There would be 1024 possible outcomes on a 5 question test with each question having 4 possible answers.
Based on the given information, there are 4 possible ways for each of the 5 questions.
4 possible ways to answer Question # 1
4 possible ways to answer Question # 2
4 possible ways to answer Question # 3
4 possible ways to answer Question # 4
4 possible ways to answer Question # 5
Fundamental Principle of Counting, also called the counting rule, is the method to count how many ways multiple independent events can occur.
Thus, by Fundamental Principle of Counting, the number of possible outcomes is
4 x 4 x 4 x 4 x 4 = 1024
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Christian buys 18 bottles of grapefruit juice at the corner store for a total cost of $15.66. If each bottle costs the same amount, how much is 3 bottles of juice?
Answer:$2.61
Step-by-step explanation:
18=$15.66
÷6 ÷6
3=$2.61
The cost of 3 bottles of juice based on the given ratio will be $2.61.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
18 bottles cost = $15.66
1 bottle cost = $15.66/18 = $0.87/ bottle
For 3 bottles = 3 × $0.87 = $2.61
Hence "The cost of 3 bottles of juice based on the given ratio will be $2.61".
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David picked 15 pears. Jenna picked p fewer pears than David. Write an expression that shows how many pears Jenna picked.
Answer:
15-p
Step-by-step explanation:
15-p
Write the equation of the graph shown below in factored form.
a graph that starts at the top left and continues down through the x axis at negative one to a minimum around y equals negative twelve point two five and goes up to touch the x axis at two and the goes back down to a minimum around y equals negative one half and goes back up through the x axis at two.
f(x) = (x − 2)2(x + 1)(x − 3)
f(x) = (x + 2)2(x − 1)(x + 3)
f(x) = (x + 2)2(x + 1)(x + 3)
f(x) = (x − 2)2(x − 1)(x − 3)
The answer is
f(x) = (x - 1) 2(x +1)(x - 3 ).
Given equation
f(x) = (x − 2)2(x + 1)(x − 3)
f(x) = (x + 2)2(x − 1)(x + 3)
f(x) = (x + 2)2(x + 1)(x + 3)
f(x) = (x − 2)2(x − 1)(x − 3)
Factored form is a product of stayed and linear elements.
by checking of the red line cross the x-axis.it will give you the zero.
it passes at -1, touches at 1, and crosses again at 3.
This implies that the zeroes are -1, 1 and 3.
The factors 2(x+1), (x - 3), and (x - 1) must be evaluated.
Therefore the answer is
f(x) = (x - 1) 2(x +1)(x - 3 ).
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help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The distance that Evan has left to hike is 13/30 mile.
How to calculate the distance left?From the information, Eva is hiking a real that has a length of 5/6 miles.
He has also hiked 2/5 miles. Therefore, in this situation, the distance that he has left will gotten by subtracting the fractions.
This will be:.
Distance left = Total distance - Distance hiked
Distance left = 5/6 - 2/5
= 25/30 - 12/30
= 13/30
The distance is 13/30 miles.
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the drying times for a certain type of cement are normally distributed with a standard deviation of 62 minutes. a researcher wishes to estimate the mean drying time for this type of cement. find the least sample size needed to assure with 90% confidence that the sample mean will not differ from the population mean by more than 5 minutes.
The least sample size needed to assure with 90% confidence that the sample mean will not differ from the population mean by more than 5 minutes will be 416.16.
What is normal distribution?A normal distribution is a data set design in which the majority of values cluster around the middle of the range and the remainder taper off symmetrically toward either end. Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central location, with values decreasing as one moves out from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are all the same. The normal distribution, like any other probability distribution, defines how the values of a variable are distributed. Because it properly captures the distribution of values for many natural occurrences, it is the most important probability distribution in statistics.
