Answer:
Let's call the speed of the bus on the winding road "s". Then we know that the bus traveled at a speed of "s + 20" on the level road. We also know that the time spent on the winding road was 4 hours, so the distance traveled on the winding road is:
distance = speed × time = s × 4
Similarly, the distance traveled on the level road is:
distance = speed × time = (s + 20) × 4
Since the entire trip was 400 miles, we can write:
4s + 4(s + 20) = 400
Simplifying this equation, we get:
8s + 80 = 400
8s = 320
s = 40
Therefore, the speed of the bus on the winding road was 40 mph, and the speed on the level road was 40 + 20 = 60 mph.
To check that this solution is correct, we can calculate the distance traveled on each road:
distance on winding road = 40 × 4 = 160 miles
distance on level road = 60 × 4 = 240 miles
The total distance traveled is indeed 160 + 240 = 400 miles, so our solution is correct.
Therefore, the average speed on the level road was 60 miles per hour.
In one of the rental parking lots at rent-and-save auto, there are 5 trucks, 9 cars, and 1 van. What is the probability that a randomly selected vehicle from this lot would be a car?
The probability of selecting a car from the rental parking lot is 0.6 or 60%.
What is a probability?Probability of selection refers to the likelihood or chance of selecting a particular item or event from a group or population. It is a mathematical concept used in statistics, mathematics, and science to describe the likelihood of an event occurring, given the set of possible outcomes.
The probability of selecting a car from the rental parking lot can be found by dividing the number of cars by the total number of vehicles:
P(Car) = Number of Cars / Total Number of Vehicles
In this case, there are 5 trucks, 9 cars, and 1 van, so the total number of vehicles is:
Total Number of Vehicles = 5 + 9 + 1 = 15
Number of Cars = 9
Therefore, the probability of selecting a car from the rental parking lot is:
P(Car) = Number of Cars / Total Number of Vehicles
= 9 / 15
= 3 / 5
= 0.6
So the probability of selecting a car from the rental parking lot is 0.6 or 60%.
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1. In his closet, John has one red shirt, one blue shirt, one pair of shorts, one pair of jeans, and a pair of
slacks. List all of the possible shirt-and-pant combinations below. -(4 points)
Since he has two shirts, and only 3 pants the possible number of combination would be 2 x 3 = 6
2. John discovered that he also has a pair of boots and a pair of dress shoes in his closet. Make a tree
diagram showing all of the possible shirt, pant, and shoe combinations. (4 points)
3. Jenny has six tlouses, four different skirts, 20 different pairs of socks, and four pairs of shoes in her
closet at the end of the week.
Part 1: Explain why the methods used in the previous two problems would be inefficient in
determining the number of different outfits Jenny could wear (2 points)
The total number of possible outcomes of shirt and pants are
Red shirt and shorts
Red shirt and jeans
Red shirt and slacks
Blue shirt and shorts
Blue shirt and jeans
Blue shirt and slacks
Given data ,
John has one red shirt, one blue shirt, one pair of shorts, one pair of jeans, and a pair of slacks
Now , total number of possible outcomes of shirt and pants are
A = 2 x 3 = 6 outcomes
Red shirt and shorts
Red shirt and jeans
Red shirt and slacks
Blue shirt and shorts
Blue shirt and jeans
Blue shirt and slacks
Hence , the possible outcomes are solved
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Y=2X squared -12 X +20 for quadratic formula
x = (12 ± √(-16)) / 4,The solutions would be complex numbers.
What is the quadratic formula?To solve quadratic equations of the form ax2 + bx + c = 0, use the quadratic formula. For this situation, your condition is as of now as a quadratic condition, with a = 2, b = - 12, and c = 20.
The quadratic formula is:
x = (-b ± √[tex](b^2 - 4ac)[/tex]) / 2a
Plugging in the values for a, b, and c, we get:
x = (-(-12) ± √[tex]((-12)^2 - 4(2)(20)))[/tex] / 2(2)
Simplifying the expression inside the square root:
x = (12 ± √[tex](144 - 160)[/tex]) / 4
x = (12 ± √(-16)) / 4
Since the square foundation of a negative number is definitely not a genuine number, this condition has no genuine arrangements. Complex numbers would provide the answers.
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Meghan is spending money at a constant rate. Suppose she initially has $1100, and after 4 months, she has $720.
Express the rate at which Meghan's amount of money is changing.
95$
Step-by-step explanation:
Based on the given conditions, formulate ( 1100 - 720 ) ÷ 4
Calculate the sum or difference = 380/4
Cross out the common factor = 95
PLEASE HELP
The scatter plot shows the time spent studying, X, and the midterm score, y, for each of 25students.
Time spent studying (in hours)
Use the equation of the line of best fit, y=3.84×+16.64, to answer the questions below.
Give exact answers, not rounded approximations.
(a) For an increase of one hour in the time spent studying,
what is the predicted increase in the midterm score?
(b) What is the predicted midterm score for a student who
doesn't spend any time studying?
(c) What is the predicted midterm score for a student who
studies for 12 hours?
Which is the graph of f(x) = -(x+3)(x + 1)?
Using functions, we can find that the given equation is a quadratic equation so, the graph will be a parabola.
Option B is correct.
How to graph a function?Simple functions like linear and quadratic functions are simple to graph. The fundamental concept behind graphing functions is to locate the shape, if at all possible. A line would be the graph of a linear function of the type f(x) = axe + b, for instance; a parabola would be the graph of a quadratic function of the form f(x) = ax² + bx + c.
By replacing some random x values into the function, one can locate some spots on it by determining the corresponding y values for each value.
Here in the question,
Given equation will be:
-(x+3)(x + 1)
Solving it we get:
= -x² -x + 3x + 3
= -x² + 2x + 3
So, graph for this function will be a parabola as the function is a quadratic function.
Therefore, the graph of the function will be the 2nd graph. Option B is correct.
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Surface area of the shape
The total surface area of diagram is 119.1 unit
Define rectangular pyramid?A rectangular pyramid is a three-layered strong item that comprises of a rectangular base and four three-sided faces that meet at a typical point, called the summit.
In the figure below is a cuboid and upside is Square Pyramid;
Surface area of cuboid = 2 (l×h + l×w+ h×w)
Surface area of cuboid = 2 (6×3 + 6×3+ 3×3) = 2 (18+18+9)
Surface area of cuboid = 90 unit²
The slant height is the hypotenuse of a right triangle whose height is 3 inches and half the base of the triangular (3/2 = 1.5 inches). Using the Pythagorean theorem,
slant height = [tex]\sqrt{3^2 + 1.5^2}[/tex] [tex]= \sqrt{11.25}[/tex]
slant height = 3.35 unit
Surface Area of a Square Pyramid = base² + 2×base×slant height
Surface Area of a Square Pyramid = 3² + 2×3×3.35
Surface Area of a Square Pyramid = 9 + 20.1
Surface Area of a Square Pyramid = 29.1 unit²
The total area of these two faces = Surface area of cuboid + Surface area of pyramid.
The total Surface area = 90 + 29.1 = 119.1 unit²
Therefore total area of diagram is 119.1 unit²
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A box contains 10 balls that each have a dollar amount on them. A person is charged $10 to randomly choose a ball. The person will receive the amount of money that is on the ball. In the box, there are 5 balls with $1, 2 with $2, and 3 balls with $30.
Find the expected value of this game.
$0.10
$0.50
$9.50
$11.00
Answer:
A I'm pretty sure
Step-by-step explanation:
To find the expected value, we need to multiply each possible outcome by its probability and add up the results.The probability of drawing a ball with $1 is 5/10 = 0.5.
The probability of drawing a ball with $2 is 2/10 = 0.2.
The probability of drawing a ball with $30 is 3/10 = 0.3.
