Answer: So, the value of the function f(x) = 2x + 3x^2 when x = 1/3 is 1.
Step-by-step explanation: To evaluate the function f(x) = 2x + 3x^2 at x = 1/3, we can substitute the value of x into the function. This gives us:
f(1/3) = 2(1/3) + 3(1/3)^2
Solving this expression following the order of operations, we first solve the exponent:
f(1/3) = 2(1/3) + 3(1/9)
Then we solve the multiplication:
f(1/3) = 2/3 + 3/9
= 6/9 + 3/9
= 9/9
= 1
So, the value of the function f(x) = 2x + 3x^2 when x = 1/3 is 1.
Aisha just got a new bike. Her old bike has 3 gears.
The new bike has 7 times as many gears as the old bike.
How many gears does the new bike have?
»Let g stand for the number of gears the new bike has.
Which bar model represents the problem?
Old bike 3
New bike 3 3 3 3 3 3
Old bike 3
New bike 3 3
3
g
3
g
3
لی
3
3
New bike 3
Old bike
New bike
Old bike
3
3 3 3
3 3 3
g
3
g
3 3 3
3 3
3
Answer: 21
Step-by-step explanation:
If U={a,c,e,s,i,k}, then which of the following are proper subsets of U?
Option 1, 3 and 6 are the proper subsets of the set U = {a, c, e, g, i, k}.
The subsets of U that do not include all of its components are the correct subsets of U. Given that it doesn't include any items of U, Option 1, A = empty set, is a valid subset of U. In the case of option 2, B = "a, c, e, g, i, k" is the set U itself and is not a legitimate subset of U because it contains all of U's components.
Now, option 4, D = {b, d, f, h}, is not a subset of U as it contains elements that are not in U. Option 5 is not correct as it includes both A and B, which is not a proper subset of U. In option 6, both 1 and 3 are given, hence, it is correct.
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Complete question - If U = {a, c, e, g, i, k} then which of the following are proper subsets of U?
Choose one 4 points
1. A = emptyset
2. B = {a, c, e, g, i, k}
3. C = {a, c, e, g}
4. D = {b, d, f, h}
5. Set A, set B and set C
6. Set A, and set C
Two homebuyers are financing $137,000 to purchase a condominium. They obtained a 15-year, fixed-rate loan with a rate of 5.05%. They have been given the option of purchasing up to four points to lower their rate to 4.81%. How much will the four points cost them?
$1,370
$1,730
$4,580
$5,480
Answer: $4,580
Step-by-step explanation:
First, we need to calculate the monthly payment for the 15-year, fixed-rate loan at the original rate of 5.05%. We can use the formula for the monthly payment of a mortgage loan:
P = L[c(1 + c)^n]/[(1 + c)^n - 1],
where P is the monthly payment, L is the loan amount, c is the monthly interest rate (which is the annual interest rate divided by 12), and n is the total number of payments (which is the number of years multiplied by 12).
Plugging in the given values, we get:
L = $137,000
c = 0.0505/12 = 0.0042083 (rounded to 7 decimal places)
n = 15 x 12 = 180
P = $1,071.18
Next, we need to calculate the monthly payment at the lower rate of 4.81% if the buyers purchase four points. Each point costs 1% of the loan amount, so four points will cost 4% of the loan amount.
The new rate after purchasing four points is:
5.05% - 0.24% = 4.81%
The new loan amount after purchasing four points is:
$137,000 - (4% x $137,000) = $131,920
Using the same formula for the monthly payment, but with the new values for the loan amount and monthly interest rate, we get:
L = $131,920
c = 0.0481/12 = 0.0040083 (rounded to 7 decimal places)
n = 15 x 12 = 180
P = $1,030.98
The monthly savings due to the lower interest rate is:
$1,071.18 - $1,030.98 = $40.20
To calculate the cost of the four points, we need to divide the upfront cost of the points by the monthly savings:
Cost of four points = ($40.20 x 180)/0.0024 = $3,015
Therefore, the cost of the four points is $3,015, which is closest to $4,580.
The four points that the homebuyers are purchasing to lower their rate from 5.05% to 4.81% will cost them D. $5,480.
What are the points in loans?The points purchased for loans are charges that the borrower pays upfront to lower their interest rates.
Each point equals a percentage of the loan amount.
For example, four points on a $137,000 loan are 4 percent of the loan amount, or $5,480.
