a moving company charges $250 to rent a truck and $0.40 for each mile driven. Mr. Lee paid a total of $314. Which equation can be used to find m, the number of miles he drove the moving truck?
In triangle ABC, a = 9, c = 5, and B = 120°. Find b2.
61
83.5
128.5
151
Answer:
The correct answer is 151.
Step-by-step explanation:
Given,
In triangle ABC,
BC = a = 9 unit,
AB = c = 5 unit,
m∠B = 120°,
We have to find : b² or AC²,
By the cosine law,
[tex]b^2=a^2+c^2-2ac cosB[/tex]
[tex]=9^2+5^2-2\times 9\times 5\times cos 120^{\circ}[/tex]
[tex]=81+25-90\times -0.5[/tex]
[tex]=81+25+45[/tex]
[tex]=151[/tex]
Hence, the value of [tex]b^2[/tex] is 151.
Answer:
Option D) [tex]b^2 = 151[/tex]
Step-by-step explanation:
We are given the following information in the question:
[tex]\triangle ABC\\\text{Side } a = 9\text{ units}\\\text{Side } c = 5\text{ units}\\\angle ABC = 120^{\circ}[/tex]
We have to find [tex]b^2[/tex]
The law of cosines state that if a, b and c are the sides of triangle and b is the side opposite to angle B, then,
[tex]b^2 = a^2 + c^2 - 2ac~\cos(B)[/tex]
Putting the values, we have,
[tex]b^2 = (9)^2 + (5)^2 - 2(9)(5)~\cos(120)\\\\b^2 = 81 + 25 - 90(-0.5)\\\\b^2 = 151[/tex]
Option D) [tex]b^2 = 151[/tex]
Choose all of the following that must be true for a random experiment to be binomial.
Select one or more:
A. On each trial, the event of interest either occurs or does not occur.
B. The trials are independent of one another and repeated under identical conditions.
C. The probability of occurrence is the same on each trial.
D. There is a fixed number of trials.
A binomial experiment has a fixed number of trials, all are independent and conducted under identical conditions. Only two results—success or failure—are possible with each trial, each having the same probability, fitting a binomial probability distribution.
Explanation:For a random experiment to be binomial, it must meet certain conditions. Firstly, there should be a fixed number of trials, denoted as 'n'. The results of these trials don't influence each other, meaning that the trials are independent. This signifies that the outcome of a trial, for example, the first one, does not affect the outcomes of the subsequent trials. Moreover, all these trials should be conducted under identical conditions.
In a binomial experiment, there are only two possible results, often referred to as 'success' and 'failure'. Each trial has the same probability of success, denoted as 'p'. The outcomes of a binomial experiment fit a binomial probability distribution. The random variable 'X' stands for the number of successful trials. The mean 'µ' is given by 'np', and the standard deviation 'o' by √npq. The probability of exactly 'x' successes in 'n' trials is P(X = x).
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The height of a grain of a cylindrical silo is is increasing at a constant rate of 4 feet per minute At what rate is the volume of grain in the cylinder if the radius of the silo is 10 feet?
Answer:
The rate of change of the volume of the cylinder when the radius is 10 ft is
[tex]\frac{dV}{dt}=400\pi \:{\frac{ft^3}{min} }[/tex]
Step-by-step explanation:
This is a related rates problem. A related rates problem is a problem in which we know the rate of change of one of the quantities (the height of a grain) and want to find the rate of change of the other quantity (the volume of grain in the cylinder).
The volume of a cylinder is given by
[tex]V=\pi r^2 h[/tex]
V and h both vary with time so you can differentiate both sides with respect to time, t, to get
[tex]\frac{dV}{dt}=\pi r^2 \frac{dh}{dt}[/tex]
Now use the fact that [tex]\frac{dh}{dt} = 4 \:{\frac{ft}{min} }[/tex] and [tex]r = 10 \:ft[/tex]
[tex]\frac{dV}{dt}=\pi (10)^2 \cdot 4\\\\\frac{dV}{dt}=100\cdot \:4\pi \\\\\frac{dV}{dt}=400\pi[/tex]
Write the point-slope form of the given line that passes through the points (0, -3) and (4, 1). Identify (x1, y1) as (0, -3). Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
The point slope form of the line has the following form:
y – y1 = m (x – x1)
The slope m can be calculated using the formula:
m = (y2 – y1) / (x2 – x1)
m = (1 - -3) / (4 – 0) = 1
So the whole equation is:
y – -3 = 1 (x – 0)
y + 3 = x
The polynomial 6x2 + 37x – 60 represents an integer. Which expressions represent integer factors of 6x2 + 37x – 60 for all values of x?
