Answers
Answer:
1st and last one
Step-by-step explanation:
the first and the last one are the only ones that represent a function because for each value of x there is only one corresponding value of y.
A graph represents a function if each value of x corresponds uniquely to a value of y. These graphs, often called line graphs, can depict various types of functions like linear, quadratic, etc. The slope and position of the line will vary depending on the function's formula.
Explanation:
In the subject of Mathematics, specifically when dealing with functions and graphs, a graph represents a function if each value of x corresponds to a unique value of y. This means that different values of x will produce different values of y. Graphs can be produced using specific pairs of (x,y) data points.
These graphs may be named line graphs as they showcase the relationship between two variables: one measured on the horizontal axis (x) and the other on the vertical axis (y). An example could be a function where y = a + bx. If b > 0, the line of the graph slopes upward to the right. If b = 0, the line is horizontal. If b < 0, the line slopes downward to the right.
Graphs may also represent other types of functions like linear, quadratic, inverse, or exponential, depending on the equation of the relation between x and y. It's also important to note that there can be other types of graphs, such as a specific type of line graph shown, where the x-axis consists of data values and the y-axis consists of frequency points.
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Related Questions
for lunch , you must choose a sandwich, a piece of fruit, and a drink. your choices include a ham sandwich, tuna sandwich, or cheese sandwich; an apple or an orange; and skim milk, whole milk, fruit juice, or bottle water. how many combinations of choices are possible
Answers
PLEASE HELP ME ASAP!!!
1. The average cost per ounce for glass cleaner is 7.7 cents with a standard deviation of 2.5 cents. What is the z-score of glass cleaner with a cost of 10.1 cents per ounce?
A. 0.96
B. 1.31
C. 1.94
D. 4.04
E. none of the above
2. A candy bar takes an average of 3.4 hours to move through an assembly line. If the standard deviation is 0.5 hours, what is the probability that the candy bar will take between 3 and 4 hours to move through the line?
A. .2119
B. .2295
C. .6731
D. .3270
E. .8849
3. The average noise level in a diner is 30 decibels with a standard deviation of decibels. 99% of the time, the noise level is below what value?
A. 16.04
B. 30.00
C. 36.00
D. 43.96
E. 48.00
4. The mean income per household in a certain state is $29,500 with a standard deviation of $5,750. The middle 95% of incomes is between what two values? The incomes are normally distributed.
A. $23, 750 and $35,250
B. $18,000 and $41,000
C. $29,500 and $41,000
D. $12,250 and $46,750
E. $12,325 and $81,550
Answers
The z-score of a value, a, given the mean, μ, and the standard deviation, σ, is given by
[tex]z= \frac{a-\mu}{\sigma} [/tex]
Thus, given that the average cost per ounce for glass cleaner is 7.7 cents with a standard deviation of 2.5 cents.
The z-score of glass cleaner with a cost of 10.1 cents per ounce is given by
[tex]z= \frac{10.1-7.7}{2.5} = \frac{2.4}{2.5} =\bold{0.96}[/tex]
Part 2:
Assuming the data is normally distribution, the probability that a normally distributed data is between two values a and b is given by
[tex]P(a\ \textless \ X\ \textless \ b)=P(X\ \textless \ b)-P(X\ \textless \ a) \\ \\ =P\left(z\ \textless \ \frac{b-\mu}{\sigma} \right)-P\left(z\ \textless \ \frac{a-\mu}{\sigma} \right)[/tex]
Thus, given that a candy bar takes an average of 3.4 hours to move through an assembly line and that the standard deviation is 0.5 hours.