The loan amount for the purchase of the condominium = $137,000
Fixed interest rate = 5.05%
Loan period = 15 years
Loan option rate = 4.81%
Hence, Four points = $137,000 x 4%
= $5,480
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Match the base to the corresponding height. Base (b) Height (h)
Answer:
1:2
2:1
3:3
Explanation:
1 on the left is with 2 on the right (1:2) because base and height are inversed, so the same explanation is for 2:1.
3:3 because the hypotenuse (the base) is calculated with the height of the right angles.
Hope I helped and that I get brainliest ;)
15 5/8 minus 15 4/5 I need to know soon pleaseeeeeee
Answer:
15 5/8 - 15 4/5
= 15 25/40 - 15 32/40 (15-15 = 0)
= 25/40 - 32/40
= -7/40
Brainliest, please:)
What is the slope of the equation y=5/4x-7/4
Answer:
Step-by-step explanation:
m=5/4
write a related multiplication sentence to solve 1/5 ÷3
1/5 ÷3 is equal to 1/15
I hope this helps
simplify this expression to have no negative exponents. -2^3a^4b^-5/ 24a^7b^3 *b^10/a^-2b^-4
The expression -2³a⁴b⁻⁵/ 24a⁷b³ × b¹⁰/a⁻²b⁻⁴ with no negative exponents is -a⁵b⁶/3
The given expression is -2³a⁴b⁻⁵/ 24a⁷b³ × b¹⁰/a⁻²b⁻⁴
a and b are the variable in the expression
We have to find the expression without negative exponents
[tex]\frac{a^m}{a^n}=a^m^-^n[/tex]
-8a⁴b⁻⁵/ 24a⁷b³ × b¹⁰/a⁻²b⁻⁴
-a³/3b⁸ × a²b¹⁴
-a⁵b⁶/3
Hence, the expression with no negative exponents is -a⁵b⁶/3
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Identify equation in point-slope form for the line perpendicular to
y=1/4x-7 that passes through (-2,-6).
Answer: y + 6 = -4 (x+2)
Step-by-step explanation:
Which statement best defines a circle?
A.
points in a plane that surround a given point called the center
B.
the set of all points in a plane that are the same distance from each other surrounding a given point called the center
C.
the set of all points that are the same distance from a given point called the center
D.
the set of all points in a plane that are the same distance from a given point called the center
Answer:
The statement that best defines a circle is:
C. The set of all points that are the same distance from a given point called the center.
A circle is a geometric shape consisting of all the points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle through the center is called the diameter. Therefore, a circle is defined as the set of all points that are the same distance (equal to the radius) from a given point (the center).
Answer: The answer should be B
The data given below is for 259 randomly selected 10-minute intervals, where the number of people entering the atrium of a large mall were recorded. Calculate the class width.
The class width is 0.3877.
In order to analyze data, it is often helpful to group it into categories, or intervals, and then determine how frequently each interval occurs. This process is known as frequency distribution.
To calculate the class width, you need to determine the range of each interval. The range is the difference between the upper and lower limits of the interval. For example, the first interval is 160-179, so the range is 179-160=19.
In mathematical terms, the formula for class width is:
Class Width = (Range of all intervals) / (Number of intervals)
In your case, the range of the intervals are:
19, 19, 19, 19, and 19
And the number of intervals is:
53 + 24 + 93 + 27 + 48 = 245
So, the class width can be calculated as follows:
Class Width = (19+19+19+19+19) / 245
Class Width = 95 / 245
Class Width = 0.3877
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Complete Question:
The data given below is for 245 randomly selected 10-minute intervals, where the number of people entering the atrium of a large mall were recorded. Calculate the class width.
Number of Guests Frequency
160 - 179 53
180- 199 24
200 - 219 93
220 - 239 27
240 - 259 48
Help please, I don’t know what to do
The vector that satisfies the equation v = 2u - 3w, where u = (5, -4) and w = (4, -2), is v = (-2, -2).
What is vector?A vector is a mathematical quantity that represents a magnitude (length) and direction in space, usually represented as an ordered set of numbers or coordinates, used to describe physical quantities and geometric objects.
What is equation?An equation is a mathematical statement that indicates the equality of two expressions or quantities, often containing variables, used to describe relationships and solve problems in various fields of mathematics and science.
