The domain of the function is [1, ∞) and the range of the function is [0,∞).
Domain and range:
The domain and range of a function are refers the set of all the inputs and outputs a function can give respectively.
Basically, domain takes all the possible input values from the set of real numbers whereas the range takes all the output values of the function.
Given,
Here we have the function
y = √x - 1
Now, here we need to find the domain and range of the function.
The given function is rewritten as,
√x - 1 > 0
Square both sides then we get,
x - 1 > 0
Add 1 on both sides then we get,
x > 1
Therefore, the domain is [1, ∞).
Similarly, let us consider, y ≥ 0
Therefore, the range is [0,∞).
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Suppose you have $10,000 in savings when the price level index is 100.
Instructions: Round your responses to the nearest whole number.
a. What is the real value of your savings if the price level increases by 10 percent for the year?
b. What is the real value of your savings if, instead, the price level declines by 5 percent for the year?
Answer:
a. $9,090.91
b. $10,526.32
Step-by-step explanation:
You want to know the value of your $10,000 savings when the price level (a) increases by 10%, and (b) decreases by 5%.
Price levelAs the price level goes up, the number of items that can be purchased with a given dollar amount goes down in inverse proportion.
a. Price level increaseWhen the price level increases by 10%, it is multiplied by 1 +10% = 1.10. The effective purchasing power of the savings will be inversely proportional to that:
$10,000/1.10 = $9,090.91 . . . "real value" of savings
b. Price level decreaseWhen the price level decreases by 5%, it is multiplied by 1 -5% = 0.95. The effective purchasing power of the savings will be inversely proportional, so will be ...
$10,000/0.95 = $10,526.32 . . . "real value" of savings
__
Additional comment
The price level index is usually normalized to a value of 100 at some specified point in time. An increase of 10% in price level would be reflected in an index value of 100×1.10 = 110. Effectively, this means that what did cost $100 at the reference time now costs $110.
With $10,000, you could have purchased 100 of those items, but now you can purchase only 90.91 of those items. Your purchasing power has changed in inverse proportion to the price level.
For the entire year, $9091 will be spent if prices rise by 10%.
In the event that prices drop by 5% for the entire year, $10,526.32
What is a Whole number?Integers include zero, a positive natural number, and a negative integer represented by a minus sign. The negative numbers are the inverse additions of the comparable positive numbers.
Given,
If the price index is 100, savings equal $10,000.
a) If prices increase by 10% annually, the following formula will be used to calculate the true value of the savings:
Real Value = Nominal Value x Prior Year CPI / Current Year CPI
According to the CPI:
= 100 + (100 x 10/100)
For the current year, = 110%.
The resultant value will be
= $10000 x 100/110
= $9090.90
b) If prices decline by 5% annually, the following formula will be used to calculate the true value of the savings:
Real Value = Nominal Value x Prior Year CPI / Current Year CPI
According to the CPI:
= 100 - (100 x 5/100)
for the current year, = 95%
Consequently, the true value will be:
= $10000 x 100/95
=$10,526.32
As a result, your savings would actually be worth $9090.90 if prices rose by 10% annually.
Alternatively, if prices fall by 5% over the course of the year, the actual worth of your savings is $10,526.32.
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Julie is given two points, (x,y) and (w,z). Which process can she use to find the distance between the points?
One option is to use the distance formula.
In this case, this is what Julie would be working with:
[tex]d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(x-w)^2+(y-z)^2}\\\\[/tex]
If Julie knew the values of x, y, w, and z, then she could find a numeric result for the distance (d).
Find the y intercept of the line y
4x+12
Answer:
12
Step-by-step explanation:
y = mx + b is the slope intercept form of a line. The b is the y-intercept.
In the equation y = 4x + 12, 12 is in the b spot.
Answer:
y- intercept = 12
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 4x + 12 ← is in slope- intercept form
with y- intercept c = 12
Suppose that the cost of an item, excluding tax, is $2.75x describes the cost , in dollars, of purchasing x units of that item. Evaluate the algebraic expression when x=90
The cost of the item is $247.5 when x=90
Let x represent the number of units of the item
Cost of item excluding tax = $2.75x
Algebra: The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. Creating a meaningful mathematical expression, it requires variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every discipline of mathematics, including trigonometry, calculus, and coordinate geometry.
Finding the cost of the item excluding tax when x=90 we get:
= 2.75*90
= 247.5
So, the cost is 247.5
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if 6 bushels of apples is equal to 24pecks of apples,what is the ratio of bushels of bushels to pecks?
Explanation:
6 bushels = 24 pecks
1 bushel = ??
