The inverse of the given function f(x) = -5x-3, is f⁻¹(x) = -x/5-3/5
What is an inverse function?An inverse function is a function that undoes the action of the another function. A function g is the inverse of a function f if whenever y=f(x) then x=g(y).
Given that a finction f(x) = -5x-3, we need to find the inverse of the function,
We can write,
y = -5x-3,
Interplace, x and y,
x = -5y-3
-5y = x+3
y = -(x+3)/5
y = -x/5-3/5
f⁻¹(x) = -x/5-3/5
Hence, the inverse of the given function f(x) = -5x-3, is f⁻¹(x) = -x/5-3/5
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When creating a serial dilution from 1/10 to 1/1000, the first dilution will be [a] part sample and [b] parts diluent (what you dilute the sample in). The second dilution will be one part [c] and nine parts [d]. The final dilution will be one part [e] and nine parts diluent.
The answer is: 1 part sample, 9 parts diluent, 1 part of the first dilution, 9 parts diluent, 1 part of the second dilution, 9 parts diluent
When creating a serial dilution, the starting concentration is typically given as a ratio of sample to diluent. For example, a 1/10 dilution would mean that there is one part of sample and nine parts of diluent.
Now when we create a serial dilution from 1/10 to 1/1000, the first dilution will be 1 part sample and 9 parts diluent. The second dilution will be one part of the first dilution and nine parts diluent. The final dilution will be one part of the second dilution and nine parts diluent.
Thus, the answer is:
1 part sample
9 parts diluent
1 part of the first dilution
9 parts diluent
1 part of the second dilution
9 parts diluent
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____ The given question is incorrect, the correct question is given below:
When creating a serial dilution from 1/10 to 1/1000, the first dilution will be _______ part sample and ______ parts diluent. The second dilution will be one part ____ and nine parts _____. The final dilution will be one part _____ and nine parts diluent.
Choices:
1(one)
9(nine)
1/10 dilution
1/100 dilution
1/1000 dilution
diluent
How many ways can
4 candy bars be chosen
from a store that sells 30 candy bars?
Permutation or combination?
The count of the ways in which to chose 4 candies from a store that sells 30 candy bars, obtained by the combination formula, are 27405 ways
What is a combination in mathematics?A mathematical combination, is the ways in which a number of items can be chosen from a set of items, excluding a reference to the order in which the items are selected.
The number of ways k items can be chosen from n items, can be found by using the following combinations formula;
[tex]\binom{n}{k} = \frac{n!}{k!\cdot (n-k)!}[/tex]
Therefore, the number of ways 4 candies can be chosen from a store that sells 30 candy bars can be found by plugging in k = 4, and n = 30 as follows;
[tex]\binom{30}{4} = \frac{30!}{4!\cdot (30-4)!} = 27405[/tex]
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What is the value of 186 lb in kg
The formula for converting pounds (lb) to kilograms (kg) is 1 lb = 0.45359237 kg. To convert from lb to kg, you simply multiply the value in lb by 0.45359237.
For example, to convert 186 lb to kg, you would need to perform the following calculation: 186 lb × 0.45359237 kg/lb = 83.99 kg. Therefore, the answer to the question is that 186 lb is equivalent to 83.99 kg. This can be written in a short form as 186 lb = 83.99 kg. It is important to note that this conversion is based on the International System of Units (SI) and is the most commonly used method for measuring weight. When converting between measurements, it is also important to consider the accuracy of the conversion. In this case, the conversion is accurate to nine decimal places. This means that the result is accurate to within 0.000000001 kg, which is an extremely small amount. As such, this conversion should be suitable for most practical applications.
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I don’t get this math problem4/5 + 3/4
Answer:
AS a fraction: 1[tex]\frac{11}{20}[/tex]
AS a decimal: 1.55
Step-by-step explanation:
4/5 + 3/4
least common multiple of 5 and 4 is 20. Conver [tex]\frac{4}{5}[/tex] and [tex]\frac{3}{4}[/tex] to fractions with denominator 20.
16/20 + 15/20
since [tex]\frac{16}{20} and \frac{15}{20}[/tex] have the same denominator, add them by adding their numerators.
[tex]\frac{16 + 15}{20}[/tex]
Add 16 and 15 to get 31.
[tex]\frac{31}{20}[/tex]
[tex]\frac{31}{2^{2}x5 } = 1\frac{11}{20}[/tex]
Hope that helps and have a great day! =) ~sunshine~
19. The total number of students T who traveled for spring break
consists of two groups: students who flew to their destinations F and students who
drove to their destination D. The number (in thousands) of students who flew and
the total number of students who flew or drove can be modeled by the following
equations, where n is the number of years since 1995.
T = 14n + 21
F = 8n + 7
a. Write an equation that models the number of students who drove to their
destination for this time period. /
b. Predict the number of students who will drive to their destination in 2012.
c. How many students will drive or fly to their destination in 2015?
(asap help!)
Explain step by step please
The inequality form is 4/3<x<11.
What are logarithms?In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.
The given inequality is log₂(3x-4)<log₂(2x+7)
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form: 4/3<x<11
Interval Notation:(4/3,11)
Therefore, the inequality form is 4/3<x<11.
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7. A 16-inch pizza is cut into 8 equal slices. If
Thomas ate 3 slices, approximately how
many square inches of pizza did she eat?
Answer: 6 square inches
Step-by-step explanation:
Since the pizza is 16 inches and there is 8 slices divide.
16 inches ÷ 8 slices = 2 inches per slice
Each slice is 2 inches.
Since each slice is 2 inches multiply by 3 slices to get how many square inches she ate.
2 inches per slice x 3 slices = 6 square inches
Therefore she ate 6 square inches of pizza.
1. A number is less than one-fourth the sum of eight times the number and four.
We can write the inequality as -
{x} < (1/4){8x + 4}
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the statement as -
"A number is less than one-fourth the sum of eight times the number and four"
We can write the statement as follows.
Let the number be {x}. Then, we can write the inequality as -
{x} < (1/4){8x + 4}
Therefore, we can write the inequality as -
{x} < (1/4){8x + 4}
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A school orchestra has 60 members 20%of the members are percussionists,how many orchestra members are percussionist
Answer:
12
Step-by-step explanation:
10% * 60 = 6
20% * 60 = 12
You want to purchase
a pair of shoes for the
summer. Normally
they cost $79.99.
They are on sale for
15% off, or you also
have a $10 off
coupon. Including
sales tax at 10.3%,
what is the total
savings between
using the coupon and
taking the discount?
Answer:
$2.21
Step-by-step explanation:
You want to know the savings between using a $10 off coupon and taking a 15% discount, if the tax rate is 10.3%.
CouponThe price with the coupon is ...
$79.99 -10.00 = $69.99
When tax is added, the total becomes ...
$69.99 × 1.103 ≈ $77.20
DiscountThe price with the discount is ...
$79.99 × (1 -0.15) ≈ $67.99
When tax is added, the total becomes ...
$67.99 × 1.103 ≈ $74.99
SavingsThe savings by making use of the discount is ...
$77.20 -74.99 = $2.21
The total savings between the coupon and the discount is $2.21. That is, you save $2.21 more by using the discount instead of the coupon.
__
Additional comment
The question seems a bit ambiguous. The word "or" suggests you cannot use both discounts. If you do, the total amount saved will depend on the order in which they are applied.
You get the best result by taking the $10 off the sale price. Doing that gives you a total savings of about $24.27 off the normal price with tax.
If a system graphs as parallel lines, the system would have how many solutions?
Answer:
zero
Step-by-step explanation:
If a system of equations is graphed as 2 lines, then if the lines intersect, they intersect at one single point, and that point is the solution. There is one solution.
If the lines are parallel and do not intersect, then there is no solution. The number of solutions is zero.
Answer: zero
You want to estimate the mean SAT score for a population of students with a 80% confidence interval. Assume that the population standard deviation is s = 120. If you want the margin of error to be approximately 10, you will need a sample size of_____
The sample size for the given data is 17
What is sample size?The sample size is a term used in market research for defining the number of subjects included in a sample size.
Given that, a sample size has an 80% confidence interval, the population standard deviation is s = 120, the margin of error to be approximately 10, We need to find the sample size,
Sample size = (z-score)²×SD×(1-SD) / (confidence interval)²
z-score of 80% confidence interval = 1.28
Sample size = (1.28)²×0.12(1-0.12)/0.10²
= 1.6384×0.12×0.88/0.01
= 17.30
Hence, the sample size for the given data is 17
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ASAP
will give brainliest to correct answer
20pts
Answer:
5, 18 and 7 respectively
Step-by-step explanation:
4+9+5=18
18+7=35
Answer:The top box is 11 making the middle boxes 15 20
Step-by-step explanation:
4 11 9
4+11 11+9
15 20
15+20
35
Write some examples of quadrilaterals
A two-dimensional form having four sides, four vertices, and four angles is referred to as a quadrilateral. Examples are: Trapezium, Parallelogram, Rectangle, Rhombus, Square and Kite.
A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
The Latin words quadra, which means four, and latus, which means sides, are combined to form the English term quadrilateral. A quadrilateral does not always have to have equal lengths on each of its four sides. As a result, depending on the sides and angles, we might have several sorts of quadrilaterals. Hence a Quadrilateral is of 4 sides, vertices and angles. It consists of 360 degrees.
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4. Suppose you draw four balls from a bag containing seven pink, four white, three yellow, and two stripped balls. What is the probability of drawing 1 pink, 2 yellow and, stripped ball in succession without replacing the ball each time?
5. If a pair of dice is rolled, what is the probability that we roll a total of five if we are given that the total is less than nine?
6. Suppose a card is chosen at random from a deck of cards, replaced, and a second card is chosen. What is the probability that both cards are 7s?
7. It cost $1 to play a game in which two dice are rolled. If both dice show the same number you win $5; otherwise, you lose. What is the expected value of this game?
4. The probability of drawing 1 pink, 2 yellow and, stripped ball in succession without replacing the ball each time is (7/16) x (1/35) x (1/13) = 1/2540.
5. The probability that we roll a total of five if we are given that the total is less than nine is (1/36) / (4/36) = 1/4.
6. The probability that both cards are 7s is (6/36) x ($5 - $1) + (30/36) x (-$1) = -$0.17.
7. The expected value of the game is a loss of 17 cents per play.
Probabilities of Games4. The probability of drawing 1 pink ball, 2 yellow balls, and 1 stripped ball in succession is given by the product of the probabilities of drawing each ball without replacement.
The probability of drawing 1 pink ball is 7/16, the probability of drawing 2 yellow balls is (3/15) x (2/14) = 1/35 (because there are 3 yellow balls in the bag out of 15 total balls on the first draw, and 2 yellow balls out of 14 total balls on the second draw), and the probability of drawing 1 stripped ball is 2/13. Therefore, the probability of drawing 1 pink ball, 2 yellow balls, and 1 stripped ball in succession is:
(7/16) x (1/35) x (1/13) = 1/2540
5. If the total is less than nine, then there are only 4 possible outcomes: (1, 4), (2, 3), (3, 2), and (4, 1). The probability of rolling each of these outcomes is 1/36, since each die has 6 equally likely outcomes. The only outcome that adds up to 5 is (1, 4), which has probability 1/36. Therefore, the probability of rolling a total of 5, given that the total is less than nine, is:
(1/36) / (4/36) = 1/4
6. The probability of drawing a 7 on the first card is 4/52, since there are four 7s in a deck of 52 cards. Since the card is replaced, the probability of drawing a 7 on the second card is also 4/52. Therefore, the probability of drawing two 7s in a row is:
(4/52) x (4/52) = 1/169
7. The expected value of the game is the sum of the products of the outcomes and their probabilities. There are 6 x 6 = 36 possible outcomes, each with probability 1/36. Of these outcomes, 6 are winning outcomes (where both dice show the same number), and 30 are losing outcomes. The payout for a winning outcome is $5, and the cost of playing the game is $1. Therefore, the expected value is:
(6/36) x ($5 - $1) + (30/36) x (-$1) = -$0.17
Therefore, the expected value of the game is a loss of 17 cents per play.
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A kaleidoscope shaped like the prism below has mirrors covering the lateral surfaces. The bases are equilateral triangles. Find the total
square centimeters of mirrors covering the lateral surfaces.
The total square centimeters of mirrors covering the lateral surfaces is
171.5 cm².
What is surface area?
The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface.
Given:
Perpendicular height = 14.3
So, the Surface area of Prism is
= 5 x 10 x 3 + 1/2 x 5 x 4.3 x 2
= 150 + 21.5
= 171.5
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Write an explicit formula for a(n) the n^th term of the sequence 36,−6,1
how much 10 ml in teaspoon?
There are approximately 1 teaspoon in 5 milliliters. Therefore, in 10 milliliters we have 2 teaspoons approximately.
When converting between milliliters and teaspoons, it's important to know that 1 teaspoon is equal to approximately 5 milliliters. Therefore, to convert 10 milliliters to teaspoons, you would divide 10 by 5, which gives you 2. This means that there are approximately 2 teaspoons in 10 milliliters. It's worth noting that while teaspoons are commonly used in the United States and other countries that use the imperial system of measurement, most countries use the metric system, which uses milliliters as the standard unit of volume. Therefore, it can be helpful to know how to convert between these units of measurement, particularly if you're following a recipe or taking medication that uses a different system than what you're used to.
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Convert 8400 kilograms into tons. Round your answer to the nearest hundredth.
Answer:
9.26 tons
Step-by-step explanation:
8400 kilograms is 9.259415 tons and when you round to the nearest hundredth it is 9.26.
Students make a big mess in the cafeteria at lunch. 9 students had 30 minutes to clean up the mess.They got mad and named 3 others that were guilty. The principal added their names to the clean up crew and changed the time limit. How much time should she give them to complete the job?
Answer:
22.5 minutes
Step-by-step explanation:
Initially, there were 9 students with 30 minutes to clean up the mess. This means they had a total of 9 · 30 = 270 student minutes to clean up the mess.
After the 3 additional students were added, there were a total of 9 + 3 = 12 students on the clean-up crew.
Now, let's assume the time they need to clean up the mess is "t" minutes. Since the number of students and the time are inversely proportional to the amount of work done, we can set up the following equation based on the idea that the amount of work done is the same before and after the addition of the 3 students:
9 · 30 = 12 · t
Solving for "t":
270 = 12t
t = 270 / 12
t = 22.5
So, the principal should give them approximately 22.5 minutes to complete the job with the new crew of 12 students.
divide 3x^3-2x^2+4x-3 by x^2+3x+3
On dividing (3x³ - 2x² + 4x - 3) by (x² + 3x + 3), we get -
h(x) = 3x - 11 + {(28x + 30)/(x² + 3x + 3)}.
What is algebraic expression?An algebraic expression is a combination of terms both constants and variables. For example -
2x + 3y + z
3x + y
Given is to divide (3x³ - 2x² +4x - 3) by (x² + 3x + 3).
Let us assume that -
f(x) = (3x³ - 2x² + 4x - 3)
g(x) = (x² + 3x + 3)
We can write -
h(x) = f(x)/g(x)
h(x) = (3x³ - 2x² + 4x - 3)/(x² + 3x + 3)
h(x) = 3x + {(- 11x² - 5x - 3)/(x² + 3x + 3)}
h(x) = 3x - 11 + {(28x + 30)/(x² + 3x + 3)}
Therefore, on dividing (3x³ - 2x² + 4x - 3) by (x² + 3x + 3), we get -
h(x) = 3x - 11 + {(28x + 30)/(x² + 3x + 3)}.
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PLS HELP...... 4. John and Carol have both set up a proportion to solve for x in the diagram below.
John :
Carol:
Who is correct? Then solve for x.
There are 128 teams in a softball tournament. In each
round, half of the teams are eliminated. Which function
can be used to find the number of teams remaining in
the tournament after x rounds?
We can say that function (C) y = 128(0.5)ˣ will help us to determine the number of teams remaining after x number of rounds.
What are functions?A relation between a collection of inputs and outputs is known as a function.
A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
Each function has a range, codomain, and domain.
The usual way to refer to a function is as f(x), where x is the input.
One function, many. function onto (Surjective Function) into perform.
The function of a polynomial.
So, by observation we can find out the function:
y = 128(0.5)ˣ
Assume the teams after 1st round:
y = 128(0.5)ˣ
y = 128(0.5)¹
y = 128*0.5
y = 64 (Half od 128)
Therefore, we can say that function (C) y = 128(0.5)ˣ will help us to determine the number of teams remaining after x number of rounds.
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[tex]\lim_{x\to \023}[/tex][tex]\sqrt{x+2}-5/x-23[/tex]
The limit of the expression [tex]\lim_{x \to \223} \sqrt{x+2} -\frac{5\\}{x} -23[/tex] when evaluated is -18.22
What is a Limit?Limit is a value that a function approaches the output for the given input values.
How to determine the limit of the expressionFrom the question, we have the following limit expression that can be used in our computation:
[tex]\lim_{x \to \223} \sqrt{x+2} -\frac{5\\}{x} -23[/tex]
To find the limit tends to 23, we substitute 23 for x in the above equation
So, we have the following representation
[tex]\lim_{x \to \223} \sqrt{23+2} -\frac{5\\}{23} -23[/tex]
Evaluate the sum in the expression
[tex]\lim_{x \to \223} \sqrt{25} -\frac{5\\}{23} -23[/tex]
Evaluate the exponent and the fractions
Limit = 5 -5/23 -23
When the expression is evaluated, we have
Limit = -18.2173913043
Approximate
Limit = -18.22
Hence, the solution is -18.22
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Tyler is working two summer jobs, making $25 per hour tutoring and making $9 per
hour clearing tables. In a given week, he can work no more than 18 total hours and
must earn a minimum of $270. If a represents the number of hours tutoring and y
represents the number of hours clearing tables, write and solve a system of
inequalities graphically and determine one possible solution.
One possible solution is to tutor for 11 hours and clear tables for 5 hours
How to write and solve a system of inequalities graphicallyFrom the question, we have the following parameters that can be used in our computation:
$25 per hour tutoring and making $9 per hour clearing tables. He can work no more than 18 total hours and must earn a minimum of $270Using the above as a guide, we have the following:
25x + 9y ≥ 270
x + y ≤ 18
Where
x = hours tutoring
y = hours cleaning tables
Next, we plot the graph (see attachment)
One solution from the graph is (11, 5)
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please answer this for me
Answer:
Step-by-step explanation:
where is the equation?
Answer:
Step-by-step explanation:
Multiply 4.75 by 2 to find out how much money Maurice gets when finishing 2 chores. $4.75 x 2 = $9.50. So, write $9.50 under 2. For three chores, multiply $4.75 by 3. $4.75 x 3 = $14.25. Write $14.25 under 3.
Naomi has taken six science tests so far this year. The tests are out of 100 points, and she has gotten the following scores.
64, 88, 92, 86, 81, 92
What is the median of her scores?
no median
83.8
92
87
A successful lawyer ownsthree vintage cars. The ratio of car is value to 1's value is 3:4. The ratio of car 2's value tocar 3's is 8:5. d the total value of three cars is $1115900, fins the value of each car
Answer: Let's represent the value of car 1 as x. Then, the value of car 2 is 3/4 of x, and the value of car 3 is 4/5 of the value of car 2.
So, we can write the following equations:
x = (3/4) * y
y = (4/5) * z
Where y is the value of car 2, and z is the value of car 3.
Adding all the values, we have:
x + y + z = 1115900
We can substitute the values of y and z in terms of x:
x + (3/4) * x + (4/5) * (3/4) * x = 1115900
Simplifying the expression on the left side, we get:
7/4 * x = 1115900
Finally, dividing both sides by 7/4, we get:
x = 359900
So, the value of car 1 is $359900, the value of car 2 is (3/4) * x = (3/4) * 359900 = 269925, and the value of car 3 is (4/5) * (3/4) * x = (4/5) * (3/4) * 359900 = 213140.
Step-by-step explanation:
Answer: the value of car 1 is $467125, the value of car 2 is $623033.33, and the value of car 3 is $350937.5.
Step-by-step explanation:
Let's call the value of car 1 "x".
From the first ratio, we know that the value of car 2 is 4/3 times greater than the value of car 1, and the value of car 3 is 3/4 times greater than the value of car 1.
So, the value of car 2 is 4/3 * x, and the value of car 3 is 3/4 * x.
From the second ratio, we know that the value of car 2 is 8/5 times greater than the value of car 3.
So, the value of car 2 is 8/5 * (3/4 * x) = 6/5 * x.
The total value of all three cars is $1115900, so we can set up an equation to solve for x:
x + 4/3 * x + 3/4 * x = 1115900
Expanding and simplifying the right side:
x + 4/3 * x + 3/4 * x = 1115900
8/3 * x = 1115900
x = 1115900 * 3 / 8
x = 467125
So, the value of car 1 is $467125, the value of car 2 is $623033.33, and the value of car 3 is $350937.5.
The regular price on a pair of jeans is $54. The store advertises a back to school sale at 40% of the regular price of the jeans. Two weeks later, the store advertises a sale at an additional 20% off the sale price of the jeans. Two friends decided to purchase the jeans. Shannon says these jeans are now 60% of the regular price. Mary disagrees because she figures that the total discount is less than 60%. What is the cost of the jeans at the 40% off back-to-school sale. What is the cost of the jeans during the additional 20% off sale
Answer:
See explanation
Step-by-step explanation:
40% of the original $54 is $21.60, therefore the pants are $21.60 off of their original price. This makes the pants $32.40.
20% of the new $32.40 is $6.48, therefore the pants are $6.48 off of the 40%-off price. This makes the pants $25.92 for their final price.
Graph and find the area of the figure with vertices (-3,-2),(-2,-),(1,1), (0,-2) NEED help pls
Answer: The formula for finding the area of a triangle is A = 1/2(x1)(y2-y3)+(x2)(y3-y1)+(x3)(y1-y2).
Plugging in the given coordinates, the area of the triangle is:
A = 1/2(-3)(-1-1) + (-2)(1-(-2)) + (1)(-2-(-1))
A = 1/2(-3)(-2)+(-2)(3)+1(-3)
A = -9+6-3
A = 4
Step-by-step explanation: Step 1: Identify the formula for finding the area of a triangle: A = 1/2(x1)(y2-y3)+(x2)(y3-y1)+(x3)(y1-y2).
Step 2: Plug the given coordinates into the formula: A = 1/2(-3)(-1-1) + (-2)(1-(-2)) + (1)(-2-(-1)).
Step 3: Simplify the equation: A = 1/2(-3)(-2)+(-2)(3)+1(-3).
Step 4: Solve the equation: A = -9+6-3.
Step 5: Find the area of the triangle: A = 4.