The value of the travel trailer after 5 years is $8306 .
in the question ,
it is given that
the price of the travel trailer(a) = $35000
rate of decrease(r) = 0.25
time (x) = 5 years
The exponential expression for the decrease in price after x years is given by the formula
price = a(1-r)ˣ
where, a is the initial amount ,
r is the decay rate ,
x is the time period .
Substituting the values from above in the formula ,
we get
price = 35000(1-0.25)⁵
= 35000(0.75)⁵
= 8305.664
≈8306
Therefore , the value of the travel trailer after 5 years is $8306 .
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64 (5x+4) solve for x (angles)
Answer: 320x + 256
Step-by-step explanation:
freddy is having a fall harvant party for his friends they have 30 to decorate and 36 sets of material to make mini scarecrows how many kids decorate pumpkins and make scarecrows if he wants each person to have the same amount of crafts with nno left overs material
Based on the highest common factor, the number of kids that can decorate 30 pumpkins equally and make scarecrows from the materials without leftovers is 5.
What is the highest common factor?The highest common factor (HCF) is the number that can divide between 30 and 36 without a remainder.
Pumpkins Materials
Units 30 36
HCF 6 6
Average used 5 6
Thus, dividing 30 and 36 by their HCF of 6, respectively, shows that 5 kids can decorate the 30 pumpkins using 6 materials each to make the scarecrows.
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The number of kids who can decorate 30 pumpkins equally and make scarecrows from the materials without leftovers would be; 5.
What is factorization?factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.
The highest common factor (HCF) is defined as the number which can divide between 30 and 36 without a remainder.
Given that they have 30 to decorate and 36 sets of material to make mini scarecrows.
Their HCF is 6. The averages used are 5 and 6 respectively.
Hence, their HCF of 6, shows that 5 kids can decorate the 30 pumpkins by using 6 materials each to make the scarecrows.
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How many terms are in this expression?
7a+ 1 + 8b
Answer:
3
Step-by-step explanation:
There are 3 terms. The terms are separated by + signs. They can also be separated by - signs.
The terms are 7a, 1, 8b.
If there was a minus sign in front of the term you need to keep it with the term because it is a negative term.
Answer:
There are a total of 3 terms
Step-by-step explanation:
A term is either a single number or variable, or the product of several numbers or variables. Terms are separated by a + or - sign in an overall expression. We are basically counting how many individual mathematical expressions
7a is a term
1 is a term, and it's a constant
8b is a term
Which inequality is equivalent to 22 ≤x-9?
(A) 13sx
(B) 13zx
(C) 31sx
(D) 31zx
Answer:
31 ≤ x
Step-by-step explanation:
22 ≤ x - 9;
22 + 9 ≤ x - 9 + 9;
31 ≤ x
40 ounces of granola cost $6.52 how much does a granola cost per ounce(give your answer to the nearest cent)
Answer: $0.2
Step-by-step explanation:
To find the answer you divide 6.52 by 40 which will get 0.163. To check the answer and make sure its correct you can multiply 0.163 by 40 to get 6.52 making the answer correct so 0.2 is the answer to the nearest cent. Hope this helps :)
Does anyone know why this is wrong??
[tex]=-10x^4-4x^3+6x^2[/tex]
Which expression represents the quotient of d and 11d÷11d×11d-11d+11
Answer:
A. d ÷ 11
Explanation:
The quotient of two terms is the division of the first term by the other term.
If we say the quotient of d and 11, we write it mathematically as:
[tex]d\div11[/tex]The correct choice is A.
the combined math and verbal scores for students taking a national standardized examination for college admission, is normally distributed with a mean of 800 and a standard deviation of 150. if a college requires a student to be in the top 15 % of students taking this test, what is the minimum score that such a student can obtain and still qualify for admission at the college? answer:(round to the nearest integer)
The student needs a minimum score of 956 to stay in the top 15% of the normal distribution.
Normal distributions are fundamental to statistics because they are widely used in the social and natural sciences to represent real-valued regressors with uncertain distributions.
Some of its importance may be due to the central limit theory.This statement asserts that, under certain conditions, the mean of many samples (observations) of a stochastic process with small mean and variance creates itself as a random variable, whose distributions converge to a normal distribution as the sample size increases.Because of this, physical value distributions that are expected to be the sum of a large number of independent occurrences, such as error margins, are typically near to normal.Now top 15%
Therefore P=0.15
P(X<x) = 1 -0.15 = 0.85
Z-score = 1.04
Now we know that
z=(x-μ)/σ
Solving we get :
1.04 = (x - 800)/150
or, x = 956
hence the minimum score is 956.
