The difference between f(8) and f(4) lies between -16 and 12, inclusive. Therefore, we can estimate that f(8) - f(4) is between -16 and 12.
The Mean Value Theorem is a fundamental result in calculus that relates the average rate of change of a function over an interval to its instantaneous rate of change at some point within the interval. It states that if a function f(x) is continuous on a closed interval [a,b] and differentiable on the open interval (a,b), then there exists some c in (a,b) such that:
f'(c) = [f(b) - f(a)] / (b - a)
In this problem, we are given that f(x) is continuous on [4,8] and differentiable on (4,8), and we are asked to estimate f(8) - f(4) using the Mean Value Theorem.
To do this, we first apply the Mean Value Theorem to obtain an expression for f(8) - f(4) in terms of f'(c) for some c in (4,8):
f'(c) = [f(8) - f(4)] / (8 - 4)
Rearranging, we get:
f(8) - f(4) = f'(c) [tex]\times[/tex] 4
So we need to find an estimate for f'(c) to find an estimate for f(8) - f(4).
We are given that −4≤f′(x)≤3 for all x in (4,8), which means that f'(x) lies between -4 and 3 for all x in (4,8). Since c is also in (4,8), it follows that f'(c) is also between -4 and 3. Therefore, we can say that:
-4 ≤ f'(c) ≤ 3
Substituting this inequality into our expression for f(8) - f(4), we get:
-4 * 4 ≤ f(8) - f(4) ≤ 3 [tex]\times[/tex] 4
Simplifying, we get:
-16 ≤ f(8) - f(4) ≤ 12
This means that the difference between f(8) and f(4) lies between -16 and 12, inclusive. Therefore, we can estimate that f(8) - f(4) is between -16 and 12.
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40 mm
34.6 mm
40 mm
Please help me with this question
I remember doing this but I don’t seem to remember sorry
Andre studies 7 hours this week for end-of-year exams. He spends 1 hour on English and an equal number of hours each on math, science, and history.
Answer:
Step-by-step explanation:
The population P(t) of a culture of the pseudomonas aeruginosa is given by P(t) = -1709t^2 + 80,000t + 10,000, where t is the time in hours since the culture was started. What is the maximum?
Check the picture below.
so the path of the population P(t) is parabolic, more or less like the one in the picture, so it reaches its maximum at the vertex and at "t" time of the x-coordinate of the vertex.
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ P(t)=\stackrel{\stackrel{a}{\downarrow }}{-1709}t^2\stackrel{\stackrel{b}{\downarrow }}{+80000}t\stackrel{\stackrel{c}{\downarrow }}{+10000} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\left(-\cfrac{ 80000}{2(-1709)}~~~~ ,~~~~ 10000-\cfrac{ (80000)^2}{4(-1709)}\right) \implies \left( - \cfrac{ 80000 }{ -3418 }~~,~~10000 - \cfrac{ 6400000000 }{ -6836 } \right) \\\\\\ \left( \cfrac{ -40000 }{ -1709 } ~~~~ ,~~~~ 10000 + \cfrac{ 1600000000 }{ 1709 } \right) ~~ \approx ~~ (\stackrel{ hours }{\text{\LARGE 23}}~~,~~946220)[/tex]
the equation
4x-2y=4
-4x+2y=-3
have the same/different what slopes and the same/different what y-intercepts?
Answer:
They both have the same slope of 2. Their y-intercepts are different. One is -2 and the other is -3/2.
Step-by-step explanation:
4x-2y=4
4x - 4 = 2y
(divide 2 by both sides)
2x-2=y
-4x+2y=-3
2y=4x-3
(divide 2 both sides)
y = 2x - 3/2
ME HELP PLEASE JSJS
The complete solution and complete answer of the questions provided are mentioned below respectively.
What is an integer?An integer is a whole number that can be either positive, negative or zero, but does not include fractions or decimals. Examples of integers include -5,-4,-3, -2, -1, 0, 1, 2, 3, 4, 5.
1.To find out how much money is in Lane's account now, we need to substitute x = 0 in the given expression:
500(1.05)⁰ = 500(1) = 500
Therefore, Lane has $500 in his account now.