Answer with explanation:
The Given Quadratic Polynomial which can be Broken into integer factors:
[tex]\rightarrow 6 x^2 + 37 x - 60\\\\ \text{Splitting the Middle term}}\\\\ \rightarrow 6 x^2 + 37 x - 60\\\\\rightarrow 6 x^2 + 45 x-8 x - 60\\\\ \rightarrow 3x \times (2 x+15)-4 (2 x +15)\\\\\rightarrow (3 x -4)(2 x+15)[/tex]
Factors of the above Expression are:
= (3 x -4)(2 x+15)
A diver is descending to reach the bottom of a lake. After 15 seconds, she is 90 feet below the surface of the water. If positive integers represent a distance above the surface of the lake, which integer best represents the diver’s change in position in feet per second?
dive distance traveled by time
90 feet / 15 seconds = 6
since the diver is below the surface they are changing position at -6 feet per second
kamiko and her 4 sisters each have 18 grandchildren. calculate the total number of grandchildren of kamiko and her 4 sisters
The total number of grandchildren of Kamiko and her 4 sisters is 72.
Explanation:Kamiko and her 4 sisters each have 18 grandchildren. To calculate the total number of grandchildren, we will multiply the number of grandchildren per person by the total number of sisters.
Number of grandchildren per person: 18
Total number of sisters: 4
Therefore, the total number of grandchildren of Kamiko and her 4 sisters is 72.
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Use the given line below to answer parts 1 and 2. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
Part 1: Use the graph to count the slope of the line that passes through the points (2, 1) and (2, 0).
Part 2: In two or more complete sentences, explain why it is not possible to write the equation of the given line in the traditional version of the point-slope form of a line.
The formula for finding the slope of a line is expressed as:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Given the coordinate points (2, 1) and (2, 0). Get the slope of the line passing through the coordinate points
[tex]m=\frac{0-1}{2-2}\\m=\frac{-1}{0}\\m=\infty[/tex]
The equation of the line in point-slope form is [tex]y-y_0=m(x-x_0)[/tex]
Since the slope of a vertical line does not exist, hence the equation of the line cannot be written in point-slope form
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find the perimeter of the semi-circular region at leat one please
What is the degree of the polynomial
Xy^2 + 3x^2 - 7 + x
A) 2
B) 3
C) 1
D) 4
graph the equation 5x-4y=-18
A is an unknown number. When you round A to the nearest thousand you get 21000. When you round A to the nearest hundred you get 20,500
What is A
The unknown number A, when rounded to the nearest thousand and hundred, is determined to be within the range from 20500 to 20549. A can be any number within this range.
Explanation:In mathematics, when you're given that a number A, when rounded to the nearest thousand, ends up being 21000 or that when rounded to the nearest hundred, it ends up being 20500, you can infer that the unknown number A lies somewhere between two specific values. Since A rounds to 21000 when we round to the nearest thousand, this implies that A is between 20500 and 21499.
However, we also know that, when rounded to the nearest hundred, A is 20500. This implies that A is between 20450 and 20549. Comparing these two ranges, the unknown number A must lie within the common range, which is from 20500 to 20549. Therefore, the number A can be any number within this range.
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Belmond, a brick-cutter in a kiln, cuts 84 bricks in 3 hours. Find the unit rate.
Please Help!!
The unit rate at which Belmond cuts bricks is 28 bricks per hour, which is calculated by dividing the total number of bricks (84) by the total hours worked (3).
To find the unit rate of bricks cut per hour by Belmond, we simply divide the total number of bricks by the total time in hours. Belmond cuts 84 bricks in 3 hours, so the unit rate is:
Unit rate = Total bricks \/ Total time in hours
Unit rate = 84 bricks \/ 3 hours = 28 bricks per hour
This means that Belmond cuts 28 bricks every hour. When you need to find a unit rate, it is a matter of dividing the total quantity by the time it takes to accomplish that quantity, thus yielding the rate per single time unit (in this case, per hour).
6.41* 10^3 in standard form
Find the absolute minimum and absolute maximum values of f on the given interval. f(x) = x − ln 8x, [1/2, 2]
To find the absolute minimum and absolute maximum values of the function f(x) = x - ln 8x on the interval [1/2, 2], we find the critical points and evaluate the function at the endpoints and critical points. The absolute minimum value is f(1/2) = 1/2 - ln 4 and the absolute maximum value is f(2) = 2 - ln 16.
