Answers
y=ab^x
Where a is the y-intercept/starting point and b is the value that x exponentially grows or decays.
From the given equation, the two graphs with other intercepts (not 4) can be removed.
Since b is between 0 and one, this function should be decaying.
Next calculate the value of x when y=1.
1=4(0.5)^x
1/4=(1/2)^x
log₀₋₅(1/4)=x
2=x
Check which of the graphs have y=1, x=2. This would be the second graph, which would represent the equation y=4(0.5)^x
Hope I helped :)
In this exercise we have to be aware of the type of graph we have and identify its formula, like this:
The second graph
As it is a graph of the equation of an exponential, we have that its form is given by:
[tex]y=ab^x[/tex]
Where:
y-intercept/starting point b is the value x exponentially grows or decays.Calculating the value of X when Y is equal to 1, we have:
[tex]1=4(0.5)^x \\1/4=(1/2)^x \\log_{0.5}(1/4)=x \\x=2[/tex]
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Related Questions
The formula v = square root of 64h gives the velocity v in feet per second of an object that has fallen h feet. find the velocity of an object that has fallen 76 feet. round to the nearest hundredth.
Answers
h = 76
V = sqrt (64 * 76)
V = sqrt 4864
V = 69.742 rounds to 69.74 feet per second <=
Answer:
69.74 feet per second is the velocity of an object that has fallen 76 feet
Step-by-step explanation:
As per the statement:
The formula v = square root of 64h gives the velocity v in feet per second of an object that has fallen h feet.
⇒[tex]v = \sqrt{64h}[/tex]
where, v is the velocity in feet per second and an object that has fallen h feet.
We have to find the velocity of an object that has fallen 76 feet.
⇒ h = 76 feet.
Substitute in the given formula we have;
[tex]v = \sqrt{64 \cdot 76} = \sqrt{4864} = 69.7423831[/tex] feet per second
Therefore, the velocity of an object that has fallen 76 feet to the nearest hundredth is, 69.74 feet per second
Jonas bought 3 books. Each book was the same price. He also used a coupon that takes $20 off the total cost. What expression can be used to represent the total purchase?
Answers
Final answer:
The expression to represent Jonas's total purchase is 3x - $20, where x is the price of one book.
Explanation:
To create an expression that represents the total purchase of Jonas's books, let's denote the price of each book as x. Jonas bought 3 books at the same price, so the cost of the books is 3x. However, with the coupon, Jonas gets $20 off the total cost. Therefore, the expression that represents the total purchase is:
3x - $20
This expression first calculates the total cost of the books (3 times the price of one book) and then subtracts the $20 discount from the coupon.
Percy works two part-time jobs to help pay for college classes. On Monday, he works 3 hours at the library and 2 hours at the coffee cart and earns $36.50. On Tuesday, he works 2 hours at the library and 5 hours at the coffee cart and earns $50. His hourly wage at the library, x, and hourly wage at the coffee cart, y, can be determined using the system of equations below. 3x + 2y = 36.50 2x + 5y = 50.00 At which job does Percy earn the greater hourly wage? How much does Percy earn each hour at this job? Percy earns a greater hourly wage of $7.00 at the library. Percy earns a greater hourly wage of $7.00 at the coffee cart. Percy earns a greater hourly wage of $7.50 at the library. Percy earns a greater hourly wage of $7.50 at the coffee cart.
Answers
Answer:
Percy earns a greater hourly wage of $7.50 at the library.
Step-by-step explanation:
A rancher needs to enclose two adjacent rectangular corrals, one for cattle and one for sheep. if the river forms one side of the corrals and 330330 yd of fencing is available, find the largest total area that can be enclosed.
Answers
The sides to be fenced is three equal sides plus one other side. Let the length of the coral be x, then the perimeter of the sides to be fenced is given by 3x + the other side = 330
Thus, the sides sides of the rectangle formed by the two adjacent corals are x and 330 - 3x.