The expected value is:
(0.5 * 1) + (0.2 * 2) + (0.3 * 30) = 0.5 + 0.4 + 9 = 9.9
However, the person paid $10 to play, so we need to subtract that from the expected value:9.9 - 10 = -0.1
Therefore, the expected value of this game is -$0.10. Answer choice (A) is correct.
Answer: $9.50
Step-by-step explanation:
r x 24 = 161
what is the answer
Answer:are you trying to solve for R or? sorry if im wrong i have hard time paying attention in math
Step-by-step explanation:
if you are the answer is in exact form its r= 161/24 in decimal form its r=6.7083 and in mixed number form its r= 6 17/24
Magdalene creates the scale drawing shown of a rectangular field.
7.2 cm
Scale
1 cm = 4.5m
3 cm
What is the area, in square meters (m²), of the actual field?
The scale of the drawing is 1 cm = 4.5 m. This means that each centimeter in the drawing represents 4.5 meters in the actual field. The length of the field in the drawing is 7.2 cm, so the actual length of the field is 7.2 cm × 4.5 m/cm = 32.4 m. The width of the field in the drawing is 3 cm, so the actual width of the field is 3 cm × 4.5 m/cm = 13.5 m. The area of a rectangle is found by multiplying its length by its width, so the area of the actual field is 32.4 m × 13.5 m = 437.4 m²
Note :- I'm sorry to bother you but can you please mark me BRAINLEIST if this ans is helpfull
IQ test scores are normally distributed with a mean of 99 and a standard deviation of 11. An individual's IQ score is found to be 128. Find the z-score corresponding to this value.
According to the given data the z-score corresponding to an IQ score is [tex]2.64[/tex].
What do you mean by z-score?A z-score (or standard score) is a measure of how many standard deviations an observation or data point is away from the mean of its distribution.
It is calculated by subtracting the mean of the distribution from the observed value, and then dividing the difference by the standard deviation of the distribution.
Given ; Data in the problem
∴μ[tex]= 99[/tex] , σ[tex]= 11[/tex] , [tex]x = 128[/tex]
so, z - score =( [tex]x -[/tex]μ)/σ
[tex]\frac{(128-99)}{11} \\=\frac{29}{11} \\= 2.64[/tex]
Therefore the z-score corresponding to an IQ score of [tex]128[/tex] is approximately [tex]2.64[/tex]
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how to plot 4x-5y less than equal to -15
The answer of the given question based on the plotting graph , the steps are given below .
What is Inequality?An inequality is a statement that compares two values or expressions and indicates that one is greater than, less than, or equal to the other. Inequalities can be solved or simplified using various algebraic techniques, such as adding, subtracting, multiplying, or dividing both sides by the same quantity, or factoring and finding the roots of the expressions
To plot the inequality 4x - 5y ≤ -15, you can follow these steps:
First, rearrange the inequality to solve for y:4x - 5y ≤ -15
-5y ≤ -4x - 15
y ≥ (4/5)x + 3
This gives you the equation of the boundary line. Plot this line on a graph by plotting two points and drawing a straight line through them. To plot the line, you can choose any two values of x and find the corresponding values of y using the equation.Let's choose x = 0 and x = 5.
When x = 0: y = (4/5)(0) + 3 = 3, so one point is (0, 3).
When x = 5: y = (4/5)(5) + 3 = 7, so another point is (5, 7).
Plot these two points and draw straight line through them.
Now, to shade the region that satisfies the inequality, choose a point that is not on the boundary line. The easiest point to choose is (0,0). Substitute x and y values of this point into inequality.4x - 5y ≤ -15
4(0) - 5(0) ≤ -15
0 ≤ -15
Since this is not true, the point (0,0) is not in the region that satisfies the inequality. Shade the region above the boundary line to show the region that satisfies the inequality.
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This is untrue since the point (0,0) is not located in the area where the inequality is satisfied. To highlight the area that satisfies the inequality, shade the area above the boundary line.
What is Inequality?An inequality is a comparison that shows that one value or expression is larger than, less than, or equal to another. Different algebraic methods, such as adding, subtracting, multiplying, or dividing both sides by the same amount, or factoring and determining the roots of the equations, can be used to resolve or simplify inequalities.
Plotting the inequality 4x - 5y ≤-15 can be done by doing the following:
To solve for y, rearrange the inequality first:
4x - 5y ≤ -15
-5y ≤ -4x - 15
y ≥ (4/5)x + 3
You are then provided with the boundary line's equation. Plot two points on a graph, then draw a straight line through them to represent this line. You can use the equation to determine the values of y that correspond to any two x values to plot the line.
Let's choose x = 0 and x = 5.
When x = 0: y = (4/5)(0) + 3 = 3, so one point is (0, 3).
When x = 5: y = (4/5)(5) + 3 = 7, so another point is (5, 7).
Plot these two spots and a line should be drawn directly between them.
Now select a point that is not on the border line to shade the area that satisfies the inequality. (0, 0) is the simplest position to select. In the inequality, replace the x and y values of this point.
4x - 5y ≤ -15
4(0) - 5(0) ≤ -15
0 ≤ -15
Since this is untrue, the point (0,0) is not located in the area where the inequality is satisfied. To highlight the area that satisfies the inequality, shade the area above the boundary line.
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Need your help guys
Based on the information, we lack credible evidence to assume an association between a student's academic success and if they are either a boarder or day student at a significance level of 0.05.
How to explain the hypothesisThe statistic for the chi-square test is given as follows:
X² = ∑ [(observed value - expected value)² / expected value]
Through employing a significance level of 0.05, accompanied by 1 degree of freedom (due to two categories and three degrees of performance), the critical value for the chi-square distribution is calculated at 3.84.
The computed chi-square test statistic is measured to be:
X² = [(130-147.43)²/147.43] + [(180-195.57)²/195.57] + [(240-222.57)²/222.57] + [(305-289.43)²/289.43] + [(100-111.43)²/111.43] + [(200-188.57)²/188.57]
X² = 5.61
Given that 5.61 is lower than 3.84, we dismiss the null hypothesis. Ultimately, we lack credible evidence to assume an association between a student's academic success and if they are either a boarder or day student at a significance level of 0.05.
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Find the surface area
Will give branliest
The surface area of the square base pyramid is 138 inches².
How to find the surface area of a pyramid?The pyramid above is a square base pyramid. The surface area of the pyramid can be calculated as follows:
Therefore,
surface area of the pyramid = base area + 2al
where
a = base lengthl = height of the pyramidTherefore,
a = 6 inches
l = 8.5 inches
Hence,
base area = 6² = 36 inches²
a = 6 inches
l = 8.5 inches
Therefore,
surface area of the pyramid = 36 + 2 × 6 × 8.5
surface area of the pyramid = 36 + 102
surface area of the pyramid = 138 inches²
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Carla and Hattie are playing a game and trying to decide who will start first. Which method assures that each of them has a fair chance of being selected to go first? Flip a fair coin. If it lands on heads, Carla will go first. If it lands on tails, Hattie will go first. Create a spinner with four equal-sized regions. Color each region a different color: red, green, blue, and purple. If the spinner lands on red, Carla will go first. If the spinner lands on green, Hattie will go first. If the spinner lands on blue, Carla will go first. If the spinner lands on purple, spin again. Roll a number cube with numbers from 1 to 6. If the number rolled is greater than 4, Carla will go first. Otherwise, Hattie will go first. Draw a card from an ordinary deck of 52 playing cards. If the drawn card is a club, Hattie will go first. If the drawn card is a diamond, Carla will go first. If the drawn card is a heart, Hattie will go first. If the drawn card is a spade, draw again.
The selection method that assures a fair chance of being selected to go first between Carla and Hattie is A) Flip a fair coin. If it lands on heads, Carla will go first. If it lands on tails, Hattie will go first.
What is a fair chance?A fair chance is based on an equal probability of being selected.
A fair coin of head and tail offers a fair chance to two contenders on who should play the game first.
In this situation, since Carla gets the heads, he has 50% chance of being selected to go first.
Equally, Hattie has a 50% chance to go first getting the tails.
Thus, the correct selection method is Option A.
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The length of a rectangurlar frame is 15 inches and the width of the frame is 8 inches what is the length of the frame
the correct length of the frame is 17 inches.
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees. Area of rectangle is A = a*b
Based on the information given, it should be noted that the diagonal will be the longest side. Therefore, we'll use the Pythagoras theorem to solve the question.
This will be:
d² = 15² + 8²
d² = 225 + 64
d² = 289
d = ✓289
d = 17
Therefore, the correct option is 17 inches.
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there are 40 students in ms. vitales wednesday night aerobics class of the 40 students 30% are african american 45% are caucasian and the rest are hispanic how many of the students in the aerobics class are hispanic
Hence ,10 Hispanic students in Ms. Vitals Wednesday night aerobics class.
What is the aerobics class?Aerobics is a form of physical exercise that combines rhythmic aerobic exercise with strength and stretching training routines with the goal of improving all elements of fitness ( cardio-vascular fitness, flexibility and muscular strength ).
How to find percentage?The percentage can be found by dividing the value by the total value and then multiplying the result by 100. The formula used to calculate the percentage is: [tex]\frac{value}{total value}[/tex]×100%.
To find out how many of the students in Ms. Vitals aerobics class are Hispanic,
first of all to determine the percentage of students are not African American or Caucasian.
The percentage of students are African American is 30%, and the percentage are Caucasian is 45%. Therefore, the percentage of students are not African American or Caucasian is;
100% - 30% - 45% = 25%
So, 25% of the students in the aerobics class are Hispanic.
To find the number of students are Hispanic, we need to calculate 25% of the total number of students;
25% of 40 students = [tex]\frac{25}{100}[/tex] x 40 = 0.25×40=10 students
Therefore, there are 10 Hispanic students in Ms. Vitals Wednesday night aerobics class.
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According to a poll, 80% of Americans report being afflicted by stress. Suppose a random sample of 1,200 Americans is selected. Complete parts (a) through (d) below.
a. What percentage of the sample would we expect to report being afflicted by stress?
The percentage of the sample selected at random that would be expected to be afflicted by stress would also be = 80%
How to calculate the percentage afflicted by stress?The percentage of a data set is when part of the data is represented per 100 with a symbol of %.
It was stated in the question that 80% of Americans report being afflicted by stress.
Therefore when a sample is randomly selected from an American population, the percentage that is expected to be afflicted by stress should also be 80%.
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Suppose you work for a company that manufactures electronics. The development analysts estimate that 1% of their flagship product will fail within 2 years of the purchase date, with a replacement cost of $ 1300.
A newly hired associate at the company proposes to charge $ 5 for a 2 year warranty.
The company can expect to earn $5 per product sold if they offer a warranty, compared to an expected loss of $13 per product sold if they do not offer a warranty. It is a profitable decision for the company to offer the warranty.
What is binomial distribution?In a binomial probability distribution, the number of "Successes" in a series of n experiments is represented as either success/yes/true/one (probability p) or failure/no/false/zero (probability q = 1 p), depending on the outcome's boolean value.
Assuming that the failure of the flagship product follows a binomial distribution with a probability of 1% of failure within 2 years of purchase, let's calculate the expected cost to the company without a warranty and with the warranty.
Without the warranty, the expected cost to the company is given by:
Expected cost without warranty = 0.01 x $1300 = $13
With the warranty, the expected cost to the company is given by:
Expected cost with warranty = $5 - (0.99 x $0) = $5
Therefore, the company can expect to earn $5 per product sold if they offer a warranty, compared to an expected loss of $13 per product sold if they do not offer a warranty. It is a profitable decision for the company to offer the warranty.
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A group of friends decided to go out of town to a championship football game. The group pays $85 per ticket plus a one-time convenience fee of $35. They also pay $26 each to ride a tour bus to the game. If the group sent $3,587 in total, how many friends are in the group?
Answer: The group size is 32 friends.
Step-by-step explanation:
We will consider the total number of friends as x
The total expenditure can be broken down into the following equation:
85*x + 35 + 26*x = 3587
111x = 3587-35
111x = 3552
x = 3552/111
x = 32
Please help me with this due tomorrow
Answer:
Step-by-step explanation:
you have to match the numbers on the lines of the plane, they have to match up with each other it goes (x,y) the x line is the one going to the side, and the y is the one going up to down
The plane region is revolved completely about the x-axis to sweep out a solid of revolution. Find its volume in terms of PI .
The correct answer is C. 320×pi
How to solveWhat occurs when something is rotated around a pole? What kind of shape is the point closest to the pole making?
Obviously, a circle.
that means rotating the rectangle around the x-axis creates a round object (with the bottom area being a circle).
so, all answers about a prism (rectangular bottom shape) are automatically wrong.
again, just imagine to rotate a small sheet of paper around a pole (the x-axis acts like one in this scenario).
the result is solid with a circular bottom area, and it maintains this shape all the way to the top.
it is a cylinder!
and what is its radius?
well, the outermost point of the rectangle is 8 points away from the x-axis. when we rotate this rectangle, that attribute remains, of course. and every point on the side surface of the resulting cylinder has the same distance from the central x-axis : 8.
so, the radius is 8.
and the volume of a cylinder is
ground area × height = pi×r² × height
in our case
pi×8² × 5 (the width or "height" of the rectangle) = pi×64 × 5 = 320×pi
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Natalia paid $40 for 4 t-shirts and a necklace.
If Natalia paid $12 for the necklace, how much did each shirt cost?
If Natalia paid $12 for the necklace, then Each t- shirt cost $7.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit.
We are given that Natalia paid $40 for 4 t-shirts and a necklace.
If Natalia paid $12 for the necklace, then;
We need to find the cost of each shirt.
Therefore,
cost of 4 t- shirt + 1 neclace = 40
40 - 12 = 28
Cost of 4 t- shirt = 28
Cost of 1 t- shirt = 28/4 = 7
Hence, the cost of each t shirt is $7.
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A bank account earns 4.1% APR compounded monthly. Find the doubling time of the account.
It would take 211 months for the bank account to double in value at a 4.1% APR compounded monthly.
What is the doubling time of the account?We are going to use the rule of 72 which states that the number of years it takes for an investment to double is approximately equal to 72 divided by the annual interest rate.
The annual interest rate is 4.1% compounded monthly.
Monthly interest rate = 4.1% / 12
Monthly interest rate = 0.0034166667
Now we can use the rule of 72:
Doubling time = 72 / (0.0034166667 x 100)
Doubling time = 210.731705261
Doubling time = 211 months.
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Solve the following equation for x, giving your answer in the form lnp/lnq
2 × 5^(3x+2) = 6 x 7^(1-2x)
Answer:
[tex]x=\dfrac{\ln \left(\frac{21}{25}\right)}{\ln 6125}[/tex]
Step-by-step explanation:
Given equation:
[tex]2 \cdot 5^{3x+2} = 6 \cdot 7^{1-2x}[/tex]
Divide both sides of the equation by 2:
[tex]\implies 5^{3x+2} = 3 \cdot 7^{1-2x}[/tex]
Take natural logs of both sides:
[tex]\implies \ln \left(5^{3x+2}\right) = \ln \left(3 \cdot 7^{1-2x}\right)[/tex]
[tex]\textsf{Apply the product law:} \quad \ln xy=\ln x + \ln y[/tex]
[tex]\implies \ln 5^{3x+2} = \ln 3 + \ln 7^{1-2x}[/tex]
[tex]\textsf{Apply the power law:} \quad \ln x^n=n \ln x[/tex]
[tex]\implies (3x+2)\ln 5 = \ln 3 + (1-2x)\ln7[/tex]
Expand:
[tex]\implies 3x\ln 5+2\ln 5=\ln 3+\ln7-2x\ln7[/tex]
Collect the terms in x on the left side and the constants on the right side of the equation:
[tex]\implies 3x\ln 5+2x\ln7=\ln 3+\ln7-2\ln 5[/tex]
Factor out the common term x on the left side:
[tex]\implies x(3\ln 5+2\ln7)=\ln 3+\ln7-2\ln 5[/tex]
[tex]\textsf{Apply the power law:} \quad n \ln x=\ln x^n[/tex]
[tex]\implies x(\ln 5^3+\ln7^2)=\ln 3+\ln7-\ln 5^2[/tex]
Simplify:
[tex]\implies x(\ln 125+\ln 49)=\ln 3+\ln7-\ln 25[/tex]
[tex]\textsf{Apply the product law:} \quad \ln x + \ln y=\ln xy[/tex]
[tex]\implies x(\ln (125 \cdot 49))=\ln (3\cdot 7)-\ln 25[/tex]
[tex]\implies x(\ln 6125)=\ln 21-\ln 25[/tex]
[tex]\textsf{Apply the quotient law:} \quad \ln x - \ln y=\ln \left(\dfrac{x}{y}\right)[/tex]
[tex]\implies x(\ln 6125)=\ln \left(\dfrac{21}{25}\right)[/tex]
Divide both sides of the equation by ln 6125:
[tex]\implies x=\dfrac{\ln \left(\frac{21}{25}\right)}{\ln 6125}[/tex]
A rectangular prism has a surface area is 484 square centimeters and the edge lengths are consecutive integers. Determine the longest segment that can be drawn to connect two vertices.
The longest segment that can be drawn to connect two vertices is 10 cm
Determining the longest segment that can be drawn to connect two vertices.From the question, we have the following parameters that can be used in our computation:
A rectangular prism has a surface area is 484 square centimeters The edge lengths are consecutive integers.Represent the smallest length with x
So, we have
SA = 2 * (x(x + 1) + x(x + 2) + (x + 1)(x + 2))
Substitute the known values in the above equation, so, we have the following representation
2 * (x(x + 1) + x(x + 2) + (x + 1)(x + 2)) = 484
So, we have
(x(x + 1) + x(x + 2) + (x + 1)(x + 2)) = 242
When solved using a graph, we have
x = 8
So, we have
Longest edge = 8 + 2
Longest edge = 10
Hence, the longest segment that can be drawn to connect two vertices is 10 cm
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4) Amy traveled to the recycling plan
back. It took one hour less time to get
there than it did to get back. The average
speed on the trip there was 50 km/h. The
average speed on the way back was 40
km/h. How many hours did the trip there
take?
The time taken by Amy to travel to the place was t = 4 hours.
What is average speed?A measure of average speed is the amount of distance travelled in a given amount of time. It is determined by dividing the overall mileage by the overall time required to cover that mileage.
In physics and other sciences, average speed is frequently employed to describe how objects move. For instance, it is possible to estimate how long it will take to go a certain distance or assess a car's fuel economy by looking at its average speed over a given distance. By dividing the whole distance travelled by the total time required, average speed may also be used to characterise the speed of an object that is moving at various speeds at different points along its path.
Let the time taken to get back = t + 1.
Now, it took one hour less time to get there thus time = t.
Now, average speed is given as:
average speed = total distance / total time
Substituting the values:
50 km/h = d / t
d = 50t .........(1)
40 km/h = d / (t + 1)
d = 40(t + 1)......(2)
Setting the value of d as equal we have:
50t = 40(t + 1)
50t = 40t + 40
10t = 40
t = 4
Hence, the time taken by Amy to travel to the place was t = 4 hours.
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Given that -6i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable.
f(x)=x^4-15x³ + 90x² - 540x + 1944
Answer:
Step-by-step explanation:
The Conjugate Roots Theorem states that imaginary roots come in pairs. If -8i is a root of the polynomial, then so is +8i.
If both -8i and +8i are factors, we rewrite them as (x + 8i) and (x - 8i) in factored form. Since imaginary terms aren't accepted, you can FOIL these to get a quadratic with no imaginary terms.
x2 - 8ix + 8ix - 64i2
Simplify. Replace i2 with -1 because √-1 = i
x2 - 64(-1)
x2 + 64
The quadratic x2 + 64 has roots -8i and 8i. You can use the quadratic formula to verify this.
Now, let's tackle the rest of the polynomial. If x2 + 64 is a factor of the polynomial
x4 + 10x3 + 85x2 + 640x + 1344, divide it out to see what is left. I will use long division of polynomials. Note, I am using the square root symbol as a division symbol.
x2 + 10x + 21
x2 + 64 √ (x4 + 10x3 + 85x2 + 640x + 1344)
x4 + 64x2
_____________
10x3 + 21x2
10x3 + 640x
__________
21x2 +1344
21x2 + 1344
___________
0
There is no remainder, meaning x2 + 64 went in evenly. The quotient left when we divide out x2 + 64 from
x4 + 10x3 + 85x2 + 640x + 1344 is x2 + 10x + 21. Factor the quotient to get (x + 7)(x + 3).
x4 + 10x3 + 85x2 + 640x + 1344 = (x2 + 64)(x + 7)(x + 3)
You can check this factored form by FOILing out, and you should get the original polynomial.
find the greatest common factor of
1/4n^2m^3,
5/20n^7m^8,
3/12n^2m^8
options are
n^3m^2
1/4 n^3m^2
n^2m^3
1/4 n^2m^3
To find the greatest common factor of these three terms, we need to factor each one and identify the highest power of each factor that is common to all three. Then, we can multiply those factors together to find the GCF.
Let's begin by factoring each term:
1/4n^2m^3 = (1/4) * n^2 * m^3
5/20n^7m^8 = (1/4) * n^7 * m^8
3/12n^2m^8 = (1/4) * n^2 * m^8
Now, we can see that each term has a common factor of 1/4, so we can factor that out:
1/4 * (n^2 * m^3)
1/4 * (n^7 * m^8)
1/4 * (n^2 * m^8)
To find the highest power of each factor that is common to all three terms, we need to look at the exponents. The highest power of "n" that is common to all three terms is 2, and the highest power of "m" that is common to all three terms is 3. Therefore, the GCF is:
1/4 * n^2 * m^3
This simplifies to:
n^2m^3/4
So, the correct option is (c) n^2m^3/4.
A display case is made of one rectangular prism stacked on top of a second rectangular prism. What is the volume of the display case? A.24 B.36 C.60 D.84,is it b right?
The volume of the display case is 60 + 120 = 180. The correct answer is B. 36.
What is volume?Volume is a measure of the three-dimensional space something occupies or contains. It is often expressed as a calculation of length x width x height. It can also refer to the amount of something, such as the volume of a liquid, or the amount of space a container holds. Volume is an important concept in mathematics, science, engineering, and many other fields. It is used to measure the size of a solid, liquid, or gas, and to quantify the amount of material in an object or a space.
The volume of a rectangular prism is determined by multiplying its length, width, and height. The volume of a display case made of one rectangular prism stacked on top of a second rectangular prism is equal to the sum of the volumes of each rectangular prism.
The volume of the first rectangular prism is 3 x 4 x 5 = 60.
The volume of the second rectangular prism is 4 x 5 x 6 = 120.
Therefore, the volume of the display case is 60 + 120 = 180. The correct answer is B. 36.
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