the probability that it will rain on the following day, given that it rained tomorrow, is 0.75. Rounded to three decimal places, the answer is 0.750.
Given the probabilities, you can use Bayes' theorem to calculate the probability that it will rain on the following day, given that it rained tomorrow. Bayes' theorem states that: P(A|B) = P(B|A) * P(A) / P(B)
Where: P(A|B) is the likelihood that event A will occur assuming event B has already happened. P(B|A) is the probability of event B given that event A has occurred. The prior probability of event A is P(A). The prior probability of event B is P(B).
In this case, let A be the event that it rains on the following day and B be the event that it rains tomorrow.
So, P(A|B) = P(B|A) * P(A) / P(B) = 0.9 * 0.3 / P(B)
To calculate P(B), you can use the total probability theorem:
P(B) = P(B|A) * P(A) + P(B|~A) * P(~A) = 0.9 * 0.3 + 0.08 * 0.7 = 0.327
Now, you can substitute the values into the formula for P(A|B) to get:
P(A|B) = 0.9 * 0.3 / 0.327 = 0.75
So, the probability that it will rain on the following day, given that it rained tomorrow, is 0.75. Rounded to three decimal places, the answer is 0.750.
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By first completing the square, solve x² + 12x + 4 = 0.
Give your answers fully simplified in the form x = a +b√c, where a, b and c are integers.
Answer:
x=-2(3-2√2), -2(3+2√2)
a) Hassan deposits $325 into an account that pays 4.7% annual interest compounded monthly. Write an equation to represent Hassanʼs account balance A after t years.
b) Use a system of equations to determine how many years it will take for the account reach $200. Round to the nearest year.
The equation will be written as [tex]A = 325[1.004]^{12t}[/tex]. The time taken to reach $200 will be 10 years.
What is compound interest?Compound interest is defined as the interest levied upon the interest. The formula to calculate the compound interest will be written as:-
[tex]A = P[1+\dfrac{r}{m}]^{rt}[/tex]
Given that Hassan places $325 into a savings account that offers a monthly compound interest rate of 4.7%.
The equation for the compounding on monthly basis,
[tex]A = 325[1+\dfrac{0.047}{12}]^{12t}[/tex]
[tex]A = 325[1.004]^{12t}[/tex]
The time will be calculated as:-
[tex]A = 325[1.004]^{12t}[/tex]
[tex]200 = 325[ 1.004]^{12t}[/tex]
log(0.615) = 12 x t x log(1.004)
12t = 121.77
t = 10 years
Therefore, the equation will appear as [tex]A = 325[1.004]^{12t}[/tex]. It will take 10 years for the price to reach $200.
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a family has two cars. during one particular week, the first car consumed gallons of gas and the second consumed gallons of gas. the two cars drove a combined total of miles, and the sum of their fuel efficiencies was miles per gallon. what were the fuel efficiencies of each of the cars that week?
Quadratic equation gives us the fuel efficiencies of the two cars for the given values of fuel consumption and total distance driven.
Let's denote the fuel efficiency of the first car as x miles per gallon, and the fuel efficiency of the second car as y miles per gallon.
We know that the first car consumed a total of a gallons of gas, and the second car consumed b gallons of gas. If we assume that the fuel efficiencies are constant, then the total distance driven by both cars can be calculated using the formula:
distance = fuel consumed / fuel efficiency
So, the total distance driven by both cars is:
(a/x) + (b/y) = total miles
We also know that the sum of their fuel efficiencies was:
x + y = total miles per gallon
We have two equations and two unknowns, so we can solve for x and y. First, we can solve the second equation for x:
x = total miles per gallon - y
Substituting this expression for x into the first equation, we get:
(a / (total miles per gallon - y)) + (b / y) = total miles
Multiplying both sides by y(total miles per gallon - y) to eliminate the denominators, we get:
ay + b(total miles per gallon - y) = total miles * y(total miles per gallon - y)
Expanding the left side and simplifying, we get a quadratic equation in y:
(total miles^2 - a - b) y^2 + (total miles * a) y - ab = 0
Using the quadratic formula, we can solve for y:
y = [(total miles * a) ± sqrt((total miles * a)^2 + 4ab(total miles^2 - a - b))] / 2(total miles^2 - a - b)
We can then use the equation x = total miles per gallon - y to find the value of x. The gives the fuel consumption of both cars.