The probability that the candy bar will take between 3 and 4 hours to move through the line is given by
[tex]P(3\ \textless \ X\ \textless \ 4)=P(X\ \textless \ 4)-P(X\ \textless \ 3) \\ \\ =P\left(z\ \textless \ \frac{4-3.4}{0.5} \right)-P\left(z\ \textless \ \frac{3-3.4}{0.5} \right)=P(z\ \textless \ 1.2)-P(z\ \textless \ -0.8) \\ \\ =0.88493-0.21186=\bold{0.6731}[/tex]
Part 3
Given that the average noise level in a diner is 30 decibels with a standard deviation of 4 decibels.
The value for which the noice level is below 99% of the time is the value for which the probability that the noice level is below that value is 0.99.
Assuming the data is normally distribution, the probability that a normally distributed data is less than a value, a, is given by
[tex]P(X\ \textless \ a)=P\left(z\ \textless \ \frac{a-\mu}{\sigma} \right)[/tex]
Thus, given that the average noise level in a diner is 30 decibels with a standard deviation of 4 decibels.
The value for which 99% of the time, the noise level is below is obtained as follows:
[tex]P(X\ \textless \ a)=0.99 \\ \\ \Rightarrow P\left(z\ \textless \ \frac{a-30}{4} \right)=P(z\ \textless \ 2.33) \\ \\ \Rightarrow\frac{a-30}{4}=2.33 \\ \\ \Rightarrow a=4(2.33)+30=\bold{39.32}[/tex]
Note: there is standard deviation value was omitted in the question post but I used 4 as my standard deviation. So you can substitute the appropriate standard deviation for you question.
Part 4:
From the empirical rule, it is known that for a normally distributed data that 95% of the data are within 2 standard deviations.
Thus, given that the mean income per household in a certain state is $29,500 with a standard deviation of $5,750.
The values between which 95% of the incomes lies is obtained as follows:
[tex]95\% \ of \ the \ data \ lies \ between \ \mu\pm2\sigma=\$29,500\pm2(\$5,750) \\ \\ =\$29,500-\$11,500 \ and \ \$29,500+\$11,500=\bold{\$18,000 \ and \ \$41,000}[/tex]
Final answer:
The student's questions involve calculating z-scores and applying knowledge of normal distributions to determine probabilities and percentile ranges within a set of data. Correct answers include finding the z-score for glass cleaner costs, determining the probability of assembly line time for a candy bar, identifying the noise level not exceeded 99% of the time in a diner, and calculating the income range for the middle 95% in a state.
Explanation:
To solve these problems related to standard normal distribution and probabilities, we'll follow a step-by-step process. For each question, you'll either need to calculate a z-score or apply knowledge of normal distributions.
The z-score for a glass cleaner costing 10.1 cents per ounce when the mean cost is 7.7 cents and the standard deviation is 2.5 cents is calculated as: z = (10.1 - 7.7) / 2.5 = 0.96. The correct answer is A.The probability of a candy bar taking between 3 and 4 hours through the assembly line involves finding the area under the normal curve between these two z-scores: z for 3 hours and z for 4 hours. Use z-tables or calculators to find P(3 < X < 4) = P(Z < (4 - 3.4) / 0.5) - P(Z < (3 - 3.4) / 0.5) which gives us C. 0.6731.To find the noise level that is not exceeded 99% of the time, use the z-score that corresponds to 99% in the standard normal distribution and multiply by the standard deviation and add to the mean. This gives us 43.96 decibels, with D being the correct answer.The middle 95% of normally distributed incomes is found using z-scores that correspond to the 2.5th percentile and 97.5th percentile because 95% is in between. The correct answer is A. $18,000 and $41,000.5c+2(10−c) ????????
(x+8) - (X-8) ?????
Answers
[tex]5c + 2(10-c) Use the distributive property =5c+(2)(10)+(2)(-c) =5c + 20 -2c = 3c + 20 -------------------------- (x+8)-(x-8) x + 8 - x + 8 = 16 Best of luck! [/tex]
Suppose you're given the formula R = s + 2t. If you know that s is three times greater than t, how could you rewrite the formula?
A. R=3 (s+t)
B. R=5s
C. R=5t
D.R=3(s+2r)
Answers
r=s+2t
s=3t
so R = 3T+2T=5T
Answer:the answer is C
Step-by-step explanation:
what are the zeros of f(x)=x^2+7x+5
Answers
How many people lost their jobs when minimum wage increased from $12 to $18?
Answers
Answer:
15 people lost their jobs when minimum wage increased from $12 to $18
Step-by-step explanation:
When the minimum wage is $12
Then by looking at the given graph :
Number of labors supplied = 33
Number of labors in demand = 33
So, it is an equilibrium wage for the system.
Now, when the minimum wage increased from $12 to $18
From the given graph :
Number of labors supplied = 45
Number of labors in demand = 18
⇒ Number of labors working when wage is $12 = 33
And when the wage is $18, no. of labors working or are in demand = 18
⇒ Number of workers who lost their job = 33 - 18 = 15
Hence, 15 people lost their jobs when minimum wage increased from $12 to $18
How to know if a line is parallel perpendicular or neither?
Answers
Gail owns a small business. There was a profit of $43 on Saturday and a loss of $48 on Sunday. Find the total profit or loss for the weekend.
A) $5 profit
B) $5 loss
C) $91 loss
D) $91 profit
Answers
Samantha is planting a garden in her backyard that is going to be 600 square inches. She loves tomatoes and wants them to cover 60% of the garden. She then put lettuce in 1/3 of what was left. The remaining part of her garden was used for fresh herbs. What is the area of the garden that is fresh herbs?
Answers
10% of 600 is 60
60×6=360
so 360 sq inches are used for tomatoes.
600-360=240
240 square inches are left
240/3 = 80 square inches used for lettuce
240-80=160
therefore she uses 160 square inches of garden for fresh herbs! :)
What is 12.1167 rounded to the nearest hundredth?
Answers
Boats can travel anywhere between 50 and 150 kilometers per hour. Choose a speed between 50 and 150. Convert the speed you chose into meters per second and explain how you set up the conversion factor.
Answers
HELPS ASAP PLEASE!!!!
Find the product of -9 and -3.
A. 27
B. -27
C. 3
D. -3
Answers
You are dealt one card from a 52-card deck. find the probability that you are not dealt: a heart.
Answers
PLEASE HELP ME!!! WORTH 10 POINTS!!!
Write the equation of the line, in point-slope form. Identify (x1, y1) as the point (1, 2). Use the box provided or the upload option to submit all of your calculations and final answer.
Answers
Formula for slope: [tex] \frac{y2-y1}{x2-x1} [/tex]
Plug in values: [tex] \frac{-2-2}{-1-1} = - \frac{4}{2} = 2[/tex]
Slope: [tex]2[/tex]
Second, we must plug into point-slope form.
Formula for point-slope: [tex]y-y1=m(x-x1)[/tex]
Plug in the values: [tex]y-2=2(x-1)[/tex]
And there you have your answer in point-slope form
We first need to find the slope.
Slope formula : m = y₂-y₁ / x₂-x₁
The graph gives us 2 points : (1, 2) & (-1, -2)
Simply plug everything in! :)
m = -2 - 2 / -1 -1
Simplify.
m = -4/-2
Simplify.
m = 2
So, our slope is 2.
Now that we have the slope as well as a plot, we can plug this into the point-slope formula.
Remember : y - y₁ = m(x - x₁) is the point-slope formula.
m = 2 ; Passes through (1, 2)
Plug everything in :)
y - 2 = 2(x - 1)
~hope I helped!~
Megan is starting a business selling cookies. She researched other businesses to determine the price that people are willing to pay for a dozen cookies her results can be represented by the equation n=-2p+16 where P is the price per dozen cookies and N is the number of dozens sold where does the graph of the equation cross the x-axis?
Answers
n = -2p + 16
0 = -2p + 16
2p = 16
p = 8
(8, 0)
Option C.
Which of the following is the quadratic parent function
Answers
Answer:
A. F(x)=x^2
Step-by-step explanation:
Answer: Option A F(x)=[tex]x^{2}[/tex]
Explanation:
Quadratic function is the function which has degree two
Degree is the highest power of a polynomial
In option B we have |x| in which degree is one hence, discarded
In option C we have [tex]x^{3}[/tex] in which degree is three hence, discarded
In option D we have x which is a linear function being of degree one. Hence, discarded.
What is 4.14 trillion in scientific notation?
Answers
The given data can be written in scientific notation as 4.14 × 10¹².
How to write a number in scientific notation?In order to write a number in scientific notation, express the number in terms of the product of a number between 0 to 10 and the power of 10.
For example, 32 can be written as 3.2 × 10¹.
Here, 3.2 is between 0 and 10 and the power of 10 is 1
The given data is 4.14 trillion.
Since, one trillion can be written as,
1 trillion = 1,000,000,000,000
The number of zeros is 12.
In the scientific notation 4.14 trillion can be written as below,
4.14 × 10¹²
Hence, the scientific notation of the given data is 4.14 × 10¹².
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find the product of (a²+b)(2a²-5b)
Answers
I really need help doing this spelling plz answer really Quick
Answers
12. = reptiles
13. = rodeos
14. = countries
15. = taxes
16. = zeroes
17. = difficulties
18. = lashes
19. = abilities
20. = losses
A. Matching Definitions:
1 small whirls - eddies
2. snake teeth - fangs
3. rattlesnakes - rattles
4. defeats; failures - losses
5. freedoms - liberties
6. skills; talents - abilities
7. bunches or groups - batches
8. eyelid hairs - lashes
9. nations - countries
10. accepted truths - beliefs
How to perform the completing sentences11. The cook put potatoes and carrots in the stew.
12. Are crocodiles and alligators reptiles?
13. Many rodeos have riding and roping events.
14. The travelers were happy in their new surroundings.
15. Our taxes will be used to build new schools.
16. The numeral 100 has two zeroes.
17. He searched the paper for job opportunities.
18. You can use an ax to put notches in a log.
19. The clever criminal had many different identities.
20. Pioneers faced many difficulties in the wilderness.
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A shop advertised a 27% off sale. If a coat originally sold for 253 , find the decrease in price and the sale price
Answers
253-68.31 OR 253*0.73= 184.69 (sale price)
How many diagonals can be drawn from one vertex of a hexagon
Answers
Nine diagonals can be drawn from the vertex of a hexagon.
What is diagonal?A diagonal of a polygon is a line segment joining two vertex points, excluding the sides of the polygon.
The formula used to find the number of diagonals of a polygon is
(n(n-3))/2
where n is the number of sides of the polygon.
A hexagon has six sides. So, n=6.
The number of diagonals in a hexagon is given by
(6(6-3))/2=9
Hence, a hexagon has nine diagonals.
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Quadratic inequalities
Answers
if f(x)= 5x +40 what is f(x) when x= -5
Answers
f(-25)=5+40.
f(-25) is your answer.
Find the real roots of the equation x^4-5x^2-36=0
Answers
Then x^4 - 5x^2 - 36 = 0 becomes p^2 - 5p - 36 = 0.
This factors nicely, to (p-9)(p+4) = 0. Then p = 9 and p = -4.
Equating 9 and x^2, we find that x=3 or x=-3.
Equating -4 and x^2, we see that there's no real solution.
Show that both x=3 and x=-3 are real roots of x^4 - 5x^2 - 36 = 0.
Three interior angles of a quadrilateral measure 55, 117 and 120 degrees. What is the measure of the fourth interior angle?
Answers
4 angles = 360
120 + 117 +55 = 292
360-292 = 68
4th angle = 68 degrees
The typical flight of stairs has 12 steps. Billy is on a new fitness regimen that requires him to climb at least 300 steps each day. His fitness tracker says he has already climbed 175 steps.
Let n represent the number of flights of stairs Billy has yet to climb.
Create the inequality that symbolizes this situation.
Then answer this.
If Billy climbs 10 more flights of stairs, will he meet his required 300 steps?
Answers
and No because he would have only climbed 295 steps.
You would base your equation as 300 ≤ n + 175.
But, you need to fix the equation on one unit. Let's go with the stairs route.
If he goes up 10 more flights, you can multiply the amount of steps per flight (12) by the amount of flights (10).
10 × 12 = 120
So, you need to figure out if 300 ≤ 120 + 170 is a true statement. Solving it would be adding 120 to 170.
120 + 170 = 290
Well, 300 is not ≤ 290, so the answer would be no, he wouldn't reach his goal.
Write an algebraic expression for the phrase. 8 times the quantity d minus 3 8d – 3 8(d – 3) d(8 – 3)
Answers
The quantity is what is in the parentheses which is d-3. Then, you multiply that quantity by 8 because it it's being "timesed"? (multiplied) 8 times.
Which function below is the inverse of f(x) = the quantity of two x plus three, over five.?f−1(x) = the quantity of five x plus three, over twof−1(x) = the quantity of five x minus three, over twof−1(x) = five over the quantity of two x plus threef−1(x) = five over the quantity of three minus two x?
Answers
[change f(x) to y]: y=(2x+3)/5
[swap x and y]: x=(2y+3)/5
[solve again for y]: 5x=2y+3
y=(5x-3)/2
f-1(x) = (5x-3)/2..."The quantity five x minus three, over two
Answer:
[tex]f^{-1}(x)=\dfrac{5x-3}{2}[/tex]
f⁻¹(x) = the quantity of five x minus three, over two
C is correct
Step-by-step explanation:
Given: [tex]f(x)=\dfrac{2x+3}{5}[/tex]
We need to find inverse of function f(x)
Step 1: Set f(x)=y
[tex]y=\dfrac{2x+3}{5}[/tex]
Step 2: Switch x and y
[tex]x=\dfrac{2y+3}{5}[/tex]
Step 3: Solve for y (isolate y)
[tex]5x=2y+3[/tex]
[tex]2y=5x-3[/tex]
[tex]y=\dfrac{5x-3}{2}[/tex]
Therefore, [tex]f^{-1}(x)=\dfrac{5x-3}{2}[/tex]
Now we write as sentence form,
Inverse of f(x) is 5 times of x minus 3 over 2.
Hence, f⁻¹(x) = the quantity of five x minus three, over two
Find the volume of a cube that will hold sixty-four 4.19 in3 toy bouncy balls. (round to nearest whole number)
Answers
we know that
The volume of the ball (sphere) is equal to
[tex]V=\frac{4}{3} \pi r^{3}[/tex]
In this problem we have
[tex]V=4.19\ in^{3}[/tex]
Find the radius of the sphere
[tex]r=\sqrt[3]{\frac{3V}{4\pi}}[/tex]
Substitute the value of V
[tex]r=\sqrt[3]{\frac{3*4.19}{4\pi}}=1\ in[/tex]
for the calculation of the total volume I will assume that each ball is a cube
The volume of each ball is
[tex]V=b^{3}[/tex]
where
b is the diameter of the ball
[tex]b=1*2=2\ in[/tex]
Substitute
[tex]V=2^{3}=8\ in^{3}[/tex] ------> volume of each ball in the shape of cube
so
Multiply by [tex]64[/tex]
[tex]64*8=512\ in^{3}[/tex]
therefore
the answer is
[tex]512\ in^{3}[/tex]
If the width of the rectangle is three times the length and the perimeter of the rectangle is 72 ft, what are the length and width of the rectangle?
Answers
W+W+L+L=72
Replace W with 3L: 3L+3L+L+L=72
8L=72
L=9
W=27