6. Oliver is playing a game in which he has to choose one of two numbers (2 or 7) and then one of five vowels (a, e, i, o, or u). How many possible outcomes are there? 2 7 There are possible outcomes.
Answer
Number of possible outcomes for everything = 240 ways
Explanation
The number of possible outcomes can be calculated by taking each of these two groups.
First group contains 2 elements
Number of possible ways to pick the elements = 2! = 2 × 1 = 2 ways
Second group contains 5 elements
Number of possible ways to pick the elements = 5! = 5 × 4 × 3 × 2 × 1 = 120 ways
Number of possible outcomes for everything = 2! × 5! = 2 × 120 = 240 ways
Hope this Helps!!!
Mick O'Meara budgeted $315 per month for electricity and $238 per month for gas. His expenses for a twelve-month period were $3,950 for electricity and $3,055 for gas.How much less did he budget annually for the two expenses than he needed?$339$344$357$369None of these choices are correct.
In order to know how much he budgeted annually for each expense, we need to multiply each month budget by 12:
annual budget for electricity: 12 * 315 = 3780
annual budget for gas: 12 * 238 = 2856
So, the total annual budget was:
3780 + 2856 = 6636
On the other hand, his real expenses for that year were:
3950 + 3055 = 7005
Then, to find how much less he budget than he needed, we can find the difference between those two values:
7005 - 6636 = 369
Therefore, the last option is correct.
The function f(x) is graphed below. what is true about the graph on the interval from x = y to x = ∞?* it is positive and increasing* it is positive and decreasing * it is negative and increasing* it is negative and decreasing
Looking at the graph, we will the following:
The portion ab is increasing
The portion bc is decreasing
The portion cd is decreasing
The portion de is increasing
The portion ef is increasing
The portion fg is decreasing
The portion beyond g is increasing
In the interval x = y to x = ∞, we will observe that the graph is positive & increasing
Hence, the first option is correct (it is positive and increasing)
9km 87 m equals
option A = 9.087km
option B= 90.87km
option c = 0.9087km
option D= 908.7km
option e= none of these
please don't give wrong answer
The dose of a drug is critical. Too small a dose may be treat a patient effectively, A nurse must give a patient 40mg of a drug for each kilogram of the patient’s mass. If the patient weighs 165lbs how many milligrams of the drug should be given?
EXPLANATION
We need to multiply the number of needed milligrams by the weight of the patient, but first turning the weight in lbs into kilograms,
[tex]?Kilograms=165lbs*\frac{0.453}{1lb}=74.745Kg[/tex]Now, multiplying the obtained weight by the number of miligrams, give us the dose:
[tex]Dose=40\frac{mg}{Kg}*74.745Kg=2989.8mg[/tex]In conclusion, the nurse should give 2989 mg of the drug.
help pleasesjjsnsbsbbbsbs
Student asking the same question for third time in less than ten minutes. Can't help him or her out with additional information to complete the exercise.
Closing the session!
Factoring
64v^4-225w^10
I come up with
(8v^2+15w^2)(8v^2-15w^5) can I simplify it?
Your answer can't be simplified but it's also slightly incorrect. No worries!
You can simplify (64v^4 - 225w^10) by applying the difference of squares --> a^2 - b^2 = (a + b)(a - b)
Here, (64v^4) is a^2, and (225w^10) is b^2.
[tex]\sqrt{64v^4 }[/tex] = a = 8v^2
[tex]\sqrt{225w^{10} }[/tex] = b = 15w^5
Substitute the values:
(8v^2 + 15w^5)(8v^2 - 15w^5)
Therefore, the factorization of [tex]64x^{4} -225w^{10}[/tex] is:
[tex](8v^{2} + 15w^5)(8v^2-15w^5)[/tex]
The factorization is already the simplest. It can't be simplified further.
What is 4527 written in scientific notation?A.4.527B.4.527 x 10*2C.4.527 x 10*3D.4.527 x 10*4
Solution
- The question would like us to convert the number 4527 to scientific notation.
