Ronaldo's family drove a total of 6.90 kilometres to get from their house to the store.
What expression used to determine number of kilograms?To determine the total distance Ronaldo's family drove, we need to add the distance from their house to the gas station and the distance from the gas station to the store. We can write this as:
[tex]4 6/10 km + 2 30/100 km[/tex]
To add these two distances, we need to find a common denominator for the fractions. The smallest common denominator for 10 and 100 is 100, so we can convert the first distance to an equivalent fraction with a denominator of 100:
[tex]4 6/10 km = 4 60/100 km = 4.60 km[/tex]
Then we can add the two distances:
[tex]4.60 km + 2.30 km = 6.90 km[/tex]
Therefore, Ronaldo's family drove a total of 6.90 kilometres to get from their house to the store.
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Ricardo throws a stone off a bridge into a river below.
The stone's height (in meters above the water), x seconds after Ricardo threw it, is modeled by
w ( x ) = − 5 ( x − 8 ) ( x + 4 )
How many seconds after being thrown will the stone reach its maximum height?
Therefore , the solution of the given problem of equation comes out to be the stone will reach its maximum height 2 seconds after being thrown.
What is an equation?Variable words are widely used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic figures. Think about the information that y + 7 provides. When paired with construct y + 7, elevating results in b + 7 in this circumstance rather than another method that may divide 12 equal two halves.
Here,
The height of the stone above the water is given by the function:
=> w(x) = -5(x-8)(x+4)
To find the time when the stone reaches its maximum height, we need to find the vertex of the parabola that represents this function. We can do this by using the formula:
=> x = -b / 2a
where a = -5 and b = -5(8+(-4)) = -20.
Substituting these values into the formula, we get:
=> x = -(-20) / 2(-5) = 2
Therefore, the stone will reach its maximum height 2 seconds after being thrown.
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find the measure in degrees of the angle
Answer:
120°
Step-by-step explanation:
We know that the exterior angle of a triangle is equal to the sum of the interior opposite angles.
Let the unknown angle be x.
Accordingly,
70° + 50° = x
120° = x
its special angles, please show work
Answer:
H=25
I=36
Step-by-step explanation:
i need this paper finished within 2 hours to stay in honors math. help? (2 attachments for 50 points)
Answers:
Q.1 B. 6.88.
Q2. Sorry Not clearly visible its blurred
Q3. The closest answer choice is C. 4.9
Q4. 2.94
Q5. Set B
Q6. C
Step-by-step explanation:
Q1.
To find the mean absolute deviation, we first need to find the mean of the data set
Data: 32, 43, 38, 28, 51
Mean = (32 + 43 + 38 + 28 + 51) / 5 = 38.4
Next, we need to find the absolute deviations of each number from the mean
|32 - 38.4| = 6.4
|43 - 38.4| = 4.6
|38 - 38.4| = 0.4
|28 - 38.4| = 10.4
|51 - 38.4| = 12.6
To find the mean absolute deviation, we need to take the average of these absolute deviations
Mean Absolute Deviation = (6.4 + 4.6 + 0.4 + 10.4 + 12.6) / 5 = 6.88
Therefore, the answer is B. 6.88.
Q3.
To find the mean absolute deviation, we first need to find the mean of the data set
Data: 12.7, 22, 23.5, 24, 11, 22
Mean = (12.7 + 22 + 23.5 + 24 + 11 + 22) / 6= 18.2
Next, we need to find the absolute deviations of each number from the mean
|12.7 - 18.2| = 5.5
|22 - 18.2| = 3.8
|23.5 - 18.2| = 5.3
|24 - 18.2| = 5.8
|11 - 18.2| = 7.2
|22 - 18.2| = 3.8
To find the mean absolute deviation, we need to take the average of these absolute deviations
Mean Absolute Deviation = (5.5 + 3.8 + 5.3 + 5.8 + 7.2 + 3.8) / 6 = 5.9
Therefore, the closest answer choice is C. 4.9. However, this answer is not correct as the calculated value is 5.9.
Q4.
