1. use the quadratic equation to find the exact solutions to this equation, and simplify your answer: 2x^2 6x 12
As per the given statement, the quadratic equation is to be used to find the exact solutions to this equation, and the quadratic equation is given by [tex]ax² + bx + c = 0[/tex].
To solve the quadratic equation, we can use the quadratic formula given by[tex]x = (-b ± sqrt(b² - 4ac)) / 2a[/tex] Where x is the variable, a, b, and c are coefficients with a ≠ 0, and sqrt is the square root symbol.To find the exact solutions to this equation, we can use the quadratic formula with a = 2, b = 6, and c = 12.
Substituting these values in the quadratic formula, we get
[tex]x = (-6 ± sqrt(6² - 4 × 2 × 12)) / 2 × 2= (-6 ± sqrt(36 - 96)) / 4= (-6 ± sqrt(-60)) / 4= (-6 ± i√60) / 4= (-3 ± i√15) / 2[/tex]
Hence, the exact solutions to the given equation are [tex](-3 + i√15) / 2 and (-3 - i√15) / 2.[/tex]
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x^2-3x-40=0 solve for x
Answer:
Step-by-step explanation:
x^2-3x-40=0
x^2-3x=40
2x-6x=40
-4x=40
-4x/4 = 40/-4
x= -10
Answer:
x=8 or x=-5
Step-by-step explanation:
x²-3x-40=0
x²-8x+5x-40=0
x(x-8)+5(x-8)=0
(x-8)(x+5)=0
⇒x=8 or x=-5
PACKAGING A video game system is packaged in a box that is in the shape of a cube. The length of the packaging box is 4x^2 y^5 . What is the volume of the packaging box in terms of x and y?
Answer: 64x^6y^15
Step-by-step explanation:
If the packaging box is in the shape of a cube, then all its sides are equal in length. Let's call the length of each side "s".
We know that the length of the packaging box is 4x^2 y^5, so:
s = 4x^2 y^5
To find the volume of the packaging box, we need to calculate s^3 (since the box is a cube).
s^3 = (4x^2 y^5)^3
s^3 = 4^3 (x^2)^3 (y^5)^3
s^3 = 64x^6 y^15
Therefore, the volume of the packaging box in terms of x and y is 64x^6 y^15.
A scientist measures the amount of water collected in a tub at different times during the day. The table shows the time the water had been running and the amount of water in the tub.
Based on the information in the table, write an equation that can be used to find t, the number of minutes it took to collect w liters of water in the tub.
As a result, the following equation can be used to determine t, or how many minutes it took to fill the tub with w liters of water: t = (w - 0.2) / 0.4
what is slope ?Slope is a unit used to describe how steep or slope a line is. The ratio of the vertical change (rise) to the horizontal change (run) between any two locations on the line is what is referred to as the slope. In other words, the slope of the line going through the two points (x1, y1) and (x2, y2), which are on a line, is given by: Slope is equal to y2 - y1 / x2 - x1. Positive, negative, zero, or undefinable slopes are all possible.
given
With the slope and y-intercept in hand, we can now write the line's equation:
y = 0.4x + 0.2
Given a value for y, we wish to find a solution to this equation for x. In this instance, we're looking for t, or how many minutes it took to fill the tub with w liters of water. We can solve for x by substituting w for y:
w = 0.4t + 0.2
0.4t = w - 0.2
t = (w - 0.2) / 0.4
As a result, the following equation can be used to determine t, or how many minutes it took to fill the tub with w liters of water: t = (w - 0.2) / 0.4.
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Prove that the following statement is false. There exists an integer n such that 6n2 + 27 is prime. To prove the statement is false, prove the negation is true. Write the negation of the statement. For every integer n, 6n² + 27 is prime. For every integer n, 6n2 + 27 is not prime. There exists an integer n, such that 6n2 + 27 is not prime. There exists a composite number q = 6n2 + 27, such that n is an integer. There exists an integer n, such that 6n2 + 27 is prime. Now prove the negation. Suppose n is any integer. Express 6n2 + 27 as the following product: 6n2 + 2 Now is an integer because sums and products of integers are integers. Thus, 6n2 + 27 is not prime because it is a
The negation of the statement "There exists an integer n such that 6n2 + 27 is prime" is "For every integer n, 6n2 + 27 is not prime."