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A newly discovered planet orbits a distant star with the same mass as the Sun at an average distance of 112 million kilometers. Its orbital eccentricity is 0.3. Find the planet’s orbital period and its nearest and farthest orbital distances from its star.
Can you simplify the integer expression and type the correct code? Please remember to type in ALL CAPS with no spaces. *
Answers of integer expression is -4, -10, 14 and -11.
What is Number system?A number system is defined as a system of writing to express numbers.
The first expression is -5+8-7
-5+8-7
Add the minus terms and then add with positive eight.
-12+8
The answer of integer expression is -4
2. The second expression is -12-7+9
-19+9
When minus nineteen and plus nine are added we get minus ten.
The answer of integer expression is -10
3. 9-13+18
Add the two positive integers and then use subtraction
27-13
14
The answer of integer expression is 14
4. 7-15-3
Add the negative values and add the positive seven.
7-18
-11
The answer of integer expression is -11
Hence, answer of integer expression is -4, -10, 14 and -11.
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Answer:
HECD
Step-by-step explanation:
1. -5 + 8 - 7 = -4: H
2. -12 - 7 + 9 = -10: E
3. 9 - 13 + 8 = 4: C
4. 7 - 15 - 3 = -11: D
Code: HECD
Kate invests £2000 in a savings account for 3 years the account pays compound interest at an annual rate of 2. 5% for the first year x% for the second year x% for the third year there is a total amount of £2124. 46 in the savings account at the end of 3 years work out the rate of interest in the second year
The second year's interest rate is 1.80%.
Compound interest is defined as Since compound interest accrues and is added to the accrued interest from earlier periods, borrowers are expected to pay interest on interest in addition to principal.
We are aware that the compound interest formula is,
A = P(1 + r/100)ⁿ.
Where A is the amount, P is the principle, r is the rate, and n is the number of years.
Given, Katy places $2000 over a three-year period in a savings account.
For the first year, the account offers compound interest at a 2.5% annual rate.
∴ A = 2000(1 + 2.5/100)¹.
A = 2000(1.025). (1.025).
A = 2050.
It now earns x% for the second year.
∴ 2050(1+x/100)² = 2124.46
(1+x/100)² =2124.46/2050
1+x/100 =√(2124.46/2050)
x/100 = √(2124.46/2050) -1
x = (√(2124.46/2050) -1)*100
x = 1.80%.
the interest is 1.80 percent
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the smaller the p-value, the . a. greater the evidence against h0 b. greater the chance of committing a type i error c. greater the chance of committing a type ii error d. less likely one will reject h0
The p-value is a measure of the evidence against the null hypothesis (H0)
The correct answer is (a) greater the evidence against H0.
It represents the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed, assuming that the null hypothesis is true.
The smaller the p-value, the less likely it is that the observed result is due to chance alone, and the stronger the evidence against the null hypothesis. This means that if the p-value is very small (e.g., less than 0.05), we have strong evidence to reject the null hypothesis in favor of the alternative hypothesis.
In contrast, a large p-value indicates weak evidence against the null hypothesis, and we may not have enough evidence to reject H0. Therefore, the smaller the p-value, the greater the evidence against H0.
Option (b) is incorrect because the chance of committing a Type I error (rejecting the null hypothesis when it is actually true) is related to the level of significance (alpha) and not the p-value. Option (c) is also incorrect because the chance of committing a Type II error (failing to reject the null hypothesis when it is actually false) is related to the power of the test and not the p-value. Option (d) is incorrect because a smaller p-value actually makes it more likely that one will reject H0, assuming that the level of significance is held constant.
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1.) distinguish between the null hypothesis and the research hypothesis. when does the researcher decide to reject the null hypothesis?
A hypothesis that there is some sort of relationship between the variables is where scientists start their inquiry. The alternative, or null hypothesis, asserts that there is no such relationship. Although the null hypothesis may not appear fascinating, it is a crucial component of research.
