The global extreme values of the function f(x, y) = x² + 2(y²) on the circle x² + y² = 1 are,
The maximum value of f on the circle x² + y² = 1 is,
⇒ f(0, ±1) = 2
And, the minimum value is,
⇒ f(±1, 0) = 1
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
Function is,
f(x, y) = x² + 2(y²)
And, Equations of circle is,
x² + y² = 1
Hence, The maximum value of f on the circle x² + y² = 1 is,
⇒ f(0, ±1) = 0² + 2(1²) = 2
And, the minimum value is,
⇒ f(±1, 0) = 1² + 2 × 0 = 1
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Identify the horizontal and vertical asymptotes, if any, of the given function.
f(x) = (x^2 - 16) / (-x^2 - 16)
Separate multiple answers by commas. Enter DNE if an asymptote does not exist. a) Horizontal asymptote(s): y =___?
b) Vertical asymptote(s): x=____?
The vertical asymptote of the function are 4. -4 and the horizontal asymptote is -1.
What are asymptotes?An asymptote is a line that a curve approaches but never touches. i.e., an asymptote is a line to which the graph of a function converges. When graphing functions, asymptotes are typically not required. However, when we graph them using dotted lines (imaginary lines), we have to be careful that the curve doesn't hit the asymptote. The asymptotes are therefore essentially made-up lines.
Given that, the function:
f(x) = (x² - 16) / (-x² - 16)
The horizontal asymptote of the function when both the degrees of numerator and denominator are equal is:
HA = Leading coefficient of numerator / leading coefficient of denominator
HA = 1 / -1
HA = -1
To calculate the vertical asymptote simplify the function:
f(x) = (x² - 16) / (-x² - 16)
f(x) = (x - 4) (x + 4) / (-x - 4) (-x + 4)
Equate the denominator to 0:
-x - 4 = 0, x= -4
- x + 4 = 0, x = 4
Hence, the vertical asymptotes of the function are 4. -4 and the horizontal asymptote is -1.
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Helppppppppppppppppppppp
Answer:The answer is letter E
Step-by-step explanation:
If you divide 4/15 you get 0.2666.
If you solve all of the choices letter E is equivalent to the expression.
In 1999, a sample of a radioactive substance had a mass of 750 milligrams. Since then, the sample has decayed by 7.1% each year.
Let t be the number of years since 1999. Let y be the mass of the substance in milligrams,
Write an exponential function showing the relationship between y and t.
Answer:
Below
Step-by-step explanation:
If it decays 7.1 % ( which is .071 in decimal ) then .929 remains at the end of each year and the equation becomes
y = 750 (.929^t) where t is years since 1999 and y is mg
A certain instructor asked the girls in his class to estimate his weight. Their responses were
190, 230, 105, 180, 130, 160, and 170 pounds.
a. Compute the sample mean.
b. What is the sample median?
Answer: sample mean is 166,4285714285714
and sample median is 170
Step-by-step explanation: sorry if its wrong
Answer:
Step-by-step explanation:
a. To compute the sample, mean, we add up all the weights and divide by the number of responses (in this case, 7):
(190 + 230 + 105 + 180 + 130 + 160 + 170) / 7 = 1265 / 7 ≈ 180.71
Therefore, the sample mean weight estimate is approximately 180.71 pounds.
b. To find the sample median, we need to put the responses in order from smallest to largest and then find the middle value. In this case, the ordered list of weights is:
105, 130, 160, 170, 180, 190, 230
The middle value is the average of the two values in the middle of the list, which in this case is:
(170 + 180) / 2 = 175
Therefore, the sample median weight estimate is 175 pounds.
A $5070 investment earns interest at
compounded quarterly
5% per year
over 15 years.
Use the compound interest formula to
calculate the value of this investment
to the nearest cent.
Answer:
Step-by-step explanation:
The value of the investment can be calculated using the compound interest formula:
A = P * (1 + (r/n))^(nt)
Where:
A = final amount
P = principal amount (5070)
r = annual interest rate (0.05)
n = number of times the interest is compounded in a year (4)
t = number of years (15)
So,
A = 5070 * (1 + (0.05/4))^(4*15)
A = 5070 * (1.0125)^60
A = 5070 * 2.693260689
A = 13,652.14
The value of the investment after 15 years compounded quarterly at 5% per year is $13,652.14, rounded to the nearest cent.