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f(x)=4x+2; Find f(8)
We have:
[tex]f(x)=4x+2[/tex]And want to find f(8), for this we simply replace x with 8 and operate:
[tex]f(8)=4(8)+2\Rightarrow f(8)=34[/tex]101x^2+231x-334=-2 find the A,B,C
The roots of the equation is 1 and 3.28
The given equation is a quadratic
To find the roots of a quadratic equation, the formula is
[tex]\frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]
The equation is 101x^2+231x-334=-2 we need to find the A,B,C
101x^2+231x-332 = 0
here a is 101, b is 231, and c is -332
[tex]\frac{-b + \sqrt{b^{2} - 4ac } }{2a}\\\frac{-231 + \sqrt{231^{2} - 4(101)(-332) } }{2(101)}\\\frac{-231 + \sqrt{53361 + 134128 } }{202}\\\frac{-231 + \sqrt{187489 } }{202}\\\\\frac{-231 + \sqrt{187489 } }{202}\\\\\frac{-231 + 433 }{202}\\\\=\frac{202}{202}\\\\ 1[/tex]
[tex]\frac{-b - \sqrt{b^{2} - 4ac } }{2a}\\\frac{-231 - \sqrt{231^{2} - 4(101)(-332) } }{2(101)}\\\frac{-231 - \sqrt{53361 + 134128 } }{202}\\\frac{-231 - \sqrt{187489 } }{202}\\\\\frac{-231 - \sqrt{187489 } }{202}\\\\\frac{-231 -433 }{202}\\\\=\frac{664}{202}\\\\ 3.28[/tex]
Therefore, the roots of the equation is 1 and 3.28
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which integers represent each situation? a) a debt of $10b) 6 degrees below 0 c) deposit of $25 someone please help fast
An integer that represent the debt of $10 can be express below
[tex]-\text{ \$10}[/tex]An integer that represent 6 degree below 0 is expressed below
[tex]0-6=\text{ -6 degre}e[/tex]An integer that represent a deposit of $25 can be express below
[tex]+\text{ \$25= \$25}[/tex]Which inequality represebts the graph shown below
Answer:
x > -2
Step-by-step explanation:
I just need a little help
Which table represents a function?
Answer:
A would be the correct answer because to find a function when you draw a line on the graph, the line cannot cross each other. Even if the line is verticle, it is still crossing each other.
Step-by-step explanation:
PLSS HELP I DO NOT UNDERSTAND THIS PLSSS
The rate of change is 18 units and 24 ≤ x ≤ 96 is 24 < 42, 60, 78 < 96.
What is the rate of change?The rate at which a variable alters over a predetermined amount of time. It is frequently used when discussing momentum and is typically expressed as a ratio of one variable's change to another's corresponding change. This ratio is graphically represented by a line's slope.So, the rate of change in column 'x':
24 - 6 = 18The rate of change per unit is 18.
Now, 24 ≤ x ≤ 96.
Between 24 and 96, there are three values given in the column which are:
426078So, x can be 42, 60, and 78.
Therefore, the rate of change is 18 units and 24 ≤ x ≤ 96 is 24 < 42, 60, 78 < 96.
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Susie has a part-time job at the video store. She makes between $41.89 and $47.91 a day. Which is a reasonable amount of money that Susie makes for working 7 days?
The amount of money that Susie makes for 7 working days will be;
⇒ $314.3
What is mean by Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Susie has a part-time job at the video store and she makes between $41.89 and $47.91 a day.
Now,
The amount of money for a day = ($41.89 + $47.91) / 2
The amount of money for a day = $89.8 / 2
The amount of money for a day = $44.9
Thus, The amount of money that Susie makes for 7 working days is;
= 7 x $44.9
= $314.3
Hence,
The amount of money that Susie makes for 7 working days will be;
⇒ $314.3
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PLEASE HELP!!!!!!!!!!!!
The stem-and-leaf plot shows kilometers walked by participants in a charity benefit walk. Use it to answer the questions.
A stem and leaf plot shows the number of kilometers walked for charity.
The plot is titled 'Kilometers Walked for Charity.' The numbers 12, 13, 14, 15, 16, and 17 are in a vertical column to the left of a vertical line.
· On the same line as 12 but on the right of the vertical line are the numbers 3, 3, 6, 7, 9, and 9.
· On the same line as 13 but on the right of the vertical line are the numbers 1, 1, 4, 5, and 5.
· On the same line as 14 but on the right of the vertical line are the numbers 0, 0, 2, 3, 3, 8, 8, and 9.
· On the same line as 15 but on the right of the vertical line are the numbers 2, 2, 2, 2, 2, 3, 5, 5, and 7.
· On the same line as 16 but on the right of the vertical line are the numbers 4, 5, 5, 9, and 9.
· On the same line as 17 but on the right of the vertical line are the numbers 3 and 5.