The area of a rectangle is given by length x width.
Thus, the area of the corals to be enclosed is given by
[tex]Area=x(330-3x)=330x-3x^2[/tex]
For the area to be maximum, the differentiation of the area with rexpect to x will equal 0.
Thus,
[tex] \frac{dA}{dx} =330-6x=0 \\ \\ \Rightarrow6x=330 \\ \\ \Rightarrow x=55[/tex]
Therefore, the largest total area that can be enclosed is given by
[tex]Area=330x-3x^2 \\ \\ =330(55)-3(55)^2 \\ \\ =18,150-9,075 \\ \\ =9,075\ yd^2[/tex]
I'm not sure how to answer this question. Could someone please help explain it?
use the graph of the parent function, f(x)=sqrt x, to describe the transformation for the graph of g(x)=sqrt x-5
A. The graph of g(x) is the graph of f(x) shifted up 5 units
B. The graph of g(x) is the graph of f(x) shifted down 5 units
C. The graph of g(x) is the graph of f(x) shifted right 5 units
D. The graph of g(x) is the graph of f(x) shifted left 5 units.
I think the answer should either be down 5 or right 5 but I still don't quite understand.
thank you!
Answers
The function f, takes a number x, and produces the square root of it, for example we have the points:
(1, 1), (4, 2), (25, 5), (100, 10).
The function [tex]\displaystyle{ g(x)= \sqrt{x-5} [/tex], takes a value x, subtracts it 5, and then produces the square root of this difference.
So to produce the values 1, 2, 5, 10 given in the previous function, we need to
plug in the function not 1, 4, 25, and 100, but 6, 9, 30, 105.
Comparing : (1, 1), (4, 2), (25, 5), (100, 10) of (x, f(x)) with
(6, 1), (9, 2), (30, 5), (105, 10) of (x, g(x)),
we see that the graph of g is the same as the graph of f shifted 5 units right.
In general, the graph of y=f(x-a), where a is a positive number, is the graph of y=f(x) shifted a units right.
Answer: C
Every square is ____ a rectangle.
A. always
B. sometimes
C. never
Answers
Your answer is A.
Suppose a college student pays $650 for tuition fees. However, she also has to pay $325 for her textbooks (ouch!). What percent of her total education costs does she pay for her books?
Answer: Her books represent
percent (as a decimal) of her total costs.
Write your answer to the nearest tenth of a percent, but in decimal form. For example, if you saved 34.67%, you would round to 34.7% and enter .347 as your answer.
Answers
Five divided by the difference of a number and 4 equals the quotient of 10 and the sum of the number and 2. find the number.
Answers
Along the Oregon trail the trading post in fort Laramie, Wyoming, sold a 16 pound of beef je rky for 5.92 what was the cost per pound
Answers
So 5.92 divide by 166= $0.37 per pound.
the LCD of 6y/5x and 8/12x is 60x. true or false?
Answers
Answer:
true....
Step-by-step explanation:
For a quadrilateral to be a parallelogram, its opposite sides and _____ must be congruent.
Answers
For a quadrilateral to be a parallelogram, its opposite sides and angles must be congruent.
What is congruency?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.
A quadrilateral is a closed shape in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral. The word "quadrilateral" is derived from the Latin "quadra" (four) and "latus" (sides).
For a quadrilateral to be a parallelogram, its opposite sides and angles must be congruent.
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For high school wrestling competitions, the wrestling mat must be a square with an area of 1444 square feet. _ feet is the length of each side of the wrestling mat.
Answers
A = a^2
A = 1444
1444 = a^2....take the sqrt of both sides, eliminating the ^2
sqrt 1444 = a
38 = a.....so each side is 38 ft <==
The length of each side of the wrestling mat is, 38 feet.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
For high school wrestling competitions, the wrestling mat must be a square with an area of 1444 square feet.
Let the length of each side of the wrestling mat is, x
Hence, We get;
⇒ x² = 1444
⇒ x = √1444
⇒ x = 38 feet
Thus, The length of each side of the wrestling mat is, 38 feet.
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Test scores are normally distributed with a mean of 100 and a standard deviation of 15. an individual's iq score is found to be 90. find the z-score corresponding to this value.
Answers
z=(90-100)/15=-0.6666666667
The z-score corresponding to this value will be negative 0.6667.
What is the z-score?The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The z-score is given as
z = (x - μ) / σ
Where μ is the mean, σ is the standard deviation, and x is the sample.
Test scores are typically conveyed with a mean of 100 and a standard deviation of 15. A singular's level of intelligence score is viewed as 90.
The z-value is given as,
z = (90 - 100) / 15
z = - 10 / 15
z = - 0.6667
The z-score relating to this worth will be negative 0.6667.
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What is the unit rate for $1 for 12lbs
Answers
You can get 12 for 1. Unit rate is the simplified fraction in which the denominator is 1.
hamburger selling $1.25 a pound contains 30% fat. how much does the consumer pay for the meat without the fat?
Answers
Answer : $0.88
(Hopefully its right)
Find the real or imaginary solutions of the equation by factoring. X^4-10x^2=-9
Answers
Rearranging to get [tex]x^4-10x^2+9=0[/tex]
Let [tex]x^2[/tex] be [tex]p[/tex], then we have [tex]p^2-10p+9=0[/tex]
Factorising we get [tex](p-1)(p-9)=0[/tex]
Solving for [tex]p[/tex], we have [tex]p=1[/tex] and [tex]p = 9[/tex]
Rewriting [tex]p[/tex] back as [tex]x^2[/tex], we have:
[tex]x^2=1[/tex] and [tex]x^2=9[/tex]
[tex]x= \sqrt{1} [/tex] and [tex]x= \sqrt{9} [/tex]
[tex]x = (+1) and (-1)[/tex] and [tex]x=(+3) and (-3)[/tex] ⇒ Final answers
If $4500 is invested at an interest rate of 7.25% per year, compounded continuously, find the value of the investment after the given number of years. (round your answers to the nearest cent.)
Answers
Final answer:
The value of an investment of $4500 at a 7.25% annual interest rate, compounded continuously, is calculated using the compound interest formula [tex]P = P_0e^{rt}[/tex], where P0 is the initial amount, r is the rate as a decimal, and t is the time in years.
Explanation:
The subject of this question is Mathematics, and it falls under the High School grade level. To find the value of an investment compounded continuously, we use the formula:
[tex]P = P_0e^{rt}[/tex]
Where:
P0 is the initial amount investedr is the annual interest rate (in decimal form)t is the time in yearse is the base of the natural logarithm, approximately equal to 2.71828Given a $4500 investment at a 7.25% annual interest rate, compounded continuously, we can calculate the future value of the investment after t years. Convert the percentage to a decimal by dividing by 100:
r = 7.25 / 100 = 0.0725
So the formula becomes:
[tex]P = $4500e^{0.0725t}[/tex]
Plug in the number of years into 't' to calculate the future value for that specific duration.
After 2, 4, and 6 years of continuous compounding, the investment values are approximately $5198.85, $6014.70, and $6953.85 respectively.
To find the value of the investment after a certain number of years with continuous compounding, we use the formula:
[tex]\[ A = P e^{rt} \][/tex]
Given:
- P = $4500
- r = 7.25% = 0.0725 (as a decimal)
We need to calculate the value of the investment after 2, 4, and 6 years.
