To double, the population must increase by a factor of 2, which would take ln(2) / ln(6) = ln(2) / ln(6) * 10 hours = 2.817 hours.
To solve for the time it took for the bacterial population to double, we need to use the exponential growth formula:
[tex]N(t) = N_0 * e^{(kt)[/tex]
where N0 is the initial population, N(t) is the population at time t, k is the growth rate, and e is the base of the natural logarithm (approximately 2.71828).
Since the population is increased sixfold in 10 hours, we can set up the equation as:
[tex]N_0 * e^{(kt)} = 6 * N_0[/tex]
Taking the natural logarithm of both sides gives:
kt = ln(6).
Dividing both sides by k and using the fact that the natural logarithm of 2 is approximately 0.693,
ln(2) / ln(6) = ln(2) / ln(6) * 10 hours = 2.817 hours.
So it took approximately 2.817 hours for the population to double.
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Someone help fast I need the answer (In a live class)
Answer:
216 in^3
Step-by-step explanation:
Volume = 6 in. * 4 in. * 9 in. = 216 in^3
help me with the question, please
have a good day
Answer:
3 liters
Step-by-step explanation:
If he took the 2 fullest containers, he took the two dots that are at 4 1/2, which is also 4.5
Now since there are two, we multiply by 2.
4.5 = 9 liters
It then says he will divide the milk evenly between 3 containers. So now we divide.
9/3 = 3
`h\left(x\right)=\frac{1}{2}x-14`
`h\left(-4\right)=`
Answer:
-16
Step-by-step explanation:
[tex]h\left(x\right)=\frac{1}{2}x-14\\h\left(-4\right)=-4/2-14=-2-14=-16[/tex]
Which algebraic expression is a polynomial term?
A polynomial term is an expression composed of constants, variables, and exponents.
A polynomial term is an expression composed of constants, variables, and exponents. Constants are the numerical values that don't change, while variables are values that can change. Exponents are numbers that indicate how many times a number is multiplied by itself. For example, 2^3 means 2 multiplied by itself 3 times, or 8. A polynomial term is an expression that combines constants, variables, and exponents, such as 6x^2 - 3x + 5. In this expression, 6, -3, and 5 are constants, x is a variable, and 2 and 1 are exponents. A polynomial term can also contain fractions, such as (2x + 1)/3. In this case, 2, 1, and 3 are constants, and x is a variable. Polynomial terms are the building blocks of polynomials, which are equations that consist of multiple polynomial terms.
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LB =
Round your answer to the nearest hundredth.
B
?
CT
5
4
A
C
3
Measure of angle B is 36.87°.
What are Trigonometric Functions?Trigonometric functions are defined as the real functions or the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.
Given is a right angled triangle.
We have to find measure of angle B.
Cosine of an angle in a right angled triangle is equal to the ratio of it's adjacent side to the hypotenuse.
Hypotenuse = AB = 5
Adjacent side to B = CB = 4
Cos B = 4/5
∠B = Cos⁻¹ (4/5)
= 0.6435 radians
= 36.87°
Hence the measure of the angle B is 36.87°.
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John and Paul both run on the same track each morning. The ratio of the number of miles John runs to the number of miles Paul runs is 5:8.
Which statement correctly represents the situation?
The statement correctly represents the situation is "Paul runs 5/8 mile for every one mile that John runs".
How to determine which statement correctly represents the situation?Ratio is used to compare two or more quantities. It is used to indicate how big or small a quantity is when compared to another.
The ratio of the number of runs that John and Paul do is 5:8, which means that for every 5 runs that John does, Paul does 8 runs.
Let J and P number of miles John and Paul run respectively. We can write:
P : J = 5 : 8
P / J = 5 / 8
P = (5/8)J
Therefore, Paul runs 5/8 mile for every one mile that John runs
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Complete Question
John and Paul both run on the same track each morning. The ratio of the number of John runs to the number of Paul runs is 5:8 Which statement correctly represents the situation?
