Answer:
(A)62.8 square feet
Step-by-step explanation:
Height of the barrels = 5 feet
Radius of the barrels= 2 feet
[tex]\pi[/tex]=3.14
The barrel is in the shape of a cylinder and the area of the label the company needs is that of the round sides(curved surface area) of the cylinder.
Curved Surface Area of a Cylinder=[tex]2\pi rh[/tex]
=2X3.14X2X5
=62.8 square feet
The company need 62.8 square feet of label.
Madison Middle School has a math and science club that holds meetings after school. The club has decided to enter a two-day competition that involves different a math science challenges. The first day of competition involves solving multi-step math problems. Teams will receive two points for every problem they get correct in the morning session and three points for every question they get correct in the afternoon session.
a. Write an equation to represent the situation. Remember to define your variable(s)
b. The team scores four points in the morning session, but finishes the day with 28 points. Solve the equation and interpret the solution in the context of the problem.
c. The second day of the competition the science portion, involving hands-on science problems. Each correct science problem is worth 5 points. If the team started the day with 28 points and ended with 53 points, how many science problems did they get correct? Write and solve the an equation to answer the question.
Answer:
Please see attached picture for full solution.
Final answer:
The math and science club scored points by solving problems in a competition, with a total of 8 math problems solved on the first day and 5 science problems on the second day.
Explanation:
The situation from Madison Middle School's math and science club competition can be represented and solved with mathematical equations. Let's break down each part of the problem.
Part A: Equation Representation
Let m be the number of problems solved in the morning, and a the number in the afternoon. The equation representing the total points for the day is: 2m + 3a = Total Points.
Part B: Solving for the Afternoon Session
The team scored 4 points in the morning, meaning they solved 2 problems (as each is worth 2 points). This gives us the equation 2*2 + 3a = 28. Solving this, we find a = 8. Thus, the team solved 8 problems in the afternoon session to finish the day with 28 points.
Part C: Science Portion on the Second Day
On the second day, the team starts with 28 points and ends with 53 points, all from solving science problems worth 5 points each. The equation is 5s + 28 = 53, where s is the number of science problems solved. This simplifies to s = 5, indicating the team solved 5 science problems.
Find f (1) pleaseeee
Answer:
f(1) = 4
Step-by-step explanation:
f(1) = 3(1)^2 -(1) + 2 = 4
Just replace all the x's with 1.
Students were divided into two groups. Students in one group were ignored when they talked without raising their hands. Students in the other group were attended to in the teacher's usual manner. The independent variable in this experiment was _____.
Answer:
The independent variable in this experiment was the attention students gets from the teacher
Step-by-step explanation:
An independent variables are variables in maths, statistics and experimental sciences that stands alone and isn't affected by the other variables you are trying to measure.
Final answer:
The independent variable was the teacher's response to the student behavior of either ignoring or attending to students when they talked without raising their hands.
Explanation:
The independent variable in this experiment was the strategy used by the teacher regarding whether or not to ignore the students when they talked without raising their hands.
In experimental design, the independent variable is the condition that is manipulated by the researcher to observe its effects on the dependent variable.
In this case, students in one group were ignored when they spoke without raising their hands, making them the experimental group.
The other group, which the teacher attended to in their usual manner, acted as the control group.
Since the independent variable is the only factor that is intentionally changed to test its impact on outcomes, observing changes in the students' behavior helped determine the effects of this teaching strategy.
i desperate for help plz come help
Which of the following are ordered pairs for the equation y =x - 3?
(0,3) (-2,-1) (2,5)
(0,3) (2,1) (-2,-5)
(0,-3) (2,-1) (-2,-5)
(0,-3) (2,-1) (-2,5)
A forest ranger sights a fire directly to the south. A second ranger, 99 miles east of the first ranger, also sights the fire. The bearing from the second ranger to the fire is Upper S 29 degrees Upper WS 29° W. How far is the first ranger from the fire?
Answer:
The first ranger is approximately 54.88 miles away from the fire.
Step-by-step explanation:
We have drawn the diagram for your reference.
Given:
Distance between first ranger and second ranger (AB)= 99 miles
Angle between fire and second ranger [tex]\angle B[/tex] = [tex]29\°[/tex]
We need to find the distance between the first ranger from the fire.
Solution:
Let the distance between the first ranger from the fire (AC) be 'x'.
So we can say that;
We know that;
tan of angle B is equal to opposite side divided by adjacent side.
