Use interval notation to write the intervals over which fis (a) increasing, (b) decreasing, and (c) constant.
y =f(x)
The intervals of each behavior of the function are given as follows:
a) Increasing: (-∞, -1).
b) Decreasing: (-1, 1).
c) Constant: (1, 3).
How to classify the function as increasing, decreasing or constant?The function is increasing when the graph moves right and up.The function is decreasing when the graph moves right and down.The function is constant when the graph of the function is an horizontal line.More can be learned about functions at https://brainly.com/question/24808124
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¿Qué volumen de solución de ácido a 60% debe mezclarse con una solución a 30% para producir
300 mililitros de solución al 50%?
Answer:
Step-by-step explanation:
To solve this problem, we must first use an equation that reflects the amount of acid in each solution and its relationship to the total volume of the resulting solution. We can use the following equation:
(C1 * V1) + (C2 * V2) = (C3 * V3)
Where:
C1 = concentration of the acid solution at 60% (in percent)
V1 = volume of the acid solution at 60% (in ml)
C2 = concentration of the acid solution at 30% (in percent)
V2 = volume of the 30% acid solution (in ml)
C3 = concentration of the resulting 50% acid solution (in percent)
V3 = volume of the resulting 50% acid solution (in ml)
In this case, we know the total volume of the resulting solution (V3 = 300 ml) and the desired concentration (C3 = 50%). We also know the concentration of one of the original solutions (C1 = 60%). So we can plug the known values into the equation:
(60 * V1) + (30 * V2) = (50 * 300)
Clearing V1:
V1 = (300 * 50 - 30 * V2) / 60
Now that we have V1 as a function of V2, we can solve the problem to find the volume of the 60% acid solution to mix with the 30% solution. Substitute the known values into the equation:
V1 = (300 * 50 - 30 * V2) / 60
V1 = (15000 - 30 * V2) / 60
V1 = 250 - (V2 / 2)
We can use this last equation to find the volume of the 30% solution that we must mix with the 60% solution:
V2 = 2 * (250 - V1)
Clearing V1:
V1 = 250 - (V2 / 2)
V1 = 250 - (2 * (250 - V1) / 2)
V1 = 250 - 250 + V1
V1 = 250
Therefore, we must mix 250 ml of 60% acid solution with 250 ml of 30% solution to produce 300 ml of 50% solution.
Solve for x Each figure is a trapezoid
The value of x in the trapezoid is 12
How to determine the valueIt is important to note that the properties of a trapezoid are;
Opposite sides of a trapezoid are equalOpposite angles of a trapezoid are equalThe diagonals bisect each other at right angleThe sum of the interior angles is 360 degreesNow, let's equate the angles, we getl
7x + 21 = 105
collect the like terms, we get;
7x = 105 - 21
subtract the like terms
7x = 84
Make 'x' the subject of formula
x = 84/7
Divide the values
x = 12
Hence, the value is 12
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8m
6m
10m
5m what is the area of this shape
The area of the given composite shape with two rectangles is 68 m²
What is a rectangle?
There are four right angles on the quadrilateral that forms the rectangle. Every corner or vertex has a right angle where the two sides meet. It differs from a square, which has all of its sides of equal length, in that the opposite sides of the rectangle are equal in length. Two dimensions and flatness combine to make a rectangle.
The figure can be divided into a rectangle with a length of 8m and breadth of 6m and another rectangle of length 5m and breadth = (10-6) = 4m.
To find the area of the whole figure, we first find the areas of small and big rectangles and sum their areas.
Area of small rectangle = length * breadth = 5*4 = 20 m²
Area of big rectangle = length * breadth = 8 * 6 = 48 m²
Therefore the area of the given composite shape with two rectangles is 20+48 = 68 m².
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What is the total surface area of the rectangular prism?
Answer:a rectangular prism has height 4m, length 6m & width 5m
thus the surface consist of two 4*6 vertical surfaces
two 4*5 vertical surfaces
& two 6*5 top & bottom surfaces
that is
2(4*6) = 48
2(4*5) = 40
2(6*5) = 60
total surface area = 48+40+60 = 148m²
Step-by-step explanation:
Please help me with this please
Answer:
He will need 64 ft of fencing
Step-by-step explanation:
To determine the amount of fencing, we need to find the perimeter.
