For the given condition the correct inequality is,
⇒ x ≥ 20
Where, x represent the number of questions.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
A student decides to solve at least 20 math problems every day to better their grade if they self and math problems every day.
Let number of questions done by a student = x
So, The inequality for the given condition is,
⇒ x ≥ 20
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For each inequality, show it on the number line and write all one-digit integers that satisfy it. k≥0
For the inequality k≥0, all the integers which satisfies the given inequality are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
What are inequalities?Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.
We use these symbols to represent inequalities, '>' , '<', '≥', '≤'
Given that,
The inequality,
k ≥ 0
The inequality k ≥ 0 means that k is greater than or equal to 0. This can be represented on a number line as follows:
-------------k-------------
where the line represents all real numbers and the arrow points to the right to indicate that k can be any real number greater than or equal to 0.
All one-digit integers that satisfy the inequality k ≥ 0 are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
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Ten letter tiles are placed in a bag. Once a tile has been drawn, it is not placed back in the bag. What is the probability that someone will randomly select the letter tiles in order to spell STATISTICS?
The probability that the word formed STATISTICS will be; 1/10! = 1/3628800
What is meant by probability?The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. According to the probability formula, the likelihood that an event will occur is equal to the proportion of favourable outcomes to all outcomes.
The total number of tiles in a bag is; 10
WE are given that once a tile is drawn, we will not place the tile back in the bag.
We should find the probability that randomly selected tiles spell the word, STATISTICS, that is a 10 letter word.
Now when we draw the first tile,
1 st tile = 1/10
Now there are only 9 tiles left.
2nd tile probability = 1/9
Now only 8 tiles left then
3rd tile probability = 1/8
Therefore the probability that the word formed is STATISTICS would be
= 1/10 * 1/9 * 1/8 * 1/7 * 1/6 * 1/5 * 1/4 * 1/3 * 1/2
= 1/10! = 1/3628800
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Which equation would create a line parallel to y= 5x +10
Answer:
y=1/5x +4
Step-by-step explanation:
Write an equation for the line that is parallel to the given line and passes through the given point. y = 5x + 10; (2, 14) y=1/5x +4
WILL MARK BRAINLIEST!!!!!
Liam said that the following graph shows a positive correlation between ice cream sales and temperature.
Is he correct? Why or why not?
Liam’s friend Armonte said he believes this represents causation instead of a correlation. Is Liam or Armonte correct? Give at least two reasons to help support your claim.
Yes, Liam is correct as the graph depicts a positive correlation as the temperature increases the ice cream sales also increases.
What do you mean by correlation and causation?A correlation between two variables shows a statistical connection between them. Causation is the process whereby a change in one variable causes a change in another.
While conducting research, you may have come across the proverb "correlation doesn't imply causality." Although correlation and causality are related ideas, understanding how they differ helps improve your capacity to assess and critically analyze scientific data.
Armonte said the graph depicts causation and yes Armonte is correct as causation means that changes in one variable bring about changes in the other; there is a cause-and-effect relationship between variables. The two variables are correlated with each other and there is also a causal link between them.
So here the change in the temperature brought about the change in the ice cream sales. As the temperature rose the ice cream sales too started increasing.
Now two reasons as to why this represents causation instead of correlation:
The third variable problem states that a confounding variable has an effect on two variables, providing the false appearance that they are causally related. The directionality problem occurs when two variables correlate and maybe have a causal relationship, but it is impossible to pinpoint which variable has an impact on the other.Therefore, the graph shows a positive correlation, but it represents causation.
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A sector with a central angle measure of \purpleD{175\degree}175°start color #7854ab, 175, degree, end color #7854ab has a radius of \maroonD{12\,\text{cm}}12cmstart color #ca337c, 12, start text, c, m, end text, end color #ca337c.
A circle with a radius of twelve centimeters. A sector is highlighted. The central angle is equals one hundred seventy-five degrees.
A circle with a radius of twelve centimeters. A sector is highlighted. The central angle is equals one hundred seventy-five degrees.
What is the area of the sector?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
\dfrac{35}{3}\pi\,\text{cm}^2
3
35
πcm
2
start fraction, 35, divided by, 3, end fraction, pi, start text, c, m, end text, squared
(Choice B)
B
24\pi\,\text{cm}^224πcm
2
24, pi, start text, c, m, end text, squared
(Choice C)
C
70\pi\,\text{cm}^270πcm
2
70, pi, start text, c, m, end text, squared
(Choice D)
D
144\pi\,\text{cm}^2144πcm
2
The area of the sector is evaluated to be equal to 220 square centimeters.
