As per the temperature, the population of Salmonella bacteria in the salad will double approximately every 2.87 hours if the conditions for growth remain constant.
The population of Salmonella bacteria can increase over time if they have the necessary nutrients and temperature for growth. In this case, we have a cutting board contaminated with Salmonella bacteria, which ends up in a salad. The number of bacteria present in the salad after t hours is given by the formula S(t) = 250 x 6t, where t is the time in hours.
To understand how often the population of bacteria doubles, we need to look at the growth rate of the bacteria.
To calculate the doubling time, we can use the formula Td = ln(2) / r, where Td is the doubling time, ln is the natural logarithm, and r is the exponential growth rate. In this case, the growth rate can be found by taking the derivative of S(t) with respect to t, which gives us r = 6ln(6).
Plugging in the values, we get Td = ln(2) / 6ln(6) = 2.87 hours
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Consider the following information:
Observations 1 2 3 4 5 6
Num. of defects 10 18 13 15 9 12
The number of runs above and below the sample median is:
Multiple Choice
a. 3.
b. 4.
c. none of these.
d. 5.
e. 6.
The number of runs above and below the sample median is: option a) 3. There are 3 runs above and below the sample median.
Sort the data in ascending order and find the median, we get
observations......5; 1; 6; 3; 4; 2
no. of defects....9; 10; 12; 13; 15; 18
Median = mean of the 6th and 3rd sample values
= (12+13)/2 = 12.5
When we count the samples in their occurrence order whether they are below or above the median.
we get that observation 1, 5 and 6 are below the median and observation 2, 3 and 4 are above the median,
Now we need to count 'Runs' from the beginning and count an additional run only when there is a transition from A to B or the vice versa.
Therefore, we get that there are 3 runs above and below the sample median.
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The plot below shows the graphs of three functions, f. 9, and h, all of which determine the population of a certain city (in thousands of people in terms of the number of years a since 2000. 80 60 20 a. The population of City A in 2000 was 50 thousand people and the population increased by 12% each year. The function / determines the population of this city (in thousands of people) in terms of r i. Write a function formula for f f(x)50e 0 12x w Preview ii. Which graph above represents f? The sold. bluegraph a. The population of City A in 2000 was 50 thousand people and the population ncreased by 12% each year. The function determines the population of this city (in thousands of people) in terms of z. i Write a function formula for f (z)50e0 12x ii which graph above represents The solid, blue graph b The population of City B in 2000 was 50 thousand people and the population increased by 16% each year. The function g determines the population of this city (in thousands of people) in terms of a i. Write a function formula for g g(x) 50 0 16x ii Which graph above represents g? u Preview The dotted green graph c. The population of City C in 2000 was 50 thousand people and the population increased by 20 thousand people each year. The function h determines the population of this city (in thousands of people) in terms of r i Write a function formula for h Preview The dashed red graph
The graphs which shows the following cities A, B, C are solid blue represents f(x), dashed red represents g(x) and dotted green graph represents the function h(x).
A graph is a structure that amounts to a set of items where certain pairs of the objects are in some manner "connected" in discrete mathematics, more especially in graph theory. The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
For x % increase, the 1-year growth factor g is given by
g = 1 + (x/100)
a) i) In this case
x = 12%
Therefore,
g = 1 + (12/100) = 1 + 0.12 = 1.12
Population after x years = (Population in 2000) * (1-year growth factor)x
=> f(x) = 50 (1.12)x
ii) The population growth is exponential in this case. The solid blue graph represents the function f(x).
b) i) In this case
x = 16%
Therefore,
g = 1 + (16/100) = 1 + 0.16 = 1.16
Population after x years = (Population in 2000) * (1-year growth factor)x
=> g(x) = 50 (1.16)x
ii) The population growth is exponential in this case . So, the dashed red graph represents the function g(x).
c) i) In this case, the growth of population is linear.