The probability that a randomly selected education major received a starting salary offer greater than $52,350 is . The probability that a randomly selected education major received a starting salary offer between $45,000 and $52,350 is . (Hint: The standard normal distribution is perfectly symmetrical about the mean, the area under the curve to the left (and right) of the mean is 0.5. Therefore, the area under the curve between the mean and a z-score is computed by subtracting the area to the left (or right) of the z-score from 0.5.) Twenty percent of education majors were offered a starting salary greater than?
The area under the curve between the mean and a z-score
P (Z > - 1.80) - P (Z < - 0.3)1 - P (Z < - 1.80) - P (Z < - 0.3)1 - 0.0359 - 0.3821 = 0.582 = 58.2%What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
1. z = (x[tex]- \mu) /\sigma[/tex]
z= (52350 - 46292)/ 4320
z = 1.40
P(X> 52350 )= P( z> 1.40) = P(z< -1.40)
P(Z>1.40) = 0.0808, which is 8.08%
2. Now, z = (x[tex]- \mu) /\sigma[/tex]
z= (45000- 46292)/ 4320
z = -0.30
and, z = (x[tex]- \mu) /\sigma[/tex]
z= (52350 - 46292)/ 4320
z = 1.40
Then, you must find the area between Z = -0.30 and Z = 1.40
So, P(Z<1.40) - P(Z < - 0.30)
= P(Z > - 1.40) - P(Z < - 0.30)
= 1 - P(Z< -1.40) - P( Z < -0.30)
The area under the curve to the left= 1 - 0.0808 - 0.3821 = 0.5371
3. z = (x[tex]- \mu) /\sigma[/tex]
z= (38500- 46292)/ 4320
z = -1.8
Thus, the area under the curve to the right of Z = - 1.80 and to the left of Z = - 0.3
P (Z > - 1.80) - P (Z < - 0.3)1 - P (Z < - 1.80) - P (Z < - 0.3)1 - 0.0359 - 0.3821 = 0.582 = 58.2%Learn more about Probability here:
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Michael has a granola recipe that requires 1 4 pounds of oats to make one batch of granola. If Michael uses 4 5 pounds of oats while making granola, how many batches has he made?
Michael has made 3.21 batches of granola.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
Michael has a granola recipe that requires 14 pounds of oats to make one batch of granola.
If Michael uses 45 pounds of oats while making granola,
then number of batches he made,
= 45 /14
= 3.21
Hence, he made 3.21 batches.
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Explain/describe in your own words what happens to the graph when
k
increases.
For the graph [tex]f(x)= a(x-h)^{2}+k[/tex] The graph goes upward if k > 0, but it shifts downward if k < 0.
A quadratic function is represented in its standard form as [tex]f(x)= a(x-h)^{2}+k[/tex], where (h, k) is the vertex. This form is also referred to as the vertex form of a quadratic function because the vertex occurs in the quadratic function's standard form.
To understand how the graph differs from the graph of y = x², the standard form is helpful. This fundamental function's graph is shown in the figure below.
A constant, k, can be added to or subtracted from the graph of f(x) = x² to represent a vertical (up, down) shift.
The graph goes upward if k > 0, but it shifts downward if k < 0.
Describe graphs.Mathematicians use graphs to visually represent or chart facts or values in a logical way. Usually, a graph point will show the relationship between two or more objects.
A graph is a non-linear data structure made up of nodes, also known as vertices, and edges. The nodes, sometimes referred to as vertices, should be joined with glue. Vertices in this graph are 1, 2, 3, and 5, whereas edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of exponential development in statistical charts, such as bar charts, pie charts, and line graphs. a triangle-shaped logarithmic graph
Piecewise functions are exactly what their name implies: groups of several functions (subfunctions) on a single graph.