A. Paul runs 5/8 mile for every one mile that John runs
B. Paul runs 8/13 mile for every one mile that John runs.
C. John runs 5/8 mile for every one mile that Paul runs.
D. John runs 8/13 mile for every one mile that Paul runs.
Sam depositied 500$ in a new bank account correct answer
Answer:
Bank a/c Dr
To cash a/c
(Being deposited cash into bank)
There are 5 slices of pepperoni pizza, 1 slice of sausage pizza, and 3 slices of cheese pizza left. Without looking, Douglas took a slice of pizza, ate it, and then took another slice.
What's the probability of Douglas eating two of the same kinds of pizza?
Answer:
Step-by-step explanation:
well if there are 5 pepperoni pizzas that means that he eats 2 meaning he has 3 pepperoni slices of pizza.
A survey was conducted among a group of employees to find the average time they spent online each day. The answers of the employees (in minutes) are shown in the box. 25, 45, 60, 30, 35, 20, 40, 45, 15, 30 Which of these scales would be most appropriate on the y -axis to represent this data on a bar graph? Responses
An appropriate scale for the y-axis would be to have each unit represent 5 minutes of time.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Since the data represents the average time employees spent online, the y-axis of the bar graph should represent time in minutes.
To choose an appropriate scale for the y-axis.
we need to consider the range of values in the data set.
The lowest value is 15 minutes
and the highest value is 60 minutes
Range of values is 60 - 15 = 45 minutes.
It's best to choose a scale that divides the range of values into equal intervals.
One possible option is to use a scale where each unit represents 5 minutes of time. This would allow us to represent the data accurately without making the bars too small or too large.
Therefore, an appropriate scale for the y-axis would be to have each unit represent 5 minutes of time.
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The height of a hill, h(x), in a painting can be written as a
function of x, the distance from the left side of the
painting. Both h(x) and x are measured in inches.
h(x) = -(x)(x-13)
Mark this and return
4
What is the height of the hill in the painting 3 inches from
the left side of the picture?
O 6 inches
O
13 inches
O 30 inches
O 150 inches
Save and Exit
Next
Submit
The height of the hill in the painting 3 inches from the left side of the picture is 30 Inches. Option C
How to determine the height
From the information given, we have that;
h(x) represents the height of a hill, h(x), in a paintingx represents the distance from the left side of the paintingBoth the height and the distance are measured in inchesWe also have that the function is;
h(x) =-(x)(x-13)
Given that the distance is 3 inches
Substitute the values, we have;
h(3)= -(3)(3-13)
substract the values
h(3) = (-3)(-10)
multiply the values
h(3) = 30 inches
Hence, the value is 30 inches
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A factory has 1,254 tires each new car needs 4 tires how many new cars can be made
The total number of new cars made by a factory from 1,254 tires as each car required four tires is equal to 314 ( round off to nearest whole number ).
Total number of tires in the factory is equal to 1,254
Number of tires required by each new car is equal to 4 tires.
The total number of new car made by a factory is equal to :
4 tires = 1 new car
⇒ 1 tire = ( 1 / 4 ) new car
⇒ 1,254 tires = 1,254 × ( 1 / 4 ) new car
⇒ 1,254 tires = ( 1,254 / 4 ) new cars
⇒ 1,254 tires = 313.5 new cars
But number of new cars cannot be in the decimals or fraction.
Round off to the nearest whole number .
⇒ 1,254 tires = 314 new cars ( nearest whole number )
Therefore the total number of new cars made by a factory is equal to 314 new cars.
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according to internet security experts, approximately 90% of all e-mail messages are spam (unsolicited commercial e-mail), while the remaining 10% are legitimate. a system administrator wishes to see if the same percentages hold true for the e-mail traffic on her servers. she randomly selects e-mail messages and checks to see whether or not each one is legitimate. (unless otherwise specified, round all probabilities below to four decimal places; i.e. your answer should look like 0.1234, not 12.34%). a) assuming that 90% of the messages on these servers are also spam, compute the probability that the first legitimate e-mail she finds is the sixth message she checks.
The probability that the first legitimate e-mail she finds is the sixth message she checks is 0.0656.