[tex]\frac{6}{24}=\frac{1}{4}[/tex]Answer:
The ratio of bushels to pecks is 1/4
what is 10 divided by 3 1/3
Answer:
10 divided by 3 1/3 is;
[tex]3[/tex]Explanation:
We want to divide 10 by 3 1/3;
[tex]10\div3\frac{1}{3}[/tex]Firstly, let us convert the mixed fraction to improper fraction;
[tex]\begin{gathered} 10\div\text{ }\frac{3(3)+1}{3} \\ =10\text{ }\div\text{ }\frac{10}{3} \end{gathered}[/tex]Then we can proceed to divide;
[tex]\begin{gathered} 10\text{ }\div\text{ }\frac{10}{3} \\ 10\times\frac{3}{10} \\ =\frac{30}{10} \\ =3 \end{gathered}[/tex]Therefore, 10 divided by 3 1/3 is;
[tex]3[/tex]. 2 1 3 LAU 5 16 7 DO If angle 1 is x+74 and angle 8 is 2x - 1, what are the measures of angle and 87
Consider that the Alternate Exterior Angles are always equal for a transversal passing through two parallel lines.
The given diagram depicts two incline parallel lines and the vertical line acts as a transversal to them.
Now, angle 1 and angle 8 are alternate exterior angles so they must be equal,
[tex]\begin{gathered} m\angle1=m\angle8 \\ x+74=2x-1 \\ 2x-x=74+1 \\ x=75 \end{gathered}[/tex]So the measure of the angles is given by,
[tex]\begin{gathered} m\angle1=x+74 \\ m\angle1=75+74 \\ m\angle1=149 \end{gathered}[/tex]Thus, both the angles measure 149 degrees.
Since 12:00 am., a cold front has caused the tempurature in a particular city to decrease at a constant rate. At 2:00 a.m., the tempurature was 54 degrees Farenheit, and at 5:00 a.m., the tempurature was 45 degrees Fahrenheit. Which of the following statements is correct?
A. The tempurature at 12:00 a.m. was 57 degrees Fahrenheit.
B. The tempurature at 12.00 a.m was 60 degrees Fahrenheit.
C. The tempurature at 12:00 a.m was 63 degrees Fahrenheit.
D. The tempurature is decreasingn at a rate of 9 degrees Fahrenheit per hour.
Answer: B.
Step-by-step explanation: First, you find the difference between 2 and 5 =( 3 ), and 54 and 45 ( -9 ). Meaning the unit rate is -3. (-9/3 = -3)
The difference between 12:00 am and 2:00 am is 2 hours meaning 2 x 3 is 6. 54 + 6 = 60 meaning at 12:00 am it was 60 degrees Fahrenheit.
y=(x-5)^2 quadratic function and state the functions domain and graph
help with this question in attachment below
The value of x is 7 units
Length = 4x + 2 = 4 x 7 + 2
=> length = 30units
Breadth = 5x = 5(7 )= 35
Breadth = 35 units
Given,
Perimeter of the rectangle is 130 units
Length of the rectangle = 4x + 2
Breadth of the rectangle = 5x
To find the value of x
Now According to the question:
We know that;
Perimeter of a Rectangle = 2(l + b)
where, l = length of the rectangle
b = breadth of the rectangle
Now, plug the values in above formula :
130 = 2(4x + 2 + 5x)
130 = 2(9x + 2)
130 = 18x + 4
130 - 4 = 18x
126 = 18x
x = 126/ 18
x = 7
Hence, The value of x is 7 units .
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A species of animal is discovered on an island. Suppose that the population size P (t) of the species can be modeled by the following function, where time t is measured in years.P (t) = 800/(1+4e^-0.31t)
To find the initial population, we evaluate
[tex]P(t)=\frac{800}{1+4e^{-0.31t}}[/tex]at t=0:
[tex]\begin{gathered} P(0)=\frac{8_{}00}{1+4e^{-0.31\cdot0}}=\frac{8_{}00}{1+4e^0} \\ =\frac{8_{}00}{1+4}=\frac{800}{5}=160. \end{gathered}[/tex]Therefore, the initial population was 160 individuals.
To find the population after 10 years, we evaluate the given function at t=10:
[tex]\begin{gathered} P(10)=\frac{800}{1+4e^{-0.31\times10}}=\frac{800}{1+4e^{-3.1}} \\ \approx678. \end{gathered}[/tex]Therefore, the population after 10 years is 678 individuals.
Answer:
The initial population was 160 individuals.
The population after 10 years is 678 individuals.
