Answer:
To solve this problem, we can use the formula for exponential growth:
V(t) = V0 * (1 + r)^t
where:
V(t) is the value of the equipment at time t
V0 is the initial value of the equipment ($15,000)
r is the annual growth rate (15.9% or 0.159)
t is the time in years
We want to find the time t when the value of the equipment will be less than $7500. So we can set up the following inequality:
V(t) < 7500
Substituting the formula for V(t), we get:
V0 * (1 + r)^t < 7500
Substituting the given values, we get:
15000 * (1 + 0.159)^t < 7500
Simplifying and solving for t,
we get:(1 + 0.159)^t < 0.5
t * log(1 + 0.159) < log(0.5)
t > log(0.5) / log(1 + 0.159)
Using a calculator, we get:
t > 2.64
So the company's new equipment will be worth less than $7500 after about 2.64 years.
Step-by-step explanation:
A function is given.
f(x) = x3 − 7x2; x = 0, x = 10
(a) Determine the net change between the given values of the variable.
(b) Determine the average rate of change between the given values of the variable.
On solving the provided question, we can say that the function is
[tex]f(z) = 3 - 4z^2[/tex] and f(-2) = -13 and f(0) = 3.
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
the function is
[tex]f(z) = 3 - 4z^2[/tex]
[tex]f(-2) = 3 - 4(-2)^2[/tex]
= 3 - 4(4)
= 3 - 16
=-13
[tex]f(0) = 3 - 4(0)^2[/tex]
= 3 - 4(0)
= 3 - 0
= 3
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Sketch an angle θ in standard position such that θ has the least possible positive measure and the point (−3,4) is on the terminal side of θ. Then find the exact values of the six trigonometric functions for θ.
To sketch the angle θ in standard position, you can start by plotting the point ( -3, 4 ) on the coordinate plane. Next, you draw a line from the origin ( 0, 0 ) to the point ( -3, 4 ), which represents the terminal side of the angle.
Now, you can use the six trigonometric functions to find the exact values for θ:
Cosine ( cos θ ) = x / r = -3 / 5
Sine ( sin θ ) = y / r = 4 / 5
Tangent ( tan θ ) = y / x = 4 / -3
Secant ( sec θ ) = 1 / cos θ = -5 / 3
Cosecant ( csc θ ) = 1 / sin θ = -5 / 4
Cotangent ( cot θ ) = 1 / tan θ = -3 / 4
Here, r represents the distance from the origin to the point ( -3, 4 ), which is 5 units. Note that these values are for the least positive measure of the angle, which is in the second quadrant.
select the equivalent expression.
Answer:
Step-by-step explanation: Option A is correct.
please help me with math i’ll give you brainlist!!
Answer: A) Dashed line with shading below
Step-by-step explanation:
because, as you can see the < sign is only less than not 'less than and equal to' so it will be dashed...
Answer:
A
Step-by-step explanation:
A dashed line is used if < or > is used to indicate that the boundary is not part of the solution. Then shade the appropriate region.
As in the question, y is less than 4/3x + 2 therefore, the region below the line is shaded.
Please help!!!!! Due tomorrow need to understand how to properly do this question :(
Answer:
f(x)=3x^2+2
Step-by-step explanation:
use pm
Give the domain of
s(x)=6/25-x^2
Answer: The domain of a function is the set of all possible input values (x-values) for which the function is defined and produces a valid output (y-value).
In this case, the function s(x) = 6/25 - x^2 has no restrictions on the input values for x, so the domain of the function is all real numbers.
Therefore, the domain of the function s(x) = 6/25 - x^2 is:
(-∞, ∞)
This means that the function can be evaluated for any real value of x.
Step-by-step explanation:
A and C are right angles. Mp=. Degrees
The required measure of angle p in triangle DBC is given as ∠p = 59.14°.
What are trig ratios?If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.
Here,
Consider triangle ABD
Apply the Pythagorean theorem to determine the measure of DB,
DB² = AD² + AB²
DB² = 6² + 5²
DB² = 61
DB = 7.81
Now,
Apply the trig ratio in triangle DCB,
cosp = 4/7.81
p = 59.14°
Thus, the required measure of angle p in triangle DBC is given as ∠p = 59.14°.
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Help me with my last question…..
Answer:
C
Step-by-step explanation:
An irrational number cannot be shown as a simple fraction. If the number has decimals that are non-repeating (so not 7.85555555... or. 9.121212121...), cannot be shown as fractions (not 1.50000000... as it can be written as 3/2), and does not terminate (aka end). C is the answer you're looking for, as it cannot be shown as a fraction, the numbers after the decimal go on indefinitely, and the number's don't follow a noticeable repeatable pattern.
Answer:
Step-by-step explanation:
Suppose
−5x−15≤f(x)≤x2+3x+1
Use this to compute the following limit.
limx→−4f(x)
The limits lim x→ −4 f(x) is 5
The method is substitution method
How to determine the limitsFrom the question, we have the following parameters that can be used in our computation:
−5x − 15 ≤ f(x) ≤ x² + 3x + 1
The limits is given as
lim x→ −4 f(x)
By direct substitution, we have
−5(-4) − 15 ≤ f(x) ≤ (-4)² + 3(-4) + 1
Evaluate the exponents and the products
20 − 15 ≤ f(x) ≤ 16 - 12 + 1
Evaluate the difference
5 ≤ f(x) ≤ 5
This means that
f(x) = 5
So, we have
lim x→ −4 f(x) = 5
The method used is the direct substitution method
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How many rotational symmetries does this figure have?
The figure: F
The number of rotational symmetries that the figure has would be C. 1 at 360 degrees.
What is rotational symmetry ?The number of times the geometric figure is similar to the original figure after undergoing a full revolution is known as the order of rotational symmetry. The order of rotational symmetry is determined by how many times the rotated figure perfectly fits within the original figure.
When the Figure F is rotated, the only times that it can be rotated to be able to give the same figure of F, is once, and that once has to be a full revolution of 360 degrees.
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PLS HELP <33
Which of the numbers listed below are solutions to the equation? Check all
that apply.
|x = -25
A. 25
B. 0
C. 5
D. -5
E.-25
F. None of these
Answer:
There is no value of x that makes the equation be true since an absolute value can never be negative.
No solution
Step-by-step explanation:
Final question no more lives
who ever gives me correct answer will get brainliest
The time take to fill the pool will be 494 hours.
How to calculate the TimeInlet pipe fills in 38 hours = 1 pool
Inlet pipe fills in 1 hours = 1/38
Drain pipe empty in 39 hours = 1 pool
Drain pipe empty in 1 hour = 1/39
If both pipes are opened together then in pool fills in 1 hour = 1/38 - 1/39
= 1/1482
Therefore, 1/1482 fills in 1 hour.
. Therefore, 1/3 will be:
= 1/3 × 1482
= 494 hours.
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Solve it down guys :)
Refer to the attached images.
**Should be arctan(tanx)=x on the last page**
when x is equal to two the square root of another number ,s, plus the square root of two which one of the following formula correctly expressthis statement
Answer:
The correct formula that expresses the statement "when x is equal to the square root of another number, s, plus the square root of two" is:
x = √s + √2
This formula says that x is equal to the square root of s plus the square root of 2.
(1,-3),(4,-5),(2,2),(1,9) function or not function
Answer: Function
Step-by-step explanation:
How many quarts are in8.25 gallons?
Answer:
8.25 gallan=33 quart
Step-by-step explanation:
what is the perimeter of the following shapes
(a) 1.4 cm 0.7 cm 0.7 cm
The perimeter of each shape is obtained adding all of their outer side lengths.
How to obtain the perimeter of the polygon?The perimeter of a polygon is composed by the sum of the lengths of the outer edges of the figure.
Hence, for each polygon, you must identify the outer side lengths, and then add them.