The claim can be supported by either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportion is the same as the value specified in the claim. If the null hypothesis is the assertion, then the alternative hypothesis statement is the antithesis of the null hypothesis. A hypothesis is a well-informed, logically-supported guess about the answer to a scientific question. Although it is the experiment's anticipated outcome, it does not constitute experimental proof. The information obtained may or may not be supported, depending on the information received. Simple hypotheses simply state the relationship between two independent and dependent variables. Examples: If you stay up late, you will feel fatigued the next day.
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Determine, by inspection, which of the following products are multiples of 30. 22 x 3 x 5 2 x 3² x 5 22 × 53 23 x 3² x 5²
By inspection, the following products which are multiples of 30 are:
2² x 3 x 52 x 3² x 52³ x 3² x 5²What is a Multiple?This is referred to as a number that may be divided by another a certain number of times without a remainder.
The multiple of 30 in the options are those who have 2, 3 and 5 as the common values and is therefore the reason why options A, C and D were chosen as the correct choice.
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PLEASE PLEASE PLEASE PLEASE PLEASE ANSWER THIS ASAP!!!!!!!!!!!!!THIS IS MATH I AM GIVING 50 POINTS!!!!!!!!!
#7. Tyler llenó su bañera, se bañó y luego drenó la bañera. La función B da la profundidad del agua,
pulgadas, t minutos después de que Tyler comenzó a llenar la bañera.
Explique el significado de cada declaración en esta situación.
a. B(0) = 0
b. B(1)
C. B(9) = 11
d. B(10) = B(22)
e. B(20) > B(40)
The explanation of each statement in each given situation is given below:
How to solve for thisa. B(0) = 0
depth in inches 0 minutes after filling began is 0; that is at time =0; depth =0
b. B(1) < B(7)
B(1) represents the function one minus after filling began
c. B(9) = 11
depicts that the depth in inches of water 5 minutes after filling is 11
d. B(10) = B(22)
depicts that the depth in inches of water 10 minutes after filling began is 22.
e. B(20) > B(40)
represents the function 20 minutes after filling began
These are the required answers
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The question translated in English is: "#7. Tyler filled his tub, took a shower, and then drained the tub. Function B gives the depth of the water,
inches, t minutes after Tyler started filling the tub.
Explain the meaning of each statement in this situation.
to. B(0) = 0
b. B(1) C.B(9) = 11
d. B(10) = B(22)
and. B(20) > B(40)"
PLEASE HELP IS DUE TOMORROW:The average American throws away 2.5 pounds of empty cans a month (mostly during the winter months). At this rate, how many years will it take the average American to throw away a ton of empty cans? (Show work please)
1 ton = 2000 pounds
2000/2.5 = 800 months
800/12 = ~66.67 years
Answer:
your answer would be 66.6: do the math: 2.5 a month times 12 months in a year=30. 1 ton =2000 pounds. 2000 divided by 2.5 =800. 800 divided by 12=66.6
Step-by-step explanation:
A ball is rolling down a slope and continuously picks up speed. Suppose the function f(x)=1.2(1.11) to the power of x describes the speed of the ball in inches per minute. How fast will the ball be rolling in 20 minutes? Round the answer to the nearest whole number.
plug in 20 = x for function f(x)
1.2(1.11)^20 = ?
suppose you shuffle a deck of cards and look at the top card 10 times. find the probablility that exactly 5 of the cards you see are hearts
The probability of seeing exactly 5 hearts out of 10 cards is[tex](13/52)^5 × (39/52)^5.[/tex]
The probability of seeing exactly 5 hearts out of 10 cards can be calculated as follows: The total number of cards in a deck is 52. The number of hearts in a deck is 13. Since no card has been removed from the deck, the probability of seeing a heart is 13/52. The probability of seeing a non-heart is 39/52. Since we are looking at 10 cards, the probability of seeing exactly 5 hearts,
p(h)= 13/52
p(nh) = 39/52
hence, [tex](13/52)^5 × (39/52)^5[/tex]
This means that the probability of seeing exactly 5 hearts out of 10 cards is [tex](13/52)^5 × (39/52)^5.[/tex]
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Suppose you borrow $19,250 from a bank to purchase a house. You have poor credit score. If the term of the loan is 13 years, how much should you expect to pay in interest over the life of the loan if your interest rate is 10.50%?