Here,
The z value at the 90 percent confidence interval is 1.645.
t ≥ z*s/√n
5≥1.645*62/√n
√n≥20.398
√n≥20.4
n≥416.16
The smallest sample size required to ensure that the sample mean does not deviate from the population mean by more than 5 minutes with 90% confidence is 416.16.
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A ditch used to drain storm water has the shape of a trapezoid with the wider base being 24 feet and the height being 6 feet. The shorter base has an unknown length of x-feet. Set up and solve an equation to find the value of x if the drainage ditch as an area of 96 square feet.
The value of the shorter base which is x is 8 feet.
What is a trapezium?A trapezium is a quadrilateral with exactly one pair of opposite sides parallel to each other. The trapezium is a two-dimensional shape that appears as a table when drawn on a sheet of paper.
It has four sides and four vertices.
The trapezium is made of a rectangle and triangles.
Area of a trapezium = 1/2 (a + b ) h
where a = small base, b = big base and h = height.
from the above, b = 24 feet, h = 6 feet, a = x and area = 96 square feet
substituting the above into the equation
1/2 ( 24 + x) x 6 = 96
6(24 + x) = 96 x 2
6(24 + x ) = 192
multiplying the terms by 6
144 + 6x = 192
6x = 192 - 144
6x = 48
x = 48/6
x = 8 feet
In conclusion, the value of x is 8 feet
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suppose for a particular week, the forecasted sales were $4,000. the actual sales were $3,000. what is the value of the mean absolute percentage error?
The mean absolute percentage error is 33.3%
The mean absolute percentage error measures the forecast accuracy by determining how well a particular forecasting method is able to reproduce the time series data that are already available.
This method is referred to as the forecasts of accuracy, which help to measure the number of errors that are in a former forecast.
Then this would factor these errors into a new forecast while making adjustments to the new forecast.
Forecasted sales were $4,000
Actual sales were $3,000
Absolute error = |Actual sales - Forecasted sales|
= |3,000-4,000|
= 1000
Mean Absolute error percentage = (Absolute error / Actual sales) *100%
=(1000/3000)*100
= 33.33%
Hence, The Mean Absolute error percentage is 33.3%
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Redondea 5.2 al número entero más cercano
The nearest whole number to the number 5.2 is 5.
Given number:
= 5.2
we can determine the whole number of any decimals using the properties that is,
if decimal part < .5 its nearest whole number is 0.
example = 0.5 whole number is 0.
if decimal part > 0.5 its nearest whole number is 1.
In this case,
= 5.2
decimal part = 0.2 < 0
so the nearest whole number is 5.
Therefore the nearest whole number to the number 5.2 is 5.
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Select ALL the correct answers. Figure A is a polygon that has been graphed on a coordinate grid. Which of the following transformations will result in a similar image to figure A? Reflect figure A across the y-axis, and dilate it by a scale factor of 4. Reduce the measurement of each angle by half, and reflect the figure across the x-axis. Translate figure A down 4 units and left 6 units, and dilate it by a scale factor of 3. Double the measurement of each angle by 2, and dilate it by a scale factor of 2. Increase the length of one side of figure A by 2 units, and rotate the figure 90° counterclockwise about its center.
=> Translate figure A down 4 units and left 6 units, and dilate it by a scale factor of 3.
=> Reflect figure A across the y-axis, and dilate it by a scale factor of 4.
Given,
In the question:
Figure A is a polygon that has been graphed on a coordinate grid.
To select the option:
Which of the following transformations will result in a similar image to figure A?
Now, According to the question;
The correct options are:
=> Translate figure A down 4 units and left 6 units, and dilate it by a scale factor of 3.
=> Reflect figure A across the y-axis, and dilate it by a scale factor of 4.
{If the two figures are similar, then their angles are not changed. The ratio of length are the same.}
Hence, => Translate figure A down 4 units and left 6 units, and dilate it by a scale factor of 3.
=> Reflect figure A across the y-axis, and dilate it by a scale factor of 4.
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What are some Mathematical Concepts for Slopes and equations? Any kind of help would be much appreciated.
Answer:25256
Step-by-step explanation:
at an academically challenging high school, the average gpa of a high school senior is known to be normally distributed with a variance of 0.45. a sample of 15 seniors is taken and their average gpa is found to be 2.83. assume that and . the 90% confidence interval for the population mean gpa is:
The 90% confidence interval for the population mean gpa is [2.545,3.114].
The confidence interval for population mean is:
µ ± z* . σ/√n
Where, μ is population mean, σ is standard deviation, z* is the value of z-score and n is number of samples.
The z-score value for 90% confidence interval is 1.645.
The average gpa is found to be 2.83, so μ=2.83. The variance is 0.45, it means
σ² = 0.45
σ = √0.45
σ = 0.67
The 90% confidence interval for population mean is:
2.83 ± 1.645 . 0.67/√15
[2.83 - 1.645.0.67/√15 , 2.83+1.645.0.67/√15]
[2.545 , 3.114]
Therefore, the 90% confidence interval for the population mean gpa is :
[2.545 , 3.114]
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answer:
The correct statements are:
- 6x + 15 < 10 - 5x ⇒ 3rd answer
Step-by-step explanation
An open circle is at 5 and a bold line starts at 5 and is pointing to the right ⇒ 4th answer
Step-by-step explanation:
∵ The inequality is -3(2x - 5) < 5(2 - x)
At first simplify each side
∵ -3(2x - 5) = -3(2x) + -3(-5)
Remember (-)(-) = (+)
∴ -3(2x - 5) = - 6x + 15
∵ 5(2 - x) = 5(2) + 5(-x)
Remember (+)(-) = (-)
∴ 5(2 - x) = 10 - 5x
∴ - 6x + 15 < 10 - 5x
Subtract 15 from both sides
∴ - 6x < -5 - 5x
Add 5x to both sides
∴ - x < - 5
Remember the coefficient of x is negative, then when you divide both sides by it you must reverse the sign of inequality
∵ The coefficient of x is -1
∴ Divide both sides by -1
∴ x > 5
in right angles , side of all angles. how am I supposed to know what is adjacent to angle I'm trying to find and what is opposite from it.
I know the hypotenuse because it is the biggest one
2x+y=4 1x-y=11 adding subtracting equations to solve systems.
By solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3
What is meant by an equation?An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign =. In French, an equation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions coupled with an equals sign.
An equation is composed of two expressions joined by an equals sign (=). The expressions on the two sides of the equals sign are referred to as the equation's left-hand side and right-hand side. The right side of an equation is frequently considered to be zero.
Given,
2x+y=4
x-y=1
By solving above two equations we get,
2x+y=4
x-y=1
3x=5
x=5/3
y=-1+x
y=(5/3)-1
y=2/3
Therefore, by solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3
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Write and Solve the equation: A printing company charges $0.15 per copy in addition to a service fee of $3. Write an equation to represent the cost, y, the company charges for x numbers of copies. How much would 250 copies cost?
The equation representing the cost is y = 0.15x + 3 where x ix the number of copies and y is total cost.
Cost for 250 copies is $40.5
What is equation?The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, a printing company charges $0.15 per copy in addition to a service fee of $3,
Therefore, according to question, the total cost y for printing x copies is,
y = 0.15x + 3
For x = 250
y = 0.15*250 + 3
y = $40.5
Hence, The equation representing the cost is y = 0.15x + 3 where x ix the number of copies and y is total cost.
Cost for 250 copies is $40.5
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please help!!
the function shown in the graph is f(x)= ???