- In order to write a number to its scientific notation, we need to follow these steps:
1. Move the decimal place to the right of the first digit of the number. Make sure you count each step as you move the decimal point from right to left or left to right.
2. The number of steps corresponds to the exponent of 10 that multiplies the decimal form of the original number.
- We can apply these steps to solve the question given as follows:
- Thus, we have that the scientific notation of the number 4527 is
[tex]4.527\times10^3[/tex]Final Answer
The scientific notation of the number 4527 is
[tex]4.527\times10^3\text{ (OPTION C)}[/tex]
what is the surface are of this cone rounded to the nearest tenth of a square foot?
ANSWER
[tex]282.7ft^2[/tex]EXPLANATION
Recall, the formula for calculating the surface area of a cone is;
[tex]A=\pi r^2+\pi r\sqrt{r^2+h^2}[/tex]Given;
[tex]\begin{gathered} radius(r)=5 \\ height(h)=12 \end{gathered}[/tex]Substitute the values into the formula;
[tex]\begin{gathered} A=\pi 5^2+\pi 5\sqrt{5^2+12^2} \\ =\pi5^2+\pi5\sqrt{25+144} \\ =25\pi+5\pi\times13 \\ =25\pi+65\pi \\ =90\pi \\ =90\times3.14 \\ =282.74 \\ \cong282.7 \end{gathered}[/tex]Analyze the general equation of a linear function, y = mx. No matter what value the constant m has, which pair of numerical values (x, y) always satisfies this mathematical equation? Justify your answer.
The pair of numerical values (x,y) that always satisfies the mathematical equation of linear equation y = mx is (0,0).
A two-variable linear equation can be thought of as a linear relationship between x and y, or two variables whose values rely on one another.
The slop-intercept form of a linear equation is y = mx + b.
For y = mx, b = 0.
If we put x = 0 in y = mx, y = 0.
Therefore, y = mx line always passes through (0,0) for any value of m because (0,0) always satisfies the equation y = mx.
Hence, (x,y) = (0,0).
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Which of the following graphs shows a negative linear relationship with a correlation coefficient, r, close to -0.5?A. Graph AB. Graph BC. Graph CD. Graph D
A negative linear relationship occurs when for increasing x values, the values of y are decreasing.
Observing the graphs, we can see a positive linear relationship for graphs A and C (x - increases, y - increases).
For Graph D, we can observe no correlation.
For graph B, we can observe a negative linear relationship (x - increases, y - decreases).
Answer: Graph B
Find the slope of the tangent line when x=3 using the limit definition f(x) = X^2 - 5
SOLUTION
From the limit definition, we have that
[tex]f^{\prime}(x)=\lim _{h\to0}\frac{f(x+h)-f(x)}{h}[/tex]Now applying we have
[tex]\begin{gathered} f\mleft(x\mright)=x^2-5 \\ f^{\prime}(x)=\lim _{h\to0}\frac{f(x+h)-f(x)}{h} \\ =\lim _{h\to0}\frac{((x+h)^2-5)-(x^2-5)}{h} \\ =\lim _{h\to0}\frac{x^2+2xh+h^2^{}-5-(x^2-5)}{h} \\ =\lim _{h\to0}\frac{x^2+2xh+h^2-5-x^2+5}{h} \\ =\lim _{h\to0}\frac{x^2-x^2+2xh+h^2-5+5}{h} \\ =\lim _{h\to0}\frac{2xh+h^2}{h} \end{gathered}[/tex]factorizing for h, we have
[tex]\begin{gathered} =\lim _{h\to0}\frac{h(2x+h)^{}}{h} \\ \text{cancelling h} \\ =\lim _{h\to0}2x+h \\ =2x \end{gathered}[/tex]So, when x = 3, we have
[tex]\begin{gathered} =2x \\ =2\times3 \\ =6 \end{gathered}[/tex]Hence, the answer is 6
What Is the inverse of.. (ignore pencil writing) -matrices- (there may be more than one answer
To find the inverse of the matrix, first let's find the determinant:
[tex]\begin{gathered} |A|\text{ = 3(2) - 5(1)} \\ |A|\text{ = 6 - 5} \\ |A|\text{ = 1} \end{gathered}[/tex]Then, we'll find the Adjunct of the matrix:
[tex]\begin{gathered} \begin{bmatrix}{3} & {5} & {} \\ {1} & {2} & {} \\ {} & {} & {}\end{bmatrix}\text{ : interchange }3\text{ and 2. negate 1 and 5} \\ \text{Adjunct = }\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex][tex]\begin{gathered} In\text{verse of the matrix = }\frac{1}{|A|}\times\text{ adjunct} \\ A^{-1}\text{ = }\frac{1}{1}(\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix}) \\ A^{-1}\text{ =}\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix}\text{ (option B)} \\ \end{gathered}[/tex]Neegan paddles a kayak 21 miles upstream in 4.2 hours. The return trip downstream takes him 3 hours. What isthe rate that Neegan paddles in still water? What is the rate of the current?
