Determine whether y varies directly with x If so, find the constant of variation and write the function rule.
Does y vary directly with x?
No
Yes
What is the constant of variation? Select the correct choice and fill in any answer boxes in your choice below.
A. k=__ (Simplify your answer. Type an integer or a fraction.)
B. There is no constant of variation.
What is the function rule? Select the correct choice and fill in any answer boxes in your choice below.
A. y=_____
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
B. There is no function rule.
Answers
The value of y varies directly with x, and the constant of variation is 3, and function rule y = 3x.
What is Direct Variation?When one value is dependent on another i.e if one value increases with respect to another or if one value decreases with respect to another then we can say that the two quantities are in direct variation.
In simple words, It is the relationship between two variables where one of the variables is a constant multiple of the other.
When two values a and b are varies directly then the relation between them can be shown as given below
=> a ∝ b
=> a = kb here 'k' constant of variation
Here we have
x values 57 63 66
y values 19 21 22
Let's assume that y varies directly with x
=> y ∝ x
=> y = kx ---- (1)
Where k is the proportionality constant
From (1)
We can write k = x/y
From the above calculations, if y varies directly with x then x/y must be a constant.
Now check whether the given value can give a constant
At x = 57 and y = 19
[tex]= > \frac{x}{y} = \frac{57}{19} = 3[/tex]
At x = 63 and y = 21
[tex]= > \frac{x}{y} = \frac{63}{21} = 3[/tex]
At x = 66 and y = 22
[tex]= > \frac{x}{y} = \frac{66}{22} = 3[/tex]
From the above calculation,
For given x and y values, x/y is always constant
Therefore,
It is true that y varies directly with x, and the constant of variation is 3
Here the function rule will be y = x × constant of variation
=> y = 3x
Therefore,
The value of y varies directly with x, and the constant of variation is 3, and function rule y = 3x
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Related Questions
What is the solution of the inequality −3x−3>12 ?
Answers
Answer:
[tex]x < -5[/tex]
Step-by-step explanation:
-3x-3>12
Divide by -3, since you are dividing by a negative, flip the equality sign:
x+1<-4
Subtract 1 from both sides:
x<-5
Hello,
I hope you and your family are doing well!
To solve the inequality −3x−3>12, you can start by moving everything to one side of the inequality by adding 3 to both sides. This gives you −3x>15.
Next, you can divide both sides of the inequality by -3 to get x<-5.
Finally, you can simplify the inequality to its final form by flipping the direction of the inequality symbol, since you divided it by a negative number. This gives you the final solution: x>-5.
So, the solution to the inequality −3x−3>12 is x>-5. This means that any value of x that is greater than -5 will satisfy the inequality.
The answer is: x > -5
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Use Pythagoras' theorem to work out the height of the equilateral
triangle below.
Give your answer in centimetres (cm) to 1 d.p.
N
10 cm
allowed
M
10 cm
10 cm
Answers
The hypotenuse (longest side) of each right triangle is 10 cm, and its base is 5 cm (since there are two right triangles, we have to divide the base length of the equilateral triangle by 2, so 10/2=5).
Let’s call the hypotenuse of each right triangle ‘a’, the base ‘b’ and the height ‘c’
Pythagorean theorem = a^2 + b^2 = c^2
We need to find the height ‘c’ so:
a = 10 cm
b = 5 cm
c = ?
10^2 + 5^2 = c^2
100 + 25 = c^2
125 = c^2
c = square root of 125
c = 11.18 cm
So the height of the total equilateral triangle is 11.18 cm.
Here’s a picture to help you understand:
In the right-angled triangle ABC, cos C = 4/5 and BC = 16 cm, find the following:
i) AC
ii) AB
Answers
The value of (i) AC is the right angled triangle is 20 cm, For (ii) AB is 12 cm.
What is a right angled triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle.
(i) To calculate the value of /AC/, we use the formula below.
/AC/ = BC/cosC..................... Equation 1From the question,
Given:
BC = 16 cmcosC = 4/5Substitute these values into equation 1
AC = 16/(4/5)AC = 20 cm(ii) To calculate AB, use Pythagoras formula:
a² = b²+c².................. Equation 2From the diagram,
a = AC = 20 cmb = AB = ?c = BC = 16 cmSubstitute these values into equation 2 and solve for AB
20² = b²+16²b² = 20²-16²b² = 400-256b² = 144b = √144b = 12 cmAB = 12 cmLearn more about right angle triangle here: https://brainly.com/question/25016594
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Find the measure of each numbered angle.
m∠1=_____ and m∠2=_____
Answers
Answer:
m∠1 = m∠2 = 17°
Step-by-step explanation:
You want to know the measures of the base angles of an isosceles triangle with an a.pex angle of 146°.
Angle sum theoremThe sum of angles in a triangle is 180°. We can use x to represent the measures of each of the two congruent base angles of the isosceles triangle:
x + 146° +x = 180°
2x = 34° . . . . . . subtract 146°
x = 17° . . . . . . . divide by 2
The measures of the angles are ...
m∠1 = m∠2 = 17°
The solution to a system of equation is (1, 5).
Choose two equations that might make up the system.
(Select all that apply.)
y+ -3x-6
Y= 2x+3
Y= -7x+1
Y=x+4
Y=-2x-9
Answers
Answer:
y = 2x + 3 and y = x + 4
Step-by-step explanation:
the first equation:
y = -3x - 6
(5) =-3(1) - 6
5 = 3-6
5≠-3
second equation:
y = 2x + 3
(5) = 2(1) + 3
5 = 2 + 3
5 = 5
third equation:
y = -7x + 1
(5) = -7(1) + 1
5 = -7 + 1
5 ≠ -6
fourth equation:
y = x + 4
(5) = 1 + 4
5 = 5
last equation:
y = -2x - 9
(5) = -2(1) - 9
5 = -2 - 9
5 ≠ -11
Scenario: A researcher is interested in estimating the proportion of the population on a
particular construct characteristic within the researcher's area of scholarly interest [Fill
in with something that would be appropriate for your area of research interest]. A
measurement instrument has been created that can be used to categorize respondents as
either demonstrating the characteristic, or not. The researcher has obtained a population
frame to draw a sample from. The frame contains 3400 records.
Question: How large of a random sample is needed to estimate the population
proportion to within plus or minus 2% and be 95% sure the estimate is correct? Do
NOT take nonresponse into account. Remember, this is a sample size estimate, which
means you should round UP for your final answer.
Answers
To estimate the population proportion to within plus or minus 2% with 95% confidence, a sample size of at least 804 is needed.
How do we get the sample size for estimating a population proportion?This can be calculated using the formula for determining sample size for estimating a population proportion:
n = (Z^2 * p * (1-p)) / (E^2)
Where n is the sample size, Z is the z-score corresponding to the desired level of confidence (1.96 for 95% confidence), p is the estimated proportion of the population with the characteristic of interest (assumed to be 0.5 for this calculation), and E is the maximum margin of error desired (2% in this case). Plugging these values into the formula, we get:
n = (1.96^2 * 0.5 * (1-0.5)) / (0.02^2) = 803.84
Since this is a sample size estimate, we should round up to the next whole number, resulting in a sample size of 804.
Therefore, the correct answer is as given above
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If the following data were transformed, and points with the coordinates
(x, log(y)) were plotted, what points would be plotted? Round log(y) to three
decimal places.
A. (1.690, 49), (2.535, 343), (3.380, 2401)
B. (49, 1.690), (343, 2.535), (2401, 3.380)
C. (1.690, 2), (2.535, 3), (3.380, 4)
D. (2, 1.690), (3, 2.535), (4, 3.380)
Answers
The points that would be plotted are (2, 1.690), (3, 2.535), and (4, 3.380).
What are the coordinates?
Any one of a group of numbers used to describe where a point is on a line, a surface, or in space coordinates of latitude and longitude
Here, we have
If the following data were transformed and points with coordinates (x, log(y)) were plotted then we have to find what points would be plotted.
From the table:
At x = 2 and y = 49 ⇒ (x,log(y)) = ( 2 , log 49 ) = (2, 1.690)
At x = 3 and y = 343 ⇒(x,log(y)) = ( 3 , log 343) = (3, 2.535)
At x = 4 and y = 2401 ⇒(x,log(y)) = ( 4 , log 2401) =(4, 3.380)
Hence, The points that would be plotted are (2, 1.690), (3, 2.535), and (4, 3.380).
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The slope of a curve at each point (x,y) is given by 4x - 1. Which one of the following is an equation fo curve if it passes through the point (-2,3)? A) y = 4x^2 - x - 15 B) y = 2x^2 - x C)y=2r^2-r+7 D) y= 2x^2-1-7
Answers
The following is an equation fo curve if it passes through the point (-2,3) is y=2 x^2-x-7.
What is Slope?
A graph is a set of vertices—points—and edges—the lines connecting those vertices in discrete mathematics. Graphs come in a variety of forms, including connected and disconnected graphs, bipartite graphs, weighted graphs, directed and undirected graphs, and simple graphs.
Slope of the carne at (x, y) is 4 x-1
Let the curve is: y=2 x^2-x-7
[tex]$$\begin{gathered}\text { Slope: } \frac{d y}{d x}=\frac{d}{d x}\left[2 x^2-x-7\right] \\\frac{d y}{d x}=4 x-1\end{gathered}$$[/tex]
And passes Iowa's the point (-2,3).
[tex]$$\begin{aligned}& y=2 x^2-x-7 \\& 3=2(-2)^2-(-2)-7 \\& 3=8+2-7 \\& 3=10-7 \\& 3=3\end{aligned}$$[/tex]
Satisfied.
y=2 x^2-x-7
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given s : t : u = 4 : 9 : 3 and t - u = 30. find the value of s
Answers
The value of s from the proportion s : t : u = 4 : 9 : 3 is s = 20
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
Let the proportion be in the form s : t : u
where the value of the proportion is
s : t : u = 4 : 9 : 3
And , t - u = 30
Now , assume the value of s = 4x
where x is the unknown we have to calculate
So , the value of t = 9x
And , the value of u = 3x
From the equation , t - u = 30
Substitute the value of t and u in the equation , we get
9x - 3x = 30
6x = 30
Divide by 6 on both sides of the equation , we get
x = 5
Therefore , the value of x is 5
Now , substituting the value of x in the above equation , we get
s = 4x
s = 4 x 5
s = 20
Therefore , the value of s from the proportion is 20
Hence , The value of s from the proportion s : t : u = 4 : 9 : 3 is s = 20
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Part 1: Two custodians are painting the hallway in the school, starting
at opposite ends at 10:00 a.m. By noon, if Jon has painted 1/5 of the
hallway and Dan has painted 25% of the hallway, who has painted the
most?
25
Part 2: What percentage of the job needs to be completed after lunch
Answers
Answer: Part 1: Dan, Part 2: 55%
Step-by-step explanation:
1. By noon, Jon has painted 1/5 (or 20%) of the hallway and Dan has painted 25% of the hallway. Therefore, Dan has painted more of the hallway than Jon.
2. In total, the two have painted 45% (20% + 25% = 45%) of the hallway by lunchtime. Therefore, 55% (100% - 45% = 55%) needs to be painted after lunch.
How many pages are necessary to make 1,050 copies of a manuscript that is 423 pages long? (Print on one side only.)
Answers
Answer:
Step-by-step explanation:
hi!!! i’d appreciate it sm if someone could do 25 and 26 i’m thing to turn my work in tomorrow and these are the last ones i need, i’ll mark u brainliest when it pops up :) thank you
Answers
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} \implies \cfrac{-4}{2 +1} \implies \cfrac{ -4 }{ 3 } \implies - \cfrac{ 4 }{ 3 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{- \cfrac{ 4 }{ 3 }}(x-\stackrel{x_1}{(-1)}) \implies y -3 = - \cfrac{ 4 }{ 3 } ( x +1) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y-3)=3\left( - \cfrac{ 4 }{ 3 } ( x +1) \right)}\implies 3y-9=-4(x+1)\implies 3y-9=-4x-4 \\\\\\ 3y=-4x+5\implies \text{\LARGE 4}x+3y=5[/tex]
help meeeeeeeeeee pleaseee
Answers
The pressure of 28 inches of mercury occurs about 6 miles from the eye of hurricane.
How to solve function?A function having the formula f(x) = ax' + b is said to be linear.
It appears to be a standard linear equation, except the linear function symbol is f rather than y. (x).
You would be given the value of f(x) and asked to locate x when solving a linear function.
F(x) is the barometric air pressure in inches of mercury.
x is the distance in miles from the eye of a severe hurricane.
It is given pressure 28inches of mercury
Put F(x) equal to 28
F(x) = 0.48ln(x+2) +27
28 = 0.48ln(x+2)+ 27
28-27= 0.48ln(x+2)
1= 0.48ln(x+2)
1/0.48= ㏑(x+2)
25/12= ㏑(x+2)
x+2= e^(25/12)
x+2=8.03119
x=8.03119-2
x= 6.03119
x = 6(round off)
Therefore, for 28 inches of mercury occurs about 6 miles from the eye of hurricane.
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4. The number of minutes a person uses each month often varies. Suppose that a Verizon customer uses the total number of minutes shown below.
Which plan would cost the consumer the least amount money over the year?
Answers
The annual cost for the 450 Plan is $645.03.
What is cost price?
The cost price represents the particular worth that represents unit worth purchased.
Main Body;
This consumer used less than 450 minutes a month every month except June and December. In June, they used 178 extra minutes and in December they used 189 extra minutes. In total, they used 367
extra minutes throughout the year. The basic fee for the 450 Plan is $39.99 per month so their annual cost is
annual cost = monthly fee* months + cost per minutes* extra minutes
=39.99 *12 +0.45* 367
=479.88+ 165.15
=645.03
Annual Cost Monthly fee months cost per minute extra minutes
The annual cost for the 450 Plan is $645.03.
The 900 Plan costs $59.99 per month for all 12 months for a total cost of $719.88. Even though the consumer had to pay extra during June and December, the 450 Plan was still less expensive than the 900 Plan.
Hence , The annual cost for the 450 Plan is $645.03.
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What is the correct answer to this problem? g(x)=x2+6 find g(-3)=
Answers
Answer:
15
Step-by-step explanation:
If 7 is added to twice a number and
this sum is multiplied by 2, the result is
the same as if the number is multiplied by
13 and 9 is added to the product. What is
the number?
Answers
Answer: x= -5
Step-by-step explanation:
2(7+2x) = 3x+9
14+4x=3x+9
isolate x
x=-5
I need help!
The value of __ divided by 32 is greater than 1
Does anyone know?
Answers
[tex]x\div 32 > 1\implies \cfrac{x}{32} > 1\implies 32\left( \cfrac{x}{32} \right) > 32(1)\implies x > 32[/tex]
and that can be any value, so long is greater than that, 33 will do, but so does 1,000,000, and so on.
Answer: and that can be any value, so long is greater than that, 33 will do, but so does 1,000,000, and so on.
Step-by-step explanation:and that can be any value, so long is greater than that, 33 will do, but so does 1,000,000, and so on.
and that can be any value, so long is greater than that, 33 will do, but so does 1,000,000, and so on.
In the 1960 Olympics, Wilma Rudolph of the United States won the women's 100 meter run in 11.0 seconds. In 1988, Florence Griffith-Joyner, also of
the United States, won with a time of 10.49 seconds, which is still the fastest women's time to this date. Find the percent of decrease in the winning
time. Round to the nearest tenth
% decrease
Answers
Hello,
I hope you and your family are doing well!
To find the percent of decrease in the winning time, you can use the following formula:
percent decrease = (old value - new value) / old value * 100%
Plugging in the values from the problem, we get:
percent decrease = (11.0 seconds - 10.49 seconds) / 11.0 seconds * 100% = 0.51 seconds / 11.0 seconds * 100% = 4.636363636363636%
Rounding to the nearest tenth, the percent of the decrease in the winning time is:
4.6%
This means that the winning time decreased by 4.6% between the 1960 Olympics and the 1988 Olympics.
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8. A parabola has its focus at (1,2) and its directrix is y = -2. The equation of this parabola could be
1) y = 8(x + 1)²
2)y=1/8(x + 1)²
3)y =8(x-1)²
4)y=1/8(x-1)²
Answers
The equation of a parabola is y=1/8 (x-1)². Therefore, option 4 is the correct answer.
What is the parabola?A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
Given that, parabola has its focus at (1,2) and its directrix is y= -2.
From graph, vertex is (h, k)=(1, 0) and p=2
Substitute (h, k)=(1,0) and p=2 in (x-h)²=4p(y-k), we get
(x-1)²=4(2)(y-0)
⇒ (x-1)²=8y
⇒ y=1/8 (x-1)²
The equation of a parabola is y=1/8 (x-1)². Therefore, option 4 is the correct answer.
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Problem Solving Strategy: Write an
Equation
Write an equation for each problem using the variable -n. Then solve and check the equation.
6) Allan has 84 baseball cards. This is 19 fewer cards than Mike. How many baseball cards does Mike have?
7) Jamie can ride her bike 3 times as fast as Michelle can jog. If Jamie rides her bike at a rate of 12 miles per hour, how fast can Michelle jog?
Problem Solving Strategy: Mental Math
Answers
Hence, the equation for the question (7) is [tex]n + 19 = 84[/tex] and equation for (8) is [tex]3n = 12[/tex]. It can be solved by linear equation in one variable.
What is a linear equation in one variable?
A linear equation in one variable is written as [tex]ax+b = 0[/tex]. Here, [tex]a[/tex] and [tex]b[/tex] are constants and [tex]x[/tex] is a variable.
(7)
Consider n number of baseball cards does Mike have. Since this is 19 less then the cards Allan have hence, as you add 19 in n then it will give 84.
[tex]n + 19 = 84[/tex]
(8)
Consider the speed of Michelle is n. As, it is 3 times less than the speed of the Jamie hence, it you multiply 3 with n then it will give 12.
[tex]3n = 12[/tex]
Hence, the equation for the question (7) is [tex]n + 19 = 84[/tex] and equation for (8) is [tex]3n = 12[/tex].
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2. Zac has earned $ 200 and earns $ 20 every week walking his neighbor's dog. Jon is $ 100 in debt and earns $ 25 every week cleaning his neighbor's pool. In how many weeks ( w ) will both Zac and Jon earnings be the same?
A student claims the solution to the equation 200+20 w=-100+25 w is w=50 He shows his steps.
Given : 2 0 0+2 0 w=- 1 0 0}+2 5 w
Step 1: 300+20 w=25 w
Step 2: 300=5 w
Step 3: 60=w
Select the two correct justifications for the given steps.
Step 1: Addition Property of Equality
Step 2: Subtraction Property of Equality
Step 3: Division Property of Equality
Answers
1. In 60 weeks, both Zac and Jon will earn the same amount, equating to their different earnings.
2. The student's claim that the solution to the equation 200 + 20w = -100 + 25w is w = 50 is false as the solution shows that w = 60.
3. The two correct justifications for the given steps used in solving w are:
Step 1: Combining like termsStep 3: Division Property of Equality.How the equations are determined?The fixed earnings of Zac = $200
Zac's earnings per week = $20
The total earnings of Zac in w weeks = 200 + 20w
Jon's fixed debt so far = $100
Jon's earnings per week = $25
The total earnings of Jon in w weeks = -100 + 25w
To determine the weeks when the total earnings of Zac and Jon will be equal, we can equate the two expressions above as follows and solve for w:
200 + 20w = -100 + 25w
20w - 25w = -300
-5w = - 300
w = -300/-5
w = 60
Thus, we can conclude that in 60 weeks, the earnings of Zac and Jon will become equal.
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Find two consecutive integers between which the solution to each equation is located. x^2=3
Answers
Step-by-step explanation:
Using squares of integers numbers, it is found that the solution of the equation is located between the integers x = 1 and x = 2.
The equation given is:
x^2=3
The solution of the equation given is:
X=√3
The squares of the integers numbers until the square root of 3 are:
1^2=1
2^2=4
Since , the square root of 3, which is the solution to the equation, is located between the integers x = 1 and x = 2.
Marvin and Alicia are putting new carpet in there living room. The carpet cost $4.15 per square foot and $97 to have it stalled. Their total bill is $1, 789.50 how many square feet 9s their living room
Answers
There are 407.83 square feet living room.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
The carpet cost $4.15 per square foot and $97 to have it stalled.
And, Their total bill is $1, 789.50.
Now,
Let number of square feet living room = x
So, We can formulate;
⇒ 4.15x + 97 = 1,789.50
Solve for x as;
⇒ 4.15x = 1,789.50 - 97
⇒ 4.15x = 1,692.5
⇒ x = 1,692.5 / 4.15
⇒ x = 407.83 square feet
Thus, There are 407.83 square feet living room.
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What are the equations of the asymptotes of the hyperbola?
(x+1)^2/25−(y−3)^2/16=1
Answers
The horizontal and vertical asymptotes of the hyperbola equation (x + 1)² / 25 - (y - 3)² / 16 = 1 are y = 4x / 5 + 19 / 5 and y = -4x / 5 + 11/5 respectively
Equation of AsymptotesAn asymptote of the curve y = f(x) or in the implicit form: f(x,y) = 0 is a straight line such that the distance between the curve and the straight line lends to zero when the points on the curve approach infinity. This can be said to be a line that a curve approaches but never touches.
Basically, we have three types of asymptotes which are horizontal asymptotes, vertical asymptotes and oblique asymptotes.
In the hyperbola equation given
(x + 1)² / 25 - (y - 3)² / 16 = 1
The equation of asymptotes are;
Horizontal asymptotes : y = 4x / 5 + 19 / 5
Vertical asymptotes : y = -4x / 5 + 11/5
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Name
Chapter
4
Test B (continued)
8. You deposit $300 in an account that earns simple interest at an annual rate of 5%.
How much money is in the account after 6 years?
Answers
Answer:
90
Step-by-step explanation:
To solve, you have to use the formula
I=Prt
I is the dollars of of simple interest earned
P is principal in dollars
R is the annual interest rate (decimal form)
T is the time in years
I=Prt
I =300*0.05*6
I = 90
Answer:
we use bodmas!
Step-by-step explanation:
Question 1 of 10, Step 1 of 1
Correct
An economist wants to estimate the mean per capita Income (in thousands of dollars) for a major city in California. He believes that the mean Income is $21.3, and the
variance is known to be $32.49. How large of a sample would be required in order to estimate the mean per capita income at the 99 % level of confidence with an
error of at most $0.39? Round your answer up to the next integer.
Answers
n=1422 is the sample that would be required in order to estimate the mean per capita income at the 99 % level of confidence with an error of at most $0.39.