The graph y= f(x) is shown. Translate it to get the graph of y = f(x-2)
The translation of two units right of the graph of y = x is graphed at the end of the answer.
TranslationTranslation is a transformation to the graph of a function or of a figure that keeps everything such as orientation and inclination stable, changing only the position of the graph.
The translations are movements to left, right, up or down, and each movement is represented as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.In this problem, the definition of the translation is given as follows:
y = f(x - 2).
Hence a = 2, and the function is shifted right 2 units.
Considering function y = x, the translated function is:
y = f(x - 2) = x - 2.
(each instance of x in the function is replaced by x - 2).
The graph of the two functions is shown at the end of the answer, which x - 2 being a shift right of 2 units of f(x).
Missing InformationThe function is not given, hence we suppose that it is of y = x.
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To indirectly measure the distance across a river, Kiran stands on one side of the river and uses sight-lines to a landmark on the opposite bank. Kiran draws the diagram below to show the lengths and angles that he measured. Find PR, the distance across the river. Round your answer to the nearest foot.
Okay, here we have this:
Considering the provided information and figure, we are going to calculate the requested measure, so we obtain the following:
We can see that the two triangles are similar because they have the same angles, so from this we have:
PR/RE=PO/OC
PR/195=(PR+160)/305
PR*305=(PR+160)195
305PR=195PR+31200
305PR-195PR=31200
110PR=31200
PR=31200/110
PR=3120/11
PR≈294 ft
Finally we obtain that PR, the distance across the river is approximately 294 ft.
Which of the following statements is false?A. A rhombus is a quadrilateral.B. A quadrilateral is a polygon with four angles.C. In quadrilateral PQRS, ∠P and ∠S are opposite angles.D. The diagonals of a rhombus are perpendicular and bisect each other.
We have the following statements and results.
A. A rhombus is a quadrilateral.
True. A rhombus is a quadrilateral all of which sides have the same length.
B. A quadrilateral is a polygon with four angles.
True. A polygon is a plane figure with at least three straight sides and angles, and typically five or more.
C. In quadrilateral PQRS, ∠P and ∠S are opposite angles.
False. If we have a quadrilateral PQRS, that means that ∠P and ∠S are consecutive angles, not opposite.
D. The diagonals of a rhombus are perpendicular and bisect each other.
True. It is true that the diagonals of a rhombus are always perpendicular and bisect each other.
Answer.
Statement C is false.
Usain Bolt is considered to be the fastest person on earth. He holds the record for the fastest 100 m (meters), ,which he ran in 9.58 s (seconds), in 2009. We'll assume that Bolt ran the race at a constant speed.
Which of the following equations, where t represents time in seconds and d represents distance in meters, describe a speed greater than Bolt's record-breaking speed in 2009?
Choose all answers that apply!
A. d=10t
B. d=10.2t
C. d=10.4t
D. d=10.45t
Khan Academy - Rates & proportional relationships
according to City high school's alumni records 375 students graduated in college in 2001 are these graduates 176 were female 100 and 47 of whom were accepted into college of the male graduate 100 were accepted to college.A) what is the probability that a 2001 graduate of City high School was accepted into collegeB) what is the probability that 2001 graduate of City high School was not a female C)what is the probability that a 2001 graduate of City high School was accepted into college or maleD) what is the probability of being a female given you were accepted into college.
We are asked to determine probabilities from a population of high school graduates. Let's remember that probability is defined as the quotient of desired events and the number of total events.
a) what is the probability that a 2001 graduate of City High School was accepted into college
To determine the probability we need to find the quotient of the number of students that were accepted into college and the total number of students. The total number of students accepted into college is 145 female plus 100 males, therefore, the probability is:
[tex]P(a)=\frac{145+100}{375}=\frac{245}{375}=0.653[/tex]Therefore, the probability is 65.3%.
b)what is the probability that 2001 graduate of City high School was not a female
To do this we will use the fact that the sum of the probabilities that a student is a female plus the probability that the student is not a female must be equal to 1.
[tex]P(\text{female)}+P(\text{not female)=1}[/tex]Therefore, solving for the probability that the student is not a female we get:
[tex]P(\text{not female)=1-P(female)}[/tex]The probability that the student is female is the quotient between the number of female students and the total number of students, therefore:
[tex]\begin{gathered} P(\text{not female)=1-}\frac{176}{375} \\ \\ P(\text{not female)=1-0.461} \\ P(\text{not female)=0.539} \end{gathered}[/tex]Therefore, the probability that the student is not a female is 53.9%.
c) what is the probability that a 2001 graduate of City high School was accepted into college or male
To determine this probability we need to have into account that the probability of event A or event B happening is the sum of both probabilities minus the probability of both events happening at the same time, therefore:
[tex]P(\text{accepted or male)=P(accepted)+P(male)}-P(\text{accepted and male)}[/tex]Replacing the probabilities we get:
[tex]P(\text{accepted or male)=}0.653+\frac{375-176}{375}-\frac{100}{375}[/tex]Solving the operations:
[tex]\begin{gathered} P(\text{accepted or male)=0.653+0.53-0.267} \\ P(\text{accepted or male)=0.916} \end{gathered}[/tex]Therefore, the probability that a student is accepted or male is 91.6%
d) what is the probability of being a female given you were accepted into college.
The probability of event A given event B is given by the following formula:
[tex]P(A\parallel B)=\frac{P(AandB)}{P(B)}[/tex]In this case, we have:
[tex]P(female\parallel accepted)=\frac{P(\text{female and accepted)}}{P(accepted)}[/tex]Replacing the probabilities:
[tex]\begin{gathered} P(female\parallel accepted)=\frac{\frac{147}{375}}{0.653} \\ \\ P(female\parallel accepted)=\frac{0.392}{0.653} \\ \\ P(\text{female}\parallel accepted)=0.6 \end{gathered}[/tex]Therefore, the probability is 60%.
Ronald's lemon cookie recipe calls for 3 1/3 cups of sugar. How much sugar would Ronald use to make 4 batches of cookies?
To make 4 batches of lemon cookie, Ronald will need 13.3 cups of sugar.
Firstly converting mixed fraction to fraction, thus getting the amount of cups of sugar required for 1 batch.
Number of cups of sugar required for 1 batch = (3×3 + 1)/3
Performing multiplication and addition in numerator
Number of cups of sugar required for 1 batch = 10/3
Number of cups of sugar required for 4 batches = 10/3 × 4
Performing multiplication to find the number of cups of sugar required
Number of cups of sugar required for 4 batches = 40/3
Performing division to find the number of cups in decimal
Number of cups of sugar required for 4 batches = 13.3
Thus, 13.3 cups of sugar will be needed by Ronald.
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What is the functional value of the ceiling function: f(1.5)
f is the ceiling function
f(1.5) = 2
Julie plans to put a fence around her square shaped backyard. The length of one side measures 2n-3feet. Write a simplified expression to represent the perimeter of the backyard.
We have the following:
Since it is a square, the sides are equal, and the perimeter is the sum of all the sides, therefore it would be
[tex]\begin{gathered} p=4\cdot l \\ l=2n-3 \\ \text{replacing} \\ p=4\cdot(2n-3) \\ p=8n-12 \end{gathered}[/tex]The answer is 8n - 12
which of the following is the graph of y=-5+2x
we have the equation
y=5+2x
this is the equation of the line
the slope is positive m=2
the y-intercept is (0,5)
the x-intercept is (-2.5,0)
using a graphing tool
the graph in the attached image
please wait a minute
answer is option CI'll give brainliest!
Answer: it is 40 times greater
Step-by-step explanation:
please give brainlyist
Answer:
40x larger
Step-by-step explanation:
9.6 is 4 times larger than 2.4
and 10^4 is 10 times larger than 10^3
Which expression is NOT equivalent to 40 + 20?
O 5(8+20)
O2(20 + 10)
○ 5(8+4)
○ 10(4+2)
Submit Answer
Answer:
Option 1
Step-by-step explanation:
[tex]40+20=60 \\ \\
5(8+20)=5(28)=140 \\ \\ 2(20+10)=2(30)=60 \\ \\ 5(8+4)=5(12)=60 \\ \\ 10(4+2)=10(6)=60[/tex]
Calculate the area of each figure. Which figure has the greatest area?
a) Area of the parallelogram = b x h
= 9 cm x 7 cm
= 63 cm^2
Find the APR (rounded to the nearest tenth of a percent) for the loan. Purchase a living room set for $3,600 at 8 % add- on interest for 3 years.
The annual percentage rate (APR) for the loan of $3,600 at 8% add-on interest for 3 years is 15.6%.
What is the annual percentage rate?The annual percentage rate is the nominal or effective interest rate charged on a loan for a year, unlike the Monthly Percentage Rate (MPR), which is a monthly rate.
The annual percentage rate can be calculated by using the formula:
APR = 2Nr/N + 1
N = number of payments
r = the add-on interest rate
N = 3 years = 36 months (12 x 3)
r = 8% or 0.08 (8/100)
APR = (2 x 36 x 0.08)/(36 + 1)
= 5.76/37
= 0.15.57
= 15.57%
= 15.6%
Thus, with an 8% interest rate for 3 years, the APR is 15.6%.