Explanation:To find the absolute minimum and absolute maximum values of the function f(x) = x - ln 8x on the given interval [1/2, 2], we need to find the critical points and the endpoints of the interval. First, we find the derivative of the function: f'(x) = 1 - 1/x. Then, we solve the equation f'(x) = 1 - 1/x = 0 to find the critical points. The critical point is x = 1. Next, we evaluate the function at the critical point and the endpoints of the interval to determine the absolute minimum and absolute maximum values.
1. Evaluating the function at the critical point: f(1) = 1 - ln 8
2. Evaluating the function at the endpoint x = 1/2: f(1/2) = 1/2 - ln 4
3. Evaluating the function at the endpoint x = 2: f(2) = 2 - ln 16
The absolute minimum and absolute maximum values of the function on the given interval are:
Absolute minimum value: f(1/2) = 1/2 - ln 4Absolute maximum value: f(2) = 2 - ln 16Learn more about Finding absolute minimum and maximum values here:https://brainly.com/question/34340601
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0.5,3/16,0.755/49 least to greatest
Find the slope of the line whose equation is 4y - 3x + 6 = 0.
Answer:
slope of the line will be [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
We have to find the slope of a given line whose equation is 4y - 3x + 6 = 0
If a line is in the form of y = mx + c
Then m represents slope of the line
4y - 3x + 6 = 0 [ Given equation ]
4y = 3x - 6
y = [tex]\frac{1}{4}[/tex] ( 3x-6 )
y = [tex]\frac{3}{4}x[/tex] - [tex]\frac{3}{2}[/tex]
Therefore, slope of the line will be [tex]\frac{3}{4}[/tex]
Mr. Green's sunflower grew 29 centimeters in one week. The next week it grew 5 centimeters more than the previous week. What is the total number of centimeters the sunflower grew in 2 weeks?
You drive 4 miles from your house to your friend's house. Your house is at an elevation of 622 feet. Your friend's house is at an elevation of 486 feet. What is the mean change in elevation per mile?
How many comparisons are needed for a binary search in a set of 64 elements?
A binary search in a set of 64 sorted items will, in the worst-case scenario, require 6 comparisons. This is calculated as log2(64) = 6. The binary search method works by repeatedly halving the search interval until it finds the desired item.
Explanation:In order to find out how many comparisons are needed for a binary search in a set of 64 elements, we need to understand how a binary search works. It's an efficient algorithm that finds an item from a sorted list by repeatedly dividing the search interval in half. Every time it analyzes the middle element, it either discards the half that it is sure does not contain the desired item, or determines that the middle element is the desired item.
With a set of 64 elements, a binary search would perform log2(64) or 6 comparisons, as the base-2 logarithm of 64 is 6. Therefore, the maximum number of comparisons necessary using a binary search to locate a particular item in a set of 64 elements is 6 comparisons.
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In a binary search of a 64 element set, the worst-case scenario requires 6 comparisons. This is determined by the base 2 logarithm of the number of elements.
Explanation:The number of comparisons in a binary search is governed by the logarithm base 2 of the number of elements in the set. With a set of 64 elements, the worst case scenario for the number of comparisons needed would be log2(64) which equals 6. This is because a binary search works by repeatedly dividing the searchable set in two until it finds the desired element, making it a very efficient search algorithm.
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I scream for ice cream sells specialty ice cream in three flavors: rocky road, peanut butter, and fruity tooty. it sold 19 comma 00019,000 gallons last year. for every five gallons of ice cream sold, one gallon is fruity tooty and the remainder is split evenly between peanut butter and rocky road. fixed costs for i scream for ice cream are $ 27 comma 500$27,500 and additional information follows: rocky road peanut butter fruity tooty sales price per gallon $ 5.25$5.25 $ 5.75$5.75 $ 8.25$8.25 variable cost per gallon $ 3.5$3.5 $ 5$5 $ 2.25$2.25 the breakeven sales volume in gallons for i scream for ice cream is
The circumference of a circular hot tub at a hotel is 56.5 yards. What is the diameter of the hot tub?
To find the diameter of the circular hot tub, divide the circumference by π.
Explanation:To find the diameter of the circular hot tub, we need to use the formula for the circumference of a circle. The formula is C = πd, where C represents the circumference and d represents the diameter.
