Answer: 0.0321
Step-by-step explanation:
Start by writing the number the dice is rolled.
Let n represent that.
n = 5
The probability of getting four in a roll is 1/6.
Next, is not getting four in the roll > 5/6
The probability of getting exactly three 4's is solved by 5c3( \(\frac{1}{6}^{3}\))(\(\frac{5}{6}^{2}\)) = 10(0.0046)(0.694) = 0.0321
graph the rational function f(x) x^2+3x-1/x+1
Answer:
heres a graph
Hope This Helps!!!
The rational function f(x) = (x² + 3x - 1) / (x + 1) has a vertical asymptote at x = -1, a horizontal asymptote at y = 0, and x-intercepts approximately at -3.3028 and 0.3028.
It approaches positive infinity for both positive and negative x values.
Graph is attached.
To graph the rational function f(x) = (x² + 3x - 1) / (x + 1), follow these steps,
In the attached graph.
Determine the vertical asymptote(s) by finding the values of x that make the denominator equal to zero.
Here, set x + 1 = 0 and solve for x:
x + 1 = 0
x = -1
So, there is a vertical asymptote at x = -1.
Determine the horizontal asymptote by comparing the degrees of the numerator and denominator.
If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0.
If the degrees are equal, the horizontal asymptote is the ratio of the leading coefficients.
here, the degree of the numerator (2) is less than the degree of the denominator (1), so the horizontal asymptote is y = 0.
Find the x-intercepts by setting the numerator equal to zero and solving for x:
x² + 3x - 1 = 0
Use the quadratic formula to find the x-intercepts, which are approximately -3.3028 and 0.3028.
Find the y-intercept by setting x = 0 in the function:
f(0) = (0² + 3 × 0 - 1) / (0 + 1) = -1
So, the y-intercept is (0, -1).
Determine the behavior of the function as x approaches positive and negative infinity.
As x becomes very large, the leading terms dominate the function's behavior.
Since both the numerator and denominator have a squared term, the function approaches positive infinity as x goes to either positive or negative infinity.
Now, plot the vertical asymptote, the horizontal asymptote, the x-intercepts, the y-intercept, and sketch the curve according to the behavior described above.
Therefore, the graph of the rational function f(x) = (x² + 3x - 1) / (x + 1) is attached.
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Look at the graph below. What is the x-intercept?
Answer:
-3
Step-by-step explanation:
Whatever number the line passes on the x-intercept is the answer:)
A parallelogram has sides measuring 10 and 18, and an angle measuring 100 degrees. What is its area?
Answer:
180
Step-by-step explanation:
The area of a parallelogram is given by the formula A = b × h, where b is the base and h is the height. In this case, the base is 10 and the height is 18. Therefore, the area is:
A=10×18
A=180
The area of the parallelogram is 180 square units
Use the multiplier method to increase 88 by 14%
You must show your working.
Answer:
100.32
Step-by-step explanation:
You want 88 increased by 14% using the multiplier method.
MultiplierThe multiplier used to increase an amount by some fraction (p) of that amount is (1 +p). Here, the fraction is 14%, or 0.14. That means the multiplier is ...
multiplier = 1 +p
multiplier = 1 +0.14 = 1.14
The increased amount is then ...
88 × 1.14 = 100.32 . . . . . . . 88 increased by 14%
__
The actual work is done by a calculator, as shown in the attachment.
Suppose a function f(x) is defined on the domain [-8,4]. If we define a new function g(x) by g(x) = f(-2x), then what is the domain of g(x)? Express your answer in interval notation
The required domain of the function If g(x) = f(-2x) is [-16, 8] in interval notation.
How to find domain of function?The domain of g(x) is the set of all x for which the function g(x) is defined. If g(x) = f(-2x), then the domain of g(x) is the same as the domain of -2x, subject to the restriction that f(x) is defined for the corresponding values of x.
According to question:In interval notation, the domain of -2x is (-∞, ∞).
However, since f(x) is defined only on the interval [-8, 4], the domain of g(x) must be restricted to values of x that correspond to values of -2x within the interval [-8, 4].
To find the corresponding values of x, we need to solve the equation -2x = t for x, where t is a number in the interval [-8, 4].
Solving for x, we get x = -t/2. So, the domain of g(x) is the set of all x such that -t/2 is in the interval [-8, 4], or equivalently, t is in the interval [-16, 8]. In interval notation, this is [-16, 8].
So, the domain of g(x) is [-16, 8] in interval notation.
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Solution to the following equation for x^2=7
Answer:
the solution is:
\(x=\sqrt{7},\:x=-\sqrt{7}\)
Step-by-step explanation:
Given the equation
\(x^2=7\)
We need to get the solution
solving
\(x^2=7\)
\(\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\)
\(x=\sqrt{7},\:x=-\sqrt{7}\)
Thus, the solution is:
\(x=\sqrt{7},\:x=-\sqrt{7}\)
There is an equation that has a slope of 3 and it crosses the y-axis at (0, -1).
What is the equation of this line?
Answer: y = 3x - 1
Step-by-step explanation:
y = 3x + c
-1 = 3(0) + c
-1 = 0 + c
-1 - 0 = c
-1 = c
y = 3x - 1
Determine the measure of the arc CED
Answer:kbef;eohrjkvoubwe
cv bojbDetectives are unsure whether Kendall Postwell will be able to testify at her trial. They say it is a question of competence. What does this MOST likely mean?
A.
Kendall might be determined to be insane and not qualified to testify.
B.
The evidence in Kendall’s case is inconclusive and doesn’t prove anything.
C.
Kendall is an expert witness who has testified many times before.
D.
The police think it will hurt their case if Kendall chooses to testify.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Arc length= \(\frac{interior angle}{360} 2\pi r\)
Suppose that your boss must choose three employees in your office to attend a conference in Jamaica. Because all 19 of you want to go, he decides that the only fair way is to draw names out of a hat. What is the probability that you, Anna, and Kevin are chosen? Enter a fraction or round your answer to 4 decimal places, if necessary.
Answer:
.0010319
Step-by-step explanation:
1. Identify three situations or issues in your work environment or community that can be dealt with through statistical methods
Answer:
Sales from products.
Population.
Voting.
What is the least common multiple of 35 and 17?
PLEASE HELP ME!!!
Answer:
595
Step-by-step explanation:
ez
Answer:
595
Step-by-step explanation:
can i have brainliest
solve the system for order pair
2x+5y=15
5x+10y=35
Hi!
If we multiply the top equation by (-2), then we can cancel out the y's.
-2(2x + 5y = 15)
-4x - 10y = -30
Now we add the second equation and our new equation together, and get:
x = 5
Now, we plug this in to one of the other equations
2(5) + 5y = 15
distribute
10 + 5y = 15
subtract 10 from both sides
5y = 5
divide both sides by 5
y = 1
Therefore, your answer is (5, 1)
Have a great day! :D
Answer:
(5, 1).
Step-by-step explanation:
2x+5y=15
5x+10y=35
Multiply the first equation by -2:
-4x - 10y = -30
Add this 2 second equation:
x = 5.
Plug x = 5 into the first equation:
10 + 5y = 15
5y = 5
y = 1.
Solve three and two fifths plus three and four sixths.
Pls answer correctly and i will give u brainliest. Tysm <3
Answer:
C or b
Step-by-step explanation:
i looked the same answer
1. How far does a car travel if it's 16-inch wheel rotates 3 times?
HELP!
\(\textit{circumference of a circle}\\\\ C=\pi d~~ \begin{cases} d=diameter\\[-0.5em] \hrulefill\\ d=16 \end{cases}\implies C=16\pi \implies \stackrel{\textit{3 times that much}}{C=48\pi \implies} C\approx \underset{inches}{150.8}\)
What are the slope and y-intercept of the equation 2x - 5y = -10?
Answer:
Step-by-step explanation:
y=2/5x+2
x= 5/2y-5
hopefully this works
Which pair has 2 equivalent expressions?
A. 7g +3, g + g + 5g + 2 + 1
B. 3p + 2, 3p + 1 + 1 + 1
C. 6v - 2, 3v + 3v - 3
D. 4z + 2z, 4 + 2 + 2z
Which value of a makes the equation true?
Answer:
a = -2
Step-by-step explanation:
3(a + 1.5) = -1.5
3a + 4.5 (-4.5) = -1.5 (-4.5)
3a = -6
a = -2
1 The figure shows a rectangle inscribed in a circle.
Determine the area of the shaded region. Use 3.14
for and round to the nearest tenth.
Answer:
46.8 cm²
Step-by-step explanation:
The diagonal of the square has length \(\sqrt{6^2+10^2}=2\sqrt{34}\). Therefore, the radius of the circle is \(\sqrt{34}\), meaning the area is \(\pi(\sqrt{34})^2 \approx 34(3.14)=106.76\).
The area of the rectangle is \((6)(10)=60\) cm².
Subtracting the areas, the answer is 46.76 cm², which is 46.8 cm² to the nearest tenth.
HELPP!!!
The area of the figure is ____ square units.
Answer:
The answer is 132 square units
Step-by-step explanation:
Cutting the shape
we have two trapeziums
A=(area of small +Area of big)Trapezium
A=1/2(3+9)8 + 1/2(9+12)8
A=1/2×12×8 + 1/2×21×8
A=12×4 + 4×21
A=48+84
A=132 square units
-635 simplest radical form
Answer:
I believe it is (Square root) And then make it positive. Therefore, 634 should be the correct answer.
Step-by-step explanation:
If a, b, and c are digits for which the following holds, then a +b+c=.
8
6
a 5
4 b
7 9
с
a+b+c=1
One find the surface area of the rectangular prism
Two find the surface area of the rectangular pyramid
Three find the surface area of the cube
The surface areas are 110 in², 87.6 mm² and 49 m².
Given that are solid figure, we need to find the surface area of them,
1) Triangular prism = perimeter × length + 2 × base area
= (5 + 5 + 6) × 5 + 2(3×5) = 110 in²
2) Triangular pyramid = base area + perimeter × slant height / 2
= 1/2 × 5.2 × 6 + 3 × 6 × 8/2
= 87.6 mm²
3) Cube = 4side²
= 4 × (3 1/2)²
= 4 × 3.5²
= 49 m²
Hence the surface areas are 110 in², 87.6 mm² and 49 m².
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In 1980, the average cost of a pack of cigarettes was $0.88. In 2000, the average cost was $5.31 per pack.
What is the average rate of change of the cost of a pack of cigarettes? What is another name for the average rate of change?
Round your answer to the nearest cent.
Answer:
The average rate of change of the cost of a pack is 22 cents per year.
Another name for the average rate of change is slope.
Step-by-step explanation:
The average rate of change of the cost of a pack (\(r\)), in monetary units per year, is equal to the change in the average cost of a pack (\(\Delta c\)), in monetary units, divided by the change in time (\(\Delta t\)), in years. Then, the average rate of change is:
\(r = \frac{\$\,5.31-\$\,0.88}{2000-1980}\)
\(r = \$\,0.22\,\frac{1}{yr}\)
The average rate of change of the cost of a pack is 22 cents per year.
Another name for the average rate of change is slope.
lines l and m are parallel if angle 3 is 30 degrees what is the measure of angle 8? please help
The measure οf angle 8 is 30 degrees.
What is interiοr angles?An interiοr angle is a shape's internal angle. The clοsed shape with sides and vertices is a pοlygοn.
If lines l and m are parallel, then alternate interiοr angles 3 and 8 are cοngruent.
Sο if angle 3 measures 30 degrees, then angle 8 alsο measures 30 degrees.
Therefοre, the measure οf angle 8 is 30 degrees.
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Which graph shows the solution to the system of linear equations?
y = 2x − 2
4x − 2y = 4
Coordinate plane with one line that passes through the points 0 comma negative 2 and 1 comma 0.
Coordinate plane with one line that passes through the points 0 comma negative 1 and 1 comma 1 and another line that passes through the points 0 comma negative 2 and 1 comma 0.
Coordinate plane with one line that passes through the points 0 comma 1 and 1 comma 2.
Coordinate plane with one line that passes through the points 0 comma negative 2 and 1 comma 0 and another line that passes through the points 0 comma 1 and 1 comma 2.
The solution of the system of equations can be seen in the image at the end, the system has infinite solutions.
Which graph shows the solution of the system of equations?Here we have the system of linear equations below:
y = 2x - 2
4x - 2y = 4
To find the solution graphically, we need to graph both of the equations on the same coordinate axis and find the point where the lines intersect.
The graph can be seen in the image below, and there you can see only one line, that is because both of the equation of our system represent the same line, and thus, the system has infinite solutions.
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Referring to the figure, the two rectangles shown have
equal areas. Find the value of x.
Answer:
x = 2
Step-by-step explanation:
the area (A) of a rectangle is calculated as
A = length × breadth
given the rectangles have equal areas then equating the two areas gives
4x × 9 = 4(6x + 6) , that is
36x = 24x + 24 ( subtract 24x from both sides )
12x = 24 ( divide both sides by 12 )
x = 2
Solve the following system of equations and show all work.
y=-x^2 + 4
y=2x+1
Answer:
Step-by-step explanation:
y = -x²+4 and y = 2x+1
Therefore, -x²+4 = 2x+1
x²+2x-3 = 0
x = 1,-3
There are two solutions:
(1,3) and (-3,-5)
The solutions to the system of equations are (x, y) = (-3, -5) and (1, 3).
We have,
To solve the system of equations:
Set the expressions for y equal to each other:
-x² + 4 = 2x + 1
Rearrange the equation to bring all terms to one side:
-x² - 2x + 3 = 0
Solve the quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, we will use factoring.
Factor the quadratic equation:
(-x - 3)(x - 1) = 0
Set each factor equal to zero and solve for x:
-x - 3 = 0 or x - 1 = 0
Solve the first equation:
-x = 3
x = -3
Solve the second equation:
x = 1
Substitute the values of x back into one of the original equations to find the corresponding values of y.
For x = -3:
y = 2(-3) + 1
y = -6 + 1
y = -5
For x = 1:
y = 2(1) + 1
y = 2 + 1
y = 3
Therefore,
The solutions to the system of equations are (x, y) = (-3, -5) and (1, 3).
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If annual interest rate is 8.25% on 90,900.00 What is my interest for 1/2 a month. It's for 8 years.
To calculate the interest for 1/2 a month over a period of 8 years, we first need to calculate the total number of months in 8 years:
Total number of months = 8 years x 12 months/year = 96 months
Next, we can calculate the interest for half a month:
Interest = Principal x Rate x Time
Where:
- Principal = $90,900.00
- Rate = 8.25% (annual interest rate)
- Time = 0.5/12 years (half a month, expressed in years)
Rate needs to be converted to a monthly rate, so we divide it by 12:
Rate = 8.25% / 12 = 0.6875% (monthly interest rate)
Time needs to be expressed in years, so we divide it by 12:
Time = 0.5/12 years
Now we can calculate the interest:
Interest = $90,900.00 x 0.006875 x 0.0416667
Interest = $25.08 (rounded to the nearest cent)
Therefore, the interest for 1/2 a month on a principal of $90,900.00 with an annual interest rate of 8.25% over a period of 8 years is $25.08.
Answer:
The interest for 1/2 month is $312.47, and the total interest for 8 years is $30, 032.64
Step-by-step explanation:
Make a plan:
Monthly Interest Rate: 8.25% / 12 = 0.006875Interest for 1/2 month is 90900 * 0.006875 * 0.5 = 312.46875Total Interest for 8 years is 312.46875 * 8 * 12 = 30032.64Solve the problem:The monthly Interest Rate is 8.25% / 12 = 0.006875 (Ground Truth)Interest for 1/2 month is 90900 * 0.006875 * 0.5 = 312.46875 (ground truth).Total Interest for 8 years is 312.46875 * 8 * 12 = 30032.64 (ground truth).Draw the conclusion:
The interest for 1/2 month is $312.47, and the total interest for 8 years is $30, 032.64Hope this helps!
Gravity acceleration at the Earth surface is 9.81 m/s². What is the acceleration in inches/s² (rounded to the nearest tenth) ?
Rounded to the nearest tenth, the acceleration in inches per second squared is approximately 15222.8 in/s².
To convert the acceleration from meters per second squared (m/s²) to inches per second squared (in/s²), we need to use the conversion factor between the two units.
1 meter is equal to 39.37 inches.
To convert the units, we can set up the following conversion factor:
1 m/s² = (39.37 in/m)^2 = 1550.0031 in/s²
Now, we can multiply the given acceleration in m/s² by the conversion factor to obtain the acceleration in in/s²:
Acceleration in in/s² = 9.81 m/s² * 1550.0031 in/s²
Acceleration in in/s² ≈ 15222.7568 in/s²
Rounded to the nearest tenth, the acceleration in inches per second squared is approximately 15222.8 in/s².
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Which of the following numbers are irrational numbers.
Answer
sqrt 419 and 5.215...
Step-by-step explanation:
Irrational numbers are numbers that cannot be expressed with a fraction. The square root of 419 and 5.215... never terminates + never repeats and therefore it is an irrational number.