Answer:
The answer is x^{3}-2x^{2}-5x+6
Step-by-step explanation:
This is because only a Cubic Function would have such a shape. That leaves x^3 functions from there just substitute points and check
Which step contains a mistake in solving for the system of equations?
x + 2y = 5
y = 3x - 8
1. x + 2(3x) - 8 = 5
2. x + 6x - 8 = 5
3. 7x = 13
4. x = 13/7
5. 7x 8 5
Answer:
First step, correct answer is (3,1)
Step-by-step explanation:
1.it should be x+2(3x-8)=5
2. x+6x-16=5
3.7x=21
4. 7x/7=21/7
5. x=3
then you can eitheir take x+2y=5 or y=3x-8 i suggets taking second option as it is easier, just input values for x in
) 3x-8=y
6. 3(3)-8= 1
7. x=3, y=1
125 = 7m - 1 please answer
Answer:
m=18
Step-by-step explanation:
Simplify. (4i+1)^2
show all work
(4i+1)² can be simplified to 8i-15
What is Complex number?A complex number is a number of the form a + bi, where a and b are real numbers
Given expression is (4i+1)²
four times of i plus one whole square.
(4i+1)² can be expanded by using algebraic identity
(a+b)²=a²+b²+2ab
(4i+1)²
Now put a as 4i and b as 1
(4i+1)²=16i²+1+2(4i)(1)
Where i²=-1
=-16+1+8i
=8i-15
Hence (4i+1)² can be simplified to 8i-15
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Find the length of each side of triangle XYZ, then classify the triangle by its side: X(7,6), Y(5,1), Z(9,1) show work, please!!!
Answer:
(9,1), Z(5,1)
Step-by-step explanation:
describe a situation that could be represented by f(x) // pls help
Answer: “y is a function of x.” The letter x represents the input value or independent variable. The letter y, or f(x), represents the output value, or dependent variable.
Step-by-step explanation:lol i have no idea
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The curve -3[tex]x^{2}[/tex] + 18x +3 has a maximum value of 30 at x = 3
What is a maximum point?In mathematics, a point at which a function’s value is greatest. If the value is greater than or equal to all other function values, it is an absolute maximum. if it is merely greater than any nearby point, it is a relative, or local, maximum. In calculus, the derivative equals zero or does not exist at a function’s maximum point.
Differentiate f(x) = -3[tex]x^{2}[/tex] + 18x +3 ,
we have dy/dx = -6x + 18.
at turning point, dy/dx = 0
-6x + 18 = 0
6x = 18
x =18/3
x = 3
to check if x = 3 is a minimum or maximum point, we take the second derivate
which is [tex]\frac{d^{2}y }{dx^{2} }[/tex] = -6
since [tex]\frac{d^{2}y }{dx^{2} }[/tex] < 0
F(x) is a maximum,
so maximum value of x, we substitute x = 3 into the function
f(x) = -3[tex](3)^{2}[/tex] + 18(3) + 3
f(x) = 30
In conclusion, the maximum value for the function is 30 at x = 3
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on saturday leon biked an average speed of 14.5 miles per hour for 1.5 hours. then on sunday he biked an average speed of 15 miles per hour for 2.75. what was the total distance leon biked in miles that weekend
The total distance leon biked in miles that weekend is 19.5 miles.
The answer provided below has been developed in a clear step by step manner.
On Saturday, Leon biked 1.5 hours at a speed of 14.5 miles per hour that means distance = 14.5 * 1.5 = 21.75 miles
On Sunday, he biked 2.75 hours at a speed of 15 miles per hour that means distance =15 * 2.75 =41.25 miles
Distance = speed*time use this formula
He farther did in sunday = 41.25 - 21.75 miles = 19.5 miles
Therefore, that weekend Leon rode his bike a total of 19.5 miles.
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Use the diagram shown.
Ж
If mz1 equals (4x + 2)° and mz2 equals 110°, what is the value of x?
О А. 14
O B. 15
О С. 16
O D. 17
By using the concept of straight angle, the value of x obtained is 17°
What is straight angle?
At first it is important to know about angle
When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle
Straight angle is the angle whose measure is 180°
Here,
[tex]m\angle 1 =(4x +2)\\m\angle 2 = 110\\[/tex]
[tex]\angle 1 \ and \ \angle 2[/tex] forms a straight angle
[tex]m\angle 1 + m\angle 2 = 180[/tex] [Angle on a straight line]
[tex]4x + 2 + 110 = 180\\4x +112 = 180\\4x =180-112\\4x = 68\\x = \frac{68}{4}\\x = 17[/tex]
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The function f(x) is given in the graph below. Find its average rate of change between the followin
points. Show the calculations that lead to your answer.
(a) x=-6 to x = 4
(b) x=-2 to x=2.
a) x = -6 to x =4
[tex](x_{1} , y_{1} ) (x_{2} , y_{2} ) = (-6,1) (4,3)[/tex]
Slope(m)[tex]= \frac{Y_{2}-Y_{1}}{x_{2}-x_{1}}[/tex]
[tex]= \frac{1-3}{-6-4-}[/tex]
[tex]= \frac{-2}{-10}[/tex]
[tex]m = \frac{1}{5}[/tex]
Slope (m) of the function is 1/5.
b) x = -2 to x = 2
[tex](x_{1} , y_{1} ) (x_{2} , y_{2} ) = (-2,-1) (2,-3)[/tex]
slope (m)[tex]= \frac{Y_{2}-Y_{1}}{x_{2}-x_{1}}[/tex]
[tex]= \frac{-3-(-1)}{-2-2}[/tex]
[tex]= \frac{-2}{-4}[/tex]
slope(m) [tex]= \frac{1}{2}[/tex]
Slope(m) of the given function is 1/2.
What is fraction ?
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.
In a simple fraction, both are integers.
A complex fraction has a fraction in the numerator or denominator.
In a proper fraction, the numerator is less than the denominator.
Define slope(m)?
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
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Translate the expression “the product of triple a number and 19”
Answer: 3x+19
Step-by-step explanation:
Please help! I need help solving this final problem for geometry.
Eric's city took a telephone poll about a plan to build a new hotel downtown. 200 people took
the poll. 25% of them were in favor of the new hotel. How many people were in favor of the
new hotel?
Answer:
50 people
Step-by-step explanation:
Solution
25% as a fraction is 25/100 which reduces down to 1/4. What this tells you is that 1/4 of the people asked want the hotel
1/4 * 200 = 50
50 people want the hotel.
10. On a school trip the ratio of the number of teachers to the number of students is 1 : 15
The ratio of the number of male students to the number of female students is 7:5
Work out what percentage of all the people on the trip are female students.
Give your answer correct to the nearest whole number.
There are 39% of all the people on the trip are female students on a school trip.
What is meant by the term ratio?Mathematicians use the term "ratio" to compare two numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another. Two quantities being compared using division in a ratio.One to fifteen teachers are assigned to every hundred students.
and there are 7:5 more female students than male students.
Let's say there are x teachers. Students multiply by 15 as a result.
Take the ratio of male to female as 7 years for the male and 5 years for the female.
The total student trip is made up of both male and female pupils.
Thus,
15x = 7y + 5y
15x = 12y
5x = 4y
x = 4/5y ...eq 1
Then, the percentage of the female students.
5y/(x + 5x)×100
5y/16x ×100
Put the value of x from eq 1
625/ 16 = 39%
Thus, there are 39% of all the people on the trip are female students.
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which statements is true of the function f(x)= x2 + 6x3 - 4 + 2x5?
A. the function is positive for all values of x
B. the end behavior of the graph f(x) is similar to that of g(x) = -x
C.the graph has exactly one x-intercept
D. the function is increasing for all real numbers
The statements is true of the function f(x)= x^2 + 6x^3 - 4 + 2x^5 is C.the graph has exactly one x-intercept
How to show that the function has one interceptIt is shown that the function has one intercept in the x direction by plotting the graph of the polynomial
The graph showed one x intercept is at the coordinate (0.778, 0)
x intercept refers to the value of x when y is zero
The graph is plotted and attached
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