If we have two fractions a/b and c/d:
[tex]\frac{a}{b}(\text{ })\frac{c}{d}[/tex]To determine which one of them is greater we make the cross product:
[tex]ad(\text{ })bc[/tex]We have 3 cases:
- If ad is greater than bc, then a/b is greater than c/d
- If bc is greater than ad, then c/d is greater than a/b
- If ad is equal to bc, then a/b is equal to c/d
For 1/2 and 2/7:
[tex]\begin{gathered} \frac{1}{2}(\text{ })\frac{2}{7} \\ 7\cdot1(_{\square})2\cdot2 \\ 7>4 \\ \Rightarrow\frac{1}{2}>\frac{2}{7} \end{gathered}[/tex]Supposed to go out to a dinner and you spend $42 you want to leave a 20% tip how much money should you leave for a tip round your answer to the nearest cent
Answer:
$8.4
Explanation:
To find how much money you should leave for a tip, we need to find how much is 20% of $42. So, to calculate this, we need to multiply 42 by 20 and then divide by 100, so:
$42 x 20% = 42 x 20 / 100 = 840 / 100 = 8.4
Therefore, the answer is $8.4
what percent of $717 is $239?
what percent of $717 is $239?
we have that
717 represent the 100%
so
Apply proportion
100/717=x/239
solve for x
x=(100/717)*239
x=
Please solve #24 for me.I’m struggling badly with systems of equations and need some help solving problems with it.Please explain the steps of it as best and basic as possible.
Data
• Small cones (s): $2
,• Large cones (L): $3.50
,• Total sold (T): $163
,• The number of L sold was 12 more than the number of ,s.
Procedure
We have to build a system of equations based on the information given.
• Equation 1:, she sold $163 of small and large cones
[tex]2s+3.50L=163[/tex]• Equation 2: ,the number of L sold was 12 more than the number of ,s.
[tex]L=s+12[/tex]As we have L isolated in the second equation, it is convenient to use this expression in the first equation to have it in terms of one variable:
[tex]2s+3.50\times\left(s+12\right)=163[/tex]Simplifying the parenthesis we get:
[tex]2s+3.50s+42=163[/tex]As we have two terms with an s we can group in each side of the equation the common terms and simplify them as follows:
[tex]2s+3.50s=163-42[/tex][tex]5.50s=121[/tex][tex]s=\frac{121}{5.50}[/tex][tex]s=22[/tex]Now that we have s, we just have to replace this value in equation 2:
[tex]L=22+12=34[/tex]Answer:
• Small snow cones: 22
,• Large snow cones: 34
Use the table of values for f and g below to find the indicated compositions. (f \circ g)(8) =Answerg(f(3))=Answerf(f(1))=Answer (g \circ g)(6) =Answer
In order to find the value of a composition of functions at x = a, (f º g)(a), we first find the value of g(a), then find the value of f(x) at x = g(a).
(f º g)(a) = f(g(a))
In this problem, the values of f(x) and g(x) are shown in the table, for integer values of x from 0 to 9.
So, we have:
1. (f º g)(8) = f(g(8))
From the table, we see that
g(8) = 4 (value of g(x) in the line corresponding to x = 8)
Then:
f(g(8)) = f(4) = 4 (value of f(x) in the line corresponding to x = 4)
Thus:
[tex]\mleft(f\circ g\mright)\mleft(8\mright)=4[/tex]2. g(f(3))
f(3) = 8
g(8) = 4
Thus:
[tex]g(f(3))=4[/tex]3. f(f(1))
f(1) = 6
f(6) = 2
Thus:
[tex]f(f(1))=2[/tex]4. (g º g)(6) = g(g(6))
g(6) = 7
g(7) = 3
Thus:
[tex]\mleft(g\circ g\mright)\mleft(6\mright)=3[/tex]
5.65 less than a number equals 49
Let
x ------> the number
the algebraic expression is equal to
x-65=-49
solve for x
adds 65 both sides -------> by addition equality property
x=-49+65
x=16
the number is 16
Use the substitution method to solve the system of equations.3x + 2y = 13y = x - 1O A. (2,1)O B. (2,3)O C. (3,2)O D. (1,2)
3x + 2y = 13
y = x - 1
We want to substitute the second equation into the first equation.