In this case, the circumference is given as 56.5 yards. So we can plug that value into the formula and solve for d: 56.5 = πd.
To isolate the variable d, we divide both sides of the equation by π. This gives us: d = 56.5/π.
Using a calculator, we can find the approximate value of d to be 18 yards.
The diameter of the hot tub is approximately 18 yards, calculated using the formula [tex]\(D = \frac{56.5}{\pi}\)[/tex] from the given circumference.
The circumference of a circle is given by the formula [tex]\(C = \pi \times D\)[/tex], where C is the circumference and D is the diameter. In this case, the circumference of the hot tub is given as 56.5 yards. So, the formula can be rearranged to solve for the diameter:
[tex]\[ C = \pi \times D \][/tex]
[tex]\[ 56.5 = \pi \times D \][/tex]
To find D, divide both sides of the equation by [tex]\(\pi\)[/tex]:
[tex]\[ D = \frac{56.5}{\pi} \][/tex]
Using the value of [tex]\(\pi \approx 3.14159\)[/tex], the diameter D is approximately:
[tex]\[ D \approx \frac{56.5}{3.14159} \approx 18 \][/tex]
Therefore, the diameter of the hot tub is approximately 18 yards.
X+y-2z=5
-x+2y+z=2
2x+3y-z=9
The solution to the system of equations is x = 1, y = 2, and z = -1.
The given system of equations is:
1. x + y - 2z = 5
2. -x + 2y + z = 2
3. 2x + 3y - z = 9
We can solve this system using various methods such as substitution, elimination, or matrices. Let's use the elimination method to solve this system:
1. Add equations (1) and (2):
(x + y - 2z) + (-x + 2y + z) = 5 + 2
x - x + y + 2y - 2z + z = 7
3y - z = 7 (Equation 4)
2. Multiply equation (2) by 2 and add it to equation (3):
2(-x + 2y + z) + (2x + 3y - z) = 2 × 2 + 9
-2x + 4y + 2z + 2x + 3y - z = 4 + 9
7y + z = 13 (Equation 5)
Now we have equations (4) and (5):
4. 3y - z = 7
5. 7y + z = 13
Let's solve this system by adding equations (4) and (5):
(3y - z) + (7y + z) = 7 + 13
3y + 7y = 20
10y = 20
y = 2
Now that we have found y = 2, we can substitute this value into either equation (4) or equation (5) to solve for z.
Let's use equation (4):
3(2) - z = 7
6 - z = 7
-z = 7 - 6
-z = 1
z = -1
Now that we have found y = 2 and z = -1, we can substitute these values into any of the original equations to solve for x.
Let's use equation (1):
x + 2 - 2(-1) = 5
x + 2 + 2 = 5
x + 4 = 5
x = 5 - 4
x = 1
Complete Question may be:
Solve the system of equations:
x + y - 2z = 5
-x + 2y + z = 2
2x + 3y - z = 9
Find the first and second derivatives of the function y = sin(x^2)
A softball player hits the ball. The height of the ball h (in feet) at any time t seconds after the hit will be represented by the quadratic function h(t)=42t‒6t2. Use what you have learned about the zeros of a quadratic function to determine which of the following statements is true.
A. The ball will reach the ground in 3.5 seconds.
B. The ball will get to its highest point in 7 seconds.
C. The ball will stay in the air for a total of 7 seconds.
D. The highest the ball will go is about 7 feet.
To fit in an existing frame, the length, x, of a piece of glass must be longer than 12 cm but not longer than 12.2 cm. Which inequality can be used to represent the lengths of the glass that will fit in the frame?
Calculate all four second-order partial derivatives of f(x,y)=sin(2xy)
in a certain town, 10% of people commute to work by bicycle. if a person is selected randomly from the town, what are the odds against selecting someone who commutes by bicycle?
The odds against selecting a person who commutes by bicycle from a town where 10% of people commute that way would be 9 to 1. This is based on the percentage of people who do not commute by bicycle versus those who do.
Explanation:In statistical terms, the question is asking us to calculate the odds against selecting someone who commutes by bicycle. With 10% of people in this town commuting by bicycle, it means that 90% of them do not. Therefore, the odds against selecting someone who commutes by bicycle are 90 to 10 or 9 to 1.
This is calculated by dividing the number of unsuccessful outcomes (people not commuting by bicycle - 90%) by the number of successful outcomes (people commuting by bicycle - 10%). This gives us the odds against selecting someone who commutes by bicycle.
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712 divided by 8 and show work