How to evaluate for the area of the sector.The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius and π = 22/7.
We have the angle of the sector = 175° and radius = 12 cm, hence the area of the sector is calculated as follows:
(175°/360°) × 22/7 × 12 × 12
we simplify by division and multiplication
(35/72) × 22/7 × 12cm × 12cm
{35/7 = 5 and 72/12 = 6}
(5/6) × 22 × 12cm²
{12/6 = 2}
5 × 22 × 2cm²
220 cm².
Therefore, the area of the sector is evaluated to be equal to 220 square centimeters.
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Use the Empirical Rule to estimate
The number of farms whose land and building values are between $1,200 and $1,400 is given as follows:
50 farms.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of approximately 68%.The percentage of scores within two standard deviations of the mean of the distribution is of approximately 95%.The percentage of scores within three standard deviations of the mean off the distribution is of approximately 99.7%.Considering the mean of $1,300 and the standard deviation of $100, measures between $1,200 and $1,400 are within one standard deviation of the mean, hence the percentage is of 68%.
The total amount is of 74 farms, hence the amount relative to 68% of 74 is of:
0.68 x 74 = 50 farms. (rounded).
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Linear equation that passes through the points of (0,1) and (5,3)
Answer:
y=2/5x+1
Step-by-step explanation:
Answer:
y = 2/5 x + 1
Step-by-step explanation:
The slope is the change in y over the change in x
[tex]\frac{3-1}{5-0}[/tex] = [tex]\frac{2}{5}[/tex]
slope: [tex]\frac{2}{5}[/tex]
The y-intercept is 1. When x = 0, the y is the intercept. (0,1)
Let X be a continuous distribution with the density function f_X. Derive the random variable Y = | X-1 | density function f_Y. If X ~Unif (-1,0), what is the distribution of Y?
The density function of Y = | X-1 | is given by:
f_Y(y) = {f_X(y + 1), if 0 < y < 1;
{f_X(1 - y), if 1 < y < 2;
{0, otherwise.
Continuous distribution is a type of probability distribution that describes the likelihood of a variable taking on any value within a given range, rather than just specific values
If X ~Unif (-1,0), then the density function of Y is given by:
f_Y(y) = {1/2, if 0 < y < 1;
{1/2, if 1 < y < 2;
{0, otherwise.
Therefore, Y ~Unif (0,2).
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Danton is rolling a fair six-sided die, each face with a number 1-6. He rolls 20 times and gets a “4” 6 times. What is the theoretical probability of rolling a 4 on this die?
The theoretical probability of rolling a 4 on the die is 0.0647
What is a Binomial Distribution?The binomial distribution is a type of probability distribution that predicts the likelihood of obtaining one of two outcomes given a set of inputs. It summarizes the number of tries where each trial has the equal chance of producing the same result.
The formula for Binomial Distribution is given by
P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ
where
n = number of trials
x = number of successes
p = probability of getting a success in one trial
q = probability of getting a failure in one trial
q = 1 - p
Given data ,
Let the number of trials n = 20
Let the probability of getting a 4 on the die be = 1/6
So , the value of p = 1/6
And , the probability of getting a failure q = 5/6
So , theoretical probability of rolling a 4 on this die = P ( x = 4 )
And , the Binomial Distribution is given by
P ( x = 6 ) = [ 20! / ( 20 - 6 )! 6! ] ( 1/6 )⁶ ( 5/6 )¹⁴
On simplifying the equation , we get
P ( x = 6 ) = [ 20 x 19 x 18 x 17 x 16 x 15 / 6 x 5 x 4 x 3 x 2 x 1 ) ( 1/6 )⁶ ( 5/6 )¹⁴
On further simplification , we get
P ( x = 6 ) = 0.0647
P ( x = 6 ) = 6.047 %
Hence , the probability of rolling a 4 is 0.0647
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Help me ASAP!!!!!!!!!!
The difference in height of the two checkpoints is 3487 feet.
What do you mean by above sea level?The term above mean sea level (AMSL) refers to the elevation (on the ground) or altitude (in the air) of any object, relative to the average sea level datum.
Given here: The table containing the altitude of different checkpoints in a race.
Height above mean sea level is a measure of the vertical distance (height, elevation or altitude) of a location in reference to a historic mean sea level taken as a vertical datum.
The altitude of checkpoint 1 is -164 and Checkpoint 2 as 3487
Thus Difference in the height of the two checkpoints is
3487-(-164)
3651 feet lower.
