Answers
The most appropriate choice for functions will be given by -
First and second options are correct
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here Domain of function is obtained from x axis and range of the function is obtained from y axis
For the first option
Every element of domain has a unique image
So first graph is a function.
First option is correct
For the second option
Every element of domain has a unique image
So second graph is a function.
Second option is correct
For the third option
x = 3 has been mapped to every element of y axis
So ]x = 3 has infinite number of images.
Third graph is not a function.
Third option is wrong
For the fourth option
Every point on x axis has been mapped to two elements
So every element of x axis has two images.
Fourth graph is not a function
Fourth option is wrong.
So First and second option are correct
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Related Questions
A 95% confidence interval for the mean hours freshmen spent on social media per day was calculated to be (2.5 hr,3.1 hr). The confidence interval was based on an SRS of
size n=50 and was calculated using a Normal distribution. The population standard
deviation is (show all work).
Answers
The standard deviation of the population is 1.0823
Given
95% confidence interval
Mean fresh men hours on phone 2.5 hr, 3.1 hr
ME is calculated as follows:
Margin of Error = Z a/2 * (sd/ [tex]\sqrt{n}[/tex]) = (Upper
Where sd = standard deviation
n = size of population
interval - Lower Interval) / 2 = (3.1 - 2.5) / 2 = 0.3
Where,
x = Mean
Standard Deviation
(Confidence Level/100) - 1
Z = a/2× ([tex]sd/\sqrt{n}[/tex]), where
([tex]sd/\sqrt{50}[/tex]) = 0.3 = 1.96
Standard deviation equals [tex]0.3\sqrt{\frac{50}{96} }[/tex],
which is 1.0823
Hence the population standard deviation is 1.0823
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In the diagram, the length of segment VS is 39 units.What is the length of segment TV?14 unitsnQ19 units3x + 438 unitsR50 units2x + 56x - 3Save and ExitNextSubmUnmark this question
Answers
From the diagram we know that:
[tex]\begin{gathered} TR=RV \\ TS=\text{VS} \end{gathered}[/tex]Therefore:
[tex]6x-3=39[/tex]Solving for x we get:
[tex]\begin{gathered} 6x=42 \\ x=7 \end{gathered}[/tex]Then:
[tex]\begin{gathered} TV=TR+RV=2RV=2(2x+5)=2(2\cdot7+5) \\ TV=2(19)=38 \end{gathered}[/tex]Answer: 38 units.
Convert the following phrase into a mathematical expression. Use x as the variable. Combine like terms when possible.A number multiplied by - 9, subtracted from the sum of 15 and two times the numberThe expression is(Simplify your answer.)
Answers
Given:
A number multiplied by - 9, subtracted from the sum of 15 and two times the number.
Let the number = x
A number multiplied by - 9 ⇒ -9x
The sum of 15 and 2 times the number ⇒ 15 + 2x
So, the expression will be ⇒ 15 + 2x - (-9x) = 11x + 15
So, the answer will be ⇒ 11x + 15
If $14,000 is invested at 8% interest compounded quarterly, find the interest earned in 12 years.
Answers
Using the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
P = Principal = $14000
r = interest rate = 8% = 0.08
t = time = 12
n = Number of times interest is compounded = 4
Therefore:
[tex]\begin{gathered} A=14000(1+\frac{0.08}{4})^{4\cdot12} \\ A=36218.99 \end{gathered}[/tex]1/4 of a 24-hour period to read 1/3 of his book. At this rate, how many hoursto complete the book?
Answers
We have:
That in 1/4th of 24 hours someone reads 1/3rd of a book, in other words:
[tex]h=\frac{24}{4}\Rightarrow h=6[/tex]So in 6 hours someone reads 1/3rd of a book, now:
If in 6 hours someone reads 1/3 of a book, then how many hours will it take to read the whole book.
In order to solve for the ammount of hours to read the whole book, we multiply the ammount of hours it takes to read 1/3rd of the book (6h) times the total of the book (1 book) and divide by the ammount of book that is read in 6 hours (1/3rd); that is:
[tex]T=\frac{6\cdot1}{(\frac{1}{3})}\Rightarrow T=18[/tex]Therefore the total ammount of time it will take to read the whole book are 18 hours.
5. Order from least to greatest -1/5, 10.5], 0.25, 5/10
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
-1/5, 10.5, 0.25, 5/10
Step 02:
-1/5 = -0.2
5/10 = 0.5
from least to greatest
- 1/5 , 0.25 , 5/10 , 10.5
That is the solution.
Save Submit Melanie and Joseph are raising money for their class trip to the zoo. They each need $30 to pay for the trip and are selling boxes of cookies for $4 each to earn the money. Joseph has sold 5 boxes and Melanie has sold 3 boxes. How much more money does Melanie need than Joseph? A) $10 B) $12 $18 DY $8
Answers
Save Submit Melanie and Joseph are raising money for their class trip to the zoo. They each need $30 to pay for the trip and are selling boxes of cookies for $4 each to earn the money. Joseph has sold 5 boxes and Melanie has sold 3 boxes. How much more money does Melanie need than Joseph? A) $10 B) $12 $18 DY $8
Joseph -------> has sold 5 boxes
5*($4)=$20 --------> need 30-20=$10
Melanie -------> has sold 3 boxes
3*($4)=$12 ------> need 30-12=$18
therefore
18-10=$8
answer is $8Carol says that 83 + 96 + 74 is greater than 300.
Is Carol correct? Why or why not?
Answers
Answer:
that girl is wrong because if you add 83+96+74 it equals 253, and that is not greater than 300
Step-by-step explanation:
Simplify the expression [tex]\sqrt[3]{32a^{7} }b\fracx^{9}[/tex] . Assume a ≠ 0 and b ≠ 0.
Enter the correct answer in the box.
Answers
The result obtained when we simplify the expression ³√(32a⁷b⁹) is ³√(2⁵ × a⁷) × b³
How to simplify ³√(32a⁷b⁹)The simplification of ³√(32a⁷b⁹) can be obatined as illustrated below:
³√(32a⁷b⁹)
We shall simplify the individual term. This is shown below
³√32 = ³√2⁵
³√a⁷ = ³√a⁷
³√b⁹ = b^(9/3) = b³
Combining the above, we have
³√(32a⁷b⁹) = ³√2⁵ × ³√a⁷ × b³
³√(32a⁷b⁹) = ³√(2⁵ × a⁷) × b³
From the above illustration, we can conclude that simplifying ³√(32a⁷b⁹) results in ³√(2⁵ × a⁷) × b³
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x/-6≥-20help meeee[tex] \frac{x}{ - 6 } \geqslant - 20[/tex]
Answers
We need to solve an inequality given in the form:
[tex]\frac{x}{-6}\ge-20[/tex]So we need to isolate "x" on one side to the inequality symbol.
In order to do that, we need to multiply both sides by the number "-6" (which will cancel out the denominator that "x" has). Bit we need to recall that when we multipkynor divide by a negative number boths sides of an inequality, the symbol flips direction. having that in mind, we proceed to multiply and solve for "x":
[tex]\begin{gathered} \frac{x}{-6}\ge-20 \\ x\leq(-20)\cdot(-6) \\ x\leq120 \end{gathered}[/tex]So the answer is: all real x-values less than or equal to 120.
If we need to give the answer in graphic form, we draw a number line with the origin (0), and mark on the right of it a point that we name "120". Then we highlight the line from the point 120 towards the left, and we make sure that we draw a solid dot on the 120 point mark to indicate that the point is included in the set.
Estimate each sum 22+ 23 + 19 + 20 + 18 + 19 + 22
Answers
Two students were competing to have the
highest amount of sales at a bake sale.
Together they made $132. If each
student had made $15 more in sales, one
student would have made twice as much
as the other student.
How much money did the winning
student make, in dollars?
Answers
Amount of money made by thee winning student as per the given conditions is equal to $93.
As given in the question,
Let x dollars be the money made by winning student
And y be the amount made by other student
As per given conditions:
x + y = $132 ___(1)
x + 15 = 2(y+15)
⇒ x +15 = 2y +30
⇒ x-2y =15 ____(2)
Multiply (1) by 2 and add it to (2)
2x +2y = 264
x - 2y = 15
3x = 279
⇒x =$93
Hence, y = 132 -93
= $39
Therefore, amount of money made by thee winning student as per the given conditions is equal to $93.
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It says to find the area of the figure. Round to the nearest hundredth where necessary. Please Help!
Answers
Answer:
309.76 mm²
Explanation:
The given figure is a square with:
• Side length, s = 17.6 mm
The area of a square with side length, s is found by using the formula:
[tex]A=s^2[/tex]Therefore:
[tex]\begin{gathered} \text{The area of the figure}=17.6^2 \\ =17.6\times17.6 \\ =309.76\; mm^2 \end{gathered}[/tex].The area of the figure is 309.76 mm².
The retail price for Jamaican allspice is $4.69 per ounce. You buy 8 ounces of allspice on sale for $4.62 per ounce. How much money do you save?
Answers
Answer:
Step-by-step explanation
56 cents
Explanation: The deal is 7 cents less per ounce, you need to buy 8 ounces, multiply 7 by 8, equaling 56 cents
Greg bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $350 more than the desktop. He paid for the computers using two different financing plans. For the desktop the interest rate was 7.5% per year, and for the laptop it was 8% per year. The total finance charges for one year were $400. How much did each computer cost before finance charges?
Answers
the cost of laptop and cost of desktop is $1,800 and $2,100 respectively does each computer cost before finance charges.
What are mathematics operations?
• A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.
• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.
From the question above, we can see that the laptop costs $350 more than the desktop, therefore, we say:
let x represent the cost of the laptop ;
then x-350 will be the cost of the desktop .
We can also see that the total finance charge of $400 is equal to 8% of the cost of the laptop and 7.5% of the cost of the desktop, we solve as follows:
400 = 0.08(x) + 0.075(x - 350)
252 = 0.08x + 0.075x - 26.25
252 26.75 = 0.155x
278.75 = 0.155x
x = 278.75/0.155
x = 1798
Recall that:
cost of desktop = x -350
therefore:
1,798- 350 = 1448
cost of laptop = $1798
cost of desktop = $1448
Thus, the cost of laptop and cost of desktop is $1,800 and $2,100 respectively does each computer cost before finance charges.
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Let f(x) = 2x + 7 and g(x) = 3(2x +7). The y-intercept of g is Choose... the y-intercept of f, and the x-intercept of g is Choose... the x-intercept of f.
Answers
The y-intercept of .f(x) = 2x + 7 is 7; its x-intercept is -7/2.
The y-intercept of .f(x) = 2x + 7 is 7; its x-intercept is -21/6.
What is the Y-intercept and the X-intercept of a Function?A function is expressed in slope-intercept form as .f(x) = mx + b, where the y-intercept is represented by the value of b.
On the other hand, to determine the value of the x-intercept for a function, .f(x) = mx + b, substitute .f(x) = 0 into the equation .f(x) = mx + b and solve for the value of x in the equation.
Find the y-intercept and the x-intercept of .f(x) = 2x + 7:
y-intercept of the function (b) = 7
To find the x-intercept, substitute .f(x) = 0 into f(x) = 2x + 7:
0 = 2x + 7
Subtract 7 from both sides
0 - 7 = 2x + 7 - 7
-7 = 2x
Divide both sides by 2
-7/2 = 2x/2
-7/2 = x
x = -7/2
Therefore, the x-intercept is: -7/2.
Find the y-intercept and the x-intercept of g(x) = 3(2x +7):
g(x) = 3(2x +7)
g(x) = 6x + 21
The y-intercept is: 21.
Find the x-intercept by substituting g(x) = 0 into g(x) = 6x + 21:
0 = 6x + 21
-21 = 6x
-21/6 = 6x/6
-21/6 = x
x = -21/6.
x-intercept is: -21/6.
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The function f(x) is a cubic function and the zeros of f(x) are −2, 1 and 2. The y-
intercept of f(x) is -8. Write the equation of the cubic polynomial in standard
form.
Answers
In linear equation, p(x) = -2x³ - 6x² - 12x - 8 is the equation of the cubic polynomial in standard form.
What is linear equation in math?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.Given the roots x1, x2, and x3 of a cubic polynomial, the equation can be written
p(x) = a( x - x₁ ) ( x - x₂) ( x - x₃ )
Where a is the leading coefficient.
We know the three roots of the polynomial −2, 1 and 2.
p( x ) = a( x + 2) ( x + 1 ) ( x + 2 )
Since the y-intercept of the polynomial is y= - 8 when x=0
- 8 = a( 0 + 2 ) ( 0 + 1 ) ( 0 + 2 )
- 8 = a * 4
- 8 = 4a
a = -8/4
a = -2
The polynomial is
p( x ) = -2( x + 2) ( x + 1 ) ( x + 2 )
We must write it in standard form, so we have to multiply all of the factors as follows
p(x) = -2 ( x + 1 )² ( x + 1 )
p(x) = -2 ( x² + 4 + 2x ) ( x+ 1 )
p(x) = -2 ( x₃ + 3x² + 6x + 4 )
p(x) = -2x³ - 6x² - 12x - 8
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How would I begin to find the equation for this? I will post picture of problem below if I can figure out how to upload photo. It's a graph. I have 10 extra credit of these to do...teachers always make extra credit on things we've never even seen before, ugh. Thanks in advance!
Answers
The equation of the parabola is y = (x + 2)² - 2, and the value of f(-1) is -1 after plugging x = -1 in the function.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
From the graph the vertex form of the parabola:
(-2, -2)
h = -2
k = -2
The vertex form of the parabola:
y = a(x - h)² + k
y = a(x + 2)² - 2
Plug x = 0
y = 2
a = 1
y = (x + 2)² - 2
Or
f(x) = (x + 2)² - 2
f(-1) = (-1 + 2)² - 2
f(-1) = -1
Thus, the equation of the parabola is y = (x + 2)² - 2, and the value of f(-1) is -1 after plugging x = -1 in the function.
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The average life span in years of different species of zoo animals are shown: 35, 16, 12, 8, 14, 8, 5, 8, 1, 121. Indentify the number summary. Using 1.5 interquartile ranges up from Q3 and down from Q1, identify any outliers. Min:Max:Q1:Q2:Q3:IQR:Outliers:2. Sketch and label a box-and-whisker plot of the data. Use an appropriate scale.<-----I-----I-----I-----I-----I-----I-----I-----I-----I-----I-----I----->3. What is the mean average life span?Mean:4. What is the MAD for the average life span?MAD:5. Explain what the MAD means in the context of the data
Answers
1)First, lets arrange our data in ascending order:
[tex]1,5,8,8,8,12,12,14,16,35[/tex]notice that we have the following:
[tex]\begin{gathered} \min =1 \\ \max =35 \end{gathered}[/tex]now, since we have ten elements in your data set, we can find the median by adding the two central elements. In this case we have:
[tex]\begin{gathered} \operatorname{median}=\frac{8+12}{2}=\frac{20}{2}=10 \\ \operatorname{median}=10 \end{gathered}[/tex]Next, notice that we can divide our data set in two equal parts:
[tex]\mleft\lbrace1,5,8,8,8\mright\rbrace,\mleft\lbrace12,12,14,16,35\mright\rbrace[/tex]the median in these two subsets are going to be or first and third quartile, therefore, we have that:
[tex]\begin{gathered} Q_1=8 \\ Q_2=10 \\ Q_3=14 \end{gathered}[/tex]Now we can find the IQR:
[tex]\begin{gathered} \text{IQR}=Q_3-Q_1 \\ \Rightarrow IQR=14-8=6 \\ \text{IQR}=6 \end{gathered}[/tex]Finally, the outliers are the following for 1.5 interquantile:
[tex]\begin{gathered} 1.5\cdot\text{IQR}=(1.5)(6)=9 \\ \Rightarrow Outliers\colon Q_1-9=8-9=-1 \\ Q_2+9=14+9=23 \end{gathered}[/tex]2)The box and whisker plot would be the following:
3)We can find the mean with the following formula:
[tex]\operatorname{mean}=\frac{\sum ^n_{i=1}x_i}{n}[/tex]In this case, the mean is:
[tex]\begin{gathered} \operatorname{mean}=\frac{1+5+8+8+8+12+12+14+16+35}{10}=\frac{119}{10}=11.9 \\ \operatorname{mean}=11.9 \end{gathered}[/tex]therefore, the average life span is 11.9
$)We can find the mean absolute deviation (or MAD), with the following expression:
[tex]\text{MAD}=\frac{\sum ^{}_{}|x_i-\operatorname{mean}|}{n}[/tex]with this expression we can find out the variability of the dataset.
In this case, we have the following:
[tex]\begin{gathered} \text{MAD}=\frac{|1-11.9|+|5-11.9|+|8-11.9|+|8-11.9|+|8-11.9|+|12-11.9|+|12-11.9|+|14-11.9|+|16-11.9|+|35-11.9}{10} \\ =\frac{10.9+6.9+3.9+3.9+3.9+0.1+0.1+2.1+4.1+23.1}{10} \\ =\frac{59}{10}=5.9 \\ \text{MAD}=5.9 \end{gathered}[/tex]We have that the MAD for the average lifespan is 5.9
5) Since the mean absolute deviation is 5.9, we can estimate that the values of the dataset are approximately 5.9 units away from the mean. therefore, there is a high variability in the life span of the animals
Are you able to help? If you are thank you
Answers
From the graph of the function, the polynomial has the next roots: -2 (double), -1 (simple), and 3 (simple). Then, its equation is:
[tex]\begin{gathered} y=(x-(-2))^2(x-(-1))(x-3) \\ y=(x+2)^2(x+1)(x-3) \end{gathered}[/tex]Selecting all the correct answers. Which represents the inverse of this statement? Is the inverse true or false?
Answers
Given: A statement- A number is negative if and only if it is less than 0.
p: A number is negative.
q: A number is less than 0.
Required: To find the inverse of the given statement and state if it is true or false.
Explanation: The inverse of the statement will be-
A number is positive if and only if it is greater than 0.
p: A number is positive.
q: A number is greater than 0.
The statement is always true since a positive number is always greater than 0.
Now p and q both are true since any positive number is greater than 0 and any number greater than 0 is always a positive number.
Hence we can write
[tex]\text{\textasciitilde}p\leftrightarrow\text{\textasciitilde}q\text{ }[/tex]The inverse of the given statement is true.
Final Answer: Option D and Option F are correct.
At a dinner table, the meal cost $22 and a sales tax of $1.87 was added to the bill. How much would the sales tax be on a $66 meal? What is the tax rate for the meals in this city?
Answers
Calculate the percentage for the tax rate
using this analysis
[tex]1.87\cdot\frac{100}{22}=8.5[/tex]The tax rate for meals in this city is 8.5%
Calculate the tax for the $66 meal.
[tex]66\cdot0.085\cdot=5.61[/tex]The tax for a $66 meal should be $5.61
Simplify: 3(s + 5)3s + 153s + 58s18s
Answers
The given equation is 3(s + 5)
and it will be simplified as
3(s + 5) = 3s + 15
So option A is correct
you are buying one flower for each member of the swim team to wear at an awards tonight there are 19 members on the team you have decided to buy pink roses and yellow roses the pink roses cost $3 and the yellow roses cost $2 you will spend $50 Let x represent pink roses and y represent yellow roses . If there's a solution graph them
Answers
Let:
x = Number of pink roses
y = Number of yellow roses
there are 19 members on the team, so:
[tex]x+y\le19[/tex]the pink roses cost $3 and the yellow roses cost $2 you will spend $50, so:
[tex]3x+2y\le50[/tex]so:
[tex]\begin{gathered} y\le19-x \\ y\le\frac{1}{2}(50-3x) \end{gathered}[/tex]A shirt is on sale for 25% off. Sandy paid $7.50 for the shirt. What was the shirt's regular price?
Answers
Ik cause I took the quiz
The radius of a circle is 10 centimeters. What is the area?Give the exact answer in simplest form. _____ square centimeters (pi, fraction)
Answers
The radius of the circle can be computed using the equation
[tex]A=\pi r^2[/tex]The radius of the circle is provided in the problem, which is 10 cm. Just plug it in on the equation above and compute, we get
[tex]A=\pi(10cm)^2=100\pi cm^2[/tex]The exact answer is 100π square centimeters.
Can you please help me out with this I’m stuck
Answers
Given
Find
the value of x
Explanation
given m is parallel to n.
so, these are corresponding angles.
hence
[tex]\begin{gathered} 4x-23=2x+17 \\ 2x=17+23 \\ 2x=40 \\ x=20 \end{gathered}[/tex]so, x = 20
Final Answer
The value of x is 20
about 7 out of 20 homes have a dishwahser on a street with 60homes, how many would you expect to have?
Answers
On a street with 60 homes, about 7 out of 20 have a dish washer, and 21 expect to have one.
Explain about the equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.Expressions that add up to one another make form an equation. A formula is an equation containing two or more variables that shows how the variables relate to one another. A line with the equation y=mx+b, where m denotes the slope and b the y-intercept, is an example of a linear equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.A ratio can be used to resolve this 7/20=x/60 is the ratio.
20x=420
x=21
The answer is 21
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True or False: It does not matter which side you get the variable as stated by the symmetric property.
Answers
Answer: True
Step-by-step explanation: As the Symmetric property states you can put a variable on either side of a problem, or an equation.
rewrite the expression in standard form (use the Fewest number of symbols and characters possible) a. 5g + yh
Answers
a) 5y
b) 7de
c) 20yz
d) 90d
Explanation:[tex]1a)\text{ }5\times y=5y[/tex][tex]b)\text{ }7\times d\times e=7de[/tex][tex]\begin{gathered} c)\text{ }5\times2\times2\times\times y\times z \\ 5\times2\times2=20 \\ \text{ }y\times z\text{ = yz} \\ 5\times2\times2\times\times y\times z\text{ = 20yz} \\ \end{gathered}[/tex][tex]\begin{gathered} d)\text{ }3\times3\times2\times5\times d\text{ } \\ 3\times3\times2\times5\text{ = 90} \\ 3\times3\times2\times5\times d=\text{ 90d} \end{gathered}[/tex]