To prove the negation, we can use algebraic manipulation to show that 6n2 + 27 is always composite.
Suppose n is any integer. We can factor out 3 from 6n2 + 27 to get 3(2n2 + 9). Since 2n2 + 9 is always odd (2 times any integer is even, and adding 9 makes it odd), we can further factor it as (2n2 + 9) = (2n2 + 6n + 9 - 6n) = [(2n+3)(n+3)] - 6n.
Substituting this expression back into 3(2n2 + 9), we get 3[(2n+3)(n+3) - 6n]. Since (2n+3)(n+3) - 6n is an integer, 3[(2n+3)(n+3) - 6n] is composite for every integer n. Therefore, 6n2 + 27 is not prime for any integer n.
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Annabelle works in a deli and has been tracking the daily sales of different items over several months. Annabelle found that when there was an increase in the number of cups of hot chocolate sold, the number of cups of coffee sold also increased. Similarly, when there was a decrease in the number of cups of hot chocolate sold, the number of cups of coffee also decreased.
Which of the following is a valid conclusion?
A.
There is no correlation between the sale of hot chocolate and the sale of coffee.
B.
The increase in the sale of hot chocolate caused an increase in the sale of coffee.
C.
The increase in the sale of hot chocolate is correlated to, but not caused by, the sale of coffee.
D.
No conclusion can be drawn about the correlation or causation of the sale of hot chocolate and the sale of coffee.
Option C is the correct answer. The increase in the sale of hot chocolate is correlated to, but not caused by, the sale of coffee.
What is correlation?
Correlation is a statistical measure that shows how closely two or more variables are linked to one another. It is a measurement of the strength and direction of the linear connection between two variables, in other words.
Based on the information provided, it can be concluded that there is a correlation between the sale of hot chocolate and the sale of coffee.
Option A can't be considered because it conflicts with the material provided.
Option B indicates a causal relationship that cannot be proven merely on the basis of the observed correlation between the sales of hot chocolate and coffee.
Option D is untrue as well because a correlation has been found.
Therefore, option C is the valid conclusion that can be drawn from the given information, stating that the increase in the sale of hot chocolate is correlated to, but not necessarily caused by, the sale of coffee.
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A business owner applies for a credit card to cover $14,000 in emergency expenses. The credit card charges 16.99% annual interest compounded continuously. If no payments are made for 2 years, what will the balance on the card be, rounded to the nearest penny?
Credit card charges $19665.33 will the balance on the card be, rounded to the nearest penny.
What is interest in simple words?
When you borrow money, you must pay interest, and when you lend money, you must charge interest. The most common way to represent interest is as a percentage of a loan's total amount per year. The interest rate for the loan is denoted by this proportion.
Interest is the cost of borrowing money and is typically stated as a percentage, such an annual percentage rate (APR). Lenders may charge interest to borrowers for the use of their funds, or borrowers may charge interest to lenders for the use of their funds.
amount applied for = $14,000
interest rate = 16.99%
the balance after 2 years
P₀ = $1400
r = 16.99% = 0.1699
t = 2
[tex]P_{0} = P_{0}e^{rt}[/tex]
[tex]P_{2} = 1400e^{0.1699 * 2}[/tex]
≈ $19665.33
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3 2/5 -1 3/5!!
Please i need help!
Answer:
Step-by-step explanation:
3 2/5 -1 3/5 = 1.8
studies have shown that bats can consume an average of 10 mosquitoes per minute. what is the probability that a bat does not consume any mosquitoes in a 30-second interval?
The probability that a bat does not consume any mosquitoes in a 30-second interval is 0.0067379 or 0.67%.
In this case, the average rate of mosquitoes consumed by a bat is 10 per minute.
To find the rate for a 30-second interval, calculate the rate for 1 minute and then adjust it for the 30-second interval:
Average rate for 1 minute = 10 mosquitoes
Rate for 30 seconds = [tex]\dfrac{10 \,mosquitoes}{1 \,minute} \times \dfrac{1}{2}[/tex]
= 5 mosquitoes
The Poisson distribution probability mass function is given by:
[tex]\[ P(X = k) = \dfrac{e^{-\lambda} \cdot \lambda^k}{k!} \][/tex]
Where:
[tex]\(\lambda\)[/tex] is the average rate of events.