P = 2 (l+w) where l is the length and w is the width
P = 2(22+10)
P = 2(32)
P = 64
He will need 64 ft of fencing
A group of friends wants to go to the amusement park. They have no more than $295
to spend on parking and admission. Parking is $11.50, and tickets cost $39
person, including tax. Which inequality can be used to determine x, the maximum
number of people who can go to the amusement park?
Answer:
295>_ 39x+11.50
Step-by-step explanation:
the >_ means less than or equal to.
Maya had $32. She spent all the money on buying 3 notebooks for x dollars each and 4
packs of index cards for y dollars each. If Maya had bought 5 notebooks and 5 packs of
index cards, she would have been short $18. Which system of equations represents this
situation?
O 3x + 4y = 32 and 5x + 5y = 50
O 3x+4y= 32 and 5x + 5y = 18
O 3x + 4y = 50 and 5x - 5y = 18
O 3x - 4y= 32 and 5x - 5y = 50
The system of equations which represents this
situation is 3x+4y= 32 and 5x + 5y = 18.
The correct answer choice is option B
Which system of equations represents the situation?Amount with Maya = $32
Amount spent on each notebook = x
Number of notebook = 3
Amount spent on each pack of index cards = y
Number of index cards = 4
Maya bought 5 notebooks and 5 packs of
index cards
$18 short = $32 - $18
= $14
3x + 4y = 32
5x + 5y = 14
In conclusion, the system of equation is 3x+4y= 32 and 5x + 5y = 18.
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Circles and answers please just need help tthank you so mwa
On solving the provided question, we can say that In decimals r = 3.8799 and d = 7.7598
What is decimal?Integer and non-integer numbers are οften expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded tο include non-integer values. Decimal notation is the name fοr the method used to represent numbers in the decimal system.
A decimal is a number with a whοle and a fractional component. Decimal numbers, which are in between integers, are used tο express the numerical value οf full and partially whole amounts.
the lengths (in inches) οf the radius and the diameter οf a circle with area 47.25 in'.
Area = πr²
47.25 = 3.14 × r × r
r × r = 15.0541401274
In decimals
r = 3.8799
d = 7.7598
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How do we find X and Y?
Step-by-step explanation:
answer is in the picture
Multiple Step-Find the value of X.
117
93
(6x+9)
87
The value of x is given as follows:
x = 9.
How to obtain the sum of the interior angle measures?The sum of the interior angle measures of a polygon with n sides is given by the equation presented as follows:
S(n) = 180 x (n - 2).
The figure for this problem has four sides, hence the sum of the internal angle measures is given as follows:
S(4) = 180 x (4 x 2)
S(4) = 360º.
Adding the four angle measures and equaling them to 360º, the value of x is obtained as follows:
117 + 93 + 87 + 6x + 9 = 360
306 + 6x = 360
6x = 54
x = 54/6
x = 9.
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How far did Mai run in her first 30 minutes
A researcher recorded the number of people in each vehicle that passed through a checkpoint. The table above shows the percent distribution for the 420 vehicles that passed through the checkpoint yesterday morning. How many of the 420 vehicles contained at least 3 people?
*
1 point
Total 105 of the 420 vehicles contained at least 3 people. Therefore , option C is correct.
Given :
percent distribution : 40% , 35% , 15% , 7% , 3%
Vehicles : 420
First, add the percentage of cars containing 3 people, 4 people, and 5 or more people:
15% + 7% + 3% = 25%
Thus, 25% of the cars contained at least 3 people, so use that to calculate the number of cars:
420 × 0.25 = 105 cars.
Hence , Total 105 of the 420 vehicles contained at least 3 people. Therefore , option C is correct.
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Complete question:
A researcher recorded the number of people in each vehicle that passed through a checkpoint. The table above shows the percent distribution for the 420 vehicles that passed through the checkpoint yesterday morning.
How many of the 420 vehicles contained at least 3 people?
A. 42
B. 63
C. 105
D. 315
Name the relationship
1). Adjacent angle
2). Alternate angles
3). Corresponding angles
4). Vertical angles
5). Supplementary angles
It looks like 1) adjacent angles.
According to a 2009 Reader's Digest article, people throw away approximately 13% of what they buy
at the grocery store. Assume this is the true proportion and you plan to randomly survey 90 grocery
shoppers to investigate their behavior. What is the probability that the sample proportion exceeds
0.12?
Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.
(Enter your answer as a number accurate to 4 decimal places.)
The probability that the sample proportion exceeds 0.12 is given as follows:
0.6103 = 61.03%.
How to obtain probabilities using the normal distribution?
The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].The parameters of the binomial distribution are given as follows:
n = 90, p = 0.13.
Hence the mean and the standard error are given as follows:
[tex]\mu = 0.13[/tex][tex]s = \sqrt{\frac{0.13(0.87)}{90}} = 0.0354[/tex]The probability that the sample proportion exceeds 0.12 is one subtracted by the p-value of Z when X = 0.12, hence:
Z = (0.12 - 0.13)/0.0354
Z = -0.28
Z = -0.28 has a p-value of 0.3897.
Hence:
1 - 0.3897 = 0.6103.
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Select the correct answer.
Which statement describes the solutions of this equation?
(X/3) + (x-1/x+4) = (x+3/x+4) help please
The statement describes the solutions of this equation is
The Equation have two valid solution and No Extraneous solution.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
x/3 + (x-1)/ (x+ 4)= (x+3)/ (x+4)
Now, simplifying the above Expression
(x² + 4x + 3x - 3) / 3(x+4) = (x+3)/ (x+4)
(x² + 4x + 3x - 3) / 3 = (x+3)
x² + 7x -3 = 3(x+3)
x² + 7x -3 - 3x - 9 = 0
x² + 4x - 12 = 0
Solving the above Quadratic Equation
x² + 6x- 2x - 12 = 0
x(x+6)- 2(x+6)= 0
(x-2)(x+6)= 0
x= 2, -6.
So, the Equation have two valid solution and No Extraneous solution.
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For every 3 lemons you buy at a farm stand, the total cost increases by $1.80.
The constant of proportionality is
An equation that relates the total cost y and the number of lemons x is y=____x
Use the equation you wrote to complete the table.
The constant of proportionality is 0.60
The equation is y = $0.60x.
Here is the completed table
Number of lemons Total cost
4 $2.40
7 $4.20
15 $9
18 $10.80
What is the total cost of lemons?Direct variation is when two variables move in the same direction. As the number of lemons bought increases, the total cost increases.
The equation that represents direct variation is:
y = kx
Where:
y = total cost k = constant of proportionality x = number of lemons$1.80 = 3k
k = $1.80 / 3
k = $0.60
y = $0.60x
Total cost of 4 lemons= $0.60 x 4 = $2.40
Total cost of 18 lemons= $0.60 x 18 = $10.80
Number of lemons that cost $4.20 : 4.20 / 0.6 = 7
Number of lemons that cost $9 : 9 / 0.60 = 15
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Find the common ratio of the geometric sequence
17,51,153
Answer:
Common ratio, r = 3
Step-by-step explanation:
Common ratio is given by the ratio of one of the terms to the previous term and is a constant for the entire sequence
Here the first term is 17
Second term is 51
Second Term ÷ First Term
= 51 ÷ 17 =3
Third Term ÷ Second Term
= 153 ÷ 51 = 3
So common ratio is 3
In general, if aₙ is the nth term and aₙ₊₁ then the common ratio is given by:
aₙ₊₁ / aₙ
RECORDING SNEET
Naper is buying fabric to make pillows. At the store, 3 yards of
annel fabric costs $12.60, and 5 feet of fleece fabric costs $8.75.
know the units need to be the same to compare the prices.
suy the length of the flannel fabric to feet.
From unit prices gotten, the price of one feet of annel fabric is cheaper than the price of one feet of fleece fabric.
How to find unit prices?A unit price is defined as the price for one item or measurement, such as a pound, a kilogram, or a pint. This can be used to compare the same type of goods sold in varying weights and amounts.
The parameters are;
3 yards of annel fabric costs $12.60
5 feet of fleece fabric costs $8.75.
From conversion units;
1 yard = 3 feet
Thus;
3 yards = 3 * 3 = 9 ft
Thus;
Unit price of Annel fabric = 12.6/9 = $1.4 per ft
Unit price of fleece fabric = 8.75/5 = $1.75 per ft
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The perimeter of a triangle is 39 inches. If the length of the shortest side is 1/2 the length of the longest side, and the length of the third side is 1 less than the length of the longest side, what is the length of each side?