System of Equations
When Neegan paddles the kayak upstream, the real rate (speed) is the difference between the rate that Neegan paddles in still water and the rate of the water against his paddling.
When he goes downstream, the real rate is the sum of the rates because the water and Neegan push in the same direction.
He takes 4.2 hours to paddle for 21 miles against the current, so the real rate is 21/4.2 = 5 mi/h
He takes only 3 hours to return, so the real speed is 21 / 3 = 7 mi/h.
Let:
x = rate at which Neegan paddles in still water
y = rate of the current.
We set the system of equations:
x - y = 5
x + y = 7
Adding both equations:
2x = 12
Divide by 2:
x = 6
Substituting in the second equation:
6 + y = 7
Subtracting 6:
y = 1
Neegan paddles at 6 mi/h in still water. The rate of the current is 1 mi/h
(Third choice)
Line Graph: This time you will not have the numbers on the x and y axis. You will need to decide which number to use (1, 2, 3... or 2,4,5.... Or 5, 10, 15...) 3: Creating Graphs Create a single line graph using the following table. Time goes on the x axis Rainfall goes on the y axis Make sure to do the following: Label the x and y axis Create a title 10 15 20 Time (minutes) 25 30 35 40 25 55 45 60 50 35 40 Speed (of car) (km/min)
Line Graph:
A line graph is used to show how the data points are changing with respect to time.
For Example:
A line graph may be used to show the average rainfall over the entire month.
For the given scenario we have,
X-axis = Time in minutes
Y-axis = Speed of car in km/min
Title of graph = Speed of Car Vs Time
Data points for time = 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
Data points for speed = 25, 30, 35, 40, 25, 55, 45, 60 50 35 40
This is how the line graph looks like.
It is showing the speed of the car in km/min over an interval of 60 minutes in steps of 5 minutes.n steps of
Procedure:
• Draw and label the x-axis and y-axis.
,• Label the data points on both axis.
,• Draw the data points.
,• Join the data points with a line.
,• We are done.
,•
I need help with question 12 please in a hurry I understand already
Trigonometric Ratios
The figure is a triangle with hypotenuse of h = 25 feet. The angle of elevation is 35°.
In right triangle QRS, m S=73. In right triangle TUV m V=73.
To find:
Which theorem used to prove that both triangles are congruent.
Solution:
It is given that both triangles are right triangles. So, each one of the corresponding angles is 90 degrees.
angle M is given 73 degrees and angle V is given 73 degrees. So, we can see that two pairs of angles are equal in triangle.
Thus, AA similarity postulate can be use to prove that both triangles are congruent.
Thus, option C is correct.
Approximate when the function is positive, negative, increasing, or decreasing.
Describe the end behavior of the function.
The function y = - | x | + 1 is increasing on ( - ∞, 0 ) and decreases on ( 0, ∞ ).
A relationship between a group of inputs with each output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Consider the function,
y = - | x | + 1
The non-negative value of a real number x, represented by the symbol |x|, is the absolute value or modulus of x, regardless of its sign.
From the graph, we can approximate that the function is increasing from negative infinity to zero and the function decreases from zero to infinity.
Increasing on: ( - ∞, 0 )
Decreasing on: ( 0, ∞ )
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A Parks and Recreation department in a small city conducts a survey to determine what recreational activities for children it should offer. Of the 1200 respondents,400 parents wanted soccer offered625 parents wanted baseball/softball offered370 parents wanted tennis offered150 parents wanted soccer and tennis offered315 parents wanted soccer and baseball/softball offered230 parents wanted baseball/softball and tennis offered75 parents wanted all three sports offeredHow many parents didn’t want any of these sports offered?a) 155b) 75c) 0d) 425
There were 1200 respondents:
400 parents wanted soccer offered
370 parents wanted tennis offered
625 parents wanted baseball/softball offered
150 parents wanted soccer and tennis offered
315 parents wanted soccer and baseball/softball offered
230 parents wanted baseball/softball and tennis offered
75 parents wanted all three sports offered
Therefore:
We have to add all the options that were mixed with different sports:
150 + 315 + 230 = 695 - 75= 620 (We subtract 75 because it's already included in the other values as we can see in the diagram)
We have to add all the parents that chose only one sport:
400 + 370 + 625= 1395
We have to subtract 620 from 1395:
1395 - 620= 775 parents who chose any sport
Now:
1200 - 775 = 425 respondents who didn't want any.
Therefore, 425 parents didn't want any of the sports offered.
The answer is D) 425.
The coordinates of point F are (8,4) and the coordinates of point G are (-4,9). What is the slope of the line that is perpendicular to line FG. Enter the answer as a simplified fraction.
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
The formula for finding slope is
m = (y2 - y1)/(x2 - x1)
y2 and y1 are the final and initial values of y
x2 and x1 are the final and initial values of x
From the given points ,
x1 = 8, y1 = 4
x2 = - 4, y2 = 9
m = (9 - 4)/(- 4 - 8) = 5/- 12 = - 5/12
Recall, if two lines are perpendicular, it means that the slope of one line is equal to the negative reciprocal of the slope of the other line. The negative reciprocal of - 5/12 is 12/5
Thus, the slope of the perpendicular to line FG is 12/5
If 1 is added to a number and the sum is tripled, the result is 5 more than the number. Find the number
Answer;
[tex]n=1[/tex]Explanation;
Here, we want to get a number
Since the number is not known at the moment, we can start by identifying the number with an a;phabet
Let us call this n
If 1 is added to the number
mathematical representation;
[tex]1+n[/tex]And the sum is tripled;
[tex]3(1+n)[/tex]The result is 5 more than the number
5 more than the number is simply;
[tex]5+n[/tex]So, we equate this to what we had initially as follows;
[tex]5+n=3(1+n)[/tex]We can now solve this equation for n
[tex]\begin{gathered} 5+n=3+3n \\ 5-3=3n-n \\ 2n=2 \\ n=\frac{2}{2} \\ n=1 \end{gathered}[/tex]Find the domain. Then use the drop down menu to select the correct symbols to indicate your answer in interval notation. If a number is not an integer then round it to the nearest hundredth. To indicate positive infinifty ( \infty ) type the three letters "inf". To indicate negative infinity(-\infty ) type "-inf" with no spaces between characters. \frac{ \sqrt[]{x-4} }{\sqrt[]{x-6}} AnswerAnswer,AnswerAnswer
The domain of a function is all values of x the function can have.