In this case, to find the probability that k = 0.
So, let's plug in the values:
[tex]\(\lambda = 5\)[/tex]
[tex]\(k = 0\)[/tex], back to the formula as
[tex]\[ P(X = 0) = \dfrac{e^{-5} \cdot 5^0}{0!} \][/tex]
Calculating the probability as
[tex]\[ P(X = 0) = e^{-5}[/tex]
[tex]= 0.0067379[/tex]
Therefore, the probability is 0.0067379 or 0.67%.
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given the following frequency table of values, is the mean, median, or mode likely to be the best measure of the center for the data set? valuefrequency 351 364 376 386 395 631
For the given following frequency table of values 351, 362, 373, 381, 391, The mode is likely to be the best measure of the center for the data set.
The given frequency table is as follows:
Value frequency 351, 362, 373, 381, 391.
To find the most appropriate measure of central tendency for a dataset, we need to analyze the spread of data.
The mean, median, and mode are measures of central tendency in statistics.
We can find the following measures from the given data set:
Mean: It is calculated by summing up all the values and then dividing the result by the total number of values. This measure of central tendency is appropriate when the data are symmetrical.
Median: It is the middle value of the data set when arranged in order. It is suitable for skewed data.
Mode: It is the most common value in the data set. It is appropriate when data is discrete. The data in the frequency table appear to be discrete.
Because the data are discrete, the most appropriate measure of central tendency is the mode. So, the mode is likely to be the best measure of the center for the given value frequency data set.
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at 3:25 p.m., two trains left kalamazoo, michigan. one train traveled westward at a constant rate of
When they are 111 miles apart, the current time is 4:10 p.m.
If the time taken for two trains to be apart by 111 miles by "t" time.
Then at that time, t, the train which is at 82 mph, should have traveled a distance of 82T miles.
d1 = 82t
At the same time, t, the train which is at 66 mph, should have traveled a distance of 66T miles.
d2= 66t
The total distance traveled by both trains is d1 + d2 = D
D = 82t + 66t
D = 148t
From the given data, D = 111
Hence, 148t = 111
Solving the equation, the time t
t = 111÷148
t = 0.75
Converting it into minutes,
t = 0.75*60
t = 45 mins.
The current time ( T ) = the time at which both the trains left ( t1 ) + 45 mins.
T = t1+t
T = 3:25 + 45 min.
T =4:10 pm
Therefore, the current time is 4:10 p.m
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The complete question is-
At 3:25 p.m., two trains left Kalamazoo, Michigan. one train traveled westward at a constant rate of 82 miles per hour, while the other traveled eastward at a constant rate of 66 miles per hour. if they are now 111 miles apart, what time is it now? show your work on how you solved this situation.
Line segment AB in the coordinate plane has endpoints with coordinates A (1,5) and B (9,17). Which of the following is true?
The correct option- The perpendicular bisector of AB has the slope -1/3.
Explain about the slope of line?The difference between the change in y-values and the change in x-values is known as the slope of a line. This figure represents the slope of a line.
A quantity called the slope of a line is used to quantify how steep a line is. This number may be zero, positive, or negative. Moreover, it may be unreasonable or rational.Any two lines with the same slope are said to be parallel. When a line is rotated 90 degrees, it becomes perpendicular and becomes parallel. Four 90 degree angles result from the intersection of two perpendicular lines.Formula for slope m = (y2 - y1)/(x2 - x1)
Line segment AB coordinates :
A (1,5) and B (9,17).
Slope m1 = (17 - 5)/(9 - 5)
m1 = 12/4
m1 = 3
The line perpendicular to AB.
Let the slope of m2.
The relation between the slopes of perpendicular lines:
m1 x m2 = -1
3 x m2 = -1
m2 = -1/3.
Thus, the slope of the line perpendicular to the given line AB is found as: -1/3.
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Complete question:
AB in the coordinate plane has endpoints with coordinates A (1,5) and B (9,17). Which of the following is true?
The perpendicular bisector of AB has slope 3/2.
The perpendicular bisector of AB has slope -2/3.
The perpendicular bisector of AB has slope -2/3.
The perpendicular bisector of AB has slope -1/3.
Which of the following is a point of tangency on the circle below?
A. Point Y
B. Point Z
C. Point W
D. Point X
Based on the diagram, the point of tangency is Point Z. Therefore, the answer is B.
What is point of tangency?A point of tangency is a point at which a straight line, called a tangent line, touches a curve or a circle at only one point.
At the point of tangency, the tangent line is perpendicular to the radius of the circle that intersects the point of tangency.
The point of tangency is the point where a tangent line to the circle touches the circle at only one point.
In the given diagram, the line segment XZ appears to be a tangent to the circle.
Therefore, the point of tangency is the point where the line segment XZ touches the circle.
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5. the number of people arriving for treatment at an emergency room can be modeled by a poisson process with a mean of 5 people per hour. how many people do you expect to arrive during a 45-min period?
If the number of people arriving for treatment at an emergency room is modeled by a Poisson process with a mean of 5 people per hour, we can use this information to estimate the expected number of people who will arrive during a 45-minute period.
The Poisson distribution describes the probability of a certain number of events occurring in a fixed interval of time, given the average rate at which the events occur. In this case, the Poisson distribution can be used to estimate the number of people who will arrive during a 45-minute period, given that the mean arrival rate is 5 people per hour.
To calculate the expected number of arrivals, we first need to convert the 45-minute time period into hours. There are 60 minutes in an hour, so 45 minutes is equivalent to 0.75 hours.
Next, we can use the Poisson distribution formula, which is:
P(X = k) = (e^(-λ) * λ^k) / k!
where λ is the mean arrival rate (in this case, 5 people per hour), k is the number of arrivals we are interested in, and e is Euler's number (approximately 2.71828).
Expected number of arrivals = λ * t = 5 * 0.75 = 3.75
Therefore, we can expect approximately 3.75 people to arrive for treatment during a 45-minute period, assuming that the number of arrivals follows a Poisson distribution with a mean of 5 people per hour.
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Ethan is older than Jordan. Their ages are consecutive integers. Find Ethan’s age if the sum of the square of Ethan’s age is 4 times Jordan’s age is 56.
If the square of Ethan's age is added to Jordan's age, the result is [tex]56[/tex], which equals Ethan's age. The answer is that Ethan is [tex]6[/tex] years old.
How can you calculate age using maths?A person's birth date is compared to the day on which their age has to be computed as part of the age calculation process. The age of the individual is calculated by subtracting the person's age from the given date. Provided Date - Birthdate is used to compute age.
How can ageing be quantified?A person's age is merely a measurement of how long they have been living. These metrics don't adequately describe who you are or what you have accomplished. At any age, either old or young, one may do anything.
The solution states that [tex]56[/tex] is equal to [tex]4[/tex] times Jordan's age multiplied by the square of Ethan's age. This may be expressed as an equation:
[tex]x^2 + 4(x-1) = 56[/tex]
Simplifying the equation:
[tex]x^2 + 4x - 4 = 56[/tex]
[tex]x^2 + 4x - 60 = 0[/tex]
We can solve this quadratic equation by factoring:
(x+10)(x-6) = 0
Therefore, [tex]x = -10[/tex] or [tex]x = 6[/tex]. We can discard the negative value since age cannot be negative, so Ethan's age is [tex]6[/tex].
To check, we can substitute x=6 into the original equation:
[tex]6^2 + 4(6-1) = 36 + 20 = 56[/tex]
So the solution is Ethan is [tex]6[/tex] years old.
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Given f(x)=5x+7 and g(x)=2x+2, find g(g(1-3w))
Enter as the final value or expression without parentheses
As a result, the final number or expression is g(g(1-3w)) ≈ -12w + 10 (without parenthesis).
Which of these are they known as?When adding extraneous information or perhaps an afterthought to a sentence, parentheses, a pair or punctuation marks, are most frequently utilized. Two curving vertical lines can be seen in parentheses: ( ).
We must first evaluate g(1-3w) and then re-insert that result into g(x) in order to determine g(g(1-3w)).
We must first determine g(1-3w):
Substitute x with 1-3w to get g(x) ≈ 2x + 2 and g(1-3w) ≈ 2(1-3w) + 2.
g(1-3w) ≈ 2 - 6w + 2 (distribute the 2)
g(1-3w) ≈ -6w + 4 (combine similar terms) (combine like terms)
We can again again enter the result of g(1-3w) into g(x):
If you substitute g(1-3w) for x, then g(x) ≈ 2x + 2 g(g(1-3w)) ≈ 2(-6w Plus 4) + 2
g(g(1-3w)) ≈ -12w + 8 + 2 (allocate the 2) (distribute the 2)
g(g(1-3w)) ≈ -12w + 10 (combine comparable terms) (combine like terms)
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where is the water table in a swamp? group of answer choices well below the surface. at the surface. well above the surface. generally, 2 miles below the surface.
Generally, the water table in a swamp is located 2 miles below the surface.
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What is the simplest form of 8(5k+7)−10(6k−7)
The simplest form of the given expression is -20k + 126.
To find the simplest form of the expression 8(5k+7)−10(6k−7), follow these steps:
1. Distribute the numbers outside the parentheses to the terms inside the parentheses:
8 × 5k + 8 × 7 - 10 × 6k + 10 × 7
2. Perform the multiplication:
40k + 56 - 60k + 70
3. Combine like terms (terms with the same variable and exponent):
(40k - 60k) + (56 + 70)
4. Simplify the expression by performing the subtraction and addition:
-20k + 126
The simplest form of the given expression is -20k + 126.
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I need help with dis math
Determine the surface area of the cylinder. (Use π = 3. 14)
net of a cylinder where radius of base is labeled 5 inches and a rectangle with a height labeled 4 inches
157 in2
219. 8 in2
282. 6 in2
314 in2
The surface area of the cylinder with radius 5 inches and rectangle with height 4 inches is equal to 282.6 square inches.
Radius of the base = 5 inches
Height of the rectangle = 4 inches
Surface area of a cylinder
= area of the top and bottom circular faces + the area of the curved surface.
Here,
Rectangle represents the curved surface of the cylinder, with a height of 4 inches and a length equal to the circumference of the base.
Circumference of the base is equal to,
Circumference
= 2πr
= 2 x 3.14 x 5
= 31.4 inches (approx.)
Area of the curved surface of the cylinder is ,
Curved surface area
= Length x Height
= 31.4 inches x 4 inches
= 125.6 square inches
Area of each circular face of the cylinder is ,
Circular face area
= πr²
= 3.14 x 5²
= 78.5 square inches
Substitute the value to get total surface area of the cylinder we have,
Total surface area of the cylinder
= 2 x Circular face area + Curved surface area
= 2 x 78.5 square inches + 125.6 square inches
= 282.6 square inches (approx.)
Therefore, the surface area of the cylinder is approximately equal to 282.6 square inches.
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there is a group of five children, where two of the children are twins. in how many ways can i distribute $8$ identical pieces of candy to the children, if the twins must get an equal amount of candy?
There are 1960 different ways to distribute 8 identical pieces of candy to the five children, where the twins get an equal amount of candy.
First, distribute the candy to the twins.
Split the 8 pieces of candy into two equal parts for the twins using combinations:
C(8, 4)
This means selecting 4 pieces of candy from the 8 identical pieces for one twin, and the remaining 4 pieces will automatically go to the other twin.
C(8, 4) is calculated as:
[tex]^8C_4 = \dfrac{8!}{4!(8-4)!}[/tex]
= 8! / (4! * 4!)
= (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1)
= 70
Now, you have distributed 4 pieces of candy to each of the twins. Y
In this case, you have 6 pieces of candy to distribute among 3 children, and you can use two dividers (bars) to separate the candy for each child.
This can be represented as:
OO|OO|OO
The two bars split the 6 pieces of candy into three sections for the three children.
So, you have C(6 + 2, 2) ways to distribute the remaining candy:
[tex]^{6+2}C_2 = \dfrac{8!}{2!(8-2)!}[/tex]
= 8! / (2!(8 - 2)!)