According to the given information:
To find the vector that satisfies the given equation:
v = 2u - 3w
we need to first calculate the vectors u and w using the given points:
u = (5 - 0, 1 - 5) = (5, -4)
w = (4 - 0, 3 - 5) = (4, -2)
Substituting these values into the equation:
v = 2u - 3w
v = 2(5, -4) - 3(4, -2)
v = (10, -8) - (12, -6)
v = (-2, -2)
Therefore, the vector that satisfies the given equation is (-2, -2).
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Find the volume of the oblique rectangular prism below. Round your
answer to the nearest tenth if necessary.
1
9
The volume of the oblique rectangular prism is 629.1 unit² .
The length of the oblique rectangular prism = 6 unit
The width of the oblique rectangular prism = 9 unit
Using trigonometry the height will be
tan θ = perpendicular / base
Perpendicular = h
Base = 9
h/9 = tan (59)
h = 1.66 (9)
h = 11.6 unit
The height of the oblique rectangular prism = 11.6 unit
The volume of the oblique rectangular prism = l × b ×h
The volume of the oblique rectangular prism = 6 × 9 ×11.6
The volume of the oblique rectangular prism = 629.1 unit²
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Data Set 1 has a mean of 54 and a MAD of 4. Data Set 2 has a mean of 60 and a MAD of 2.
What can be concluded about the two distributions?
Select each correct answer.
A} The distributions are similar.
B} The distributions are somewhat similar.
C} The means-to-MAD ratio is 3.
D} The means-to-MAD ratio is 1.5.
The correct option about the two data set's distribution is B) The distributions are somewhat similar.
Given that,
For data set 1,
Mean = 54 and MAD = 4
For data set 2,
Mean = 60 and MAD = 2
Means to MAD ratio = (60 - 54) / (2 - 4) = 6 / -2 = -3
So means to MAD ratio is -3, not 3.
Now, it is clear that the distributions are not fully similar.
But it appears to be somewhat similar since Mean absolute deviation is somewhat similar, which is close.
Hence the correct option is B.
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When m = 2 and p = 1/4,j=32. Ifj varies directly with m and inversely with p, what is the constant of variation?
-4
-16
-64
-256
Answer:
Step-by-step explanation:
yees
A x+40
B 80
C x+50
D x+5
E 125
Sum of interior angles=
x=
A=
C=
D=
The sum of the measures of the interior angles of the pentagon is given as follows:
540º.
Hence the angle measures are given as follows:
<A = 120º.<C = 130º.<D = 85º.How to obtain the 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).
A pentagon has five sides, that is, n = 5, hence the sum is given as follows:
S(5) = 180 x (5 - 2)
S(5) = 540º.
Then the value of x is obtained as follows:
x + 40 + 80 + x + 50 + x + 5 + 125 = 540
3x + 300 = 540
3x = 240
x = 80º.
Then the angle measures are given as follows:
<A = 80 + 40 = 120º.<C = 80 + 50 = 130º.<D = 80 + 5 = 85º.More can be learned about the sum of the interior angle measures of a polygon brainly.com/question/224658
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HELP ASAP PLEASE! Mrs. Smith has 6 activity tables she wants to place side by side in her classroom.
(a) In how many ways can she arrange all 6 tables? Show your work.
(b) If she only wants to have 4 of the tables set up, in how many ways can she choose the tables she wishes to have set up? Show your work.
a) There are 720 different ways to arrange all six tables in a row. b) There are also 15 other methods to select four of the six tables.
A combination is a technique for calculating the number of alternative arrangements in a set of objects where the order of the selection is irrelevant.
Given this,
Mrs. Smith wants to arrange six activity tables side by side in her classroom.
After aligning all six tables in a straight line, we can use the factorial function to compute the product of all positive integers up to a specified value. We could write:
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
As a result, there are 720 different ways to arrange all six tables in a row.
And, to select four of the six tables, we can use the combination function, which computes the number of ways to select k things from n different items, regardless of their order. We could write:
⁶C₄ = 6! / (4! x 2!)
= (6 x 5 x 4 x 3 × 2 × 1) / [(4 x 3 x 2 x 1) × (2 × 1)]
= (6 x 5 x 4 x 3) / (4 x 3 x 2 x 1)
= 15
As a result, there are 15 different methods to select four of the six tables.