To find the average distance of these points from the mean of the data, we need to first find the mean of the data.
The mean of the data can be found by adding up all the values and dividing by the total number of values:
Mean = (-8 + 6.2 + 2.5 + 12 - 2 - 1.3 + 15 - 2 + 0 + 7) / 10
= 29.4 / 10
= 2.94
The average distance from the mean is found by taking the absolute value of the difference between each value and the mean, adding them up, and dividing by the total number of values:
Average Distance from Mean = (|(-8) - 2.94| + |6.2 - 2.94| + |2.5 - 2.94| + |12 - 2.94| + |-2 - 2.94| + |-1.3 - 2.94| + |15 - 2.94| + |-2 - 2.94| + |0 - 2.94| + |7 - 2.94|) / 10
= (10.94 + 3.26 + 0.44 + 9.06 + 4.94 + 4.24 + 12.06 + 4.94 + 2.94 + 4.06) / 10
= 5.688
Therefore, the average distance of these points from the mean of the data is 5.688, which is option D.
Q5.
o find out if the mean and median are equal in a set of data, we need to calculate both the mean and median and compare them.
Mean is calculated by adding up all the values and dividing by the total number of values.
Median is the middle value of the data when it is arranged in order.
Let's calculate the mean and median of both data sets:
A. (5, 3, 5, 8, 2, 5)
Mean = (5 + 3 + 5 + 8 + 2 + 5) / 6
= 4.6667
To calculate the median, we first need to arrange the data in order:
2, 3, 5, 5, 5, 8
Since the data set has an even number of values, the median is the average of the middle two values:
Median = (5 + 5) / 2
= 5
Since the mean and median of set A are not equal (4.6667 ≠ 5), set A is not the correct answer.
B. (7, 3, 5, 11, 5, 3)
Mean = (7 + 3 + 5 + 11 + 5 + 3) / 6
= 5.8333
To calculate the median, we first need to arrange the data in order:
3, 3, 5, 5, 7, 11
Since the data set has an even number of values, the median is the average of the middle two values:
Median = (5 + 5) / 2
= 5
Since the mean and median of set B are equal (5.8333 ≈ 5), set B is the correct answer.
Therefore, the set of data in which the mean and median are equal is set B: (7, 3, 5, 11, 5, 3). Answer: B.
Q6.
To answer this question, we need to first find the mean, median, and range of the data:
Data: 10, 23, 52, 18, 5, 60, 35
Mean = (10 + 23 + 52 + 18 + 5 + 60 + 35) / 7
= 28.57
Median = 23
To find the range, we need to subtract the smallest value from the largest value:
Range = 60 - 5
= 55
Now, let's evaluate each statement:
A. The mean is greater than the range.
- 28.57 > 55
- This statement is false.
B. The range is 50.
- The range is 55, not 50.
- This statement is false.
C. The median is less than the mean.
- The median is 23 and the mean is 28.57
- This statement is true.
D. The median is greater than the range.
- 23 > 55
- This statement is false.
Therefore, the statement that is true is C. The median is less than the mean.
Evaluate. 547+233×5−142 whats this answer
The answer to the expression 547 + 233 × 5 - 142 is 1752. To solve the expression, we must follow the order of operations, which is PEMDAS: Parentheses, Exponents, Multiplication, and Division (performed left to right), and Addition and Subtraction (performed left to right).
Since there are no parentheses or exponents in this expression, we start with multiplication and division. In this case, we have to multiply 233 by 5, which gives us 1165. Then, we add 547 to 1165, which gives us 1712. Finally, we subtract 142 from 1712, which gives us the final answer of 1752. Therefore, the result of the expression 547 + 233 × 5 - 142 is 1752, which can be obtained by following the order of operations and performing the arithmetic operations in the correct order.
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Juan has a large bag of rice that he placed in three different containers. He put 3.253.25 pounds into the first container. He put three times as much into the second container. He put twice as much into the third container as he put into the second container.
What is the weight in pounds of the rice in the second container and the third container?
Answer:
he puts 3.354.235 pounds in it
Step-by-step explanation:
because the synapses hypural torminal that's the only answer that make since.
In which quadrant does the point (-18 , 17) lie?
A.
Quadrant II
B.
Quadrant IV
C.
Quadrant III
D.
Quadrant I
Answer:quadrant ll
Step-by-step explanation:
Find Sum to infinity of the given series: a. 1 + 2x + 3x² + 4x³+... to ∞ (|x| <1)
The sum to infinity of the series 1 + 2x + 3x² + 4x³ + ... is 1/[(1-x)²] when |x| < 1.
How do we calculate?The formula for the sum of an infinite geometric series when |x| < 1 is given as:
S = a/(1-r)
We have a = 1 and r = x/1.
S = 1/(1-x) + 2x/(1-x)² + 3x²/(1-x)³ + 4x³/(1-x)⁴ + ...
we multiply both sides of this equation by (1-x)²,
S(1-x)² = (1-x) + 2x + 3x²(1-x) + 4x³(1-x)² + ...
S(1-x)² = 1 + x + x² + x³ + ... eqn (1)
Using the formula for the sum of an infinite geometric series when |x| < 1, we have:
1/(1-x) = 1 + x + x² + x³ + ...
Substituting this into equation (1), we get:
S(1-x)² = 1/(1-x)
S = 1/[(1-x)²]
In conclusion, the sum to infinity of the series 1 + 2x + 3x² + 4x³ + ... is 1/[(1-x)²] when |x| < 1
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Pls i need help on this question
The length of the missing side is 3√17 ft. Option B is the correct option.
What is the hypotenuse?
The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry. The Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.
The △ABC is a right-angled triangle.
Thus the sum of squares of the legs of the triangle is equal to the square of the hypotenuse.
The hypotenue is 13 ft.
Assume that the missing leg is equal to x.
The legs of the triangle are x and 4ft.
Apply Pythagorean theorem:
13² = 4² + x²
x² = 169 -16
x² = 157
x = √(3×3×17)
x = 3 √17
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How do you put fractions in order from least to greatest?
To put fractions in order from least to greatest, you need to compare their values by finding the common denominator.
Here are the steps to follow:Step 1: Find a common denominator for all the fractions.
Step 2: Convert each fraction to an equivalent fraction with the common denominator.
Step 3: Compare the numerators of the equivalent fractions. The fraction with the smallest numerator is the smallest fraction, and the fraction with the largest numerator is the largest fraction.
Step 4: If two or more fractions have the same numerator, compare their denominators. The fraction with the smallest denominator is the smallest fraction, and the fraction with the largest denominator is the largest fraction.
Step 5: Write the fractions in order from least to greatest.
For example, let's say you need to put the fractions 1/3, 2/5, and 3/8 in order from least to greatest.
Step 1: The common denominator for 3, 5, and 8 is 120.
Step 2: Convert each fraction to an equivalent fraction with a denominator of 120.
1/3 = 40/120
2/5 = 48/120
3/8 = 45/120
Step 3: Compare the numerators of the equivalent fractions: 40 < 45 < 48
Step 4: Since 40 is not equal to 45 or 48, we don't need to compare the denominators.
Step 5: Write the fractions in order from least to greatest: 1/3 < 3/8 < 2/5.
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suppose that the number of log-ons to a computer network follow a poisson process with an average of three counts per minute, a. what is the mean time between counts? b. what is the standard deviation of the time between counts?
a) Mean time between counts is 0.3333 minutes.
b) Standard deviation of time between counts is 0.5774 minutes.
a. Mean time between counts: The mean time between counts can be computed as the inverse of the Poisson rate parameter (λ): Mean time between counts = 1/λ.
The average of 3 counts per minute is the same as the rate parameter λ in a Poisson process. Thus, the mean time between counts is: Mean time between counts = 1/λ = 1/3 = 0.3333 minutes (20 seconds approximately).
b. Standard deviation of the time between counts: The standard deviation of a Poisson process is equal to the square root of the mean.
Therefore, the standard deviation of the time between counts can be calculated as follows: Standard deviation of time between counts = sqrt(mean) = sqrt(1/λ) = sqrt(1/3) = 0.5774 minutes (approximately 35 seconds).
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if repairing a machine has already taken two hours and the repair person is not done, what is the probability that it will take 3 or more hours to repair the machine?
The probability of the repair person taking 3 or more hours to fix the machine is 0.3, or 30%.
As an AI language model, I do not have the specific information needed to answer this question. However, we can use probability theory to solve this problem.
Let's assume that the probability of repairing the machine in 2 hours or less is p, and the probability of taking more than 2 hours is q (which is the same as saying the probability of taking 3 or more hours).
We know that p + q = 1, meaning that the sum of the probabilities of repairing in 2 hours or less and taking more than 2 hours is equal to 1, which represents the total probability.
Now, if we know the value of p, we can easily calculate q by subtracting it from 1:
q = 1 - p
For example, if we assume that the probability of repairing in 2 hours or less is 0.7, then the probability of taking more than 2 hours is:
q = 1 - 0.7 = 0.3
So, in this case, the probability of the repair person taking 3 or more hours to fix the machine is 0.3, or 30%.
However, without knowing the specific probabilities of the repair person finishing within 2 hours or the probabilities of taking longer, we cannot provide an accurate answer to this question.
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A triangle has two sides 4 and 15 what value could the length of the third side be
The answers
are 12, 15, 13
__________________________________________________________
The sum of two sides must be equal to or greater than the third side.
4+15 = 19; 4 + 19 = 23; 15 + 19 = 34.
19 is a possible answer.
4 + 15 = 19; 15 + 15 = 30
15 is a possible answer.
4 + 15 = 19; 4 + 13 = 17; 15 + 13 = 28
13 is a possible answer.
4 + 12 = 16; 4 + 15 = 19; 15 + 12 = 27
12 is a possible answer.
4 + 11 = 15; 4 + 15 = 19; 11 + 15 = 26
11 is a possible answer.
15 + 4 = 19; 4 + 4 = 8
4 is NOT a possible answer because 4 + 4 is less than 15.
--------------------------------------HAVE A NICE DAY--------------------------------------------
The scale factor of two similar hexagons is 7:3.
The area of the smaller hexagon is 18 m2.
What is the area of the larger hexagon?
Question options:
5832 m2
324 m2
42 m2
98 m2
36 m2
Answer:
42 m2
Step-by-step explanation:
3=18
7=?
=7 × 13 ÷ 3
=42
The number of milligrams D(h) in a patient’s bloodstream h hours after the drug is injected is modeled by the following function D (h) =50e^-0.2h
Find the initial amount injected and the amount in the bloodstream after 7 hours. Round your answers to the nearest hundredth as necessary
The initial amount injected was 50 milligrams and after 7 hours, there are approximately 16.08 milligrams of the drug in the patient's bloodstream.
How to calculate initial amount injected and the amount in the bloodstream after 7 hours.The function that models the number of milligrams D(h) in a patient's bloodstream h hours after the drug is injected is:
D(h) = 50e^(-0.2h)
To find the initial amount injected, we can evaluate D(0):
D(0) = 50e^(-0.2*0) = 50e^0 = 50
Therefore, the initial amount injected was 50 milligrams.
To find the amount in the bloodstream after 7 hours, we can evaluate D(7):
D(7) = 50e^(-0.2*7) ≈ 16.08
Therefore, after 7 hours, there are approximately 16.08 milligrams of the drug in the patient's bloodstream.
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Blake decides to estimate the volume of a coffee cup by modeling it as a right cylinder. Blake measures its radius as 2.7 cm and its volume as 174 cubic centimeters. Find the height of the cup in centimeters. Round your answer to the nearest tenth if necessary.
The height of the coffee cup is approximately 4.1 cm.
Equations
h = V / (π[tex]r^{2}[/tex])
Plugging in the given values, we get:
h = 174 / (π × [tex]2.7^{2}[/tex])
h ≈ 4.1 cm
Therefore, the height of the coffee cup is approximately 4.1 cm.
What is the difference between total surface area and lateral surface area of a cylinder?The total surface area of a cylinder is the sum of the areas of its curved surface and its two circular bases, while the lateral surface area of a cylinder is the area of its curved surface only, without the bases.
To be more precise, if a cylinder has a height of "h", a radius of "r", and a base circumference of "c", then:
The total surface area of the cylinder is given by: 2πr² + 2πrh = 2πr(r+h) + 2πr² = 2πr(r+h+c)
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in three combined decks of cards, what is the fewest number of cards you must pick at random to be guaranteed at least one four-of-a-kind?
four is the minimal because you want to draw all four to the four of a kind
Help me please on the linear function from a table
The missing numbers to complete the linear equation that gives the rule for this table are y = 11x-10
Describe Linear Equation?A linear equation is an equation that describes a line in a two-dimensional coordinate system. It can be written in the form:
y = mx + b
where y and x are variables representing coordinates on the vertical and horizontal axes, respectively, m is the slope of the line, and b is the y-intercept (the point where the line crosses the y-axis).
The slope of the line represents the rate of change between y and x, or the steepness of the line. A positive slope indicates that the line is increasing from left to right, while a negative slope indicates that the line is decreasing from left to right. A slope of zero indicates a horizontal line, while a slope that is undefined (such as when x is constant) indicates a vertical line.
To find the equation that gives the rule for this table, we need to determine the slope and y-intercept of the line that passes through these points.
We can start by using the two given points (4, 34) and (5, 45) to find the slope:
slope = (change in y) / (change in x)
slope = (45 - 34) / (5 - 4)
slope = 11
Now we can use the point-slope form of a linear equation to write the equation for this line, using the point (4, 34):
y - 34 = 11(x - 4)
Simplifying this equation gives:
y = 11x - 10
So the missing numbers to complete the linear equation that gives the rule for this table are:
y = 11x-10
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There are 3.2 liters of iced tea in a pitcher. How many milliliters of iced tea are in the pitcher?
Answer:3200
Step-by-step explanation:
there are 1000 ml per liter
Roberto plays on the school baseball team. In the last 10 games, Roberto was at bat 44 times. While at bat, Roberto got 11 hits and struck out 33 times. What is the experimental probability that Roberto will get a hit during his next time at bat?
The experimental probability that Roberto will get a hit during his next time at bat is 0.25 or 25%.
The experimental probability of an event is calculated by dividing the number of times the event occurred by the total number of trials.
In this case, the event is "getting a hit" and the number of times it occurred is 11. The total number of trials is 44, which represents the number of times Roberto was at bat.
Experimental probability of getting a hit = Number of times Roberto got a hit / Total number of times at bat
Experimental probability of getting a hit = 11 / 44
Experimental probability of getting a hit = 0.25 or 25%
Therefore, the experimental probability that Roberto will get a hit during his next time at bat is 0.25 or 25%.
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for each model, choose categorical or numeric for the explanatory and response variables. for simple linear regression, the explanatory variable is
For simple linear regression, the explanatory variable is numeric.
What is simple linear regression?Simple linear regression is a statistical method that allows researchers to understand the relationship between two continuous variables. A simple linear regression model is used to represent the relationship between a dependent variable (Y) and an independent variable (X) by making a linear equation of the form
Y = a + bX, where a is the constant, and b is the regression coefficient.
In simple linear regression, the explanatory variable is of numeric type. This statistical method involves the use of two numeric variables, namely the explanatory (independent) variable and the response (dependent) variable, which are analyzed to establish a linear relationship between them.
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a poll was taken asking people if they agreed with the positions of the 4 candidates for a county office. does the pie chart present a good representation of this data? explain.
The pie chart accurately represents the data from the poll, as it accurately shows the proportion of people who agreed with each candidate's positions.
The pie chart presents a good representation of the data from the poll taken asking people if they agreed with the positions of the 4 candidates for a county office. This is because the pie chart accurately shows the proportion of people who agreed with each candidate's positions. For example, the chart indicates that 26% of the people agreed with Candidate A's positions, 28% agreed with Candidate B's positions, 29% agreed with Candidate C's positions, and 17% agreed with Candidate D's positions. In order to calculate the proportions, the total number of people who responded to the poll was divided by each individual candidate's number of supporters. For example, for Candidate A, the proportion of people who agreed with their positions was calculated by dividing the total number of people responding to the poll (100) by the number of people who agreed with Candidate A's positions (26), resulting in a proportion of 0.26 or 26%. This same approach was used to calculate the proportions of each candidate's supporters. Therefore, the pie chart accurately presents the data from the poll and is a good representation of the data.
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A 3.0kg ball and a 1.0kg ball are placed at opposite ends of a massless beam so that the system is i equilibrium as shown. What is the value of the ratio of the lengths, b/a?
To find the value of the ratio b/a for the 3.0 kg ball and the 1.0 kg ball placed at opposite ends of a massless beam in equilibrium, we can use the principle of moments.
Solution:
Step 1: Identify the forces and distances involved. The 3.0 kg ball has a force of 3.0g (g represents gravity) acting at distance a from the pivot point. The 1.0 kg ball has a force of 1.0g acting at distance b from the pivot point.
Step 2: Apply the principle of moments. For the system to be in equilibrium, the clockwise moment and anticlockwise moment must be equal. This means that the product of the force and distance for each ball must be equal:
3.0g × a = 1.0g × b
Step 3: Solve for the ratio b/a. First, divide both sides of the equation by g:
3.0a = 1.0b
Now, divide both sides of the equation by 3.0a:
b/a = 1/3
The value of the ratio b/a is 1/3.
The ratio is 1:3
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A plant in my garden is growing 2/3 of a foot every 3/4 of a month. How much does it grow per month?
The plant is growing 0.89 feet per month.
To calculate how much a plant grows per month, you need to first convert the measurements into one unit of measurement.
Since the plant is growing 2/3 of a foot every 3/4 of a month,
we can first convert the fractions of a foot and a month into decimal equivalents.
2/3 of a foot is 0.67 feet, and 3/4 of a month is 0.75 months.
We can then calculate the amount of growth per month by dividing the amount of growth per 3/4 of a month by the amount of time that is 3/4 of a month (0.75).
The equation is 0.67 feet / 0.75 months = 0.89 feet per month.
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what is the probability that at least 67 out of 100 cars stopped at a roadblock will not be given a ticket? local authorities report that tickets usually are given to 23% of cars stopped
The probability that at least 67 out of 100 cars stopped at a roadblock will not be given a ticket is 2.37.
Given Probability of giving tickets to cars that are stopped = 0.23
Probability of not giving tickets to cars that are stopped = 1 - 0.23 = 0.77
the probability that at least 67 out of 100 cars stopped at a roadblock will not be given a ticket
Here n = 100, p = 0.77, q = 0.23
mean = np = 100*0.77 = 77
standard deviation = [tex](sigma = \sqrt{(100)*(0.77)*(0.23) } = 4.208[/tex]
[tex]P(X\geq 67) = \frac{67 - 77}{4.208}[/tex] = 2.37
P-VALUE is 0.99126 from z-table
Probability is a fundamental concept in mathematics that helps us quantify the likelihood of events occurring and is applicable to a wide range of fields. It is a measure of the uncertainty of an event, expressed as a number between 0 and 1. An event with probability 0 is impossible, while an event with probability 1 is certain.For example, the probability of rolling a six on a fair six-sided die is 1/6, since there is only one favorable outcome out of six possible outcomes.
Probability theory has wide applications in fields such as statistics, finance, engineering, and physics, among others. It is used to model and analyze various phenomena, including weather patterns, stock prices, quantum mechanics, and more.
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the area of one lateral face of a right pyramid with an equilateral triangular base is 75 square meters. if the slant height is 30 meters, what is the length of the side of its base, in meters?
A right pyramid with an equilateral triangular base has a lateral face with a surface area of 75 square meters. The side of the base of a slant with a height of 30 meters is 5 meters long.
Let’s call the side length of the equilateral triangular base “s”. We know that the area of one lateral face is 75 square meters, and that face is a triangle with base s and height 30 meters (the slant height). We can use the formula for the area of a triangle to solve for s:
Area = (1/2) * base * height
75 = (1/2) * s * 30
Simplifying the equation, we get:
75 = 15s
s = 75/15
s = 5
Therefore, the length of the side of the equilateral triangular base is 5 meters.
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Pls just say a b c or d
Answer: theres no attachment
Step-by-step explanation:
Determine whether it is possible to find values of L 0 so that the given boundary-value problem has precisely one nontrivial solution, more than one solution, no solution, and the trivial solution. (Let k represent an arbitrary integer. If an answer does not exist, enter DNE.) y" + 16y=0, y(0)= 1, y(L) = 1 (a) precisely one nontrivial solution (b) more than one solution (c) no solution (d) the trivial solution
There is no solution if the boundary conditions are inconsistent, i.e., if y(0) ≠ y(L) = 1.
We are given the boundary-value problem:
y" + 16y = 0, y(0) = 1, y(L) = 1
The characteristic equation is r^2 + 16 = 0, which has roots r = ±4i.
The general solution to the differential equation is then y(x) = c1cos(4x) + c2sin(4x).
Using the boundary conditions, we get:
y(0) = c1 = 1
y(L) = c1cos(4L) + c2sin(4L) = 1
Substituting c1 = 1 into the second equation, we get:
cos(4L) + c2*sin(4L) = 1
Solving for c2, we get:
c2 = (1 - cos(4L))/sin(4L)
Thus, the general solution to the differential equation that satisfies the given boundary conditions is:
y(x) = cos(4x) + (1 - cos(4L))/sin(4L)*sin(4x)
Now, we can answer the questions:
(a) To have precisely one nontrivial solution, we need the coefficients c1 and c2 to be uniquely determined. From the above expression for c2, we see that this is only possible if sin(4L) is nonzero. Thus, if sin(4L) ≠ 0, there exists precisely one nontrivial solution.
(b) If sin(4L) = 0, then c2 is undefined and we have a family of solutions that differ by a constant multiple of sin(4x). Hence, there are infinitely many solutions.
(c) There is no solution if the boundary conditions are inconsistent, i.e., if y(0) ≠ y(L) = 1.
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GIVING BRAINLIEST AND MANY POINTS FOR CORRECT ANSWER!!
Let's say you decide to go for a walk. You start out at home and walk 500 meters total, making a few turns here and there. You stop for a moment and realize you have ended up only 100 meters east of where you started.
What distance did you travel?
What was your displacement?
Answer:
500 meters.
Step-by-step explanation:
to begin a bacteria study, a petri dish had 2800 bacteria cells. each hour since, the number of cells has increased by 3.3%. let t be the number of hours since the start of the study. let y be the number of bacteria cells. write an exponential function showing the relationship between y and t.
[tex]y = 2800(1.033)^t[/tex] is the exponential function for starting population of 2800 bacterium cells that is shown to multiply exponentially over time using this function, increasing by a factor of 1.033 every hour.
We can use an exponential function of the type y = abt to simulate the development of bacteria cells over time, where y stands for the number of cells, t for the number of hours, and a and b for constants that we must establish.
Since we now know there are 2800 bacterium cells, we can enter this number into the equation to obtain:
[tex]2800 = ab^0[/tex]
By simplifying this equation, we obtain a = 2800, which informs us that there are 2800 bacterium cells in the initial population.
We must use the knowledge that the number of cells rises by 3.3% every hour to get the value of b. By dividing this percentage growth by 100, we can convert it to a decimal, yielding a growth rate of 0.033. The value of b can then be obtained by multiplying this growth rate by 1:
b = 1 + 0.033 = 1.033
These values of a and b are what we obtain when we enter them into our exponential function:
[tex]y = 2800(1.033)^t[/tex]
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