The key to the stem and leaf plot identifies that 12 vertical line 3 means 12.3.
a. How many people participated in the walk?
b. How many of the walkers traveled more than 14 kilometers?
Answer:
35 participants for A
22 participants traveled more than 14 km for B.
Step-by-step explanation:
What is the equation of a line that passes though the pointe (8, -3) and has a slope of 1/4?
Answer:
y = (1/4)x - 5
Step-by-step explanation:
We'll look for an equation having the form y=mx+b, where m is the slope and b is the y-intercept, the value of y when x=0.
We are told the slope, m, is (1/4):
y = (1/4)x+ b
We need to find a value of b such that it forces the line to go through point (8,-3). Enter that point in the equation:
y = (1/4)x + b
-3 = (1/4)(8) + b for (8,-3)
-3 = 2 + b
b = -5
The equation is y = (1/4)x - 5
See attached graph.
(03.03)
The point R is halfway between the integers on the number line below and represents the number ____. (Use the hyphen for negative numbers and write the answer as a decimal, such as -6.4). please help
The point R represents the number -2.5 on the number line
How to determine the location of the point R?From the question, we understand that the point R is halfway between the integers on the number line
This means that
Point R = 1/2 * (a + b)
Where variables a and b represent the boundaries of the integers
In this case, we have
a =-2
b = -3
Substitute a =-2 and b = -3 in the equation Point R = 1/2 * (a + b)
So, we have
Point R = 1/2 * (-2 - 3)
Evaluate the difference
Point R = 1/2 * -5
Evaluate the product
Point R = -2.5
Hence, the location of R on the number line is -2.5
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There are two spinners. one spinner has three equally sized sectors that are numbered 1, 2, and 4. the second spinner has four equally sized sectors that are labeled a, b, c, and d. each spinner is spun once. how many outcomes do not show c? responses 4 4, 6 6, 7 7, 9
The number of outcomes that do not show c is calculated to be 9 if each spinner is spun once.
The three possible outcomes of the first spinner are 1,2 and 4 and the possible outcomes of the second spinner are a,b,c and d; so if the two spinners are spun together, the possible outcome will be:
a1, a2, a4
b1, b2, b4
c1, c2, c4
d1, d2, d4
Therefore, there are a total of 12 possible outcomes, and 3 out of these possible outcomes show c. Now the outcomes that do not show c can be calculated by subtraction as follows;
Outcome not showing c = Total outcomes - Outcomes showing c
Outcome not showing c = 12 - 3
Outcome not showing c = 9
Therefore, 9 outcomes do not show c if each spinner is spun once.
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Answer: 6
Step-by-step explanation:
for her final project, stacy plans on surveying a random sample of 50 students on whether they plan to go to florida for spring break. from past years, she guesses that about 10% of the class goes. is it reasonable for her to use a normal model for the sampling distribution of the sample proportion? why or why not?
It is not reasonable to use a normal model for the sampling distribution of the sample because the data doesn't meet the success or failure consideration.
How to illustrate the information?The sample has a size of 50 students. The probability that she guesses that about 10% of the class goes is 10%
This will be illustrated as:
1 - p = 1 - 10% = 1 - 0.10 = 0.90
np = 50 × 0.1 = 5. This implies the number of successes.
In this case, the number of successes is less than 10. This is because 5 is less than 10. Therefore, the data doesn't meet the condition.
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i need this asap pleasee 44 points
Answer:
Step-by-step explanation:
i think its the 3rd one
What are we missing in the triangle in the picture?
Looking at the triangle, we missing a side. This side represents the leg.
Now, we can find this missing side using the Pythagorean Theorem because the half represents a right triangle.
- The hypotenuse is the largest side, then hypotenuse = 5ft.
Using
5x^2-25=100 solve by taking square root
Answer:
x=5,−5
Step-by-step explanation:
-3(0.5+3p)=-6(p-5.9) show work
help
Answer:
p=12.3
Step-by-step explanation:
-1.5-9p= -6p+35.4
36.9=3p
p=12.3
Find the mean for n = 200 and p = 0.24 when the conditions for the binomial distribution are met.
The mean value of expected value for a binomial distribution is given by the next formula:
[tex]\mu_x=n\cdot p[/tex]Where n is the number of trials and p is the probability of success. So, using the given data:
[tex]\begin{gathered} \mu_x=200\cdot0.24 \\ \mu_x=48 \end{gathered}[/tex]So the expected value or mean is 48
Which statement best describes how to slice a cone so that the resulting cross section is an ellipse
Cutting at less than a right angle to the axis but more than the angle made by the side of the cone produces an ellipse.
Therefore, with this above statement, the statement which best describes how to slice a cone so that the resulting cross-section is an ellipse is
A plane slicing the cone diagonally without intersecting the base
The correct option, therefore, is OPTION B
A guy wire runs from the top of a cell tower to a metal stake in the ground. Hannah
places a 6-foot tall pole to support the guy wire. After placing the pole, Hannah
measures the distance from the stake to the pole to be 1 ft. She then measures the
distance from the pole to the tower to be 12 ft. Find the length of the guy wire, to the
nearest foot.
The length of the guy wire, to the nearest foot is 1548 ft.
What is the Pythagoras theorem?The right-angled triangle's relationship between its three sides is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The square of a triangle's hypotenuse is equal to the sum of its other two sides' squares, according to the Pythagoras theorem. The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized
After sketching the information given, we have two similar right triangles, ΔABE and ΔCDE.
CD = 6 ft
DE = 1 ft
BD = 12 ft
Since ΔABE ~ ΔCDE, therefore,
AB/CD = BE/DE (proportional sides)
Plug in the values
AB/6 = (12 + 1)/2
AB/6 = 13/2
Cross multiply
AB = 13(3)
AB = 39 ft
AE = √(AB² + BE²)
AE = √(39² + 12²)
AE = 1548 ft (nearest foot)
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Answer: The length of the guy wire, to the nearest foot is 1548 ft.
Step-by-step explanation:
The cost to rent a paddle boat at the country park is $8 per hour plus a non-refundable deposit of $10. The cost can be modeled by the function f(h) = 8h + 10, where h represents the number of hours the boat is rented. Describe the graph g(h) as it relates to f(h) if the non-refundable deposit increases to %15. PLEASEE HELPP!!
The relationship between the graph of f(h) and graph of g(h)
Both graphs have same slope of 8The y intercept of f(h) = 10The y intercept of g(h) = 11.5both graphs are straight line graph representing linear functions.What is a graph ?A graph is a pictorial representation of information
How to find the increment in the non refundable depositThe difference in the two graphs is the part of the non refundable deposit which will affect the intercept.
In f(h) = 8h + 10, the non refundable deposit 10 and the increment is 15%
The increment is solved below
solving the percentage increased
15% of $10 = 0.15 * 10 = $1.5
adding to the initial deposit
10 + 1.5 = 11.5
g(h) = 8h + 11.5
The graph of g(h) will have same slope as graph of f(h) which is 8
The y intercept of the graph if g(h) will be 11.5 while that of the graph of f(h) is 10
both graphs will form parallel lines
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type the correct answer in each box. use numerals instead of words if neasary
This is given point in the fourth quadrant.
In this point, the adjacent is
[tex]\frac{5}{13}[/tex]The opposite is y.
Find hypotenuse h using the pythagorean theorem:
[tex]\begin{gathered} h^2=(\frac{5}{13})^2+y^2 \\ h=\sqrt[]{\frac{25}{169}+y^2} \end{gathered}[/tex][tex]\sec (\theta)[/tex]is equal to hypotenuse by adjacent.
[tex]\cot (\theta)[/tex]is equal to adjacent by opposite.
In the fourth quadrant,
[tex]\sec \theta[/tex]is positive , and
[tex]\cot \theta[/tex]is negative.
So,
[tex]\begin{gathered} \sec \theta=\frac{h}{\frac{5}{13}} \\ =\frac{13\sqrt[]{\frac{25}{169}+y^2}}{5} \\ \cot \theta=\frac{\frac{5}{13}}{-y} \\ =-\frac{5}{13y} \end{gathered}[/tex]Element X decays radioactively with a half life of 5 minutes. If there are 860 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 230 grams? y = a(.5) k
The amount of time it would take Element X to decay to a mass of 230 grams is 9.5 minutes.
How to determine the amount of time to decay?Mathematically, the mass of a radioactive element that is remaining after time (t-hours) is given by this exponential function:
A(t) = A₀·e^{t/τ}
Where:
A(t) represents the mass remaining or current mass measured in grams.A₀ represents the initial mass measured in grams.τ is the time constant measured in minutes.t represents the half-life or time to decay measured in minutes.Next, we would determine the time constant by using this mathematical expression:
Time constant, τ = t/ln2
Time constant, τ = 5/0.6932
Time constant, τ = 7.2130 minutes.
Now, we can determine the amount of time to decay by making half-life (t) the subject of formula as follows:
A(t) = A₀·e^{t/τ}
Half-life, t = -τ·ln(A(t)/A₀)
Substituting the parameters into the formula, we have;
Half-life, t = -7.2130·ln(230/860)
Half-life, t = -7.2130 × ln(0.2674)
Half-life, t = -7.2130 × -1.3190
Half-life, t = 9.51 ≈ 9.5 minutes.
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