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Bonita has 15% more stamps than Jessica. If Bonita has 150 more stamps than Jessica, how many stamps do they have altogether?
The number of stamps that Jessica and Bonita have altogether if the percent increase in stamps with Bonita is 15% more is 2150.
Given that,
Bonita has 15 percent more stamps than Jessica.
Let x be the number of stamps that Jessica has.
Then,
Number of stamps that Bonita has = x + 150
x + 150 = x + 15% of x
x + 150 = x + (0.15)x
x + 150 = 1.15x
0.15x = 150
x = 1000
Hence the number of stamps that Jessica has = 1000
Number of stamps that Bonita has = 1150
Total number of stamps = 1000 + 1150 = 2150
Hence the total number of stamps is 2150.
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Round to the nearest dollar (but give me the answer before you round also please)
The total selling price, as per the percent rule, is $9,000.
You must first determine the selling price of each toy in order to determine the overall selling price.
As per the percent rule, the cost price plus the markup equals the selling price.
The cost price of each toy is $24, so the markup is 25% of $24, which is $6.
Therefore, the selling price of each toy is $24 + $6 = $30.
To find the total selling price, you need to multiply the selling price of each toy by the number of toys sold.
The store bought 300 toys, so the total selling price is 300 x $30 = $9,000.
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Use the quadratic formula to find all degree solutions and if
0° ≤ x < 360°.
Use a calculator to approximate all answers to the nearest tenth of a degree. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
cos^2 (x) + cos (x) − 1 = 0
(a) all degree solutions (Let k be any integer.)
The degree solutions of the equation are 51.82 degrees and 128.17 degrees
Finding all degree solutions of the equationFrom the question, we have the following parameters that can be used in our computation:
cos² (x) + cos (x) − 1 = 0
Let y = cos(x)
So, we have
y² + y - 1 = 0
When solved graphically, we have
y = ±0.618
This means that
cos(x) = ±0.618
Take the arccos of both sides
x = cos-1(±0.618)
Evaluate
x = 51.82 degrees and 128.17 degrees
Hence, the angles are 51.82 degrees and 128.17 degrees
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4. The table shows when the tickets for a concert are sold and the types of tickets that are sold.
What is the probability that a randomly selected person attending the concert is an adult or has
purchased the ticket in advance?
SOLUTION broken down in steps:
Step 1: Find the probability that a person attending the concert is an adult:
Step 2: Find the probability that a person purchased the ticket in advance:
Step 3: Find the probability that a selected person attending the concert is an adult AND has purchased
the ticket in advance.
Answer: Probability that a person attending the concert is an adult + probability that a person purchased
the ticket in advance - the probability that a selected person attending the concert is an adult AND has
purchased the ticket in advance. (Step 1 +Step 2-Step 3)
The probability that the randomly selected person attending the concert is an adult or has purchased the ticket in advance is 188/250.
We have,
Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Given a table which shows when the tickets for a concert are sold and the types of tickets that are sold.
The probability of A or B can be calculated as,
P(A or B) = P(A) + P(B) - P(A and B)
Let A denote the people is an adult.
Let B denote the people who has purchased the ticket in advance.
P(A) = 148/250
P(B) = 140/250
P(A and B) = 100/250
Probability that a randomly selected person attending the concert is an adult or has purchased the ticket in advance is,
P(A or B) = 148/250 + 140/250 - 100/250
= 288/250 - 100/250
= 188/250
Hence the required probability is 188/250.
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Which point on the number line has a value that is the opposite of 15?
The point on the number line that has a value that is the opposite of 15 must be -15
Calculating the point on the number lineFrom the question, we have the following parameters that can be used in our computation:
Point = 15
The opposite of 15 is
Opposite = -15
This means that the point must have a value of -15
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-4x + 4x
please help asap!
Answer:
0 they cancel each other out..
Step-by-step explanation:
The expression -4x + 4x simplifies to zero:
-4x + 4x = (-4 + 4)x = 0x = 0
Therefore, the result is zero.
a painter can paint a house in 6 days how many houses can a painter finish painting in 222 days?
paint 1 house in = 6 days
paint ? house in = 222 days
= 222 ÷ 6 = 37 houses
Answer: A painter can paint 37 houses in 222 days
Find the equation of a line that passes through the point (1,2) and has a gradient of -3. Leave your answer in the form y = mx + C
Answer: y = -3x + 5
Step-by-step explanation:
We are given that the line passes through the point (1,2) and has a slope of -3. To find the y-intercept, we can use the point-slope form of a line:
y - y1 = m(x - x1)
where (x1, y1) is the point the line passes through.
Substituting the values we have:
y - 2 = -3(x - 1)
Expanding the brackets and rearranging:
y - 2 = -3x + 3
y = -3x + 5
Therefore, the equation of the line is y = -3x + 5, in slope-intercept form.
Wesley deposits 2,000 in an account that earns 4.5% annual interest compounded continuously . If no other deposits or withdrawals are made the amount ,A, in dollars the account after t years Can be modeled by the funtion A(t)=2000e^0.045
The time it will take for the money in the account to reach $4,000 is about 15.407 years.
To solve for the number of years it takes for the amount in the account to reach $4,000, we need to solve the equation:
[tex]4000 = 2000e^{0.045t[/tex]
Dividing both sides by 2000, we get:
[tex]2 = e^{(0.045t)[/tex]
To solve for t, we can take the natural logarithm of both sides:
[tex]ln 2 = ln e^{(0.045t)[/tex]
Using the property that ln [tex]e^x = x[/tex], we can simplify this to:
[tex]ln 2 = 0.045t[/tex]
Dividing both sides by 0.045, we get:
t = (ln 2)/0.045
Using a calculator, we can evaluate this expression to get:
[tex]t = 15.407[/tex]
Therefore, it will take about 15.407 years for the amount in the account to reach $4,000.
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Find the length of the missing side. round to the nearest tenth, 9 6
The length of the missing side is 3 < x < 13.
We have, two measurement of triangle is 9 and 6 unit.
Also, we know that the length of third side of a triangles lies in between the sum of sides and difference of sides.
So, Sum of sides = 9 + 6= 13 unit
Difference of side= 9-6 = 3 unit
Then, the measure of third side is 3 < x < 13.
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Solve the equation below
Property of logarithms: The property of logarithms that we used in this problem states that if loga(b) ≥ loga(c), then b ≥ c. This property is true for any base of the logarithm. Note that the inequality symbol flips when you move from the logarithmic expression to the exponential expression.
Solving linear inequalities: To solve a linear inequality like ax + b > c, you need to isolate the variable on one side of the inequality. This involves adding or subtracting terms and possibly multiplying or dividing by constants. You need to be careful when multiplying or dividing by a negative number, as this flips the inequality symbol.
Domain restrictions: When solving logarithmic inequalities, you need to make sure that the argument of the logarithm is positive. This means that the expression inside the logarithm cannot be zero or negative. You need to check for domain restrictions and make sure that any values that make the argument zero or negative are not included in the solution.
Check the solution: After solving the inequality, it's always a good idea to check the solution to make sure that it satisfies the original inequality. You can plug in the solution to the inequality and make sure that both sides of the inequality are still true. If not, you may have made a mistake in solving the inequality.
To solve log2(7x-3) ≥ log2(x+12), you can start by using the fact that if loga(b) ≥ loga(c), then b ≥ c:
Using this property, you can rewrite the inequality as:
7x - 3 ≥ x + 12
Simplifying the inequality by subtracting x and adding 3 from both sides, you get:
6x ≥ 15
Dividing both sides of the inequality by 6, you get:
x ≥ 2.5
Therefore, the solution to the inequality is x ≥ 2.5 which is option C.
Note that when you use the property of logarithms to simplify an inequality, you need to make sure that the argument of the logarithm is positive. In this case, both arguments are positive as long as x > 3/7 and x > -12, respectively. However, these conditions are automatically satisfied when x ≥ 2.5, so there is no need to check them separately.
Janae is at a carnival. She won 420 tickets. She rides two rides for 75 tickets each and attends a concert for 180 tickets. If she can exchange 10 tickets for one prize, how many prizes can she get with her tickets
Answer:
9 Prizes
Step-by-step explanation:
She begins with 420 tickets.
She goes on 2 rides for 75 tickets each so 420-75-75= 270
She then attends the concert for 180 tickets so 270-180= 90
Now she is left with 90 tickets. 10 tickets = 1 prize therefore you can do 90/10 = 9
9 PRIZES
You flip a coin twice. What is the probability of getting a heads and then a tails?
Answer:
25%
Step-by-step explanation:
