The function's domain is (a) all real numbers.
What is the domain in math?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set. A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.
How do you identify the domain?The formula for the function is: f(x) = Negative 5/6. X in superscript?
The function mentioned above is exponential
There are no input value restrictions for exponential functions
Consequently, the function's domain is (a) all real numbers.
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what is the total amount that First Consumer Bank will receive after lending Jane $7,000 for three years at an interest rate of 5 percent, compounded annually
Answer: it is 8103.38
Step-by-step explanation:
(a) at least how many sets must be printed to be sure of having at least 4 identical subsets on the list?
The number of sets to be printed to ascertain at least 4 identical subset is there on the list when a computer is printing out subsets of a 5 element set is 97.
The total number of subset for a n element set is 2^{n}. Therefore, for a 5 element set is 2^{5} = 32.
Thus to ensure there are at least 4 identical subset, the computer should print 3 times the total number of subsets possible plus 1 additional subset, i.e. 3×32 + 1 = 97.
-- The question is incomplete, the correct question is as follows --
"A computer is printing out subsets of a 5 element set (possibly including the empty set). a. at least how many sets must be printed to be sure of having at least 4 identical subsets on the list?"
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Dean is training for a 20 kilometre race. He wants to beat his personal best time of 3 hr 14 min 45 sec. If it takes him 9 minutes and 30 seconds to run one kilometre, will he beat his personal best? Calculate by how much will Dean beat/not beat his personal best time?
Dean will take a total time of 3 hours and 10 minutes to complete the race and will beat his personal best time
What is an 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.
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 data ,
Let the personal best time of Dean be = A
Now , the value of A = 3 hours 14 minutes 45 seconds
And ,
The time taken by Dean to complete 1 km = 9 minutes 30 seconds
Now , the total distance of the race lap = 20 km
So , the equation will be
Total time taken by Dean to complete 20 km race B = 20 x time taken by Dean to complete 1 km
Substituting the values in the equation , we get
Total time taken by Dean to complete 20 km race = 20 x 9 minutes 30 seconds
Total time taken by Dean to complete 20 km race = 20 x 9 minutes + 20 x 30 seconds
Total time taken by Dean to complete 20 km race = 180 minutes + 600 seconds
1 hour = 60 minutes
1 minute = 60 seconds
180 minutes = 3 hours
600 seconds = 10 minutes
So , the equation is
Total time taken by Dean to complete 20 km race B = 3 hours 10 minutes
So , the value of B < value of A
Therefore , the Dean will beat his personal best time and the race is completed in 3 hours 10 minutes
Hence , Dean will take a total time of 3 hours and 10 minutes to complete the race and will beat his personal best time
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7. What is the number?
The number is between 10 and 20.
The number is composite.
The number is odd.
Answer:
The number is 15
Answer:
15
Step-by-step explanation:
The number is between 10 and 20.
10 11 12 13 14 15 16 17 18 19 20
The number is composite or have more than 2 factors.
10 12 14 15 16 18 20
The number is odd.
15
The expression below is the factorization of what polynomial? Write
exponents with the caret (^). For example, enter x² as x^2.
(2x+3)(3x + 5)
what is x and what is the reason why (circle theorems)
Check the picture below.
Please help, I'm having trouble.
Compared to the graph of y = x graph y = -x/3 is a negative slope
Compared to the graph of y = x graph y = -x/3 intersects the y axis at same point
Compared to the graph of y = x graph y = x - 2 is a parallel line
Compared to the graph of y = x graph y = x - 2 intersects the y axis at 2 units down
How to make the graph comparisonThe two graphs compared are linear function graphs
A linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
c = y intercept
y = x
slope = 1
c = 0
y = -x/3
slope = -1/3
c = 0
y = x - 2
slope = 1
equal slopes means the lines are parallel
c = -2 (down 2 units)
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Given that log,m=n, express 25n+2 in terms of m.
Answer:
25n+2 can be expressed as log,m^25+2.
Step-by-step explanation:
Since log,m=n, we can write 25n+2 as 25*log,m+2.
Using the property of logarithms that log,a+log,b=log,ab, we can rewrite 25*log,m as log,m^25.
What value of x makes the perimeters of the figures below equal? (see imagine attached) :)
The value of x that makes the perimeters of the figures equal is; x = 3.
What is the Perimeter of a Figure?To find the perimeter of a figure, add all its side together. That is, the sum of all its sides will give you the perimeter.
Perimeter of the triangle = (x + 6) + 5x + (3x + 3)
Open the bracket and simplify
x + 6 + 5x + 3x + 3
Combine like terms
= 9x + 9
Perimeter of the square = 4(x + 6)
= 4(x) + 4(6)
= 4x + 24
Make both equation equal to each other and find x:
9x + 9 = 4x + 24
9x - 4x = -9 + 24
5x = 15
x = 3
The value of x is 3.
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Twice last month, Judy Carter rented a car from a car rental company and traveled around the Southwest on business. The company rents its car for a daily fee, plus an
additional charge per mile driven. Judy recalls that her first trip lasted 4 days, she drove 450 miles, and the rental cost her $256.00. On her second business trip she drove
200 miles in 3 days, and paid $159.00 for the rental. Find the daily fee, and find the mileage charge.
Answer:
the daily fee is 37 and the mileage charge is .24 per mile.
Step-by-step explanation:
256 = 450x + 4b
159 = 200x + 3b
Multiple the top equations by -3 all the way through the bottom equations by 4 all the way through then add the equation together.
-768 = -1350x -12b
636 = 800x + 12b
-132 = -550x Divide both sides by -550
.24 = x This is the charge per mile.
Plug in .24 for x into either of the original 2 equations to solve for b which is the daily fee.
256 = 450(.24) = 4b
256 = 108 + 4b Subtract 108 from both sides
148 = 4b Divide both sides by 4
37 = b This is the daily fee.
Ome of the children at a chool arrive by car
- 30% of the tudent at the chool are boy
- 60% of the boy at the chool arrive by car
- 80% of the girl at the chool arrive by car
what i the probability a child choen at random from the chool arrive by car
The probability that a child chosen at random from the school arrives by car is the total of the column Car 74%.
Describe probability using an example?
By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained.
The most basic illustration is a coin toss. There are only two outcomes that can occur when you flip a coin: either heads or tails.
You can build a two-way relative frequency table to represent the data:
These are the columns and rows:
Car No car Total
Boys
Girl
Total
Fill the table
30% of the children at the school are boys
Car No car Total
Boys 30%
Girl
Total
60% of the boys at the school arrive by car
That is 60% of 30% = 0.6 × 30% = 18%
Car No car Total
Boys 18% 30%
Girls
Total
By difference you can fill the cell of Boy and No car: 30% - 18% = 12%
Car No car Total
Boy 18% 12% 30%
Girl
Total
Also, you know that the grand total is 100%
Car No car Total
Boy 18% 12% 30%
Girl
Total 100%
By difference you fill the total of Girls: 100% - 30% = 70%
Car No car Total
Boy 18% 12% 30%
Girl 70%
Total 100%
80% of the girls at the school arrive by car
That is 80% of 70% = 0.8 × 70% = 56%
Car No car Total
Boy 18% 12% 30%
Girl 56% 70%
Total 100%
Now you can finish filling in the whole table calculating the differences:
Car No car Total
Boy 18% 12% 30%
Girl 56% 14% 70%
Total 74% 26% 100%
Having the table completed you can find any relevant probability.
The probability that a child chosen at random from the school arrives by car is the total of the column Car 74%.
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Example An investor Saved #120,000 For 7 years in a bank which pays interest of 11½% per annum Calculate the a. Interest which accrued b balance if # 25,000 was withdrawn from the account (N 28,276) 00
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$120000\\ r=rate\to 11.5\%\to \frac{11.5}{100}\dotfill &0.115\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &7 \end{cases}[/tex]
[tex]A=120000\left(1+\frac{0.115}{1}\right)^{1\cdot 7} \implies A \approx 257101.92 \\\\\\ \underset{earned~interest}{\stackrel{257101.92 - 120000}{\text{\LARGE 137101.92}}}\hspace{10em}\underset{adjusted~balance}{\stackrel{257101.92 - 25000}{\text{\LARGE 232101.92}}}[/tex]
At what number of square feet of countertop would the cost from each company be the same?
The cost from company A and company B will be the same at 40 square feet of countertop
At what number of square feet of countertop would the cost from each company be the same?Given that:
Company A will sell Mikayla a countertop according to the given
graph, which includes a $1, 000 installation fee.
