Compare the -intercepts and the rates of change of the following items.
A.The y-intercepts are the same, but the rates of change are different.
B.The items have the same y-intercept and the same rate of change.
C.The items have different y-intercepts and different rates of change.
D.The rates of change are the same, but the y-intercepts are different.
Answers
Answer:
C. The items have different y-intercepts and different rates of change
Step-by-step explanation:
Figure I shows a linear equation in the form y = mx + b, where "m" is the rate of change and "b" is the y-intercept. That means for y = 1/4 * x - 1/2, 1/4 is the slope and 1/2 is the y-intercept.
Figure II shows a table. The y-intercept is when x = 0, so look at where x = 0 is in the table and see the y-value which corresponds to it. The y-value in this case would be -0.25. To find the rate of change, assuming Table II is changing at a constant rate, subtract the subsequent y-value from a proceeding y-value and divide that by subtracting the corresponding x-values (any two sets of x and y-values should work): (3.75 - 7.75)/(-1 - -2) = -4/(-1 + 2) = -4/-1 = 4.
Thus, we know that the rates of change are different and the y-intercepts are different for both functions.
Related Questions
ASAPPP PLEAse 25 pointss
Show work it's already solved but show work\
`its 2 questions
Answers
Volume First Cylinder: 50.24 in³
Volume Second Cylinder: 127.5625 inch³
Volume Third Cylinder: 904.32 inch³
Volume First Cylinder:
= πr²h
= 3.14(2)² (4)
= 3.14 x 16
= 50.24 in³
Volume Second Cylinder:
= πr²h
= 3.14(2.5)² (6.5)
=3.14 (6.25)(6.5)
= 127.5625 inch³
Volume Third Cylinder:
= πr²h
= 3.14(6)² (8)
=3.14 (36)(8)
= 904.32 inch³
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Hallar la ecuación de la parábola cuya directriz es la recta x= - 6 y su foco es F(0,0).
Answers
The required equation of the parabola is y² = 24x for focus (6,0) and directrix x= -6 .
The focus and directrix of the required parabola are as,
Focus (6, 0)
and, Directrix x = - 6
Since the focus of the parabola lies on the x- axis, the x- axis is said to be the axis of the parabola.
Therefore, the equation of the parabola is either of the form,
y² = 4ax
or, y2 = - 4ax
depending on which axis the parabola is in, that is whether negative or positive axis.
It is also seen that the directrix, x = - 6 which implies it is to the left of the y- axis while the focus is (6, 0) which implies it is to the right of the y-axis.
Hence, the parabola is of the form y² = 4ax.
Since, a = 6
Thus, the equation of the parabola is y² = 4(6)x
⇒ y² = 24x
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cylinder radius2 cm height7 cm
13. What is the shape of the bases?
Answers
Answer:
88
Step-by-step explanation:
y=2cm h=7cm
CSA=22/7×4×7
the sevens get crossed out and then 22/1 ×4=88.
Consider the following random sample of diameter measurements (in inches) of 14 softballs.
4.75, 4.71, 4.78, 4.81, 4.69, 4.89, 4.68, 4.86, 4.84, 4.86, 4.75, 4.72, 4.71, 4.69
Send data to calculator Send data to Excel
If we assume that the diameter measurements are normally distributed, find a 99% confidence interval for
the mean diameter of a softball. Give the lower limit and upper limit of the 99% confidence interval.
Answers
Step-by-step explanation:
sadly, we have only 14 data points. that is a very small sample to find a more or less reliable standard deviation for the production of softballs.
because to create the desired answer we need to calculate the mean value and the standard deviation. and we need to mix that with the Z- value of the standard normal distribution table representing the 99% confidence (= coverage of 99% of the area under the normal distribution curve, meaning therefore from 99.5% to 0.5%).
the confidence interval limits are
mean ± Z×sd/sqrt(n)
mean = mean value of the sample.
sd = standard deviation (either of - preferred - the entire population or of the sample)
n = number of data points (here 14).
Z = Z value of the standard normal distributing table for 99% (2.576).
here a little table for different confidence intervals :
Confidence Interval Z
80% 1.282
85% 1.440
90% 1.645
95% 1.960
99% 2.576
99.5% 2.807
99.9% 3.291
mean value = sum of all data points divided by the number of data points :
mean = 66.74/14 = 4.767142857...
sd = sqrt(sum((data point difference to mean)²)/n)
let's use some calculation tool like Excel (after all, the mean value is not a simple number, and to write this all up here takes a lot of space).
sd = 0.069941667...
the confidence interval limits are then
4.767142857... ± 2.576×0.069941667.../sqrt(14) =
= 4.767142857... ± 0.048152387...
upper limit = 4.815295244 ... ≈ 4.82
lower limit = 4.71899047 ... ≈ 4.72
that means, we are 99% sure that the true mean value across all produced softballs is between these 2 limits.
in other words, for 99% of such samples we can pick, their mean values will be between these 2 limits. and 1 % of such samples we expect to have a mean value outside of these 2 limits.
Find the maximize z = 4x + y. Subject to the constraints x + y ≤ 50, 3x + y ≤ 90, x,y ≥ 0
Answers
The maximum value of z = 4x + y subject to the given constraints is 180, which occurs at x = 45 and y = 0.
How to deal with inequality?To find the maximum value of z = 4x + y subject to the given constraints, we can use linear programming.
Graph the constraints:
First, we will graph the constraints to visualize the feasible region.
The constraint x + y ≤ 50 represents the region below the line x + y = 50:
The constraint 3x + y ≤ 90 represents the region below the line 3x + y = 90:
The feasible region is the shaded region that satisfies both constraints:
Identify the corner points of the feasible region:
The feasible region has four corner points: (0, 0), (0, 50), (30, 20), and (45, 0).
Evaluate z at each corner point:
z(0, 0) = 4(0) + 0 = 0
z(0, 50) = 4(0) + 50 = 50
z(30, 20) = 4(30) + 20 = 140
z(45, 0) = 4(45) + 0 = 180
Compare the values of z at the corner points:
The largest value of z is 180, which occurs at the corner point (45, 0).
Therefore, the maximum value of z = 4x + y subject to the given constraints is 180, which occurs at x = 45 and y = 0.
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Please what is the answer?
Answers
Answer:
When we have a set of points, we can find the distance between them using the formula:
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex], where d is the distance, x1 and x2 are one point and y1 and y2 are another point.
OB:
Thus, for OB, we can allow O(6, 6) to be our x1 and x2 point and we can allow B(9, 6) to be our y1 and y2 point:
[tex]d=\sqrt{(6-9)^2+(6-6)^2} \\d=\sqrt{(-3)^2+(0)^2} \\d=\sqrt{(-9)} \\d=3[/tex]
Thus, the first part/step in the equation is your subtraction expression to find the length of OB.
AB:
For AB, we can allow A(9, 10) to be our x1 and x2 point and we can allow B (9, 6) to be our y1 and y2 point:
[tex]d=\sqrt{(9-9)^2+(10-6)^2}\\ d=\sqrt{(0)^2+(4)^2}\\ d=\sqrt{16}\\ d=4[/tex]
The first part/step is your subtraction expression for the length of AB.
. According to the National Highway Traffic Safety Administration, seat belt using among American
drivers and front-seat passengers passed 90% for the first time in 2016. At that time, 90.1% of
people used seat belts. If four people are selected at random, find the probability that all four
regularly use seat belts.
Answers
The probability that all four people regularly use seat belts is approximately 0.656 or 65.6%.
To find the probability that all four people regularly use seat belts, we need to use the multiplication rule of probability which states that the probability of two or more independent events occurring together is the product of their individual probabilities.
The probability that the first person uses a seat belt is 0.901, and assuming that the events of seat belt use by different people are independent, the probability that the second person also uses a seat belt is 0.901.
The probability that the third person uses a seat belt is also 0.901, and the probability that the fourth person uses a seat belt is also 0.901.
Therefore, the probability that all four people regularly use seat belts is:
P(all four use seat belts) = P(person 1 uses seat belt) x P(person 2 uses seat belt) x P(person 3 uses seat belt) x P(person 4 uses seat belt)
P(all four use seat belts) = 0.901 x 0.901 x 0.901 x 0.901
P(all four use seat belts) = 0.656
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Sarah is borrowing money from a friend. She is paying 5% interest. after 18 months, she paid her friend the principal plus $45. what was the original amount she borrowed?
Answers
The interest rate is 5%, which means that Sarah would owe 5% of the principal for each year that she borrows the money. Since she borrowed the money for 18 months, or 1.5 years, she would owe 5% * 1.5 = 7.5% interest.
So the total amount that Sarah owed her friend after 18 months is:
P + 0.075P = 1.075P
We know that Sarah paid her friend the principal plus $45, so we can set up the following equation:
1.075P = P + 45
Simplifying this equation, we get:
0.075P = 45
Dividing both sides by 0.075, we get:
P = 600
Therefore, the original amount that Sarah borrowed was $600.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
g°f = -9 So, the correct answer is (B) -9.To find g°f, we need to first apply the function f to -3, and then apply the function g to the result.
what is function ?
In mathematics, a function is a relation between two sets, called the domain and the range, that assigns to each element of the domain exactly one element of the range.
In the given question,
To find g°f, we need to first apply the function f to -3, and then apply the function g to the result.
Step 1: Apply f to -3
f(x) = 3x + 7
f(-3) = 3(-3) + 7 = -2
Step 2: Apply g to the result of f(-3)
g(x) = 2x - 5
g(-2) = 2(-2) - 5 = -9
Therefore, g°f = -9.
So, the correct answer is (B) -9.
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The area of this rhombus is 20 square miles. One of its diagonals is 10 miles. What is the length of the missing diagonal?
Answers
========================================================
Work Shown:
[tex]d_1 = \text{ one of the diagonals} = 10\\\\d_2 = \text{ the other diagonal}= \text{x}\\\\A = \text{ area of the rhombus} = 20\\\\A = \frac{d_1*d_2}{2}\\\\20 = \frac{10\text{x}}{2}\\\\20*2 = 10\text{x}\\\\40 = 10\text{x}\\\\\text{x} = 40/10\\\\\text{x} = 4[/tex]
The other diagonal is 4 miles long.
A dance instructor ears $75 for teaching 3 classes. The instructor receives a 10% raise. Enter how much the instructor earns, in dollars, per class after the raise.
Answers
Consider the following.
f(x) = x^5 − x^3 + 4, −1 ≤ x ≤ 1
(a) Use a graph to find the absolute maximum and minimum values of the function to two decimal places.
Answers
The function has a local maximum at x = 1 and a local minimum at x = 1/5, as shown in the graph, and the absolute maximum and minimum occur at x = 0 and x = (3/5), respectively.
what is function?Numbers and their variants, equations and related structures, forms and their arrangements, and the places where they might be found are all topics covered in mathematics. The term "function" describes the relationship between a collection of inputs, each of which has a corresponding output.
A function is an association between inputs and outputs that yields one unique outcome for each input. Every function has a domain and a codomain, often known as a scope. Functions are commonly represented with the letter f. (x). As input, an x is used. On functions, one-to-one functions, many-to-one functions, within functions, and on functions are the four fundamental types of functions available.
To obtain the absolute maximum and lowest values of the function over the interval −1 ≤ x ≤ 1, we must examine the critical points and the interval endpoints.
We first take the derivative of f(x) and set it to zero to determine the critical points:
The function is then assessed at these pivotal points and the interval's endpoints:
As we can see from the information above, f(x) has a maximum value of 4 and occurs at the values x = 0 and x = 1. The absolute minimum value of f(x) is approximately 2.65 for x = (3/5).
We can corroborate these findings by charting the graph of f(x) across the 1 x 1 interval: graph of f(x) = x5 x3 + 4
According to the graph, the function has a local maximum at x = 1 and a local minimum at x = 1/5, but the absolute maximum and lowest are, respectively, x = 0 and x = (3/5).
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A 2-pound package of hamburger costs $7.00, and you pay $10.50 for a 3-pound package of hamburger.
Answers
A 2-pound package of hamburger costs $7.00, and you pay $10.50 for a 3-pound package of hamburger.
To find the cost per pound of hamburger, we need to divide the total cost by the weight in pounds.
For the 2-pound package
Cost per pound = Total cost / Weight in pounds
Cost per pound = $7.00 / 2 lbs
Cost per pound = $3.50 per pound
For the 3-pound package
Cost per pound = Total cost / Weight in pounds
Cost per pound = $10.50 / 3 lbs
Cost per pound = $3.50 per pound
Therefore, the cost per pound of hamburger is the same for both packages, at $3.50 per pound.
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1) You're traveling to Spain this
summer. You'll have $200 to spend on
memorabilia items. How much euros
do you have to spend on memorabilia
items? Note: $1=0.84 E
Answers
Using the conversion factor we know that we will spend 180.69€ on memorabilia items.
What is the conversion factor?A conversion factor is a number that is used to multiply or divide one set of units into another.
If a conversion is required, it must be done using the correct conversion factor to get an identical value.
A fraction that is equal to "1" is a conversion factor.
The numerator and denominator are the same amounts, but they are expressed in different units. It is used to change a number's unit of measurement.
By multiplying the initial number by the fraction that is equal to "1," you can change the units without changing the original number's value.
So, in the given situation:
$200 = euros?
We know that:
$1 = 0.90€
Then,
$200 = 180.69€
Therefore, using the conversion factor we know that we will spend 180.69€ on memorabilia items.
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The committee spends $462 on costumes for 24 people. Each costume costs the same amount of money.
How much did each costume cost, in dollars?
Answers
Answer:
Step-by-step explanation: 462 Divided by 24 = 19.25$
Proof: 19.25 x 24 = 462
Answer: 19.25$
How many times smaller is 1.2 × 106 than 1.47 × 107?
Answers
Answer: It is 1.24x smaller.
Step-by-step explanation:
1.2(106)= 127.2
1.47(107)= 157.3
157.3/127.2 = 1.24x smaller
Please help studying for next grade:
192-84÷(71+16)x3
Answers
Answer:
189.1034.
Step-by-step explanation:
The result of the expression is approximately 189.1035.
To calculate the expression 192 - 84 ÷ (71 + 16) x 3, follow the order of operations, which is commonly remembered by the acronym PEMDAS:
Parentheses: Perform the operation within the parentheses first.
71 + 16 = 87
Division: Perform the division.
84 ÷ 87 ≈ 0.9655 (rounded to four decimal places)
Multiplication: Perform the multiplication.
0.9655 * 3 ≈ 2.8965 (rounded to four decimal places)
Subtraction: Finally, perform the subtraction.
192 - 2.8965 ≈ 189.1035 (rounded to four decimal places)
The result of the expression is approximately 189.1035.
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Use the power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1. 18sin^2(x)cos^2(x)
Answers
An equivalent expression to 18sin^2(x)cos^2(x) that does not contain powers of trigonometric functions greater than 1 is 9 - 9cos(4x)/8.
How did we get the value?The power-reducing formulas state that:
sin^2(x) = (1 - cos(2x))/2
cos^2(x) = (1 + cos(2x))/2
Using these formulas, we can rewrite the expression 18sin^2(x)cos^2(x) as:
18sin^2(x)cos^2(x) = 18[(1 - cos(2x))/2][(1 + cos(2x))/2]
Expanding the right-hand side of the equation, we get:
18[(1 - cos^2(2x))/4]
Using the identity cos^2(2x) = (1 + cos(4x))/2, we can simplify further:
18[(1 - (1 + cos(4x))/2)/4] = 9 - 9cos(4x)/8
Therefore, an equivalent expression to 18sin^2(x)cos^2(x) that does not contain powers of trigonometric functions greater than 1 is 9 - 9cos(4x)/8.
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Use w for the unknown.
"A number split into 3 equal parts"
Answers
Answer:
[tex] \frac{w}{3} [/tex]
Which step is missing?
OA.
ADCA
ADCA
OC. ADAC
OD. ADAC
B.
ABCA by ASA
ABCA by SAS
ABCA by SAS
ABCA by ASA
Answers
The missing step in the two column proof is
Statement Reason
Δ DAC ≅ ΔBCA ASA congruence theorem
What is ASA theorem?The ASA theorem, also known as the angle side angle theorem, is a rule used in geometry to determine whether two triangles are congruent (meaning they have the same shape and size).
The angle side angle theorem states uses the side two parameters which includes:
angle and included sideThe parameters are used for the theorem to say that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
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I need help please!!!
Answers
Answer:
a. Plot the points on the graphing calculator, then generate a logarithmic regression equation.
y = 34.17860108 - 5.682632245ln(x)
b. Setting this equation equal to 10, we have x = 70.44 mph
c. If x = 75 mph, then y = 9.64.
Enter the value for x that makes the equation 3(2x+5)=x-10 true.
Answers
Answer:
Step-by-step explanation:
6x + 15 = x - 10
5x + 15 = -10
5x = -25
x = -5
NO LINKS!! URGENT HEL PLEASE!!!
Use tests for symmetry to determine which graphs from the lists below are symmetric with respect to the y-axis, the x-axis, and the origin. (Select all that apply)
a. symmetric with respect to the y-axis
Answers
Using the tests for symmetry, the following are symmetric with respect to y-axis:
y = - x + 7y = - 7x²x = - y² + 9How to determine symmetricity?A graph is symmetric with respect to the y-axis if replacing x with -x produces an equivalent equation.
A graph is symmetric with respect to the x-axis if replacing y with -y produces an equivalent equation.
A graph is symmetric with respect to the origin if replacing x with -x and y with -y produces an equivalent equation.
(a) symmetric with respect to the y-axis:
y = 7x - 4 (no)
y = - x + 7 (yes)
y = - 7x² (yes)
y = 6x² - 9 (no)
x = 1/4 × y² (no)
x = - y² + 9 (yes)
y = - 1/6 × x³ (no)
y = x³ - 1 (no)
y = √(x) (no)
y = √(x) - 6 (no)
Therefore, the graphs that are symmetric with respect to the y-axis are:
y = - x + 7
y = - 7x²
x = - y² + 9
None of the graphs are symmetric with respect to the x-axis or the origin.
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help please quick i need these
Answers
ANSWER:
368
EXPLANATION:
youre given:
l=14
w=5
h=5
just plug those into the given formula,
2×(14×5)+2×(14×6)+2×(5×6)
(you should do it yourself to check my math...)
What should be added to
[tex] \frac{17}{24} [/tex]
get
[tex] \frac{ - 5}{12} [/tex]
Answers
Answer:
See the below process
Step-by-step explanation:
let the Unknown value be x.
Now
[tex] \frac{17}{24} + x = \frac{ - 5}{12} [/tex]
[tex]x = \frac{ - 5}{12} - \frac{17}{24}[/tex]
Taking LCM
[tex]x = \frac{ - 10 - 17}{24} [/tex]
[tex]x = \frac{ - 27}{24} \\ = \frac{8}{9} [/tex]
we should add 8/9 to 17/24 to get -5/12
I hope it helped you
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The probability that the friend is at least 22 minutes late is
Answers
The probability that the friend is at least 22 minutes late is 0.266
Uniform density function for a friend = x minutes late
The Friend is at least 21 minutes late
Based on the above information, the probability that the friend is at least 21 minutes late is
= (Total minutes - minimum minutes)/Total minutes
=30-22/30
=8/30
=0.266
Based on the above formula we can easily find out the probability for the friend who is at least 22 minutes late
Hence, the probability that the friend is at least 22 minutes late is 0.266
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The population of a city increases by 3.5% per year. If this year's population is
p, which expression does NOT represent next year's population?
3.5p
O (1+0.035)p
1.035p
O 1p+ 0.035p
Answers
The expression that does NOT represent next year's population is: [tex]O(1p +0.035)p[/tex]
What is an expression ?Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. Mathematical operations include addition, subtraction, multiplication, and division.
An example is the expression x + y, which combines the terms x and y with an addition operator.
In mathematics, there are two different types of expressions: algebraic expressions, which also include variables, and numerical expressions, which solely comprise numbers.
A number is [tex]6[/tex] more than half of the other number, which is x. This statement is represented by the mathematical equation [tex]\frac{x}{2} +6[/tex]. Mathematical expressions are used to solve complicated puzzles.
According to the problem,
The expression that does NOT represent next year's population is: [tex]O(1p +0.035)p[/tex]
This is because it incorrectly adds [tex]1p to 0.035p[/tex], which would result in an overestimation of the population growth.
The correct way to calculate next year's population with a growth rate of [tex]3.5[/tex]% is to multiply the current population (p) by [tex]1[/tex] + [tex]0.035[/tex], as shown in the other three expressions: [tex]3.5p, 1.035p, (1+0.035)p[/tex].
Therefore,the expression that does NOT represent next year's population is: [tex]O(1p +0.035)p[/tex]
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for your land line phone service monthly bill, you pay 3¢ for each minute you use plus a $10 monthly charge. you budget yourself to spend no more than $40 on your phone bill. what is the range of minutes you can use this month?
Answers
Answer:
100 Minutes
Step-by-step explanation:
Step 1: Break it down-
3¢ can be expressed as 0.3
Step 2: Add monthly charge-
Since there is a 10$ monthly charge: 40-10=30
Step 3: Subtract-
Now divide: 30 ÷ 0.3
Step 4: Final Answer-
Hence the amount of minutes per month= 100
What is the slope of the line
Answers
Answer:
- 2/1
Step-by-step explanation:
if u look at the graph/line it's going up by 2 then across 1
Chanasia buys a plastic bucket. The bucket weighs 460 g. The label on the bucket says made with 20% recycled plastic. How many grams of recycled plastic are used to make Chanasia’s bucket?
please help and please show work
Answers
92 grams of recycled plastic were used to make Chanasia's bucket
How to calculate the amount of recycled plastic that was used to make Chanasia's bucket?Chanasia buys a plastic bucket
The bucket weighs 460 grams
The label on the bucket says it was made with 20% recycled plastic
The number of grams of recycled plastic that was used to make the bucket can be calculated as follows
= 460/100
= 4.6
= 4.6 × 20
= 92
Hence 92 grams of recycled plastic was used to make the bucket
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