What is 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%. The higher the likelihood, the more likely it is that the event will take place.
Here, we have
Given: according to internet security experts, approximately 90% of all e-mail messages are spam (unsolicited commercial e-mail), while the remaining 10% are legitimate.
For each message, we have the following probabilities:
90% probability it is spam.
10% probability it is legitimate.
Compute the probability that the first legitimate e-mail she finds is the fifth message she checks:
The first four are all spam, each with a 90% probability.
The fifth is legitimate, with a 10% probability.
P = (0.9)⁴×0.1
P = 0.0656
Hence, the probability that the first legitimate e-mail she finds is the sixth message she checks is 0.0656.
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A bouncy ball is dropped such that the height of its first bounce is 5 feet and each
successive bounce is 68% of the previous bounce's height. What would be the height
of the 9th bounce of the ball? Round to the nearest tenth (if necessary).
I know, I answer quick. What do you expect I'm Johnny Sins to help you with your homework. :)
Anyways,
The height of the nth bounce can be calculated using the formula:
h_n = h_1 * 0.68^(n-1)
Where h_1 is the height of the first bounce, h_n is the height of the nth bounce, and 0.68 is the percentage of the height lost with each successive bounce.
Substituting the given values, we have:
h_9 = 5 * 0.68^(9-1)
h_9 = 5 * 0.68^8
h_9 = 5 * 0.265
h_9 = 1.325
So the height of the 9th bounce would be approximately 1.3 feet, rounded to the nearest tenth.
_________________________________________________________
Thanks for the support, love you brother!
Love Johnny Sins
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Question 2 1 pts In a density curve, proportion of data is represented by area above the curve area under the curve: the shape of the curve: intervals of values on the vertical axis_ intervals of values on the horizontal axis. the length of the curve: Question 3 1 pts Which ONE of the following is a correct classification of shapes of density curves? All v Symmetric Uniform Normal All - Nonsymmetric Bell = Normal AIl = Nonsymmetric Symmetric - Normal AII + Bell 7 Symmetric Normal All v Symmetric Bell v Normal All + Uniform Bell 7 Normal
In a density curve, the proportion of data is represented by the area under the curve. So option B is correct.
What is Density curve?The probability that an observation chosen at random falls within a given interval is represented by the area under a density curve, which is a smooth representation of a probability distribution. As a result, the area under the curve between the respective points is proportional to the percentage of data that falls inside a given range.
The area under the curve that directly represents the proportion of data. The intervals of values on the vertical and horizontal axes are used to plot the curve and are important for interpreting the graph, but they do not directly represent the proportion of data. The length of the curve is not relevant for determining the proportion of data, as it can vary depending on the scaling of the graph.
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Mr. Lopez must drive 340 miles to
attend an origami convention. His
car averages 28 miles per gallon and so far he has traveled 102 miles. How much gasoline must be left in his tank if he wants to complete the trip without stopping?
made
The quantity of gasoline that must be left in his tank if he wants to complete the trip without stopping is 8.5 gallons of gasoline.
What is the slope-intercept form?Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x represents the quantity of gasoline.y represents the total distance.c represents the y-intercept or initial value.In this context, an equation that models the situation is given by:
y = mx + c
340 = 28x + 102
28x = 340 - 102
28x = 238
x = 238/28
x = 8.5 gallons of gasoline.
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i need help please!!!!!!!!!!
A person's height and speed to reach mars are the two things cοnsidered to be measured.
What does precision mean?Precision is a number that expresses the value οf the number and indicates how many informational digits are there. Fοr instance, 3.14 is an approximation οf pi that is reasonable and accurate. Hοwever, the precision digit, which is 3.199, is less than the precise digit.
1. A person's height and the speed necessary tο reach Mars are two things you could measure. We dοn't need to be extremely precise because it's possible to measure the person's height with a mοdest level of accuracy. If we said something like, "that individual is rοughly 6 feet tall," the person listening wοuld have an idea of their height. For a rocket speed to Mars, hοwever, we require excellent accuracy because getting this number incοrrect could have disastrous consequences in the future. In οrder to ensure that we strike the necessary οbjective in space, extremely difficult mathematics is required.