Company B will sell a countertop according to the values given in the
table, which includes an $800 installation fee and a constant rate of change
With this information, you can make cost function for both Company A and Company B
Company A
A linear function is of the form y = mx + c
where c is the y-intercept (starting point) and m is the slope (rate)
c = 1000 (from the graph)
m = 1150-1000 / 10-0 (By using the 2 points on the graph: m = y2-y1/x2-x1)
m = 15
y = mx + c
y = 15x+1000
Company B
c = 800 (given)
m = 1100-1000 / 15-10 (From table)
m = 100/5 = 20
y = mx + c
y = 20x+800
Equate the two cost functions and solve for x:
20x+800 = 15x+1000
20x-15x = 1000-800
5x = 200
x = 200/5
x = 40 square feet
Therefore, at 40 square feet of countertop, the cost from each company will be the same
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9. You decide to invest $500 into a 4-year CD that pays 2.85% interest
compounded monthly.
Use the compound interest formula A = P(1 + r/n) ^nt to give:
a. The future value in 4 years.
b. The interest gained in 4 years.
The compound interest formula [tex]A = P(1 + r/n) ^nt[/tex] Monthly compounding is a common strategy used by interest-bearing CDs to boost returns. The annual interest rate is divided by twelve in this scenario.
How to calculate interest ?After 4 years, you should have $763 in your account.After four years of saving $4 every month, your funds may reach $762.90. This includes a $500.00 initial balance and a 2.85% yearly rate of return.
Invest $500 in a 4-year certificate of deposit (CD) earning 2.85% interest compounded monthly.utilizing the compound interest formula [tex]A = P ( 1 + r / n ) ^{nt}[/tex]
The formula for calculating simple interest is S.I. = P R T, where P stands for principal, R for the annual percentage rate of interest, and T for time, which is typically expressed as the number of years. The interest rate is expressed as a percentage, or r%, and should be represented as r/100.
Many interest-bearing CDs use monthly compounding to increase returns. This model divides the annual interest rate by twelve.
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identify the maximum or minimum volume to the domain and range of the graph of the function y=2(x-3)^2-4
The minimum value of the function y = 2(x - 3)² - 4 is -4. Domain of the function is set of all real numbers and the range is all real numbers ≥ -4.
What is Domain and Range of a function?Domain of a function y = f(x) is the set of all the values of x where the function is defined.
The range of the function is the set of all values of the function on the defined domain.
The given function is,
y = 2(x - 3)² - 4
y = 2(x² - 6x +9) - 4
y = 2x² - 12x + 14
This is a quadratic function and the graph of the function will be a parabola.
The parabola is directed upwards if the coefficient of x² in a quadratic equation is positive and so will be having a minimum value.
The parabola is directed downwards if the coefficient of x² is negative and so will be having the maximum value for the function.
Here, coefficient of x² = 2, is positive.
So there will be a minimum value.
The value of [tex]\frac{-b}{2a}[/tex] in the quadratic equation ax² + bx + c, is the x value of the vertex of the parabola.
x = - (-12) / (2 × 2) = 3
∴ Minimum value, y = 2 (3 - 3)² - 4 = -4
Domain of the function will be the set of all real numbers because the function is defined for all real numbers.
The range will be all real numbers ≥ -4, because any values of x in the function does not make the value of the function less than -4.
Hence the minimum value of the function is -4 and the domain and the range of the function is set of all real numbers and all real numbers ≥ -4 respectively.
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Add. State the sum in simplest terms.
16-p
(p+4)(p-6)
+ 1⁄4 › P‡ − 4,6
p+4
The sum in simplest terms is 1/(p-6)
What is LCM?
Least Common Multiple is the meaning of the acronym LCM. The smallest number that both numbers can divide by is known as the least common multiple (LCM) of two numbers. It can also be computed for two or more different numbers. There are numerous ways to calculate the LCM of a given collection of numbers. Utilizing the prime factorization of each number and then calculating the product of the highest powers of the common prime factors yields the LCM of two integers in a short amount of time.
(16-p)/[ (p+4)(p-6) ] + 2/ (p+4)
Take LCM = (p+4)(p-6)
= [ 16-p + 2(p-6) ] / [ (p+4)(p-6) ]
= [ 16-p + 2p-12) ] / [ (p+4)(p-6) ]
= ( p +4 ) / [ (p+4)(p-6) ]
= 1/(p-6)
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Hillary is using the figure shown below to prove Pythagorean Theorem using triangle similarity: In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC. The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC. Which of these could be a step to prove that BC2 = AB2 + AC2? (6 points) By the addition property of equality, AC2 plus AD2 = AB multiplied by DC plus AD2. By the addition property of equality, AC2 plus AD2 = BC multiplied by DC plus AD2. By the addition property of equality, AC2 plus AB2 = AB multiplied by DC plus AB2. By the addition property of equality, AC2 plus AB2 = BC multiplied by DC plus AB2.
