The claim that if x is even then 9x - 5 is odd is false for all x < 0, as demonstrated by an example where x = -2 and 9x - 5 = -17, which is an even number.
The smallest counterexample method is used to prove that a claim is false by providing an example that does not follow the claim. To prove the claim that if x is even then 9x 5 is odd, for all x < 0, we can use the smallest counterexample method by finding the smallest value of x that would disprove the claim.
Let x = -2, then 9(-2) - 5 = -17. Since -17 is even, it does not follow the claim that if x is even then 9x - 5 is odd, thus disproving the claim for all x < 0.
To explain this with formula and calculation, let x = -2, then 9x - 5 = 9(-2) - 5 = -17. Since -17 is even, the claim that if x is even then 9x - 5 is odd is false. Therefore, the claim is false for all x < 0.
The claim that if x is even then 9x - 5 is odd is false for all x < 0, as demonstrated by an example where x = -2 and 9x - 5 = -17, which is an even number.
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Personality types are broadly defined according to four main preferences. Do married couples choose similar or different personality types in their mates? Suppose the following data were collected to attempt to answer this question.
a) The probability that the married couples will have 0, 1, 2, 3, or 4 preferences in common is as follows:
All four 0.07Three 0.32Two 0.30One 0.16None 0.15.b) Yes, the probabilities add up to 1.
c) The above result does make sense. The table values add up to 375 as the probabilities sum up to 1.
d) The sample space in this problem is C. 0, 1, 2, 3, 4 personality preferences in common.
What is the probability?Probability refers to the odds, chance, or likelihood of an expected outcome occurring given many possible outcomes.
Probability is a fractional value, lying between 0 and 1, in most instances, except when it is 100% uncertain or certain.
Random Sample = 375 married couples
Number of Similar Number of Probability of
Preferences Married Couples Common Preferences
All four 26 6.93% (26/375) or 0.07
Three 120 32.00% (120/375) or 0.32
Two 113 30.13% (113/375) or 0.30
One 61 16.27% (61/375) or 0.16
None 55 14.67% (55/375) or 0.15
Total 375 100% or 1
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a 400-gal tank initially contains 100 gal of brine containing 50 lb of salt. brine containing 1 lb of salt per gallon enters the tank at the rate of 5 gal/s, and the well-mixed brine in the tank flows out at the rate of 3 gal/s. use x (t) to represent the number of pounds of salt in the tank at time t, where t is measured in seconds. answer the following, stating the units in each part. (a) what is the initial amount of salt in the tank? (b) what is the initial volume of solution in the tank? (c) what is the concentration of salt being added to the tank? (d) what is the rate at which the solution being added to the tank? (e) what is the rate at which the solution is being removed from the tank? (f) what is the volume of the solution in the tank at time t. (g) what is the concentration of the salt in the tank at time t? (h) write a differential equation with initial conditions that models this mixture problem. (do your units make sense?)
This differential equation states that the rate of change of the amount of salt in the tank is equal to the difference between the rate at which brine containing salt is being added to the tank.
(a) The initial amount of salt in the tank is 50 lbs.
(b) The initial volume of solution in the tank is 100 gal.
(c) The concentration of salt being added to the tank is 1 lb of salt per gallon of brine.
(d) The rate at which the solution is being added to the tank is 5 gal/s.
(e) The rate at which the solution is being removed from the tank is 3 gal/s.
(f) The volume of the solution in the tank at time t can be represented by V(t) = 100 + (5 - 3)t = 100 + 2t gal.
(g) The concentration of salt in the tank at time t can be represented by C(t) = x(t) / V(t), where x(t) represents the number of pounds of salt in the tank at time t.
(h) A differential equation with initial conditions that models this mixture problem is:
dx/dt = 5 - 3 = 2 (lb/s), where x(0) = 50 lbs.
This differential equation states that the rate of change of the amount of salt in the tank is equal to the difference between the rate at which brine containing salt is being added to the tank and the rate at which brine is being removed from the tank. The initial condition x(0) = 50 lbs states that the initial amount of salt in the tank is 50 lbs. The units in this differential equation make sense as the rate of change of the amount of salt in the tank is in lbs/s and the amount of salt in the tank is in lbs.
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Find
�
∠
�
m∠Bm, angle, B.
Round to the nearest degree.
∘
∘
degrees
The angle ∠Bm is equal to the measure of the angle in degrees rounded to the nearest degree.
