Answer:
Step-by-step explanation:
To find the probability of choosing a random number that starts with 2, we need to find two things:
1. The total number of valid four-digit numbers that can be created from the digits 0-9 where the first and last digits are even and no digit can repeat.
2. The number of valid four-digit numbers that start with 2 and meet the other criteria.
Let's begin by calculating the total number of valid four-digit numbers.
There are 5 even digits (0, 2, 4, 6, 8) to choose from for the first and last digits. For the second digit, there are 9 digits to choose from (since 0 cannot be repeated), for the third digit there are 8 digits to choose from (since we used one digit already and neither the first nor last digit can be repeated), and for the last digit there are only 4 choices left (since we used 5 for the first digit, and one more can’t be repeated). Therefore, the total number of valid four-digit numbers is:
5 * 9 * 8 * 4 = 1,440
Now we need to calculate the number of valid four-digit numbers that start with 2.
We already determined that there are 5 even digits to choose from for the last digit, leaving 8 digits for the second and 7 for the third digit (since the first digit is fixed). So the number of valid four-digit numbers that start with 2 is:
5 * 8 * 7 * 1 = 280
Therefore, the probability of choosing a random number that starts with 2 is:
280 / 1,440 = 0.1944 rounded to 4 decimal places.
So the answer to the problem is 97/500, which simplifies to 0.1940 when rounded to 4 decimal places.
∠A = x + 2 and ∠B = 2x + 4. What is the measurement of ∠A
Answer:
(B) 60 degrees
Step-by-step explanation:
You want the measure of angle A = x+2, given that it forms a linear pair with angle B = 2x+4.
Linear PairThe sum of angles in a linear pair is 180°
A +B = 180
(x +2) +(2x +4) = 180 . . . . use the given expressions
3x +6 = 180 . . . . . . . . . simplify
x +2 = 60 . . . . . . . . . divide by 3. Angle A = x+2 = 60
The measure of angle A is 60 degrees.
Four pipes can fill a tank in 16 hours. How long will it take to fill the tank if twelve
pipes of the same dimensions are used ?
Answer:
5.333 hours
Step-by-step explanation:
We know
4 Pipes fill a tank in 16 hours.
How long will it take to fill the tank if 12 pipes of the same dimensions are used?
We Take
16 x 1/3 = 5.333 hours
So, it takes about 5.333 hours to fill the tank.
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Answer:
The midpoint of the diameter is (4, 1)
This is the center of the circle
=====================================================
Explanation:
Add up the x coordinates and divide in half
(-1+9)/2 = 8/2 = 4
The x coordinate of the midpoint is x = 4
Repeat for the y coordinates
(4 + (-2))/2 = (4-2)/2 = 2/2 = 1
The y coordinate of the midpoint is y = 1
The midpoint is located at (x,y) = (4,1)
The midpoint of any diameter is the center of the circle. This is because all diameters go through the center.
The distance from the center to either endpoint represents the radius of the circle (aka half the diameter).
In baseball, each time a player attempts to hit the ball, it is recorded. The ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most. For the season so far, Jana has hit the ball 8 times out of 10 attempts. Tasha has hit the ball 9 times out of 12 attempts. Which player has a ratio that means they have a better batting average?
Tasha, because she has the lowest ratio since 0.75 < 0.8
Tasha, because she has the highest ratio since 48 over 60 is greater than 45 over 60
Jana, because she has the lowest ratio since 0.75 < 0.8
Jana, because she has the highest ratio since 48 over 60 is greater than 45 over 60
Jana, because she has the highest ratio since 8/10 is greater than 9/12.
What is ratio?A ratio is a comparison of two numbers or quantities expressed in relation to each other. It represents the relative size or magnitude of one quantity with respect to another. Ratios are typically written as a fraction, with the first number being the numerator and the second number being the denominator, and can also be expressed as a decimal or percentage.
What is batting average?Batting average is a statistical measure used in baseball to evaluate a player's performance at the plate. It is calculated as the ratio of a player's total number of hits to their total number of at-bats (the number of times they attempt to hit the ball).
In the given question,
A higher batting average indicates a better performance, since it means the player is successfully hitting the ball more often.
In this case, we are given the number of hits and attempts for two players, Jana and Tasha. To compare their batting averages, we need to calculate the ratio of their hits to their attempts.
Jana has hit the ball 8 times out of 10 attempts, so her batting average is 8/10 = 0.8.