If the top of a hill rises 291 feet above checkpoint 1 we get
-164+291=127 feet
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independent and dependent variables maze
The independent variable affects the dependent variable. The correct option is B.
What are variables?A variable is something whose value can change and is not fixed. Typically, the letters x, y, z, etc. are used to indicate variables. (b) Constants: An object whose value is fixed for the current circumstance is referred to as a constant. The constant's value may not be known, but we do know that it is fixed.
A variable is an object that you are trying to measure. It has two types; independent and dependent variables. An independent variable is a variable that is not affected b other variables.
A dependent variable on the other hand is a variable that depends on other variables. Suppose you want to know the quality of sleep of the students in their academic performance. The quality of sleep is the independent variable and academic performance is the dependent variable.
The complete question is given below.
What is the relationship between the independent variable and the dependent variable?
a. The dependent variable affects the independent variable.
b. The independent variable affects the dependent variable.
c. Both the independent variable and the dependent variable affect each other.
d. Neither the dependent variable nor the independent variable affects each other.
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can someone pls help with the question that have stars
The answers for each polynomial are:
a) 4x³ - 8: degree is 3, and the number of terms is 2.
b) 2x⁴ - 7x² - 5x + 1: degree is 4, and there are 4 terms.
c) x³ +5x² + 28 - x: standard form is: x³ +5x² - x + 28 And the leading coefficient is 1.
d) 24 - x³ + x: standard form is: -x³ + x + 24 and the leading coefficient is -1.
How to classify the polynomials?The degree of a polynomial is equal to the maximum exponent in the variable, and the number of terms is just the number of "elements" separated by the symbols + or -.
For the first one:
4x³ - 8
The degree is 3, and the number of terms is 2.
For the second one:
2x⁴ - 7x² - 5x + 1
The degree is 4, and there are 4 terms.
In the next part you need to write them in standard form and write the leading coefficient. The leading coefficient is the coefficient on the term with the largest exponent.
For the first one:
x³ +5x² + 28 - x
The standard form is:
x³ +5x² - x + 28
And the leading coefficient is 1.
And the last one is:
24 - x³ + x
The standard form is:
-x³ + x + 24
The leading coefficient is -1.
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Given that P={2,3} Q={2,4} and U={1,2,3,4} find P and Q
The intersection of sets P and Q is given as follows:
P and Q = {2}.
How to obtain the intersection between sets P and Q?The sets P and Q for this problem are defined as follows:
P = {2,3}.Q = {2,4}.The intersection between two sets is composed by the elements that belong to both of the sets.
Hence the intersection of sets P and Q is given as follows:
P and Q = {2}.
As the element 2 belongs to both sets P and Q.
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A tank contains 22 gallons of water when all of a sudden the water begins draining at a constant rate of 2 gallons per hour. Let t represent the number of hours since the water began draining and let v represent the volume of water in the tank. a. Write a formula that expresses v in terms of t
b. As t increases from 3 to 5, v varies from___ to ____
c. As t varies from 3 to 5, how much do t and v change by?
a). The formula that expresses v in terms of t is v = 22 - 2t, b). As t increases from 3 to 5, v varies from 16 to 12, c). As t varies from 3 to 5, v changes by 16 - 12 = 4.
What is the volume?
'Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m3, cm3, in3, etc. Sometimes, volume is also termed capacity.
a). The volume of water in the tank, v, decreases by 2 gallons per hour, so the formula for v in terms of t is v = 22 - 2t.
b). As t increases from 3 to 5, v varies from 16 to 12. That is, as t goes from 3 to 5, v decreases from 22 - 2(3) = 16 to 22 - 2(5) = 12.
c). As t varies from 3 to 5, t changes by 5 - 3 = 2, and v changes by 16 - 12 = 4.
Hence, a). The formula that expresses v in terms of t is v = 22 - 2t, b). As t increases from 3 to 5, v varies from 16 to 12, c). As t varies from 3 to 5, v changes by 16 - 12 = 4.
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Reduce the equation to one of the standard forms, classify the surface, and sketch it. (a) z^2 = 4x^2 + 9y^2 + 36 (b) x = 2y^2 + 3z^2 (c) 4x^2 + y^2 + 4z^2 - 4y - 24z + 36 = 0 (d) x^2 - y^2 + z^2 - 4x - 2y - 2z = 0
Reduced the equation to one of the standard forms
(a) z²/36 = 4x²/36 + 9y²/36 + 1
(b) x = 2y² + 3z
(c) (x + y + 2z)²
(d) (x - y + z)²
What do you mean by equation?It is represented by an equal sign (=) and is used to solve for unknown values or to describe relationships between variables. Equations can be simple or complex, involving basic arithmetic operations or advanced mathematical concepts like trigonometry and calculus.