What is meant by angle and how to find angle?The angle is the amount of deviation from a straight line. It is measured in degrees, with a full circle being 360 degrees. Angles can be either acute, obtuse, right, or reflex. An acute angle is less than 90 degrees, an obtuse angle is greater than 90 degrees but less than 180 degrees, a right angle is exactly 90 degrees, and a reflex angle is greater than 180 degrees but less than 360 degrees. Angles can be used in a variety of ways, from measuring distances and directions to constructing shapes and figures. They are an important part of mathematics and can provide a useful way of understanding the world around us.
To find this, calculate the measure of the angle in degrees and then round it to the nearest degree.
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Find m∠B
Note that
m∠B is acute. Round to the nearest degree.
algebra please helppp
Answer:
its 2 i think
Step-by-step explanation:
can you match these prefixes, suffixes, and word roots with their definitions? resethelp same: blanktarget 1 of 10 self: blanktarget 2 of 10 to produce: blanktarget 3 of 10 color: target 4 of 10 both, double: blanktarget 5 of 10 single: target 6 of 10 without, lack of, not: blanktarget 7 of 10 body: target 8 of 10 chromosomes: blanktarget 9 of 10 small:
The area of a circle is [tex]A = πr2[/tex], where A is the area, π is 3.14, and r is the radius of the circle.
Prefix: Self - referring to one's self or own self;
Suffix: -produce - to create, make or cause something;
Word Root: Color - the sensation of light that is seen by the eye;
Prefix: Both/Double - referring to two or more;
Suffix: -single - indicating one only;
Prefix: Without/Lack of/Not - indicating the absence of something;
Word Root: Body - referring to the physical structure or anatomy of a living organism;
Word Root: Chromosomes - a thread-like structure made up of DNA found in the nucleus of cells;
Suffix: -small - indicating a size that is lesser than the average.
For example, let's say we want to calculate the area of a circle. We can use the formula [tex]A = πr2[/tex], where A is the area, π is 3.14, and r is the radius of the circle. We can plug in the numbers to calculate the area: [tex]A = 3.14 × 42 = 50.24 cm2[/tex]. This formula allows us to calculate the area of the circle with accuracy, and also allows us to use it for different shapes
The formula and calculation used to calculate the area of a circle is [tex]A = πr2[/tex], where A is the area, π is 3.14, and r is the radius of the circle.
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Which function has a horizontal asymptote of y = 3?
f(x) = 3(2x)
f(x) = 2(4)x–3
f(x) = 2(3x)
f(x) = 2(4x) + 3
The function that has a horizontal asymptote of y = 3 is f(x) = 2(4x) + 3.
option D.
What is horizontal asymptote?A horizontal asymptote is a horizontal line that a function approaches as the input of the function approaches positive or negative infinity. It is a limiting value of the function as the input gets very large in magnitude
Based on the given question,
The function has a horizontal asymptote of y = 3.
f(x) = 3(2x) = 6x
Put x = 0
f(x) = 0 (not horizontal asymptote)
f(x) = 2(4)x–3
put x = 0
f(x) = -3
f (x) ≠ 3 (not horizontal asymptote)
f(x) = 2(4x) + 3
Put x =0
f(x) = 3.
Thus, the horizontal asymptote of y = 3 is f(x) = 2(4x)+3.
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s) a fair, six-sided dice is rolled until the number 6 is rolled. find the expected value of the sum of all rolls, including the final roll of
The expected value of the number of rolls necessary to roll a specific number is 6. This is because each roll has an equal probability of rolling the desired number, which is 1/6.
The expected value of the number of rolls necessary to roll a specific number can be calculated by multiplying the probability of rolling the desired number by the total number of rolls. In this case, since the random number generator is a six-sided die, the probability of rolling a specific number, such as a six, is 1/6. Therefore, the expected value of the number of rolls necessary to roll a six would be 6 (1/6 x 6 = 6). This is because each roll has an equal probability of rolling the desired number. To calculate the expected value for any number, simply multiply the probability of rolling the desired number (1/6) by the total number of rolls. For example, if the desired number is a five, the expected value would be 5 (1/6 x 5 = 5). If the desired number is a three, the expected value would be 3 (1/6 x 3 = 3). Thus, the expected value of the number of rolls necessary to roll a specific number is equal to the number itself.
The complete question: Given a discrete random number generator, such as a six-sided die, what is the expected value of the number of rolls necessary to roll a specific number (e.g. a six)?