Since this function has radicals, and the value inside a radical needs to be positive or zero, and also the denominator of a fraction can't be zero, we have the following conditions:
[tex]\begin{gathered} x-4\ge0 \\ x\ge4 \\ \\ x-6>0 \\ x>6 \end{gathered}[/tex]Since the first condition contains the second, so the domain set is represented by the second condition:
[tex](6,\text{inf)}[/tex]Need help asap please and thank you
Answer:
y=[tex]\frac{1}{2}[/tex]x+1
Step-by-step explanation:
y=mx+b
m is the slope of the line, which you find by counting the rise over run between two points. In this case its up one, and right two, or [tex]\frac{1}{2}[/tex].
b is the y intercept, or where the line crosses the y axis
a) Jayla says that the equation y=2*3 matches the graph Substitute the ordered pairs (from part() into the equation to prove that jayla is correct. Make sure to show ALL steps
From the graph let's take the points as the ordered pairs:
(3, 3), (4, 5), and (5, 7)
Given the equation:
y = 2x - 3
Let's verify for all points, if the equation matches the graph:
a) (x, y) ==> (3, 3)
Substitute 3 for x and 3 for y in the equation
y = 2x - 3
3 = 3(3) - 3
3 = 6 - 3
3 = 3
b) (x, y) ==> (4, 5)
Substitute 4 for x and 5 for y:
y = 2x - 3
5 = 2(4) - 3
5 = 8 - 3
5 = 5
c) (x, y) ==> (5, 7)
Substitute 5 for x and 7 for y:
y = 2x - 3
7 = 5(2) - 3
7 = 10 - 3
7 = 7
Since the left side equals the right side of the equation, the equation
y=2x-3 matches the graph.
Therefore, Jayla is correct.
A number times the sum of 12 and 32 (write as an algebraic expression)
ANSWER
x(12 + 32)
EXPLANATION
Let x be 'the number'.
A number times... means 'a number multiplied by...'
The sum of 12 and 32 is (12 + 32)
The complete algebraic expression is x(12 + 32)
Find the domain of the function represented by the list of ordered pairs
The domain of a function is always represented by the values of X. In the ordered pair, they are always the first value of the pair.
The domain is the first number of each pair.
Domain: {-1, -10, 8, 6}.
20) Determine if the number is rational (R) or irrational (I)
EXPLANATION:
Given;
Consider the number below;
[tex]97.33997[/tex]Required;
We are required to determine if the number is rational or irrational.
Solution;
A number can be split into the whole and the decimal. The decimal part of it can be a recurring decimal or terminating decimal. A recurring decimal has its decimal digits continuing into infinity, whereas a terminating decimal has a specified number of decimal digits.
The decimal digits for this number can be expressed in fraction as;
[tex]Fraction=\frac{33997}{100000}[/tex]In other words, the number can also be expressed as;
[tex]97\frac{33997}{100000}[/tex]Therefore,
ANSWER: This is a RATIONAL number
what is the GCF of 6x+18/x^2-x-12
The GCF of the expression 6x+18/x^2-x-12 is (x+3)
How to find the GCF of the expression?The GCF (Greatest Common Factor) of two or more numbers or expressions is the greatest number or expression among all the common factors of the given numbers or expressions
Given 6x+18/x²-x-12
We can write 6x+18/x²-x-12 as:
6x+18/x²-x-12 = 6x+18/x²-4x+3x-12 By factorization:
= 6(x+3) / (x+3)(x-4)
Since (x+3) is common to both the numerator and the denominator. Therefore, the greatest common factor (GCF) is (x+3)
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Which equation is equivalent to: 3r=78+14 ?A. −3r=−78+14B. 3r−14=78C. 3r=78−14D. −3r=78−14
IF log x = 1/₂, find log (10x²)
Answer:
2
Step-by-step explanation:
log ab = log a + log b
Similarly,
log 10x² = log 10 + log x²
log a^b = b log a
Similarly,
log 10x² = 2 log x
= 2 * 1/2
= 2/2
= 1
Note :-
The value of log 10 = 1
Hence,
log 10x²
= log 10 + log x²
= 1 + 1
= 2