(a) For 2 years:
[tex]\( A = 4500 \times e^{0.0725 \times 2} \)\\\( A = 4500 \times e^{0.145} \)\\\( A \approx 4500 \times 1.1553 \)\\\( A \approx \$5198.85 \)[/tex]
(b) For 4 years:
[tex]\( A = 4500 \times e^{0.0725 \times 4} \)\\\( A = 4500 \times e^{0.29} \)\\\( A \approx 4500 \times 1.3366 \)\\\( A \approx \$6014.70 \)[/tex]
(c) For 6 years:
[tex]\( A = 4500 \times e^{0.0725 \times 6} \)\\\(A = 4500 \times e^{0.435} \)\\\(A \approx 4500 \times 1.5453 \)\\\( A \approx \$6953.85 \)[/tex]
So, the values of the investment after 2, 4, and 6 years respectively are approximately:
(a) $5198.85
(b) $6014.70
(c) $6953.85
Complete Question:
If $ 4500 is invested at an interest rate of 7.25% per year, compounded continuously, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)
(a) 2 years
(b) 4 years
(c) 6 years
In order to make an A on her project, Sarah needs at least 160 points. She has already turned in part of her work and has been given 125 point so far. Write and solve an inequality that models this situation and find out how many points Sarah needs on the last part of her project to get an A.
Answers
to get an A, she needs >=160 points and she already has 125 points
let 'x' be the number of points on the last part of her project then
125 + x >= 160
x >= 160 - 125
x >= 35
Sarah needs at least 35 points on the last part of her project.
Answer:
P ≥ 35
Step-by-step explanation:
Naming P to the Points needed for the last part of Sarah's project,
we can define an inequation modelling in which cases Sarah will have enough points for an A or better:
It is stated that:
An A is achieved with 160 points.Sarah already has been given 125 points.Then the inequation can be written:
[Points-so-far] + [Points-needed] greater or equal than 160
In math symbols:
[tex]125+P\geq 160\\P\geq 160-125\\P\geq 35[/tex]
involves triangle centroid
Answers
[tex]\bf TW-TX=XW\implies \cfrac{8a}{5}+\cfrac{1}{10}-\left(a +\cfrac{4}{5} \right)=XW \\\\\\ \cfrac{8a}{5}+\cfrac{1}{10}-a-\cfrac{4}{5}=XW\implies \cfrac{3a}{5}-\cfrac{7}{10}=XW\\\\ -------------------------------\\\\[/tex]
[tex]\bf TX:XW\qquad 2:1\qquad \cfrac{TX}{XW}=\cfrac{2}{1}\implies \cfrac{a+\frac{4}{5}}{\frac{3a}{5}-\frac{7}{10}}=\cfrac{2}{1} \\\\\\ \cfrac{\frac{5a+4}{5}}{\frac{6a-7}{10}}=\cfrac{2}{1}\implies \cfrac{5a+4}{5}\cdot \cfrac{10}{6a-7}=\cfrac{2}{1}\implies \cfrac{10a+8}{6a-7}=\cfrac{2}{1} \\\\\\ 10a+8=12a-14\implies 22=2a\implies \cfrac{22}{2}=a\implies 11=a[/tex]
1. You will use 25% of your budget to rent business space and pay for utilities. Write an algebraic expression that indicates how much money will be spent on business space and utilities. Do not include commas for large numbers. Do not solve.
2. How much money will rent and utilities cost? Enter your answer as a number, without any commas or dollar signs.
Answers
then budget used for rent business space and pay for utility = 25% of x
= [tex] \frac{25}{100} [/tex] × x
= [tex] \frac{1}{4} [/tex] × x
= [tex] \frac{x}{4} [/tex]
2. $1 for total budget of $4.
Assume that the budget you have is x.
You will spend 25% of this budget on rental and utilities' cost.
This means that you will spend 25% * x on rental and utilities' cost.
Transforming this into an equation:
cost of rent and utilities = 0.25x
Part (b):
You should really add you budget so that we can solve this part. Since you haven't, I;ll just assume a budget and you can follow the same steps of calculations based on the budget you have.
Assume that the budget is 100$.
This means that:
money spent on rent and utilities = 0.25(100) = 25$
remaining money = 100 - 25 = 75$
The corresponding angles postulate states that if two parallel lines are cut by a transversal, then the pairs of corresponding angles are
Answers
Which of the following is not greater than 7/16?
A.)1/2
B.)31/62
C.)15/17
D.)3/8
Answers
Which polygon is always regular
Answers
In the united states, 40% of the population has brown eyes. if 14 people are randomly selected, find the probability that at most 11 of them have brown eyes.
Answers
The probability that at most 11 of them have brown eyes is 0.9994
What is Binomial Distribution Function?
If a random variable X denotes the number of successes in n trials each with probability of success p, then we say that X ∼ Bin (n, p) , and the probability of exactly x successes in n trials P [X = x] is given by the binomial distribution function, f(x) , where f(x) is
[tex]f(x) = P[X=x] = (\frac{n}{x} ) p^{x} (1-p)^{n-x}[/tex]
where x = successes , n = trials
Therefore , [tex]f(x) = \frac{n!}{x!(n-x)!} p^{x} (1-p)^{n-x}[/tex]
Given data , we have
p = 40 % = 0.4
n = 14
Let X be the number out of a sample of 14 whose eyes are brown.
So the probability that at most 11 of them have brown eyes is calculated as P( X [tex]\leq[/tex] 11 ) and
P( X [tex]\leq[/tex] 11 ) = 1 - P( X > 11 )
where P( X > 11 ) = 0.0006
Therefore , P( X [tex]\leq[/tex] 11 ) = 1 - 0.0006
= 0.9994
Hence , the probability that at most 11 of them have brown eyes is 0.9994.
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2 more than twice a number w
Answers
So your answer is 2w + 2
Hope this helped!
hope this helps
-4.2+3.3=
Write answer in decimal form.
Answers
The value of the given expression is -0.9
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that, an expression -4.2+3.3 = ? we need to find the answer in the decimal form,
To find the same, we have to simply subtract 3.3 from 4.2 and since the greater number is in negative the result will also be in negative,
3.3-4.2 = -0.9
Hence, the value of the given expression is -0.9
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Bill owns a grocery store chain with 2,000 total employees. Nine hundred of his employees are managers. What can we assume about the total productivity of Bill’s chain?
Answers
We can assume that Bill's store is in danger of experiencing a diseconomy of scale.
Given Bill's grocery store chain's 2,000 total employees, 900 of whom are managers, it may be more logical to believe that Bill's store is in danger of suffering a diseconomy of scale.
Diseconomies of scale relate to a situation in which a company expands so much that its costs per unit rise.
When a corporation suffers diseconomies of scale, needless expenditures frequently develop as a result of greater management issues and inefficiencies in the flow of work and commodities.
Almost half of Bill's employees are managers of some kind. This will reduce his company's productivity and cause costs to increase as output expands.
Complete question:
Bill owns a grocery store chain with 2,000 total employees. nine hundred of his employees are managers. what can we assume about the total productivity of bill’s chain?
a. bill’s store is in danger of experiencing a diseconomy of scale
b. the grocery store is experiencing a constant return to scale
c. the grocery store is experiencing an economy of scale
d. bill’s store is run very efficiently.
An online weather report says the temperature is between 40 degrees and 50 degrees, when it is really 54.4 degrees outside. Which of the following is true?
Answers
Please Help! I don't want an exact answer, just a brief explanation of what the question actually means.
IF THE STUDENTS HIKE AT A SPEED OF 4 KM/H, WHAT IS THE TOTAL DISTANCE THE STUDENTS WILL HIKE?
Answers
Answer:
21km i beileve srry im late
Step-by-step explanation:
please help!
create an expression equal to 6/5
what you have to work with:
1/16, (7/10, -, 5/8), ÷
Answers
In addition, 6/5=96/80. To get this, we'd want 6 as the numerator and 5 as the denominator. Noting that we have parenthesis (meaning that (7/10 has to start with the parenthesis and 5/8) has to end it), we can also notice that (56-50)/80=6/80 and since 1/16=5/80, we can divide them to get (6/80)/(5/80)=
(6*80)/(5*80)=6/5