Tasha has hit the ball 9 times out of 12 attempts, so her batting average is 9/12 = 0.75.
To determine which player has the better batting average, we compare their ratios. Since 0.8 is greater than 0.75, Jana has the higher ratio and therefore the better batting average.
So, the answer is Jana, because she has the highest ratio (8/10 = 0.8), which means she has the better batting average compared to Tasha (9/12 = 0.75).
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The exponential 12 (3) 2x-12 has been converted to 12(k)*-6, what is the value of k?
Answer:
The solution set is (13,− 32). A quadratic equation of the form x 2= k can be solved by factoring with the following sequence of equivalent equations.
Step-by-step explanation:
use the trapezoidal rule and simpson's rule to approximate the value of the definite integral for the given value of n. round your answer to four decimal places and compare the results with the exact value of the definite integral. 4 x x2 1 0 dx, n
The Trapezoidal rule and Simpson's rule are two methods used to approximate the value of a definite integral. The Trapezoidal rule approximates the integral by dividing the region between the lower and upper limits of the integral into n trapezoids, each with a width h. The approximate value of the integral is then calculated as the sum of the areas of the trapezoids. The Simpson's rule is similar, except the region is divided into n/2 trapezoids and then the integral is approximated using the weighted sum of the area of the trapezoids.
For the given integral 4 x x2 1 0 dx, with n = 200, the Trapezoidal rule and Simpson's rule approximate the integral to be 7.4528 and 7.4485 respectively, rounded to four decimal places. The exact value of the integral is 7.4527. The difference between the exact and approximate values is very small, thus indicating that both the Trapezoidal rule and Simpson's rule are accurate approximations.
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Verify that W is a subspace of V. Assume that V has the standard operations.
W is the set of all 3x2 matrices of the form [a,b;(a+b),0;0,c] and V=M[-subscript-(3,2)]
The zero vector: The zero vector 0 = [0,0;0,0;0,0] is also a member of W. Thus, the third criterion is satisfied.
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Ray has 9 identical shoe boxes like the one shown. What is the total volume of all the shoe boxes?
Answer:
Step-by-step explanation:
You need to find the volume if one shoe box by doing:
Length x Width x Height
Of the shoe box
Then multiply by 30 to get the volume for all the shoe boxes
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Here is a solid.
What would be the cross section resulting from the intersection of the solid and the given plane? Be specific about the resulting shape.
Responses
a right triangle
a right triangle
an isosceles triangle
an isosceles triangle
a scalene triangle
a scalene triangle
a square
a square
a rectangle
a rectangle
a circle
A right square pyramid formed by the junction of the solid would have a square-shaped cross section.
Why would be the cross section resulting from the intersection of the solid be a square shape?This is thus because a square pyramid has four triangular sides that meet at a shared vertex on its square base. The cross section of a pyramid formed when a plane meets it parallel to the base and perpendicular to one of the triangular sides is a square. Because the pyramid's base is square, the intersecting plane will cut all four of the triangle faces at the same distance from the peak, giving the pyramid a square shape.
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A rectangular pyramid has a volume of 100 cm? What is the volume of a rectangular prism in cubic centimeters with the same dimensions?
The volume of the rectangular prism with the same dimensions as the rectangular pyramid is 300 cubic centimeters.
What is rectangular prism?A rectangular prism, also known as a rectangular parallelepiped, is a three-dimensional solid shape with six rectangular faces, where each pair of opposite faces are congruent (i.e., have the same dimensions) and parallel to each other.
The rectangular prism is defined by three dimensions: length, width, and height. The length is the longest dimension of the prism, the width is the second-longest dimension, and the height is the shortest dimension, perpendicular to both length and width. The volume of a rectangular prism is given by the formula: V = l * w * h.
In the given question,
Let's assume that the rectangular pyramid has a rectangular base with length l, width w, and height h. The formula for the volume of a rectangular pyramid is given by:
V_pyramid = (1/3) * base_area * height
where base_area = l * w is the area of the rectangular base of the pyramid.
We know that the volume of the rectangular pyramid is 100 cm^3, so we can write: 100 = (1/3) * l * w * h
Simplifying this equation, we get:
l * w * h = 300
Now, let's find the volume of the rectangular prism with the same dimensions. The formula for the volume of a rectangular prism is given by: V_prism = base_area * height
where base_area = l * w is the area of the rectangular base of the prism.