An equation can be used to solve for a single unknown value, for example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving us 2x = 4 and then dividing both sides by 2, giving us x = 2. In this example, x = 2 is the solution to the equation.
(a) The equation z² = 4x² + 9y² + 36 can be reduced to the standard form of an ellipsoid by dividing both sides by 36:
z²/36 = 4x²/36 + 9y²/36 + 1
This is the equation of an ellipsoid with center at the origin and semi-axes of length 3, 3/2, and 6, respectively. The surface is a solid and is classified as an oblate ellipsoid.
(b) The equation x = 2y² + 3z² is a standard parabolic cylinder equation. The surface is a cylinder and is classified as a parabolic cylinder.
(c) The equation 4x² + y² + 4z² - 4y - 24z + 36 = 0 can be reduced to the standard form of an ellipsoid by dividing both sides by 36:
x² + y² + 4z² - 4y - 24z + 36 = 0
= (x + y + 2z)²
This is the equation of an ellipsoid with center at the origin and semi-axes of length 3, 3, and 6, respectively. The surface is a solid and is classified as an oblate ellipsoid.
(d) The equation x² - y² + z² - 4x - 2y - 2z = 0 can be reduced to the standard form of a hyperboloid of two sheets by subtracting 1 from both sides:
x² - y² + z² - 4x - 2y - 2z + 1 = 1
= (x - y + z)²
This is the equation of a hyperboloid of two sheets with center at the point (-2, -1, -1) and semi-axes of length √2, √2, and √6, respectively. The surface is a solid and is classified as a hyperboloid of two sheets.
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After reducing the equation to one of the standard forms, the equations will be (a) z²/36 = 4x²/36 + 9y²/36 + 1, (b) x = 2y² + 3z, (c) (x + y + 2z)², and (d) (x - y + z)²
What do you mean by equation?It is represented by an equal sign (=) and is used to solve for unknown values or to describe relationships between variables. Equations can be simple or complex, involving basic arithmetic operations or advanced mathematical concepts like trigonometry and calculus.
An equation can be used to solve for a single unknown value, for example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving us 2x = 4 and then dividing both sides by 2, giving us x = 2. In this example, x = 2 is the solution to the equation.
(a) The equation z² = 4x² + 9y² + 36 can be reduced to the standard form of an ellipsoid by dividing both sides by 36:
z²/36 = 4x²/36 + 9y²/36 + 1
This is the equation of an ellipsoid with center at the origin and semi-axes of length 3, 3/2, and 6, respectively. The surface is a solid and is classified as an oblate ellipsoid.
(b) The equation x = 2y² + 3z² is a standard parabolic cylinder equation. The surface is a cylinder and is classified as a parabolic cylinder.
(c) The equation 4x² + y² + 4z² - 4y - 24z + 36 = 0 can be reduced to the standard form of an ellipsoid by dividing both sides by 36:
x² + y² + 4z² - 4y - 24z + 36 = 0
= (x + y + 2z)²
This is the equation of an ellipsoid with center at the origin and semi-axes of length 3, 3, and 6, respectively. The surface is a solid and is classified as an oblate ellipsoid.
(d) The equation x² - y² + z² - 4x - 2y - 2z = 0 can be reduced to the standard form of a hyperboloid of two sheets by subtracting 1 from both sides:
x² - y² + z² - 4x - 2y - 2z + 1 = 1
= (x - y + z)²
This is the equation of a hyperboloid of two sheets with center at the point (-2, -1, -1) and semi-axes of length √2, √2, and √6, respectively. The surface is a solid and is classified as a hyperboloid of two sheets.
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What is an angle that is supplementary to ∠CGD
Answer:
Step-by-step explanation:
angle DGF
Paul wants to buy a new car, but rather than take out a loan, he decides to save $150 a month in an account that earns 2.5% interest, compounded monthly. How much will he have saved up after three years have passed?
Answer:
Step-by-step explanation: To calculate the total amount of money Paul will have saved after three years, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A = the total amount after t years
P = the initial principal, which is $150
r = the annual interest rate, which is 2.5% or 0.025
n = the number of times the interest is compounded per year, which is 12 since it is compounded monthly
t = the number of years, which is 3
Substituting the values into the formula, we get:
A = 150 * (1 + 0.025/12)^(12*3)
= 150 * 1.081567
= $162.23
Therefore, Paul will have saved up $162.23 after three years have passed.
PLease help 50 points
Answer:
Step-by-step explanation:
multiple by the domanatior to get the answer
Change from base 10 to base 4. It will be helpful to create a place value chart for base 4 before doing this problem. Show your thinking.
9^10
15^10
29^10
72^10
Challenge: 259^10
9¹⁰ can be expressed as base 4 with 22 and 15¹⁰ can be expressed as 33.
What is Expression?An expression is combination of variables, numbers and operators.
To change from base 10 to base 4, we need to express each number in terms of powers of 4. Here's how you can do this for each number:
9¹⁰ in base 4:
9 in base 10 can be expressed as 22
Base 4
So, (22)¹⁰ = 4¹⁰ x 2¹⁰ = 1048576 x 1024
= 1073741824 in base 10.
15¹⁰ in base 4
15 in base 10 can be expressed as 33 in base 4
Hence, 9¹⁰ can be expressed as base 4 with 22 and 15¹⁰ can be expressed as 33.
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87+3 ? pls help me i dont know any answer /clue
Answer:the answer is 90
Step-by-step explanation:
Answer:9
Step-by-step explanation:
Troy set a goal for the total distance he wants to jog this week. He divided his goal evenly among the 5 jogs he planned for the week. Troy determined that each jog should be at least 2.8 miles to meet his goal.
Let x represent how many miles Troy wants to jog in all. Which inequality describes the problem?
The inequality describing the given problem is x/5 ≥ 2.8 and Troy should at least jog for 14 miles in total.
What is inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given that, Troy set a goal for the total distance he wants to jog this week. He divided his goal evenly among the 5 jogs he planned for the week. Troy determined that each jog should be at least 2.8 miles to meet his goal.
x represent how many miles Troy wants to jog in all. We need to find an inequality describes the problem.
Since, he has divided his goal into 5 jogs and in total he did x jogs, therefore, jog for 1 day = x/5
Now, he set that each jog should be at least 2.8 miles to meet his goal.
That mean, he can jog 2.8 miles or more than it but not less than it,
Therefore, inequality will be,
x/5 ≥ 2.8
Now, finding x,
Multiply both sides by 5,
x ≥ 14
Hence, the inequality describing the given problem is x/5 ≥ 2.8 and Troy should at least jog for 14 miles in total.
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NEEED HELP’’’’’!!!….
63, 69, 75 and 81 is the first four terms of the seqence
Finding the recursive formula for a sequenceGiven the recursive formula of the given sequence
an = 63 + (n - 1)*6
We need to determine the first four terms of the sequence
When n = 1;
a1 = 63 + (1 - 1)*6
a1 = 63
When n = 2;
a2 = 63 + (2 - 1)*6
a2 = 69
When n = 3;
a3 = 63 + (3 - 1)*6
a3 = 75
When n = 4;
a4 = 63 + (4 - 1)*6
a4 = 81
Hence the first four terms of the sequence are 63, 69, 75 and 81.
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Please help me with the answer to this question
Answer:
1/36
Step-by-step explanation:
above is the answer
is "What is the area of the floor in this classroom?" a statistical question? Explain your reasoning.
"What is the area of the floor in this classroom?" is not a statistical question.
What is statistical reasoning?Statistical Reasoning is the first course in statistics for students whose college and career paths require knowledge of the fundamentals of the collection, analysis, and interpretation of data.
All statistical questions contain gathering numerical statistics (normally from a set of human beings) after which studying it to attract conclusions approximately the reviews of human beings of a positive phenomenon because the statistics vary relying on the reaction of every person.
This method isn't required to decide the location of the ground due to the fact this has a completely unique solution and might certainly be located via way of means of measuring the peak and width of the school room after which multiplying each number.
therefore, this doesn't mean accumulating loads of statistics and the statistics does now no longer vary.
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A water sport shop sells tubes, kayaks, canoes, skis, and rafts. The circle graph below shows the sales from january.
There were 400 items sales in january. Based on the circle graph, how many of those sales were tubes or rafts?
A. 160
B. 200
C. 240
D. 300
Answer: B. 200
Step-by-step explanation:
Since "rafts" and "tubes" takes up exactly 50% of the circle graph, the answer is 50% of 400, or 200. The correct answer is option B. 200
PLEASE HELP!