2. As already mentiοned, anything involving space travel requires extreme precision. The spacecraft might sοmehow crash if the calculations are off. Engineers utilized the incοrrect parameters in one instance, causing the Mars lander tο smash into the planet rather than land safely. Given the expensive cost οf such space exploration missions, it is imperative to οbtain exact data that is as accurate as feasible. It's nοt necessary to be extremely accurate while discussing someοne's height because we can merely give approximatiοns to anyone we're speaking tο. Cοmpared to something like a rοcket launch, the level of accuracy required in this informal situation is lοwer.
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. three coins are tossed up in the air, one at a time. what is the probability that two of them will land heads up and one will land tails up?
The probability of receiving two heads and one tail is 3/8, or 0.375.
One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it .Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. Mathematics has incorporated probability to forecast the likelihood of various events.
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What number is exactly halfway between 61 and 547?
Answer:
304
Step-by-step explanation
it was on my quiz
Answer:
The number 304 is exactly halfway between 61 and 547.
Step-by-step explanation:
To find the halfway point between two given numbers we can simply add them together then divide them by 2.
Note:
let [tex]N[/tex] be the number that is halfway
[tex]N=\frac{547+61}{2}[/tex]
[tex]N=\frac{608}{2}[/tex]
[tex]N=304[/tex]
In a class & 60 students the most number of students who passed Ga is 6 more than the number that passed fante. Every student passed at least one of the two subjects and 8 students passed both subjects (1) How many students passed Ga?
Answer: 37
Step-by-step explanation:
let x be the number of students who pass "fante". Then the number of students who passed "Ga" will be x + 6.
with the added information that 8 students passed both we can say:
(x + x + 6) - 8 = 60
2x + 6 = 68
2x = 62
x = 31
.: x + 6 = "only Ga pass" = 37
The question does not make it clear if it is asking for students who *only* passed Ga, or students who passed Ga + those who passed both. I'll assume the former though. Otherwise the answer would be 37 + 8 = 45 students
use the rule to complete the table below Multiply by 2 and then add 3
The values in the table are 7, 11, 15, and 19.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
We are assuming the table to be:
x value
2 2x2 + 3 = 7
4 4x2 + 3 = 11
6 6x2 + 3 = 15
8 8x2 + 3 = 19
Thus,
The values in the table are 7, 11, 15, and 19.
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Anand's math teacher finds that there's roughly a linear relationship between the
amount of time students spend on their homework and their weekly quiz scores. This.
relationship can be represented by the equation y = 7.2x + 55, where y represents
the expected quiz score and a represents hours spent on homework that week. What
is the meaning of the 2-value when y = 77?
The number of hours a student should spend on their homework to expect a
score of 77 on the quiz.
A student's expected quiz score if they spent 77 hours on their homework.
The change in expected quiz score for every additional one hour students spend
on their homework.
A student's expected quiz score if they spent no time on their homework.
Submit Answer
To get 77 marks on a quiz the student has to spend approximately 3 hrs.
The expected quiz score if a student spends no time on homework is 55.
What is meant by a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, occasionally referred to as a "linear equation of two variables."
It is given that y = 7.2x + 55
where y is the expected quiz score.
x is the number of hours spent on homework that week.
If the value of y=77
77=7.2x+55
22=7.2x
x is approximately 3 hrs.
If the student spends no time on their homework:
x=0
y=0+55
y=55.
Therefore to get 77 marks on a quiz the student has to spend approximately 3 hrs.
The expected quiz score if the student spends no time on home work is 55.
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1. Cam has just completed her first year of
college, and she has decided to put her
possessions in a self-storage facility while
she's visiting her family during summer
vacation. She will be charged a flat fee of
$35.00 plus $0.45 for each day of storage. If
Cam stores her possessions for d days and
is charged a total of $63.80, which of the
following equations can be used to solve for
d?
A. 35+0.45 + d = 63.80
B. 35+0.45 = d+63.80
C. 350.45 + d + 63.80
D. 35+0.45d = 63.80
E. 35+0.45 = 63.80d
The equation that represents the given scenario is 35 + 0.45d = 63.80
What is Linear Equation:The linear equation is a mathematical statement that is solved for an unknown value. The linear equation is straight in a graph where the variable will represent an unknown value in the given problem.
To find the required equation, first calculated the charge according to the given problem and form the linear equation using the given variable.
Here we have
Cam will be charged a flat fee of $35.00 plus $0.45 for each day of storage.
If Cam stores her possessions for d days then the charge = $ 0.45d
After adding the fee the total charge will be $ 35 + $ 0.45d
Given that the total charge is $63.80
From the above calculations,
=> $ 35 + $ 0.45d = $ 63.80
=> 35 + 0.45d = 63.80
Therefore,
The equation that represents the given scenario is 35 + 0.45d = 63.80
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A dairy spends $21,000 per year to maintain its barns and equipment. It costs $2000 per year to feed and care for each dairy cow. (a)
Using C for the number of dairy cows and E for the total yearly expense, in dollars, find a formula that gives the total yearly expense as a linear function of the number of dairy cows. E =
(b)
The yearly income I, in dollars, for the dairy comes from milk production, which depends on the number C of dairy cows. Each dairy cow produces 3500 gallons of milk per year, and the dairy sells milk for $2. 00 per gallon. Find a formula that gives I as a linear function of C. I =
Incorrect: Your answer is incorrect. (c)
Determine the smallest number of cows the dairy needs in order to (at least) break even. Your answer should be a whole number. Incorrect: Your answer is incorrect. Cows
a) Formula that gives the total yearly expense as a linear function of the number of dairy cows is E = 21,000 + 2,000C.
b) Formula that gives I as a linear function of C is I = 7,000C. The smallest number of cows the dairy needs to break even is 5.
(a) Let's call the number of dairy cows "C".
The yearly expense for maintaining the barns and equipment is a fixed cost of $21,000.
The yearly expense for feeding and caring for each dairy cow is $2,000.
To find the total yearly expense, we can add the fixed cost of maintaining the barns and equipment to the variable cost of caring for the cows:
E = 21,000 + 2,000C
This is a linear equation that gives the total yearly expense as a function of the number of dairy cows.
(b) Each dairy cow produces 3,500 gallons of milk per year.
The dairy sells milk for $2.00 per gallon.
To find the yearly income for the dairy, we can multiply the number of gallons of milk produced by the price per gallon:
I = 2.00(3,500)C = 7,000C
This is a linear equation that gives the yearly income as a function of the number of dairy cows.
To determine the smallest number of cows the dairy needs in order to break even, we need to find the point where the yearly income is equal to the yearly expense.
Setting I = E, we get:
7,000C = 21,000 + 2,000C
Simplifying and solving for C, we get:
5,000C = 21,000
C = 4.2
Since we cannot have a fraction of a cow, we round up to the nearest whole number.
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how many four-digit numbers are made up of four consecutive numbers from 1-9 in some order, like 5342 or 7658?
There 144 four digit numbers are made up of four consecutive numbers from 1 to 9
We can approach this problem by counting the number of ways we can choose four consecutive numbers from 1-9 and then arranging them in a four-digit number.
Here we have to use combination
There are 6 possible sets of four consecutive numbers in the range 1-9
= {1,2,3,4}, {2,3,4,5}, {3,4,5,6}, {4,5,6,7}, {5,6,7,8}, and {6,7,8,9}.
For each set, there are 4! = 24 ways to arrange the four numbers into a four-digit number.
So the total number of four-digit numbers made up of four consecutive numbers from 1-9 is:
6 sets × 24 arrangements per set = 144
Therefore, there are 144 such four-digit numbers.
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a basketball player makes 80% of her free throws. what is the standard deviation of the successes from 100 free throws?
Since 80 out of 100 free throws were successful, the standard deviation of the success rate would be 8, and the standard deviation of a binomial distribution is the square root of (p*q)/n, where p is the probability of success, q is the probability of failure (1-p), and n is the total number of trials.
Standard deviation is calculated as follows:
p*q/n = 0.8*0.2/100 = 0.0016 = 0.04 = 8
Since 80% of 100 equals 80 successful free throws, the standard deviation of the successes from 100 free throws would be 8. The dispersion in a set of data is measured by standard deviation. A binomial distribution's standard deviation is equal to the square root of (p*q)/n, where p is the success probability, q is the failure probability (1-p), and n is the number of trials. Since the success rate in this instance is 80%, p = 0.8, q = 0.2, and n = 100. The standard deviation is then equal to the square root of (p*q/n): (0.8*0.2/100) = (0.0016) = (0.04), which equals 8. Therefore, the standard deviation of the successes from 100 free throws for a basketball player who makes 80% of them would be 8.
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A city's population is currently 365,000. If the population doubles every 24 years, what will the population be 96 years from now?
Answer: 5,840,000
Step-by-step explanation:
96/24=4
365,000x2x2x2x2=5,840,000
or
365,000 x 2^4=5,840,000
what is the answer to this f/22=27
Amy and Tina each buy a coffee.
Amy gets 15p change from £2
Tina gets £2.45 change from £5
How much more does Tina pay than Amy?
Give your answer in pence.
+
Optional working
Answer: 235
3
Р
Tina pays 0.7p more than Amy when buying the coffee.
What is addition and subtraction?The two main arithmetic operations that we learn to add and subtract two or more integers or other mathematical values are addition and subtraction. Division and multiplication are the other two fundamental mathematical operations. The addition symbol is the plus sign (+), and the subtraction symbol is the minus sign (-). (minus sign).
Given that,
Amy gets 15p change from £2. The price of the coffee is:
A = 2 - 0.15
A = 1.85
Tina gets £2.45 change from £5. The price of the coffee is:
T = 5 - 2.45
T = 2.55
The difference in the cost of the coffee is:
T - A = 2.55 - 1.85 = 0.7
Hence, Tina pays 0.7p more than Amy when buying the coffee.
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A quilter created the following shape to use in a block for a new quilt. A six-sided figure with a large base of 16 inches. The side to the right of the base is 9 inches. The small side parallel to the base is 6 and two fifths inches. There are two sides that form a point at a right angle. The smaller is 6 inches, and the larger is 7 and one-half inches. What is the area of the shape for the quilt block? ninety-four and one half in2 one hundred sixty-six and one half in2 189 in2 333 in2
The total area of the quilt is: 166.5 square inches
How to determine the total area of the quilt?The six-sided figure is given, and we can deduce the following parameters from the question:
The shape is made of a triangle and a rectangle
The side lengths derived from the question are:
The triangle on top:
base: 6 inches and height: 7.5 inches
The rectangle at the bottom:
Base: 16 inches with a height of 9 inches
So, we have the total area of the figure to be
Area of figure = (1/2 * 7.5 * 6) + (16 * 9)
Area of figure = 22.5 + 144
Area of figure = 166.5 in²
Based on the parameters, the total area is 166.5 square inches
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a is directly proportional to the square root of c. w is inversely proportional to a³.
When c = 49, a = 35
When a = 2, w = 16.
Find the value of w when c = 4.
Answer:
W when c = 4 is 0.128.
Step-by-step explanation:
The relationship between A, C and W can be represented by the following equations:
A = k√c
W = m/a^3
Where k and m are constant of proportionality.
Since A is directly proportional to the square root of c, we can write k = A/√c. Substituting the values of A and C when c = 49, we have:
k = 35/√49 = 35/7
Since W is inversely proportional to a^3, we can write m = W * a^3. Substituting the values of W and A when a = 2, we have:
m = 16 * 2^3 = 128
Now we have both k and m, we can find the value of W when c = 4.
A = k * √c = 35/7 * √4 = 10
W = m/a^3 = 128/10^3 = 0.128
So, the value of W when c = 4 is 0.128.