2.To write an expression for the amount of money in Lane's account in 20 years, we need to substitute x = 20 in the given expression:
500(1.05)²⁰ ≈ 1326.65
Therefore, the expression for the amount of money in Lane's account in 20 years is 1326.65.
3.To write an expression for the amount of money in Lane's account 5 years ago, we need to subtract the amount of interest earned in the last 5 years from the current balance of his account. The amount of interest earned in the last 5 years is:
500(1.05)² - 500(1.05)⁰≈ $154.13
Therefore, the expression for the amount of money in Lane's account 5 years ago is 500 - 154.13 = $345.87.
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1. Lane has $500 in his account now.
2. The given expression: 500(1.05)²⁰ ≈ 1326.65
3. The calculation for Lane's account balance five years ago is $345.87.
What is an integer?An integer is a whole number, which does not include fractions or digits and can be positive, negative, or zero.
Integer examples include -5,-4,-3, -2, -1, 0, 1, 2, 3, 4, 5.
1. The following equation must be changed to read x = 0 in order to determine how much money is currently in Lane's account:
500(1.05)⁰ = 500(1) = 500
Lane now has $500 in his account as a result.
2. We must replace x with 20 in the provided expression in order to create an expression for the sum of money that will be in Lane's account in 20 years:
500(1.05)²⁰ ≈ 1326.65
As a result, the phrase for Lane's account balance in 20 years is 1326.65.
3. We must deduct the amount of interest earned over the previous five years from Lane's account balance in order to calculate the balance five years back. The income earned over the previous five years is:
500(1.05)² - 500(1.05)⁰≈ $154.13
Since there was money in Lane's account five years ago, the phrase is 500 - 154.13 = $345.87.
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Need help with homework, thanks in advance.
Equation of block pattern is: n² + 2n + 4
Define the term equation?A statement that shows the equality of two mathematical expressions is known as an equation. The goal is typically to ascertain the values of the variables that keep the equation true, and it may have one or more variables. In that both sides must be equal for an equation to hold true, it might be likened to a balance scale.
A block pattern is a type of organizational structure used in writing and presenting information. It involves dividing the information into distinct blocks or sections, with each block focusing on a particular aspect of the topic being discussed. This pattern is often used in writing comparison and contrast essays, where the writer wants to explore the similarities and differences between two or more subjects.
Equation of block pattern is: n² + 2n + 4
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increase £142 by 34%
Add £48.28 to £142 so you get £190.28
AnswerAnswerAnswerAnswer:
190.28
Step-by-step explanation:
£142 + 34% = £142 x 1.34 = 190.28
Solve the system of equations by graphing on the given coordinate plane. y = 2x – 5 y = –x + 4
Answer:
(3,1)
Step-by-step explanation:
I just graphed it using desmos but I could show you algebraically if you want
:)
how many solutions does this have?
x + 5 = 24
5x = 12 − y
In conclusion there is only one solution to the system of equations and that is for x and y that satisfies both equations: x = 19 and y = -83.
How to solve and what does an equation mean?
We have two equations:
x + 5 = 24
5x = 12 - y
For the first equation, we can isolate x by subtracting 5 from both sides:
x = 19
Now we can substitute x = 19 into the second equation:
5(19) = 12 - y
95 = 12 - y
y = -83
So we have found a unique solution for x and y that satisfies both equations: x = 19 and y = -83.
Therefore, there is only one solution to the system of equations.
An equation is a mathematical statement that says that two things are equal. It consists of two expressions separated by an equal sign (=). For example, 2 + 3 = 5 is an equation that says that the sum of 2 and 3 is equal to 5.
Equations can be written in a variety of forms, depending on the type of problem being solved. In algebra, equations often involve variables, which are letters or symbols that represent unknown quantities.
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If sin∠X = cos∠Y and m∠X = 72°, what is the measure of ∠Y?
Given sin∠X = cos∠Y and m∠X = 72°, we can find the measure of angle Y to be 18° since angles X and Y are complementary.
The problem states that sin∠X = cos∠Y and m∠X = 72°, and we are asked to find the measure of angle Y.
The first thing to notice is that sin∠X = cos∠Y means that the sine of angle X is equal to the cosine of angle Y. By the definition of sine and cosine, we know that:
sin∠X = opposite/hypotenuse
cos∠Y = adjacent/hypotenuse
where "opposite" and "adjacent" are the lengths of the sides of a right triangle that correspond to angles X and Y, respectively, and "hypotenuse" is the length of the hypotenuse of the triangle.
Since sin∠X = cos∠Y, we can set the two expressions equal to each other:
sin∠X = cos∠Y
opposite/hypotenuse = adjacent/hypotenuse
opposite = adjacent
This tells us that the lengths of the opposite and adjacent sides of the right triangle are equal. Since these sides are opposite and adjacent to angles X and Y, respectively, this means that angles X and Y are complementary angles (i.e., the sum of their measures is 90°).
We know that angle X has a measure of 72°, so we can use the fact that angles X and Y are complementary to find the measure of angle Y:
m∠Y = 90° - m∠X
m∠Y = 90° - 72°
m∠Y = 18°
Therefore, the measure of angle Y is 18°.
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In circle H with m \angle GHJ= 90m∠GHJ=90 and GH=20GH=20 units, find the length of arc GJ.
HELP!!
Answer:
Since $\angle GHJ=90^\circ$, arc $GJ$ is a quarter of the circumference of circle $H$. The formula for the circumference of a circle is $C=2\pi r$, where $r$ is the radius, so the circumference of circle $H$ is:
$$C=2\pi \cdot 20 = 40\pi$$
Since arc $GJ$ is a quarter of the circumference, its length is:
$$\frac{1}{4} \cdot 40\pi = 10\pi$$
Therefore, the length of arc $GJ$ is $10\pi$ units.
The data table to the right represents the volumes of a generic soda brand Volumes of soda (oz) 65 80 70 75 70 85 80 75 70 75 65 70 Complete parts (a) through (c) below 508:5 a. Which plot represents a dotplot of the data? 50 60 70 80 9 50 60 70 80 9 Volumes of soda (oz) Volumes of soda (oz) Oc. 50 60 70 80 90 50 60 70 80 9 Volumes of soda (oz) Volumes of soda (oz) b. Does the configuration of the points appear to suggest that the volumes are from a population with a normal distribution? A. Yes, the population appears to have a normal distribution because the dotplot resembles a "bell shape B. No, the population does not appear to have a normal distribution because the frequencies of the volume decrease from left to right. C. No, the population does not appear to have a normal distribution because the dotplot does not resemble a "bell" shape D. Yes, the population appears to have a normal distribution because the frequencies of the volume increase from left to right. c. Are there any outliers? A. Yes, the volumes of 0 oz and 200 oz appear to be outliers because they are far away from the other temperatures O B. No, there does not appear to be any outliers ° C. Yes, the volume of 50 oz appears to be an outlier because it is far away from the other volumes ( D. Yes, the volume of 70 oz appears to be an outlier because many sodas had this as their volume
a) The plot that represents a dot plot of the data is plot (B).
b) The answer is (C)
c) The answer is (B)
Define the term normal distribution?A normal distribution is a continuous probability distribution that has a symmetric bell-shaped curve, with the mean, median, and mode all being equal.
(a) The plot that represents a dot plot of the data is plot (B).
(b) The configuration of the points does not suggest that the volumes are from a population with a normal distribution. The answer is (C) - The dot plot does not approximate a "bell" form, hence the population does not seem to have a normal distribution.
(c) There are no outliers in the data. The answer is (B) - No, there does not appear to be any outliers.
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The answers are:
1). B. The plot that depicts a data dot plot is plot (B).
2). C. Because the dotplot does not match a "bell" shape, the population does not appear to have a normal distribution.
3). B. No, there does not appear to be any outlie
What is meant by Normal distribution?A normal distribution is a kind of continuous distribution of probability in which the majority of data points cluster in the centre of the range, while the remainder taper off symmetrically towards either extreme. The mean of the distribution is also known as the centre of the range.
Because of its flared form, a normal distribution resembles a bell curve graphically. The exact shape can vary depending on the population's value distribution. The population is the total number of data elements in the distribution.
a). The plot depicts a data dot plot and is called plot. (B).
b). Because the dot plot does not resemble a "bell" form.(C).
c). The data does not contain any anomalies. (B).
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The Complete question is,
a). question a is attached below.
b). Does the configuration of the points appear to suggest that the volumes are from a population with a normal distribution?
A. Yes, the population appears to have a normal distribution because the dotplot resembles a "bell shape
B. No, the population does not appear to have a normal distribution because the frequencies of the volume decrease from left to right.
C. No, the population does not appear to have a normal distribution because the dotplot does not resemble a "bell" shape
D. Yes, the population appears to have a normal distribution because the frequencies of the volume increase from left to right.
c). Are there any outliers?
A. Yes, the volumes of 0 oz and 200 oz appear to be outliers because they are far away from the other temperatures
B. No, there does not appear to be any outliers °
C. Yes, the volume of 50 oz appears to be an outlier because it is far away from the other volumes
D. Yes, the volume of 70 oz appears to be an outlier because many sodas had this as their volume
Carlos purchased a new computer for $1,350. One year later, a popular tech website valued the same computer at $810. The website predicts that the value of the computer will continue depreciating each year. Write an exponential equation in the form y=a(b)x that can model the value of the computer, y, x years after purchase. Use whole numbers, decimals, or simplified fractions for the values of a and b. y = To the nearest ten dollars, what can Carlos expect the value of the computer to be 3 years after purchase?
Answer:
Step-by-step explanation:
Carlos can expect the value of the computer to be $580 in 3 years after purchase.
To find the exponential equation in the form y=a(b)ˣ that models the value of the computer, we need to determine the initial value and the rate of decay.
The initial value of the computer is $1,350, and its value after one year is $810.
We can use this information to find the rate of decay as follows:
810 = 1350 × b¹
b = 0.6
So the exponential equation is:
y = 1350(0.6)ˣ
To find the value of the computer 3 years after purchase, we can substitute x = 3 into the equation:
y = 1350(0.6)³= 583.2
Hence, Carlos can expect the value of the computer to be $580 in 3 years after purchase.
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let f(x)=−8(2)3x 3. evaluate f(0) without using a calculator. do not include f(0) in your answer.
For the given function f(x)= [tex]-8(2)^{3x}[/tex] + 3 which contains variable x , whose value on substituting as zero is found to be (calculated without using calculator)
What is variable?
Variable is a term used in algebra or algebraic expressions and equations to represent the unknown values or whose value is not fixed. variables and constants are combined to form algebraic expressions or equations. The difference between expression and an equation is that expressions do not contain 'equal to' sign and equations shows balance between left hand side and the right side using 'equal to' sign.
Here the function is f(x)= [tex]-8(2)^{3x}[/tex] + 3
To find the value of given function at x= 0 , we need to substititute zero in place of x.
f(x) at x=0 will be [tex]-8(2)^{3(0)}[/tex] + 3
= [tex]-8(2)^{0}[/tex] + 3
= [tex]-8(1)[/tex] + 3 { we know that [tex]m^{0} = 1[/tex] }
= - 8 + 3
= -5
∴The value of function at x=0 is found to be -5
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Refer to the attachment for complete question
A group of 17 men and 24 women each banquet table can sit eight people what is the least number of tables need it for the banquet
Answer:
5
Step-by-step explanation:17+24=41
41/8=5.125
So The least you can get for the banquet table is 5.
Select the correct answer. Suppose x varies indirectly as y, and x = 5 when y = 24. What is the value of x when y = 8? A. 15 B. 1. 67 C. 960 D. 38. 40 Re
The value of x is 15 when y =8
If x varies indirectly as y, then we can write:
x = k/y
where k is the constant of variation. To find the value of k, we can use the given information that x = 5 when y = 24:
5 = k/24
Multiplying both sides by 24, we get:
k = 120
Now we can use this value of k to find x when y = 8:
x = 120/8 = 15
Therefore, the answer is A. 15.
A ratio that depicts the association between the independent variable (x) and the dependent variable is known as a constant of variation (k) (y). In the event that both of those variables have known values, it can be calculated by dividing y by x.
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Find h please math help plsssss help
The height of the triangle is approximately 7.31 units.
What is Pythagorean theorem ?
The Pythagorean theorem is a fundamental theorem in geometry that relates to the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In mathematical notation, the Pythagorean theorem can be written as:
a^2 + b^2 = c^2
where a and b are the lengths of the legs (the sides adjacent to the right angle) and c is the length of the hypotenuse.
According to the question:
Since triangle ABC is a right triangle with angle B = 90 degrees, we can use the Pythagorean theorem to find the length of side BC:
[tex]BC^2 = AC^2 - AB^2[/tex]
[tex]BC^2 = 30^2 - h^2[/tex]
[tex]BC = \sqrt{30^2 - h^2}[/tex]
Now, let's consider triangle ABD. We know that AD = 25 and DC = 11, so BD = BC - DC:
BD = BC - DC
[tex]BD = \sqrt{30^2 - h^2} - 11[/tex]
Since the line passing through vertex A is perpendicular to BC, we know that triangles ABD and ABC are similar. Therefore, we can use the ratio of corresponding sides to find the value of h:
h/AB = AB/AC
h/AB = AB/30
[tex]AB^2 = h*30[/tex]
[tex]AB =\ sqrt{h*30}[/tex]
Now, using the fact that AD + DC = BC, we can write:
AD + DC = BD + AB
[tex]25 + 11 = \sqrt{30^2 - h^2} - 11 +\sqrt{h*30}[/tex]
[tex]36 = \sqrt{30^2 - h^2} + \sqrt{h*30}[/tex]
Squaring both sides, we get:
[tex]1296 = 30^2 - h^2 + 2\sqrt{h*30}\sqrt{30^2 - h^2} + h*30[/tex]
[tex]1296 = 900 - h^2 + 2\sqrt{30h - h^3} + 30*h[/tex]
[tex]396 = 32\sqrt{30*h - h^3}[/tex]
Squaring again, we get:
[tex]156816 = 960h^2 - 96h^4[/tex]
[tex]h^4 - 10h^2 + 1639/12 = 0[/tex]
Using the quadratic formula, we get:
[tex]h^2 = (10 \± \sqrt{10^2 - 4(1)(1639/12))}/2[/tex]
[tex]h^2 = (10 \± \sqrt{1561})/2[/tex]
Since h must be positive, we take the positive square root:
[tex]h = \sqrt{(10 + sqrt(1561)}/2) \approx 7.31[/tex]
Therefore, the height of the triangle is approximately 7.31 units.
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Find the greatest common factor of 509089201 and 509089201.
Answer:
GCF = 509089201
for the values 509089201, 509089201
Solution by Factorization:
The factors of 509089201 are: 1, 107, 1663, 2861, 177941, 306127, 4757843, 509089201
The factors of 509089201 are: 1, 107, 1663, 2861, 177941, 306127, 4757843, 509089201
Then the greatest common factor is 509089201.
Answer: 509089201
Step-by-step explanation: The multiples would be 1, 107, 1663 and so on until 509089201, which makes 509089201 the gcf
A department store wants to send codes for $15 off a $75 purchase to the subscribers of its email list. The coupon code will have three letters followed by one digit followed by one letter. The letters PQNR will not be used so there are 23 letters and 10 digits that will be used. Assume that the letters can be repeated how many such coupon codes can be generated.
there are 407,230 possible coupon codes that can be generated using the given format.
To find the number of possible coupon codes, we need to count the total number of ways to choose three letters from 23, one digit from 10, and one letter from 23 (since we can repeat letters). Combinations
The number of ways to choose three letters from 23 is:
23[tex]C_{3}[/tex] = (232221)/(321) = 1771
The number of ways to choose one digit from 10 is simply 10.
The number of ways to choose one letter from 23 (allowing repetition) is 23.
Therefore, the total number of possible coupon codes is:
1771 * 10 * 23 = 407,230
So there are 407,230 possible coupon codes that can be generated using the given format.
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(06.02 LC) Line AB contains points A (0, 1) and B (1, 5). The slope of line AB is (5 points) Group of answer choices −4 negative 1 over 4 1 over 4 4
General equation of line is [tex]y=mx+n[/tex] where m is slope and n is point on y-axis. So just use points in question to determine what m and n must be. Let me show you.
For A(0,1), put this point in [tex]y=mx+n[/tex] then you have [tex]1=m.0+n[/tex] Hence [tex]n=1[/tex]
Now use second one that is B(1,5), then you get [tex]5=m.1+1[/tex] since [tex]n=1[/tex]. Finally you get [tex]m=4[/tex] that is slope.
Therefore, D is the correct answer.
if you were to have simply guessed the answer for each of the two questions, four choices each, what is the mathematical probability that you would have gotten them both right?
If you were to simply guess the answer to both questions, you would have a 6.25% chance of getting both answers right according to probability
Assuming that each answer choice is equally likely to be correct, the probability of guessing the correct answer to one question is 1/4 or 0.25. Since there are two questions, the probability of guessing both correctly is the product of the probabilities of guessing each question correctly.
P(guessing both questions correctly) = P(guessing first question correctly) x P(guessing second question correctly)
P(guessing both questions correctly) = (1/4) x (1/4)
P(guessing both questions correctly) = 1/16 or 0.0625
Therefore, the probability of guessing both questions correctly is 1/16 or 0.0625.
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Use a trigonometric ratio to solve for x. Round to two
decimal places as necessary.
X
10
14
Step-by-step explanation:
For RIGHT triangles , remember S-O-H-C-A-H-T-O-A
sin 14° = opposite leg / hypotenuse
sin 14° = x / 10
10* sin 14° = x
x = 2.42 units
sin 37° = 10 / a
a = 10 / sin 37°
a = 16.62 units
In a survey 80 students were asked to name their favorite subjects. Thirty students said that English was their favorite. What percent of the student surge said that English was their favorite subject
Answer:
37.5%
Step-by-step explanation:
Based on the given conditions, formulate: 30/80
Reduce the fraction: 3/8
Rewrite a fraction as a decimal: 0.375
Multiply a number to both the numerator and the denominator:
0.375 * 100/100
Write as a single fraction:
0.375 * 100 / 100
Calculate the product or quotient:
37.5/100
Rewrite a fraction with denominator equals 100 to a percentage:
37.5%
Answer:
37.5%
[50 POINTS!!!] I posted a Screen shot of the question down below!
Answer:
C; as x-> infinite, f(x) -> infinite, as x-> neg. infinite, f(x) -> neg. infinite
Step-by-step explanation:
Graphing the equation will help with knowing the end behavior.
X^3 graphs tend to increase infinitely when x is going infinitely positive and decrease infinitely when x is going infinitely negative.
The volume of prism R is 40 m³. Prism R and prism S have the same height. The area of the base of prism S is half the area of the base of prism R. What is the volume of prism S? 1) 10 m³ 2) 20 m³ 3) 40 m³ 4) 80 m³
2) 20 m³ is the answer
the top face of a portable digital device measures 3.01 inches by 1.23 inches. find the area of the face of the device
The area of the face of the portable digital device is approximately 3.7033 square inches.
Area is a measurement of the amount of space inside a two-dimensional figure or shape. It is expressed in square units and can be calculated by multiplying the length and width of a rectangle or the base and height of a triangle, or by using specific formulas for other shapes such as circles, trapezoids, or parallelograms.
The area of the face of the portable digital device can be found by multiplying the length by the width
Area = Length x Width
Area = 3.01 inches x 1.23 inches
Area = 3.7033 square inches (rounded to four decimal places)
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twenty five cards are marked with the numbers 1 through 25. amira randomly picks two cards without replacement. blanca then randomly picked two of the remaining cards without replacement. what is the probability that at least one of blanca's cards has a number greater than at least one of amira's cards?
The probability that at least one of Blanca's cards has a number greater than at least one of Amira's cards is 0.705 or approximately 70.5%.
The total number of ways in which Blanca can choose two cards out of 23 is given by the combination formula C(23, 2), which is equal to 253.
The value of k can range from 3 (if Amira's cards are 1 and 2) to 25 (if Amira's cards are 24 and 25). Therefore, the total number of ways in which Blanca can pick two cards that are both greater than Amira's cards is:
C(23, 2) - C(2, 2) - C(3, 2) - ... - C(23, 2) = 23C(23, 1) - (C(2, 2) + C(3, 2) + ... + C(23, 2)) = 253 - 276 = -23
Since the result is negative, it means that there are no ways in which Blanca can pick two cards that are both greater than Amira's cards. Therefore, the probability of this case is 0.
P(Case 2) = (number of ways in which Blanca can pick one card greater than Amira's and one card less than Amira's) / (total number of ways in which Blanca can pick two cards out of 23) = 44,550 / C(23, 2) = 0.705
Finally, the probability of at least one of Blanca's cards having a number greater than at least one of Amira's cards is given by the sum of the probabilities of Case 1 and Case 2:
P(at least one of Blanca's cards is greater) = P(Case 1) + P(Case 2) = 0 + 0.705 = 0.705 or 70.5%
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find f0.05 where v1=8 and v2=11
a) 2.95
b) 2.30
c) 4.74
d) 3.66
The correct answer for F-distribution f0.05 is d) 3.66
How to find F-distribution f0.05?To find f0.05 with v1=8 and v2=11, you can use an F-distribution table or an online calculator.
Here's a step-by-step explanation:
1. Locate the row in the F-distribution table corresponding to the degrees of freedom for the numerator (v1), which is 8 in this case.
2. Locate the column corresponding to the degrees of freedom for the denominator (v2), which is 11 in this case.
3. Find the intersection of the row and column to get the critical value for f0.05.
Using an F-distribution table or calculator, you will find that the f0.05 value for v1=8 and v2=11 is approximately 3.66.
So, the correct answer is:
d) 3.66
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it’s a 2 part question
The missing values in the figure is solved using central angle theorem to get
angle FHG = 122 degreesHow to find angle FHGThe measure of an central angle is equal to the measure of the intercepted arc according to the central angle theorem.
From the figure we have that the intercepted arc is FG = 122 degrees. Using the central angle theorem, the central angle is angle FHG
central angle = intercepted arc
angle FHG = arc FG
angle FHG = 122 degrees
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11. The velocity, V of a car moving with a constant acceleration is partly constant and partly
varies as the time taken, t. The velocity of the car after 8s and 12s are 9 m/s and 11
m/s respectively. Find
(i)
(ii)
The relationship between the velocity and the time taken.
The time taken when the velocity is 15 m/s.
Based on the information provided, the relationship between velocity and time taken is V = 4 + 0.5t.
How to find the velocity between the two variables?We can start by using the formula for velocity with constant acceleration:
V = Vo + at
where V is the final velocity, Vo is the initial velocity, a is the constant acceleration, and t is the time taken.
We know that the velocity is partly constant and partly varies with time, so we can write:
V = Vc + Vv
where Vc is the constant part of the velocity and Vv is the part that varies with time.
Using the given information, we can set up a system of equations:
9 = Vc + Vv (when t = 8s)
11 = Vc + Vv (when t = 12s)
Subtracting the first equation from the second, we get:
11 - 9 = (Vc + Vv) - (Vc + Vv)
2 = Vv (when t = 12s) - Vv (when t = 8s)
2 = Vv (12) - Vv (8)
2 = 4Vv
Vv = 0.5 m/s
Now we can use either of the two original equations to find Vc:
9 = Vc + 0.5(8)
Vc = 4 m/s
Therefore, the relationship between the velocity and the time taken is:
V = 4 + 0.5t
where V is the velocity in m/s and t is the time taken in seconds.
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