The final amount after a certain rate of decrease over a period of time can be calculated by Xₙ = X₀ (1-r)ⁿ. From calculations the sales after 6 weeks are 13286.025.
If the percent increase or decrease, period of time and initial amount are given, the final amount can be calculated using the equation Xₙ = X₀ (1±r)ⁿ. Here the percentage decrease is given. So the equation is
Xₙ = X₀ (1-r)ⁿ
Xₙ is the final amount
X₀ is the initial amount
r is the rate
n is the period of time
Here percent is given as 10%. So the rate, r = 10/100 = 0.10
Xₙ = X₀ (1-r)ⁿ
= 25000× (1-0.10)⁶
= 13286.025
So the sales after 6 weeks are 13286.025
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At the end of each month, Bianca deposits $100 into an account with an interest rate of 4.25%, compounded monthly. If no money is withdrawn from the account, what will her balance be after 5 years?
Answer:
123.630189899 or A. $1,257.72
Step-by-step explanation:
[tex]\frac{4.25}{100}=0.0425\\ 100(1 + \frac{0.0425}{12})^{12(5)} \\= 123.630189899[/tex]
Given the two functions, which statement is true?
f(x) = e^x, g(x) = e^x-2
g(x) is translated down 2 units compared to f(x)
g(x) is translated right 2 units compared to f(x)
g(x) is translated left 2 units compared to f(x)
g(x) is translated up 2 units compared to f(x)
Determine the exact value of cot 3pi/2
put steps please
By trigonometric functions and trigonometric formulas, the exact value of cot (3π / 2) is equal to 0.
How to determine the exact value of a trigonometric function
In this problem we have the case of trigonometric function whose exact value must be found by means of trigonometric functions and trigonometric formulas. Now we proceed to present the entire procedure:
cot (3π / 2)
1 / tan (3π / 2)
Rewrite the function in terms of fundamental trigonometric functions: (sine, cosine)
1 / [sin (3π / 2) / cos (3π / 2)]
cos (3π / 2) / sin (3π / 2)
Then, we get the following exact value:
0 / (- 1)
0
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Find the value of x in the acute scalene triangle that has the angles 93° and 46°
The third angle of acute scalene triangle is 41°
Now, According to the question:
The first angle of acute scalene triangle is 93°
The second angle of acute scalene triangle is 46°
Let the third angle of acute scalene triangle is x
We know that:
The sum of the interior angles is always equal to 180 degrees.
Now, 93° + 46° + x = 180°
139° + x = 180°
x = 180° - 139°
x = 41°
Hence, the third angle of acute scalene triangle is 41°
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The revenue (R) made on the sale of tickets is a function of the price (p) of each
ticket, where R(p) = -40p^2 +400p-640
Pls help!!!
The revenue is maximized when the derivative of R(p) is equal to 0.
R'(p) = -80p + 400 = 0
p = 5
What is a function?A function is a mathematical relationship between two or more variables, where one variable (the output) is determined by the values of the other variables (the inputs). A function can be expressed as an equation, and it describes how the output changes in relation to the inputs.
Therefore, the maximum revenue is achieved when the price of each ticket is $5.
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The product of two consecutive even integers is 168. Find the integers.
What are the negative integers?
Answer:
We can use algebra to find the two consecutive even integers whose product is 168.
Let's call the first even integer x. Since it is consecutive to another even integer, the next one will be x+2. The product of these two integers is:
x * (x+2) = 168
We can solve for x by simplifying the equation:
x^2 + 2x = 168
x^2 + 2x - 168 = 0
We can factor the left side of the equation:
(x-14)(x+12) = 0
So the two solutions for x are -12 and 14.
The negative integers are -12 and -14.
The two integers that multiply to give 168 are -12 and -14, but keep in mind that they are not consecutive integers.
Nicole is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 18 meters from the building. The angle of elevation from her eyes to the roof ((point AA)) is 41^{\circ} ∘ , and the angle of elevation from her eyes to the top of the antenna ((point BB)) is 44^{\circ} ∘ . If her eyes are 1.68 meters from the ground, find the height of the antenna ((the distance from point AA to point BB)). Round your answer to the nearest meter if necessary.
The height of the antenna is 17m approximately to the nearest metre using the trigonometric ratio of tangent for angleof elevation 44°.
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
Considering the right triangle formed by the point of Nicole's eyes E with an angle of elevation 44°, top of the roof A (90°) and the top of the antenna B,
we shall evaluate for the height of the antenna AB as follows:
tan 44° = AB/18m {opposite/adjacent}
AB = 18m × tan 44° {cross multiplication}
AB = 18m × 0.9657
AB = 17.3826m
Therefore, the height of the antenna to the nearest metre is 17 metres using the trigonometric ratio of tangent for angleof elevation 44°.
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Answer:
2 meters
I got it correct in my hw (check the photos)
also mark me brainleist
A line includes the points (0, -8) and (3, 3) find the rate of change of the line
Answer:
11/3 or 11/3x
Step-by-step explanation:
Another term for "Rate of change" is slope.
The usual slope equation is (y2-y1)/(x2-x1)
Plugging in the points we get
(3 - (-8)) / (3 - 0)
(3+8)/(3-0)
(11)/(3)
Which makes the slope 11/3 or 11/3x
Please Help me on this 3rd last question I'm on I'm a bit stuck on it it would be very amazing if you did help me.
Answer:
c
Step-by-step explanation:
If Elayna bought 18 bags of topsoil and each bag contains 36 pounds, how many total bags did she buy?
Answer: To find the total weight of the bags of topsoil, you can multiply the number of bags by the weight of each bag.
18 bags * 36 pounds/bag = 648 pounds
So, Elayna bought 18 bags of topsoil which is 648 pounds in total.
Step-by-step explanation:
n engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 280 engines and the mean pressure was 6.6 lbs/square inch. assume the variance is known to be 1 . if the valve was designed to produce a mean pressure of 6.7 lbs/square inch, is there sufficient evidence at the 0.1 level that the valve performs below the specifications? state the null and alternative hypotheses for the above scenario.
Null hypothesis: valve meets specifications. Alternative hypothesis: valve doesn't meet specifications, t-test with p-value < 0.1 to reject Null.
What is null hypothesis ?
The null hypothesis is a arithmetic theory suggesting that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.
To test the null hypothesis, we can use a one-sample t-test. The t-statistic for this test is calculated as:
t = (x - μ) / (s / √n)
where x is the sample mean, μ is the population mean (6.7 lbs/square inch in this case), s is the population standard deviation (assumed to be 1), and n is the sample size (280 engines).
The p-value for this test can be calculated using the t-distribution table or a t-test calculator. If the p-value is less than the significance level of 0.1, then we can reject the null hypothesis and conclude that there is sufficient evidence that the valve performs below the specifications.
Null hypothesis: valve meets specifications. Alternative hypothesis: valve doesn't meet specifications, t-test with p-value < 0.1 to reject Null.
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3 Points
Steven rents an apartment in an all-wood building in the city suburbs. The
value of the belongings in the apartment is about $15,000. If Steven wants to
insure his belongings while renting, how much will he have to pay for
insurance per year?
Annual Premium per $100 of coverage
Brick. . Steel
Mixed
Wood
Area Building Contents Building Contents Building Contents Building Contents
rating
City 0. 39 0. 43 0. 5 0. 54 0. 55 0. 65 0. 66 0. 76
Suburb 0. 45 0. 52 0. 56 0. 63 0. 72 0. 74 083 085
Rural 0. 6 0. 69 0. 71 0. 8 0. 89 0. 91 1 | 102
O A. $150. 00
O B. $107. 50
OC. $127. 50
O D. $173. 50
Steven will have to pay $127. 50 for the insurance per year.
The correct answer is an option (C)
First, we need to find the corresponding value for the all-wood building in the city suburbs.
From given table, we will use the value 0.85 because he wishes to ensure his belongings.
Here, the value of the belongings in the apartment is about $15,000
Steven wants to insure his belongings while renting.
Now we can calculate the amount of money he will have to pay for insurance per year as follows:
15000 × (0.85 / 100)
= 127. 50 dollars
Therefore, he will have to pay 127. 50 dollars for insurance.
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Please help!!!!
If f(x)=-9x+13 and f(x) = -41, find x
The numerical value of x in the function f(x) = -9x + 13 when f(x) = -41 is 6.