[tex]tan 29\°= \frac{AC}{AB}\\\\tan 29\° = \frac{x}{99}\\\\x= 99\times tan29\°\\\\x \approx 54.88\ mi[/tex]
Hence the first ranger is approximately 54.88 miles away from the fire.
The variable z is directly proportional to x, and inversely proportional to y. When x is 14 and y is 10, z has the value 26.6.
What is the value of z when x= 24, and y= 15
Answer:
Step-by-step explanation:
If two variables are directly proportional, it means that an increase in one variable will cause a corresponding increase in the other variable.
If two variables are inversely proportional, it means that an increase in one variable will cause a corresponding decrease in the other variable.
The variable z is directly proportional to x, and inversely proportional to y. If we introduce a constant k, the equation would be
z = kx/y
When x is 14 and y is 10, z has the value 26.6. It means that
26.6 = 14k/10
Cross multiplying, it becomes
26.6 × 10 = 14k
266 = 14k
k = 266/14
k = 19
The equation becomes
z = 19x/y
When x = 24, and y = 15, the value of z would be
z = 19 × 24/15
z = 30.4
A restaurant charges an automatic gratuity of 18% on tables with more than 6 people. A party of 8 had a bill of p. Which expression can be used to find the total cost of the meal with the gratuity?
0.18p
0.82p
1.18p
18.00p
The expression 1.18p can be used to find the total cost of the meal with gratuity.
Step-by-step explanation:
Step 1:
If there are more than 6 people, the restaurant charges an automatic gratuity of 18%.
Since there are 8 people this charge will also be applied here.
If the bill amount is p and 18% of p is added, the options 0.18p and 0.82p cannot be the total cost of the meal.
Step 2:
We need to determine how much 18% is in terms of p.
18% of p [tex]= \frac{18}{100} (p) = 0.18p.[/tex]
So the total cost of the meal = Cost of the meal + Gratuity charges [tex]=p + 0.18p = 1.18p.[/tex]
So the total cost is the third option 1.18p.
Answer:
1.18
Step-by-step explanation:
A trampolinist steps off from 15 feet above ground to a trampoline 13 feet below. The function h (t) = -16 t 2 + 15, where t represents the time in seconds, gives the height h, in feet, of the trampolinist above the ground as he falls. When will the trampolinist land on the trampoline?
Answer:
Trampolinist will land on the trampoline after 0.9 seconds.
Step-by-step explanation:
The function h(t) = -16t² + 15 represents the relation between height 'h' above the ground and the time 't' of the trampolinist.
We have to find the time when trampolinist lands on the ground.
That means we have to find the value of 't' when h(t) = 15 - 13 = 2
[Since trampoline is 2 feet above the ground]
When we plug in the value h(t) = 2
2 = -16t² + 15
2 + 16t² = -16t² + 16t² + 15
16t² + 2 = 15
16t² + 2 - 2 = 15 - 2
16t² = 13
[tex]\frac{16t^{2}}{16}=\frac{13}{16}[/tex]
[tex]t^{2}=\frac{13}{16}[/tex]
t = [tex]\sqrt{\frac{13}{16}}[/tex]
t ≈ 0.9 seconds
Therefore, trampolinist will land on the trampoline at 0.9 seconds.
An air force pilot is flying at a cruising altitude of 9000 feet and is forced to eject from her aircraft. The function h(t)=-16t+128t+900. Determine and state the vertex of h(t)
Answer:
(t, h(t)) = (4, 9256)
Step-by-step explanation:
We assume you intend the h(t) function to be ...
h(t) = -16t^2 +128t +9000
The equation can be written in vertex form as follows:
h(t) = -16(t^2 -8t) +9000
h(t) = -16(t^2 -8t +16) +9000 -(-16)(16) . . . . add and subtract -16(16) to complete the square
h(t) = -16(t -4)^2 +9256 . . . . . vertex form of the height function
The vertex of h(t) is (4, 9256), an altitude of 9256 feet after 4 seconds.
We would like to construct a 66% confidence interval for the proportion of voters that support building a new prison. What is the appropriate multiplier (z) that would be used in this situation?
Answer:
The appropriate z multiplier for 66% confidence interval is 0.95
Step-by-step explanation:
We are given the following in the question:
Confidence interval:
[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
We have to make a 66% confidence interval for the proportion of voters.
Confidence level = 66%
Significance level =
[tex]\alpha = 1 - 0.66 = 0.34[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.34} = \pm 0.95[/tex]
Thus, the appropriate z multiplier for 66% confidence interval is 0.95
As of a certain date, there had been a total of 14,404 performances of two shows on Broadway, with 2384 more performances of Show A than Show B. How many performances were there of each show?
Answer: show A had 8394 performances.
Show B had 6010 performances.
Step-by-step explanation:
Let x represent the number of performances of show A.
Let y represent the number of performances of show B.
As of a certain date, there had been a total of 14,404 performances of two shows on Broadway. This means that
x + y = 14404 - - - - - - - - - -1
There was 2384 more performances of Show A than Show B. It means that
x = y + 2384
Substituting x = y + 2384 into equation 1, it becomes
y + 2384 + y = 14404
2y = 14404 - 2384
2y = 12020
y = 12020/2
y = 6010
x = y + 2384 = 6010 + 2384
x = 8394
Answer:
show A had 8394 performances.
Show B had 6010 performances.
Step-by-step explanation:
Let x represent the number of performances of show A.
Let y represent the number of performances of show B.
As of a certain date, there had been a total of 14,404 performances of two shows on Broadway. This means that
x + y = 14404 - - - - - - - - - -1
There was 2384 more performances of Show A than Show B. It means that
x = y + 2384
Substituting x = y + 2384 into equation 1, it becomes
y + 2384 + y = 14404
2y = 14404 - 2384
2y = 12020
y = 12020/2
y = 6010
x = y + 2384 = 6010 + 2384
x = 8394
Step-by-step explanation:
A daycare charges a base fee of 333 dollars plus 0.500.500, point, 50 dollars per minute for late (after closing time) pick-ups. Albin had to pay 10.5010.5010, point, 50 dollars for a late pick-up. Albin uses the equation, 10.50=0.50a+310.50=0.50a+310, point, 50, equals, 0, point, 50, a, plus, 3 to represent the situation.
Answer:
a represents the Number of Minutes Late, (a=15 in this case)
Step-by-step explanation:
If the daycare charges a base fee of $3 plus $0.50 per minute late for late pickups(after closing time).
Albin on arrival for pickup had to pay $10.50;
She uses the equation
10.50=0.50a+3
0.50a=10.50-3
0.50a=7.50
a=7.50/0.5
a= 15
It means Albin was 15 minutes late to a pickup.
The vertex of a parabolic function is located at (5,−4). One of its zeros (x-intercepts) occurs at x = 7. Where will its other zero (x-intercept) be located?
Answer:
The answer to the question is
Its other zero (x-intercept) will be located at x = -5
Step-by-step explanation:
To solve the question, we note that a parabolic function is of the form
ax² + bx +c = 0
Therefore we have the vertex occurring at the extremum where the slope = 0
or dy/dx =2a+b = 0 also the x intercept occurs at x = 7, therefore when
ax² + bx +c = 0, x = 7 which is one of the solution
when x = 5, y = -4
That is a*25 +5*b + c = -4 also
49*a + 7*b + c = 0
2*a + b = 0
Solving the system of equations we get
a = 0.2, b = -0.4 and c = -7
That is 0.2x² -0.4x -7 = 0 which gives
(x+5)(x-7)×0.2 = 0
Therefore the x intercepts are 7 and -5
the second intercept will be located at x = -5
Final answer:
The other zero of the parabolic function with a vertex at (5, -4), and one zero at x = 7, will be located at x = 3, since it will be symmetrically placed with respect to the vertex.
Explanation:
The vertex of a parabolic function represents the highest or lowest point on the graph, depending on whether the parabola opens upwards or downwards. The fact that the vertex of the function is given as (5, -4) and one zero is at x = 7 leads to the conclusion that the other zero must be equidistant from the vertex on the x-axis because a parabola is symmetric about its vertex. Since the distance from the vertex (5) to the given zero (7) is 2 units to the right, the other zero must be 2 units to the left of the vertex. Therefore, the other zero will be at x = 5 - 2, which is x = 3.
Flip a coin 25 times and keep track of the results. What is the experimental probability of landing on tails? What is the theoretical probability of landing on heads or tails?
Answer:
you must flip a coin 25 times and record it on a table for experimental. Theoretical would be 50% chance ( showing working)
The theoretical probability of landing on heads or tails is always 0.5 or 50%. The experimental probability of landing on tails is determined by dividing the number of times you land tails by the total number of flips. Over the long term, thanks to the Law of Large Numbers, these values tend to converge.
