are driving. Kojo is 14 meters below the surface of the water. Duku is 5 meters above kojo.What is Duku position relative to the surface of the water ?
Duku is 9 meters below the surface of the water, calculated by adding Duku's 5 meters above Kojo's position to Kojo's 14 meters below the surface.
Explanation:The question asks about Duku's position relative to the surface of the water given Kojo is 14 meters below the surface and Duku is 5 meters above Kojo. To find Duku's position, subtract 5 meters (Duku's position above Kojo) from -14 meters (Kojo's position below the surface). Therefore, Duku's position relative to the surface of the water is -14 meters + 5 meters = -9 meters. This means Duku is 9 meters below the surface of the water.
(50 Points & Brainliest, please show work)
The function f(x) = 2x + 210 represents the number of calories burned when exercising, where x is the number of hours spent exercising.
The function g(x) = 2x + 125 represents the calorie deficit that occurs when following a particular diet, where x is the number of hours spent exercising.
What is (f + g)(3)?
Show all work and explain your answer
Answer:
(f+g)(3) = 347 calories
Step-by-step explanation:
f(x) = 2x + 210
g(x) = 2x + 125
(f+g)(x) is the sum of the functions
(f+g)(x) = 2x+210 + 2x+125
Combining like terms
=4x+335
Now let x = 3
(f+g)(3) = 4*3 +335
= 12 +335
= 347
(f+g)(3) = 347 calories
Answer:
347
Step-by-step explanation:
f(x) = 2x + 210
g(x) = 2x + 125
we know that (f+g)(x)=f(x)+g(x)
so (f+g)(x)= 2x + 210 + 2x + 125 = 4x + 335
(f+g)(3) simply means that x=3
therefore
(f+g)(3) = 12 + 335 = 347
A force of 10 pounds is required to stretch a spring 4 inches beyond its natural length. Assuming Hooke's law applies, how much work is done in stretching the spring from its natural length to 6 inches beyond its natural length?
Answer:
The work done is 5.084 J
Step-by-step explanation:
From Hooke's law of elasticity,
F = ke
F/e = k
F1/e1 = F2/e2
F2 = F1e2/e1
F1 = 10 lbf, e2 = 6 in, e1 = 4 in
F2 = 10×6/4 = 15 lbf
Work done (W) = 1/2F2e2
F2 = 15 lbf = 15×4.4482 = 66.723 N
e2 = 6 in = 6×0.0254 = 0.1524 m
W = 1/2×66.723×0.1524 = 5.084 J
What is the measure of side FD?
3.4 units
5.9 units
5.8 units
72.4 units
Give an example of a research experiment, indicating the independent and dependent variables, as well as the experimental and the control groups.
Answer:
In a study to determine whether how long a student sleeps affects test scores, the independent variable is the length of time spent sleeping while the dependent variable is the test score. You want to compare brands of paper towels, to see which holds the most liquid.
hopes it helps
Given the lines, AB and CD, determine the slope of line CD. Type a numerical answer in the space provided. If necessary, use the / key to represent a fraction bar. Do not put spaces in your answer.
A(0,-1)
B(5,3)
C(2,3)
D(6,2)
Answer:
The slope is = -1/4
Step-by-step explanation:
We are looking for the slope of the line CD. You are given the coordinates for each point as follows:
A(0,-1) B(5,3) C(2,3) D(6,2)
To find the slope of a straight line, you use the formula:
slope (m) = (y2 - y1)/(x2 - x1)
In other words the slope is the "rise over run":
rise (change in y) over the run (change in x) between two coordinates of the points:Remember: the coordinates of a point are (x;y). Choose one of the points to be point 1 and the other to be point 2. I would suggest that you follow the order they have given you ie. CD:
So if our points are C (2; 3) and D (6, 2) we can say point C is point 1 and point D is point 2. Plug into the formula:
slope (m) = (y2-y1)/(x2-x1)
y1 = 3
y2 = 2
x1 = 2
x2 = 6
∴ m = (2-3)/(6-2)
= -1/4
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)
The scale on a model railroad train set is 3.5 millimeters to 1 foot. If the length of a model car in the set is 150 millimeters, what is the approximate length of the actual car?
Answer:
The approximate length of the actual car is 43 feet.
Step-by-step explanation:
Given:
The scale on a model railroad train set is 3.5 millimeters to 1 foot. If the length of a model car in the set is 150 millimeters.
Now, to find the approximate length of the actual car.
Let the actual length of the car is [tex]x.[/tex]
The length of a model car in the set is 150 millimeters.
As, given the scale on a model railroad train set is 3.5 millimeters to 1 foot.
So, 3.5 millimeters equivalent to 1 foot.
Thus, 150 millimeters to [tex]x[/tex].
Now, to get the actual length of the car by using cross multiplication method:
[tex]\frac{3.5}{1} =\frac{150}{x}[/tex]
By using cross multiplying we get:
[tex]3.5x=150[/tex]
Dividing both sides by 3.5 we get:
[tex]x=42.85\ feet.[/tex]
The approximate length of the actual car = 43 feet.
Therefore, the approximate length of the actual car is 43 feet.
Answer:
43ft
Step-by-step explanation:
The answer is B.
Here's another way to solve this problem.
1. Write the scale ratio
3.5 mm
1 ft
2. Choose a variable, such as r, to represent the approximate length of the actual railroad car
3. Write the ratio of the length of the model car to the length of the actual car:
150 mm
r ft
4. Write a proportion
3.5=150
1= r
5. Cross multiply
3.5
r=150
3.5
r=42.9, which rounds to 43.
so the, approximate length of the actual car is 43 feet
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.
Mandi learned that each 10% of charge on her cell phone gave her an hour and twenty minutes of use. While playing a game today on her phone, she noticed the charge drop from 81% to 57% how long did mandi play the game?
Answer:
3hrs 12 mins
Step-by-step explanation:
For every 10% charge she gets 1hr 20mins (or 80 mins)
Charge drop = (81% - 57%) = 24%
Since 10% gives 80 mins;
24% gives (24/10) x 80 mins = 192 mins
since 1hr = 60 mins
192 mins = 192/60 = 3hrs 12 mins
Final answer:
Mandi played the game on her phone for 3 hours and 12 minutes, as she experienced a 24% drop in battery charge, with each 10% equating to 1 hour and 20 minutes of playtime.
Explanation:
The student's question involves calculating the duration of time Mandi played a game on her phone based on the percentage drop in battery charge. Mandi’s phone loses 10% charge for every 1 hour and 20 minutes of use. The charge dropped from 81% to 57%, which is a 24% drop. To find out how long she played the game, we calculate the number of 10% intervals in 24% and then multiply by the duration of one interval.
First, we determine how many 10% intervals are in 24%, which is calculated as 24% ÷ 10% = 2.4 intervals. Each interval equates to 1 hour and 20 minutes (which is the same as 80 minutes). Therefore, Mandi played for 2.4 intervals × 80 minutes per interval:
2.4 intervals × 80 minutes/interval = 192 minutes.
To convert minutes into hours and minutes, we divide by 60:
192 minutes ÷ 60 minutes/hour = 3 hours and 12 minutes.
So, Mandi played the game for 3 hours and 12 minutes.
HELP PLEASEEE
What are the exact and approximate circumference of a circle whose diameter is 2 1 over 3 km ?
Use 3.14 for π when finding the approximate circumference. Round your answer to the nearest hundreth
Enter your answers in the boxes
The exact circumference of the circle is [tex]7 \frac{49}{150} k m[/tex]
The approximate circumference of the circle is [tex]7.33 k m[/tex]
Explanation:
The diameter of the circle is [tex]2 \frac{1}{3} \mathrm{km}[/tex]
Now, we shall find the circumference of the circle.
The formula to determine the circumference of the circle is given by
[tex]C=\pi d[/tex]
Where C is the circumference , [tex]\pi[/tex] is 3.14 and [tex]d=2 \frac{1}{3} \mathrm[/tex] is the diameter of the circle.
The exact circumference of the circle is given by
[tex]\begin{aligned}C &=\pi d \\&=(3.14)\left(2 \frac{1}{3}\right) \\&=(3.14)\left(\frac{7}{3}\right) \\&=\frac{21.98}{3}\end{aligned}[/tex]
Multiply both numerator and denominator by 100, we get,
[tex]C=\frac{2198}{300} \\C=\frac{1099}{150}[/tex]
Converting [tex]\frac{1099}{150}[/tex] into mixed fraction, we get,
[tex]C=7 \frac{49}{150}[/tex]
Thus, the exact circumference of the circle is [tex]7 \frac{49}{150} k m[/tex]
The approximate value of the circumference can be determined by dividing the value [tex]\frac{1099}{150}[/tex]
[tex]C=\frac{1099}{150}=7.327[/tex]
[tex]C=7.33km[/tex]
Thus, the approximate circumference of the circle is [tex]7.33 k m[/tex]