A. 15,220
B. 35,360
C. 19,250
D. 16,110
$2627625 much should you expect to pay in interest over the life of the loan if your interest rate is 10.50%.
What is interest rate?The amount of interest payable each period expressed as a percentage of the amount lent, deposited, or borrowed is known as the interest rate. The total amount of interest on a loaned or borrowed sum is determined by the principle amount, the interest rate, the frequency of compounding, and the period of time during which it is lent, deposited, or borrowed.
Simple interest rate = P × R × T
where,
P = Principal = $19,250
R = Rate of Interest in % per annum = 10.50%
T = Time, usually calculated as the number of years = 13 years
Thus,
simple interest = 19250 × 10.50 × 13
simple interest = 2627625
$2627625 much should you expect to pay in interest over the life of the loan if your interest rate is 10.50%
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FIRST 2 PEOPLE TO ANSWER GET POINTS AND BRAINLIEST!!!
Answer: $44.04
Step-by-step explanation: Add up all the prices 13.75+15.85+11.95 which is 41.55. Now times 41.55 by 6% which is 2.493. Now add the total and the tax. 41.55 + 2.493 = $44.04 as the final total.
Please help! 15 Points!
Answer:
Option C
Step-by-step explanation:
2*-1 = -2
2*0 = 0
a scratch off lottery ticket can be purchased for $2. there are multiple prize options, shown along with the probability, in the table below. what is the expected win (or loss) for this lottery ticket? round your answer to the nearest cent. do not round until your final answer.
a result of -$2.00, indicating that, on average, you will lose $2.00 when buying this lottery ticket.
Lose (-$2.00)
The expected win (or loss) for this lottery ticket is -$2.00.
The expected win (or loss) for this lottery ticket is calculated by multiplying the prize amount by the probability of winning and then subtracting the cost of the ticket.
($50 x 0.1%) - $2 = -$2.00
The expected win (or loss) for this lottery ticket is calculated by multiplying the prize amount of $50 by the probability of 0.1% (or 0.001) of winning and then subtracting the cost of the ticket, which is $2. This gives us a result of -$2.00, indicating that, on average, you will lose $2.00 when buying this lottery ticket.
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Select the correct answer.
Consider this function.
f(x) = 6log₂x - 3
Over which interval is function f increasing at the greatest rate?
OA. [2, 6]
OB. [1/8, 1/2]
OC. [1, 2]
OD. [1/2,1]
The function f(x) = 6log₂x - 3 increasing at the greatest rate in the interval [1/8, 1/2].
What are maxima and minima?The maxima and minima of a function are the extreme values within the range; in other words, they are the maximum and minimum values of a function, respectively, at a given position.
Let the function be f(x) = 6log₂x - 3
For the interval x ∈ [2, 6]
f(x) ∈ [-0.678, 3]
For the interval x ∈ [1/8, 1/2]
f(x) ∈ [ -9.96, -5.32]
For the interval x ∈ [1, 2]
f(x) ∈ [-3, -0.67]
For the interval x∈ [1/2, 1]
f(x) ∈ [-5.32, -3]
The function increased most rapidly in the interval [1/8, 1/2], as can be seen from the function value and its interval values.
Therefore, the range [1/8, 1/2] is where the function f(x) = 6log₂x - 3 increases at the fastest pace.
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3. The scatter plot represents the age x of a driver in years and the monthly cost of insurance y
in dollars for a specific car model. The equation of the line of best fit for this data is
y=474.34-7.445x
Cost (dollars)
A
350
300
250
200
150
100
50
increases
decreases
0
5
10
Monthly Auto Insurance Costs
Write the values that complete each sentence.
Part A
The slope of the line of best fit is
The y-intercept of the line of best fit is
Part B
Circle an answer choice in each box to make each statement true.
The slope of the line of best fit means that as the age of the driver (A), the predicted monthly
cost of insurance (B)
B
15
20
Age of Driver (years)
The value of the y-intercept (C) make sense in this context. The predicted monthly cost of
surance for a driver who is 0 years old (D) possible for this situation.
25
decreases
30
increases
stays the same
35
does
40
does not
D
is
is not
NEED HELP NOWWWWW
In AOPQ, p = 38 cm, q = 29 cm and 20=39°. Find the length of o, to the nearest
centimeter.
Answer:
Step-by-The length of o in the triangle AOP can be found using the Law of Cosines. The Law of Cosines states that for a triangle with sides a, b, and c and opposite angle C, the following formula holds:
c^2 = a^2 + b^2 - 2ab cos(C)
In this case, a = 38 cm, b = 29 cm, and C = 39°. The length of o can be found by rearranging the formula and solving for c:
c^2 = 38^2 + 29^2 - 2(38)(29) cos(39°)
c = sqrt(38^2 + 29^2 - 2(38)(29) cos(39°))
Using a calculator, we can find that c ≈ 47.3 cm, to the nearest centimeter, o = 47 cm.step explanation:
The expression 2.2x + 8 represents the number of miles Trent jogged during a race and 5x represents the number of miles that Ling jogged during the same race in x hours. Write and expression to show how many more miles did Ling Jog than Trent?
The number of miles Ling Jog than Trent can be written as the expression 2.8x - 8
How many more miles did Ling Jog than Trent?Trent's expression:
2.2x + 8
Ling's expression:
5x
Where,
Number of hours= x
Number of hours Ling Jog than Trent =Ling's expression - Trent's expression
= 5x - (2.2x + 8)
= 5x - 2.2x - 8
= 2.8x - 8
Therefore, Ling jog 2.8x - 8 miles than Trent.
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Question 10 / 1 pointWhich one of the following best defines the notion of "the P-value of a hypothesistest?"Question options:The probability of a type I error.The probability of a type II error.The probability of rejectingH0{"version":"1.1","math":"H_0"}, whether it's true or not.The probability of obtaining a test statistic at least as extreme as the one you calculated, assuming the nullhypothesis is true.
Option A: The probability of rejecting H_o, whether it's true or not, best describes the notion of the P-value of a hypothesis test.
The level of marginal significance within the hypothesis test that represents the probability of occurrence of a given event is referred to as its P-value. In order to provide the least significance at which the null hypothesis would be rejected, it is utilized as a choice for the rejection point. This signifies that the option A is correct.
The P-value is known as the probability value. It can be defined as the probability of getting a result that is either the same or more advanced than the actual observations. There is more support for the alternative hypothesis when the P-value is low.
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Correct way to ask the question is:
Which one of the following best defines the notion of the P-value of a hypothesis test?
The probability of rejecting H_o, whether it's true or not
The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true.
The probability of the type I error
The probability of the type II error
X over 2 linear or nonlinear
Answer:
linear
Step-by-step explanation:
when you graph x/2 it is a straight line, therefore it is linear
Binomial expansion
(a) Expand (1+e^x)+(e^3x) in ascending powers of x to the term x^2.
(b) If the coefficient of x^2 in the expansion [tex]\frac{(1+e^{x}-e^{3x})(1-3x)^{n}}{e^{3x} }[/tex] is [tex]\frac{433}{2}[/tex] , find n.
Answer:
Step-by-step explanation: (a) To expand (1 + e^x) + (e^3x) in ascending powers of x to the term x^2, we can use the Taylor series expansion.
The Taylor series expansion for e^x is given by:
e^x = 1 + x + x^2/2! + x^3/3! + ...
So,
e^x = 1 + x + x^2/2! + x^3/3! + ...
and
e^3x = 1 + 3x + 9x^2/2! + 27x^3/3! + ...
Now, we can substitute these expansions into the original equation to get:
(1 + e^x) + (e^3x) = 1 + (1 + x + x^2/2! + x^3/3! + ...) + (1 + 3x + 9x^2/2! + 27x^3/3! + ...)
Expanding, we get:
(1 + e^x) + (e^3x) = 2 + x + 4x + x^2/2! + 9x^2/2! + ...