Explanation:The subject of the question is the probability of landing on heads or tails when flipping a coin 25 times. The experimental probability of landing on tails can only be determined empirically by actually performing the experiment. After flipping the coin 25 times, you would calculate the experimental probability of landing on tails by dividing the number of times you landed on tails by the total number of flips (25).
On the other hand, the theoretical probability of landing on heads or tails on a single flip of a fair coin is always 0.5, or 50%, due to the nature of the coin having two equally likely outcomes. This is known as the Law of Large Numbers, which states that as the number of trials of a random experiment increases, the experimental probability approaches the theoretical probability.
For example, if we talk about Karl Pearson's experiment, after flipping a coin 24,000 times, he obtained heads 12,012 times. The relative frequency of heads is 12,012/24,000 = 0.5005, which is very close to the theoretical probability (0.5).
Learn more about Probability here:https://brainly.com/question/32117953
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5. Solve for x in the equation 6x = 42.
A. x = 48
B. x = 7
- C.x=6
D. x = 36
Answer:
B. x= 7
Step-by-step explanation:
6x = 42
x = 42 / 6
x = 7
The 6 is multiplying because of the x, this passes to the other side of the equal to split.
After years of practicing at the local bowling alley, Allan has determined that his distribution of bowling scores is roughly symmetric, unimodal, and bell-shaped, with a mean of 182 points and a standard deviation of 23 points. How likely is it that Allan will roll a perfect game (300 points), just by random chance?
Answer:
P(x = 300) = 1.45 × 10⁻⁷
Step-by-step explanation:
This is a normal distribution problem with mean number of points = μ = 182 points
Standard deviation = σ = 23 points
Probability that Allan will roll a perfect game (300 points), just by random chance.
First of, we need to normalize/standardize 300.
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (300 - 182)/23 = 5.13
300 is 5.13 Standard deviation from the mean
Probability of scoring 300 points = P(x = 300) = P(z = 5.13)
Using the normal distribution formula which is presented in the attached image to this question,
The mean = μ = 182
Standard deviation = σ = 23
x = variable whose probability is required = 300
P(x = 300) = P(z = 5.13) = 1.449193 × 10⁻⁷
Extremely unlikely!
Hope this helps!!!
A prism with a base area of 8 cm² and a height of 6 cm is dilated by a factor of 54 .
What is the volume of the dilated prism?
Enter your answer, as a decimal, in the box.
cm³
Answer:
New base area = 8 x 25/16 = 25/2 = 12•5 cm²
New height = 7•5 cm²
V = 7•5 x 12•5 cm³
V = 93•75 cm³
Step-by-step explanation:
A disc of unit radius is tossed at random onto a large rectangular floor, which is tiled with $4 \times 6$ tiles. Find the probability that the disc is contained entirely in a rectangular tile (and does not intersect the border between two tiles).
Answer:
1/3
Step-by-step explanation:
In order for the disc to be entirely contained in a rectangular tile, its center must be at least 1 unit from the nearest edge. Which means there's a 2 by 4 region that the center can lie in.
So the probability is (2×4) / (4×6) = 8/24 = 1/3.
The ratio of the number of teachers to students in a school is 3:35. The ratio of the number of male students to the number of female students is 2:5 there are 500 female students. How many teachers are there
Answer:
60
Step-by-step explanation:
There are 2+5 = 7 ratio units of students. If we multiply the numbers by 5, we can have a total of 35 ratio units of students: 10 : 25.
Now, we can substitute this into the ratio of teachers to students:
teachers : students = 3 : 35
teachers : (male students : female students) = 3 : (10 : 25)
Then the number of teachers is seen to be 3/25 of the number of female students:
(3/25)(500) = 60 . . . teachers
DONT SKIP PLZ
Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (-3, -1) and point (-2, -4) rounded to the nearest tenth?
3.2 units
2.9 units
3.4 units
4.1 units
Answer:
The first one: 3.2 units
Answer: 3.2 units
Step-by-step explanation:
The formula for determining the distance between two points on a straight line is expressed as
Distance = √(x2 - x1)² + (y2 - y1)²
Where
x2 represents final value of x on the horizontal axis
x1 represents initial value of x on the horizontal axis.
y2 represents final value of y on the vertical axis.
y1 represents initial value of y on the vertical axis.
From the graph given,
x2 = -2
x1 = - 3
y2 = - 4
y1 = - 1
Therefore,
Distance = √(- 2 - - 3)² + (-4 - - 1)²
Distance = √1² + - 3² = √1 + 9 = √10
Distance = 3.2
Ty has 5 goats and 19 carrots. He gives each goat the same number of carrots, and he uses as many carrots as he can. How many carrots does Ty give each goat? How many carrots are left?