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After checking the conditions are met, you perform a significance test of H0: μ = 1 versus Ha: μ≠ 1. You obtain a P-value of 0.022. Which of the following must be true?
answer choices
A 95% confidence interval for μ will include the value 1
A 95% confidence interval for μ will include the value 0
A 99% confidence interval for μ will include the value 1
A 99% confidence interval for μ will include the value 0
None of these is necessarily true
After checking the conditions are met, you perform a significance test of H0: μ = 1 versus Ha: μ≠ 1. You obtain a P-value of 0.022. the correct option is
None of these is necessarily trueWhat is p value?A P-value is the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true. In this case, the P-value of 0.022 means that there is a 2.2% chance of observing the test statistic if the null hypothesis (μ = 1) were true.
A confidence interval, on the other hand, provides a range of values that are believed to contain the true population mean with a certain level of confidence. The confidence level (e.g. 95%) indicates the degree of certainty that the interval contains the true mean.
A low P-value suggests that the data provide strong evidence against the null hypothesis, and a confidence interval that does not contain the null value supports the alternative hypothesis. However, it is not guaranteed that a 95% or 99% confidence interval will include the value 1 or 0 just based on the P-value obtained from a hypothesis test. The confidence interval depends on multiple factors such as sample size, variability of the data, and estimation method used.
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1) Researchers in a city are studying bloodstream infection in two different hospitals. There are 50 patients with bloodstream infections in hospital A with a patient population of 500. And 10 patients with bloodstream infection in hospital B with a patient population of 450. In each city half of the population was exposed to chemical substance that is being studied to evaluate its effect on bloodstream infections and 10% of the diseased population was exposed to a chemical substances.
a) What is the relative risk of bloodstream infection in hospital A?
b) What is the relative risk of bloodstream infection in hospital B?
The function f(x) = 3x + 10 represents the number of animals adopted at one shelter, where x is the number of months.
The function g(x) = x + 5 represents the number of animals adopted at another shelter, where x is the number of months.
Part A: What is (f + g)(x)? Show all necessary steps. (2 points)
Part B: Evaluate (f + g)(6). Show your work. (2 points)
Part C: Explain what your answer represents in terms of the scenario. (2 points)
The answers are a) (f+g)x = 4x+15, b) 39 and c) the animals adopted in 6 months are 24 and there were already 15 animal at the shelter.
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable) is called a function.
Given that, the function f(x) = 3x + 10 represents the number of animals adopted at one shelter, and the function g(x) = x + 5 represents the number of animals adopted at another shelter, where x is the number of months.
a) (f+g)x = f(x) + g(x)
= 3x+10 + x+5
= 4x+15
∴ (f+g)x = 4x+15
b) (f + g)(6)
Put x = 6 in (f+g)x = 4x+15
∴ (f + g)(6) = 4(6)+15
= 24+15
= 39
c) It means, the animals adopted in 6 months are 24 and there were already 15 animal at the shelter.
Hence, the answers are a) (f+g)x = 4x+15, b) 39 and c) the animals adopted in 6 months are 24 and there were already 15 animal at the shelter.
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Answer:
Step-by-step explanation:
Part A: (f + g)(x) = 4x + 15.
My work for Part A:
Step 1: Write the functions without the parentheses: x + 5 + 3x + 10 .
Step 2: Rewrite the function so like terms are next to each other: x + 3x + 5 + 10.
Step 3: Combine like terms: x + 3x = 4x, and 5 + 10 = 15.
Step 4: Write the final function in standard form: (f + g)(x) = 4x + 15.
Part B: (f + g)(6) = 39.
My work for Part B:
Step 1: Write the first function substituting x for 4: f(6) = 6 + 5.
Step 2: Solve the function: f(6) = 6 + 5 = 11.
Step 3: Write the final answer for the first function: f(6) = 11.
Step 4: Write the second function substituting x for 4: g(4) = 3 x 6 + 10.
Step 5: Solve the function: g(4) = 3 x 6 = 18, and 18 + 10 = 28.
Write the final answer for the second function: g(4) = 28.
Step 6: Add the output answers together: 11 + 28 = 39.
Step 7: Write the final output answer for both functions: (f + g)(4) = 39.
Part C: 39 represents the total number of animals adopted at two shelters in 6 months.
Rob borrows $15.00 from his father, and then he borrows $3.00 more.
Drag numbers to write an equation using negative integers to represent Rob's debt and complete the
sentence to show how much money Rob owes his father. Numbers may be used once, more than once, or not at
The equation which represents Rob's debt is -$15 + -$3 = -$18
How to write an equation using negative integers to represent Rob's debt?Directed numbers, also known as integers, are numbers that have a direction or sign, either positive (+) or negative (-). They are used to represent quantities that have direction, such as temperature, height, weight, etc.
Rob borrows 15 dollars first
He later borrows 3 dollars.
Since we are to drag numbers to write an equation using NEGATIVE integers only,
We have -$15 + -$3 = -$18 which is Rob's debt
If numbers may be used more than once, the equation is
-$5 + -$3 + -$5 + -$2 + -$3 = -$18 which is Rob's debt.
Hence Rob owes his father $18. The debt is represented by the negative sign "-"
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Last month Carlos paid $1210 on rent but next month he must pay $1370. What is the Percent increase or decrease?
PIECEWISE FUNCTION PROBLEM HELP PLEASE!
The total charge as a function of time is
C(t) = 10t + 2, for t < 2C(t) = 17 for t = 2C(t) = 25 for t > 2How to determine the total charge as a function of timeFrom the question, we have the following parameters that can be used in our computation:
Time Price
1/2 hour $7.00
1 hour $12.00
2 hours $17.00
All day $25.00
For 1/2 hour to 1 hour, we have
Rate = (12 - 7)/(1 - 1/2)
Rate = 10
So, we have
C(t) = 10t + c
Where c is the initial value
So, we have
c = C(t) - 10t
c = 7 - 10 * 1/2 = 2
So, we have
C(t) = 10t + 2, for t < 2
For 2 hours, the rate is
C(t) = 17 for t = 2
Lastly, we have
C(t) = 25 for t > 2
The above represent the piecewise function
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compute 16/36 + 2/36
someone please help me with this i suck at math and im losing my mind right now thank you.
The factors of the cubic function f(x) = 27x³ + 8 are ( 3x + 2) and ( 9x² - 6x + 4 ).
What are the factors of the cubic function?Given the function in the question;
f(x) = 27x³ + 8
To determine the factors, first rewrite 27x³ as (3x)² and 8 as 2³
27x³ + 8
(3x)² + 2³
Since both terms are perfect cubes, factor using the sum of cubes formula.
a³ + b³ = (a+b)(a² - ab + b² )
Here, a = 3x and b = 2
Plug in these values
(a+b)(a² - ab + b² )
( 3x + 2)( (3x)² - (3x)×2 + 2² )
Simplify
( 3x + 2)( (3x × 3x) - (3x)×2 + 2² )
( 3x + 2)( 9x² - 6x + 4 )
Therefore, the factors are ( 3x + 2) and ( 9x² - 6x + 4 ).
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What are the first five terms of the recursive sequence?
an= 3a n-1 +3 where a1= 9
9, 30, 93, 282, 849
9, 15, 21, 27, 33
9, 24, 69, 204, 609
9, 27, 81, 243, 729
Answer:
The first five terms of the recursive sequence are:
an = 3an-1 + 3
a1 = 9
a2 = 3a1 + 3 = 3 * 9 + 3 = 30
a3 = 3a2 + 3 = 3 * 30 + 3 = 93
a4 = 3a3 + 3 = 3 * 93 + 3 = 282
a5 = 3a4 + 3 = 3 * 282 + 3 = 849
So the first five terms are: 9, 30, 93, 282, 849.
Step-by-step explanation:
Try This question out and I’ll give you brainliest
Answer:
(d) ρ = 0.83 g/cm
Step-by-step explanation:
You want the density of a piece of driftwood that has a mass of 25 g and a volume of 30 cm³.
DensityUse the given formula with the given numbers, and do the arithmetic.
ρ = m ÷ V
ρ = (25 g)÷(30 cm³) = (25/30) g/cm³ = 0.83 g/cm³
The solution is Option D.
The density of the driftwood is given by the equation D = 0.83 kg/cm³
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 density of the material be represented as D
Now , the equation will be
The mass of the material = m
The value of m = 25 grams
The volume of the material = v
The value of v = 30 cm³
So , density D = m / v
Substituting the values in the equation , we get
Density of driftwood D = 25/30
On simplifying the equation , we get
Density of driftwood = 0.83 kg/cm³
Hence , the equation is D = 0.83 kg/cm³
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textrequest reports that adults years old send and receive texts every day. suppose we take a sample of year olds to see if their mean number of daily texts differs from the mean for year olds reported by textrequest. a. select the null hypothesis we should use to test whether the population mean daily number of texts for year olds differs from the population daily mean number of texts for year olds.
Null hypothesis: The population mean daily number of texts for 18-24 year olds is equal to the population mean daily number of texts for 25-34 year olds.
To test whether the population mean daily number of texts for 18-24 year olds differs from the population mean daily number of texts for 25-34 year olds, we need to set up a null hypothesis. The null hypothesis states that the population mean daily number of texts for 18-24 year olds is equal to the population mean daily number of texts for 25-34 year olds. This means that there is no difference in the mean daily number of texts between the two groups. We can then use this null hypothesis to test the data from our sample to see if the difference in means is statistically significant. If the test results show that the difference in means is statistically significant, then we can reject the null hypothesis and conclude that the two population means are significantly different.
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Find the greatest common factor for the list of the terms. 70x² , 30x³ , 60x⁸
Answer: 70x²= 1 30x ALSO= 1 60x⁸= 1 again
Step-by-step explanation: To find the Greatest Common Factor of these three terms you must first factor each term separately:
If X and Y are jointly continuous with joint density function fx,y(x,y), show that X + Y is continuous with density function fx+y(t) = | sx.x(8,6 – u)dx
X + Y is continuous with density function fx+y(t) = |sx.x(8,6-u)|dxdy.
Let X and Y be jointly continuous random variables with joint density function fx,y(x,y). The density function of the sum of X and Y, X + Y, is given by the convolution of fx,y(x,y) and is denoted by fx+y(t). The convolution of fx,y(x,y) is calculated as follows:
fx+y(t) = ∫∫infinityfX,Y(x,y)dydx
= ∫∫∞fX,Y(x,y)dxdy
= ∫∫∞fX,Y(x,y)sx.(x(8,6-u))dxdy
= ∫∫∞|sx.x(8,6-u)|dxdy
Hence, X + Y is continuous with density function fx+y(t) = |sx.x(8,6-u)|dxdy.
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You download 5 songs on your music player. If you play the songs using the random
shuffle option, how many different ways can the sequence of songs be played?
In 120 different ways can the sequence of songs be played.
What is Music?The art of arranging sound is called music. It is one of the defining characteristics of all human societies' cultures. Styles that highlight, de-emphasize, or exclude common components of organized sound, such as rhythm, loudness, and pitch, can be used to characterize the music.
Tempos and meters can be used to specify rhythm, and pitch variation and juxtaposition are frequently coordinated.
Individual sounds have timbres or textures that significantly affect the music's overall personality.
Music player:
A tool or program that plays digital audio files.
Solution -
To find the ways, multiply 5×4×3×2 .
⇒ 20 × 3 × 2
⇒ 120
Therefore, songs can be played in 120 ways.
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Shane believes that the sum of the
interior angles of an octagon is 1440°.
What mistake did Shane make? How
would you explain the correct solution to
Shane?
Answer:
The formula for calculating the sum of the interior angles of a polygon is (n - 2) * 180, where n is the number of sides.
Since an octagon has 8 sides, Shane needed to use the formula (8 - 2) * 180 to get 1080.
The only way Shane could have gotten 1440 is by inputting 10 for n since (10 - 2) * 180 = 1440.
identify the terms that are substituted for supply chain. (check all that apply.) multiple select question. supply web supply network extended enterprise demand chain lean operation
The following phrases are used in place of supply chain:
Supply network ; Demand chain ; Extended enterprise ; Supply web.
Explain about the supply chain?The supply chain is a networked system of businesses, people, information, and assets created to locate, produce, and transport items from their point of origin to their final destination, which is often from the a supplier to a customer.
Modern supply chains sometimes span several nations and involve numerous processes, making them exceedingly complicated.
The fundamental steps in such a supply chain are as follows:
original source or raw material extractiontransforming raw materials into simple componentsputting together basic components into completed goodsdistributing finished goods to customersdelivering completed goods to customers or end usersThus, the following phrases are used in place of supply chain:
Supply network ; Demand chain ; Extended enterprise ; Supply web.
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The maximum height a Rüppel's
Vulture can fly is 37,000 feet, which is 8,000 feet more than a Bar-headed Goose. Write and solve an equation to find the maximum flight height for a Bar-headed Goose.
The maximum flight height for a Bar headed Goose is 29,000 feet.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given that,
Maximum height that Rüppel's Vulture can fly = 37,000 feet
It is given that this height is 8,000 feet more than a Bar-headed Goose.
Let x be the maximum flight height of Bar-headed Goose.
We can write the equation as,
x + 8000 = 37000
Solving this,
x = 37000 - 8000
x = 29,000
Hence a Bar-headed Goose can fly to a maximum height of 29,000 feet.
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Please help
AD=BC
Find Angle B
The measure of m ∠ABC is 50°.
What is angle?In Euclidean geometry -
an angle is the figure formed by two rays known as the sides of the angle and sharing a common endpoint known as the vertex of the angle.
Given is a triangle as shown in the image.
We can write -
∠ACD = 180 - (60 + 40)
∠ACD = 80 ...... Eq { 1 }
Now, -
∠ABC + (180 - ∠ACD) + (90 - ∠DAC) = 180
∠ABC + 100 + 30 = 180
∠ABC = 50°
Therefore, the measure of m ∠ABC is 50°.
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Is this a function (or linear)
Yes or no
Answer: no
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
It's not a linear function because
3 and 5 have the same y and its not a linear function
The Hawaii Visitors Bureau collects data on visitors to Hawaii. The following questions were among 16 asked in a questionnaire handed out to passengers during incoming airline flights.
• This trip to Hawaii is my: 1st, 2nd, 3rd, 4th, etc.
• The primary reason for this trip is: (10 categories, including vacation, convention, honeymoon)
• Where I plan to stay: (11 categories, including hotel, apartment, relatives, camping)
• Total days in Hawaii
a. What is the population being studied?
b. Is the use of a questionnaire a good way to reach the population of passengers on incoming airline flights?
c. Comment on each of the four questions in terms of whether it will provide categorical or quantitative data.
a. Passengers on incoming airline flights, b. Yes, it is a good way, c. 1st, categorical; Reason, categorical; Stay, categorical; Days, quantitative.
The population being studied is passengers on incoming airline flights. Using a questionnaire to collect data from this population is a good way to reach a large number of travelers quickly and easily. The first question is asking about the number of visits to Hawaii, which will provide categorical data. The second question is asking about the primary reason for the trip, which will also provide categorical data. The third question is asking about where the person plans to stay, which will also provide categorical data. The fourth question is asking about the total days in Hawaii, which will provide quantitative data.
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Belinda is making bracelets for an auction fundraiser. The number of beads varies directly with the number of inches of string used to make the
bracelets. Use the information in the table to write an equation.
Number of Inches of String.
X
+
I
x
+
2
4
6
8
old
ď vo vo
Number of Beads,
y
18
36
54
72
2
(0)
11
The equation representing the number of beads varies directly with the number of inches of the string is y = 9x.
What are ratio and proportion?In its most basic form, a ratio is a comparison between two comparable quantities.
There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.
If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.
Given, The number of beads varies directly with the number of inches of string.
Therefore, y ∝ x.
y = kx.
From the table,
18 = 2k.
k = 9.
So, y = 9x.
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A person deposited $5,000 into a bank account and made no other withdrawals or deposits. Each year, 2.7% interest was added to the account.
Write an exponential function for the situation.
Answer:
Let y be the amount of money in the bank account after t years, where t >= 0.
The exponential function for this situation is:
y = 5000 * (1 + 0.027)^t
This function models the amount of money in the bank account after t years, given the initial deposit of $5,000 and an annual interest rate of 2.7%.
Step-by-step explanation:
10. Here are five shape
Four of the shapes are squares and one of the shapes is a circle.
One square is black. Three squares are white.
The circle is black. The five shapes are put in a bag.
(a) Jasmine takes a shape at random from the bag 150 times. She replaces the shape each time.
Work out an estimate for the number of times she will take a white square.
(3)
(b) Alec takes a shape at random from the bag and does not replace it. Bashir then takes a shape at random from the bag.
Work out the probability that
(i) they both take a square,
(ii) they take shapes
The probability that they both take shapes 3 / 8.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that there are five shapes, Four of the shapes are squares and one of the shapes is a circle, One square is black, three squares are white, circle is black.
Jasmine takes a shape at random from the bag 150 times
3 / 5 ×150 = 90 times.
If Alec takes a shape at random from the bag and does not replace it, there are now 4 shapes left in the bag.
The probability that they both take a square is 3 / 4 × 3 / 3 = 3 / 4.
The probability that Bashir takes a square is 2 / 4 = 1 / 2.
If Alec takes a circle, the probability that Bashir takes a square is 3 / 4. The overall probability that they both take shapes
(3 / 4) × (1 / 2) + (1 / 4)× (3 / 4) = 3 / 8.
Hence, the probability that they both take shapes 3 / 8.
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