What is the value of x in the given function?A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.
Given the data in the question;
f(x) = -9x + 13f(x) = -41x = ?To find the value of x, replace the occurrence of f(x) with -41 in the function and simplify.
f(x) = -9x + 13
-41 = -9x + 13
Collect like terms
9x = 41 + 13
Add 41 and 13
9x = 54
Divide both sides by 9
9x/9 = 54/9
x = 54/9
x = 6
Therefore, the input value x is 6.
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Find a2, a3, and a4.
a1=0
an=an–1+15
Write your answers as integers or fractions in simplest form.
The values of the terms are a₂ = 15, a₃ = 30 and a₄ = 45
How to determine the value of the terms?The definition of the function is given as
a₁= 0
aₙ = aₙ₋₁ + 15
The above definitions imply that we simply add 15 to the previous term to get the current term
Using the above as a guide,
So, we have the following representation
a₂ = 0 + 15
a₂ = 15
Also, we have
a₃ = 15 + 15
a₃ = 30
Lastly, we have
a₄ = 30 + 15
Evaluate the equation
a₄ = 45
Hence, the value of a₄ is 45
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Factor the quadratic expression completely.
-3x² +172-20=
Answer: The given quadratic expression is -3x²+172x-20. To factor this expression, we look for two numbers that multiply to -20 and add to 172.
We can start by dividing -20 by different numbers and checking if the product and the sum of the divisors equals -20 and 172 respectively.
-20/1 = -20, 1+-20 = -19
-20/2 = -10, 2+-10 = -8
-20/4 = -5, 4+-5 = -1
-20/-1 = 20, -1+20 = 19
-20/-2 = 10, -2+10 = 8
-20/-4 = 5, -4+5 = 1
We can see that the divisors that multiply to -20 and add to 172 are (x+8)(x-5)
So, we can factor the quadratic expression as:
-3x²+172x-20 = -3(x+8)(x-5)
Hope this helps!
Step-by-step explanation:
Chase tried to evaluate an expression. Here is his work: 2(12÷2)2–14+6 = Step 1262–14+6 = Step 2236–14+6 = Step 372–14+6 = Step 472–20 = Step 552 Is Chase's work correct? PLEASE HELP FAST THIS IS FOR 6th GRADE IXL
No Chase's work is not correct. He has made a mistake in working the brackets out. The BODMAS Rule has to be used here.
We have 2(12 ÷ 2)2 – 14 + 6
Here according to the BODMAS rule which stands for Brackets Of Division Multiplication Addition Subtraction, we will first solve the brackets.
Now any number to the left or right of the brackets without any sign in between the bracket and the number has to be multiplied by the answer we get by solving the bracket.
12 ÷ 2 = 6
Hence we get
2 X 6 X 2 - 14 + 6
Now we need to multiply.
2 X 6 X 2 = 12 X 2 = 24
Hence we get
24 - 14 + 6
Now we need to add the numbers up.
24 + 6 = 30 hence we get
30 - 14
= 16
Hence Chase's work is not correct.
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8.A rocket travels at an approximate speed of 7.9 kilometers per second.
Which statements about the rocket are true?
Select all that apply.
The statement below about the rocket is true:
A rocket travels at an approximate speed of 7.9 *10⁵ cm per second.
What is Unit conversion?A statement of the connection between units that are used to alter the units of a measured quantity without affecting the value is called a conversion factor. A conversion ratio (or unit factor), if the numerator and denominator have the same value represented in various units, always equals one (1).
Given, A rocket travels at an approximate speed of 7.9 kilometers per second.
Since, some unit conversion:
1 kilometer = 1000 meteres
1 kilometer = 100000 centimeteres = 10⁵ cm
1 kilometer = 10000000 milimeteres = 10⁷ mm
thus we can say that from the given options only "f" is correct that states:
A rocket travels at an approximate speed of 7.9 *10⁵ cm per second.
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determine the minimum distance (ft) it will take for a driver going at the speed limit to come to stop at the traffic light after the traffic light turns yellow. b) what will be minimum stopping distance if the driver was going at 45 mph (5 mph over the speed limit)? express it in ft and also as % of the distance you found in part a). c) what will be the minimum stopping distance if the driver was going at 50 mph (10 mph over the speed limit)? express it in ft and also as % of the distance you found in part a). g
The minimum stopping distance is 800 ft.
Part A: The minimum stopping distance for a driver going at the speed limit (40 mph) is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (40 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 800 ft.
Part B: For a driver going at 45 mph, the minimum stopping distance is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (45 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 925 ft, which is 15.6% greater than the stopping distance for the speed limit.
Part C: For a driver going at 50 mph, the minimum stopping distance is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (50 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 1250 ft, which is 56.3% greater than the stopping distance for the speed limit.
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Select the correct statement in the table.
Tennis balls are traditionally sold in a cylinder which contains three balls. The volume of space in the cylinder not occupied by a
tennis ball is modeled in the following function, where r is the radius of a tennis ball, in inches.
V =
(²) (67)
477-3
Select the true statement in the table below.
-
The factor T2² represents the volume of the can.
The factor 6r represents the width of the can.
The term 41³ represents the volume of the three tennis balls.
The term (1²)(6r) represents the volume of one tennis ball.
The distance between the tennis balls and the cans is 49.46 cubic inches.
What is meant by volume?A measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units. Volume and the notion of length are connected.
Given: Each ball has a diameter of three inches.
Three tennis balls are contained in each can, which is how they are sold.
Each can has a cylindrical shape.
We start by determining each tennis ball's volume.
Because of their spherical shape, their volume is determined by
[tex]$V=\frac{4}{3} \pi r^3$[/tex]
Where [tex]$r=\frac{d}{2}=\frac{3 \text { in }}{2}=1.5 i$[/tex] in
Replacing the radius and using [tex]$\pi \approx 3.14$[/tex], we have
[tex]$V=\frac{4}{3}(3.14)(1.5 \mathrm{in})^3=14.13 \mathrm{in}^3$$[/tex]
Therefore, the volume of each tennis ball exists 14.13 cubic inches, approximately.
Assuming that the diameter of each ball exists congruent with the diameter of the can, we contain the volume of a cylinder defined by
[tex]$V=\pi r^2 h$[/tex]
Where, r = 1.5 in and h = 3(3 in)=9 in, because each can has three balls, and the height exists the sum of all three diameters.
[tex]$V=3.14(1.5 i n)^2(9 i n)=63.59 n^3$$[/tex]
Therefore, the volume of each can exists 63.59 cubic inches, approximately.
The complete question is:
Tennis balls with a 3 inch Diameter are sold in cans of three. The can is a cylinder
A)what is the volume of one tennis ball ?
B)what is the volume of the cylinder ?
C)how much space is not occupied by the tennis balls in the can?
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glassdoor four players pick a real number from [0,1]. the players with the middle two numbers are paired together, while the players with the two extreme numbers are paired together. the pair with a lower sum has to each pay the difference to the pair with a higher sum. if you are allowed to choose your number (while everyone else draws uniformly at random), which number should you choose?
The expected value of the sum of the two extreme numbers is 1/2.
Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen.
The optimal strategy for you would be to choose the number 0.5, as it maximizes the probability that your pair will have the highest sum, and minimizes the probability that your pair will have the lowest sum.
This is because if all players choose a number uniformly at random, the expected value of the lowest and highest numbers will be 0 and 1 respectively, and the expected value of the middle two numbers will be 0.5. Therefore, by choosing 0.5, you have the best chance of having the highest sum, which means you will have to pay the least amount of money.
Therefore, the expected value of the sum of the two extreme numbers is 1/2.
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How do I find the median of this trapezoid?
Answer:
23.37
Step-by-step explanation:
There ya go
:)
simplify the expression 5^3b+2
Answer:
125b+2
Step-by-step explanation:
5^3b+2
5x5x5=125
125b+2
Cannot be simplified any futher
Which equation represents this graph? This graphic illustrates the mathematical word problem described in the accompanying text.
Answer:
Step-by-step explanation:
that a huge prob but yah
25-2x≤5(2-x) pls solve w/ steps
Answer: X has to be greater than or equal to 15/7 for the inequality to be true.
Step-by-step explanation:
here are the steps to solve the inequality 25-2x≤5(2-x):
Start by simplifying the right side of the inequality: 5(2-x) = 10 - 5x
Now we can substitute this back into the original inequality: 25 - 2x ≤ 10 - 5x
Next, we need to combine like terms on both sides of the inequality: 25 - 7x ≤ 10
Now we'll add 7x to both sides: 25 ≤ 10 + 7x
Subtract 10 from both sides: 15 ≤ 7x
Finally, divide both sides by 7: 15/7 ≤ x
The solution set is x ≥ 15/7.
So x has to be greater than or equal to 15/7 for the inequality to be true.
Answer:
-5 ≥ x or x ≤ -5
Step-by-step explanation:
25 - 2x ≤ 5(2 - x)
distribute the 5 to eliminate the parentheses:
25 - 2x ≤ 10 - 5x
now combine like terms:
15 - 2x ≤ -5x
15 ≤ -3x
-5 ≥ x or x ≤ -5
the inequality symbol gets switched whenever you multiply or divide by a negative value
What is 2/3+3/7? I CAN'T FIGURE IT OUT! Work it out!
The total cost (in dollars) of a cell phone plan after x months can be represented by c(x) = 35x + 20. Find the inverse function. Then find the number of months
when the total cost is $1700.
The number of months when the total cost is $1700 is 48 months
What is a function?
A function can be defined as an expression, equation, law or rule that shows the relationship between two variables.
These variables are;
Dependent variableIndependent variableFrom the information given, we have that;
The function for the total cost is c(x) = 35x + 20x represents the number of monthsNow, substitute the values, we have;
1700 = 35x + 20
collect like terms
35x = 1700 - 20
subtract the like terms
35x = 1680
Make 'x' the subject of formula
x = 48 months
Hence, the value is 48 months
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if it takes you 2 hours to shape 48 baguettes, how many could you make in 30 minutes? how long would it take for you to make 1 baguette?
Answer:
12. & 2.5mins
Step-by-step explanation:
2 hours = 120 mins for 48 baguettes. so 120/48 = 2.5 mins per baguette
30 mins is 1/4 of 2 hours. so 12 baguettes
from a pack of cards, 2 cards are drawn in succession and the selected card is not replaced. what is the probability that both the drawn cards are diamonds? (refer to the deck of cards material shared in reference material to get better understanding of cards)
Two cards are drawn in succession from a standard deck. The probability that both the drawn cards are diamonds is 143/2,652
Probability is defined as the ratio of the number of favorable events to the the number of possible outcomes. The probability of an event A is defined as:
P(A) = n(A)/n(S)
Where:
n(A) = number of possible ways the event A occurs
n(S) = total possible outcomes
In a standard deck, there are 52 cards. The number of diamond suit = 13 cards.
First drawn: number of diamond = 13
Hence, P1(diamond) = 13/52
In the second drawn, the number of diamonds left is 13 - 1 = 12, and total number of cards left is 52 - 1 = 51.
Hence, the probability of the second card will be a diamond is:
P2(diamond) = 12/51.
Since those 2 events are independent, the probability that both cards are diamonds is:
P(diamonds) = P1 (diamond) x P2 (diamond)
= (13/52) x (11/51) = 143/2,652
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Solve the inequality. -1.5x < 7.5
Answer: x > -5
Step-by-step explanation:
-1.5x < 7.5
x > -5 (When multiplying both sides by a negative, the inequality is flipped)
[tex]-1.5x < 7.5[/tex]
Divide both sides by -1.5:
[tex]\dfrac{-1.5x}{-1.5} < \dfrac{7.5}{-1.5}[/tex]
When dividing by a negative number, the inequality sign will reverse.
Answer:
[tex]x > -5[/tex]
Quinn ran five times
this week for a total
distance greater than
40 miles. He says that
means he ran, on average,
more than 8 miles on
each run.
For an indirect proof,
what does he need to
assume?
We can assume linear inequality 8x>40 for x>8 for an indirect proof.
What are linear inequalities?
Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.
The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.
e.g. y>x+2
Now,
Given,
Quinn ran total distance>40 mile
No. of times he ran=5
average distance for each run>8
also let x>8 where x=average distance for each run
Hence,
We can assume linear inequality 8x>40 for x>8
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