Since the rectangular prism has the same dimensions as the rectangular base of the pyramid, its volume is given by: V_prism = l * w * h
Substituting the value of l * w * h from the equation we derived earlier, we get: V_prism = 300
Therefore, the volume of the rectangular prism with the same dimensions as the rectangular pyramid is 300 cubic centimeters.
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three cards are drawn with replacement from a standard deck of 52 cards. find the the probability that the first card will be a club, the second card will be a red card, and the third card will be the six of hearts.
The probability of drawing a club, a red card, and the six of hearts in that order from a standard deck of 52 cards is [tex]1/13,552.[/tex]
This is because the probability of drawing a club is 1/4, and the probability of drawing a red card is 1/2, and the probability of drawing the six of hearts is 1/52.
Since the cards are drawn with replacement, the total probability is the product of the individual probabilities, which is equal to [tex]1/4 * 1/2 * 1/52 = 1/13,552[/tex].
It is important to note that if the cards were not drawn with replacement, then the probability of drawing the three cards would be slightly different. The total probability would be equal to [tex]1/4 * 1/2 * 1/51 = 1/12,600.[/tex]
It is also important to note that since this is a probability question, the answer can be expressed as a decimal or percentage. In decimal form, the probability of drawing the three cards is 0.000074, and in percentage form, the probability of drawing the three cards is 0.0074%.
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50 POINTS!!!!! NEED HELP ASAP!!!!! RUNNING OUT OF TIME!!!!!
Answer:17.6 cm
Step-by-step explanation:
if you can see the graph it can be seen as 17.6 cm.
Five cars start out on a cross-country race. The probability that a car breaks down and drops out of the race is 0.2. Cars break down independently of each other.
(a) What is the probability that exactly two cars finish the race?
(b) What is the probability that at most two cars finish the race?
(c) What is the probability that at least three cars finish the race?
(a) The probability that exactly two cars finish the race is 0.0512.
(b) The probability that at most two cars finish the race is 0.05792.
(c) The probability that at least three cars finish the race is 0.94208.
(a) To determine the probability that exactly two cars finish the race, we have to use binomial distribution. In this case, we have n = 5 trials, and p = 0.8 is the probability that a car finishes the race (1 - 0.2). Using the binomial distribution formula:
P(X = k) = (nCk)(p^k)(1 - p)^(n - k)
Where X is the number of cars that finish the race, we get:
P(X = 2) = (5C2)(0.8²)(0.2)³= (10)(0.64)(0.008)= 0.0512
Therefore, the probability that exactly two cars finish the race is 0.0512.
(b) To determine the probability that at most two cars finish the race, we have to calculate the probabilities of 0, 1, and 2 cars finishing the race and add them up.
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)= (5C0)(0.8⁰)(0.2)⁵ + (5C1)(0.8¹)(0.2)⁴ + (5C2)(0.8²)(0.2)³= 0.00032 + 0.0064 + 0.0512= 0.05792
Therefore, the probability that at most two cars finish the race is 0.05792.
(c) To determine the probability that at least three cars finish the race, we can calculate the probability of 0, 1, and 2 cars finishing the race and subtract it from 1, which gives us the probability of at least three cars finishing the race.
P(X ≥ 3) = 1 - [P(X = 0) + P(X = 1) + P(X = 2)]= 1 - (0.00032 + 0.0064 + 0.0512)= 0.94208
Therefore, the probability that at least three cars finish the race is 0.94208.
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in an experiment, it takes you one hour to memorize all the terms on a list. two years later you relearn them in 45 minutes. the time difference of 15 minutes, or 25 percent (15 divided by 60 times 100), is called the
The time difference of 15 minutes, or 25 percent (15 divided by 60 times 100), is called the time saved.
What is an experiment?An experiment is a controlled study in which a scientist manipulates a variable in order to determine its effects. An experiment must have a testable hypothesis, be replicable, and produce empirical evidence.
Discussing the time difference in an experiment. In an experiment, it takes one hour to memorize all of the words on a list, and two years later, they are relearned in 45 minutes.
The time difference of 15 minutes, or 25 percent (15 divided by 60 times 100), is referred to as the time saved.
Time saved is the difference between the total time it takes to finish a process with a particular method and the total time it would take to complete the same process without that method.
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Evaluate
(
3
7
)
−
2
Give your answer as an improper fraction in its simplest form
The value of (37)-2 is 1/1369, in its simplest form as an improper fraction.
An improper fraction is a fraction where the numerator is greater than or equal to the denominator. In other words, it is a fraction that is larger than a whole number.
When an expression is written in the form of [tex]x^{(-n)[/tex], it means the reciprocal of [tex]x^n.[/tex] In this case, we have the expression[tex](37)^{(-2)[/tex] which means the reciprocal of 37².
The expression (37)-2 means 37 raised to the power of -2, or 1/(37²). To simplify this fraction, we can multiply the numerator and denominator by 1,296 (37²):
1/(37²) = 1 * 1 / (37 * 37)
= 1/1369
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Graph the function f(x)=-(√x+2)+3
State the domain and range of the function.
Determine the vertex and 4 more points.
If you could help me with this, I would really appreciate it. Thank you!
Vertex: The vertex of the function is at the point (-2, 3).
What is domain?The domain of a function is the set of all possible input values (often represented as x) for which the function is defined. In other words, it is the set of all values that can be plugged into a function to get a valid output. The domain can be limited by various factors such as the type of function, restrictions on the input values, or limitations of the real-world scenario being modeled.
What is Range?The range of a function refers to the set of all possible output values (also known as the dependent variable) that the function can produce for each input value (also known as the independent variable) in its domain. In other words, the range is the set of all values that the function can "reach" or "map to" in its output.
In the given question,
Domain: The domain of the function is all real numbers greater than or equal to -2, since the square root of a negative number is not defined in the real number system.
Range: The range of the function is all real numbers less than or equal to 3, since the maximum value of the function occurs at x=-2, where f(x)=3.
Vertex: The vertex of the function is at the point (-2, 3).
Four additional points:When x=-1, f(x)=-(√(-1)+2)+3 = -1, so (-1,-1) is a point on the graph.
When x=0, f(x)=-(√0+2)+3 = 1, so (0,1) is a point on the graph.
When x=1, f(x)=-(√1+2)+3 = 2, so (1,2) is a point on the graph.
When x=4, f(x)=-(√4+2)+3 = -1, so (4,-1) is a point on the graph
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1 Find the value of x.
i’m like struggling
Answer: 23 degrees
Step-by-step explanation:
Assuming that 117 is the entire angle we can find that:
94+x = 117
Subtract 94 from both sides:
x = 117-94
x = 23 degrees
Help me please I need to show my work
Answer:
x=33
Step-by-step explanation:
all angles in a triangle sum to 180 degrees
x+2x+(2x+15) = 180 <---- simplify this
5x+15 = 180
5x=165
x = 33
This question has two parts. First, answer Part A. Thenanswer Part B
Part A
BAKERY Aisha can work up to 20 hours per week Working at a bakery, she earns $7 per hour most of the time and $ 8.50 per hour during the early morning shift. Aisha needs to earn at least $150 this week to pay for a trip with her friends. Determine the number of regular and early morning hours that Aisha could work
Part A Select the correct system and graph. Let r=regular hours and m = early morning hours
R<20
7r+8.5m>=150
R+m <=20
r+m<=150
r+m<= 20
7r+ 8.5m >= 150
7r+8.5m>20
7r+8.5m>= 150
Part B
Drag every viable solution to the bin.
The other solutions are not viable because either they exceed the maximum number of hours Aisha can work (20 hours) or they do not meet the minimum amount Aisha needs to earn ($150).
What is an illustration of a workable solution?If the ongoing research is successful, this approach might be an effective remedy. The only real way to resolve the problem is through negotiations between the military administration and the various opposition movements.
Part A: The correct system and graph to represent Aisha's situation is:
r + m ≤ 20 (maximum number of hours Aisha can work)
7r + 8.5m ≥ 150 (minimum amount Aisha needs to earn)
Part B: The viable solutions are:
r = 20, m = 0 (Aisha works only regular hours for 20 hours at $7 per hour)
r = 14, m = 6 (Aisha works 14 regular hours and 6 early morning hours at $7 per hour and $8.50 per hour, respectively)
r = 0, m = 18 (Aisha works only early morning hours for 18 hours at $8.50 per hour)
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Use the diagram shown. Lines p and q are parallel.
Select all the correct measures for ∠1, ∠2,
and ∠3.
Answer:
<1= 61
<2= 61
<3= 119
Step-by-step explanation:
The function
�
=
�
(
�
)
y=f(x) is graphed below. What is the average rate of change of the function
�
(
�
)
f(x) on the interval
−
6
≤
�
≤
5
−6≤x≤5?
Answer:
-10/11
Step-by-step explanation:
You want the average rate of change of f(x) on the interval [-6, 5].