1. what are the three equations that are used.
2. what are the lengths of the sides?
(the shortest side, the longest side, and the third side.
The equations used are:
Longest side = a
Shortest side = 1/2 x a = 1/2a
Third side = a - 1
The shortest side is 8 inches, the longest side is 16 inches and the third side is 15 inches.
What are the length of the sides?The perimeter of a triangle is the sum of the length of the three sides of the triangle.
Let the following expressions represent the lengths of the sides of the triangle:
Longest side = a
Shortest side = 1/2 x a = 1/2a
Third side = a - 1
Perimeter = a + 1/2a + a - 1 = 39
a + 1/2a + a = 39 + 1
2a + 1/2a = 40
2 1/2a = 40
5/2a = 40
a = 40 x 2/5
a = 16 inches
Shortest side = 1/2 x 16 = 8 inches
Third side = 16 - 1 = 15 inches
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16. At Target, a shirt that costs $25 goes on sale for $15. What is the
percent of decrease in the price?
O 40 percent increase
O 7 percent decrease
O40 percent decrease
O7 percent increase
Answer: Decreased 40%
Step-by-step explanation:
Alright, we know they reduced $10.00 (25-15)
Now all we have to do is find the percentage, 10 is how much of 25?
10/25 =0.4
(to get 0.4 to a percentage multiply by 100)
The price was decreased by 40%
The area of a certain desert (Desert 1) is six times the area of another desert (Desert 2). If the sum of
their areas is 21,000,000 square miles, find the area of each desert.
Area of desert 1 is 18,000,000 square miles and area of desert 2 is 3,000,000 square miles.
What is meant by Area?Area of a two dimensional shape is the total region which is bounded by the object's shape.
Let A₁ and A₂ be the area of Desert 1 and Desert 2 respectively.
Given,
Area of a Desert 1 is six times the area of Desert 2.
A₁ = 6 A₂
The sum of their areas is 21,000,000 square miles.
A₁ + A₂ = 21,000,000
Substituting A₁ = 6 A₂ in A₁ + A₂ = 21,000,000 ,
6 A₂ + A₂ = 21,000,000
7 A₂ = 21,000,000
A₂ = 21,000,000 / 7
A₂ = 3,000,000 square miles
A₁ = 6 A₂
= 6 × 3,000,000
= 18,000,000 square miles
Hence the areas of each desert is 18,000,000 square miles and 3,000,000 square miles.
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PLEASE HELP (IMAGE ATTACHED)
It says my answer needs to be more simplified but I don’t understand
Answer:
-5x⁵ +2x² -3/x³
Step-by-step explanation:
You want the quotient and remainder of (-15x⁸ +6x⁵ -9)/(3x³).
DivisionThe quotient and remainder can be found by dividing term by term.
[tex]\dfrac{-15x^8+6x^5-9}{3x^3}=\dfrac{-15x^8}{3x^3}+\dfrac{6x^5}{3x^3}-\dfrac{9}{3x^3}\\\\\\=\boxed{-5x^5+2x^2-\dfrac{3}{x^3}}[/tex]
__
Additional comment
The exponent rule is (a^b)/(a^c) = a^(b-c).
<95141404393>
Explain how you would solve negative x = 9 algebraically what inverse operation ?should be used is there an invisible number in front of x ?if so what is it? if not how do you solve this?
The solution to the equation "negative x = 9" is "x = -9". There is no invisible number in front of "x" in this equation.
Solving the equation "negative x = 9" algebraicallyTo solve the equation "negative x = 9" algebraically, we want to isolate the variable "x" on one side of the equation.
First, we notice that "negative x" means "-x", so we can rewrite the equation as:
-x = 9
To isolate "x", we need to perform an inverse operation on both sides of the equation. Since "-x" means the opposite of "x", we need to perform the opposite operation, which is to add "x" to both sides:
-x + x = 9 + x
Simplifying the left-hand side by canceling out the "-x" and "+x", we get:
0 = 9 + x
We can further simplify this equation by subtracting 9 from both sides:
0 - 9 = 9 + x - 9
-9 = x
So the solution to the equation "negative x = 9" is "x = -9".
There is no invisible number in front of "x" in this equation, so we don't need to worry about any additional steps or calculations.
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A new bank customer with $3,000 wants to open a money market account. The bank is offering a simple interest rate of 1.2%
Answer:
Alright, so we want to know how much that can be earned in one year. So that's going to be 3000. And this is simple interest. So this is one plus 0.011, which equals $3,033. And that's the solution to this exercise.
Answer:
$3,036
Step-by-step explanation:
The new customer can open a money market account. The bank will deposit $3,000 into the account.
The bank will pay 1.2% (0.012) in interest every year. This interest will increase the original amount to $3,036.
Gabrielle's age is three times Mikhail's age. The sum of their ages is 64. What is Mikhail's age?
Answer:
16 years old
Step-by-step explanation:
Let's call Mikhail's age "x". Gabrielle's age is 3 times that, so her age is 3x. The sum of their ages is 64, so:
x + 3x = 64
4x = 64
x = 16
So, Mikhail's age is 16 years old.
What is the average rate of change? Problem in the picture
The average rate of change over the interval (-1, 2) is; 3
What is the average rate of change over an interval?The formula for the average rate of change over an interval (a, b) is expressed as;
f'(x) = [f(b) - f(a)]/[b - a]
We want to find the average rate of change over the interval (-1, 2). Thus;
a = -1 and b = 2
Thus;
f(-1) = -4
f(2) = 5
Thus;
f'(x) = (5 - (-4))/(2 - (-1))
f'(x) = 9/3
f'(x) = 3
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Anyone know the answers for Domain and rqnge digital escape puzzle 3?
The domain and the range of a function/graph/relation are defined as follows:
Domain: set of input values.Range: set of output values.What are the domain and range of a function?The domain of a function is the set that contains all possible input values of the function/relation, hence it is composed by the values of x.The range of a function is the set that contains all possible output values of the function/relation, hence it is composed by the values of y.Missing InformationThe problem is incomplete, hence the concepts of domain and range are presented, and then they are used to obtain the domain and the range.
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HURRRRRRYYYYYYYYYYYYYYYYYYYYYYYY Drag numbers to show which are closest to ‐1
and ‐1/4
on the number line.
The number that is closest to -1 is -0.82 while the number that is closest to -1/4 is -0.28.
What are the closest numbers?In order to obtain the numbers that are close to a given number, we need to place the numbers side by side for a better understanding. For instance, the number 3 is closer to number 1 while the number 9 is closer to number 10.
Given the number line above, we can arrive at the conclusion that -0.82 is closer to -1 because by approximating the decimal, we will arrive at figure 1. Also, the number, -0.28 is closer to -1/4 or - 0.25 when converted to decimal.
Options;
A. -0.28
B. -0.82
C. -4/5
D. -1/5
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Required information
[The following information applies to the questions displayed below.]
University Car Wash built a deluxe car wash across the street from campus. The new machines cost $219,000 including
installation. The company estimates that the equipment will have a residual value of $19,500. University Car Wash also
estimates it will use the machine for six years or about 12,500 total hours. Actual use per year was as follows:
Year
123456
Hours Used
2,800
1,400
1,500
2,500
2,300
2,000
Answer:
Step-by-step explanation:
Calculate the total hours used: We add up the hours used each year to find the total hours used:
2,800 + 1,400 + 1,500 + 2,500 + 2,300 + 2,000 = 12,500
Calculate the total depreciation: We subtract the residual value from the cost to find the total depreciation:
$219,000 - $19,500 = $199,500
Calculate the annual depreciation expense: We divide the total depreciation by the number of years to find the annual depreciation expense:
$199,500 / 6 = $33,250
Calculate the depreciation expense per hour: We divide the annual depreciation expense by the estimated total hours to find the depreciation expense per hour:
$33,250 / 12,500 = $2.66
So the depreciation expense per hour is $2.66.
Calculate the depreciation expense for each year: We multiply the hours used each year by the depreciation expense per hour to find the depreciation expense for each year:
Year 1: 2,800 * $2.66 = $7,448
Year 2: 1,400 * $2.66 = $3,724
Year 3: 1,500 * $2.66 = $3,990
Year 4: 2,500 * $2.66 = $6,650
Year 5: 2,300 * $2.66 = $6,118
Year 6: 2,000 * $2.66 = $5,320
So the depreciation expense for each year is:
Year 1: $7,448
Year 2: $3,724
Year 3: $3,990
Year 4: $6,650
Year 5: $6,118
Year 6: $5,320