The linear relationship is given by
h(x) = mx + b
Population in 2000 = 50 thousand
In this case, m = 20
h(x) = 20x + 50
ii) The dotted green graph represents the function h(x) as the population growth is linear.
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rectangle opqr is dilated by a scale factor of 66 to form rectangle o'p'q'r'. side r'o' measures 9696. what is the measure of side ro?
The measure of side ro is 147 and the scale factor is 66, so the measure of side r'o' is 147 * 66 = 9696.
The measure of side ro can be found by dividing the measure of side r'o' by the scale factor. In this case, the measure of side r'o' is 9696 and the scale factor is 66. So, we can find the measure of side ro by doing the following calculation:
ro = r'o' / scale factor
ro = 9696 / 66
ro = 147
Therefore, the measure of side ro is 147.
In general, when a rectangle is dilated by a scale factor, the measures of the sides are multiplied by the scale factor. So, if the measure of a side is x and the scale factor is y, the measure of the dilated side will be x * y. In this case, the measure of side ro is 147 and the scale factor is 66, so the measure of side r'o' is 147 * 66 = 9696.
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Help with geometry homework with rectangles. Given rectangle ABCD with m < BEC = 62 degrees. Determine the measure of ABD.
Answer:
62°
Step-by-step explanation:
Alternate interior angles are congruent.
Helping in the name of Jesus.
What is the correct numerical expression for "9 times 4 added to the difference of 3 and 2?"
A. 9 x 4 + (3 − 2)
B. 9 x (4 + 3) − 2
C. 9 + (4 x 3) ÷ 2
D. 9 − 2 x 4 + 3
The correct numerical expression for "9 times 4 added to the difference of 3 and 2" is:
9 x 4 + (3 - 2)
what is expression?
In mathematics, an expression is a combination of numbers, variables, operators, and/or functions that can be evaluated to produce a value. Expressions can be simple or complex, and can involve arithmetic operations (such as addition, subtraction, multiplication, and division), as well as more advanced mathematical concepts such as exponents, logarithms, and trigonometric functions.
Expressions are often used in mathematical equations and formulas, and can be used to represent real-world situations and problems. For example, the expression "2x + 3y" might be used to represent the cost of buying two items that cost x dollars each and three items that cost y dollars each.
It's important to distinguish expressions from equations, which are statements that assert that two expressions are equal to each other. An equation involves an expression on each side of the equal sign, whereas an expression does not contain an equal sign.
The correct numerical expression for "9 times 4 added to the difference of 3 and 2" is:
9 x 4 + (3 - 2)
First, we evaluate the difference between 3 and 2, which is 1. Then we multiply 9 and 4, which is 36. Finally, we add 36 and 1 to get the answer:
36 + 1 = 37
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2) A garden is in the shape of a rectangle. The gardener put a
diagonal fence across the garden to separate his vegetables from
his fruit trees. The length of the garden is 22 ft and the width of the
garden is 17 feet. What is the length of the fence?
The barrier measures about 27.8 feet in length, according to the provided statement.
Pythagorean Theorem is what degree of mathematics?The Pythagorean Theorem is crucial to mathematics. Although you'll likely hear about it for your initial time in algebra, you'll actually use it in all subsequent math classes, including precalculus, calculus, geometry, and trigonometry.
The Pythagorean formula can be used to determine how long the vertical barrier is. According to the Pythagorean theorem, the square for the dimension of the hypotenuse, the longest side in a right triangle, is equivalent to the total of the squares of the remaining two sides.
In this case, the length and width of the garden form the two legs of a right triangle, and the diagonal fence is the hypotenuse. So we have:
Length of hypotenuse² = Length² + Width²
Substituting the given values, we get:
Length of hypotenuse² = 22² + 17²
Length of hypotenuse² = 484 + 289
Length of hypotenuse² = 773
Length of hypotenuse = √(773)
Using a calculator or simplifying by hand, we get:
Length of hypotenuse ≈ 27.8 feet
Therefore, the length of the fence is approximately 27.8 feet.
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Wanda says that if –3 > –8 then it must be true that 3 > 8. Is Wanda correct? Explain.
Group of answer choices
She is correct because a 3 will always be to the right of 8 on a number line, negative or not.
She is correct because the only thing that changed is the signs.
She is incorrect because 3 is to the left of 8 on a number line, which means it is less than 8.
She is incorrect because a 3 will always be to the left of 8 on a number line, negative or not.
The correct response is b. She is correct because the only thing that changed is the signs.
The term "sign" in mathematics describes a quantity's ability to be either positive or negative. Every real number with a sign that is not zero is either positive or negative. Zero itself is signless, or without a sign. The conjunction operator takes two or more inputs to build a Boolean-valued function, and it only returns true if all of its arguments are true. identical signs ADD and Retain that sign. Various indicators of the bigger absolute value SUBTRACT and KEEP. Rule 1: An integer that is both positive and negative cannot be added. RULE 2: Two positive integers add up to a positive number. The sum of two negative integers is positive, according to Rule 3. Rule 1: An integer that is both positive and negative cannot be multiplied together.
Determine whether -3>-8 is true or false:
True.
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A computer that originally cost $929 was returned to the electronics store. Because the box was opened, the store put it on the clearance rack for 35% off. What is the price of the computer?
Answer:
$603.85
Step-by-step explanation:
METHOD ONE:
to quickly shorten your way of finding the answer, find your discount number first.
it says 35% is the actual discount number.
100% - 35% = 65%
multiply:
929 x 0.65= $603.85
METHOD TWO:
do it the regular way.
929 x 0.35 = 325.15
929 - 325.15 = $603.85
he cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 50 to 70 minutes. find the mean and variance of the cycle times for the trucks.
The mean cycle time for the trucks hauling concrete to a highway construction site is 60 minutes, and the variance of the cycle times is 100/3 minutes squared.
The cycle time for the trucks hauling concrete is uniformly distributed over the interval 50 to 70 minutes. This means that any value within the interval has an equal chance of being the cycle time for the trucks. The probability density function (PDF) for a uniform distribution is given by:
f(x) = 1/(b-a), for a ≤ x ≤ b
where a = 50 minutes (the lower limit of the interval) and b = 70 minutes (the upper limit of the interval).
To find the mean of the cycle times, we can use the formula:
mean = (a + b)/2
Substituting the values of a and b, we get:
mean = (50 + 70)/2 = 60
Therefore, the mean cycle time for the trucks hauling concrete is 60 minutes.
To find the variance of the cycle times, we can use the formula:
variance = (b - a)² / 12
Substituting the values of a and b, we get:
variance = (70 - 50)² / 12 = 100/3
Therefore, the variance of the cycle times for the trucks hauling concrete is 100/3 minutes squared.
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Given that z is a standard normal random variable, find z for each situation. (Round your answers to two decimal places.)
(a) The area to the left of z is 0.9750.
(b) The area between 0 and z is 0.4750.
(c) The area to the left of z is 0.7517.
(d) The area to the right of z is 0.1292.
(e) The area to the left of z is 0.7794.
(f) The area to the right of z is 0.2206.
(a) The area to the left of z is 0.9750. Z = 1.96.
(b) The area between 0 and z is 0.4750. The area in the left tail of the distribution is 0.475/2 = 0.2375. Since the distribution is symmetric, then the area to the left of z is 0.5 + 0.2375 = 0.7375. The value of z with an area of 0.7375 to its left is z = 0.72.
(c) The area to the left of z is 0.7517. Z = 0.99.
(d) The area to the right of z is 0.1292. The area to the left of z is 1 - 0.1292 = 0.8708. Z = 1.15.
(e) The area to the left of z is 0.7794. Z = 0.81.
(f) The area to the right of z is 0.2206. The area to the left of z is 1 - 0.2206 = 0.7794. Z = 0.81.
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Find a formula for this function. Please
The formula for the given function y = 0.9cos(2π/?(x-[ ])) + [ ] is : y = 0.9cos(2π/4(x - 0.55))
What is function?A function is a relation between a set of inputs and a set of possible outputs, with each input corresponding to exactly one output.
Based on the given graph values of 0.3, 2.2, 0.6, and 2.1, we can determine the formula for the function y = 0.9cos(2π/?(x-[a])) + b as follows:
Amplitude: The given function oscillates between a maximum value of 0.9 and a minimum value of -0.9. Hence, the amplitude of the function is 0.9.
Period: From the graph, we can see that the function completes one full cycle between x = 0 and x = 4. Therefore, the period of the function is 4.
Phase Shift: The given function attains its maximum value at x = 2.2, which is not at the starting point of the graph (x = 0). Therefore, the function is horizontally shifted to the right. We need to find the amount of this shift.
The distance between x = 0 and x = 2.2 is 2.2 units. Since the period of the function is 4 units, the phase shift is 2.2/4 = 0.55 units.
Vertical Shift: From the graph, we can see that the midline of the function (i.e., the horizontal line passing through the center of the oscillation) is at y = 0. Therefore, the vertical shift of the function is also 0.
Frequency: The frequency of the function is the number of cycles completed by the function in one unit of the input. From the period, we know that the function completes one full cycle in 4 units. Therefore, the frequency of the function is 1/4.
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Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. a) 2+0.5 +0.125+0.03125 (4pts)
Sn = 2/(1-0.5) = 4.
The given geometric series is convergent, as the ratio between each term is always less than 1 (in this case, 0.5). The sum of the series can be found using the formula Sn=a₁/(1-r), where a₁ is the first term of the series (2 in this case), and r is the common ratio between terms (0.5 in this case).
Therefore, the sum of the series is Sn = 2/(1-0.5) = 4.
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subtitution solve for x and y
y = x + 7
x + + 2y = -16
Answer:
x = -10 and y = -3
Step-by-step explanation:
given y = x+7
substitute in x + 2y = -16
=> x + 2(x+7) = -16
=> x + 2x + 14 = -16
=> 3x = -16 - 14
=> 3x = -30
=> x = -30/3
x = -10substitute in y = x + 7
=> y = -10 + 7
y = -3PLS MRK ME BRAINLIEST
OMG HELPPPPP
Match the math word to the correct part of the equation below:
3x + 8 = 7
Question 4 options:
3
8 and 7
x
1.
Coefficient(s)
2.
Variable(s)
3.
Constant(s)
The words with the part of the equations are
Coefficient = 3Variable = xConstant = 8 and 7How to match the words with the part of the equationsFrom the question, we have the following parameters that can be used in our computation:
3x + 8 = 7
Consider an equation represented as
ax + b = c
Where the variable is x, we have the following labels
Variable = x
Coefficient = a
Constant = b and c
Using the above as a guide, we have the following:
Variable = x
Coefficient = 3
Constant = 8 and 7
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jeanette rows at an average speed or 2m/s. how long does it take her to row 70m?
Answer:
35s
Step-by-step explanation:
Speed = distance/time
When distance is 70m and speed is 2m/s,
2 = 70/time
time = 70/2
= 35s
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you buy a lottery ticket to a lottery that costs $10 per ticket. there are only 100 tickets available to be sold in this lottery. in this lottery there are one $415 prize, two $115 prizes, and four $20 prizes. find your expected gain or loss. (if this is a loss, enter a negative number.)
The expected gain or loss for buying a lottery ticket in this lottery is a loss of $2.75.
The expected gain or loss for the lottery ticket bought can be found by calculating the expected value, which is the sum of the products of the probability of each outcome and its associated gain or loss.
The given probabilities can be found as follows:
There is only one $415 prize,
so the probability of winning this prize is : 1/100 = 0.01
There are two $115 prizes, so the probability of winning any one of these prizes is : 2/100 = 0.02.
There are four $20 prizes, so the probability of winning any one of these prizes is: 4/100 = 0.04
Now, the expected gain can be found by multiplying the probability of winning each prize by the amount of money to be won and then adding all the products.
The expected gain is : ($415 × 0.01) + ($115 × 0.02) + ($20 × 0.04)
= $4.15 + $2.30 + $0.80
= $7.25
The expected loss can be found by subtracting the cost of the ticket from the expected gain.
The expected loss is: $7.25 − $10.00 = −$2.75.
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The least common multiple of 6 and 9 is
Answer:
18
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
The Least Common Multiple or Lowest Common Multiple of 6 and 9 is 18.
The price of a computer component is decreasing at a rate of 14% per year. State whether this decrease is linear or exponential. If the component costs $60 today, what will it cost in three years?
Simplify the following expression.
3/11/5: 3-9/5
○ A. 12
○ B. 1
12
oc.
O D.
81
1
81
Using the product rule of exponents, the expression can be simplified to 3²⁰/25.
What is expression?
Expression in math is a combination of numbers, symbols, and other mathematical terms used to represent a quantity or an operation. It can be defined as a statement that uses mathematical symbols to form a mathematical equation or to express a mathematical relationship. Expressions are used to calculate the value of a mathematical equation and to determine the solution to a problem. They can also be used to represent relationships between different variables.
The given expression can be simplified using the product rule of exponents which states that when two terms with the same base are multiplied together, the exponents can be added together.
Therefore, 3¹¹/5 ÷ 3⁻⁹/⁵ can be rewritten as 3¹¹/5 x 3⁻⁹/⁵
Using the product rule of exponents, the expression can be simplified to 3²⁰/25.
Therefore, the simplified expression is 3²⁰/25.
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Complete questions as follows-
Simplify the following expression. 3^11/5 divided by 3^-9/5
THE QUATION WHEN QUNITYOF 17PLUS P IS DIVIED BY 8
This expression is an example of an algebraic fraction, where the numerator (17 + p) is divided by the denominator (8).
The quantity 17 plus p is represented as (17 + p) in parentheses. This means that we add 17 and p together before doing anything else with the expression.
The entire quantity (17 + p) is then divided by 8. This means we take the sum of 17 and p and divide it by 8.
We can simplify the expression further if needed, depending on the context of the problem. For example, if we are asked to find the value of the expression when p equals 5, we would substitute 5 for p and evaluate:
(17 + 5) / 8 = 22 / 8 = 2.75
So the value of the expression when p equals 5 is 2.75.
In general, "(17 + p) / 8" represents a number that is obtained by adding 17 and p and then dividing the result by 8. The expression is often used in algebraic equations or problems that involve dividing a sum of numbers by a constant value (in this case, 8).
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The question "When the quantity of 17 plus p is divided by 8?
can yall help me again plsssssssss!!!!!!!!!!!!!!!
After solving the given expression we get a = b = 12 and q = r = 24.
What is fractiοn?A fractiοn is a numerical quantity that represents a part οf a whοle οr a ratiο between twο quantities. It is written as a tοp number (numeratοr) οver a bοttοm number (denοminatοr), separated by a hοrizοntal line.
Tο subtract 2/3 - 1/4, we need tο find a cοmmοn denοminatοr fοr the twο fractiοns. The smallest cοmmοn denοminatοr is 12, sο we'll cοnvert each fractiοn tο an equivalent fractiοn with a denοminatοr οf 12:
2/3 = 8/12 (multiply bοth numeratοr and denοminatοr by 4)
1/4 = 3/12 (multiply bοth numeratοr and denοminatοr by 3)
Nοw we can subtract the twο fractiοns:
8/12 - 3/12 = 5/12
Sο 2/3 - 1/4 = 5/12.
Tο express the result as a fractiοn in the fοrm x/y, we can simply use the answer we fοund: x = 5, y = 12, sο:
2/3 - 1/4 = 5/12 = 5/12
Similarly, tο express the result as a fractiοn in the fοrm a/b, we need tο find anοther equivalent fractiοn with a cοmmοn denοminatοr. We can use 24 as a cοmmοn denοminatοr this time:
2/3 = 16/24 (multiply bοth numeratοr and denοminatοr by 8)
1/4 = 6/24 (multiply bοth numeratοr and denοminatοr by 6)
Nοw we can subtract the twο fractiοns:
16/24 - 6/24 = 10/24
Sο 2/3 - 1/4 = 10/24.
Tο express the result as a fractiοn in the fοrm a/b, we can simplify the fractiοn by dividing bοth numeratοr and denοminatοr by their greatest cοmmοn factοr, which is 2:
10/24 = (10 ÷ 2) / (24 ÷ 2) = 5/12
Sο we get a=b=12 and q=r=24.
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Given are five observations for two variables, x and y
xi 1 8 11 13 16
yi 59 58 40 22 10
The estimated regression equation for these data is y=71.01-3.39x.
Compute SSE, SST, and SSR.
SSE (to 2 decimals)
SST (to 2 decimals)
SSR (to 2 decimals)
b. Compute the coefficient of determination r2. Comment on the goodness of fit.
BLANK (to 3 decimals)
The least squares line provided an (GOOD/BAD) fit- Select your answer; BLANK % of the variability in y has been explained by the estimated regression equation (to 1 decimal).
c. Compute the sample correlation coefficient. Enter negative value as negative number.
BLANK (to 3 decimals)
SSE: 2129.59
SST: 13243.6
SSR: 11113.0
To compute SSE, SST, and SSR, we first need to calculate the mean of x and y:
mean(x) = (1 + 8 + 11 + 13 + 16) / 5 = 9.8
mean(y) = (59 + 58 + 40 + 22 + 10) / 5 = 37.8
Using these means and the estimated regression equation y = 71.01 - 3.39x, we can compute SSE, SST, and SSR:
SSE = Σ(yi - ŷi)² = Σ(yi - (a + bx))² = Σ(yi - 71.01 + 3.39xi)² = 2129.59
SST = Σ(yi - ȳ)² = Σ(yi - 37.8)² = 13243.6
SSR = Σ(ŷi - ȳ)² = Σ(71.01 - 3.39xi - 37.8)² = 11113.0
Therefore, SSE = 2129.59, SST = 13243.6, and SSR = 11113.0.
To compute the coefficient of determination r², we can use the formula:
r² = SSR / SST
Substituting the values we found, we get:
r² = 11113.0 / 13243.6 ≈ 0.839
The coefficient of determination r² is 0.839. This indicates a reasonably good fit between the estimated regression equation and the data, as a large proportion of the variability in y is explained by the regression model.
The sample correlation coefficient can be found using the formula:
r = Σ[(xi - mean(x))(yi - mean(y))] / √[Σ(xi - mean(x))² Σ(yi - mean(y))²]
Substituting the values we found, we get:
r = [(-8.8)(21) + (-0.8)(20) + (1.2)(2) + (3.2)(56) + (6.2)(84)] / √[(84.8)(860.8)] ≈ 0.917
Therefore, the sample correlation coefficient is approximately 0.917.
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Antarctica is roughly a semicircular, with a radius of 2.00×103 km. The average thickness of the ice cover is 3.00×103 m. How many cubic centimeters of ice does Antarctica contain ?
Antarctica is roughly a semicircular, with a radius of 2.00×103 km. The average thickness of the ice cover is 3.00×103 m. How many cubic centimeters of ice does Antarctica contain is Antarctica is roughly semicircular with a radius of 2.00 × 103 km, with an average ice cover thickness of 3.00 × 103 m. In cubic centimeters, (3.14 × 2.00×106 km^2) x (3.00×103 m) =6.0114 × 1019 cm3.
the total ice content of Antarctica may be estimated. We have to change the measurement system from kilometers to centimeters and from meters to centimeters, and then we can do the arithmetic calculation. We know that the radius of the earth is 6371 km.
According to the formula 2πr, the circumference of the earth is (2 × 3.14 × 6371) km = 40075.4 km.Since the Antarctic is a semicircle, half of its perimeter would be 20,038 km long. The ice cover's total surface area would be given by multiplying this by the ice cover's average thickness (3.00 × 103 m).
As a result, the total ice volume in cubic meters would be given by multiplying the ice cover's surface area by its thickness. As a result, we have: V = surface area x thickness= (20,038 × 103 m) x (3.00 × 103 m)= 6.0114 × 1010 m3We may now convert cubic meters to cubic centimeters since we want the solution in cubic centimeters.= (6.0114 × 1010) m3 x (100 × 100 × 100) cm3/m3= 6.0114 × 1010 x 1.00 × 109 cm3= 6.0114 × 1019 cm3.
Therefore, the total ice content of Antarctica is 6.0114 × 1019 cm3. This is how we can determine the cubic centimeters of ice that Antarctica contains.
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suppose the value of y changes from y = − 1.8 to y = − 6.2 . what is the corresponding change in y ?
The corresponding change in y is −4.4 when the value of y changes from y = − 1.8 to y = − 6.2
The corresponding change in y can be found by subtracting the initial value of y from the final value of y. In this case, the initial value of y is y = − 1.8 and the final value of y is y = − 6.2.
To find the corresponding change in y, we can use the following formula:
Change in y = Final value of y - Initial value of y
Substituting the given values into the formula, we get:
Change in y = (− 6.2) - (− 1.8)
Change in y = − 6.2 + 1.8
Change in y = − 4.4
Therefore, the corresponding change in y is − 4.4.
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What are the greatest common divisors of these pairs of integers? a) 2^2.3^3.5^5, 2^5. 3^3 . 5^2 b) 2.3.5.7.11 · 13, 2^11.3^9 . 11. 17^14 c) 17, 17^17 d) 2^2. 7,5^3 . 13 e) 0,5 f) 2.3.5.7,2.3.5.7
a) The prime factors of the GCD must be the minimum of the exponents in each prime factorization. Therefore, GCD = 2^2.3^3.5^2.
b) The only shared prime factors are 2, 3, and 11. The exponent of 2 is 1 in the first number and 11 in the second number, so we take 2^1. The exponent of 3 is 1 in the first number and 9 in the second number, so we take 3^1. The exponent of 11 is 1 in both numbers, so we take 11^1. Therefore, GCD = 2^1.3^1.11^1 = 66.
c) The two numbers are the same, so the GCD is simply 17.
d) The only shared prime factor is 1. Therefore, GCD = 1.
e) By definition, any integer divides 0. Therefore, the GCD is undefined.
f) The two numbers are the same, so the GCD is simply 2.3.5.7 = 210.
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create a conversion factor between grains of sand and mass based on the data you have collected. use this conversion factor to determine the grains of sand in your 50-ml beaker.
There are 0.001 grains of sand in your 50-ml beaker.
To create a conversion factor between grains of sand and mass, you need to determine the mass of one grain of sand. Once you have that information, you can create a conversion factor by dividing the mass of one grain of sand by the mass of the 50-ml beaker. This will give you the number of grains of sand per unit mass.
For example, if one grain of sand has a mass of 0.001 grams and the 50-ml beaker has a mass of 50 grams, the conversion factor would be 0.001 grams/grain of sand ÷ 50 grams = 0.00002 grains of sand/gram.
To determine the grains of sand in your 50-ml beaker, you can multiply the conversion factor by the mass of the beaker. In this case, 0.00002 grains of sand/gram x 50 grams = 0.001 grains of sand.
Therefore, there are 0.001 grains of sand in your 50-ml beaker.
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Consider the following. T is the clockwise rotation (theta is negative) of 60 degree in R^2, v = (1, 4). (a) Find the standard matrix A for the linear transformation T. A = [___ ____ ____ ____] (b) Use A to find the image of the vector v. T(v) = ____
The standard matrix A for the linear transformation T is
A = [1/2 -√3/2]
[√3/2 1/2]
Using this matrix, the image of the vector v under T is given by T(v) = A * v = (2√3, 5/2).
(a) The standard matrix A for the linear transformation T is given by:
A = [cos(-60°) sin(-60°)]
[-sin(-60°) cos(-60°)]
Since cos(-60°) = cos(60°) = 1/2 and sin(-60°) = -sin(60°) = -√3/2, we have:
A = [1/2 -√3/2]
[√3/2 1/2]
(b) To find the image of the vector v = (1, 4) under the transformation T, we multiply the matrix A by v:
T(v) = A * v
[1/2 -√3/2] [1]
= [√3/2 1/2] * [4]
= [1/2 -√3/2] [1] [1/2 -2√3]
= [√3/2 1/2] * [4] = [2√3 2]
= [1/2 -√3/2] [1] [1/2 -2√3]
= [√3/2 1/2] [4] = [2√3 2]
= [1/2 -√3/2] * 1 + [√3/2 1/2] * 4, [1/2 -2√3] + [2√3 2]
= [2√3 5/2]
Therefore, T(v) = (2√3, 5/2).
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4. Write an equation that relates the measure of
Answer:
2x - 8 = 50
Step-by-step explanation:
∠ CBD and ∠ ABE are vertically opposite angles and are congruent , then
2x - 8 = 50
What is the fifth term when the first term is 6 and the common ratio is 0.5?
To find the fifth term of a geometric sequence, we need to use the formula:
a_n = a_1 * r^(n-1)
where a_n is the nth term of the sequence, a_1 is the first term, r is the common ratio, and n is the number of the term we want to find.
In this case, we are given that the first term (a_1) is 6 and the common ratio (r) is 0.5. We want to find the fifth term (a_5).
Using the formula, we have:
a_5 = a_1 * r^(5-1)
a_5 = 6 * 0.5^(4)
a_5 = 6 * 0.0625
a_5 = 0.375
Therefore, the fifth term of the sequence is 0.375.
A quality inspector plans to test a sample of 40 bottles of soft drink labeled as 20 ounces. If she finds the mean content to be less than 19.8 ounces, she will have the bottling machinery stopped and recalibrated. If it is known that the machine operates with a standard deviation of 0.75 ounces, what is the probability that the inspector will mistakenly stop a machine that is delivering a mean of at least 20 ounces per bottle?
A) .023
B) .046
C) .050
D) .092
E) .119
The probability that the inspector will mistakenly stop a machine that is delivering a mean of at least 20 ounces per bottle is 0.023 (option A).
The null hypothesis is that the mean content of the bottles is 20 ounces, and the alternative hypothesis is that the mean content is less than 19.8 ounces.
Let's assume that the true mean content of the bottles is μ = 20 ounces, and the standard deviation is σ = 0.75 ounces.
The sample size is n = 40, which is large enough for the central limit theorem to apply.
The z-score for a sample mean of 19.8 ounces is:
z = (x-bar - μ) / (σ / √n) = (19.8 - 20) / (0.75 / √40) = -2.83
The probability of getting a sample mean of less than 19.8 ounces if the true mean is 20 ounces is:
P(z < -2.83) = 0.0023
This is the level of significance or the probability of making a Type I error.
The probability of not stopping the machine when it is delivering a mean of at least 20 ounces per bottle is:
1 - 0.0023 = 0.9977
Therefore, the probability of mistakenly stopping the machine is:
0.0023 or 0.023%
Thus, the answer is A) 0.023.
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