What is meant by confidence level?The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The parameter's true value, for instance, should be present in 95% of all intervals computed at the 95% level. The range of values within the 95% confidence interval represents the population's actual mean, with 95% confidence. The sample mean (the center of the CI) will differ between samples due to natural sampling variability. The process itself, not a certain CI, is what inspires confidence. According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, hence to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.
At 99% confidence interval the critical value is [tex]z_{0.005}[/tex]=2.58
Margin of error=0.39
Or, [tex]z_{0.005}[/tex](σ/√n)=0.39
Or, 2.58(5.7/√n)=0.39
Or, n=(2.58×(5.7/0.39)²
Or, n=1422
n=1422 is the sample that would be required in order to estimate the mean per capita income at the 99 % level of confidence with an error of at most $0.39.
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Question 1 of 5
A canoe travels 5 miles per hour downstream and 1 mile per hour upstream.
Let x represent the canoe's speed with no water current (in still water) and y
represent the speed of the water current, in miles per hour. Then the situation
can be represented by this system of equations:
Choose the two correct options.
x + y = 5
x - y = 1
h
A. The speed of the water current is 3 miles per hour.
B. The speed of the canoe in still water is 3 miles per hour.
C. The speed of the canoe in still water is 2 miles per hour.
D. The speed of the water current is 2 miles per hour.
Answers
The speed of the canoe in still water is 3 miles per hour and the speed of the water current is 2 miles per hour. The correct options are B and D.
What is the system of equation?One or many equation having same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given that the system of equations;
x + y = 5
x - y = 1
Solving the above equations by elimination we get
x = 3 and y = 2
Where, x represents the canoe's speed with no water current (in still water) and y represents the speed of the water current, in miles per hour.
Therefore, the speed of the canoe in still water is 3 miles per hour and
the speed of the water current is 2 miles per hour.
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A large community college has professors and lecturers. The total number of faculty members is 228. The school reported that they have 5 professors every 14 lecturers How many of each type of faculty member does the community college employ?
Answers
There are 60 professors and 168 lecturers according to the given information.
What is arithmetic?
Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots.
Main BODY:
Let X be the number of professors and Y be the number of lecturers. As the total of both is 228:
X + Y = 228
Then, as there are 5 professors for every 14 lecturers:
5 X = 14 Y or X = (14/5) Y
Replacing this last value of X on the first equation:
(14/5) Y + Y = 228
(14/5) Y + (5/5) Y = 228
(19/5) Y = 228
Y = 228 * (5/19)
Y = (228*5)/19
Y = 1140 / 19
Y = 60
Then we can find X:
X = (14/5) Y = (14/5) * 60 = 168
X = 168
Hence thre are 60 professors and 168 lecturers.
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Scott's Heating and Air
Conditioning
charges $80.00 for a service call and $30.00
for each hour of work. Create a graph to
show the relationship between the number
of hours worked and total cost of the repair
bill.
Answers
Cost function is fixed cost added with number of hours times the variable cost.
What is cost ?
The two primary categories of costs that organizations face are fixed and variable costs. While variable costs fluctuate with output, fixed costs do not.
Sometimes, fixed costs are referred to as overhead costs. They are incurred regardless of whether a company produces 100 or 1,000 widgets.
Given that charge for a service call is $80.00 and $30.00 for each hour of work. So fixed cost is 80 and variable cost is 30.
Cost function is fixed cost added with number of hours times the variable cost.
Thus we have the cost function here,
where x is the hours of work.
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Alfred is looking for a new part-time job as a butler. He responds to an ad position that pays $110,200 a year.
What would his weekly salary be to the nearest cent if he gets the job?
Answers
Alfred gets pay as $2119.23 per week for a new part-time job as a butler.
What is the division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Given that, Alfred responds to an ad position that pays $110,200 a year.
We know that, there are 52 weeks in a year
Salary for one week =110,200/52
= $2119.23
Therefore, the weekly pay for Alfred is $2119.23.
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