Average rate of changeThe average rate of change of function f(x) on the interval [a, b] is ...
AROC = (f(b) -f(a))/(b -a)
= (f(5) -f(-6))/(5 -(-6))
= (-20 -(-10))/5 +6 = (-20 +10)/(5 +6)
AROC = -10/11
The average rate of change on the interval is -10/11.
Find the outer perimeter.
6 ft
4 ft
15 ft
10 ft
P = [?] ft
Round to the nearest
hundredth.
Answer:
P= 40 ft
Step-by-step explanation:
Perimeter is the sum of all the lengths
So,
Perimeter= 6+4+15+10ft
= 35ft
Nearest ten can be 40ft or 30ft
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the amount of bacteria present in a medium after t hours is given by a (t )equals 16 e to the power of 0.32 t end exponent. at what rate is the amount of bacteria changing after 12 hours?
The rate at which the amount of bacteria is changing after 12 hours is 21.698 units/hour.
What is the rate at which the amount of bacteria changing after 12 hours?The given formula for the amount of bacteria present in a medium after t hours is:
[tex]a(t) = 16e^ (0.32t)[/tex]
Now, we need to find out at what rate the amount of bacteria is changing after 12 hours.
This means we need to find out the derivative of a(t) with respect to t and then substitute t = 12 in the derivative formula to get the rate of change of bacteria after 12 hours.
Differentiating the given formula for a(t) with respect to t, we get:
a'(t) = [tex]16(0.32)e^(0.32t)[/tex]
On substituting, t = 12, we get
a'(12) = [tex]16(0.32)e^ (0.32X12)[/tex]
On solving this, we get a'(12) = 21.698.
Therefore, the rate at which the amount of bacteria is changing after 12 hours is 21.698 units/hour.
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[Complex Analysis] Is there a polynomial P(z) such that Pe^(1/z) is entire?
There is no polynomials such that [tex]P(z)e^{\frac{1}{z} }[/tex] is entire.
Sums of elements of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the equation 3x+2x-5. a description of polynomials.
By the Taylor expansion, [tex]e^{\frac{1}{z} }[/tex] = ∑∞n= 0.
Let P(z)= (ad)zd+.......+a0.
For n>0, the coefficient of z-n in the expansion of [tex]P(z)e^{\frac{1}{z} }[/tex] is :-
[tex]tn= n^{a0} 1 + (n+1)!+.......+(n+d)![/tex]
So the Laurent expansion of [tex]P(z)e^{\frac{1}{z} } = 0[/tex]will have terms of the form tn2-n where an is not equal to zero.
if r is the smallest non negative integer such that ar is not equal to zero, then we see that we can rewrite:-
[tex]tn= (n^{1} +r)![ar+n^{ar+1} +1+.....+(n+r+d)....(n+d)][/tex]
as we know that [tex]\lim_{n \to \infty} (n+r+1+....+(n+r+d).....(n+d)=0[/tex]
so there exists an N∈N, such that:-
[tex]/ar/ > n+r+1+....+(n+r+d)....(n+d)=0[/tex]
HenHence tn is non zero for all n>N. In other words, expansion contains terms of negative powers.
So, apart from P(z)=0, there is no polynomials such that [tex]P(z)e^{\frac{1}{z} } .[/tex]
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A hawk flying at 19 m/s at an altitude of 228 m accidentally drops its prey. The parabolic trajectory of the falling prey is described by the equation y = 228 − x^2/57 until it hits the ground, where y is its height above the ground and x is its horizontal distance traveled in meters. Calculate the distance traveled by the prey from the time it is dropped until the time it hits the ground. Express your answer correct to the nearest tenth of a meter.
The parabolic trajectory of the falling prey can be described by the equation y = 228 – x2/57, where y is the height above the ground and x is the horizontal distance traveled in meters. In this case, the prey was dropped at a height of 228 m and flying at 19 m/s. To calculate the total distance traveled by the prey, we can use the equation for the parabola to solve for x.
We can rearrange the equation y = 228 – x2/57 to solve for x, which gives us[tex]x = √(57*(228 – y))[/tex]. When the prey hits the ground, the height (y) is 0. Plugging this into the equation for x, we can calculate that the total distance traveled by the prey is[tex]x = √(57*(228 - 0)) = √(57*228) = 84.9 m.\\[/tex] Expressing this answer to the nearest tenth of a meter gives us the final answer of 84.9 m.
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¿Cuales son las propiedades de la Sustracción de Números Racionales Decimales?
The following characteristics of racional decimal number abstraction apply: Conmutative property: The order of the remaining rational decimal numbers has no bearing on the operation's outcome,
Proprietary property: The racional decimal numbers may remain in various groups without affecting the operation's ultimate outcome, i.e., (a - b) - c = a - (b - c). Distributive property: Subtracting one racional decimal number from a sum of racional decimal numbers equals the sum of the subtractions of each one of them, or a - (b + c) = a - b - c. Neutral element: If a racional decimal number is left at zero, the outcome is the same number, i.e., a - 0 = a. Estas propiedades son útiles para simplificar y realizar cálculos más complejos con números racionales decimales.
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Tina started a project with two 1 -gallon cans of paint. One can us now 4/10 full, and the other can is 5/8. Which one less than 1/2 full?
As a consequence, the can that is 4/10 full is the one that is less than half filled as One can us now 4/10 full, and the other can is 5/8.
what is fractions ?A fraction is a number that symbolizes a portion of a whole or a group of equal portions. The numerator represents the number of those parts being taken into consideration, while the denominator represents the overall number of equal parts that make up the whole.
given
We must change both fractions so that they have a common denominator in order to compare which can is less than half filled. 10 and 8 have a least common multiple (LCM) of 40.
20/40 is equivalent to 1/2.
So,
4/10 is equal to (4/10) x (4/4) Equals 16/40.
The formula for 5/8 is (5/8) x (5/5) = 25/40.
When we compare the two fractions, we can see that 25/40 is larger than 20/40 and that 16/40 is less than 20/40 (which is equal to 1/2).
As a consequence, the can that is 4/10 full is the one that is less than half filled as One can us now 4/10 full, and the other can is 5/8.
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The data in Exercise 1 were taken from the following functions. Compute the actual errors in Exercise 1, and find error bounds using the error formulas.
a. f ( x ) = sin x b. f (x) = ex − 2x2 + 3x – 1
The actual errors for Exercise 1 can be computed by subtracting the calculated values from the true values of the functions. For example, the actual error for sin(1.1) can be found by subtracting sin(1.1) = 0.8912 from the calculated value of 0.8890. The actual error in this case is 0.0022.
Error bounds for these functions can be found using the error formulas. For the function f(x) = sin x, the error bound can be found using the formula |E| <= M|x-a|, where M is the maximum value of the first derivative of the function, and a is the value of x at which the error is computed. In this case, M = 1 and a = 1.1, so the error bound is |E| <= 1 * |1.1 - 1.1| = 0.
For the function f(x) = ex - 2x2 + 3x - 1, the error bound can be found using the formula |E| <= M|x-a|2, where M is the maximum value of the second derivative of the function, and a is the value of x at which the error is computed. In this case, M = e and a = 1.1, so the error bound is |E| <= e * |1.1 - 1.1|2 = 0.
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a reaseacher tests the null hypothesis that the mean body temperature of residents in a nursing home is 98.6 f. which statistical test could the researcher use?
The statistical test that a researcher could use to test the null hypothesis that the mean body temperature of residents in a nursing home is 98.6°F is a one-sample t-test.
What is a statistical test?A statistical test is a method that enables the comparison of the collected data with the assumed distribution of the data. A statistical test aids in determining if the outcomes of the experiment or research are caused by the treatment or if they are due to the random variation in the data.
A null hypothesis is a type of hypothesis that predicts the absence of a relationship between variables or groups. The null hypothesis claims that no difference exists between two variables or groups, and that any observed differences are due to chance.
Alternative hypotheses are used to reject null hypotheses, as they predict the presence of a relationship between variables or groups.
The significance level, which is the probability of committing a Type I error, is often used to set the null hypothesis. The statistical test that a researcher could use to test the null hypothesis that the mean body temperature of residents in a nursing home is 98.6°F is a one-sample t-test.
The t-test will aid in determining if the difference between the mean body temperature of residents in the nursing home and 98.6°F is statistically significant.
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A square is inscribed in a right triangle with leg lengths 6 and 8 so that they have a common right angle. FInd the square's side length.
Answer:
10 units
Step-by-step explanation:
Here, legs = base and perpendiculars.
So, Clearly given Base = 6 units Perpendicular = 8 cm
Square's Side = Hypotenuse.
By Pythagoras theorem,
H² = B²+P²
H ² = 6²+8²
H² = 36+64 = (10)²
H = 10 units.
Square's Side length = 10 units