Solve the formula for the specified variable
V= APT for A
A=
It says a=v/pt is wrong
Making A the subject of the equation V = APT gives A = V/(PT)
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Given the equation:
V = APT
We need to make A the subject of the formula.
Firstly, divide both sides of the equation by P:
V/P = APT/P
AT = V/P
Secondly divide both sides of the equation by T:
(AT)/T = (V/P)/T
A = V/(PT)
The value is A = V/(PT)
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An account that compounds interest monthly has an annual percentage yield of 5.9%.
What is the annual interest rate for the account?
Answer: The annual percentage yield (APY) is the total amount of interest earned on an investment over a year, expressed as a percentage of the initial investment. The annual interest rate is simply the interest rate per year, expressed as a percentage.
To convert the APY to the annual interest rate, we can divide the APY by the number of times the interest is compounded in a year. If the interest is compounded monthly, then the number of times the interest is compounded in a year is 12.
So, the annual interest rate for the account is given by:
Annual interest rate = APY / number of times compounded in a year
= 5.9% / 12
= 0.49%
Therefore, the annual interest rate for the account is 0.49%.
Step-by-step explanation:
20. While packing for a trip to Spain a traveler wishes to weigh their luggage to make
sure it doesn't exceed 23 kilograms. Unfortunately, their bathroom scale for some
reason can only weigh in ounces. How many ounces should the luggage weigh?
The traveler's luggage should weigh around 806.722 ounces.
How to convert kilogram to ounces?To convert kilograms to ounces, you can use the conversion factor of 35.274 ounces per kilogram.
Here's the formula to convert kilograms to ounces:
Ounces = Kilograms * 35.274
When it comes to measuring weight, the metric system and the imperial system use different units of measurement. The metric system uses kilograms as its unit of measurement for weight, while the imperial system uses ounces.
To convert between the two systems, it is necessary to know the conversion factor between kilograms and ounces. One kilogram is approximately equal to 35.274 ounces. This means that to convert from kilograms to ounces, you can multiply the number of kilograms by 35.274.
In the case of the traveler in Spain, they wanted to ensure that their luggage did not exceed 23 kilograms in weight. To determine this weight in ounces, they multiplied 23 kilograms by the conversion factor of 35.274 ounces/kilogram, which gives a result of 806.722 ounces.
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Given f(x) = 8x ^ 2 + 16x + 6 and (g - f)(x) g(x) = x ^ 3 - 3x ^ 2 - 9 find (g-f)(x).
A) - x ^ 3 + 11x ^ 2 + 16x + 15
B) x ^ 3 + 5x ^ 2 + 16x - 3
C) x ^ 3 - 11x ^ 2 - 16x - 15
D) - x ^ 3 + 5x ^ 2 - 16x - 3
The combination of the difference of the functions (g - f)(x), where; f(x) = 8·x² + 16·x + 6 and g(x) = x³ - 3·x² - 9 is; x³ - 11·x² - 16·x - 15
The correct option is option C
C) x³ - 11·x² - 16·x - 15
What are some of the formula for the combination of functions?The combinations of functions can be found as follows;
Addition; (f + g)(x) = f(x) + g(x)
Subtraction; (f - g) = f(x) - g(x)
Multiplication; (f·g) = f(x) × g(x)
Division; (f/g)(x) = f(x)/g(x)
What is a function?
A function is a rule or law that maps an input variable into an output variable such that each element in the set of input variable is mapped to exactly one element in the set of the output variables.
The f(x) = 8·x² + 16·x + 6
g(x) = x³ - 3·x² - 9
Therefore;
(g - f)(x) = g(x) - f(x)
(g - f)(x) = x³ - 3·x² - 9 - (8·x² + 16·x + 6) = x³ - 11·x² - 16·x - 15
The correct option is therefore option C
C) x³ - 11·x² - 16·x - 15
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a meal in a restaurant cost $40 in 2000. What was it's price in 1992 dollars? Contemporary math
The cost of the meal that cost $40 in 2000 would have cost $32.16 in 1992.
What is average inflation rate?The average rate at which the prices of goods and services change within a year is called the average inflation rate.
Given that, a meal in a restaurant cost $40 in 2000, we need to find its price in 1992 dollars,
The dollar had an average inflation rate of 2.45% per year between 1992 and today,
The year change = 2000 - 1992 = 8
Therefore, the $40 in 1992 =
= 40 - (40 × 8 × 2.45 / 100)
= 40 - (7.84)
= 32.16
Hence, the cost of the meal that cost $40 in 2000 would have cost $32.16 in 1992.
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