Answer: By the addition property of equality, AC2 plus AB2 = BC multiplied by DC plus AB2.
Jack is running on a treadmill at a speed of 7. 2 miles per hour a slim y equals total distance and x equals number of hours
Need help pls important!!!!!!!!
Given that he is running on a treadmill at a pace of 7.2 miles per hour, the necessary expression will be y=7.2x.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.
Here,
Speed of him=7.2 miles/hour
Let y be the total distance and x be the number of hours,
speed=distance/time
7.2=y/x
y=7.2x
The required expression will be y=7.2x as he is running on a treadmill at a speed of 7. 2 miles per hour.
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PLEASE HELP ASAP!!!!
Answer:
statements 2 and 3 are true
Step-by-step explanation:
using the rule of exponents
[tex]a^{0}[/tex] = 1
then
1 [tex]a^{0}[/tex]≠ a ← lie
2 [tex]x^{0}[/tex] = 1 ← true
3 [tex]5^{0}[/tex] = 1 ← true
A washer and dryer cost a total of $1132. The cost of the washer is three times the cost of the dryer. Find the cost of each item.
Cost of washer:
Cost of dryer:
Answer:
Washer = $849
Dryer = $283
Step-by-step explanation:
Dryer = x
Washer = 3x
3x + x = 1132
Simplify:
4x = 1132
Divide both sides by 4:
x = 283
The dryer costs $283, and since the washer is three times the cost of the dryer, the washer is:
283x3 = 849
Shelley is searching online for airline tickets. Two weeks ago, the cost to fly from Hartford to Orlando was $210. Now the cost is $320. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
The percent increase is 56%
The percent increase if the airline charges an additional $50 baggage fee with the new ticket price is 76%
How to determine the percent increaseThe formula for determining percent increase is expressed as;
Percent increase = x₂ - x₁/x₁ × 100/ 1
Where;
x₁ is the initial valuex₂ is the final valueNow, substitute the values, we have;
Percent increase = $320 - $210/$210 × 100/ 1
Find the difference
Percent increase = $110/$210 × 100/ 1
Percent increase = 0. 52 × 100/ 1
Multiply through
Percent increase = 52%
If there is an increase of $50
Percent increase = $370-210/210 × 100/ 1
= 160/210 × 100/ 1
= 76%
Hence, the values are 52% and 76% respectively,
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A hospital is going to be built in the land of the shape of a rhomus having its
diagonals 250 m and 480 m respectively in a mountainous district of Nepal. Find
the area covered by the hospital in Ropani. (1 Ropani = 508.72 m²).
Answer:
117.94 Ropani
Step-by-step explanation:
Area Of Rhombus=½×d1×d2
=½×480×250
=60,000m²
1Ropani=508.72 {As Given}
60,000m²=(60,000÷508.72)Ropani
=117.94 Ropani
Answer:
60000 m^2
117.943 ropani
Step-by-step explanation:
the area of rhombus = 250 × 480 ÷2=60000 m^2
60000 m^2 = 117.943 ropani
Write 2/5 and 1/4 with the same denominator
Answer:
Make the denominators equal by L.C.M
--> 8/20 + 5/20
--> 13/20
Ben bought one share of stock for $40. He watched the
price of his stock every day for a week. On Monday, the
stock moved 2.5 points up. On Tuesday, it moved 1.75
points down. On Wednesday, it moved p points. On
Thursday and Friday, the stock moved 0.75 points up
each day. If the price of the stock was $45 at the end of
the week, what is the value of p?
Answer:2p
Step-by-step explanation:
What is an algebraic expression for 16 more than the product of 43 and a number?
A: 16 − 43y
B: 43y(16)
C: 43y − 16
D: 43y + 16
The algebraic expression that can be represented by the statement is 43y + 16
How to make a algebraic expression that can be represented by the statement?From the question, we have the following statement that can be used in our computation:
16 more than the product of 43 and a number
Represent the variable with y
So, we have the following representation
16 more than the product of 43 and y
Express the product as an actual product
So, we have the following representation
16 more than 43y
more than as used here means addition
So, we have
43y + 16
Hence, the expression is (d) 43y + 16
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Answer: 43y + 16
Step-by-step explanation:
i did the test
geologists unearth a sample of zircon that appears to be a closed system. they find 0.686 microgram of 206pb for 1.000 microgram of 238u present. approximately how old is the sample? yrs
geologists unearth a sample of zircon that appears to be a closed system. they find 0.686 micro gram of 206 Pb for 1.000 micro gram of 238U present. approximately 3.7973 × 10⁹ years old is the sample.
What is decay constant?The reciprocal of the time period during which the number of atoms in the radioactive element drops to almost A. 50% of its initial number is the decay constant.
According to the radioactive decay law, a nucleus's likelihood of decaying is a constant that is independent of time.
t1/2 of U₂₃₈ is 4.5 × 10⁹ years
moles of U₂₃₈ : (1 × 10⁻⁶ / 238) moles
moles of Pb₂₀₆ : (0.686 × 10⁻⁶ / 206) moles
Now, U₂₃₈ → Pb₂₀₆
As Pb₂₀₆ comes from U₂₃₈ hence,
moles of U₂₃₈ decayed = moles of Pb₂₀₆
= (0.686 × 10⁻⁶ / 206) moles
Therefore, initial moles of U₂₃₈:
N₀ = [(1 × 10⁻⁶ / 238) + (0.686 × 10⁻⁶ / 206)] moles
and N = (1 × 10⁻⁶ / 238) moles
Now, λ (decay constant) = 0.693 / (t1/2)
= 0.693 / ( 4.5 × 10⁹ years)
So,
t = 2.303 / λ × log (N₀ / N)
t = 2.303 / [0.693 / ( 4.5 × 10⁹ years)] × log [1 + (0.686/206)/(1/238)]
t = 14.95 × 10⁹ × 0.254
t = 3.7973 × 10⁹ years.
Thus, the sample is: 3.7973 × 10⁹ years old.
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Whats the scale factor of triangle PQR to triangle STU.
PR =8 SU=12
RQ=6 UT=9
QP=10 TS=15
The scale factor of triangle PQR to triangle STU is 3/2
How to find the scale factor of the two trianglesScale factors are used to increase or decrease image. The situation of increment is usually called magnifying.
Taking a point of reference say PR and SU
PR = 8
SU = 12
let the scale factor be r such that
8 * r = 12
r = 12 / 8
r = 3/2
checking with other sides
PR to UT
6 * 2/3 = 9 correct
QP to TS
10 * 3/2 = 15 correct
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What is the equation of the parabola with focus (1, 6) and directrix y = 1?
An equation of the parabola with focus (1, 6) and directrix y = 1 is: C. y = 1/10(x²) - 1/5(x) + 18/5
How to determine the equation of a parabola?Mathematically, the standard equation of the directrix lines for any parabola is given by:
y = a(x - h)² + 2.
Where:
h and k are the vertex.a is a point.Since the directrix is horizontal, the axis of symmetry would be vertical. Therefore, the equation of this parabola would be modeled by this standard mathematical expression;
(x - h)² = 4p(y - k)
Where:
h = 1
In Mathematics, the focus for either a right or left parabola is modeled by this mathematical expression (h + p, k) while its directrix is modeled by this mathematical expression x = h - p;
k + p = 6
k - p = 1
Solving the set of linear equations simultaneously, we have:
2k = 7
k = 7/2
For the value of p, we have;
p = 6 - k
p = 6 - 7/2
p = 5/2
Substituting the given parameters into the formula, we have;
(x - 1)² = 4(5/2)(y - 7/2)
x² - 2x + 1 = 10(y - 7/2)
x² - 2x + 1 = 10y - 35
10y = x² - 2x + 1 + 35
10y = x² - 2x + 36
y = (x² - 2x + 36)/10
y = x²/10 - x/5 + 18/5
y = 1/10(x²) - 1/5(x) + 18/5
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Solve each system by elimination: x+5y=4 3x-7y=-10
Answer: x= -1 y= 1
Step-by-step explanation: Times -3 to get the same x
-3x - 15y = -12
3x - 7y = -10
-22y = -22
y= 1
Then put 1 back in for letter y and you get x= - 1
Sam goes to lunch with a friend. The total cost of lunch is $15. Sam leaves $1.50 as a tip. What percent of the total did he tip?