In the first equation, everytime we see "y" substitute x-1
3x +2y = 13
3x + 2( x-1) = 13
Distribute
3x +2x -2 = 13
Combine like terms
5x -2 = 13
Add 2 to each side
5x-2+2 = 13+2
5x = 15
Divide each side by 5
5x/5 = 15/5
x = 3
Noe we can find the value of y by using the second equation
y = x-1
y = 3-1
y =2
The solution is
( 3,2)
The graph of a quadratic function with the vertex 2,3 is shown in the figure below.Find the domain in the range. Write your answers as inequalities, using X or Y as appropriate. Or, you may instead write “empty set” or “all reals” as the answer.domain=range=
From the graph, we are asked to find the domain and randge./.
First lets know what domain and range.
Domain of a function is the set of values that are allowed is the plug into our function.
The domain and rang of the function written in an inequality form are:
Domain:
-1 < x < 4
Range:
-10 < y < 3
sue writes three different numbers. the numbers are all between 30 and 60 . the numbers all have 6 ones . what numbers does sue write
EXPLANATION
The three numbers are 36, 46 and 56. This is because the only three numbers that have 6 ones and wich are included between 30 and 60 are 36, 46 and 56, no other number can comply that condition.
What’s your question represents our relationship shown in the graph
Given the graph of a line
As shown the line passes through the point (0, 0)
So, the relation has the form:
[tex]y=kx[/tex]We will find the value of k using one point lying on the line
As shown the line passes through the point (4, 14)
So, when x = 4, y = 14
Substitute with x and y into the equation: y = k * x
so,
[tex]\begin{gathered} 14=k\cdot4 \\ \\ k=\frac{14}{4}=3.5 \end{gathered}[/tex]so, the answer will be option C) y = 3.5x
The total area of a polygon is 176 sq.ft. Find the value of x in the drawing
Answer:
x=6 ft
Explanation:
The given polygon is a trapezium in which:
• The parallel sides are a=16 ft and b=(16+2x) ft
,• The height, h = 8 ft
,• Area = 176 sq.ft.
The area of a trapezium is calculated using the formula:
[tex]\begin{gathered} A=\frac{1}{2}(a+b)h \\ a,b\text{ are the parallel sides} \\ h\text{ is the perpendicular height} \end{gathered}[/tex]Substitute all the known values:
[tex]\begin{gathered} 176=\frac{1}{2}\times8(16+16+2x) \\ 176=4(32+2x) \end{gathered}[/tex]Divide both sides by 4.
[tex]\begin{gathered} \frac{176}{4}=32+2x \\ 44=32+2x \end{gathered}[/tex]Subtract 32 from both sides:
[tex]\begin{gathered} 44-32=32-32+2x \\ 12=2x \end{gathered}[/tex]Divide both sides by 2.
[tex]\begin{gathered} \frac{12}{2}=\frac{2x}{2} \\ x=6\text{ feet} \end{gathered}[/tex]The value of x in the drawing is 6 feet.
Answer:
X=6
Step-by-step explanation:
First multiply 8 by 16 to get 128. Then subtract that from 176 to get 48. Then divide by to because there are two triangles to get 24, so each triangle is 24 square feet. Find a number that multiplied by 8 equals 48 (this will be x). The reason that I did this is because of the formula for area of a triangle (B*H/2=A). After you divide by 48 by 2 you will get 24. The number that was multiplied by 8 is x (x=6).
Angle AED is 146 degrees. Ray EC bisects angle AED. What is the measure of angle AEC?
STEP 1
We draw a diagram to represent the information.
[tex]\begin{gathered} <\text{AEC}=\frac{In conclusion, the answer is 73 degreesHow would I create a logic proof for this question?
Let us represent the premises given:
[tex]\begin{gathered} \text{Let } \\ A=\text{John is aardvark} \\ C=\text{Charles has a blue eye} \\ B=\text{Bob counts} \\ E=\text{Edna drives a truck} \\ D=\text{Dan edits} \end{gathered}[/tex]Then
We can subdivide the argument into substatement
Statement 1: If John is an aardvark then either Charlene has blue eyes or Bob counts
[tex]A\Rightarrow(C\lor B)[/tex]Statement 2: If Charlene has a blue eye then Edna drives a truck
[tex]C\Rightarrow E[/tex]Statement 3: Either John is an aadvark or Dan edits
[tex]A\lor D[/tex]Statement 4: Moly claims that either Bob counts or Edna drives a truck, but Moly is wrong
[tex]\begin{gathered} (B\lor E),\text{ But} \\ \sim(B\lor E) \end{gathered}[/tex]Therefor D
[tex]\therefore D[/tex]The above hypothesis and conclusion can be summarized below as;
Using a truth table calculator, the validity of the above arguments is shown below
Hence, we can conclude that the above is a valid argument.
Whats the vertex of f(x)= 2x^2-8
write a polynomial function in standard form with the given zeros. This is not a test nor homework, I am preparing for the ACT and my teacher said these problems would be on there and therefore I need help1. -1, 3, 42. -3, 0, 0, 53. -2 multiplicity 34. (x+3)^2(x+1)
For question 1
The zeros of the polynomial are -1, 3 , 4, it means x = -1, x=3 and x=4
therefore,
[tex]\begin{gathered} x\text{ + 1, , x-3, and x-4 are factors of the polynomial} \\ \text{ f(x)= (x+1)(x-3)(x-4) } \\ f(x)=(x^2-3x+x-3)(x-4)^{} \\ =(x^2\text{ -2x -3)(x -4)} \\ =x^3-4x^2-2x^2+8x-3x+12 \\ f(x)=\text{ }x^3-6x^2+5x+12 \end{gathered}[/tex]For question 2
The zeros of the polynomial are -3, 0, 0, 5 it means x = -3, x=0, x=0 and x=5
therefore,
[tex]\begin{gathered} (x+3),\text{ (x-0), (x-0), and (x-5) are factors} \\ f(x)=\text{ (x+3) (x) (x) (x-5)} \\ =x^2(x+3)(x-5)=x^2(x^2-5x+3x-15)=x^2(x^2-2x-15) \\ f(x)=x^4-2x^3-15x^2 \end{gathered}[/tex]For question 3
The zeros of the polynomial are -2, -2, -2 it means x = -2, x=-2, , x=-2
therefore,
[tex]\begin{gathered} (x+2),(x+2),(x+2)\text{ are factors of the polynomial} \\ f(x)\text{ = (x+2)(x+2)(x+2)} \\ =(x^2+2x+2x+4)(x+2)=(x^2+4x+4)(x+2) \\ =x^3+2x^2+4x^2+8x+4x+8 \\ f(x)=x^3+6x^2+12x+8 \end{gathered}[/tex]An online auction company charges sellers a commission fee of 5.25% of an items final selling price. If you sell an item for 55$ what fee will you pay to the auction company ?
The selling price of the item is $55.
The money charged by the auction company is;
[tex]\begin{gathered} 5.25\text{ \% of \$55} \\ \frac{5.25}{100}\times55 \\ =\text{ \$2.89} \end{gathered}[/tex]The fee paid to the auction company is $2.89
What is the component form of the vector represented by 8a when a=(-4,2)
Given the vector represented by:
[tex]8a[/tex]You know that:
[tex]a\langle-4,2\rangle[/tex]By definition, the Component Form of a vector is:
[tex]\vec{V}=\langle x,y\rangle[/tex]In this case, you only need to multiply the coordinates of "a" by 8, in order to find the Component Form of:
[tex]8a[/tex]Therefore, you get:
[tex]=\langle(8)(-4),(8)(2)\rangle=\langle-32,16\rangle[/tex]Hence, the answer is:
[tex]\langle-32,16\rangle[/tex]The slope of this regression line is 0.8 .What does this tell you about the relationship between the amount of fertilizer and the height of the seedlings?
The slope of a line shows the relation between a unitary increment in the x-variable and the corresponding change in the y-variable.
In this case, the x-variable represents the amount of fertilizer, in grams, and the y-variable represents the height of the seedings, in cm.
Then, the slope of 0.8 means that when the x-variable increases in 1 unit, the y-variable increases 0.8 units. Or more specifically, for each additional gram of fertilizer used, the height of the seedings increases by about 0.8 cm on average.
If an object is shot upward with an initial velocity, vo, in feet per second (fu/s), the velocity, v, in fus is given by the formula v = vo - 321,where ris time in seconds. Find the initial velocity of an object if the velocity after 2 seconds is 38 ft/s.
The final velocity function is given to be:
[tex]v=v_0-32t[/tex][tex]\begin{gathered} We\text{ are to find the initial velocity;} \\ v_0,\text{ given final velocity v to be 38ft/s and time t to be 2secs} \end{gathered}[/tex]Thus, we have:
[tex]\begin{gathered} v=v_0-32t \\ 38=v_0-32(2) \\ 38=v_0-64 \\ 38+64=v_0 \\ 102=v_0 \\ v_0=102\text{ft/s} \end{gathered}[/tex]Hence, the initial velocity of the object is 102ft/s
Simple random sampling uses a sample of size from a population of size to obtain data that can be used to make inferences about the characteristics of a population. Suppose that, from a population of bank accounts, we want to take a random sample of four accounts in order to learn about the population. How many different random samples of four accounts are possible?
There will be 1,215,450 different random samples of four accounts are possible.
What is combination and permutation?There are two methods to calculate the number of ways a certain event can happen. Both are used in different circumstances, such as, when the order of arrangement does not matter we use the combination and when the order matters we use permutation.
Given,
Population size, N = 75
Sample size, n = 4
We have selected a random sample of 4 accounts in order to learn about the population because these accounts can not be repeated and can be in any order, so we will use combination without repetition. According to this, the number of ways by which n subjects can be chosen from N subjects are given by,
[tex]\frac{N}{n}[/tex] = [tex]\frac{N!}{n!(N-n)!}[/tex]
Therefore, required number of ways are,
= 75!/4!(75-4)!
= 75!/4!*71!
= 75*74*73*72*/4*3*2
= 1,215,450
Hence, There will be 1,215,450 different random samples of four accounts are possible.
For more references on combination and permutation, click;
https://brainly.com/question/13387529
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Can you help me understand the steps to number 21 I think I got it wrong
The probability of an event is determined a follows;
[tex]P\lbrack E\rbrack=\frac{\text{Number of required outcomes}}{Number\text{ of possible outcomes}}[/tex]We shall begin with the probability of selecting an even number as shown below;
[tex]\begin{gathered} P\lbrack\text{even\rbrack}=\frac{6}{12} \\ P\lbrack\text{even\rbrack}=\frac{1}{2} \end{gathered}[/tex]Next we shall calculate the probability of selecting a number less than 5 as shown below;
[tex]\begin{gathered} P\lbrack\text{less than 5\rbrack=}\frac{4}{12} \\ P\lbrack\text{less than 5\rbrack=}\frac{1}{3} \end{gathered}[/tex]The probability of event A OR event B occuring is calculated a follows;
[tex]\begin{gathered} P\lbrack A\rbrack\text{ OR P\lbrack{}B\rbrack=P\lbrack{}A\rbrack+P\lbrack{}B\rbrack} \\ P\lbrack\text{even\rbrack OR P\lbrack{}less than 5\rbrack=}\frac{1}{2}+\frac{1}{3} \\ P\lbrack\text{even\rbrack OR P\lbrack{}less than 5\rbrack=}\frac{3+2}{6} \\ P\lbrack\text{even\rbrack OR P\lbrack{}less than 5\rbrack=}\frac{5}{6} \end{gathered}[/tex]The probability of selecting an even number or a number less than 5 is therefore
[tex]\frac{5}{6}[/tex]The correct answer is option A
Find the conditional relative frequency that a student surveyed prefers cats as pets, given that the student is a girl
To find the relative frequency asked, you have to divide the number of girls who prefer cats by the number of girls:
[tex]\frac{6}{28}\approx0.2143\Rightarrow21.43\text{percent}[/tex]About 21.43% of the girls prefer cats as pets
Can you please help me out with a question
Step 1 :
We use the Intersecting Chord Theorem which states that :
When two chords intersect each other inside a circle, the products of their segments are equal.
This theorem states that A×B is always equal to C×D
(no matter where the chords are).
From the question, A = 15, B = 12, C = ? , D = 18
Step 2 :
Using the equation, where AB = CD
[tex]\begin{gathered} 15\text{ x 12 = C x 18} \\ 180\text{ = 18 C} \\ \text{Divide both sides by 18, we have that:} \\ C\text{ = 10 units.} \end{gathered}[/tex]CONCLUSION :
The value of C = 10 units
what do you do after you multiply an equation in the elimination method?2x -3y=-11x+3y = 8
1) Let's multiply the second equation by -2, to eliminate x
2x -3y=-11
x+3y = 8
2) Now let's add both equations
2x -3y=-11
-2x-6y = -16
--------------------
-9y = -27
3) Divide both by -9
y=3
4) Plug y=3 into the simpler original equation, to make calculations easier:
x +3y=8
x+3(3) =8
x +9 =8 Subtract 9 from both sides
x = 8-9
x=-1
So, after multiplying it we add both equations to eliminate one variable either x or y.
parallelogram pqrs has diagonals PR and SQ that intersect at T find the value of X and Y
If a parallelogram PQRS has diagonals PR and SQ that intersects at T, then, T is the midpoint of PR and T is the midpoint of SQ
Given
[tex]\begin{gathered} PT=y \\ TR=3x+1 \end{gathered}[/tex][tex]y=3x+1[/tex]Also
[tex]\begin{gathered} QT=3y \\ TS=4x+13 \end{gathered}[/tex][tex]3y=4x+13[/tex]Now we are going to solve the system of equations with two unknowns
[tex]\begin{gathered} y=3x+1 \\ 3y=4x+13 \end{gathered}[/tex]Substitute equation 1 into 2
[tex]\begin{gathered} 3(3x+1)=4x+13 \\ 9x+3=4x+13 \\ 9x-4x=13-3 \\ 5x=10 \\ x=\frac{10}{5} \\ x=2 \\ \end{gathered}[/tex]x = 2
Substitute x = 2 into equation 1
[tex]\begin{gathered} y=3x+1 \\ y=3(2)+1 \\ y=6+1 \\ y=7 \end{gathered}[/tex]y = 7
The answer would be x = 2, y = 7
(10,-5)(10-9) what is the linear equation
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
point 1 (10 , - 5) x1 = 10 y1 = -5
point 2 (10, - 9) x2 = 10 y2 = -9
linear equation = ?
Step 02:
Slope formula
[tex]m\text{ = }\frac{y2\text{ -y1}}{x2-x1}[/tex][tex]m\text{ = }\frac{-9-(-5)}{10-10}=\frac{-9+5}{0}=\frac{-4}{0}=\infty[/tex]The answer is:
The equation of the line is a vertical line in x = 10, since the slope is infinite.
Dylan looked at the function .and said, "This function is always greater than 0, so 0 is the absolute minimum." Explain why Dylan is incorrect.
Given data:
The given function is f(x)=4(1/2)^x.
The given function always greater than zero, the given function never become equal to zero, the asymptote at y=0.
Thus, zero can't be consider as the absolute minima of the function.
Find the slope of the line passing trough the given points point (3 , 2). Point (1, -1)
For this question we will use the formula for the slope of a line passing through two points:
[tex]s=\frac{y_2-y_1}{x_2-x_1}\text{.}[/tex]Substituting the given points we get:
[tex]s=\frac{-1-2}{1-3}=\frac{-3}{-2}=\frac{3}{2}\text{.}[/tex]Answer:
[tex]\frac{3}{2}\text{.}[/tex]Lin ran 234 miles in 2/5 of an hour. Noah ran 823 miles in 4/3 of an hour.Who ran faster, Noah or Lin?How far would Lin run in 1 hour?How far did Noah run in 1 hour?How long would it take Lin to run 1 mile at that rate?How long would it take Noah to run 1 mile at that rate?
Given:
• For Lin:
Distance = 234 miles
Time = 2/5 of an hour
• For Noah:
Distance = 823 miles
Time = 4/3 of an hour
Let's determine who ran faster.
Let's find the time of each runner by multplying by 60.
Where:
60 minutes = 1 hour
To determine the speed of each of them, apply the formula:
[tex]speed=\frac{dis\tan ce}{time}[/tex]• To find Lin's speed, we have:
[tex]\text{ Lin's sp}eed=\frac{dis\tan ce}{\text{time}}=\frac{234}{\frac{2}{5}\ast60}=\frac{234}{24}=9.75\text{ mph}[/tex]Therefore, Lin's speed is 9.75 miles per hour.
• To find Noah's speed, we have:
[tex]undefined[/tex]What is the quotient? 7-^1/7^2
Hello there. To solve this question, we'll have to remember some properties about powers.
We have to determine the following quotient:
[tex]undefined[/tex]Tell whether the following statement is always, sometimes, or never true for numbers greater than zero. Explain. In equivalent ratios, if the numerator of the first ratio is greater than the denominator of the first ratio, then the numerator of the second ratio is greater than the denominator of the second ratio.
Answer
The statement is always true.
Explanation
Since equivalent ratios reduce to essentially the same fundamental ratios, if the numerator of one of the ratios is greater than its denominator, then the numerator of each of the equivalent ratios must be greater than each of their corresponding denominators too.
So, this statement is always true!
Hope this Helps!!!