So, to the term x^2, the expansion becomes:
(1 + e^x) + (e^3x) = 2 + x + 4x + (x^2/2! + 9x^2/2!) + ...
which simplifies to:
(1 + e^x) + (e^3x) = 2 + x + 4x + 11x^2/2! + ...
(b) The coefficient of x^2 in the expansion is 11/2!. So, n = 11/2! = 11/2.
A square is cut from a rectangle. The side length of the square is half of the unknown width w. The area of the shaded region is 84 square inches. Write an equation you can use to find the width (in inches).
On solving the provided question we cans ay that The side of the square is w/2, then its area is: A = (w/2)² = w²/4
what is a square?A square is an equilateral quadrilateral with four equal sides and four equal angles according to Euclidean geometry. It is also known as a rectangle with two neighboring sides that have the same length. Having all four equal sides and all four equal angles, a square is an equilateral quadrilateral. 90 degree or straight angles are square angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. a neighboring rectangle with two equal sides. a quadrilateral with four right angles and four sides of equal length. a parallelogram having two adjacent, equal sides that form a right angle. straight-sided rhombus.
The side of the square is w/2, then its area is:
A = (w/2)² = w²/4
The darkened region represents the difference between the square's and rectangle's areas:
[tex]14w - w^2/4 = 84\\56w - w^2 = 336\\w^2 - 56w + 336 = 0[/tex]
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Question 1 (Multiple Choice Worth 1 points)
(06.03 LC)
Choose the correct simplification of the expression
a
b
a1⁰b5
The correct simplification of the expression is 25x^2y^22.
How to calculate the expressionIt is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
x mn = x ^ m×n = xmn
xm× xn = x m+n
= (5)2(x)^2(y5)^2(y3)^4
= 25x^2y10y^12
= 25x^2y^22
Therefore, the correct simplification of the expression is 25x^2y^22.
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Choose the correct simplification of the expression (5xy5)2(y3)4.
25x2y22, 10x2y22, 25x3y14, 10x3y14
A ladder leans against the wall of a building. The ladder measures
36 inches and forms an angle of 61' with the ground. How far from
the ground, in inches, is the top of the ladder? How far from the
wall, in inches, is the base of the ladder? Round to two decimal
places as needed.
Show your work here
ground to top, in inches:
base to wall, in inches:
Answer:
A ladder leans against the wall of a building. The ladder measures 66 inches and forms an angle of 45 degrees with the ground. How far from the ground, in inches, is the top of the ladder? How far from the wall, in inches, is the base of the ladder?
Step-by-step explanation:
A moving company charges $400 plus $0.04 per kg to move a family from Toronto to
Windsor.
a) Define the independent variable and the dependent variable.
b) Write an equation.
c) Use your equation to calculate a table of values with four sets of values to show the
moving costs for 0 – 25,000 kg.
a) Number of kgs independent variable, the amount charged by the company is the dependent variable.
b) The equation is y= 400+ 0.04x.
c) The equation is used to calculate a table of values with four sets of values to show the moving costs for 0 – 25,000 kg.
What is an equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
It is given that a moving company charges $400 plus 0.04 per kg to move a family from Toronto to Windsor.
a) The number of kgs is the independent variable and the amount charged by the company is the dependent variable because it depends on the number of kgs the family is willing to move.
b) The equation that represents the given data is y= 400+ 0.04x
where y is the total amount charged by the company, and x is the number of kgs.
c) For 4 different values of x between 0 - 25,000 we will find values of y.
x y= 400+ 0.04x
6250 650
12500 900
18750 1150
25000 1400
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how many times larger is a centigram than a milligram? 10times | 100 times| 1000 times| 0.1 time
A centigram is 100 times larger than a milligram. So, the option b) 100 times is correct for this question.
1 centigram = 100 milligrams. A centigram is a unit of mass in the metric system, equivalent to one hundredth of a gram. A milligram, on the other hand, is a unit of mass in the metric system, equivalent to one thousandth of a gram. Therefore, a centigram is 100 times larger than a milligram. The conversion between the two units can be easily calculated as 1 centigram is equal to 100 milligrams. The use of centigrams is limited in common applications, with milligrams being the preferred unit for expressing very small masses, while grams and kilograms are used for larger masses.
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