= 8! / (2! * 6!)
= (8 * 7) / (2 * 1)
= 28
Now, the total number of ways to distribute the candy
Total ways = C(8, 4) * C(8, 2) = 70 * 28 = 1960
So, there are 1960 different ways to distribute.
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.. Sasha Abbott earns $62,550.00 in taxable income each year. The tax rate is 3.6%, and she takes zero deductions. How much tax does her employer withhold each year? A $2,380.50 B $2,251.80 C $2,500.40 D $1,823.20
Answer: B $2,251.80
Step-by-step explanation:
:)
what is the value of t?
Answer:
t=36°
Step-by-step explanation:
90-54=36
opposite angles are equal so t=36°
consider the differential equation given by[math equation]the goal of this problem is to solve this differential equation numerically, analytically and compare the solutions. find the exact solution (i.e. the analytical solution) use euler's method to solve the differential equation with a step size h=0,001; (this is the numerical solution)
The number of iterations increases. If there is a significant difference between the two solutions, we may need to investigate the numerical method used or check for errors in our analytical solution.
Step-by-step explanation:
The differential equation is missing in your question. However, I will give a general overview of how to solve a differential equation numerically using Euler's method and how to find an analytical solution.
Numerical Solution using Euler's Method:
Suppose we have a first-order differential equation of the form y' = f(x, y), where y' represents the derivative of y with respect to x. To solve this numerically using Euler's method, we need to start with an initial condition y(x0) = y0, and we want to find the value of y at some other point x1 = x0 + h.
The Euler's method involves approximating the derivative y' by the difference quotient (y1 - y0) / h, where y1 is the value of y at x1. Rearranging this equation, we get:
y1 = y0 + h * f(x0, y0)
Using this equation, we can iteratively compute the value of y at different points by using the previous value of y. For example, to find y2, we can use the equation:
y2 = y1 + h * f(x1, y1)
We continue this process until we reach the desired endpoint.
Analytical Solution:
An analytical solution to a differential equation is an explicit expression for y(x) that satisfies the differential equation for all values of x. To find an analytical solution, we may use techniques such as separation of variables, integrating factors, or other methods specific to the type of differential equation.
For example, if we have a differential equation of the form y' = k * y, where k is a constant, we can use separation of variables to obtain:
dy / y = k * dx
Integrating both sides, we get:
ln|y| = k * x + C
where C is an arbitrary constant of integration. Solving for y, we get:
y = Ce^(kx)
where C = ±e^C is a constant determined by the initial condition.
Comparison of Solutions:
Once we have the numerical and analytical solutions, we can compare them by plotting the graphs of y(x) for each method. If the numerical solution was computed with a small enough step size, it should converge to the analytical solution as the number of iterations increases. If there is a significant difference between the two solutions, we may need to investigate the numerical method used or check for errors in our analytical solution.
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Translate the figure 5 units left and 5 units up. -10-9 Plot all of the points of the translated figure. You may click a plotted point to delete it.
I hoped this helped!
: )
Step-by-step explanation:
originally - (6,-1) After translation - (1,4)
originally - (8,-1) After translation - (3,4)
originally - (4,-7) After translation - (-1,-2)
originally - (7,-9) After translation - (3,-4)
originally - (9,-9) After translation - (4,-4)
When the temperature drops below 15°C in a building, the furnace turns on.
At what temperatures will the heater turn on? Write an inequality to represent
this situation, and graph the solution on a number line.
The inequality to represent this situation is T < 15°C, where T is the temperature.
What is inequality?Inequality is a statement that two values, expressions, or quantities are not equal. Inequality is usually represented by the symbols ">", "<", "≥", or "≤".
This inequality can be graphed on the number line by representing 15°C as a point on the number line. Any values to the left of 15°C, such as 14°C, 13°C, and so on, would be represented as points to the left of 15°C on the number line.
Less than inequality is used to compare two values to see if one is less than the other. In this case, the inequality T < 15°C states that the temperature T must be less than 15°C in order for the furnace to turn on.
Graphically, the solution to this inequality is represented by a number line with a point at 15°C and all points to the left of 15°C represented in the solution set.
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fatima is 1.27m tall. charlotte is 0.89m tall lila is taller than charlotte by half the difference betweem fatimas height and charlottes height. how tall in meters is lila?
Lila's height is 0.89 + 0.19 = 1.08m.
What is height ?
Height typically refers to the measurement of an object or person from the base to the top, usually measured vertically. It is often used in reference to the physical dimension of a person or object, such as the height of a building, tree, or individual.
According to the question:
In the context of the given problem, height refers to the height of Fatima, Charlotte, and Lila.
Fatima is 1.27 meters tall, Charlotte is 0.89 meters tall, and Lila is taller than Charlotte by half the difference between Fatima's height and Charlotte's height.
The difference between Fatima's height and Charlotte's height is 1.27 - 0.89 = 0.38m.
Half of that difference is 0.38/2 = 0.19m.
So, Lila is taller than Charlotte by 0.19m.
Therefore, Lila's height is 0.89 + 0.19 = 1.08m.
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How do I solve for x and y?
Answer:
x = 80
y = 160
Step-by-step explanation:
The sum of all arc measures that make up a circle is 360°. Therefore:
[tex]\implies 200^{\circ} + y^{\circ} = 360^{\circ}[/tex]
[tex]\implies 200^{\circ} + y^{\circ} - 200^{\circ} = 360^{\circ} - 200^{\circ}[/tex]
[tex]\implies y^{\circ} = 160^{\circ}[/tex]
[tex]\implies y=160[/tex]
Tangent and Intersected Chord TheoremIf a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one-half the measure of its intercepted arc.
Therefore, according to the Tangent and Intersected Chord Theorem, the measure of angle x is equal to half of the measure of arc y:
[tex]\implies x^{\circ}=\dfrac{1}{2} y^{\circ}[/tex]
[tex]\implies x^{\circ}=\dfrac{1}{2} \cdot 160^{\circ}[/tex]
[tex]\implies x^{\circ}=80^{\circ}[/tex]
[tex]\implies x=80[/tex]
[tex]\hrulefill[/tex]
Circle Theorem vocabularyChord: A straight line joining two points on the circle.Tangent: A straight line that touches a circle at only one point.Arc: the curve between two points on the circumference of a circleIntercepted arc: The curve between the points where two chords or line segments intercept the circumference of a circle.a high school baseball player has a 0.253 batting average. in one game, he gets 8 at bats. what is the probability he will get at least 6 hits in the game?
The probability of a high school baseball player getting at least 6 hits in one game, given a 0.253 batting average, when he gets 8 at-bats, is 0.0197 or approximately 2%.
Given, the high school baseball player's batting average is 0.253, which means in 100 times he hits the ball, he will make 25.3 hits on average. We need to find the probability of getting at least 6 hits in a game when he gets 8 at-bats.
We will calculate the probability using the Binomial Probability formula. Here, the number of trials is 8, and the probability of success is 0.253. We need to find the probability of getting at least 6 hits.
P(X≥6) = 1 - P(X<6)
P(X<6) = ∑P(X=i), i=0 to 5
We can use the Binomial Probability Table to find these probabilities or use the Binomial Probability formula.
P(X<6) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)
= C(8,0) (0.253)^0 (1 - 0.253)^8 + C(8,1) (0.253)^1 (1 - 0.253)^7 + C(8,2) (0.253)^2 (1 - 0.253)^6 + C(8,3) (0.253)^3 (1 - 0.253)^5 + C(8,4) (0.253)^4 (1 - 0.253)^4 + C(8,5) (0.253)^5 (1 - 0.253)^3
≈ 0.9799
Therefore, P(X≥6) = 1 - 0.9799
= 0.0201 or approximately 2%.
Hence, approximately 0.0197 or 1.97% is the probability of a high school baseball player, who has a batting average of 0.253, obtaining at least 6 hits when given 8 at-bats during a single game.
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. In which step does a mistake first occur?
(24+3 + 10)-14 + 2
Step 1: (8 + 10) -14 + 2
Step 2: 18 -14+2
Step 3: 4 +2
Step 4: 2
NEED HELP ASAP !!
TY
Answer:
The first one...............