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Evolution and Scientists. A professor claims that more than 77% of all scientists believe in evolution. In a 2014 Pew Research survey of a representative sample of 115 scientists connected to the American Association for the Advancement of Science (AAAS), 104 of these scientists say they believe in evolution. Perform a hypothesis test of the professor's claim using these data.
(b) Find the p-value (round to 4 decimals).
A professor asserts that more than 77% of all scientists believe in evolution, and the p-value for the two-tailed test is 2 mincdf(x), 1 - cdf(x).
what is null hypothesis ?A type of statistic hypothesis known as a hypothesis claims that a certain group of data has no statistical power. The viability of hypotheses is investigated using sample data. Sometimes refer to as "zero," and represented as H0. The premise that researchers make is that there is a link between the variables. The null hypothesis, on the contrary hand, asserts that such a link does not exist. Despite its inability to seem relevant, the null hypothesis is a critical component of research.
given
You must understand the distribution of your test statistic on the supposition that the null hypothesis is correct in order to calculate the p-value.
Left-tailed test: cdf as the p-value (x).
Test with a right-tail: p-value = 1 - cdf (x).
p-value for the two-tailed test is 2 mincdf(x), 1 - cdf(x).
A professor asserts that more than 77% of all scientists believe in evolution, and the p-value for the two-tailed test is 2 mincdf(x), 1 - cdf(x).
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the quotient of a number and -5, decreased by 9, is 2.”
The quotient of a number and -5, decreased by 9, is 2.”So, the number is -55.
In arithmetic, what exactly is a quotient?The dividend is the quantity being divided (15 in this case), and the divisor is the quantity being divided (3 in this case). Quotient is what remains after division. A quotient is the result of dividing one number by another. It is the number of times one number is contained within the other, or the answer to a division problem.
The name of which quotient?It is known as the quotient to divide two numbers. Six times two is the ratio, which equals three. The Latin word for ratio, "how many times," is quotient. This is very logical: by dividing two numbers, you are calculating "how many times" the second number enters the first.
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A city held a bike parade. 10 bikers rode recumbent bicycles, and 82 bikers rode other types of bicycle. What is the probability that a randomly chosen bike in the parade was a recumbent bicycle? Write your answer as a fraction or whole number. P(recumbent bicycle)=
The probability that a randomly chosen bike in the parade was a recumbent bicycle will be 5/46.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the chance is given as,
P = (Favorable event) / (Total event)
A city held a bike parade. 10 bikers rode recumbent bicycles, and 82 bikers rode other types of bicycles.
The total number of bikers is given as,
Total bikers = 82 + 10
Total bikers = 92
Then the probability is given as,
P = 10 / 92
P = 5 / 46
The probability that a randomly chosen bike in the parade was a recumbent bicycle will be 5/46.
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the range of temperature, t on the surface of a planet is from -150°c to 18c. translate this statement into algebraic or compound inequality.
Answer:
-150 ≤ t ≤ 18
Step-by-step explanation:
When you divide 33 from a natural number (n) you get the remainder 5. What are all possible values of n? PLEASE HELP I HAVE RSM IN TWO DAYS I NEED THIS ITS MY LAST QUESTION PLS
The possible values of n are 5 and 6.
What is the division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Given that, divide 33 from a natural number (n) you get the remainder 5.
Now, 33/n =5
n=33/5
n=5.5
So, the possible values are 5 and 6
Therefore, the possible values of n are 5 and 6.
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A fully loaded and fueled spacecraft can weigh close to 3.9
million pounds. What is this weight converted to tons?
Answer:1950 US tons
Step-by-step explanation:
A container is 90% filled with chemical solution the container holds 1490 L of chemical solution how many liters of chemical solution are needed to fill the container to the top
The amount of chemical solution needed to fill the container to the top is 165.56 L.
If the container is already 90% filled with a chemical solution, then the remaining empty space is 10% of the total volume. We can calculate the total volume of the container using the formula:
total volume = volume of solution/fraction of container filled
Plugging in the given values, we get:
total volume = 1490 / 0.9
total volume = 1655.56 L
So, the total volume of the container is 1655.56 L. To fill the container to the top, we need to add the amount of solution that fills the remaining 10% of the container. This is equivalent to:
volume of remaining space = 0.1 * 1655.56
volume of remaining space = 165.56 L
Therefore, we need to add 165.56 L of a chemical solution to fill the container to the top.
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Find the diameter of the object. A circular switch with a radius of 3/5 centimeters.
Answer:
1.2
Step-by-step explanation:
To find the diameter, you must multiply the radius by two
Select the correct answer from the drop-down menu.
Three segments AB, AC, and AE share a common endpoint A. Point D lies on segment AB. Arc BC and arc DE is drawn. The length of arc between segments AB and AC is 1.18 radians. The length of arc between segments AE and AC is 2.36 radians.
If AD=2/3 AB , the ratio of the length of BC to the length of DE is [1/6, 1/4, 3/2, 3/4].
The ratio of the length of BC to the length of DE is 1/2.
What is Arc Length?Arc length is defined as the distance between any two points on a section of a circle or curve.
The figure in the question is given below.
The formula to find the length of an arc is given as,
Arc length, l = rθ, where r is the radius and θ is the central angle in radians.
Given that,
Central angle for arc BC, θ = 1.18 radians.
Radius for arc BC, r = AC = AB
Arc length of BC = rθ
= 1.18 (AB)
Central angle for arc DE, θ = 1.18 + 2.36 = 3.54 radians
Radius for arc DE, r = AE = AD = 2/3 AB
Arc length of DE = rθ
= 3.54 × (2/3) AB
= 2.36 (AB)
Arc length of BC / Arc length of DE = 1.18 (AB) / 2.36 (AB) = 1/2
Hence the ratio of BC to DE is 1/2.
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Answer:
DE: 3/4
Step-by-step explanation:
PlatoGang
Select the correct answer. What is the coefficient of x2 in the expansion of (x + 2)3?
The coefficient of x^2 in the expansion of (x + 2)^3 is 6
How to determine the coefficient of x2From the question, we have the following parameters that can be used in our computation:
(x + 2)^3
Next, we expand the expression
So, we have the following representation
(x + 2)^3 = x^3 + 3x^2 * 2 + 3x * 2^2 + 2^3
Evaluate the expression
(x + 2)^3 = x^3 + 6x^2 + 12x + 8
The coefficient of x^2 in the expression x^3 + 6x^2 + 12x + 8 is 6
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One link in a chain was made from a cylinder that has a radius of 3 cm and a height of 25 cm. How much plastic coating would be needed to coat the surface of the chain link? Use 3.14 for π.
The plastic coating required to cover the surface of the coating is 527.52 cm²
What is the area and volume of a right circular cylinder?The volume of a Right Circular Cylinder. In general, the volume of a right cylinder is the area of the base times the height of the cylinder. The area of the circular base is given by the formula A = πr². Substitute to get V = πr²h.
Given here: The radius is 3 cm and a height 25 cm
We know the total surface area of the cylinder is
TSA=2πrh + 2π r².
=2πr(r+h)
=2×3.14×3(3+25)
=527.52 cm²
The plastic coating required to cover the surface of the coating is 527.52 cm²
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Answer:
To find the surface area of the cylinder that makes up the chain link, we need to add the area of the top and bottom circles (which are congruent) to the lateral surface area of the cylinder.
Therefore, we need approximately 527.52 square centimeters of plastic coating to coat the surface of the chain link. The closest answer choice is 471, but that is not correct. The closest answer to the actual surface area is 345.4 cm².
Step-by-step explanation:
The formula for the lateral surface area of a cylinder is:
Lateral surface area = 2πrh
where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is 3.14.
The formula for the area of a circle is:
Area of circle = πr²
Substituting the given values, we get:
Area of top and bottom circles = 2 x π x 3²
Area of top and bottom circles = 56.52 cm² (rounded to two decimal places)
Lateral surface area = 2 x 3.14 x 3 x 25
Lateral surface area = 471 cm²
Total surface area = Area of top and bottom circles + Lateral surface area
Total surface area = 56.52 + 471
Total surface area = 527.52 cm²
Kaitlin and her husband are each starting a saving plan. Kaitlin will initially set aside $650 and then add $155 every month to the savings. The amount A (in dollars) saved this way is given by the function =A+155N650, where N is the number of months she has been saving.
Her husband will not set an initial amount aside but will add $585 to the savings every month. The amount B (in dollars) saved using this plan is given by the function =B585N.
Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N. Simplify your answer as much as possible.
The linear function for the total amount added to the account each month is given as follows:
T(n) = 650 + 740n.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the amount added each month.The intercept b represent the initial amount.Then the parameters for this problem are given as follows:
m = 155 + 585 = 740.b = 650.Hence the function is given as follows:
T(n) = 650 + 740n.
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What is the measure of QR?
Answer:
Step-by-step explanation:
The answer to the question is 15
classify each angle as acute , right , obtuse , or straight
Based on the picture above:
numbers 1,5,6 and 8 including the obtuse angle numbers 2,3,9 and 10 include the acute angle number 4 is a straight angle number 7 is the right angle How to determine what type of anglesFrom the answer above, the way to determine the type of angle is to measure the angle.
if the angle is 90° then it is a right angle.
If the angle is 0-90° then it's an acute angle
If the angle is above 90° and below 180° then it is an obtuse angle
If the angle is 180° then it is called a straight angle.
The following is a more complete explanation:
1. Right Angles
Right angles have a measure of 90º and are perpendicular in shape. This angle is usually denoted by ∟. Examples of surrounding objects that have right angles include books, tables, cupboards, clock hands that show 3 o'clock, and so on.
2. Straight Angle
A straight angle has an angle of 180º. As the name implies, this angle is straight and flat. Examples of objects that have straight angles include a ruler and clock hands that show 6 o'clock.
3. Acute Angles
Acute angles have angles greater than 0º and less than 90º. As the name implies, this angle is pointed. Objects that have acute angles such as pencil tips, pizza slices, iron tips, and clock hands that show 1 and 2 o'clock.
4. Obtuse Angle
Contrary to an acute angle, an obtuse angle has an angle greater than 90º but less than 180º. As the name suggests, objects that have this angle are obtuse, such as laptops wide open, beach chairs, camping tents, and clock hands that show 4 and 5 o'clock.
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find the mean and standard deviation for each binomial random value: of n = 26, pi = .90
The mean and standard deviation for each binomial random value: of n = 26, pi = .90
Mean = 23.4
Standard Deviation = 1.53
What is mean?In one of the branches of mathematics called statistics, We use one term known as mean; it generally tells us what is the central tendency of the data set.
Generally, we use three terms for measurement of central tendency like, mean, median, mode.
In simple words, mean is an average of all the dataset.
formula;
Mean = Sum of all the dataset/Total number of dataset
Given that,
A binomial distribution with parameters,
n = 26 and p = 0.9,
the mean (expected value) of the distribution is given by:
E(X) = n x p
= 26 x 0.9
= 23.4
The standard deviation of the distribution is given by:
σ = √(n x p x (1 - p))
= √(26 x 0.9 x (1 - 0.9))
= √(26 x 0.9 x 0.1)
= √(2.34)
= 1.53
So the mean of the distribution is 23.4 and the standard deviation is 1.53.
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5. If the figure below is rotated 180° counterclockwise. What will the new coordinates of B' be?
O (-1, -3)
O (3, 1)
O (-3,1)
O (1, -3)
-10
The new coordinates of B' is (-3, 1)
What will the new coordinates of B' be?From the question, we have the following parameters that can be used in our computation:
B = (3, -1)
The figure is rotated 180° counterclockwise.
This is represented as
(x, y) = (−x,−y)
Substitute the known values in the above equation, so, we have the following representation
B' = (-3, 1)
Hence, the image poont is (-3, 1)
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Find the explicit formula for the geometric sequence tn given below. Note that t1=7.
7,14,28,56,112,…
The explicit formula for the geometric sequence is,
⇒ tn = 7 (2ⁿ - 1)
What is Geometric sequence?An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.
Given that;
The geometric sequence is,
⇒ 7,14,28,56,112,…
Here, First term = 7
And, Common ratio = 14 / 7 = 2
We know that;
The explicit formula for the geometric sequence is,
⇒ tn = t₁ (rⁿ - 1) / (r - 1)
Substitute all the values we get;
The explicit formula for the geometric sequence is,
⇒ tn = 7 (2ⁿ - 1) / (2 - 1)
⇒ tn = 7 (2ⁿ - 1)
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5 kilograms 45 grams help needed
5 kilograms 45 grams is equal to 5045 grams.
What do you mean by weight units?Weight is a measure of the force of gravity acting on an object, and weight units are units of measurement used to express the weight of an object. There are several different weight units used in different parts of the world, but some of the most common weight units include grams, kilograms, pounds, and ounces.
Grams are a metric unit of weight commonly used in the scientific and medical communities, as well as for small items like jewelry and food ingredients.
Kilograms are also a metric unit of weight, equivalent to 1000 grams. Kilograms are often used to express the weight of larger objects, such as people, animals, and heavy packages.
Pounds and ounces are units of weight used primarily in the United States and the United Kingdom. Pounds are equivalent to 16 ounces, and are used to express the weight of larger objects. Ounces are a smaller unit of weight and are often used for items like food and small packages.
To convert kilograms to grams, we multiply the number of kilograms by 1000. Therefore, 5 kilograms is equal to 5 x 1000 = 5000 grams.
Adding the 45 grams, we get 5000 + 45 = 5045 grams.
So, 5 kilograms 45 grams is equal to 5045 grams.
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Please help :(!!!!!!
The procedure to determine the function's behavior is explained in this problem.
How to classify the function as increasing, decreasing or constant?The function is increasing when the graph moves right and up.The function is decreasing when the graph moves right and down.The function is constant when the graph of the function is an horizontal line.Missing InformationThe problem is incomplete, hence the general procedure to obtain the function's behavior was presented.
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is the process of selecting and prioritizing innovation projects to ensure that they are consistent with a firm's strategy and development capacity.
This statement describes the process of innovation portfolio management.
What is statement?A statement in mathematics is a declarative utterance that is either true or untrue but not both. A proposal is another name for a statement. The main point is that there should be no uncertainty. A sentence cannot be both true and untrue in order to be a statement. A mathematical statement is made up of two components. The hypothesis or assumptions come first, followed by the conclusion. When a mathematical sentence makes a mathematically accurate statement, it is true.
Here,
This statement describes the process of innovation portfolio management. Innovation portfolio management involves evaluating and selecting innovation projects in line with an organization's goals and resources, and ensuring that these projects are aligned with the overall strategy of the firm. The aim of innovation portfolio management is to optimize the allocation of resources and maximize the return on investment in innovation.
By selecting and prioritizing innovation projects, companies can ensure that they are working on initiatives that have the greatest potential to drive growth and success, while also balancing risk and resource constraints.
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A random sample of 130 full-grown lobsters had a mean weight of 21 ounces and a standard
deviation of 3.0 ounces. Construct a 98% confidence interval for the population mean μ.
20 oz<μ<22 oz
O21 oz <μ< 23 oz
0 19 oz <μ< 21 oz
20 oz <μ< 23 oz
The 98% confidence interval for the population mean μ is 20 < μ < 22
How to construct a 98% confidence interval for the population mean μ.From the question, we have the following parameters that can be used in our computation:
n = 130
μ = 21
σ = 3
To construct a 98% confidence interval for the population mean μ, we can use the following formula:
μ ± (z * σ / √n)
Where
z = 2.33 i.e. the Z-score for a 98% confidence level
So, we have
21 ± (2.33 * 3 / √130)
Evaluate
21 ± 0.61
This gives
20.39 < μ < 21.61
Approximate
20 < μ < 22
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Find the volume of the figure. Express the answer in terms of pi and then round to the nearest whole number.
Answer:
see below
Step-by-step explanation:
memorize this formula for cone volume:
V = 1/3 * π r²*h
so r = 18/2 =9
h = 3
solve V = 81π = 254
Answer:
254.47
Step-by-step explanation: