The range of possible values for the population parameter can be estimated using the margin of error, which is calculated as the critical value times the standard error.
Assuming a 95% confidence level, the critical value is approximately 1.96. The standard error for a sample proportion can be calculated as:
SE = sqrt[(p * (1 - p)) / n]
Where p is the sample proportion and n is the sample size. Substituting the values given in the question, we get:
SE = sqrt[(0.65 * 0.35) / n]
We do not know the sample size, so we cannot calculate the standard error exactly. However, we can use a rule of thumb that states that if the sample size is at least 30, we can use the normal distribution to estimate the margin of error.
With a sample proportion of 0.65, the margin of error can be estimated as:
ME = 1.96 * sqrt[(0.65 * 0.35) / n]
We do not know the sample size, so we cannot calculate the margin of error exactly. However, we can use the rule of thumb that a margin of error of about ±5% is typical for a 95% confidence level.
Using this margin of error, we can construct the following range of possible values for the population parameter:
0.65 ± 0.05
This range can be expressed as (0.6, 0.7), which corresponds to option A.
Therefore, the correct answer is option A) (0.6, 0.69).
what is 27% in a equivalent form using the two other forms of notian: fraction,decimal,or percent
You can write 27% as a fraction like this: [tex]\frac{27}{100}[/tex] . (27/100).
Or as a decimal 0.27.
The number 1.3 is both a(n) __________ and a(n) __________ number.
The number 1.3 is both a rational and an irrational number.
What is the number 1.3?The number 1.3 is a rational number because it can be expressed as the quotient of two integers, namely 13/10.
The number 1.3 an irrational number because it cannot be expressed as the ratio of two integers, without repeating or terminating decimals, and its decimal representation goes on forever without repeating.
So we can conclude that the number 1.3 is both rational and irrational number.
Learn more about rational numbers here: https://brainly.com/question/19079438
#SPJ1
A bag contains 40 marbles. 12 of the marbles are red. What is the percent of red marbles in the bag?
Answer:
the percentage of red marbles in the bag is 30%.
Step-by-step explanation:
To find the percentage of red marbles in the bag, we need to divide the number of red marbles by the total number of marbles and then multiply by 100:
Percentage of red marbles = (Number of red marbles / Total number of marbles) x 100
Number of red marbles = 12
Total number of marbles = 40
Percentage of red marbles = (12/40) x 100
= 0.3 x 100
= 30%
Therefore, the percentage of red marbles in the bag is 30%.
The rear window of Alex's van is shaped like a trapezoid with an upper base
measuring 36 inches, a lower base measuring 48 inches, and a height of 21 inches.
An 18-inch rear window wiper clears a 150° sector of a circle on the rear window, as
shown in the diagram below.
36 in.
21 in.
150 degrees
18 in.
48 in.
a. What is the area, in square inches, of the entire trapezoidal rear window? Show or explain how you got your answer.
b. What fractional part of a complete circle is cleared on the rear window by the 18-inch wiper? Show or explain how you got your answer.
c. What is the area, in square inches, of the part of the rear window that is cleared by the wiper? Show or explain how you got your answer.
d. What percent of the area of the entire rear window is cleared by the wiper? Show or explain how you got your answer.
a) The area of the entire trapezoidal rear window = 882 sq.in.
b) The fractional part of a complete circle is cleared on the rear window by the 18-inch wiper = 5/12
c) The area of the part of the rear window that is cleared by the wiper = 424.12 sq. in.
d) The percent of the area of the entire rear window is cleared by the wiper = 48.09%
We know that the formula for the area of trapezoid,
A = ((a + b) / 2) × h
Here, a = 36 in., b = 48 in. and height of the trapezoid h=21 in
Using above formula, the area of the entire trapezoidal rear window would be,
A = ((36 + 48) / 2) × 21
A = 882 sq.in.
Here, the 18-inch rear window wiper clears a 150° sector of a circle on the rear window.
We know that the measure of entire circle = 360°
So, the fractional part of a complete circle is cleared on the rear window by the 18-inch wiper would be,
150° / 360° = 5/12
Now we need to find the area of the part of the rear window that is cleared by the wiper.
We know that the formula for the area of sector of a circle is:
A = (θ/360) × πr²
Here, the central angle θ = 150° and radius r = 18 in.
A = (θ/360) × πr²
A = (150/360) × π × 18²
A = 424.12 sq. in.
Now we need to find the percent of the area of the entire rear window is cleared by the wiper.
P = [(area of the part of the rear window cleared by the wiper) / (area of the entire trapezoidal rear window)] × 100
P = (424.12 / 882) × 100
P = 48.09%
Learn more about the area of trapezoid here:
https://brainly.com/question/15640807
#SPJ1
A student is establishing the A.A criterion for the similarity of triangles [MN and [QR. The student writes LMLN ~ ZQLR What other information can the student use to establish the AA criterion?
The other information can the student use to establish the AA criterion is Angle LMN congruent angle LQR or angle LMN congruent angle LRQ
The student can use the following information to establish the AA criterion:
Angle MLN congruent angle QLR (already given)Angle LMN congruent angle LQR or angle LMN congruent angle LRQ (either one will work)These two angles correspond to the two angles in the other triangle (LQR or LRQ) that are not congruent to the angle already known to be congruent (angle QLR).
Therefore, the AA congruent for similarity can be congruent .
Learn more about Similarity here:
https://brainly.com/question/26451866
#SPJ1
A bag consists of 5 marbles. There is 1 yellow, 1 red marble, 1 clear marble, 1 green marble, and 1 blue marble. Which table shows the sample space for choosing 2 marbles from the bag with replacement? Answer by looking at the images below!
Table C shows the sample space for choosing 2 marbles from the bag with replacement. The probabity and there are 25 possible pairs.
The sample space for choosing 2 marbles from the bag with replacement consists of all possible pairs of marbles that can be chosen, where the order in which they are chosen does not matter.
Since there are 5 marbles in the bag and we are choosing 2 of them, there are 5 choices for the first marble and 5 choices for the second marble, for a total of [tex]5*5 = 25[/tex] possible pairs.
Table C shows the sample space for choosing 2 marbles from the bag with replacement. Each row and column in the table represents a different marble that can be chosen, and each cell represents a pair of marbles that can be chosen.
For example, the cell in row 2 and column 3 represents the pair of marbles consisting of the red marble and the clear marble. Tables A and B show the sample space for choosing 2 marbles from the bag without replacement. In this case, the order in which the marbles are chosen does matter, and each marble can only be chosen once.
Therefore, there are only 5 choices for the first marble, but only 4 choices for the second marble (since one marble has already been chosen), for a total of[tex]5 * 4 = 20[/tex] possible pairs.
To learn more about probabilities, refer:
https://brainly.com/question/21336179
#SPJ1
The complete question is:
A bag contains five green marbles, three blue marbles, two red marbles, and two yellow marbles. One marble is drawn out randomly.
a) Are the four different colour outcomes equally likely? Explain.
b) Find the probability of drawing each colour marble i.e., P(green), P(blue), P(red) and P(yellow)
c) Find the sum of their probabilities.
Teena uses 1/4 cup of oil for a cake. How many cakes can she make if she has 6 cups of oil?
Answer:
24 cakes.
Step-by-step explanation:
6 cups of oil divided by 1/4 cup oil per cake = 24 cakes
6/(1/4) = 24
or 6/(0.25) = 24
She can make 24 cakes with 6 cups of oil.
johnny can build in 3 1/2 lego planes in 60 minutes. how many can he build in 40 minutes?
The number of lego planes that can be build in 40 minutes is A = 2.33
Given data ,
Johnny can build in 3 1/2 lego planes in 60 minutes
On dividing the number of planes he can build in 60 minutes (3 1/2) by 60:
From the proportion , we get
To find out how many planes he can build in 40 minutes, we can multiply the amount he can build in one minute by 40:
3.5 / 60 = A / 40
Multiply by 40 on both sides , we get
A = 2.33
Hence , Johnny can build approximately 2.33 lego planes in 40 minutes
To learn more about proportion click :
https://brainly.com/question/7096655
#SPJ1
Need help asap, please and thank you
If the population in the year 2007 is 111.3 million, then the population in the year 2044 will be 148.37 million.
In order to find the population in the year 2044, we use the population growth formula; which is : P = P₀ × (1 + r)ⁿ;
where P = future population, P₀ = initial population, r = annual growth rate, and n = number of years;
Substituting the values,
We get;
⇒ P = (111.3 million) × (1 + 0.0078)²⁰⁴⁴⁻²⁰⁰⁷;
Simplifying this expression,
We get;
⇒ P = (111.3 million) × (1.0078)³⁷;
⇒ P ≈ 148.37 million;
Therefore, the population in the year 2044 is estimated to be approximately 148.37 million.
Learn more about Growth Rate here
https://brainly.com/question/29203229
#SPJ1
Part A: Jan INCORRECTLY
finds the surface area of the
cone using the following
work. Explain Jan's error
and find the
correct volume AND
surface area of the cone.
The volume of the cone is 2786.2 cubic meters and the surface area of the cone is 1229.51 square meters.
Given the height (h) of a cone as 22 m and the diameter (d) of its circular base as 22 m, we can find the radius (r) of the circular base using the formula:
r = d/2 = 22/2 = 11 m
Here, Jan made a mistake in the work of the surface area of the cone because she used the wrong value of slant height (l=22) in the calculation.
The volume (V) of a cone is given by the formula:
V = (1/3)πr²h
Substituting the values of r and h, we get:
V = (1/3)π(11)²(22)
V = 2786.2 cubic meters
The surface area (A) of a cone is given by the formula:
A = πr(r + l)
here l is the slant height of the cone, which can be found using the Pythagorean theorem:
l = √(r² + h²)
l = √(11² + 22²)
l = √(605)
l = 24.6
Substituting the values of r and l, we get:
A = π(11)(11 + 24.6)
A ≈ 1229.51 square meters
Therefore, the volume of the cone is 2786.2 cubic meters and the surface area of the cone is 1229.51 square meters.
Learn more about the volume of the cone here:
brainly.com/question/1578538
#SPJ1
Find the y intercept for a line with a slope or 2 that goes through (5, 4)
Answer:
y- intercept = - 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here slope m = 2 , then
y = 2x + c ← is the partial equation
to find c substitute (5, 4 ) into the partial equation
4 = 2(5) + c = 10 + c ( subtract 10 from both sides )
- 6 = c
that is the y- intercept c = - 6
NO LINKS!! URGENT PLEASE!!!
1. Vanessa invested $2500 into an account that will increase in value by 3.5% each year. Write an exponential function to model this situation, then find when the account will have $5000?
2. The average price of a movie ticket in 1990 was $4.22. Since then, the price has increased by approximately 3.1% each year. Write an exponential function to model this situation, then find how many years until tickets cost $9.33.
The exponential function that model this situation is [tex]A(t) = 2500(1 + 0.035)^t.[/tex]
The account will have $5000 in 20 years.
What is the exponential function for Vanessa's investment growth?Let A be the amount in the account after t years.
Then, we can model this situation with the function A(t) = 2500(1 + 0.035)^t with the use of compound intererst formula which is [tex]P = A*(1+r)^t[/tex]
To find when the account will have $5000, we can set A(t) = 5000 and solve:
5000 = 2500(1 + 0.035)^t
2 = (1.035)^t
Taking the natural logarithm:
ln(2) = t ln(1.035)
t = ln(2)/ln(1.035)
t = 20.148791684
t = 20 years.
Read more about exponential function
brainly.com/question/2456547
#SPJ1
Answer:
1) 21 years
2) 26 years
Step-by-step explanation:
Question 1To model the account balance of Vanessa's account at t years, we can use an exponential function in the form:
[tex]\large\boxed{A(t) = A_0(1 + r)^t}[/tex]
where:
A(t) is the value of the investment after t years.A₀ is the initial amount of the investment.r is the annual interest rate (as a decimal).t is the time elapsed (in years).Given Vanessa invested $2500 into the account and it will increase in value by 3.5% each year:
A₀ = $2500r = 3.5% = 0.035Substitute these values into the formula to create an equation for A in terms of t:
[tex]A(t) = 2500(1 + 0.035)^t[/tex]
[tex]A(t) = 2500(1.035)^t[/tex]
To find when the account balance will be $5000, set A(t) equal to $5000 and solve for t:
[tex]A(t)=5000[/tex]
[tex]2500(1.035)^t=5000[/tex]
[tex](1.035)^t=\dfrac{5000}{2500}[/tex]
[tex](1.035)^t=2[/tex]
[tex]\ln (1.035)^t=\ln 2[/tex]
[tex]t \ln 1.035=\ln 2[/tex]
[tex]t=\dfrac{\ln 2}{ \ln 1.035}[/tex]
[tex]t=20.1487916...[/tex]
[tex]t=20.15\; \sf years\;(2\;d.p.)[/tex]
Therefore, it will take approximately 20.15 years for Vanessa's account to reach a value of $5000.
Since the interest rate is an annual rate of 3.5%, it means that the interest is applied once per year, at the end of the year. Therefore, we need to round up the number of years to the next whole number.
So Vanessa's account will have $5,000 after 21 years.
Note: After 20 years, the account balance will be $4,974.47. After 21 years, the account balance will be $5,148.58.
[tex]\hrulefill[/tex]
Question 2To model the increase in movie ticket prices over time, we can use an exponential function in the form:
[tex]\large\boxed{P(t) = P_0(1 + r)^t}[/tex]
where:
P(t) is the price of the ticket (in dollars) after t years.P₀ is the initial price of the ticket (in dollars).r is the annual growth rate (as a decimal).t is the time elapsed (in years).Given the initial price of the ticket was $4.22 and the price has increased by 3.1% each year:
P₀ = $4.22r = 3.1% = 0.031Substitute these values into the formula to create an equation for P in terms of t:
[tex]P(t) = 4.22(1 + 0.031)^t[/tex]
[tex]P(t) = 4.22(1.031)^t[/tex]
To find how many years until tickets cost $9.33, we can set P(t) equal to $9.33 and solve for t:
[tex]P(t)=9.33[/tex]
[tex]4.22(1.031)^t=9.33[/tex]
[tex](1.031)^t=\dfrac{9.33}{4.22}[/tex]
[tex]\ln (1.031)^t=\ln \left(\dfrac{9.33}{4.22}\right)[/tex]
[tex]t \ln (1.031)=\ln \left(\dfrac{9.33}{4.22}\right)[/tex]
[tex]t =\dfrac{\ln \left(\dfrac{9.33}{4.22}\right)}{\ln (1.031)}[/tex]
[tex]t=25.9882262...[/tex]
Therefore, it will take approximately 26 years for movie ticket prices to reach $9.33, assuming the annual growth rate remains constant at 3.1%.
MA.7.AR.4.1
Johnny and Eleanor went to their local gas station to collect information about the cost of
fuel for compact cars. They observed both regular and premium gas purchases that day and
recorded their data in the table below.
Gallons Purchased 11.5 7.2
10
14.3 6.8
9.7
Cost
$25.23 $15.80 $21.94 $40.63 $14.92 $27.56
Part A. Is there a proportional relationship between the number of gallons of gas sold and
the cost? Explain your answer.
Part B. If the relationship is not proportional, which data value or values should be
changed to make the relationship proportional? What could explain this
difference?
a) The fourth and sixth data points have significantly different ratios.
a) Let's calculate the ratios:
For the first data point:
= 11.5 gallons / $25.23 = 0.4555 gallons per dollar
For the second data point:
= 7.2 gallons / $15.80 = 0.4557 gallons per dollar
For the third data point:
= 10 gallons / $21.94 = 0.4556 gallons per dollar
For the fourth data point:
= 14.3 gallons / $40.63 = 0.3519 gallons per dollar
For the fifth data point:
= 6.8 gallons / $14.92 = 0.4555 gallons per dollar
For the sixth data point:
= 9.7 gallons / $27.56 = 0.3517 gallons per dollar
However, the fourth and sixth data points have significantly different ratios.
b) If the relationship is not proportional, the data values that should be changed to make the relationship proportional are the fourth and sixth data points.
The difference in ratios could be explained by factors such as fluctuations in gas prices or differences in gas grades.
To establish a proportional relationship, it would be necessary to collect data where the price per gallon remains constant for all data points or to separate the data based on gas grades and analyze each grade separately.
Learn more about Ratio here:
https://brainly.com/question/31945112
#SPJ2
You roll a 6-sided number cube and toss a coin. Let event A = Toss a heads.
What outcomes are in event A?
What outcomes are in event AC?
1. Event A includes the outcomes of H and T,
2. while event AC includes all the possible outcomes of rolling a number cube, which are 1, 2, 3, 4, 5, and 6.
1. Event A is defined as tossing a heads on a coin, regardless of the outcome of rolling a number cube. Therefore, the outcomes in event A are H (heads) and T (tails), since either of these outcomes could occur when rolling a number cube and tossing a coin.
2. Event AC is the complement of event A, i.e., it is the set of outcomes that are not in event A. Since event A contains H and T, the outcomes in event AC are the remaining outcomes that are not in event A, which are all the possible outcomes when rolling a number cube: 1, 2, 3, 4, 5, and 6.
Learn more about probability here;
https://brainly.com/question/24756209
#SPJ1
Instructions: Find the missing probability.
P(B)=1/2P(A|B)=11/25P(AandB)=
Diondra wants to know the most popular movie of this year but is unsure of the best way to determine this answer. Which of the following questions would Diondra ask that does NOT allow for variability?
Which movie did her best friend like the most?
How many awards did each movie win?
What is the total dollar amount that each movie made from ticket sales?
How many weeks did each movie play in the theater?
The question that Diondra would ask that does not allow for variability is A. Which movie did her best friend like the most?
How does this question not show variability ?The other three questions ("How many awards did each movie win?", "What is the total dollar amount that each movie made from ticket sales?", and "How many weeks did each movie play in the theater?") all offer metrics by which a movie's popularity could be measured, and those measurements could vary from movie to movie.
However, the question about her best friend's favorite movie depends solely on the opinion of one individual, not a variable measure, and therefore doesn't allow for variability.
Find out more on variability at https://brainly.com/question/12872866
#SPJ1
Please help. Is the answer even there?
The critical values t₀ for a two-sample t-test is ± 2.0.6
To find the critical values t₀ for a two-sample t-test to test the claim that the population means are equal (i.e., µ₁ = µ₂), we need to use the following formula:
t₀ = ± t_(α/2, df)
where t_(α/2, df) is the critical t-value with α/2 area in the right tail and df degrees of freedom.
The degrees of freedom are calculated as:
df = (s₁²/n₁ + s₂²/n₂)² / [(s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1)]
n₁ = 14, n₂ = 12, X₁ = 6,X₂ = 7, s₁ = 2.5 and s₂ = 2.8
α = 0.05 (two-tailed)
First, we need to calculate the degrees of freedom:
df = (s₁²/n₁ + s₂²/n₂)² / [(s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1)]
= (2.5²/14 + 2.8²/12)² / [(2.5²/14)²/13 + (2.8²/12)²/11]
= 24.27
Since this is a two-tailed test with α = 0.05, we need to find the t-value with an area of 0.025 in each tail and df = 24.27.
From a t-distribution table, we find:
t_(0.025, 24.27) = 2.0639 (rounded to four decimal places)
Finally, we can calculate the critical values t₀:
t₀ = ± t_(α/2, df) = ± 2.0639
To learn more on Statistics click:
https://brainly.com/question/30218856
#SPJ1
Out of 1000 students who appeared in an examination,60% passed the examination.60% of the failing students failed in mathematics and 50% of the failing students failed in English.If the students failed in English and Mathematics only, find the number of students who failed in both subjects.
The value of number of students who failed in both mathematics and English is 40.
Since, Given that;
60% of the 1000 students passed the examination,
Hence, we can calculate the number of students who passed the exam as follows:
60/100 x 1000 = 600
So, 600 students passed the examination.
Now, let's find the number of students who failed the examination.
Since 60% of the students passed, the remaining 40% must have failed. Therefore, the number of students who failed the examination is:
40/100 x 1000 = 400
Of the 400 failing students, we know that 60% failed in mathematics.
So, the number of students who failed in mathematics is:
60/100 x 400 = 240
Similarly, we know that 50% of the failing students failed in English.
So, the number of students who failed in English is:
50/100 x 400 = 200
Now, we need to find the number of students who failed in both subjects.
We can use the formula:
Total = A + B - Both
Where A is the number of students who failed in mathematics, B is the number of students who failed in English, and Both is the number of students who failed in both subjects.
Substituting the values we have, we get:
400 = 240 + 200 - Both
Solving for Both, we get:
Both = 240 + 200 - 400
Both = 40
Therefore, the number of students who failed in both mathematics and English is 40.
Learn more about the subtraction visit:
https://brainly.com/question/17301989
#SPJ1
LUUK al uit grapii velow.
Part B
-4
Part A
-3-2
Part C
3
2
-2
-3
Part D
Which part of the graph best represents the solution set to the system of
inequalities y ≥x+1 and y + x>-1? (5 points)
The solution set of given inequalities are represented by Part A.
The given inequalities are
⇒ y ≥ x + 1 and y + x > -1
Hence, The related equations of both inequalities are
y = x + 1
Put x=0, to find the y-intercept and put y=0, to find x intercept.
y = 0 + 1
y = 1
And, 0 = x + 1
x = - 1
Therefore, x-intercept of the equation is (-1,0) and y-intercept is (0,1).
Similarly, for the second related equation
y + x = - 1
y + 0 = - 1
y = - 1
0 + x = - 1
x = - 1
Therefore x-intercept of the equation is (-1,0) and y-intercept is (0,-1).
Now, join the x and y-intercepts of both lines to draw the line.
Now check the given inequalities by (0,0).
0 ≥ 0 + 1
0 ≥ 1
It is a false statement, therefore the shaded region is in the opposite side of origin.
0 + 0 ≥ - 1
0 ≥ - 1
It is a true statement, therefore the shaded region is about the origin.
Hence, From the below figure we can say that the solution set of given inequalities are represented by Part A.
Learn more about the inequality visit:
https://brainly.com/question/25944814
#SPJ1
HELP PLEASE ASAP PHOTO INCLUDED
The volume of water that the pool can hold is 150.72 cubic centimeters.
How to find the volume of the pool?Remember that the volume of a cylinder of radius R and height H is:
V = pi*R²*H
Where pi = 3.14
For the pool we know that the height is H = 3ft, and the diameter is 8ft, then the radius is R = 8ft/2 = 4ft
Replacing that in the volume formula we will get:
V = 3.14*(4cm)²*3cm
V = 150.72 cubic centimeters.
Learn more about cylinders at:
https://brainly.com/question/9554871
#SPJ1
What function is the inverse of the exponential function y = 4*?
OA
1
y=z.
OC y = log₂ 4
O B. y=(¹)²
O
D. y = log, z
The function that is the inverse of the exponential function y = 4ˣ is lnx/ln4
The inverse of a function f is denoted by [tex]f^{-1[/tex] and it exists only when f is both one-one and onto function. Note that [tex]f^{-1[/tex] is NOT the reciprocal of f. The composition of the function f and the reciprocal function [tex]f^{-1[/tex] gives the domain value of x.
(f o [tex]f^{-1[/tex] ) (x) = ( [tex]f^{-1[/tex] o f) (x) = x
For a function 'f' to be considered an inverse function, each element in the range y ∈ Y has been mapped from some element x ∈ X in the domain set, and such a relation is called a one-one relation or an injunction relation.
The standard exponential function is given as y = abˣ
Given the function,
y = 4ˣ
Replace y with x
[tex]x = 4^y[/tex]
Make y the subject of the formula,
[tex]lnx = ln4^y\\\\lnx = yln4[/tex]
Divide both sides by ln4
lnx/ln4 = y
Hence the function that is the inverse of the exponential function y = 4ˣ is lnx/ln4
Learn more on inverse function here: brainly.com/question/2873333
#SPJ1
Scores on a final exam in a large class were normally distributed with a mean of 75 and a standard deviation of 8. What percent of the students scored above an 83?
Using z - score, the percentage of students above 83 is 15.9%
What is the percentage of students that scored above 83?To find the number of students that scored above 83 can be calculated using z - score formula.
This is given as
z = x - μ / σ
μ = meanσ = standard deviationx = scoreSubstituting the values into the formula;
z = 83 - 75 / 8
z = 1
The z-score is 1
Let's find the percentage of z -score under the score
p(x > 83) = 1 - P(x < 83) = 0.15866
p = 15.9%
Learn more on z-score here;
https://brainly.com/question/29367643
#SPJ1
determine what type of model bets fits the given situation: A $500 raise in salary each year
The type of model that best fits the situation of a $500 raise in salary each year is a linear model.
In a linear model, the dependent variable changes a constant amount for constant increments of the independent variable.
In the given case, the dependent variable is the salary and the independent variable is the year.
You may build a table to show that for increments of 1 year the increments of the salary is $500:
Year Salary Change in year Change in salary
2010 A - -
2011 A + 500 2011 - 2010 = 1 A + 500 - 500 = 500
2012 A + 1,000 2012 - 2011 = 1 A + 1,000 - (A + 500) = 500
So, you can see that every year the salary increases the same amount ($500).
In general, a linear model is represented by the general equation y = mx + b, where x is the change of y per unit change of x, and b is the initial value (y-intercept).
In this case, m = $500 and b is the starting salary: y = 500x + b.
A top travels 8 centimeters each time it is spun. if it is spun 7 times what distance does it travel?
If a top travels 8 centimeters each time it is spun and it is spun 7 times, the total distance it travels is 56 centimeters.
How the total distance is determined:The total distance is determined by multiplication of the distance traveled per spin and the number of spins.
Multiplication involves the multiplicand, the multiplier, and the product.
The traveling distance per spun = 8 centimeters
The number of spinning of the top = 7 times
The total distance = 56 centimeters (8 x 7)
Thus, using multiplication, the total distance the top travels after the 7th spin is 56 centimeters.
Learn more about multiplication at https://brainly.com/question/4721701.
#SPJ1
Raphael and his four friends are having lunch. They agree to split the bill evenly at the end after adding a 20% tip. If the total bill is $85.60, how much will each person end up paying? A. $25.68 B. $20.54 C. $18.68 D. $17.12
The total amount to each person end up paying $20.54.
To find the total amount each person will pay, first calculate the 20% tip on the total bill and then divide the sum by the number of people.
To split the bill evenly among Raphael and his four friends, we first need to find the total cost including the 20% tip.
The tip is 20% of the original bill, which is equivalent to 0.20 x $85.60 = $17.12.
Therefore, the total cost of the bill with the tip is $85.60 + $17.12 = $102.72.
To split this evenly among the five people, we divide by 5:
$102.72 ÷ 5 = $20.54
So each person will end up paying $20.54.
20% of $85.60 is ($85.60 * 0.20) = $17.12
Add the tip to the total bill:
$85.60 + $17.12 = $102.72
Divide the total amount by the number of people (5): $102.72 / 5 = $20.54
Therefore, the answer is B. $20.54.
For similar question on total amount:
https://brainly.com/question/11807738
#SPJ11
The parabola y = x^2 is scaled vertically by a factor of 1/10
The parabola y = x² scaled vertically by a factor of 1/10 gives y = x²/10
Calculating the image of the vertical scaleFrom the question, we have the following parameters that can be used in our computation:
The parabola y = x² is scaled vertically by a factor of 1/10
The rule of this transformation is
Image = (x, ay)
Where
a = 1/10
So, we have
y = 1/10 * x²
Evaluate
y = x²/10
Hence, the image of the function is y = x²/10
Read more about transformation at
https://brainly.com/question/27224272
#SPJ1
7. $60.00 in 5 hours
a. 12 hours for one dollar
b. 5/60
c. $12 per hour
d. $1.20 per hour
The calculated value of the unit rate of the situation is (c) $12 per hour
Calculating the unit rate of the situationFrom the question, we have the following parameters that can be used in our computation:
$60.00 in 5 hours
This means that
Time = 5 hours
Total costs = $60.00
using the above as a guide, we have the following:
Unit rate = Total costs / time
substitute the known values in the above equation, so, we have the following representation
Unit rate = 60.00/5
Evaluate
Unit rate = 12
Hence, the unit rate of the situation is (c) $12 per hour
Read more about unit rate at
https://brainly.com/question/4895463
#SPJ1
1. The vertices of APQR are P(1, 3), Q(5, 4) and
R(5, 15). Find the length of the perpendicular
from Q to PR.
The distance of the perpendicular from Q to line PR is D = 2.2135 units
Given data ,
Let the triangle be represented as ΔPQR
Now , the coordinates are P(1, 3), Q(5, 4) and R(5, 15)
And , the equation of line of PR is given by
Slope m = ( 15 - 3 ) / ( 5 - 1 )
m = 3
y - 3 = 3 ( x - 1 )
Adding 3 on both sides , we get
y = 3x
y - 3x = 0
And , the point is Q(5, 4)
Now , distance of a point to line D = | Ax₀ + By₀ + C | / √ ( A² + B² )
D = | ( 1 ) ( 5 ) + ( -3 ) ( 4 ) + 0 | / √ ( 1 )² + ( 3 )²
D = | 5 - 12 | / √10
D = 7/√10
D = 2.2135 units
Hence , the distance is 2.2135 units
To learn more about distance of point to line click :
https://brainly.com/question/21096072
#SPJ1
Hi. Could someone please help me with this !!
Answer:
The slope is 5.
Hope this helps!
Step-by-step explanation:
( x, y )
( 6, 50 ) and ( 12, 80 )
[tex]\frac{80-50}{12 - 6} < = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
[tex]\frac{30}{6} = \frac{5}{1} = 5[/tex]
The slope is 5.
7. Given right triangle ABC below, determine sin(A).
The value of Sin A is 5/13.
Option A is the correct answer.
We have,
Sin A = Perpendicular / Hypotenuse
Sin A = BC / AB
And,
BC = 5
AB = 13
Substituting.
Sin A = 5/13
Thus,
The value of Sin A is 5/13.
Learn more about trigonometric identities here:
https://brainly.com/question/14746686
#SPJ1