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A restaurant frequently offers a special prix fixe meal and has been charging $140 per person for the event. At that price, they’ve been averaging 50 customers each time. Their marketing firm has convinced them that they’ll gain a customer for every dollar they lower the cost of the event, and conversely lose a customer for every dollar they raise the cost. Their fixed cost per event is $2600 and preparing each customer’s meal costs an additional $40. What are the break-even points in terms of customers served? Write the exact answer. Do not round. Separate multiple answers with a comma.
The milestones at which we will be profitable in terms of the number of consumers serviced are going to be (20, $170), and (130, $60).
How to calculate the break-even point?In several aspects of commerce and finance, a break-even point is an important concept to understand. In the context of finance and accounting, it is a reference to the level of output at which the total production income matches the entire production expenses.
When it comes to financing, the moment at which an investment is considered to have broken even is known as the "break-even point."
When the market price of an underlying asset hits the level at which a buyer will not incur a loss, this is referred to as the break-even point in the options trading market.
In contrast, the point at which a buyer will not incur a loss.
The following will serve as examples of the model:
n - n1 = m(p - p1)
n - 50 = -1(p - 140)
n = -p + 190
Where
Revenue = price * quantity
Revenue = p * n
Revenue = (190 - n) * n
[tex]Revenue= 190n - n^2[/tex]
Cost = 40n +2600
At break-even, revenue = cost
[tex]190n - n^2 = 40n + 2600[/tex]
[tex]n^2 - 150n + 2600 = 0.[/tex]
n = 20 p = 170
n = 130 p = 60
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Find the percent of change
Original $85 new $68
Answer: -20%
Step-by-step explanation:
new-old divided by old
68-85=-17
-17/85=-0.2
-0.2x100=-20
-20%
Which of the following is equal to the expression below?(4 53ОА.1415B.1OB.142O c. – 42D. -415
Recall the following properties of exponentials:
[tex]\begin{gathered} (a^n)^m=a^{n\times m} \\ \\ a^{-n}=\frac{1}{a^n} \end{gathered}[/tex]Use these two properties in that order to find another expression for the same number:
[tex](4^{-5})^3=4^{-5\times3}=4^{-15}=\frac{1}{4^{15}}[/tex]Therefore, the correct choice is option A)
[tex]\frac{1}{4^{15}}[/tex]Simplify [tex](\sqrt{5})(\sqrt[3]{5})[/tex]
The value of the indices given will be
[tex](\sqrt{5}) (\sqrt[3]{5})[/tex] simplifies to give [tex]5^{\frac{5}{6} }[/tex] or [tex]\sqrt[6]{3125}[/tex][tex]\sqrt[6]{3125}[/tex]
How can to simply [tex](\sqrt{5}) (\sqrt[3]{5})[/tex]The indices concept can be used for this simplification. An index is the small number which tells us how many times a term had been multiplied by itself.
[tex](\sqrt{5}) (\sqrt[3]{5}) = 5^{\frac{1}{2} } . 5^{\frac{1}{3} }\\\\(\sqrt{5}) (\sqrt[3]{5}) =5^{\frac{1}{2} +\frac{1}{3} }\\\\(\sqrt{5}) (\sqrt[3]{5}) =5^{\frac{2+3}{6}[/tex]
[tex](\sqrt{5}) (\sqrt[3]{5}) = 5^{\frac{5}{6}} = \sqrt[6]{5^{5} } = \sqrt[6]{3125}[/tex]
Therefore, the result of the simplification is [tex]5^{\frac{5}{6} }[/tex] or [tex]\sqrt[6]{3125}[/tex]
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Please help with math question
Answer:
x-intercept is at (18, 0)
y-intercept is at (0, 360)
In a cricket match, you have a squad of 15 players and you need to select 11 for a game. The two opening batsmans are fixed and the rest of the players are flexible. How many batting orders are possible for the game?
1365 batting orders are possible for the game.
Given,
In the question:
In a cricket match, you have a squad of 15 players and you need to select 11 for a game.
To find the how many batting orders are possible for the game?
Let's Know:
What are combination?
Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects.
Combination formula
ⁿCr = n! / ((n – r)! r!
n = the number of items.
r = how many items are taken at a time.
Substitute the values in above formula :
15! / 11! (15 - 11)!
= 15! / 11! 4!
= 15 × 14 × 13 × 12 / 4 × 3 × 2
= 1365 orders
Hence, 1365 batting orders are possible for the game.
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