Missing InformationThe problem is incomplete, hence the standard procedure to find the polygon of a shape was presented.
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Every month, the bakery orders blueberries to use in their blueberry muffins. They had a stock of 1.38 kilograms of blueberries. Last month, they used 1.12 kilograms. This month, they need a total of 1.26 kilograms of blueberries.
How many kilograms of blueberries do they need to order?
0.12
0.26
1
1.26
help me, please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The value of x in the proportion equals 50.
What is Proportion?Proportion is referred to as a part, share, or number considered in comparative relation to a whole. Proportion can be defined as when two ratios are equivalent, they are in proportion. It is an equation or statement used to show that two ratios or fractions are equal.
In proportion, if two sets of numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. Proportions are denoted using the symbol ":" or "=".
16/50 = x/156.25
x = 156.25 x 16 / 50
x = 2500 / 50
x = 50
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Consider the two triangles. How can the triangles be proven similar by the SSS similarity theorem?
Answer:if their corresponding sides are proportional.
Step-by-step explanation:
Faith needs 300 milliliters of a 57% acid solution for a chemistry experiment. She has two acid solutions, A and B, that can be mixed together to form the solution. Solution A is 50% acid, and Solution B is 60% acid. How much of each solution should she use to create the mixture?
She should use milliliters of Solution A.
She should use milliliters of Solution B.
The needed amount of each solution is given as follows:
90 milliliters of Solution B.210 milliliters of Solution B.How to obtain the amounts?The amounts are obtained using a system of equations, for which the variables are given as follows:
Variable x: amount of Solution A.Variable y: amount of Solution B.Faith needs 300 milliliters of the solution, hence:
x + y = 300.
x = 300 - y.
The percentage is of 57%, hence:
0.5x + 0.6y = 0.57 x 300
0.5x + 0.6y = 171.
Replacing the first equation into the second, the value of y is obtained as follows:
0.5(300 - y) + 0.6y = 171
0.1y = 21
y = 21/0.1
y = 210.
The value of x is then given as follows:
x = 300 - 210
x = 90.
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Find the values of x and y.
The value of x is 5, while the value of y is 24
How to solve for x and yIn order to get the value of x we would first have to find the value of y
The sum of angles on a straight line = 180
hence we would have:
5y + 2y + 12 = 180
7y = 180 - 12
7y = 168
y = 24 degrees
The angle that is made at R is 90 degrees
we would have
2y + 12 + 5x = 90
y = 24
2 * 24 + 12 + 5x = 90
60 + 5x = 90
5x = 90 - 60
5x = 30
x = 30 / 6
x = 5
Hence the value of x is 5
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(b) At the beginning of the term, Caroline bought p notebooks and Bert bought 5 notebooks less than Caroline. During the term, Caroline gave 2 of her notebooks to her sister. Caroline then had twice as many notebooks as Bert. By writing a suitable equation, calculate the number of notebooks Caroline now has.
The number of Caroline's textbook is 8
What is word problem?A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you've ever taken a math class, you've probably solved a word problem.
Represent the Notebook bought by Bert as q
q = p-5
p-2= 2q
p = 2q +2
substitute 2q +2
q = 2q+2-5
2q-q = 3
q = 3
substitute 3 for q
3 = p-5
p = 5+3
p= 8
Therefore Caroline's number of notebook is 8
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How to solve evaluate the limit
Step-by-step explanation:
for z -> 3 (3z - 2) -> (3×3 - 2) = 7
70°
160
What is the size in degrees of the missing angle
Answer:
40°
Step-by-step explanation:
The sum of interior angles in a quadrilateral is 360°, from the picture we have a 90°, 160° and 70°.
so
take off from 360° the know angles and we will find the angle "?"
360 - 90 - 160 - 70 =
40° (your answer)
I will give brainliest and ratings if you get this correct
The first order derivative of the given function is f'(x) = [tex](1+\frac{1}{2(x+x^{\frac{1}{2} })}(1+\frac{1}{2x^{\frac{1}{2} }} )) \frac{1}{2(x+(x+x^{\frac{1}{2} })^{\frac{1}{2} })^{\frac{1}{2} }}[/tex].
What is the differentiation?The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.
The given function is [tex]f(x)=\sqrt{x+\sqrt{x+\sqrt{x} } }[/tex].
The derivative using the chain and power rules is
f'(x) = [tex](1+\frac{1}{2(x+x^{\frac{1}{2} })}(1+\frac{1}{2x^{\frac{1}{2} }} )) \frac{1}{2(x+(x+x^{\frac{1}{2} })^{\frac{1}{2} })^{\frac{1}{2} }}[/tex]
Therefore, the first order derivative is f'(x) = [tex](1+\frac{1}{2(x+x^{\frac{1}{2} })}(1+\frac{1}{2x^{\frac{1}{2} }} )) \frac{1}{2(x+(x+x^{\frac{1}{2} })^{\frac{1}{2} })^{\frac{1}{2} }}[/tex].
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The angle y° and 49° are complementary,find the value y
Answer:
41°
Step-by-step explanation:
We know that,
y°+49°= 90°
y° = 90°-49°
y=41°
So, the value of y is 41°
The probability that someone files their taxes late is 0.351. If you are questioning 10 people, what is the probability
that 6 of them filed their taxes on time.
Answer:
0.209.
Step-by-step explanation:
The probability that someone files their taxes on time is 1 - 0.351 = 0.649.
To find the probability that 6 out of 10 people file their taxes on time, we can use the binomial distribution. The binomial formula for the probability of k success in n trials is given by:
P(k) = (n choose k) * p^k * (1-p)^(n-k)
Where (n choose k) is the number of combinations of n items taken k at a time, and p is the probability of success in a single trial.
So, for the problem at hand:
P(6) = (10 choose 6) * 0.649^6 * (1 - 0.649)^(10 - 6) = 0.209
Therefore, the probability that 6 out of 10 people file their taxes on time is approximately 0.209.
Jason wants to dine at five different restaurants during a summer getaway. If three of nine available restaurants serve seafood, find the number of ways that at least one
of the selected restaurants will serve seafood given the following conditions.
(a) The order of selection is important.
(b) The order of selection is not important.
(a) If the order is important, then the number of ways that at least one of the selected restaurants will serve seafood is
answer
C(9, 5) - C(6, 5) + C(3, 1) = 126 - 6 + 3 = 123
explanation
The first term, C(9, 5), represents the number of ways to select 5 restaurants out of 9, regardless of type. The second term, C(6, 5), represents the number of ways to select 5 non-seafood restaurants out of 6. To find the number of ways that at least one of the selected restaurants will serve seafood, we subtract the number of ways to select 5 non-seafood restaurants and add the number of ways to select exactly 1 seafood restaurant, represented by C(3, 1).
The result, 123, represents the number of ways that at least one of the selected restaurants will serve seafood.
Grant is thinking of two numbers. He says one of the numbers is twice the other number and the sum of the number is 42. What are the numbers?
On solving the provided question, we can say that by linear equation If The Grant is thinking of two numbers, they are 13 and 26.
What is a linear equation?A linear equatiοn is one that has the form y = mx+b in algebra. B is the slοpe, and m is the y-intercept. It's usual to refer tο the previous clause as a "linear equation with twο variables" because y and x are variables. The twο-variable linear equations knοwn as bivariate linear equations.
There are several instances οf linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred tο as being linear when an equation has the fοrm y = mx+b, where m stands for the slοpe and b for the y-intercept. When an equatiοn has the formula y = mx+b, with m denοting the slope and b the y-intercept, it is referred tο as being linear.
x be the first number and y be the secοnd number:
x = 2y
x + y = 39
Plug x = 2y in the other equation:
2y + y = 39
3y = 39
y = 13
x = 26
If The Grant is thinking of two numbers, they are 13 and 26. He claims that the total of the two numbers is 39 and that one of the numbers is double the other.
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