Each goat gets 3 carrots.
After giving 3 carrots to each of the goat, 4 carrots are left with Ty in total.
Step-by-step explanation:
Here, the total number of carrots = 19
The total number of goats = 5
So, in the given condition:
19 is the DIVIDEND
5 is the DIVISOR
Now, dividing 19 by 5, we get:
19 = 5 x 3 + 4
Here, 3 = Quotient
4 = Remainder
So, by the given equation. we can say that:
Each goat gets 3 carrots.
After giving 3 carrots to each of the goat, 4 carrots are left with Ty in total.
Factor the expression. 16j2 + 24j + 9
(4j – 3)Factor the expression. 16j2 + 24j + 9
(4j – 3)2
(4j + 3)(4j – 3)
(4j + 3)^2
(4j – 9)(4j + 1)^2
(4j + 3)(4j – 3)
(4j + 3)^2
(4j – 9)(4j + 1)
Option C: [tex](4 j+3)^{2}[/tex] is the correct answer.
Explanation:
The given expression is [tex]16 j^{2}+24 j+9[/tex]
We need to factor the expression.
Let us rewrite the expression as
[tex](4j)^{2}+24 j+(3)^2[/tex]
Also, we can rewrite the term [tex]24j[/tex] as [tex]2(4)(3)j[/tex]
Thus, we have,
[tex](4j)^{2}+2(4j)(3)+(3)^2[/tex]
Hence, the equation is of the form,
[tex](a+b)^{2}=a^{2}+2 a b+b^{2}[/tex]
where [tex]a=4 j[/tex] and [tex]b=3[/tex]
Hence, the factor of the expression can be written as [tex](4 j+3)^{2}[/tex]
Thus, the factored expression is [tex](4 j+3)^{2}[/tex]
Therefore, Option C is the correct answer.
Final answer:
The factored form of the expression 16j^2 + 24j + 9 is (4j + 3)².
Explanation:
To factor the expression 16j2 + 24j + 9, we look for two binomials ((aj + b)(cj + d)) that when multiplied together, give us the original quadratic expression. The factors of 16j2 are 4j imes 4j, and the factors of 9 are 3 imes 3. Our binomial factors will have the format (4j + 3).
Expanding the binomial (4j + 3)², we have:
(4j + 3) imes (4j + 3)
= 16j2 + 12j + 12j + 9
= 16j2 + 24j + 9
This matches the original expression exactly, so the factored form of the expression is (4j + 3)².
Cara bought a DVD for $22 and a CD for less than the cost of the DVD let C represent the the cost of the CD write an inequality to show the cost of the CD
Answer:
C < 22
Step-by-step explanation:
Find the indicated term of the given geometric sequence.
a = –5, r = –2, n = 3
Question 16 options:
–20
–41
10
40
Answer: the first option is correct.
Step-by-step explanation:
In a geometric sequence, each consecutive term differ by a common ratio, r.
The formula for determining the nth term of a geometric progression is expressed as
an = a1r^(n - 1)
Where
a1 represents the first term of the sequence.
r represents the common ratio.
n represents the number of terms.
From the information given,
a = - 5
r = - 2
n = 3
Therefore, the 3rd term, T3 is
T3 = - 5 × - 2^(3 - 1)
T3 = - 5 × - 2^2
T3 = - 5 × 4
T3 = - 20
Henry is trapped at the roof top of a burning building, which is 24 feet high. In order to rescue him, his father, Diego, must find a ladder which will be used to cross the river, which is 7 feet wide, and go up directly to the top of the building. Help Diego to find the appropriate length of ladder from the other side of the river to the top of the building
Answer: the ladder should be 25 feet
Step-by-step explanation:
The ladder forms a right angle triangle with the building and the river. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the top of the ladder to the base of the building represents the opposite side of the right angle triangle.
The distance from the bottom of the ladder to the base of the building represents the adjacent side of the right angle triangle.
To determine the length of the required ladder h, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
h² = 24² + 7² = 576 + 49
h² = 625
h = √625 = 25 feet
The scale on a map is 2 centimeters= 50 kilometres.Two rivers on a map are located 9.3 centimeters apart.What is The actual distance between the two rivers
Answer:
The actual distance between the two rivers is 232.5 kilometers.
Step-by-step explanation:
GIven:
The scale on a map is 2 centimeters= 50 kilometres.Two rivers on a map are located 9.3 centimeters apart.
Now, to find the actual distance between the two rivers.
Let the actual distance between the two rivers is [tex]x.[/tex]
The two rivers on the map is located apart of 9.3 centimeters.
According to the scale on the map is 2 centimeters = 50 kilometers.
So, 2 centimeters is equivalent to 50 kilometers.
Thus, 9.3 centimeters is equivalent to [tex]x.[/tex]
Now, to solve by using cross multiplication method:
[tex]\frac{2}{50} =\frac{9.3}{x}[/tex]
By cross multiplying we get:
[tex]2x=465[/tex]
Dividing both sides by 2 we get:
[tex]x=232.5\ kilometers.[/tex]
Therefore, the actual distance between the two rivers is 232.5 kilometers.
Just answer what it asks in the picture PLEASE
m∠1 = 30° (by Vertical angle theorem)
m∠A = 80° (by Triangle sum theorem)
m∠D = 80° (by Triangle sum theorem)
The value of x is 7.5 and y is 9.
Solution:
∠ACB and ∠DCE are vertically opposite angles.
Vertical angle theorem:
If two lines are intersecting, then vertically opposite angles are congruent.
⇒ m∠DCE = m∠ACB
⇒ m∠1 = 30° (by Vertical angle theorem)
In triangle ACD,
Triangle sum property:
Sum of the interior angles of the triangle = 180°
⇒ m∠A + m∠C + m∠B = 180°
⇒ m∠A + 30° + 70° = 180°
⇒ m∠A + 100° = 180°
⇒ m∠A = 100° – 180°
⇒ m∠A = 80° (by Triangle sum theorem)
Similarly, m∠D = 80° (by Triangle sum theorem)
In ΔACD and ΔDCE,
All the angles are congruent, so ΔACD and ΔDCE are similar triangles.
In similar triangle corresponding sides are in the same ratio.
[tex]$\frac{9}{12}=\frac{x}{10}[/tex]
Do cross multiplication.
90 = 12x
7.5 = x
Now, to find y:
[tex]$\frac{9}{12}=\frac{6}{y}[/tex]
Do cross multiplication.
9y = 72
Divide by 9, we get
y = 8
Hence the value of x is 7.5 and y is 9.
what number can you add to √7 to get a rational nember?
Answer:
you will add -√7
Step-by-step explanation:
the only reason you would do that is so that the equation could equal 0
walnuts cost $3.60 per pound and peanuts cost $2.70 per pound. For a fundraiser, the softball team will be selling bags of mixed nuts. How many punds of walnuts and how many pounds of peanuts should the team buy in order to make a 60 pound . ixture that will sell for $3.00 per pound?
Answer: 20 pounds of walnuts should be mixed with 40 pounds of peanuts.
Step-by-step explanation:
Let x represent the number of pounds of walnuts that should be in the mixture.
Let y represent the number of pounds of peanuts that should be in the mixture.
The number of pounds of the mixture to be made is 60. This means that
x + y = 60
Walnuts cost $3.60 per pound and peanuts cost $2.70 per pound. The mixture will sell for $3.00 per pound. It means that the total cost of the mixture is 3 × 60 = $180. The expression would be
3.6x + 2.7y = 180- - - - - - - - - - - - -1
Substituting x = 60 - y into equation 1, it becomes
3.6(60 - y) + 2.7y = 180
216 - 3.6y + 2.7y = 180
- 3.6y + 2.7y = 180 - 216
- 0.9y = - 36
y = - 36/ - 0.9
y = 40
x = 60 - y = 60 - 40
x = 20
Find the constant of variation k for the inverse variation. Then write an equation for the inverse variation.
y = 2.5 when x = 9
1) k = 3.6; xy = 3.6
2) k = 22.5; y = 22.5x
3) k = 22.5; xy = 22.5
4) k= 3.6; y = 3.6
Answer: 3) k = 22.5; xy = 22.5
Step-by-step explanation:
If two variables are inversely proportional, it means that an increase in the value of one variable would cause a corresponding decrease in the other variable. Also, a decrease in the value of one variable would cause a corresponding increase in the other variable.
Given that y varies directly with x, if we introduce a constant of proportionality, k, the expression becomes
y = k/x
If y = 2.5 when x = 9, then
2.5 = k/9
k = 9 × 2.5 = 22.5
Therefore, an equation for the inverse variation is
y = 22.5/x
xy = 22.5
Answer: (3)
k = 22.5; xy = 22.5
Step-by-step explanation: